1,1,29,0,0.384446," ","integrate(x^2*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{3} x^{3} a A"," ",0,"1/7*x^7*b*B + 1/5*x^5*a*B + 1/5*x^5*b*A + 1/3*x^3*a*A","A",0
2,1,29,0,0.370956," ","integrate(x*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b B + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + \frac{1}{2} x^{2} a A"," ",0,"1/6*x^6*b*B + 1/4*x^4*a*B + 1/4*x^4*b*A + 1/2*x^2*a*A","A",0
3,1,26,0,0.399012," ","integrate((b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b B + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + x a A"," ",0,"1/5*x^5*b*B + 1/3*x^3*a*B + 1/3*x^3*b*A + x*a*A","A",0
4,1,25,0,0.473674," ","integrate((b*x^2+a)*(B*x^2+A)/x,x, algorithm=""fricas"")","\frac{1}{4} \, B b x^{4} + \frac{1}{2} \, {\left(B a + A b\right)} x^{2} + A a \log\left(x\right)"," ",0,"1/4*B*b*x^4 + 1/2*(B*a + A*b)*x^2 + A*a*log(x)","A",0
5,1,28,0,0.402640," ","integrate((b*x^2+a)*(B*x^2+A)/x^2,x, algorithm=""fricas"")","\frac{B b x^{4} + 3 \, {\left(B a + A b\right)} x^{2} - 3 \, A a}{3 \, x}"," ",0,"1/3*(B*b*x^4 + 3*(B*a + A*b)*x^2 - 3*A*a)/x","A",0
6,1,30,0,0.482910," ","integrate((b*x^2+a)*(B*x^2+A)/x^3,x, algorithm=""fricas"")","\frac{B b x^{4} + 2 \, {\left(B a + A b\right)} x^{2} \log\left(x\right) - A a}{2 \, x^{2}}"," ",0,"1/2*(B*b*x^4 + 2*(B*a + A*b)*x^2*log(x) - A*a)/x^2","A",0
7,1,29,0,0.414816," ","integrate((b*x^2+a)*(B*x^2+A)/x^4,x, algorithm=""fricas"")","\frac{3 \, B b x^{4} - 3 \, {\left(B a + A b\right)} x^{2} - A a}{3 \, x^{3}}"," ",0,"1/3*(3*B*b*x^4 - 3*(B*a + A*b)*x^2 - A*a)/x^3","A",0
8,1,31,0,0.479468," ","integrate((b*x^2+a)*(B*x^2+A)/x^5,x, algorithm=""fricas"")","\frac{4 \, B b x^{4} \log\left(x\right) - 2 \, {\left(B a + A b\right)} x^{2} - A a}{4 \, x^{4}}"," ",0,"1/4*(4*B*b*x^4*log(x) - 2*(B*a + A*b)*x^2 - A*a)/x^4","A",0
9,1,29,0,0.455042," ","integrate((b*x^2+a)*(B*x^2+A)/x^6,x, algorithm=""fricas"")","-\frac{15 \, B b x^{4} + 5 \, {\left(B a + A b\right)} x^{2} + 3 \, A a}{15 \, x^{5}}"," ",0,"-1/15*(15*B*b*x^4 + 5*(B*a + A*b)*x^2 + 3*A*a)/x^5","A",0
10,1,29,0,0.426497," ","integrate((b*x^2+a)*(B*x^2+A)/x^7,x, algorithm=""fricas"")","-\frac{6 \, B b x^{4} + 3 \, {\left(B a + A b\right)} x^{2} + 2 \, A a}{12 \, x^{6}}"," ",0,"-1/12*(6*B*b*x^4 + 3*(B*a + A*b)*x^2 + 2*A*a)/x^6","A",0
11,1,53,0,0.401940," ","integrate(x^2*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{5} x^{5} a^{2} B + \frac{2}{5} x^{5} b a A + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/9*x^9*b^2*B + 2/7*x^7*b*a*B + 1/7*x^7*b^2*A + 1/5*x^5*a^2*B + 2/5*x^5*b*a*A + 1/3*x^3*a^2*A","A",0
12,1,53,0,0.381698," ","integrate(x*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{2} B + \frac{1}{3} x^{6} b a B + \frac{1}{6} x^{6} b^{2} A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/8*x^8*b^2*B + 1/3*x^6*b*a*B + 1/6*x^6*b^2*A + 1/4*x^4*a^2*B + 1/2*x^4*b*a*A + 1/2*x^2*a^2*A","A",0
13,1,50,0,0.380884," ","integrate((b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{2} B + \frac{2}{5} x^{5} b a B + \frac{1}{5} x^{5} b^{2} A + \frac{1}{3} x^{3} a^{2} B + \frac{2}{3} x^{3} b a A + x a^{2} A"," ",0,"1/7*x^7*b^2*B + 2/5*x^5*b*a*B + 1/5*x^5*b^2*A + 1/3*x^3*a^2*B + 2/3*x^3*b*a*A + x*a^2*A","A",0
14,1,49,0,0.478895," ","integrate((b*x^2+a)^2*(B*x^2+A)/x,x, algorithm=""fricas"")","\frac{1}{6} \, B b^{2} x^{6} + \frac{1}{4} \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}"," ",0,"1/6*B*b^2*x^6 + 1/4*(2*B*a*b + A*b^2)*x^4 + A*a^2*log(x) + 1/2*(B*a^2 + 2*A*a*b)*x^2","A",0
15,1,53,0,0.473946," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^2,x, algorithm=""fricas"")","\frac{3 \, B b^{2} x^{6} + 5 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 15 \, A a^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{15 \, x}"," ",0,"1/15*(3*B*b^2*x^6 + 5*(2*B*a*b + A*b^2)*x^4 - 15*A*a^2 + 15*(B*a^2 + 2*A*a*b)*x^2)/x","A",0
16,1,54,0,0.445088," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^3,x, algorithm=""fricas"")","\frac{B b^{2} x^{6} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 4 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2} \log\left(x\right) - 2 \, A a^{2}}{4 \, x^{2}}"," ",0,"1/4*(B*b^2*x^6 + 2*(2*B*a*b + A*b^2)*x^4 + 4*(B*a^2 + 2*A*a*b)*x^2*log(x) - 2*A*a^2)/x^2","A",0
17,1,52,0,0.427266," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^4,x, algorithm=""fricas"")","\frac{B b^{2} x^{6} + 3 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - A a^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/3*(B*b^2*x^6 + 3*(2*B*a*b + A*b^2)*x^4 - A*a^2 - 3*(B*a^2 + 2*A*a*b)*x^2)/x^3","A",0
18,1,55,0,0.413405," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^5,x, algorithm=""fricas"")","\frac{2 \, B b^{2} x^{6} + 4 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{4 \, x^{4}}"," ",0,"1/4*(2*B*b^2*x^6 + 4*(2*B*a*b + A*b^2)*x^4*log(x) - A*a^2 - 2*(B*a^2 + 2*A*a*b)*x^2)/x^4","A",0
19,1,53,0,0.419940," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^6,x, algorithm=""fricas"")","\frac{15 \, B b^{2} x^{6} - 15 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 3 \, A a^{2} - 5 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{15 \, x^{5}}"," ",0,"1/15*(15*B*b^2*x^6 - 15*(2*B*a*b + A*b^2)*x^4 - 3*A*a^2 - 5*(B*a^2 + 2*A*a*b)*x^2)/x^5","A",0
20,1,55,0,0.407526," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^7,x, algorithm=""fricas"")","\frac{12 \, B b^{2} x^{6} \log\left(x\right) - 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 2 \, A a^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/12*(12*B*b^2*x^6*log(x) - 6*(2*B*a*b + A*b^2)*x^4 - 2*A*a^2 - 3*(B*a^2 + 2*A*a*b)*x^2)/x^6","A",0
21,1,53,0,0.430129," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{2} x^{6} + 35 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 15 \, A a^{2} + 21 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{105 \, x^{7}}"," ",0,"-1/105*(105*B*b^2*x^6 + 35*(2*B*a*b + A*b^2)*x^4 + 15*A*a^2 + 21*(B*a^2 + 2*A*a*b)*x^2)/x^7","A",0
22,1,53,0,0.418121," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^9,x, algorithm=""fricas"")","-\frac{12 \, B b^{2} x^{6} + 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 3 \, A a^{2} + 4 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{24 \, x^{8}}"," ",0,"-1/24*(12*B*b^2*x^6 + 6*(2*B*a*b + A*b^2)*x^4 + 3*A*a^2 + 4*(B*a^2 + 2*A*a*b)*x^2)/x^8","A",0
23,1,125,0,0.362676," ","integrate(x^9*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{22} x^{22} b^{5} B + \frac{1}{4} x^{20} b^{4} a B + \frac{1}{20} x^{20} b^{5} A + \frac{5}{9} x^{18} b^{3} a^{2} B + \frac{5}{18} x^{18} b^{4} a A + \frac{5}{8} x^{16} b^{2} a^{3} B + \frac{5}{8} x^{16} b^{3} a^{2} A + \frac{5}{14} x^{14} b a^{4} B + \frac{5}{7} x^{14} b^{2} a^{3} A + \frac{1}{12} x^{12} a^{5} B + \frac{5}{12} x^{12} b a^{4} A + \frac{1}{10} x^{10} a^{5} A"," ",0,"1/22*x^22*b^5*B + 1/4*x^20*b^4*a*B + 1/20*x^20*b^5*A + 5/9*x^18*b^3*a^2*B + 5/18*x^18*b^4*a*A + 5/8*x^16*b^2*a^3*B + 5/8*x^16*b^3*a^2*A + 5/14*x^14*b*a^4*B + 5/7*x^14*b^2*a^3*A + 1/12*x^12*a^5*B + 5/12*x^12*b*a^4*A + 1/10*x^10*a^5*A","A",0
24,1,125,0,0.365875," ","integrate(x^8*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{5} B + \frac{5}{19} x^{19} b^{4} a B + \frac{1}{19} x^{19} b^{5} A + \frac{10}{17} x^{17} b^{3} a^{2} B + \frac{5}{17} x^{17} b^{4} a A + \frac{2}{3} x^{15} b^{2} a^{3} B + \frac{2}{3} x^{15} b^{3} a^{2} A + \frac{5}{13} x^{13} b a^{4} B + \frac{10}{13} x^{13} b^{2} a^{3} A + \frac{1}{11} x^{11} a^{5} B + \frac{5}{11} x^{11} b a^{4} A + \frac{1}{9} x^{9} a^{5} A"," ",0,"1/21*x^21*b^5*B + 5/19*x^19*b^4*a*B + 1/19*x^19*b^5*A + 10/17*x^17*b^3*a^2*B + 5/17*x^17*b^4*a*A + 2/3*x^15*b^2*a^3*B + 2/3*x^15*b^3*a^2*A + 5/13*x^13*b*a^4*B + 10/13*x^13*b^2*a^3*A + 1/11*x^11*a^5*B + 5/11*x^11*b*a^4*A + 1/9*x^9*a^5*A","A",0
25,1,125,0,0.389010," ","integrate(x^7*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{20} x^{20} b^{5} B + \frac{5}{18} x^{18} b^{4} a B + \frac{1}{18} x^{18} b^{5} A + \frac{5}{8} x^{16} b^{3} a^{2} B + \frac{5}{16} x^{16} b^{4} a A + \frac{5}{7} x^{14} b^{2} a^{3} B + \frac{5}{7} x^{14} b^{3} a^{2} A + \frac{5}{12} x^{12} b a^{4} B + \frac{5}{6} x^{12} b^{2} a^{3} A + \frac{1}{10} x^{10} a^{5} B + \frac{1}{2} x^{10} b a^{4} A + \frac{1}{8} x^{8} a^{5} A"," ",0,"1/20*x^20*b^5*B + 5/18*x^18*b^4*a*B + 1/18*x^18*b^5*A + 5/8*x^16*b^3*a^2*B + 5/16*x^16*b^4*a*A + 5/7*x^14*b^2*a^3*B + 5/7*x^14*b^3*a^2*A + 5/12*x^12*b*a^4*B + 5/6*x^12*b^2*a^3*A + 1/10*x^10*a^5*B + 1/2*x^10*b*a^4*A + 1/8*x^8*a^5*A","A",0
26,1,125,0,0.383484," ","integrate(x^6*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{19} x^{19} b^{5} B + \frac{5}{17} x^{17} b^{4} a B + \frac{1}{17} x^{17} b^{5} A + \frac{2}{3} x^{15} b^{3} a^{2} B + \frac{1}{3} x^{15} b^{4} a A + \frac{10}{13} x^{13} b^{2} a^{3} B + \frac{10}{13} x^{13} b^{3} a^{2} A + \frac{5}{11} x^{11} b a^{4} B + \frac{10}{11} x^{11} b^{2} a^{3} A + \frac{1}{9} x^{9} a^{5} B + \frac{5}{9} x^{9} b a^{4} A + \frac{1}{7} x^{7} a^{5} A"," ",0,"1/19*x^19*b^5*B + 5/17*x^17*b^4*a*B + 1/17*x^17*b^5*A + 2/3*x^15*b^3*a^2*B + 1/3*x^15*b^4*a*A + 10/13*x^13*b^2*a^3*B + 10/13*x^13*b^3*a^2*A + 5/11*x^11*b*a^4*B + 10/11*x^11*b^2*a^3*A + 1/9*x^9*a^5*B + 5/9*x^9*b*a^4*A + 1/7*x^7*a^5*A","A",0
27,1,124,0,0.353681," ","integrate(x^5*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{5} B + \frac{5}{16} x^{16} b^{4} a B + \frac{1}{16} x^{16} b^{5} A + \frac{5}{7} x^{14} b^{3} a^{2} B + \frac{5}{14} x^{14} b^{4} a A + \frac{5}{6} x^{12} b^{2} a^{3} B + \frac{5}{6} x^{12} b^{3} a^{2} A + \frac{1}{2} x^{10} b a^{4} B + x^{10} b^{2} a^{3} A + \frac{1}{8} x^{8} a^{5} B + \frac{5}{8} x^{8} b a^{4} A + \frac{1}{6} x^{6} a^{5} A"," ",0,"1/18*x^18*b^5*B + 5/16*x^16*b^4*a*B + 1/16*x^16*b^5*A + 5/7*x^14*b^3*a^2*B + 5/14*x^14*b^4*a*A + 5/6*x^12*b^2*a^3*B + 5/6*x^12*b^3*a^2*A + 1/2*x^10*b*a^4*B + x^10*b^2*a^3*A + 1/8*x^8*a^5*B + 5/8*x^8*b*a^4*A + 1/6*x^6*a^5*A","A",0
28,1,125,0,0.377969," ","integrate(x^4*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{17} x^{17} b^{5} B + \frac{1}{3} x^{15} b^{4} a B + \frac{1}{15} x^{15} b^{5} A + \frac{10}{13} x^{13} b^{3} a^{2} B + \frac{5}{13} x^{13} b^{4} a A + \frac{10}{11} x^{11} b^{2} a^{3} B + \frac{10}{11} x^{11} b^{3} a^{2} A + \frac{5}{9} x^{9} b a^{4} B + \frac{10}{9} x^{9} b^{2} a^{3} A + \frac{1}{7} x^{7} a^{5} B + \frac{5}{7} x^{7} b a^{4} A + \frac{1}{5} x^{5} a^{5} A"," ",0,"1/17*x^17*b^5*B + 1/3*x^15*b^4*a*B + 1/15*x^15*b^5*A + 10/13*x^13*b^3*a^2*B + 5/13*x^13*b^4*a*A + 10/11*x^11*b^2*a^3*B + 10/11*x^11*b^3*a^2*A + 5/9*x^9*b*a^4*B + 10/9*x^9*b^2*a^3*A + 1/7*x^7*a^5*B + 5/7*x^7*b*a^4*A + 1/5*x^5*a^5*A","A",0
29,1,123,0,0.378501," ","integrate(x^3*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{16} x^{16} b^{5} B + \frac{5}{14} x^{14} b^{4} a B + \frac{1}{14} x^{14} b^{5} A + \frac{5}{6} x^{12} b^{3} a^{2} B + \frac{5}{12} x^{12} b^{4} a A + x^{10} b^{2} a^{3} B + x^{10} b^{3} a^{2} A + \frac{5}{8} x^{8} b a^{4} B + \frac{5}{4} x^{8} b^{2} a^{3} A + \frac{1}{6} x^{6} a^{5} B + \frac{5}{6} x^{6} b a^{4} A + \frac{1}{4} x^{4} a^{5} A"," ",0,"1/16*x^16*b^5*B + 5/14*x^14*b^4*a*B + 1/14*x^14*b^5*A + 5/6*x^12*b^3*a^2*B + 5/12*x^12*b^4*a*A + x^10*b^2*a^3*B + x^10*b^3*a^2*A + 5/8*x^8*b*a^4*B + 5/4*x^8*b^2*a^3*A + 1/6*x^6*a^5*B + 5/6*x^6*b*a^4*A + 1/4*x^4*a^5*A","A",0
30,1,124,0,0.370990," ","integrate(x^2*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{5} B + \frac{5}{13} x^{13} b^{4} a B + \frac{1}{13} x^{13} b^{5} A + \frac{10}{11} x^{11} b^{3} a^{2} B + \frac{5}{11} x^{11} b^{4} a A + \frac{10}{9} x^{9} b^{2} a^{3} B + \frac{10}{9} x^{9} b^{3} a^{2} A + \frac{5}{7} x^{7} b a^{4} B + \frac{10}{7} x^{7} b^{2} a^{3} A + \frac{1}{5} x^{5} a^{5} B + x^{5} b a^{4} A + \frac{1}{3} x^{3} a^{5} A"," ",0,"1/15*x^15*b^5*B + 5/13*x^13*b^4*a*B + 1/13*x^13*b^5*A + 10/11*x^11*b^3*a^2*B + 5/11*x^11*b^4*a*A + 10/9*x^9*b^2*a^3*B + 10/9*x^9*b^3*a^2*A + 5/7*x^7*b*a^4*B + 10/7*x^7*b^2*a^3*A + 1/5*x^5*a^5*B + x^5*b*a^4*A + 1/3*x^3*a^5*A","A",0
31,1,124,0,0.374536," ","integrate(x*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{5} B + \frac{5}{12} x^{12} b^{4} a B + \frac{1}{12} x^{12} b^{5} A + x^{10} b^{3} a^{2} B + \frac{1}{2} x^{10} b^{4} a A + \frac{5}{4} x^{8} b^{2} a^{3} B + \frac{5}{4} x^{8} b^{3} a^{2} A + \frac{5}{6} x^{6} b a^{4} B + \frac{5}{3} x^{6} b^{2} a^{3} A + \frac{1}{4} x^{4} a^{5} B + \frac{5}{4} x^{4} b a^{4} A + \frac{1}{2} x^{2} a^{5} A"," ",0,"1/14*x^14*b^5*B + 5/12*x^12*b^4*a*B + 1/12*x^12*b^5*A + x^10*b^3*a^2*B + 1/2*x^10*b^4*a*A + 5/4*x^8*b^2*a^3*B + 5/4*x^8*b^3*a^2*A + 5/6*x^6*b*a^4*B + 5/3*x^6*b^2*a^3*A + 1/4*x^4*a^5*B + 5/4*x^4*b*a^4*A + 1/2*x^2*a^5*A","B",0
32,1,121,0,0.367466," ","integrate((b*x^2+a)^5*(B*x^2+A),x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{5} B + \frac{5}{11} x^{11} b^{4} a B + \frac{1}{11} x^{11} b^{5} A + \frac{10}{9} x^{9} b^{3} a^{2} B + \frac{5}{9} x^{9} b^{4} a A + \frac{10}{7} x^{7} b^{2} a^{3} B + \frac{10}{7} x^{7} b^{3} a^{2} A + x^{5} b a^{4} B + 2 x^{5} b^{2} a^{3} A + \frac{1}{3} x^{3} a^{5} B + \frac{5}{3} x^{3} b a^{4} A + x a^{5} A"," ",0,"1/13*x^13*b^5*B + 5/11*x^11*b^4*a*B + 1/11*x^11*b^5*A + 10/9*x^9*b^3*a^2*B + 5/9*x^9*b^4*a*A + 10/7*x^7*b^2*a^3*B + 10/7*x^7*b^3*a^2*A + x^5*b*a^4*B + 2*x^5*b^2*a^3*A + 1/3*x^3*a^5*B + 5/3*x^3*b*a^4*A + x*a^5*A","A",0
33,1,117,0,0.411008," ","integrate((b*x^2+a)^5*(B*x^2+A)/x,x, algorithm=""fricas"")","\frac{1}{12} \, B b^{5} x^{12} + \frac{1}{10} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + \frac{5}{8} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + \frac{5}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + A a^{5} \log\left(x\right) + \frac{5}{4} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}"," ",0,"1/12*B*b^5*x^12 + 1/10*(5*B*a*b^4 + A*b^5)*x^10 + 5/8*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 5/3*(B*a^3*b^2 + A*a^2*b^3)*x^6 + A*a^5*log(x) + 5/4*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 1/2*(B*a^5 + 5*A*a^4*b)*x^2","A",0
34,1,121,0,0.427331," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^2,x, algorithm=""fricas"")","\frac{63 \, B b^{5} x^{12} + 77 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 495 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1386 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 693 \, A a^{5} + 1155 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 693 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{693 \, x}"," ",0,"1/693*(63*B*b^5*x^12 + 77*(5*B*a*b^4 + A*b^5)*x^10 + 495*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1386*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 693*A*a^5 + 1155*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 693*(B*a^5 + 5*A*a^4*b)*x^2)/x","A",0
35,1,123,0,0.442845," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^3,x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{12} + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 60 \, A a^{5} + 300 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 120 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2} \log\left(x\right)}{120 \, x^{2}}"," ",0,"1/120*(12*B*b^5*x^12 + 15*(5*B*a*b^4 + A*b^5)*x^10 + 100*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 300*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 60*A*a^5 + 300*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 120*(B*a^5 + 5*A*a^4*b)*x^2*log(x))/x^2","A",0
36,1,121,0,0.403089," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^4,x, algorithm=""fricas"")","\frac{7 \, B b^{5} x^{12} + 9 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 63 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 21 \, A a^{5} + 315 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{63 \, x^{3}}"," ",0,"1/63*(7*B*b^5*x^12 + 9*(5*B*a*b^4 + A*b^5)*x^10 + 63*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 210*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 21*A*a^5 + 315*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 63*(B*a^5 + 5*A*a^4*b)*x^2)/x^3","A",0
37,1,123,0,0.417418," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^5,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{12} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 6 \, A a^{5} + 120 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} \log\left(x\right) - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{24 \, x^{4}}"," ",0,"1/24*(3*B*b^5*x^12 + 4*(5*B*a*b^4 + A*b^5)*x^10 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 120*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 6*A*a^5 + 120*(B*a^4*b + 2*A*a^3*b^2)*x^4*log(x) - 12*(B*a^5 + 5*A*a^4*b)*x^2)/x^4","A",0
38,1,121,0,0.420849," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^6,x, algorithm=""fricas"")","\frac{15 \, B b^{5} x^{12} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 175 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 21 \, A a^{5} - 525 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 35 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{105 \, x^{5}}"," ",0,"1/105*(15*B*b^5*x^12 + 21*(5*B*a*b^4 + A*b^5)*x^10 + 175*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1050*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 21*A*a^5 - 525*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 35*(B*a^5 + 5*A*a^4*b)*x^2)/x^5","A",0
39,1,123,0,0.468539," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^7,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{12} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} \log\left(x\right) - 2 \, A a^{5} - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/12*(2*B*b^5*x^12 + 3*(5*B*a*b^4 + A*b^5)*x^10 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 120*(B*a^3*b^2 + A*a^2*b^3)*x^6*log(x) - 2*A*a^5 - 30*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 3*(B*a^5 + 5*A*a^4*b)*x^2)/x^6","A",0
40,1,121,0,0.417377," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^8,x, algorithm=""fricas"")","\frac{21 \, B b^{5} x^{12} + 35 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 525 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} - 1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 15 \, A a^{5} - 175 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 21 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{105 \, x^{7}}"," ",0,"1/105*(21*B*b^5*x^12 + 35*(5*B*a*b^4 + A*b^5)*x^10 + 525*(2*B*a^2*b^3 + A*a*b^4)*x^8 - 1050*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 15*A*a^5 - 175*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 21*(B*a^5 + 5*A*a^4*b)*x^2)/x^7","A",0
41,1,123,0,0.427291," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^9,x, algorithm=""fricas"")","\frac{6 \, B b^{5} x^{12} + 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 120 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} \log\left(x\right) - 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 3 \, A a^{5} - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{24 \, x^{8}}"," ",0,"1/24*(6*B*b^5*x^12 + 12*(5*B*a*b^4 + A*b^5)*x^10 + 120*(2*B*a^2*b^3 + A*a*b^4)*x^8*log(x) - 120*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 3*A*a^5 - 30*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 4*(B*a^5 + 5*A*a^4*b)*x^2)/x^8","A",0
42,1,121,0,0.730903," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^10,x, algorithm=""fricas"")","\frac{21 \, B b^{5} x^{12} + 63 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} - 315 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} - 210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 7 \, A a^{5} - 63 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 9 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{63 \, x^{9}}"," ",0,"1/63*(21*B*b^5*x^12 + 63*(5*B*a*b^4 + A*b^5)*x^10 - 315*(2*B*a^2*b^3 + A*a*b^4)*x^8 - 210*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 7*A*a^5 - 63*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 9*(B*a^5 + 5*A*a^4*b)*x^2)/x^9","A",0
43,1,123,0,0.430703," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^11,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{12} + 120 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} \log\left(x\right) - 300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} - 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 12 \, A a^{5} - 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{120 \, x^{10}}"," ",0,"1/120*(60*B*b^5*x^12 + 120*(5*B*a*b^4 + A*b^5)*x^10*log(x) - 300*(2*B*a^2*b^3 + A*a*b^4)*x^8 - 300*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 12*A*a^5 - 100*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 15*(B*a^5 + 5*A*a^4*b)*x^2)/x^10","A",0
44,1,121,0,0.457260," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^12,x, algorithm=""fricas"")","\frac{693 \, B b^{5} x^{12} - 693 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} - 1155 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} - 1386 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 63 \, A a^{5} - 495 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 77 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{693 \, x^{11}}"," ",0,"1/693*(693*B*b^5*x^12 - 693*(5*B*a*b^4 + A*b^5)*x^10 - 1155*(2*B*a^2*b^3 + A*a*b^4)*x^8 - 1386*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 63*A*a^5 - 495*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 77*(B*a^5 + 5*A*a^4*b)*x^2)/x^11","A",0
45,1,123,0,0.438243," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^13,x, algorithm=""fricas"")","\frac{120 \, B b^{5} x^{12} \log\left(x\right) - 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} - 150 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} - 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} - 10 \, A a^{5} - 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{120 \, x^{12}}"," ",0,"1/120*(120*B*b^5*x^12*log(x) - 60*(5*B*a*b^4 + A*b^5)*x^10 - 150*(2*B*a^2*b^3 + A*a*b^4)*x^8 - 200*(B*a^3*b^2 + A*a^2*b^3)*x^6 - 10*A*a^5 - 75*(B*a^4*b + 2*A*a^3*b^2)*x^4 - 12*(B*a^5 + 5*A*a^4*b)*x^2)/x^12","A",0
46,1,121,0,0.409283," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^14,x, algorithm=""fricas"")","-\frac{9009 \, B b^{5} x^{12} + 3003 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 9009 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 12870 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 693 \, A a^{5} + 5005 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 819 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{9009 \, x^{13}}"," ",0,"-1/9009*(9009*B*b^5*x^12 + 3003*(5*B*a*b^4 + A*b^5)*x^10 + 9009*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 12870*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 693*A*a^5 + 5005*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 819*(B*a^5 + 5*A*a^4*b)*x^2)/x^13","A",0
47,1,121,0,0.428299," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^15,x, algorithm=""fricas"")","-\frac{42 \, B b^{5} x^{12} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 70 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 6 \, A a^{5} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{84 \, x^{14}}"," ",0,"-1/84*(42*B*b^5*x^12 + 21*(5*B*a*b^4 + A*b^5)*x^10 + 70*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 105*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 6*A*a^5 + 42*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 7*(B*a^5 + 5*A*a^4*b)*x^2)/x^14","B",0
48,1,121,0,0.403924," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^16,x, algorithm=""fricas"")","-\frac{15015 \, B b^{5} x^{12} + 9009 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 32175 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 50050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 3003 \, A a^{5} + 20475 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 3465 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{45045 \, x^{15}}"," ",0,"-1/45045*(15015*B*b^5*x^12 + 9009*(5*B*a*b^4 + A*b^5)*x^10 + 32175*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 50050*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 3003*A*a^5 + 20475*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 3465*(B*a^5 + 5*A*a^4*b)*x^2)/x^15","A",0
49,1,121,0,0.450750," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^17,x, algorithm=""fricas"")","-\frac{84 \, B b^{5} x^{12} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 210 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 336 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 21 \, A a^{5} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 24 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{336 \, x^{16}}"," ",0,"-1/336*(84*B*b^5*x^12 + 56*(5*B*a*b^4 + A*b^5)*x^10 + 210*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 336*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 21*A*a^5 + 140*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 24*(B*a^5 + 5*A*a^4*b)*x^2)/x^16","A",0
50,1,121,0,0.395809," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^18,x, algorithm=""fricas"")","-\frac{153153 \, B b^{5} x^{12} + 109395 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 425425 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 696150 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 45045 \, A a^{5} + 294525 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 51051 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{765765 \, x^{17}}"," ",0,"-1/765765*(153153*B*b^5*x^12 + 109395*(5*B*a*b^4 + A*b^5)*x^10 + 425425*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 696150*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 45045*A*a^5 + 294525*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 51051*(B*a^5 + 5*A*a^4*b)*x^2)/x^17","A",0
51,1,121,0,0.406278," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^19,x, algorithm=""fricas"")","-\frac{168 \, B b^{5} x^{12} + 126 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 504 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 840 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 56 \, A a^{5} + 360 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{1008 \, x^{18}}"," ",0,"-1/1008*(168*B*b^5*x^12 + 126*(5*B*a*b^4 + A*b^5)*x^10 + 504*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 840*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 56*A*a^5 + 360*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 63*(B*a^5 + 5*A*a^4*b)*x^2)/x^18","A",0
52,1,121,0,0.417374," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^20,x, algorithm=""fricas"")","-\frac{415701 \, B b^{5} x^{12} + 323323 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 1322685 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 2238390 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 153153 \, A a^{5} + 969969 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 171171 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{2909907 \, x^{19}}"," ",0,"-1/2909907*(415701*B*b^5*x^12 + 323323*(5*B*a*b^4 + A*b^5)*x^10 + 1322685*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 2238390*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 153153*A*a^5 + 969969*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 171171*(B*a^5 + 5*A*a^4*b)*x^2)/x^19","A",0
53,1,121,0,0.421218," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^21,x, algorithm=""fricas"")","-\frac{630 \, B b^{5} x^{12} + 504 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 2100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 3600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 252 \, A a^{5} + 1575 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 280 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{5040 \, x^{20}}"," ",0,"-1/5040*(630*B*b^5*x^12 + 504*(5*B*a*b^4 + A*b^5)*x^10 + 2100*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 3600*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 252*A*a^5 + 1575*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 280*(B*a^5 + 5*A*a^4*b)*x^2)/x^20","A",0
54,1,121,0,0.454056," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^22,x, algorithm=""fricas"")","-\frac{323323 \, B b^{5} x^{12} + 264537 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 1119195 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1939938 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 138567 \, A a^{5} + 855855 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 153153 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{2909907 \, x^{21}}"," ",0,"-1/2909907*(323323*B*b^5*x^12 + 264537*(5*B*a*b^4 + A*b^5)*x^10 + 1119195*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1939938*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 138567*A*a^5 + 855855*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 153153*(B*a^5 + 5*A*a^4*b)*x^2)/x^21","A",0
55,1,121,0,0.439702," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^23,x, algorithm=""fricas"")","-\frac{2772 \, B b^{5} x^{12} + 2310 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 9900 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 17325 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 1260 \, A a^{5} + 7700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 1386 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{27720 \, x^{22}}"," ",0,"-1/27720*(2772*B*b^5*x^12 + 2310*(5*B*a*b^4 + A*b^5)*x^10 + 9900*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 17325*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 1260*A*a^5 + 7700*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 1386*(B*a^5 + 5*A*a^4*b)*x^2)/x^22","A",0
56,1,228,0,0.459647," ","integrate(x^6*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{30 \, B b^{3} x^{7} - 42 \, {\left(B a b^{2} - A b^{3}\right)} x^{5} + 70 \, {\left(B a^{2} b - A a b^{2}\right)} x^{3} - 105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 210 \, {\left(B a^{3} - A a^{2} b\right)} x}{210 \, b^{4}}, \frac{15 \, B b^{3} x^{7} - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{5} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{3} + 105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 105 \, {\left(B a^{3} - A a^{2} b\right)} x}{105 \, b^{4}}\right]"," ",0,"[1/210*(30*B*b^3*x^7 - 42*(B*a*b^2 - A*b^3)*x^5 + 70*(B*a^2*b - A*a*b^2)*x^3 - 105*(B*a^3 - A*a^2*b)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 210*(B*a^3 - A*a^2*b)*x)/b^4, 1/105*(15*B*b^3*x^7 - 21*(B*a*b^2 - A*b^3)*x^5 + 35*(B*a^2*b - A*a*b^2)*x^3 + 105*(B*a^3 - A*a^2*b)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 105*(B*a^3 - A*a^2*b)*x)/b^4]","A",0
57,1,75,0,0.447852," ","integrate(x^5*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{6} - 3 \, {\left(B a b^{2} - A b^{3}\right)} x^{4} + 6 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} - 6 \, {\left(B a^{3} - A a^{2} b\right)} \log\left(b x^{2} + a\right)}{12 \, b^{4}}"," ",0,"1/12*(2*B*b^3*x^6 - 3*(B*a*b^2 - A*b^3)*x^4 + 6*(B*a^2*b - A*a*b^2)*x^2 - 6*(B*a^3 - A*a^2*b)*log(b*x^2 + a))/b^4","A",0
58,1,178,0,0.476856," ","integrate(x^4*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, B b^{2} x^{5} - 10 \, {\left(B a b - A b^{2}\right)} x^{3} - 15 \, {\left(B a^{2} - A a b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 30 \, {\left(B a^{2} - A a b\right)} x}{30 \, b^{3}}, \frac{3 \, B b^{2} x^{5} - 5 \, {\left(B a b - A b^{2}\right)} x^{3} - 15 \, {\left(B a^{2} - A a b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 15 \, {\left(B a^{2} - A a b\right)} x}{15 \, b^{3}}\right]"," ",0,"[1/30*(6*B*b^2*x^5 - 10*(B*a*b - A*b^2)*x^3 - 15*(B*a^2 - A*a*b)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 30*(B*a^2 - A*a*b)*x)/b^3, 1/15*(3*B*b^2*x^5 - 5*(B*a*b - A*b^2)*x^3 - 15*(B*a^2 - A*a*b)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 15*(B*a^2 - A*a*b)*x)/b^3]","A",0
59,1,51,0,0.432402," ","integrate(x^3*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\frac{B b^{2} x^{4} - 2 \, {\left(B a b - A b^{2}\right)} x^{2} + 2 \, {\left(B a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{4 \, b^{3}}"," ",0,"1/4*(B*b^2*x^4 - 2*(B*a*b - A*b^2)*x^2 + 2*(B*a^2 - A*a*b)*log(b*x^2 + a))/b^3","A",0
60,1,129,0,0.461401," ","integrate(x^2*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B b x^{3} - 3 \, {\left(B a - A b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, {\left(B a - A b\right)} x}{6 \, b^{2}}, \frac{B b x^{3} + 3 \, {\left(B a - A b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 3 \, {\left(B a - A b\right)} x}{3 \, b^{2}}\right]"," ",0,"[1/6*(2*B*b*x^3 - 3*(B*a - A*b)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*(B*a - A*b)*x)/b^2, 1/3*(B*b*x^3 + 3*(B*a - A*b)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 3*(B*a - A*b)*x)/b^2]","A",0
61,1,30,0,0.385355," ","integrate(x*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\frac{B b x^{2} - {\left(B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(B*b*x^2 - (B*a - A*b)*log(b*x^2 + a))/b^2","A",0
62,1,99,0,0.456174," ","integrate((B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, B a b x + {\left(B a - A b\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b^{2}}, \frac{B a b x - {\left(B a - A b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b^{2}}\right]"," ",0,"[1/2*(2*B*a*b*x + (B*a - A*b)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^2), (B*a*b*x - (B*a - A*b)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^2)]","A",0
63,1,32,0,0.466434," ","integrate((B*x^2+A)/x/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, A b \log\left(x\right) + {\left(B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"1/2*(2*A*b*log(x) + (B*a - A*b)*log(b*x^2 + a))/(a*b)","A",0
64,1,105,0,0.453531," ","integrate((B*x^2+A)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(B a - A b\right)} \sqrt{-a b} x \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, A a b}{2 \, a^{2} b x}, \frac{{\left(B a - A b\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) - A a b}{a^{2} b x}\right]"," ",0,"[1/2*((B*a - A*b)*sqrt(-a*b)*x*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*A*a*b)/(a^2*b*x), ((B*a - A*b)*sqrt(a*b)*x*arctan(sqrt(a*b)*x/a) - A*a*b)/(a^2*b*x)]","A",0
65,1,47,0,0.455915," ","integrate((B*x^2+A)/x^3/(b*x^2+a),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} x^{2} \log\left(b x^{2} + a\right) - 2 \, {\left(B a - A b\right)} x^{2} \log\left(x\right) + A a}{2 \, a^{2} x^{2}}"," ",0,"-1/2*((B*a - A*b)*x^2*log(b*x^2 + a) - 2*(B*a - A*b)*x^2*log(x) + A*a)/(a^2*x^2)","A",0
66,1,135,0,0.446215," ","integrate((B*x^2+A)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 6 \, {\left(B a - A b\right)} x^{2} + 2 \, A a}{6 \, a^{2} x^{3}}, -\frac{3 \, {\left(B a - A b\right)} x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left(B a - A b\right)} x^{2} + A a}{3 \, a^{2} x^{3}}\right]"," ",0,"[-1/6*(3*(B*a - A*b)*x^3*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 6*(B*a - A*b)*x^2 + 2*A*a)/(a^2*x^3), -1/3*(3*(B*a - A*b)*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*(B*a - A*b)*x^2 + A*a)/(a^2*x^3)]","A",0
67,1,73,0,0.472878," ","integrate((B*x^2+A)/x^5/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, {\left(B a b - A b^{2}\right)} x^{4} \log\left(b x^{2} + a\right) - 4 \, {\left(B a b - A b^{2}\right)} x^{4} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} - A a b\right)} x^{2}}{4 \, a^{3} x^{4}}"," ",0,"1/4*(2*(B*a*b - A*b^2)*x^4*log(b*x^2 + a) - 4*(B*a*b - A*b^2)*x^4*log(x) - A*a^2 - 2*(B*a^2 - A*a*b)*x^2)/(a^3*x^4)","A",0
68,1,184,0,0.482365," ","integrate((B*x^2+A)/x^6/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a b - A b^{2}\right)} x^{5} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 30 \, {\left(B a b - A b^{2}\right)} x^{4} + 6 \, A a^{2} + 10 \, {\left(B a^{2} - A a b\right)} x^{2}}{30 \, a^{3} x^{5}}, \frac{15 \, {\left(B a b - A b^{2}\right)} x^{5} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 15 \, {\left(B a b - A b^{2}\right)} x^{4} - 3 \, A a^{2} - 5 \, {\left(B a^{2} - A a b\right)} x^{2}}{15 \, a^{3} x^{5}}\right]"," ",0,"[-1/30*(15*(B*a*b - A*b^2)*x^5*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 30*(B*a*b - A*b^2)*x^4 + 6*A*a^2 + 10*(B*a^2 - A*a*b)*x^2)/(a^3*x^5), 1/15*(15*(B*a*b - A*b^2)*x^5*sqrt(b/a)*arctan(x*sqrt(b/a)) + 15*(B*a*b - A*b^2)*x^4 - 3*A*a^2 - 5*(B*a^2 - A*a*b)*x^2)/(a^3*x^5)]","A",0
69,1,98,0,0.448994," ","integrate((B*x^2+A)/x^7/(b*x^2+a),x, algorithm=""fricas"")","-\frac{6 \, {\left(B a b^{2} - A b^{3}\right)} x^{6} \log\left(b x^{2} + a\right) - 12 \, {\left(B a b^{2} - A b^{3}\right)} x^{6} \log\left(x\right) - 6 \, {\left(B a^{2} b - A a b^{2}\right)} x^{4} + 2 \, A a^{3} + 3 \, {\left(B a^{3} - A a^{2} b\right)} x^{2}}{12 \, a^{4} x^{6}}"," ",0,"-1/12*(6*(B*a*b^2 - A*b^3)*x^6*log(b*x^2 + a) - 12*(B*a*b^2 - A*b^3)*x^6*log(x) - 6*(B*a^2*b - A*a*b^2)*x^4 + 2*A*a^3 + 3*(B*a^3 - A*a^2*b)*x^2)/(a^4*x^6)","A",0
70,1,234,0,0.449664," ","integrate((B*x^2+A)/x^8/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a b^{2} - A b^{3}\right)} x^{7} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 210 \, {\left(B a b^{2} - A b^{3}\right)} x^{6} - 70 \, {\left(B a^{2} b - A a b^{2}\right)} x^{4} + 30 \, A a^{3} + 42 \, {\left(B a^{3} - A a^{2} b\right)} x^{2}}{210 \, a^{4} x^{7}}, -\frac{105 \, {\left(B a b^{2} - A b^{3}\right)} x^{7} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 105 \, {\left(B a b^{2} - A b^{3}\right)} x^{6} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{4} + 15 \, A a^{3} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x^{2}}{105 \, a^{4} x^{7}}\right]"," ",0,"[-1/210*(105*(B*a*b^2 - A*b^3)*x^7*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 210*(B*a*b^2 - A*b^3)*x^6 - 70*(B*a^2*b - A*a*b^2)*x^4 + 30*A*a^3 + 42*(B*a^3 - A*a^2*b)*x^2)/(a^4*x^7), -1/105*(105*(B*a*b^2 - A*b^3)*x^7*sqrt(b/a)*arctan(x*sqrt(b/a)) + 105*(B*a*b^2 - A*b^3)*x^6 - 35*(B*a^2*b - A*a*b^2)*x^4 + 15*A*a^3 + 21*(B*a^3 - A*a^2*b)*x^2)/(a^4*x^7)]","A",0
71,1,172,0,0.394872," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{10} - {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} x^{8} + 2 \, {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{6} + 12 \, B a^{5} - 12 \, A a^{4} b - 6 \, {\left(5 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{4} - 12 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x^{2} + 12 \, {\left(5 \, B a^{5} - 4 \, A a^{4} b + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{24 \, {\left(b^{7} x^{2} + a b^{6}\right)}}"," ",0,"1/24*(3*B*b^5*x^10 - (5*B*a*b^4 - 4*A*b^5)*x^8 + 2*(5*B*a^2*b^3 - 4*A*a*b^4)*x^6 + 12*B*a^5 - 12*A*a^4*b - 6*(5*B*a^3*b^2 - 4*A*a^2*b^3)*x^4 - 12*(4*B*a^4*b - 3*A*a^3*b^2)*x^2 + 12*(5*B*a^5 - 4*A*a^4*b + (5*B*a^4*b - 4*A*a^3*b^2)*x^2)*log(b*x^2 + a))/(b^7*x^2 + a*b^6)","A",0
72,1,350,0,0.472135," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{60 \, B b^{4} x^{9} - 12 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{7} + 28 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{5} - 140 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{3} - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 210 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} x}{420 \, {\left(b^{6} x^{2} + a b^{5}\right)}}, \frac{30 \, B b^{4} x^{9} - 6 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{7} + 14 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{5} - 70 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{3} + 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} x}{210 \, {\left(b^{6} x^{2} + a b^{5}\right)}}\right]"," ",0,"[1/420*(60*B*b^4*x^9 - 12*(9*B*a*b^3 - 7*A*b^4)*x^7 + 28*(9*B*a^2*b^2 - 7*A*a*b^3)*x^5 - 140*(9*B*a^3*b - 7*A*a^2*b^2)*x^3 - 105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 210*(9*B*a^4 - 7*A*a^3*b)*x)/(b^6*x^2 + a*b^5), 1/210*(30*B*b^4*x^9 - 6*(9*B*a*b^3 - 7*A*b^4)*x^7 + 14*(9*B*a^2*b^2 - 7*A*a*b^3)*x^5 - 70*(9*B*a^3*b - 7*A*a^2*b^2)*x^3 + 105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 105*(9*B*a^4 - 7*A*a^3*b)*x)/(b^6*x^2 + a*b^5)]","A",0
73,1,148,0,0.418869," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{4} x^{8} - {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} x^{6} - 6 \, B a^{4} + 6 \, A a^{3} b + 3 \, {\left(4 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + 6 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2} - 6 \, {\left(4 \, B a^{4} - 3 \, A a^{3} b + {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{6} x^{2} + a b^{5}\right)}}"," ",0,"1/12*(2*B*b^4*x^8 - (4*B*a*b^3 - 3*A*b^4)*x^6 - 6*B*a^4 + 6*A*a^3*b + 3*(4*B*a^2*b^2 - 3*A*a*b^3)*x^4 + 6*(3*B*a^3*b - 2*A*a^2*b^2)*x^2 - 6*(4*B*a^4 - 3*A*a^3*b + (4*B*a^3*b - 3*A*a^2*b^2)*x^2)*log(b*x^2 + a))/(b^6*x^2 + a*b^5)","A",0
74,1,298,0,0.472782," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{12 \, B b^{3} x^{7} - 4 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{5} + 20 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3} - 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 30 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} x}{60 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, \frac{6 \, B b^{3} x^{7} - 2 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{5} + 10 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3} - 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} x}{30 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/60*(12*B*b^3*x^7 - 4*(7*B*a*b^2 - 5*A*b^3)*x^5 + 20*(7*B*a^2*b - 5*A*a*b^2)*x^3 - 15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 30*(7*B*a^3 - 5*A*a^2*b)*x)/(b^5*x^2 + a*b^4), 1/30*(6*B*b^3*x^7 - 2*(7*B*a*b^2 - 5*A*b^3)*x^5 + 10*(7*B*a^2*b - 5*A*a*b^2)*x^3 - 15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 15*(7*B*a^3 - 5*A*a^2*b)*x)/(b^5*x^2 + a*b^4)]","A",0
75,1,121,0,0.405457," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{B b^{3} x^{6} - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} x^{4} + 2 \, B a^{3} - 2 \, A a^{2} b - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{2} + 2 \, {\left(3 \, B a^{3} - 2 \, A a^{2} b + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/4*(B*b^3*x^6 - (3*B*a*b^2 - 2*A*b^3)*x^4 + 2*B*a^3 - 2*A*a^2*b - 2*(2*B*a^2*b - A*a*b^2)*x^2 + 2*(3*B*a^3 - 2*A*a^2*b + (3*B*a^2*b - 2*A*a*b^2)*x^2)*log(b*x^2 + a))/(b^5*x^2 + a*b^4)","A",0
76,1,240,0,0.427190," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B b^{2} x^{5} - 4 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x^{3} - 3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 6 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} x}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{2 \, B b^{2} x^{5} - 2 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 3 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} x}{6 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/12*(4*B*b^2*x^5 - 4*(5*B*a*b - 3*A*b^2)*x^3 - 3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 6*(5*B*a^2 - 3*A*a*b)*x)/(b^4*x^2 + a*b^3), 1/6*(2*B*b^2*x^5 - 2*(5*B*a*b - 3*A*b^2)*x^3 + 3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 3*(5*B*a^2 - 3*A*a*b)*x)/(b^4*x^2 + a*b^3)]","A",0
77,1,81,0,0.411754," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{B b^{2} x^{4} + B a b x^{2} - B a^{2} + A a b - {\left(2 \, B a^{2} - A a b + {\left(2 \, B a b - A b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/2*(B*b^2*x^4 + B*a*b*x^2 - B*a^2 + A*a*b - (2*B*a^2 - A*a*b + (2*B*a*b - A*b^2)*x^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3)","A",0
78,1,208,0,0.460137," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, B a b^{2} x^{3} + {\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} x}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, \frac{2 \, B a b^{2} x^{3} - {\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, B a^{2} b - A a b^{2}\right)} x}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/4*(4*B*a*b^2*x^3 + (3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(3*B*a^2*b - A*a*b^2)*x)/(a*b^4*x^2 + a^2*b^3), 1/2*(2*B*a*b^2*x^3 - (3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*B*a^2*b - A*a*b^2)*x)/(a*b^4*x^2 + a^2*b^3)]","A",0
79,1,44,0,0.409352," ","integrate(x*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x^{2} + B a\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/2*(B*a - A*b + (B*b*x^2 + B*a)*log(b*x^2 + a))/(b^3*x^2 + a*b^2)","A",0
80,1,182,0,0.464700," ","integrate((B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(B a^{2} b - A a b^{2}\right)} x}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(B a^{2} b - A a b^{2}\right)} x}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/4*((B*a^2 + A*a*b + (B*a*b + A*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(B*a^2*b - A*a*b^2)*x)/(a^2*b^3*x^2 + a^3*b^2), 1/2*((B*a^2 + A*a*b + (B*a*b + A*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (B*a^2*b - A*a*b^2)*x)/(a^2*b^3*x^2 + a^3*b^2)]","A",0
81,1,70,0,0.426399," ","integrate((B*x^2+A)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{B a^{2} - A a b + {\left(A b^{2} x^{2} + A a b\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(A b^{2} x^{2} + A a b\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"-1/2*(B*a^2 - A*a*b + (A*b^2*x^2 + A*a*b)*log(b*x^2 + a) - 2*(A*b^2*x^2 + A*a*b)*log(x))/(a^2*b^2*x^2 + a^3*b)","A",0
82,1,210,0,0.482115," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, A a^{2} b - 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} - {\left({\left(B a b - 3 \, A b^{2}\right)} x^{3} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}, -\frac{2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} - {\left({\left(B a b - 3 \, A b^{2}\right)} x^{3} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}\right]"," ",0,"[-1/4*(4*A*a^2*b - 2*(B*a^2*b - 3*A*a*b^2)*x^2 - ((B*a*b - 3*A*b^2)*x^3 + (B*a^2 - 3*A*a*b)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^2*x^3 + a^4*b*x), -1/2*(2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x^2 - ((B*a*b - 3*A*b^2)*x^3 + (B*a^2 - 3*A*a*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^2*x^3 + a^4*b*x)]","A",0
83,1,117,0,0.414597," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{A a^{2} - {\left(B a^{2} - 2 \, A a b\right)} x^{2} + {\left({\left(B a b - 2 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 2 \, A a b\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(B a b - 2 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 2 \, A a b\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}"," ",0,"-1/2*(A*a^2 - (B*a^2 - 2*A*a*b)*x^2 + ((B*a*b - 2*A*b^2)*x^4 + (B*a^2 - 2*A*a*b)*x^2)*log(b*x^2 + a) - 2*((B*a*b - 2*A*b^2)*x^4 + (B*a^2 - 2*A*a*b)*x^2)*log(x))/(a^3*b*x^4 + a^4*x^2)","A",0
84,1,250,0,0.458797," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{4} + 4 \, A a^{2} + 4 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2} + 3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{12 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}, -\frac{3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{4} + 2 \, A a^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2} + 3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[-1/12*(6*(3*B*a*b - 5*A*b^2)*x^4 + 4*A*a^2 + 4*(3*B*a^2 - 5*A*a*b)*x^2 + 3*((3*B*a*b - 5*A*b^2)*x^5 + (3*B*a^2 - 5*A*a*b)*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^3*b*x^5 + a^4*x^3), -1/6*(3*(3*B*a*b - 5*A*b^2)*x^4 + 2*A*a^2 + 2*(3*B*a^2 - 5*A*a*b)*x^2 + 3*((3*B*a*b - 5*A*b^2)*x^5 + (3*B*a^2 - 5*A*a*b)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^3*b*x^5 + a^4*x^3)]","A",0
85,1,154,0,0.434144," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{4} + A a^{3} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} x^{2} - 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{6} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{4}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{6} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left(a^{4} b x^{6} + a^{5} x^{4}\right)}}"," ",0,"-1/4*(2*(2*B*a^2*b - 3*A*a*b^2)*x^4 + A*a^3 + (2*B*a^3 - 3*A*a^2*b)*x^2 - 2*((2*B*a*b^2 - 3*A*b^3)*x^6 + (2*B*a^2*b - 3*A*a*b^2)*x^4)*log(b*x^2 + a) + 4*((2*B*a*b^2 - 3*A*b^3)*x^6 + (2*B*a^2*b - 3*A*a*b^2)*x^4)*log(x))/(a^4*b*x^6 + a^5*x^4)","A",0
86,1,308,0,0.459295," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{30 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 20 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} - 12 \, A a^{3} - 4 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2} - 15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{7} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{60 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}}, \frac{15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} - 6 \, A a^{3} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2} + 15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{7} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{30 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}}\right]"," ",0,"[1/60*(30*(5*B*a*b^2 - 7*A*b^3)*x^6 + 20*(5*B*a^2*b - 7*A*a*b^2)*x^4 - 12*A*a^3 - 4*(5*B*a^3 - 7*A*a^2*b)*x^2 - 15*((5*B*a*b^2 - 7*A*b^3)*x^7 + (5*B*a^2*b - 7*A*a*b^2)*x^5)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^4*b*x^7 + a^5*x^5), 1/30*(15*(5*B*a*b^2 - 7*A*b^3)*x^6 + 10*(5*B*a^2*b - 7*A*a*b^2)*x^4 - 6*A*a^3 - 2*(5*B*a^3 - 7*A*a^2*b)*x^2 + 15*((5*B*a*b^2 - 7*A*b^3)*x^7 + (5*B*a^2*b - 7*A*a*b^2)*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^4*b*x^7 + a^5*x^5)]","A",0
87,1,184,0,0.465059," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{6} - 2 \, A a^{4} + 3 \, {\left(3 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{4} - {\left(3 \, B a^{4} - 4 \, A a^{3} b\right)} x^{2} - 6 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{8} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{6}\right)} \log\left(b x^{2} + a\right) + 12 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{8} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{6}\right)} \log\left(x\right)}{12 \, {\left(a^{5} b x^{8} + a^{6} x^{6}\right)}}"," ",0,"1/12*(6*(3*B*a^2*b^2 - 4*A*a*b^3)*x^6 - 2*A*a^4 + 3*(3*B*a^3*b - 4*A*a^2*b^2)*x^4 - (3*B*a^4 - 4*A*a^3*b)*x^2 - 6*((3*B*a*b^3 - 4*A*b^4)*x^8 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^6)*log(b*x^2 + a) + 12*((3*B*a*b^3 - 4*A*b^4)*x^8 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^6)*log(x))/(a^5*b*x^8 + a^6*x^6)","A",0
88,1,231,0,0.440400," ","integrate(x^11*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, B b^{6} x^{12} - 2 \, {\left(3 \, B a b^{5} - 2 \, A b^{6}\right)} x^{10} + 5 \, {\left(3 \, B a^{2} b^{4} - 2 \, A a b^{5}\right)} x^{8} + 66 \, B a^{6} - 54 \, A a^{5} b - 20 \, {\left(3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} x^{6} - 6 \, {\left(34 \, B a^{4} b^{2} - 21 \, A a^{3} b^{3}\right)} x^{4} - 12 \, {\left(4 \, B a^{5} b - A a^{4} b^{2}\right)} x^{2} + 60 \, {\left(3 \, B a^{6} - 2 \, A a^{5} b + {\left(3 \, B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} x^{4} + 2 \, {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{24 \, {\left(b^{9} x^{4} + 2 \, a b^{8} x^{2} + a^{2} b^{7}\right)}}"," ",0,"1/24*(3*B*b^6*x^12 - 2*(3*B*a*b^5 - 2*A*b^6)*x^10 + 5*(3*B*a^2*b^4 - 2*A*a*b^5)*x^8 + 66*B*a^6 - 54*A*a^5*b - 20*(3*B*a^3*b^3 - 2*A*a^2*b^4)*x^6 - 6*(34*B*a^4*b^2 - 21*A*a^3*b^3)*x^4 - 12*(4*B*a^5*b - A*a^4*b^2)*x^2 + 60*(3*B*a^6 - 2*A*a^5*b + (3*B*a^4*b^2 - 2*A*a^3*b^3)*x^4 + 2*(3*B*a^5*b - 2*A*a^4*b^2)*x^2)*log(b*x^2 + a))/(b^9*x^4 + 2*a*b^8*x^2 + a^2*b^7)","A",0
89,1,205,0,0.430655," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{10} - {\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} x^{8} + 4 \, {\left(5 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{6} - 27 \, B a^{5} + 21 \, A a^{4} b + 3 \, {\left(21 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{4} + 6 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} x^{2} - 12 \, {\left(5 \, B a^{5} - 3 \, A a^{4} b + {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{4} + 2 \, {\left(5 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}}"," ",0,"1/12*(2*B*b^5*x^10 - (5*B*a*b^4 - 3*A*b^5)*x^8 + 4*(5*B*a^2*b^3 - 3*A*a*b^4)*x^6 - 27*B*a^5 + 21*A*a^4*b + 3*(21*B*a^3*b^2 - 11*A*a^2*b^3)*x^4 + 6*(B*a^4*b + A*a^3*b^2)*x^2 - 12*(5*B*a^5 - 3*A*a^4*b + (5*B*a^3*b^2 - 3*A*a^2*b^3)*x^4 + 2*(5*B*a^4*b - 3*A*a^3*b^2)*x^2)*log(b*x^2 + a))/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6)","A",0
90,1,179,0,0.447316," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{B b^{4} x^{8} - 2 \, {\left(2 \, B a b^{3} - A b^{4}\right)} x^{6} + 7 \, B a^{4} - 5 \, A a^{3} b - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{4} + 2 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(2 \, B a^{4} - A a^{3} b + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} x^{4} + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}"," ",0,"1/4*(B*b^4*x^8 - 2*(2*B*a*b^3 - A*b^4)*x^6 + 7*B*a^4 - 5*A*a^3*b - (11*B*a^2*b^2 - 4*A*a*b^3)*x^4 + 2*(B*a^3*b - 2*A*a^2*b^2)*x^2 + 6*(2*B*a^4 - A*a^3*b + (2*B*a^2*b^2 - A*a*b^3)*x^4 + 2*(2*B*a^3*b - A*a^2*b^2)*x^2)*log(b*x^2 + a))/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5)","A",0
91,1,142,0,0.430020," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{6} + 4 \, B a b^{2} x^{4} - 5 \, B a^{3} + 3 \, A a^{2} b - 4 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} - 2 \, {\left({\left(3 \, B a b^{2} - A b^{3}\right)} x^{4} + 3 \, B a^{3} - A a^{2} b + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}"," ",0,"1/4*(2*B*b^3*x^6 + 4*B*a*b^2*x^4 - 5*B*a^3 + 3*A*a^2*b - 4*(B*a^2*b - A*a*b^2)*x^2 - 2*((3*B*a*b^2 - A*b^3)*x^4 + 3*B*a^3 - A*a^2*b + 2*(3*B*a^2*b - A*a*b^2)*x^2)*log(b*x^2 + a))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)","A",0
92,1,89,0,0.424703," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, B a^{2} - A a b + 2 \, {\left(2 \, B a b - A b^{2}\right)} x^{2} + 2 \, {\left(B b^{2} x^{4} + 2 \, B a b x^{2} + B a^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/4*(3*B*a^2 - A*a*b + 2*(2*B*a*b - A*b^2)*x^2 + 2*(B*b^2*x^4 + 2*B*a*b*x^2 + B*a^2)*log(b*x^2 + a))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","A",0
93,1,42,0,0.437901," ","integrate(x*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{2 \, B b x^{2} + B a + A b}{4 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*B*b*x^2 + B*a + A*b)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
94,1,119,0,0.451349," ","integrate((B*x^2+A)/x/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, A a b^{2} x^{2} - B a^{3} + 3 \, A a^{2} b - 2 \, {\left(A b^{3} x^{4} + 2 \, A a b^{2} x^{2} + A a^{2} b\right)} \log\left(b x^{2} + a\right) + 4 \, {\left(A b^{3} x^{4} + 2 \, A a b^{2} x^{2} + A a^{2} b\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"1/4*(2*A*a*b^2*x^2 - B*a^3 + 3*A*a^2*b - 2*(A*b^3*x^4 + 2*A*a*b^2*x^2 + A*a^2*b)*log(b*x^2 + a) + 4*(A*b^3*x^4 + 2*A*a*b^2*x^2 + A*a^2*b)*log(x))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)","A",0
95,1,197,0,0.554188," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{4} - 2 \, A a^{3} + 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{2} - 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{6} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{6} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}"," ",0,"1/4*(2*(B*a^2*b - 3*A*a*b^2)*x^4 - 2*A*a^3 + 3*(B*a^3 - 3*A*a^2*b)*x^2 - 2*((B*a*b^2 - 3*A*b^3)*x^6 + 2*(B*a^2*b - 3*A*a*b^2)*x^4 + (B*a^3 - 3*A*a^2*b)*x^2)*log(b*x^2 + a) + 4*((B*a*b^2 - 3*A*b^3)*x^6 + 2*(B*a^2*b - 3*A*a*b^2)*x^4 + (B*a^3 - 3*A*a^2*b)*x^2)*log(x))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)","B",0
96,1,229,0,0.432439," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{6} + A a^{4} + 9 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{4} + 2 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} x^{2} - 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{8} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{6} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{4}\right)} \log\left(b x^{2} + a\right) + 12 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{8} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{6} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left(a^{5} b^{2} x^{8} + 2 \, a^{6} b x^{6} + a^{7} x^{4}\right)}}"," ",0,"-1/4*(6*(B*a^2*b^2 - 2*A*a*b^3)*x^6 + A*a^4 + 9*(B*a^3*b - 2*A*a^2*b^2)*x^4 + 2*(B*a^4 - 2*A*a^3*b)*x^2 - 6*((B*a*b^3 - 2*A*b^4)*x^8 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^6 + (B*a^3*b - 2*A*a^2*b^2)*x^4)*log(b*x^2 + a) + 12*((B*a*b^3 - 2*A*b^4)*x^8 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^6 + (B*a^3*b - 2*A*a^2*b^2)*x^4)*log(x))/(a^5*b^2*x^8 + 2*a^6*b*x^6 + a^7*x^4)","B",0
97,1,267,0,0.435516," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{8} + 18 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{6} - 2 \, A a^{5} + 4 \, {\left(3 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{4} - {\left(3 \, B a^{5} - 5 \, A a^{4} b\right)} x^{2} - 12 \, {\left({\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} x^{10} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{8} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{6}\right)} \log\left(b x^{2} + a\right) + 24 \, {\left({\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} x^{10} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{8} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{6}\right)} \log\left(x\right)}{12 \, {\left(a^{6} b^{2} x^{10} + 2 \, a^{7} b x^{8} + a^{8} x^{6}\right)}}"," ",0,"1/12*(12*(3*B*a^2*b^3 - 5*A*a*b^4)*x^8 + 18*(3*B*a^3*b^2 - 5*A*a^2*b^3)*x^6 - 2*A*a^5 + 4*(3*B*a^4*b - 5*A*a^3*b^2)*x^4 - (3*B*a^5 - 5*A*a^4*b)*x^2 - 12*((3*B*a*b^4 - 5*A*b^5)*x^10 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*x^8 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*x^6)*log(b*x^2 + a) + 24*((3*B*a*b^4 - 5*A*b^5)*x^10 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*x^8 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*x^6)*log(x))/(a^6*b^2*x^10 + 2*a^7*b*x^8 + a^8*x^6)","A",0
98,1,468,0,0.471082," ","integrate(x^10*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{80 \, B b^{5} x^{11} - 16 \, {\left(11 \, B a b^{4} - 7 \, A b^{5}\right)} x^{9} + 48 \, {\left(11 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{7} - 336 \, {\left(11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{5} - 1050 \, {\left(11 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{3} - 315 \, {\left(11 \, B a^{5} - 7 \, A a^{4} b + {\left(11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{4} + 2 \, {\left(11 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 630 \, {\left(11 \, B a^{5} - 7 \, A a^{4} b\right)} x}{560 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}}, \frac{40 \, B b^{5} x^{11} - 8 \, {\left(11 \, B a b^{4} - 7 \, A b^{5}\right)} x^{9} + 24 \, {\left(11 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{7} - 168 \, {\left(11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{5} - 525 \, {\left(11 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{3} + 315 \, {\left(11 \, B a^{5} - 7 \, A a^{4} b + {\left(11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{4} + 2 \, {\left(11 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 315 \, {\left(11 \, B a^{5} - 7 \, A a^{4} b\right)} x}{280 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}}\right]"," ",0,"[1/560*(80*B*b^5*x^11 - 16*(11*B*a*b^4 - 7*A*b^5)*x^9 + 48*(11*B*a^2*b^3 - 7*A*a*b^4)*x^7 - 336*(11*B*a^3*b^2 - 7*A*a^2*b^3)*x^5 - 1050*(11*B*a^4*b - 7*A*a^3*b^2)*x^3 - 315*(11*B*a^5 - 7*A*a^4*b + (11*B*a^3*b^2 - 7*A*a^2*b^3)*x^4 + 2*(11*B*a^4*b - 7*A*a^3*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 630*(11*B*a^5 - 7*A*a^4*b)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6), 1/280*(40*B*b^5*x^11 - 8*(11*B*a*b^4 - 7*A*b^5)*x^9 + 24*(11*B*a^2*b^3 - 7*A*a*b^4)*x^7 - 168*(11*B*a^3*b^2 - 7*A*a^2*b^3)*x^5 - 525*(11*B*a^4*b - 7*A*a^3*b^2)*x^3 + 315*(11*B*a^5 - 7*A*a^4*b + (11*B*a^3*b^2 - 7*A*a^2*b^3)*x^4 + 2*(11*B*a^4*b - 7*A*a^3*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 315*(11*B*a^5 - 7*A*a^4*b)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6)]","A",0
99,1,416,0,0.460417," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{48 \, B b^{4} x^{9} - 16 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{7} + 112 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{5} + 350 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3} - 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} x}{240 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}, \frac{24 \, B b^{4} x^{9} - 8 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{7} + 56 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{5} + 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3} - 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} x}{120 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}\right]"," ",0,"[1/240*(48*B*b^4*x^9 - 16*(9*B*a*b^3 - 5*A*b^4)*x^7 + 112*(9*B*a^2*b^2 - 5*A*a*b^3)*x^5 + 350*(9*B*a^3*b - 5*A*a^2*b^2)*x^3 - 105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^4 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(9*B*a^4 - 5*A*a^3*b)*x)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5), 1/120*(24*B*b^4*x^9 - 8*(9*B*a*b^3 - 5*A*b^4)*x^7 + 56*(9*B*a^2*b^2 - 5*A*a*b^3)*x^5 + 175*(9*B*a^3*b - 5*A*a^2*b^2)*x^3 - 105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^4 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(9*B*a^4 - 5*A*a^3*b)*x)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5)]","A",0
100,1,358,0,0.448264," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, B b^{3} x^{7} - 16 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{5} - 50 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{3} - 15 \, {\left({\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{4} + 7 \, B a^{3} - 3 \, A a^{2} b + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 30 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} x}{48 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}, \frac{8 \, B b^{3} x^{7} - 8 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{5} - 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{3} + 15 \, {\left({\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{4} + 7 \, B a^{3} - 3 \, A a^{2} b + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} x}{24 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}\right]"," ",0,"[1/48*(16*B*b^3*x^7 - 16*(7*B*a*b^2 - 3*A*b^3)*x^5 - 50*(7*B*a^2*b - 3*A*a*b^2)*x^3 - 15*((7*B*a*b^2 - 3*A*b^3)*x^4 + 7*B*a^3 - 3*A*a^2*b + 2*(7*B*a^2*b - 3*A*a*b^2)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 30*(7*B*a^3 - 3*A*a^2*b)*x)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4), 1/24*(8*B*b^3*x^7 - 8*(7*B*a*b^2 - 3*A*b^3)*x^5 - 25*(7*B*a^2*b - 3*A*a*b^2)*x^3 + 15*((7*B*a*b^2 - 3*A*b^3)*x^4 + 7*B*a^3 - 3*A*a^2*b + 2*(7*B*a^2*b - 3*A*a*b^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 15*(7*B*a^3 - 3*A*a^2*b)*x)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)]","A",0
101,1,328,0,0.498994," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{16 \, B a b^{3} x^{5} + 10 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3} + 3 \, {\left({\left(5 \, B a b^{2} - A b^{3}\right)} x^{4} + 5 \, B a^{3} - A a^{2} b + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} x}{16 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{8 \, B a b^{3} x^{5} + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3} - 3 \, {\left({\left(5 \, B a b^{2} - A b^{3}\right)} x^{4} + 5 \, B a^{3} - A a^{2} b + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} x}{8 \, {\left(a b^{6} x^{4} + 2 \, a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/16*(16*B*a*b^3*x^5 + 10*(5*B*a^2*b^2 - A*a*b^3)*x^3 + 3*((5*B*a*b^2 - A*b^3)*x^4 + 5*B*a^3 - A*a^2*b + 2*(5*B*a^2*b - A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(5*B*a^3*b - A*a^2*b^2)*x)/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4), 1/8*(8*B*a*b^3*x^5 + 5*(5*B*a^2*b^2 - A*a*b^3)*x^3 - 3*((5*B*a*b^2 - A*b^3)*x^4 + 5*B*a^3 - A*a^2*b + 2*(5*B*a^2*b - A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(5*B*a^3*b - A*a^2*b^2)*x)/(a*b^6*x^4 + 2*a^2*b^5*x^2 + a^3*b^4)]","A",0
102,1,301,0,0.460150," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3} + {\left({\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + 3 \, B a^{3} + A a^{2} b + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} x}{16 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}, -\frac{{\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3} - {\left({\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + 3 \, B a^{3} + A a^{2} b + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} x}{8 \, {\left(a^{2} b^{5} x^{4} + 2 \, a^{3} b^{4} x^{2} + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*B*a^2*b^2 - A*a*b^3)*x^3 + ((3*B*a*b^2 + A*b^3)*x^4 + 3*B*a^3 + A*a^2*b + 2*(3*B*a^2*b + A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(3*B*a^3*b + A*a^2*b^2)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3), -1/8*((5*B*a^2*b^2 - A*a*b^3)*x^3 - ((3*B*a*b^2 + A*b^3)*x^4 + 3*B*a^3 + A*a^2*b + 2*(3*B*a^2*b + A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*B*a^3*b + A*a^2*b^2)*x)/(a^2*b^5*x^4 + 2*a^3*b^4*x^2 + a^4*b^3)]","A",0
103,1,300,0,0.438971," ","integrate((B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{3} - {\left({\left(B a b^{2} + 3 \, A b^{3}\right)} x^{4} + B a^{3} + 3 \, A a^{2} b + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x}{16 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}, \frac{{\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{3} + {\left({\left(B a b^{2} + 3 \, A b^{3}\right)} x^{4} + B a^{3} + 3 \, A a^{2} b + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x}{8 \, {\left(a^{3} b^{4} x^{4} + 2 \, a^{4} b^{3} x^{2} + a^{5} b^{2}\right)}}\right]"," ",0,"[1/16*(2*(B*a^2*b^2 + 3*A*a*b^3)*x^3 - ((B*a*b^2 + 3*A*b^3)*x^4 + B*a^3 + 3*A*a^2*b + 2*(B*a^2*b + 3*A*a*b^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(B*a^3*b - 5*A*a^2*b^2)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2), 1/8*((B*a^2*b^2 + 3*A*a*b^3)*x^3 + ((B*a*b^2 + 3*A*b^3)*x^4 + B*a^3 + 3*A*a^2*b + 2*(B*a^2*b + 3*A*a*b^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (B*a^3*b - 5*A*a^2*b^2)*x)/(a^3*b^4*x^4 + 2*a^4*b^3*x^2 + a^5*b^2)]","A",0
104,1,324,0,0.463057," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, A a^{3} b - 6 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} - 10 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} - 3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{5} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{3} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{16 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}, -\frac{8 \, A a^{3} b - 3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} - 3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{5} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{3} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{8 \, {\left(a^{4} b^{3} x^{5} + 2 \, a^{5} b^{2} x^{3} + a^{6} b x\right)}}\right]"," ",0,"[-1/16*(16*A*a^3*b - 6*(B*a^2*b^2 - 5*A*a*b^3)*x^4 - 10*(B*a^3*b - 5*A*a^2*b^2)*x^2 - 3*((B*a*b^2 - 5*A*b^3)*x^5 + 2*(B*a^2*b - 5*A*a*b^2)*x^3 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x), -1/8*(8*A*a^3*b - 3*(B*a^2*b^2 - 5*A*a*b^3)*x^4 - 5*(B*a^3*b - 5*A*a^2*b^2)*x^2 - 3*((B*a*b^2 - 5*A*b^3)*x^5 + 2*(B*a^2*b - 5*A*a*b^2)*x^3 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^3*x^5 + 2*a^5*b^2*x^3 + a^6*b*x)]","A",0
105,1,368,0,0.480076," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{30 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 50 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + 16 \, A a^{3} + 16 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2} + 15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{5} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{48 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}, -\frac{15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2} + 15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{5} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{24 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}\right]"," ",0,"[-1/48*(30*(3*B*a*b^2 - 7*A*b^3)*x^6 + 50*(3*B*a^2*b - 7*A*a*b^2)*x^4 + 16*A*a^3 + 16*(3*B*a^3 - 7*A*a^2*b)*x^2 + 15*((3*B*a*b^2 - 7*A*b^3)*x^7 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^5 + (3*B*a^3 - 7*A*a^2*b)*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3), -1/24*(15*(3*B*a*b^2 - 7*A*b^3)*x^6 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^4 + 8*A*a^3 + 8*(3*B*a^3 - 7*A*a^2*b)*x^2 + 15*((3*B*a*b^2 - 7*A*b^3)*x^7 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^5 + (3*B*a^3 - 7*A*a^2*b)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)]","A",0
106,1,426,0,0.451282," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{210 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{8} + 350 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{6} - 48 \, A a^{4} + 112 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{4} - 16 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x^{2} - 105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{9} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{7} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{240 \, {\left(a^{5} b^{2} x^{9} + 2 \, a^{6} b x^{7} + a^{7} x^{5}\right)}}, \frac{105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{8} + 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{6} - 24 \, A a^{4} + 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{4} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x^{2} + 105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{9} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{7} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{120 \, {\left(a^{5} b^{2} x^{9} + 2 \, a^{6} b x^{7} + a^{7} x^{5}\right)}}\right]"," ",0,"[1/240*(210*(5*B*a*b^3 - 9*A*b^4)*x^8 + 350*(5*B*a^2*b^2 - 9*A*a*b^3)*x^6 - 48*A*a^4 + 112*(5*B*a^3*b - 9*A*a^2*b^2)*x^4 - 16*(5*B*a^4 - 9*A*a^3*b)*x^2 - 105*((5*B*a*b^3 - 9*A*b^4)*x^9 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^7 + (5*B*a^3*b - 9*A*a^2*b^2)*x^5)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^5*b^2*x^9 + 2*a^6*b*x^7 + a^7*x^5), 1/120*(105*(5*B*a*b^3 - 9*A*b^4)*x^8 + 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^6 - 24*A*a^4 + 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^4 - 8*(5*B*a^4 - 9*A*a^3*b)*x^2 + 105*((5*B*a*b^3 - 9*A*b^4)*x^9 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^7 + (5*B*a^3*b - 9*A*a^2*b^2)*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^5*b^2*x^9 + 2*a^6*b*x^7 + a^7*x^5)]","A",0
107,1,12,0,0.402063," ","integrate((b*x^2+a)/(x^2+1),x, algorithm=""fricas"")","b x + {\left(a - b\right)} \arctan\left(x\right)"," ",0,"b*x + (a - b)*arctan(x)","A",0
108,1,23,0,0.466188," ","integrate((b*x^2+a)/(-x^2+1),x, algorithm=""fricas"")","-b x + \frac{1}{2} \, {\left(a + b\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(a + b\right)} \log\left(x - 1\right)"," ",0,"-b*x + 1/2*(a + b)*log(x + 1) - 1/2*(a + b)*log(x - 1)","B",0
109,1,10,0,0.410614," ","integrate((x^2+1)/(x^2-1)^2,x, algorithm=""fricas"")","-\frac{x}{x^{2} - 1}"," ",0,"-x/(x^2 - 1)","A",0
110,1,9,0,0.426986," ","integrate((-x^2+1)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{x}{x^{2} + 1}"," ",0,"x/(x^2 + 1)","A",0
111,1,20,0,0.412504," ","integrate((2*x^2+3)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) + x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(5*(x^2 + 1)*arctan(x) + x)/(x^2 + 1)","A",0
112,1,21,0,0.408994," ","integrate((x^2-2)/(x^2+1)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} + 1\right)} \arctan\left(x\right) + 3 \, x}{2 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/2*((x^2 + 1)*arctan(x) + 3*x)/(x^2 + 1)","A",0
113,1,19,0,0.410649," ","integrate((x^2+3)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) + x}{x^{2} + 1}"," ",0,"(2*(x^2 + 1)*arctan(x) + x)/(x^2 + 1)","A",0
114,1,14,0,0.412569," ","integrate((b*x^2+a)/(b*x^2-a)^2,x, algorithm=""fricas"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
115,1,14,0,0.605338," ","integrate((b*x^2+a)/(-b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
116,1,98,0,0.454116," ","integrate((B*x^2+A)/(-b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{2 \, B a b x - {\left(B a + A b\right)} \sqrt{a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{a b} x + a}{b x^{2} - a}\right)}{2 \, a b^{2}}, -\frac{B a b x + {\left(B a + A b\right)} \sqrt{-a b} \arctan\left(\frac{\sqrt{-a b} x}{a}\right)}{a b^{2}}\right]"," ",0,"[-1/2*(2*B*a*b*x - (B*a + A*b)*sqrt(a*b)*log((b*x^2 + 2*sqrt(a*b)*x + a)/(b*x^2 - a)))/(a*b^2), -(B*a*b*x + (B*a + A*b)*sqrt(-a*b)*arctan(sqrt(-a*b)*x/a))/(a*b^2)]","A",0
117,1,39,0,0.481842," ","integrate((x^2+1)/(x^2+16)^3,x, algorithm=""fricas"")","\frac{76 \, x^{3} + 19 \, {\left(x^{4} + 32 \, x^{2} + 256\right)} \arctan\left(\frac{1}{4} \, x\right) - 704 \, x}{8192 \, {\left(x^{4} + 32 \, x^{2} + 256\right)}}"," ",0,"1/8192*(76*x^3 + 19*(x^4 + 32*x^2 + 256)*arctan(1/4*x) - 704*x)/(x^4 + 32*x^2 + 256)","A",0
118,1,16,0,0.760902," ","integrate((2*x^2+1)/x^5/(x^2+1)^3,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(x^{8} + 2 \, x^{6} + x^{4}\right)}}"," ",0,"-1/4/(x^8 + 2*x^6 + x^4)","A",0
119,1,1,0,0.698463," ","integrate((-x^2+1)^2/(x^2-1)^2,x, algorithm=""fricas"")","x"," ",0,"x","A",0
120,1,6,0,0.603911," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{1}{4} \, c x^{4}"," ",0,"1/4*c*x^4","A",0
121,1,6,0,0.666442," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{1}{3} \, c x^{3}"," ",0,"1/3*c*x^3","A",0
122,1,6,0,0.599301," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, c x^{2}"," ",0,"1/2*c*x^2","A",0
123,1,3,0,0.603784," ","integrate((b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""fricas"")","c x"," ",0,"c*x","A",0
124,1,4,0,0.622861," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a),x, algorithm=""fricas"")","c \log\left(x\right)"," ",0,"c*log(x)","A",0
125,1,6,0,0.617796," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a),x, algorithm=""fricas"")","-\frac{c}{x}"," ",0,"-c/x","A",0
126,1,6,0,0.634430," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a),x, algorithm=""fricas"")","-\frac{c}{2 \, x^{2}}"," ",0,"-1/2*c/x^2","A",0
127,1,24,0,0.650292," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b c x^{2} - a c \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(b*c*x^2 - a*c*log(b*x^2 + a))/b^2","A",0
128,1,86,0,0.602315," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{c \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 2 \, c x}{2 \, b}, -\frac{c \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - c x}{b}\right]"," ",0,"[1/2*(c*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 2*c*x)/b, -(c*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - c*x)/b]","A",0
129,1,14,0,0.610410," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{c \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*c*log(b*x^2 + a)/b","A",0
130,1,69,0,0.768569," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} c \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b}, \frac{\sqrt{a b} c \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b}\right]"," ",0,"[-1/2*sqrt(-a*b)*c*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a))/(a*b), sqrt(a*b)*c*arctan(sqrt(a*b)*x/a)/(a*b)]","A",0
131,1,21,0,0.705822," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{c \log\left(b x^{2} + a\right) - 2 \, c \log\left(x\right)}{2 \, a}"," ",0,"-1/2*(c*log(b*x^2 + a) - 2*c*log(x))/a","A",0
132,1,86,0,0.562572," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{c x \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, c}{2 \, a x}, -\frac{c x \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + c}{a x}\right]"," ",0,"[1/2*(c*x*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*c)/(a*x), -(c*x*sqrt(b/a)*arctan(x*sqrt(b/a)) + c)/(a*x)]","A",0
133,1,36,0,0.614480," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b c x^{2} \log\left(b x^{2} + a\right) - 2 \, b c x^{2} \log\left(x\right) - a c}{2 \, a^{2} x^{2}}"," ",0,"1/2*(b*c*x^2*log(b*x^2 + a) - 2*b*c*x^2*log(x) - a*c)/(a^2*x^2)","A",0
134,1,40,0,0.604108," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{a c + {\left(b c x^{2} + a c\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/2*(a*c + (b*c*x^2 + a*c)*log(b*x^2 + a))/(b^3*x^2 + a*b^2)","A",0
135,1,128,0,0.658255," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, a b c x + {\left(b c x^{2} + a c\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, -\frac{a b c x - {\left(b c x^{2} + a c\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*b*c*x + (b*c*x^2 + a*c)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^3*x^2 + a^2*b^2), -1/2*(a*b*c*x - (b*c*x^2 + a*c)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a*b^3*x^2 + a^2*b^2)]","A",0
136,1,16,0,0.564926," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{c}{2 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"-1/2*c/(b^2*x^2 + a*b)","A",0
137,1,128,0,0.577916," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, a b c x - {\left(b c x^{2} + a c\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{a b c x + {\left(b c x^{2} + a c\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}\right]"," ",0,"[1/4*(2*a*b*c*x - (b*c*x^2 + a*c)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^2*x^2 + a^3*b), 1/2*(a*b*c*x + (b*c*x^2 + a*c)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^2*b^2*x^2 + a^3*b)]","A",0
138,1,54,0,0.640791," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{a c - {\left(b c x^{2} + a c\right)} \log\left(b x^{2} + a\right) + 2 \, {\left(b c x^{2} + a c\right)} \log\left(x\right)}{2 \, {\left(a^{2} b x^{2} + a^{3}\right)}}"," ",0,"1/2*(a*c - (b*c*x^2 + a*c)*log(b*x^2 + a) + 2*(b*c*x^2 + a*c)*log(x))/(a^2*b*x^2 + a^3)","A",0
139,1,144,0,0.584165," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, b c x^{2} - 3 \, {\left(b c x^{3} + a c x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 4 \, a c}{4 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}, -\frac{3 \, b c x^{2} + 3 \, {\left(b c x^{3} + a c x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, a c}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}\right]"," ",0,"[-1/4*(6*b*c*x^2 - 3*(b*c*x^3 + a*c*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 4*a*c)/(a^2*b*x^3 + a^3*x), -1/2*(3*b*c*x^2 + 3*(b*c*x^3 + a*c*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*a*c)/(a^2*b*x^3 + a^3*x)]","A",0
140,1,80,0,0.528571," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{2 \, a b c x^{2} + a^{2} c - 2 \, {\left(b^{2} c x^{4} + a b c x^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left(b^{2} c x^{4} + a b c x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}"," ",0,"-1/2*(2*a*b*c*x^2 + a^2*c - 2*(b^2*c*x^4 + a*b*c*x^2)*log(b*x^2 + a) + 4*(b^2*c*x^4 + a*b*c*x^2)*log(x))/(a^3*b*x^4 + a^4*x^2)","A",0
141,1,53,0,0.499031," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{11} x^{11} d b^{2} + \frac{1}{9} x^{9} c b^{2} + \frac{2}{9} x^{9} d b a + \frac{2}{7} x^{7} c b a + \frac{1}{7} x^{7} d a^{2} + \frac{1}{5} x^{5} c a^{2}"," ",0,"1/11*x^11*d*b^2 + 1/9*x^9*c*b^2 + 2/9*x^9*d*b*a + 2/7*x^7*c*b*a + 1/7*x^7*d*a^2 + 1/5*x^5*c*a^2","A",0
142,1,53,0,0.537396," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{10} x^{10} d b^{2} + \frac{1}{8} x^{8} c b^{2} + \frac{1}{4} x^{8} d b a + \frac{1}{3} x^{6} c b a + \frac{1}{6} x^{6} d a^{2} + \frac{1}{4} x^{4} c a^{2}"," ",0,"1/10*x^10*d*b^2 + 1/8*x^8*c*b^2 + 1/4*x^8*d*b*a + 1/3*x^6*c*b*a + 1/6*x^6*d*a^2 + 1/4*x^4*c*a^2","A",0
143,1,53,0,0.535404," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{9} x^{9} d b^{2} + \frac{1}{7} x^{7} c b^{2} + \frac{2}{7} x^{7} d b a + \frac{2}{5} x^{5} c b a + \frac{1}{5} x^{5} d a^{2} + \frac{1}{3} x^{3} c a^{2}"," ",0,"1/9*x^9*d*b^2 + 1/7*x^7*c*b^2 + 2/7*x^7*d*b*a + 2/5*x^5*c*b*a + 1/5*x^5*d*a^2 + 1/3*x^3*c*a^2","A",0
144,1,53,0,0.436026," ","integrate(x*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{8} x^{8} d b^{2} + \frac{1}{6} x^{6} c b^{2} + \frac{1}{3} x^{6} d b a + \frac{1}{2} x^{4} c b a + \frac{1}{4} x^{4} d a^{2} + \frac{1}{2} x^{2} c a^{2}"," ",0,"1/8*x^8*d*b^2 + 1/6*x^6*c*b^2 + 1/3*x^6*d*b*a + 1/2*x^4*c*b*a + 1/4*x^4*d*a^2 + 1/2*x^2*c*a^2","A",0
145,1,50,0,0.529077," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{1}{7} x^{7} d b^{2} + \frac{1}{5} x^{5} c b^{2} + \frac{2}{5} x^{5} d b a + \frac{2}{3} x^{3} c b a + \frac{1}{3} x^{3} d a^{2} + x c a^{2}"," ",0,"1/7*x^7*d*b^2 + 1/5*x^5*c*b^2 + 2/5*x^5*d*b*a + 2/3*x^3*c*b*a + 1/3*x^3*d*a^2 + x*c*a^2","A",0
146,1,49,0,0.566706," ","integrate((b*x^2+a)^2*(d*x^2+c)/x,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} d x^{6} + \frac{1}{4} \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c \log\left(x\right) + \frac{1}{2} \, {\left(2 \, a b c + a^{2} d\right)} x^{2}"," ",0,"1/6*b^2*d*x^6 + 1/4*(b^2*c + 2*a*b*d)*x^4 + a^2*c*log(x) + 1/2*(2*a*b*c + a^2*d)*x^2","A",0
147,1,53,0,0.599625," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} d x^{6} + 5 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} - 15 \, a^{2} c + 15 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}}{15 \, x}"," ",0,"1/15*(3*b^2*d*x^6 + 5*(b^2*c + 2*a*b*d)*x^4 - 15*a^2*c + 15*(2*a*b*c + a^2*d)*x^2)/x","A",0
148,1,54,0,0.570868," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^3,x, algorithm=""fricas"")","\frac{b^{2} d x^{6} + 2 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} + 4 \, {\left(2 \, a b c + a^{2} d\right)} x^{2} \log\left(x\right) - 2 \, a^{2} c}{4 \, x^{2}}"," ",0,"1/4*(b^2*d*x^6 + 2*(b^2*c + 2*a*b*d)*x^4 + 4*(2*a*b*c + a^2*d)*x^2*log(x) - 2*a^2*c)/x^2","A",0
149,1,52,0,0.491189," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^4,x, algorithm=""fricas"")","\frac{b^{2} d x^{6} + 3 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} - a^{2} c - 3 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/3*(b^2*d*x^6 + 3*(b^2*c + 2*a*b*d)*x^4 - a^2*c - 3*(2*a*b*c + a^2*d)*x^2)/x^3","A",0
150,1,94,0,0.535627," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{2} b^{2} + \frac{2}{11} x^{11} d c b^{2} + \frac{2}{11} x^{11} d^{2} b a + \frac{1}{9} x^{9} c^{2} b^{2} + \frac{4}{9} x^{9} d c b a + \frac{1}{9} x^{9} d^{2} a^{2} + \frac{2}{7} x^{7} c^{2} b a + \frac{2}{7} x^{7} d c a^{2} + \frac{1}{5} x^{5} c^{2} a^{2}"," ",0,"1/13*x^13*d^2*b^2 + 2/11*x^11*d*c*b^2 + 2/11*x^11*d^2*b*a + 1/9*x^9*c^2*b^2 + 4/9*x^9*d*c*b*a + 1/9*x^9*d^2*a^2 + 2/7*x^7*c^2*b*a + 2/7*x^7*d*c*a^2 + 1/5*x^5*c^2*a^2","A",0
151,1,94,0,0.474333," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{12} x^{12} d^{2} b^{2} + \frac{1}{5} x^{10} d c b^{2} + \frac{1}{5} x^{10} d^{2} b a + \frac{1}{8} x^{8} c^{2} b^{2} + \frac{1}{2} x^{8} d c b a + \frac{1}{8} x^{8} d^{2} a^{2} + \frac{1}{3} x^{6} c^{2} b a + \frac{1}{3} x^{6} d c a^{2} + \frac{1}{4} x^{4} c^{2} a^{2}"," ",0,"1/12*x^12*d^2*b^2 + 1/5*x^10*d*c*b^2 + 1/5*x^10*d^2*b*a + 1/8*x^8*c^2*b^2 + 1/2*x^8*d*c*b*a + 1/8*x^8*d^2*a^2 + 1/3*x^6*c^2*b*a + 1/3*x^6*d*c*a^2 + 1/4*x^4*c^2*a^2","A",0
152,1,94,0,0.502729," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} d^{2} b^{2} + \frac{2}{9} x^{9} d c b^{2} + \frac{2}{9} x^{9} d^{2} b a + \frac{1}{7} x^{7} c^{2} b^{2} + \frac{4}{7} x^{7} d c b a + \frac{1}{7} x^{7} d^{2} a^{2} + \frac{2}{5} x^{5} c^{2} b a + \frac{2}{5} x^{5} d c a^{2} + \frac{1}{3} x^{3} c^{2} a^{2}"," ",0,"1/11*x^11*d^2*b^2 + 2/9*x^9*d*c*b^2 + 2/9*x^9*d^2*b*a + 1/7*x^7*c^2*b^2 + 4/7*x^7*d*c*b*a + 1/7*x^7*d^2*a^2 + 2/5*x^5*c^2*b*a + 2/5*x^5*d*c*a^2 + 1/3*x^3*c^2*a^2","A",0
153,1,94,0,0.625756," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d^{2} b^{2} + \frac{1}{4} x^{8} d c b^{2} + \frac{1}{4} x^{8} d^{2} b a + \frac{1}{6} x^{6} c^{2} b^{2} + \frac{2}{3} x^{6} d c b a + \frac{1}{6} x^{6} d^{2} a^{2} + \frac{1}{2} x^{4} c^{2} b a + \frac{1}{2} x^{4} d c a^{2} + \frac{1}{2} x^{2} c^{2} a^{2}"," ",0,"1/10*x^10*d^2*b^2 + 1/4*x^8*d*c*b^2 + 1/4*x^8*d^2*b*a + 1/6*x^6*c^2*b^2 + 2/3*x^6*d*c*b*a + 1/6*x^6*d^2*a^2 + 1/2*x^4*c^2*b*a + 1/2*x^4*d*c*a^2 + 1/2*x^2*c^2*a^2","A",0
154,1,91,0,0.743763," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} d^{2} b^{2} + \frac{2}{7} x^{7} d c b^{2} + \frac{2}{7} x^{7} d^{2} b a + \frac{1}{5} x^{5} c^{2} b^{2} + \frac{4}{5} x^{5} d c b a + \frac{1}{5} x^{5} d^{2} a^{2} + \frac{2}{3} x^{3} c^{2} b a + \frac{2}{3} x^{3} d c a^{2} + x c^{2} a^{2}"," ",0,"1/9*x^9*d^2*b^2 + 2/7*x^7*d*c*b^2 + 2/7*x^7*d^2*b*a + 1/5*x^5*c^2*b^2 + 4/5*x^5*d*c*b*a + 1/5*x^5*d^2*a^2 + 2/3*x^3*c^2*b*a + 2/3*x^3*d*c*a^2 + x*c^2*a^2","A",0
155,1,82,0,0.671277," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x,x, algorithm=""fricas"")","\frac{1}{8} \, b^{2} d^{2} x^{8} + \frac{1}{3} \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + \frac{1}{4} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} \log\left(x\right) + {\left(a b c^{2} + a^{2} c d\right)} x^{2}"," ",0,"1/8*b^2*d^2*x^8 + 1/3*(b^2*c*d + a*b*d^2)*x^6 + 1/4*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2*log(x) + (a*b*c^2 + a^2*c*d)*x^2","A",0
156,1,87,0,0.701562," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} d^{2} x^{8} + 42 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 35 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 105 \, a^{2} c^{2} + 210 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}{105 \, x}"," ",0,"1/105*(15*b^2*d^2*x^8 + 42*(b^2*c*d + a*b*d^2)*x^6 + 35*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 105*a^2*c^2 + 210*(a*b*c^2 + a^2*c*d)*x^2)/x","A",0
157,1,88,0,0.569916," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^3,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{8} + 3 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 3 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 3 \, a^{2} c^{2} + 12 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} \log\left(x\right)}{6 \, x^{2}}"," ",0,"1/6*(b^2*d^2*x^8 + 3*(b^2*c*d + a*b*d^2)*x^6 + 3*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 3*a^2*c^2 + 12*(a*b*c^2 + a^2*c*d)*x^2*log(x))/x^2","A",0
158,1,87,0,0.695311," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} x^{8} + 10 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 15 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 5 \, a^{2} c^{2} - 30 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}{15 \, x^{3}}"," ",0,"1/15*(3*b^2*d^2*x^8 + 10*(b^2*c*d + a*b*d^2)*x^6 + 15*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 5*a^2*c^2 - 30*(a*b*c^2 + a^2*c*d)*x^2)/x^3","A",0
159,1,135,0,0.559021," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} d^{3} b^{2} + \frac{3}{13} x^{13} d^{2} c b^{2} + \frac{2}{13} x^{13} d^{3} b a + \frac{3}{11} x^{11} d c^{2} b^{2} + \frac{6}{11} x^{11} d^{2} c b a + \frac{1}{11} x^{11} d^{3} a^{2} + \frac{1}{9} x^{9} c^{3} b^{2} + \frac{2}{3} x^{9} d c^{2} b a + \frac{1}{3} x^{9} d^{2} c a^{2} + \frac{2}{7} x^{7} c^{3} b a + \frac{3}{7} x^{7} d c^{2} a^{2} + \frac{1}{5} x^{5} c^{3} a^{2}"," ",0,"1/15*x^15*d^3*b^2 + 3/13*x^13*d^2*c*b^2 + 2/13*x^13*d^3*b*a + 3/11*x^11*d*c^2*b^2 + 6/11*x^11*d^2*c*b*a + 1/11*x^11*d^3*a^2 + 1/9*x^9*c^3*b^2 + 2/3*x^9*d*c^2*b*a + 1/3*x^9*d^2*c*a^2 + 2/7*x^7*c^3*b*a + 3/7*x^7*d*c^2*a^2 + 1/5*x^5*c^3*a^2","A",0
160,1,135,0,0.444406," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} d^{3} b^{2} + \frac{1}{4} x^{12} d^{2} c b^{2} + \frac{1}{6} x^{12} d^{3} b a + \frac{3}{10} x^{10} d c^{2} b^{2} + \frac{3}{5} x^{10} d^{2} c b a + \frac{1}{10} x^{10} d^{3} a^{2} + \frac{1}{8} x^{8} c^{3} b^{2} + \frac{3}{4} x^{8} d c^{2} b a + \frac{3}{8} x^{8} d^{2} c a^{2} + \frac{1}{3} x^{6} c^{3} b a + \frac{1}{2} x^{6} d c^{2} a^{2} + \frac{1}{4} x^{4} c^{3} a^{2}"," ",0,"1/14*x^14*d^3*b^2 + 1/4*x^12*d^2*c*b^2 + 1/6*x^12*d^3*b*a + 3/10*x^10*d*c^2*b^2 + 3/5*x^10*d^2*c*b*a + 1/10*x^10*d^3*a^2 + 1/8*x^8*c^3*b^2 + 3/4*x^8*d*c^2*b*a + 3/8*x^8*d^2*c*a^2 + 1/3*x^6*c^3*b*a + 1/2*x^6*d*c^2*a^2 + 1/4*x^4*c^3*a^2","A",0
161,1,135,0,0.669748," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} d^{3} b^{2} + \frac{3}{11} x^{11} d^{2} c b^{2} + \frac{2}{11} x^{11} d^{3} b a + \frac{1}{3} x^{9} d c^{2} b^{2} + \frac{2}{3} x^{9} d^{2} c b a + \frac{1}{9} x^{9} d^{3} a^{2} + \frac{1}{7} x^{7} c^{3} b^{2} + \frac{6}{7} x^{7} d c^{2} b a + \frac{3}{7} x^{7} d^{2} c a^{2} + \frac{2}{5} x^{5} c^{3} b a + \frac{3}{5} x^{5} d c^{2} a^{2} + \frac{1}{3} x^{3} c^{3} a^{2}"," ",0,"1/13*x^13*d^3*b^2 + 3/11*x^11*d^2*c*b^2 + 2/11*x^11*d^3*b*a + 1/3*x^9*d*c^2*b^2 + 2/3*x^9*d^2*c*b*a + 1/9*x^9*d^3*a^2 + 1/7*x^7*c^3*b^2 + 6/7*x^7*d*c^2*b*a + 3/7*x^7*d^2*c*a^2 + 2/5*x^5*c^3*b*a + 3/5*x^5*d*c^2*a^2 + 1/3*x^3*c^3*a^2","A",0
162,1,134,0,0.485599," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} d^{3} b^{2} + \frac{3}{10} x^{10} d^{2} c b^{2} + \frac{1}{5} x^{10} d^{3} b a + \frac{3}{8} x^{8} d c^{2} b^{2} + \frac{3}{4} x^{8} d^{2} c b a + \frac{1}{8} x^{8} d^{3} a^{2} + \frac{1}{6} x^{6} c^{3} b^{2} + x^{6} d c^{2} b a + \frac{1}{2} x^{6} d^{2} c a^{2} + \frac{1}{2} x^{4} c^{3} b a + \frac{3}{4} x^{4} d c^{2} a^{2} + \frac{1}{2} x^{2} c^{3} a^{2}"," ",0,"1/12*x^12*d^3*b^2 + 3/10*x^10*d^2*c*b^2 + 1/5*x^10*d^3*b*a + 3/8*x^8*d*c^2*b^2 + 3/4*x^8*d^2*c*b*a + 1/8*x^8*d^3*a^2 + 1/6*x^6*c^3*b^2 + x^6*d*c^2*b*a + 1/2*x^6*d^2*c*a^2 + 1/2*x^4*c^3*b*a + 3/4*x^4*d*c^2*a^2 + 1/2*x^2*c^3*a^2","B",0
163,1,131,0,0.588930," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} d^{3} b^{2} + \frac{1}{3} x^{9} d^{2} c b^{2} + \frac{2}{9} x^{9} d^{3} b a + \frac{3}{7} x^{7} d c^{2} b^{2} + \frac{6}{7} x^{7} d^{2} c b a + \frac{1}{7} x^{7} d^{3} a^{2} + \frac{1}{5} x^{5} c^{3} b^{2} + \frac{6}{5} x^{5} d c^{2} b a + \frac{3}{5} x^{5} d^{2} c a^{2} + \frac{2}{3} x^{3} c^{3} b a + x^{3} d c^{2} a^{2} + x c^{3} a^{2}"," ",0,"1/11*x^11*d^3*b^2 + 1/3*x^9*d^2*c*b^2 + 2/9*x^9*d^3*b*a + 3/7*x^7*d*c^2*b^2 + 6/7*x^7*d^2*c*b*a + 1/7*x^7*d^3*a^2 + 1/5*x^5*c^3*b^2 + 6/5*x^5*d*c^2*b*a + 3/5*x^5*d^2*c*a^2 + 2/3*x^3*c^3*b*a + x^3*d*c^2*a^2 + x*c^3*a^2","A",0
164,1,125,0,0.559973," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x,x, algorithm=""fricas"")","\frac{1}{10} \, b^{2} d^{3} x^{10} + \frac{1}{8} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + \frac{1}{6} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} + a^{2} c^{3} \log\left(x\right) + \frac{1}{4} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + \frac{1}{2} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}"," ",0,"1/10*b^2*d^3*x^10 + 1/8*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 1/6*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 + a^2*c^3*log(x) + 1/4*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 1/2*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2","A",0
165,1,129,0,0.565203," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^2,x, algorithm=""fricas"")","\frac{35 \, b^{2} d^{3} x^{10} + 45 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 63 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 315 \, a^{2} c^{3} + 105 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + 315 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}}{315 \, x}"," ",0,"1/315*(35*b^2*d^3*x^10 + 45*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 63*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 315*a^2*c^3 + 105*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 315*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x","A",0
166,1,131,0,0.661226," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{3} x^{10} + 4 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 6 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 12 \, a^{2} c^{3} + 12 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + 24 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2} \log\left(x\right)}{24 \, x^{2}}"," ",0,"1/24*(3*b^2*d^3*x^10 + 4*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 6*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 12*a^2*c^3 + 12*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 24*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2*log(x))/x^2","A",0
167,1,129,0,0.710629," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^4,x, algorithm=""fricas"")","\frac{15 \, b^{2} d^{3} x^{10} + 21 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 35 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 35 \, a^{2} c^{3} + 105 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 105 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}}{105 \, x^{3}}"," ",0,"1/105*(15*b^2*d^3*x^10 + 21*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 35*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 35*a^2*c^3 + 105*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 105*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x^3","A",0
168,1,302,0,0.630706," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{30 \, b^{2} d^{3} x^{7} - 42 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{5} + 70 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} + 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - 210 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x}{210 \, d^{4}}, \frac{15 \, b^{2} d^{3} x^{7} - 21 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{5} + 35 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x}{105 \, d^{4}}\right]"," ",0,"[1/210*(30*b^2*d^3*x^7 - 42*(b^2*c*d^2 - 2*a*b*d^3)*x^5 + 70*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^3 + 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(-c/d)*log((d*x^2 + 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - 210*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x)/d^4, 1/105*(15*b^2*d^3*x^7 - 21*(b^2*c*d^2 - 2*a*b*d^3)*x^5 + 35*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^3 + 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x)/d^4]","A",0
169,1,101,0,0.460020," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{3} x^{6} - 3 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{4} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \log\left(d x^{2} + c\right)}{12 \, d^{4}}"," ",0,"1/12*(2*b^2*d^3*x^6 - 3*(b^2*c*d^2 - 2*a*b*d^3)*x^4 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^2 - 6*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*log(d*x^2 + c))/d^4","A",0
170,1,228,0,0.573079," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{6 \, b^{2} d^{2} x^{5} - 10 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{3} + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) + 30 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{30 \, d^{3}}, \frac{3 \, b^{2} d^{2} x^{5} - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{3} - 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{15 \, d^{3}}\right]"," ",0,"[1/30*(6*b^2*d^2*x^5 - 10*(b^2*c*d - 2*a*b*d^2)*x^3 + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) + 30*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/d^3, 1/15*(3*b^2*d^2*x^5 - 5*(b^2*c*d - 2*a*b*d^2)*x^3 - 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/d^3]","A",0
171,1,66,0,0.900983," ","integrate(x*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{4} - 2 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, d^{3}}"," ",0,"1/4*(b^2*d^2*x^4 - 2*(b^2*c*d - 2*a*b*d^2)*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x^2 + c))/d^3","A",0
172,1,179,0,0.837482," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, b^{2} c d^{2} x^{3} - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x}{6 \, c d^{3}}, \frac{b^{2} c d^{2} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x}{3 \, c d^{3}}\right]"," ",0,"[1/6*(2*b^2*c*d^2*x^3 - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 6*(b^2*c^2*d - 2*a*b*c*d^2)*x)/(c*d^3), 1/3*(b^2*c*d^2*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 3*(b^2*c^2*d - 2*a*b*c*d^2)*x)/(c*d^3)]","A",0
173,1,59,0,0.848379," ","integrate((b*x^2+a)^2/x/(d*x^2+c),x, algorithm=""fricas"")","\frac{b^{2} c d x^{2} + 2 \, a^{2} d^{2} \log\left(x\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, c d^{2}}"," ",0,"1/2*(b^2*c*d*x^2 + 2*a^2*d^2*log(x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x^2 + c))/(c*d^2)","A",0
174,1,164,0,0.879155," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{2 \, b^{2} c^{2} d x^{2} - 2 \, a^{2} c d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d} x \log\left(\frac{d x^{2} + 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{2 \, c^{2} d^{2} x}, \frac{b^{2} c^{2} d x^{2} - a^{2} c d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d} x \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{c^{2} d^{2} x}\right]"," ",0,"[1/2*(2*b^2*c^2*d*x^2 - 2*a^2*c*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d)*x*log((d*x^2 + 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c^2*d^2*x), (b^2*c^2*d*x^2 - a^2*c*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)*x*arctan(sqrt(c*d)*x/c))/(c^2*d^2*x)]","A",0
175,1,74,0,0.872163," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c),x, algorithm=""fricas"")","-\frac{a^{2} c d - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \log\left(d x^{2} + c\right) - 2 \, {\left(2 \, a b c d - a^{2} d^{2}\right)} x^{2} \log\left(x\right)}{2 \, c^{2} d x^{2}}"," ",0,"-1/2*(a^2*c*d - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*log(d*x^2 + c) - 2*(2*a*b*c*d - a^2*d^2)*x^2*log(x))/(c^2*d*x^2)","A",0
176,1,192,0,0.578415," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c d} x^{3} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, a^{2} c^{2} d + 6 \, {\left(2 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{2}}{6 \, c^{3} d x^{3}}, \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d} x^{3} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - a^{2} c^{2} d - 3 \, {\left(2 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{2}}{3 \, c^{3} d x^{3}}\right]"," ",0,"[-1/6*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c*d)*x^3*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*a^2*c^2*d + 6*(2*a*b*c^2*d - a^2*c*d^2)*x^2)/(c^3*d*x^3), 1/3*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)*x^3*arctan(sqrt(c*d)*x/c) - a^2*c^2*d - 3*(2*a*b*c^2*d - a^2*c*d^2)*x^2)/(c^3*d*x^3)]","A",0
177,1,98,0,0.891782," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} \log\left(d x^{2} + c\right) - 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} \log\left(x\right) + a^{2} c^{2} + 2 \, {\left(2 \, a b c^{2} - a^{2} c d\right)} x^{2}}{4 \, c^{3} x^{4}}"," ",0,"-1/4*(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4*log(d*x^2 + c) - 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4*log(x) + a^2*c^2 + 2*(2*a*b*c^2 - a^2*c*d)*x^2)/(c^3*x^4)","A",0
178,1,236,0,1.118017," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{5} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 30 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} - 6 \, a^{2} c^{2} - 10 \, {\left(2 \, a b c^{2} - a^{2} c d\right)} x^{2}}{30 \, c^{3} x^{5}}, -\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{5} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} + 5 \, {\left(2 \, a b c^{2} - a^{2} c d\right)} x^{2}}{15 \, c^{3} x^{5}}\right]"," ",0,"[1/30*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^5*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 30*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4 - 6*a^2*c^2 - 10*(2*a*b*c^2 - a^2*c*d)*x^2)/(c^3*x^5), -1/15*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^5*sqrt(d/c)*arctan(x*sqrt(d/c)) + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4 + 3*a^2*c^2 + 5*(2*a*b*c^2 - a^2*c*d)*x^2)/(c^3*x^5)]","A",0
179,1,136,0,0.623459," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c),x, algorithm=""fricas"")","\frac{6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} \log\left(d x^{2} + c\right) - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} \log\left(x\right) - 2 \, a^{2} c^{3} - 6 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x^{4} - 3 \, {\left(2 \, a b c^{3} - a^{2} c^{2} d\right)} x^{2}}{12 \, c^{4} x^{6}}"," ",0,"1/12*(6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^6*log(d*x^2 + c) - 12*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^6*log(x) - 2*a^2*c^3 - 6*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x^4 - 3*(2*a*b*c^3 - a^2*c^2*d)*x^2)/(c^4*x^6)","A",0
180,1,400,0,0.795611," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{12 \, b^{2} d^{3} x^{7} - 4 \, {\left(7 \, b^{2} c d^{2} - 10 \, a b d^{3}\right)} x^{5} + 20 \, {\left(7 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{3} + 15 \, {\left(7 \, b^{2} c^{3} - 10 \, a b c^{2} d + 3 \, a^{2} c d^{2} + {\left(7 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) + 30 \, {\left(7 \, b^{2} c^{3} - 10 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x}{60 \, {\left(d^{5} x^{2} + c d^{4}\right)}}, \frac{6 \, b^{2} d^{3} x^{7} - 2 \, {\left(7 \, b^{2} c d^{2} - 10 \, a b d^{3}\right)} x^{5} + 10 \, {\left(7 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{3} - 15 \, {\left(7 \, b^{2} c^{3} - 10 \, a b c^{2} d + 3 \, a^{2} c d^{2} + {\left(7 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + 15 \, {\left(7 \, b^{2} c^{3} - 10 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x}{30 \, {\left(d^{5} x^{2} + c d^{4}\right)}}\right]"," ",0,"[1/60*(12*b^2*d^3*x^7 - 4*(7*b^2*c*d^2 - 10*a*b*d^3)*x^5 + 20*(7*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*x^3 + 15*(7*b^2*c^3 - 10*a*b*c^2*d + 3*a^2*c*d^2 + (7*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*x^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) + 30*(7*b^2*c^3 - 10*a*b*c^2*d + 3*a^2*c*d^2)*x)/(d^5*x^2 + c*d^4), 1/30*(6*b^2*d^3*x^7 - 2*(7*b^2*c*d^2 - 10*a*b*d^3)*x^5 + 10*(7*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*x^3 - 15*(7*b^2*c^3 - 10*a*b*c^2*d + 3*a^2*c*d^2 + (7*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*x^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + 15*(7*b^2*c^3 - 10*a*b*c^2*d + 3*a^2*c*d^2)*x)/(d^5*x^2 + c*d^4)]","A",0
181,1,161,0,0.596887," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{3} x^{6} + 2 \, b^{2} c^{3} - 4 \, a b c^{2} d + 2 \, a^{2} c d^{2} - {\left(3 \, b^{2} c d^{2} - 4 \, a b d^{3}\right)} x^{4} - 4 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} x^{2} + 2 \, {\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(d^{5} x^{2} + c d^{4}\right)}}"," ",0,"1/4*(b^2*d^3*x^6 + 2*b^2*c^3 - 4*a*b*c^2*d + 2*a^2*c*d^2 - (3*b^2*c*d^2 - 4*a*b*d^3)*x^4 - 4*(b^2*c^2*d - a*b*c*d^2)*x^2 + 2*(3*b^2*c^3 - 4*a*b*c^2*d + a^2*c*d^2 + (3*b^2*c^2*d - 4*a*b*c*d^2 + a^2*d^3)*x^2)*log(d*x^2 + c))/(d^5*x^2 + c*d^4)","A",0
182,1,342,0,0.803941," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b^{2} c d^{3} x^{5} - 4 \, {\left(5 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3}\right)} x^{3} - 3 \, {\left(5 \, b^{2} c^{3} - 6 \, a b c^{2} d + a^{2} c d^{2} + {\left(5 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 6 \, {\left(5 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{12 \, {\left(c d^{5} x^{2} + c^{2} d^{4}\right)}}, \frac{2 \, b^{2} c d^{3} x^{5} - 2 \, {\left(5 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{3} - 6 \, a b c^{2} d + a^{2} c d^{2} + {\left(5 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 3 \, {\left(5 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{6 \, {\left(c d^{5} x^{2} + c^{2} d^{4}\right)}}\right]"," ",0,"[1/12*(4*b^2*c*d^3*x^5 - 4*(5*b^2*c^2*d^2 - 6*a*b*c*d^3)*x^3 - 3*(5*b^2*c^3 - 6*a*b*c^2*d + a^2*c*d^2 + (5*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 6*(5*b^2*c^3*d - 6*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c*d^5*x^2 + c^2*d^4), 1/6*(2*b^2*c*d^3*x^5 - 2*(5*b^2*c^2*d^2 - 6*a*b*c*d^3)*x^3 + 3*(5*b^2*c^3 - 6*a*b*c^2*d + a^2*c*d^2 + (5*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 3*(5*b^2*c^3*d - 6*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c*d^5*x^2 + c^2*d^4)]","A",0
183,1,101,0,0.795325," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{4} + b^{2} c d x^{2} - b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} - 2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(d^{4} x^{2} + c d^{3}\right)}}"," ",0,"1/2*(b^2*d^2*x^4 + b^2*c*d*x^2 - b^2*c^2 + 2*a*b*c*d - a^2*d^2 - 2*(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)*log(d*x^2 + c))/(d^4*x^2 + c*d^3)","A",0
184,1,302,0,0.915040," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b^{2} c^{2} d^{2} x^{3} + {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{4 \, {\left(c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}, \frac{2 \, b^{2} c^{2} d^{2} x^{3} - {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x}{2 \, {\left(c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}\right]"," ",0,"[1/4*(4*b^2*c^2*d^2*x^3 + (3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c^2*d^4*x^2 + c^3*d^3), 1/2*(2*b^2*c^2*d^2*x^3 - (3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)/(c^2*d^4*x^2 + c^3*d^3)]","B",0
185,1,116,0,0.654668," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{3} - a^{2} c d^{2} + {\left(b^{2} c^{2} d - a^{2} d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left(a^{2} d^{3} x^{2} + a^{2} c d^{2}\right)} \log\left(x\right)}{2 \, {\left(c^{2} d^{3} x^{2} + c^{3} d^{2}\right)}}"," ",0,"1/2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^3 - a^2*c*d^2 + (b^2*c^2*d - a^2*d^3)*x^2)*log(d*x^2 + c) + 2*(a^2*d^3*x^2 + a^2*c*d^2)*log(x))/(c^2*d^3*x^2 + c^3*d^2)","A",0
186,1,305,0,0.798471," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} c^{2} d^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2} - {\left({\left(b^{2} c^{2} d + 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-c d} \log\left(\frac{d x^{2} + 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{4 \, {\left(c^{3} d^{3} x^{3} + c^{4} d^{2} x\right)}}, -\frac{2 \, a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2} - {\left({\left(b^{2} c^{2} d + 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{2 \, {\left(c^{3} d^{3} x^{3} + c^{4} d^{2} x\right)}}\right]"," ",0,"[-1/4*(4*a^2*c^2*d^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2 - ((b^2*c^2*d + 2*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (b^2*c^3 + 2*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-c*d)*log((d*x^2 + 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c^3*d^3*x^3 + c^4*d^2*x), -1/2*(2*a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2 - ((b^2*c^2*d + 2*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (b^2*c^3 + 2*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(c*d)*arctan(sqrt(c*d)*x/c))/(c^3*d^3*x^3 + c^4*d^2*x)]","A",0
187,1,159,0,0.890703," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} c^{2} d + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + 2 \, a^{2} c d^{2}\right)} x^{2} + 2 \, {\left({\left(a b c d^{2} - a^{2} d^{3}\right)} x^{4} + {\left(a b c^{2} d - a^{2} c d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) - 4 \, {\left({\left(a b c d^{2} - a^{2} d^{3}\right)} x^{4} + {\left(a b c^{2} d - a^{2} c d^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(c^{3} d^{2} x^{4} + c^{4} d x^{2}\right)}}"," ",0,"-1/2*(a^2*c^2*d + (b^2*c^3 - 2*a*b*c^2*d + 2*a^2*c*d^2)*x^2 + 2*((a*b*c*d^2 - a^2*d^3)*x^4 + (a*b*c^2*d - a^2*c*d^2)*x^2)*log(d*x^2 + c) - 4*((a*b*c*d^2 - a^2*d^3)*x^4 + (a*b*c^2*d - a^2*c*d^2)*x^2)*log(x))/(c^3*d^2*x^4 + c^4*d*x^2)","B",0
188,1,356,0,0.789032," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} c^{3} d - 6 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{4} + 4 \, {\left(6 \, a b c^{3} d - 5 \, a^{2} c^{2} d^{2}\right)} x^{2} + 3 \, {\left({\left(b^{2} c^{2} d - 6 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{5} + {\left(b^{2} c^{3} - 6 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{12 \, {\left(c^{4} d^{2} x^{5} + c^{5} d x^{3}\right)}}, -\frac{2 \, a^{2} c^{3} d - 3 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{4} + 2 \, {\left(6 \, a b c^{3} d - 5 \, a^{2} c^{2} d^{2}\right)} x^{2} - 3 \, {\left({\left(b^{2} c^{2} d - 6 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{5} + {\left(b^{2} c^{3} - 6 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{6 \, {\left(c^{4} d^{2} x^{5} + c^{5} d x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^2*c^3*d - 6*(b^2*c^3*d - 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^4 + 4*(6*a*b*c^3*d - 5*a^2*c^2*d^2)*x^2 + 3*((b^2*c^2*d - 6*a*b*c*d^2 + 5*a^2*d^3)*x^5 + (b^2*c^3 - 6*a*b*c^2*d + 5*a^2*c*d^2)*x^3)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c^4*d^2*x^5 + c^5*d*x^3), -1/6*(2*a^2*c^3*d - 3*(b^2*c^3*d - 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^4 + 2*(6*a*b*c^3*d - 5*a^2*c^2*d^2)*x^2 - 3*((b^2*c^2*d - 6*a*b*c*d^2 + 5*a^2*d^3)*x^5 + (b^2*c^3 - 6*a*b*c^2*d + 5*a^2*c*d^2)*x^3)*sqrt(c*d)*arctan(sqrt(c*d)*x/c))/(c^4*d^2*x^5 + c^5*d*x^3)]","A",0
189,1,522,0,0.713061," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{16 \, b^{2} c d^{4} x^{7} - 16 \, {\left(7 \, b^{2} c^{2} d^{3} - 6 \, a b c d^{4}\right)} x^{5} - 10 \, {\left(35 \, b^{2} c^{3} d^{2} - 30 \, a b c^{2} d^{3} + 3 \, a^{2} c d^{4}\right)} x^{3} - 3 \, {\left(35 \, b^{2} c^{4} - 30 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 6 \, {\left(35 \, b^{2} c^{4} d - 30 \, a b c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3}\right)} x}{48 \, {\left(c d^{7} x^{4} + 2 \, c^{2} d^{6} x^{2} + c^{3} d^{5}\right)}}, \frac{8 \, b^{2} c d^{4} x^{7} - 8 \, {\left(7 \, b^{2} c^{2} d^{3} - 6 \, a b c d^{4}\right)} x^{5} - 5 \, {\left(35 \, b^{2} c^{3} d^{2} - 30 \, a b c^{2} d^{3} + 3 \, a^{2} c d^{4}\right)} x^{3} + 3 \, {\left(35 \, b^{2} c^{4} - 30 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 3 \, {\left(35 \, b^{2} c^{4} d - 30 \, a b c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3}\right)} x}{24 \, {\left(c d^{7} x^{4} + 2 \, c^{2} d^{6} x^{2} + c^{3} d^{5}\right)}}\right]"," ",0,"[1/48*(16*b^2*c*d^4*x^7 - 16*(7*b^2*c^2*d^3 - 6*a*b*c*d^4)*x^5 - 10*(35*b^2*c^3*d^2 - 30*a*b*c^2*d^3 + 3*a^2*c*d^4)*x^3 - 3*(35*b^2*c^4 - 30*a*b*c^3*d + 3*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 30*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(35*b^2*c^3*d - 30*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 6*(35*b^2*c^4*d - 30*a*b*c^3*d^2 + 3*a^2*c^2*d^3)*x)/(c*d^7*x^4 + 2*c^2*d^6*x^2 + c^3*d^5), 1/24*(8*b^2*c*d^4*x^7 - 8*(7*b^2*c^2*d^3 - 6*a*b*c*d^4)*x^5 - 5*(35*b^2*c^3*d^2 - 30*a*b*c^2*d^3 + 3*a^2*c*d^4)*x^3 + 3*(35*b^2*c^4 - 30*a*b*c^3*d + 3*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 30*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(35*b^2*c^3*d - 30*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 3*(35*b^2*c^4*d - 30*a*b*c^3*d^2 + 3*a^2*c^2*d^3)*x)/(c*d^7*x^4 + 2*c^2*d^6*x^2 + c^3*d^5)]","A",0
190,1,178,0,0.988378," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{3} x^{6} + 4 \, b^{2} c d^{2} x^{4} - 5 \, b^{2} c^{3} + 6 \, a b c^{2} d - a^{2} c d^{2} - 2 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2} - 2 \, {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d + {\left(3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}}"," ",0,"1/4*(2*b^2*d^3*x^6 + 4*b^2*c*d^2*x^4 - 5*b^2*c^3 + 6*a*b*c^2*d - a^2*c*d^2 - 2*(2*b^2*c^2*d - 4*a*b*c*d^2 + a^2*d^3)*x^2 - 2*(3*b^2*c^3 - 2*a*b*c^2*d + (3*b^2*c*d^2 - 2*a*b*d^3)*x^4 + 2*(3*b^2*c^2*d - 2*a*b*c*d^2)*x^2)*log(d*x^2 + c))/(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)","A",0
191,1,475,0,0.738044," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{16 \, b^{2} c^{2} d^{3} x^{5} + 2 \, {\left(25 \, b^{2} c^{3} d^{2} - 10 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{3} + {\left(15 \, b^{2} c^{4} - 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(15 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} - a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(c^{2} d^{6} x^{4} + 2 \, c^{3} d^{5} x^{2} + c^{4} d^{4}\right)}}, \frac{8 \, b^{2} c^{2} d^{3} x^{5} + {\left(25 \, b^{2} c^{3} d^{2} - 10 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{3} - {\left(15 \, b^{2} c^{4} - 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(15 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} - a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(c^{2} d^{6} x^{4} + 2 \, c^{3} d^{5} x^{2} + c^{4} d^{4}\right)}}\right]"," ",0,"[1/16*(16*b^2*c^2*d^3*x^5 + 2*(25*b^2*c^3*d^2 - 10*a*b*c^2*d^3 + a^2*c*d^4)*x^3 + (15*b^2*c^4 - 6*a*b*c^3*d - a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(15*b^2*c^4*d - 6*a*b*c^3*d^2 - a^2*c^2*d^3)*x)/(c^2*d^6*x^4 + 2*c^3*d^5*x^2 + c^4*d^4), 1/8*(8*b^2*c^2*d^3*x^5 + (25*b^2*c^3*d^2 - 10*a*b*c^2*d^3 + a^2*c*d^4)*x^3 - (15*b^2*c^4 - 6*a*b*c^3*d - a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (15*b^2*c^4*d - 6*a*b*c^3*d^2 - a^2*c^2*d^3)*x)/(c^2*d^6*x^4 + 2*c^3*d^5*x^2 + c^4*d^4)]","B",0
192,1,108,0,0.605471," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2} + 4 \, {\left(b^{2} c d - a b d^{2}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} x^{4} + 2 \, b^{2} c d x^{2} + b^{2} c^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(d^{5} x^{4} + 2 \, c d^{4} x^{2} + c^{2} d^{3}\right)}}"," ",0,"1/4*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2 + 4*(b^2*c*d - a*b*d^2)*x^2 + 2*(b^2*d^2*x^4 + 2*b^2*c*d*x^2 + b^2*c^2)*log(d*x^2 + c))/(d^5*x^4 + 2*c*d^4*x^2 + c^2*d^3)","A",0
193,1,449,0,0.775795," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - 3 \, a^{2} c d^{4}\right)} x^{3} + {\left(3 \, b^{2} c^{4} + 2 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(3 \, b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(c^{3} d^{5} x^{4} + 2 \, c^{4} d^{4} x^{2} + c^{5} d^{3}\right)}}, -\frac{{\left(5 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - 3 \, a^{2} c d^{4}\right)} x^{3} - {\left(3 \, b^{2} c^{4} + 2 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 2 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 2 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(3 \, b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(c^{3} d^{5} x^{4} + 2 \, c^{4} d^{4} x^{2} + c^{5} d^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - 3*a^2*c*d^4)*x^3 + (3*b^2*c^4 + 2*a*b*c^3*d + 3*a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 2*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(3*b^2*c^4*d + 2*a*b*c^3*d^2 - 5*a^2*c^2*d^3)*x)/(c^3*d^5*x^4 + 2*c^4*d^4*x^2 + c^5*d^3), -1/8*((5*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - 3*a^2*c*d^4)*x^3 - (3*b^2*c^4 + 2*a*b*c^3*d + 3*a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 2*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 2*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (3*b^2*c^4*d + 2*a*b*c^3*d^2 - 5*a^2*c^2*d^3)*x)/(c^3*d^5*x^4 + 2*c^4*d^4*x^2 + c^5*d^3)]","B",0
194,1,163,0,1.178432," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{4} + 2 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + 2 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)} x^{2} + 2 \, {\left(a^{2} d^{4} x^{4} + 2 \, a^{2} c d^{3} x^{2} + a^{2} c^{2} d^{2}\right)} \log\left(d x^{2} + c\right) - 4 \, {\left(a^{2} d^{4} x^{4} + 2 \, a^{2} c d^{3} x^{2} + a^{2} c^{2} d^{2}\right)} \log\left(x\right)}{4 \, {\left(c^{3} d^{4} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{5} d^{2}\right)}}"," ",0,"-1/4*(b^2*c^4 + 2*a*b*c^3*d - 3*a^2*c^2*d^2 + 2*(b^2*c^3*d - a^2*c*d^3)*x^2 + 2*(a^2*d^4*x^4 + 2*a^2*c*d^3*x^2 + a^2*c^2*d^2)*log(d*x^2 + c) - 4*(a^2*d^4*x^4 + 2*a^2*c*d^3*x^2 + a^2*c^2*d^2)*log(x))/(c^3*d^4*x^4 + 2*c^4*d^3*x^2 + c^5*d^2)","B",0
195,1,475,0,0.854032," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a^{2} c^{3} d^{2} - 2 \, {\left(b^{2} c^{3} d^{2} + 6 \, a b c^{2} d^{3} - 15 \, a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 10 \, a b c^{3} d^{2} + 25 \, a^{2} c^{2} d^{3}\right)} x^{2} - {\left({\left(b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - 15 \, a^{2} d^{4}\right)} x^{5} + 2 \, {\left(b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - 15 \, a^{2} c d^{3}\right)} x^{3} + {\left(b^{2} c^{4} + 6 \, a b c^{3} d - 15 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{-c d} \log\left(\frac{d x^{2} + 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{16 \, {\left(c^{4} d^{4} x^{5} + 2 \, c^{5} d^{3} x^{3} + c^{6} d^{2} x\right)}}, -\frac{8 \, a^{2} c^{3} d^{2} - {\left(b^{2} c^{3} d^{2} + 6 \, a b c^{2} d^{3} - 15 \, a^{2} c d^{4}\right)} x^{4} + {\left(b^{2} c^{4} d - 10 \, a b c^{3} d^{2} + 25 \, a^{2} c^{2} d^{3}\right)} x^{2} - {\left({\left(b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - 15 \, a^{2} d^{4}\right)} x^{5} + 2 \, {\left(b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - 15 \, a^{2} c d^{3}\right)} x^{3} + {\left(b^{2} c^{4} + 6 \, a b c^{3} d - 15 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{8 \, {\left(c^{4} d^{4} x^{5} + 2 \, c^{5} d^{3} x^{3} + c^{6} d^{2} x\right)}}\right]"," ",0,"[-1/16*(16*a^2*c^3*d^2 - 2*(b^2*c^3*d^2 + 6*a*b*c^2*d^3 - 15*a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 10*a*b*c^3*d^2 + 25*a^2*c^2*d^3)*x^2 - ((b^2*c^2*d^2 + 6*a*b*c*d^3 - 15*a^2*d^4)*x^5 + 2*(b^2*c^3*d + 6*a*b*c^2*d^2 - 15*a^2*c*d^3)*x^3 + (b^2*c^4 + 6*a*b*c^3*d - 15*a^2*c^2*d^2)*x)*sqrt(-c*d)*log((d*x^2 + 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c^4*d^4*x^5 + 2*c^5*d^3*x^3 + c^6*d^2*x), -1/8*(8*a^2*c^3*d^2 - (b^2*c^3*d^2 + 6*a*b*c^2*d^3 - 15*a^2*c*d^4)*x^4 + (b^2*c^4*d - 10*a*b*c^3*d^2 + 25*a^2*c^2*d^3)*x^2 - ((b^2*c^2*d^2 + 6*a*b*c*d^3 - 15*a^2*d^4)*x^5 + 2*(b^2*c^3*d + 6*a*b*c^2*d^2 - 15*a^2*c*d^3)*x^3 + (b^2*c^4 + 6*a*b*c^3*d - 15*a^2*c^2*d^2)*x)*sqrt(c*d)*arctan(sqrt(c*d)*x/c))/(c^4*d^4*x^5 + 2*c^5*d^3*x^3 + c^6*d^2*x)]","A",0
196,1,256,0,0.680603," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} c^{3} d - 2 \, {\left(2 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{4} + {\left(b^{2} c^{4} - 6 \, a b c^{3} d + 9 \, a^{2} c^{2} d^{2}\right)} x^{2} + 2 \, {\left({\left(2 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{6} + 2 \, {\left(2 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{4} + {\left(2 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) - 4 \, {\left({\left(2 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{6} + 2 \, {\left(2 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{4} + {\left(2 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(c^{4} d^{3} x^{6} + 2 \, c^{5} d^{2} x^{4} + c^{6} d x^{2}\right)}}"," ",0,"-1/4*(2*a^2*c^3*d - 2*(2*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^4 + (b^2*c^4 - 6*a*b*c^3*d + 9*a^2*c^2*d^2)*x^2 + 2*((2*a*b*c*d^3 - 3*a^2*d^4)*x^6 + 2*(2*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^4 + (2*a*b*c^3*d - 3*a^2*c^2*d^2)*x^2)*log(d*x^2 + c) - 4*((2*a*b*c*d^3 - 3*a^2*d^4)*x^6 + 2*(2*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^4 + (2*a*b*c^3*d - 3*a^2*c^2*d^2)*x^2)*log(x))/(c^4*d^3*x^6 + 2*c^5*d^2*x^4 + c^6*d*x^2)","B",0
197,1,536,0,0.927716," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a^{2} c^{4} d - 6 \, {\left(3 \, b^{2} c^{3} d^{2} - 30 \, a b c^{2} d^{3} + 35 \, a^{2} c d^{4}\right)} x^{6} - 10 \, {\left(3 \, b^{2} c^{4} d - 30 \, a b c^{3} d^{2} + 35 \, a^{2} c^{2} d^{3}\right)} x^{4} + 16 \, {\left(6 \, a b c^{4} d - 7 \, a^{2} c^{3} d^{2}\right)} x^{2} + 3 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{7} + 2 \, {\left(3 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{5} + {\left(3 \, b^{2} c^{4} - 30 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{3}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right)}{48 \, {\left(c^{5} d^{3} x^{7} + 2 \, c^{6} d^{2} x^{5} + c^{7} d x^{3}\right)}}, -\frac{8 \, a^{2} c^{4} d - 3 \, {\left(3 \, b^{2} c^{3} d^{2} - 30 \, a b c^{2} d^{3} + 35 \, a^{2} c d^{4}\right)} x^{6} - 5 \, {\left(3 \, b^{2} c^{4} d - 30 \, a b c^{3} d^{2} + 35 \, a^{2} c^{2} d^{3}\right)} x^{4} + 8 \, {\left(6 \, a b c^{4} d - 7 \, a^{2} c^{3} d^{2}\right)} x^{2} - 3 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{7} + 2 \, {\left(3 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{5} + {\left(3 \, b^{2} c^{4} - 30 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{3}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right)}{24 \, {\left(c^{5} d^{3} x^{7} + 2 \, c^{6} d^{2} x^{5} + c^{7} d x^{3}\right)}}\right]"," ",0,"[-1/48*(16*a^2*c^4*d - 6*(3*b^2*c^3*d^2 - 30*a*b*c^2*d^3 + 35*a^2*c*d^4)*x^6 - 10*(3*b^2*c^4*d - 30*a*b*c^3*d^2 + 35*a^2*c^2*d^3)*x^4 + 16*(6*a*b*c^4*d - 7*a^2*c^3*d^2)*x^2 + 3*((3*b^2*c^2*d^2 - 30*a*b*c*d^3 + 35*a^2*d^4)*x^7 + 2*(3*b^2*c^3*d - 30*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^5 + (3*b^2*c^4 - 30*a*b*c^3*d + 35*a^2*c^2*d^2)*x^3)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)))/(c^5*d^3*x^7 + 2*c^6*d^2*x^5 + c^7*d*x^3), -1/24*(8*a^2*c^4*d - 3*(3*b^2*c^3*d^2 - 30*a*b*c^2*d^3 + 35*a^2*c*d^4)*x^6 - 5*(3*b^2*c^4*d - 30*a*b*c^3*d^2 + 35*a^2*c^2*d^3)*x^4 + 8*(6*a*b*c^4*d - 7*a^2*c^3*d^2)*x^2 - 3*((3*b^2*c^2*d^2 - 30*a*b*c*d^3 + 35*a^2*d^4)*x^7 + 2*(3*b^2*c^3*d - 30*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^5 + (3*b^2*c^4 - 30*a*b*c^3*d + 35*a^2*c^2*d^2)*x^3)*sqrt(c*d)*arctan(sqrt(c*d)*x/c))/(c^5*d^3*x^7 + 2*c^6*d^2*x^5 + c^7*d*x^3)]","A",0
198,1,75,0,0.782002," ","integrate(x^5*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d x^{6} + 3 \, {\left(b^{3} c - a b^{2} d\right)} x^{4} - 6 \, {\left(a b^{2} c - a^{2} b d\right)} x^{2} + 6 \, {\left(a^{2} b c - a^{3} d\right)} \log\left(b x^{2} + a\right)}{12 \, b^{4}}"," ",0,"1/12*(2*b^3*d*x^6 + 3*(b^3*c - a*b^2*d)*x^4 - 6*(a*b^2*c - a^2*b*d)*x^2 + 6*(a^2*b*c - a^3*d)*log(b*x^2 + a))/b^4","A",0
199,1,178,0,0.939400," ","integrate(x^4*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, b^{2} d x^{5} + 10 \, {\left(b^{2} c - a b d\right)} x^{3} - 15 \, {\left(a b c - a^{2} d\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 30 \, {\left(a b c - a^{2} d\right)} x}{30 \, b^{3}}, \frac{3 \, b^{2} d x^{5} + 5 \, {\left(b^{2} c - a b d\right)} x^{3} + 15 \, {\left(a b c - a^{2} d\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 15 \, {\left(a b c - a^{2} d\right)} x}{15 \, b^{3}}\right]"," ",0,"[1/30*(6*b^2*d*x^5 + 10*(b^2*c - a*b*d)*x^3 - 15*(a*b*c - a^2*d)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 30*(a*b*c - a^2*d)*x)/b^3, 1/15*(3*b^2*d*x^5 + 5*(b^2*c - a*b*d)*x^3 + 15*(a*b*c - a^2*d)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 15*(a*b*c - a^2*d)*x)/b^3]","A",0
200,1,51,0,0.748427," ","integrate(x^3*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{b^{2} d x^{4} + 2 \, {\left(b^{2} c - a b d\right)} x^{2} - 2 \, {\left(a b c - a^{2} d\right)} \log\left(b x^{2} + a\right)}{4 \, b^{3}}"," ",0,"1/4*(b^2*d*x^4 + 2*(b^2*c - a*b*d)*x^2 - 2*(a*b*c - a^2*d)*log(b*x^2 + a))/b^3","A",0
201,1,129,0,0.847350," ","integrate(x^2*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, b d x^{3} - 3 \, {\left(b c - a d\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, {\left(b c - a d\right)} x}{6 \, b^{2}}, \frac{b d x^{3} - 3 \, {\left(b c - a d\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 3 \, {\left(b c - a d\right)} x}{3 \, b^{2}}\right]"," ",0,"[1/6*(2*b*d*x^3 - 3*(b*c - a*d)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*(b*c - a*d)*x)/b^2, 1/3*(b*d*x^3 - 3*(b*c - a*d)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 3*(b*c - a*d)*x)/b^2]","A",0
202,1,29,0,0.762269," ","integrate(x*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{b d x^{2} + {\left(b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(b*d*x^2 + (b*c - a*d)*log(b*x^2 + a))/b^2","A",0
203,1,98,0,0.761606," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a b d x + \sqrt{-a b} {\left(b c - a d\right)} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a b^{2}}, \frac{a b d x + \sqrt{a b} {\left(b c - a d\right)} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a b^{2}}\right]"," ",0,"[1/2*(2*a*b*d*x + sqrt(-a*b)*(b*c - a*d)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a*b^2), (a*b*d*x + sqrt(a*b)*(b*c - a*d)*arctan(sqrt(a*b)*x/a))/(a*b^2)]","A",0
204,1,33,0,0.739395," ","integrate((d*x^2+c)/x/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, b c \log\left(x\right) - {\left(b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"1/2*(2*b*c*log(x) - (b*c - a*d)*log(b*x^2 + a))/(a*b)","A",0
205,1,105,0,0.658407," ","integrate((d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a b} {\left(b c - a d\right)} x \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, a b c}{2 \, a^{2} b x}, -\frac{\sqrt{a b} {\left(b c - a d\right)} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) + a b c}{a^{2} b x}\right]"," ",0,"[1/2*(sqrt(-a*b)*(b*c - a*d)*x*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*a*b*c)/(a^2*b*x), -(sqrt(a*b)*(b*c - a*d)*x*arctan(sqrt(a*b)*x/a) + a*b*c)/(a^2*b*x)]","A",0
206,1,48,0,0.785437," ","integrate((d*x^2+c)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{{\left(b c - a d\right)} x^{2} \log\left(b x^{2} + a\right) - 2 \, {\left(b c - a d\right)} x^{2} \log\left(x\right) - a c}{2 \, a^{2} x^{2}}"," ",0,"1/2*((b*c - a*d)*x^2*log(b*x^2 + a) - 2*(b*c - a*d)*x^2*log(x) - a*c)/(a^2*x^2)","A",0
207,1,136,0,1.163393," ","integrate((d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 6 \, {\left(b c - a d\right)} x^{2} + 2 \, a c}{6 \, a^{2} x^{3}}, \frac{3 \, {\left(b c - a d\right)} x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left(b c - a d\right)} x^{2} - a c}{3 \, a^{2} x^{3}}\right]"," ",0,"[-1/6*(3*(b*c - a*d)*x^3*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 6*(b*c - a*d)*x^2 + 2*a*c)/(a^2*x^3), 1/3*(3*(b*c - a*d)*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*(b*c - a*d)*x^2 - a*c)/(a^2*x^3)]","A",0
208,1,138,0,0.785284," ","integrate(x^5*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} d^{2} x^{8} + 4 \, {\left(2 \, b^{4} c d - a b^{3} d^{2}\right)} x^{6} + 6 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} - 12 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2} + 12 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \log\left(b x^{2} + a\right)}{24 \, b^{5}}"," ",0,"1/24*(3*b^4*d^2*x^8 + 4*(2*b^4*c*d - a*b^3*d^2)*x^6 + 6*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4 - 12*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2 + 12*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*log(b*x^2 + a))/b^5","A",0
209,1,304,0,0.766167," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{30 \, b^{3} d^{2} x^{7} + 42 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{5} + 70 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + 105 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 210 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x}{210 \, b^{4}}, \frac{15 \, b^{3} d^{2} x^{7} + 21 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{5} + 35 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + 105 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 105 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x}{105 \, b^{4}}\right]"," ",0,"[1/210*(30*b^3*d^2*x^7 + 42*(2*b^3*c*d - a*b^2*d^2)*x^5 + 70*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3 + 105*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 210*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)/b^4, 1/105*(15*b^3*d^2*x^7 + 21*(2*b^3*c*d - a*b^2*d^2)*x^5 + 35*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3 + 105*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 105*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)/b^4]","A",0
210,1,102,0,0.613934," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{2} x^{6} + 3 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{4} + 6 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2} - 6 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, b^{4}}"," ",0,"1/12*(2*b^3*d^2*x^6 + 3*(2*b^3*c*d - a*b^2*d^2)*x^4 + 6*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2 - 6*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*log(b*x^2 + a))/b^4","A",0
211,1,230,0,0.925987," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, b^{2} d^{2} x^{5} + 10 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{3} + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 30 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{30 \, b^{3}}, \frac{3 \, b^{2} d^{2} x^{5} + 5 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{3} - 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{15 \, b^{3}}\right]"," ",0,"[1/30*(6*b^2*d^2*x^5 + 10*(2*b^2*c*d - a*b*d^2)*x^3 + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 30*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/b^3, 1/15*(3*b^2*d^2*x^5 + 5*(2*b^2*c*d - a*b*d^2)*x^3 - 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/b^3]","A",0
212,1,67,0,1.050214," ","integrate(x*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{4} + 2 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, b^{3}}"," ",0,"1/4*(b^2*d^2*x^4 + 2*(2*b^2*c*d - a*b*d^2)*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x^2 + a))/b^3","A",0
213,1,181,0,0.779121," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a b^{2} d^{2} x^{3} - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x}{6 \, a b^{3}}, \frac{a b^{2} d^{2} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x}{3 \, a b^{3}}\right]"," ",0,"[1/6*(2*a*b^2*d^2*x^3 - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(2*a*b^2*c*d - a^2*b*d^2)*x)/(a*b^3), 1/3*(a*b^2*d^2*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(2*a*b^2*c*d - a^2*b*d^2)*x)/(a*b^3)]","A",0
214,1,59,0,0.853632," ","integrate((d*x^2+c)^2/x/(b*x^2+a),x, algorithm=""fricas"")","\frac{a b d^{2} x^{2} + 2 \, b^{2} c^{2} \log\left(x\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a b^{2}}"," ",0,"1/2*(a*b*d^2*x^2 + 2*b^2*c^2*log(x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x^2 + a))/(a*b^2)","A",0
215,1,164,0,0.861064," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b d^{2} x^{2} - 2 \, a b^{2} c^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a b} x \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{2 \, a^{2} b^{2} x}, \frac{a^{2} b d^{2} x^{2} - a b^{2} c^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{a^{2} b^{2} x}\right]"," ",0,"[1/2*(2*a^2*b*d^2*x^2 - 2*a*b^2*c^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*b)*x*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^2*b^2*x), (a^2*b*d^2*x^2 - a*b^2*c^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)*x*arctan(sqrt(a*b)*x/a))/(a^2*b^2*x)]","A",0
216,1,73,0,0.823733," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a),x, algorithm=""fricas"")","-\frac{a b c^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \log\left(b x^{2} + a\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d\right)} x^{2} \log\left(x\right)}{2 \, a^{2} b x^{2}}"," ",0,"-1/2*(a*b*c^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*log(b*x^2 + a) + 2*(b^2*c^2 - 2*a*b*c*d)*x^2*log(x))/(a^2*b*x^2)","A",0
217,1,190,0,0.888871," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a b} x^{3} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, a^{2} b c^{2} - 6 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d\right)} x^{2}}{6 \, a^{3} b x^{3}}, \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b} x^{3} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - a^{2} b c^{2} + 3 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d\right)} x^{2}}{3 \, a^{3} b x^{3}}\right]"," ",0,"[-1/6*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*b)*x^3*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*a^2*b*c^2 - 6*(a*b^2*c^2 - 2*a^2*b*c*d)*x^2)/(a^3*b*x^3), 1/3*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)*x^3*arctan(sqrt(a*b)*x/a) - a^2*b*c^2 + 3*(a*b^2*c^2 - 2*a^2*b*c*d)*x^2)/(a^3*b*x^3)]","A",0
218,1,220,0,0.839023," ","integrate(x^5*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{12 \, b^{5} d^{3} x^{10} + 15 \, {\left(3 \, b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{8} + 20 \, {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{6} + 30 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{4} - 60 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{2} + 60 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \log\left(b x^{2} + a\right)}{120 \, b^{6}}"," ",0,"1/120*(12*b^5*d^3*x^10 + 15*(3*b^5*c*d^2 - a*b^4*d^3)*x^8 + 20*(3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^6 + 30*(b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^4 - 60*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x^2 + 60*(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*log(b*x^2 + a))/b^6","A",0
219,1,468,0,0.753358," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{70 \, b^{4} d^{3} x^{9} + 90 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{7} + 126 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{5} + 210 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{3} - 315 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 630 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x}{630 \, b^{5}}, \frac{35 \, b^{4} d^{3} x^{9} + 45 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{7} + 63 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{5} + 105 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{3} + 315 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 315 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x}{315 \, b^{5}}\right]"," ",0,"[1/630*(70*b^4*d^3*x^9 + 90*(3*b^4*c*d^2 - a*b^3*d^3)*x^7 + 126*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^5 + 210*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^3 - 315*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 630*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x)/b^5, 1/315*(35*b^4*d^3*x^9 + 45*(3*b^4*c*d^2 - a*b^3*d^3)*x^7 + 63*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^5 + 105*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^3 + 315*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 315*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x)/b^5]","A",0
220,1,169,0,1.039962," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} d^{3} x^{8} + 4 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{6} + 6 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{4} + 12 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{2} - 12 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \log\left(b x^{2} + a\right)}{24 \, b^{5}}"," ",0,"1/24*(3*b^4*d^3*x^8 + 4*(3*b^4*c*d^2 - a*b^3*d^3)*x^6 + 6*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^4 + 12*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^2 - 12*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*log(b*x^2 + a))/b^5","A",0
221,1,364,0,0.785527," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{30 \, b^{3} d^{3} x^{7} + 42 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{5} + 70 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} - 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{210 \, b^{4}}, \frac{15 \, b^{3} d^{3} x^{7} + 21 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{5} + 35 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} - 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{105 \, b^{4}}\right]"," ",0,"[1/210*(30*b^3*d^3*x^7 + 42*(3*b^3*c*d^2 - a*b^2*d^3)*x^5 + 70*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^3 - 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x)/b^4, 1/105*(15*b^3*d^3*x^7 + 21*(3*b^3*c*d^2 - a*b^2*d^3)*x^5 + 35*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^3 - 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x)/b^4]","A",0
222,1,120,0,0.655267," ","integrate(x*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{6} + 3 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{4} + 6 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(b x^{2} + a\right)}{12 \, b^{4}}"," ",0,"1/12*(2*b^3*d^3*x^6 + 3*(3*b^3*c*d^2 - a*b^2*d^3)*x^4 + 6*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x^2 + a))/b^4","A",0
223,1,292,0,1.046934," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a b^{3} d^{3} x^{5} + 10 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 30 \, {\left(3 \, a b^{3} c^{2} d - 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x}{30 \, a b^{4}}, \frac{3 \, a b^{3} d^{3} x^{5} + 5 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 15 \, {\left(3 \, a b^{3} c^{2} d - 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x}{15 \, a b^{4}}\right]"," ",0,"[1/30*(6*a*b^3*d^3*x^5 + 10*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^3 + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 30*(3*a*b^3*c^2*d - 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x)/(a*b^4), 1/15*(3*a*b^3*d^3*x^5 + 5*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^3 + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 15*(3*a*b^3*c^2*d - 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x)/(a*b^4)]","A",0
224,1,101,0,0.514440," ","integrate((d*x^2+c)^3/x/(b*x^2+a),x, algorithm=""fricas"")","\frac{a b^{2} d^{3} x^{4} + 4 \, b^{3} c^{3} \log\left(x\right) + 2 \, {\left(3 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(b x^{2} + a\right)}{4 \, a b^{3}}"," ",0,"1/4*(a*b^2*d^3*x^4 + 4*b^3*c^3*log(x) + 2*(3*a*b^2*c*d^2 - a^2*b*d^3)*x^2 - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x^2 + a))/(a*b^3)","A",0
225,1,253,0,0.750721," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b^{2} d^{3} x^{4} - 6 \, a b^{3} c^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a b} x \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{2}}{6 \, a^{2} b^{3} x}, \frac{a^{2} b^{2} d^{3} x^{4} - 3 \, a b^{3} c^{3} - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{2}}{3 \, a^{2} b^{3} x}\right]"," ",0,"[1/6*(2*a^2*b^2*d^3*x^4 - 6*a*b^3*c^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*b)*x*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^2)/(a^2*b^3*x), 1/3*(a^2*b^2*d^3*x^4 - 3*a*b^3*c^3 - 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)*x*arctan(sqrt(a*b)*x/a) + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^2)/(a^2*b^3*x)]","A",0
226,1,105,0,0.924975," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{a^{2} b d^{3} x^{4} - a b^{2} c^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2} \log\left(b x^{2} + a\right) - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d\right)} x^{2} \log\left(x\right)}{2 \, a^{2} b^{2} x^{2}}"," ",0,"1/2*(a^2*b*d^3*x^4 - a*b^2*c^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2*log(b*x^2 + a) - 2*(b^3*c^3 - 3*a*b^2*c^2*d)*x^2*log(x))/(a^2*b^2*x^2)","A",0
227,1,256,0,0.586802," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a^{3} b d^{3} x^{4} - 2 \, a^{2} b^{2} c^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a b} x^{3} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d\right)} x^{2}}{6 \, a^{3} b^{2} x^{3}}, \frac{3 \, a^{3} b d^{3} x^{4} - a^{2} b^{2} c^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b} x^{3} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d\right)} x^{2}}{3 \, a^{3} b^{2} x^{3}}\right]"," ",0,"[1/6*(6*a^3*b*d^3*x^4 - 2*a^2*b^2*c^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*b)*x^3*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(a*b^3*c^3 - 3*a^2*b^2*c^2*d)*x^2)/(a^3*b^2*x^3), 1/3*(3*a^3*b*d^3*x^4 - a^2*b^2*c^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)*x^3*arctan(sqrt(a*b)*x/a) + 3*(a*b^3*c^3 - 3*a^2*b^2*c^2*d)*x^2)/(a^3*b^2*x^3)]","A",0
228,1,72,0,0.693059," ","integrate(x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{a^{2} d^{2} \log\left(b x^{2} + a\right) - b^{2} c^{2} \log\left(d x^{2} + c\right) + {\left(b^{2} c d - a b d^{2}\right)} x^{2}}{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}"," ",0,"1/2*(a^2*d^2*log(b*x^2 + a) - b^2*c^2*log(d*x^2 + c) + (b^2*c*d - a*b*d^2)*x^2)/(b^3*c*d^2 - a*b^2*d^3)","A",0
229,1,391,0,0.948730," ","integrate(x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{a d \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + b c \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} + 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c - a d\right)} x}{2 \, {\left(b^{2} c d - a b d^{2}\right)}}, \frac{2 \, a d \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - b c \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} + 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) + 2 \, {\left(b c - a d\right)} x}{2 \, {\left(b^{2} c d - a b d^{2}\right)}}, -\frac{2 \, b c \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + a d \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 2 \, {\left(b c - a d\right)} x}{2 \, {\left(b^{2} c d - a b d^{2}\right)}}, \frac{a d \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - b c \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + {\left(b c - a d\right)} x}{b^{2} c d - a b d^{2}}\right]"," ",0,"[-1/2*(a*d*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + b*c*sqrt(-c/d)*log((d*x^2 + 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - 2*(b*c - a*d)*x)/(b^2*c*d - a*b*d^2), 1/2*(2*a*d*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - b*c*sqrt(-c/d)*log((d*x^2 + 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) + 2*(b*c - a*d)*x)/(b^2*c*d - a*b*d^2), -1/2*(2*b*c*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + a*d*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 2*(b*c - a*d)*x)/(b^2*c*d - a*b*d^2), (a*d*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - b*c*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + (b*c - a*d)*x)/(b^2*c*d - a*b*d^2)]","A",0
230,1,42,0,0.781671," ","integrate(x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{a d \log\left(b x^{2} + a\right) - b c \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c d - a b d^{2}\right)}}"," ",0,"-1/2*(a*d*log(b*x^2 + a) - b*c*log(d*x^2 + c))/(b^2*c*d - a*b*d^2)","A",0
231,1,309,0,0.838819," ","integrate(x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, -\frac{2 \, \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, \frac{2 \, \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right)}{2 \, {\left(b c - a d\right)}}, -\frac{\sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right)}{b c - a d}\right]"," ",0,"[-1/2*(sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)))/(b*c - a*d), -1/2*(2*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)))/(b*c - a*d), 1/2*(2*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)))/(b*c - a*d), -(sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - sqrt(c/d)*arctan(d*x*sqrt(c/d)/c))/(b*c - a*d)]","A",0
232,1,31,0,0.962943," ","integrate(x/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{\log\left(b x^{2} + a\right) - \log\left(d x^{2} + c\right)}{2 \, {\left(b c - a d\right)}}"," ",0,"1/2*(log(b*x^2 + a) - log(d*x^2 + c))/(b*c - a*d)","A",0
233,1,292,0,0.885362," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, -\frac{2 \, \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{2 \, {\left(b c - a d\right)}}, \frac{2 \, \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{2 \, {\left(b c - a d\right)}}, \frac{\sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{b c - a d}\right]"," ",0,"[-1/2*(sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/(b*c - a*d), -1/2*(2*sqrt(d/c)*arctan(x*sqrt(d/c)) + sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(b*c - a*d), 1/2*(2*sqrt(b/a)*arctan(x*sqrt(b/a)) - sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/(b*c - a*d), (sqrt(b/a)*arctan(x*sqrt(b/a)) - sqrt(d/c)*arctan(x*sqrt(d/c)))/(b*c - a*d)]","A",0
234,1,54,0,1.002108," ","integrate(1/x/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{b c \log\left(b x^{2} + a\right) - a d \log\left(d x^{2} + c\right) - 2 \, {\left(b c - a d\right)} \log\left(x\right)}{2 \, {\left(a b c^{2} - a^{2} c d\right)}}"," ",0,"-1/2*(b*c*log(b*x^2 + a) - a*d*log(d*x^2 + c) - 2*(b*c - a*d)*log(x))/(a*b*c^2 - a^2*c*d)","A",0
235,1,384,0,1.200689," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{b c x \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + a d x \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, b c - 2 \, a d}{2 \, {\left(a b c^{2} - a^{2} c d\right)} x}, \frac{2 \, a d x \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - b c x \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, b c + 2 \, a d}{2 \, {\left(a b c^{2} - a^{2} c d\right)} x}, -\frac{2 \, b c x \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + a d x \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, b c - 2 \, a d}{2 \, {\left(a b c^{2} - a^{2} c d\right)} x}, -\frac{b c x \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - a d x \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + b c - a d}{{\left(a b c^{2} - a^{2} c d\right)} x}\right]"," ",0,"[-1/2*(b*c*x*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + a*d*x*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*b*c - 2*a*d)/((a*b*c^2 - a^2*c*d)*x), 1/2*(2*a*d*x*sqrt(d/c)*arctan(x*sqrt(d/c)) - b*c*x*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*b*c + 2*a*d)/((a*b*c^2 - a^2*c*d)*x), -1/2*(2*b*c*x*sqrt(b/a)*arctan(x*sqrt(b/a)) + a*d*x*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*b*c - 2*a*d)/((a*b*c^2 - a^2*c*d)*x), -(b*c*x*sqrt(b/a)*arctan(x*sqrt(b/a)) - a*d*x*sqrt(d/c)*arctan(x*sqrt(d/c)) + b*c - a*d)/((a*b*c^2 - a^2*c*d)*x)]","A",0
236,1,99,0,1.236384," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{b^{2} c^{2} x^{2} \log\left(b x^{2} + a\right) - a^{2} d^{2} x^{2} \log\left(d x^{2} + c\right) - a b c^{2} + a^{2} c d - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2} \log\left(x\right)}{2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{2}}"," ",0,"1/2*(b^2*c^2*x^2*log(b*x^2 + a) - a^2*d^2*x^2*log(d*x^2 + c) - a*b*c^2 + a^2*c*d - 2*(b^2*c^2 - a^2*d^2)*x^2*log(x))/((a^2*b*c^3 - a^3*c^2*d)*x^2)","A",0
237,1,560,0,1.156664," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{3 \, b^{2} c^{2} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 3 \, a^{2} d^{2} x^{3} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, a b c^{2} - 2 \, a^{2} c d - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{6 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{3}}, -\frac{6 \, a^{2} d^{2} x^{3} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 3 \, b^{2} c^{2} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, a b c^{2} - 2 \, a^{2} c d - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{6 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{3}}, \frac{6 \, b^{2} c^{2} x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, a^{2} d^{2} x^{3} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, a b c^{2} + 2 \, a^{2} c d + 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{6 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{3}}, \frac{3 \, b^{2} c^{2} x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, a^{2} d^{2} x^{3} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - a b c^{2} + a^{2} c d + 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{3 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{3}}\right]"," ",0,"[-1/6*(3*b^2*c^2*x^3*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 3*a^2*d^2*x^3*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*a*b*c^2 - 2*a^2*c*d - 6*(b^2*c^2 - a^2*d^2)*x^2)/((a^2*b*c^3 - a^3*c^2*d)*x^3), -1/6*(6*a^2*d^2*x^3*sqrt(d/c)*arctan(x*sqrt(d/c)) + 3*b^2*c^2*x^3*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*a*b*c^2 - 2*a^2*c*d - 6*(b^2*c^2 - a^2*d^2)*x^2)/((a^2*b*c^3 - a^3*c^2*d)*x^3), 1/6*(6*b^2*c^2*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*a^2*d^2*x^3*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*a*b*c^2 + 2*a^2*c*d + 6*(b^2*c^2 - a^2*d^2)*x^2)/((a^2*b*c^3 - a^3*c^2*d)*x^3), 1/3*(3*b^2*c^2*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*a^2*d^2*x^3*sqrt(d/c)*arctan(x*sqrt(d/c)) - a*b*c^2 + a^2*c*d + 3*(b^2*c^2 - a^2*d^2)*x^2)/((a^2*b*c^3 - a^3*c^2*d)*x^3)]","A",0
238,1,127,0,3.086428," ","integrate(1/x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} x^{4} \log\left(b x^{2} + a\right) - 2 \, a^{3} d^{3} x^{4} \log\left(d x^{2} + c\right) + a^{2} b c^{3} - a^{3} c^{2} d - 4 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{4} \log\left(x\right) - 2 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{2}}{4 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{4}}"," ",0,"-1/4*(2*b^3*c^3*x^4*log(b*x^2 + a) - 2*a^3*d^3*x^4*log(d*x^2 + c) + a^2*b*c^3 - a^3*c^2*d - 4*(b^3*c^3 - a^3*d^3)*x^4*log(x) - 2*(a*b^2*c^3 - a^3*c*d^2)*x^2)/((a^3*b*c^4 - a^4*c^3*d)*x^4)","A",0
239,1,669,0,1.016676," ","integrate(1/x^6/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{15 \, b^{3} c^{3} x^{5} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 15 \, a^{3} d^{3} x^{5} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 6 \, a^{2} b c^{3} - 6 \, a^{3} c^{2} d + 30 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{4} - 10 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{2}}{30 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{5}}, \frac{30 \, a^{3} d^{3} x^{5} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 15 \, b^{3} c^{3} x^{5} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 6 \, a^{2} b c^{3} + 6 \, a^{3} c^{2} d - 30 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{4} + 10 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{2}}{30 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{5}}, -\frac{30 \, b^{3} c^{3} x^{5} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 15 \, a^{3} d^{3} x^{5} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 6 \, a^{2} b c^{3} - 6 \, a^{3} c^{2} d + 30 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{4} - 10 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{2}}{30 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{5}}, -\frac{15 \, b^{3} c^{3} x^{5} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 15 \, a^{3} d^{3} x^{5} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 3 \, a^{2} b c^{3} - 3 \, a^{3} c^{2} d + 15 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{4} - 5 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{2}}{15 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{5}}\right]"," ",0,"[-1/30*(15*b^3*c^3*x^5*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 15*a^3*d^3*x^5*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 6*a^2*b*c^3 - 6*a^3*c^2*d + 30*(b^3*c^3 - a^3*d^3)*x^4 - 10*(a*b^2*c^3 - a^3*c*d^2)*x^2)/((a^3*b*c^4 - a^4*c^3*d)*x^5), 1/30*(30*a^3*d^3*x^5*sqrt(d/c)*arctan(x*sqrt(d/c)) - 15*b^3*c^3*x^5*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 6*a^2*b*c^3 + 6*a^3*c^2*d - 30*(b^3*c^3 - a^3*d^3)*x^4 + 10*(a*b^2*c^3 - a^3*c*d^2)*x^2)/((a^3*b*c^4 - a^4*c^3*d)*x^5), -1/30*(30*b^3*c^3*x^5*sqrt(b/a)*arctan(x*sqrt(b/a)) + 15*a^3*d^3*x^5*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 6*a^2*b*c^3 - 6*a^3*c^2*d + 30*(b^3*c^3 - a^3*d^3)*x^4 - 10*(a*b^2*c^3 - a^3*c*d^2)*x^2)/((a^3*b*c^4 - a^4*c^3*d)*x^5), -1/15*(15*b^3*c^3*x^5*sqrt(b/a)*arctan(x*sqrt(b/a)) - 15*a^3*d^3*x^5*sqrt(d/c)*arctan(x*sqrt(d/c)) + 3*a^2*b*c^3 - 3*a^3*c^2*d + 15*(b^3*c^3 - a^3*d^3)*x^4 - 5*(a*b^2*c^3 - a^3*c*d^2)*x^2)/((a^3*b*c^4 - a^4*c^3*d)*x^5)]","A",0
240,1,155,0,4.457509," ","integrate(1/x^7/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{6 \, b^{4} c^{4} x^{6} \log\left(b x^{2} + a\right) - 6 \, a^{4} d^{4} x^{6} \log\left(d x^{2} + c\right) - 2 \, a^{3} b c^{4} + 2 \, a^{4} c^{3} d - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x^{6} \log\left(x\right) - 6 \, {\left(a b^{3} c^{4} - a^{4} c d^{3}\right)} x^{4} + 3 \, {\left(a^{2} b^{2} c^{4} - a^{4} c^{2} d^{2}\right)} x^{2}}{12 \, {\left(a^{4} b c^{5} - a^{5} c^{4} d\right)} x^{6}}"," ",0,"1/12*(6*b^4*c^4*x^6*log(b*x^2 + a) - 6*a^4*d^4*x^6*log(d*x^2 + c) - 2*a^3*b*c^4 + 2*a^4*c^3*d - 12*(b^4*c^4 - a^4*d^4)*x^6*log(x) - 6*(a*b^3*c^4 - a^4*c*d^3)*x^4 + 3*(a^2*b^2*c^4 - a^4*c^2*d^2)*x^2)/((a^4*b*c^5 - a^5*c^4*d)*x^6)","A",0
241,1,162,0,1.070282," ","integrate(x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{a^{2} b c d - a^{3} d^{2} + {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(a b^{4} c^{2} d - 2 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3} + {\left(b^{5} c^{2} d - 2 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*(a^2*b*c*d - a^3*d^2 + (2*a^2*b*c*d - a^3*d^2 + (2*a*b^2*c*d - a^2*b*d^2)*x^2)*log(b*x^2 + a) - (b^3*c^2*x^2 + a*b^2*c^2)*log(d*x^2 + c))/(a*b^4*c^2*d - 2*a^2*b^3*c*d^2 + a^3*b^2*d^3 + (b^5*c^2*d - 2*a*b^4*c*d^2 + a^2*b^3*d^3)*x^2)","A",0
242,1,718,0,1.024177," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a d^{2} x^{2} + a c d\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - {\left(b c^{2} - 3 \, a c d + {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c^{2} - a c d\right)} x}{4 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left(a d^{2} x^{2} + a c d\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - {\left(b c^{2} - 3 \, a c d + {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c^{2} - a c d\right)} x}{4 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2}\right)}}, \frac{{\left(b c^{2} - 3 \, a c d + {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + {\left(a d^{2} x^{2} + a c d\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - {\left(b c^{2} - a c d\right)} x}{2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(a d^{2} x^{2} + a c d\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + {\left(b c^{2} - 3 \, a c d + {\left(b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - {\left(b c^{2} - a c d\right)} x}{2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(a*d^2*x^2 + a*c*d)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - (b*c^2 - 3*a*c*d + (b*c*d - 3*a*d^2)*x^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - 2*(b*c^2 - a*c*d)*x)/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2), 1/4*(4*(a*d^2*x^2 + a*c*d)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - (b*c^2 - 3*a*c*d + (b*c*d - 3*a*d^2)*x^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - 2*(b*c^2 - a*c*d)*x)/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2), 1/2*((b*c^2 - 3*a*c*d + (b*c*d - 3*a*d^2)*x^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + (a*d^2*x^2 + a*c*d)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - (b*c^2 - a*c*d)*x)/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2), 1/2*(2*(a*d^2*x^2 + a*c*d)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + (b*c^2 - 3*a*c*d + (b*c*d - 3*a*d^2)*x^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - (b*c^2 - a*c*d)*x)/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2)]","A",0
243,1,117,0,0.857337," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{b c^{2} - a c d + {\left(a d^{2} x^{2} + a c d\right)} \log\left(b x^{2} + a\right) - {\left(a d^{2} x^{2} + a c d\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2}\right)}}"," ",0,"-1/2*(b*c^2 - a*c*d + (a*d^2*x^2 + a*c*d)*log(b*x^2 + a) - (a*d^2*x^2 + a*c*d)*log(d*x^2 + c))/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2)","A",0
244,1,705,0,1.048213," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c d^{2} x^{2} + c^{2} d\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - {\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x}{4 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}, \frac{{\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(c d^{2} x^{2} + c^{2} d\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + {\left(b c^{2} d - a c d^{2}\right)} x}{2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}, -\frac{4 \, {\left(c d^{2} x^{2} + c^{2} d\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 2 \, {\left(b c^{2} d - a c d^{2}\right)} x}{4 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}, -\frac{2 \, {\left(c d^{2} x^{2} + c^{2} d\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(b c^{2} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - {\left(b c^{2} d - a c d^{2}\right)} x}{2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(c*d^2*x^2 + c^2*d)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - (b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(b*c^2*d - a*c*d^2)*x)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2), 1/2*((b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (c*d^2*x^2 + c^2*d)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + (b*c^2*d - a*c*d^2)*x)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2), -1/4*(4*(c*d^2*x^2 + c^2*d)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 2*(b*c^2*d - a*c*d^2)*x)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2), -1/2*(2*(c*d^2*x^2 + c^2*d)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (b*c^2 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - (b*c^2*d - a*c*d^2)*x)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2)]","A",0
245,1,103,0,0.794780," ","integrate(x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{b c - a d + {\left(b d x^{2} + b c\right)} \log\left(b x^{2} + a\right) - {\left(b d x^{2} + b c\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)}}"," ",0,"1/2*(b*c - a*d + (b*d*x^2 + b*c)*log(b*x^2 + a) - (b*d*x^2 + b*c)*log(d*x^2 + c))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^2)","A",0
246,1,711,0,1.308322," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c d - a d^{2}\right)} x}{4 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}, -\frac{{\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(b c d - a d^{2}\right)} x}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}, \frac{4 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b c d - a d^{2}\right)} x}{4 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(b c d x^{2} + b c^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(b c d - a d^{2}\right)} x}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b*c*d*x^2 + b*c^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(b*c*d - a*d^2)*x)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2), -1/2*((3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (b*c*d*x^2 + b*c^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (b*c*d - a*d^2)*x)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2), 1/4*(4*(b*c*d*x^2 + b*c^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(b*c*d - a*d^2)*x)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2), 1/2*(2*(b*c*d*x^2 + b*c^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) - (3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (b*c*d - a*d^2)*x)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)]","A",0
247,1,219,0,2.647509," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{a b c^{2} d - a^{2} c d^{2} + {\left(b^{2} c^{2} d x^{2} + b^{2} c^{3}\right)} \log\left(b x^{2} + a\right) - {\left(2 \, a b c^{2} d - a^{2} c d^{2} + {\left(2 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) - 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2} + {\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*(a*b*c^2*d - a^2*c*d^2 + (b^2*c^2*d*x^2 + b^2*c^3)*log(b*x^2 + a) - (2*a*b*c^2*d - a^2*c*d^2 + (2*a*b*c*d^2 - a^2*d^3)*x^2)*log(d*x^2 + c) - 2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^2)*log(x))/(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2 + (a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x^2)","B",0
248,1,1005,0,1.522351," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, b^{2} c^{3} - 8 \, a b c^{2} d + 4 \, a^{2} c d^{2} + 2 \, {\left(2 \, b^{2} c^{2} d - 5 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{4 \, {\left({\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x^{3} + {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x\right)}}, -\frac{2 \, b^{2} c^{3} - 4 \, a b c^{2} d + 2 \, a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - 5 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2} - {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{2 \, {\left({\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x^{3} + {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x\right)}}, -\frac{4 \, b^{2} c^{3} - 8 \, a b c^{2} d + 4 \, a^{2} c d^{2} + 2 \, {\left(2 \, b^{2} c^{2} d - 5 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{4 \, {\left({\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x^{3} + {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x\right)}}, -\frac{2 \, b^{2} c^{3} - 4 \, a b c^{2} d + 2 \, a^{2} c d^{2} + {\left(2 \, b^{2} c^{2} d - 5 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{2 \, {\left({\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x^{3} + {\left(a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2}\right)} x\right)}}\right]"," ",0,"[-1/4*(4*b^2*c^3 - 8*a*b*c^2*d + 4*a^2*c*d^2 + 2*(2*b^2*c^2*d - 5*a*b*c*d^2 + 3*a^2*d^3)*x^2 - 2*(b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + ((5*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x^3 + (a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x), -1/2*(2*b^2*c^3 - 4*a*b*c^2*d + 2*a^2*c*d^2 + (2*b^2*c^2*d - 5*a*b*c*d^2 + 3*a^2*d^3)*x^2 - ((5*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x^3 + (a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x), -1/4*(4*b^2*c^3 - 8*a*b*c^2*d + 4*a^2*c*d^2 + 2*(2*b^2*c^2*d - 5*a*b*c*d^2 + 3*a^2*d^3)*x^2 + 4*(b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + ((5*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x^3 + (a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x), -1/2*(2*b^2*c^3 - 4*a*b*c^2*d + 2*a^2*c*d^2 + (2*b^2*c^2*d - 5*a*b*c*d^2 + 3*a^2*d^3)*x^2 + 2*(b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) - ((5*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x^3 + (a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2)*x)]","A",0
249,1,302,0,4.994191," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2} - {\left(b^{3} c^{3} d x^{4} + b^{3} c^{4} x^{2}\right)} \log\left(b x^{2} + a\right) + {\left({\left(3 \, a^{2} b c d^{3} - 2 \, a^{3} d^{4}\right)} x^{4} + {\left(3 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left({\left(b^{3} c^{3} d - 3 \, a^{2} b c d^{3} + 2 \, a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} - 3 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{4} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x^{2}\right)}}"," ",0,"-1/2*(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2 - (b^3*c^3*d*x^4 + b^3*c^4*x^2)*log(b*x^2 + a) + ((3*a^2*b*c*d^3 - 2*a^3*d^4)*x^4 + (3*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x^2)*log(d*x^2 + c) + 2*((b^3*c^3*d - 3*a^2*b*c*d^3 + 2*a^3*d^4)*x^4 + (b^3*c^4 - 3*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2)*log(x))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^4 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x^2)","B",0
250,1,1281,0,3.283984," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 4 \, a^{3} c^{2} d^{2} - 6 \, {\left(2 \, b^{3} c^{3} d - 7 \, a^{2} b c d^{3} + 5 \, a^{3} d^{4}\right)} x^{4} - 4 \, {\left(3 \, b^{3} c^{4} - a b^{2} c^{3} d - 7 \, a^{2} b c^{2} d^{2} + 5 \, a^{3} c d^{3}\right)} x^{2} - 6 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 3 \, {\left({\left(7 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{5} + {\left(7 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{12 \, {\left({\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{5} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, a b^{2} c^{4} - 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2} - 3 \, {\left(2 \, b^{3} c^{3} d - 7 \, a^{2} b c d^{3} + 5 \, a^{3} d^{4}\right)} x^{4} - 2 \, {\left(3 \, b^{3} c^{4} - a b^{2} c^{3} d - 7 \, a^{2} b c^{2} d^{2} + 5 \, a^{3} c d^{3}\right)} x^{2} + 3 \, {\left({\left(7 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{5} + {\left(7 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 3 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{6 \, {\left({\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{5} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{4 \, a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 4 \, a^{3} c^{2} d^{2} - 6 \, {\left(2 \, b^{3} c^{3} d - 7 \, a^{2} b c d^{3} + 5 \, a^{3} d^{4}\right)} x^{4} - 4 \, {\left(3 \, b^{3} c^{4} - a b^{2} c^{3} d - 7 \, a^{2} b c^{2} d^{2} + 5 \, a^{3} c d^{3}\right)} x^{2} - 12 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left({\left(7 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{5} + {\left(7 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{12 \, {\left({\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{5} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, a b^{2} c^{4} - 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2} - 3 \, {\left(2 \, b^{3} c^{3} d - 7 \, a^{2} b c d^{3} + 5 \, a^{3} d^{4}\right)} x^{4} - 2 \, {\left(3 \, b^{3} c^{4} - a b^{2} c^{3} d - 7 \, a^{2} b c^{2} d^{2} + 5 \, a^{3} c d^{3}\right)} x^{2} - 6 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left({\left(7 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{5} + {\left(7 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{6 \, {\left({\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{5} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a*b^2*c^4 - 8*a^2*b*c^3*d + 4*a^3*c^2*d^2 - 6*(2*b^3*c^3*d - 7*a^2*b*c*d^3 + 5*a^3*d^4)*x^4 - 4*(3*b^3*c^4 - a*b^2*c^3*d - 7*a^2*b*c^2*d^2 + 5*a^3*c*d^3)*x^2 - 6*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 3*((7*a^2*b*c*d^3 - 5*a^3*d^4)*x^5 + (7*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^5 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x^3), -1/6*(2*a*b^2*c^4 - 4*a^2*b*c^3*d + 2*a^3*c^2*d^2 - 3*(2*b^3*c^3*d - 7*a^2*b*c*d^3 + 5*a^3*d^4)*x^4 - 2*(3*b^3*c^4 - a*b^2*c^3*d - 7*a^2*b*c^2*d^2 + 5*a^3*c*d^3)*x^2 + 3*((7*a^2*b*c*d^3 - 5*a^3*d^4)*x^5 + (7*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 3*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^5 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x^3), -1/12*(4*a*b^2*c^4 - 8*a^2*b*c^3*d + 4*a^3*c^2*d^2 - 6*(2*b^3*c^3*d - 7*a^2*b*c*d^3 + 5*a^3*d^4)*x^4 - 4*(3*b^3*c^4 - a*b^2*c^3*d - 7*a^2*b*c^2*d^2 + 5*a^3*c*d^3)*x^2 - 12*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*((7*a^2*b*c*d^3 - 5*a^3*d^4)*x^5 + (7*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^5 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x^3), -1/6*(2*a*b^2*c^4 - 4*a^2*b*c^3*d + 2*a^3*c^2*d^2 - 3*(2*b^3*c^3*d - 7*a^2*b*c*d^3 + 5*a^3*d^4)*x^4 - 2*(3*b^3*c^4 - a*b^2*c^3*d - 7*a^2*b*c^2*d^2 + 5*a^3*c*d^3)*x^2 - 6*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*((7*a^2*b*c*d^3 - 5*a^3*d^4)*x^5 + (7*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^5 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x^3)]","A",0
251,1,290,0,0.898795," ","integrate(x^5/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + a^{4} d^{2} + 2 \, {\left(2 \, a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2} + 2 \, {\left(b^{4} c^{2} x^{4} + 2 \, a b^{3} c^{2} x^{2} + a^{2} b^{2} c^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b^{4} c^{2} x^{4} + 2 \, a b^{3} c^{2} x^{2} + a^{2} b^{2} c^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3} + {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} x^{4} + 2 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/4*(3*a^2*b^2*c^2 - 4*a^3*b*c*d + a^4*d^2 + 2*(2*a*b^3*c^2 - 3*a^2*b^2*c*d + a^3*b*d^2)*x^2 + 2*(b^4*c^2*x^4 + 2*a*b^3*c^2*x^2 + a^2*b^2*c^2)*log(b*x^2 + a) - 2*(b^4*c^2*x^4 + 2*a*b^3*c^2*x^2 + a^2*b^2*c^2)*log(d*x^2 + c))/(a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3 + (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*x^4 + 2*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*x^2)","B",0
252,1,1573,0,1.658818," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{3} d^{2} - 6 \, a b c^{2} d^{3} + 5 \, a^{2} c d^{4}\right)} x^{3} - 8 \, {\left(a c d^{4} x^{4} + 2 \, a c^{2} d^{3} x^{2} + a c^{3} d^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - {\left(b^{2} c^{4} - 6 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 2 \, {\left(b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 3 \, a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5} + {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} x^{4} + 2 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{{\left(b^{2} c^{3} d^{2} - 6 \, a b c^{2} d^{3} + 5 \, a^{2} c d^{4}\right)} x^{3} + {\left(b^{2} c^{4} - 6 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 4 \, {\left(a c d^{4} x^{4} + 2 \, a c^{2} d^{3} x^{2} + a c^{3} d^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - {\left(b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 3 \, a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5} + {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} x^{4} + 2 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{3} d^{2} - 6 \, a b c^{2} d^{3} + 5 \, a^{2} c d^{4}\right)} x^{3} + 16 \, {\left(a c d^{4} x^{4} + 2 \, a c^{2} d^{3} x^{2} + a c^{3} d^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(b^{2} c^{4} - 6 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - 2 \, {\left(b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 3 \, a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5} + {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} x^{4} + 2 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{{\left(b^{2} c^{3} d^{2} - 6 \, a b c^{2} d^{3} + 5 \, a^{2} c d^{4}\right)} x^{3} + 8 \, {\left(a c d^{4} x^{4} + 2 \, a c^{2} d^{3} x^{2} + a c^{3} d^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(b^{2} c^{4} - 6 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - {\left(b^{2} c^{4} d + 2 \, a b c^{3} d^{2} - 3 \, a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5} + {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} x^{4} + 2 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(b^2*c^3*d^2 - 6*a*b*c^2*d^3 + 5*a^2*c*d^4)*x^3 - 8*(a*c*d^4*x^4 + 2*a*c^2*d^3*x^2 + a*c^3*d^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - (b^2*c^4 - 6*a*b*c^3*d - 3*a^2*c^2*d^2 + (b^2*c^2*d^2 - 6*a*b*c*d^3 - 3*a^2*d^4)*x^4 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 2*(b^2*c^4*d + 2*a*b*c^3*d^2 - 3*a^2*c^2*d^3)*x)/(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5 + (b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*x^4 + 2*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^2), 1/8*((b^2*c^3*d^2 - 6*a*b*c^2*d^3 + 5*a^2*c*d^4)*x^3 + (b^2*c^4 - 6*a*b*c^3*d - 3*a^2*c^2*d^2 + (b^2*c^2*d^2 - 6*a*b*c*d^3 - 3*a^2*d^4)*x^4 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 4*(a*c*d^4*x^4 + 2*a*c^2*d^3*x^2 + a*c^3*d^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - (b^2*c^4*d + 2*a*b*c^3*d^2 - 3*a^2*c^2*d^3)*x)/(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5 + (b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*x^4 + 2*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^2), 1/16*(2*(b^2*c^3*d^2 - 6*a*b*c^2*d^3 + 5*a^2*c*d^4)*x^3 + 16*(a*c*d^4*x^4 + 2*a*c^2*d^3*x^2 + a*c^3*d^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (b^2*c^4 - 6*a*b*c^3*d - 3*a^2*c^2*d^2 + (b^2*c^2*d^2 - 6*a*b*c*d^3 - 3*a^2*d^4)*x^4 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - 2*(b^2*c^4*d + 2*a*b*c^3*d^2 - 3*a^2*c^2*d^3)*x)/(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5 + (b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*x^4 + 2*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^2), 1/8*((b^2*c^3*d^2 - 6*a*b*c^2*d^3 + 5*a^2*c*d^4)*x^3 + 8*(a*c*d^4*x^4 + 2*a*c^2*d^3*x^2 + a*c^3*d^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (b^2*c^4 - 6*a*b*c^3*d - 3*a^2*c^2*d^2 + (b^2*c^2*d^2 - 6*a*b*c*d^3 - 3*a^2*d^4)*x^4 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 - 3*a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - (b^2*c^4*d + 2*a*b*c^3*d^2 - 3*a^2*c^2*d^3)*x)/(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5 + (b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*x^4 + 2*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^2)]","B",0
253,1,256,0,0.788431," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{3} - a^{2} c d^{2} + 2 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b d^{3} x^{4} + 2 \, a b c d^{2} x^{2} + a b c^{2} d\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(a b d^{3} x^{4} + 2 \, a b c d^{2} x^{2} + a b c^{2} d\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(b^{3} c^{5} d - 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{3} d^{3} - a^{3} c^{2} d^{4} + {\left(b^{3} c^{3} d^{3} - 3 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} d^{2} - 3 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c^{2} d^{4} - a^{3} c d^{5}\right)} x^{2}\right)}}"," ",0,"-1/4*(b^2*c^3 - a^2*c*d^2 + 2*(a*b*c*d^2 - a^2*d^3)*x^2 + 2*(a*b*d^3*x^4 + 2*a*b*c*d^2*x^2 + a*b*c^2*d)*log(b*x^2 + a) - 2*(a*b*d^3*x^4 + 2*a*b*c*d^2*x^2 + a*b*c^2*d)*log(d*x^2 + c))/(b^3*c^5*d - 3*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 - a^3*c^2*d^4 + (b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5 - a^3*d^6)*x^4 + 2*(b^3*c^4*d^2 - 3*a*b^2*c^3*d^3 + 3*a^2*b*c^2*d^4 - a^3*c*d^5)*x^2)","B",0
254,1,1587,0,1.864857," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3} - 8 \, {\left(b c^{2} d^{3} x^{4} + 2 \, b c^{3} d^{2} x^{2} + b c^{4} d\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - {\left(3 \, b^{2} c^{4} + 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4} + {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3} + {\left(3 \, b^{2} c^{4} + 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - 4 \, {\left(b c^{2} d^{3} x^{4} + 2 \, b c^{3} d^{2} x^{2} + b c^{4} d\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + {\left(5 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4} + {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(3 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3} - 16 \, {\left(b c^{2} d^{3} x^{4} + 2 \, b c^{3} d^{2} x^{2} + b c^{4} d\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(3 \, b^{2} c^{4} + 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(5 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4} + {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(3 \, b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} x^{3} - 8 \, {\left(b c^{2} d^{3} x^{4} + 2 \, b c^{3} d^{2} x^{2} + b c^{4} d\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(3 \, b^{2} c^{4} + 6 \, a b c^{3} d - a^{2} c^{2} d^{2} + {\left(3 \, b^{2} c^{2} d^{2} + 6 \, a b c d^{3} - a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d + 6 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(5 \, b^{2} c^{4} d - 6 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4} + {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(3*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - a^2*c*d^4)*x^3 - 8*(b*c^2*d^3*x^4 + 2*b*c^3*d^2*x^2 + b*c^4*d)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - (3*b^2*c^4 + 6*a*b*c^3*d - a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(5*b^2*c^4*d - 6*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4 + (b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^4 + 2*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^2), 1/8*((3*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - a^2*c*d^4)*x^3 + (3*b^2*c^4 + 6*a*b*c^3*d - a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - 4*(b*c^2*d^3*x^4 + 2*b*c^3*d^2*x^2 + b*c^4*d)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + (5*b^2*c^4*d - 6*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4 + (b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^4 + 2*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^2), 1/16*(2*(3*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - a^2*c*d^4)*x^3 - 16*(b*c^2*d^3*x^4 + 2*b*c^3*d^2*x^2 + b*c^4*d)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (3*b^2*c^4 + 6*a*b*c^3*d - a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(5*b^2*c^4*d - 6*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4 + (b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^4 + 2*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^2), 1/8*((3*b^2*c^3*d^2 - 2*a*b*c^2*d^3 - a^2*c*d^4)*x^3 - 8*(b*c^2*d^3*x^4 + 2*b*c^3*d^2*x^2 + b*c^4*d)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (3*b^2*c^4 + 6*a*b*c^3*d - a^2*c^2*d^2 + (3*b^2*c^2*d^2 + 6*a*b*c*d^3 - a^2*d^4)*x^4 + 2*(3*b^2*c^3*d + 6*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (5*b^2*c^4*d - 6*a*b*c^3*d^2 + a^2*c^2*d^3)*x)/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4 + (b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*x^4 + 2*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*x^2)]","B",0
255,1,254,0,0.561769," ","integrate(x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} x^{4} + 2 \, b^{2} c d x^{2} + b^{2} c^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b^{2} d^{2} x^{4} + 2 \, b^{2} c d x^{2} + b^{2} c^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x^{2}\right)}}"," ",0,"1/4*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x^2 + 2*(b^2*d^2*x^4 + 2*b^2*c*d*x^2 + b^2*c^2)*log(b*x^2 + a) - 2*(b^2*d^2*x^4 + 2*b^2*c*d*x^2 + b^2*c^2)*log(d*x^2 + c))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*x^4 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x^2)","B",0
256,1,1585,0,2.643210," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} + 8 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{{\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 4 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{2 \, {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} - 16 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{16 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}, -\frac{{\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{3} - 8 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(15 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(9 \, b^{2} c^{3} d - 14 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x}{8 \, {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3} + {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{6} d - 3 \, a b^{2} c^{5} d^{2} + 3 \, a^{2} b c^{4} d^{3} - a^{3} c^{3} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(2*(7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 + 8*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/8*((7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 4*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/16*(2*(7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 - 16*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2), -1/8*((7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^3 - 8*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (15*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^4 + 2*(15*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (9*b^2*c^3*d - 14*a*b*c^2*d^2 + 5*a^2*c*d^3)*x)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3 + (b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5)*x^4 + 2*(b^3*c^6*d - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3 - a^3*c^3*d^4)*x^2)]","B",0
257,1,520,0,8.892444," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{5 \, a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 3 \, a^{3} c^{2} d^{3} + 2 \, {\left(2 \, a b^{2} c^{3} d^{2} - 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x^{2} + 2 \, {\left(b^{3} c^{3} d^{2} x^{4} + 2 \, b^{3} c^{4} d x^{2} + b^{3} c^{5}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(3 \, a b^{2} c^{4} d - 3 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(3 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{3} d^{2} - 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) - 4 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3} + {\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{4} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x^{2}\right)}}"," ",0,"-1/4*(5*a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 3*a^3*c^2*d^3 + 2*(2*a*b^2*c^3*d^2 - 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x^2 + 2*(b^3*c^3*d^2*x^4 + 2*b^3*c^4*d*x^2 + b^3*c^5)*log(b*x^2 + a) - 2*(3*a*b^2*c^4*d - 3*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (3*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4 + a^3*d^5)*x^4 + 2*(3*a*b^2*c^3*d^2 - 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x^2)*log(d*x^2 + c) - 4*(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*x^4 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x^2)*log(x))/(a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3 + (a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^4 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x^2)","B",0
258,1,1991,0,4.425725," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, b^{3} c^{5} - 48 \, a b^{2} c^{4} d + 48 \, a^{2} b c^{3} d^{2} - 16 \, a^{3} c^{2} d^{3} + 2 \, {\left(8 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 42 \, a^{2} b c d^{4} - 15 \, a^{3} d^{5}\right)} x^{4} + 2 \, {\left(16 \, b^{3} c^{4} d - 61 \, a b^{2} c^{3} d^{2} + 70 \, a^{2} b c^{2} d^{3} - 25 \, a^{3} c d^{4}\right)} x^{2} + 8 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left({\left(35 \, a b^{2} c^{2} d^{3} - 42 \, a^{2} b c d^{4} + 15 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(35 \, a b^{2} c^{3} d^{2} - 42 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{3} + {\left(35 \, a b^{2} c^{4} d - 42 \, a^{2} b c^{3} d^{2} + 15 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{16 \, {\left({\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x^{3} + {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3}\right)} x\right)}}, -\frac{8 \, b^{3} c^{5} - 24 \, a b^{2} c^{4} d + 24 \, a^{2} b c^{3} d^{2} - 8 \, a^{3} c^{2} d^{3} + {\left(8 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 42 \, a^{2} b c d^{4} - 15 \, a^{3} d^{5}\right)} x^{4} + {\left(16 \, b^{3} c^{4} d - 61 \, a b^{2} c^{3} d^{2} + 70 \, a^{2} b c^{2} d^{3} - 25 \, a^{3} c d^{4}\right)} x^{2} - {\left({\left(35 \, a b^{2} c^{2} d^{3} - 42 \, a^{2} b c d^{4} + 15 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(35 \, a b^{2} c^{3} d^{2} - 42 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{3} + {\left(35 \, a b^{2} c^{4} d - 42 \, a^{2} b c^{3} d^{2} + 15 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 4 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{8 \, {\left({\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x^{3} + {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3}\right)} x\right)}}, -\frac{16 \, b^{3} c^{5} - 48 \, a b^{2} c^{4} d + 48 \, a^{2} b c^{3} d^{2} - 16 \, a^{3} c^{2} d^{3} + 2 \, {\left(8 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 42 \, a^{2} b c d^{4} - 15 \, a^{3} d^{5}\right)} x^{4} + 2 \, {\left(16 \, b^{3} c^{4} d - 61 \, a b^{2} c^{3} d^{2} + 70 \, a^{2} b c^{2} d^{3} - 25 \, a^{3} c d^{4}\right)} x^{2} + 16 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left({\left(35 \, a b^{2} c^{2} d^{3} - 42 \, a^{2} b c d^{4} + 15 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(35 \, a b^{2} c^{3} d^{2} - 42 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{3} + {\left(35 \, a b^{2} c^{4} d - 42 \, a^{2} b c^{3} d^{2} + 15 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{16 \, {\left({\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x^{3} + {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3}\right)} x\right)}}, -\frac{8 \, b^{3} c^{5} - 24 \, a b^{2} c^{4} d + 24 \, a^{2} b c^{3} d^{2} - 8 \, a^{3} c^{2} d^{3} + {\left(8 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 42 \, a^{2} b c d^{4} - 15 \, a^{3} d^{5}\right)} x^{4} + {\left(16 \, b^{3} c^{4} d - 61 \, a b^{2} c^{3} d^{2} + 70 \, a^{2} b c^{2} d^{3} - 25 \, a^{3} c d^{4}\right)} x^{2} + 8 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left({\left(35 \, a b^{2} c^{2} d^{3} - 42 \, a^{2} b c d^{4} + 15 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(35 \, a b^{2} c^{3} d^{2} - 42 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{3} + {\left(35 \, a b^{2} c^{4} d - 42 \, a^{2} b c^{3} d^{2} + 15 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{8 \, {\left({\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x^{3} + {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3}\right)} x\right)}}\right]"," ",0,"[-1/16*(16*b^3*c^5 - 48*a*b^2*c^4*d + 48*a^2*b*c^3*d^2 - 16*a^3*c^2*d^3 + 2*(8*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 42*a^2*b*c*d^4 - 15*a^3*d^5)*x^4 + 2*(16*b^3*c^4*d - 61*a*b^2*c^3*d^2 + 70*a^2*b*c^2*d^3 - 25*a^3*c*d^4)*x^2 + 8*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + ((35*a*b^2*c^2*d^3 - 42*a^2*b*c*d^4 + 15*a^3*d^5)*x^5 + 2*(35*a*b^2*c^3*d^2 - 42*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^3 + (35*a*b^2*c^4*d - 42*a^2*b*c^3*d^2 + 15*a^3*c^2*d^3)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^5 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x^3 + (a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3)*x), -1/8*(8*b^3*c^5 - 24*a*b^2*c^4*d + 24*a^2*b*c^3*d^2 - 8*a^3*c^2*d^3 + (8*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 42*a^2*b*c*d^4 - 15*a^3*d^5)*x^4 + (16*b^3*c^4*d - 61*a*b^2*c^3*d^2 + 70*a^2*b*c^2*d^3 - 25*a^3*c*d^4)*x^2 - ((35*a*b^2*c^2*d^3 - 42*a^2*b*c*d^4 + 15*a^3*d^5)*x^5 + 2*(35*a*b^2*c^3*d^2 - 42*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^3 + (35*a*b^2*c^4*d - 42*a^2*b*c^3*d^2 + 15*a^3*c^2*d^3)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 4*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^5 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x^3 + (a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3)*x), -1/16*(16*b^3*c^5 - 48*a*b^2*c^4*d + 48*a^2*b*c^3*d^2 - 16*a^3*c^2*d^3 + 2*(8*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 42*a^2*b*c*d^4 - 15*a^3*d^5)*x^4 + 2*(16*b^3*c^4*d - 61*a*b^2*c^3*d^2 + 70*a^2*b*c^2*d^3 - 25*a^3*c*d^4)*x^2 + 16*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + ((35*a*b^2*c^2*d^3 - 42*a^2*b*c*d^4 + 15*a^3*d^5)*x^5 + 2*(35*a*b^2*c^3*d^2 - 42*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^3 + (35*a*b^2*c^4*d - 42*a^2*b*c^3*d^2 + 15*a^3*c^2*d^3)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^5 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x^3 + (a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3)*x), -1/8*(8*b^3*c^5 - 24*a*b^2*c^4*d + 24*a^2*b*c^3*d^2 - 8*a^3*c^2*d^3 + (8*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 42*a^2*b*c*d^4 - 15*a^3*d^5)*x^4 + (16*b^3*c^4*d - 61*a*b^2*c^3*d^2 + 70*a^2*b*c^2*d^3 - 25*a^3*c*d^4)*x^2 + 8*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) - ((35*a*b^2*c^2*d^3 - 42*a^2*b*c*d^4 + 15*a^3*d^5)*x^5 + 2*(35*a*b^2*c^3*d^2 - 42*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^3 + (35*a*b^2*c^4*d - 42*a^2*b*c^3*d^2 + 15*a^3*c^2*d^3)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^5 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x^3 + (a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3)*x)]","B",0
259,1,640,0,18.490508," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a b^{3} c^{6} - 6 \, a^{2} b^{2} c^{5} d + 6 \, a^{3} b c^{4} d^{2} - 2 \, a^{4} c^{3} d^{3} + 2 \, {\left(a b^{3} c^{4} d^{2} - 6 \, a^{2} b^{2} c^{3} d^{3} + 8 \, a^{3} b c^{2} d^{4} - 3 \, a^{4} c d^{5}\right)} x^{4} + {\left(4 \, a b^{3} c^{5} d - 19 \, a^{2} b^{2} c^{4} d^{2} + 24 \, a^{3} b c^{3} d^{3} - 9 \, a^{4} c^{2} d^{4}\right)} x^{2} - 2 \, {\left(b^{4} c^{4} d^{2} x^{6} + 2 \, b^{4} c^{5} d x^{4} + b^{4} c^{6} x^{2}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left({\left(6 \, a^{2} b^{2} c^{2} d^{4} - 8 \, a^{3} b c d^{5} + 3 \, a^{4} d^{6}\right)} x^{6} + 2 \, {\left(6 \, a^{2} b^{2} c^{3} d^{3} - 8 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x^{4} + {\left(6 \, a^{2} b^{2} c^{4} d^{2} - 8 \, a^{3} b c^{3} d^{3} + 3 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 4 \, {\left({\left(b^{4} c^{4} d^{2} - 6 \, a^{2} b^{2} c^{2} d^{4} + 8 \, a^{3} b c d^{5} - 3 \, a^{4} d^{6}\right)} x^{6} + 2 \, {\left(b^{4} c^{5} d - 6 \, a^{2} b^{2} c^{3} d^{3} + 8 \, a^{3} b c^{2} d^{4} - 3 \, a^{4} c d^{5}\right)} x^{4} + {\left(b^{4} c^{6} - 6 \, a^{2} b^{2} c^{4} d^{2} + 8 \, a^{3} b c^{3} d^{3} - 3 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{6} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{4} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*a*b^3*c^6 - 6*a^2*b^2*c^5*d + 6*a^3*b*c^4*d^2 - 2*a^4*c^3*d^3 + 2*(a*b^3*c^4*d^2 - 6*a^2*b^2*c^3*d^3 + 8*a^3*b*c^2*d^4 - 3*a^4*c*d^5)*x^4 + (4*a*b^3*c^5*d - 19*a^2*b^2*c^4*d^2 + 24*a^3*b*c^3*d^3 - 9*a^4*c^2*d^4)*x^2 - 2*(b^4*c^4*d^2*x^6 + 2*b^4*c^5*d*x^4 + b^4*c^6*x^2)*log(b*x^2 + a) + 2*((6*a^2*b^2*c^2*d^4 - 8*a^3*b*c*d^5 + 3*a^4*d^6)*x^6 + 2*(6*a^2*b^2*c^3*d^3 - 8*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x^4 + (6*a^2*b^2*c^4*d^2 - 8*a^3*b*c^3*d^3 + 3*a^4*c^2*d^4)*x^2)*log(d*x^2 + c) + 4*((b^4*c^4*d^2 - 6*a^2*b^2*c^2*d^4 + 8*a^3*b*c*d^5 - 3*a^4*d^6)*x^6 + 2*(b^4*c^5*d - 6*a^2*b^2*c^3*d^3 + 8*a^3*b*c^2*d^4 - 3*a^4*c*d^5)*x^4 + (b^4*c^6 - 6*a^2*b^2*c^4*d^2 + 8*a^3*b*c^3*d^3 - 3*a^4*c^2*d^4)*x^2)*log(x))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^6 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^4 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x^2)","B",0
260,1,2397,0,12.309915," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a b^{3} c^{6} - 48 \, a^{2} b^{2} c^{5} d + 48 \, a^{3} b c^{4} d^{2} - 16 \, a^{4} c^{3} d^{3} - 6 \, {\left(8 \, b^{4} c^{4} d^{2} - 63 \, a^{2} b^{2} c^{2} d^{4} + 90 \, a^{3} b c d^{5} - 35 \, a^{4} d^{6}\right)} x^{6} - 2 \, {\left(48 \, b^{4} c^{5} d - 8 \, a b^{3} c^{4} d^{2} - 315 \, a^{2} b^{2} c^{3} d^{3} + 450 \, a^{3} b c^{2} d^{4} - 175 \, a^{4} c d^{5}\right)} x^{4} - 16 \, {\left(3 \, b^{4} c^{6} - 2 \, a b^{3} c^{5} d - 12 \, a^{2} b^{2} c^{4} d^{2} + 18 \, a^{3} b c^{3} d^{3} - 7 \, a^{4} c^{2} d^{4}\right)} x^{2} + 24 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 3 \, {\left({\left(63 \, a^{2} b^{2} c^{2} d^{4} - 90 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{7} + 2 \, {\left(63 \, a^{2} b^{2} c^{3} d^{3} - 90 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{5} + {\left(63 \, a^{2} b^{2} c^{4} d^{2} - 90 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{48 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{5} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x^{3}\right)}}, -\frac{8 \, a b^{3} c^{6} - 24 \, a^{2} b^{2} c^{5} d + 24 \, a^{3} b c^{4} d^{2} - 8 \, a^{4} c^{3} d^{3} - 3 \, {\left(8 \, b^{4} c^{4} d^{2} - 63 \, a^{2} b^{2} c^{2} d^{4} + 90 \, a^{3} b c d^{5} - 35 \, a^{4} d^{6}\right)} x^{6} - {\left(48 \, b^{4} c^{5} d - 8 \, a b^{3} c^{4} d^{2} - 315 \, a^{2} b^{2} c^{3} d^{3} + 450 \, a^{3} b c^{2} d^{4} - 175 \, a^{4} c d^{5}\right)} x^{4} - 8 \, {\left(3 \, b^{4} c^{6} - 2 \, a b^{3} c^{5} d - 12 \, a^{2} b^{2} c^{4} d^{2} + 18 \, a^{3} b c^{3} d^{3} - 7 \, a^{4} c^{2} d^{4}\right)} x^{2} + 3 \, {\left({\left(63 \, a^{2} b^{2} c^{2} d^{4} - 90 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{7} + 2 \, {\left(63 \, a^{2} b^{2} c^{3} d^{3} - 90 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{5} + {\left(63 \, a^{2} b^{2} c^{4} d^{2} - 90 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 12 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{24 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{5} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x^{3}\right)}}, -\frac{16 \, a b^{3} c^{6} - 48 \, a^{2} b^{2} c^{5} d + 48 \, a^{3} b c^{4} d^{2} - 16 \, a^{4} c^{3} d^{3} - 6 \, {\left(8 \, b^{4} c^{4} d^{2} - 63 \, a^{2} b^{2} c^{2} d^{4} + 90 \, a^{3} b c d^{5} - 35 \, a^{4} d^{6}\right)} x^{6} - 2 \, {\left(48 \, b^{4} c^{5} d - 8 \, a b^{3} c^{4} d^{2} - 315 \, a^{2} b^{2} c^{3} d^{3} + 450 \, a^{3} b c^{2} d^{4} - 175 \, a^{4} c d^{5}\right)} x^{4} - 16 \, {\left(3 \, b^{4} c^{6} - 2 \, a b^{3} c^{5} d - 12 \, a^{2} b^{2} c^{4} d^{2} + 18 \, a^{3} b c^{3} d^{3} - 7 \, a^{4} c^{2} d^{4}\right)} x^{2} - 48 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left({\left(63 \, a^{2} b^{2} c^{2} d^{4} - 90 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{7} + 2 \, {\left(63 \, a^{2} b^{2} c^{3} d^{3} - 90 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{5} + {\left(63 \, a^{2} b^{2} c^{4} d^{2} - 90 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{48 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{5} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x^{3}\right)}}, -\frac{8 \, a b^{3} c^{6} - 24 \, a^{2} b^{2} c^{5} d + 24 \, a^{3} b c^{4} d^{2} - 8 \, a^{4} c^{3} d^{3} - 3 \, {\left(8 \, b^{4} c^{4} d^{2} - 63 \, a^{2} b^{2} c^{2} d^{4} + 90 \, a^{3} b c d^{5} - 35 \, a^{4} d^{6}\right)} x^{6} - {\left(48 \, b^{4} c^{5} d - 8 \, a b^{3} c^{4} d^{2} - 315 \, a^{2} b^{2} c^{3} d^{3} + 450 \, a^{3} b c^{2} d^{4} - 175 \, a^{4} c d^{5}\right)} x^{4} - 8 \, {\left(3 \, b^{4} c^{6} - 2 \, a b^{3} c^{5} d - 12 \, a^{2} b^{2} c^{4} d^{2} + 18 \, a^{3} b c^{3} d^{3} - 7 \, a^{4} c^{2} d^{4}\right)} x^{2} - 24 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left({\left(63 \, a^{2} b^{2} c^{2} d^{4} - 90 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{7} + 2 \, {\left(63 \, a^{2} b^{2} c^{3} d^{3} - 90 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{5} + {\left(63 \, a^{2} b^{2} c^{4} d^{2} - 90 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{24 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{5} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[-1/48*(16*a*b^3*c^6 - 48*a^2*b^2*c^5*d + 48*a^3*b*c^4*d^2 - 16*a^4*c^3*d^3 - 6*(8*b^4*c^4*d^2 - 63*a^2*b^2*c^2*d^4 + 90*a^3*b*c*d^5 - 35*a^4*d^6)*x^6 - 2*(48*b^4*c^5*d - 8*a*b^3*c^4*d^2 - 315*a^2*b^2*c^3*d^3 + 450*a^3*b*c^2*d^4 - 175*a^4*c*d^5)*x^4 - 16*(3*b^4*c^6 - 2*a*b^3*c^5*d - 12*a^2*b^2*c^4*d^2 + 18*a^3*b*c^3*d^3 - 7*a^4*c^2*d^4)*x^2 + 24*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 3*((63*a^2*b^2*c^2*d^4 - 90*a^3*b*c*d^5 + 35*a^4*d^6)*x^7 + 2*(63*a^2*b^2*c^3*d^3 - 90*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^5 + (63*a^2*b^2*c^4*d^2 - 90*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^7 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^5 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x^3), -1/24*(8*a*b^3*c^6 - 24*a^2*b^2*c^5*d + 24*a^3*b*c^4*d^2 - 8*a^4*c^3*d^3 - 3*(8*b^4*c^4*d^2 - 63*a^2*b^2*c^2*d^4 + 90*a^3*b*c*d^5 - 35*a^4*d^6)*x^6 - (48*b^4*c^5*d - 8*a*b^3*c^4*d^2 - 315*a^2*b^2*c^3*d^3 + 450*a^3*b*c^2*d^4 - 175*a^4*c*d^5)*x^4 - 8*(3*b^4*c^6 - 2*a*b^3*c^5*d - 12*a^2*b^2*c^4*d^2 + 18*a^3*b*c^3*d^3 - 7*a^4*c^2*d^4)*x^2 + 3*((63*a^2*b^2*c^2*d^4 - 90*a^3*b*c*d^5 + 35*a^4*d^6)*x^7 + 2*(63*a^2*b^2*c^3*d^3 - 90*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^5 + (63*a^2*b^2*c^4*d^2 - 90*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 12*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^7 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^5 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x^3), -1/48*(16*a*b^3*c^6 - 48*a^2*b^2*c^5*d + 48*a^3*b*c^4*d^2 - 16*a^4*c^3*d^3 - 6*(8*b^4*c^4*d^2 - 63*a^2*b^2*c^2*d^4 + 90*a^3*b*c*d^5 - 35*a^4*d^6)*x^6 - 2*(48*b^4*c^5*d - 8*a*b^3*c^4*d^2 - 315*a^2*b^2*c^3*d^3 + 450*a^3*b*c^2*d^4 - 175*a^4*c*d^5)*x^4 - 16*(3*b^4*c^6 - 2*a*b^3*c^5*d - 12*a^2*b^2*c^4*d^2 + 18*a^3*b*c^3*d^3 - 7*a^4*c^2*d^4)*x^2 - 48*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*((63*a^2*b^2*c^2*d^4 - 90*a^3*b*c*d^5 + 35*a^4*d^6)*x^7 + 2*(63*a^2*b^2*c^3*d^3 - 90*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^5 + (63*a^2*b^2*c^4*d^2 - 90*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^7 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^5 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x^3), -1/24*(8*a*b^3*c^6 - 24*a^2*b^2*c^5*d + 24*a^3*b*c^4*d^2 - 8*a^4*c^3*d^3 - 3*(8*b^4*c^4*d^2 - 63*a^2*b^2*c^2*d^4 + 90*a^3*b*c*d^5 - 35*a^4*d^6)*x^6 - (48*b^4*c^5*d - 8*a*b^3*c^4*d^2 - 315*a^2*b^2*c^3*d^3 + 450*a^3*b*c^2*d^4 - 175*a^4*c*d^5)*x^4 - 8*(3*b^4*c^6 - 2*a*b^3*c^5*d - 12*a^2*b^2*c^4*d^2 + 18*a^3*b*c^3*d^3 - 7*a^4*c^2*d^4)*x^2 - 24*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*((63*a^2*b^2*c^2*d^4 - 90*a^3*b*c*d^5 + 35*a^4*d^6)*x^7 + 2*(63*a^2*b^2*c^3*d^3 - 90*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^5 + (63*a^2*b^2*c^4*d^2 - 90*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^7 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^5 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x^3)]","B",0
261,1,17,0,0.964875," ","integrate(x/(x^2+1)/(x^2+4),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(x^{2} + 4\right) + \frac{1}{6} \, \log\left(x^{2} + 1\right)"," ",0,"-1/6*log(x^2 + 4) + 1/6*log(x^2 + 1)","A",0
262,1,240,0,0.946090," ","integrate(x^4*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, b^{2} d x^{5} + 4 \, {\left(3 \, b^{2} c - 5 \, a b d\right)} x^{3} - 3 \, {\left(3 \, a b c - 5 \, a^{2} d + {\left(3 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, {\left(3 \, a b c - 5 \, a^{2} d\right)} x}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{2 \, b^{2} d x^{5} + 2 \, {\left(3 \, b^{2} c - 5 \, a b d\right)} x^{3} - 3 \, {\left(3 \, a b c - 5 \, a^{2} d + {\left(3 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 3 \, {\left(3 \, a b c - 5 \, a^{2} d\right)} x}{6 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[1/12*(4*b^2*d*x^5 + 4*(3*b^2*c - 5*a*b*d)*x^3 - 3*(3*a*b*c - 5*a^2*d + (3*b^2*c - 5*a*b*d)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*(3*a*b*c - 5*a^2*d)*x)/(b^4*x^2 + a*b^3), 1/6*(2*b^2*d*x^5 + 2*(3*b^2*c - 5*a*b*d)*x^3 - 3*(3*a*b*c - 5*a^2*d + (3*b^2*c - 5*a*b*d)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 3*(3*a*b*c - 5*a^2*d)*x)/(b^4*x^2 + a*b^3)]","A",0
263,1,78,0,1.009164," ","integrate(x^3*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d x^{4} + a b d x^{2} + a b c - a^{2} d + {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/2*(b^2*d*x^4 + a*b*d*x^2 + a*b*c - a^2*d + (a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3)","A",0
264,1,202,0,0.918396," ","integrate(x^2*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a b^{2} d x^{3} + {\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(a b^{2} c - 3 \, a^{2} b d\right)} x}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, \frac{2 \, a b^{2} d x^{3} + {\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - {\left(a b^{2} c - 3 \, a^{2} b d\right)} x}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/4*(4*a*b^2*d*x^3 + (a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(a*b^2*c - 3*a^2*b*d)*x)/(a*b^4*x^2 + a^2*b^3), 1/2*(2*a*b^2*d*x^3 + (a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - (a*b^2*c - 3*a^2*b*d)*x)/(a*b^4*x^2 + a^2*b^3)]","A",0
265,1,45,0,0.845883," ","integrate(x*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{b c - a d - {\left(b d x^{2} + a d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"-1/2*(b*c - a*d - (b*d*x^2 + a*d)*log(b*x^2 + a))/(b^3*x^2 + a*b^2)","A",0
266,1,181,0,0.802572," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(a b^{2} c - a^{2} b d\right)} x}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(a b^{2} c - a^{2} b d\right)} x}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/4*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(a*b^2*c - a^2*b*d)*x)/(a^2*b^3*x^2 + a^3*b^2), 1/2*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (a*b^2*c - a^2*b*d)*x)/(a^2*b^3*x^2 + a^3*b^2)]","A",0
267,1,71,0,0.839578," ","integrate((d*x^2+c)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{a b c - a^{2} d - {\left(b^{2} c x^{2} + a b c\right)} \log\left(b x^{2} + a\right) + 2 \, {\left(b^{2} c x^{2} + a b c\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}"," ",0,"1/2*(a*b*c - a^2*d - (b^2*c*x^2 + a*b*c)*log(b*x^2 + a) + 2*(b^2*c*x^2 + a*b*c)*log(x))/(a^2*b^2*x^2 + a^3*b)","A",0
268,1,214,0,0.950574," ","integrate((d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b c + 2 \, {\left(3 \, a b^{2} c - a^{2} b d\right)} x^{2} - {\left({\left(3 \, b^{2} c - a b d\right)} x^{3} + {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}, -\frac{2 \, a^{2} b c + {\left(3 \, a b^{2} c - a^{2} b d\right)} x^{2} + {\left({\left(3 \, b^{2} c - a b d\right)} x^{3} + {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{3} b^{2} x^{3} + a^{4} b x\right)}}\right]"," ",0,"[-1/4*(4*a^2*b*c + 2*(3*a*b^2*c - a^2*b*d)*x^2 - ((3*b^2*c - a*b*d)*x^3 + (3*a*b*c - a^2*d)*x)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^2*x^3 + a^4*b*x), -1/2*(2*a^2*b*c + (3*a*b^2*c - a^2*b*d)*x^2 + ((3*b^2*c - a*b*d)*x^3 + (3*a*b*c - a^2*d)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^2*x^3 + a^4*b*x)]","A",0
269,1,122,0,0.845413," ","integrate((d*x^2+c)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x^{2} - {\left({\left(2 \, b^{2} c - a b d\right)} x^{4} + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left({\left(2 \, b^{2} c - a b d\right)} x^{4} + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}"," ",0,"-1/2*(a^2*c + (2*a*b*c - a^2*d)*x^2 - ((2*b^2*c - a*b*d)*x^4 + (2*a*b*c - a^2*d)*x^2)*log(b*x^2 + a) + 2*((2*b^2*c - a*b*d)*x^4 + (2*a*b*c - a^2*d)*x^2)*log(x))/(a^3*b*x^4 + a^4*x^2)","A",0
270,1,250,0,1.016304," ","integrate((d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(5 \, b^{2} c - 3 \, a b d\right)} x^{4} - 4 \, a^{2} c + 4 \, {\left(5 \, a b c - 3 \, a^{2} d\right)} x^{2} - 3 \, {\left({\left(5 \, b^{2} c - 3 \, a b d\right)} x^{5} + {\left(5 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{12 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}, \frac{3 \, {\left(5 \, b^{2} c - 3 \, a b d\right)} x^{4} - 2 \, a^{2} c + 2 \, {\left(5 \, a b c - 3 \, a^{2} d\right)} x^{2} + 3 \, {\left({\left(5 \, b^{2} c - 3 \, a b d\right)} x^{5} + {\left(5 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right)}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[1/12*(6*(5*b^2*c - 3*a*b*d)*x^4 - 4*a^2*c + 4*(5*a*b*c - 3*a^2*d)*x^2 - 3*((5*b^2*c - 3*a*b*d)*x^5 + (5*a*b*c - 3*a^2*d)*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/(a^3*b*x^5 + a^4*x^3), 1/6*(3*(5*b^2*c - 3*a*b*d)*x^4 - 2*a^2*c + 2*(5*a*b*c - 3*a^2*d)*x^2 + 3*((5*b^2*c - 3*a*b*d)*x^5 + (5*a*b*c - 3*a^2*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)))/(a^3*b*x^5 + a^4*x^3)]","A",0
271,1,400,0,0.956327," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{12 \, b^{3} d^{2} x^{7} + 4 \, {\left(10 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{5} + 20 \, {\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{3} + 15 \, {\left(3 \, a b^{2} c^{2} - 10 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 30 \, {\left(3 \, a b^{2} c^{2} - 10 \, a^{2} b c d + 7 \, a^{3} d^{2}\right)} x}{60 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, \frac{6 \, b^{3} d^{2} x^{7} + 2 \, {\left(10 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{5} + 10 \, {\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{3} - 15 \, {\left(3 \, a b^{2} c^{2} - 10 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 15 \, {\left(3 \, a b^{2} c^{2} - 10 \, a^{2} b c d + 7 \, a^{3} d^{2}\right)} x}{30 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/60*(12*b^3*d^2*x^7 + 4*(10*b^3*c*d - 7*a*b^2*d^2)*x^5 + 20*(3*b^3*c^2 - 10*a*b^2*c*d + 7*a^2*b*d^2)*x^3 + 15*(3*a*b^2*c^2 - 10*a^2*b*c*d + 7*a^3*d^2 + (3*b^3*c^2 - 10*a*b^2*c*d + 7*a^2*b*d^2)*x^2)*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 30*(3*a*b^2*c^2 - 10*a^2*b*c*d + 7*a^3*d^2)*x)/(b^5*x^2 + a*b^4), 1/30*(6*b^3*d^2*x^7 + 2*(10*b^3*c*d - 7*a*b^2*d^2)*x^5 + 10*(3*b^3*c^2 - 10*a*b^2*c*d + 7*a^2*b*d^2)*x^3 - 15*(3*a*b^2*c^2 - 10*a^2*b*c*d + 7*a^3*d^2 + (3*b^3*c^2 - 10*a*b^2*c*d + 7*a^2*b*d^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 15*(3*a*b^2*c^2 - 10*a^2*b*c*d + 7*a^3*d^2)*x)/(b^5*x^2 + a*b^4)]","A",0
272,1,160,0,1.001186," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{2} x^{6} + 2 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2} + {\left(4 \, b^{3} c d - 3 \, a b^{2} d^{2}\right)} x^{4} + 4 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} b c d + 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 4 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/4*(b^3*d^2*x^6 + 2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 + (4*b^3*c*d - 3*a*b^2*d^2)*x^4 + 4*(a*b^2*c*d - a^2*b*d^2)*x^2 + 2*(a*b^2*c^2 - 4*a^2*b*c*d + 3*a^3*d^2 + (b^3*c^2 - 4*a*b^2*c*d + 3*a^2*b*d^2)*x^2)*log(b*x^2 + a))/(b^5*x^2 + a*b^4)","A",0
273,1,342,0,0.782984," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a b^{3} d^{2} x^{5} + 4 \, {\left(6 \, a b^{3} c d - 5 \, a^{2} b^{2} d^{2}\right)} x^{3} - 3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 6 \, {\left(a b^{3} c^{2} - 6 \, a^{2} b^{2} c d + 5 \, a^{3} b d^{2}\right)} x}{12 \, {\left(a b^{5} x^{2} + a^{2} b^{4}\right)}}, \frac{2 \, a b^{3} d^{2} x^{5} + 2 \, {\left(6 \, a b^{3} c d - 5 \, a^{2} b^{2} d^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 3 \, {\left(a b^{3} c^{2} - 6 \, a^{2} b^{2} c d + 5 \, a^{3} b d^{2}\right)} x}{6 \, {\left(a b^{5} x^{2} + a^{2} b^{4}\right)}}\right]"," ",0,"[1/12*(4*a*b^3*d^2*x^5 + 4*(6*a*b^3*c*d - 5*a^2*b^2*d^2)*x^3 - 3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 6*(a*b^3*c^2 - 6*a^2*b^2*c*d + 5*a^3*b*d^2)*x)/(a*b^5*x^2 + a^2*b^4), 1/6*(2*a*b^3*d^2*x^5 + 2*(6*a*b^3*c*d - 5*a^2*b^2*d^2)*x^3 + 3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 3*(a*b^3*c^2 - 6*a^2*b^2*c*d + 5*a^3*b*d^2)*x)/(a*b^5*x^2 + a^2*b^4)]","A",0
274,1,101,0,0.549049," ","integrate(x*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{4} + a b d^{2} x^{2} - b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} + 2 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/2*(b^2*d^2*x^4 + a*b*d^2*x^2 - b^2*c^2 + 2*a*b*c*d - a^2*d^2 + 2*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*log(b*x^2 + a))/(b^4*x^2 + a*b^3)","A",0
275,1,297,0,0.930868," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b^{2} d^{2} x^{3} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x}{4 \, {\left(a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}, \frac{2 \, a^{2} b^{2} d^{2} x^{3} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x}{2 \, {\left(a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}\right]"," ",0,"[1/4*(4*a^2*b^2*d^2*x^3 + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x)/(a^2*b^4*x^2 + a^3*b^3), 1/2*(2*a^2*b^2*d^2*x^3 + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (a*b^3*c^2 - 2*a^2*b^2*c*d + 3*a^3*b*d^2)*x)/(a^2*b^4*x^2 + a^3*b^3)]","A",0
276,1,117,0,0.885775," ","integrate((d*x^2+c)^2/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} - {\left(a b^{2} c^{2} - a^{3} d^{2} + {\left(b^{3} c^{2} - a^{2} b d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"1/2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 - (a*b^2*c^2 - a^3*d^2 + (b^3*c^2 - a^2*b*d^2)*x^2)*log(b*x^2 + a) + 2*(b^3*c^2*x^2 + a*b^2*c^2)*log(x))/(a^2*b^3*x^2 + a^3*b^2)","A",0
277,1,308,0,0.975259," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b^{2} c^{2} + 2 \, {\left(3 \, a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2} - {\left({\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 2 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2} x\right)}}, -\frac{2 \, a^{2} b^{2} c^{2} + {\left(3 \, a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2} + {\left({\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 2 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2} x\right)}}\right]"," ",0,"[-1/4*(4*a^2*b^2*c^2 + 2*(3*a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2 - ((3*b^3*c^2 - 2*a*b^2*c*d - a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - 2*a^2*b*c*d - a^3*d^2)*x)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^3*x^3 + a^4*b^2*x), -1/2*(2*a^2*b^2*c^2 + (3*a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2 + ((3*b^3*c^2 - 2*a*b^2*c*d - a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - 2*a^2*b*c*d - a^3*d^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^3*x^3 + a^4*b^2*x)]","A",0
278,1,159,0,0.901882," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2} - 2 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{4} + {\left(a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 4 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{4} + {\left(a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}"," ",0,"-1/2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2 - 2*((b^3*c^2 - a*b^2*c*d)*x^4 + (a*b^2*c^2 - a^2*b*c*d)*x^2)*log(b*x^2 + a) + 4*((b^3*c^2 - a*b^2*c*d)*x^4 + (a*b^2*c^2 - a^2*b*c*d)*x^2)*log(x))/(a^3*b^2*x^4 + a^4*b*x^2)","B",0
279,1,356,0,0.905695," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{3} b c^{2} - 6 \, {\left(5 \, a b^{3} c^{2} - 6 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{4} - 4 \, {\left(5 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d\right)} x^{2} + 3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{5} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{12 \, {\left(a^{4} b^{2} x^{5} + a^{5} b x^{3}\right)}}, -\frac{2 \, a^{3} b c^{2} - 3 \, {\left(5 \, a b^{3} c^{2} - 6 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d\right)} x^{2} - 3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{5} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{6 \, {\left(a^{4} b^{2} x^{5} + a^{5} b x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^3*b*c^2 - 6*(5*a*b^3*c^2 - 6*a^2*b^2*c*d + a^3*b*d^2)*x^4 - 4*(5*a^2*b^2*c^2 - 6*a^3*b*c*d)*x^2 + 3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^5 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^2*x^5 + a^5*b*x^3), -1/6*(2*a^3*b*c^2 - 3*(5*a*b^3*c^2 - 6*a^2*b^2*c*d + a^3*b*d^2)*x^4 - 2*(5*a^2*b^2*c^2 - 6*a^3*b*c*d)*x^2 - 3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^5 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^2*x^5 + a^5*b*x^3)]","A",0
280,1,580,0,0.954191," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{20 \, b^{4} d^{3} x^{9} + 12 \, {\left(7 \, b^{4} c d^{2} - 3 \, a b^{3} d^{3}\right)} x^{7} + 28 \, {\left(5 \, b^{4} c^{2} d - 7 \, a b^{3} c d^{2} + 3 \, a^{2} b^{2} d^{3}\right)} x^{5} + 140 \, {\left(b^{4} c^{3} - 5 \, a b^{3} c^{2} d + 7 \, a^{2} b^{2} c d^{2} - 3 \, a^{3} b d^{3}\right)} x^{3} - 105 \, {\left(a b^{3} c^{3} - 5 \, a^{2} b^{2} c^{2} d + 7 \, a^{3} b c d^{2} - 3 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 5 \, a b^{3} c^{2} d + 7 \, a^{2} b^{2} c d^{2} - 3 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 210 \, {\left(a b^{3} c^{3} - 5 \, a^{2} b^{2} c^{2} d + 7 \, a^{3} b c d^{2} - 3 \, a^{4} d^{3}\right)} x}{140 \, {\left(b^{6} x^{2} + a b^{5}\right)}}, \frac{10 \, b^{4} d^{3} x^{9} + 6 \, {\left(7 \, b^{4} c d^{2} - 3 \, a b^{3} d^{3}\right)} x^{7} + 14 \, {\left(5 \, b^{4} c^{2} d - 7 \, a b^{3} c d^{2} + 3 \, a^{2} b^{2} d^{3}\right)} x^{5} + 70 \, {\left(b^{4} c^{3} - 5 \, a b^{3} c^{2} d + 7 \, a^{2} b^{2} c d^{2} - 3 \, a^{3} b d^{3}\right)} x^{3} - 105 \, {\left(a b^{3} c^{3} - 5 \, a^{2} b^{2} c^{2} d + 7 \, a^{3} b c d^{2} - 3 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 5 \, a b^{3} c^{2} d + 7 \, a^{2} b^{2} c d^{2} - 3 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 105 \, {\left(a b^{3} c^{3} - 5 \, a^{2} b^{2} c^{2} d + 7 \, a^{3} b c d^{2} - 3 \, a^{4} d^{3}\right)} x}{70 \, {\left(b^{6} x^{2} + a b^{5}\right)}}\right]"," ",0,"[1/140*(20*b^4*d^3*x^9 + 12*(7*b^4*c*d^2 - 3*a*b^3*d^3)*x^7 + 28*(5*b^4*c^2*d - 7*a*b^3*c*d^2 + 3*a^2*b^2*d^3)*x^5 + 140*(b^4*c^3 - 5*a*b^3*c^2*d + 7*a^2*b^2*c*d^2 - 3*a^3*b*d^3)*x^3 - 105*(a*b^3*c^3 - 5*a^2*b^2*c^2*d + 7*a^3*b*c*d^2 - 3*a^4*d^3 + (b^4*c^3 - 5*a*b^3*c^2*d + 7*a^2*b^2*c*d^2 - 3*a^3*b*d^3)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 210*(a*b^3*c^3 - 5*a^2*b^2*c^2*d + 7*a^3*b*c*d^2 - 3*a^4*d^3)*x)/(b^6*x^2 + a*b^5), 1/70*(10*b^4*d^3*x^9 + 6*(7*b^4*c*d^2 - 3*a*b^3*d^3)*x^7 + 14*(5*b^4*c^2*d - 7*a*b^3*c*d^2 + 3*a^2*b^2*d^3)*x^5 + 70*(b^4*c^3 - 5*a*b^3*c^2*d + 7*a^2*b^2*c*d^2 - 3*a^3*b*d^3)*x^3 - 105*(a*b^3*c^3 - 5*a^2*b^2*c^2*d + 7*a^3*b*c*d^2 - 3*a^4*d^3 + (b^4*c^3 - 5*a*b^3*c^2*d + 7*a^2*b^2*c*d^2 - 3*a^3*b*d^3)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 105*(a*b^3*c^3 - 5*a^2*b^2*c^2*d + 7*a^3*b*c*d^2 - 3*a^4*d^3)*x)/(b^6*x^2 + a*b^5)]","A",0
281,1,254,0,0.829028," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} d^{3} x^{8} + 6 \, a b^{3} c^{3} - 18 \, a^{2} b^{2} c^{2} d + 18 \, a^{3} b c d^{2} - 6 \, a^{4} d^{3} + {\left(9 \, b^{4} c d^{2} - 4 \, a b^{3} d^{3}\right)} x^{6} + 3 \, {\left(6 \, b^{4} c^{2} d - 9 \, a b^{3} c d^{2} + 4 \, a^{2} b^{2} d^{3}\right)} x^{4} + 18 \, {\left(a b^{3} c^{2} d - 2 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{2} + 6 \, {\left(a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} - 4 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 6 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} - 4 \, a^{3} b d^{3}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{12 \, {\left(b^{6} x^{2} + a b^{5}\right)}}"," ",0,"1/12*(2*b^4*d^3*x^8 + 6*a*b^3*c^3 - 18*a^2*b^2*c^2*d + 18*a^3*b*c*d^2 - 6*a^4*d^3 + (9*b^4*c*d^2 - 4*a*b^3*d^3)*x^6 + 3*(6*b^4*c^2*d - 9*a*b^3*c*d^2 + 4*a^2*b^2*d^3)*x^4 + 18*(a*b^3*c^2*d - 2*a^2*b^2*c*d^2 + a^3*b*d^3)*x^2 + 6*(a*b^3*c^3 - 6*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 - 4*a^4*d^3 + (b^4*c^3 - 6*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 - 4*a^3*b*d^3)*x^2)*log(b*x^2 + a))/(b^6*x^2 + a*b^5)","B",0
282,1,508,0,0.957098," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{4} d^{3} x^{7} + 4 \, {\left(15 \, a b^{4} c d^{2} - 7 \, a^{2} b^{3} d^{3}\right)} x^{5} + 20 \, {\left(9 \, a b^{4} c^{2} d - 15 \, a^{2} b^{3} c d^{2} + 7 \, a^{3} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 15 \, a^{3} b c d^{2} - 7 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 15 \, a^{2} b^{2} c d^{2} - 7 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 30 \, {\left(a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 15 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{60 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}, \frac{6 \, a b^{4} d^{3} x^{7} + 2 \, {\left(15 \, a b^{4} c d^{2} - 7 \, a^{2} b^{3} d^{3}\right)} x^{5} + 10 \, {\left(9 \, a b^{4} c^{2} d - 15 \, a^{2} b^{3} c d^{2} + 7 \, a^{3} b^{2} d^{3}\right)} x^{3} + 15 \, {\left(a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 15 \, a^{3} b c d^{2} - 7 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 15 \, a^{2} b^{2} c d^{2} - 7 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 15 \, {\left(a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 15 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{30 \, {\left(a b^{6} x^{2} + a^{2} b^{5}\right)}}\right]"," ",0,"[1/60*(12*a*b^4*d^3*x^7 + 4*(15*a*b^4*c*d^2 - 7*a^2*b^3*d^3)*x^5 + 20*(9*a*b^4*c^2*d - 15*a^2*b^3*c*d^2 + 7*a^3*b^2*d^3)*x^3 + 15*(a*b^3*c^3 - 9*a^2*b^2*c^2*d + 15*a^3*b*c*d^2 - 7*a^4*d^3 + (b^4*c^3 - 9*a*b^3*c^2*d + 15*a^2*b^2*c*d^2 - 7*a^3*b*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 30*(a*b^4*c^3 - 9*a^2*b^3*c^2*d + 15*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/(a*b^6*x^2 + a^2*b^5), 1/30*(6*a*b^4*d^3*x^7 + 2*(15*a*b^4*c*d^2 - 7*a^2*b^3*d^3)*x^5 + 10*(9*a*b^4*c^2*d - 15*a^2*b^3*c*d^2 + 7*a^3*b^2*d^3)*x^3 + 15*(a*b^3*c^3 - 9*a^2*b^2*c^2*d + 15*a^3*b*c*d^2 - 7*a^4*d^3 + (b^4*c^3 - 9*a*b^3*c^2*d + 15*a^2*b^2*c*d^2 - 7*a^3*b*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 15*(a*b^4*c^3 - 9*a^2*b^3*c^2*d + 15*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/(a*b^6*x^2 + a^2*b^5)]","A",0
283,1,181,0,0.994792," ","integrate(x*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{6} - 2 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3} + 3 \, {\left(2 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/4*(b^3*d^3*x^6 - 2*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + 3*(2*b^3*c*d^2 - a*b^2*d^3)*x^4 + 2*(3*a*b^2*c*d^2 - 2*a^2*b*d^3)*x^2 + 6*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2)*log(b*x^2 + a))/(b^5*x^2 + a*b^4)","B",0
284,1,442,0,0.967413," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b^{3} d^{3} x^{5} + 4 \, {\left(9 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{3} - 3 \, {\left(a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 9 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 9 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 6 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x}{12 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}, \frac{2 \, a^{2} b^{3} d^{3} x^{5} + 2 \, {\left(9 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d - 9 \, a^{3} b c d^{2} + 5 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2} d - 9 \, a^{2} b^{2} c d^{2} + 5 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x}{6 \, {\left(a^{2} b^{5} x^{2} + a^{3} b^{4}\right)}}\right]"," ",0,"[1/12*(4*a^2*b^3*d^3*x^5 + 4*(9*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^3 - 3*(a*b^3*c^3 + 3*a^2*b^2*c^2*d - 9*a^3*b*c*d^2 + 5*a^4*d^3 + (b^4*c^3 + 3*a*b^3*c^2*d - 9*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 6*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x)/(a^2*b^5*x^2 + a^3*b^4), 1/6*(2*a^2*b^3*d^3*x^5 + 2*(9*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^3 + 3*(a*b^3*c^3 + 3*a^2*b^2*c^2*d - 9*a^3*b*c*d^2 + 5*a^4*d^3 + (b^4*c^3 + 3*a*b^3*c^2*d - 9*a^2*b^2*c*d^2 + 5*a^3*b*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x)/(a^2*b^5*x^2 + a^3*b^4)]","B",0
285,1,178,0,0.848699," ","integrate((d*x^2+c)^3/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{a^{2} b^{2} d^{3} x^{4} + a^{3} b d^{3} x^{2} + a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3} - {\left(a b^{3} c^{3} - 3 \, a^{3} b c d^{2} + 2 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 3 \, a^{2} b^{2} c d^{2} + 2 \, a^{3} b d^{3}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left(b^{4} c^{3} x^{2} + a b^{3} c^{3}\right)} \log\left(x\right)}{2 \, {\left(a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"1/2*(a^2*b^2*d^3*x^4 + a^3*b*d^3*x^2 + a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3 - (a*b^3*c^3 - 3*a^3*b*c*d^2 + 2*a^4*d^3 + (b^4*c^3 - 3*a^2*b^2*c*d^2 + 2*a^3*b*d^3)*x^2)*log(b*x^2 + a) + 2*(b^4*c^3*x^2 + a*b^3*c^3)*log(x))/(a^2*b^4*x^2 + a^3*b^3)","B",0
286,1,412,0,0.580442," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{3} b^{2} d^{3} x^{4} - 4 \, a^{2} b^{3} c^{3} - 6 \, {\left(a b^{4} c^{3} - a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{2} - 3 \, {\left({\left(b^{4} c^{3} - a b^{3} c^{2} d - a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{3} + {\left(a b^{3} c^{3} - a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + a^{4} d^{3}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{4 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3} x\right)}}, \frac{2 \, a^{3} b^{2} d^{3} x^{4} - 2 \, a^{2} b^{3} c^{3} - 3 \, {\left(a b^{4} c^{3} - a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{2} - 3 \, {\left({\left(b^{4} c^{3} - a b^{3} c^{2} d - a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{3} + {\left(a b^{3} c^{3} - a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + a^{4} d^{3}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{2 \, {\left(a^{3} b^{4} x^{3} + a^{4} b^{3} x\right)}}\right]"," ",0,"[1/4*(4*a^3*b^2*d^3*x^4 - 4*a^2*b^3*c^3 - 6*(a*b^4*c^3 - a^2*b^3*c^2*d + a^3*b^2*c*d^2 - a^4*b*d^3)*x^2 - 3*((b^4*c^3 - a*b^3*c^2*d - a^2*b^2*c*d^2 + a^3*b*d^3)*x^3 + (a*b^3*c^3 - a^2*b^2*c^2*d - a^3*b*c*d^2 + a^4*d^3)*x)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^3*b^4*x^3 + a^4*b^3*x), 1/2*(2*a^3*b^2*d^3*x^4 - 2*a^2*b^3*c^3 - 3*(a*b^4*c^3 - a^2*b^3*c^2*d + a^3*b^2*c*d^2 - a^4*b*d^3)*x^2 - 3*((b^4*c^3 - a*b^3*c^2*d - a^2*b^2*c*d^2 + a^3*b*d^3)*x^3 + (a*b^3*c^3 - a^2*b^2*c^2*d - a^3*b*c*d^2 + a^4*d^3)*x)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^3*b^4*x^3 + a^4*b^3*x)]","A",0
287,1,209,0,0.885640," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{2} c^{3} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{2} - {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d + a^{3} b d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + a^{4} d^{3}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d\right)} x^{4} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{3} x^{4} + a^{4} b^{2} x^{2}\right)}}"," ",0,"-1/2*(a^2*b^2*c^3 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x^2 - ((2*b^4*c^3 - 3*a*b^3*c^2*d + a^3*b*d^3)*x^4 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + a^4*d^3)*x^2)*log(b*x^2 + a) + 2*((2*b^4*c^3 - 3*a*b^3*c^2*d)*x^4 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d)*x^2)*log(x))/(a^3*b^3*x^4 + a^4*b^2*x^2)","B",0
288,1,458,0,0.679542," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{3} b^{2} c^{3} - 6 \, {\left(5 \, a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} - 4 \, {\left(5 \, a^{2} b^{3} c^{3} - 9 \, a^{3} b^{2} c^{2} d\right)} x^{2} + 3 \, {\left({\left(5 \, b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right)}{12 \, {\left(a^{4} b^{3} x^{5} + a^{5} b^{2} x^{3}\right)}}, -\frac{2 \, a^{3} b^{2} c^{3} - 3 \, {\left(5 \, a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 9 \, a^{3} b^{2} c^{2} d\right)} x^{2} - 3 \, {\left({\left(5 \, b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right)}{6 \, {\left(a^{4} b^{3} x^{5} + a^{5} b^{2} x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^3*b^2*c^3 - 6*(5*a*b^4*c^3 - 9*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 - 4*(5*a^2*b^3*c^3 - 9*a^3*b^2*c^2*d)*x^2 + 3*((5*b^4*c^3 - 9*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x^5 + (5*a*b^3*c^3 - 9*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 + a^4*d^3)*x^3)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)))/(a^4*b^3*x^5 + a^5*b^2*x^3), -1/6*(2*a^3*b^2*c^3 - 3*(5*a*b^4*c^3 - 9*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 - 2*(5*a^2*b^3*c^3 - 9*a^3*b^2*c^2*d)*x^2 - 3*((5*b^4*c^3 - 9*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 + a^3*b*d^3)*x^5 + (5*a*b^3*c^3 - 9*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 + a^4*d^3)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x/a))/(a^4*b^3*x^5 + a^5*b^2*x^3)]","A",0
289,1,726,0,1.099650," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, a b c - a^{2} d + {\left(3 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 2 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} + 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - 2 \, {\left(a b c - a^{2} d\right)} x}{4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}, -\frac{{\left(3 \, a b c - a^{2} d + {\left(3 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - {\left(b^{2} c x^{2} + a b c\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} + 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) - {\left(a b c - a^{2} d\right)} x}{2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}, \frac{4 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - {\left(3 \, a b c - a^{2} d + {\left(3 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 2 \, {\left(a b c - a^{2} d\right)} x}{4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}, -\frac{{\left(3 \, a b c - a^{2} d + {\left(3 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 2 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - {\left(a b c - a^{2} d\right)} x}{2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((3*a*b*c - a^2*d + (3*b^2*c - a*b*d)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 2*(b^2*c*x^2 + a*b*c)*sqrt(-c/d)*log((d*x^2 + 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - 2*(a*b*c - a^2*d)*x)/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2), -1/2*((3*a*b*c - a^2*d + (3*b^2*c - a*b*d)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - (b^2*c*x^2 + a*b*c)*sqrt(-c/d)*log((d*x^2 + 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) - (a*b*c - a^2*d)*x)/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2), 1/4*(4*(b^2*c*x^2 + a*b*c)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - (3*a*b*c - a^2*d + (3*b^2*c - a*b*d)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 2*(a*b*c - a^2*d)*x)/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2), -1/2*((3*a*b*c - a^2*d + (3*b^2*c - a*b*d)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 2*(b^2*c*x^2 + a*b*c)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - (a*b*c - a^2*d)*x)/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2)]","A",0
290,1,117,0,0.818468," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{a b c - a^{2} d + {\left(b^{2} c x^{2} + a b c\right)} \log\left(b x^{2} + a\right) - {\left(b^{2} c x^{2} + a b c\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}"," ",0,"1/2*(a*b*c - a^2*d + (b^2*c*x^2 + a*b*c)*log(b*x^2 + a) - (b^2*c*x^2 + a*b*c)*log(d*x^2 + c))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2)","A",0
291,1,704,0,1.016804," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 2 \, {\left(a b^{2} x^{2} + a^{2} b\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} x}{4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{2}\right)}}, \frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(a b^{2} x^{2} + a^{2} b\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) - {\left(a b^{2} c - a^{2} b d\right)} x}{2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{2}\right)}}, -\frac{4 \, {\left(a b^{2} x^{2} + a^{2} b\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + {\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} x}{4 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{2}\right)}}, \frac{{\left(a b c + a^{2} d + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 2 \, {\left(a b^{2} x^{2} + a^{2} b\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) - {\left(a b^{2} c - a^{2} b d\right)} x}{2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 2*(a*b^2*x^2 + a^2*b)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 2*(a*b^2*c - a^2*b*d)*x)/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x^2), 1/2*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (a*b^2*x^2 + a^2*b)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) - (a*b^2*c - a^2*b*d)*x)/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x^2), -1/4*(4*(a*b^2*x^2 + a^2*b)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + (a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(a*b^2*c - a^2*b*d)*x)/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x^2), 1/2*((a*b*c + a^2*d + (b^2*c + a*b*d)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 2*(a*b^2*x^2 + a^2*b)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) - (a*b^2*c - a^2*b*d)*x)/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x^2)]","A",0
292,1,103,0,0.571810," ","integrate(x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{b c - a d + {\left(b d x^{2} + a d\right)} \log\left(b x^{2} + a\right) - {\left(b d x^{2} + a d\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)}}"," ",0,"-1/2*(b*c - a*d + (b*d*x^2 + a*d)*log(b*x^2 + a) - (b*d*x^2 + a*d)*log(d*x^2 + c))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)","A",0
293,1,699,0,0.915130," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) - 2 \, {\left(b^{2} c - a b d\right)} x}{4 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}, \frac{4 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(b^{2} c - a b d\right)} x}{4 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}, \frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + {\left(b^{2} c - a b d\right)} x}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}, \frac{{\left(a b c - 3 \, a^{2} d + {\left(b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(b^{2} c - a b d\right)} x}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*(a*b*d*x^2 + a^2*d)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) - 2*(b^2*c - a*b*d)*x)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2), 1/4*(4*(a*b*d*x^2 + a^2*d)*sqrt(d/c)*arctan(x*sqrt(d/c)) - (a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(b^2*c - a*b*d)*x)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2), 1/2*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (a*b*d*x^2 + a^2*d)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + (b^2*c - a*b*d)*x)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2), 1/2*((a*b*c - 3*a^2*d + (b^2*c - 3*a*b*d)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*(a*b*d*x^2 + a^2*d)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (b^2*c - a*b*d)*x)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)]","A",0
294,1,218,0,2.616453," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{a b^{2} c^{2} - a^{2} b c d - {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + {\left(b^{3} c^{2} - 2 \, a b^{2} c d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2} + {\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{2}\right)}}"," ",0,"1/2*(a*b^2*c^2 - a^2*b*c*d - (a*b^2*c^2 - 2*a^2*b*c*d + (b^3*c^2 - 2*a*b^2*c*d)*x^2)*log(b*x^2 + a) - (a^2*b*d^2*x^2 + a^3*d^2)*log(d*x^2 + c) + 2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)*log(x))/(a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2 + (a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^2)","B",0
295,1,1003,0,1.626384," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{4 \, a b^{2} c^{2} - 8 \, a^{2} b c d + 4 \, a^{3} d^{2} + 2 \, {\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x^{2} + {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{4 \, {\left({\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{3} + {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x\right)}}, -\frac{4 \, a b^{2} c^{2} - 8 \, a^{2} b c d + 4 \, a^{3} d^{2} + 2 \, {\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x^{2} + 4 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{4 \, {\left({\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{3} + {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x\right)}}, -\frac{2 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x^{2} + {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{2 \, {\left({\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{3} + {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x\right)}}, -\frac{2 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x^{2} + {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{2 \, {\left({\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{3} + {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} x\right)}}\right]"," ",0,"[-1/4*(4*a*b^2*c^2 - 8*a^2*b*c*d + 4*a^3*d^2 + 2*(3*b^3*c^2 - 5*a*b^2*c*d + 2*a^2*b*d^2)*x^2 + ((3*b^3*c^2 - 5*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^3 + (a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x), -1/4*(4*a*b^2*c^2 - 8*a^2*b*c*d + 4*a^3*d^2 + 2*(3*b^3*c^2 - 5*a*b^2*c*d + 2*a^2*b*d^2)*x^2 + 4*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(d/c)*arctan(x*sqrt(d/c)) + ((3*b^3*c^2 - 5*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^3 + (a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x), -1/2*(2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 + (3*b^3*c^2 - 5*a*b^2*c*d + 2*a^2*b*d^2)*x^2 + ((3*b^3*c^2 - 5*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) - (a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^3 + (a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x), -1/2*(2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 + (3*b^3*c^2 - 5*a*b^2*c*d + 2*a^2*b*d^2)*x^2 + ((3*b^3*c^2 - 5*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^3 + (a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*x)]","A",0
296,1,303,0,5.584387," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d + a^{4} c d^{2} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + a^{3} b c d^{2}\right)} x^{2} - {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d\right)} x^{4} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - {\left(a^{3} b d^{3} x^{4} + a^{4} d^{3} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d + a^{3} b d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + a^{4} d^{3}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{3} c^{4} - 2 \, a^{4} b^{2} c^{3} d + a^{5} b c^{2} d^{2}\right)} x^{4} + {\left(a^{4} b^{2} c^{4} - 2 \, a^{5} b c^{3} d + a^{6} c^{2} d^{2}\right)} x^{2}\right)}}"," ",0,"-1/2*(a^2*b^2*c^3 - 2*a^3*b*c^2*d + a^4*c*d^2 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + a^3*b*c*d^2)*x^2 - ((2*b^4*c^3 - 3*a*b^3*c^2*d)*x^4 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d)*x^2)*log(b*x^2 + a) - (a^3*b*d^3*x^4 + a^4*d^3*x^2)*log(d*x^2 + c) + 2*((2*b^4*c^3 - 3*a*b^3*c^2*d + a^3*b*d^3)*x^4 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + a^4*d^3)*x^2)*log(x))/((a^3*b^3*c^4 - 2*a^4*b^2*c^3*d + a^5*b*c^2*d^2)*x^4 + (a^4*b^2*c^4 - 2*a^5*b*c^3*d + a^6*c^2*d^2)*x^2)","B",0
297,1,1281,0,3.477949," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b^{2} c^{3} - 8 \, a^{3} b c^{2} d + 4 \, a^{4} c d^{2} - 6 \, {\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 2 \, a^{3} b d^{3}\right)} x^{4} - 4 \, {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + 3 \, a^{4} d^{3}\right)} x^{2} + 3 \, {\left({\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 6 \, {\left(a^{3} b d^{3} x^{5} + a^{4} d^{3} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{12 \, {\left({\left(a^{3} b^{3} c^{4} - 2 \, a^{4} b^{2} c^{3} d + a^{5} b c^{2} d^{2}\right)} x^{5} + {\left(a^{4} b^{2} c^{4} - 2 \, a^{5} b c^{3} d + a^{6} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{4 \, a^{2} b^{2} c^{3} - 8 \, a^{3} b c^{2} d + 4 \, a^{4} c d^{2} - 6 \, {\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 2 \, a^{3} b d^{3}\right)} x^{4} - 4 \, {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + 3 \, a^{4} d^{3}\right)} x^{2} - 12 \, {\left(a^{3} b d^{3} x^{5} + a^{4} d^{3} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 3 \, {\left({\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{12 \, {\left({\left(a^{3} b^{3} c^{4} - 2 \, a^{4} b^{2} c^{3} d + a^{5} b c^{2} d^{2}\right)} x^{5} + {\left(a^{4} b^{2} c^{4} - 2 \, a^{5} b c^{3} d + a^{6} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, a^{2} b^{2} c^{3} - 4 \, a^{3} b c^{2} d + 2 \, a^{4} c d^{2} - 3 \, {\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 2 \, a^{3} b d^{3}\right)} x^{4} - 2 \, {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + 3 \, a^{4} d^{3}\right)} x^{2} - 3 \, {\left({\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left(a^{3} b d^{3} x^{5} + a^{4} d^{3} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{6 \, {\left({\left(a^{3} b^{3} c^{4} - 2 \, a^{4} b^{2} c^{3} d + a^{5} b c^{2} d^{2}\right)} x^{5} + {\left(a^{4} b^{2} c^{4} - 2 \, a^{5} b c^{3} d + a^{6} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, a^{2} b^{2} c^{3} - 4 \, a^{3} b c^{2} d + 2 \, a^{4} c d^{2} - 3 \, {\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d + 2 \, a^{3} b d^{3}\right)} x^{4} - 2 \, {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + 3 \, a^{4} d^{3}\right)} x^{2} - 3 \, {\left({\left(5 \, b^{4} c^{3} - 7 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 7 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 6 \, {\left(a^{3} b d^{3} x^{5} + a^{4} d^{3} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{6 \, {\left({\left(a^{3} b^{3} c^{4} - 2 \, a^{4} b^{2} c^{3} d + a^{5} b c^{2} d^{2}\right)} x^{5} + {\left(a^{4} b^{2} c^{4} - 2 \, a^{5} b c^{3} d + a^{6} c^{2} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^2*b^2*c^3 - 8*a^3*b*c^2*d + 4*a^4*c*d^2 - 6*(5*b^4*c^3 - 7*a*b^3*c^2*d + 2*a^3*b*d^3)*x^4 - 4*(5*a*b^3*c^3 - 7*a^2*b^2*c^2*d - a^3*b*c*d^2 + 3*a^4*d^3)*x^2 + 3*((5*b^4*c^3 - 7*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 7*a^2*b^2*c^2*d)*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 6*(a^3*b*d^3*x^5 + a^4*d^3*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^3*c^4 - 2*a^4*b^2*c^3*d + a^5*b*c^2*d^2)*x^5 + (a^4*b^2*c^4 - 2*a^5*b*c^3*d + a^6*c^2*d^2)*x^3), -1/12*(4*a^2*b^2*c^3 - 8*a^3*b*c^2*d + 4*a^4*c*d^2 - 6*(5*b^4*c^3 - 7*a*b^3*c^2*d + 2*a^3*b*d^3)*x^4 - 4*(5*a*b^3*c^3 - 7*a^2*b^2*c^2*d - a^3*b*c*d^2 + 3*a^4*d^3)*x^2 - 12*(a^3*b*d^3*x^5 + a^4*d^3*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 3*((5*b^4*c^3 - 7*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 7*a^2*b^2*c^2*d)*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^3*b^3*c^4 - 2*a^4*b^2*c^3*d + a^5*b*c^2*d^2)*x^5 + (a^4*b^2*c^4 - 2*a^5*b*c^3*d + a^6*c^2*d^2)*x^3), -1/6*(2*a^2*b^2*c^3 - 4*a^3*b*c^2*d + 2*a^4*c*d^2 - 3*(5*b^4*c^3 - 7*a*b^3*c^2*d + 2*a^3*b*d^3)*x^4 - 2*(5*a*b^3*c^3 - 7*a^2*b^2*c^2*d - a^3*b*c*d^2 + 3*a^4*d^3)*x^2 - 3*((5*b^4*c^3 - 7*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 7*a^2*b^2*c^2*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*(a^3*b*d^3*x^5 + a^4*d^3*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^3*c^4 - 2*a^4*b^2*c^3*d + a^5*b*c^2*d^2)*x^5 + (a^4*b^2*c^4 - 2*a^5*b*c^3*d + a^6*c^2*d^2)*x^3), -1/6*(2*a^2*b^2*c^3 - 4*a^3*b*c^2*d + 2*a^4*c*d^2 - 3*(5*b^4*c^3 - 7*a*b^3*c^2*d + 2*a^3*b*d^3)*x^4 - 2*(5*a*b^3*c^3 - 7*a^2*b^2*c^2*d - a^3*b*c*d^2 + 3*a^4*d^3)*x^2 - 3*((5*b^4*c^3 - 7*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 7*a^2*b^2*c^2*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 6*(a^3*b*d^3*x^5 + a^4*d^3*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^3*b^3*c^4 - 2*a^4*b^2*c^3*d + a^5*b*c^2*d^2)*x^5 + (a^4*b^2*c^4 - 2*a^5*b*c^3*d + a^6*c^2*d^2)*x^3)]","A",0
298,1,356,0,12.768841," ","integrate(1/x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{a^{3} b^{2} c^{4} - 2 \, a^{4} b c^{3} d + a^{5} c^{2} d^{2} - 2 \, {\left(3 \, a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + a^{4} b c d^{3}\right)} x^{4} - {\left(3 \, a^{2} b^{3} c^{4} - 4 \, a^{3} b^{2} c^{3} d - a^{4} b c^{2} d^{2} + 2 \, a^{5} c d^{3}\right)} x^{2} + 2 \, {\left({\left(3 \, b^{5} c^{4} - 4 \, a b^{4} c^{3} d\right)} x^{6} + {\left(3 \, a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d\right)} x^{4}\right)} \log\left(b x^{2} + a\right) + 2 \, {\left(a^{4} b d^{4} x^{6} + a^{5} d^{4} x^{4}\right)} \log\left(d x^{2} + c\right) - 4 \, {\left({\left(3 \, b^{5} c^{4} - 4 \, a b^{4} c^{3} d + a^{4} b d^{4}\right)} x^{6} + {\left(3 \, a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + a^{5} d^{4}\right)} x^{4}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{4} b^{3} c^{5} - 2 \, a^{5} b^{2} c^{4} d + a^{6} b c^{3} d^{2}\right)} x^{6} + {\left(a^{5} b^{2} c^{5} - 2 \, a^{6} b c^{4} d + a^{7} c^{3} d^{2}\right)} x^{4}\right)}}"," ",0,"-1/4*(a^3*b^2*c^4 - 2*a^4*b*c^3*d + a^5*c^2*d^2 - 2*(3*a*b^4*c^4 - 4*a^2*b^3*c^3*d + a^4*b*c*d^3)*x^4 - (3*a^2*b^3*c^4 - 4*a^3*b^2*c^3*d - a^4*b*c^2*d^2 + 2*a^5*c*d^3)*x^2 + 2*((3*b^5*c^4 - 4*a*b^4*c^3*d)*x^6 + (3*a*b^4*c^4 - 4*a^2*b^3*c^3*d)*x^4)*log(b*x^2 + a) + 2*(a^4*b*d^4*x^6 + a^5*d^4*x^4)*log(d*x^2 + c) - 4*((3*b^5*c^4 - 4*a*b^4*c^3*d + a^4*b*d^4)*x^6 + (3*a*b^4*c^4 - 4*a^2*b^3*c^3*d + a^5*d^4)*x^4)*log(x))/((a^4*b^3*c^5 - 2*a^5*b^2*c^4*d + a^6*b*c^3*d^2)*x^6 + (a^5*b^2*c^5 - 2*a^6*b*c^4*d + a^7*c^3*d^2)*x^4)","B",0
299,1,1489,0,6.929028," ","integrate(1/x^6/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\left[-\frac{12 \, a^{3} b^{2} c^{4} - 24 \, a^{4} b c^{3} d + 12 \, a^{5} c^{2} d^{2} + 30 \, {\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d + 2 \, a^{4} b d^{4}\right)} x^{6} + 20 \, {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d - a^{4} b c d^{3} + 3 \, a^{5} d^{4}\right)} x^{4} - 4 \, {\left(7 \, a^{2} b^{3} c^{4} - 9 \, a^{3} b^{2} c^{3} d - 3 \, a^{4} b c^{2} d^{2} + 5 \, a^{5} c d^{3}\right)} x^{2} + 15 \, {\left({\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d\right)} x^{7} + {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d\right)} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 30 \, {\left(a^{4} b d^{4} x^{7} + a^{5} d^{4} x^{5}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{60 \, {\left({\left(a^{4} b^{3} c^{5} - 2 \, a^{5} b^{2} c^{4} d + a^{6} b c^{3} d^{2}\right)} x^{7} + {\left(a^{5} b^{2} c^{5} - 2 \, a^{6} b c^{4} d + a^{7} c^{3} d^{2}\right)} x^{5}\right)}}, -\frac{12 \, a^{3} b^{2} c^{4} - 24 \, a^{4} b c^{3} d + 12 \, a^{5} c^{2} d^{2} + 30 \, {\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d + 2 \, a^{4} b d^{4}\right)} x^{6} + 20 \, {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d - a^{4} b c d^{3} + 3 \, a^{5} d^{4}\right)} x^{4} - 4 \, {\left(7 \, a^{2} b^{3} c^{4} - 9 \, a^{3} b^{2} c^{3} d - 3 \, a^{4} b c^{2} d^{2} + 5 \, a^{5} c d^{3}\right)} x^{2} + 60 \, {\left(a^{4} b d^{4} x^{7} + a^{5} d^{4} x^{5}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 15 \, {\left({\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d\right)} x^{7} + {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d\right)} x^{5}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{60 \, {\left({\left(a^{4} b^{3} c^{5} - 2 \, a^{5} b^{2} c^{4} d + a^{6} b c^{3} d^{2}\right)} x^{7} + {\left(a^{5} b^{2} c^{5} - 2 \, a^{6} b c^{4} d + a^{7} c^{3} d^{2}\right)} x^{5}\right)}}, -\frac{6 \, a^{3} b^{2} c^{4} - 12 \, a^{4} b c^{3} d + 6 \, a^{5} c^{2} d^{2} + 15 \, {\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d + 2 \, a^{4} b d^{4}\right)} x^{6} + 10 \, {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d - a^{4} b c d^{3} + 3 \, a^{5} d^{4}\right)} x^{4} - 2 \, {\left(7 \, a^{2} b^{3} c^{4} - 9 \, a^{3} b^{2} c^{3} d - 3 \, a^{4} b c^{2} d^{2} + 5 \, a^{5} c d^{3}\right)} x^{2} + 15 \, {\left({\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d\right)} x^{7} + {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d\right)} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 15 \, {\left(a^{4} b d^{4} x^{7} + a^{5} d^{4} x^{5}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{30 \, {\left({\left(a^{4} b^{3} c^{5} - 2 \, a^{5} b^{2} c^{4} d + a^{6} b c^{3} d^{2}\right)} x^{7} + {\left(a^{5} b^{2} c^{5} - 2 \, a^{6} b c^{4} d + a^{7} c^{3} d^{2}\right)} x^{5}\right)}}, -\frac{6 \, a^{3} b^{2} c^{4} - 12 \, a^{4} b c^{3} d + 6 \, a^{5} c^{2} d^{2} + 15 \, {\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d + 2 \, a^{4} b d^{4}\right)} x^{6} + 10 \, {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d - a^{4} b c d^{3} + 3 \, a^{5} d^{4}\right)} x^{4} - 2 \, {\left(7 \, a^{2} b^{3} c^{4} - 9 \, a^{3} b^{2} c^{3} d - 3 \, a^{4} b c^{2} d^{2} + 5 \, a^{5} c d^{3}\right)} x^{2} + 15 \, {\left({\left(7 \, b^{5} c^{4} - 9 \, a b^{4} c^{3} d\right)} x^{7} + {\left(7 \, a b^{4} c^{4} - 9 \, a^{2} b^{3} c^{3} d\right)} x^{5}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 30 \, {\left(a^{4} b d^{4} x^{7} + a^{5} d^{4} x^{5}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{30 \, {\left({\left(a^{4} b^{3} c^{5} - 2 \, a^{5} b^{2} c^{4} d + a^{6} b c^{3} d^{2}\right)} x^{7} + {\left(a^{5} b^{2} c^{5} - 2 \, a^{6} b c^{4} d + a^{7} c^{3} d^{2}\right)} x^{5}\right)}}\right]"," ",0,"[-1/60*(12*a^3*b^2*c^4 - 24*a^4*b*c^3*d + 12*a^5*c^2*d^2 + 30*(7*b^5*c^4 - 9*a*b^4*c^3*d + 2*a^4*b*d^4)*x^6 + 20*(7*a*b^4*c^4 - 9*a^2*b^3*c^3*d - a^4*b*c*d^3 + 3*a^5*d^4)*x^4 - 4*(7*a^2*b^3*c^4 - 9*a^3*b^2*c^3*d - 3*a^4*b*c^2*d^2 + 5*a^5*c*d^3)*x^2 + 15*((7*b^5*c^4 - 9*a*b^4*c^3*d)*x^7 + (7*a*b^4*c^4 - 9*a^2*b^3*c^3*d)*x^5)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 30*(a^4*b*d^4*x^7 + a^5*d^4*x^5)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^4*b^3*c^5 - 2*a^5*b^2*c^4*d + a^6*b*c^3*d^2)*x^7 + (a^5*b^2*c^5 - 2*a^6*b*c^4*d + a^7*c^3*d^2)*x^5), -1/60*(12*a^3*b^2*c^4 - 24*a^4*b*c^3*d + 12*a^5*c^2*d^2 + 30*(7*b^5*c^4 - 9*a*b^4*c^3*d + 2*a^4*b*d^4)*x^6 + 20*(7*a*b^4*c^4 - 9*a^2*b^3*c^3*d - a^4*b*c*d^3 + 3*a^5*d^4)*x^4 - 4*(7*a^2*b^3*c^4 - 9*a^3*b^2*c^3*d - 3*a^4*b*c^2*d^2 + 5*a^5*c*d^3)*x^2 + 60*(a^4*b*d^4*x^7 + a^5*d^4*x^5)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 15*((7*b^5*c^4 - 9*a*b^4*c^3*d)*x^7 + (7*a*b^4*c^4 - 9*a^2*b^3*c^3*d)*x^5)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^4*b^3*c^5 - 2*a^5*b^2*c^4*d + a^6*b*c^3*d^2)*x^7 + (a^5*b^2*c^5 - 2*a^6*b*c^4*d + a^7*c^3*d^2)*x^5), -1/30*(6*a^3*b^2*c^4 - 12*a^4*b*c^3*d + 6*a^5*c^2*d^2 + 15*(7*b^5*c^4 - 9*a*b^4*c^3*d + 2*a^4*b*d^4)*x^6 + 10*(7*a*b^4*c^4 - 9*a^2*b^3*c^3*d - a^4*b*c*d^3 + 3*a^5*d^4)*x^4 - 2*(7*a^2*b^3*c^4 - 9*a^3*b^2*c^3*d - 3*a^4*b*c^2*d^2 + 5*a^5*c*d^3)*x^2 + 15*((7*b^5*c^4 - 9*a*b^4*c^3*d)*x^7 + (7*a*b^4*c^4 - 9*a^2*b^3*c^3*d)*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 15*(a^4*b*d^4*x^7 + a^5*d^4*x^5)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^4*b^3*c^5 - 2*a^5*b^2*c^4*d + a^6*b*c^3*d^2)*x^7 + (a^5*b^2*c^5 - 2*a^6*b*c^4*d + a^7*c^3*d^2)*x^5), -1/30*(6*a^3*b^2*c^4 - 12*a^4*b*c^3*d + 6*a^5*c^2*d^2 + 15*(7*b^5*c^4 - 9*a*b^4*c^3*d + 2*a^4*b*d^4)*x^6 + 10*(7*a*b^4*c^4 - 9*a^2*b^3*c^3*d - a^4*b*c*d^3 + 3*a^5*d^4)*x^4 - 2*(7*a^2*b^3*c^4 - 9*a^3*b^2*c^3*d - 3*a^4*b*c^2*d^2 + 5*a^5*c*d^3)*x^2 + 15*((7*b^5*c^4 - 9*a*b^4*c^3*d)*x^7 + (7*a*b^4*c^4 - 9*a^2*b^3*c^3*d)*x^5)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 30*(a^4*b*d^4*x^7 + a^5*d^4*x^5)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^4*b^3*c^5 - 2*a^5*b^2*c^4*d + a^6*b*c^3*d^2)*x^7 + (a^5*b^2*c^5 - 2*a^6*b*c^4*d + a^7*c^3*d^2)*x^5)]","A",0
300,1,410,0,19.484134," ","integrate(1/x^7/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{2 \, a^{4} b^{2} c^{5} - 4 \, a^{5} b c^{4} d + 2 \, a^{6} c^{3} d^{2} + 6 \, {\left(4 \, a b^{5} c^{5} - 5 \, a^{2} b^{4} c^{4} d + a^{5} b c d^{4}\right)} x^{6} + 3 \, {\left(4 \, a^{2} b^{4} c^{5} - 5 \, a^{3} b^{3} c^{4} d - a^{5} b c^{2} d^{3} + 2 \, a^{6} c d^{4}\right)} x^{4} - {\left(4 \, a^{3} b^{3} c^{5} - 5 \, a^{4} b^{2} c^{4} d - 2 \, a^{5} b c^{3} d^{2} + 3 \, a^{6} c^{2} d^{3}\right)} x^{2} - 6 \, {\left({\left(4 \, b^{6} c^{5} - 5 \, a b^{5} c^{4} d\right)} x^{8} + {\left(4 \, a b^{5} c^{5} - 5 \, a^{2} b^{4} c^{4} d\right)} x^{6}\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(a^{5} b d^{5} x^{8} + a^{6} d^{5} x^{6}\right)} \log\left(d x^{2} + c\right) + 12 \, {\left({\left(4 \, b^{6} c^{5} - 5 \, a b^{5} c^{4} d + a^{5} b d^{5}\right)} x^{8} + {\left(4 \, a b^{5} c^{5} - 5 \, a^{2} b^{4} c^{4} d + a^{6} d^{5}\right)} x^{6}\right)} \log\left(x\right)}{12 \, {\left({\left(a^{5} b^{3} c^{6} - 2 \, a^{6} b^{2} c^{5} d + a^{7} b c^{4} d^{2}\right)} x^{8} + {\left(a^{6} b^{2} c^{6} - 2 \, a^{7} b c^{5} d + a^{8} c^{4} d^{2}\right)} x^{6}\right)}}"," ",0,"-1/12*(2*a^4*b^2*c^5 - 4*a^5*b*c^4*d + 2*a^6*c^3*d^2 + 6*(4*a*b^5*c^5 - 5*a^2*b^4*c^4*d + a^5*b*c*d^4)*x^6 + 3*(4*a^2*b^4*c^5 - 5*a^3*b^3*c^4*d - a^5*b*c^2*d^3 + 2*a^6*c*d^4)*x^4 - (4*a^3*b^3*c^5 - 5*a^4*b^2*c^4*d - 2*a^5*b*c^3*d^2 + 3*a^6*c^2*d^3)*x^2 - 6*((4*b^6*c^5 - 5*a*b^5*c^4*d)*x^8 + (4*a*b^5*c^5 - 5*a^2*b^4*c^4*d)*x^6)*log(b*x^2 + a) - 6*(a^5*b*d^5*x^8 + a^6*d^5*x^6)*log(d*x^2 + c) + 12*((4*b^6*c^5 - 5*a*b^5*c^4*d + a^5*b*d^5)*x^8 + (4*a*b^5*c^5 - 5*a^2*b^4*c^4*d + a^6*d^5)*x^6)*log(x))/((a^5*b^3*c^6 - 2*a^6*b^2*c^5*d + a^7*b*c^4*d^2)*x^8 + (a^6*b^2*c^6 - 2*a^7*b*c^5*d + a^8*c^4*d^2)*x^6)","B",0
301,1,1407,0,1.558029," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3} - {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) + 4 \, {\left(a b c^{2} - a^{2} c d\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3} - 2 \, {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{2} - 2 \, d x \sqrt{-\frac{c}{d}} - c}{d x^{2} + c}\right) + 4 \, {\left(a b c^{2} - a^{2} c d\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3} + 2 \, {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) - {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 4 \, {\left(a b c^{2} - a^{2} c d\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, \frac{{\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3} - {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x \sqrt{\frac{c}{d}}}{c}\right) + 2 \, {\left(a b c^{2} - a^{2} c d\right)} x}{2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b^2*c^2 - a^2*d^2)*x^3 - ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) + 4*(a*b*c^2 - a^2*c*d)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), 1/4*(2*(b^2*c^2 - a^2*d^2)*x^3 - 2*((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(-c/d)*log((d*x^2 - 2*d*x*sqrt(-c/d) - c)/(d*x^2 + c)) + 4*(a*b*c^2 - a^2*c*d)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), 1/4*(2*(b^2*c^2 - a^2*d^2)*x^3 + 2*((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) - ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 4*(a*b*c^2 - a^2*c*d)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), 1/2*((b^2*c^2 - a^2*d^2)*x^3 - ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(c/d)*arctan(d*x*sqrt(c/d)/c) + 2*(a*b*c^2 - a^2*c*d)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)]","B",0
302,1,296,0,1.400964," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{2 \, a b c^{2} - 2 \, a^{2} c d + {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2} + {\left({\left(b^{2} c d + a b d^{2}\right)} x^{4} + a b c^{2} + a^{2} c d + {\left(b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - {\left({\left(b^{2} c d + a b d^{2}\right)} x^{4} + a b c^{2} + a^{2} c d + {\left(b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}"," ",0,"1/2*(2*a*b*c^2 - 2*a^2*c*d + (b^2*c^2 - a^2*d^2)*x^2 + ((b^2*c*d + a*b*d^2)*x^4 + a*b*c^2 + a^2*c*d + (b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x^2)*log(b*x^2 + a) - ((b^2*c*d + a*b*d^2)*x^4 + a*b*c^2 + a^2*c*d + (b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x^2)*log(d*x^2 + c))/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)","B",0
303,1,1387,0,1.949522," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, -\frac{4 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + 2 \, {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, -\frac{4 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} - 2 \, {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{4 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}, -\frac{2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} - {\left({\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + a b c^{2} + 3 \, a^{2} c d + {\left(b^{2} c^{2} + 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left({\left(3 \, b^{2} c d + a b d^{2}\right)} x^{4} + 3 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*(b^2*c*d - a*b*d^2)*x^3 + ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^2*c^2 - a^2*d^2)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), -1/4*(4*(b^2*c*d - a*b*d^2)*x^3 + 2*((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(b^2*c^2 - a^2*d^2)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), -1/4*(4*(b^2*c*d - a*b*d^2)*x^3 - 2*((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^2*c^2 - a^2*d^2)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2), -1/2*(2*(b^2*c*d - a*b*d^2)*x^3 - ((b^2*c*d + 3*a*b*d^2)*x^4 + a*b*c^2 + 3*a^2*c*d + (b^2*c^2 + 4*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + ((3*b^2*c*d + a*b*d^2)*x^4 + 3*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (b^2*c^2 - a^2*d^2)*x)/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)]","B",0
304,1,253,0,1.045865," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} - a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)}}"," ",0,"-1/2*(b^2*c^2 - a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x^2 + 2*(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)*log(b*x^2 + a) - 2*(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)*log(d*x^2 + c))/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)","B",0
305,1,1681,0,3.056618," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + 2 \, {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + 2 \, {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{4 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}, \frac{{\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{3} + {\left(a b^{2} c^{3} - 5 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(5 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(5 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{4} + {\left(5 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(b^{3} c^{3} - a b^{2} c^{2} d + a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{2 \, {\left(a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + {\left(a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + 2*(5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/4*(2*(b^3*c^2*d - a^2*b*d^3)*x^3 + 2*(a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2), 1/2*((b^3*c^2*d - a^2*b*d^3)*x^3 + (a*b^2*c^3 - 5*a^2*b*c^2*d + (b^3*c^2*d - 5*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 4*a*b^2*c^2*d - 5*a^2*b*c*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (5*a^2*b*c^2*d - a^3*c*d^2 + (5*a*b^2*c*d^2 - a^2*b*d^3)*x^4 + (5*a*b^2*c^2*d + 4*a^2*b*c*d^2 - a^3*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (b^3*c^3 - a*b^2*c^2*d + a^2*b*c*d^2 - a^3*d^3)*x)/(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + (a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2)]","B",0
306,1,540,0,11.967775," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{a b^{3} c^{4} - a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(a b^{3} c^{3} d - a^{3} b c d^{3}\right)} x^{2} - {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - {\left(3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(3 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3} + {\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{4} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x^{2}\right)}}"," ",0,"1/2*(a*b^3*c^4 - a^2*b^2*c^3*d + a^3*b*c^2*d^2 - a^4*c*d^3 + (a*b^3*c^3*d - a^3*b*c*d^3)*x^2 - (a*b^3*c^4 - 3*a^2*b^2*c^3*d + (b^4*c^3*d - 3*a*b^3*c^2*d^2)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2)*x^2)*log(b*x^2 + a) - (3*a^3*b*c^2*d^2 - a^4*c*d^3 + (3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (3*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)*log(d*x^2 + c) + 2*(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x^2)*log(x))/(a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3 + (a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^4 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x^2)","B",0
307,1,2113,0,6.148870," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a b^{3} c^{4} - 12 \, a^{2} b^{2} c^{3} d + 12 \, a^{3} b c^{2} d^{2} - 4 \, a^{4} c d^{3} + 2 \, {\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} + 7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{4} c^{4} - 5 \, a b^{3} c^{3} d + 5 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{2} - {\left({\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - {\left({\left(7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{5} + {\left(7 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{3} + {\left(7 \, a^{3} b c^{2} d^{2} - 3 \, a^{4} c d^{3}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{4 \, {\left({\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{5} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x^{3} + {\left(a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3}\right)} x\right)}}, -\frac{4 \, a b^{3} c^{4} - 12 \, a^{2} b^{2} c^{3} d + 12 \, a^{3} b c^{2} d^{2} - 4 \, a^{4} c d^{3} + 2 \, {\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} + 7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{4} c^{4} - 5 \, a b^{3} c^{3} d + 5 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{2} + 2 \, {\left({\left(7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{5} + {\left(7 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{3} + {\left(7 \, a^{3} b c^{2} d^{2} - 3 \, a^{4} c d^{3}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - {\left({\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{4 \, {\left({\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{5} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x^{3} + {\left(a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3}\right)} x\right)}}, -\frac{4 \, a b^{3} c^{4} - 12 \, a^{2} b^{2} c^{3} d + 12 \, a^{3} b c^{2} d^{2} - 4 \, a^{4} c d^{3} + 2 \, {\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} + 7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{4} c^{4} - 5 \, a b^{3} c^{3} d + 5 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{2} + 2 \, {\left({\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - {\left({\left(7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{5} + {\left(7 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{3} + {\left(7 \, a^{3} b c^{2} d^{2} - 3 \, a^{4} c d^{3}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{4 \, {\left({\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{5} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x^{3} + {\left(a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3}\right)} x\right)}}, -\frac{2 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3} + {\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} + 7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{4} + {\left(3 \, b^{4} c^{4} - 5 \, a b^{3} c^{3} d + 5 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{2} + {\left({\left(3 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(3 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left({\left(7 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x^{5} + {\left(7 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} x^{3} + {\left(7 \, a^{3} b c^{2} d^{2} - 3 \, a^{4} c d^{3}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{2 \, {\left({\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{5} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x^{3} + {\left(a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3}\right)} x\right)}}\right]"," ",0,"[-1/4*(4*a*b^3*c^4 - 12*a^2*b^2*c^3*d + 12*a^3*b*c^2*d^2 - 4*a^4*c*d^3 + 2*(3*b^4*c^3*d - 7*a*b^3*c^2*d^2 + 7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^4 + 2*(3*b^4*c^4 - 5*a*b^3*c^3*d + 5*a^3*b*c*d^3 - 3*a^4*d^4)*x^2 - ((3*b^4*c^3*d - 7*a*b^3*c^2*d^2)*x^5 + (3*b^4*c^4 - 4*a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2)*x^3 + (3*a*b^3*c^4 - 7*a^2*b^2*c^3*d)*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - ((7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^5 + (7*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*x^3 + (7*a^3*b*c^2*d^2 - 3*a^4*c*d^3)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^5 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x^3 + (a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3)*x), -1/4*(4*a*b^3*c^4 - 12*a^2*b^2*c^3*d + 12*a^3*b*c^2*d^2 - 4*a^4*c*d^3 + 2*(3*b^4*c^3*d - 7*a*b^3*c^2*d^2 + 7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^4 + 2*(3*b^4*c^4 - 5*a*b^3*c^3*d + 5*a^3*b*c*d^3 - 3*a^4*d^4)*x^2 + 2*((7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^5 + (7*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*x^3 + (7*a^3*b*c^2*d^2 - 3*a^4*c*d^3)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)) - ((3*b^4*c^3*d - 7*a*b^3*c^2*d^2)*x^5 + (3*b^4*c^4 - 4*a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2)*x^3 + (3*a*b^3*c^4 - 7*a^2*b^2*c^3*d)*x)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^5 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x^3 + (a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3)*x), -1/4*(4*a*b^3*c^4 - 12*a^2*b^2*c^3*d + 12*a^3*b*c^2*d^2 - 4*a^4*c*d^3 + 2*(3*b^4*c^3*d - 7*a*b^3*c^2*d^2 + 7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^4 + 2*(3*b^4*c^4 - 5*a*b^3*c^3*d + 5*a^3*b*c*d^3 - 3*a^4*d^4)*x^2 + 2*((3*b^4*c^3*d - 7*a*b^3*c^2*d^2)*x^5 + (3*b^4*c^4 - 4*a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2)*x^3 + (3*a*b^3*c^4 - 7*a^2*b^2*c^3*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) - ((7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^5 + (7*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*x^3 + (7*a^3*b*c^2*d^2 - 3*a^4*c*d^3)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^5 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x^3 + (a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3)*x), -1/2*(2*a*b^3*c^4 - 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 2*a^4*c*d^3 + (3*b^4*c^3*d - 7*a*b^3*c^2*d^2 + 7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^4 + (3*b^4*c^4 - 5*a*b^3*c^3*d + 5*a^3*b*c*d^3 - 3*a^4*d^4)*x^2 + ((3*b^4*c^3*d - 7*a*b^3*c^2*d^2)*x^5 + (3*b^4*c^4 - 4*a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2)*x^3 + (3*a*b^3*c^4 - 7*a^2*b^2*c^3*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + ((7*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x^5 + (7*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*x^3 + (7*a^3*b*c^2*d^2 - 3*a^4*c*d^3)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^5 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x^3 + (a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3)*x)]","B",0
308,1,667,0,25.063670," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + 2 \, {\left(a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{4} + {\left(2 \, a b^{4} c^{5} - 3 \, a^{2} b^{3} c^{4} d + 3 \, a^{4} b c^{2} d^{3} - 2 \, a^{5} c d^{4}\right)} x^{2} - 2 \, {\left({\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2}\right)} x^{6} + {\left(b^{5} c^{5} - a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{6} + {\left(2 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} - a^{5} d^{5}\right)} x^{4} + {\left(2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 4 \, {\left({\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} + 2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{6} + {\left(b^{5} c^{5} - a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} - a^{5} d^{5}\right)} x^{4} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{6} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{4} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + 2*(a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^4 + (2*a*b^4*c^5 - 3*a^2*b^3*c^4*d + 3*a^4*b*c^2*d^3 - 2*a^5*c*d^4)*x^2 - 2*((b^5*c^4*d - 2*a*b^4*c^3*d^2)*x^6 + (b^5*c^5 - a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d)*x^2)*log(b*x^2 + a) - 2*((2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^6 + (2*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 - a^5*d^5)*x^4 + (2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2)*log(d*x^2 + c) + 4*((b^5*c^4*d - 2*a*b^4*c^3*d^2 + 2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^6 + (b^5*c^5 - a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 - a^5*d^5)*x^4 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2)*log(x))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^6 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^4 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x^2)","B",0
309,1,2457,0,13.745413," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b^{3} c^{5} - 12 \, a^{3} b^{2} c^{4} d + 12 \, a^{4} b c^{3} d^{2} - 4 \, a^{5} c^{2} d^{3} - 6 \, {\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2} + 9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{6} - 2 \, {\left(15 \, b^{5} c^{5} - 17 \, a b^{4} c^{4} d - 18 \, a^{2} b^{3} c^{3} d^{2} + 18 \, a^{3} b^{2} c^{2} d^{3} + 17 \, a^{4} b c d^{4} - 15 \, a^{5} d^{5}\right)} x^{4} - 20 \, {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2} - 3 \, {\left({\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 4 \, a b^{4} c^{4} d - 9 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 9 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 3 \, {\left({\left(9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{7} + {\left(9 \, a^{3} b^{2} c^{2} d^{3} + 4 \, a^{4} b c d^{4} - 5 \, a^{5} d^{5}\right)} x^{5} + {\left(9 \, a^{4} b c^{2} d^{3} - 5 \, a^{5} c d^{4}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{12 \, {\left({\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{7} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{5} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x^{3}\right)}}, -\frac{4 \, a^{2} b^{3} c^{5} - 12 \, a^{3} b^{2} c^{4} d + 12 \, a^{4} b c^{3} d^{2} - 4 \, a^{5} c^{2} d^{3} - 6 \, {\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2} + 9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{6} - 2 \, {\left(15 \, b^{5} c^{5} - 17 \, a b^{4} c^{4} d - 18 \, a^{2} b^{3} c^{3} d^{2} + 18 \, a^{3} b^{2} c^{2} d^{3} + 17 \, a^{4} b c d^{4} - 15 \, a^{5} d^{5}\right)} x^{4} - 20 \, {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2} - 6 \, {\left({\left(9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{7} + {\left(9 \, a^{3} b^{2} c^{2} d^{3} + 4 \, a^{4} b c d^{4} - 5 \, a^{5} d^{5}\right)} x^{5} + {\left(9 \, a^{4} b c^{2} d^{3} - 5 \, a^{5} c d^{4}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 3 \, {\left({\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 4 \, a b^{4} c^{4} d - 9 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 9 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{12 \, {\left({\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{7} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{5} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x^{3}\right)}}, -\frac{4 \, a^{2} b^{3} c^{5} - 12 \, a^{3} b^{2} c^{4} d + 12 \, a^{4} b c^{3} d^{2} - 4 \, a^{5} c^{2} d^{3} - 6 \, {\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2} + 9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{6} - 2 \, {\left(15 \, b^{5} c^{5} - 17 \, a b^{4} c^{4} d - 18 \, a^{2} b^{3} c^{3} d^{2} + 18 \, a^{3} b^{2} c^{2} d^{3} + 17 \, a^{4} b c d^{4} - 15 \, a^{5} d^{5}\right)} x^{4} - 20 \, {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2} - 6 \, {\left({\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 4 \, a b^{4} c^{4} d - 9 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 9 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left({\left(9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{7} + {\left(9 \, a^{3} b^{2} c^{2} d^{3} + 4 \, a^{4} b c d^{4} - 5 \, a^{5} d^{5}\right)} x^{5} + {\left(9 \, a^{4} b c^{2} d^{3} - 5 \, a^{5} c d^{4}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{12 \, {\left({\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{7} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{5} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x^{3}\right)}}, -\frac{2 \, a^{2} b^{3} c^{5} - 6 \, a^{3} b^{2} c^{4} d + 6 \, a^{4} b c^{3} d^{2} - 2 \, a^{5} c^{2} d^{3} - 3 \, {\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2} + 9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{6} - {\left(15 \, b^{5} c^{5} - 17 \, a b^{4} c^{4} d - 18 \, a^{2} b^{3} c^{3} d^{2} + 18 \, a^{3} b^{2} c^{2} d^{3} + 17 \, a^{4} b c d^{4} - 15 \, a^{5} d^{5}\right)} x^{4} - 10 \, {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x^{2} - 3 \, {\left({\left(5 \, b^{5} c^{4} d - 9 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 4 \, a b^{4} c^{4} d - 9 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 9 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left({\left(9 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x^{7} + {\left(9 \, a^{3} b^{2} c^{2} d^{3} + 4 \, a^{4} b c d^{4} - 5 \, a^{5} d^{5}\right)} x^{5} + {\left(9 \, a^{4} b c^{2} d^{3} - 5 \, a^{5} c d^{4}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{6 \, {\left({\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{7} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{5} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^2*b^3*c^5 - 12*a^3*b^2*c^4*d + 12*a^4*b*c^3*d^2 - 4*a^5*c^2*d^3 - 6*(5*b^5*c^4*d - 9*a*b^4*c^3*d^2 + 9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^6 - 2*(15*b^5*c^5 - 17*a*b^4*c^4*d - 18*a^2*b^3*c^3*d^2 + 18*a^3*b^2*c^2*d^3 + 17*a^4*b*c*d^4 - 15*a^5*d^5)*x^4 - 20*(a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2 - 3*((5*b^5*c^4*d - 9*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 4*a*b^4*c^4*d - 9*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 9*a^2*b^3*c^4*d)*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 3*((9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^7 + (9*a^3*b^2*c^2*d^3 + 4*a^4*b*c*d^4 - 5*a^5*d^5)*x^5 + (9*a^4*b*c^2*d^3 - 5*a^5*c*d^4)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^7 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^5 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x^3), -1/12*(4*a^2*b^3*c^5 - 12*a^3*b^2*c^4*d + 12*a^4*b*c^3*d^2 - 4*a^5*c^2*d^3 - 6*(5*b^5*c^4*d - 9*a*b^4*c^3*d^2 + 9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^6 - 2*(15*b^5*c^5 - 17*a*b^4*c^4*d - 18*a^2*b^3*c^3*d^2 + 18*a^3*b^2*c^2*d^3 + 17*a^4*b*c*d^4 - 15*a^5*d^5)*x^4 - 20*(a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2 - 6*((9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^7 + (9*a^3*b^2*c^2*d^3 + 4*a^4*b*c*d^4 - 5*a^5*d^5)*x^5 + (9*a^4*b*c^2*d^3 - 5*a^5*c*d^4)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 3*((5*b^5*c^4*d - 9*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 4*a*b^4*c^4*d - 9*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 9*a^2*b^3*c^4*d)*x^3)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^7 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^5 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x^3), -1/12*(4*a^2*b^3*c^5 - 12*a^3*b^2*c^4*d + 12*a^4*b*c^3*d^2 - 4*a^5*c^2*d^3 - 6*(5*b^5*c^4*d - 9*a*b^4*c^3*d^2 + 9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^6 - 2*(15*b^5*c^5 - 17*a*b^4*c^4*d - 18*a^2*b^3*c^3*d^2 + 18*a^3*b^2*c^2*d^3 + 17*a^4*b*c*d^4 - 15*a^5*d^5)*x^4 - 20*(a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2 - 6*((5*b^5*c^4*d - 9*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 4*a*b^4*c^4*d - 9*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 9*a^2*b^3*c^4*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*((9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^7 + (9*a^3*b^2*c^2*d^3 + 4*a^4*b*c*d^4 - 5*a^5*d^5)*x^5 + (9*a^4*b*c^2*d^3 - 5*a^5*c*d^4)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^7 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^5 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x^3), -1/6*(2*a^2*b^3*c^5 - 6*a^3*b^2*c^4*d + 6*a^4*b*c^3*d^2 - 2*a^5*c^2*d^3 - 3*(5*b^5*c^4*d - 9*a*b^4*c^3*d^2 + 9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^6 - (15*b^5*c^5 - 17*a*b^4*c^4*d - 18*a^2*b^3*c^3*d^2 + 18*a^3*b^2*c^2*d^3 + 17*a^4*b*c*d^4 - 15*a^5*d^5)*x^4 - 10*(a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x^2 - 3*((5*b^5*c^4*d - 9*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 4*a*b^4*c^4*d - 9*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 9*a^2*b^3*c^4*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*((9*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x^7 + (9*a^3*b^2*c^2*d^3 + 4*a^4*b*c*d^4 - 5*a^5*d^5)*x^5 + (9*a^4*b*c^2*d^3 - 5*a^5*c*d^4)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^7 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^5 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x^3)]","B",0
310,1,2859,0,2.898288," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b^{3} c^{3} d^{2} + 2 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4}\right)} x^{5} + 2 \, {\left(5 \, b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3} + 12 \, {\left(a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{2} d^{3} + a b c d^{4}\right)} x^{6} + {\left(2 \, b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) - 3 \, {\left(a b^{2} c^{4} + 6 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(b^{3} c^{2} d^{2} + 6 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 8 \, a b^{2} c^{3} d + 13 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 6 \, {\left(3 \, a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} x}{16 \, {\left(a b^{4} c^{7} d - 4 \, a^{2} b^{3} c^{6} d^{2} + 6 \, a^{3} b^{2} c^{5} d^{3} - 4 \, a^{4} b c^{4} d^{4} + a^{5} c^{3} d^{5} + {\left(b^{5} c^{5} d^{3} - 4 \, a b^{4} c^{4} d^{4} + 6 \, a^{2} b^{3} c^{3} d^{5} - 4 \, a^{3} b^{2} c^{2} d^{6} + a^{4} b c d^{7}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d^{2} - 7 \, a b^{4} c^{5} d^{3} + 8 \, a^{2} b^{3} c^{4} d^{4} - 2 \, a^{3} b^{2} c^{3} d^{5} - 2 \, a^{4} b c^{2} d^{6} + a^{5} c d^{7}\right)} x^{4} + {\left(b^{5} c^{7} d - 2 \, a b^{4} c^{6} d^{2} - 2 \, a^{2} b^{3} c^{5} d^{3} + 8 \, a^{3} b^{2} c^{4} d^{4} - 7 \, a^{4} b c^{3} d^{5} + 2 \, a^{5} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{3 \, {\left(b^{3} c^{3} d^{2} + 2 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4}\right)} x^{5} + {\left(5 \, b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3} + 3 \, {\left(a b^{2} c^{4} + 6 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(b^{3} c^{2} d^{2} + 6 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 8 \, a b^{2} c^{3} d + 13 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + 6 \, {\left(a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{2} d^{3} + a b c d^{4}\right)} x^{6} + {\left(2 \, b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{2} - 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 3 \, {\left(3 \, a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} x}{8 \, {\left(a b^{4} c^{7} d - 4 \, a^{2} b^{3} c^{6} d^{2} + 6 \, a^{3} b^{2} c^{5} d^{3} - 4 \, a^{4} b c^{4} d^{4} + a^{5} c^{3} d^{5} + {\left(b^{5} c^{5} d^{3} - 4 \, a b^{4} c^{4} d^{4} + 6 \, a^{2} b^{3} c^{3} d^{5} - 4 \, a^{3} b^{2} c^{2} d^{6} + a^{4} b c d^{7}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d^{2} - 7 \, a b^{4} c^{5} d^{3} + 8 \, a^{2} b^{3} c^{4} d^{4} - 2 \, a^{3} b^{2} c^{3} d^{5} - 2 \, a^{4} b c^{2} d^{6} + a^{5} c d^{7}\right)} x^{4} + {\left(b^{5} c^{7} d - 2 \, a b^{4} c^{6} d^{2} - 2 \, a^{2} b^{3} c^{5} d^{3} + 8 \, a^{3} b^{2} c^{4} d^{4} - 7 \, a^{4} b c^{3} d^{5} + 2 \, a^{5} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{6 \, {\left(b^{3} c^{3} d^{2} + 2 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4}\right)} x^{5} + 2 \, {\left(5 \, b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3} - 24 \, {\left(a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{2} d^{3} + a b c d^{4}\right)} x^{6} + {\left(2 \, b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) - 3 \, {\left(a b^{2} c^{4} + 6 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(b^{3} c^{2} d^{2} + 6 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 8 \, a b^{2} c^{3} d + 13 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{-c d} \log\left(\frac{d x^{2} - 2 \, \sqrt{-c d} x - c}{d x^{2} + c}\right) + 6 \, {\left(3 \, a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} x}{16 \, {\left(a b^{4} c^{7} d - 4 \, a^{2} b^{3} c^{6} d^{2} + 6 \, a^{3} b^{2} c^{5} d^{3} - 4 \, a^{4} b c^{4} d^{4} + a^{5} c^{3} d^{5} + {\left(b^{5} c^{5} d^{3} - 4 \, a b^{4} c^{4} d^{4} + 6 \, a^{2} b^{3} c^{3} d^{5} - 4 \, a^{3} b^{2} c^{2} d^{6} + a^{4} b c d^{7}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d^{2} - 7 \, a b^{4} c^{5} d^{3} + 8 \, a^{2} b^{3} c^{4} d^{4} - 2 \, a^{3} b^{2} c^{3} d^{5} - 2 \, a^{4} b c^{2} d^{6} + a^{5} c d^{7}\right)} x^{4} + {\left(b^{5} c^{7} d - 2 \, a b^{4} c^{6} d^{2} - 2 \, a^{2} b^{3} c^{5} d^{3} + 8 \, a^{3} b^{2} c^{4} d^{4} - 7 \, a^{4} b c^{3} d^{5} + 2 \, a^{5} c^{2} d^{6}\right)} x^{2}\right)}}, \frac{3 \, {\left(b^{3} c^{3} d^{2} + 2 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4}\right)} x^{5} + {\left(5 \, b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} - 5 \, a^{3} c d^{4}\right)} x^{3} - 12 \, {\left(a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{2} d^{3} + a b c d^{4}\right)} x^{6} + {\left(2 \, b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 3 \, {\left(a b^{2} c^{4} + 6 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(b^{3} c^{2} d^{2} + 6 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 8 \, a b^{2} c^{3} d + 13 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{c d} \arctan\left(\frac{\sqrt{c d} x}{c}\right) + 3 \, {\left(3 \, a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} x}{8 \, {\left(a b^{4} c^{7} d - 4 \, a^{2} b^{3} c^{6} d^{2} + 6 \, a^{3} b^{2} c^{5} d^{3} - 4 \, a^{4} b c^{4} d^{4} + a^{5} c^{3} d^{5} + {\left(b^{5} c^{5} d^{3} - 4 \, a b^{4} c^{4} d^{4} + 6 \, a^{2} b^{3} c^{3} d^{5} - 4 \, a^{3} b^{2} c^{2} d^{6} + a^{4} b c d^{7}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d^{2} - 7 \, a b^{4} c^{5} d^{3} + 8 \, a^{2} b^{3} c^{4} d^{4} - 2 \, a^{3} b^{2} c^{3} d^{5} - 2 \, a^{4} b c^{2} d^{6} + a^{5} c d^{7}\right)} x^{4} + {\left(b^{5} c^{7} d - 2 \, a b^{4} c^{6} d^{2} - 2 \, a^{2} b^{3} c^{5} d^{3} + 8 \, a^{3} b^{2} c^{4} d^{4} - 7 \, a^{4} b c^{3} d^{5} + 2 \, a^{5} c^{2} d^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(6*(b^3*c^3*d^2 + 2*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4)*x^5 + 2*(5*b^3*c^4*d + 9*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3 + 12*(a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^2*d^3 + a*b*c*d^4)*x^6 + (2*b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + (b^2*c^4*d + 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) - 3*(a*b^2*c^4 + 6*a^2*b*c^3*d + a^3*c^2*d^2 + (b^3*c^2*d^2 + 6*a*b^2*c*d^3 + a^2*b*d^4)*x^6 + (2*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 + a^3*d^4)*x^4 + (b^3*c^4 + 8*a*b^2*c^3*d + 13*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 6*(3*a*b^2*c^4*d - 2*a^2*b*c^3*d^2 - a^3*c^2*d^3)*x)/(a*b^4*c^7*d - 4*a^2*b^3*c^6*d^2 + 6*a^3*b^2*c^5*d^3 - 4*a^4*b*c^4*d^4 + a^5*c^3*d^5 + (b^5*c^5*d^3 - 4*a*b^4*c^4*d^4 + 6*a^2*b^3*c^3*d^5 - 4*a^3*b^2*c^2*d^6 + a^4*b*c*d^7)*x^6 + (2*b^5*c^6*d^2 - 7*a*b^4*c^5*d^3 + 8*a^2*b^3*c^4*d^4 - 2*a^3*b^2*c^3*d^5 - 2*a^4*b*c^2*d^6 + a^5*c*d^7)*x^4 + (b^5*c^7*d - 2*a*b^4*c^6*d^2 - 2*a^2*b^3*c^5*d^3 + 8*a^3*b^2*c^4*d^4 - 7*a^4*b*c^3*d^5 + 2*a^5*c^2*d^6)*x^2), 1/8*(3*(b^3*c^3*d^2 + 2*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4)*x^5 + (5*b^3*c^4*d + 9*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3 + 3*(a*b^2*c^4 + 6*a^2*b*c^3*d + a^3*c^2*d^2 + (b^3*c^2*d^2 + 6*a*b^2*c*d^3 + a^2*b*d^4)*x^6 + (2*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 + a^3*d^4)*x^4 + (b^3*c^4 + 8*a*b^2*c^3*d + 13*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + 6*(a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^2*d^3 + a*b*c*d^4)*x^6 + (2*b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + (b^2*c^4*d + 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2)*sqrt(-a*b)*log((b*x^2 - 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 3*(3*a*b^2*c^4*d - 2*a^2*b*c^3*d^2 - a^3*c^2*d^3)*x)/(a*b^4*c^7*d - 4*a^2*b^3*c^6*d^2 + 6*a^3*b^2*c^5*d^3 - 4*a^4*b*c^4*d^4 + a^5*c^3*d^5 + (b^5*c^5*d^3 - 4*a*b^4*c^4*d^4 + 6*a^2*b^3*c^3*d^5 - 4*a^3*b^2*c^2*d^6 + a^4*b*c*d^7)*x^6 + (2*b^5*c^6*d^2 - 7*a*b^4*c^5*d^3 + 8*a^2*b^3*c^4*d^4 - 2*a^3*b^2*c^3*d^5 - 2*a^4*b*c^2*d^6 + a^5*c*d^7)*x^4 + (b^5*c^7*d - 2*a*b^4*c^6*d^2 - 2*a^2*b^3*c^5*d^3 + 8*a^3*b^2*c^4*d^4 - 7*a^4*b*c^3*d^5 + 2*a^5*c^2*d^6)*x^2), 1/16*(6*(b^3*c^3*d^2 + 2*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4)*x^5 + 2*(5*b^3*c^4*d + 9*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3 - 24*(a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^2*d^3 + a*b*c*d^4)*x^6 + (2*b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + (b^2*c^4*d + 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) - 3*(a*b^2*c^4 + 6*a^2*b*c^3*d + a^3*c^2*d^2 + (b^3*c^2*d^2 + 6*a*b^2*c*d^3 + a^2*b*d^4)*x^6 + (2*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 + a^3*d^4)*x^4 + (b^3*c^4 + 8*a*b^2*c^3*d + 13*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2)*sqrt(-c*d)*log((d*x^2 - 2*sqrt(-c*d)*x - c)/(d*x^2 + c)) + 6*(3*a*b^2*c^4*d - 2*a^2*b*c^3*d^2 - a^3*c^2*d^3)*x)/(a*b^4*c^7*d - 4*a^2*b^3*c^6*d^2 + 6*a^3*b^2*c^5*d^3 - 4*a^4*b*c^4*d^4 + a^5*c^3*d^5 + (b^5*c^5*d^3 - 4*a*b^4*c^4*d^4 + 6*a^2*b^3*c^3*d^5 - 4*a^3*b^2*c^2*d^6 + a^4*b*c*d^7)*x^6 + (2*b^5*c^6*d^2 - 7*a*b^4*c^5*d^3 + 8*a^2*b^3*c^4*d^4 - 2*a^3*b^2*c^3*d^5 - 2*a^4*b*c^2*d^6 + a^5*c*d^7)*x^4 + (b^5*c^7*d - 2*a*b^4*c^6*d^2 - 2*a^2*b^3*c^5*d^3 + 8*a^3*b^2*c^4*d^4 - 7*a^4*b*c^3*d^5 + 2*a^5*c^2*d^6)*x^2), 1/8*(3*(b^3*c^3*d^2 + 2*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4)*x^5 + (5*b^3*c^4*d + 9*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 - 5*a^3*c*d^4)*x^3 - 12*(a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^2*d^3 + a*b*c*d^4)*x^6 + (2*b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + (b^2*c^4*d + 3*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 3*(a*b^2*c^4 + 6*a^2*b*c^3*d + a^3*c^2*d^2 + (b^3*c^2*d^2 + 6*a*b^2*c*d^3 + a^2*b*d^4)*x^6 + (2*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 + a^3*d^4)*x^4 + (b^3*c^4 + 8*a*b^2*c^3*d + 13*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x^2)*sqrt(c*d)*arctan(sqrt(c*d)*x/c) + 3*(3*a*b^2*c^4*d - 2*a^2*b*c^3*d^2 - a^3*c^2*d^3)*x)/(a*b^4*c^7*d - 4*a^2*b^3*c^6*d^2 + 6*a^3*b^2*c^5*d^3 - 4*a^4*b*c^4*d^4 + a^5*c^3*d^5 + (b^5*c^5*d^3 - 4*a*b^4*c^4*d^4 + 6*a^2*b^3*c^3*d^5 - 4*a^3*b^2*c^2*d^6 + a^4*b*c*d^7)*x^6 + (2*b^5*c^6*d^2 - 7*a*b^4*c^5*d^3 + 8*a^2*b^3*c^4*d^4 - 2*a^3*b^2*c^3*d^5 - 2*a^4*b*c^2*d^6 + a^5*c*d^7)*x^4 + (b^5*c^7*d - 2*a*b^4*c^6*d^2 - 2*a^2*b^3*c^5*d^3 + 8*a^3*b^2*c^4*d^4 - 7*a^4*b*c^3*d^5 + 2*a^5*c^2*d^6)*x^2)]","B",0
311,1,598,0,1.176713," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{5 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d - a^{3} c d^{2} + 2 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} x^{4} + {\left(3 \, b^{3} c^{3} + 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x^{2} + 2 \, {\left({\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{6} + a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + {\left(2 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} + 4 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{6} + a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + {\left(2 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} + 4 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{4} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x^{2}\right)}}"," ",0,"1/4*(5*a*b^2*c^3 - 4*a^2*b*c^2*d - a^3*c*d^2 + 2*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*x^4 + (3*b^3*c^3 + 4*a*b^2*c^2*d - 5*a^2*b*c*d^2 - 2*a^3*d^3)*x^2 + 2*((b^3*c*d^2 + 2*a*b^2*d^3)*x^6 + a*b^2*c^3 + 2*a^2*b*c^2*d + (2*b^3*c^2*d + 5*a*b^2*c*d^2 + 2*a^2*b*d^3)*x^4 + (b^3*c^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)*x^2)*log(b*x^2 + a) - 2*((b^3*c*d^2 + 2*a*b^2*d^3)*x^6 + a*b^2*c^3 + 2*a^2*b*c^2*d + (2*b^3*c^2*d + 5*a*b^2*c*d^2 + 2*a^2*b*d^3)*x^4 + (b^3*c^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)*x^2)*log(d*x^2 + c))/(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^6 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^4 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x^2)","B",0
312,1,2891,0,4.600406," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(11 \, b^{3} c^{2} d^{2} - 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{5} + 2 \, {\left(17 \, b^{3} c^{3} d - 11 \, a b^{2} c^{2} d^{2} - 5 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{3} - 4 \, {\left(a b^{2} c^{4} + 5 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 5 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 11 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 7 \, a b^{2} c^{3} d + 10 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(15 \, a b^{2} c^{4} + 10 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2} + {\left(15 \, b^{3} c^{2} d^{2} + 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{6} + {\left(30 \, b^{3} c^{3} d + 35 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{4} + {\left(15 \, b^{3} c^{4} + 40 \, a b^{2} c^{3} d + 19 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{3} c^{4} + 5 \, a b^{2} c^{3} d - 10 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x}{16 \, {\left(a b^{4} c^{7} - 4 \, a^{2} b^{3} c^{6} d + 6 \, a^{3} b^{2} c^{5} d^{2} - 4 \, a^{4} b c^{4} d^{3} + a^{5} c^{3} d^{4} + {\left(b^{5} c^{5} d^{2} - 4 \, a b^{4} c^{4} d^{3} + 6 \, a^{2} b^{3} c^{3} d^{4} - 4 \, a^{3} b^{2} c^{2} d^{5} + a^{4} b c d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d - 7 \, a b^{4} c^{5} d^{2} + 8 \, a^{2} b^{3} c^{4} d^{3} - 2 \, a^{3} b^{2} c^{3} d^{4} - 2 \, a^{4} b c^{2} d^{5} + a^{5} c d^{6}\right)} x^{4} + {\left(b^{5} c^{7} - 2 \, a b^{4} c^{6} d - 2 \, a^{2} b^{3} c^{5} d^{2} + 8 \, a^{3} b^{2} c^{4} d^{3} - 7 \, a^{4} b c^{3} d^{4} + 2 \, a^{5} c^{2} d^{5}\right)} x^{2}\right)}}, -\frac{{\left(11 \, b^{3} c^{2} d^{2} - 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{5} + {\left(17 \, b^{3} c^{3} d - 11 \, a b^{2} c^{2} d^{2} - 5 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{3} + {\left(15 \, a b^{2} c^{4} + 10 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2} + {\left(15 \, b^{3} c^{2} d^{2} + 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{6} + {\left(30 \, b^{3} c^{3} d + 35 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{4} + {\left(15 \, b^{3} c^{4} + 40 \, a b^{2} c^{3} d + 19 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 2 \, {\left(a b^{2} c^{4} + 5 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 5 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 11 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 7 \, a b^{2} c^{3} d + 10 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(4 \, b^{3} c^{4} + 5 \, a b^{2} c^{3} d - 10 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x}{8 \, {\left(a b^{4} c^{7} - 4 \, a^{2} b^{3} c^{6} d + 6 \, a^{3} b^{2} c^{5} d^{2} - 4 \, a^{4} b c^{4} d^{3} + a^{5} c^{3} d^{4} + {\left(b^{5} c^{5} d^{2} - 4 \, a b^{4} c^{4} d^{3} + 6 \, a^{2} b^{3} c^{3} d^{4} - 4 \, a^{3} b^{2} c^{2} d^{5} + a^{4} b c d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d - 7 \, a b^{4} c^{5} d^{2} + 8 \, a^{2} b^{3} c^{4} d^{3} - 2 \, a^{3} b^{2} c^{3} d^{4} - 2 \, a^{4} b c^{2} d^{5} + a^{5} c d^{6}\right)} x^{4} + {\left(b^{5} c^{7} - 2 \, a b^{4} c^{6} d - 2 \, a^{2} b^{3} c^{5} d^{2} + 8 \, a^{3} b^{2} c^{4} d^{3} - 7 \, a^{4} b c^{3} d^{4} + 2 \, a^{5} c^{2} d^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left(11 \, b^{3} c^{2} d^{2} - 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{5} + 2 \, {\left(17 \, b^{3} c^{3} d - 11 \, a b^{2} c^{2} d^{2} - 5 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{3} - 8 \, {\left(a b^{2} c^{4} + 5 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 5 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 11 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 7 \, a b^{2} c^{3} d + 10 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, a b^{2} c^{4} + 10 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2} + {\left(15 \, b^{3} c^{2} d^{2} + 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{6} + {\left(30 \, b^{3} c^{3} d + 35 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{4} + {\left(15 \, b^{3} c^{4} + 40 \, a b^{2} c^{3} d + 19 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{3} c^{4} + 5 \, a b^{2} c^{3} d - 10 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x}{16 \, {\left(a b^{4} c^{7} - 4 \, a^{2} b^{3} c^{6} d + 6 \, a^{3} b^{2} c^{5} d^{2} - 4 \, a^{4} b c^{4} d^{3} + a^{5} c^{3} d^{4} + {\left(b^{5} c^{5} d^{2} - 4 \, a b^{4} c^{4} d^{3} + 6 \, a^{2} b^{3} c^{3} d^{4} - 4 \, a^{3} b^{2} c^{2} d^{5} + a^{4} b c d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d - 7 \, a b^{4} c^{5} d^{2} + 8 \, a^{2} b^{3} c^{4} d^{3} - 2 \, a^{3} b^{2} c^{3} d^{4} - 2 \, a^{4} b c^{2} d^{5} + a^{5} c d^{6}\right)} x^{4} + {\left(b^{5} c^{7} - 2 \, a b^{4} c^{6} d - 2 \, a^{2} b^{3} c^{5} d^{2} + 8 \, a^{3} b^{2} c^{4} d^{3} - 7 \, a^{4} b c^{3} d^{4} + 2 \, a^{5} c^{2} d^{5}\right)} x^{2}\right)}}, -\frac{{\left(11 \, b^{3} c^{2} d^{2} - 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{5} + {\left(17 \, b^{3} c^{3} d - 11 \, a b^{2} c^{2} d^{2} - 5 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{3} - 4 \, {\left(a b^{2} c^{4} + 5 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 5 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 11 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 7 \, a b^{2} c^{3} d + 10 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(15 \, a b^{2} c^{4} + 10 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2} + {\left(15 \, b^{3} c^{2} d^{2} + 10 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{6} + {\left(30 \, b^{3} c^{3} d + 35 \, a b^{2} c^{2} d^{2} + 8 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{4} + {\left(15 \, b^{3} c^{4} + 40 \, a b^{2} c^{3} d + 19 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(4 \, b^{3} c^{4} + 5 \, a b^{2} c^{3} d - 10 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x}{8 \, {\left(a b^{4} c^{7} - 4 \, a^{2} b^{3} c^{6} d + 6 \, a^{3} b^{2} c^{5} d^{2} - 4 \, a^{4} b c^{4} d^{3} + a^{5} c^{3} d^{4} + {\left(b^{5} c^{5} d^{2} - 4 \, a b^{4} c^{4} d^{3} + 6 \, a^{2} b^{3} c^{3} d^{4} - 4 \, a^{3} b^{2} c^{2} d^{5} + a^{4} b c d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{6} d - 7 \, a b^{4} c^{5} d^{2} + 8 \, a^{2} b^{3} c^{4} d^{3} - 2 \, a^{3} b^{2} c^{3} d^{4} - 2 \, a^{4} b c^{2} d^{5} + a^{5} c d^{6}\right)} x^{4} + {\left(b^{5} c^{7} - 2 \, a b^{4} c^{6} d - 2 \, a^{2} b^{3} c^{5} d^{2} + 8 \, a^{3} b^{2} c^{4} d^{3} - 7 \, a^{4} b c^{3} d^{4} + 2 \, a^{5} c^{2} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(2*(11*b^3*c^2*d^2 - 10*a*b^2*c*d^3 - a^2*b*d^4)*x^5 + 2*(17*b^3*c^3*d - 11*a*b^2*c^2*d^2 - 5*a^2*b*c*d^3 - a^3*d^4)*x^3 - 4*(a*b^2*c^4 + 5*a^2*b*c^3*d + (b^3*c^2*d^2 + 5*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 11*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 7*a*b^2*c^3*d + 10*a^2*b*c^2*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (15*a*b^2*c^4 + 10*a^2*b*c^3*d - a^3*c^2*d^2 + (15*b^3*c^2*d^2 + 10*a*b^2*c*d^3 - a^2*b*d^4)*x^6 + (30*b^3*c^3*d + 35*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 - a^3*d^4)*x^4 + (15*b^3*c^4 + 40*a*b^2*c^3*d + 19*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^3*c^4 + 5*a*b^2*c^3*d - 10*a^2*b*c^2*d^2 + a^3*c*d^3)*x)/(a*b^4*c^7 - 4*a^2*b^3*c^6*d + 6*a^3*b^2*c^5*d^2 - 4*a^4*b*c^4*d^3 + a^5*c^3*d^4 + (b^5*c^5*d^2 - 4*a*b^4*c^4*d^3 + 6*a^2*b^3*c^3*d^4 - 4*a^3*b^2*c^2*d^5 + a^4*b*c*d^6)*x^6 + (2*b^5*c^6*d - 7*a*b^4*c^5*d^2 + 8*a^2*b^3*c^4*d^3 - 2*a^3*b^2*c^3*d^4 - 2*a^4*b*c^2*d^5 + a^5*c*d^6)*x^4 + (b^5*c^7 - 2*a*b^4*c^6*d - 2*a^2*b^3*c^5*d^2 + 8*a^3*b^2*c^4*d^3 - 7*a^4*b*c^3*d^4 + 2*a^5*c^2*d^5)*x^2), -1/8*((11*b^3*c^2*d^2 - 10*a*b^2*c*d^3 - a^2*b*d^4)*x^5 + (17*b^3*c^3*d - 11*a*b^2*c^2*d^2 - 5*a^2*b*c*d^3 - a^3*d^4)*x^3 + (15*a*b^2*c^4 + 10*a^2*b*c^3*d - a^3*c^2*d^2 + (15*b^3*c^2*d^2 + 10*a*b^2*c*d^3 - a^2*b*d^4)*x^6 + (30*b^3*c^3*d + 35*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 - a^3*d^4)*x^4 + (15*b^3*c^4 + 40*a*b^2*c^3*d + 19*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 2*(a*b^2*c^4 + 5*a^2*b*c^3*d + (b^3*c^2*d^2 + 5*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 11*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 7*a*b^2*c^3*d + 10*a^2*b*c^2*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (4*b^3*c^4 + 5*a*b^2*c^3*d - 10*a^2*b*c^2*d^2 + a^3*c*d^3)*x)/(a*b^4*c^7 - 4*a^2*b^3*c^6*d + 6*a^3*b^2*c^5*d^2 - 4*a^4*b*c^4*d^3 + a^5*c^3*d^4 + (b^5*c^5*d^2 - 4*a*b^4*c^4*d^3 + 6*a^2*b^3*c^3*d^4 - 4*a^3*b^2*c^2*d^5 + a^4*b*c*d^6)*x^6 + (2*b^5*c^6*d - 7*a*b^4*c^5*d^2 + 8*a^2*b^3*c^4*d^3 - 2*a^3*b^2*c^3*d^4 - 2*a^4*b*c^2*d^5 + a^5*c*d^6)*x^4 + (b^5*c^7 - 2*a*b^4*c^6*d - 2*a^2*b^3*c^5*d^2 + 8*a^3*b^2*c^4*d^3 - 7*a^4*b*c^3*d^4 + 2*a^5*c^2*d^5)*x^2), -1/16*(2*(11*b^3*c^2*d^2 - 10*a*b^2*c*d^3 - a^2*b*d^4)*x^5 + 2*(17*b^3*c^3*d - 11*a*b^2*c^2*d^2 - 5*a^2*b*c*d^3 - a^3*d^4)*x^3 - 8*(a*b^2*c^4 + 5*a^2*b*c^3*d + (b^3*c^2*d^2 + 5*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 11*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 7*a*b^2*c^3*d + 10*a^2*b*c^2*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*a*b^2*c^4 + 10*a^2*b*c^3*d - a^3*c^2*d^2 + (15*b^3*c^2*d^2 + 10*a*b^2*c*d^3 - a^2*b*d^4)*x^6 + (30*b^3*c^3*d + 35*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 - a^3*d^4)*x^4 + (15*b^3*c^4 + 40*a*b^2*c^3*d + 19*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^3*c^4 + 5*a*b^2*c^3*d - 10*a^2*b*c^2*d^2 + a^3*c*d^3)*x)/(a*b^4*c^7 - 4*a^2*b^3*c^6*d + 6*a^3*b^2*c^5*d^2 - 4*a^4*b*c^4*d^3 + a^5*c^3*d^4 + (b^5*c^5*d^2 - 4*a*b^4*c^4*d^3 + 6*a^2*b^3*c^3*d^4 - 4*a^3*b^2*c^2*d^5 + a^4*b*c*d^6)*x^6 + (2*b^5*c^6*d - 7*a*b^4*c^5*d^2 + 8*a^2*b^3*c^4*d^3 - 2*a^3*b^2*c^3*d^4 - 2*a^4*b*c^2*d^5 + a^5*c*d^6)*x^4 + (b^5*c^7 - 2*a*b^4*c^6*d - 2*a^2*b^3*c^5*d^2 + 8*a^3*b^2*c^4*d^3 - 7*a^4*b*c^3*d^4 + 2*a^5*c^2*d^5)*x^2), -1/8*((11*b^3*c^2*d^2 - 10*a*b^2*c*d^3 - a^2*b*d^4)*x^5 + (17*b^3*c^3*d - 11*a*b^2*c^2*d^2 - 5*a^2*b*c*d^3 - a^3*d^4)*x^3 - 4*(a*b^2*c^4 + 5*a^2*b*c^3*d + (b^3*c^2*d^2 + 5*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 11*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 7*a*b^2*c^3*d + 10*a^2*b*c^2*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (15*a*b^2*c^4 + 10*a^2*b*c^3*d - a^3*c^2*d^2 + (15*b^3*c^2*d^2 + 10*a*b^2*c*d^3 - a^2*b*d^4)*x^6 + (30*b^3*c^3*d + 35*a*b^2*c^2*d^2 + 8*a^2*b*c*d^3 - a^3*d^4)*x^4 + (15*b^3*c^4 + 40*a*b^2*c^3*d + 19*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (4*b^3*c^4 + 5*a*b^2*c^3*d - 10*a^2*b*c^2*d^2 + a^3*c*d^3)*x)/(a*b^4*c^7 - 4*a^2*b^3*c^6*d + 6*a^3*b^2*c^5*d^2 - 4*a^4*b*c^4*d^3 + a^5*c^3*d^4 + (b^5*c^5*d^2 - 4*a*b^4*c^4*d^3 + 6*a^2*b^3*c^3*d^4 - 4*a^3*b^2*c^2*d^5 + a^4*b*c*d^6)*x^6 + (2*b^5*c^6*d - 7*a*b^4*c^5*d^2 + 8*a^2*b^3*c^4*d^3 - 2*a^3*b^2*c^3*d^4 - 2*a^4*b*c^2*d^5 + a^5*c*d^6)*x^4 + (b^5*c^7 - 2*a*b^4*c^6*d - 2*a^2*b^3*c^5*d^2 + 8*a^3*b^2*c^4*d^3 - 7*a^4*b*c^3*d^4 + 2*a^5*c^2*d^5)*x^2)]","B",0
313,1,507,0,0.933528," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{4} + 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{6} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{4} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(b^{3} d^{3} x^{6} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{4} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x^{2}\right)} \log\left(d x^{2} + c\right)}{4 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{4} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*b^3*c^3 + 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + a^3*d^3 + 6*(b^3*c*d^2 - a*b^2*d^3)*x^4 + 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x^2 + 6*(b^3*d^3*x^6 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^4 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x^2)*log(b*x^2 + a) - 6*(b^3*d^3*x^6 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^4 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x^2)*log(d*x^2 + c))/(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^6 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^4 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x^2)","B",0
314,1,3239,0,8.744472," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + 2 \, {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} - 4 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{16 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) - 2 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{8 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + 2 \, {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + 8 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right) + 2 \, {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{16 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{{\left(4 \, b^{4} c^{3} d^{2} + 7 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{5} + {\left(8 \, b^{4} c^{4} d + 5 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3} - 9 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + 4 \, {\left(a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 7 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 13 \, a b^{3} c^{3} d^{2} - 7 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 5 \, a b^{3} c^{4} d - 14 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + {\left(35 \, a^{2} b^{2} c^{4} d - 14 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + {\left(35 \, a b^{3} c^{2} d^{3} - 14 \, a^{2} b^{2} c d^{4} + 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(70 \, a b^{3} c^{3} d^{2} + 7 \, a^{2} b^{2} c^{2} d^{3} - 8 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{4} + {\left(35 \, a b^{3} c^{4} d + 56 \, a^{2} b^{2} c^{3} d^{2} - 25 \, a^{3} b c^{2} d^{3} + 6 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + {\left(4 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 13 \, a^{2} b^{2} c^{3} d^{2} - 18 \, a^{3} b c^{2} d^{3} + 5 \, a^{4} c d^{4}\right)} x}{8 \, {\left(a^{2} b^{4} c^{8} - 4 \, a^{3} b^{3} c^{7} d + 6 \, a^{4} b^{2} c^{6} d^{2} - 4 \, a^{5} b c^{5} d^{3} + a^{6} c^{4} d^{4} + {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{7} d - 7 \, a^{2} b^{4} c^{6} d^{2} + 8 \, a^{3} b^{3} c^{5} d^{3} - 2 \, a^{4} b^{2} c^{4} d^{4} - 2 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} x^{4} + {\left(a b^{5} c^{8} - 2 \, a^{2} b^{4} c^{7} d - 2 \, a^{3} b^{3} c^{6} d^{2} + 8 \, a^{4} b^{2} c^{5} d^{3} - 7 \, a^{5} b c^{4} d^{4} + 2 \, a^{6} c^{3} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(2*(4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + 2*(8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 - 4*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/8*((4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + (8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) - 2*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + (4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/16*(2*(4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + 2*(8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + 8*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)) + 2*(4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2), 1/8*((4*b^4*c^3*d^2 + 7*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^5 + (8*b^4*c^4*d + 5*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3 - 9*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + 4*(a*b^3*c^5 - 7*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 7*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 13*a*b^3*c^3*d^2 - 7*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 5*a*b^3*c^4*d - 14*a^2*b^2*c^3*d^2)*x^2)*sqrt(b/a)*arctan(x*sqrt(b/a)) + (35*a^2*b^2*c^4*d - 14*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3 + (35*a*b^3*c^2*d^3 - 14*a^2*b^2*c*d^4 + 3*a^3*b*d^5)*x^6 + (70*a*b^3*c^3*d^2 + 7*a^2*b^2*c^2*d^3 - 8*a^3*b*c*d^4 + 3*a^4*d^5)*x^4 + (35*a*b^3*c^4*d + 56*a^2*b^2*c^3*d^2 - 25*a^3*b*c^2*d^3 + 6*a^4*c*d^4)*x^2)*sqrt(d/c)*arctan(x*sqrt(d/c)) + (4*b^4*c^5 - 4*a*b^3*c^4*d + 13*a^2*b^2*c^3*d^2 - 18*a^3*b*c^2*d^3 + 5*a^4*c*d^4)*x)/(a^2*b^4*c^8 - 4*a^3*b^3*c^7*d + 6*a^4*b^2*c^6*d^2 - 4*a^5*b*c^5*d^3 + a^6*c^4*d^4 + (a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6)*x^6 + (2*a*b^5*c^7*d - 7*a^2*b^4*c^6*d^2 + 8*a^3*b^3*c^5*d^3 - 2*a^4*b^2*c^4*d^4 - 2*a^5*b*c^3*d^5 + a^6*c^2*d^6)*x^4 + (a*b^5*c^8 - 2*a^2*b^4*c^7*d - 2*a^3*b^3*c^6*d^2 + 8*a^4*b^2*c^5*d^3 - 7*a^5*b*c^4*d^4 + 2*a^6*c^3*d^5)*x^2)]","B",0
315,1,1058,0,30.216985," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{2 \, a b^{4} c^{6} - 2 \, a^{2} b^{3} c^{5} d + 7 \, a^{3} b^{2} c^{4} d^{2} - 10 \, a^{4} b c^{3} d^{3} + 3 \, a^{5} c^{2} d^{4} + 2 \, {\left(a b^{4} c^{4} d^{2} + 2 \, a^{2} b^{3} c^{3} d^{3} - 4 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5}\right)} x^{4} + {\left(4 \, a b^{4} c^{5} d + 3 \, a^{2} b^{3} c^{4} d^{2} - 4 \, a^{3} b^{2} c^{3} d^{3} - 5 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x^{2} - 2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3}\right)} x^{6} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{4} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 8 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{6} + {\left(12 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{4} + {\left(6 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 4 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{6} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{4} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4} + {\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{6} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{4} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x^{2}\right)}}"," ",0,"1/4*(2*a*b^4*c^6 - 2*a^2*b^3*c^5*d + 7*a^3*b^2*c^4*d^2 - 10*a^4*b*c^3*d^3 + 3*a^5*c^2*d^4 + 2*(a*b^4*c^4*d^2 + 2*a^2*b^3*c^3*d^3 - 4*a^3*b^2*c^2*d^4 + a^4*b*c*d^5)*x^4 + (4*a*b^4*c^5*d + 3*a^2*b^3*c^4*d^2 - 4*a^3*b^2*c^3*d^3 - 5*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x^2 - 2*(a*b^4*c^6 - 4*a^2*b^3*c^5*d + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3)*x^6 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3)*x^4 + (b^5*c^6 - 2*a*b^4*c^5*d - 8*a^2*b^3*c^4*d^2)*x^2)*log(b*x^2 + a) - 2*(6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^6 + (12*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^4 + (6*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x^2)*log(d*x^2 + c) + 4*(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^6 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^4 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x^2)*log(x))/(a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4 + (a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^6 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^4 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x^2)","B",0
316,1,3753,0,19.647599," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a b^{4} c^{6} - 64 \, a^{2} b^{3} c^{5} d + 96 \, a^{3} b^{2} c^{4} d^{2} - 64 \, a^{4} b c^{3} d^{3} + 16 \, a^{5} c^{2} d^{4} + 6 \, {\left(4 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{6} + 2 \, {\left(24 \, b^{5} c^{5} d - 64 \, a b^{4} c^{4} d^{2} + 81 \, a^{2} b^{3} c^{3} d^{3} - 27 \, a^{3} b^{2} c^{2} d^{4} - 29 \, a^{4} b c d^{5} + 15 \, a^{5} d^{6}\right)} x^{4} + 2 \, {\left(12 \, b^{5} c^{6} - 20 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2} + 81 \, a^{3} b^{2} c^{3} d^{3} - 82 \, a^{4} b c^{2} d^{4} + 25 \, a^{5} c d^{5}\right)} x^{2} + 12 \, {\left({\left(b^{5} c^{4} d^{2} - 3 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(2 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(b^{5} c^{6} - a b^{4} c^{5} d - 6 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 3 \, {\left({\left(21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{7} + {\left(42 \, a^{2} b^{3} c^{3} d^{3} - 15 \, a^{3} b^{2} c^{2} d^{4} - 8 \, a^{4} b c d^{5} + 5 \, a^{5} d^{6}\right)} x^{5} + {\left(21 \, a^{2} b^{3} c^{4} d^{2} + 24 \, a^{3} b^{2} c^{3} d^{3} - 31 \, a^{4} b c^{2} d^{4} + 10 \, a^{5} c d^{5}\right)} x^{3} + {\left(21 \, a^{3} b^{2} c^{4} d^{2} - 18 \, a^{4} b c^{3} d^{3} + 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{16 \, {\left({\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{5} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4}\right)} x\right)}}, -\frac{8 \, a b^{4} c^{6} - 32 \, a^{2} b^{3} c^{5} d + 48 \, a^{3} b^{2} c^{4} d^{2} - 32 \, a^{4} b c^{3} d^{3} + 8 \, a^{5} c^{2} d^{4} + 3 \, {\left(4 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{6} + {\left(24 \, b^{5} c^{5} d - 64 \, a b^{4} c^{4} d^{2} + 81 \, a^{2} b^{3} c^{3} d^{3} - 27 \, a^{3} b^{2} c^{2} d^{4} - 29 \, a^{4} b c d^{5} + 15 \, a^{5} d^{6}\right)} x^{4} + {\left(12 \, b^{5} c^{6} - 20 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2} + 81 \, a^{3} b^{2} c^{3} d^{3} - 82 \, a^{4} b c^{2} d^{4} + 25 \, a^{5} c d^{5}\right)} x^{2} + 3 \, {\left({\left(21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{7} + {\left(42 \, a^{2} b^{3} c^{3} d^{3} - 15 \, a^{3} b^{2} c^{2} d^{4} - 8 \, a^{4} b c d^{5} + 5 \, a^{5} d^{6}\right)} x^{5} + {\left(21 \, a^{2} b^{3} c^{4} d^{2} + 24 \, a^{3} b^{2} c^{3} d^{3} - 31 \, a^{4} b c^{2} d^{4} + 10 \, a^{5} c d^{5}\right)} x^{3} + {\left(21 \, a^{3} b^{2} c^{4} d^{2} - 18 \, a^{4} b c^{3} d^{3} + 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 6 \, {\left({\left(b^{5} c^{4} d^{2} - 3 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(2 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(b^{5} c^{6} - a b^{4} c^{5} d - 6 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{8 \, {\left({\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{5} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4}\right)} x\right)}}, -\frac{16 \, a b^{4} c^{6} - 64 \, a^{2} b^{3} c^{5} d + 96 \, a^{3} b^{2} c^{4} d^{2} - 64 \, a^{4} b c^{3} d^{3} + 16 \, a^{5} c^{2} d^{4} + 6 \, {\left(4 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{6} + 2 \, {\left(24 \, b^{5} c^{5} d - 64 \, a b^{4} c^{4} d^{2} + 81 \, a^{2} b^{3} c^{3} d^{3} - 27 \, a^{3} b^{2} c^{2} d^{4} - 29 \, a^{4} b c d^{5} + 15 \, a^{5} d^{6}\right)} x^{4} + 2 \, {\left(12 \, b^{5} c^{6} - 20 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2} + 81 \, a^{3} b^{2} c^{3} d^{3} - 82 \, a^{4} b c^{2} d^{4} + 25 \, a^{5} c d^{5}\right)} x^{2} + 24 \, {\left({\left(b^{5} c^{4} d^{2} - 3 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(2 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(b^{5} c^{6} - a b^{4} c^{5} d - 6 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left({\left(21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{7} + {\left(42 \, a^{2} b^{3} c^{3} d^{3} - 15 \, a^{3} b^{2} c^{2} d^{4} - 8 \, a^{4} b c d^{5} + 5 \, a^{5} d^{6}\right)} x^{5} + {\left(21 \, a^{2} b^{3} c^{4} d^{2} + 24 \, a^{3} b^{2} c^{3} d^{3} - 31 \, a^{4} b c^{2} d^{4} + 10 \, a^{5} c d^{5}\right)} x^{3} + {\left(21 \, a^{3} b^{2} c^{4} d^{2} - 18 \, a^{4} b c^{3} d^{3} + 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} - 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{16 \, {\left({\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{5} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4}\right)} x\right)}}, -\frac{8 \, a b^{4} c^{6} - 32 \, a^{2} b^{3} c^{5} d + 48 \, a^{3} b^{2} c^{4} d^{2} - 32 \, a^{4} b c^{3} d^{3} + 8 \, a^{5} c^{2} d^{4} + 3 \, {\left(4 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{6} + {\left(24 \, b^{5} c^{5} d - 64 \, a b^{4} c^{4} d^{2} + 81 \, a^{2} b^{3} c^{3} d^{3} - 27 \, a^{3} b^{2} c^{2} d^{4} - 29 \, a^{4} b c d^{5} + 15 \, a^{5} d^{6}\right)} x^{4} + {\left(12 \, b^{5} c^{6} - 20 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2} + 81 \, a^{3} b^{2} c^{3} d^{3} - 82 \, a^{4} b c^{2} d^{4} + 25 \, a^{5} c d^{5}\right)} x^{2} + 12 \, {\left({\left(b^{5} c^{4} d^{2} - 3 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(2 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(b^{5} c^{6} - a b^{4} c^{5} d - 6 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 3 \, {\left({\left(21 \, a^{2} b^{3} c^{2} d^{4} - 18 \, a^{3} b^{2} c d^{5} + 5 \, a^{4} b d^{6}\right)} x^{7} + {\left(42 \, a^{2} b^{3} c^{3} d^{3} - 15 \, a^{3} b^{2} c^{2} d^{4} - 8 \, a^{4} b c d^{5} + 5 \, a^{5} d^{6}\right)} x^{5} + {\left(21 \, a^{2} b^{3} c^{4} d^{2} + 24 \, a^{3} b^{2} c^{3} d^{3} - 31 \, a^{4} b c^{2} d^{4} + 10 \, a^{5} c d^{5}\right)} x^{3} + {\left(21 \, a^{3} b^{2} c^{4} d^{2} - 18 \, a^{4} b c^{3} d^{3} + 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{8 \, {\left({\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{5} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4}\right)} x\right)}}\right]"," ",0,"[-1/16*(16*a*b^4*c^6 - 64*a^2*b^3*c^5*d + 96*a^3*b^2*c^4*d^2 - 64*a^4*b*c^3*d^3 + 16*a^5*c^2*d^4 + 6*(4*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^6 + 2*(24*b^5*c^5*d - 64*a*b^4*c^4*d^2 + 81*a^2*b^3*c^3*d^3 - 27*a^3*b^2*c^2*d^4 - 29*a^4*b*c*d^5 + 15*a^5*d^6)*x^4 + 2*(12*b^5*c^6 - 20*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2 + 81*a^3*b^2*c^3*d^3 - 82*a^4*b*c^2*d^4 + 25*a^5*c*d^5)*x^2 + 12*((b^5*c^4*d^2 - 3*a*b^4*c^3*d^3)*x^7 + (2*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3)*x^5 + (b^5*c^6 - a*b^4*c^5*d - 6*a^2*b^3*c^4*d^2)*x^3 + (a*b^4*c^6 - 3*a^2*b^3*c^5*d)*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 3*((21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^7 + (42*a^2*b^3*c^3*d^3 - 15*a^3*b^2*c^2*d^4 - 8*a^4*b*c*d^5 + 5*a^5*d^6)*x^5 + (21*a^2*b^3*c^4*d^2 + 24*a^3*b^2*c^3*d^3 - 31*a^4*b*c^2*d^4 + 10*a^5*c*d^5)*x^3 + (21*a^3*b^2*c^4*d^2 - 18*a^4*b*c^3*d^3 + 5*a^5*c^2*d^4)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^7 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^5 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4)*x), -1/8*(8*a*b^4*c^6 - 32*a^2*b^3*c^5*d + 48*a^3*b^2*c^4*d^2 - 32*a^4*b*c^3*d^3 + 8*a^5*c^2*d^4 + 3*(4*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^6 + (24*b^5*c^5*d - 64*a*b^4*c^4*d^2 + 81*a^2*b^3*c^3*d^3 - 27*a^3*b^2*c^2*d^4 - 29*a^4*b*c*d^5 + 15*a^5*d^6)*x^4 + (12*b^5*c^6 - 20*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2 + 81*a^3*b^2*c^3*d^3 - 82*a^4*b*c^2*d^4 + 25*a^5*c*d^5)*x^2 + 3*((21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^7 + (42*a^2*b^3*c^3*d^3 - 15*a^3*b^2*c^2*d^4 - 8*a^4*b*c*d^5 + 5*a^5*d^6)*x^5 + (21*a^2*b^3*c^4*d^2 + 24*a^3*b^2*c^3*d^3 - 31*a^4*b*c^2*d^4 + 10*a^5*c*d^5)*x^3 + (21*a^3*b^2*c^4*d^2 - 18*a^4*b*c^3*d^3 + 5*a^5*c^2*d^4)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 6*((b^5*c^4*d^2 - 3*a*b^4*c^3*d^3)*x^7 + (2*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3)*x^5 + (b^5*c^6 - a*b^4*c^5*d - 6*a^2*b^3*c^4*d^2)*x^3 + (a*b^4*c^6 - 3*a^2*b^3*c^5*d)*x)*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^7 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^5 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4)*x), -1/16*(16*a*b^4*c^6 - 64*a^2*b^3*c^5*d + 96*a^3*b^2*c^4*d^2 - 64*a^4*b*c^3*d^3 + 16*a^5*c^2*d^4 + 6*(4*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^6 + 2*(24*b^5*c^5*d - 64*a*b^4*c^4*d^2 + 81*a^2*b^3*c^3*d^3 - 27*a^3*b^2*c^2*d^4 - 29*a^4*b*c*d^5 + 15*a^5*d^6)*x^4 + 2*(12*b^5*c^6 - 20*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2 + 81*a^3*b^2*c^3*d^3 - 82*a^4*b*c^2*d^4 + 25*a^5*c*d^5)*x^2 + 24*((b^5*c^4*d^2 - 3*a*b^4*c^3*d^3)*x^7 + (2*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3)*x^5 + (b^5*c^6 - a*b^4*c^5*d - 6*a^2*b^3*c^4*d^2)*x^3 + (a*b^4*c^6 - 3*a^2*b^3*c^5*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*((21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^7 + (42*a^2*b^3*c^3*d^3 - 15*a^3*b^2*c^2*d^4 - 8*a^4*b*c*d^5 + 5*a^5*d^6)*x^5 + (21*a^2*b^3*c^4*d^2 + 24*a^3*b^2*c^3*d^3 - 31*a^4*b*c^2*d^4 + 10*a^5*c*d^5)*x^3 + (21*a^3*b^2*c^4*d^2 - 18*a^4*b*c^3*d^3 + 5*a^5*c^2*d^4)*x)*sqrt(-d/c)*log((d*x^2 - 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^7 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^5 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4)*x), -1/8*(8*a*b^4*c^6 - 32*a^2*b^3*c^5*d + 48*a^3*b^2*c^4*d^2 - 32*a^4*b*c^3*d^3 + 8*a^5*c^2*d^4 + 3*(4*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^6 + (24*b^5*c^5*d - 64*a*b^4*c^4*d^2 + 81*a^2*b^3*c^3*d^3 - 27*a^3*b^2*c^2*d^4 - 29*a^4*b*c*d^5 + 15*a^5*d^6)*x^4 + (12*b^5*c^6 - 20*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2 + 81*a^3*b^2*c^3*d^3 - 82*a^4*b*c^2*d^4 + 25*a^5*c*d^5)*x^2 + 12*((b^5*c^4*d^2 - 3*a*b^4*c^3*d^3)*x^7 + (2*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3)*x^5 + (b^5*c^6 - a*b^4*c^5*d - 6*a^2*b^3*c^4*d^2)*x^3 + (a*b^4*c^6 - 3*a^2*b^3*c^5*d)*x)*sqrt(b/a)*arctan(x*sqrt(b/a)) + 3*((21*a^2*b^3*c^2*d^4 - 18*a^3*b^2*c*d^5 + 5*a^4*b*d^6)*x^7 + (42*a^2*b^3*c^3*d^3 - 15*a^3*b^2*c^2*d^4 - 8*a^4*b*c*d^5 + 5*a^5*d^6)*x^5 + (21*a^2*b^3*c^4*d^2 + 24*a^3*b^2*c^3*d^3 - 31*a^4*b*c^2*d^4 + 10*a^5*c*d^5)*x^3 + (21*a^3*b^2*c^4*d^2 - 18*a^4*b*c^3*d^3 + 5*a^5*c^2*d^4)*x)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^7 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^5 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4)*x)]","B",0
317,1,1227,0,72.333030," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b^{4} c^{7} - 8 \, a^{3} b^{3} c^{6} d + 12 \, a^{4} b^{2} c^{5} d^{2} - 8 \, a^{5} b c^{4} d^{3} + 2 \, a^{6} c^{3} d^{4} + 2 \, {\left(2 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} + 3 \, a^{5} b c d^{6}\right)} x^{6} + {\left(8 \, a b^{5} c^{6} d - 18 \, a^{2} b^{4} c^{5} d^{2} + 25 \, a^{3} b^{3} c^{4} d^{3} - 10 \, a^{4} b^{2} c^{3} d^{4} - 11 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{4} + {\left(4 \, a b^{5} c^{7} - 6 \, a^{2} b^{4} c^{6} d - 4 \, a^{3} b^{3} c^{5} d^{2} + 25 \, a^{4} b^{2} c^{4} d^{3} - 28 \, a^{5} b c^{3} d^{4} + 9 \, a^{6} c^{2} d^{5}\right)} x^{2} - 2 \, {\left({\left(2 \, b^{6} c^{5} d^{2} - 5 \, a b^{5} c^{4} d^{3}\right)} x^{8} + {\left(4 \, b^{6} c^{6} d - 8 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{6} + {\left(2 \, b^{6} c^{7} - a b^{5} c^{6} d - 10 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{4} + {\left(2 \, a b^{5} c^{7} - 5 \, a^{2} b^{4} c^{6} d\right)} x^{2}\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(10 \, a^{3} b^{3} c^{2} d^{5} - 10 \, a^{4} b^{2} c d^{6} + 3 \, a^{5} b d^{7}\right)} x^{8} + {\left(20 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} - 4 \, a^{5} b c d^{6} + 3 \, a^{6} d^{7}\right)} x^{6} + {\left(10 \, a^{3} b^{3} c^{4} d^{3} + 10 \, a^{4} b^{2} c^{3} d^{4} - 17 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{4} + {\left(10 \, a^{4} b^{2} c^{4} d^{3} - 10 \, a^{5} b c^{3} d^{4} + 3 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 4 \, {\left({\left(2 \, b^{6} c^{5} d^{2} - 5 \, a b^{5} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{2} d^{5} - 10 \, a^{4} b^{2} c d^{6} + 3 \, a^{5} b d^{7}\right)} x^{8} + {\left(4 \, b^{6} c^{6} d - 8 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3} + 20 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} - 4 \, a^{5} b c d^{6} + 3 \, a^{6} d^{7}\right)} x^{6} + {\left(2 \, b^{6} c^{7} - a b^{5} c^{6} d - 10 \, a^{2} b^{4} c^{5} d^{2} + 10 \, a^{3} b^{3} c^{4} d^{3} + 10 \, a^{4} b^{2} c^{3} d^{4} - 17 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{4} + {\left(2 \, a b^{5} c^{7} - 5 \, a^{2} b^{4} c^{6} d + 10 \, a^{4} b^{2} c^{4} d^{3} - 10 \, a^{5} b c^{3} d^{4} + 3 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)} \log\left(x\right)}{4 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{8} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{6} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{4} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*a^2*b^4*c^7 - 8*a^3*b^3*c^6*d + 12*a^4*b^2*c^5*d^2 - 8*a^5*b*c^4*d^3 + 2*a^6*c^3*d^4 + 2*(2*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3 + 10*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 + 3*a^5*b*c*d^6)*x^6 + (8*a*b^5*c^6*d - 18*a^2*b^4*c^5*d^2 + 25*a^3*b^3*c^4*d^3 - 10*a^4*b^2*c^3*d^4 - 11*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^4 + (4*a*b^5*c^7 - 6*a^2*b^4*c^6*d - 4*a^3*b^3*c^5*d^2 + 25*a^4*b^2*c^4*d^3 - 28*a^5*b*c^3*d^4 + 9*a^6*c^2*d^5)*x^2 - 2*((2*b^6*c^5*d^2 - 5*a*b^5*c^4*d^3)*x^8 + (4*b^6*c^6*d - 8*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3)*x^6 + (2*b^6*c^7 - a*b^5*c^6*d - 10*a^2*b^4*c^5*d^2)*x^4 + (2*a*b^5*c^7 - 5*a^2*b^4*c^6*d)*x^2)*log(b*x^2 + a) - 2*((10*a^3*b^3*c^2*d^5 - 10*a^4*b^2*c*d^6 + 3*a^5*b*d^7)*x^8 + (20*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 - 4*a^5*b*c*d^6 + 3*a^6*d^7)*x^6 + (10*a^3*b^3*c^4*d^3 + 10*a^4*b^2*c^3*d^4 - 17*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^4 + (10*a^4*b^2*c^4*d^3 - 10*a^5*b*c^3*d^4 + 3*a^6*c^2*d^5)*x^2)*log(d*x^2 + c) + 4*((2*b^6*c^5*d^2 - 5*a*b^5*c^4*d^3 + 10*a^3*b^3*c^2*d^5 - 10*a^4*b^2*c*d^6 + 3*a^5*b*d^7)*x^8 + (4*b^6*c^6*d - 8*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3 + 20*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 - 4*a^5*b*c*d^6 + 3*a^6*d^7)*x^6 + (2*b^6*c^7 - a*b^5*c^6*d - 10*a^2*b^4*c^5*d^2 + 10*a^3*b^3*c^4*d^3 + 10*a^4*b^2*c^3*d^4 - 17*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^4 + (2*a*b^5*c^7 - 5*a^2*b^4*c^6*d + 10*a^4*b^2*c^4*d^3 - 10*a^5*b*c^3*d^4 + 3*a^6*c^2*d^5)*x^2)*log(x))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^8 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^6 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^4 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x^2)","B",0
318,1,4225,0,47.778397," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\left[-\frac{16 \, a^{2} b^{4} c^{7} - 64 \, a^{3} b^{3} c^{6} d + 96 \, a^{4} b^{2} c^{5} d^{2} - 64 \, a^{5} b c^{4} d^{3} + 16 \, a^{6} c^{3} d^{4} - 6 \, {\left(20 \, b^{6} c^{5} d^{2} - 44 \, a b^{5} c^{4} d^{3} + 99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{8} - 2 \, {\left(120 \, b^{6} c^{6} d - 224 \, a b^{5} c^{5} d^{2} - 88 \, a^{2} b^{4} c^{4} d^{3} + 495 \, a^{3} b^{3} c^{3} d^{4} - 253 \, a^{4} b^{2} c^{2} d^{5} - 155 \, a^{5} b c d^{6} + 105 \, a^{6} d^{7}\right)} x^{6} - 2 \, {\left(60 \, b^{6} c^{7} - 52 \, a b^{5} c^{6} d - 184 \, a^{2} b^{4} c^{5} d^{2} + 176 \, a^{3} b^{3} c^{4} d^{3} + 319 \, a^{4} b^{2} c^{3} d^{4} - 494 \, a^{5} b c^{2} d^{5} + 175 \, a^{6} c d^{6}\right)} x^{4} - 16 \, {\left(5 \, a b^{5} c^{7} - 13 \, a^{2} b^{4} c^{6} d + 2 \, a^{3} b^{3} c^{5} d^{2} + 22 \, a^{4} b^{2} c^{4} d^{3} - 23 \, a^{5} b c^{3} d^{4} + 7 \, a^{6} c^{2} d^{5}\right)} x^{2} + 12 \, {\left({\left(5 \, b^{6} c^{5} d^{2} - 11 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(10 \, b^{6} c^{6} d - 17 \, a b^{5} c^{5} d^{2} - 11 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(5 \, b^{6} c^{7} - a b^{5} c^{6} d - 22 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(5 \, a b^{5} c^{7} - 11 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 3 \, {\left({\left(99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{9} + {\left(198 \, a^{3} b^{3} c^{3} d^{4} - 121 \, a^{4} b^{2} c^{2} d^{5} - 40 \, a^{5} b c d^{6} + 35 \, a^{6} d^{7}\right)} x^{7} + {\left(99 \, a^{3} b^{3} c^{4} d^{3} + 88 \, a^{4} b^{2} c^{3} d^{4} - 185 \, a^{5} b c^{2} d^{5} + 70 \, a^{6} c d^{6}\right)} x^{5} + {\left(99 \, a^{4} b^{2} c^{4} d^{3} - 110 \, a^{5} b c^{3} d^{4} + 35 \, a^{6} c^{2} d^{5}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{48 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{7} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{5} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x^{3}\right)}}, -\frac{8 \, a^{2} b^{4} c^{7} - 32 \, a^{3} b^{3} c^{6} d + 48 \, a^{4} b^{2} c^{5} d^{2} - 32 \, a^{5} b c^{4} d^{3} + 8 \, a^{6} c^{3} d^{4} - 3 \, {\left(20 \, b^{6} c^{5} d^{2} - 44 \, a b^{5} c^{4} d^{3} + 99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{8} - {\left(120 \, b^{6} c^{6} d - 224 \, a b^{5} c^{5} d^{2} - 88 \, a^{2} b^{4} c^{4} d^{3} + 495 \, a^{3} b^{3} c^{3} d^{4} - 253 \, a^{4} b^{2} c^{2} d^{5} - 155 \, a^{5} b c d^{6} + 105 \, a^{6} d^{7}\right)} x^{6} - {\left(60 \, b^{6} c^{7} - 52 \, a b^{5} c^{6} d - 184 \, a^{2} b^{4} c^{5} d^{2} + 176 \, a^{3} b^{3} c^{4} d^{3} + 319 \, a^{4} b^{2} c^{3} d^{4} - 494 \, a^{5} b c^{2} d^{5} + 175 \, a^{6} c d^{6}\right)} x^{4} - 8 \, {\left(5 \, a b^{5} c^{7} - 13 \, a^{2} b^{4} c^{6} d + 2 \, a^{3} b^{3} c^{5} d^{2} + 22 \, a^{4} b^{2} c^{4} d^{3} - 23 \, a^{5} b c^{3} d^{4} + 7 \, a^{6} c^{2} d^{5}\right)} x^{2} - 3 \, {\left({\left(99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{9} + {\left(198 \, a^{3} b^{3} c^{3} d^{4} - 121 \, a^{4} b^{2} c^{2} d^{5} - 40 \, a^{5} b c d^{6} + 35 \, a^{6} d^{7}\right)} x^{7} + {\left(99 \, a^{3} b^{3} c^{4} d^{3} + 88 \, a^{4} b^{2} c^{3} d^{4} - 185 \, a^{5} b c^{2} d^{5} + 70 \, a^{6} c d^{6}\right)} x^{5} + {\left(99 \, a^{4} b^{2} c^{4} d^{3} - 110 \, a^{5} b c^{3} d^{4} + 35 \, a^{6} c^{2} d^{5}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right) + 6 \, {\left({\left(5 \, b^{6} c^{5} d^{2} - 11 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(10 \, b^{6} c^{6} d - 17 \, a b^{5} c^{5} d^{2} - 11 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(5 \, b^{6} c^{7} - a b^{5} c^{6} d - 22 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(5 \, a b^{5} c^{7} - 11 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right)}{24 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{7} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{5} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x^{3}\right)}}, -\frac{16 \, a^{2} b^{4} c^{7} - 64 \, a^{3} b^{3} c^{6} d + 96 \, a^{4} b^{2} c^{5} d^{2} - 64 \, a^{5} b c^{4} d^{3} + 16 \, a^{6} c^{3} d^{4} - 6 \, {\left(20 \, b^{6} c^{5} d^{2} - 44 \, a b^{5} c^{4} d^{3} + 99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{8} - 2 \, {\left(120 \, b^{6} c^{6} d - 224 \, a b^{5} c^{5} d^{2} - 88 \, a^{2} b^{4} c^{4} d^{3} + 495 \, a^{3} b^{3} c^{3} d^{4} - 253 \, a^{4} b^{2} c^{2} d^{5} - 155 \, a^{5} b c d^{6} + 105 \, a^{6} d^{7}\right)} x^{6} - 2 \, {\left(60 \, b^{6} c^{7} - 52 \, a b^{5} c^{6} d - 184 \, a^{2} b^{4} c^{5} d^{2} + 176 \, a^{3} b^{3} c^{4} d^{3} + 319 \, a^{4} b^{2} c^{3} d^{4} - 494 \, a^{5} b c^{2} d^{5} + 175 \, a^{6} c d^{6}\right)} x^{4} - 16 \, {\left(5 \, a b^{5} c^{7} - 13 \, a^{2} b^{4} c^{6} d + 2 \, a^{3} b^{3} c^{5} d^{2} + 22 \, a^{4} b^{2} c^{4} d^{3} - 23 \, a^{5} b c^{3} d^{4} + 7 \, a^{6} c^{2} d^{5}\right)} x^{2} - 24 \, {\left({\left(5 \, b^{6} c^{5} d^{2} - 11 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(10 \, b^{6} c^{6} d - 17 \, a b^{5} c^{5} d^{2} - 11 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(5 \, b^{6} c^{7} - a b^{5} c^{6} d - 22 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(5 \, a b^{5} c^{7} - 11 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left({\left(99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{9} + {\left(198 \, a^{3} b^{3} c^{3} d^{4} - 121 \, a^{4} b^{2} c^{2} d^{5} - 40 \, a^{5} b c d^{6} + 35 \, a^{6} d^{7}\right)} x^{7} + {\left(99 \, a^{3} b^{3} c^{4} d^{3} + 88 \, a^{4} b^{2} c^{3} d^{4} - 185 \, a^{5} b c^{2} d^{5} + 70 \, a^{6} c d^{6}\right)} x^{5} + {\left(99 \, a^{4} b^{2} c^{4} d^{3} - 110 \, a^{5} b c^{3} d^{4} + 35 \, a^{6} c^{2} d^{5}\right)} x^{3}\right)} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{2} + 2 \, c x \sqrt{-\frac{d}{c}} - c}{d x^{2} + c}\right)}{48 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{7} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{5} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x^{3}\right)}}, -\frac{8 \, a^{2} b^{4} c^{7} - 32 \, a^{3} b^{3} c^{6} d + 48 \, a^{4} b^{2} c^{5} d^{2} - 32 \, a^{5} b c^{4} d^{3} + 8 \, a^{6} c^{3} d^{4} - 3 \, {\left(20 \, b^{6} c^{5} d^{2} - 44 \, a b^{5} c^{4} d^{3} + 99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{8} - {\left(120 \, b^{6} c^{6} d - 224 \, a b^{5} c^{5} d^{2} - 88 \, a^{2} b^{4} c^{4} d^{3} + 495 \, a^{3} b^{3} c^{3} d^{4} - 253 \, a^{4} b^{2} c^{2} d^{5} - 155 \, a^{5} b c d^{6} + 105 \, a^{6} d^{7}\right)} x^{6} - {\left(60 \, b^{6} c^{7} - 52 \, a b^{5} c^{6} d - 184 \, a^{2} b^{4} c^{5} d^{2} + 176 \, a^{3} b^{3} c^{4} d^{3} + 319 \, a^{4} b^{2} c^{3} d^{4} - 494 \, a^{5} b c^{2} d^{5} + 175 \, a^{6} c d^{6}\right)} x^{4} - 8 \, {\left(5 \, a b^{5} c^{7} - 13 \, a^{2} b^{4} c^{6} d + 2 \, a^{3} b^{3} c^{5} d^{2} + 22 \, a^{4} b^{2} c^{4} d^{3} - 23 \, a^{5} b c^{3} d^{4} + 7 \, a^{6} c^{2} d^{5}\right)} x^{2} - 12 \, {\left({\left(5 \, b^{6} c^{5} d^{2} - 11 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(10 \, b^{6} c^{6} d - 17 \, a b^{5} c^{5} d^{2} - 11 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(5 \, b^{6} c^{7} - a b^{5} c^{6} d - 22 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(5 \, a b^{5} c^{7} - 11 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - 3 \, {\left({\left(99 \, a^{3} b^{3} c^{2} d^{5} - 110 \, a^{4} b^{2} c d^{6} + 35 \, a^{5} b d^{7}\right)} x^{9} + {\left(198 \, a^{3} b^{3} c^{3} d^{4} - 121 \, a^{4} b^{2} c^{2} d^{5} - 40 \, a^{5} b c d^{6} + 35 \, a^{6} d^{7}\right)} x^{7} + {\left(99 \, a^{3} b^{3} c^{4} d^{3} + 88 \, a^{4} b^{2} c^{3} d^{4} - 185 \, a^{5} b c^{2} d^{5} + 70 \, a^{6} c d^{6}\right)} x^{5} + {\left(99 \, a^{4} b^{2} c^{4} d^{3} - 110 \, a^{5} b c^{3} d^{4} + 35 \, a^{6} c^{2} d^{5}\right)} x^{3}\right)} \sqrt{\frac{d}{c}} \arctan\left(x \sqrt{\frac{d}{c}}\right)}{24 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{7} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{5} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x^{3}\right)}}\right]"," ",0,"[-1/48*(16*a^2*b^4*c^7 - 64*a^3*b^3*c^6*d + 96*a^4*b^2*c^5*d^2 - 64*a^5*b*c^4*d^3 + 16*a^6*c^3*d^4 - 6*(20*b^6*c^5*d^2 - 44*a*b^5*c^4*d^3 + 99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^8 - 2*(120*b^6*c^6*d - 224*a*b^5*c^5*d^2 - 88*a^2*b^4*c^4*d^3 + 495*a^3*b^3*c^3*d^4 - 253*a^4*b^2*c^2*d^5 - 155*a^5*b*c*d^6 + 105*a^6*d^7)*x^6 - 2*(60*b^6*c^7 - 52*a*b^5*c^6*d - 184*a^2*b^4*c^5*d^2 + 176*a^3*b^3*c^4*d^3 + 319*a^4*b^2*c^3*d^4 - 494*a^5*b*c^2*d^5 + 175*a^6*c*d^6)*x^4 - 16*(5*a*b^5*c^7 - 13*a^2*b^4*c^6*d + 2*a^3*b^3*c^5*d^2 + 22*a^4*b^2*c^4*d^3 - 23*a^5*b*c^3*d^4 + 7*a^6*c^2*d^5)*x^2 + 12*((5*b^6*c^5*d^2 - 11*a*b^5*c^4*d^3)*x^9 + (10*b^6*c^6*d - 17*a*b^5*c^5*d^2 - 11*a^2*b^4*c^4*d^3)*x^7 + (5*b^6*c^7 - a*b^5*c^6*d - 22*a^2*b^4*c^5*d^2)*x^5 + (5*a*b^5*c^7 - 11*a^2*b^4*c^6*d)*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 3*((99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^9 + (198*a^3*b^3*c^3*d^4 - 121*a^4*b^2*c^2*d^5 - 40*a^5*b*c*d^6 + 35*a^6*d^7)*x^7 + (99*a^3*b^3*c^4*d^3 + 88*a^4*b^2*c^3*d^4 - 185*a^5*b*c^2*d^5 + 70*a^6*c*d^6)*x^5 + (99*a^4*b^2*c^4*d^3 - 110*a^5*b*c^3*d^4 + 35*a^6*c^2*d^5)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^9 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^7 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^5 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x^3), -1/24*(8*a^2*b^4*c^7 - 32*a^3*b^3*c^6*d + 48*a^4*b^2*c^5*d^2 - 32*a^5*b*c^4*d^3 + 8*a^6*c^3*d^4 - 3*(20*b^6*c^5*d^2 - 44*a*b^5*c^4*d^3 + 99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^8 - (120*b^6*c^6*d - 224*a*b^5*c^5*d^2 - 88*a^2*b^4*c^4*d^3 + 495*a^3*b^3*c^3*d^4 - 253*a^4*b^2*c^2*d^5 - 155*a^5*b*c*d^6 + 105*a^6*d^7)*x^6 - (60*b^6*c^7 - 52*a*b^5*c^6*d - 184*a^2*b^4*c^5*d^2 + 176*a^3*b^3*c^4*d^3 + 319*a^4*b^2*c^3*d^4 - 494*a^5*b*c^2*d^5 + 175*a^6*c*d^6)*x^4 - 8*(5*a*b^5*c^7 - 13*a^2*b^4*c^6*d + 2*a^3*b^3*c^5*d^2 + 22*a^4*b^2*c^4*d^3 - 23*a^5*b*c^3*d^4 + 7*a^6*c^2*d^5)*x^2 - 3*((99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^9 + (198*a^3*b^3*c^3*d^4 - 121*a^4*b^2*c^2*d^5 - 40*a^5*b*c*d^6 + 35*a^6*d^7)*x^7 + (99*a^3*b^3*c^4*d^3 + 88*a^4*b^2*c^3*d^4 - 185*a^5*b*c^2*d^5 + 70*a^6*c*d^6)*x^5 + (99*a^4*b^2*c^4*d^3 - 110*a^5*b*c^3*d^4 + 35*a^6*c^2*d^5)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)) + 6*((5*b^6*c^5*d^2 - 11*a*b^5*c^4*d^3)*x^9 + (10*b^6*c^6*d - 17*a*b^5*c^5*d^2 - 11*a^2*b^4*c^4*d^3)*x^7 + (5*b^6*c^7 - a*b^5*c^6*d - 22*a^2*b^4*c^5*d^2)*x^5 + (5*a*b^5*c^7 - 11*a^2*b^4*c^6*d)*x^3)*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^9 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^7 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^5 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x^3), -1/48*(16*a^2*b^4*c^7 - 64*a^3*b^3*c^6*d + 96*a^4*b^2*c^5*d^2 - 64*a^5*b*c^4*d^3 + 16*a^6*c^3*d^4 - 6*(20*b^6*c^5*d^2 - 44*a*b^5*c^4*d^3 + 99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^8 - 2*(120*b^6*c^6*d - 224*a*b^5*c^5*d^2 - 88*a^2*b^4*c^4*d^3 + 495*a^3*b^3*c^3*d^4 - 253*a^4*b^2*c^2*d^5 - 155*a^5*b*c*d^6 + 105*a^6*d^7)*x^6 - 2*(60*b^6*c^7 - 52*a*b^5*c^6*d - 184*a^2*b^4*c^5*d^2 + 176*a^3*b^3*c^4*d^3 + 319*a^4*b^2*c^3*d^4 - 494*a^5*b*c^2*d^5 + 175*a^6*c*d^6)*x^4 - 16*(5*a*b^5*c^7 - 13*a^2*b^4*c^6*d + 2*a^3*b^3*c^5*d^2 + 22*a^4*b^2*c^4*d^3 - 23*a^5*b*c^3*d^4 + 7*a^6*c^2*d^5)*x^2 - 24*((5*b^6*c^5*d^2 - 11*a*b^5*c^4*d^3)*x^9 + (10*b^6*c^6*d - 17*a*b^5*c^5*d^2 - 11*a^2*b^4*c^4*d^3)*x^7 + (5*b^6*c^7 - a*b^5*c^6*d - 22*a^2*b^4*c^5*d^2)*x^5 + (5*a*b^5*c^7 - 11*a^2*b^4*c^6*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*((99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^9 + (198*a^3*b^3*c^3*d^4 - 121*a^4*b^2*c^2*d^5 - 40*a^5*b*c*d^6 + 35*a^6*d^7)*x^7 + (99*a^3*b^3*c^4*d^3 + 88*a^4*b^2*c^3*d^4 - 185*a^5*b*c^2*d^5 + 70*a^6*c*d^6)*x^5 + (99*a^4*b^2*c^4*d^3 - 110*a^5*b*c^3*d^4 + 35*a^6*c^2*d^5)*x^3)*sqrt(-d/c)*log((d*x^2 + 2*c*x*sqrt(-d/c) - c)/(d*x^2 + c)))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^9 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^7 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^5 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x^3), -1/24*(8*a^2*b^4*c^7 - 32*a^3*b^3*c^6*d + 48*a^4*b^2*c^5*d^2 - 32*a^5*b*c^4*d^3 + 8*a^6*c^3*d^4 - 3*(20*b^6*c^5*d^2 - 44*a*b^5*c^4*d^3 + 99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^8 - (120*b^6*c^6*d - 224*a*b^5*c^5*d^2 - 88*a^2*b^4*c^4*d^3 + 495*a^3*b^3*c^3*d^4 - 253*a^4*b^2*c^2*d^5 - 155*a^5*b*c*d^6 + 105*a^6*d^7)*x^6 - (60*b^6*c^7 - 52*a*b^5*c^6*d - 184*a^2*b^4*c^5*d^2 + 176*a^3*b^3*c^4*d^3 + 319*a^4*b^2*c^3*d^4 - 494*a^5*b*c^2*d^5 + 175*a^6*c*d^6)*x^4 - 8*(5*a*b^5*c^7 - 13*a^2*b^4*c^6*d + 2*a^3*b^3*c^5*d^2 + 22*a^4*b^2*c^4*d^3 - 23*a^5*b*c^3*d^4 + 7*a^6*c^2*d^5)*x^2 - 12*((5*b^6*c^5*d^2 - 11*a*b^5*c^4*d^3)*x^9 + (10*b^6*c^6*d - 17*a*b^5*c^5*d^2 - 11*a^2*b^4*c^4*d^3)*x^7 + (5*b^6*c^7 - a*b^5*c^6*d - 22*a^2*b^4*c^5*d^2)*x^5 + (5*a*b^5*c^7 - 11*a^2*b^4*c^6*d)*x^3)*sqrt(b/a)*arctan(x*sqrt(b/a)) - 3*((99*a^3*b^3*c^2*d^5 - 110*a^4*b^2*c*d^6 + 35*a^5*b*d^7)*x^9 + (198*a^3*b^3*c^3*d^4 - 121*a^4*b^2*c^2*d^5 - 40*a^5*b*c*d^6 + 35*a^6*d^7)*x^7 + (99*a^3*b^3*c^4*d^3 + 88*a^4*b^2*c^3*d^4 - 185*a^5*b*c^2*d^5 + 70*a^6*c*d^6)*x^5 + (99*a^4*b^2*c^4*d^3 - 110*a^5*b*c^3*d^4 + 35*a^6*c^2*d^5)*x^3)*sqrt(d/c)*arctan(x*sqrt(d/c)))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^9 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^7 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^5 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x^3)]","B",0
319,1,379,0,1.259273," ","integrate(x^m*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{3} m^{4} + 16 \, B b^{3} m^{3} + 86 \, B b^{3} m^{2} + 176 \, B b^{3} m + 105 \, B b^{3}\right)} x^{9} + {\left({\left(3 \, B a b^{2} + A b^{3}\right)} m^{4} + 405 \, B a b^{2} + 135 \, A b^{3} + 18 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m^{3} + 104 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m^{2} + 222 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m\right)} x^{7} + 3 \, {\left({\left(B a^{2} b + A a b^{2}\right)} m^{4} + 189 \, B a^{2} b + 189 \, A a b^{2} + 20 \, {\left(B a^{2} b + A a b^{2}\right)} m^{3} + 130 \, {\left(B a^{2} b + A a b^{2}\right)} m^{2} + 300 \, {\left(B a^{2} b + A a b^{2}\right)} m\right)} x^{5} + {\left({\left(B a^{3} + 3 \, A a^{2} b\right)} m^{4} + 315 \, B a^{3} + 945 \, A a^{2} b + 22 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{3} + 164 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{2} + 458 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m\right)} x^{3} + {\left(A a^{3} m^{4} + 24 \, A a^{3} m^{3} + 206 \, A a^{3} m^{2} + 744 \, A a^{3} m + 945 \, A a^{3}\right)} x\right)} x^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((B*b^3*m^4 + 16*B*b^3*m^3 + 86*B*b^3*m^2 + 176*B*b^3*m + 105*B*b^3)*x^9 + ((3*B*a*b^2 + A*b^3)*m^4 + 405*B*a*b^2 + 135*A*b^3 + 18*(3*B*a*b^2 + A*b^3)*m^3 + 104*(3*B*a*b^2 + A*b^3)*m^2 + 222*(3*B*a*b^2 + A*b^3)*m)*x^7 + 3*((B*a^2*b + A*a*b^2)*m^4 + 189*B*a^2*b + 189*A*a*b^2 + 20*(B*a^2*b + A*a*b^2)*m^3 + 130*(B*a^2*b + A*a*b^2)*m^2 + 300*(B*a^2*b + A*a*b^2)*m)*x^5 + ((B*a^3 + 3*A*a^2*b)*m^4 + 315*B*a^3 + 945*A*a^2*b + 22*(B*a^3 + 3*A*a^2*b)*m^3 + 164*(B*a^3 + 3*A*a^2*b)*m^2 + 458*(B*a^3 + 3*A*a^2*b)*m)*x^3 + (A*a^3*m^4 + 24*A*a^3*m^3 + 206*A*a^3*m^2 + 744*A*a^3*m + 945*A*a^3)*x)*x^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
320,1,215,0,0.931356," ","integrate(x^m*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} m^{3} + 9 \, B b^{2} m^{2} + 23 \, B b^{2} m + 15 \, B b^{2}\right)} x^{7} + {\left({\left(2 \, B a b + A b^{2}\right)} m^{3} + 42 \, B a b + 21 \, A b^{2} + 11 \, {\left(2 \, B a b + A b^{2}\right)} m^{2} + 31 \, {\left(2 \, B a b + A b^{2}\right)} m\right)} x^{5} + {\left({\left(B a^{2} + 2 \, A a b\right)} m^{3} + 35 \, B a^{2} + 70 \, A a b + 13 \, {\left(B a^{2} + 2 \, A a b\right)} m^{2} + 47 \, {\left(B a^{2} + 2 \, A a b\right)} m\right)} x^{3} + {\left(A a^{2} m^{3} + 15 \, A a^{2} m^{2} + 71 \, A a^{2} m + 105 \, A a^{2}\right)} x\right)} x^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((B*b^2*m^3 + 9*B*b^2*m^2 + 23*B*b^2*m + 15*B*b^2)*x^7 + ((2*B*a*b + A*b^2)*m^3 + 42*B*a*b + 21*A*b^2 + 11*(2*B*a*b + A*b^2)*m^2 + 31*(2*B*a*b + A*b^2)*m)*x^5 + ((B*a^2 + 2*A*a*b)*m^3 + 35*B*a^2 + 70*A*a*b + 13*(B*a^2 + 2*A*a*b)*m^2 + 47*(B*a^2 + 2*A*a*b)*m)*x^3 + (A*a^2*m^3 + 15*A*a^2*m^2 + 71*A*a^2*m + 105*A*a^2)*x)*x^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
321,1,92,0,0.765741," ","integrate(x^m*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b m^{2} + 4 \, B b m + 3 \, B b\right)} x^{5} + {\left({\left(B a + A b\right)} m^{2} + 5 \, B a + 5 \, A b + 6 \, {\left(B a + A b\right)} m\right)} x^{3} + {\left(A a m^{2} + 8 \, A a m + 15 \, A a\right)} x\right)} x^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"((B*b*m^2 + 4*B*b*m + 3*B*b)*x^5 + ((B*a + A*b)*m^2 + 5*B*a + 5*A*b + 6*(B*a + A*b)*m)*x^3 + (A*a*m^2 + 8*A*a*m + 15*A*a)*x)*x^m/(m^3 + 9*m^2 + 23*m + 15)","B",0
322,0,0,0,0.776220," ","integrate(x^m*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} x^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((B*x^2 + A)*x^m/(b*x^2 + a), x)","F",0
323,0,0,0,0.874695," ","integrate(x^m*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} x^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*x^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
324,0,0,0,1.092517," ","integrate(x^m*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} x^{m}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*x^m/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
325,1,773,0,1.205065," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} d^{3} m^{5} + 25 \, b^{2} d^{3} m^{4} + 230 \, b^{2} d^{3} m^{3} + 950 \, b^{2} d^{3} m^{2} + 1689 \, b^{2} d^{3} m + 945 \, b^{2} d^{3}\right)} x^{11} + {\left({\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} m^{5} + 3465 \, b^{2} c d^{2} + 2310 \, a b d^{3} + 27 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} m^{4} + 262 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} m^{3} + 1122 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} m^{2} + 2041 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} m\right)} x^{9} + {\left({\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} m^{5} + 4455 \, b^{2} c^{2} d + 8910 \, a b c d^{2} + 1485 \, a^{2} d^{3} + 29 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} m^{4} + 302 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} m^{3} + 1366 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} m^{2} + 2577 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} m\right)} x^{7} + {\left({\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} m^{5} + 2079 \, b^{2} c^{3} + 12474 \, a b c^{2} d + 6237 \, a^{2} c d^{2} + 31 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} m^{4} + 350 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} m^{3} + 1730 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} m^{2} + 3489 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} m\right)} x^{5} + {\left({\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} m^{5} + 6930 \, a b c^{3} + 10395 \, a^{2} c^{2} d + 33 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} m^{4} + 406 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} m^{3} + 2262 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} m^{2} + 5353 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} m\right)} x^{3} + {\left(a^{2} c^{3} m^{5} + 35 \, a^{2} c^{3} m^{4} + 470 \, a^{2} c^{3} m^{3} + 3010 \, a^{2} c^{3} m^{2} + 9129 \, a^{2} c^{3} m + 10395 \, a^{2} c^{3}\right)} x\right)} x^{m}}{m^{6} + 36 \, m^{5} + 505 \, m^{4} + 3480 \, m^{3} + 12139 \, m^{2} + 19524 \, m + 10395}"," ",0,"((b^2*d^3*m^5 + 25*b^2*d^3*m^4 + 230*b^2*d^3*m^3 + 950*b^2*d^3*m^2 + 1689*b^2*d^3*m + 945*b^2*d^3)*x^11 + ((3*b^2*c*d^2 + 2*a*b*d^3)*m^5 + 3465*b^2*c*d^2 + 2310*a*b*d^3 + 27*(3*b^2*c*d^2 + 2*a*b*d^3)*m^4 + 262*(3*b^2*c*d^2 + 2*a*b*d^3)*m^3 + 1122*(3*b^2*c*d^2 + 2*a*b*d^3)*m^2 + 2041*(3*b^2*c*d^2 + 2*a*b*d^3)*m)*x^9 + ((3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*m^5 + 4455*b^2*c^2*d + 8910*a*b*c*d^2 + 1485*a^2*d^3 + 29*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*m^4 + 302*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*m^3 + 1366*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*m^2 + 2577*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*m)*x^7 + ((b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*m^5 + 2079*b^2*c^3 + 12474*a*b*c^2*d + 6237*a^2*c*d^2 + 31*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*m^4 + 350*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*m^3 + 1730*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*m^2 + 3489*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*m)*x^5 + ((2*a*b*c^3 + 3*a^2*c^2*d)*m^5 + 6930*a*b*c^3 + 10395*a^2*c^2*d + 33*(2*a*b*c^3 + 3*a^2*c^2*d)*m^4 + 406*(2*a*b*c^3 + 3*a^2*c^2*d)*m^3 + 2262*(2*a*b*c^3 + 3*a^2*c^2*d)*m^2 + 5353*(2*a*b*c^3 + 3*a^2*c^2*d)*m)*x^3 + (a^2*c^3*m^5 + 35*a^2*c^3*m^4 + 470*a^2*c^3*m^3 + 3010*a^2*c^3*m^2 + 9129*a^2*c^3*m + 10395*a^2*c^3)*x)*x^m/(m^6 + 36*m^5 + 505*m^4 + 3480*m^3 + 12139*m^2 + 19524*m + 10395)","B",0
326,1,442,0,1.043283," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} d^{2} m^{4} + 16 \, b^{2} d^{2} m^{3} + 86 \, b^{2} d^{2} m^{2} + 176 \, b^{2} d^{2} m + 105 \, b^{2} d^{2}\right)} x^{9} + 2 \, {\left({\left(b^{2} c d + a b d^{2}\right)} m^{4} + 135 \, b^{2} c d + 135 \, a b d^{2} + 18 \, {\left(b^{2} c d + a b d^{2}\right)} m^{3} + 104 \, {\left(b^{2} c d + a b d^{2}\right)} m^{2} + 222 \, {\left(b^{2} c d + a b d^{2}\right)} m\right)} x^{7} + {\left({\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} m^{4} + 189 \, b^{2} c^{2} + 756 \, a b c d + 189 \, a^{2} d^{2} + 20 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} m^{3} + 130 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} m^{2} + 300 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} m\right)} x^{5} + 2 \, {\left({\left(a b c^{2} + a^{2} c d\right)} m^{4} + 315 \, a b c^{2} + 315 \, a^{2} c d + 22 \, {\left(a b c^{2} + a^{2} c d\right)} m^{3} + 164 \, {\left(a b c^{2} + a^{2} c d\right)} m^{2} + 458 \, {\left(a b c^{2} + a^{2} c d\right)} m\right)} x^{3} + {\left(a^{2} c^{2} m^{4} + 24 \, a^{2} c^{2} m^{3} + 206 \, a^{2} c^{2} m^{2} + 744 \, a^{2} c^{2} m + 945 \, a^{2} c^{2}\right)} x\right)} x^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"((b^2*d^2*m^4 + 16*b^2*d^2*m^3 + 86*b^2*d^2*m^2 + 176*b^2*d^2*m + 105*b^2*d^2)*x^9 + 2*((b^2*c*d + a*b*d^2)*m^4 + 135*b^2*c*d + 135*a*b*d^2 + 18*(b^2*c*d + a*b*d^2)*m^3 + 104*(b^2*c*d + a*b*d^2)*m^2 + 222*(b^2*c*d + a*b*d^2)*m)*x^7 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*m^4 + 189*b^2*c^2 + 756*a*b*c*d + 189*a^2*d^2 + 20*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*m^3 + 130*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*m^2 + 300*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*m)*x^5 + 2*((a*b*c^2 + a^2*c*d)*m^4 + 315*a*b*c^2 + 315*a^2*c*d + 22*(a*b*c^2 + a^2*c*d)*m^3 + 164*(a*b*c^2 + a^2*c*d)*m^2 + 458*(a*b*c^2 + a^2*c*d)*m)*x^3 + (a^2*c^2*m^4 + 24*a^2*c^2*m^3 + 206*a^2*c^2*m^2 + 744*a^2*c^2*m + 945*a^2*c^2)*x)*x^m/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
327,1,215,0,1.025810," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} d m^{3} + 9 \, b^{2} d m^{2} + 23 \, b^{2} d m + 15 \, b^{2} d\right)} x^{7} + {\left({\left(b^{2} c + 2 \, a b d\right)} m^{3} + 21 \, b^{2} c + 42 \, a b d + 11 \, {\left(b^{2} c + 2 \, a b d\right)} m^{2} + 31 \, {\left(b^{2} c + 2 \, a b d\right)} m\right)} x^{5} + {\left({\left(2 \, a b c + a^{2} d\right)} m^{3} + 70 \, a b c + 35 \, a^{2} d + 13 \, {\left(2 \, a b c + a^{2} d\right)} m^{2} + 47 \, {\left(2 \, a b c + a^{2} d\right)} m\right)} x^{3} + {\left(a^{2} c m^{3} + 15 \, a^{2} c m^{2} + 71 \, a^{2} c m + 105 \, a^{2} c\right)} x\right)} x^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"((b^2*d*m^3 + 9*b^2*d*m^2 + 23*b^2*d*m + 15*b^2*d)*x^7 + ((b^2*c + 2*a*b*d)*m^3 + 21*b^2*c + 42*a*b*d + 11*(b^2*c + 2*a*b*d)*m^2 + 31*(b^2*c + 2*a*b*d)*m)*x^5 + ((2*a*b*c + a^2*d)*m^3 + 70*a*b*c + 35*a^2*d + 13*(2*a*b*c + a^2*d)*m^2 + 47*(2*a*b*c + a^2*d)*m)*x^3 + (a^2*c*m^3 + 15*a^2*c*m^2 + 71*a^2*c*m + 105*a^2*c)*x)*x^m/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
328,0,0,0,1.285269," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} x^{m}}{d x^{2} + c}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*x^m/(d*x^2 + c), x)","F",0
329,0,0,0,1.012376," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} x^{m}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*x^m/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
330,0,0,0,1.183954," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} x^{m}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*x^m/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
331,0,0,0,1.278486," ","integrate(x^m*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}\right)} x^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3)*x^m/(b*x^2 + a), x)","F",0
332,0,0,0,1.185301," ","integrate(x^m*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} x^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*x^m/(b*x^2 + a), x)","F",0
333,0,0,0,1.008337," ","integrate(x^m*(d*x^2+c)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} x^{m}}{b x^{2} + a}, x\right)"," ",0,"integral((d*x^2 + c)*x^m/(b*x^2 + a), x)","F",0
334,0,0,0,1.159414," ","integrate(x^m/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(x^m/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
335,0,0,0,1.096058," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}}, x\right)"," ",0,"integral(x^m/(b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2), x)","F",0
336,0,0,0,1.004780," ","integrate(x^m/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{3} d x^{8} + {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{6} + 3 \, {\left(a b^{2} c + a^{2} b d\right)} x^{4} + a^{3} c + {\left(3 \, a^{2} b c + a^{3} d\right)} x^{2}}, x\right)"," ",0,"integral(x^m/(b^3*d*x^8 + (b^3*c + 3*a*b^2*d)*x^6 + 3*(a*b^2*c + a^2*b*d)*x^4 + a^3*c + (3*a^2*b*c + a^3*d)*x^2), x)","F",0
337,0,0,0,0.743492," ","integrate(x^m*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}\right)} x^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3)*x^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
338,0,0,0,1.140059," ","integrate(x^m*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{4} + 2 \, c d x^{2} + c^{2}\right)} x^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d^2*x^4 + 2*c*d*x^2 + c^2)*x^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
339,0,0,0,1.056564," ","integrate(x^m*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{2} + c\right)} x^{m}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*x^2 + c)*x^m/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
340,0,0,0,1.184448," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}}, x\right)"," ",0,"integral(x^m/(b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2), x)","F",0
341,0,0,0,0.965575," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} d^{2} x^{8} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}, x\right)"," ",0,"integral(x^m/(b^2*d^2*x^8 + 2*(b^2*c*d + a*b*d^2)*x^6 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + a^2*c^2 + 2*(a*b*c^2 + a^2*c*d)*x^2), x)","F",0
342,0,0,0,1.274448," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b^{2} d^{3} x^{10} + {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} + a^{2} c^{3} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}}, x\right)"," ",0,"integral(x^m/(b^2*d^3*x^10 + (3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 + a^2*c^3 + (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + (2*a*b*c^3 + 3*a^2*c^2*d)*x^2), x)","F",0
343,1,32,0,1.018949," ","integrate(x^(7/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{1989} \, {\left(117 \, B b x^{8} + 153 \, {\left(B a + A b\right)} x^{6} + 221 \, A a x^{4}\right)} \sqrt{x}"," ",0,"2/1989*(117*B*b*x^8 + 153*(B*a + A*b)*x^6 + 221*A*a*x^4)*sqrt(x)","A",0
344,1,32,0,0.709408," ","integrate(x^(5/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, B b x^{7} + 105 \, {\left(B a + A b\right)} x^{5} + 165 \, A a x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*B*b*x^7 + 105*(B*a + A*b)*x^5 + 165*A*a*x^3)*sqrt(x)","A",0
345,1,32,0,0.986104," ","integrate(x^(3/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, B b x^{6} + 65 \, {\left(B a + A b\right)} x^{4} + 117 \, A a x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*B*b*x^6 + 65*(B*a + A*b)*x^4 + 117*A*a*x^2)*sqrt(x)","A",0
346,1,30,0,1.023034," ","integrate((b*x^2+a)*(B*x^2+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{231} \, {\left(21 \, B b x^{5} + 33 \, {\left(B a + A b\right)} x^{3} + 77 \, A a x\right)} \sqrt{x}"," ",0,"2/231*(21*B*b*x^5 + 33*(B*a + A*b)*x^3 + 77*A*a*x)*sqrt(x)","A",0
347,1,29,0,0.833174," ","integrate((b*x^2+a)*(B*x^2+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(5 \, B b x^{4} + 9 \, {\left(B a + A b\right)} x^{2} + 45 \, A a\right)} \sqrt{x}"," ",0,"2/45*(5*B*b*x^4 + 9*(B*a + A*b)*x^2 + 45*A*a)*sqrt(x)","A",0
348,1,29,0,1.006210," ","integrate((b*x^2+a)*(B*x^2+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b x^{4} + 7 \, {\left(B a + A b\right)} x^{2} - 21 \, A a\right)}}{21 \, \sqrt{x}}"," ",0,"2/21*(3*B*b*x^4 + 7*(B*a + A*b)*x^2 - 21*A*a)/sqrt(x)","A",0
349,1,29,0,1.036977," ","integrate((b*x^2+a)*(B*x^2+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b x^{4} + 15 \, {\left(B a + A b\right)} x^{2} - 5 \, A a\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*B*b*x^4 + 15*(B*a + A*b)*x^2 - 5*A*a)/x^(3/2)","A",0
350,1,29,0,0.847428," ","integrate((b*x^2+a)*(B*x^2+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b x^{4} - 15 \, {\left(B a + A b\right)} x^{2} - 3 \, A a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(5*B*b*x^4 - 15*(B*a + A*b)*x^2 - 3*A*a)/x^(5/2)","A",0
351,1,56,0,1.069903," ","integrate(x^(7/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{13923} \, {\left(663 \, B b^{2} x^{10} + 819 \, {\left(2 \, B a b + A b^{2}\right)} x^{8} + 1547 \, A a^{2} x^{4} + 1071 \, {\left(B a^{2} + 2 \, A a b\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/13923*(663*B*b^2*x^10 + 819*(2*B*a*b + A*b^2)*x^8 + 1547*A*a^2*x^4 + 1071*(B*a^2 + 2*A*a*b)*x^6)*sqrt(x)","A",0
352,1,56,0,1.070325," ","integrate(x^(5/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, B b^{2} x^{9} + 1463 \, {\left(2 \, B a b + A b^{2}\right)} x^{7} + 3135 \, A a^{2} x^{3} + 1995 \, {\left(B a^{2} + 2 \, A a b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/21945*(1155*B*b^2*x^9 + 1463*(2*B*a*b + A*b^2)*x^7 + 3135*A*a^2*x^3 + 1995*(B*a^2 + 2*A*a*b)*x^5)*sqrt(x)","A",0
353,1,56,0,1.326928," ","integrate(x^(3/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{9945} \, {\left(585 \, B b^{2} x^{8} + 765 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 1989 \, A a^{2} x^{2} + 1105 \, {\left(B a^{2} + 2 \, A a b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9945*(585*B*b^2*x^8 + 765*(2*B*a*b + A*b^2)*x^6 + 1989*A*a^2*x^2 + 1105*(B*a^2 + 2*A*a*b)*x^4)*sqrt(x)","A",0
354,1,54,0,1.166941," ","integrate((b*x^2+a)^2*(B*x^2+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, B b^{2} x^{7} + 105 \, {\left(2 \, B a b + A b^{2}\right)} x^{5} + 385 \, A a^{2} x + 165 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*B*b^2*x^7 + 105*(2*B*a*b + A*b^2)*x^5 + 385*A*a^2*x + 165*(B*a^2 + 2*A*a*b)*x^3)*sqrt(x)","A",0
355,1,53,0,1.339962," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, B b^{2} x^{6} + 65 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 585 \, A a^{2} + 117 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*B*b^2*x^6 + 65*(2*B*a*b + A*b^2)*x^4 + 585*A*a^2 + 117*(B*a^2 + 2*A*a*b)*x^2)*sqrt(x)","A",0
356,1,53,0,1.172211," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, B b^{2} x^{6} + 33 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 231 \, A a^{2} + 77 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)}}{231 \, \sqrt{x}}"," ",0,"2/231*(21*B*b^2*x^6 + 33*(2*B*a*b + A*b^2)*x^4 - 231*A*a^2 + 77*(B*a^2 + 2*A*a*b)*x^2)/sqrt(x)","A",0
357,1,53,0,1.079226," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{2} x^{6} + 9 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 15 \, A a^{2} + 45 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)}}{45 \, x^{\frac{3}{2}}}"," ",0,"2/45*(5*B*b^2*x^6 + 9*(2*B*a*b + A*b^2)*x^4 - 15*A*a^2 + 45*(B*a^2 + 2*A*a*b)*x^2)/x^(3/2)","A",0
358,1,53,0,1.045285," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} x^{6} + 35 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} - 21 \, A a^{2} - 105 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)}}{105 \, x^{\frac{5}{2}}}"," ",0,"2/105*(15*B*b^2*x^6 + 35*(2*B*a*b + A*b^2)*x^4 - 21*A*a^2 - 105*(B*a^2 + 2*A*a*b)*x^2)/x^(5/2)","A",0
359,1,78,0,1.234229," ","integrate(x^(7/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{348075} \, {\left(13923 \, B b^{3} x^{12} + 16575 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{10} + 61425 \, {\left(B a^{2} b + A a b^{2}\right)} x^{8} + 38675 \, A a^{3} x^{4} + 26775 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/348075*(13923*B*b^3*x^12 + 16575*(3*B*a*b^2 + A*b^3)*x^10 + 61425*(B*a^2*b + A*a*b^2)*x^8 + 38675*A*a^3*x^4 + 26775*(B*a^3 + 3*A*a^2*b)*x^6)*sqrt(x)","A",0
360,1,78,0,0.793145," ","integrate(x^(5/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{168245} \, {\left(7315 \, B b^{3} x^{11} + 8855 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + 33649 \, {\left(B a^{2} b + A a b^{2}\right)} x^{7} + 24035 \, A a^{3} x^{3} + 15295 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/168245*(7315*B*b^3*x^11 + 8855*(3*B*a*b^2 + A*b^3)*x^9 + 33649*(B*a^2*b + A*a*b^2)*x^7 + 24035*A*a^3*x^3 + 15295*(B*a^3 + 3*A*a^2*b)*x^5)*sqrt(x)","A",0
361,1,78,0,1.279699," ","integrate(x^(3/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""fricas"")","\frac{2}{69615} \, {\left(3315 \, B b^{3} x^{10} + 4095 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{8} + 16065 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} + 13923 \, A a^{3} x^{2} + 7735 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/69615*(3315*B*b^3*x^10 + 4095*(3*B*a*b^2 + A*b^3)*x^8 + 16065*(B*a^2*b + A*a*b^2)*x^6 + 13923*A*a^3*x^2 + 7735*(B*a^3 + 3*A*a^2*b)*x^4)*sqrt(x)","A",0
362,1,76,0,0.893265," ","integrate((b*x^2+a)^3*(B*x^2+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, B b^{3} x^{9} + 1463 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{7} + 5985 \, {\left(B a^{2} b + A a b^{2}\right)} x^{5} + 7315 \, A a^{3} x + 3135 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/21945*(1155*B*b^3*x^9 + 1463*(3*B*a*b^2 + A*b^3)*x^7 + 5985*(B*a^2*b + A*a*b^2)*x^5 + 7315*A*a^3*x + 3135*(B*a^3 + 3*A*a^2*b)*x^3)*sqrt(x)","A",0
363,1,75,0,0.761051," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3315} \, {\left(195 \, B b^{3} x^{8} + 255 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 1105 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + 3315 \, A a^{3} + 663 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/3315*(195*B*b^3*x^8 + 255*(3*B*a*b^2 + A*b^3)*x^6 + 1105*(B*a^2*b + A*a*b^2)*x^4 + 3315*A*a^3 + 663*(B*a^3 + 3*A*a^2*b)*x^2)*sqrt(x)","A",0
364,1,75,0,1.030994," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, B b^{3} x^{8} + 105 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 495 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} - 1155 \, A a^{3} + 385 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)}}{1155 \, \sqrt{x}}"," ",0,"2/1155*(77*B*b^3*x^8 + 105*(3*B*a*b^2 + A*b^3)*x^6 + 495*(B*a^2*b + A*a*b^2)*x^4 - 1155*A*a^3 + 385*(B*a^3 + 3*A*a^2*b)*x^2)/sqrt(x)","A",0
365,1,75,0,1.017172," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45 \, B b^{3} x^{8} + 65 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 351 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} - 195 \, A a^{3} + 585 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)}}{585 \, x^{\frac{3}{2}}}"," ",0,"2/585*(45*B*b^3*x^8 + 65*(3*B*a*b^2 + A*b^3)*x^6 + 351*(B*a^2*b + A*a*b^2)*x^4 - 195*A*a^3 + 585*(B*a^3 + 3*A*a^2*b)*x^2)/x^(3/2)","A",0
366,1,75,0,1.178762," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{3} x^{8} + 55 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 385 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} - 77 \, A a^{3} - 385 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)}}{385 \, x^{\frac{5}{2}}}"," ",0,"2/385*(35*B*b^3*x^8 + 55*(3*B*a*b^2 + A*b^3)*x^6 + 385*(B*a^2*b + A*a*b^2)*x^4 - 77*A*a^3 - 385*(B*a^3 + 3*A*a^2*b)*x^2)/x^(5/2)","A",0
367,1,714,0,0.990285," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\frac{180 \, b^{3} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{6} \sqrt{-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}} + {\left(B^{2} a^{4} - 2 \, A B a^{3} b + A^{2} a^{2} b^{2}\right)} x} b^{10} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{3}{4}} + {\left(B a^{2} b^{10} - A a b^{11}\right)} \sqrt{x} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{3}{4}}}{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}\right) + 45 \, b^{3} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{1}{4}} - {\left(B a^{2} - A a b\right)} \sqrt{x}\right) - 45 \, b^{3} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{B^{4} a^{9} - 4 \, A B^{3} a^{8} b + 6 \, A^{2} B^{2} a^{7} b^{2} - 4 \, A^{3} B a^{6} b^{3} + A^{4} a^{5} b^{4}}{b^{13}}\right)^{\frac{1}{4}} - {\left(B a^{2} - A a b\right)} \sqrt{x}\right) + 4 \, {\left(5 \, B b^{2} x^{4} + 45 \, B a^{2} - 45 \, A a b - 9 \, {\left(B a b - A b^{2}\right)} x^{2}\right)} \sqrt{x}}{90 \, b^{3}}"," ",0,"1/90*(180*b^3*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(1/4)*arctan((sqrt(b^6*sqrt(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13) + (B^2*a^4 - 2*A*B*a^3*b + A^2*a^2*b^2)*x)*b^10*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(3/4) + (B*a^2*b^10 - A*a*b^11)*sqrt(x)*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(3/4))/(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)) + 45*b^3*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(1/4)*log(b^3*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(1/4) - (B*a^2 - A*a*b)*sqrt(x)) - 45*b^3*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(1/4)*log(-b^3*(-(B^4*a^9 - 4*A*B^3*a^8*b + 6*A^2*B^2*a^7*b^2 - 4*A^3*B*a^6*b^3 + A^4*a^5*b^4)/b^13)^(1/4) - (B*a^2 - A*a*b)*sqrt(x)) + 4*(5*B*b^2*x^4 + 45*B*a^2 - 45*A*a*b - 9*(B*a*b - A*b^2)*x^2)*sqrt(x))/b^3","B",0
368,1,899,0,0.933122," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","\frac{84 \, b^{2} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{10} - 6 \, A B^{5} a^{9} b + 15 \, A^{2} B^{4} a^{8} b^{2} - 20 \, A^{3} B^{3} a^{7} b^{3} + 15 \, A^{4} B^{2} a^{6} b^{4} - 6 \, A^{5} B a^{5} b^{5} + A^{6} a^{4} b^{6}\right)} x - {\left(B^{4} a^{7} b^{5} - 4 \, A B^{3} a^{6} b^{6} + 6 \, A^{2} B^{2} a^{5} b^{7} - 4 \, A^{3} B a^{4} b^{8} + A^{4} a^{3} b^{9}\right)} \sqrt{-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}}} b^{3} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{5} b^{3} - 3 \, A B^{2} a^{4} b^{4} + 3 \, A^{2} B a^{3} b^{5} - A^{3} a^{2} b^{6}\right)} \sqrt{x} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{1}{4}}}{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}\right) - 21 \, b^{2} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{1}{4}} \log\left(b^{8} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{5} - 3 \, A B^{2} a^{4} b + 3 \, A^{2} B a^{3} b^{2} - A^{3} a^{2} b^{3}\right)} \sqrt{x}\right) + 21 \, b^{2} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{1}{4}} \log\left(-b^{8} \left(-\frac{B^{4} a^{7} - 4 \, A B^{3} a^{6} b + 6 \, A^{2} B^{2} a^{5} b^{2} - 4 \, A^{3} B a^{4} b^{3} + A^{4} a^{3} b^{4}}{b^{11}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{5} - 3 \, A B^{2} a^{4} b + 3 \, A^{2} B a^{3} b^{2} - A^{3} a^{2} b^{3}\right)} \sqrt{x}\right) + 4 \, {\left(3 \, B b x^{3} - 7 \, {\left(B a - A b\right)} x\right)} \sqrt{x}}{42 \, b^{2}}"," ",0,"1/42*(84*b^2*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(1/4)*arctan((sqrt((B^6*a^10 - 6*A*B^5*a^9*b + 15*A^2*B^4*a^8*b^2 - 20*A^3*B^3*a^7*b^3 + 15*A^4*B^2*a^6*b^4 - 6*A^5*B*a^5*b^5 + A^6*a^4*b^6)*x - (B^4*a^7*b^5 - 4*A*B^3*a^6*b^6 + 6*A^2*B^2*a^5*b^7 - 4*A^3*B*a^4*b^8 + A^4*a^3*b^9)*sqrt(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11))*b^3*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(1/4) + (B^3*a^5*b^3 - 3*A*B^2*a^4*b^4 + 3*A^2*B*a^3*b^5 - A^3*a^2*b^6)*sqrt(x)*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(1/4))/(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)) - 21*b^2*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(1/4)*log(b^8*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(3/4) - (B^3*a^5 - 3*A*B^2*a^4*b + 3*A^2*B*a^3*b^2 - A^3*a^2*b^3)*sqrt(x)) + 21*b^2*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(1/4)*log(-b^8*(-(B^4*a^7 - 4*A*B^3*a^6*b + 6*A^2*B^2*a^5*b^2 - 4*A^3*B*a^4*b^3 + A^4*a^3*b^4)/b^11)^(3/4) - (B^3*a^5 - 3*A*B^2*a^4*b + 3*A^2*B*a^3*b^2 - A^3*a^2*b^3)*sqrt(x)) + 4*(3*B*b*x^3 - 7*(B*a - A*b)*x)*sqrt(x))/b^2","B",0
369,1,660,0,1.292433," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{20 \, b^{2} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{4} \sqrt{-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x} b^{7} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{3}{4}} + {\left(B a b^{7} - A b^{8}\right)} \sqrt{x} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{3}{4}}}{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}\right) + 5 \, b^{2} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{1}{4}} \log\left(b^{2} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) - 5 \, b^{2} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-b^{2} \left(-\frac{B^{4} a^{5} - 4 \, A B^{3} a^{4} b + 6 \, A^{2} B^{2} a^{3} b^{2} - 4 \, A^{3} B a^{2} b^{3} + A^{4} a b^{4}}{b^{9}}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) - 4 \, {\left(B b x^{2} - 5 \, B a + 5 \, A b\right)} \sqrt{x}}{10 \, b^{2}}"," ",0,"-1/10*(20*b^2*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(1/4)*arctan((sqrt(b^4*sqrt(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x)*b^7*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(3/4) + (B*a*b^7 - A*b^8)*sqrt(x)*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(3/4))/(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)) + 5*b^2*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(1/4)*log(b^2*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(1/4) - (B*a - A*b)*sqrt(x)) - 5*b^2*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(1/4)*log(-b^2*(-(B^4*a^5 - 4*A*B^3*a^4*b + 6*A^2*B^2*a^3*b^2 - 4*A^3*B*a^2*b^3 + A^4*a*b^4)/b^9)^(1/4) - (B*a - A*b)*sqrt(x)) - 4*(B*b*x^2 - 5*B*a + 5*A*b)*sqrt(x))/b^2","B",0
370,1,834,0,1.130704," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{4 \, B x^{\frac{3}{2}} - 12 \, b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)} x - {\left(B^{4} a^{5} b^{3} - 4 \, A B^{3} a^{4} b^{4} + 6 \, A^{2} B^{2} a^{3} b^{5} - 4 \, A^{3} B a^{2} b^{6} + A^{4} a b^{7}\right)} \sqrt{-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}}} b^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{3} b^{2} - 3 \, A B^{2} a^{2} b^{3} + 3 \, A^{2} B a b^{4} - A^{3} b^{5}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{1}{4}}}{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) + 3 \, b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{1}{4}} \log\left(a b^{5} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 3 \, A B^{2} a^{2} b + 3 \, A^{2} B a b^{2} - A^{3} b^{3}\right)} \sqrt{x}\right) - 3 \, b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{1}{4}} \log\left(-a b^{5} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a b^{7}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 3 \, A B^{2} a^{2} b + 3 \, A^{2} B a b^{2} - A^{3} b^{3}\right)} \sqrt{x}\right)}{6 \, b}"," ",0,"1/6*(4*B*x^(3/2) - 12*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(1/4)*arctan((sqrt((B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)*x - (B^4*a^5*b^3 - 4*A*B^3*a^4*b^4 + 6*A^2*B^2*a^3*b^5 - 4*A^3*B*a^2*b^6 + A^4*a*b^7)*sqrt(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7)))*b^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(1/4) + (B^3*a^3*b^2 - 3*A*B^2*a^2*b^3 + 3*A^2*B*a*b^4 - A^3*b^5)*sqrt(x)*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(1/4))/(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)) + 3*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(1/4)*log(a*b^5*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(3/4) - (B^3*a^3 - 3*A*B^2*a^2*b + 3*A^2*B*a*b^2 - A^3*b^3)*sqrt(x)) - 3*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(1/4)*log(-a*b^5*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a*b^7))^(3/4) - (B^3*a^3 - 3*A*B^2*a^2*b + 3*A^2*B*a*b^2 - A^3*b^3)*sqrt(x)))/b","B",0
371,1,645,0,0.821701," ","integrate((B*x^2+A)/(b*x^2+a)/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{2} b^{2} \sqrt{-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x} a^{2} b^{4} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{3}{4}} + {\left(B a^{3} b^{4} - A a^{2} b^{5}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{3}{4}}}{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) + b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(a b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) - b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} \log\left(-a b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{5}}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) + 4 \, B \sqrt{x}}{2 \, b}"," ",0,"1/2*(4*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(1/4)*arctan((sqrt(a^2*b^2*sqrt(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5)) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x)*a^2*b^4*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(3/4) + (B*a^3*b^4 - A*a^2*b^5)*sqrt(x)*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(3/4))/(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)) + b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(1/4)*log(a*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(1/4) - (B*a - A*b)*sqrt(x)) - b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(1/4)*log(-a*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^5))^(1/4) - (B*a - A*b)*sqrt(x)) + 4*B*sqrt(x))/b","B",0
372,1,843,0,1.127162," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{4 \, a x \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)} x - {\left(B^{4} a^{7} b - 4 \, A B^{3} a^{6} b^{2} + 6 \, A^{2} B^{2} a^{5} b^{3} - 4 \, A^{3} B a^{4} b^{4} + A^{4} a^{3} b^{5}\right)} \sqrt{-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}}} a b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{4} b - 3 \, A B^{2} a^{3} b^{2} + 3 \, A^{2} B a^{2} b^{3} - A^{3} a b^{4}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{1}{4}}}{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) - a x \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \log\left(a^{4} b^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 3 \, A B^{2} a^{2} b + 3 \, A^{2} B a b^{2} - A^{3} b^{3}\right)} \sqrt{x}\right) + a x \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{1}{4}} \log\left(-a^{4} b^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 3 \, A B^{2} a^{2} b + 3 \, A^{2} B a b^{2} - A^{3} b^{3}\right)} \sqrt{x}\right) - 4 \, A \sqrt{x}}{2 \, a x}"," ",0,"1/2*(4*a*x*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(1/4)*arctan((sqrt((B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)*x - (B^4*a^7*b - 4*A*B^3*a^6*b^2 + 6*A^2*B^2*a^5*b^3 - 4*A^3*B*a^4*b^4 + A^4*a^3*b^5)*sqrt(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3)))*a*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(1/4) + (B^3*a^4*b - 3*A*B^2*a^3*b^2 + 3*A^2*B*a^2*b^3 - A^3*a*b^4)*sqrt(x)*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(1/4))/(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)) - a*x*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(1/4)*log(a^4*b^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(3/4) - (B^3*a^3 - 3*A*B^2*a^2*b + 3*A^2*B*a*b^2 - A^3*b^3)*sqrt(x)) + a*x*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(1/4)*log(-a^4*b^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^3))^(3/4) - (B^3*a^3 - 3*A*B^2*a^2*b + 3*A^2*B*a*b^2 - A^3*b^3)*sqrt(x)) - 4*A*sqrt(x))/(a*x)","B",0
373,1,653,0,1.406164," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{12 \, a x^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{4} \sqrt{-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x} a^{5} b \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{3}{4}} + {\left(B a^{6} b - A a^{5} b^{2}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{3}{4}}}{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) + 3 \, a x^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{1}{4}} \log\left(a^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) - 3 \, a x^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{1}{4}} \log\left(-a^{2} \left(-\frac{B^{4} a^{4} - 4 \, A B^{3} a^{3} b + 6 \, A^{2} B^{2} a^{2} b^{2} - 4 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{7} b}\right)^{\frac{1}{4}} - {\left(B a - A b\right)} \sqrt{x}\right) + 4 \, A \sqrt{x}}{6 \, a x^{2}}"," ",0,"-1/6*(12*a*x^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(1/4)*arctan((sqrt(a^4*sqrt(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b)) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x)*a^5*b*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(3/4) + (B*a^6*b - A*a^5*b^2)*sqrt(x)*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(3/4))/(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)) + 3*a*x^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(1/4)*log(a^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(1/4) - (B*a - A*b)*sqrt(x)) - 3*a*x^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(1/4)*log(-a^2*(-(B^4*a^4 - 4*A*B^3*a^3*b + 6*A^2*B^2*a^2*b^2 - 4*A^3*B*a*b^3 + A^4*b^4)/(a^7*b))^(1/4) - (B*a - A*b)*sqrt(x)) + 4*A*sqrt(x))/(a*x^2)","B",0
374,1,883,0,1.037436," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{20 \, a^{2} x^{3} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{6} b^{2} - 6 \, A B^{5} a^{5} b^{3} + 15 \, A^{2} B^{4} a^{4} b^{4} - 20 \, A^{3} B^{3} a^{3} b^{5} + 15 \, A^{4} B^{2} a^{2} b^{6} - 6 \, A^{5} B a b^{7} + A^{6} b^{8}\right)} x - {\left(B^{4} a^{9} b - 4 \, A B^{3} a^{8} b^{2} + 6 \, A^{2} B^{2} a^{7} b^{3} - 4 \, A^{3} B a^{6} b^{4} + A^{4} a^{5} b^{5}\right)} \sqrt{-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}}} a^{2} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{5} b - 3 \, A B^{2} a^{4} b^{2} + 3 \, A^{2} B a^{3} b^{3} - A^{3} a^{2} b^{4}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{1}{4}}}{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}\right) - 5 \, a^{2} x^{3} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{1}{4}} \log\left(a^{7} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} b - 3 \, A B^{2} a^{2} b^{2} + 3 \, A^{2} B a b^{3} - A^{3} b^{4}\right)} \sqrt{x}\right) + 5 \, a^{2} x^{3} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{1}{4}} \log\left(-a^{7} \left(-\frac{B^{4} a^{4} b - 4 \, A B^{3} a^{3} b^{2} + 6 \, A^{2} B^{2} a^{2} b^{3} - 4 \, A^{3} B a b^{4} + A^{4} b^{5}}{a^{9}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} b - 3 \, A B^{2} a^{2} b^{2} + 3 \, A^{2} B a b^{3} - A^{3} b^{4}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(B a - A b\right)} x^{2} + A a\right)} \sqrt{x}}{10 \, a^{2} x^{3}}"," ",0,"-1/10*(20*a^2*x^3*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(1/4)*arctan((sqrt((B^6*a^6*b^2 - 6*A*B^5*a^5*b^3 + 15*A^2*B^4*a^4*b^4 - 20*A^3*B^3*a^3*b^5 + 15*A^4*B^2*a^2*b^6 - 6*A^5*B*a*b^7 + A^6*b^8)*x - (B^4*a^9*b - 4*A*B^3*a^8*b^2 + 6*A^2*B^2*a^7*b^3 - 4*A^3*B*a^6*b^4 + A^4*a^5*b^5)*sqrt(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9))*a^2*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(1/4) + (B^3*a^5*b - 3*A*B^2*a^4*b^2 + 3*A^2*B*a^3*b^3 - A^3*a^2*b^4)*sqrt(x)*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(1/4))/(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)) - 5*a^2*x^3*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(1/4)*log(a^7*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(3/4) - (B^3*a^3*b - 3*A*B^2*a^2*b^2 + 3*A^2*B*a*b^3 - A^3*b^4)*sqrt(x)) + 5*a^2*x^3*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(1/4)*log(-a^7*(-(B^4*a^4*b - 4*A*B^3*a^3*b^2 + 6*A^2*B^2*a^2*b^3 - 4*A^3*B*a*b^4 + A^4*b^5)/a^9)^(3/4) - (B^3*a^3*b - 3*A*B^2*a^2*b^2 + 3*A^2*B*a*b^3 - A^3*b^4)*sqrt(x)) + 4*(5*(B*a - A*b)*x^2 + A*a)*sqrt(x))/(a^2*x^3)","B",0
375,1,748,0,1.606375," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(b^{4} x^{2} + a b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{6} \sqrt{-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}} + {\left(81 \, B^{2} a^{2} - 90 \, A B a b + 25 \, A^{2} b^{2}\right)} x} b^{10} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{3}{4}} + {\left(9 \, B a b^{10} - 5 \, A b^{11}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{3}{4}}}{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}\right) + 5 \, {\left(b^{4} x^{2} + a b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{1}{4}} \log\left(b^{3} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{1}{4}} - {\left(9 \, B a - 5 \, A b\right)} \sqrt{x}\right) - 5 \, {\left(b^{4} x^{2} + a b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-b^{3} \left(-\frac{6561 \, B^{4} a^{5} - 14580 \, A B^{3} a^{4} b + 12150 \, A^{2} B^{2} a^{3} b^{2} - 4500 \, A^{3} B a^{2} b^{3} + 625 \, A^{4} a b^{4}}{b^{13}}\right)^{\frac{1}{4}} - {\left(9 \, B a - 5 \, A b\right)} \sqrt{x}\right) - 4 \, {\left(4 \, B b^{2} x^{4} - 45 \, B a^{2} + 25 \, A a b - 4 \, {\left(9 \, B a b - 5 \, A b^{2}\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"-1/40*(20*(b^4*x^2 + a*b^3)*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(1/4)*arctan((sqrt(b^6*sqrt(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13) + (81*B^2*a^2 - 90*A*B*a*b + 25*A^2*b^2)*x)*b^10*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(3/4) + (9*B*a*b^10 - 5*A*b^11)*sqrt(x)*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(3/4))/(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)) + 5*(b^4*x^2 + a*b^3)*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(1/4)*log(b^3*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(1/4) - (9*B*a - 5*A*b)*sqrt(x)) - 5*(b^4*x^2 + a*b^3)*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(1/4)*log(-b^3*(-(6561*B^4*a^5 - 14580*A*B^3*a^4*b + 12150*A^2*B^2*a^3*b^2 - 4500*A^3*B*a^2*b^3 + 625*A^4*a*b^4)/b^13)^(1/4) - (9*B*a - 5*A*b)*sqrt(x)) - 4*(4*B*b^2*x^4 - 45*B*a^2 + 25*A*a*b - 4*(9*B*a*b - 5*A*b^2)*x^2)*sqrt(x))/(b^4*x^2 + a*b^3)","B",0
376,1,925,0,1.450887," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(117649 \, B^{6} a^{6} - 302526 \, A B^{5} a^{5} b + 324135 \, A^{2} B^{4} a^{4} b^{2} - 185220 \, A^{3} B^{3} a^{3} b^{3} + 59535 \, A^{4} B^{2} a^{2} b^{4} - 10206 \, A^{5} B a b^{5} + 729 \, A^{6} b^{6}\right)} x - {\left(2401 \, B^{4} a^{5} b^{5} - 4116 \, A B^{3} a^{4} b^{6} + 2646 \, A^{2} B^{2} a^{3} b^{7} - 756 \, A^{3} B a^{2} b^{8} + 81 \, A^{4} a b^{9}\right)} \sqrt{-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}}} b^{3} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{1}{4}} + {\left(343 \, B^{3} a^{3} b^{3} - 441 \, A B^{2} a^{2} b^{4} + 189 \, A^{2} B a b^{5} - 27 \, A^{3} b^{6}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{1}{4}}}{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}\right) - 3 \, {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{1}{4}} \log\left(a b^{8} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{3}{4}} - {\left(343 \, B^{3} a^{3} - 441 \, A B^{2} a^{2} b + 189 \, A^{2} B a b^{2} - 27 \, A^{3} b^{3}\right)} \sqrt{x}\right) + 3 \, {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{1}{4}} \log\left(-a b^{8} \left(-\frac{2401 \, B^{4} a^{4} - 4116 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 756 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a b^{11}}\right)^{\frac{3}{4}} - {\left(343 \, B^{3} a^{3} - 441 \, A B^{2} a^{2} b + 189 \, A^{2} B a b^{2} - 27 \, A^{3} b^{3}\right)} \sqrt{x}\right) - 4 \, {\left(4 \, B b x^{3} + {\left(7 \, B a - 3 \, A b\right)} x\right)} \sqrt{x}}{24 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"-1/24*(12*(b^3*x^2 + a*b^2)*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(1/4)*arctan((sqrt((117649*B^6*a^6 - 302526*A*B^5*a^5*b + 324135*A^2*B^4*a^4*b^2 - 185220*A^3*B^3*a^3*b^3 + 59535*A^4*B^2*a^2*b^4 - 10206*A^5*B*a*b^5 + 729*A^6*b^6)*x - (2401*B^4*a^5*b^5 - 4116*A*B^3*a^4*b^6 + 2646*A^2*B^2*a^3*b^7 - 756*A^3*B*a^2*b^8 + 81*A^4*a*b^9)*sqrt(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11)))*b^3*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(1/4) + (343*B^3*a^3*b^3 - 441*A*B^2*a^2*b^4 + 189*A^2*B*a*b^5 - 27*A^3*b^6)*sqrt(x)*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(1/4))/(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)) - 3*(b^3*x^2 + a*b^2)*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(1/4)*log(a*b^8*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(3/4) - (343*B^3*a^3 - 441*A*B^2*a^2*b + 189*A^2*B*a*b^2 - 27*A^3*b^3)*sqrt(x)) + 3*(b^3*x^2 + a*b^2)*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(1/4)*log(-a*b^8*(-(2401*B^4*a^4 - 4116*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 756*A^3*B*a*b^3 + 81*A^4*b^4)/(a*b^11))^(3/4) - (343*B^3*a^3 - 441*A*B^2*a^2*b + 189*A^2*B*a*b^2 - 27*A^3*b^3)*sqrt(x)) - 4*(4*B*b*x^3 + (7*B*a - 3*A*b)*x)*sqrt(x))/(b^3*x^2 + a*b^2)","B",0
377,1,725,0,1.009359," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{2} b^{4} \sqrt{-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}} + {\left(25 \, B^{2} a^{2} - 10 \, A B a b + A^{2} b^{2}\right)} x} a^{2} b^{7} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{3}{4}} + {\left(5 \, B a^{3} b^{7} - A a^{2} b^{8}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{3}{4}}}{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) + {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(a b^{2} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{1}{4}} - {\left(5 \, B a - A b\right)} \sqrt{x}\right) - {\left(b^{3} x^{2} + a b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{1}{4}} \log\left(-a b^{2} \left(-\frac{625 \, B^{4} a^{4} - 500 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 20 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{9}}\right)^{\frac{1}{4}} - {\left(5 \, B a - A b\right)} \sqrt{x}\right) + 4 \, {\left(4 \, B b x^{2} + 5 \, B a - A b\right)} \sqrt{x}}{8 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/8*(4*(b^3*x^2 + a*b^2)*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(1/4)*arctan((sqrt(a^2*b^4*sqrt(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9)) + (25*B^2*a^2 - 10*A*B*a*b + A^2*b^2)*x)*a^2*b^7*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(3/4) + (5*B*a^3*b^7 - A*a^2*b^8)*sqrt(x)*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(3/4))/(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)) + (b^3*x^2 + a*b^2)*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(1/4)*log(a*b^2*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(1/4) - (5*B*a - A*b)*sqrt(x)) - (b^3*x^2 + a*b^2)*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(1/4)*log(-a*b^2*(-(625*B^4*a^4 - 500*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 20*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^9))^(1/4) - (5*B*a - A*b)*sqrt(x)) + 4*(4*B*b*x^2 + 5*B*a - A*b)*sqrt(x))/(b^3*x^2 + a*b^2)","B",0
378,1,912,0,1.208187," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(B a - A b\right)} x^{\frac{3}{2}} + 4 \, {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, B^{6} a^{6} + 1458 \, A B^{5} a^{5} b + 1215 \, A^{2} B^{4} a^{4} b^{2} + 540 \, A^{3} B^{3} a^{3} b^{3} + 135 \, A^{4} B^{2} a^{2} b^{4} + 18 \, A^{5} B a b^{5} + A^{6} b^{6}\right)} x - {\left(81 \, B^{4} a^{7} b^{3} + 108 \, A B^{3} a^{6} b^{4} + 54 \, A^{2} B^{2} a^{5} b^{5} + 12 \, A^{3} B a^{4} b^{6} + A^{4} a^{3} b^{7}\right)} \sqrt{-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}}} a b^{2} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{1}{4}} - {\left(27 \, B^{3} a^{4} b^{2} + 27 \, A B^{2} a^{3} b^{3} + 9 \, A^{2} B a^{2} b^{4} + A^{3} a b^{5}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{1}{4}}}{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) - {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \log\left(a^{4} b^{5} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} a^{3} + 27 \, A B^{2} a^{2} b + 9 \, A^{2} B a b^{2} + A^{3} b^{3}\right)} \sqrt{x}\right) + {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{1}{4}} \log\left(-a^{4} b^{5} \left(-\frac{81 \, B^{4} a^{4} + 108 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 12 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} a^{3} + 27 \, A B^{2} a^{2} b + 9 \, A^{2} B a b^{2} + A^{3} b^{3}\right)} \sqrt{x}\right)}{8 \, {\left(a b^{2} x^{2} + a^{2} b\right)}}"," ",0,"-1/8*(4*(B*a - A*b)*x^(3/2) + 4*(a*b^2*x^2 + a^2*b)*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(1/4)*arctan((sqrt((729*B^6*a^6 + 1458*A*B^5*a^5*b + 1215*A^2*B^4*a^4*b^2 + 540*A^3*B^3*a^3*b^3 + 135*A^4*B^2*a^2*b^4 + 18*A^5*B*a*b^5 + A^6*b^6)*x - (81*B^4*a^7*b^3 + 108*A*B^3*a^6*b^4 + 54*A^2*B^2*a^5*b^5 + 12*A^3*B*a^4*b^6 + A^4*a^3*b^7)*sqrt(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7)))*a*b^2*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(1/4) - (27*B^3*a^4*b^2 + 27*A*B^2*a^3*b^3 + 9*A^2*B*a^2*b^4 + A^3*a*b^5)*sqrt(x)*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(1/4))/(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)) - (a*b^2*x^2 + a^2*b)*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(1/4)*log(a^4*b^5*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(3/4) + (27*B^3*a^3 + 27*A*B^2*a^2*b + 9*A^2*B*a*b^2 + A^3*b^3)*sqrt(x)) + (a*b^2*x^2 + a^2*b)*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(1/4)*log(-a^4*b^5*(-(81*B^4*a^4 + 108*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 12*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^7))^(3/4) + (27*B^3*a^3 + 27*A*B^2*a^2*b + 9*A^2*B*a*b^2 + A^3*b^3)*sqrt(x)))/(a*b^2*x^2 + a^2*b)","B",0
379,1,717,0,1.151526," ","integrate((B*x^2+A)/(b*x^2+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{4} b^{2} \sqrt{-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}} + {\left(B^{2} a^{2} + 6 \, A B a b + 9 \, A^{2} b^{2}\right)} x} a^{5} b^{4} \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{3}{4}} - {\left(B a^{6} b^{4} + 3 \, A a^{5} b^{5}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{3}{4}}}{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}\right) + {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(a^{2} b \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + {\left(B a + 3 \, A b\right)} \sqrt{x}\right) - {\left(a b^{2} x^{2} + a^{2} b\right)} \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} \log\left(-a^{2} b \left(-\frac{B^{4} a^{4} + 12 \, A B^{3} a^{3} b + 54 \, A^{2} B^{2} a^{2} b^{2} + 108 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{5}}\right)^{\frac{1}{4}} + {\left(B a + 3 \, A b\right)} \sqrt{x}\right) - 4 \, {\left(B a - A b\right)} \sqrt{x}}{8 \, {\left(a b^{2} x^{2} + a^{2} b\right)}}"," ",0,"1/8*(4*(a*b^2*x^2 + a^2*b)*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(1/4)*arctan((sqrt(a^4*b^2*sqrt(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5)) + (B^2*a^2 + 6*A*B*a*b + 9*A^2*b^2)*x)*a^5*b^4*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(3/4) - (B*a^6*b^4 + 3*A*a^5*b^5)*sqrt(x)*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(3/4))/(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)) + (a*b^2*x^2 + a^2*b)*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(1/4)*log(a^2*b*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(1/4) + (B*a + 3*A*b)*sqrt(x)) - (a*b^2*x^2 + a^2*b)*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(1/4)*log(-a^2*b*(-(B^4*a^4 + 12*A*B^3*a^3*b + 54*A^2*B^2*a^2*b^2 + 108*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^5))^(1/4) + (B*a + 3*A*b)*sqrt(x)) - 4*(B*a - A*b)*sqrt(x))/(a*b^2*x^2 + a^2*b)","B",0
380,1,920,0,1.054251," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} b x^{3} + a^{3} x\right)} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{6} - 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} - 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} - 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)} x - {\left(B^{4} a^{9} b - 20 \, A B^{3} a^{8} b^{2} + 150 \, A^{2} B^{2} a^{7} b^{3} - 500 \, A^{3} B a^{6} b^{4} + 625 \, A^{4} a^{5} b^{5}\right)} \sqrt{-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}}} a^{2} b \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{5} b - 15 \, A B^{2} a^{4} b^{2} + 75 \, A^{2} B a^{3} b^{3} - 125 \, A^{3} a^{2} b^{4}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{1}{4}}}{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}\right) - {\left(a^{2} b x^{3} + a^{3} x\right)} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \log\left(a^{7} b^{2} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 15 \, A B^{2} a^{2} b + 75 \, A^{2} B a b^{2} - 125 \, A^{3} b^{3}\right)} \sqrt{x}\right) + {\left(a^{2} b x^{3} + a^{3} x\right)} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{1}{4}} \log\left(-a^{7} b^{2} \left(-\frac{B^{4} a^{4} - 20 \, A B^{3} a^{3} b + 150 \, A^{2} B^{2} a^{2} b^{2} - 500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{3}}\right)^{\frac{3}{4}} - {\left(B^{3} a^{3} - 15 \, A B^{2} a^{2} b + 75 \, A^{2} B a b^{2} - 125 \, A^{3} b^{3}\right)} \sqrt{x}\right) + 4 \, {\left({\left(B a - 5 \, A b\right)} x^{2} - 4 \, A a\right)} \sqrt{x}}{8 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}"," ",0,"1/8*(4*(a^2*b*x^3 + a^3*x)*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(1/4)*arctan((sqrt((B^6*a^6 - 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 - 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 - 18750*A^5*B*a*b^5 + 15625*A^6*b^6)*x - (B^4*a^9*b - 20*A*B^3*a^8*b^2 + 150*A^2*B^2*a^7*b^3 - 500*A^3*B*a^6*b^4 + 625*A^4*a^5*b^5)*sqrt(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3)))*a^2*b*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(1/4) + (B^3*a^5*b - 15*A*B^2*a^4*b^2 + 75*A^2*B*a^3*b^3 - 125*A^3*a^2*b^4)*sqrt(x)*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(1/4))/(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)) - (a^2*b*x^3 + a^3*x)*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(1/4)*log(a^7*b^2*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(3/4) - (B^3*a^3 - 15*A*B^2*a^2*b + 75*A^2*B*a*b^2 - 125*A^3*b^3)*sqrt(x)) + (a^2*b*x^3 + a^3*x)*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(1/4)*log(-a^7*b^2*(-(B^4*a^4 - 20*A*B^3*a^3*b + 150*A^2*B^2*a^2*b^2 - 500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^3))^(3/4) - (B^3*a^3 - 15*A*B^2*a^2*b + 75*A^2*B*a*b^2 - 125*A^3*b^3)*sqrt(x)) + 4*((B*a - 5*A*b)*x^2 - 4*A*a)*sqrt(x))/(a^2*b*x^3 + a^3*x)","B",0
381,1,741,0,1.603428," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{6} \sqrt{-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}} + {\left(9 \, B^{2} a^{2} - 42 \, A B a b + 49 \, A^{2} b^{2}\right)} x} a^{8} b \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{3}{4}} + {\left(3 \, B a^{9} b - 7 \, A a^{8} b^{2}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{3}{4}}}{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}\right) + 3 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{1}{4}} \log\left(a^{3} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{1}{4}} - {\left(3 \, B a - 7 \, A b\right)} \sqrt{x}\right) - 3 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{1}{4}} \log\left(-a^{3} \left(-\frac{81 \, B^{4} a^{4} - 756 \, A B^{3} a^{3} b + 2646 \, A^{2} B^{2} a^{2} b^{2} - 4116 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b}\right)^{\frac{1}{4}} - {\left(3 \, B a - 7 \, A b\right)} \sqrt{x}\right) - 4 \, {\left({\left(3 \, B a - 7 \, A b\right)} x^{2} - 4 \, A a\right)} \sqrt{x}}{24 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}}"," ",0,"-1/24*(12*(a^2*b*x^4 + a^3*x^2)*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(1/4)*arctan((sqrt(a^6*sqrt(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b)) + (9*B^2*a^2 - 42*A*B*a*b + 49*A^2*b^2)*x)*a^8*b*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(3/4) + (3*B*a^9*b - 7*A*a^8*b^2)*sqrt(x)*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(3/4))/(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)) + 3*(a^2*b*x^4 + a^3*x^2)*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(1/4)*log(a^3*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(1/4) - (3*B*a - 7*A*b)*sqrt(x)) - 3*(a^2*b*x^4 + a^3*x^2)*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(1/4)*log(-a^3*(-(81*B^4*a^4 - 756*A*B^3*a^3*b + 2646*A^2*B^2*a^2*b^2 - 4116*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b))^(1/4) - (3*B*a - 7*A*b)*sqrt(x)) - 4*((3*B*a - 7*A*b)*x^2 - 4*A*a)*sqrt(x))/(a^2*b*x^4 + a^3*x^2)","B",0
382,1,974,0,1.436634," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, B^{6} a^{6} b^{2} - 168750 \, A B^{5} a^{5} b^{3} + 759375 \, A^{2} B^{4} a^{4} b^{4} - 1822500 \, A^{3} B^{3} a^{3} b^{5} + 2460375 \, A^{4} B^{2} a^{2} b^{6} - 1771470 \, A^{5} B a b^{7} + 531441 \, A^{6} b^{8}\right)} x - {\left(625 \, B^{4} a^{11} b - 4500 \, A B^{3} a^{10} b^{2} + 12150 \, A^{2} B^{2} a^{9} b^{3} - 14580 \, A^{3} B a^{8} b^{4} + 6561 \, A^{4} a^{7} b^{5}\right)} \sqrt{-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}}} a^{3} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{1}{4}} + {\left(125 \, B^{3} a^{6} b - 675 \, A B^{2} a^{5} b^{2} + 1215 \, A^{2} B a^{4} b^{3} - 729 \, A^{3} a^{3} b^{4}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{1}{4}}}{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}\right) - 5 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{1}{4}} \log\left(a^{10} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{3}{4}} - {\left(125 \, B^{3} a^{3} b - 675 \, A B^{2} a^{2} b^{2} + 1215 \, A^{2} B a b^{3} - 729 \, A^{3} b^{4}\right)} \sqrt{x}\right) + 5 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{1}{4}} \log\left(-a^{10} \left(-\frac{625 \, B^{4} a^{4} b - 4500 \, A B^{3} a^{3} b^{2} + 12150 \, A^{2} B^{2} a^{2} b^{3} - 14580 \, A^{3} B a b^{4} + 6561 \, A^{4} b^{5}}{a^{13}}\right)^{\frac{3}{4}} - {\left(125 \, B^{3} a^{3} b - 675 \, A B^{2} a^{2} b^{2} + 1215 \, A^{2} B a b^{3} - 729 \, A^{3} b^{4}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(5 \, B a b - 9 \, A b^{2}\right)} x^{4} + 4 \, A a^{2} + 4 \, {\left(5 \, B a^{2} - 9 \, A a b\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}"," ",0,"-1/40*(20*(a^3*b*x^5 + a^4*x^3)*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(1/4)*arctan((sqrt((15625*B^6*a^6*b^2 - 168750*A*B^5*a^5*b^3 + 759375*A^2*B^4*a^4*b^4 - 1822500*A^3*B^3*a^3*b^5 + 2460375*A^4*B^2*a^2*b^6 - 1771470*A^5*B*a*b^7 + 531441*A^6*b^8)*x - (625*B^4*a^11*b - 4500*A*B^3*a^10*b^2 + 12150*A^2*B^2*a^9*b^3 - 14580*A^3*B*a^8*b^4 + 6561*A^4*a^7*b^5)*sqrt(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13))*a^3*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(1/4) + (125*B^3*a^6*b - 675*A*B^2*a^5*b^2 + 1215*A^2*B*a^4*b^3 - 729*A^3*a^3*b^4)*sqrt(x)*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(1/4))/(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)) - 5*(a^3*b*x^5 + a^4*x^3)*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(1/4)*log(a^10*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(3/4) - (125*B^3*a^3*b - 675*A*B^2*a^2*b^2 + 1215*A^2*B*a*b^3 - 729*A^3*b^4)*sqrt(x)) + 5*(a^3*b*x^5 + a^4*x^3)*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(1/4)*log(-a^10*(-(625*B^4*a^4*b - 4500*A*B^3*a^3*b^2 + 12150*A^2*B^2*a^2*b^3 - 14580*A^3*B*a*b^4 + 6561*A^4*b^5)/a^13)^(3/4) - (125*B^3*a^3*b - 675*A*B^2*a^2*b^2 + 1215*A^2*B*a*b^3 - 729*A^3*b^4)*sqrt(x)) + 4*(5*(5*B*a*b - 9*A*b^2)*x^4 + 4*A*a^2 + 4*(5*B*a^2 - 9*A*a*b)*x^2)*sqrt(x))/(a^3*b*x^5 + a^4*x^3)","B",0
383,1,793,0,1.171422," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{2} b^{6} \sqrt{-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}} + {\left(81 \, B^{2} a^{2} - 18 \, A B a b + A^{2} b^{2}\right)} x} a^{2} b^{10} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{3}{4}} + {\left(9 \, B a^{3} b^{10} - A a^{2} b^{11}\right)} \sqrt{x} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{3}{4}}}{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) + 5 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(5 \, a b^{3} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - 5 \, {\left(9 \, B a - A b\right)} \sqrt{x}\right) - 5 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(-5 \, a b^{3} \left(-\frac{6561 \, B^{4} a^{4} - 2916 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 36 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - 5 \, {\left(9 \, B a - A b\right)} \sqrt{x}\right) + 4 \, {\left(32 \, B b^{2} x^{4} + 45 \, B a^{2} - 5 \, A a b + 9 \, {\left(9 \, B a b - A b^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/64*(20*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(1/4)*arctan((sqrt(a^2*b^6*sqrt(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13)) + (81*B^2*a^2 - 18*A*B*a*b + A^2*b^2)*x)*a^2*b^10*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(3/4) + (9*B*a^3*b^10 - A*a^2*b^11)*sqrt(x)*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(3/4))/(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)) + 5*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(1/4)*log(5*a*b^3*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(1/4) - 5*(9*B*a - A*b)*sqrt(x)) - 5*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(1/4)*log(-5*a*b^3*(-(6561*B^4*a^4 - 2916*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 36*A^3*B*a*b^3 + A^4*b^4)/(a^3*b^13))^(1/4) - 5*(9*B*a - A*b)*sqrt(x)) + 4*(32*B*b^2*x^4 + 45*B*a^2 - 5*A*a*b + 9*(9*B*a*b - A*b^2)*x^2)*sqrt(x))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","B",0
384,1,990,0,1.307213," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(117649 \, B^{6} a^{6} + 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} + 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} + 42 \, A^{5} B a b^{5} + A^{6} b^{6}\right)} x - {\left(2401 \, B^{4} a^{7} b^{5} + 1372 \, A B^{3} a^{6} b^{6} + 294 \, A^{2} B^{2} a^{5} b^{7} + 28 \, A^{3} B a^{4} b^{8} + A^{4} a^{3} b^{9}\right)} \sqrt{-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}}} a b^{3} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{1}{4}} - {\left(343 \, B^{3} a^{4} b^{3} + 147 \, A B^{2} a^{3} b^{4} + 21 \, A^{2} B a^{2} b^{5} + A^{3} a b^{6}\right)} \sqrt{x} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{1}{4}}}{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}\right) - 3 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(27 \, a^{4} b^{8} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{3}{4}} + 27 \, {\left(343 \, B^{3} a^{3} + 147 \, A B^{2} a^{2} b + 21 \, A^{2} B a b^{2} + A^{3} b^{3}\right)} \sqrt{x}\right) + 3 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(-27 \, a^{4} b^{8} \left(-\frac{2401 \, B^{4} a^{4} + 1372 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 28 \, A^{3} B a b^{3} + A^{4} b^{4}}{a^{5} b^{11}}\right)^{\frac{3}{4}} + 27 \, {\left(343 \, B^{3} a^{3} + 147 \, A B^{2} a^{2} b + 21 \, A^{2} B a b^{2} + A^{3} b^{3}\right)} \sqrt{x}\right) + 4 \, {\left({\left(11 \, B a b - 3 \, A b^{2}\right)} x^{3} + {\left(7 \, B a^{2} + A a b\right)} x\right)} \sqrt{x}}{64 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"-1/64*(12*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(1/4)*arctan((sqrt((117649*B^6*a^6 + 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 + 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 + 42*A^5*B*a*b^5 + A^6*b^6)*x - (2401*B^4*a^7*b^5 + 1372*A*B^3*a^6*b^6 + 294*A^2*B^2*a^5*b^7 + 28*A^3*B*a^4*b^8 + A^4*a^3*b^9)*sqrt(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11)))*a*b^3*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(1/4) - (343*B^3*a^4*b^3 + 147*A*B^2*a^3*b^4 + 21*A^2*B*a^2*b^5 + A^3*a*b^6)*sqrt(x)*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(1/4))/(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)) - 3*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(1/4)*log(27*a^4*b^8*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(3/4) + 27*(343*B^3*a^3 + 147*A*B^2*a^2*b + 21*A^2*B*a*b^2 + A^3*b^3)*sqrt(x)) + 3*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(1/4)*log(-27*a^4*b^8*(-(2401*B^4*a^4 + 1372*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 28*A^3*B*a*b^3 + A^4*b^4)/(a^5*b^11))^(3/4) + 27*(343*B^3*a^3 + 147*A*B^2*a^2*b + 21*A^2*B*a*b^2 + A^3*b^3)*sqrt(x)) + 4*((11*B*a*b - 3*A*b^2)*x^3 + (7*B*a^2 + A*a*b)*x)*sqrt(x))/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)","B",0
385,1,806,0,1.203131," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{4} b^{4} \sqrt{-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}} + {\left(25 \, B^{2} a^{2} + 30 \, A B a b + 9 \, A^{2} b^{2}\right)} x} a^{5} b^{7} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{3}{4}} - {\left(5 \, B a^{6} b^{7} + 3 \, A a^{5} b^{8}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{3}{4}}}{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}\right) + {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(a^{2} b^{2} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{1}{4}} + {\left(5 \, B a + 3 \, A b\right)} \sqrt{x}\right) - {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(-a^{2} b^{2} \left(-\frac{625 \, B^{4} a^{4} + 1500 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 540 \, A^{3} B a b^{3} + 81 \, A^{4} b^{4}}{a^{7} b^{9}}\right)^{\frac{1}{4}} + {\left(5 \, B a + 3 \, A b\right)} \sqrt{x}\right) - 4 \, {\left(5 \, B a^{2} + 3 \, A a b + {\left(9 \, B a b - A b^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"1/64*(4*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(1/4)*arctan((sqrt(a^4*b^4*sqrt(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9)) + (25*B^2*a^2 + 30*A*B*a*b + 9*A^2*b^2)*x)*a^5*b^7*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(3/4) - (5*B*a^6*b^7 + 3*A*a^5*b^8)*sqrt(x)*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(3/4))/(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)) + (a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(1/4)*log(a^2*b^2*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(1/4) + (5*B*a + 3*A*b)*sqrt(x)) - (a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(1/4)*log(-a^2*b^2*(-(625*B^4*a^4 + 1500*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 540*A^3*B*a*b^3 + 81*A^4*b^4)/(a^7*b^9))^(1/4) + (5*B*a + 3*A*b)*sqrt(x)) - 4*(5*B*a^2 + 3*A*a*b + (9*B*a*b - A*b^2)*x^2)*sqrt(x))/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)","B",0
386,1,1005,0,0.872809," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, B^{6} a^{6} + 7290 \, A B^{5} a^{5} b + 30375 \, A^{2} B^{4} a^{4} b^{2} + 67500 \, A^{3} B^{3} a^{3} b^{3} + 84375 \, A^{4} B^{2} a^{2} b^{4} + 56250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)} x - {\left(81 \, B^{4} a^{9} b^{3} + 540 \, A B^{3} a^{8} b^{4} + 1350 \, A^{2} B^{2} a^{7} b^{5} + 1500 \, A^{3} B a^{6} b^{6} + 625 \, A^{4} a^{5} b^{7}\right)} \sqrt{-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}}} a^{2} b^{2} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{1}{4}} - {\left(27 \, B^{3} a^{5} b^{2} + 135 \, A B^{2} a^{4} b^{3} + 225 \, A^{2} B a^{3} b^{4} + 125 \, A^{3} a^{2} b^{5}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{1}{4}}}{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}\right) - {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(a^{7} b^{5} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} a^{3} + 135 \, A B^{2} a^{2} b + 225 \, A^{2} B a b^{2} + 125 \, A^{3} b^{3}\right)} \sqrt{x}\right) + {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(-a^{7} b^{5} \left(-\frac{81 \, B^{4} a^{4} + 540 \, A B^{3} a^{3} b + 1350 \, A^{2} B^{2} a^{2} b^{2} + 1500 \, A^{3} B a b^{3} + 625 \, A^{4} b^{4}}{a^{9} b^{7}}\right)^{\frac{3}{4}} + {\left(27 \, B^{3} a^{3} + 135 \, A B^{2} a^{2} b + 225 \, A^{2} B a b^{2} + 125 \, A^{3} b^{3}\right)} \sqrt{x}\right) - 4 \, {\left({\left(3 \, B a b + 5 \, A b^{2}\right)} x^{3} - {\left(B a^{2} - 9 \, A a b\right)} x\right)} \sqrt{x}}{64 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}"," ",0,"-1/64*(4*(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(1/4)*arctan((sqrt((729*B^6*a^6 + 7290*A*B^5*a^5*b + 30375*A^2*B^4*a^4*b^2 + 67500*A^3*B^3*a^3*b^3 + 84375*A^4*B^2*a^2*b^4 + 56250*A^5*B*a*b^5 + 15625*A^6*b^6)*x - (81*B^4*a^9*b^3 + 540*A*B^3*a^8*b^4 + 1350*A^2*B^2*a^7*b^5 + 1500*A^3*B*a^6*b^6 + 625*A^4*a^5*b^7)*sqrt(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7)))*a^2*b^2*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(1/4) - (27*B^3*a^5*b^2 + 135*A*B^2*a^4*b^3 + 225*A^2*B*a^3*b^4 + 125*A^3*a^2*b^5)*sqrt(x)*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(1/4))/(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)) - (a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(1/4)*log(a^7*b^5*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(3/4) + (27*B^3*a^3 + 135*A*B^2*a^2*b + 225*A^2*B*a*b^2 + 125*A^3*b^3)*sqrt(x)) + (a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(1/4)*log(-a^7*b^5*(-(81*B^4*a^4 + 540*A*B^3*a^3*b + 1350*A^2*B^2*a^2*b^2 + 1500*A^3*B*a*b^3 + 625*A^4*b^4)/(a^9*b^7))^(3/4) + (27*B^3*a^3 + 135*A*B^2*a^2*b + 225*A^2*B*a*b^2 + 125*A^3*b^3)*sqrt(x)) - 4*((3*B*a*b + 5*A*b^2)*x^3 - (B*a^2 - 9*A*a*b)*x)*sqrt(x))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)","B",0
387,1,793,0,0.606639," ","integrate((B*x^2+A)/(b*x^2+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{12 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{6} b^{2} \sqrt{-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}} + {\left(B^{2} a^{2} + 14 \, A B a b + 49 \, A^{2} b^{2}\right)} x} a^{8} b^{4} \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{3}{4}} - {\left(B a^{9} b^{4} + 7 \, A a^{8} b^{5}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{3}{4}}}{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}\right) + 3 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(3 \, a^{3} b \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(B a + 7 \, A b\right)} \sqrt{x}\right) - 3 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)} \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{3} b \left(-\frac{B^{4} a^{4} + 28 \, A B^{3} a^{3} b + 294 \, A^{2} B^{2} a^{2} b^{2} + 1372 \, A^{3} B a b^{3} + 2401 \, A^{4} b^{4}}{a^{11} b^{5}}\right)^{\frac{1}{4}} + 3 \, {\left(B a + 7 \, A b\right)} \sqrt{x}\right) - 4 \, {\left(3 \, B a^{2} - 11 \, A a b - {\left(B a b + 7 \, A b^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}"," ",0,"1/64*(12*(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(1/4)*arctan((sqrt(a^6*b^2*sqrt(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5)) + (B^2*a^2 + 14*A*B*a*b + 49*A^2*b^2)*x)*a^8*b^4*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(3/4) - (B*a^9*b^4 + 7*A*a^8*b^5)*sqrt(x)*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(3/4))/(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)) + 3*(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(1/4)*log(3*a^3*b*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(1/4) + 3*(B*a + 7*A*b)*sqrt(x)) - 3*(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(1/4)*log(-3*a^3*b*(-(B^4*a^4 + 28*A*B^3*a^3*b + 294*A^2*B^2*a^2*b^2 + 1372*A^3*B*a*b^3 + 2401*A^4*b^4)/(a^11*b^5))^(1/4) + 3*(B*a + 7*A*b)*sqrt(x)) - 4*(3*B*a^2 - 11*A*a*b - (B*a*b + 7*A*b^2)*x^2)*sqrt(x))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)","B",0
388,1,988,0,0.822949," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(B^{6} a^{6} - 54 \, A B^{5} a^{5} b + 1215 \, A^{2} B^{4} a^{4} b^{2} - 14580 \, A^{3} B^{3} a^{3} b^{3} + 98415 \, A^{4} B^{2} a^{2} b^{4} - 354294 \, A^{5} B a b^{5} + 531441 \, A^{6} b^{6}\right)} x - {\left(B^{4} a^{11} b - 36 \, A B^{3} a^{10} b^{2} + 486 \, A^{2} B^{2} a^{9} b^{3} - 2916 \, A^{3} B a^{8} b^{4} + 6561 \, A^{4} a^{7} b^{5}\right)} \sqrt{-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}}} a^{3} b \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{1}{4}} + {\left(B^{3} a^{6} b - 27 \, A B^{2} a^{5} b^{2} + 243 \, A^{2} B a^{4} b^{3} - 729 \, A^{3} a^{3} b^{4}\right)} \sqrt{x} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{1}{4}}}{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}\right) - 5 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(125 \, a^{10} b^{2} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{3}{4}} - 125 \, {\left(B^{3} a^{3} - 27 \, A B^{2} a^{2} b + 243 \, A^{2} B a b^{2} - 729 \, A^{3} b^{3}\right)} \sqrt{x}\right) + 5 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(-125 \, a^{10} b^{2} \left(-\frac{B^{4} a^{4} - 36 \, A B^{3} a^{3} b + 486 \, A^{2} B^{2} a^{2} b^{2} - 2916 \, A^{3} B a b^{3} + 6561 \, A^{4} b^{4}}{a^{13} b^{3}}\right)^{\frac{3}{4}} - 125 \, {\left(B^{3} a^{3} - 27 \, A B^{2} a^{2} b + 243 \, A^{2} B a b^{2} - 729 \, A^{3} b^{3}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, {\left(B a b - 9 \, A b^{2}\right)} x^{4} - 32 \, A a^{2} + 9 \, {\left(B a^{2} - 9 \, A a b\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}"," ",0,"1/64*(20*(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(1/4)*arctan((sqrt((B^6*a^6 - 54*A*B^5*a^5*b + 1215*A^2*B^4*a^4*b^2 - 14580*A^3*B^3*a^3*b^3 + 98415*A^4*B^2*a^2*b^4 - 354294*A^5*B*a*b^5 + 531441*A^6*b^6)*x - (B^4*a^11*b - 36*A*B^3*a^10*b^2 + 486*A^2*B^2*a^9*b^3 - 2916*A^3*B*a^8*b^4 + 6561*A^4*a^7*b^5)*sqrt(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3)))*a^3*b*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(1/4) + (B^3*a^6*b - 27*A*B^2*a^5*b^2 + 243*A^2*B*a^4*b^3 - 729*A^3*a^3*b^4)*sqrt(x)*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(1/4))/(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)) - 5*(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(1/4)*log(125*a^10*b^2*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(3/4) - 125*(B^3*a^3 - 27*A*B^2*a^2*b + 243*A^2*B*a*b^2 - 729*A^3*b^3)*sqrt(x)) + 5*(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(1/4)*log(-125*a^10*b^2*(-(B^4*a^4 - 36*A*B^3*a^3*b + 486*A^2*B^2*a^2*b^2 - 2916*A^3*B*a*b^3 + 6561*A^4*b^4)/(a^13*b^3))^(3/4) - 125*(B^3*a^3 - 27*A*B^2*a^2*b + 243*A^2*B*a*b^2 - 729*A^3*b^3)*sqrt(x)) + 4*(5*(B*a*b - 9*A*b^2)*x^4 - 32*A*a^2 + 9*(B*a^2 - 9*A*a*b)*x^2)*sqrt(x))/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)","B",0
389,1,809,0,1.144240," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{84 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{8} \sqrt{-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}} + {\left(9 \, B^{2} a^{2} - 66 \, A B a b + 121 \, A^{2} b^{2}\right)} x} a^{11} b \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{3}{4}} + {\left(3 \, B a^{12} b - 11 \, A a^{11} b^{2}\right)} \sqrt{x} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{3}{4}}}{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}\right) + 21 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{1}{4}} \log\left(7 \, a^{4} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{1}{4}} - 7 \, {\left(3 \, B a - 11 \, A b\right)} \sqrt{x}\right) - 21 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{1}{4}} \log\left(-7 \, a^{4} \left(-\frac{81 \, B^{4} a^{4} - 1188 \, A B^{3} a^{3} b + 6534 \, A^{2} B^{2} a^{2} b^{2} - 15972 \, A^{3} B a b^{3} + 14641 \, A^{4} b^{4}}{a^{15} b}\right)^{\frac{1}{4}} - 7 \, {\left(3 \, B a - 11 \, A b\right)} \sqrt{x}\right) - 4 \, {\left(7 \, {\left(3 \, B a b - 11 \, A b^{2}\right)} x^{4} - 32 \, A a^{2} + 11 \, {\left(3 \, B a^{2} - 11 \, A a b\right)} x^{2}\right)} \sqrt{x}}{192 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)}}"," ",0,"-1/192*(84*(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2)*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(1/4)*arctan((sqrt(a^8*sqrt(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b)) + (9*B^2*a^2 - 66*A*B*a*b + 121*A^2*b^2)*x)*a^11*b*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(3/4) + (3*B*a^12*b - 11*A*a^11*b^2)*sqrt(x)*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(3/4))/(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)) + 21*(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2)*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(1/4)*log(7*a^4*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(1/4) - 7*(3*B*a - 11*A*b)*sqrt(x)) - 21*(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2)*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(1/4)*log(-7*a^4*(-(81*B^4*a^4 - 1188*A*B^3*a^3*b + 6534*A^2*B^2*a^2*b^2 - 15972*A^3*B*a*b^3 + 14641*A^4*b^4)/(a^15*b))^(1/4) - 7*(3*B*a - 11*A*b)*sqrt(x)) - 4*(7*(3*B*a*b - 11*A*b^2)*x^4 - 32*A*a^2 + 11*(3*B*a^2 - 11*A*a*b)*x^2)*sqrt(x))/(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2)","B",0
390,1,1043,0,1.467654," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{180 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, B^{6} a^{6} b^{2} - 243750 \, A B^{5} a^{5} b^{3} + 1584375 \, A^{2} B^{4} a^{4} b^{4} - 5492500 \, A^{3} B^{3} a^{3} b^{5} + 10710375 \, A^{4} B^{2} a^{2} b^{6} - 11138790 \, A^{5} B a b^{7} + 4826809 \, A^{6} b^{8}\right)} x - {\left(625 \, B^{4} a^{13} b - 6500 \, A B^{3} a^{12} b^{2} + 25350 \, A^{2} B^{2} a^{11} b^{3} - 43940 \, A^{3} B a^{10} b^{4} + 28561 \, A^{4} a^{9} b^{5}\right)} \sqrt{-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}}} a^{4} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{1}{4}} + {\left(125 \, B^{3} a^{7} b - 975 \, A B^{2} a^{6} b^{2} + 2535 \, A^{2} B a^{5} b^{3} - 2197 \, A^{3} a^{4} b^{4}\right)} \sqrt{x} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{1}{4}}}{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}\right) - 45 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{1}{4}} \log\left(729 \, a^{13} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{3}{4}} - 729 \, {\left(125 \, B^{3} a^{3} b - 975 \, A B^{2} a^{2} b^{2} + 2535 \, A^{2} B a b^{3} - 2197 \, A^{3} b^{4}\right)} \sqrt{x}\right) + 45 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{1}{4}} \log\left(-729 \, a^{13} \left(-\frac{625 \, B^{4} a^{4} b - 6500 \, A B^{3} a^{3} b^{2} + 25350 \, A^{2} B^{2} a^{2} b^{3} - 43940 \, A^{3} B a b^{4} + 28561 \, A^{4} b^{5}}{a^{17}}\right)^{\frac{3}{4}} - 729 \, {\left(125 \, B^{3} a^{3} b - 975 \, A B^{2} a^{2} b^{2} + 2535 \, A^{2} B a b^{3} - 2197 \, A^{3} b^{4}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, {\left(5 \, B a b^{2} - 13 \, A b^{3}\right)} x^{6} + 81 \, {\left(5 \, B a^{2} b - 13 \, A a b^{2}\right)} x^{4} + 32 \, A a^{3} + 32 \, {\left(5 \, B a^{3} - 13 \, A a^{2} b\right)} x^{2}\right)} \sqrt{x}}{320 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}"," ",0,"-1/320*(180*(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(1/4)*arctan((sqrt((15625*B^6*a^6*b^2 - 243750*A*B^5*a^5*b^3 + 1584375*A^2*B^4*a^4*b^4 - 5492500*A^3*B^3*a^3*b^5 + 10710375*A^4*B^2*a^2*b^6 - 11138790*A^5*B*a*b^7 + 4826809*A^6*b^8)*x - (625*B^4*a^13*b - 6500*A*B^3*a^12*b^2 + 25350*A^2*B^2*a^11*b^3 - 43940*A^3*B*a^10*b^4 + 28561*A^4*a^9*b^5)*sqrt(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17))*a^4*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(1/4) + (125*B^3*a^7*b - 975*A*B^2*a^6*b^2 + 2535*A^2*B*a^5*b^3 - 2197*A^3*a^4*b^4)*sqrt(x)*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(1/4))/(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)) - 45*(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(1/4)*log(729*a^13*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(3/4) - 729*(125*B^3*a^3*b - 975*A*B^2*a^2*b^2 + 2535*A^2*B*a*b^3 - 2197*A^3*b^4)*sqrt(x)) + 45*(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(1/4)*log(-729*a^13*(-(625*B^4*a^4*b - 6500*A*B^3*a^3*b^2 + 25350*A^2*B^2*a^2*b^3 - 43940*A^3*B*a*b^4 + 28561*A^4*b^5)/a^17)^(3/4) - 729*(125*B^3*a^3*b - 975*A*B^2*a^2*b^2 + 2535*A^2*B*a*b^3 - 2197*A^3*b^4)*sqrt(x)) + 4*(45*(5*B*a*b^2 - 13*A*b^3)*x^6 + 81*(5*B*a^2*b - 13*A*a*b^2)*x^4 + 32*A*a^3 + 32*(5*B*a^3 - 13*A*a^2*b)*x^2)*sqrt(x))/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)","B",0
391,1,56,0,1.048158," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{2}{13923} \, {\left(663 \, b^{2} d x^{10} + 819 \, {\left(b^{2} c + 2 \, a b d\right)} x^{8} + 1547 \, a^{2} c x^{4} + 1071 \, {\left(2 \, a b c + a^{2} d\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/13923*(663*b^2*d*x^10 + 819*(b^2*c + 2*a*b*d)*x^8 + 1547*a^2*c*x^4 + 1071*(2*a*b*c + a^2*d)*x^6)*sqrt(x)","A",0
392,1,56,0,0.847486," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, b^{2} d x^{9} + 1463 \, {\left(b^{2} c + 2 \, a b d\right)} x^{7} + 3135 \, a^{2} c x^{3} + 1995 \, {\left(2 \, a b c + a^{2} d\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/21945*(1155*b^2*d*x^9 + 1463*(b^2*c + 2*a*b*d)*x^7 + 3135*a^2*c*x^3 + 1995*(2*a*b*c + a^2*d)*x^5)*sqrt(x)","A",0
393,1,56,0,1.156388," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""fricas"")","\frac{2}{9945} \, {\left(585 \, b^{2} d x^{8} + 765 \, {\left(b^{2} c + 2 \, a b d\right)} x^{6} + 1989 \, a^{2} c x^{2} + 1105 \, {\left(2 \, a b c + a^{2} d\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9945*(585*b^2*d*x^8 + 765*(b^2*c + 2*a*b*d)*x^6 + 1989*a^2*c*x^2 + 1105*(2*a*b*c + a^2*d)*x^4)*sqrt(x)","A",0
394,1,54,0,0.761599," ","integrate((b*x^2+a)^2*(d*x^2+c)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(77 \, b^{2} d x^{7} + 105 \, {\left(b^{2} c + 2 \, a b d\right)} x^{5} + 385 \, a^{2} c x + 165 \, {\left(2 \, a b c + a^{2} d\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/1155*(77*b^2*d*x^7 + 105*(b^2*c + 2*a*b*d)*x^5 + 385*a^2*c*x + 165*(2*a*b*c + a^2*d)*x^3)*sqrt(x)","A",0
395,1,53,0,1.270051," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{585} \, {\left(45 \, b^{2} d x^{6} + 65 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} + 585 \, a^{2} c + 117 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/585*(45*b^2*d*x^6 + 65*(b^2*c + 2*a*b*d)*x^4 + 585*a^2*c + 117*(2*a*b*c + a^2*d)*x^2)*sqrt(x)","A",0
396,1,53,0,1.078543," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, b^{2} d x^{6} + 33 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} - 231 \, a^{2} c + 77 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)}}{231 \, \sqrt{x}}"," ",0,"2/231*(21*b^2*d*x^6 + 33*(b^2*c + 2*a*b*d)*x^4 - 231*a^2*c + 77*(2*a*b*c + a^2*d)*x^2)/sqrt(x)","A",0
397,1,53,0,0.819739," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{2} d x^{6} + 9 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} - 15 \, a^{2} c + 45 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)}}{45 \, x^{\frac{3}{2}}}"," ",0,"2/45*(5*b^2*d*x^6 + 9*(b^2*c + 2*a*b*d)*x^4 - 15*a^2*c + 45*(2*a*b*c + a^2*d)*x^2)/x^(3/2)","A",0
398,1,53,0,0.782671," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{2} d x^{6} + 35 \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} - 21 \, a^{2} c - 105 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)}}{105 \, x^{\frac{5}{2}}}"," ",0,"2/105*(15*b^2*d*x^6 + 35*(b^2*c + 2*a*b*d)*x^4 - 21*a^2*c - 105*(2*a*b*c + a^2*d)*x^2)/x^(5/2)","A",0
399,1,90,0,1.038777," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{2}{348075} \, {\left(13923 \, b^{2} d^{2} x^{12} + 33150 \, {\left(b^{2} c d + a b d^{2}\right)} x^{10} + 20475 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{8} + 38675 \, a^{2} c^{2} x^{4} + 53550 \, {\left(a b c^{2} + a^{2} c d\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/348075*(13923*b^2*d^2*x^12 + 33150*(b^2*c*d + a*b*d^2)*x^10 + 20475*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^8 + 38675*a^2*c^2*x^4 + 53550*(a*b*c^2 + a^2*c*d)*x^6)*sqrt(x)","A",0
400,1,90,0,0.891230," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{2}{504735} \, {\left(21945 \, b^{2} d^{2} x^{11} + 53130 \, {\left(b^{2} c d + a b d^{2}\right)} x^{9} + 33649 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{7} + 72105 \, a^{2} c^{2} x^{3} + 91770 \, {\left(a b c^{2} + a^{2} c d\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/504735*(21945*b^2*d^2*x^11 + 53130*(b^2*c*d + a*b*d^2)*x^9 + 33649*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^7 + 72105*a^2*c^2*x^3 + 91770*(a*b*c^2 + a^2*c*d)*x^5)*sqrt(x)","A",0
401,1,90,0,1.272291," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{2}{69615} \, {\left(3315 \, b^{2} d^{2} x^{10} + 8190 \, {\left(b^{2} c d + a b d^{2}\right)} x^{8} + 5355 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{6} + 13923 \, a^{2} c^{2} x^{2} + 15470 \, {\left(a b c^{2} + a^{2} c d\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/69615*(3315*b^2*d^2*x^10 + 8190*(b^2*c*d + a*b*d^2)*x^8 + 5355*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^6 + 13923*a^2*c^2*x^2 + 15470*(a*b*c^2 + a^2*c*d)*x^4)*sqrt(x)","A",0
402,1,88,0,0.692926," ","integrate((b*x^2+a)^2*(d*x^2+c)^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{21945} \, {\left(1155 \, b^{2} d^{2} x^{9} + 2926 \, {\left(b^{2} c d + a b d^{2}\right)} x^{7} + 1995 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{5} + 7315 \, a^{2} c^{2} x + 6270 \, {\left(a b c^{2} + a^{2} c d\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/21945*(1155*b^2*d^2*x^9 + 2926*(b^2*c*d + a*b*d^2)*x^7 + 1995*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^5 + 7315*a^2*c^2*x + 6270*(a*b*c^2 + a^2*c*d)*x^3)*sqrt(x)","A",0
403,1,87,0,0.962897," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{9945} \, {\left(585 \, b^{2} d^{2} x^{8} + 1530 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 1105 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + 9945 \, a^{2} c^{2} + 3978 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/9945*(585*b^2*d^2*x^8 + 1530*(b^2*c*d + a*b*d^2)*x^6 + 1105*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + 9945*a^2*c^2 + 3978*(a*b*c^2 + a^2*c*d)*x^2)*sqrt(x)","A",0
404,1,87,0,1.048289," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, b^{2} d^{2} x^{8} + 210 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 165 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 1155 \, a^{2} c^{2} + 770 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}{1155 \, \sqrt{x}}"," ",0,"2/1155*(77*b^2*d^2*x^8 + 210*(b^2*c*d + a*b*d^2)*x^6 + 165*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 1155*a^2*c^2 + 770*(a*b*c^2 + a^2*c*d)*x^2)/sqrt(x)","A",0
405,1,87,0,0.870660," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(45 \, b^{2} d^{2} x^{8} + 130 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 117 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 195 \, a^{2} c^{2} + 1170 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}{585 \, x^{\frac{3}{2}}}"," ",0,"2/585*(45*b^2*d^2*x^8 + 130*(b^2*c*d + a*b*d^2)*x^6 + 117*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 195*a^2*c^2 + 1170*(a*b*c^2 + a^2*c*d)*x^2)/x^(3/2)","A",0
406,1,87,0,1.086619," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, b^{2} d^{2} x^{8} + 330 \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + 385 \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} - 231 \, a^{2} c^{2} - 2310 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}{1155 \, x^{\frac{5}{2}}}"," ",0,"2/1155*(105*b^2*d^2*x^8 + 330*(b^2*c*d + a*b*d^2)*x^6 + 385*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 - 231*a^2*c^2 - 2310*(a*b*c^2 + a^2*c*d)*x^2)/x^(5/2)","A",0
407,1,132,0,0.873861," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{2}{10094175} \, {\left(348075 \, b^{2} d^{3} x^{14} + 403767 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{12} + 480675 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{10} + 1121575 \, a^{2} c^{3} x^{4} + 593775 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{8} + 776475 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/10094175*(348075*b^2*d^3*x^14 + 403767*(3*b^2*c*d^2 + 2*a*b*d^3)*x^12 + 480675*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^10 + 1121575*a^2*c^3*x^4 + 593775*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^8 + 776475*(2*a*b*c^3 + 3*a^2*c^2*d)*x^6)*sqrt(x)","A",0
408,1,132,0,0.768738," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{2}{4542615} \, {\left(168245 \, b^{2} d^{3} x^{13} + 197505 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{11} + 239085 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{9} + 648945 \, a^{2} c^{3} x^{3} + 302841 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{7} + 412965 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/4542615*(168245*b^2*d^3*x^13 + 197505*(3*b^2*c*d^2 + 2*a*b*d^3)*x^11 + 239085*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^9 + 648945*a^2*c^3*x^3 + 302841*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^7 + 412965*(2*a*b*c^3 + 3*a^2*c^2*d)*x^5)*sqrt(x)","A",0
409,1,132,0,0.753376," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{2}{348075} \, {\left(13923 \, b^{2} d^{3} x^{12} + 16575 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{10} + 20475 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{8} + 69615 \, a^{2} c^{3} x^{2} + 26775 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{6} + 38675 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/348075*(13923*b^2*d^3*x^12 + 16575*(3*b^2*c*d^2 + 2*a*b*d^3)*x^10 + 20475*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^8 + 69615*a^2*c^3*x^2 + 26775*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^6 + 38675*(2*a*b*c^3 + 3*a^2*c^2*d)*x^4)*sqrt(x)","A",0
410,1,130,0,0.845999," ","integrate((b*x^2+a)^2*(d*x^2+c)^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{504735} \, {\left(21945 \, b^{2} d^{3} x^{11} + 26565 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{9} + 33649 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{7} + 168245 \, a^{2} c^{3} x + 45885 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{5} + 72105 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/504735*(21945*b^2*d^3*x^11 + 26565*(3*b^2*c*d^2 + 2*a*b*d^3)*x^9 + 33649*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^7 + 168245*a^2*c^3*x + 45885*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^5 + 72105*(2*a*b*c^3 + 3*a^2*c^2*d)*x^3)*sqrt(x)","A",0
411,1,129,0,0.817541," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{69615} \, {\left(3315 \, b^{2} d^{3} x^{10} + 4095 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 5355 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} + 69615 \, a^{2} c^{3} + 7735 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + 13923 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/69615*(3315*b^2*d^3*x^10 + 4095*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 5355*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 + 69615*a^2*c^3 + 7735*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 13923*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)*sqrt(x)","A",0
412,1,129,0,1.071383," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, b^{2} d^{3} x^{10} + 1463 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 1995 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 21945 \, a^{2} c^{3} + 3135 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + 7315 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{21945 \, \sqrt{x}}"," ",0,"2/21945*(1155*b^2*d^3*x^10 + 1463*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 1995*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 21945*a^2*c^3 + 3135*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 7315*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/sqrt(x)","A",0
413,1,129,0,1.284783," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(585 \, b^{2} d^{3} x^{10} + 765 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 1105 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 3315 \, a^{2} c^{3} + 1989 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + 9945 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{9945 \, x^{\frac{3}{2}}}"," ",0,"2/9945*(585*b^2*d^3*x^10 + 765*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 1105*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 3315*a^2*c^3 + 1989*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 9945*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x^(3/2)","A",0
414,1,129,0,1.025190," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(77 \, b^{2} d^{3} x^{10} + 105 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + 165 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} - 231 \, a^{2} c^{3} + 385 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 1155 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{1155 \, x^{\frac{5}{2}}}"," ",0,"2/1155*(77*b^2*d^3*x^10 + 105*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 165*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 - 231*a^2*c^3 + 385*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 1155*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x^(5/2)","A",0
415,1,1334,0,1.408676," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{2340 \, d^{4} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{d^{8} \sqrt{-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}} + {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} x} d^{13} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{3}{4}} - {\left(b^{2} c^{3} d^{13} - 2 \, a b c^{2} d^{14} + a^{2} c d^{15}\right)} \sqrt{x} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{3}{4}}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right) + 585 \, d^{4} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{1}{4}} \log\left(d^{4} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{x}\right) - 585 \, d^{4} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{1}{4}} \log\left(-d^{4} \left(-\frac{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}{d^{17}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, b^{2} d^{3} x^{6} - 585 \, b^{2} c^{3} + 1170 \, a b c^{2} d - 585 \, a^{2} c d^{2} - 65 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{4} + 117 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{1170 \, d^{4}}"," ",0,"1/1170*(2340*d^4*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(1/4)*arctan((sqrt(d^8*sqrt(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17) + (b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*x)*d^13*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(3/4) - (b^2*c^3*d^13 - 2*a*b*c^2*d^14 + a^2*c*d^15)*sqrt(x)*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(3/4))/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)) + 585*d^4*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(1/4)*log(d^4*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(1/4) + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(x)) - 585*d^4*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(1/4)*log(-d^4*(-(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)/d^17)^(1/4) + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(x)) + 4*(45*b^2*d^3*x^6 - 585*b^2*c^3 + 1170*a*b*c^2*d - 585*a^2*c*d^2 - 65*(b^2*c*d^2 - 2*a*b*d^3)*x^4 + 117*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^2)*sqrt(x))/d^4","B",0
416,1,1701,0,1.208946," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","\frac{924 \, d^{3} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{12} c^{16} - 12 \, a b^{11} c^{15} d + 66 \, a^{2} b^{10} c^{14} d^{2} - 220 \, a^{3} b^{9} c^{13} d^{3} + 495 \, a^{4} b^{8} c^{12} d^{4} - 792 \, a^{5} b^{7} c^{11} d^{5} + 924 \, a^{6} b^{6} c^{10} d^{6} - 792 \, a^{7} b^{5} c^{9} d^{7} + 495 \, a^{8} b^{4} c^{8} d^{8} - 220 \, a^{9} b^{3} c^{7} d^{9} + 66 \, a^{10} b^{2} c^{6} d^{10} - 12 \, a^{11} b c^{5} d^{11} + a^{12} c^{4} d^{12}\right)} x - {\left(b^{8} c^{11} d^{7} - 8 \, a b^{7} c^{10} d^{8} + 28 \, a^{2} b^{6} c^{9} d^{9} - 56 \, a^{3} b^{5} c^{8} d^{10} + 70 \, a^{4} b^{4} c^{7} d^{11} - 56 \, a^{5} b^{3} c^{6} d^{12} + 28 \, a^{6} b^{2} c^{5} d^{13} - 8 \, a^{7} b c^{4} d^{14} + a^{8} c^{3} d^{15}\right)} \sqrt{-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}}} d^{4} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{1}{4}} - {\left(b^{6} c^{8} d^{4} - 6 \, a b^{5} c^{7} d^{5} + 15 \, a^{2} b^{4} c^{6} d^{6} - 20 \, a^{3} b^{3} c^{5} d^{7} + 15 \, a^{4} b^{2} c^{4} d^{8} - 6 \, a^{5} b c^{3} d^{9} + a^{6} c^{2} d^{10}\right)} \sqrt{x} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{1}{4}}}{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}\right) - 231 \, d^{3} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{1}{4}} \log\left(d^{11} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{8} - 6 \, a b^{5} c^{7} d + 15 \, a^{2} b^{4} c^{6} d^{2} - 20 \, a^{3} b^{3} c^{5} d^{3} + 15 \, a^{4} b^{2} c^{4} d^{4} - 6 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} \sqrt{x}\right) + 231 \, d^{3} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{1}{4}} \log\left(-d^{11} \left(-\frac{b^{8} c^{11} - 8 \, a b^{7} c^{10} d + 28 \, a^{2} b^{6} c^{9} d^{2} - 56 \, a^{3} b^{5} c^{8} d^{3} + 70 \, a^{4} b^{4} c^{7} d^{4} - 56 \, a^{5} b^{3} c^{6} d^{5} + 28 \, a^{6} b^{2} c^{5} d^{6} - 8 \, a^{7} b c^{4} d^{7} + a^{8} c^{3} d^{8}}{d^{15}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{8} - 6 \, a b^{5} c^{7} d + 15 \, a^{2} b^{4} c^{6} d^{2} - 20 \, a^{3} b^{3} c^{5} d^{3} + 15 \, a^{4} b^{2} c^{4} d^{4} - 6 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} \sqrt{x}\right) + 4 \, {\left(21 \, b^{2} d^{2} x^{5} - 33 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{3} + 77 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x\right)} \sqrt{x}}{462 \, d^{3}}"," ",0,"1/462*(924*d^3*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(1/4)*arctan((sqrt((b^12*c^16 - 12*a*b^11*c^15*d + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a^11*b*c^5*d^11 + a^12*c^4*d^12)*x - (b^8*c^11*d^7 - 8*a*b^7*c^10*d^8 + 28*a^2*b^6*c^9*d^9 - 56*a^3*b^5*c^8*d^10 + 70*a^4*b^4*c^7*d^11 - 56*a^5*b^3*c^6*d^12 + 28*a^6*b^2*c^5*d^13 - 8*a^7*b*c^4*d^14 + a^8*c^3*d^15)*sqrt(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15))*d^4*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(1/4) - (b^6*c^8*d^4 - 6*a*b^5*c^7*d^5 + 15*a^2*b^4*c^6*d^6 - 20*a^3*b^3*c^5*d^7 + 15*a^4*b^2*c^4*d^8 - 6*a^5*b*c^3*d^9 + a^6*c^2*d^10)*sqrt(x)*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(1/4))/(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)) - 231*d^3*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(1/4)*log(d^11*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(3/4) + (b^6*c^8 - 6*a*b^5*c^7*d + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a^5*b*c^3*d^5 + a^6*c^2*d^6)*sqrt(x)) + 231*d^3*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(1/4)*log(-d^11*(-(b^8*c^11 - 8*a*b^7*c^10*d + 28*a^2*b^6*c^9*d^2 - 56*a^3*b^5*c^8*d^3 + 70*a^4*b^4*c^7*d^4 - 56*a^5*b^3*c^6*d^5 + 28*a^6*b^2*c^5*d^6 - 8*a^7*b*c^4*d^7 + a^8*c^3*d^8)/d^15)^(3/4) + (b^6*c^8 - 6*a*b^5*c^7*d + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a^5*b*c^3*d^5 + a^6*c^2*d^6)*sqrt(x)) + 4*(21*b^2*d^2*x^5 - 33*(b^2*c*d - 2*a*b*d^2)*x^3 + 77*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)*sqrt(x))/d^3","B",0
417,1,1268,0,1.374080," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""fricas"")","-\frac{180 \, d^{3} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{d^{6} \sqrt{-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x} d^{10} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{3}{4}} - {\left(b^{2} c^{2} d^{10} - 2 \, a b c d^{11} + a^{2} d^{12}\right)} \sqrt{x} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{3}{4}}}{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}\right) + 45 \, d^{3} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{1}{4}} \log\left(d^{3} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 45 \, d^{3} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{1}{4}} \log\left(-d^{3} \left(-\frac{b^{8} c^{9} - 8 \, a b^{7} c^{8} d + 28 \, a^{2} b^{6} c^{7} d^{2} - 56 \, a^{3} b^{5} c^{6} d^{3} + 70 \, a^{4} b^{4} c^{5} d^{4} - 56 \, a^{5} b^{3} c^{4} d^{5} + 28 \, a^{6} b^{2} c^{3} d^{6} - 8 \, a^{7} b c^{2} d^{7} + a^{8} c d^{8}}{d^{13}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 4 \, {\left(5 \, b^{2} d^{2} x^{4} + 45 \, b^{2} c^{2} - 90 \, a b c d + 45 \, a^{2} d^{2} - 9 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{x}}{90 \, d^{3}}"," ",0,"-1/90*(180*d^3*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(1/4)*arctan((sqrt(d^6*sqrt(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x)*d^10*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(3/4) - (b^2*c^2*d^10 - 2*a*b*c*d^11 + a^2*d^12)*sqrt(x)*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(3/4))/(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)) + 45*d^3*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(1/4)*log(d^3*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 45*d^3*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(1/4)*log(-d^3*(-(b^8*c^9 - 8*a*b^7*c^8*d + 28*a^2*b^6*c^7*d^2 - 56*a^3*b^5*c^6*d^3 + 70*a^4*b^4*c^5*d^4 - 56*a^5*b^3*c^4*d^5 + 28*a^6*b^2*c^3*d^6 - 8*a^7*b*c^2*d^7 + a^8*c*d^8)/d^13)^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 4*(5*b^2*d^2*x^4 + 45*b^2*c^2 - 90*a*b*c*d + 45*a^2*d^2 - 9*(b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(x))/d^3","B",0
418,1,1629,0,1.102888," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{84 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}\right)} x - {\left(b^{8} c^{9} d^{5} - 8 \, a b^{7} c^{8} d^{6} + 28 \, a^{2} b^{6} c^{7} d^{7} - 56 \, a^{3} b^{5} c^{6} d^{8} + 70 \, a^{4} b^{4} c^{5} d^{9} - 56 \, a^{5} b^{3} c^{4} d^{10} + 28 \, a^{6} b^{2} c^{3} d^{11} - 8 \, a^{7} b c^{2} d^{12} + a^{8} c d^{13}\right)} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}}} d^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{1}{4}} - {\left(b^{6} c^{6} d^{3} - 6 \, a b^{5} c^{5} d^{4} + 15 \, a^{2} b^{4} c^{4} d^{5} - 20 \, a^{3} b^{3} c^{3} d^{6} + 15 \, a^{4} b^{2} c^{2} d^{7} - 6 \, a^{5} b c d^{8} + a^{6} d^{9}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{1}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) - 21 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{1}{4}} \log\left(c d^{8} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) + 21 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{1}{4}} \log\left(-c d^{8} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c d^{11}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(3 \, b^{2} d x^{3} - 7 \, {\left(b^{2} c - 2 \, a b d\right)} x\right)} \sqrt{x}}{42 \, d^{2}}"," ",0,"-1/42*(84*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(1/4)*arctan((sqrt((b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)*x - (b^8*c^9*d^5 - 8*a*b^7*c^8*d^6 + 28*a^2*b^6*c^7*d^7 - 56*a^3*b^5*c^6*d^8 + 70*a^4*b^4*c^5*d^9 - 56*a^5*b^3*c^4*d^10 + 28*a^6*b^2*c^3*d^11 - 8*a^7*b*c^2*d^12 + a^8*c*d^13)*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11)))*d^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(1/4) - (b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8 + a^6*d^9)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(1/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) - 21*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(1/4)*log(c*d^8*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) + 21*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(1/4)*log(-c*d^8*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c*d^11))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) - 4*(3*b^2*d*x^3 - 7*(b^2*c - 2*a*b*d)*x)*sqrt(x))/d^2","B",0
419,1,1245,0,1.284310," ","integrate((b*x^2+a)^2/(d*x^2+c)/x^(1/2),x, algorithm=""fricas"")","\frac{20 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{2} d^{4} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x} c^{2} d^{7} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{3}{4}} - {\left(b^{2} c^{4} d^{7} - 2 \, a b c^{3} d^{8} + a^{2} c^{2} d^{9}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{3}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) + 5 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left(c d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 5 \, d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left(-c d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{9}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(b^{2} d x^{2} - 5 \, b^{2} c + 10 \, a b d\right)} \sqrt{x}}{10 \, d^{2}}"," ",0,"1/10*(20*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*arctan((sqrt(c^2*d^4*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x)*c^2*d^7*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(3/4) - (b^2*c^4*d^7 - 2*a*b*c^3*d^8 + a^2*c^2*d^9)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(3/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) + 5*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*log(c*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 5*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4)*log(-c*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^9))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) + 4*(b^2*d*x^2 - 5*b^2*c + 10*a*b*d)*sqrt(x))/d^2","B",0
420,1,1636,0,0.961028," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c),x, algorithm=""fricas"")","\frac{12 \, c d x \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}\right)} x - {\left(b^{8} c^{11} d^{3} - 8 \, a b^{7} c^{10} d^{4} + 28 \, a^{2} b^{6} c^{9} d^{5} - 56 \, a^{3} b^{5} c^{8} d^{6} + 70 \, a^{4} b^{4} c^{7} d^{7} - 56 \, a^{5} b^{3} c^{6} d^{8} + 28 \, a^{6} b^{2} c^{5} d^{9} - 8 \, a^{7} b c^{4} d^{10} + a^{8} c^{3} d^{11}\right)} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}}} c d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{1}{4}} - {\left(b^{6} c^{7} d^{2} - 6 \, a b^{5} c^{6} d^{3} + 15 \, a^{2} b^{4} c^{5} d^{4} - 20 \, a^{3} b^{3} c^{4} d^{5} + 15 \, a^{4} b^{2} c^{3} d^{6} - 6 \, a^{5} b c^{2} d^{7} + a^{6} c d^{8}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{1}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) - 3 \, c d x \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{4} d^{5} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) + 3 \, c d x \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{1}{4}} \log\left(-c^{4} d^{5} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{7}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) + 4 \, {\left(b^{2} c x^{2} - 3 \, a^{2} d\right)} \sqrt{x}}{6 \, c d x}"," ",0,"1/6*(12*c*d*x*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(1/4)*arctan((sqrt((b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)*x - (b^8*c^11*d^3 - 8*a*b^7*c^10*d^4 + 28*a^2*b^6*c^9*d^5 - 56*a^3*b^5*c^8*d^6 + 70*a^4*b^4*c^7*d^7 - 56*a^5*b^3*c^6*d^8 + 28*a^6*b^2*c^5*d^9 - 8*a^7*b*c^4*d^10 + a^8*c^3*d^11)*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7)))*c*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(1/4) - (b^6*c^7*d^2 - 6*a*b^5*c^6*d^3 + 15*a^2*b^4*c^5*d^4 - 20*a^3*b^3*c^4*d^5 + 15*a^4*b^2*c^3*d^6 - 6*a^5*b*c^2*d^7 + a^6*c*d^8)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(1/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) - 3*c*d*x*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(1/4)*log(c^4*d^5*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) + 3*c*d*x*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(1/4)*log(-c^4*d^5*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^7))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) + 4*(b^2*c*x^2 - 3*a^2*d)*sqrt(x))/(c*d*x)","B",0
421,1,1253,0,0.732572," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{12 \, c d x^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{4} d^{2} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x} c^{5} d^{4} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{3}{4}} - {\left(b^{2} c^{7} d^{4} - 2 \, a b c^{6} d^{5} + a^{2} c^{5} d^{6}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{3}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) + 3 \, c d x^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(c^{2} d \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 3 \, c d x^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(-c^{2} d \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{7} d^{5}}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 4 \, {\left(3 \, b^{2} c x^{2} - a^{2} d\right)} \sqrt{x}}{6 \, c d x^{2}}"," ",0,"-1/6*(12*c*d*x^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(1/4)*arctan((sqrt(c^4*d^2*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x)*c^5*d^4*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(3/4) - (b^2*c^7*d^4 - 2*a*b*c^6*d^5 + a^2*c^5*d^6)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(3/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) + 3*c*d*x^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(1/4)*log(c^2*d*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 3*c*d*x^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(1/4)*log(-c^2*d*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^7*d^5))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 4*(3*b^2*c*x^2 - a^2*d)*sqrt(x))/(c*d*x^2)","B",0
422,1,1648,0,1.218359," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{20 \, c^{2} x^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}\right)} x - {\left(b^{8} c^{13} d - 8 \, a b^{7} c^{12} d^{2} + 28 \, a^{2} b^{6} c^{11} d^{3} - 56 \, a^{3} b^{5} c^{10} d^{4} + 70 \, a^{4} b^{4} c^{9} d^{5} - 56 \, a^{5} b^{3} c^{8} d^{6} + 28 \, a^{6} b^{2} c^{7} d^{7} - 8 \, a^{7} b c^{6} d^{8} + a^{8} c^{5} d^{9}\right)} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}}} c^{2} d \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{1}{4}} - {\left(b^{6} c^{8} d - 6 \, a b^{5} c^{7} d^{2} + 15 \, a^{2} b^{4} c^{6} d^{3} - 20 \, a^{3} b^{3} c^{5} d^{4} + 15 \, a^{4} b^{2} c^{4} d^{5} - 6 \, a^{5} b c^{3} d^{6} + a^{6} c^{2} d^{7}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{1}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) - 5 \, c^{2} x^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{1}{4}} \log\left(c^{7} d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) + 5 \, c^{2} x^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{1}{4}} \log\left(-c^{7} d^{2} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{9} d^{3}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{x}\right) + 4 \, {\left(a^{2} c + 5 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{x}}{10 \, c^{2} x^{3}}"," ",0,"-1/10*(20*c^2*x^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(1/4)*arctan((sqrt((b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)*x - (b^8*c^13*d - 8*a*b^7*c^12*d^2 + 28*a^2*b^6*c^11*d^3 - 56*a^3*b^5*c^10*d^4 + 70*a^4*b^4*c^9*d^5 - 56*a^5*b^3*c^8*d^6 + 28*a^6*b^2*c^7*d^7 - 8*a^7*b*c^6*d^8 + a^8*c^5*d^9)*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3)))*c^2*d*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(1/4) - (b^6*c^8*d - 6*a*b^5*c^7*d^2 + 15*a^2*b^4*c^6*d^3 - 20*a^3*b^3*c^5*d^4 + 15*a^4*b^2*c^4*d^5 - 6*a^5*b*c^3*d^6 + a^6*c^2*d^7)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(1/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) - 5*c^2*x^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(1/4)*log(c^7*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) + 5*c^2*x^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(1/4)*log(-c^7*d^2*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^9*d^3))^(3/4) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(x)) + 4*(a^2*c + 5*(2*a*b*c - a^2*d)*x^2)*sqrt(x))/(c^2*x^3)","B",0
423,1,1252,0,1.343059," ","integrate((b*x^2+a)^2/x^(9/2)/(d*x^2+c),x, algorithm=""fricas"")","\frac{84 \, c^{2} x^{4} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} \sqrt{-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x} c^{8} d \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{3}{4}} - {\left(b^{2} c^{10} d - 2 \, a b c^{9} d^{2} + a^{2} c^{8} d^{3}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{3}{4}}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) + 21 \, c^{2} x^{4} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{1}{4}} \log\left(c^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 21 \, c^{2} x^{4} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{1}{4}} \log\left(-c^{3} \left(-\frac{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{11} d}\right)^{\frac{1}{4}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 4 \, {\left(3 \, a^{2} c + 7 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{x}}{42 \, c^{2} x^{4}}"," ",0,"1/42*(84*c^2*x^4*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(1/4)*arctan((sqrt(c^6*sqrt(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*x)*c^8*d*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(3/4) - (b^2*c^10*d - 2*a*b*c^9*d^2 + a^2*c^8*d^3)*sqrt(x)*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(3/4))/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)) + 21*c^2*x^4*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(1/4)*log(c^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 21*c^2*x^4*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(1/4)*log(-c^3*(-(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)/(c^11*d))^(1/4) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)) - 4*(3*a^2*c + 7*(2*a*b*c - a^2*d)*x^2)*sqrt(x))/(c^2*x^4)","B",0
424,1,1686,0,1.472483," ","integrate((d*x^2+c)^2/x^(11/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{180 \, a^{3} x^{5} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{14} c^{12} - 12 \, a b^{13} c^{11} d + 66 \, a^{2} b^{12} c^{10} d^{2} - 220 \, a^{3} b^{11} c^{9} d^{3} + 495 \, a^{4} b^{10} c^{8} d^{4} - 792 \, a^{5} b^{9} c^{7} d^{5} + 924 \, a^{6} b^{8} c^{6} d^{6} - 792 \, a^{7} b^{7} c^{5} d^{7} + 495 \, a^{8} b^{6} c^{4} d^{8} - 220 \, a^{9} b^{5} c^{3} d^{9} + 66 \, a^{10} b^{4} c^{2} d^{10} - 12 \, a^{11} b^{3} c d^{11} + a^{12} b^{2} d^{12}\right)} x - {\left(a^{7} b^{9} c^{8} - 8 \, a^{8} b^{8} c^{7} d + 28 \, a^{9} b^{7} c^{6} d^{2} - 56 \, a^{10} b^{6} c^{5} d^{3} + 70 \, a^{11} b^{5} c^{4} d^{4} - 56 \, a^{12} b^{4} c^{3} d^{5} + 28 \, a^{13} b^{3} c^{2} d^{6} - 8 \, a^{14} b^{2} c d^{7} + a^{15} b d^{8}\right)} \sqrt{-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}}} a^{3} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{1}{4}} - {\left(a^{3} b^{7} c^{6} - 6 \, a^{4} b^{6} c^{5} d + 15 \, a^{5} b^{5} c^{4} d^{2} - 20 \, a^{6} b^{4} c^{3} d^{3} + 15 \, a^{7} b^{3} c^{2} d^{4} - 6 \, a^{8} b^{2} c d^{5} + a^{9} b d^{6}\right)} \sqrt{x} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{1}{4}}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right) - 45 \, a^{3} x^{5} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{1}{4}} \log\left(a^{10} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{3}{4}} + {\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} \sqrt{x}\right) + 45 \, a^{3} x^{5} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{1}{4}} \log\left(-a^{10} \left(-\frac{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}{a^{13}}\right)^{\frac{3}{4}} + {\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(45 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} + 5 \, a^{2} c^{2} - 9 \, {\left(a b c^{2} - 2 \, a^{2} c d\right)} x^{2}\right)} \sqrt{x}}{90 \, a^{3} x^{5}}"," ",0,"1/90*(180*a^3*x^5*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(1/4)*arctan((sqrt((b^14*c^12 - 12*a*b^13*c^11*d + 66*a^2*b^12*c^10*d^2 - 220*a^3*b^11*c^9*d^3 + 495*a^4*b^10*c^8*d^4 - 792*a^5*b^9*c^7*d^5 + 924*a^6*b^8*c^6*d^6 - 792*a^7*b^7*c^5*d^7 + 495*a^8*b^6*c^4*d^8 - 220*a^9*b^5*c^3*d^9 + 66*a^10*b^4*c^2*d^10 - 12*a^11*b^3*c*d^11 + a^12*b^2*d^12)*x - (a^7*b^9*c^8 - 8*a^8*b^8*c^7*d + 28*a^9*b^7*c^6*d^2 - 56*a^10*b^6*c^5*d^3 + 70*a^11*b^5*c^4*d^4 - 56*a^12*b^4*c^3*d^5 + 28*a^13*b^3*c^2*d^6 - 8*a^14*b^2*c*d^7 + a^15*b*d^8)*sqrt(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13))*a^3*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(1/4) - (a^3*b^7*c^6 - 6*a^4*b^6*c^5*d + 15*a^5*b^5*c^4*d^2 - 20*a^6*b^4*c^3*d^3 + 15*a^7*b^3*c^2*d^4 - 6*a^8*b^2*c*d^5 + a^9*b*d^6)*sqrt(x)*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(1/4))/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)) - 45*a^3*x^5*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(1/4)*log(a^10*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(3/4) + (b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*sqrt(x)) + 45*a^3*x^5*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(1/4)*log(-a^10*(-(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8)/a^13)^(3/4) + (b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*sqrt(x)) - 4*(45*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4 + 5*a^2*c^2 - 9*(a*b*c^2 - 2*a^2*c*d)*x^2)*sqrt(x))/(a^3*x^5)","B",0
425,1,1373,0,0.770756," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{180 \, {\left(d^{5} x^{2} + c d^{4}\right)} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{d^{8} \sqrt{-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}} + {\left(169 \, b^{4} c^{4} - 468 \, a b^{3} c^{3} d + 454 \, a^{2} b^{2} c^{2} d^{2} - 180 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}\right)} x} d^{13} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{3}{4}} - {\left(13 \, b^{2} c^{2} d^{13} - 18 \, a b c d^{14} + 5 \, a^{2} d^{15}\right)} \sqrt{x} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{3}{4}}}{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}\right) + 45 \, {\left(d^{5} x^{2} + c d^{4}\right)} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{1}{4}} \log\left(d^{4} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{1}{4}} + {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 45 \, {\left(d^{5} x^{2} + c d^{4}\right)} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{1}{4}} \log\left(-d^{4} \left(-\frac{28561 \, b^{8} c^{9} - 158184 \, a b^{7} c^{8} d + 372476 \, a^{2} b^{6} c^{7} d^{2} - 485784 \, a^{3} b^{5} c^{6} d^{3} + 383046 \, a^{4} b^{4} c^{5} d^{4} - 186840 \, a^{5} b^{3} c^{4} d^{5} + 55100 \, a^{6} b^{2} c^{3} d^{6} - 9000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8}}{d^{17}}\right)^{\frac{1}{4}} + {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 4 \, {\left(20 \, b^{2} d^{3} x^{6} + 585 \, b^{2} c^{3} - 810 \, a b c^{2} d + 225 \, a^{2} c d^{2} - 4 \, {\left(13 \, b^{2} c d^{2} - 18 \, a b d^{3}\right)} x^{4} + 36 \, {\left(13 \, b^{2} c^{2} d - 18 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{360 \, {\left(d^{5} x^{2} + c d^{4}\right)}}"," ",0,"-1/360*(180*(d^5*x^2 + c*d^4)*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(1/4)*arctan((sqrt(d^8*sqrt(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17) + (169*b^4*c^4 - 468*a*b^3*c^3*d + 454*a^2*b^2*c^2*d^2 - 180*a^3*b*c*d^3 + 25*a^4*d^4)*x)*d^13*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(3/4) - (13*b^2*c^2*d^13 - 18*a*b*c*d^14 + 5*a^2*d^15)*sqrt(x)*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(3/4))/(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)) + 45*(d^5*x^2 + c*d^4)*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(1/4)*log(d^4*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(1/4) + (13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*sqrt(x)) - 45*(d^5*x^2 + c*d^4)*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(1/4)*log(-d^4*(-(28561*b^8*c^9 - 158184*a*b^7*c^8*d + 372476*a^2*b^6*c^7*d^2 - 485784*a^3*b^5*c^6*d^3 + 383046*a^4*b^4*c^5*d^4 - 186840*a^5*b^3*c^4*d^5 + 55100*a^6*b^2*c^3*d^6 - 9000*a^7*b*c^2*d^7 + 625*a^8*c*d^8)/d^17)^(1/4) + (13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*sqrt(x)) - 4*(20*b^2*d^3*x^6 + 585*b^2*c^3 - 810*a*b*c^2*d + 225*a^2*c*d^2 - 4*(13*b^2*c*d^2 - 18*a*b*d^3)*x^4 + 36*(13*b^2*c^2*d - 18*a*b*c*d^2 + 5*a^2*d^3)*x^2)*sqrt(x))/(d^5*x^2 + c*d^4)","B",0
426,1,1733,0,0.837054," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{84 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(1771561 \, b^{12} c^{12} - 13528284 \, a b^{11} c^{11} d + 45943458 \, a^{2} b^{10} c^{10} d^{2} - 91492940 \, a^{3} b^{9} c^{9} d^{3} + 118659255 \, a^{4} b^{8} c^{8} d^{4} - 105323064 \, a^{5} b^{7} c^{7} d^{5} + 65490076 \, a^{6} b^{6} c^{6} d^{6} - 28724472 \, a^{7} b^{5} c^{5} d^{7} + 8825895 \, a^{8} b^{4} c^{4} d^{8} - 1855980 \, a^{9} b^{3} c^{3} d^{9} + 254178 \, a^{10} b^{2} c^{2} d^{10} - 20412 \, a^{11} b c d^{11} + 729 \, a^{12} d^{12}\right)} x - {\left(14641 \, b^{8} c^{9} d^{7} - 74536 \, a b^{7} c^{8} d^{8} + 158268 \, a^{2} b^{6} c^{7} d^{9} - 181720 \, a^{3} b^{5} c^{6} d^{10} + 122566 \, a^{4} b^{4} c^{5} d^{11} - 49560 \, a^{5} b^{3} c^{4} d^{12} + 11772 \, a^{6} b^{2} c^{3} d^{13} - 1512 \, a^{7} b c^{2} d^{14} + 81 \, a^{8} c d^{15}\right)} \sqrt{-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}}} d^{4} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{1}{4}} - {\left(1331 \, b^{6} c^{6} d^{4} - 5082 \, a b^{5} c^{5} d^{5} + 7557 \, a^{2} b^{4} c^{4} d^{6} - 5516 \, a^{3} b^{3} c^{3} d^{7} + 2061 \, a^{4} b^{2} c^{2} d^{8} - 378 \, a^{5} b c d^{9} + 27 \, a^{6} d^{10}\right)} \sqrt{x} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{1}{4}}}{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}\right) - 21 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{1}{4}} \log\left(c d^{11} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{3}{4}} + {\left(1331 \, b^{6} c^{6} - 5082 \, a b^{5} c^{5} d + 7557 \, a^{2} b^{4} c^{4} d^{2} - 5516 \, a^{3} b^{3} c^{3} d^{3} + 2061 \, a^{4} b^{2} c^{2} d^{4} - 378 \, a^{5} b c d^{5} + 27 \, a^{6} d^{6}\right)} \sqrt{x}\right) + 21 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{1}{4}} \log\left(-c d^{11} \left(-\frac{14641 \, b^{8} c^{8} - 74536 \, a b^{7} c^{7} d + 158268 \, a^{2} b^{6} c^{6} d^{2} - 181720 \, a^{3} b^{5} c^{5} d^{3} + 122566 \, a^{4} b^{4} c^{4} d^{4} - 49560 \, a^{5} b^{3} c^{3} d^{5} + 11772 \, a^{6} b^{2} c^{2} d^{6} - 1512 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c d^{15}}\right)^{\frac{3}{4}} + {\left(1331 \, b^{6} c^{6} - 5082 \, a b^{5} c^{5} d + 7557 \, a^{2} b^{4} c^{4} d^{2} - 5516 \, a^{3} b^{3} c^{3} d^{3} + 2061 \, a^{4} b^{2} c^{2} d^{4} - 378 \, a^{5} b c d^{5} + 27 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(12 \, b^{2} d^{2} x^{5} - 4 \, {\left(11 \, b^{2} c d - 14 \, a b d^{2}\right)} x^{3} - 7 \, {\left(11 \, b^{2} c^{2} - 14 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{x}}{168 \, {\left(d^{4} x^{2} + c d^{3}\right)}}"," ",0,"-1/168*(84*(d^4*x^2 + c*d^3)*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(1/4)*arctan((sqrt((1771561*b^12*c^12 - 13528284*a*b^11*c^11*d + 45943458*a^2*b^10*c^10*d^2 - 91492940*a^3*b^9*c^9*d^3 + 118659255*a^4*b^8*c^8*d^4 - 105323064*a^5*b^7*c^7*d^5 + 65490076*a^6*b^6*c^6*d^6 - 28724472*a^7*b^5*c^5*d^7 + 8825895*a^8*b^4*c^4*d^8 - 1855980*a^9*b^3*c^3*d^9 + 254178*a^10*b^2*c^2*d^10 - 20412*a^11*b*c*d^11 + 729*a^12*d^12)*x - (14641*b^8*c^9*d^7 - 74536*a*b^7*c^8*d^8 + 158268*a^2*b^6*c^7*d^9 - 181720*a^3*b^5*c^6*d^10 + 122566*a^4*b^4*c^5*d^11 - 49560*a^5*b^3*c^4*d^12 + 11772*a^6*b^2*c^3*d^13 - 1512*a^7*b*c^2*d^14 + 81*a^8*c*d^15)*sqrt(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15)))*d^4*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(1/4) - (1331*b^6*c^6*d^4 - 5082*a*b^5*c^5*d^5 + 7557*a^2*b^4*c^4*d^6 - 5516*a^3*b^3*c^3*d^7 + 2061*a^4*b^2*c^2*d^8 - 378*a^5*b*c*d^9 + 27*a^6*d^10)*sqrt(x)*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(1/4))/(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)) - 21*(d^4*x^2 + c*d^3)*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(1/4)*log(c*d^11*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(3/4) + (1331*b^6*c^6 - 5082*a*b^5*c^5*d + 7557*a^2*b^4*c^4*d^2 - 5516*a^3*b^3*c^3*d^3 + 2061*a^4*b^2*c^2*d^4 - 378*a^5*b*c*d^5 + 27*a^6*d^6)*sqrt(x)) + 21*(d^4*x^2 + c*d^3)*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(1/4)*log(-c*d^11*(-(14641*b^8*c^8 - 74536*a*b^7*c^7*d + 158268*a^2*b^6*c^6*d^2 - 181720*a^3*b^5*c^5*d^3 + 122566*a^4*b^4*c^4*d^4 - 49560*a^5*b^3*c^3*d^5 + 11772*a^6*b^2*c^2*d^6 - 1512*a^7*b*c*d^7 + 81*a^8*d^8)/(c*d^15))^(3/4) + (1331*b^6*c^6 - 5082*a*b^5*c^5*d + 7557*a^2*b^4*c^4*d^2 - 5516*a^3*b^3*c^3*d^3 + 2061*a^4*b^2*c^2*d^4 - 378*a^5*b*c*d^5 + 27*a^6*d^6)*sqrt(x)) - 4*(12*b^2*d^2*x^5 - 4*(11*b^2*c*d - 14*a*b*d^2)*x^3 - 7*(11*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*x)*sqrt(x))/(d^4*x^2 + c*d^3)","B",0
427,1,1334,0,1.159510," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{20 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{2} d^{6} \sqrt{-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}} + {\left(81 \, b^{4} c^{4} - 180 \, a b^{3} c^{3} d + 118 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x} c^{2} d^{10} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{3}{4}} - {\left(9 \, b^{2} c^{4} d^{10} - 10 \, a b c^{3} d^{11} + a^{2} c^{2} d^{12}\right)} \sqrt{x} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{3}{4}}}{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) + 5 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{1}{4}} \log\left(c d^{3} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{1}{4}} + {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) - 5 \, {\left(d^{4} x^{2} + c d^{3}\right)} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{1}{4}} \log\left(-c d^{3} \left(-\frac{6561 \, b^{8} c^{8} - 29160 \, a b^{7} c^{7} d + 51516 \, a^{2} b^{6} c^{6} d^{2} - 45720 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 5080 \, a^{5} b^{3} c^{3} d^{5} + 636 \, a^{6} b^{2} c^{2} d^{6} - 40 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{3} d^{13}}\right)^{\frac{1}{4}} + {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, b^{2} d^{2} x^{4} - 45 \, b^{2} c^{2} + 50 \, a b c d - 5 \, a^{2} d^{2} - 4 \, {\left(9 \, b^{2} c d - 10 \, a b d^{2}\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(d^{4} x^{2} + c d^{3}\right)}}"," ",0,"1/40*(20*(d^4*x^2 + c*d^3)*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(1/4)*arctan((sqrt(c^2*d^6*sqrt(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13)) + (81*b^4*c^4 - 180*a*b^3*c^3*d + 118*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*x)*c^2*d^10*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(3/4) - (9*b^2*c^4*d^10 - 10*a*b*c^3*d^11 + a^2*c^2*d^12)*sqrt(x)*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(3/4))/(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)) + 5*(d^4*x^2 + c*d^3)*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(1/4)*log(c*d^3*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(1/4) + (9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*sqrt(x)) - 5*(d^4*x^2 + c*d^3)*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(1/4)*log(-c*d^3*(-(6561*b^8*c^8 - 29160*a*b^7*c^7*d + 51516*a^2*b^6*c^6*d^2 - 45720*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 5080*a^5*b^3*c^3*d^5 + 636*a^6*b^2*c^2*d^6 - 40*a^7*b*c*d^7 + a^8*d^8)/(c^3*d^13))^(1/4) + (9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*sqrt(x)) + 4*(4*b^2*d^2*x^4 - 45*b^2*c^2 + 50*a*b*c*d - 5*a^2*d^2 - 4*(9*b^2*c*d - 10*a*b*d^2)*x^2)*sqrt(x))/(d^4*x^2 + c*d^3)","B",0
428,1,1723,0,1.460010," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(117649 \, b^{12} c^{12} - 605052 \, a b^{11} c^{11} d + 1195698 \, a^{2} b^{10} c^{10} d^{2} - 1049580 \, a^{3} b^{9} c^{9} d^{3} + 247695 \, a^{4} b^{8} c^{8} d^{4} + 184968 \, a^{5} b^{7} c^{7} d^{5} - 73604 \, a^{6} b^{6} c^{6} d^{6} - 26424 \, a^{7} b^{5} c^{5} d^{7} + 5055 \, a^{8} b^{4} c^{4} d^{8} + 3060 \, a^{9} b^{3} c^{3} d^{9} + 498 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}\right)} x - {\left(2401 \, b^{8} c^{11} d^{5} - 8232 \, a b^{7} c^{10} d^{6} + 9212 \, a^{2} b^{6} c^{9} d^{7} - 2520 \, a^{3} b^{5} c^{8} d^{8} - 1434 \, a^{4} b^{4} c^{7} d^{9} + 360 \, a^{5} b^{3} c^{6} d^{10} + 188 \, a^{6} b^{2} c^{5} d^{11} + 24 \, a^{7} b c^{4} d^{12} + a^{8} c^{3} d^{13}\right)} \sqrt{-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}}} c d^{3} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{1}{4}} + {\left(343 \, b^{6} c^{7} d^{3} - 882 \, a b^{5} c^{6} d^{4} + 609 \, a^{2} b^{4} c^{5} d^{5} + 36 \, a^{3} b^{3} c^{4} d^{6} - 87 \, a^{4} b^{2} c^{3} d^{7} - 18 \, a^{5} b c^{2} d^{8} - a^{6} c d^{9}\right)} \sqrt{x} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{1}{4}}}{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}\right) - 3 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{1}{4}} \log\left(c^{4} d^{8} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{3}{4}} - {\left(343 \, b^{6} c^{6} - 882 \, a b^{5} c^{5} d + 609 \, a^{2} b^{4} c^{4} d^{2} + 36 \, a^{3} b^{3} c^{3} d^{3} - 87 \, a^{4} b^{2} c^{2} d^{4} - 18 \, a^{5} b c d^{5} - a^{6} d^{6}\right)} \sqrt{x}\right) + 3 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{1}{4}} \log\left(-c^{4} d^{8} \left(-\frac{2401 \, b^{8} c^{8} - 8232 \, a b^{7} c^{7} d + 9212 \, a^{2} b^{6} c^{6} d^{2} - 2520 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} + 360 \, a^{5} b^{3} c^{3} d^{5} + 188 \, a^{6} b^{2} c^{2} d^{6} + 24 \, a^{7} b c d^{7} + a^{8} d^{8}}{c^{5} d^{11}}\right)^{\frac{3}{4}} - {\left(343 \, b^{6} c^{6} - 882 \, a b^{5} c^{5} d + 609 \, a^{2} b^{4} c^{4} d^{2} + 36 \, a^{3} b^{3} c^{3} d^{3} - 87 \, a^{4} b^{2} c^{2} d^{4} - 18 \, a^{5} b c d^{5} - a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(4 \, b^{2} c d x^{3} + {\left(7 \, b^{2} c^{2} - 6 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}"," ",0,"-1/24*(12*(c*d^3*x^2 + c^2*d^2)*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(1/4)*arctan((sqrt((117649*b^12*c^12 - 605052*a*b^11*c^11*d + 1195698*a^2*b^10*c^10*d^2 - 1049580*a^3*b^9*c^9*d^3 + 247695*a^4*b^8*c^8*d^4 + 184968*a^5*b^7*c^7*d^5 - 73604*a^6*b^6*c^6*d^6 - 26424*a^7*b^5*c^5*d^7 + 5055*a^8*b^4*c^4*d^8 + 3060*a^9*b^3*c^3*d^9 + 498*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)*x - (2401*b^8*c^11*d^5 - 8232*a*b^7*c^10*d^6 + 9212*a^2*b^6*c^9*d^7 - 2520*a^3*b^5*c^8*d^8 - 1434*a^4*b^4*c^7*d^9 + 360*a^5*b^3*c^6*d^10 + 188*a^6*b^2*c^5*d^11 + 24*a^7*b*c^4*d^12 + a^8*c^3*d^13)*sqrt(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11)))*c*d^3*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(1/4) + (343*b^6*c^7*d^3 - 882*a*b^5*c^6*d^4 + 609*a^2*b^4*c^5*d^5 + 36*a^3*b^3*c^4*d^6 - 87*a^4*b^2*c^3*d^7 - 18*a^5*b*c^2*d^8 - a^6*c*d^9)*sqrt(x)*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(1/4))/(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)) - 3*(c*d^3*x^2 + c^2*d^2)*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(1/4)*log(c^4*d^8*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(3/4) - (343*b^6*c^6 - 882*a*b^5*c^5*d + 609*a^2*b^4*c^4*d^2 + 36*a^3*b^3*c^3*d^3 - 87*a^4*b^2*c^2*d^4 - 18*a^5*b*c*d^5 - a^6*d^6)*sqrt(x)) + 3*(c*d^3*x^2 + c^2*d^2)*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(1/4)*log(-c^4*d^8*(-(2401*b^8*c^8 - 8232*a*b^7*c^7*d + 9212*a^2*b^6*c^6*d^2 - 2520*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 + 360*a^5*b^3*c^3*d^5 + 188*a^6*b^2*c^2*d^6 + 24*a^7*b*c*d^7 + a^8*d^8)/(c^5*d^11))^(3/4) - (343*b^6*c^6 - 882*a*b^5*c^5*d + 609*a^2*b^4*c^4*d^2 + 36*a^3*b^3*c^3*d^3 - 87*a^4*b^2*c^2*d^4 - 18*a^5*b*c*d^5 - a^6*d^6)*sqrt(x)) - 4*(4*b^2*c*d*x^3 + (7*b^2*c^2 - 6*a*b*c*d + 3*a^2*d^2)*x)*sqrt(x))/(c*d^3*x^2 + c^2*d^2)","B",0
429,1,1341,0,1.145550," ","integrate((b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{4} d^{4} \sqrt{-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}} + {\left(25 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4}\right)} x} c^{5} d^{7} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{3}{4}} + {\left(5 \, b^{2} c^{7} d^{7} - 2 \, a b c^{6} d^{8} - 3 \, a^{2} c^{5} d^{9}\right)} \sqrt{x} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{3}{4}}}{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}\right) + {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(c^{2} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} - {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{x}\right) - {\left(c d^{3} x^{2} + c^{2} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(-c^{2} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{9}}\right)^{\frac{1}{4}} - {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, b^{2} c d x^{2} + 5 \, b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}}{8 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}}"," ",0,"1/8*(4*(c*d^3*x^2 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*arctan((sqrt(c^4*d^4*sqrt(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9)) + (25*b^4*c^4 - 20*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + 9*a^4*d^4)*x)*c^5*d^7*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(3/4) + (5*b^2*c^7*d^7 - 2*a*b*c^6*d^8 - 3*a^2*c^5*d^9)*sqrt(x)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(3/4))/(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)) + (c*d^3*x^2 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*log(c^2*d^2*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4) - (5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*sqrt(x)) - (c*d^3*x^2 + c^2*d^2)*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4)*log(-c^2*d^2*(-(625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^9))^(1/4) - (5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*sqrt(x)) + 4*(4*b^2*c*d*x^2 + 5*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x))/(c*d^3*x^2 + c^2*d^2)","B",0
430,1,1739,0,1.440706," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(c^{2} d^{2} x^{3} + c^{3} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, b^{12} c^{12} + 2916 \, a b^{11} c^{11} d - 2430 \, a^{2} b^{10} c^{10} d^{2} - 19980 \, a^{3} b^{9} c^{9} d^{3} + 135 \, a^{4} b^{8} c^{8} d^{4} + 59976 \, a^{5} b^{7} c^{7} d^{5} + 6364 \, a^{6} b^{6} c^{6} d^{6} - 99960 \, a^{7} b^{5} c^{5} d^{7} + 375 \, a^{8} b^{4} c^{4} d^{8} + 92500 \, a^{9} b^{3} c^{3} d^{9} - 18750 \, a^{10} b^{2} c^{2} d^{10} - 37500 \, a^{11} b c d^{11} + 15625 \, a^{12} d^{12}\right)} x - {\left(81 \, b^{8} c^{13} d^{3} + 216 \, a b^{7} c^{12} d^{4} - 324 \, a^{2} b^{6} c^{11} d^{5} - 984 \, a^{3} b^{5} c^{10} d^{6} + 646 \, a^{4} b^{4} c^{9} d^{7} + 1640 \, a^{5} b^{3} c^{8} d^{8} - 900 \, a^{6} b^{2} c^{7} d^{9} - 1000 \, a^{7} b c^{6} d^{10} + 625 \, a^{8} c^{5} d^{11}\right)} \sqrt{-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}}} c^{2} d^{2} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{1}{4}} + {\left(27 \, b^{6} c^{8} d^{2} + 54 \, a b^{5} c^{7} d^{3} - 99 \, a^{2} b^{4} c^{6} d^{4} - 172 \, a^{3} b^{3} c^{5} d^{5} + 165 \, a^{4} b^{2} c^{4} d^{6} + 150 \, a^{5} b c^{3} d^{7} - 125 \, a^{6} c^{2} d^{8}\right)} \sqrt{x} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{1}{4}}}{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}\right) - {\left(c^{2} d^{2} x^{3} + c^{3} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{7} d^{5} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{3}{4}} - {\left(27 \, b^{6} c^{6} + 54 \, a b^{5} c^{5} d - 99 \, a^{2} b^{4} c^{4} d^{2} - 172 \, a^{3} b^{3} c^{3} d^{3} + 165 \, a^{4} b^{2} c^{2} d^{4} + 150 \, a^{5} b c d^{5} - 125 \, a^{6} d^{6}\right)} \sqrt{x}\right) + {\left(c^{2} d^{2} x^{3} + c^{3} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{1}{4}} \log\left(-c^{7} d^{5} \left(-\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{7}}\right)^{\frac{3}{4}} - {\left(27 \, b^{6} c^{6} + 54 \, a b^{5} c^{5} d - 99 \, a^{2} b^{4} c^{4} d^{2} - 172 \, a^{3} b^{3} c^{3} d^{3} + 165 \, a^{4} b^{2} c^{2} d^{4} + 150 \, a^{5} b c d^{5} - 125 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(4 \, a^{2} c d + {\left(b^{2} c^{2} - 2 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{x}}{8 \, {\left(c^{2} d^{2} x^{3} + c^{3} d x\right)}}"," ",0,"1/8*(4*(c^2*d^2*x^3 + c^3*d*x)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(1/4)*arctan((sqrt((729*b^12*c^12 + 2916*a*b^11*c^11*d - 2430*a^2*b^10*c^10*d^2 - 19980*a^3*b^9*c^9*d^3 + 135*a^4*b^8*c^8*d^4 + 59976*a^5*b^7*c^7*d^5 + 6364*a^6*b^6*c^6*d^6 - 99960*a^7*b^5*c^5*d^7 + 375*a^8*b^4*c^4*d^8 + 92500*a^9*b^3*c^3*d^9 - 18750*a^10*b^2*c^2*d^10 - 37500*a^11*b*c*d^11 + 15625*a^12*d^12)*x - (81*b^8*c^13*d^3 + 216*a*b^7*c^12*d^4 - 324*a^2*b^6*c^11*d^5 - 984*a^3*b^5*c^10*d^6 + 646*a^4*b^4*c^9*d^7 + 1640*a^5*b^3*c^8*d^8 - 900*a^6*b^2*c^7*d^9 - 1000*a^7*b*c^6*d^10 + 625*a^8*c^5*d^11)*sqrt(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7)))*c^2*d^2*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(1/4) + (27*b^6*c^8*d^2 + 54*a*b^5*c^7*d^3 - 99*a^2*b^4*c^6*d^4 - 172*a^3*b^3*c^5*d^5 + 165*a^4*b^2*c^4*d^6 + 150*a^5*b*c^3*d^7 - 125*a^6*c^2*d^8)*sqrt(x)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(1/4))/(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)) - (c^2*d^2*x^3 + c^3*d*x)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(1/4)*log(c^7*d^5*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(3/4) - (27*b^6*c^6 + 54*a*b^5*c^5*d - 99*a^2*b^4*c^4*d^2 - 172*a^3*b^3*c^3*d^3 + 165*a^4*b^2*c^2*d^4 + 150*a^5*b*c*d^5 - 125*a^6*d^6)*sqrt(x)) + (c^2*d^2*x^3 + c^3*d*x)*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(1/4)*log(-c^7*d^5*(-(81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^7))^(3/4) - (27*b^6*c^6 + 54*a*b^5*c^5*d - 99*a^2*b^4*c^4*d^2 - 172*a^3*b^3*c^3*d^3 + 165*a^4*b^2*c^2*d^4 + 150*a^5*b*c*d^5 - 125*a^6*d^6)*sqrt(x)) - 4*(4*a^2*c*d + (b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x^2)*sqrt(x))/(c^2*d^2*x^3 + c^3*d*x)","B",0
431,1,1340,0,1.377539," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(c^{2} d^{2} x^{4} + c^{3} d x^{2}\right)} \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} d^{2} \sqrt{-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}} + {\left(b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 22 \, a^{2} b^{2} c^{2} d^{2} - 84 \, a^{3} b c d^{3} + 49 \, a^{4} d^{4}\right)} x} c^{8} d^{4} \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{3}{4}} + {\left(b^{2} c^{10} d^{4} + 6 \, a b c^{9} d^{5} - 7 \, a^{2} c^{8} d^{6}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{3}{4}}}{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}\right) + 3 \, {\left(c^{2} d^{2} x^{4} + c^{3} d x^{2}\right)} \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \log\left(c^{3} d \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{1}{4}} - {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 3 \, {\left(c^{2} d^{2} x^{4} + c^{3} d x^{2}\right)} \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{1}{4}} \log\left(-c^{3} d \left(-\frac{b^{8} c^{8} + 24 \, a b^{7} c^{7} d + 188 \, a^{2} b^{6} c^{6} d^{2} + 360 \, a^{3} b^{5} c^{5} d^{3} - 1434 \, a^{4} b^{4} c^{4} d^{4} - 2520 \, a^{5} b^{3} c^{3} d^{5} + 9212 \, a^{6} b^{2} c^{2} d^{6} - 8232 \, a^{7} b c d^{7} + 2401 \, a^{8} d^{8}}{c^{11} d^{5}}\right)^{\frac{1}{4}} - {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, a^{2} c d + {\left(3 \, b^{2} c^{2} - 6 \, a b c d + 7 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{x}}{24 \, {\left(c^{2} d^{2} x^{4} + c^{3} d x^{2}\right)}}"," ",0,"-1/24*(12*(c^2*d^2*x^4 + c^3*d*x^2)*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(1/4)*arctan((sqrt(c^6*d^2*sqrt(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5)) + (b^4*c^4 + 12*a*b^3*c^3*d + 22*a^2*b^2*c^2*d^2 - 84*a^3*b*c*d^3 + 49*a^4*d^4)*x)*c^8*d^4*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(3/4) + (b^2*c^10*d^4 + 6*a*b*c^9*d^5 - 7*a^2*c^8*d^6)*sqrt(x)*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(3/4))/(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)) + 3*(c^2*d^2*x^4 + c^3*d*x^2)*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(1/4)*log(c^3*d*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(1/4) - (b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*sqrt(x)) - 3*(c^2*d^2*x^4 + c^3*d*x^2)*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(1/4)*log(-c^3*d*(-(b^8*c^8 + 24*a*b^7*c^7*d + 188*a^2*b^6*c^6*d^2 + 360*a^3*b^5*c^5*d^3 - 1434*a^4*b^4*c^4*d^4 - 2520*a^5*b^3*c^3*d^5 + 9212*a^6*b^2*c^2*d^6 - 8232*a^7*b*c*d^7 + 2401*a^8*d^8)/(c^11*d^5))^(1/4) - (b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*sqrt(x)) + 4*(4*a^2*c*d + (3*b^2*c^2 - 6*a*b*c*d + 7*a^2*d^2)*x^2)*sqrt(x))/(c^2*d^2*x^4 + c^3*d*x^2)","B",0
432,1,1737,0,1.557961," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{20 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1554 \, a^{2} b^{10} c^{10} d^{2} - 22700 \, a^{3} b^{9} c^{9} d^{3} + 205215 \, a^{4} b^{8} c^{8} d^{4} - 1188600 \, a^{5} b^{7} c^{7} d^{5} + 4443580 \, a^{6} b^{6} c^{6} d^{6} - 10697400 \, a^{7} b^{5} c^{5} d^{7} + 16622415 \, a^{8} b^{4} c^{4} d^{8} - 16548300 \, a^{9} b^{3} c^{3} d^{9} + 10195794 \, a^{10} b^{2} c^{2} d^{10} - 3542940 \, a^{11} b c d^{11} + 531441 \, a^{12} d^{12}\right)} x - {\left(b^{8} c^{15} d - 40 \, a b^{7} c^{14} d^{2} + 636 \, a^{2} b^{6} c^{13} d^{3} - 5080 \, a^{3} b^{5} c^{12} d^{4} + 21286 \, a^{4} b^{4} c^{11} d^{5} - 45720 \, a^{5} b^{3} c^{10} d^{6} + 51516 \, a^{6} b^{2} c^{9} d^{7} - 29160 \, a^{7} b c^{8} d^{8} + 6561 \, a^{8} c^{7} d^{9}\right)} \sqrt{-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}}} c^{3} d \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{1}{4}} - {\left(b^{6} c^{9} d - 30 \, a b^{5} c^{8} d^{2} + 327 \, a^{2} b^{4} c^{7} d^{3} - 1540 \, a^{3} b^{3} c^{6} d^{4} + 2943 \, a^{4} b^{2} c^{5} d^{5} - 2430 \, a^{5} b c^{4} d^{6} + 729 \, a^{6} c^{3} d^{7}\right)} \sqrt{x} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{1}{4}}}{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}\right) - 5 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{1}{4}} \log\left(c^{10} d^{2} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 327 \, a^{2} b^{4} c^{4} d^{2} - 1540 \, a^{3} b^{3} c^{3} d^{3} + 2943 \, a^{4} b^{2} c^{2} d^{4} - 2430 \, a^{5} b c d^{5} + 729 \, a^{6} d^{6}\right)} \sqrt{x}\right) + 5 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{1}{4}} \log\left(-c^{10} d^{2} \left(-\frac{b^{8} c^{8} - 40 \, a b^{7} c^{7} d + 636 \, a^{2} b^{6} c^{6} d^{2} - 5080 \, a^{3} b^{5} c^{5} d^{3} + 21286 \, a^{4} b^{4} c^{4} d^{4} - 45720 \, a^{5} b^{3} c^{3} d^{5} + 51516 \, a^{6} b^{2} c^{2} d^{6} - 29160 \, a^{7} b c d^{7} + 6561 \, a^{8} d^{8}}{c^{13} d^{3}}\right)^{\frac{3}{4}} + {\left(b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 327 \, a^{2} b^{4} c^{4} d^{2} - 1540 \, a^{3} b^{3} c^{3} d^{3} + 2943 \, a^{4} b^{2} c^{2} d^{4} - 2430 \, a^{5} b c d^{5} + 729 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(5 \, {\left(b^{2} c^{2} - 10 \, a b c d + 9 \, a^{2} d^{2}\right)} x^{4} - 4 \, a^{2} c^{2} - 4 \, {\left(10 \, a b c^{2} - 9 \, a^{2} c d\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)}}"," ",0,"-1/40*(20*(c^3*d*x^5 + c^4*x^3)*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(1/4)*arctan((sqrt((b^12*c^12 - 60*a*b^11*c^11*d + 1554*a^2*b^10*c^10*d^2 - 22700*a^3*b^9*c^9*d^3 + 205215*a^4*b^8*c^8*d^4 - 1188600*a^5*b^7*c^7*d^5 + 4443580*a^6*b^6*c^6*d^6 - 10697400*a^7*b^5*c^5*d^7 + 16622415*a^8*b^4*c^4*d^8 - 16548300*a^9*b^3*c^3*d^9 + 10195794*a^10*b^2*c^2*d^10 - 3542940*a^11*b*c*d^11 + 531441*a^12*d^12)*x - (b^8*c^15*d - 40*a*b^7*c^14*d^2 + 636*a^2*b^6*c^13*d^3 - 5080*a^3*b^5*c^12*d^4 + 21286*a^4*b^4*c^11*d^5 - 45720*a^5*b^3*c^10*d^6 + 51516*a^6*b^2*c^9*d^7 - 29160*a^7*b*c^8*d^8 + 6561*a^8*c^7*d^9)*sqrt(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3)))*c^3*d*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(1/4) - (b^6*c^9*d - 30*a*b^5*c^8*d^2 + 327*a^2*b^4*c^7*d^3 - 1540*a^3*b^3*c^6*d^4 + 2943*a^4*b^2*c^5*d^5 - 2430*a^5*b*c^4*d^6 + 729*a^6*c^3*d^7)*sqrt(x)*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(1/4))/(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)) - 5*(c^3*d*x^5 + c^4*x^3)*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(1/4)*log(c^10*d^2*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(3/4) + (b^6*c^6 - 30*a*b^5*c^5*d + 327*a^2*b^4*c^4*d^2 - 1540*a^3*b^3*c^3*d^3 + 2943*a^4*b^2*c^2*d^4 - 2430*a^5*b*c*d^5 + 729*a^6*d^6)*sqrt(x)) + 5*(c^3*d*x^5 + c^4*x^3)*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(1/4)*log(-c^10*d^2*(-(b^8*c^8 - 40*a*b^7*c^7*d + 636*a^2*b^6*c^6*d^2 - 5080*a^3*b^5*c^5*d^3 + 21286*a^4*b^4*c^4*d^4 - 45720*a^5*b^3*c^3*d^5 + 51516*a^6*b^2*c^2*d^6 - 29160*a^7*b*c*d^7 + 6561*a^8*d^8)/(c^13*d^3))^(3/4) + (b^6*c^6 - 30*a*b^5*c^5*d + 327*a^2*b^4*c^4*d^2 - 1540*a^3*b^3*c^3*d^3 + 2943*a^4*b^2*c^2*d^4 - 2430*a^5*b*c*d^5 + 729*a^6*d^6)*sqrt(x)) - 4*(5*(b^2*c^2 - 10*a*b*c*d + 9*a^2*d^2)*x^4 - 4*a^2*c^2 - 4*(10*a*b*c^2 - 9*a^2*c*d)*x^2)*sqrt(x))/(c^3*d*x^5 + c^4*x^3)","B",0
433,1,1427,0,1.440983," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{20 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{2} d^{8} \sqrt{-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}} + {\left(13689 \, b^{4} c^{4} - 21060 \, a b^{3} c^{3} d + 9270 \, a^{2} b^{2} c^{2} d^{2} - 900 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}\right)} x} c^{2} d^{13} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{3}{4}} - {\left(117 \, b^{2} c^{4} d^{13} - 90 \, a b c^{3} d^{14} + 5 \, a^{2} c^{2} d^{15}\right)} \sqrt{x} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{3}{4}}}{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}\right) + 5 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{1}{4}} \log\left(c d^{4} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{1}{4}} + {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 5 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{1}{4}} \log\left(-c d^{4} \left(-\frac{187388721 \, b^{8} c^{8} - 576580680 \, a b^{7} c^{7} d + 697317660 \, a^{2} b^{6} c^{6} d^{2} - 415092600 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 17739000 \, a^{5} b^{3} c^{3} d^{5} + 1273500 \, a^{6} b^{2} c^{2} d^{6} - 45000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{3} d^{17}}\right)^{\frac{1}{4}} + {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(32 \, b^{2} d^{3} x^{6} - 585 \, b^{2} c^{3} + 450 \, a b c^{2} d - 25 \, a^{2} c d^{2} - 32 \, {\left(13 \, b^{2} c d^{2} - 10 \, a b d^{3}\right)} x^{4} - 9 \, {\left(117 \, b^{2} c^{2} d - 90 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{320 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}}"," ",0,"1/320*(20*(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(1/4)*arctan((sqrt(c^2*d^8*sqrt(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17)) + (13689*b^4*c^4 - 21060*a*b^3*c^3*d + 9270*a^2*b^2*c^2*d^2 - 900*a^3*b*c*d^3 + 25*a^4*d^4)*x)*c^2*d^13*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(3/4) - (117*b^2*c^4*d^13 - 90*a*b*c^3*d^14 + 5*a^2*c^2*d^15)*sqrt(x)*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(3/4))/(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)) + 5*(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(1/4)*log(c*d^4*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(1/4) + (117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*sqrt(x)) - 5*(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(1/4)*log(-c*d^4*(-(187388721*b^8*c^8 - 576580680*a*b^7*c^7*d + 697317660*a^2*b^6*c^6*d^2 - 415092600*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 17739000*a^5*b^3*c^3*d^5 + 1273500*a^6*b^2*c^2*d^6 - 45000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^3*d^17))^(1/4) + (117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*sqrt(x)) + 4*(32*b^2*d^3*x^6 - 585*b^2*c^3 + 450*a*b*c^2*d - 25*a^2*c*d^2 - 32*(13*b^2*c*d^2 - 10*a*b*d^3)*x^4 - 9*(117*b^2*c^2*d - 90*a*b*c*d^2 + 5*a^2*d^3)*x^2)*sqrt(x))/(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)","B",0
434,1,1813,0,1.241953," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(208422380089 \, b^{12} c^{12} - 682109607564 \, a b^{11} c^{11} d + 881427350034 \, a^{2} b^{10} c^{10} d^{2} - 543593843100 \, a^{3} b^{9} c^{9} d^{3} + 136525986135 \, a^{4} b^{8} c^{8} d^{4} + 8334677736 \, a^{5} b^{7} c^{7} d^{5} - 7849956996 \, a^{6} b^{6} c^{6} d^{6} - 324727704 \, a^{7} b^{5} c^{5} d^{7} + 207241335 \, a^{8} b^{4} c^{4} d^{8} + 32148900 \, a^{9} b^{3} c^{3} d^{9} + 2030994 \, a^{10} b^{2} c^{2} d^{10} + 61236 \, a^{11} b c d^{11} + 729 \, a^{12} d^{12}\right)} x - {\left(35153041 \, b^{8} c^{11} d^{7} - 76697544 \, a b^{7} c^{10} d^{8} + 57274140 \, a^{2} b^{6} c^{9} d^{9} - 13854456 \, a^{3} b^{5} c^{8} d^{10} - 1457946 \, a^{4} b^{4} c^{7} d^{11} + 539784 \, a^{5} b^{3} c^{6} d^{12} + 86940 \, a^{6} b^{2} c^{5} d^{13} + 4536 \, a^{7} b c^{4} d^{14} + 81 \, a^{8} c^{3} d^{15}\right)} \sqrt{-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}}} c d^{4} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{1}{4}} + {\left(456533 \, b^{6} c^{7} d^{4} - 747054 \, a b^{5} c^{6} d^{5} + 354123 \, a^{2} b^{4} c^{5} d^{6} - 15876 \, a^{3} b^{3} c^{4} d^{7} - 13797 \, a^{4} b^{2} c^{3} d^{8} - 1134 \, a^{5} b c^{2} d^{9} - 27 \, a^{6} c d^{10}\right)} \sqrt{x} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{1}{4}}}{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}\right) - 3 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{1}{4}} \log\left(c^{4} d^{11} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{3}{4}} - {\left(456533 \, b^{6} c^{6} - 747054 \, a b^{5} c^{5} d + 354123 \, a^{2} b^{4} c^{4} d^{2} - 15876 \, a^{3} b^{3} c^{3} d^{3} - 13797 \, a^{4} b^{2} c^{2} d^{4} - 1134 \, a^{5} b c d^{5} - 27 \, a^{6} d^{6}\right)} \sqrt{x}\right) + 3 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{1}{4}} \log\left(-c^{4} d^{11} \left(-\frac{35153041 \, b^{8} c^{8} - 76697544 \, a b^{7} c^{7} d + 57274140 \, a^{2} b^{6} c^{6} d^{2} - 13854456 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} + 539784 \, a^{5} b^{3} c^{3} d^{5} + 86940 \, a^{6} b^{2} c^{2} d^{6} + 4536 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{5} d^{15}}\right)^{\frac{3}{4}} - {\left(456533 \, b^{6} c^{6} - 747054 \, a b^{5} c^{5} d + 354123 \, a^{2} b^{4} c^{4} d^{2} - 15876 \, a^{3} b^{3} c^{3} d^{3} - 13797 \, a^{4} b^{2} c^{2} d^{4} - 1134 \, a^{5} b c d^{5} - 27 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(32 \, b^{2} c d^{2} x^{5} + {\left(121 \, b^{2} c^{2} d - 66 \, a b c d^{2} + 9 \, a^{2} d^{3}\right)} x^{3} + {\left(77 \, b^{2} c^{3} - 42 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{x}}{192 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}"," ",0,"-1/192*(12*(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(1/4)*arctan((sqrt((208422380089*b^12*c^12 - 682109607564*a*b^11*c^11*d + 881427350034*a^2*b^10*c^10*d^2 - 543593843100*a^3*b^9*c^9*d^3 + 136525986135*a^4*b^8*c^8*d^4 + 8334677736*a^5*b^7*c^7*d^5 - 7849956996*a^6*b^6*c^6*d^6 - 324727704*a^7*b^5*c^5*d^7 + 207241335*a^8*b^4*c^4*d^8 + 32148900*a^9*b^3*c^3*d^9 + 2030994*a^10*b^2*c^2*d^10 + 61236*a^11*b*c*d^11 + 729*a^12*d^12)*x - (35153041*b^8*c^11*d^7 - 76697544*a*b^7*c^10*d^8 + 57274140*a^2*b^6*c^9*d^9 - 13854456*a^3*b^5*c^8*d^10 - 1457946*a^4*b^4*c^7*d^11 + 539784*a^5*b^3*c^6*d^12 + 86940*a^6*b^2*c^5*d^13 + 4536*a^7*b*c^4*d^14 + 81*a^8*c^3*d^15)*sqrt(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15)))*c*d^4*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(1/4) + (456533*b^6*c^7*d^4 - 747054*a*b^5*c^6*d^5 + 354123*a^2*b^4*c^5*d^6 - 15876*a^3*b^3*c^4*d^7 - 13797*a^4*b^2*c^3*d^8 - 1134*a^5*b*c^2*d^9 - 27*a^6*c*d^10)*sqrt(x)*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(1/4))/(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)) - 3*(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(1/4)*log(c^4*d^11*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(3/4) - (456533*b^6*c^6 - 747054*a*b^5*c^5*d + 354123*a^2*b^4*c^4*d^2 - 15876*a^3*b^3*c^3*d^3 - 13797*a^4*b^2*c^2*d^4 - 1134*a^5*b*c*d^5 - 27*a^6*d^6)*sqrt(x)) + 3*(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(1/4)*log(-c^4*d^11*(-(35153041*b^8*c^8 - 76697544*a*b^7*c^7*d + 57274140*a^2*b^6*c^6*d^2 - 13854456*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 + 539784*a^5*b^3*c^3*d^5 + 86940*a^6*b^2*c^2*d^6 + 4536*a^7*b*c*d^7 + 81*a^8*d^8)/(c^5*d^15))^(3/4) - (456533*b^6*c^6 - 747054*a*b^5*c^5*d + 354123*a^2*b^4*c^4*d^2 - 15876*a^3*b^3*c^3*d^3 - 13797*a^4*b^2*c^2*d^4 - 1134*a^5*b*c*d^5 - 27*a^6*d^6)*sqrt(x)) - 4*(32*b^2*c*d^2*x^5 + (121*b^2*c^2*d - 66*a*b*c*d^2 + 9*a^2*d^3)*x^3 + (77*b^2*c^3 - 42*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(x))/(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)","B",0
435,1,1420,0,1.292660," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{4} d^{6} \sqrt{-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}} + {\left(2025 \, b^{4} c^{4} - 900 \, a b^{3} c^{3} d - 170 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4}\right)} x} c^{5} d^{10} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{3}{4}} + {\left(45 \, b^{2} c^{7} d^{10} - 10 \, a b c^{6} d^{11} - 3 \, a^{2} c^{5} d^{12}\right)} \sqrt{x} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{3}{4}}}{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}\right) + {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{1}{4}} \log\left(c^{2} d^{3} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{1}{4}} - {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{x}\right) - {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{1}{4}} \log\left(-c^{2} d^{3} \left(-\frac{4100625 \, b^{8} c^{8} - 3645000 \, a b^{7} c^{7} d + 121500 \, a^{2} b^{6} c^{6} d^{2} + 549000 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} - 36600 \, a^{5} b^{3} c^{3} d^{5} + 540 \, a^{6} b^{2} c^{2} d^{6} + 1080 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{c^{7} d^{13}}\right)^{\frac{1}{4}} - {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(32 \, b^{2} c d^{2} x^{4} + 45 \, b^{2} c^{3} - 10 \, a b c^{2} d - 3 \, a^{2} c d^{2} + {\left(81 \, b^{2} c^{2} d - 18 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}}"," ",0,"1/64*(4*(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(1/4)*arctan((sqrt(c^4*d^6*sqrt(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13)) + (2025*b^4*c^4 - 900*a*b^3*c^3*d - 170*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 + 9*a^4*d^4)*x)*c^5*d^10*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(3/4) + (45*b^2*c^7*d^10 - 10*a*b*c^6*d^11 - 3*a^2*c^5*d^12)*sqrt(x)*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(3/4))/(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)) + (c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(1/4)*log(c^2*d^3*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(1/4) - (45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*sqrt(x)) - (c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(1/4)*log(-c^2*d^3*(-(4100625*b^8*c^8 - 3645000*a*b^7*c^7*d + 121500*a^2*b^6*c^6*d^2 + 549000*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 - 36600*a^5*b^3*c^3*d^5 + 540*a^6*b^2*c^2*d^6 + 1080*a^7*b*c*d^7 + 81*a^8*d^8)/(c^7*d^13))^(1/4) - (45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*sqrt(x)) + 4*(32*b^2*c*d^2*x^4 + 45*b^2*c^3 - 10*a*b*c^2*d - 3*a^2*c*d^2 + (81*b^2*c^2*d - 18*a*b*c*d^2 + a^2*d^3)*x^2)*sqrt(x))/(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3)","B",0
436,1,1811,0,1.581846," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(85766121 \, b^{12} c^{12} + 147027636 \, a b^{11} c^{11} d + 227542770 \, a^{2} b^{10} c^{10} d^{2} + 215040420 \, a^{3} b^{9} c^{9} d^{3} + 181522215 \, a^{4} b^{8} c^{8} d^{4} + 112905576 \, a^{5} b^{7} c^{7} d^{5} + 63002556 \, a^{6} b^{6} c^{6} d^{6} + 26882280 \, a^{7} b^{5} c^{5} d^{7} + 10290375 \, a^{8} b^{4} c^{4} d^{8} + 2902500 \, a^{9} b^{3} c^{3} d^{9} + 731250 \, a^{10} b^{2} c^{2} d^{10} + 112500 \, a^{11} b c d^{11} + 15625 \, a^{12} d^{12}\right)} x - {\left(194481 \, b^{8} c^{13} d^{5} + 222264 \, a b^{7} c^{12} d^{6} + 280476 \, a^{2} b^{6} c^{11} d^{7} + 176904 \, a^{3} b^{5} c^{10} d^{8} + 112806 \, a^{4} b^{4} c^{9} d^{9} + 42120 \, a^{5} b^{3} c^{8} d^{10} + 15900 \, a^{6} b^{2} c^{7} d^{11} + 3000 \, a^{7} b c^{6} d^{12} + 625 \, a^{8} c^{5} d^{13}\right)} \sqrt{-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}}} c^{2} d^{3} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{1}{4}} - {\left(9261 \, b^{6} c^{8} d^{3} + 7938 \, a b^{5} c^{7} d^{4} + 8883 \, a^{2} b^{4} c^{6} d^{5} + 3996 \, a^{3} b^{3} c^{5} d^{6} + 2115 \, a^{4} b^{2} c^{4} d^{7} + 450 \, a^{5} b c^{3} d^{8} + 125 \, a^{6} c^{2} d^{9}\right)} \sqrt{x} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{1}{4}}}{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}\right) - {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{1}{4}} \log\left(c^{7} d^{8} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{3}{4}} + {\left(9261 \, b^{6} c^{6} + 7938 \, a b^{5} c^{5} d + 8883 \, a^{2} b^{4} c^{4} d^{2} + 3996 \, a^{3} b^{3} c^{3} d^{3} + 2115 \, a^{4} b^{2} c^{2} d^{4} + 450 \, a^{5} b c d^{5} + 125 \, a^{6} d^{6}\right)} \sqrt{x}\right) + {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{1}{4}} \log\left(-c^{7} d^{8} \left(-\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{c^{9} d^{11}}\right)^{\frac{3}{4}} + {\left(9261 \, b^{6} c^{6} + 7938 \, a b^{5} c^{5} d + 8883 \, a^{2} b^{4} c^{4} d^{2} + 3996 \, a^{3} b^{3} c^{3} d^{3} + 2115 \, a^{4} b^{2} c^{2} d^{4} + 450 \, a^{5} b c d^{5} + 125 \, a^{6} d^{6}\right)} \sqrt{x}\right) + 4 \, {\left({\left(11 \, b^{2} c^{2} d - 6 \, a b c d^{2} - 5 \, a^{2} d^{3}\right)} x^{3} + {\left(7 \, b^{2} c^{3} + 2 \, a b c^{2} d - 9 \, a^{2} c d^{2}\right)} x\right)} \sqrt{x}}{64 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}}"," ",0,"-1/64*(4*(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(1/4)*arctan((sqrt((85766121*b^12*c^12 + 147027636*a*b^11*c^11*d + 227542770*a^2*b^10*c^10*d^2 + 215040420*a^3*b^9*c^9*d^3 + 181522215*a^4*b^8*c^8*d^4 + 112905576*a^5*b^7*c^7*d^5 + 63002556*a^6*b^6*c^6*d^6 + 26882280*a^7*b^5*c^5*d^7 + 10290375*a^8*b^4*c^4*d^8 + 2902500*a^9*b^3*c^3*d^9 + 731250*a^10*b^2*c^2*d^10 + 112500*a^11*b*c*d^11 + 15625*a^12*d^12)*x - (194481*b^8*c^13*d^5 + 222264*a*b^7*c^12*d^6 + 280476*a^2*b^6*c^11*d^7 + 176904*a^3*b^5*c^10*d^8 + 112806*a^4*b^4*c^9*d^9 + 42120*a^5*b^3*c^8*d^10 + 15900*a^6*b^2*c^7*d^11 + 3000*a^7*b*c^6*d^12 + 625*a^8*c^5*d^13)*sqrt(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11)))*c^2*d^3*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(1/4) - (9261*b^6*c^8*d^3 + 7938*a*b^5*c^7*d^4 + 8883*a^2*b^4*c^6*d^5 + 3996*a^3*b^3*c^5*d^6 + 2115*a^4*b^2*c^4*d^7 + 450*a^5*b*c^3*d^8 + 125*a^6*c^2*d^9)*sqrt(x)*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(1/4))/(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)) - (c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(1/4)*log(c^7*d^8*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(3/4) + (9261*b^6*c^6 + 7938*a*b^5*c^5*d + 8883*a^2*b^4*c^4*d^2 + 3996*a^3*b^3*c^3*d^3 + 2115*a^4*b^2*c^2*d^4 + 450*a^5*b*c*d^5 + 125*a^6*d^6)*sqrt(x)) + (c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(1/4)*log(-c^7*d^8*(-(194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(c^9*d^11))^(3/4) + (9261*b^6*c^6 + 7938*a*b^5*c^5*d + 8883*a^2*b^4*c^4*d^2 + 3996*a^3*b^3*c^3*d^3 + 2115*a^4*b^2*c^2*d^4 + 450*a^5*b*c*d^5 + 125*a^6*d^6)*sqrt(x)) + 4*((11*b^2*c^2*d - 6*a*b*c*d^2 - 5*a^2*d^3)*x^3 + (7*b^2*c^3 + 2*a*b*c^2*d - 9*a^2*c*d^2)*x)*sqrt(x))/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)","B",0
437,1,1416,0,1.556619," ","integrate((b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{6} d^{4} \sqrt{-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}} + {\left(25 \, b^{4} c^{4} + 60 \, a b^{3} c^{3} d + 246 \, a^{2} b^{2} c^{2} d^{2} + 252 \, a^{3} b c d^{3} + 441 \, a^{4} d^{4}\right)} x} c^{8} d^{7} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{3}{4}} - {\left(5 \, b^{2} c^{10} d^{7} + 6 \, a b c^{9} d^{8} + 21 \, a^{2} c^{8} d^{9}\right)} \sqrt{x} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{3}{4}}}{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}\right) + {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(c^{3} d^{2} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} + {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \sqrt{x}\right) - {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(-c^{3} d^{2} \left(-\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{c^{11} d^{9}}\right)^{\frac{1}{4}} + {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 4 \, {\left(5 \, b^{2} c^{3} + 6 \, a b c^{2} d - 11 \, a^{2} c d^{2} + {\left(9 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 7 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}}"," ",0,"1/64*(4*(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*arctan((sqrt(c^6*d^4*sqrt(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9)) + (25*b^4*c^4 + 60*a*b^3*c^3*d + 246*a^2*b^2*c^2*d^2 + 252*a^3*b*c*d^3 + 441*a^4*d^4)*x)*c^8*d^7*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(3/4) - (5*b^2*c^10*d^7 + 6*a*b*c^9*d^8 + 21*a^2*c^8*d^9)*sqrt(x)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(3/4))/(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)) + (c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*log(c^3*d^2*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4) + (5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*sqrt(x)) - (c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4)*log(-c^3*d^2*(-(625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(c^11*d^9))^(1/4) + (5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*sqrt(x)) - 4*(5*b^2*c^3 + 6*a*b*c^2*d - 11*a^2*c*d^2 + (9*b^2*c^2*d - 2*a*b*c*d^2 - 7*a^2*d^3)*x^2)*sqrt(x))/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2)","B",0
438,1,1819,0,1.841511," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(c^{3} d^{3} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{5} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, b^{12} c^{12} + 14580 \, a b^{11} c^{11} d + 55890 \, a^{2} b^{10} c^{10} d^{2} - 553500 \, a^{3} b^{9} c^{9} d^{3} - 3479625 \, a^{4} b^{8} c^{8} d^{4} + 10305000 \, a^{5} b^{7} c^{7} d^{5} + 75317500 \, a^{6} b^{6} c^{6} d^{6} - 154575000 \, a^{7} b^{5} c^{5} d^{7} - 782915625 \, a^{8} b^{4} c^{4} d^{8} + 1868062500 \, a^{9} b^{3} c^{3} d^{9} + 2829431250 \, a^{10} b^{2} c^{2} d^{10} - 11071687500 \, a^{11} b c d^{11} + 8303765625 \, a^{12} d^{12}\right)} x - {\left(81 \, b^{8} c^{15} d^{3} + 1080 \, a b^{7} c^{14} d^{4} + 540 \, a^{2} b^{6} c^{13} d^{5} - 36600 \, a^{3} b^{5} c^{12} d^{6} - 42650 \, a^{4} b^{4} c^{11} d^{7} + 549000 \, a^{5} b^{3} c^{10} d^{8} + 121500 \, a^{6} b^{2} c^{9} d^{9} - 3645000 \, a^{7} b c^{8} d^{10} + 4100625 \, a^{8} c^{7} d^{11}\right)} \sqrt{-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}}} c^{3} d^{2} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{1}{4}} + {\left(27 \, b^{6} c^{9} d^{2} + 270 \, a b^{5} c^{8} d^{3} - 315 \, a^{2} b^{4} c^{7} d^{4} - 7100 \, a^{3} b^{3} c^{6} d^{5} + 4725 \, a^{4} b^{2} c^{5} d^{6} + 60750 \, a^{5} b c^{4} d^{7} - 91125 \, a^{6} c^{3} d^{8}\right)} \sqrt{x} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{1}{4}}}{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}\right) - {\left(c^{3} d^{3} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{5} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{10} d^{5} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{3}{4}} - {\left(27 \, b^{6} c^{6} + 270 \, a b^{5} c^{5} d - 315 \, a^{2} b^{4} c^{4} d^{2} - 7100 \, a^{3} b^{3} c^{3} d^{3} + 4725 \, a^{4} b^{2} c^{2} d^{4} + 60750 \, a^{5} b c d^{5} - 91125 \, a^{6} d^{6}\right)} \sqrt{x}\right) + {\left(c^{3} d^{3} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{5} d x\right)} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{1}{4}} \log\left(-c^{10} d^{5} \left(-\frac{81 \, b^{8} c^{8} + 1080 \, a b^{7} c^{7} d + 540 \, a^{2} b^{6} c^{6} d^{2} - 36600 \, a^{3} b^{5} c^{5} d^{3} - 42650 \, a^{4} b^{4} c^{4} d^{4} + 549000 \, a^{5} b^{3} c^{3} d^{5} + 121500 \, a^{6} b^{2} c^{2} d^{6} - 3645000 \, a^{7} b c d^{7} + 4100625 \, a^{8} d^{8}}{c^{13} d^{7}}\right)^{\frac{3}{4}} - {\left(27 \, b^{6} c^{6} + 270 \, a b^{5} c^{5} d - 315 \, a^{2} b^{4} c^{4} d^{2} - 7100 \, a^{3} b^{3} c^{3} d^{3} + 4725 \, a^{4} b^{2} c^{2} d^{4} + 60750 \, a^{5} b c d^{5} - 91125 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(32 \, a^{2} c^{2} d - {\left(3 \, b^{2} c^{2} d + 10 \, a b c d^{2} - 45 \, a^{2} d^{3}\right)} x^{4} + {\left(b^{2} c^{3} - 18 \, a b c^{2} d + 81 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{x}}{64 \, {\left(c^{3} d^{3} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{5} d x\right)}}"," ",0,"1/64*(4*(c^3*d^3*x^5 + 2*c^4*d^2*x^3 + c^5*d*x)*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(1/4)*arctan((sqrt((729*b^12*c^12 + 14580*a*b^11*c^11*d + 55890*a^2*b^10*c^10*d^2 - 553500*a^3*b^9*c^9*d^3 - 3479625*a^4*b^8*c^8*d^4 + 10305000*a^5*b^7*c^7*d^5 + 75317500*a^6*b^6*c^6*d^6 - 154575000*a^7*b^5*c^5*d^7 - 782915625*a^8*b^4*c^4*d^8 + 1868062500*a^9*b^3*c^3*d^9 + 2829431250*a^10*b^2*c^2*d^10 - 11071687500*a^11*b*c*d^11 + 8303765625*a^12*d^12)*x - (81*b^8*c^15*d^3 + 1080*a*b^7*c^14*d^4 + 540*a^2*b^6*c^13*d^5 - 36600*a^3*b^5*c^12*d^6 - 42650*a^4*b^4*c^11*d^7 + 549000*a^5*b^3*c^10*d^8 + 121500*a^6*b^2*c^9*d^9 - 3645000*a^7*b*c^8*d^10 + 4100625*a^8*c^7*d^11)*sqrt(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7)))*c^3*d^2*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(1/4) + (27*b^6*c^9*d^2 + 270*a*b^5*c^8*d^3 - 315*a^2*b^4*c^7*d^4 - 7100*a^3*b^3*c^6*d^5 + 4725*a^4*b^2*c^5*d^6 + 60750*a^5*b*c^4*d^7 - 91125*a^6*c^3*d^8)*sqrt(x)*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(1/4))/(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)) - (c^3*d^3*x^5 + 2*c^4*d^2*x^3 + c^5*d*x)*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(1/4)*log(c^10*d^5*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(3/4) - (27*b^6*c^6 + 270*a*b^5*c^5*d - 315*a^2*b^4*c^4*d^2 - 7100*a^3*b^3*c^3*d^3 + 4725*a^4*b^2*c^2*d^4 + 60750*a^5*b*c*d^5 - 91125*a^6*d^6)*sqrt(x)) + (c^3*d^3*x^5 + 2*c^4*d^2*x^3 + c^5*d*x)*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(1/4)*log(-c^10*d^5*(-(81*b^8*c^8 + 1080*a*b^7*c^7*d + 540*a^2*b^6*c^6*d^2 - 36600*a^3*b^5*c^5*d^3 - 42650*a^4*b^4*c^4*d^4 + 549000*a^5*b^3*c^3*d^5 + 121500*a^6*b^2*c^2*d^6 - 3645000*a^7*b*c*d^7 + 4100625*a^8*d^8)/(c^13*d^7))^(3/4) - (27*b^6*c^6 + 270*a*b^5*c^5*d - 315*a^2*b^4*c^4*d^2 - 7100*a^3*b^3*c^3*d^3 + 4725*a^4*b^2*c^2*d^4 + 60750*a^5*b*c*d^5 - 91125*a^6*d^6)*sqrt(x)) - 4*(32*a^2*c^2*d - (3*b^2*c^2*d + 10*a*b*c*d^2 - 45*a^2*d^3)*x^4 + (b^2*c^3 - 18*a*b*c^2*d + 81*a^2*c*d^2)*x^2)*sqrt(x))/(c^3*d^3*x^5 + 2*c^4*d^2*x^3 + c^5*d*x)","B",0
439,1,1433,0,1.582460," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(c^{3} d^{3} x^{6} + 2 \, c^{4} d^{2} x^{4} + c^{5} d x^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{c^{8} d^{2} \sqrt{-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}} + {\left(9 \, b^{4} c^{4} + 252 \, a b^{3} c^{3} d + 1302 \, a^{2} b^{2} c^{2} d^{2} - 6468 \, a^{3} b c d^{3} + 5929 \, a^{4} d^{4}\right)} x} c^{11} d^{4} \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{3}{4}} + {\left(3 \, b^{2} c^{13} d^{4} + 42 \, a b c^{12} d^{5} - 77 \, a^{2} c^{11} d^{6}\right)} \sqrt{x} \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{3}{4}}}{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}\right) + 3 \, {\left(c^{3} d^{3} x^{6} + 2 \, c^{4} d^{2} x^{4} + c^{5} d x^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{1}{4}} \log\left(c^{4} d \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{1}{4}} - {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \sqrt{x}\right) - 3 \, {\left(c^{3} d^{3} x^{6} + 2 \, c^{4} d^{2} x^{4} + c^{5} d x^{2}\right)} \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{1}{4}} \log\left(-c^{4} d \left(-\frac{81 \, b^{8} c^{8} + 4536 \, a b^{7} c^{7} d + 86940 \, a^{2} b^{6} c^{6} d^{2} + 539784 \, a^{3} b^{5} c^{5} d^{3} - 1457946 \, a^{4} b^{4} c^{4} d^{4} - 13854456 \, a^{5} b^{3} c^{3} d^{5} + 57274140 \, a^{6} b^{2} c^{2} d^{6} - 76697544 \, a^{7} b c d^{7} + 35153041 \, a^{8} d^{8}}{c^{15} d^{5}}\right)^{\frac{1}{4}} - {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \sqrt{x}\right) + 4 \, {\left(32 \, a^{2} c^{2} d - {\left(3 \, b^{2} c^{2} d + 42 \, a b c d^{2} - 77 \, a^{2} d^{3}\right)} x^{4} + {\left(9 \, b^{2} c^{3} - 66 \, a b c^{2} d + 121 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{x}}{192 \, {\left(c^{3} d^{3} x^{6} + 2 \, c^{4} d^{2} x^{4} + c^{5} d x^{2}\right)}}"," ",0,"-1/192*(12*(c^3*d^3*x^6 + 2*c^4*d^2*x^4 + c^5*d*x^2)*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(1/4)*arctan((sqrt(c^8*d^2*sqrt(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5)) + (9*b^4*c^4 + 252*a*b^3*c^3*d + 1302*a^2*b^2*c^2*d^2 - 6468*a^3*b*c*d^3 + 5929*a^4*d^4)*x)*c^11*d^4*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(3/4) + (3*b^2*c^13*d^4 + 42*a*b*c^12*d^5 - 77*a^2*c^11*d^6)*sqrt(x)*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(3/4))/(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)) + 3*(c^3*d^3*x^6 + 2*c^4*d^2*x^4 + c^5*d*x^2)*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(1/4)*log(c^4*d*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(1/4) - (3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*sqrt(x)) - 3*(c^3*d^3*x^6 + 2*c^4*d^2*x^4 + c^5*d*x^2)*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(1/4)*log(-c^4*d*(-(81*b^8*c^8 + 4536*a*b^7*c^7*d + 86940*a^2*b^6*c^6*d^2 + 539784*a^3*b^5*c^5*d^3 - 1457946*a^4*b^4*c^4*d^4 - 13854456*a^5*b^3*c^3*d^5 + 57274140*a^6*b^2*c^2*d^6 - 76697544*a^7*b*c*d^7 + 35153041*a^8*d^8)/(c^15*d^5))^(1/4) - (3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*sqrt(x)) + 4*(32*a^2*c^2*d - (3*b^2*c^2*d + 42*a*b*c*d^2 - 77*a^2*d^3)*x^4 + (9*b^2*c^3 - 66*a*b*c^2*d + 121*a^2*c*d^2)*x^2)*sqrt(x))/(c^3*d^3*x^6 + 2*c^4*d^2*x^4 + c^5*d*x^2)","B",0
440,1,1832,0,2.007270," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^3,x, algorithm=""fricas"")","-\frac{20 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, b^{12} c^{12} - 1687500 \, a b^{11} c^{11} d + 78131250 \, a^{2} b^{10} c^{10} d^{2} - 2019937500 \, a^{3} b^{9} c^{9} d^{3} + 31839834375 \, a^{4} b^{8} c^{8} d^{4} - 314326575000 \, a^{5} b^{7} c^{7} d^{5} + 1936382557500 \, a^{6} b^{6} c^{6} d^{6} - 7355241855000 \, a^{7} b^{5} c^{5} d^{7} + 17434219710375 \, a^{8} b^{4} c^{4} d^{8} - 25881265273500 \, a^{9} b^{3} c^{3} d^{9} + 23425464012210 \, a^{10} b^{2} c^{2} d^{10} - 11839219392780 \, a^{11} b c d^{11} + 2565164201769 \, a^{12} d^{12}\right)} x - {\left(625 \, b^{8} c^{17} d - 45000 \, a b^{7} c^{16} d^{2} + 1273500 \, a^{2} b^{6} c^{15} d^{3} - 17739000 \, a^{3} b^{5} c^{14} d^{4} + 124525350 \, a^{4} b^{4} c^{13} d^{5} - 415092600 \, a^{5} b^{3} c^{12} d^{6} + 697317660 \, a^{6} b^{2} c^{11} d^{7} - 576580680 \, a^{7} b c^{10} d^{8} + 187388721 \, a^{8} c^{9} d^{9}\right)} \sqrt{-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}}} c^{4} d \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{1}{4}} - {\left(125 \, b^{6} c^{10} d - 6750 \, a b^{5} c^{9} d^{2} + 130275 \, a^{2} b^{4} c^{8} d^{3} - 1044900 \, a^{3} b^{3} c^{7} d^{4} + 3048435 \, a^{4} b^{2} c^{6} d^{5} - 3696030 \, a^{5} b c^{5} d^{6} + 1601613 \, a^{6} c^{4} d^{7}\right)} \sqrt{x} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{1}{4}}}{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}\right) - 5 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{1}{4}} \log\left(c^{13} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{3}{4}} + {\left(125 \, b^{6} c^{6} - 6750 \, a b^{5} c^{5} d + 130275 \, a^{2} b^{4} c^{4} d^{2} - 1044900 \, a^{3} b^{3} c^{3} d^{3} + 3048435 \, a^{4} b^{2} c^{2} d^{4} - 3696030 \, a^{5} b c d^{5} + 1601613 \, a^{6} d^{6}\right)} \sqrt{x}\right) + 5 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{1}{4}} \log\left(-c^{13} d^{2} \left(-\frac{625 \, b^{8} c^{8} - 45000 \, a b^{7} c^{7} d + 1273500 \, a^{2} b^{6} c^{6} d^{2} - 17739000 \, a^{3} b^{5} c^{5} d^{3} + 124525350 \, a^{4} b^{4} c^{4} d^{4} - 415092600 \, a^{5} b^{3} c^{3} d^{5} + 697317660 \, a^{6} b^{2} c^{2} d^{6} - 576580680 \, a^{7} b c d^{7} + 187388721 \, a^{8} d^{8}}{c^{17} d^{3}}\right)^{\frac{3}{4}} + {\left(125 \, b^{6} c^{6} - 6750 \, a b^{5} c^{5} d + 130275 \, a^{2} b^{4} c^{4} d^{2} - 1044900 \, a^{3} b^{3} c^{3} d^{3} + 3048435 \, a^{4} b^{2} c^{2} d^{4} - 3696030 \, a^{5} b c d^{5} + 1601613 \, a^{6} d^{6}\right)} \sqrt{x}\right) - 4 \, {\left(5 \, {\left(5 \, b^{2} c^{2} d - 90 \, a b c d^{2} + 117 \, a^{2} d^{3}\right)} x^{6} - 32 \, a^{2} c^{3} + 9 \, {\left(5 \, b^{2} c^{3} - 90 \, a b c^{2} d + 117 \, a^{2} c d^{2}\right)} x^{4} - 32 \, {\left(10 \, a b c^{3} - 13 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{x}}{320 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)}}"," ",0,"-1/320*(20*(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3)*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(1/4)*arctan((sqrt((15625*b^12*c^12 - 1687500*a*b^11*c^11*d + 78131250*a^2*b^10*c^10*d^2 - 2019937500*a^3*b^9*c^9*d^3 + 31839834375*a^4*b^8*c^8*d^4 - 314326575000*a^5*b^7*c^7*d^5 + 1936382557500*a^6*b^6*c^6*d^6 - 7355241855000*a^7*b^5*c^5*d^7 + 17434219710375*a^8*b^4*c^4*d^8 - 25881265273500*a^9*b^3*c^3*d^9 + 23425464012210*a^10*b^2*c^2*d^10 - 11839219392780*a^11*b*c*d^11 + 2565164201769*a^12*d^12)*x - (625*b^8*c^17*d - 45000*a*b^7*c^16*d^2 + 1273500*a^2*b^6*c^15*d^3 - 17739000*a^3*b^5*c^14*d^4 + 124525350*a^4*b^4*c^13*d^5 - 415092600*a^5*b^3*c^12*d^6 + 697317660*a^6*b^2*c^11*d^7 - 576580680*a^7*b*c^10*d^8 + 187388721*a^8*c^9*d^9)*sqrt(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3)))*c^4*d*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(1/4) - (125*b^6*c^10*d - 6750*a*b^5*c^9*d^2 + 130275*a^2*b^4*c^8*d^3 - 1044900*a^3*b^3*c^7*d^4 + 3048435*a^4*b^2*c^6*d^5 - 3696030*a^5*b*c^5*d^6 + 1601613*a^6*c^4*d^7)*sqrt(x)*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(1/4))/(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)) - 5*(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3)*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(1/4)*log(c^13*d^2*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(3/4) + (125*b^6*c^6 - 6750*a*b^5*c^5*d + 130275*a^2*b^4*c^4*d^2 - 1044900*a^3*b^3*c^3*d^3 + 3048435*a^4*b^2*c^2*d^4 - 3696030*a^5*b*c*d^5 + 1601613*a^6*d^6)*sqrt(x)) + 5*(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3)*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(1/4)*log(-c^13*d^2*(-(625*b^8*c^8 - 45000*a*b^7*c^7*d + 1273500*a^2*b^6*c^6*d^2 - 17739000*a^3*b^5*c^5*d^3 + 124525350*a^4*b^4*c^4*d^4 - 415092600*a^5*b^3*c^3*d^5 + 697317660*a^6*b^2*c^2*d^6 - 576580680*a^7*b*c*d^7 + 187388721*a^8*d^8)/(c^17*d^3))^(3/4) + (125*b^6*c^6 - 6750*a*b^5*c^5*d + 130275*a^2*b^4*c^4*d^2 - 1044900*a^3*b^3*c^3*d^3 + 3048435*a^4*b^2*c^2*d^4 - 3696030*a^5*b*c*d^5 + 1601613*a^6*d^6)*sqrt(x)) - 4*(5*(5*b^2*c^2*d - 90*a*b*c*d^2 + 117*a^2*d^3)*x^6 - 32*a^2*c^3 + 9*(5*b^2*c^3 - 90*a*b*c^2*d + 117*a^2*c*d^2)*x^4 - 32*(10*a*b*c^3 - 13*a^2*c^2*d)*x^2)*sqrt(x))/(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3)","B",0
441,1,2528,0,1.657309," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","-\frac{4620 \, b^{4} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(a^{4} b^{18} c^{18} - 18 \, a^{5} b^{17} c^{17} d + 153 \, a^{6} b^{16} c^{16} d^{2} - 816 \, a^{7} b^{15} c^{15} d^{3} + 3060 \, a^{8} b^{14} c^{14} d^{4} - 8568 \, a^{9} b^{13} c^{13} d^{5} + 18564 \, a^{10} b^{12} c^{12} d^{6} - 31824 \, a^{11} b^{11} c^{11} d^{7} + 43758 \, a^{12} b^{10} c^{10} d^{8} - 48620 \, a^{13} b^{9} c^{9} d^{9} + 43758 \, a^{14} b^{8} c^{8} d^{10} - 31824 \, a^{15} b^{7} c^{7} d^{11} + 18564 \, a^{16} b^{6} c^{6} d^{12} - 8568 \, a^{17} b^{5} c^{5} d^{13} + 3060 \, a^{18} b^{4} c^{4} d^{14} - 816 \, a^{19} b^{3} c^{3} d^{15} + 153 \, a^{20} b^{2} c^{2} d^{16} - 18 \, a^{21} b c d^{17} + a^{22} d^{18}\right)} x - {\left(a^{3} b^{21} c^{12} - 12 \, a^{4} b^{20} c^{11} d + 66 \, a^{5} b^{19} c^{10} d^{2} - 220 \, a^{6} b^{18} c^{9} d^{3} + 495 \, a^{7} b^{17} c^{8} d^{4} - 792 \, a^{8} b^{16} c^{7} d^{5} + 924 \, a^{9} b^{15} c^{6} d^{6} - 792 \, a^{10} b^{14} c^{5} d^{7} + 495 \, a^{11} b^{13} c^{4} d^{8} - 220 \, a^{12} b^{12} c^{3} d^{9} + 66 \, a^{13} b^{11} c^{2} d^{10} - 12 \, a^{14} b^{10} c d^{11} + a^{15} b^{9} d^{12}\right)} \sqrt{-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}}} b^{5} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{1}{4}} + {\left(a^{2} b^{14} c^{9} - 9 \, a^{3} b^{13} c^{8} d + 36 \, a^{4} b^{12} c^{7} d^{2} - 84 \, a^{5} b^{11} c^{6} d^{3} + 126 \, a^{6} b^{10} c^{5} d^{4} - 126 \, a^{7} b^{9} c^{4} d^{5} + 84 \, a^{8} b^{8} c^{3} d^{6} - 36 \, a^{9} b^{7} c^{2} d^{7} + 9 \, a^{10} b^{6} c d^{8} - a^{11} b^{5} d^{9}\right)} \sqrt{x} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{1}{4}}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right) - 1155 \, b^{4} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{1}{4}} \log\left(b^{14} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{3}{4}} - {\left(a^{2} b^{9} c^{9} - 9 \, a^{3} b^{8} c^{8} d + 36 \, a^{4} b^{7} c^{7} d^{2} - 84 \, a^{5} b^{6} c^{6} d^{3} + 126 \, a^{6} b^{5} c^{5} d^{4} - 126 \, a^{7} b^{4} c^{4} d^{5} + 84 \, a^{8} b^{3} c^{3} d^{6} - 36 \, a^{9} b^{2} c^{2} d^{7} + 9 \, a^{10} b c d^{8} - a^{11} d^{9}\right)} \sqrt{x}\right) + 1155 \, b^{4} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{1}{4}} \log\left(-b^{14} \left(-\frac{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}{b^{19}}\right)^{\frac{3}{4}} - {\left(a^{2} b^{9} c^{9} - 9 \, a^{3} b^{8} c^{8} d + 36 \, a^{4} b^{7} c^{7} d^{2} - 84 \, a^{5} b^{6} c^{6} d^{3} + 126 \, a^{6} b^{5} c^{5} d^{4} - 126 \, a^{7} b^{4} c^{4} d^{5} + 84 \, a^{8} b^{3} c^{3} d^{6} - 36 \, a^{9} b^{2} c^{2} d^{7} + 9 \, a^{10} b c d^{8} - a^{11} d^{9}\right)} \sqrt{x}\right) - 4 \, {\left(77 \, b^{3} d^{3} x^{7} + 105 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{5} + 165 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} + 385 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x\right)} \sqrt{x}}{2310 \, b^{4}}"," ",0,"-1/2310*(4620*b^4*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(1/4)*arctan((sqrt((a^4*b^18*c^18 - 18*a^5*b^17*c^17*d + 153*a^6*b^16*c^16*d^2 - 816*a^7*b^15*c^15*d^3 + 3060*a^8*b^14*c^14*d^4 - 8568*a^9*b^13*c^13*d^5 + 18564*a^10*b^12*c^12*d^6 - 31824*a^11*b^11*c^11*d^7 + 43758*a^12*b^10*c^10*d^8 - 48620*a^13*b^9*c^9*d^9 + 43758*a^14*b^8*c^8*d^10 - 31824*a^15*b^7*c^7*d^11 + 18564*a^16*b^6*c^6*d^12 - 8568*a^17*b^5*c^5*d^13 + 3060*a^18*b^4*c^4*d^14 - 816*a^19*b^3*c^3*d^15 + 153*a^20*b^2*c^2*d^16 - 18*a^21*b*c*d^17 + a^22*d^18)*x - (a^3*b^21*c^12 - 12*a^4*b^20*c^11*d + 66*a^5*b^19*c^10*d^2 - 220*a^6*b^18*c^9*d^3 + 495*a^7*b^17*c^8*d^4 - 792*a^8*b^16*c^7*d^5 + 924*a^9*b^15*c^6*d^6 - 792*a^10*b^14*c^5*d^7 + 495*a^11*b^13*c^4*d^8 - 220*a^12*b^12*c^3*d^9 + 66*a^13*b^11*c^2*d^10 - 12*a^14*b^10*c*d^11 + a^15*b^9*d^12)*sqrt(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19))*b^5*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(1/4) + (a^2*b^14*c^9 - 9*a^3*b^13*c^8*d + 36*a^4*b^12*c^7*d^2 - 84*a^5*b^11*c^6*d^3 + 126*a^6*b^10*c^5*d^4 - 126*a^7*b^9*c^4*d^5 + 84*a^8*b^8*c^3*d^6 - 36*a^9*b^7*c^2*d^7 + 9*a^10*b^6*c*d^8 - a^11*b^5*d^9)*sqrt(x)*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(1/4))/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)) - 1155*b^4*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(1/4)*log(b^14*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(3/4) - (a^2*b^9*c^9 - 9*a^3*b^8*c^8*d + 36*a^4*b^7*c^7*d^2 - 84*a^5*b^6*c^6*d^3 + 126*a^6*b^5*c^5*d^4 - 126*a^7*b^4*c^4*d^5 + 84*a^8*b^3*c^3*d^6 - 36*a^9*b^2*c^2*d^7 + 9*a^10*b*c*d^8 - a^11*d^9)*sqrt(x)) + 1155*b^4*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(1/4)*log(-b^14*(-(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)/b^19)^(3/4) - (a^2*b^9*c^9 - 9*a^3*b^8*c^8*d + 36*a^4*b^7*c^7*d^2 - 84*a^5*b^6*c^6*d^3 + 126*a^6*b^5*c^5*d^4 - 126*a^7*b^4*c^4*d^5 + 84*a^8*b^3*c^3*d^6 - 36*a^9*b^2*c^2*d^7 + 9*a^10*b*c*d^8 - a^11*d^9)*sqrt(x)) - 4*(77*b^3*d^3*x^7 + 105*(3*b^3*c*d^2 - a*b^2*d^3)*x^5 + 165*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^3 + 385*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x)*sqrt(x))/b^4","B",0
442,1,1898,0,1.487349," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{2340 \, b^{4} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{8} \sqrt{-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} b^{13} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{3}{4}} + {\left(b^{16} c^{3} - 3 \, a b^{15} c^{2} d + 3 \, a^{2} b^{14} c d^{2} - a^{3} b^{13} d^{3}\right)} \sqrt{x} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{3}{4}}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right) + 585 \, b^{4} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{1}{4}} \log\left(b^{4} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 585 \, b^{4} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{1}{4}} \log\left(-b^{4} \left(-\frac{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}{b^{17}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) + 4 \, {\left(45 \, b^{3} d^{3} x^{6} + 585 \, b^{3} c^{3} - 1755 \, a b^{2} c^{2} d + 1755 \, a^{2} b c d^{2} - 585 \, a^{3} d^{3} + 65 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{4} + 117 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{x}}{1170 \, b^{4}}"," ",0,"1/1170*(2340*b^4*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(1/4)*arctan((sqrt(b^8*sqrt(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x)*b^13*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(3/4) + (b^16*c^3 - 3*a*b^15*c^2*d + 3*a^2*b^14*c*d^2 - a^3*b^13*d^3)*sqrt(x)*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(3/4))/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)) + 585*b^4*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(1/4)*log(b^4*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 585*b^4*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(1/4)*log(-b^4*(-(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)/b^17)^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) + 4*(45*b^3*d^3*x^6 + 585*b^3*c^3 - 1755*a*b^2*c^2*d + 1755*a^2*b*c*d^2 - 585*a^3*d^3 + 65*(3*b^3*c*d^2 - a*b^2*d^3)*x^4 + 117*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^2)*sqrt(x))/b^4","B",0
443,1,2441,0,1.602992," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{924 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} - 18 \, a b^{17} c^{17} d + 153 \, a^{2} b^{16} c^{16} d^{2} - 816 \, a^{3} b^{15} c^{15} d^{3} + 3060 \, a^{4} b^{14} c^{14} d^{4} - 8568 \, a^{5} b^{13} c^{13} d^{5} + 18564 \, a^{6} b^{12} c^{12} d^{6} - 31824 \, a^{7} b^{11} c^{11} d^{7} + 43758 \, a^{8} b^{10} c^{10} d^{8} - 48620 \, a^{9} b^{9} c^{9} d^{9} + 43758 \, a^{10} b^{8} c^{8} d^{10} - 31824 \, a^{11} b^{7} c^{7} d^{11} + 18564 \, a^{12} b^{6} c^{6} d^{12} - 8568 \, a^{13} b^{5} c^{5} d^{13} + 3060 \, a^{14} b^{4} c^{4} d^{14} - 816 \, a^{15} b^{3} c^{3} d^{15} + 153 \, a^{16} b^{2} c^{2} d^{16} - 18 \, a^{17} b c d^{17} + a^{18} d^{18}\right)} x - {\left(a b^{19} c^{12} - 12 \, a^{2} b^{18} c^{11} d + 66 \, a^{3} b^{17} c^{10} d^{2} - 220 \, a^{4} b^{16} c^{9} d^{3} + 495 \, a^{5} b^{15} c^{8} d^{4} - 792 \, a^{6} b^{14} c^{7} d^{5} + 924 \, a^{7} b^{13} c^{6} d^{6} - 792 \, a^{8} b^{12} c^{5} d^{7} + 495 \, a^{9} b^{11} c^{4} d^{8} - 220 \, a^{10} b^{10} c^{3} d^{9} + 66 \, a^{11} b^{9} c^{2} d^{10} - 12 \, a^{12} b^{8} c d^{11} + a^{13} b^{7} d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}}} b^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{1}{4}} + {\left(b^{13} c^{9} - 9 \, a b^{12} c^{8} d + 36 \, a^{2} b^{11} c^{7} d^{2} - 84 \, a^{3} b^{10} c^{6} d^{3} + 126 \, a^{4} b^{9} c^{5} d^{4} - 126 \, a^{5} b^{8} c^{4} d^{5} + 84 \, a^{6} b^{7} c^{3} d^{6} - 36 \, a^{7} b^{6} c^{2} d^{7} + 9 \, a^{8} b^{5} c d^{8} - a^{9} b^{4} d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{1}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) - 231 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{1}{4}} \log\left(a b^{11} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 231 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{1}{4}} \log\left(-a b^{11} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a b^{15}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(21 \, b^{2} d^{3} x^{5} + 33 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{3} + 77 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{x}}{462 \, b^{3}}"," ",0,"1/462*(924*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(1/4)*arctan((sqrt((b^18*c^18 - 18*a*b^17*c^17*d + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a^17*b*c*d^17 + a^18*d^18)*x - (a*b^19*c^12 - 12*a^2*b^18*c^11*d + 66*a^3*b^17*c^10*d^2 - 220*a^4*b^16*c^9*d^3 + 495*a^5*b^15*c^8*d^4 - 792*a^6*b^14*c^7*d^5 + 924*a^7*b^13*c^6*d^6 - 792*a^8*b^12*c^5*d^7 + 495*a^9*b^11*c^4*d^8 - 220*a^10*b^10*c^3*d^9 + 66*a^11*b^9*c^2*d^10 - 12*a^12*b^8*c*d^11 + a^13*b^7*d^12)*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15)))*b^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(1/4) + (b^13*c^9 - 9*a*b^12*c^8*d + 36*a^2*b^11*c^7*d^2 - 84*a^3*b^10*c^6*d^3 + 126*a^4*b^9*c^5*d^4 - 126*a^5*b^8*c^4*d^5 + 84*a^6*b^7*c^3*d^6 - 36*a^7*b^6*c^2*d^7 + 9*a^8*b^5*c*d^8 - a^9*b^4*d^9)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(1/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) - 231*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(1/4)*log(a*b^11*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 231*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(1/4)*log(-a*b^11*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a*b^15))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 4*(21*b^2*d^3*x^5 + 33*(3*b^2*c*d^2 - a*b*d^3)*x^3 + 77*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)*sqrt(x))/b^3","B",0
444,1,1862,0,1.662490," ","integrate((d*x^2+c)^3/(b*x^2+a)/x^(1/2),x, algorithm=""fricas"")","-\frac{180 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{2} b^{6} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} a^{2} b^{10} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{3}{4}} + {\left(a^{2} b^{13} c^{3} - 3 \, a^{3} b^{12} c^{2} d + 3 \, a^{4} b^{11} c d^{2} - a^{5} b^{10} d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 45 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(a b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 45 \, b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} \log\left(-a b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{3} b^{13}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(5 \, b^{2} d^{3} x^{4} + 135 \, b^{2} c^{2} d - 135 \, a b c d^{2} + 45 \, a^{2} d^{3} + 9 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{2}\right)} \sqrt{x}}{90 \, b^{3}}"," ",0,"-1/90*(180*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*arctan((sqrt(a^2*b^6*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13)) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x)*a^2*b^10*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(3/4) + (a^2*b^13*c^3 - 3*a^3*b^12*c^2*d + 3*a^4*b^11*c*d^2 - a^5*b^10*d^3)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(3/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) + 45*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*log(a*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 45*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4)*log(-a*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^3*b^13))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 4*(5*b^2*d^3*x^4 + 135*b^2*c^2*d - 135*a*b*c*d^2 + 45*a^2*d^3 + 9*(3*b^2*c*d^2 - a*b*d^3)*x^2)*sqrt(x))/b^3","B",0
445,1,2442,0,1.554984," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{84 \, a b^{2} x \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} - 18 \, a b^{17} c^{17} d + 153 \, a^{2} b^{16} c^{16} d^{2} - 816 \, a^{3} b^{15} c^{15} d^{3} + 3060 \, a^{4} b^{14} c^{14} d^{4} - 8568 \, a^{5} b^{13} c^{13} d^{5} + 18564 \, a^{6} b^{12} c^{12} d^{6} - 31824 \, a^{7} b^{11} c^{11} d^{7} + 43758 \, a^{8} b^{10} c^{10} d^{8} - 48620 \, a^{9} b^{9} c^{9} d^{9} + 43758 \, a^{10} b^{8} c^{8} d^{10} - 31824 \, a^{11} b^{7} c^{7} d^{11} + 18564 \, a^{12} b^{6} c^{6} d^{12} - 8568 \, a^{13} b^{5} c^{5} d^{13} + 3060 \, a^{14} b^{4} c^{4} d^{14} - 816 \, a^{15} b^{3} c^{3} d^{15} + 153 \, a^{16} b^{2} c^{2} d^{16} - 18 \, a^{17} b c d^{17} + a^{18} d^{18}\right)} x - {\left(a^{3} b^{17} c^{12} - 12 \, a^{4} b^{16} c^{11} d + 66 \, a^{5} b^{15} c^{10} d^{2} - 220 \, a^{6} b^{14} c^{9} d^{3} + 495 \, a^{7} b^{13} c^{8} d^{4} - 792 \, a^{8} b^{12} c^{7} d^{5} + 924 \, a^{9} b^{11} c^{6} d^{6} - 792 \, a^{10} b^{10} c^{5} d^{7} + 495 \, a^{11} b^{9} c^{4} d^{8} - 220 \, a^{12} b^{8} c^{3} d^{9} + 66 \, a^{13} b^{7} c^{2} d^{10} - 12 \, a^{14} b^{6} c d^{11} + a^{15} b^{5} d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}}} a b^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{1}{4}} + {\left(a b^{12} c^{9} - 9 \, a^{2} b^{11} c^{8} d + 36 \, a^{3} b^{10} c^{7} d^{2} - 84 \, a^{4} b^{9} c^{6} d^{3} + 126 \, a^{5} b^{8} c^{5} d^{4} - 126 \, a^{6} b^{7} c^{4} d^{5} + 84 \, a^{7} b^{6} c^{3} d^{6} - 36 \, a^{8} b^{5} c^{2} d^{7} + 9 \, a^{9} b^{4} c d^{8} - a^{10} b^{3} d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{1}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) - 21 \, a b^{2} x \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(a^{4} b^{8} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 21 \, a b^{2} x \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{1}{4}} \log\left(-a^{4} b^{8} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{5} b^{11}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) - 4 \, {\left(3 \, a b d^{3} x^{4} - 21 \, b^{2} c^{3} + 7 \, {\left(3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{42 \, a b^{2} x}"," ",0,"-1/42*(84*a*b^2*x*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(1/4)*arctan((sqrt((b^18*c^18 - 18*a*b^17*c^17*d + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a^17*b*c*d^17 + a^18*d^18)*x - (a^3*b^17*c^12 - 12*a^4*b^16*c^11*d + 66*a^5*b^15*c^10*d^2 - 220*a^6*b^14*c^9*d^3 + 495*a^7*b^13*c^8*d^4 - 792*a^8*b^12*c^7*d^5 + 924*a^9*b^11*c^6*d^6 - 792*a^10*b^10*c^5*d^7 + 495*a^11*b^9*c^4*d^8 - 220*a^12*b^8*c^3*d^9 + 66*a^13*b^7*c^2*d^10 - 12*a^14*b^6*c*d^11 + a^15*b^5*d^12)*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11)))*a*b^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(1/4) + (a*b^12*c^9 - 9*a^2*b^11*c^8*d + 36*a^3*b^10*c^7*d^2 - 84*a^4*b^9*c^6*d^3 + 126*a^5*b^8*c^5*d^4 - 126*a^6*b^7*c^4*d^5 + 84*a^7*b^6*c^3*d^6 - 36*a^8*b^5*c^2*d^7 + 9*a^9*b^4*c*d^8 - a^10*b^3*d^9)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(1/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) - 21*a*b^2*x*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(1/4)*log(a^4*b^8*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 21*a*b^2*x*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(1/4)*log(-a^4*b^8*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^5*b^11))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) - 4*(3*a*b*d^3*x^4 - 21*b^2*c^3 + 7*(3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(x))/(a*b^2*x)","B",0
446,1,1866,0,1.362195," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{60 \, a b^{2} x^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{4} b^{4} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} a^{5} b^{7} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{3}{4}} + {\left(a^{5} b^{10} c^{3} - 3 \, a^{6} b^{9} c^{2} d + 3 \, a^{7} b^{8} c d^{2} - a^{8} b^{7} d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 15 \, a b^{2} x^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(a^{2} b^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 15 \, a b^{2} x^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{1}{4}} \log\left(-a^{2} b^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{7} b^{9}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) + 4 \, {\left(3 \, a b d^{3} x^{4} - 5 \, b^{2} c^{3} + 15 \, {\left(3 \, a b c d^{2} - a^{2} d^{3}\right)} x^{2}\right)} \sqrt{x}}{30 \, a b^{2} x^{2}}"," ",0,"1/30*(60*a*b^2*x^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(1/4)*arctan((sqrt(a^4*b^4*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9)) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x)*a^5*b^7*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(3/4) + (a^5*b^10*c^3 - 3*a^6*b^9*c^2*d + 3*a^7*b^8*c*d^2 - a^8*b^7*d^3)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(3/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) + 15*a*b^2*x^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(1/4)*log(a^2*b^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 15*a*b^2*x^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(1/4)*log(-a^2*b^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^7*b^9))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) + 4*(3*a*b*d^3*x^4 - 5*b^2*c^3 + 15*(3*a*b*c*d^2 - a^2*d^3)*x^2)*sqrt(x))/(a*b^2*x^2)","B",0
447,1,2451,0,1.468626," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{60 \, a^{2} b x^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} - 18 \, a b^{17} c^{17} d + 153 \, a^{2} b^{16} c^{16} d^{2} - 816 \, a^{3} b^{15} c^{15} d^{3} + 3060 \, a^{4} b^{14} c^{14} d^{4} - 8568 \, a^{5} b^{13} c^{13} d^{5} + 18564 \, a^{6} b^{12} c^{12} d^{6} - 31824 \, a^{7} b^{11} c^{11} d^{7} + 43758 \, a^{8} b^{10} c^{10} d^{8} - 48620 \, a^{9} b^{9} c^{9} d^{9} + 43758 \, a^{10} b^{8} c^{8} d^{10} - 31824 \, a^{11} b^{7} c^{7} d^{11} + 18564 \, a^{12} b^{6} c^{6} d^{12} - 8568 \, a^{13} b^{5} c^{5} d^{13} + 3060 \, a^{14} b^{4} c^{4} d^{14} - 816 \, a^{15} b^{3} c^{3} d^{15} + 153 \, a^{16} b^{2} c^{2} d^{16} - 18 \, a^{17} b c d^{17} + a^{18} d^{18}\right)} x - {\left(a^{5} b^{15} c^{12} - 12 \, a^{6} b^{14} c^{11} d + 66 \, a^{7} b^{13} c^{10} d^{2} - 220 \, a^{8} b^{12} c^{9} d^{3} + 495 \, a^{9} b^{11} c^{8} d^{4} - 792 \, a^{10} b^{10} c^{7} d^{5} + 924 \, a^{11} b^{9} c^{6} d^{6} - 792 \, a^{12} b^{8} c^{5} d^{7} + 495 \, a^{13} b^{7} c^{4} d^{8} - 220 \, a^{14} b^{6} c^{3} d^{9} + 66 \, a^{15} b^{5} c^{2} d^{10} - 12 \, a^{16} b^{4} c d^{11} + a^{17} b^{3} d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}}} a^{2} b^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{1}{4}} + {\left(a^{2} b^{11} c^{9} - 9 \, a^{3} b^{10} c^{8} d + 36 \, a^{4} b^{9} c^{7} d^{2} - 84 \, a^{5} b^{8} c^{6} d^{3} + 126 \, a^{6} b^{7} c^{5} d^{4} - 126 \, a^{7} b^{6} c^{4} d^{5} + 84 \, a^{8} b^{5} c^{3} d^{6} - 36 \, a^{9} b^{4} c^{2} d^{7} + 9 \, a^{10} b^{3} c d^{8} - a^{11} b^{2} d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{1}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) - 15 \, a^{2} b x^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(a^{7} b^{5} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 15 \, a^{2} b x^{3} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{1}{4}} \log\left(-a^{7} b^{5} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{9} b^{7}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, a^{2} d^{3} x^{4} - 3 \, a b c^{3} + 15 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d\right)} x^{2}\right)} \sqrt{x}}{30 \, a^{2} b x^{3}}"," ",0,"1/30*(60*a^2*b*x^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(1/4)*arctan((sqrt((b^18*c^18 - 18*a*b^17*c^17*d + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a^17*b*c*d^17 + a^18*d^18)*x - (a^5*b^15*c^12 - 12*a^6*b^14*c^11*d + 66*a^7*b^13*c^10*d^2 - 220*a^8*b^12*c^9*d^3 + 495*a^9*b^11*c^8*d^4 - 792*a^10*b^10*c^7*d^5 + 924*a^11*b^9*c^6*d^6 - 792*a^12*b^8*c^5*d^7 + 495*a^13*b^7*c^4*d^8 - 220*a^14*b^6*c^3*d^9 + 66*a^15*b^5*c^2*d^10 - 12*a^16*b^4*c*d^11 + a^17*b^3*d^12)*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7)))*a^2*b^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(1/4) + (a^2*b^11*c^9 - 9*a^3*b^10*c^8*d + 36*a^4*b^9*c^7*d^2 - 84*a^5*b^8*c^6*d^3 + 126*a^6*b^7*c^5*d^4 - 126*a^7*b^6*c^4*d^5 + 84*a^8*b^5*c^3*d^6 - 36*a^9*b^4*c^2*d^7 + 9*a^10*b^3*c*d^8 - a^11*b^2*d^9)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(1/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) - 15*a^2*b*x^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(1/4)*log(a^7*b^5*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 15*a^2*b*x^3*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(1/4)*log(-a^7*b^5*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^9*b^7))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 4*(5*a^2*d^3*x^4 - 3*a*b*c^3 + 15*(b^2*c^3 - 3*a*b*c^2*d)*x^2)*sqrt(x))/(a^2*b*x^3)","B",0
448,1,1861,0,1.452127," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{84 \, a^{2} b x^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{6} b^{2} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} a^{8} b^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{3}{4}} + {\left(a^{8} b^{7} c^{3} - 3 \, a^{9} b^{6} c^{2} d + 3 \, a^{10} b^{5} c d^{2} - a^{11} b^{4} d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 21 \, a^{2} b x^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(a^{3} b \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 21 \, a^{2} b x^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{1}{4}} \log\left(-a^{3} b \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{11} b^{5}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(21 \, a^{2} d^{3} x^{4} - 3 \, a b c^{3} + 7 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d\right)} x^{2}\right)} \sqrt{x}}{42 \, a^{2} b x^{4}}"," ",0,"-1/42*(84*a^2*b*x^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(1/4)*arctan((sqrt(a^6*b^2*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5)) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x)*a^8*b^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(3/4) + (a^8*b^7*c^3 - 3*a^9*b^6*c^2*d + 3*a^10*b^5*c*d^2 - a^11*b^4*d^3)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(3/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) + 21*a^2*b*x^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(1/4)*log(a^3*b*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 21*a^2*b*x^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(1/4)*log(-a^3*b*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^11*b^5))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 4*(21*a^2*d^3*x^4 - 3*a*b*c^3 + 7*(b^2*c^3 - 3*a*b*c^2*d)*x^2)*sqrt(x))/(a^2*b*x^4)","B",0
449,1,2459,0,1.760786," ","integrate((d*x^2+c)^3/x^(11/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{180 \, a^{3} x^{5} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} - 18 \, a b^{17} c^{17} d + 153 \, a^{2} b^{16} c^{16} d^{2} - 816 \, a^{3} b^{15} c^{15} d^{3} + 3060 \, a^{4} b^{14} c^{14} d^{4} - 8568 \, a^{5} b^{13} c^{13} d^{5} + 18564 \, a^{6} b^{12} c^{12} d^{6} - 31824 \, a^{7} b^{11} c^{11} d^{7} + 43758 \, a^{8} b^{10} c^{10} d^{8} - 48620 \, a^{9} b^{9} c^{9} d^{9} + 43758 \, a^{10} b^{8} c^{8} d^{10} - 31824 \, a^{11} b^{7} c^{7} d^{11} + 18564 \, a^{12} b^{6} c^{6} d^{12} - 8568 \, a^{13} b^{5} c^{5} d^{13} + 3060 \, a^{14} b^{4} c^{4} d^{14} - 816 \, a^{15} b^{3} c^{3} d^{15} + 153 \, a^{16} b^{2} c^{2} d^{16} - 18 \, a^{17} b c d^{17} + a^{18} d^{18}\right)} x - {\left(a^{7} b^{13} c^{12} - 12 \, a^{8} b^{12} c^{11} d + 66 \, a^{9} b^{11} c^{10} d^{2} - 220 \, a^{10} b^{10} c^{9} d^{3} + 495 \, a^{11} b^{9} c^{8} d^{4} - 792 \, a^{12} b^{8} c^{7} d^{5} + 924 \, a^{13} b^{7} c^{6} d^{6} - 792 \, a^{14} b^{6} c^{5} d^{7} + 495 \, a^{15} b^{5} c^{4} d^{8} - 220 \, a^{16} b^{4} c^{3} d^{9} + 66 \, a^{17} b^{3} c^{2} d^{10} - 12 \, a^{18} b^{2} c d^{11} + a^{19} b d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}}} a^{3} b \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{1}{4}} + {\left(a^{3} b^{10} c^{9} - 9 \, a^{4} b^{9} c^{8} d + 36 \, a^{5} b^{8} c^{7} d^{2} - 84 \, a^{6} b^{7} c^{6} d^{3} + 126 \, a^{7} b^{6} c^{5} d^{4} - 126 \, a^{8} b^{5} c^{4} d^{5} + 84 \, a^{9} b^{4} c^{3} d^{6} - 36 \, a^{10} b^{3} c^{2} d^{7} + 9 \, a^{11} b^{2} c d^{8} - a^{12} b d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{1}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) - 45 \, a^{3} x^{5} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(a^{10} b^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 45 \, a^{3} x^{5} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{1}{4}} \log\left(-a^{10} b^{2} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{3}}\right)^{\frac{3}{4}} - {\left(b^{9} c^{9} - 9 \, a b^{8} c^{8} d + 36 \, a^{2} b^{7} c^{7} d^{2} - 84 \, a^{3} b^{6} c^{6} d^{3} + 126 \, a^{4} b^{5} c^{5} d^{4} - 126 \, a^{5} b^{4} c^{4} d^{5} + 84 \, a^{6} b^{3} c^{3} d^{6} - 36 \, a^{7} b^{2} c^{2} d^{7} + 9 \, a^{8} b c d^{8} - a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(5 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 9 \, {\left(a b c^{3} - 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{x}}{90 \, a^{3} x^{5}}"," ",0,"-1/90*(180*a^3*x^5*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(1/4)*arctan((sqrt((b^18*c^18 - 18*a*b^17*c^17*d + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a^17*b*c*d^17 + a^18*d^18)*x - (a^7*b^13*c^12 - 12*a^8*b^12*c^11*d + 66*a^9*b^11*c^10*d^2 - 220*a^10*b^10*c^9*d^3 + 495*a^11*b^9*c^8*d^4 - 792*a^12*b^8*c^7*d^5 + 924*a^13*b^7*c^6*d^6 - 792*a^14*b^6*c^5*d^7 + 495*a^15*b^5*c^4*d^8 - 220*a^16*b^4*c^3*d^9 + 66*a^17*b^3*c^2*d^10 - 12*a^18*b^2*c*d^11 + a^19*b*d^12)*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3)))*a^3*b*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(1/4) + (a^3*b^10*c^9 - 9*a^4*b^9*c^8*d + 36*a^5*b^8*c^7*d^2 - 84*a^6*b^7*c^6*d^3 + 126*a^7*b^6*c^5*d^4 - 126*a^8*b^5*c^4*d^5 + 84*a^9*b^4*c^3*d^6 - 36*a^10*b^3*c^2*d^7 + 9*a^11*b^2*c*d^8 - a^12*b*d^9)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(1/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) - 45*a^3*x^5*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(1/4)*log(a^10*b^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 45*a^3*x^5*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(1/4)*log(-a^10*b^2*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^3))^(3/4) - (b^9*c^9 - 9*a*b^8*c^8*d + 36*a^2*b^7*c^7*d^2 - 84*a^3*b^6*c^6*d^3 + 126*a^4*b^5*c^5*d^4 - 126*a^5*b^4*c^4*d^5 + 84*a^6*b^3*c^3*d^6 - 36*a^7*b^2*c^2*d^7 + 9*a^8*b*c*d^8 - a^9*d^9)*sqrt(x)) + 4*(5*a^2*c^3 + 45*(b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 9*(a*b*c^3 - 3*a^2*c^2*d)*x^2)*sqrt(x))/(a^3*x^5)","B",0
450,1,1866,0,1.488021," ","integrate((d*x^2+c)^3/x^(13/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{924 \, a^{3} x^{6} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{8} \sqrt{-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} a^{11} b \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{3}{4}} + {\left(a^{11} b^{4} c^{3} - 3 \, a^{12} b^{3} c^{2} d + 3 \, a^{13} b^{2} c d^{2} - a^{14} b d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 231 \, a^{3} x^{6} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{1}{4}} \log\left(a^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 231 \, a^{3} x^{6} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{1}{4}} \log\left(-a^{4} \left(-\frac{b^{12} c^{12} - 12 \, a b^{11} c^{11} d + 66 \, a^{2} b^{10} c^{10} d^{2} - 220 \, a^{3} b^{9} c^{9} d^{3} + 495 \, a^{4} b^{8} c^{8} d^{4} - 792 \, a^{5} b^{7} c^{7} d^{5} + 924 \, a^{6} b^{6} c^{6} d^{6} - 792 \, a^{7} b^{5} c^{5} d^{7} + 495 \, a^{8} b^{4} c^{4} d^{8} - 220 \, a^{9} b^{3} c^{3} d^{9} + 66 \, a^{10} b^{2} c^{2} d^{10} - 12 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(21 \, a^{2} c^{3} + 77 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 33 \, {\left(a b c^{3} - 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{x}}{462 \, a^{3} x^{6}}"," ",0,"1/462*(924*a^3*x^6*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(1/4)*arctan((sqrt(a^8*sqrt(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b)) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*x)*a^11*b*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(3/4) + (a^11*b^4*c^3 - 3*a^12*b^3*c^2*d + 3*a^13*b^2*c*d^2 - a^14*b*d^3)*sqrt(x)*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(3/4))/(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)) + 231*a^3*x^6*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(1/4)*log(a^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 231*a^3*x^6*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(1/4)*log(-a^4*(-(b^12*c^12 - 12*a*b^11*c^11*d + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a^11*b*c*d^11 + a^12*d^12)/(a^15*b))^(1/4) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)) - 4*(21*a^2*c^3 + 77*(b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 33*(a*b*c^3 - 3*a^2*c^2*d)*x^2)*sqrt(x))/(a^3*x^6)","B",0
451,1,2512,0,1.807450," ","integrate((d*x^2+c)^3/x^(15/2)/(b*x^2+a),x, algorithm=""fricas"")","\frac{2340 \, a^{4} x^{7} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{20} c^{18} - 18 \, a b^{19} c^{17} d + 153 \, a^{2} b^{18} c^{16} d^{2} - 816 \, a^{3} b^{17} c^{15} d^{3} + 3060 \, a^{4} b^{16} c^{14} d^{4} - 8568 \, a^{5} b^{15} c^{13} d^{5} + 18564 \, a^{6} b^{14} c^{12} d^{6} - 31824 \, a^{7} b^{13} c^{11} d^{7} + 43758 \, a^{8} b^{12} c^{10} d^{8} - 48620 \, a^{9} b^{11} c^{9} d^{9} + 43758 \, a^{10} b^{10} c^{8} d^{10} - 31824 \, a^{11} b^{9} c^{7} d^{11} + 18564 \, a^{12} b^{8} c^{6} d^{12} - 8568 \, a^{13} b^{7} c^{5} d^{13} + 3060 \, a^{14} b^{6} c^{4} d^{14} - 816 \, a^{15} b^{5} c^{3} d^{15} + 153 \, a^{16} b^{4} c^{2} d^{16} - 18 \, a^{17} b^{3} c d^{17} + a^{18} b^{2} d^{18}\right)} x - {\left(a^{9} b^{13} c^{12} - 12 \, a^{10} b^{12} c^{11} d + 66 \, a^{11} b^{11} c^{10} d^{2} - 220 \, a^{12} b^{10} c^{9} d^{3} + 495 \, a^{13} b^{9} c^{8} d^{4} - 792 \, a^{14} b^{8} c^{7} d^{5} + 924 \, a^{15} b^{7} c^{6} d^{6} - 792 \, a^{16} b^{6} c^{5} d^{7} + 495 \, a^{17} b^{5} c^{4} d^{8} - 220 \, a^{18} b^{4} c^{3} d^{9} + 66 \, a^{19} b^{3} c^{2} d^{10} - 12 \, a^{20} b^{2} c d^{11} + a^{21} b d^{12}\right)} \sqrt{-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}}} a^{4} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{1}{4}} + {\left(a^{4} b^{10} c^{9} - 9 \, a^{5} b^{9} c^{8} d + 36 \, a^{6} b^{8} c^{7} d^{2} - 84 \, a^{7} b^{7} c^{6} d^{3} + 126 \, a^{8} b^{6} c^{5} d^{4} - 126 \, a^{9} b^{5} c^{4} d^{5} + 84 \, a^{10} b^{4} c^{3} d^{6} - 36 \, a^{11} b^{3} c^{2} d^{7} + 9 \, a^{12} b^{2} c d^{8} - a^{13} b d^{9}\right)} \sqrt{x} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{1}{4}}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right) - 585 \, a^{4} x^{7} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{1}{4}} \log\left(a^{13} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{3}{4}} - {\left(b^{10} c^{9} - 9 \, a b^{9} c^{8} d + 36 \, a^{2} b^{8} c^{7} d^{2} - 84 \, a^{3} b^{7} c^{6} d^{3} + 126 \, a^{4} b^{6} c^{5} d^{4} - 126 \, a^{5} b^{5} c^{4} d^{5} + 84 \, a^{6} b^{4} c^{3} d^{6} - 36 \, a^{7} b^{3} c^{2} d^{7} + 9 \, a^{8} b^{2} c d^{8} - a^{9} b d^{9}\right)} \sqrt{x}\right) + 585 \, a^{4} x^{7} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{1}{4}} \log\left(-a^{13} \left(-\frac{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}{a^{17}}\right)^{\frac{3}{4}} - {\left(b^{10} c^{9} - 9 \, a b^{9} c^{8} d + 36 \, a^{2} b^{8} c^{7} d^{2} - 84 \, a^{3} b^{7} c^{6} d^{3} + 126 \, a^{4} b^{6} c^{5} d^{4} - 126 \, a^{5} b^{5} c^{4} d^{5} + 84 \, a^{6} b^{4} c^{3} d^{6} - 36 \, a^{7} b^{3} c^{2} d^{7} + 9 \, a^{8} b^{2} c d^{8} - a^{9} b d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(585 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{6} - 45 \, a^{3} c^{3} - 117 \, {\left(a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{4} + 65 \, {\left(a^{2} b c^{3} - 3 \, a^{3} c^{2} d\right)} x^{2}\right)} \sqrt{x}}{1170 \, a^{4} x^{7}}"," ",0,"1/1170*(2340*a^4*x^7*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(1/4)*arctan((sqrt((b^20*c^18 - 18*a*b^19*c^17*d + 153*a^2*b^18*c^16*d^2 - 816*a^3*b^17*c^15*d^3 + 3060*a^4*b^16*c^14*d^4 - 8568*a^5*b^15*c^13*d^5 + 18564*a^6*b^14*c^12*d^6 - 31824*a^7*b^13*c^11*d^7 + 43758*a^8*b^12*c^10*d^8 - 48620*a^9*b^11*c^9*d^9 + 43758*a^10*b^10*c^8*d^10 - 31824*a^11*b^9*c^7*d^11 + 18564*a^12*b^8*c^6*d^12 - 8568*a^13*b^7*c^5*d^13 + 3060*a^14*b^6*c^4*d^14 - 816*a^15*b^5*c^3*d^15 + 153*a^16*b^4*c^2*d^16 - 18*a^17*b^3*c*d^17 + a^18*b^2*d^18)*x - (a^9*b^13*c^12 - 12*a^10*b^12*c^11*d + 66*a^11*b^11*c^10*d^2 - 220*a^12*b^10*c^9*d^3 + 495*a^13*b^9*c^8*d^4 - 792*a^14*b^8*c^7*d^5 + 924*a^15*b^7*c^6*d^6 - 792*a^16*b^6*c^5*d^7 + 495*a^17*b^5*c^4*d^8 - 220*a^18*b^4*c^3*d^9 + 66*a^19*b^3*c^2*d^10 - 12*a^20*b^2*c*d^11 + a^21*b*d^12)*sqrt(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17))*a^4*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(1/4) + (a^4*b^10*c^9 - 9*a^5*b^9*c^8*d + 36*a^6*b^8*c^7*d^2 - 84*a^7*b^7*c^6*d^3 + 126*a^8*b^6*c^5*d^4 - 126*a^9*b^5*c^4*d^5 + 84*a^10*b^4*c^3*d^6 - 36*a^11*b^3*c^2*d^7 + 9*a^12*b^2*c*d^8 - a^13*b*d^9)*sqrt(x)*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(1/4))/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)) - 585*a^4*x^7*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(1/4)*log(a^13*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(3/4) - (b^10*c^9 - 9*a*b^9*c^8*d + 36*a^2*b^8*c^7*d^2 - 84*a^3*b^7*c^6*d^3 + 126*a^4*b^6*c^5*d^4 - 126*a^5*b^5*c^4*d^5 + 84*a^6*b^4*c^3*d^6 - 36*a^7*b^3*c^2*d^7 + 9*a^8*b^2*c*d^8 - a^9*b*d^9)*sqrt(x)) + 585*a^4*x^7*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(1/4)*log(-a^13*(-(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)/a^17)^(3/4) - (b^10*c^9 - 9*a*b^9*c^8*d + 36*a^2*b^8*c^7*d^2 - 84*a^3*b^7*c^6*d^3 + 126*a^4*b^6*c^5*d^4 - 126*a^5*b^5*c^4*d^5 + 84*a^6*b^4*c^3*d^6 - 36*a^7*b^3*c^2*d^7 + 9*a^8*b^2*c*d^8 - a^9*b*d^9)*sqrt(x)) + 4*(585*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^6 - 45*a^3*c^3 - 117*(a*b^2*c^3 - 3*a^2*b*c^2*d + 3*a^3*c*d^2)*x^4 + 65*(a^2*b*c^3 - 3*a^3*c^2*d)*x^2)*sqrt(x))/(a^4*x^7)","B",0
452,1,2014,0,1.413475," ","integrate(x^(7/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2340 \, {\left(b^{6} x^{2} + a b^{5}\right)} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{b^{10} \sqrt{-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}} + {\left(25 \, b^{6} c^{6} - 270 \, a b^{5} c^{5} d + 1119 \, a^{2} b^{4} c^{4} d^{2} - 2276 \, a^{3} b^{3} c^{3} d^{3} + 2439 \, a^{4} b^{2} c^{2} d^{4} - 1326 \, a^{5} b c d^{5} + 289 \, a^{6} d^{6}\right)} x} b^{16} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{3}{4}} + {\left(5 \, b^{19} c^{3} - 27 \, a b^{18} c^{2} d + 39 \, a^{2} b^{17} c d^{2} - 17 \, a^{3} b^{16} d^{3}\right)} \sqrt{x} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{3}{4}}}{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}\right) + 585 \, {\left(b^{6} x^{2} + a b^{5}\right)} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{1}{4}} \log\left(b^{5} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{1}{4}} - {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 585 \, {\left(b^{6} x^{2} + a b^{5}\right)} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{1}{4}} \log\left(-b^{5} \left(-\frac{625 \, a b^{12} c^{12} - 13500 \, a^{2} b^{11} c^{11} d + 128850 \, a^{3} b^{10} c^{10} d^{2} - 718060 \, a^{4} b^{9} c^{9} d^{3} + 2603151 \, a^{5} b^{8} c^{8} d^{4} - 6477048 \, a^{6} b^{7} c^{7} d^{5} + 11369148 \, a^{7} b^{6} c^{6} d^{6} - 14225976 \, a^{8} b^{5} c^{5} d^{7} + 12631455 \, a^{9} b^{4} c^{4} d^{8} - 7783756 \, a^{10} b^{3} c^{3} d^{9} + 3168018 \, a^{11} b^{2} c^{2} d^{10} - 766428 \, a^{12} b c d^{11} + 83521 \, a^{13} d^{12}}{b^{21}}\right)^{\frac{1}{4}} - {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \sqrt{x}\right) + 4 \, {\left(180 \, b^{4} d^{3} x^{8} + 2925 \, a b^{3} c^{3} - 15795 \, a^{2} b^{2} c^{2} d + 22815 \, a^{3} b c d^{2} - 9945 \, a^{4} d^{3} + 20 \, {\left(39 \, b^{4} c d^{2} - 17 \, a b^{3} d^{3}\right)} x^{6} + 52 \, {\left(27 \, b^{4} c^{2} d - 39 \, a b^{3} c d^{2} + 17 \, a^{2} b^{2} d^{3}\right)} x^{4} + 468 \, {\left(5 \, b^{4} c^{3} - 27 \, a b^{3} c^{2} d + 39 \, a^{2} b^{2} c d^{2} - 17 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{x}}{4680 \, {\left(b^{6} x^{2} + a b^{5}\right)}}"," ",0,"1/4680*(2340*(b^6*x^2 + a*b^5)*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(1/4)*arctan((sqrt(b^10*sqrt(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21) + (25*b^6*c^6 - 270*a*b^5*c^5*d + 1119*a^2*b^4*c^4*d^2 - 2276*a^3*b^3*c^3*d^3 + 2439*a^4*b^2*c^2*d^4 - 1326*a^5*b*c*d^5 + 289*a^6*d^6)*x)*b^16*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(3/4) + (5*b^19*c^3 - 27*a*b^18*c^2*d + 39*a^2*b^17*c*d^2 - 17*a^3*b^16*d^3)*sqrt(x)*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(3/4))/(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)) + 585*(b^6*x^2 + a*b^5)*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(1/4)*log(b^5*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(1/4) - (5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*sqrt(x)) - 585*(b^6*x^2 + a*b^5)*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(1/4)*log(-b^5*(-(625*a*b^12*c^12 - 13500*a^2*b^11*c^11*d + 128850*a^3*b^10*c^10*d^2 - 718060*a^4*b^9*c^9*d^3 + 2603151*a^5*b^8*c^8*d^4 - 6477048*a^6*b^7*c^7*d^5 + 11369148*a^7*b^6*c^6*d^6 - 14225976*a^8*b^5*c^5*d^7 + 12631455*a^9*b^4*c^4*d^8 - 7783756*a^10*b^3*c^3*d^9 + 3168018*a^11*b^2*c^2*d^10 - 766428*a^12*b*c*d^11 + 83521*a^13*d^12)/b^21)^(1/4) - (5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*sqrt(x)) + 4*(180*b^4*d^3*x^8 + 2925*a*b^3*c^3 - 15795*a^2*b^2*c^2*d + 22815*a^3*b*c*d^2 - 9945*a^4*d^3 + 20*(39*b^4*c*d^2 - 17*a*b^3*d^3)*x^6 + 52*(27*b^4*c^2*d - 39*a*b^3*c*d^2 + 17*a^2*b^2*d^3)*x^4 + 468*(5*b^4*c^3 - 27*a*b^3*c^2*d + 39*a^2*b^2*c*d^2 - 17*a^3*b*d^3)*x^2)*sqrt(x))/(b^6*x^2 + a*b^5)","B",0
453,1,2542,0,1.728914," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{924 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} - 42 \, a b^{17} c^{17} d + 801 \, a^{2} b^{16} c^{16} d^{2} - 9200 \, a^{3} b^{15} c^{15} d^{3} + 71220 \, a^{4} b^{14} c^{14} d^{4} - 394392 \, a^{5} b^{13} c^{13} d^{5} + 1619684 \, a^{6} b^{12} c^{12} d^{6} - 5050512 \, a^{7} b^{11} c^{11} d^{7} + 12147630 \, a^{8} b^{10} c^{10} d^{8} - 22765820 \, a^{9} b^{9} c^{9} d^{9} + 33419166 \, a^{10} b^{8} c^{8} d^{10} - 38446992 \, a^{11} b^{7} c^{7} d^{11} + 34503236 \, a^{12} b^{6} c^{6} d^{12} - 23888280 \, a^{13} b^{5} c^{5} d^{13} + 12508500 \, a^{14} b^{4} c^{4} d^{14} - 4790000 \, a^{15} b^{3} c^{3} d^{15} + 1265625 \, a^{16} b^{2} c^{2} d^{16} - 206250 \, a^{17} b c d^{17} + 15625 \, a^{18} d^{18}\right)} x - {\left(a b^{21} c^{12} - 28 \, a^{2} b^{20} c^{11} d + 338 \, a^{3} b^{19} c^{10} d^{2} - 2316 \, a^{4} b^{18} c^{9} d^{3} + 10015 \, a^{5} b^{17} c^{8} d^{4} - 28856 \, a^{6} b^{16} c^{7} d^{5} + 57148 \, a^{7} b^{15} c^{6} d^{6} - 78968 \, a^{8} b^{14} c^{5} d^{7} + 76111 \, a^{9} b^{13} c^{4} d^{8} - 50220 \, a^{10} b^{12} c^{3} d^{9} + 21650 \, a^{11} b^{11} c^{2} d^{10} - 5500 \, a^{12} b^{10} c d^{11} + 625 \, a^{13} b^{9} d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}}} b^{5} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{1}{4}} + {\left(b^{14} c^{9} - 21 \, a b^{13} c^{8} d + 180 \, a^{2} b^{12} c^{7} d^{2} - 820 \, a^{3} b^{11} c^{6} d^{3} + 2190 \, a^{4} b^{10} c^{5} d^{4} - 3606 \, a^{5} b^{9} c^{4} d^{5} + 3716 \, a^{6} b^{8} c^{3} d^{6} - 2340 \, a^{7} b^{7} c^{2} d^{7} + 825 \, a^{8} b^{6} c d^{8} - 125 \, a^{9} b^{5} d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{1}{4}}}{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}\right) - 231 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{1}{4}} \log\left(27 \, a b^{14} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{3}{4}} - 27 \, {\left(b^{9} c^{9} - 21 \, a b^{8} c^{8} d + 180 \, a^{2} b^{7} c^{7} d^{2} - 820 \, a^{3} b^{6} c^{6} d^{3} + 2190 \, a^{4} b^{5} c^{5} d^{4} - 3606 \, a^{5} b^{4} c^{4} d^{5} + 3716 \, a^{6} b^{3} c^{3} d^{6} - 2340 \, a^{7} b^{2} c^{2} d^{7} + 825 \, a^{8} b c d^{8} - 125 \, a^{9} d^{9}\right)} \sqrt{x}\right) + 231 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{1}{4}} \log\left(-27 \, a b^{14} \left(-\frac{b^{12} c^{12} - 28 \, a b^{11} c^{11} d + 338 \, a^{2} b^{10} c^{10} d^{2} - 2316 \, a^{3} b^{9} c^{9} d^{3} + 10015 \, a^{4} b^{8} c^{8} d^{4} - 28856 \, a^{5} b^{7} c^{7} d^{5} + 57148 \, a^{6} b^{6} c^{6} d^{6} - 78968 \, a^{7} b^{5} c^{5} d^{7} + 76111 \, a^{8} b^{4} c^{4} d^{8} - 50220 \, a^{9} b^{3} c^{3} d^{9} + 21650 \, a^{10} b^{2} c^{2} d^{10} - 5500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a b^{19}}\right)^{\frac{3}{4}} - 27 \, {\left(b^{9} c^{9} - 21 \, a b^{8} c^{8} d + 180 \, a^{2} b^{7} c^{7} d^{2} - 820 \, a^{3} b^{6} c^{6} d^{3} + 2190 \, a^{4} b^{5} c^{5} d^{4} - 3606 \, a^{5} b^{4} c^{4} d^{5} + 3716 \, a^{6} b^{3} c^{3} d^{6} - 2340 \, a^{7} b^{2} c^{2} d^{7} + 825 \, a^{8} b c d^{8} - 125 \, a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(28 \, b^{3} d^{3} x^{7} + 12 \, {\left(11 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x^{5} + 44 \, {\left(7 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x^{3} - 77 \, {\left(b^{3} c^{3} - 7 \, a b^{2} c^{2} d + 11 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} x\right)} \sqrt{x}}{616 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/616*(924*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(1/4)*arctan((sqrt((b^18*c^18 - 42*a*b^17*c^17*d + 801*a^2*b^16*c^16*d^2 - 9200*a^3*b^15*c^15*d^3 + 71220*a^4*b^14*c^14*d^4 - 394392*a^5*b^13*c^13*d^5 + 1619684*a^6*b^12*c^12*d^6 - 5050512*a^7*b^11*c^11*d^7 + 12147630*a^8*b^10*c^10*d^8 - 22765820*a^9*b^9*c^9*d^9 + 33419166*a^10*b^8*c^8*d^10 - 38446992*a^11*b^7*c^7*d^11 + 34503236*a^12*b^6*c^6*d^12 - 23888280*a^13*b^5*c^5*d^13 + 12508500*a^14*b^4*c^4*d^14 - 4790000*a^15*b^3*c^3*d^15 + 1265625*a^16*b^2*c^2*d^16 - 206250*a^17*b*c*d^17 + 15625*a^18*d^18)*x - (a*b^21*c^12 - 28*a^2*b^20*c^11*d + 338*a^3*b^19*c^10*d^2 - 2316*a^4*b^18*c^9*d^3 + 10015*a^5*b^17*c^8*d^4 - 28856*a^6*b^16*c^7*d^5 + 57148*a^7*b^15*c^6*d^6 - 78968*a^8*b^14*c^5*d^7 + 76111*a^9*b^13*c^4*d^8 - 50220*a^10*b^12*c^3*d^9 + 21650*a^11*b^11*c^2*d^10 - 5500*a^12*b^10*c*d^11 + 625*a^13*b^9*d^12)*sqrt(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19)))*b^5*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(1/4) + (b^14*c^9 - 21*a*b^13*c^8*d + 180*a^2*b^12*c^7*d^2 - 820*a^3*b^11*c^6*d^3 + 2190*a^4*b^10*c^5*d^4 - 3606*a^5*b^9*c^4*d^5 + 3716*a^6*b^8*c^3*d^6 - 2340*a^7*b^7*c^2*d^7 + 825*a^8*b^6*c*d^8 - 125*a^9*b^5*d^9)*sqrt(x)*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(1/4))/(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)) - 231*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(1/4)*log(27*a*b^14*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(3/4) - 27*(b^9*c^9 - 21*a*b^8*c^8*d + 180*a^2*b^7*c^7*d^2 - 820*a^3*b^6*c^6*d^3 + 2190*a^4*b^5*c^5*d^4 - 3606*a^5*b^4*c^4*d^5 + 3716*a^6*b^3*c^3*d^6 - 2340*a^7*b^2*c^2*d^7 + 825*a^8*b*c*d^8 - 125*a^9*d^9)*sqrt(x)) + 231*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(1/4)*log(-27*a*b^14*(-(b^12*c^12 - 28*a*b^11*c^11*d + 338*a^2*b^10*c^10*d^2 - 2316*a^3*b^9*c^9*d^3 + 10015*a^4*b^8*c^8*d^4 - 28856*a^5*b^7*c^7*d^5 + 57148*a^6*b^6*c^6*d^6 - 78968*a^7*b^5*c^5*d^7 + 76111*a^8*b^4*c^4*d^8 - 50220*a^9*b^3*c^3*d^9 + 21650*a^10*b^2*c^2*d^10 - 5500*a^11*b*c*d^11 + 625*a^12*d^12)/(a*b^19))^(3/4) - 27*(b^9*c^9 - 21*a*b^8*c^8*d + 180*a^2*b^7*c^7*d^2 - 820*a^3*b^6*c^6*d^3 + 2190*a^4*b^5*c^5*d^4 - 3606*a^5*b^4*c^4*d^5 + 3716*a^6*b^3*c^3*d^6 - 2340*a^7*b^2*c^2*d^7 + 825*a^8*b*c*d^8 - 125*a^9*d^9)*sqrt(x)) + 4*(28*b^3*d^3*x^7 + 12*(11*b^3*c*d^2 - 5*a*b^2*d^3)*x^5 + 44*(7*b^3*c^2*d - 11*a*b^2*c*d^2 + 5*a^2*b*d^3)*x^3 - 77*(b^3*c^3 - 7*a*b^2*c^2*d + 11*a^2*b*c*d^2 - 5*a^3*d^3)*x)*sqrt(x))/(b^5*x^2 + a*b^4)","B",0
454,1,1961,0,1.063471," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{180 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{2} b^{8} \sqrt{-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}} + {\left(b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 279 \, a^{2} b^{4} c^{4} d^{2} - 836 \, a^{3} b^{3} c^{3} d^{3} + 1119 \, a^{4} b^{2} c^{2} d^{4} - 702 \, a^{5} b c d^{5} + 169 \, a^{6} d^{6}\right)} x} a^{2} b^{13} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{3}{4}} + {\left(a^{2} b^{16} c^{3} - 15 \, a^{3} b^{15} c^{2} d + 27 \, a^{4} b^{14} c d^{2} - 13 \, a^{5} b^{13} d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{3}{4}}}{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}\right) + 45 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(a b^{4} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 45 \, {\left(b^{5} x^{2} + a b^{4}\right)} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{1}{4}} \log\left(-a b^{4} \left(-\frac{b^{12} c^{12} - 60 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 18412 \, a^{3} b^{9} c^{9} d^{3} + 130239 \, a^{4} b^{8} c^{8} d^{4} - 535032 \, a^{5} b^{7} c^{7} d^{5} + 1365756 \, a^{6} b^{6} c^{6} d^{6} - 2272824 \, a^{7} b^{5} c^{5} d^{7} + 2520207 \, a^{8} b^{4} c^{4} d^{8} - 1853644 \, a^{9} b^{3} c^{3} d^{9} + 871026 \, a^{10} b^{2} c^{2} d^{10} - 237276 \, a^{11} b c d^{11} + 28561 \, a^{12} d^{12}}{a^{3} b^{17}}\right)^{\frac{1}{4}} - {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(20 \, b^{3} d^{3} x^{6} - 45 \, b^{3} c^{3} + 675 \, a b^{2} c^{2} d - 1215 \, a^{2} b c d^{2} + 585 \, a^{3} d^{3} + 4 \, {\left(27 \, b^{3} c d^{2} - 13 \, a b^{2} d^{3}\right)} x^{4} + 36 \, {\left(15 \, b^{3} c^{2} d - 27 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{x}}{360 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"-1/360*(180*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(1/4)*arctan((sqrt(a^2*b^8*sqrt(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17)) + (b^6*c^6 - 30*a*b^5*c^5*d + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 702*a^5*b*c*d^5 + 169*a^6*d^6)*x)*a^2*b^13*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(3/4) + (a^2*b^16*c^3 - 15*a^3*b^15*c^2*d + 27*a^4*b^14*c*d^2 - 13*a^5*b^13*d^3)*sqrt(x)*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(3/4))/(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)) + 45*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(1/4)*log(a*b^4*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(1/4) - (b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*sqrt(x)) - 45*(b^5*x^2 + a*b^4)*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(1/4)*log(-a*b^4*(-(b^12*c^12 - 60*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 18412*a^3*b^9*c^9*d^3 + 130239*a^4*b^8*c^8*d^4 - 535032*a^5*b^7*c^7*d^5 + 1365756*a^6*b^6*c^6*d^6 - 2272824*a^7*b^5*c^5*d^7 + 2520207*a^8*b^4*c^4*d^8 - 1853644*a^9*b^3*c^3*d^9 + 871026*a^10*b^2*c^2*d^10 - 237276*a^11*b*c*d^11 + 28561*a^12*d^12)/(a^3*b^17))^(1/4) - (b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*sqrt(x)) - 4*(20*b^3*d^3*x^6 - 45*b^3*c^3 + 675*a*b^2*c^2*d - 1215*a^2*b*c*d^2 + 585*a^3*d^3 + 4*(27*b^3*c*d^2 - 13*a*b^2*d^3)*x^4 + 36*(15*b^3*c^2*d - 27*a*b^2*c*d^2 + 13*a^2*b*d^3)*x^2)*sqrt(x))/(b^5*x^2 + a*b^4)","B",0
455,1,2531,0,1.386346," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{84 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(b^{18} c^{18} + 54 \, a b^{17} c^{17} d + 1089 \, a^{2} b^{16} c^{16} d^{2} + 8976 \, a^{3} b^{15} c^{15} d^{3} + 5940 \, a^{4} b^{14} c^{14} d^{4} - 279576 \, a^{5} b^{13} c^{13} d^{5} - 338844 \, a^{6} b^{12} c^{12} d^{6} + 6001776 \, a^{7} b^{11} c^{11} d^{7} - 6412626 \, a^{8} b^{10} c^{10} d^{8} - 62165180 \, a^{9} b^{9} c^{9} d^{9} + 294333534 \, a^{10} b^{8} c^{8} d^{10} - 671362704 \, a^{11} b^{7} c^{7} d^{11} + 974580036 \, a^{12} b^{6} c^{6} d^{12} - 971334936 \, a^{13} b^{5} c^{5} d^{13} + 678512340 \, a^{14} b^{4} c^{4} d^{14} - 328575984 \, a^{15} b^{3} c^{3} d^{15} + 105546969 \, a^{16} b^{2} c^{2} d^{16} - 20292426 \, a^{17} b c d^{17} + 1771561 \, a^{18} d^{18}\right)} x - {\left(a^{3} b^{19} c^{12} + 36 \, a^{4} b^{18} c^{11} d + 402 \, a^{5} b^{17} c^{10} d^{2} + 692 \, a^{6} b^{16} c^{9} d^{3} - 10017 \, a^{7} b^{15} c^{8} d^{4} - 5688 \, a^{8} b^{14} c^{7} d^{5} + 160188 \, a^{9} b^{13} c^{6} d^{6} - 486648 \, a^{10} b^{12} c^{5} d^{7} + 746703 \, a^{11} b^{11} c^{4} d^{8} - 676588 \, a^{12} b^{10} c^{3} d^{9} + 368082 \, a^{13} b^{9} c^{2} d^{10} - 111804 \, a^{14} b^{8} c d^{11} + 14641 \, a^{15} b^{7} d^{12}\right)} \sqrt{-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}}} a b^{4} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{1}{4}} - {\left(a b^{13} c^{9} + 27 \, a^{2} b^{12} c^{8} d + 180 \, a^{3} b^{11} c^{7} d^{2} - 372 \, a^{4} b^{10} c^{6} d^{3} - 3186 \, a^{5} b^{9} c^{5} d^{4} + 13194 \, a^{6} b^{8} c^{4} d^{5} - 21372 \, a^{7} b^{7} c^{3} d^{6} + 17820 \, a^{8} b^{6} c^{2} d^{7} - 7623 \, a^{9} b^{5} c d^{8} + 1331 \, a^{10} b^{4} d^{9}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{1}{4}}}{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}\right) - 21 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \log\left(a^{4} b^{11} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{3}{4}} + {\left(b^{9} c^{9} + 27 \, a b^{8} c^{8} d + 180 \, a^{2} b^{7} c^{7} d^{2} - 372 \, a^{3} b^{6} c^{6} d^{3} - 3186 \, a^{4} b^{5} c^{5} d^{4} + 13194 \, a^{5} b^{4} c^{4} d^{5} - 21372 \, a^{6} b^{3} c^{3} d^{6} + 17820 \, a^{7} b^{2} c^{2} d^{7} - 7623 \, a^{8} b c d^{8} + 1331 \, a^{9} d^{9}\right)} \sqrt{x}\right) + 21 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{1}{4}} \log\left(-a^{4} b^{11} \left(-\frac{b^{12} c^{12} + 36 \, a b^{11} c^{11} d + 402 \, a^{2} b^{10} c^{10} d^{2} + 692 \, a^{3} b^{9} c^{9} d^{3} - 10017 \, a^{4} b^{8} c^{8} d^{4} - 5688 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 486648 \, a^{7} b^{5} c^{5} d^{7} + 746703 \, a^{8} b^{4} c^{4} d^{8} - 676588 \, a^{9} b^{3} c^{3} d^{9} + 368082 \, a^{10} b^{2} c^{2} d^{10} - 111804 \, a^{11} b c d^{11} + 14641 \, a^{12} d^{12}}{a^{5} b^{15}}\right)^{\frac{3}{4}} + {\left(b^{9} c^{9} + 27 \, a b^{8} c^{8} d + 180 \, a^{2} b^{7} c^{7} d^{2} - 372 \, a^{3} b^{6} c^{6} d^{3} - 3186 \, a^{4} b^{5} c^{5} d^{4} + 13194 \, a^{5} b^{4} c^{4} d^{5} - 21372 \, a^{6} b^{3} c^{3} d^{6} + 17820 \, a^{7} b^{2} c^{2} d^{7} - 7623 \, a^{8} b c d^{8} + 1331 \, a^{9} d^{9}\right)} \sqrt{x}\right) - 4 \, {\left(12 \, a b^{2} d^{3} x^{5} + 4 \, {\left(21 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x^{3} + 7 \, {\left(3 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 21 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} x\right)} \sqrt{x}}{168 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"-1/168*(84*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(1/4)*arctan((sqrt((b^18*c^18 + 54*a*b^17*c^17*d + 1089*a^2*b^16*c^16*d^2 + 8976*a^3*b^15*c^15*d^3 + 5940*a^4*b^14*c^14*d^4 - 279576*a^5*b^13*c^13*d^5 - 338844*a^6*b^12*c^12*d^6 + 6001776*a^7*b^11*c^11*d^7 - 6412626*a^8*b^10*c^10*d^8 - 62165180*a^9*b^9*c^9*d^9 + 294333534*a^10*b^8*c^8*d^10 - 671362704*a^11*b^7*c^7*d^11 + 974580036*a^12*b^6*c^6*d^12 - 971334936*a^13*b^5*c^5*d^13 + 678512340*a^14*b^4*c^4*d^14 - 328575984*a^15*b^3*c^3*d^15 + 105546969*a^16*b^2*c^2*d^16 - 20292426*a^17*b*c*d^17 + 1771561*a^18*d^18)*x - (a^3*b^19*c^12 + 36*a^4*b^18*c^11*d + 402*a^5*b^17*c^10*d^2 + 692*a^6*b^16*c^9*d^3 - 10017*a^7*b^15*c^8*d^4 - 5688*a^8*b^14*c^7*d^5 + 160188*a^9*b^13*c^6*d^6 - 486648*a^10*b^12*c^5*d^7 + 746703*a^11*b^11*c^4*d^8 - 676588*a^12*b^10*c^3*d^9 + 368082*a^13*b^9*c^2*d^10 - 111804*a^14*b^8*c*d^11 + 14641*a^15*b^7*d^12)*sqrt(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15)))*a*b^4*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(1/4) - (a*b^13*c^9 + 27*a^2*b^12*c^8*d + 180*a^3*b^11*c^7*d^2 - 372*a^4*b^10*c^6*d^3 - 3186*a^5*b^9*c^5*d^4 + 13194*a^6*b^8*c^4*d^5 - 21372*a^7*b^7*c^3*d^6 + 17820*a^8*b^6*c^2*d^7 - 7623*a^9*b^5*c*d^8 + 1331*a^10*b^4*d^9)*sqrt(x)*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(1/4))/(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)) - 21*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(1/4)*log(a^4*b^11*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(3/4) + (b^9*c^9 + 27*a*b^8*c^8*d + 180*a^2*b^7*c^7*d^2 - 372*a^3*b^6*c^6*d^3 - 3186*a^4*b^5*c^5*d^4 + 13194*a^5*b^4*c^4*d^5 - 21372*a^6*b^3*c^3*d^6 + 17820*a^7*b^2*c^2*d^7 - 7623*a^8*b*c*d^8 + 1331*a^9*d^9)*sqrt(x)) + 21*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(1/4)*log(-a^4*b^11*(-(b^12*c^12 + 36*a*b^11*c^11*d + 402*a^2*b^10*c^10*d^2 + 692*a^3*b^9*c^9*d^3 - 10017*a^4*b^8*c^8*d^4 - 5688*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 486648*a^7*b^5*c^5*d^7 + 746703*a^8*b^4*c^4*d^8 - 676588*a^9*b^3*c^3*d^9 + 368082*a^10*b^2*c^2*d^10 - 111804*a^11*b*c*d^11 + 14641*a^12*d^12)/(a^5*b^15))^(3/4) + (b^9*c^9 + 27*a*b^8*c^8*d + 180*a^2*b^7*c^7*d^2 - 372*a^3*b^6*c^6*d^3 - 3186*a^4*b^5*c^5*d^4 + 13194*a^5*b^4*c^4*d^5 - 21372*a^6*b^3*c^3*d^6 + 17820*a^7*b^2*c^2*d^7 - 7623*a^8*b*c*d^8 + 1331*a^9*d^9)*sqrt(x)) - 4*(12*a*b^2*d^3*x^5 + 4*(21*a*b^2*c*d^2 - 11*a^2*b*d^3)*x^3 + 7*(3*b^3*c^3 - 9*a*b^2*c^2*d + 21*a^2*b*c*d^2 - 11*a^3*d^3)*x)*sqrt(x))/(a*b^4*x^2 + a^2*b^3)","B",0
456,1,1944,0,1.365094," ","integrate((d*x^2+c)^3/(b*x^2+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{60 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{4} b^{6} \sqrt{-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}} + {\left(b^{6} c^{6} + 2 \, a b^{5} c^{5} d - 9 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} + 31 \, a^{4} b^{2} c^{2} d^{4} - 30 \, a^{5} b c d^{5} + 9 \, a^{6} d^{6}\right)} x} a^{5} b^{10} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{3}{4}} - {\left(a^{5} b^{13} c^{3} + a^{6} b^{12} c^{2} d - 5 \, a^{7} b^{11} c d^{2} + 3 \, a^{8} b^{10} d^{3}\right)} \sqrt{x} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{3}{4}}}{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}\right) + 15 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(3 \, a^{2} b^{3} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} + 3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 15 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} \log\left(-3 \, a^{2} b^{3} \left(-\frac{b^{12} c^{12} + 4 \, a b^{11} c^{11} d - 14 \, a^{2} b^{10} c^{10} d^{2} - 44 \, a^{3} b^{9} c^{9} d^{3} + 127 \, a^{4} b^{8} c^{8} d^{4} + 136 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 328 \, a^{7} b^{5} c^{5} d^{7} + 1039 \, a^{8} b^{4} c^{4} d^{8} - 1932 \, a^{9} b^{3} c^{3} d^{9} + 1458 \, a^{10} b^{2} c^{2} d^{10} - 540 \, a^{11} b c d^{11} + 81 \, a^{12} d^{12}}{a^{7} b^{13}}\right)^{\frac{1}{4}} + 3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, a b^{2} d^{3} x^{4} + 5 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 75 \, a^{2} b c d^{2} - 45 \, a^{3} d^{3} + 12 \, {\left(5 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/40*(60*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*arctan((sqrt(a^4*b^6*sqrt(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13)) + (b^6*c^6 + 2*a*b^5*c^5*d - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 - 30*a^5*b*c*d^5 + 9*a^6*d^6)*x)*a^5*b^10*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(3/4) - (a^5*b^13*c^3 + a^6*b^12*c^2*d - 5*a^7*b^11*c*d^2 + 3*a^8*b^10*d^3)*sqrt(x)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(3/4))/(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)) + 15*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*log(3*a^2*b^3*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4) + 3*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(x)) - 15*(a*b^4*x^2 + a^2*b^3)*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4)*log(-3*a^2*b^3*(-(b^12*c^12 + 4*a*b^11*c^11*d - 14*a^2*b^10*c^10*d^2 - 44*a^3*b^9*c^9*d^3 + 127*a^4*b^8*c^8*d^4 + 136*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 328*a^7*b^5*c^5*d^7 + 1039*a^8*b^4*c^4*d^8 - 1932*a^9*b^3*c^3*d^9 + 1458*a^10*b^2*c^2*d^10 - 540*a^11*b*c*d^11 + 81*a^12*d^12)/(a^7*b^13))^(1/4) + 3*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*sqrt(x)) + 4*(4*a*b^2*d^3*x^4 + 5*b^3*c^3 - 15*a*b^2*c^2*d + 75*a^2*b*c*d^2 - 45*a^3*d^3 + 12*(5*a*b^2*c*d^2 - 3*a^2*b*d^3)*x^2)*sqrt(x))/(a*b^4*x^2 + a^2*b^3)","B",0
457,1,2547,0,1.272995," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(15625 \, b^{18} c^{18} - 56250 \, a b^{17} c^{17} d - 84375 \, a^{2} b^{16} c^{16} d^{2} + 570000 \, a^{3} b^{15} c^{15} d^{3} - 211500 \, a^{4} b^{14} c^{14} d^{4} - 2174040 \, a^{5} b^{13} c^{13} d^{5} + 2720004 \, a^{6} b^{12} c^{12} d^{6} + 3321072 \, a^{7} b^{11} c^{11} d^{7} - 8368866 \, a^{8} b^{10} c^{10} d^{8} + 640420 \, a^{9} b^{9} c^{9} d^{9} + 11255310 \, a^{10} b^{8} c^{8} d^{10} - 8509968 \, a^{11} b^{7} c^{7} d^{11} - 4831644 \, a^{12} b^{6} c^{6} d^{12} + 9537192 \, a^{13} b^{5} c^{5} d^{13} - 3095820 \, a^{14} b^{4} c^{4} d^{14} - 2551920 \, a^{15} b^{3} c^{3} d^{15} + 2614689 \, a^{16} b^{2} c^{2} d^{16} - 907578 \, a^{17} b c d^{17} + 117649 \, a^{18} d^{18}\right)} x - {\left(625 \, a^{5} b^{17} c^{12} - 1500 \, a^{6} b^{16} c^{11} d - 3150 \, a^{7} b^{15} c^{10} d^{2} + 11060 \, a^{8} b^{14} c^{9} d^{3} + 1071 \, a^{9} b^{13} c^{8} d^{4} - 28728 \, a^{10} b^{12} c^{7} d^{5} + 19068 \, a^{11} b^{11} c^{6} d^{6} + 27144 \, a^{12} b^{10} c^{5} d^{7} - 37665 \, a^{13} b^{9} c^{4} d^{8} + 2324 \, a^{14} b^{8} c^{3} d^{9} + 19698 \, a^{15} b^{7} c^{2} d^{10} - 12348 \, a^{16} b^{6} c d^{11} + 2401 \, a^{17} b^{5} d^{12}\right)} \sqrt{-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}}} a^{2} b^{3} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{1}{4}} - {\left(125 \, a^{2} b^{12} c^{9} - 225 \, a^{3} b^{11} c^{8} d - 540 \, a^{4} b^{10} c^{7} d^{2} + 1308 \, a^{5} b^{9} c^{6} d^{3} + 342 \, a^{6} b^{8} c^{5} d^{4} - 2430 \, a^{7} b^{7} c^{4} d^{5} + 1140 \, a^{8} b^{6} c^{3} d^{6} + 1260 \, a^{9} b^{5} c^{2} d^{7} - 1323 \, a^{10} b^{4} c d^{8} + 343 \, a^{11} b^{3} d^{9}\right)} \sqrt{x} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{1}{4}}}{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}\right) - 3 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \log\left(a^{7} b^{8} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{3}{4}} + {\left(125 \, b^{9} c^{9} - 225 \, a b^{8} c^{8} d - 540 \, a^{2} b^{7} c^{7} d^{2} + 1308 \, a^{3} b^{6} c^{6} d^{3} + 342 \, a^{4} b^{5} c^{5} d^{4} - 2430 \, a^{5} b^{4} c^{4} d^{5} + 1140 \, a^{6} b^{3} c^{3} d^{6} + 1260 \, a^{7} b^{2} c^{2} d^{7} - 1323 \, a^{8} b c d^{8} + 343 \, a^{9} d^{9}\right)} \sqrt{x}\right) + 3 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{1}{4}} \log\left(-a^{7} b^{8} \left(-\frac{625 \, b^{12} c^{12} - 1500 \, a b^{11} c^{11} d - 3150 \, a^{2} b^{10} c^{10} d^{2} + 11060 \, a^{3} b^{9} c^{9} d^{3} + 1071 \, a^{4} b^{8} c^{8} d^{4} - 28728 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} + 27144 \, a^{7} b^{5} c^{5} d^{7} - 37665 \, a^{8} b^{4} c^{4} d^{8} + 2324 \, a^{9} b^{3} c^{3} d^{9} + 19698 \, a^{10} b^{2} c^{2} d^{10} - 12348 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{a^{9} b^{11}}\right)^{\frac{3}{4}} + {\left(125 \, b^{9} c^{9} - 225 \, a b^{8} c^{8} d - 540 \, a^{2} b^{7} c^{7} d^{2} + 1308 \, a^{3} b^{6} c^{6} d^{3} + 342 \, a^{4} b^{5} c^{5} d^{4} - 2430 \, a^{5} b^{4} c^{4} d^{5} + 1140 \, a^{6} b^{3} c^{3} d^{6} + 1260 \, a^{7} b^{2} c^{2} d^{7} - 1323 \, a^{8} b c d^{8} + 343 \, a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, a^{2} b d^{3} x^{4} - 12 \, a b^{2} c^{3} - {\left(15 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 7 \, a^{3} d^{3}\right)} x^{2}\right)} \sqrt{x}}{24 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}}"," ",0,"1/24*(12*(a^2*b^3*x^3 + a^3*b^2*x)*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(1/4)*arctan((sqrt((15625*b^18*c^18 - 56250*a*b^17*c^17*d - 84375*a^2*b^16*c^16*d^2 + 570000*a^3*b^15*c^15*d^3 - 211500*a^4*b^14*c^14*d^4 - 2174040*a^5*b^13*c^13*d^5 + 2720004*a^6*b^12*c^12*d^6 + 3321072*a^7*b^11*c^11*d^7 - 8368866*a^8*b^10*c^10*d^8 + 640420*a^9*b^9*c^9*d^9 + 11255310*a^10*b^8*c^8*d^10 - 8509968*a^11*b^7*c^7*d^11 - 4831644*a^12*b^6*c^6*d^12 + 9537192*a^13*b^5*c^5*d^13 - 3095820*a^14*b^4*c^4*d^14 - 2551920*a^15*b^3*c^3*d^15 + 2614689*a^16*b^2*c^2*d^16 - 907578*a^17*b*c*d^17 + 117649*a^18*d^18)*x - (625*a^5*b^17*c^12 - 1500*a^6*b^16*c^11*d - 3150*a^7*b^15*c^10*d^2 + 11060*a^8*b^14*c^9*d^3 + 1071*a^9*b^13*c^8*d^4 - 28728*a^10*b^12*c^7*d^5 + 19068*a^11*b^11*c^6*d^6 + 27144*a^12*b^10*c^5*d^7 - 37665*a^13*b^9*c^4*d^8 + 2324*a^14*b^8*c^3*d^9 + 19698*a^15*b^7*c^2*d^10 - 12348*a^16*b^6*c*d^11 + 2401*a^17*b^5*d^12)*sqrt(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11)))*a^2*b^3*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(1/4) - (125*a^2*b^12*c^9 - 225*a^3*b^11*c^8*d - 540*a^4*b^10*c^7*d^2 + 1308*a^5*b^9*c^6*d^3 + 342*a^6*b^8*c^5*d^4 - 2430*a^7*b^7*c^4*d^5 + 1140*a^8*b^6*c^3*d^6 + 1260*a^9*b^5*c^2*d^7 - 1323*a^10*b^4*c*d^8 + 343*a^11*b^3*d^9)*sqrt(x)*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(1/4))/(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)) - 3*(a^2*b^3*x^3 + a^3*b^2*x)*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(1/4)*log(a^7*b^8*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(3/4) + (125*b^9*c^9 - 225*a*b^8*c^8*d - 540*a^2*b^7*c^7*d^2 + 1308*a^3*b^6*c^6*d^3 + 342*a^4*b^5*c^5*d^4 - 2430*a^5*b^4*c^4*d^5 + 1140*a^6*b^3*c^3*d^6 + 1260*a^7*b^2*c^2*d^7 - 1323*a^8*b*c*d^8 + 343*a^9*d^9)*sqrt(x)) + 3*(a^2*b^3*x^3 + a^3*b^2*x)*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(1/4)*log(-a^7*b^8*(-(625*b^12*c^12 - 1500*a*b^11*c^11*d - 3150*a^2*b^10*c^10*d^2 + 11060*a^3*b^9*c^9*d^3 + 1071*a^4*b^8*c^8*d^4 - 28728*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 + 27144*a^7*b^5*c^5*d^7 - 37665*a^8*b^4*c^4*d^8 + 2324*a^9*b^3*c^3*d^9 + 19698*a^10*b^2*c^2*d^10 - 12348*a^11*b*c*d^11 + 2401*a^12*d^12)/(a^9*b^11))^(3/4) + (125*b^9*c^9 - 225*a*b^8*c^8*d - 540*a^2*b^7*c^7*d^2 + 1308*a^3*b^6*c^6*d^3 + 342*a^4*b^5*c^5*d^4 - 2430*a^5*b^4*c^4*d^5 + 1140*a^6*b^3*c^3*d^6 + 1260*a^7*b^2*c^2*d^7 - 1323*a^8*b*c*d^8 + 343*a^9*d^9)*sqrt(x)) + 4*(4*a^2*b*d^3*x^4 - 12*a*b^2*c^3 - (15*b^3*c^3 - 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 7*a^3*d^3)*x^2)*sqrt(x))/(a^2*b^3*x^3 + a^3*b^2*x)","B",0
458,1,1967,0,1.419562," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x^{2}\right)} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{6} b^{4} \sqrt{-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}} + {\left(49 \, b^{6} c^{6} - 126 \, a b^{5} c^{5} d + 39 \, a^{2} b^{4} c^{4} d^{2} + 124 \, a^{3} b^{3} c^{3} d^{3} - 81 \, a^{4} b^{2} c^{2} d^{4} - 30 \, a^{5} b c d^{5} + 25 \, a^{6} d^{6}\right)} x} a^{8} b^{7} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{3}{4}} - {\left(7 \, a^{8} b^{10} c^{3} - 9 \, a^{9} b^{9} c^{2} d - 3 \, a^{10} b^{8} c d^{2} + 5 \, a^{11} b^{7} d^{3}\right)} \sqrt{x} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{3}{4}}}{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}\right) + 3 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x^{2}\right)} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \log\left(a^{3} b^{2} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{1}{4}} + {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 3 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x^{2}\right)} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{1}{4}} \log\left(-a^{3} b^{2} \left(-\frac{2401 \, b^{12} c^{12} - 12348 \, a b^{11} c^{11} d + 19698 \, a^{2} b^{10} c^{10} d^{2} + 2324 \, a^{3} b^{9} c^{9} d^{3} - 37665 \, a^{4} b^{8} c^{8} d^{4} + 27144 \, a^{5} b^{7} c^{7} d^{5} + 19068 \, a^{6} b^{6} c^{6} d^{6} - 28728 \, a^{7} b^{5} c^{5} d^{7} + 1071 \, a^{8} b^{4} c^{4} d^{8} + 11060 \, a^{9} b^{3} c^{3} d^{9} - 3150 \, a^{10} b^{2} c^{2} d^{10} - 1500 \, a^{11} b c d^{11} + 625 \, a^{12} d^{12}}{a^{11} b^{9}}\right)^{\frac{1}{4}} + {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(12 \, a^{2} b d^{3} x^{4} - 4 \, a b^{2} c^{3} - {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 15 \, a^{3} d^{3}\right)} x^{2}\right)} \sqrt{x}}{24 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x^{2}\right)}}"," ",0,"-1/24*(12*(a^2*b^3*x^4 + a^3*b^2*x^2)*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(1/4)*arctan((sqrt(a^6*b^4*sqrt(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9)) + (49*b^6*c^6 - 126*a*b^5*c^5*d + 39*a^2*b^4*c^4*d^2 + 124*a^3*b^3*c^3*d^3 - 81*a^4*b^2*c^2*d^4 - 30*a^5*b*c*d^5 + 25*a^6*d^6)*x)*a^8*b^7*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(3/4) - (7*a^8*b^10*c^3 - 9*a^9*b^9*c^2*d - 3*a^10*b^8*c*d^2 + 5*a^11*b^7*d^3)*sqrt(x)*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(3/4))/(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)) + 3*(a^2*b^3*x^4 + a^3*b^2*x^2)*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(1/4)*log(a^3*b^2*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(1/4) + (7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(x)) - 3*(a^2*b^3*x^4 + a^3*b^2*x^2)*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(1/4)*log(-a^3*b^2*(-(2401*b^12*c^12 - 12348*a*b^11*c^11*d + 19698*a^2*b^10*c^10*d^2 + 2324*a^3*b^9*c^9*d^3 - 37665*a^4*b^8*c^8*d^4 + 27144*a^5*b^7*c^7*d^5 + 19068*a^6*b^6*c^6*d^6 - 28728*a^7*b^5*c^5*d^7 + 1071*a^8*b^4*c^4*d^8 + 11060*a^9*b^3*c^3*d^9 - 3150*a^10*b^2*c^2*d^10 - 1500*a^11*b*c*d^11 + 625*a^12*d^12)/(a^11*b^9))^(1/4) + (7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(x)) - 4*(12*a^2*b*d^3*x^4 - 4*a*b^2*c^3 - (7*b^3*c^3 - 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 15*a^3*d^3)*x^2)*sqrt(x))/(a^2*b^3*x^4 + a^3*b^2*x^2)","B",0
459,1,2549,0,1.195463," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{60 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{{\left(729 \, b^{18} c^{18} - 7290 \, a b^{17} c^{17} d + 31833 \, a^{2} b^{16} c^{16} d^{2} - 78192 \, a^{3} b^{15} c^{15} d^{3} + 113940 \, a^{4} b^{14} c^{14} d^{4} - 88920 \, a^{5} b^{13} c^{13} d^{5} + 10180 \, a^{6} b^{12} c^{12} d^{6} + 46320 \, a^{7} b^{11} c^{11} d^{7} - 35970 \, a^{8} b^{10} c^{10} d^{8} - 220 \, a^{9} b^{9} c^{9} d^{9} + 12078 \, a^{10} b^{8} c^{8} d^{10} - 3600 \, a^{11} b^{7} c^{7} d^{11} - 1884 \, a^{12} b^{6} c^{6} d^{12} + 936 \, a^{13} b^{5} c^{5} d^{13} + 180 \, a^{14} b^{4} c^{4} d^{14} - 112 \, a^{15} b^{3} c^{3} d^{15} - 15 \, a^{16} b^{2} c^{2} d^{16} + 6 \, a^{17} b c d^{17} + a^{18} d^{18}\right)} x - {\left(81 \, a^{7} b^{15} c^{12} - 540 \, a^{8} b^{14} c^{11} d + 1458 \, a^{9} b^{13} c^{10} d^{2} - 1932 \, a^{10} b^{12} c^{9} d^{3} + 1039 \, a^{11} b^{11} c^{8} d^{4} + 328 \, a^{12} b^{10} c^{7} d^{5} - 644 \, a^{13} b^{9} c^{6} d^{6} + 136 \, a^{14} b^{8} c^{5} d^{7} + 127 \, a^{15} b^{7} c^{4} d^{8} - 44 \, a^{16} b^{6} c^{3} d^{9} - 14 \, a^{17} b^{5} c^{2} d^{10} + 4 \, a^{18} b^{4} c d^{11} + a^{19} b^{3} d^{12}\right)} \sqrt{-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}}} a^{3} b^{2} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{1}{4}} - {\left(27 \, a^{3} b^{11} c^{9} - 135 \, a^{4} b^{10} c^{8} d + 252 \, a^{5} b^{9} c^{7} d^{2} - 188 \, a^{6} b^{8} c^{6} d^{3} - 6 \, a^{7} b^{7} c^{5} d^{4} + 78 \, a^{8} b^{6} c^{4} d^{5} - 20 \, a^{9} b^{5} c^{3} d^{6} - 12 \, a^{10} b^{4} c^{2} d^{7} + 3 \, a^{11} b^{3} c d^{8} + a^{12} b^{2} d^{9}\right)} \sqrt{x} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{1}{4}}}{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) - 15 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \log\left(27 \, a^{10} b^{5} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{3}{4}} + 27 \, {\left(27 \, b^{9} c^{9} - 135 \, a b^{8} c^{8} d + 252 \, a^{2} b^{7} c^{7} d^{2} - 188 \, a^{3} b^{6} c^{6} d^{3} - 6 \, a^{4} b^{5} c^{5} d^{4} + 78 \, a^{5} b^{4} c^{4} d^{5} - 20 \, a^{6} b^{3} c^{3} d^{6} - 12 \, a^{7} b^{2} c^{2} d^{7} + 3 \, a^{8} b c d^{8} + a^{9} d^{9}\right)} \sqrt{x}\right) + 15 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{1}{4}} \log\left(-27 \, a^{10} b^{5} \left(-\frac{81 \, b^{12} c^{12} - 540 \, a b^{11} c^{11} d + 1458 \, a^{2} b^{10} c^{10} d^{2} - 1932 \, a^{3} b^{9} c^{9} d^{3} + 1039 \, a^{4} b^{8} c^{8} d^{4} + 328 \, a^{5} b^{7} c^{7} d^{5} - 644 \, a^{6} b^{6} c^{6} d^{6} + 136 \, a^{7} b^{5} c^{5} d^{7} + 127 \, a^{8} b^{4} c^{4} d^{8} - 44 \, a^{9} b^{3} c^{3} d^{9} - 14 \, a^{10} b^{2} c^{2} d^{10} + 4 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{13} b^{7}}\right)^{\frac{3}{4}} + 27 \, {\left(27 \, b^{9} c^{9} - 135 \, a b^{8} c^{8} d + 252 \, a^{2} b^{7} c^{7} d^{2} - 188 \, a^{3} b^{6} c^{6} d^{3} - 6 \, a^{4} b^{5} c^{5} d^{4} + 78 \, a^{5} b^{4} c^{4} d^{5} - 20 \, a^{6} b^{3} c^{3} d^{6} - 12 \, a^{7} b^{2} c^{2} d^{7} + 3 \, a^{8} b c d^{8} + a^{9} d^{9}\right)} \sqrt{x}\right) + 4 \, {\left(4 \, a^{2} b c^{3} - 5 \, {\left(9 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{4} - 12 \, {\left(3 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{x}}{40 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)}}"," ",0,"-1/40*(60*(a^3*b^2*x^5 + a^4*b*x^3)*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(1/4)*arctan((sqrt((729*b^18*c^18 - 7290*a*b^17*c^17*d + 31833*a^2*b^16*c^16*d^2 - 78192*a^3*b^15*c^15*d^3 + 113940*a^4*b^14*c^14*d^4 - 88920*a^5*b^13*c^13*d^5 + 10180*a^6*b^12*c^12*d^6 + 46320*a^7*b^11*c^11*d^7 - 35970*a^8*b^10*c^10*d^8 - 220*a^9*b^9*c^9*d^9 + 12078*a^10*b^8*c^8*d^10 - 3600*a^11*b^7*c^7*d^11 - 1884*a^12*b^6*c^6*d^12 + 936*a^13*b^5*c^5*d^13 + 180*a^14*b^4*c^4*d^14 - 112*a^15*b^3*c^3*d^15 - 15*a^16*b^2*c^2*d^16 + 6*a^17*b*c*d^17 + a^18*d^18)*x - (81*a^7*b^15*c^12 - 540*a^8*b^14*c^11*d + 1458*a^9*b^13*c^10*d^2 - 1932*a^10*b^12*c^9*d^3 + 1039*a^11*b^11*c^8*d^4 + 328*a^12*b^10*c^7*d^5 - 644*a^13*b^9*c^6*d^6 + 136*a^14*b^8*c^5*d^7 + 127*a^15*b^7*c^4*d^8 - 44*a^16*b^6*c^3*d^9 - 14*a^17*b^5*c^2*d^10 + 4*a^18*b^4*c*d^11 + a^19*b^3*d^12)*sqrt(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7)))*a^3*b^2*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(1/4) - (27*a^3*b^11*c^9 - 135*a^4*b^10*c^8*d + 252*a^5*b^9*c^7*d^2 - 188*a^6*b^8*c^6*d^3 - 6*a^7*b^7*c^5*d^4 + 78*a^8*b^6*c^4*d^5 - 20*a^9*b^5*c^3*d^6 - 12*a^10*b^4*c^2*d^7 + 3*a^11*b^3*c*d^8 + a^12*b^2*d^9)*sqrt(x)*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(1/4))/(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)) - 15*(a^3*b^2*x^5 + a^4*b*x^3)*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(1/4)*log(27*a^10*b^5*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(3/4) + 27*(27*b^9*c^9 - 135*a*b^8*c^8*d + 252*a^2*b^7*c^7*d^2 - 188*a^3*b^6*c^6*d^3 - 6*a^4*b^5*c^5*d^4 + 78*a^5*b^4*c^4*d^5 - 20*a^6*b^3*c^3*d^6 - 12*a^7*b^2*c^2*d^7 + 3*a^8*b*c*d^8 + a^9*d^9)*sqrt(x)) + 15*(a^3*b^2*x^5 + a^4*b*x^3)*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(1/4)*log(-27*a^10*b^5*(-(81*b^12*c^12 - 540*a*b^11*c^11*d + 1458*a^2*b^10*c^10*d^2 - 1932*a^3*b^9*c^9*d^3 + 1039*a^4*b^8*c^8*d^4 + 328*a^5*b^7*c^7*d^5 - 644*a^6*b^6*c^6*d^6 + 136*a^7*b^5*c^5*d^7 + 127*a^8*b^4*c^4*d^8 - 44*a^9*b^3*c^3*d^9 - 14*a^10*b^2*c^2*d^10 + 4*a^11*b*c*d^11 + a^12*d^12)/(a^13*b^7))^(3/4) + 27*(27*b^9*c^9 - 135*a*b^8*c^8*d + 252*a^2*b^7*c^7*d^2 - 188*a^3*b^6*c^6*d^3 - 6*a^4*b^5*c^5*d^4 + 78*a^5*b^4*c^4*d^5 - 20*a^6*b^3*c^3*d^6 - 12*a^7*b^2*c^2*d^7 + 3*a^8*b*c*d^8 + a^9*d^9)*sqrt(x)) + 4*(4*a^2*b*c^3 - 5*(9*b^3*c^3 - 15*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^4 - 12*(3*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)*sqrt(x))/(a^3*b^2*x^5 + a^4*b*x^3)","B",0
460,1,1955,0,0.940163," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{84 \, {\left(a^{3} b^{2} x^{6} + a^{4} b x^{4}\right)} \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{a^{8} b^{2} \sqrt{-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}} + {\left(121 \, b^{6} c^{6} - 462 \, a b^{5} c^{5} d + 639 \, a^{2} b^{4} c^{4} d^{2} - 356 \, a^{3} b^{3} c^{3} d^{3} + 39 \, a^{4} b^{2} c^{2} d^{4} + 18 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} x} a^{11} b^{4} \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{3}{4}} - {\left(11 \, a^{11} b^{7} c^{3} - 21 \, a^{12} b^{6} c^{2} d + 9 \, a^{13} b^{5} c d^{2} + a^{14} b^{4} d^{3}\right)} \sqrt{x} \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{3}{4}}}{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}\right) + 21 \, {\left(a^{3} b^{2} x^{6} + a^{4} b x^{4}\right)} \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \log\left(a^{4} b \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{1}{4}} + {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{x}\right) - 21 \, {\left(a^{3} b^{2} x^{6} + a^{4} b x^{4}\right)} \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{1}{4}} \log\left(-a^{4} b \left(-\frac{14641 \, b^{12} c^{12} - 111804 \, a b^{11} c^{11} d + 368082 \, a^{2} b^{10} c^{10} d^{2} - 676588 \, a^{3} b^{9} c^{9} d^{3} + 746703 \, a^{4} b^{8} c^{8} d^{4} - 486648 \, a^{5} b^{7} c^{7} d^{5} + 160188 \, a^{6} b^{6} c^{6} d^{6} - 5688 \, a^{7} b^{5} c^{5} d^{7} - 10017 \, a^{8} b^{4} c^{4} d^{8} + 692 \, a^{9} b^{3} c^{3} d^{9} + 402 \, a^{10} b^{2} c^{2} d^{10} + 36 \, a^{11} b c d^{11} + a^{12} d^{12}}{a^{15} b^{5}}\right)^{\frac{1}{4}} + {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, {\left(12 \, a^{2} b c^{3} - 7 \, {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3}\right)} x^{4} - 4 \, {\left(11 \, a b^{2} c^{3} - 21 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{x}}{168 \, {\left(a^{3} b^{2} x^{6} + a^{4} b x^{4}\right)}}"," ",0,"1/168*(84*(a^3*b^2*x^6 + a^4*b*x^4)*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(1/4)*arctan((sqrt(a^8*b^2*sqrt(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5)) + (121*b^6*c^6 - 462*a*b^5*c^5*d + 639*a^2*b^4*c^4*d^2 - 356*a^3*b^3*c^3*d^3 + 39*a^4*b^2*c^2*d^4 + 18*a^5*b*c*d^5 + a^6*d^6)*x)*a^11*b^4*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(3/4) - (11*a^11*b^7*c^3 - 21*a^12*b^6*c^2*d + 9*a^13*b^5*c*d^2 + a^14*b^4*d^3)*sqrt(x)*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(3/4))/(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)) + 21*(a^3*b^2*x^6 + a^4*b*x^4)*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(1/4)*log(a^4*b*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(1/4) + (11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(x)) - 21*(a^3*b^2*x^6 + a^4*b*x^4)*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(1/4)*log(-a^4*b*(-(14641*b^12*c^12 - 111804*a*b^11*c^11*d + 368082*a^2*b^10*c^10*d^2 - 676588*a^3*b^9*c^9*d^3 + 746703*a^4*b^8*c^8*d^4 - 486648*a^5*b^7*c^7*d^5 + 160188*a^6*b^6*c^6*d^6 - 5688*a^7*b^5*c^5*d^7 - 10017*a^8*b^4*c^4*d^8 + 692*a^9*b^3*c^3*d^9 + 402*a^10*b^2*c^2*d^10 + 36*a^11*b*c*d^11 + a^12*d^12)/(a^15*b^5))^(1/4) + (11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(x)) - 4*(12*a^2*b*c^3 - 7*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 3*a^3*d^3)*x^4 - 4*(11*a*b^2*c^3 - 21*a^2*b*c^2*d)*x^2)*sqrt(x))/(a^3*b^2*x^6 + a^4*b*x^4)","B",0
461,1,1422,0,7.232484," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{12 \, \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{1}{4}} b d \arctan\left(-\frac{\sqrt{a^{10} x - {\left(a^{7} b^{5} c^{2} - 2 \, a^{8} b^{4} c d + a^{9} b^{3} d^{2}\right)} \sqrt{-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}}} \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{1}{4}} {\left(b^{3} c - a b^{2} d\right)} - {\left(a^{5} b^{3} c - a^{6} b^{2} d\right)} \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{a^{7}}\right) - 12 \, \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{1}{4}} b d \arctan\left(-\frac{\sqrt{c^{10} x - {\left(b^{2} c^{9} d^{3} - 2 \, a b c^{8} d^{4} + a^{2} c^{7} d^{5}\right)} \sqrt{-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}}} \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{1}{4}} {\left(b c d^{2} - a d^{3}\right)} - {\left(b c^{6} d^{2} - a c^{5} d^{3}\right)} \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{1}{4}} \sqrt{x}}{c^{7}}\right) + 3 \, \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a^{5} \sqrt{x} + {\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{3}{4}}\right) - 3 \, \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a^{5} \sqrt{x} - {\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} \left(-\frac{a^{7}}{b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}}\right)^{\frac{3}{4}}\right) - 3 \, \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{1}{4}} b d \log\left(c^{5} \sqrt{x} + {\left(b^{3} c^{3} d^{5} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}\right)} \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{3}{4}}\right) + 3 \, \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{1}{4}} b d \log\left(c^{5} \sqrt{x} - {\left(b^{3} c^{3} d^{5} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}\right)} \left(-\frac{c^{7}}{b^{4} c^{4} d^{7} - 4 \, a b^{3} c^{3} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}}\right)^{\frac{3}{4}}\right) + 4 \, x^{\frac{3}{2}}}{6 \, b d}"," ",0,"1/6*(12*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(1/4)*b*d*arctan(-(sqrt(a^10*x - (a^7*b^5*c^2 - 2*a^8*b^4*c*d + a^9*b^3*d^2)*sqrt(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)))*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(1/4)*(b^3*c - a*b^2*d) - (a^5*b^3*c - a^6*b^2*d)*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(1/4)*sqrt(x))/a^7) - 12*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(1/4)*b*d*arctan(-(sqrt(c^10*x - (b^2*c^9*d^3 - 2*a*b*c^8*d^4 + a^2*c^7*d^5)*sqrt(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11)))*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(1/4)*(b*c*d^2 - a*d^3) - (b*c^6*d^2 - a*c^5*d^3)*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(1/4)*sqrt(x))/c^7) + 3*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(1/4)*b*d*log(a^5*sqrt(x) + (b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(3/4)) - 3*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(1/4)*b*d*log(a^5*sqrt(x) - (b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*(-a^7/(b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4))^(3/4)) - 3*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(1/4)*b*d*log(c^5*sqrt(x) + (b^3*c^3*d^5 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8)*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(3/4)) + 3*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(1/4)*b*d*log(c^5*sqrt(x) - (b^3*c^3*d^5 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8)*(-c^7/(b^4*c^4*d^7 - 4*a*b^3*c^3*d^8 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11))^(3/4)) + 4*x^(3/2))/(b*d)","B",0
462,1,1388,0,2.120831," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{4 \, \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \arctan\left(-\frac{{\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{3}{4}} \sqrt{a^{2} x + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \sqrt{-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}}} - {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{3}{4}} \sqrt{x}}{a^{5}}\right) - 4 \, \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \arctan\left(-\frac{{\left(b^{3} c^{3} d^{4} - 3 \, a b^{2} c^{2} d^{5} + 3 \, a^{2} b c d^{6} - a^{3} d^{7}\right)} \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{3}{4}} \sqrt{c^{2} x + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \sqrt{-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}}} - {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{3}{4}} \sqrt{x}}{c^{5}}\right) - \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a \sqrt{x} + \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b^{2} c - a b d\right)}\right) + \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a \sqrt{x} - \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b^{2} c - a b d\right)}\right) + \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \log\left(c \sqrt{x} + \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} {\left(b c d - a d^{2}\right)}\right) - \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \log\left(c \sqrt{x} - \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} {\left(b c d - a d^{2}\right)}\right) - 4 \, \sqrt{x}}{2 \, b d}"," ",0,"-1/2*(4*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*arctan(-((b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(3/4)*sqrt(a^2*x + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*sqrt(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))) - (a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(3/4)*sqrt(x))/a^5) - 4*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*arctan(-((b^3*c^3*d^4 - 3*a*b^2*c^2*d^5 + 3*a^2*b*c*d^6 - a^3*d^7)*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(3/4)*sqrt(c^2*x + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*sqrt(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))) - (b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(3/4)*sqrt(x))/c^5) - (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*log(a*sqrt(x) + (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*(b^2*c - a*b*d)) + (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*log(a*sqrt(x) - (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*(b^2*c - a*b*d)) + (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*log(c*sqrt(x) + (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*(b*c*d - a*d^2)) - (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*log(c*sqrt(x) - (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*(b*c*d - a*d^2)) - 4*sqrt(x))/(b*d)","B",0
463,1,1385,0,1.663795," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-2 \, \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{a^{4} x - {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} \sqrt{-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}}} {\left(b^{2} c - a b d\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} - {\left(a^{2} b^{2} c - a^{3} b d\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{a^{3}}\right) + 2 \, \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{c^{4} x - {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} \sqrt{-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}}} {\left(b c d - a d^{2}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} - {\left(b c^{3} d - a c^{2} d^{2}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \sqrt{x}}{c^{3}}\right) - \frac{1}{2} \, \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(a^{2} \sqrt{x} + {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{3}{4}}\right) + \frac{1}{2} \, \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(a^{2} \sqrt{x} - {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{3}{4}}\right) + \frac{1}{2} \, \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{2} \sqrt{x} + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{3}{4}}\right) - \frac{1}{2} \, \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{2} \sqrt{x} - {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{3}{4}}\right)"," ",0,"-2*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*arctan(-(sqrt(a^4*x - (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*sqrt(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)))*(b^2*c - a*b*d)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4) - (a^2*b^2*c - a^3*b*d)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*sqrt(x))/a^3) + 2*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*arctan(-(sqrt(c^4*x - (b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*sqrt(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7)))*(b*c*d - a*d^2)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4) - (b*c^3*d - a*c^2*d^2)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*sqrt(x))/c^3) - 1/2*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*log(a^2*sqrt(x) + (b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(3/4)) + 1/2*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*log(a^2*sqrt(x) - (b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(3/4)) + 1/2*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*log(c^2*sqrt(x) + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(3/4)) - 1/2*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*log(c^2*sqrt(x) - (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(3/4))","B",0
464,1,1249,0,1.151543," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","2 \, \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} \sqrt{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}} + x} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{3}{4}} - {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} \sqrt{x} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{3}{4}}}{a}\right) - 2 \, \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}} + x} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{3}{4}} - {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{x} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{3}{4}}}{c}\right) - \frac{1}{2} \, \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \log\left({\left(b c - a d\right)} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} + \sqrt{x}\right) + \frac{1}{2} \, \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - a d\right)} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} + \sqrt{x}\right) + \frac{1}{2} \, \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \log\left({\left(b c - a d\right)} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right) - \frac{1}{2} \, \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - a d\right)} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} + \sqrt{x}\right)"," ",0,"2*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*arctan(-((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*sqrt((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)) + x)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(3/4) - (b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*sqrt(x)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(3/4))/a) - 2*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*arctan(-((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*sqrt((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)) + x)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(3/4) - (b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*sqrt(x)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(3/4))/c) - 1/2*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*log((b*c - a*d)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4) + sqrt(x)) + 1/2*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*log(-(b*c - a*d)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4) + sqrt(x)) + 1/2*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*log((b*c - a*d)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4) + sqrt(x)) - 1/2*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*log(-(b*c - a*d)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4) + sqrt(x))","B",0
465,1,1285,0,1.155806," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","2 \, \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{b^{2} x - {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} \sqrt{-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}}} {\left(b c - a d\right)} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} - {\left(b^{2} c - a b d\right)} \sqrt{x} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}}}{b}\right) - 2 \, \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{d^{2} x - {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} \sqrt{-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}}} {\left(b c - a d\right)} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} - {\left(b c d - a d^{2}\right)} \sqrt{x} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}}}{d}\right) + \frac{1}{2} \, \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \log\left({\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{3}{4}} + b \sqrt{x}\right) - \frac{1}{2} \, \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \log\left(-{\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{3}{4}} + b \sqrt{x}\right) - \frac{1}{2} \, \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \log\left({\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{3}{4}} + d \sqrt{x}\right) + \frac{1}{2} \, \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{3}{4}} + d \sqrt{x}\right)"," ",0,"2*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*arctan(-(sqrt(b^2*x - (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*sqrt(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4)))*(b*c - a*d)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4) - (b^2*c - a*b*d)*sqrt(x)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4))/b) - 2*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*arctan(-(sqrt(d^2*x - (b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*sqrt(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4)))*(b*c - a*d)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4) - (b*c*d - a*d^2)*sqrt(x)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4))/d) + 1/2*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*log((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(3/4) + b*sqrt(x)) - 1/2*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*log(-(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(3/4) + b*sqrt(x)) - 1/2*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*log((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(3/4) + d*sqrt(x)) + 1/2*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*log(-(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(3/4) + d*sqrt(x))","B",0
466,1,1365,0,1.798742," ","integrate(1/(b*x^2+a)/(d*x^2+c)/x^(1/2),x, algorithm=""fricas"")","-2 \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \sqrt{b^{2} x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}}} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} - {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{x}}{b^{3}}\right) + 2 \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \sqrt{d^{2} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}}} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} - {\left(b^{3} c^{5} d - 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{3} d^{3} - a^{3} c^{2} d^{4}\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} \sqrt{x}}{d^{3}}\right) + \frac{1}{2} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b \sqrt{x} + {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{2} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b \sqrt{x} - {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{2} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d \sqrt{x} + {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right) + \frac{1}{2} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d \sqrt{x} - {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right)"," ",0,"-2*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*arctan(-((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*sqrt(b^2*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)))*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4) - (a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4)*sqrt(x))/b^3) + 2*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*arctan(-((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*sqrt(d^2*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4)))*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4) - (b^3*c^5*d - 3*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 - a^3*c^2*d^4)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4)*sqrt(x))/d^3) + 1/2*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*sqrt(x) + (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/2*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*sqrt(x) - (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/2*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*sqrt(x) + (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)) + 1/2*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*sqrt(x) - (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4))","B",0
467,1,1421,0,2.487748," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","-\frac{4 \, \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \arctan\left(-\frac{\sqrt{b^{8} x - {\left(a^{3} b^{7} c^{2} - 2 \, a^{4} b^{6} c d + a^{5} b^{5} d^{2}\right)} \sqrt{-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}}} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} {\left(a b c - a^{2} d\right)} - {\left(a b^{5} c - a^{2} b^{4} d\right)} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{b^{5}}\right) - 4 \, \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \arctan\left(-\frac{\sqrt{d^{8} x - {\left(b^{2} c^{5} d^{5} - 2 \, a b c^{4} d^{6} + a^{2} c^{3} d^{7}\right)} \sqrt{-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}}} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d\right)} - {\left(b c^{2} d^{4} - a c d^{5}\right)} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{d^{5}}\right) + \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(b^{4} \sqrt{x} + {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3}\right)} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{3}{4}}\right) - \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(b^{4} \sqrt{x} - {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3}\right)} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{3}{4}}\right) - \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(d^{4} \sqrt{x} + {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3}\right)} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{3}{4}}\right) + \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(d^{4} \sqrt{x} - {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3}\right)} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{3}{4}}\right) + 4 \, \sqrt{x}}{2 \, a c x}"," ",0,"-1/2*(4*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*arctan(-(sqrt(b^8*x - (a^3*b^7*c^2 - 2*a^4*b^6*c*d + a^5*b^5*d^2)*sqrt(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4)))*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*(a*b*c - a^2*d) - (a*b^5*c - a^2*b^4*d)*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*sqrt(x))/b^5) - 4*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*arctan(-(sqrt(d^8*x - (b^2*c^5*d^5 - 2*a*b*c^4*d^6 + a^2*c^3*d^7)*sqrt(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4)))*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*(b*c^2 - a*c*d) - (b*c^2*d^4 - a*c*d^5)*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*sqrt(x))/d^5) + (-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*log(b^4*sqrt(x) + (a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3)*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(3/4)) - (-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*log(b^4*sqrt(x) - (a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3)*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(3/4)) - (-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*log(d^4*sqrt(x) + (b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3)*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(3/4)) + (-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*log(d^4*sqrt(x) - (b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3)*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(3/4)) + 4*sqrt(x))/(a*c*x)","B",0
468,1,1431,0,15.950029," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{12 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \arctan\left(-\frac{{\left(a^{5} b^{3} c^{3} - 3 \, a^{6} b^{2} c^{2} d + 3 \, a^{7} b c d^{2} - a^{8} d^{3}\right)} \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{3}{4}} \sqrt{b^{4} x + {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2}\right)} \sqrt{-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}}} - {\left(a^{5} b^{5} c^{3} - 3 \, a^{6} b^{4} c^{2} d + 3 \, a^{7} b^{3} c d^{2} - a^{8} b^{2} d^{3}\right)} \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{3}{4}} \sqrt{x}}{b^{7}}\right) - 12 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \arctan\left(-\frac{{\left(b^{3} c^{8} - 3 \, a b^{2} c^{7} d + 3 \, a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3}\right)} \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{d^{4} x + {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)} \sqrt{-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}}} - {\left(b^{3} c^{8} d^{2} - 3 \, a b^{2} c^{7} d^{3} + 3 \, a^{2} b c^{6} d^{4} - a^{3} c^{5} d^{5}\right)} \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{x}}{d^{7}}\right) - 3 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \log\left(b^{2} \sqrt{x} + \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)}\right) + 3 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \log\left(b^{2} \sqrt{x} - \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)}\right) + 3 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \log\left(d^{2} \sqrt{x} + \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)}\right) - 3 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{2} \log\left(d^{2} \sqrt{x} - \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)}\right) - 4 \, \sqrt{x}}{6 \, a c x^{2}}"," ",0,"1/6*(12*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^2*arctan(-((a^5*b^3*c^3 - 3*a^6*b^2*c^2*d + 3*a^7*b*c*d^2 - a^8*d^3)*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(3/4)*sqrt(b^4*x + (a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2)*sqrt(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))) - (a^5*b^5*c^3 - 3*a^6*b^4*c^2*d + 3*a^7*b^3*c*d^2 - a^8*b^2*d^3)*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(3/4)*sqrt(x))/b^7) - 12*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^2*arctan(-((b^3*c^8 - 3*a*b^2*c^7*d + 3*a^2*b*c^6*d^2 - a^3*c^5*d^3)*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(3/4)*sqrt(d^4*x + (b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2)*sqrt(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))) - (b^3*c^8*d^2 - 3*a*b^2*c^7*d^3 + 3*a^2*b*c^6*d^4 - a^3*c^5*d^5)*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(3/4)*sqrt(x))/d^7) - 3*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^2*log(b^2*sqrt(x) + (-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*(a^2*b*c - a^3*d)) + 3*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^2*log(b^2*sqrt(x) - (-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*(a^2*b*c - a^3*d)) + 3*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^2*log(d^2*sqrt(x) + (-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*(b*c^3 - a*c^2*d)) - 3*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^2*log(d^2*sqrt(x) - (-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*(b*c^3 - a*c^2*d)) - 4*sqrt(x))/(a*c*x^2)","B",0
469,1,1484,0,21.817255," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""fricas"")","\frac{20 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \arctan\left(-\frac{\sqrt{b^{14} x - {\left(a^{5} b^{11} c^{2} - 2 \, a^{6} b^{10} c d + a^{7} b^{9} d^{2}\right)} \sqrt{-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}}} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)} - {\left(a^{2} b^{8} c - a^{3} b^{7} d\right)} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{b^{9}}\right) - 20 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \arctan\left(-\frac{\sqrt{d^{14} x - {\left(b^{2} c^{7} d^{9} - 2 \, a b c^{6} d^{10} + a^{2} c^{5} d^{11}\right)} \sqrt{-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}}} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)} - {\left(b c^{3} d^{7} - a c^{2} d^{8}\right)} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} \sqrt{x}}{d^{9}}\right) + 5 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \log\left(b^{7} \sqrt{x} + {\left(a^{7} b^{3} c^{3} - 3 \, a^{8} b^{2} c^{2} d + 3 \, a^{9} b c d^{2} - a^{10} d^{3}\right)} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{3}{4}}\right) - 5 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \log\left(b^{7} \sqrt{x} - {\left(a^{7} b^{3} c^{3} - 3 \, a^{8} b^{2} c^{2} d + 3 \, a^{9} b c d^{2} - a^{10} d^{3}\right)} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{3}{4}}\right) - 5 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \log\left(d^{7} \sqrt{x} + {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3}\right)} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{3}{4}}\right) + 5 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{3} \log\left(d^{7} \sqrt{x} - {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3}\right)} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{3}{4}}\right) + 4 \, {\left(5 \, {\left(b c + a d\right)} x^{2} - a c\right)} \sqrt{x}}{10 \, a^{2} c^{2} x^{3}}"," ",0,"1/10*(20*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^3*arctan(-(sqrt(b^14*x - (a^5*b^11*c^2 - 2*a^6*b^10*c*d + a^7*b^9*d^2)*sqrt(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4)))*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*(a^2*b*c - a^3*d) - (a^2*b^8*c - a^3*b^7*d)*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*sqrt(x))/b^9) - 20*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^3*arctan(-(sqrt(d^14*x - (b^2*c^7*d^9 - 2*a*b*c^6*d^10 + a^2*c^5*d^11)*sqrt(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4)))*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*(b*c^3 - a*c^2*d) - (b*c^3*d^7 - a*c^2*d^8)*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*sqrt(x))/d^9) + 5*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^3*log(b^7*sqrt(x) + (a^7*b^3*c^3 - 3*a^8*b^2*c^2*d + 3*a^9*b*c*d^2 - a^10*d^3)*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(3/4)) - 5*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^3*log(b^7*sqrt(x) - (a^7*b^3*c^3 - 3*a^8*b^2*c^2*d + 3*a^9*b*c*d^2 - a^10*d^3)*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(3/4)) - 5*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^3*log(d^7*sqrt(x) + (b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3)*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(3/4)) + 5*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^3*log(d^7*sqrt(x) - (b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3)*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(3/4)) + 4*(5*(b*c + a*d)*x^2 - a*c)*sqrt(x))/(a^2*c^2*x^3)","B",0
470,1,3393,0,111.542144," ","integrate(x^(11/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{6} c^{6} d^{7} - 6 \, a b^{5} c^{5} d^{8} + 15 \, a^{2} b^{4} c^{4} d^{9} - 20 \, a^{3} b^{3} c^{3} d^{10} + 15 \, a^{4} b^{2} c^{2} d^{11} - 6 \, a^{5} b c d^{12} + a^{6} d^{13}\right)} \sqrt{{\left(25 \, b^{2} c^{4} - 90 \, a b c^{3} d + 81 \, a^{2} c^{2} d^{2}\right)} x + {\left(b^{4} c^{4} d^{4} - 4 \, a b^{3} c^{3} d^{5} + 6 \, a^{2} b^{2} c^{2} d^{6} - 4 \, a^{3} b c d^{7} + a^{4} d^{8}\right)} \sqrt{-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}}} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{3}{4}} + {\left(5 \, b^{7} c^{8} d^{7} - 39 \, a b^{6} c^{7} d^{8} + 129 \, a^{2} b^{5} c^{6} d^{9} - 235 \, a^{3} b^{4} c^{5} d^{10} + 255 \, a^{4} b^{3} c^{4} d^{11} - 165 \, a^{5} b^{2} c^{3} d^{12} + 59 \, a^{6} b c^{2} d^{13} - 9 \, a^{7} c d^{14}\right)} \sqrt{x} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{3}{4}}}{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}\right) - 16 \, \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \arctan\left(\frac{{\left(b^{10} c^{6} - 6 \, a b^{9} c^{5} d + 15 \, a^{2} b^{8} c^{4} d^{2} - 20 \, a^{3} b^{7} c^{3} d^{3} + 15 \, a^{4} b^{6} c^{2} d^{4} - 6 \, a^{5} b^{5} c d^{5} + a^{6} b^{4} d^{6}\right)} \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{3}{4}} \sqrt{a^{4} x + {\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} \sqrt{-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}}} - {\left(a^{2} b^{10} c^{6} - 6 \, a^{3} b^{9} c^{5} d + 15 \, a^{4} b^{8} c^{4} d^{2} - 20 \, a^{5} b^{7} c^{3} d^{3} + 15 \, a^{6} b^{6} c^{2} d^{4} - 6 \, a^{7} b^{5} c d^{5} + a^{8} b^{4} d^{6}\right)} \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{3}{4}} \sqrt{x}}{a^{9}}\right) - 4 \, \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \log\left(a^{2} \sqrt{x} + \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{1}{4}} {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)}\right) + 4 \, \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \log\left(a^{2} \sqrt{x} - \left(-\frac{a^{9}}{b^{13} c^{8} - 8 \, a b^{12} c^{7} d + 28 \, a^{2} b^{11} c^{6} d^{2} - 56 \, a^{3} b^{10} c^{5} d^{3} + 70 \, a^{4} b^{9} c^{4} d^{4} - 56 \, a^{5} b^{8} c^{3} d^{5} + 28 \, a^{6} b^{7} c^{2} d^{6} - 8 \, a^{7} b^{6} c d^{7} + a^{8} b^{5} d^{8}}\right)^{\frac{1}{4}} {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)}\right) + {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{1}{4}} \log\left(-{\left(5 \, b c^{2} - 9 \, a c d\right)} \sqrt{x} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{1}{4}}\right) - {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{1}{4}} \log\left(-{\left(5 \, b c^{2} - 9 \, a c d\right)} \sqrt{x} - {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \left(-\frac{625 \, b^{4} c^{9} - 4500 \, a b^{3} c^{8} d + 12150 \, a^{2} b^{2} c^{7} d^{2} - 14580 \, a^{3} b c^{6} d^{3} + 6561 \, a^{4} c^{5} d^{4}}{b^{8} c^{8} d^{9} - 8 \, a b^{7} c^{7} d^{10} + 28 \, a^{2} b^{6} c^{6} d^{11} - 56 \, a^{3} b^{5} c^{5} d^{12} + 70 \, a^{4} b^{4} c^{4} d^{13} - 56 \, a^{5} b^{3} c^{3} d^{14} + 28 \, a^{6} b^{2} c^{2} d^{15} - 8 \, a^{7} b c d^{16} + a^{8} d^{17}}\right)^{\frac{1}{4}}\right) + 4 \, {\left(5 \, b c^{2} - 4 \, a c d + 4 \, {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{x}}{8 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)}}"," ",0,"1/8*(4*(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(1/4)*arctan(((b^6*c^6*d^7 - 6*a*b^5*c^5*d^8 + 15*a^2*b^4*c^4*d^9 - 20*a^3*b^3*c^3*d^10 + 15*a^4*b^2*c^2*d^11 - 6*a^5*b*c*d^12 + a^6*d^13)*sqrt((25*b^2*c^4 - 90*a*b*c^3*d + 81*a^2*c^2*d^2)*x + (b^4*c^4*d^4 - 4*a*b^3*c^3*d^5 + 6*a^2*b^2*c^2*d^6 - 4*a^3*b*c*d^7 + a^4*d^8)*sqrt(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17)))*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(3/4) + (5*b^7*c^8*d^7 - 39*a*b^6*c^7*d^8 + 129*a^2*b^5*c^6*d^9 - 235*a^3*b^4*c^5*d^10 + 255*a^4*b^3*c^4*d^11 - 165*a^5*b^2*c^3*d^12 + 59*a^6*b*c^2*d^13 - 9*a^7*c*d^14)*sqrt(x)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(3/4))/(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)) - 16*(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(1/4)*(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*arctan(((b^10*c^6 - 6*a*b^9*c^5*d + 15*a^2*b^8*c^4*d^2 - 20*a^3*b^7*c^3*d^3 + 15*a^4*b^6*c^2*d^4 - 6*a^5*b^5*c*d^5 + a^6*b^4*d^6)*(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(3/4)*sqrt(a^4*x + (b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*sqrt(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))) - (a^2*b^10*c^6 - 6*a^3*b^9*c^5*d + 15*a^4*b^8*c^4*d^2 - 20*a^5*b^7*c^3*d^3 + 15*a^6*b^6*c^2*d^4 - 6*a^7*b^5*c*d^5 + a^8*b^4*d^6)*(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(3/4)*sqrt(x))/a^9) - 4*(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(1/4)*(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*log(a^2*sqrt(x) + (-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(1/4)*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)) + 4*(-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(1/4)*(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*log(a^2*sqrt(x) - (-a^9/(b^13*c^8 - 8*a*b^12*c^7*d + 28*a^2*b^11*c^6*d^2 - 56*a^3*b^10*c^5*d^3 + 70*a^4*b^9*c^4*d^4 - 56*a^5*b^8*c^3*d^5 + 28*a^6*b^7*c^2*d^6 - 8*a^7*b^6*c*d^7 + a^8*b^5*d^8))^(1/4)*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)) + (b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(1/4)*log(-(5*b*c^2 - 9*a*c*d)*sqrt(x) + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(1/4)) - (b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(1/4)*log(-(5*b*c^2 - 9*a*c*d)*sqrt(x) - (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(-(625*b^4*c^9 - 4500*a*b^3*c^8*d + 12150*a^2*b^2*c^7*d^2 - 14580*a^3*b*c^6*d^3 + 6561*a^4*c^5*d^4)/(b^8*c^8*d^9 - 8*a*b^7*c^7*d^10 + 28*a^2*b^6*c^6*d^11 - 56*a^3*b^5*c^5*d^12 + 70*a^4*b^4*c^4*d^13 - 56*a^5*b^3*c^3*d^14 + 28*a^6*b^2*c^2*d^15 - 8*a^7*b*c*d^16 + a^8*d^17))^(1/4)) + 4*(5*b*c^2 - 4*a*c*d + 4*(b*c*d - a*d^2)*x^2)*sqrt(x))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)","B",0
471,1,3524,0,86.411182," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, c x^{\frac{3}{2}} - 4 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \sqrt{{\left(729 \, b^{6} c^{10} - 10206 \, a b^{5} c^{9} d + 59535 \, a^{2} b^{4} c^{8} d^{2} - 185220 \, a^{3} b^{3} c^{7} d^{3} + 324135 \, a^{4} b^{2} c^{6} d^{4} - 302526 \, a^{5} b c^{5} d^{5} + 117649 \, a^{6} c^{4} d^{6}\right)} x - {\left(81 \, b^{8} c^{11} d^{3} - 1080 \, a b^{7} c^{10} d^{4} + 6156 \, a^{2} b^{6} c^{9} d^{5} - 19560 \, a^{3} b^{5} c^{8} d^{6} + 37846 \, a^{4} b^{4} c^{7} d^{7} - 45640 \, a^{5} b^{3} c^{6} d^{8} + 33516 \, a^{6} b^{2} c^{5} d^{9} - 13720 \, a^{7} b c^{4} d^{10} + 2401 \, a^{8} c^{3} d^{11}\right)} \sqrt{-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}}} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{1}{4}} + {\left(27 \, b^{5} c^{7} d^{2} - 243 \, a b^{4} c^{6} d^{3} + 846 \, a^{2} b^{3} c^{5} d^{4} - 1414 \, a^{3} b^{2} c^{4} d^{5} + 1127 \, a^{4} b c^{3} d^{6} - 343 \, a^{5} c^{2} d^{7}\right)} \sqrt{x} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{1}{4}}}{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}\right) + 16 \, \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a^{10} x - {\left(a^{7} b^{5} c^{4} - 4 \, a^{8} b^{4} c^{3} d + 6 \, a^{9} b^{3} c^{2} d^{2} - 4 \, a^{10} b^{2} c d^{3} + a^{11} b d^{4}\right)} \sqrt{-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}}} \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} - {\left(a^{5} b^{3} c^{2} - 2 \, a^{6} b^{2} c d + a^{7} b d^{2}\right)} \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{1}{4}} \sqrt{x}}{a^{7}}\right) - 4 \, \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \log\left(a^{5} \sqrt{x} + {\left(b^{8} c^{6} - 6 \, a b^{7} c^{5} d + 15 \, a^{2} b^{6} c^{4} d^{2} - 20 \, a^{3} b^{5} c^{3} d^{3} + 15 \, a^{4} b^{4} c^{2} d^{4} - 6 \, a^{5} b^{3} c d^{5} + a^{6} b^{2} d^{6}\right)} \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{3}{4}}\right) + 4 \, \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \log\left(a^{5} \sqrt{x} - {\left(b^{8} c^{6} - 6 \, a b^{7} c^{5} d + 15 \, a^{2} b^{6} c^{4} d^{2} - 20 \, a^{3} b^{5} c^{3} d^{3} + 15 \, a^{4} b^{4} c^{2} d^{4} - 6 \, a^{5} b^{3} c d^{5} + a^{6} b^{2} d^{6}\right)} \left(-\frac{a^{7}}{b^{11} c^{8} - 8 \, a b^{10} c^{7} d + 28 \, a^{2} b^{9} c^{6} d^{2} - 56 \, a^{3} b^{8} c^{5} d^{3} + 70 \, a^{4} b^{7} c^{4} d^{4} - 56 \, a^{5} b^{6} c^{3} d^{5} + 28 \, a^{6} b^{5} c^{2} d^{6} - 8 \, a^{7} b^{4} c d^{7} + a^{8} b^{3} d^{8}}\right)^{\frac{3}{4}}\right) + {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{1}{4}} \log\left({\left(b^{6} c^{6} d^{5} - 6 \, a b^{5} c^{5} d^{6} + 15 \, a^{2} b^{4} c^{4} d^{7} - 20 \, a^{3} b^{3} c^{3} d^{8} + 15 \, a^{4} b^{2} c^{2} d^{9} - 6 \, a^{5} b c d^{10} + a^{6} d^{11}\right)} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{3}{4}} - {\left(27 \, b^{3} c^{5} - 189 \, a b^{2} c^{4} d + 441 \, a^{2} b c^{3} d^{2} - 343 \, a^{3} c^{2} d^{3}\right)} \sqrt{x}\right) - {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{6} c^{6} d^{5} - 6 \, a b^{5} c^{5} d^{6} + 15 \, a^{2} b^{4} c^{4} d^{7} - 20 \, a^{3} b^{3} c^{3} d^{8} + 15 \, a^{4} b^{2} c^{2} d^{9} - 6 \, a^{5} b c d^{10} + a^{6} d^{11}\right)} \left(-\frac{81 \, b^{4} c^{7} - 756 \, a b^{3} c^{6} d + 2646 \, a^{2} b^{2} c^{5} d^{2} - 4116 \, a^{3} b c^{4} d^{3} + 2401 \, a^{4} c^{3} d^{4}}{b^{8} c^{8} d^{7} - 8 \, a b^{7} c^{7} d^{8} + 28 \, a^{2} b^{6} c^{6} d^{9} - 56 \, a^{3} b^{5} c^{5} d^{10} + 70 \, a^{4} b^{4} c^{4} d^{11} - 56 \, a^{5} b^{3} c^{3} d^{12} + 28 \, a^{6} b^{2} c^{2} d^{13} - 8 \, a^{7} b c d^{14} + a^{8} d^{15}}\right)^{\frac{3}{4}} - {\left(27 \, b^{3} c^{5} - 189 \, a b^{2} c^{4} d + 441 \, a^{2} b c^{3} d^{2} - 343 \, a^{3} c^{2} d^{3}\right)} \sqrt{x}\right)}{8 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}}"," ",0,"-1/8*(4*c*x^(3/2) - 4*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(1/4)*arctan(((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*sqrt((729*b^6*c^10 - 10206*a*b^5*c^9*d + 59535*a^2*b^4*c^8*d^2 - 185220*a^3*b^3*c^7*d^3 + 324135*a^4*b^2*c^6*d^4 - 302526*a^5*b*c^5*d^5 + 117649*a^6*c^4*d^6)*x - (81*b^8*c^11*d^3 - 1080*a*b^7*c^10*d^4 + 6156*a^2*b^6*c^9*d^5 - 19560*a^3*b^5*c^8*d^6 + 37846*a^4*b^4*c^7*d^7 - 45640*a^5*b^3*c^6*d^8 + 33516*a^6*b^2*c^5*d^9 - 13720*a^7*b*c^4*d^10 + 2401*a^8*c^3*d^11)*sqrt(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15)))*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(1/4) + (27*b^5*c^7*d^2 - 243*a*b^4*c^6*d^3 + 846*a^2*b^3*c^5*d^4 - 1414*a^3*b^2*c^4*d^5 + 1127*a^4*b*c^3*d^6 - 343*a^5*c^2*d^7)*sqrt(x)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(1/4))/(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)) + 16*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*arctan((sqrt(a^10*x - (a^7*b^5*c^4 - 4*a^8*b^4*c^3*d + 6*a^9*b^3*c^2*d^2 - 4*a^10*b^2*c*d^3 + a^11*b*d^4)*sqrt(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8)))*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(1/4)*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - (a^5*b^3*c^2 - 2*a^6*b^2*c*d + a^7*b*d^2)*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(1/4)*sqrt(x))/a^7) - 4*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*log(a^5*sqrt(x) + (b^8*c^6 - 6*a*b^7*c^5*d + 15*a^2*b^6*c^4*d^2 - 20*a^3*b^5*c^3*d^3 + 15*a^4*b^4*c^2*d^4 - 6*a^5*b^3*c*d^5 + a^6*b^2*d^6)*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(3/4)) + 4*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*log(a^5*sqrt(x) - (b^8*c^6 - 6*a*b^7*c^5*d + 15*a^2*b^6*c^4*d^2 - 20*a^3*b^5*c^3*d^3 + 15*a^4*b^4*c^2*d^4 - 6*a^5*b^3*c*d^5 + a^6*b^2*d^6)*(-a^7/(b^11*c^8 - 8*a*b^10*c^7*d + 28*a^2*b^9*c^6*d^2 - 56*a^3*b^8*c^5*d^3 + 70*a^4*b^7*c^4*d^4 - 56*a^5*b^6*c^3*d^5 + 28*a^6*b^5*c^2*d^6 - 8*a^7*b^4*c*d^7 + a^8*b^3*d^8))^(3/4)) + (b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(1/4)*log((b^6*c^6*d^5 - 6*a*b^5*c^5*d^6 + 15*a^2*b^4*c^4*d^7 - 20*a^3*b^3*c^3*d^8 + 15*a^4*b^2*c^2*d^9 - 6*a^5*b*c*d^10 + a^6*d^11)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(3/4) - (27*b^3*c^5 - 189*a*b^2*c^4*d + 441*a^2*b*c^3*d^2 - 343*a^3*c^2*d^3)*sqrt(x)) - (b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(1/4)*log(-(b^6*c^6*d^5 - 6*a*b^5*c^5*d^6 + 15*a^2*b^4*c^4*d^7 - 20*a^3*b^3*c^3*d^8 + 15*a^4*b^2*c^2*d^9 - 6*a^5*b*c*d^10 + a^6*d^11)*(-(81*b^4*c^7 - 756*a*b^3*c^6*d + 2646*a^2*b^2*c^5*d^2 - 4116*a^3*b*c^4*d^3 + 2401*a^4*c^3*d^4)/(b^8*c^8*d^7 - 8*a*b^7*c^7*d^8 + 28*a^2*b^6*c^6*d^9 - 56*a^3*b^5*c^5*d^10 + 70*a^4*b^4*c^4*d^11 - 56*a^5*b^3*c^3*d^12 + 28*a^6*b^2*c^2*d^13 - 8*a^7*b*c*d^14 + a^8*d^15))^(3/4) - (27*b^3*c^5 - 189*a*b^2*c^4*d + 441*a^2*b*c^3*d^2 - 343*a^3*c^2*d^3)*sqrt(x)))/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)","B",0
472,1,3224,0,17.799894," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{6} c^{6} d^{4} - 6 \, a b^{5} c^{5} d^{5} + 15 \, a^{2} b^{4} c^{4} d^{6} - 20 \, a^{3} b^{3} c^{3} d^{7} + 15 \, a^{4} b^{2} c^{2} d^{8} - 6 \, a^{5} b c d^{9} + a^{6} d^{10}\right)} \sqrt{{\left(b^{2} c^{2} - 10 \, a b c d + 25 \, a^{2} d^{2}\right)} x + {\left(b^{4} c^{4} d^{2} - 4 \, a b^{3} c^{3} d^{3} + 6 \, a^{2} b^{2} c^{2} d^{4} - 4 \, a^{3} b c d^{5} + a^{4} d^{6}\right)} \sqrt{-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}}} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{3}{4}} + {\left(b^{7} c^{7} d^{4} - 11 \, a b^{6} c^{6} d^{5} + 45 \, a^{2} b^{5} c^{5} d^{6} - 95 \, a^{3} b^{4} c^{4} d^{7} + 115 \, a^{4} b^{3} c^{3} d^{8} - 81 \, a^{5} b^{2} c^{2} d^{9} + 31 \, a^{6} b c d^{10} - 5 \, a^{7} d^{11}\right)} \sqrt{x} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{3}{4}}}{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}\right) - 16 \, \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \arctan\left(\frac{{\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{3}{4}} \sqrt{a^{2} x + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}}} - {\left(a b^{7} c^{6} - 6 \, a^{2} b^{6} c^{5} d + 15 \, a^{3} b^{5} c^{4} d^{2} - 20 \, a^{4} b^{4} c^{3} d^{3} + 15 \, a^{5} b^{3} c^{2} d^{4} - 6 \, a^{6} b^{2} c d^{5} + a^{7} b d^{6}\right)} \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{3}{4}} \sqrt{x}}{a^{5}}\right) + {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - 5 \, a d\right)} \sqrt{x} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{1}{4}}\right) - {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - 5 \, a d\right)} \sqrt{x} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \left(-\frac{b^{4} c^{5} - 20 \, a b^{3} c^{4} d + 150 \, a^{2} b^{2} c^{3} d^{2} - 500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{8} c^{8} d^{5} - 8 \, a b^{7} c^{7} d^{6} + 28 \, a^{2} b^{6} c^{6} d^{7} - 56 \, a^{3} b^{5} c^{5} d^{8} + 70 \, a^{4} b^{4} c^{4} d^{9} - 56 \, a^{5} b^{3} c^{3} d^{10} + 28 \, a^{6} b^{2} c^{2} d^{11} - 8 \, a^{7} b c d^{12} + a^{8} d^{13}}\right)^{\frac{1}{4}}\right) - 4 \, \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \log\left(a \sqrt{x} + \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}\right) + 4 \, \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)} \log\left(a \sqrt{x} - \left(-\frac{a^{5}}{b^{9} c^{8} - 8 \, a b^{8} c^{7} d + 28 \, a^{2} b^{7} c^{6} d^{2} - 56 \, a^{3} b^{6} c^{5} d^{3} + 70 \, a^{4} b^{5} c^{4} d^{4} - 56 \, a^{5} b^{4} c^{3} d^{5} + 28 \, a^{6} b^{3} c^{2} d^{6} - 8 \, a^{7} b^{2} c d^{7} + a^{8} b d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}\right) + 4 \, c \sqrt{x}}{8 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}}"," ",0,"-1/8*(4*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(1/4)*arctan(((b^6*c^6*d^4 - 6*a*b^5*c^5*d^5 + 15*a^2*b^4*c^4*d^6 - 20*a^3*b^3*c^3*d^7 + 15*a^4*b^2*c^2*d^8 - 6*a^5*b*c*d^9 + a^6*d^10)*sqrt((b^2*c^2 - 10*a*b*c*d + 25*a^2*d^2)*x + (b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4 - 4*a^3*b*c*d^5 + a^4*d^6)*sqrt(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13)))*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(3/4) + (b^7*c^7*d^4 - 11*a*b^6*c^6*d^5 + 45*a^2*b^5*c^5*d^6 - 95*a^3*b^4*c^4*d^7 + 115*a^4*b^3*c^3*d^8 - 81*a^5*b^2*c^2*d^9 + 31*a^6*b*c*d^10 - 5*a^7*d^11)*sqrt(x)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(3/4))/(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)) - 16*(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*arctan(((b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(3/4)*sqrt(a^2*x + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))) - (a*b^7*c^6 - 6*a^2*b^6*c^5*d + 15*a^3*b^5*c^4*d^2 - 20*a^4*b^4*c^3*d^3 + 15*a^5*b^3*c^2*d^4 - 6*a^6*b^2*c*d^5 + a^7*b*d^6)*(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(3/4)*sqrt(x))/a^5) + (b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(1/4)*log(-(b*c - 5*a*d)*sqrt(x) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(1/4)) - (b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(1/4)*log(-(b*c - 5*a*d)*sqrt(x) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(-(b^4*c^5 - 20*a*b^3*c^4*d + 150*a^2*b^2*c^3*d^2 - 500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^8*c^8*d^5 - 8*a*b^7*c^7*d^6 + 28*a^2*b^6*c^6*d^7 - 56*a^3*b^5*c^5*d^8 + 70*a^4*b^4*c^4*d^9 - 56*a^5*b^3*c^3*d^10 + 28*a^6*b^2*c^2*d^11 - 8*a^7*b*c*d^12 + a^8*d^13))^(1/4)) - 4*(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*log(a*sqrt(x) + (-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(1/4)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) + 4*(-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(1/4)*(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)*log(a*sqrt(x) - (-a^5/(b^9*c^8 - 8*a*b^8*c^7*d + 28*a^2*b^7*c^6*d^2 - 56*a^3*b^6*c^5*d^3 + 70*a^4*b^5*c^4*d^4 - 56*a^5*b^4*c^3*d^5 + 28*a^6*b^3*c^2*d^6 - 8*a^7*b^2*c*d^7 + a^8*b*d^8))^(1/4)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) + 4*c*sqrt(x))/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)","B",0
473,1,3393,0,32.468444," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{{\left(b^{6} c^{6} + 18 \, a b^{5} c^{5} d + 135 \, a^{2} b^{4} c^{4} d^{2} + 540 \, a^{3} b^{3} c^{3} d^{3} + 1215 \, a^{4} b^{2} c^{2} d^{4} + 1458 \, a^{5} b c d^{5} + 729 \, a^{6} d^{6}\right)} x - {\left(b^{8} c^{9} d + 8 \, a b^{7} c^{8} d^{2} + 12 \, a^{2} b^{6} c^{7} d^{3} - 40 \, a^{3} b^{5} c^{6} d^{4} - 74 \, a^{4} b^{4} c^{5} d^{5} + 120 \, a^{5} b^{3} c^{4} d^{6} + 108 \, a^{6} b^{2} c^{3} d^{7} - 216 \, a^{7} b c^{2} d^{8} + 81 \, a^{8} c d^{9}\right)} \sqrt{-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}}} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{1}{4}} - {\left(b^{5} c^{5} d + 7 \, a b^{4} c^{4} d^{2} + 10 \, a^{2} b^{3} c^{3} d^{3} - 18 \, a^{3} b^{2} c^{2} d^{4} - 27 \, a^{4} b c d^{5} + 27 \, a^{5} d^{6}\right)} \sqrt{x} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{1}{4}}}{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}\right) - 16 \, \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a^{4} b^{2} x - {\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{4} c^{3} d + 6 \, a^{5} b^{3} c^{2} d^{2} - 4 \, a^{6} b^{2} c d^{3} + a^{7} b d^{4}\right)} \sqrt{-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} - {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} \sqrt{x}}{a^{3} b}\right) + 4 \, \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \log\left(a^{2} b \sqrt{x} + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{3}{4}}\right) - 4 \, \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \log\left(a^{2} b \sqrt{x} - {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \left(-\frac{a^{3} b}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{3}{4}}\right) - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{1}{4}} \log\left({\left(b^{6} c^{7} d^{2} - 6 \, a b^{5} c^{6} d^{3} + 15 \, a^{2} b^{4} c^{5} d^{4} - 20 \, a^{3} b^{3} c^{4} d^{5} + 15 \, a^{4} b^{2} c^{3} d^{6} - 6 \, a^{5} b c^{2} d^{7} + a^{6} c d^{8}\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{3}{4}} + {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} + 27 \, a^{3} d^{3}\right)} \sqrt{x}\right) + {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{6} c^{7} d^{2} - 6 \, a b^{5} c^{6} d^{3} + 15 \, a^{2} b^{4} c^{5} d^{4} - 20 \, a^{3} b^{3} c^{4} d^{5} + 15 \, a^{4} b^{2} c^{3} d^{6} - 6 \, a^{5} b c^{2} d^{7} + a^{6} c d^{8}\right)} \left(-\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{8} c^{9} d^{3} - 8 \, a b^{7} c^{8} d^{4} + 28 \, a^{2} b^{6} c^{7} d^{5} - 56 \, a^{3} b^{5} c^{6} d^{6} + 70 \, a^{4} b^{4} c^{5} d^{7} - 56 \, a^{5} b^{3} c^{4} d^{8} + 28 \, a^{6} b^{2} c^{3} d^{9} - 8 \, a^{7} b c^{2} d^{10} + a^{8} c d^{11}}\right)^{\frac{3}{4}} + {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} + 27 \, a^{3} d^{3}\right)} \sqrt{x}\right) - 4 \, x^{\frac{3}{2}}}{8 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}"," ",0,"-1/8*(4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(1/4)*arctan(((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt((b^6*c^6 + 18*a*b^5*c^5*d + 135*a^2*b^4*c^4*d^2 + 540*a^3*b^3*c^3*d^3 + 1215*a^4*b^2*c^2*d^4 + 1458*a^5*b*c*d^5 + 729*a^6*d^6)*x - (b^8*c^9*d + 8*a*b^7*c^8*d^2 + 12*a^2*b^6*c^7*d^3 - 40*a^3*b^5*c^6*d^4 - 74*a^4*b^4*c^5*d^5 + 120*a^5*b^3*c^4*d^6 + 108*a^6*b^2*c^3*d^7 - 216*a^7*b*c^2*d^8 + 81*a^8*c*d^9)*sqrt(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11)))*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(1/4) - (b^5*c^5*d + 7*a*b^4*c^4*d^2 + 10*a^2*b^3*c^3*d^3 - 18*a^3*b^2*c^2*d^4 - 27*a^4*b*c*d^5 + 27*a^5*d^6)*sqrt(x)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(1/4))/(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)) - 16*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*arctan((sqrt(a^4*b^2*x - (a^3*b^5*c^4 - 4*a^4*b^4*c^3*d + 6*a^5*b^3*c^2*d^2 - 4*a^6*b^2*c*d^3 + a^7*b*d^4)*sqrt(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8)))*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4) - (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*sqrt(x))/(a^3*b)) + 4*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*log(a^2*b*sqrt(x) + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(3/4)) - 4*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*log(a^2*b*sqrt(x) - (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*(-a^3*b/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(3/4)) - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(1/4)*log((b^6*c^7*d^2 - 6*a*b^5*c^6*d^3 + 15*a^2*b^4*c^5*d^4 - 20*a^3*b^3*c^4*d^5 + 15*a^4*b^2*c^3*d^6 - 6*a^5*b*c^2*d^7 + a^6*c*d^8)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(3/4) + (b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 27*a^3*d^3)*sqrt(x)) + (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(1/4)*log(-(b^6*c^7*d^2 - 6*a*b^5*c^6*d^3 + 15*a^2*b^4*c^5*d^4 - 20*a^3*b^3*c^4*d^5 + 15*a^4*b^2*c^3*d^6 - 6*a^5*b*c^2*d^7 + a^6*c*d^8)*(-(b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^8*c^9*d^3 - 8*a*b^7*c^8*d^4 + 28*a^2*b^6*c^7*d^5 - 56*a^3*b^5*c^6*d^6 + 70*a^4*b^4*c^5*d^7 - 56*a^5*b^3*c^4*d^8 + 28*a^6*b^2*c^3*d^9 - 8*a^7*b*c^2*d^10 + a^8*c*d^11))^(3/4) + (b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 27*a^3*d^3)*sqrt(x)) - 4*x^(3/2))/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","B",0
474,1,3171,0,13.986222," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{6} c^{8} d - 6 \, a b^{5} c^{7} d^{2} + 15 \, a^{2} b^{4} c^{6} d^{3} - 20 \, a^{3} b^{3} c^{5} d^{4} + 15 \, a^{4} b^{2} c^{4} d^{5} - 6 \, a^{5} b c^{3} d^{6} + a^{6} c^{2} d^{7}\right)} \sqrt{{\left(9 \, b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x + {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} \sqrt{-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}}} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{3}{4}} - {\left(3 \, b^{7} c^{9} d - 17 \, a b^{6} c^{8} d^{2} + 39 \, a^{2} b^{5} c^{7} d^{3} - 45 \, a^{3} b^{4} c^{6} d^{4} + 25 \, a^{4} b^{3} c^{5} d^{5} - 3 \, a^{5} b^{2} c^{4} d^{6} - 3 \, a^{6} b c^{3} d^{7} + a^{7} c^{2} d^{8}\right)} \sqrt{x} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{3}{4}}}{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}\right) - 16 \, \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \arctan\left(\frac{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{3}{4}} \sqrt{b^{2} x + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}}} - {\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{3}{4}} \sqrt{x}}{a b^{3}}\right) + {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left({\left(3 \, b c + a d\right)} \sqrt{x} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{1}{4}}\right) - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{1}{4}} \log\left({\left(3 \, b c + a d\right)} \sqrt{x} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \left(-\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{8} c^{11} d - 8 \, a b^{7} c^{10} d^{2} + 28 \, a^{2} b^{6} c^{9} d^{3} - 56 \, a^{3} b^{5} c^{8} d^{4} + 70 \, a^{4} b^{4} c^{7} d^{5} - 56 \, a^{5} b^{3} c^{6} d^{6} + 28 \, a^{6} b^{2} c^{5} d^{7} - 8 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}}\right)^{\frac{1}{4}}\right) - 4 \, \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \log\left(b \sqrt{x} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}}\right) + 4 \, \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \log\left(b \sqrt{x} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(-\frac{a b^{3}}{b^{8} c^{8} - 8 \, a b^{7} c^{7} d + 28 \, a^{2} b^{6} c^{6} d^{2} - 56 \, a^{3} b^{5} c^{5} d^{3} + 70 \, a^{4} b^{4} c^{4} d^{4} - 56 \, a^{5} b^{3} c^{3} d^{5} + 28 \, a^{6} b^{2} c^{2} d^{6} - 8 \, a^{7} b c d^{7} + a^{8} d^{8}}\right)^{\frac{1}{4}}\right) + 4 \, \sqrt{x}}{8 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}"," ",0,"1/8*(4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(1/4)*arctan(((b^6*c^8*d - 6*a*b^5*c^7*d^2 + 15*a^2*b^4*c^6*d^3 - 20*a^3*b^3*c^5*d^4 + 15*a^4*b^2*c^4*d^5 - 6*a^5*b*c^3*d^6 + a^6*c^2*d^7)*sqrt((9*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x + (b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*sqrt(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9)))*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(3/4) - (3*b^7*c^9*d - 17*a*b^6*c^8*d^2 + 39*a^2*b^5*c^7*d^3 - 45*a^3*b^4*c^6*d^4 + 25*a^4*b^3*c^5*d^5 - 3*a^5*b^2*c^4*d^6 - 3*a^6*b*c^3*d^7 + a^7*c^2*d^8)*sqrt(x)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(3/4))/(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)) - 16*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*arctan(((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(3/4)*sqrt(b^2*x + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))) - (b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(3/4)*sqrt(x))/(a*b^3)) + (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(1/4)*log((3*b*c + a*d)*sqrt(x) + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(1/4)) - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(1/4)*log((3*b*c + a*d)*sqrt(x) - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(-(81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(b^8*c^11*d - 8*a*b^7*c^10*d^2 + 28*a^2*b^6*c^9*d^3 - 56*a^3*b^5*c^8*d^4 + 70*a^4*b^4*c^7*d^5 - 56*a^5*b^3*c^6*d^6 + 28*a^6*b^2*c^5*d^7 - 8*a^7*b*c^4*d^8 + a^8*c^3*d^9))^(1/4)) - 4*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*log(b*sqrt(x) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)) + 4*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*log(b*sqrt(x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-a*b^3/(b^8*c^8 - 8*a*b^7*c^7*d + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a^7*b*c*d^7 + a^8*d^8))^(1/4)) + 4*sqrt(x))/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","B",0
475,1,3457,0,47.517341," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, d x^{\frac{3}{2}} + 4 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{{\left(15625 \, b^{6} c^{6} d^{2} - 18750 \, a b^{5} c^{5} d^{3} + 9375 \, a^{2} b^{4} c^{4} d^{4} - 2500 \, a^{3} b^{3} c^{3} d^{5} + 375 \, a^{4} b^{2} c^{2} d^{6} - 30 \, a^{5} b c d^{7} + a^{6} d^{8}\right)} x - {\left(625 \, b^{8} c^{11} d - 3000 \, a b^{7} c^{10} d^{2} + 5900 \, a^{2} b^{6} c^{9} d^{3} - 6120 \, a^{3} b^{5} c^{8} d^{4} + 3606 \, a^{4} b^{4} c^{7} d^{5} - 1224 \, a^{5} b^{3} c^{6} d^{6} + 236 \, a^{6} b^{2} c^{5} d^{7} - 24 \, a^{7} b c^{4} d^{8} + a^{8} c^{3} d^{9}\right)} \sqrt{-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}}} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{1}{4}} + {\left(125 \, b^{5} c^{6} d - 325 \, a b^{4} c^{5} d^{2} + 290 \, a^{2} b^{3} c^{4} d^{3} - 106 \, a^{3} b^{2} c^{3} d^{4} + 17 \, a^{4} b c^{2} d^{5} - a^{5} c d^{6}\right)} \sqrt{x} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{1}{4}}}{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}\right) + 16 \, \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{b^{8} x - {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} \sqrt{-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}}} \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{1}{4}} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} - {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{1}{4}} \sqrt{x}}{b^{5}}\right) - 4 \, \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \log\left(b^{4} \sqrt{x} + {\left(a b^{6} c^{6} - 6 \, a^{2} b^{5} c^{5} d + 15 \, a^{3} b^{4} c^{4} d^{2} - 20 \, a^{4} b^{3} c^{3} d^{3} + 15 \, a^{5} b^{2} c^{2} d^{4} - 6 \, a^{6} b c d^{5} + a^{7} d^{6}\right)} \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{3}{4}}\right) + 4 \, \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \log\left(b^{4} \sqrt{x} - {\left(a b^{6} c^{6} - 6 \, a^{2} b^{5} c^{5} d + 15 \, a^{3} b^{4} c^{4} d^{2} - 20 \, a^{4} b^{3} c^{3} d^{3} + 15 \, a^{5} b^{2} c^{2} d^{4} - 6 \, a^{6} b c d^{5} + a^{7} d^{6}\right)} \left(-\frac{b^{5}}{a b^{8} c^{8} - 8 \, a^{2} b^{7} c^{7} d + 28 \, a^{3} b^{6} c^{6} d^{2} - 56 \, a^{4} b^{5} c^{5} d^{3} + 70 \, a^{5} b^{4} c^{4} d^{4} - 56 \, a^{6} b^{3} c^{3} d^{5} + 28 \, a^{7} b^{2} c^{2} d^{6} - 8 \, a^{8} b c d^{7} + a^{9} d^{8}}\right)^{\frac{3}{4}}\right) - {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{1}{4}} \log\left({\left(b^{6} c^{10} - 6 \, a b^{5} c^{9} d + 15 \, a^{2} b^{4} c^{8} d^{2} - 20 \, a^{3} b^{3} c^{7} d^{3} + 15 \, a^{4} b^{2} c^{6} d^{4} - 6 \, a^{5} b c^{5} d^{5} + a^{6} c^{4} d^{6}\right)} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{3}{4}} - {\left(125 \, b^{3} c^{3} d - 75 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{x}\right) + {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{6} c^{10} - 6 \, a b^{5} c^{9} d + 15 \, a^{2} b^{4} c^{8} d^{2} - 20 \, a^{3} b^{3} c^{7} d^{3} + 15 \, a^{4} b^{2} c^{6} d^{4} - 6 \, a^{5} b c^{5} d^{5} + a^{6} c^{4} d^{6}\right)} \left(-\frac{625 \, b^{4} c^{4} d - 500 \, a b^{3} c^{3} d^{2} + 150 \, a^{2} b^{2} c^{2} d^{3} - 20 \, a^{3} b c d^{4} + a^{4} d^{5}}{b^{8} c^{13} - 8 \, a b^{7} c^{12} d + 28 \, a^{2} b^{6} c^{11} d^{2} - 56 \, a^{3} b^{5} c^{10} d^{3} + 70 \, a^{4} b^{4} c^{9} d^{4} - 56 \, a^{5} b^{3} c^{8} d^{5} + 28 \, a^{6} b^{2} c^{7} d^{6} - 8 \, a^{7} b c^{6} d^{7} + a^{8} c^{5} d^{8}}\right)^{\frac{3}{4}} - {\left(125 \, b^{3} c^{3} d - 75 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{x}\right)}{8 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}}"," ",0,"-1/8*(4*d*x^(3/2) + 4*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(1/4)*arctan(((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt((15625*b^6*c^6*d^2 - 18750*a*b^5*c^5*d^3 + 9375*a^2*b^4*c^4*d^4 - 2500*a^3*b^3*c^3*d^5 + 375*a^4*b^2*c^2*d^6 - 30*a^5*b*c*d^7 + a^6*d^8)*x - (625*b^8*c^11*d - 3000*a*b^7*c^10*d^2 + 5900*a^2*b^6*c^9*d^3 - 6120*a^3*b^5*c^8*d^4 + 3606*a^4*b^4*c^7*d^5 - 1224*a^5*b^3*c^6*d^6 + 236*a^6*b^2*c^5*d^7 - 24*a^7*b*c^4*d^8 + a^8*c^3*d^9)*sqrt(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8)))*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(1/4) + (125*b^5*c^6*d - 325*a*b^4*c^5*d^2 + 290*a^2*b^3*c^4*d^3 - 106*a^3*b^2*c^3*d^4 + 17*a^4*b*c^2*d^5 - a^5*c*d^6)*sqrt(x)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(1/4))/(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)) + 16*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*arctan((sqrt(b^8*x - (a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*sqrt(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8)))*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(1/4)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(1/4)*sqrt(x))/b^5) - 4*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*log(b^4*sqrt(x) + (a*b^6*c^6 - 6*a^2*b^5*c^5*d + 15*a^3*b^4*c^4*d^2 - 20*a^4*b^3*c^3*d^3 + 15*a^5*b^2*c^2*d^4 - 6*a^6*b*c*d^5 + a^7*d^6)*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(3/4)) + 4*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*log(b^4*sqrt(x) - (a*b^6*c^6 - 6*a^2*b^5*c^5*d + 15*a^3*b^4*c^4*d^2 - 20*a^4*b^3*c^3*d^3 + 15*a^5*b^2*c^2*d^4 - 6*a^6*b*c*d^5 + a^7*d^6)*(-b^5/(a*b^8*c^8 - 8*a^2*b^7*c^7*d + 28*a^3*b^6*c^6*d^2 - 56*a^4*b^5*c^5*d^3 + 70*a^5*b^4*c^4*d^4 - 56*a^6*b^3*c^3*d^5 + 28*a^7*b^2*c^2*d^6 - 8*a^8*b*c*d^7 + a^9*d^8))^(3/4)) - (b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(1/4)*log((b^6*c^10 - 6*a*b^5*c^9*d + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a^5*b*c^5*d^5 + a^6*c^4*d^6)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(3/4) - (125*b^3*c^3*d - 75*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 - a^3*d^4)*sqrt(x)) + (b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(1/4)*log(-(b^6*c^10 - 6*a*b^5*c^9*d + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a^5*b*c^5*d^5 + a^6*c^4*d^6)*(-(625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4 + a^4*d^5)/(b^8*c^13 - 8*a*b^7*c^12*d + 28*a^2*b^6*c^11*d^2 - 56*a^3*b^5*c^10*d^3 + 70*a^4*b^4*c^9*d^4 - 56*a^5*b^3*c^8*d^5 + 28*a^6*b^2*c^7*d^6 - 8*a^7*b*c^6*d^7 + a^8*c^5*d^8))^(3/4) - (125*b^3*c^3*d - 75*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 - a^3*d^4)*sqrt(x)))/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)","B",0
476,1,3310,0,55.340667," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{6} c^{11} - 6 \, a b^{5} c^{10} d + 15 \, a^{2} b^{4} c^{9} d^{2} - 20 \, a^{3} b^{3} c^{8} d^{3} + 15 \, a^{4} b^{2} c^{7} d^{4} - 6 \, a^{5} b c^{6} d^{5} + a^{6} c^{5} d^{6}\right)} \sqrt{{\left(49 \, b^{2} c^{2} d^{2} - 42 \, a b c d^{3} + 9 \, a^{2} d^{4}\right)} x + {\left(b^{4} c^{8} - 4 \, a b^{3} c^{7} d + 6 \, a^{2} b^{2} c^{6} d^{2} - 4 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} \sqrt{-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}}} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{3}{4}} + {\left(7 \, b^{7} c^{12} d - 45 \, a b^{6} c^{11} d^{2} + 123 \, a^{2} b^{5} c^{10} d^{3} - 185 \, a^{3} b^{4} c^{9} d^{4} + 165 \, a^{4} b^{3} c^{8} d^{5} - 87 \, a^{5} b^{2} c^{7} d^{6} + 25 \, a^{6} b c^{6} d^{7} - 3 \, a^{7} c^{5} d^{8}\right)} \sqrt{x} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{3}{4}}}{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}\right) + 16 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \arctan\left(\frac{{\left(a^{2} b^{6} c^{6} - 6 \, a^{3} b^{5} c^{5} d + 15 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 15 \, a^{6} b^{2} c^{2} d^{4} - 6 \, a^{7} b c d^{5} + a^{8} d^{6}\right)} \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{3}{4}} \sqrt{b^{4} x + {\left(a^{2} b^{4} c^{4} - 4 \, a^{3} b^{3} c^{3} d + 6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4}\right)} \sqrt{-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}}} - {\left(a^{2} b^{8} c^{6} - 6 \, a^{3} b^{7} c^{5} d + 15 \, a^{4} b^{6} c^{4} d^{2} - 20 \, a^{5} b^{5} c^{3} d^{3} + 15 \, a^{6} b^{4} c^{2} d^{4} - 6 \, a^{7} b^{3} c d^{5} + a^{8} b^{2} d^{6}\right)} \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{3}{4}} \sqrt{x}}{b^{7}}\right) + 4 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \log\left(b^{2} \sqrt{x} + \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}\right) - 4 \, \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \log\left(b^{2} \sqrt{x} - \left(-\frac{b^{7}}{a^{3} b^{8} c^{8} - 8 \, a^{4} b^{7} c^{7} d + 28 \, a^{5} b^{6} c^{6} d^{2} - 56 \, a^{6} b^{5} c^{5} d^{3} + 70 \, a^{7} b^{4} c^{4} d^{4} - 56 \, a^{8} b^{3} c^{3} d^{5} + 28 \, a^{9} b^{2} c^{2} d^{6} - 8 \, a^{10} b c d^{7} + a^{11} d^{8}}\right)^{\frac{1}{4}} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}\right) + {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(7 \, b c d - 3 \, a d^{2}\right)} \sqrt{x} + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}}\right) - {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(7 \, b c d - 3 \, a d^{2}\right)} \sqrt{x} - {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} - 4116 \, a b^{3} c^{3} d^{4} + 2646 \, a^{2} b^{2} c^{2} d^{5} - 756 \, a^{3} b c d^{6} + 81 \, a^{4} d^{7}}{b^{8} c^{15} - 8 \, a b^{7} c^{14} d + 28 \, a^{2} b^{6} c^{13} d^{2} - 56 \, a^{3} b^{5} c^{12} d^{3} + 70 \, a^{4} b^{4} c^{11} d^{4} - 56 \, a^{5} b^{3} c^{10} d^{5} + 28 \, a^{6} b^{2} c^{9} d^{6} - 8 \, a^{7} b c^{8} d^{7} + a^{8} c^{7} d^{8}}\right)^{\frac{1}{4}}\right) - 4 \, d \sqrt{x}}{8 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}}"," ",0,"1/8*(4*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*arctan(((b^6*c^11 - 6*a*b^5*c^10*d + 15*a^2*b^4*c^9*d^2 - 20*a^3*b^3*c^8*d^3 + 15*a^4*b^2*c^7*d^4 - 6*a^5*b*c^6*d^5 + a^6*c^5*d^6)*sqrt((49*b^2*c^2*d^2 - 42*a*b*c*d^3 + 9*a^2*d^4)*x + (b^4*c^8 - 4*a*b^3*c^7*d + 6*a^2*b^2*c^6*d^2 - 4*a^3*b*c^5*d^3 + a^4*c^4*d^4)*sqrt(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8)))*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(3/4) + (7*b^7*c^12*d - 45*a*b^6*c^11*d^2 + 123*a^2*b^5*c^10*d^3 - 185*a^3*b^4*c^9*d^4 + 165*a^4*b^3*c^8*d^5 - 87*a^5*b^2*c^7*d^6 + 25*a^6*b*c^6*d^7 - 3*a^7*c^5*d^8)*sqrt(x)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(3/4))/(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)) + 16*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*arctan(((a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5 + a^8*d^6)*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(3/4)*sqrt(b^4*x + (a^2*b^4*c^4 - 4*a^3*b^3*c^3*d + 6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4)*sqrt(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))) - (a^2*b^8*c^6 - 6*a^3*b^7*c^5*d + 15*a^4*b^6*c^4*d^2 - 20*a^5*b^5*c^3*d^3 + 15*a^6*b^4*c^2*d^4 - 6*a^7*b^3*c*d^5 + a^8*b^2*d^6)*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(3/4)*sqrt(x))/b^7) + 4*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*log(b^2*sqrt(x) + (-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)) - 4*(-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*log(b^2*sqrt(x) - (-b^7/(a^3*b^8*c^8 - 8*a^4*b^7*c^7*d + 28*a^5*b^6*c^6*d^2 - 56*a^6*b^5*c^5*d^3 + 70*a^7*b^4*c^4*d^4 - 56*a^8*b^3*c^3*d^5 + 28*a^9*b^2*c^2*d^6 - 8*a^10*b*c*d^7 + a^11*d^8))^(1/4)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)) + (b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*log(-(7*b*c*d - 3*a*d^2)*sqrt(x) + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)) - (b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)*log(-(7*b*c*d - 3*a*d^2)*sqrt(x) - (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(-(2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6 + 81*a^4*d^7)/(b^8*c^15 - 8*a*b^7*c^14*d + 28*a^2*b^6*c^13*d^2 - 56*a^3*b^5*c^12*d^3 + 70*a^4*b^4*c^11*d^4 - 56*a^5*b^3*c^10*d^5 + 28*a^6*b^2*c^9*d^6 - 8*a^7*b*c^8*d^7 + a^8*c^7*d^8))^(1/4)) - 4*d*sqrt(x))/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2)","B",0
477,1,3630,0,88.691911," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{{\left(531441 \, b^{6} c^{6} d^{8} - 1771470 \, a b^{5} c^{5} d^{9} + 2460375 \, a^{2} b^{4} c^{4} d^{10} - 1822500 \, a^{3} b^{3} c^{3} d^{11} + 759375 \, a^{4} b^{2} c^{2} d^{12} - 168750 \, a^{5} b c d^{13} + 15625 \, a^{6} d^{14}\right)} x - {\left(6561 \, b^{8} c^{13} d^{5} - 40824 \, a b^{7} c^{12} d^{6} + 109836 \, a^{2} b^{6} c^{11} d^{7} - 166824 \, a^{3} b^{5} c^{10} d^{8} + 156406 \, a^{4} b^{4} c^{9} d^{9} - 92680 \, a^{5} b^{3} c^{8} d^{10} + 33900 \, a^{6} b^{2} c^{7} d^{11} - 7000 \, a^{7} b c^{6} d^{12} + 625 \, a^{8} c^{5} d^{13}\right)} \sqrt{-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}}} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{1}{4}} + {\left(729 \, b^{5} c^{7} d^{4} - 2673 \, a b^{4} c^{6} d^{5} + 3834 \, a^{2} b^{3} c^{5} d^{6} - 2690 \, a^{3} b^{2} c^{4} d^{7} + 925 \, a^{4} b c^{3} d^{8} - 125 \, a^{5} c^{2} d^{9}\right)} \sqrt{x} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{1}{4}}}{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}\right) + 16 \, \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \arctan\left(\frac{\sqrt{b^{14} x - {\left(a^{3} b^{13} c^{4} - 4 \, a^{4} b^{12} c^{3} d + 6 \, a^{5} b^{11} c^{2} d^{2} - 4 \, a^{6} b^{10} c d^{3} + a^{7} b^{9} d^{4}\right)} \sqrt{-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}}} \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{1}{4}} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} - {\left(a b^{9} c^{2} - 2 \, a^{2} b^{8} c d + a^{3} b^{7} d^{2}\right)} \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{1}{4}} \sqrt{x}}{b^{9}}\right) - 4 \, \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \log\left(b^{7} \sqrt{x} + {\left(a^{4} b^{6} c^{6} - 6 \, a^{5} b^{5} c^{5} d + 15 \, a^{6} b^{4} c^{4} d^{2} - 20 \, a^{7} b^{3} c^{3} d^{3} + 15 \, a^{8} b^{2} c^{2} d^{4} - 6 \, a^{9} b c d^{5} + a^{10} d^{6}\right)} \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{3}{4}}\right) + 4 \, \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{1}{4}} {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \log\left(b^{7} \sqrt{x} - {\left(a^{4} b^{6} c^{6} - 6 \, a^{5} b^{5} c^{5} d + 15 \, a^{6} b^{4} c^{4} d^{2} - 20 \, a^{7} b^{3} c^{3} d^{3} + 15 \, a^{8} b^{2} c^{2} d^{4} - 6 \, a^{9} b c d^{5} + a^{10} d^{6}\right)} \left(-\frac{b^{9}}{a^{5} b^{8} c^{8} - 8 \, a^{6} b^{7} c^{7} d + 28 \, a^{7} b^{6} c^{6} d^{2} - 56 \, a^{8} b^{5} c^{5} d^{3} + 70 \, a^{9} b^{4} c^{4} d^{4} - 56 \, a^{10} b^{3} c^{3} d^{5} + 28 \, a^{11} b^{2} c^{2} d^{6} - 8 \, a^{12} b c d^{7} + a^{13} d^{8}}\right)^{\frac{3}{4}}\right) - {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{1}{4}} \log\left({\left(b^{6} c^{13} - 6 \, a b^{5} c^{12} d + 15 \, a^{2} b^{4} c^{11} d^{2} - 20 \, a^{3} b^{3} c^{10} d^{3} + 15 \, a^{4} b^{2} c^{9} d^{4} - 6 \, a^{5} b c^{8} d^{5} + a^{6} c^{7} d^{6}\right)} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{3}{4}} - {\left(729 \, b^{3} c^{3} d^{4} - 1215 \, a b^{2} c^{2} d^{5} + 675 \, a^{2} b c d^{6} - 125 \, a^{3} d^{7}\right)} \sqrt{x}\right) + {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{6} c^{13} - 6 \, a b^{5} c^{12} d + 15 \, a^{2} b^{4} c^{11} d^{2} - 20 \, a^{3} b^{3} c^{10} d^{3} + 15 \, a^{4} b^{2} c^{9} d^{4} - 6 \, a^{5} b c^{8} d^{5} + a^{6} c^{7} d^{6}\right)} \left(-\frac{6561 \, b^{4} c^{4} d^{5} - 14580 \, a b^{3} c^{3} d^{6} + 12150 \, a^{2} b^{2} c^{2} d^{7} - 4500 \, a^{3} b c d^{8} + 625 \, a^{4} d^{9}}{b^{8} c^{17} - 8 \, a b^{7} c^{16} d + 28 \, a^{2} b^{6} c^{15} d^{2} - 56 \, a^{3} b^{5} c^{14} d^{3} + 70 \, a^{4} b^{4} c^{13} d^{4} - 56 \, a^{5} b^{3} c^{12} d^{5} + 28 \, a^{6} b^{2} c^{11} d^{6} - 8 \, a^{7} b c^{10} d^{7} + a^{8} c^{9} d^{8}}\right)^{\frac{3}{4}} - {\left(729 \, b^{3} c^{3} d^{4} - 1215 \, a b^{2} c^{2} d^{5} + 675 \, a^{2} b c d^{6} - 125 \, a^{3} d^{7}\right)} \sqrt{x}\right) - 4 \, {\left(4 \, b c^{2} - 4 \, a c d + {\left(4 \, b c d - 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{x}}{8 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)}}"," ",0,"1/8*(4*((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(1/4)*arctan(((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt((531441*b^6*c^6*d^8 - 1771470*a*b^5*c^5*d^9 + 2460375*a^2*b^4*c^4*d^10 - 1822500*a^3*b^3*c^3*d^11 + 759375*a^4*b^2*c^2*d^12 - 168750*a^5*b*c*d^13 + 15625*a^6*d^14)*x - (6561*b^8*c^13*d^5 - 40824*a*b^7*c^12*d^6 + 109836*a^2*b^6*c^11*d^7 - 166824*a^3*b^5*c^10*d^8 + 156406*a^4*b^4*c^9*d^9 - 92680*a^5*b^3*c^8*d^10 + 33900*a^6*b^2*c^7*d^11 - 7000*a^7*b*c^6*d^12 + 625*a^8*c^5*d^13)*sqrt(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8)))*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(1/4) + (729*b^5*c^7*d^4 - 2673*a*b^4*c^6*d^5 + 3834*a^2*b^3*c^5*d^6 - 2690*a^3*b^2*c^4*d^7 + 925*a^4*b*c^3*d^8 - 125*a^5*c^2*d^9)*sqrt(x)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(1/4))/(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)) + 16*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(1/4)*((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*arctan((sqrt(b^14*x - (a^3*b^13*c^4 - 4*a^4*b^12*c^3*d + 6*a^5*b^11*c^2*d^2 - 4*a^6*b^10*c*d^3 + a^7*b^9*d^4)*sqrt(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8)))*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(1/4)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) - (a*b^9*c^2 - 2*a^2*b^8*c*d + a^3*b^7*d^2)*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(1/4)*sqrt(x))/b^9) - 4*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(1/4)*((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*log(b^7*sqrt(x) + (a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5 + a^10*d^6)*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(3/4)) + 4*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(1/4)*((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*log(b^7*sqrt(x) - (a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5 + a^10*d^6)*(-b^9/(a^5*b^8*c^8 - 8*a^6*b^7*c^7*d + 28*a^7*b^6*c^6*d^2 - 56*a^8*b^5*c^5*d^3 + 70*a^9*b^4*c^4*d^4 - 56*a^10*b^3*c^3*d^5 + 28*a^11*b^2*c^2*d^6 - 8*a^12*b*c*d^7 + a^13*d^8))^(3/4)) - ((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(1/4)*log((b^6*c^13 - 6*a*b^5*c^12*d + 15*a^2*b^4*c^11*d^2 - 20*a^3*b^3*c^10*d^3 + 15*a^4*b^2*c^9*d^4 - 6*a^5*b*c^8*d^5 + a^6*c^7*d^6)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(3/4) - (729*b^3*c^3*d^4 - 1215*a*b^2*c^2*d^5 + 675*a^2*b*c*d^6 - 125*a^3*d^7)*sqrt(x)) + ((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(1/4)*log(-(b^6*c^13 - 6*a*b^5*c^12*d + 15*a^2*b^4*c^11*d^2 - 20*a^3*b^3*c^10*d^3 + 15*a^4*b^2*c^9*d^4 - 6*a^5*b*c^8*d^5 + a^6*c^7*d^6)*(-(6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8 + 625*a^4*d^9)/(b^8*c^17 - 8*a*b^7*c^16*d + 28*a^2*b^6*c^15*d^2 - 56*a^3*b^5*c^14*d^3 + 70*a^4*b^4*c^13*d^4 - 56*a^5*b^3*c^12*d^5 + 28*a^6*b^2*c^11*d^6 - 8*a^7*b*c^10*d^7 + a^8*c^9*d^8))^(3/4) - (729*b^3*c^3*d^4 - 1215*a*b^2*c^2*d^5 + 675*a^2*b*c*d^6 - 125*a^3*d^7)*sqrt(x)) - 4*(4*b*c^2 - 4*a*c*d + (4*b*c*d - 5*a*d^2)*x^2)*sqrt(x))/((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)","B",0
478,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3/x^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,1,5375,0,106.840789," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{10} c^{9} - 9 \, a b^{9} c^{8} d + 36 \, a^{2} b^{8} c^{7} d^{2} - 84 \, a^{3} b^{7} c^{6} d^{3} + 126 \, a^{4} b^{6} c^{5} d^{4} - 126 \, a^{5} b^{5} c^{4} d^{5} + 84 \, a^{6} b^{4} c^{3} d^{6} - 36 \, a^{7} b^{3} c^{2} d^{7} + 9 \, a^{8} b^{2} c d^{8} - a^{9} b d^{9}\right)} \sqrt{{\left(25 \, b^{2} c^{2} + 30 \, a b c d + 9 \, a^{2} d^{2}\right)} x + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}}} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{3}{4}} - {\left(5 \, b^{11} c^{10} - 42 \, a b^{10} c^{9} d + 153 \, a^{2} b^{9} c^{8} d^{2} - 312 \, a^{3} b^{8} c^{7} d^{3} + 378 \, a^{4} b^{7} c^{6} d^{4} - 252 \, a^{5} b^{6} c^{5} d^{5} + 42 \, a^{6} b^{5} c^{4} d^{6} + 72 \, a^{7} b^{4} c^{3} d^{7} - 63 \, a^{8} b^{3} c^{2} d^{8} + 22 \, a^{9} b^{2} c d^{9} - 3 \, a^{10} b d^{10}\right)} \sqrt{x} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{3}{4}}}{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{9} c^{9} d - 9 \, a b^{8} c^{8} d^{2} + 36 \, a^{2} b^{7} c^{7} d^{3} - 84 \, a^{3} b^{6} c^{6} d^{4} + 126 \, a^{4} b^{5} c^{5} d^{5} - 126 \, a^{5} b^{4} c^{4} d^{6} + 84 \, a^{6} b^{3} c^{3} d^{7} - 36 \, a^{7} b^{2} c^{2} d^{8} + 9 \, a^{8} b c d^{9} - a^{9} d^{10}\right)} \sqrt{{\left(9 \, b^{2} c^{2} + 30 \, a b c d + 25 \, a^{2} d^{2}\right)} x + {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}}} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{3}{4}} - {\left(3 \, b^{10} c^{10} d - 22 \, a b^{9} c^{9} d^{2} + 63 \, a^{2} b^{8} c^{8} d^{3} - 72 \, a^{3} b^{7} c^{7} d^{4} - 42 \, a^{4} b^{6} c^{6} d^{5} + 252 \, a^{5} b^{5} c^{5} d^{6} - 378 \, a^{6} b^{4} c^{4} d^{7} + 312 \, a^{7} b^{3} c^{3} d^{8} - 153 \, a^{8} b^{2} c^{2} d^{9} + 42 \, a^{9} b c d^{10} - 5 \, a^{10} d^{11}\right)} \sqrt{x} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{3}{4}}}{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{1}{4}} \log\left({\left(5 \, b c + 3 \, a d\right)} \sqrt{x} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{1}{4}}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{1}{4}} \log\left({\left(5 \, b c + 3 \, a d\right)} \sqrt{x} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-\frac{625 \, a b^{4} c^{4} + 1500 \, a^{2} b^{3} c^{3} d + 1350 \, a^{3} b^{2} c^{2} d^{2} + 540 \, a^{4} b c d^{3} + 81 \, a^{5} d^{4}}{b^{13} c^{12} - 12 \, a b^{12} c^{11} d + 66 \, a^{2} b^{11} c^{10} d^{2} - 220 \, a^{3} b^{10} c^{9} d^{3} + 495 \, a^{4} b^{9} c^{8} d^{4} - 792 \, a^{5} b^{8} c^{7} d^{5} + 924 \, a^{6} b^{7} c^{6} d^{6} - 792 \, a^{7} b^{6} c^{5} d^{7} + 495 \, a^{8} b^{5} c^{4} d^{8} - 220 \, a^{9} b^{4} c^{3} d^{9} + 66 \, a^{10} b^{3} c^{2} d^{10} - 12 \, a^{11} b^{2} c d^{11} + a^{12} b d^{12}}\right)^{\frac{1}{4}}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{1}{4}} \log\left({\left(3 \, b c + 5 \, a d\right)} \sqrt{x} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{1}{4}}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{1}{4}} \log\left({\left(3 \, b c + 5 \, a d\right)} \sqrt{x} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \left(-\frac{81 \, b^{4} c^{5} + 540 \, a b^{3} c^{4} d + 1350 \, a^{2} b^{2} c^{3} d^{2} + 1500 \, a^{3} b c^{2} d^{3} + 625 \, a^{4} c d^{4}}{b^{12} c^{12} d - 12 \, a b^{11} c^{11} d^{2} + 66 \, a^{2} b^{10} c^{10} d^{3} - 220 \, a^{3} b^{9} c^{9} d^{4} + 495 \, a^{4} b^{8} c^{8} d^{5} - 792 \, a^{5} b^{7} c^{7} d^{6} + 924 \, a^{6} b^{6} c^{6} d^{7} - 792 \, a^{7} b^{5} c^{5} d^{8} + 495 \, a^{8} b^{4} c^{4} d^{9} - 220 \, a^{9} b^{3} c^{3} d^{10} + 66 \, a^{10} b^{2} c^{2} d^{11} - 12 \, a^{11} b c d^{12} + a^{12} d^{13}}\right)^{\frac{1}{4}}\right) + 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{x}}{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/8*(4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(1/4)*arctan(-((b^10*c^9 - 9*a*b^9*c^8*d + 36*a^2*b^8*c^7*d^2 - 84*a^3*b^7*c^6*d^3 + 126*a^4*b^6*c^5*d^4 - 126*a^5*b^5*c^4*d^5 + 84*a^6*b^4*c^3*d^6 - 36*a^7*b^3*c^2*d^7 + 9*a^8*b^2*c*d^8 - a^9*b*d^9)*sqrt((25*b^2*c^2 + 30*a*b*c*d + 9*a^2*d^2)*x + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12)))*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(3/4) - (5*b^11*c^10 - 42*a*b^10*c^9*d + 153*a^2*b^9*c^8*d^2 - 312*a^3*b^8*c^7*d^3 + 378*a^4*b^7*c^6*d^4 - 252*a^5*b^6*c^5*d^5 + 42*a^6*b^5*c^4*d^6 + 72*a^7*b^4*c^3*d^7 - 63*a^8*b^3*c^2*d^8 + 22*a^9*b^2*c*d^9 - 3*a^10*b*d^10)*sqrt(x)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(3/4))/(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(1/4)*arctan(-((b^9*c^9*d - 9*a*b^8*c^8*d^2 + 36*a^2*b^7*c^7*d^3 - 84*a^3*b^6*c^6*d^4 + 126*a^4*b^5*c^5*d^5 - 126*a^5*b^4*c^4*d^6 + 84*a^6*b^3*c^3*d^7 - 36*a^7*b^2*c^2*d^8 + 9*a^8*b*c*d^9 - a^9*d^10)*sqrt((9*b^2*c^2 + 30*a*b*c*d + 25*a^2*d^2)*x + (b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13)))*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(3/4) - (3*b^10*c^10*d - 22*a*b^9*c^9*d^2 + 63*a^2*b^8*c^8*d^3 - 72*a^3*b^7*c^7*d^4 - 42*a^4*b^6*c^6*d^5 + 252*a^5*b^5*c^5*d^6 - 378*a^6*b^4*c^4*d^7 + 312*a^7*b^3*c^3*d^8 - 153*a^8*b^2*c^2*d^9 + 42*a^9*b*c*d^10 - 5*a^10*d^11)*sqrt(x)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(3/4))/(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(1/4)*log((5*b*c + 3*a*d)*sqrt(x) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(1/4)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(1/4)*log((5*b*c + 3*a*d)*sqrt(x) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-(625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3 + 81*a^5*d^4)/(b^13*c^12 - 12*a*b^12*c^11*d + 66*a^2*b^11*c^10*d^2 - 220*a^3*b^10*c^9*d^3 + 495*a^4*b^9*c^8*d^4 - 792*a^5*b^8*c^7*d^5 + 924*a^6*b^7*c^6*d^6 - 792*a^7*b^6*c^5*d^7 + 495*a^8*b^5*c^4*d^8 - 220*a^9*b^4*c^3*d^9 + 66*a^10*b^3*c^2*d^10 - 12*a^11*b^2*c*d^11 + a^12*b*d^12))^(1/4)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(1/4)*log((3*b*c + 5*a*d)*sqrt(x) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(1/4)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(1/4)*log((3*b*c + 5*a*d)*sqrt(x) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(-(81*b^4*c^5 + 540*a*b^3*c^4*d + 1350*a^2*b^2*c^3*d^2 + 1500*a^3*b*c^2*d^3 + 625*a^4*c*d^4)/(b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12 + a^12*d^13))^(1/4)) + 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(x))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","B",0
489,1,5814,0,158.694047," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{{\left(729 \, b^{8} c^{6} + 7290 \, a b^{7} c^{5} d + 30375 \, a^{2} b^{6} c^{4} d^{2} + 67500 \, a^{3} b^{5} c^{3} d^{3} + 84375 \, a^{4} b^{4} c^{2} d^{4} + 56250 \, a^{5} b^{3} c d^{5} + 15625 \, a^{6} b^{2} d^{6}\right)} x - {\left(81 \, a b^{11} c^{10} + 54 \, a^{2} b^{10} c^{9} d - 675 \, a^{3} b^{9} c^{8} d^{2} - 120 \, a^{4} b^{8} c^{7} d^{3} + 2290 \, a^{5} b^{7} c^{6} d^{4} - 636 \, a^{6} b^{6} c^{5} d^{5} - 3534 \, a^{7} b^{5} c^{4} d^{6} + 2440 \, a^{8} b^{4} c^{3} d^{7} + 1725 \, a^{9} b^{3} c^{2} d^{8} - 2250 \, a^{10} b^{2} c d^{9} + 625 \, a^{11} b d^{10}\right)} \sqrt{-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}}} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{1}{4}} - {\left(27 \, b^{7} c^{6} + 54 \, a b^{6} c^{5} d - 99 \, a^{2} b^{5} c^{4} d^{2} - 172 \, a^{3} b^{4} c^{3} d^{3} + 165 \, a^{4} b^{3} c^{2} d^{4} + 150 \, a^{5} b^{2} c d^{5} - 125 \, a^{6} b d^{6}\right)} \sqrt{x} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{1}{4}}}{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{{\left(15625 \, b^{6} c^{6} d^{2} + 56250 \, a b^{5} c^{5} d^{3} + 84375 \, a^{2} b^{4} c^{4} d^{4} + 67500 \, a^{3} b^{3} c^{3} d^{5} + 30375 \, a^{4} b^{2} c^{2} d^{6} + 7290 \, a^{5} b c d^{7} + 729 \, a^{6} d^{8}\right)} x - {\left(625 \, b^{10} c^{11} d - 2250 \, a b^{9} c^{10} d^{2} + 1725 \, a^{2} b^{8} c^{9} d^{3} + 2440 \, a^{3} b^{7} c^{8} d^{4} - 3534 \, a^{4} b^{6} c^{7} d^{5} - 636 \, a^{5} b^{5} c^{6} d^{6} + 2290 \, a^{6} b^{4} c^{5} d^{7} - 120 \, a^{7} b^{3} c^{4} d^{8} - 675 \, a^{8} b^{2} c^{3} d^{9} + 54 \, a^{9} b c^{2} d^{10} + 81 \, a^{10} c d^{11}\right)} \sqrt{-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}}} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{1}{4}} - {\left(125 \, b^{6} c^{6} d - 150 \, a b^{5} c^{5} d^{2} - 165 \, a^{2} b^{4} c^{4} d^{3} + 172 \, a^{3} b^{3} c^{3} d^{4} + 99 \, a^{4} b^{2} c^{2} d^{5} - 54 \, a^{5} b c d^{6} - 27 \, a^{6} d^{7}\right)} \sqrt{x} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{1}{4}}}{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{1}{4}} \log\left({\left(a b^{9} c^{9} - 9 \, a^{2} b^{8} c^{8} d + 36 \, a^{3} b^{7} c^{7} d^{2} - 84 \, a^{4} b^{6} c^{6} d^{3} + 126 \, a^{5} b^{5} c^{5} d^{4} - 126 \, a^{6} b^{4} c^{4} d^{5} + 84 \, a^{7} b^{3} c^{3} d^{6} - 36 \, a^{8} b^{2} c^{2} d^{7} + 9 \, a^{9} b c d^{8} - a^{10} d^{9}\right)} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{3}{4}} + {\left(27 \, b^{4} c^{3} + 135 \, a b^{3} c^{2} d + 225 \, a^{2} b^{2} c d^{2} + 125 \, a^{3} b d^{3}\right)} \sqrt{x}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{1}{4}} \log\left(-{\left(a b^{9} c^{9} - 9 \, a^{2} b^{8} c^{8} d + 36 \, a^{3} b^{7} c^{7} d^{2} - 84 \, a^{4} b^{6} c^{6} d^{3} + 126 \, a^{5} b^{5} c^{5} d^{4} - 126 \, a^{6} b^{4} c^{4} d^{5} + 84 \, a^{7} b^{3} c^{3} d^{6} - 36 \, a^{8} b^{2} c^{2} d^{7} + 9 \, a^{9} b c d^{8} - a^{10} d^{9}\right)} \left(-\frac{81 \, b^{5} c^{4} + 540 \, a b^{4} c^{3} d + 1350 \, a^{2} b^{3} c^{2} d^{2} + 1500 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}}{a b^{12} c^{12} - 12 \, a^{2} b^{11} c^{11} d + 66 \, a^{3} b^{10} c^{10} d^{2} - 220 \, a^{4} b^{9} c^{9} d^{3} + 495 \, a^{5} b^{8} c^{8} d^{4} - 792 \, a^{6} b^{7} c^{7} d^{5} + 924 \, a^{7} b^{6} c^{6} d^{6} - 792 \, a^{8} b^{5} c^{5} d^{7} + 495 \, a^{9} b^{4} c^{4} d^{8} - 220 \, a^{10} b^{3} c^{3} d^{9} + 66 \, a^{11} b^{2} c^{2} d^{10} - 12 \, a^{12} b c d^{11} + a^{13} d^{12}}\right)^{\frac{3}{4}} + {\left(27 \, b^{4} c^{3} + 135 \, a b^{3} c^{2} d + 225 \, a^{2} b^{2} c d^{2} + 125 \, a^{3} b d^{3}\right)} \sqrt{x}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{1}{4}} \log\left({\left(b^{9} c^{10} - 9 \, a b^{8} c^{9} d + 36 \, a^{2} b^{7} c^{8} d^{2} - 84 \, a^{3} b^{6} c^{7} d^{3} + 126 \, a^{4} b^{5} c^{6} d^{4} - 126 \, a^{5} b^{4} c^{5} d^{5} + 84 \, a^{6} b^{3} c^{4} d^{6} - 36 \, a^{7} b^{2} c^{3} d^{7} + 9 \, a^{8} b c^{2} d^{8} - a^{9} c d^{9}\right)} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{3}{4}} + {\left(125 \, b^{3} c^{3} d + 225 \, a b^{2} c^{2} d^{2} + 135 \, a^{2} b c d^{3} + 27 \, a^{3} d^{4}\right)} \sqrt{x}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{9} c^{10} - 9 \, a b^{8} c^{9} d + 36 \, a^{2} b^{7} c^{8} d^{2} - 84 \, a^{3} b^{6} c^{7} d^{3} + 126 \, a^{4} b^{5} c^{6} d^{4} - 126 \, a^{5} b^{4} c^{5} d^{5} + 84 \, a^{6} b^{3} c^{4} d^{6} - 36 \, a^{7} b^{2} c^{3} d^{7} + 9 \, a^{8} b c^{2} d^{8} - a^{9} c d^{9}\right)} \left(-\frac{625 \, b^{4} c^{4} d + 1500 \, a b^{3} c^{3} d^{2} + 1350 \, a^{2} b^{2} c^{2} d^{3} + 540 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}}{b^{12} c^{13} - 12 \, a b^{11} c^{12} d + 66 \, a^{2} b^{10} c^{11} d^{2} - 220 \, a^{3} b^{9} c^{10} d^{3} + 495 \, a^{4} b^{8} c^{9} d^{4} - 792 \, a^{5} b^{7} c^{8} d^{5} + 924 \, a^{6} b^{6} c^{7} d^{6} - 792 \, a^{7} b^{5} c^{6} d^{7} + 495 \, a^{8} b^{4} c^{5} d^{8} - 220 \, a^{9} b^{3} c^{4} d^{9} + 66 \, a^{10} b^{2} c^{3} d^{10} - 12 \, a^{11} b c^{2} d^{11} + a^{12} c d^{12}}\right)^{\frac{3}{4}} + {\left(125 \, b^{3} c^{3} d + 225 \, a b^{2} c^{2} d^{2} + 135 \, a^{2} b c d^{3} + 27 \, a^{3} d^{4}\right)} \sqrt{x}\right) - 4 \, {\left(2 \, b d x^{3} + {\left(b c + a d\right)} x\right)} \sqrt{x}}{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/8*(4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(1/4)*arctan(-((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt((729*b^8*c^6 + 7290*a*b^7*c^5*d + 30375*a^2*b^6*c^4*d^2 + 67500*a^3*b^5*c^3*d^3 + 84375*a^4*b^4*c^2*d^4 + 56250*a^5*b^3*c*d^5 + 15625*a^6*b^2*d^6)*x - (81*a*b^11*c^10 + 54*a^2*b^10*c^9*d - 675*a^3*b^9*c^8*d^2 - 120*a^4*b^8*c^7*d^3 + 2290*a^5*b^7*c^6*d^4 - 636*a^6*b^6*c^5*d^5 - 3534*a^7*b^5*c^4*d^6 + 2440*a^8*b^4*c^3*d^7 + 1725*a^9*b^3*c^2*d^8 - 2250*a^10*b^2*c*d^9 + 625*a^11*b*d^10)*sqrt(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12)))*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(1/4) - (27*b^7*c^6 + 54*a*b^6*c^5*d - 99*a^2*b^5*c^4*d^2 - 172*a^3*b^4*c^3*d^3 + 165*a^4*b^3*c^2*d^4 + 150*a^5*b^2*c*d^5 - 125*a^6*b*d^6)*sqrt(x)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(1/4))/(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(1/4)*arctan(-((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt((15625*b^6*c^6*d^2 + 56250*a*b^5*c^5*d^3 + 84375*a^2*b^4*c^4*d^4 + 67500*a^3*b^3*c^3*d^5 + 30375*a^4*b^2*c^2*d^6 + 7290*a^5*b*c*d^7 + 729*a^6*d^8)*x - (625*b^10*c^11*d - 2250*a*b^9*c^10*d^2 + 1725*a^2*b^8*c^9*d^3 + 2440*a^3*b^7*c^8*d^4 - 3534*a^4*b^6*c^7*d^5 - 636*a^5*b^5*c^6*d^6 + 2290*a^6*b^4*c^5*d^7 - 120*a^7*b^3*c^4*d^8 - 675*a^8*b^2*c^3*d^9 + 54*a^9*b*c^2*d^10 + 81*a^10*c*d^11)*sqrt(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12)))*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(1/4) - (125*b^6*c^6*d - 150*a*b^5*c^5*d^2 - 165*a^2*b^4*c^4*d^3 + 172*a^3*b^3*c^3*d^4 + 99*a^4*b^2*c^2*d^5 - 54*a^5*b*c*d^6 - 27*a^6*d^7)*sqrt(x)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(1/4))/(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(1/4)*log((a*b^9*c^9 - 9*a^2*b^8*c^8*d + 36*a^3*b^7*c^7*d^2 - 84*a^4*b^6*c^6*d^3 + 126*a^5*b^5*c^5*d^4 - 126*a^6*b^4*c^4*d^5 + 84*a^7*b^3*c^3*d^6 - 36*a^8*b^2*c^2*d^7 + 9*a^9*b*c*d^8 - a^10*d^9)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(3/4) + (27*b^4*c^3 + 135*a*b^3*c^2*d + 225*a^2*b^2*c*d^2 + 125*a^3*b*d^3)*sqrt(x)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(1/4)*log(-(a*b^9*c^9 - 9*a^2*b^8*c^8*d + 36*a^3*b^7*c^7*d^2 - 84*a^4*b^6*c^6*d^3 + 126*a^5*b^5*c^5*d^4 - 126*a^6*b^4*c^4*d^5 + 84*a^7*b^3*c^3*d^6 - 36*a^8*b^2*c^2*d^7 + 9*a^9*b*c*d^8 - a^10*d^9)*(-(81*b^5*c^4 + 540*a*b^4*c^3*d + 1350*a^2*b^3*c^2*d^2 + 1500*a^3*b^2*c*d^3 + 625*a^4*b*d^4)/(a*b^12*c^12 - 12*a^2*b^11*c^11*d + 66*a^3*b^10*c^10*d^2 - 220*a^4*b^9*c^9*d^3 + 495*a^5*b^8*c^8*d^4 - 792*a^6*b^7*c^7*d^5 + 924*a^7*b^6*c^6*d^6 - 792*a^8*b^5*c^5*d^7 + 495*a^9*b^4*c^4*d^8 - 220*a^10*b^3*c^3*d^9 + 66*a^11*b^2*c^2*d^10 - 12*a^12*b*c*d^11 + a^13*d^12))^(3/4) + (27*b^4*c^3 + 135*a*b^3*c^2*d + 225*a^2*b^2*c*d^2 + 125*a^3*b*d^3)*sqrt(x)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(1/4)*log((b^9*c^10 - 9*a*b^8*c^9*d + 36*a^2*b^7*c^8*d^2 - 84*a^3*b^6*c^7*d^3 + 126*a^4*b^5*c^6*d^4 - 126*a^5*b^4*c^5*d^5 + 84*a^6*b^3*c^4*d^6 - 36*a^7*b^2*c^3*d^7 + 9*a^8*b*c^2*d^8 - a^9*c*d^9)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(3/4) + (125*b^3*c^3*d + 225*a*b^2*c^2*d^2 + 135*a^2*b*c*d^3 + 27*a^3*d^4)*sqrt(x)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(1/4)*log(-(b^9*c^10 - 9*a*b^8*c^9*d + 36*a^2*b^7*c^8*d^2 - 84*a^3*b^6*c^7*d^3 + 126*a^4*b^5*c^6*d^4 - 126*a^5*b^4*c^5*d^5 + 84*a^6*b^3*c^4*d^6 - 36*a^7*b^2*c^3*d^7 + 9*a^8*b*c^2*d^8 - a^9*c*d^9)*(-(625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4 + 81*a^4*d^5)/(b^12*c^13 - 12*a*b^11*c^12*d + 66*a^2*b^10*c^11*d^2 - 220*a^3*b^9*c^10*d^3 + 495*a^4*b^8*c^9*d^4 - 792*a^5*b^7*c^8*d^5 + 924*a^6*b^6*c^7*d^6 - 792*a^7*b^5*c^6*d^7 + 495*a^8*b^4*c^5*d^8 - 220*a^9*b^3*c^4*d^9 + 66*a^10*b^2*c^3*d^10 - 12*a^11*b*c^2*d^11 + a^12*c*d^12))^(3/4) + (125*b^3*c^3*d + 225*a*b^2*c^2*d^2 + 135*a^2*b*c*d^3 + 27*a^3*d^4)*sqrt(x)) - 4*(2*b*d*x^3 + (b*c + a*d)*x)*sqrt(x))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","B",0
490,1,5474,0,130.914015," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(a^{2} b^{9} c^{9} - 9 \, a^{3} b^{8} c^{8} d + 36 \, a^{4} b^{7} c^{7} d^{2} - 84 \, a^{5} b^{6} c^{6} d^{3} + 126 \, a^{6} b^{5} c^{5} d^{4} - 126 \, a^{7} b^{4} c^{4} d^{5} + 84 \, a^{8} b^{3} c^{3} d^{6} - 36 \, a^{9} b^{2} c^{2} d^{7} + 9 \, a^{10} b c d^{8} - a^{11} d^{9}\right)} \sqrt{{\left(b^{4} c^{2} + 14 \, a b^{3} c d + 49 \, a^{2} b^{2} d^{2}\right)} x + {\left(a^{2} b^{6} c^{6} - 6 \, a^{3} b^{5} c^{5} d + 15 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 15 \, a^{6} b^{2} c^{2} d^{4} - 6 \, a^{7} b c d^{5} + a^{8} d^{6}\right)} \sqrt{-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}}} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{3}{4}} - {\left(a^{2} b^{11} c^{10} - 2 \, a^{3} b^{10} c^{9} d - 27 \, a^{4} b^{9} c^{8} d^{2} + 168 \, a^{5} b^{8} c^{7} d^{3} - 462 \, a^{6} b^{7} c^{6} d^{4} + 756 \, a^{7} b^{6} c^{5} d^{5} - 798 \, a^{8} b^{5} c^{4} d^{6} + 552 \, a^{9} b^{4} c^{3} d^{7} - 243 \, a^{10} b^{3} c^{2} d^{8} + 62 \, a^{11} b^{2} c d^{9} - 7 \, a^{12} b d^{10}\right)} \sqrt{x} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{3}{4}}}{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{9} c^{11} - 9 \, a b^{8} c^{10} d + 36 \, a^{2} b^{7} c^{9} d^{2} - 84 \, a^{3} b^{6} c^{8} d^{3} + 126 \, a^{4} b^{5} c^{7} d^{4} - 126 \, a^{5} b^{4} c^{6} d^{5} + 84 \, a^{6} b^{3} c^{5} d^{6} - 36 \, a^{7} b^{2} c^{4} d^{7} + 9 \, a^{8} b c^{3} d^{8} - a^{9} c^{2} d^{9}\right)} \sqrt{{\left(49 \, b^{2} c^{2} d^{2} + 14 \, a b c d^{3} + a^{2} d^{4}\right)} x + {\left(b^{6} c^{8} - 6 \, a b^{5} c^{7} d + 15 \, a^{2} b^{4} c^{6} d^{2} - 20 \, a^{3} b^{3} c^{5} d^{3} + 15 \, a^{4} b^{2} c^{4} d^{4} - 6 \, a^{5} b c^{3} d^{5} + a^{6} c^{2} d^{6}\right)} \sqrt{-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}}} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{3}{4}} - {\left(7 \, b^{10} c^{12} d - 62 \, a b^{9} c^{11} d^{2} + 243 \, a^{2} b^{8} c^{10} d^{3} - 552 \, a^{3} b^{7} c^{9} d^{4} + 798 \, a^{4} b^{6} c^{8} d^{5} - 756 \, a^{5} b^{5} c^{7} d^{6} + 462 \, a^{6} b^{4} c^{6} d^{7} - 168 \, a^{7} b^{3} c^{5} d^{8} + 27 \, a^{8} b^{2} c^{4} d^{9} + 2 \, a^{9} b c^{3} d^{10} - a^{10} c^{2} d^{11}\right)} \sqrt{x} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{3}{4}}}{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{1}{4}} \log\left({\left(b^{2} c + 7 \, a b d\right)} \sqrt{x} + {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{1}{4}}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{1}{4}} \log\left({\left(b^{2} c + 7 \, a b d\right)} \sqrt{x} - {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b^{7} c^{4} + 28 \, a b^{6} c^{3} d + 294 \, a^{2} b^{5} c^{2} d^{2} + 1372 \, a^{3} b^{4} c d^{3} + 2401 \, a^{4} b^{3} d^{4}}{a^{3} b^{12} c^{12} - 12 \, a^{4} b^{11} c^{11} d + 66 \, a^{5} b^{10} c^{10} d^{2} - 220 \, a^{6} b^{9} c^{9} d^{3} + 495 \, a^{7} b^{8} c^{8} d^{4} - 792 \, a^{8} b^{7} c^{7} d^{5} + 924 \, a^{9} b^{6} c^{6} d^{6} - 792 \, a^{10} b^{5} c^{5} d^{7} + 495 \, a^{11} b^{4} c^{4} d^{8} - 220 \, a^{12} b^{3} c^{3} d^{9} + 66 \, a^{13} b^{2} c^{2} d^{10} - 12 \, a^{14} b c d^{11} + a^{15} d^{12}}\right)^{\frac{1}{4}}\right) + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{1}{4}} \log\left({\left(7 \, b c d + a d^{2}\right)} \sqrt{x} + {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{1}{4}}\right) - {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{1}{4}} \log\left({\left(7 \, b c d + a d^{2}\right)} \sqrt{x} - {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{2401 \, b^{4} c^{4} d^{3} + 1372 \, a b^{3} c^{3} d^{4} + 294 \, a^{2} b^{2} c^{2} d^{5} + 28 \, a^{3} b c d^{6} + a^{4} d^{7}}{b^{12} c^{15} - 12 \, a b^{11} c^{14} d + 66 \, a^{2} b^{10} c^{13} d^{2} - 220 \, a^{3} b^{9} c^{12} d^{3} + 495 \, a^{4} b^{8} c^{11} d^{4} - 792 \, a^{5} b^{7} c^{10} d^{5} + 924 \, a^{6} b^{6} c^{9} d^{6} - 792 \, a^{7} b^{5} c^{8} d^{7} + 495 \, a^{8} b^{4} c^{7} d^{8} - 220 \, a^{9} b^{3} c^{6} d^{9} + 66 \, a^{10} b^{2} c^{5} d^{10} - 12 \, a^{11} b c^{4} d^{11} + a^{12} c^{3} d^{12}}\right)^{\frac{1}{4}}\right) + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{x}}{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/8*(4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(1/4)*arctan(-((a^2*b^9*c^9 - 9*a^3*b^8*c^8*d + 36*a^4*b^7*c^7*d^2 - 84*a^5*b^6*c^6*d^3 + 126*a^6*b^5*c^5*d^4 - 126*a^7*b^4*c^4*d^5 + 84*a^8*b^3*c^3*d^6 - 36*a^9*b^2*c^2*d^7 + 9*a^10*b*c*d^8 - a^11*d^9)*sqrt((b^4*c^2 + 14*a*b^3*c*d + 49*a^2*b^2*d^2)*x + (a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5 + a^8*d^6)*sqrt(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12)))*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(3/4) - (a^2*b^11*c^10 - 2*a^3*b^10*c^9*d - 27*a^4*b^9*c^8*d^2 + 168*a^5*b^8*c^7*d^3 - 462*a^6*b^7*c^6*d^4 + 756*a^7*b^6*c^5*d^5 - 798*a^8*b^5*c^4*d^6 + 552*a^9*b^4*c^3*d^7 - 243*a^10*b^3*c^2*d^8 + 62*a^11*b^2*c*d^9 - 7*a^12*b*d^10)*sqrt(x)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(3/4))/(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(1/4)*arctan(-((b^9*c^11 - 9*a*b^8*c^10*d + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 + 9*a^8*b*c^3*d^8 - a^9*c^2*d^9)*sqrt((49*b^2*c^2*d^2 + 14*a*b*c*d^3 + a^2*d^4)*x + (b^6*c^8 - 6*a*b^5*c^7*d + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a^5*b*c^3*d^5 + a^6*c^2*d^6)*sqrt(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12)))*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(3/4) - (7*b^10*c^12*d - 62*a*b^9*c^11*d^2 + 243*a^2*b^8*c^10*d^3 - 552*a^3*b^7*c^9*d^4 + 798*a^4*b^6*c^8*d^5 - 756*a^5*b^5*c^7*d^6 + 462*a^6*b^4*c^6*d^7 - 168*a^7*b^3*c^5*d^8 + 27*a^8*b^2*c^4*d^9 + 2*a^9*b*c^3*d^10 - a^10*c^2*d^11)*sqrt(x)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(3/4))/(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(1/4)*log((b^2*c + 7*a*b*d)*sqrt(x) + (a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(1/4)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(1/4)*log((b^2*c + 7*a*b*d)*sqrt(x) - (a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-(b^7*c^4 + 28*a*b^6*c^3*d + 294*a^2*b^5*c^2*d^2 + 1372*a^3*b^4*c*d^3 + 2401*a^4*b^3*d^4)/(a^3*b^12*c^12 - 12*a^4*b^11*c^11*d + 66*a^5*b^10*c^10*d^2 - 220*a^6*b^9*c^9*d^3 + 495*a^7*b^8*c^8*d^4 - 792*a^8*b^7*c^7*d^5 + 924*a^9*b^6*c^6*d^6 - 792*a^10*b^5*c^5*d^7 + 495*a^11*b^4*c^4*d^8 - 220*a^12*b^3*c^3*d^9 + 66*a^13*b^2*c^2*d^10 - 12*a^14*b*c*d^11 + a^15*d^12))^(1/4)) + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(1/4)*log((7*b*c*d + a*d^2)*sqrt(x) + (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(1/4)) - (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(1/4)*log((7*b*c*d + a*d^2)*sqrt(x) - (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-(2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6 + a^4*d^7)/(b^12*c^15 - 12*a*b^11*c^14*d + 66*a^2*b^10*c^13*d^2 - 220*a^3*b^9*c^12*d^3 + 495*a^4*b^8*c^11*d^4 - 792*a^5*b^7*c^10*d^5 + 924*a^6*b^6*c^9*d^6 - 792*a^7*b^5*c^8*d^7 + 495*a^8*b^4*c^7*d^8 - 220*a^9*b^3*c^6*d^9 + 66*a^10*b^2*c^5*d^10 - 12*a^11*b*c^4*d^11 + a^12*c^3*d^12))^(1/4)) + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(x))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","B",0
491,-1,0,0,0.000000," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,1,99,0,1.371379," ","integrate(x^5*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, B b^{4} x^{8} + 5 \, {\left(B a b^{3} + 9 \, A b^{4}\right)} x^{6} - 16 \, B a^{4} + 24 \, A a^{3} b - 3 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{4} + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, b^{4}}"," ",0,"1/315*(35*B*b^4*x^8 + 5*(B*a*b^3 + 9*A*b^4)*x^6 - 16*B*a^4 + 24*A*a^3*b - 3*(2*B*a^2*b^2 - 3*A*a*b^3)*x^4 + 4*(2*B*a^3*b - 3*A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
505,1,257,0,1.107193," ","integrate(x^4*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, B b^{4} x^{7} + 8 \, {\left(B a b^{3} + 8 \, A b^{4}\right)} x^{5} - 2 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{4}}, \frac{3 \, {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(48 \, B b^{4} x^{7} + 8 \, {\left(B a b^{3} + 8 \, A b^{4}\right)} x^{5} - 2 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{4}}\right]"," ",0,"[-1/768*(3*(5*B*a^4 - 8*A*a^3*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*B*b^4*x^7 + 8*(B*a*b^3 + 8*A*b^4)*x^5 - 2*(5*B*a^2*b^2 - 8*A*a*b^3)*x^3 + 3*(5*B*a^3*b - 8*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^4, 1/384*(3*(5*B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (48*B*b^4*x^7 + 8*(B*a*b^3 + 8*A*b^4)*x^5 - 2*(5*B*a^2*b^2 - 8*A*a*b^3)*x^3 + 3*(5*B*a^3*b - 8*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^4]","A",0
506,1,75,0,1.289229," ","integrate(x^3*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, B b^{3} x^{6} + 3 \, {\left(B a b^{2} + 7 \, A b^{3}\right)} x^{4} + 8 \, B a^{3} - 14 \, A a^{2} b - {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, b^{3}}"," ",0,"1/105*(15*B*b^3*x^6 + 3*(B*a*b^2 + 7*A*b^3)*x^4 + 8*B*a^3 - 14*A*a^2*b - (4*B*a^2*b - 7*A*a*b^2)*x^2)*sqrt(b*x^2 + a)/b^3","A",0
507,1,206,0,0.809446," ","integrate(x^2*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, B b^{3} x^{5} + 2 \, {\left(B a b^{2} + 6 \, A b^{3}\right)} x^{3} - 3 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{3}}, -\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, B b^{3} x^{5} + 2 \, {\left(B a b^{2} + 6 \, A b^{3}\right)} x^{3} - 3 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{3}}\right]"," ",0,"[-1/96*(3*(B*a^3 - 2*A*a^2*b)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*B*b^3*x^5 + 2*(B*a*b^2 + 6*A*b^3)*x^3 - 3*(B*a^2*b - 2*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^3, -1/48*(3*(B*a^3 - 2*A*a^2*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*B*b^3*x^5 + 2*(B*a*b^2 + 6*A*b^3)*x^3 - 3*(B*a^2*b - 2*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
508,1,50,0,0.962243," ","integrate(x*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B b^{2} x^{4} - 2 \, B a^{2} + 5 \, A a b + {\left(B a b + 5 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, b^{2}}"," ",0,"1/15*(3*B*b^2*x^4 - 2*B*a^2 + 5*A*a*b + (B*a*b + 5*A*b^2)*x^2)*sqrt(b*x^2 + a)/b^2","A",0
509,1,155,0,0.929262," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(2 \, B b^{2} x^{3} + {\left(B a b + 4 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, b^{2}}, \frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B b^{2} x^{3} + {\left(B a b + 4 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, b^{2}}\right]"," ",0,"[-1/16*((B*a^2 - 4*A*a*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(2*B*b^2*x^3 + (B*a*b + 4*A*b^2)*x)*sqrt(b*x^2 + a))/b^2, 1/8*((B*a^2 - 4*A*a*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (2*B*b^2*x^3 + (B*a*b + 4*A*b^2)*x)*sqrt(b*x^2 + a))/b^2]","A",0
510,1,123,0,0.892150," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(B b x^{2} + B a + 3 \, A b\right)} \sqrt{b x^{2} + a}}{6 \, b}, \frac{3 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(B b x^{2} + B a + 3 \, A b\right)} \sqrt{b x^{2} + a}}{3 \, b}\right]"," ",0,"[1/6*(3*A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(B*b*x^2 + B*a + 3*A*b)*sqrt(b*x^2 + a))/b, 1/3*(3*A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (B*b*x^2 + B*a + 3*A*b)*sqrt(b*x^2 + a))/b]","A",0
511,1,134,0,0.951786," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a + 2 \, A b\right)} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(B b x^{2} - 2 \, A b\right)} \sqrt{b x^{2} + a}}{4 \, b x}, -\frac{{\left(B a + 2 \, A b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(B b x^{2} - 2 \, A b\right)} \sqrt{b x^{2} + a}}{2 \, b x}\right]"," ",0,"[1/4*((B*a + 2*A*b)*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(B*b*x^2 - 2*A*b)*sqrt(b*x^2 + a))/(b*x), -1/2*((B*a + 2*A*b)*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (B*b*x^2 - 2*A*b)*sqrt(b*x^2 + a))/(b*x)]","A",0
512,1,141,0,0.855241," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a + A b\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B a x^{2} - A a\right)} \sqrt{b x^{2} + a}}{4 \, a x^{2}}, \frac{{\left(2 \, B a + A b\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B a x^{2} - A a\right)} \sqrt{b x^{2} + a}}{2 \, a x^{2}}\right]"," ",0,"[1/4*((2*B*a + A*b)*sqrt(a)*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*a*x^2 - A*a)*sqrt(b*x^2 + a))/(a*x^2), 1/2*((2*B*a + A*b)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*B*a*x^2 - A*a)*sqrt(b*x^2 + a))/(a*x^2)]","A",0
513,1,137,0,0.881347," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, B a \sqrt{b} x^{3} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left({\left(3 \, B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a}}{6 \, a x^{3}}, -\frac{3 \, B a \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left({\left(3 \, B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a}}{3 \, a x^{3}}\right]"," ",0,"[1/6*(3*B*a*sqrt(b)*x^3*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*((3*B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a))/(a*x^3), -1/3*(3*B*a*sqrt(-b)*x^3*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + ((3*B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a))/(a*x^3)]","A",0
514,1,170,0,0.821495," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{a} x^{4} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, a^{2} x^{4}}, \frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, a^{2} x^{4}}\right]"," ",0,"[-1/16*((4*B*a*b - A*b^2)*sqrt(a)*x^4*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*A*a^2 + (4*B*a^2 + A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^4), 1/8*((4*B*a*b - A*b^2)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (2*A*a^2 + (4*B*a^2 + A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^4)]","A",0
515,1,55,0,0.911828," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{{\left({\left(5 \, B a b - 2 \, A b^{2}\right)} x^{4} + 3 \, A a^{2} + {\left(5 \, B a^{2} + A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, a^{2} x^{5}}"," ",0,"-1/15*((5*B*a*b - 2*A*b^2)*x^4 + 3*A*a^2 + (5*B*a^2 + A*a*b)*x^2)*sqrt(b*x^2 + a)/(a^2*x^5)","A",0
516,1,221,0,0.910863," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} \sqrt{a} x^{6} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, a^{3} x^{6}}, -\frac{3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, a^{3} x^{6}}\right]"," ",0,"[-1/96*(3*(2*B*a*b^2 - A*b^3)*sqrt(a)*x^6*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(2*B*a^2*b - A*a*b^2)*x^4 + 8*A*a^3 + 2*(6*B*a^3 + A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^6), -1/48*(3*(2*B*a*b^2 - A*b^3)*sqrt(-a)*x^6*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(2*B*a^2*b - A*a*b^2)*x^4 + 8*A*a^3 + 2*(6*B*a^3 + A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^6)]","A",0
517,1,81,0,0.883604," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^8,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(7 \, B a b^{2} - 4 \, A b^{3}\right)} x^{6} - {\left(7 \, B a^{2} b - 4 \, A a b^{2}\right)} x^{4} - 15 \, A a^{3} - 3 \, {\left(7 \, B a^{3} + A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, a^{3} x^{7}}"," ",0,"1/105*(2*(7*B*a*b^2 - 4*A*b^3)*x^6 - (7*B*a^2*b - 4*A*a*b^2)*x^4 - 15*A*a^3 - 3*(7*B*a^3 + A*a^2*b)*x^2)*sqrt(b*x^2 + a)/(a^3*x^7)","A",0
518,1,269,0,0.999328," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^9,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} \sqrt{a} x^{8} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(3 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{6} - 48 \, A a^{4} - 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{4} - 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{768 \, a^{4} x^{8}}, \frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} \sqrt{-a} x^{8} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{6} - 48 \, A a^{4} - 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{4} - 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{384 \, a^{4} x^{8}}\right]"," ",0,"[-1/768*(3*(8*B*a*b^3 - 5*A*b^4)*sqrt(a)*x^8*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(3*(8*B*a^2*b^2 - 5*A*a*b^3)*x^6 - 48*A*a^4 - 2*(8*B*a^3*b - 5*A*a^2*b^2)*x^4 - 8*(8*B*a^4 + A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^8), 1/384*(3*(8*B*a*b^3 - 5*A*b^4)*sqrt(-a)*x^8*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(8*B*a^2*b^2 - 5*A*a*b^3)*x^6 - 48*A*a^4 - 2*(8*B*a^3*b - 5*A*a^2*b^2)*x^4 - 8*(8*B*a^4 + A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^8)]","A",0
519,1,105,0,0.908173," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^10,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} x^{8} - 4 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{6} + 35 \, A a^{4} + 3 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{4} + 5 \, {\left(9 \, B a^{4} + A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, a^{4} x^{9}}"," ",0,"-1/315*(8*(3*B*a*b^3 - 2*A*b^4)*x^8 - 4*(3*B*a^2*b^2 - 2*A*a*b^3)*x^6 + 35*A*a^4 + 3*(3*B*a^3*b - 2*A*a^2*b^2)*x^4 + 5*(9*B*a^4 + A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^4*x^9)","A",0
520,1,317,0,1.094724," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^11,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5}\right)} \sqrt{a} x^{10} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(15 \, {\left(10 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{8} - 10 \, {\left(10 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{6} + 384 \, A a^{5} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{4} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{7680 \, a^{5} x^{10}}, -\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5}\right)} \sqrt{-a} x^{10} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, {\left(10 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{8} - 10 \, {\left(10 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{6} + 384 \, A a^{5} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{4} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3840 \, a^{5} x^{10}}\right]"," ",0,"[-1/7680*(15*(10*B*a*b^4 - 7*A*b^5)*sqrt(a)*x^10*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(15*(10*B*a^2*b^3 - 7*A*a*b^4)*x^8 - 10*(10*B*a^3*b^2 - 7*A*a^2*b^3)*x^6 + 384*A*a^5 + 8*(10*B*a^4*b - 7*A*a^3*b^2)*x^4 + 48*(10*B*a^5 + A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^5*x^10), -1/3840*(15*(10*B*a*b^4 - 7*A*b^5)*sqrt(-a)*x^10*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*(10*B*a^2*b^3 - 7*A*a*b^4)*x^8 - 10*(10*B*a^3*b^2 - 7*A*a^2*b^3)*x^6 + 384*A*a^5 + 8*(10*B*a^4*b - 7*A*a^3*b^2)*x^4 + 48*(10*B*a^5 + A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^5*x^10)]","A",0
521,1,124,0,0.850058," ","integrate(x^5*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(315 \, B b^{5} x^{10} + 35 \, {\left(12 \, B a b^{4} + 11 \, A b^{5}\right)} x^{8} + 5 \, {\left(3 \, B a^{2} b^{3} + 110 \, A a b^{4}\right)} x^{6} - 48 \, B a^{5} + 88 \, A a^{4} b - 3 \, {\left(6 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{4} + 4 \, {\left(6 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3465 \, b^{4}}"," ",0,"1/3465*(315*B*b^5*x^10 + 35*(12*B*a*b^4 + 11*A*b^5)*x^8 + 5*(3*B*a^2*b^3 + 110*A*a*b^4)*x^6 - 48*B*a^5 + 88*A*a^4*b - 3*(6*B*a^3*b^2 - 11*A*a^2*b^3)*x^4 + 4*(6*B*a^4*b - 11*A*a^3*b^2)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
522,1,299,0,1.028707," ","integrate(x^4*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{5} - 2 \, A a^{4} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(128 \, B b^{5} x^{9} + 16 \, {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} x^{7} + 8 \, {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} x^{5} - 10 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x^{3} + 15 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{2560 \, b^{4}}, \frac{15 \, {\left(B a^{5} - 2 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(128 \, B b^{5} x^{9} + 16 \, {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} x^{7} + 8 \, {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} x^{5} - 10 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x^{3} + 15 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{1280 \, b^{4}}\right]"," ",0,"[-1/2560*(15*(B*a^5 - 2*A*a^4*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(128*B*b^5*x^9 + 16*(11*B*a*b^4 + 10*A*b^5)*x^7 + 8*(B*a^2*b^3 + 30*A*a*b^4)*x^5 - 10*(B*a^3*b^2 - 2*A*a^2*b^3)*x^3 + 15*(B*a^4*b - 2*A*a^3*b^2)*x)*sqrt(b*x^2 + a))/b^4, 1/1280*(15*(B*a^5 - 2*A*a^4*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (128*B*b^5*x^9 + 16*(11*B*a*b^4 + 10*A*b^5)*x^7 + 8*(B*a^2*b^3 + 30*A*a*b^4)*x^5 - 10*(B*a^3*b^2 - 2*A*a^2*b^3)*x^3 + 15*(B*a^4*b - 2*A*a^3*b^2)*x)*sqrt(b*x^2 + a))/b^4]","A",0
523,1,99,0,0.838320," ","integrate(x^3*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(35 \, B b^{4} x^{8} + 5 \, {\left(10 \, B a b^{3} + 9 \, A b^{4}\right)} x^{6} + 8 \, B a^{4} - 18 \, A a^{3} b + 3 \, {\left(B a^{2} b^{2} + 24 \, A a b^{3}\right)} x^{4} - {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, b^{3}}"," ",0,"1/315*(35*B*b^4*x^8 + 5*(10*B*a*b^3 + 9*A*b^4)*x^6 + 8*B*a^4 - 18*A*a^3*b + 3*(B*a^2*b^2 + 24*A*a*b^3)*x^4 - (4*B*a^3*b - 9*A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/b^3","A",0
524,1,260,0,1.248790," ","integrate(x^2*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, B b^{4} x^{7} + 8 \, {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} x^{5} + 2 \, {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} x^{3} - 3 \, {\left(3 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{3}}, -\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(48 \, B b^{4} x^{7} + 8 \, {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} x^{5} + 2 \, {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} x^{3} - 3 \, {\left(3 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{3}}\right]"," ",0,"[-1/768*(3*(3*B*a^4 - 8*A*a^3*b)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*B*b^4*x^7 + 8*(9*B*a*b^3 + 8*A*b^4)*x^5 + 2*(3*B*a^2*b^2 + 56*A*a*b^3)*x^3 - 3*(3*B*a^3*b - 8*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^3, -1/384*(3*(3*B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (48*B*b^4*x^7 + 8*(9*B*a*b^3 + 8*A*b^4)*x^5 + 2*(3*B*a^2*b^2 + 56*A*a*b^3)*x^3 - 3*(3*B*a^3*b - 8*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
525,1,73,0,0.959446," ","integrate(x*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(5 \, B b^{3} x^{6} + {\left(8 \, B a b^{2} + 7 \, A b^{3}\right)} x^{4} - 2 \, B a^{3} + 7 \, A a^{2} b + {\left(B a^{2} b + 14 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{35 \, b^{2}}"," ",0,"1/35*(5*B*b^3*x^6 + (8*B*a*b^2 + 7*A*b^3)*x^4 - 2*B*a^3 + 7*A*a^2*b + (B*a^2*b + 14*A*a*b^2)*x^2)*sqrt(b*x^2 + a)/b^2","A",0
526,1,207,0,0.902624," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, B b^{3} x^{5} + 2 \, {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} x^{3} + 3 \, {\left(B a^{2} b + 10 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{2}}, \frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, B b^{3} x^{5} + 2 \, {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} x^{3} + 3 \, {\left(B a^{2} b + 10 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{2}}\right]"," ",0,"[-1/96*(3*(B*a^3 - 6*A*a^2*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*B*b^3*x^5 + 2*(7*B*a*b^2 + 6*A*b^3)*x^3 + 3*(B*a^2*b + 10*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^2, 1/48*(3*(B*a^3 - 6*A*a^2*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (8*B*b^3*x^5 + 2*(7*B*a*b^2 + 6*A*b^3)*x^3 + 3*(B*a^2*b + 10*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^2]","A",0
527,1,170,0,0.867574," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x,x, algorithm=""fricas"")","\left[\frac{15 \, A a^{\frac{3}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, B b^{2} x^{4} + 3 \, B a^{2} + 20 \, A a b + {\left(6 \, B a b + 5 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, b}, \frac{15 \, A \sqrt{-a} a b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, B b^{2} x^{4} + 3 \, B a^{2} + 20 \, A a b + {\left(6 \, B a b + 5 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, b}\right]"," ",0,"[1/30*(15*A*a^(3/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*B*b^2*x^4 + 3*B*a^2 + 20*A*a*b + (6*B*a*b + 5*A*b^2)*x^2)*sqrt(b*x^2 + a))/b, 1/15*(15*A*sqrt(-a)*a*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*B*b^2*x^4 + 3*B*a^2 + 20*A*a*b + (6*B*a*b + 5*A*b^2)*x^2)*sqrt(b*x^2 + a))/b]","A",0
528,1,182,0,0.709985," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(2 \, B b^{2} x^{4} - 8 \, A a b + {\left(5 \, B a b + 4 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, b x}, -\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, B b^{2} x^{4} - 8 \, A a b + {\left(5 \, B a b + 4 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, b x}\right]"," ",0,"[1/16*(3*(B*a^2 + 4*A*a*b)*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(2*B*b^2*x^4 - 8*A*a*b + (5*B*a*b + 4*A*b^2)*x^2)*sqrt(b*x^2 + a))/(b*x), -1/8*(3*(B*a^2 + 4*A*a*b)*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*B*b^2*x^4 - 8*A*a*b + (5*B*a*b + 4*A*b^2)*x^2)*sqrt(b*x^2 + a))/(b*x)]","A",0
529,1,167,0,0.909424," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, B b x^{4} + 2 \, {\left(4 \, B a + 3 \, A b\right)} x^{2} - 3 \, A a\right)} \sqrt{b x^{2} + a}}{12 \, x^{2}}, \frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, B b x^{4} + 2 \, {\left(4 \, B a + 3 \, A b\right)} x^{2} - 3 \, A a\right)} \sqrt{b x^{2} + a}}{6 \, x^{2}}\right]"," ",0,"[1/12*(3*(2*B*a + 3*A*b)*sqrt(a)*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*B*b*x^4 + 2*(4*B*a + 3*A*b)*x^2 - 3*A*a)*sqrt(b*x^2 + a))/x^2, 1/6*(3*(2*B*a + 3*A*b)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*B*b*x^4 + 2*(4*B*a + 3*A*b)*x^2 - 3*A*a)*sqrt(b*x^2 + a))/x^2]","A",0
530,1,166,0,0.978782," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B a + 2 \, A b\right)} \sqrt{b} x^{3} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(3 \, B b x^{4} - 2 \, {\left(3 \, B a + 4 \, A b\right)} x^{2} - 2 \, A a\right)} \sqrt{b x^{2} + a}}{12 \, x^{3}}, -\frac{3 \, {\left(3 \, B a + 2 \, A b\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(3 \, B b x^{4} - 2 \, {\left(3 \, B a + 4 \, A b\right)} x^{2} - 2 \, A a\right)} \sqrt{b x^{2} + a}}{6 \, x^{3}}\right]"," ",0,"[1/12*(3*(3*B*a + 2*A*b)*sqrt(b)*x^3*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(3*B*b*x^4 - 2*(3*B*a + 4*A*b)*x^2 - 2*A*a)*sqrt(b*x^2 + a))/x^3, -1/6*(3*(3*B*a + 2*A*b)*sqrt(-b)*x^3*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (3*B*b*x^4 - 2*(3*B*a + 4*A*b)*x^2 - 2*A*a)*sqrt(b*x^2 + a))/x^3]","A",0
531,1,189,0,0.935306," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{a} x^{4} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(8 \, B a b x^{4} - 2 \, A a^{2} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, a x^{4}}, \frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, B a b x^{4} - 2 \, A a^{2} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, a x^{4}}\right]"," ",0,"[1/16*(3*(4*B*a*b + A*b^2)*sqrt(a)*x^4*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(8*B*a*b*x^4 - 2*A*a^2 - (4*B*a^2 + 5*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a*x^4), 1/8*(3*(4*B*a*b + A*b^2)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (8*B*a*b*x^4 - 2*A*a^2 - (4*B*a^2 + 5*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a*x^4)]","A",0
532,1,184,0,0.818273," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, B a b^{\frac{3}{2}} x^{5} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left({\left(20 \, B a b + 3 \, A b^{2}\right)} x^{4} + 3 \, A a^{2} + {\left(5 \, B a^{2} + 6 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, a x^{5}}, -\frac{15 \, B a \sqrt{-b} b x^{5} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left({\left(20 \, B a b + 3 \, A b^{2}\right)} x^{4} + 3 \, A a^{2} + {\left(5 \, B a^{2} + 6 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, a x^{5}}\right]"," ",0,"[1/30*(15*B*a*b^(3/2)*x^5*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*((20*B*a*b + 3*A*b^2)*x^4 + 3*A*a^2 + (5*B*a^2 + 6*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a*x^5), -1/15*(15*B*a*sqrt(-b)*b*x^5*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + ((20*B*a*b + 3*A*b^2)*x^4 + 3*A*a^2 + (5*B*a^2 + 6*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a*x^5)]","A",0
533,1,222,0,0.982428," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B a b^{2} - A b^{3}\right)} \sqrt{a} x^{6} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, a^{2} x^{6}}, \frac{3 \, {\left(6 \, B a b^{2} - A b^{3}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(3 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, a^{2} x^{6}}\right]"," ",0,"[-1/96*(3*(6*B*a*b^2 - A*b^3)*sqrt(a)*x^6*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(10*B*a^2*b + A*a*b^2)*x^4 + 8*A*a^3 + 2*(6*B*a^3 + 7*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^6), 1/48*(3*(6*B*a*b^2 - A*b^3)*sqrt(-a)*x^6*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (3*(10*B*a^2*b + A*a*b^2)*x^4 + 8*A*a^3 + 2*(6*B*a^3 + 7*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^6)]","A",0
534,1,78,0,0.960493," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^8,x, algorithm=""fricas"")","-\frac{{\left({\left(7 \, B a b^{2} - 2 \, A b^{3}\right)} x^{6} + {\left(14 \, B a^{2} b + A a b^{2}\right)} x^{4} + 5 \, A a^{3} + {\left(7 \, B a^{3} + 8 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{35 \, a^{2} x^{7}}"," ",0,"-1/35*((7*B*a*b^2 - 2*A*b^3)*x^6 + (14*B*a^2*b + A*a*b^2)*x^4 + 5*A*a^3 + (7*B*a^3 + 8*A*a^2*b)*x^2)*sqrt(b*x^2 + a)/(a^2*x^7)","A",0
535,1,271,0,0.708948," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^9,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4}\right)} \sqrt{a} x^{8} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(8 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{6} + 48 \, A a^{4} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{4} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{768 \, a^{3} x^{8}}, -\frac{3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4}\right)} \sqrt{-a} x^{8} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(8 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{6} + 48 \, A a^{4} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{4} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{384 \, a^{3} x^{8}}\right]"," ",0,"[-1/768*(3*(8*B*a*b^3 - 3*A*b^4)*sqrt(a)*x^8*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(8*B*a^2*b^2 - 3*A*a*b^3)*x^6 + 48*A*a^4 + 2*(56*B*a^3*b + 3*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 9*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^8), -1/384*(3*(8*B*a*b^3 - 3*A*b^4)*sqrt(-a)*x^8*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(8*B*a^2*b^2 - 3*A*a*b^3)*x^6 + 48*A*a^4 + 2*(56*B*a^3*b + 3*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 9*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^8)]","A",0
536,1,105,0,0.996917," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^10,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(9 \, B a b^{3} - 4 \, A b^{4}\right)} x^{8} - {\left(9 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{6} - 35 \, A a^{4} - 3 \, {\left(24 \, B a^{3} b + A a^{2} b^{2}\right)} x^{4} - 5 \, {\left(9 \, B a^{4} + 10 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{315 \, a^{3} x^{9}}"," ",0,"1/315*(2*(9*B*a*b^3 - 4*A*b^4)*x^8 - (9*B*a^2*b^2 - 4*A*a*b^3)*x^6 - 35*A*a^4 - 3*(24*B*a^3*b + A*a^2*b^2)*x^4 - 5*(9*B*a^4 + 10*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^3*x^9)","A",0
537,1,317,0,1.078203," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^11,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{4} - A b^{5}\right)} \sqrt{a} x^{10} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(15 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} x^{8} - 10 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{6} - 128 \, A a^{5} - 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2}\right)} x^{4} - 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{2560 \, a^{4} x^{10}}, \frac{15 \, {\left(2 \, B a b^{4} - A b^{5}\right)} \sqrt{-a} x^{10} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} x^{8} - 10 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{6} - 128 \, A a^{5} - 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2}\right)} x^{4} - 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{1280 \, a^{4} x^{10}}\right]"," ",0,"[-1/2560*(15*(2*B*a*b^4 - A*b^5)*sqrt(a)*x^10*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(15*(2*B*a^2*b^3 - A*a*b^4)*x^8 - 10*(2*B*a^3*b^2 - A*a^2*b^3)*x^6 - 128*A*a^5 - 8*(30*B*a^4*b + A*a^3*b^2)*x^4 - 16*(10*B*a^5 + 11*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^10), 1/1280*(15*(2*B*a*b^4 - A*b^5)*sqrt(-a)*x^10*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*(2*B*a^2*b^3 - A*a*b^4)*x^8 - 10*(2*B*a^3*b^2 - A*a^2*b^3)*x^6 - 128*A*a^5 - 8*(30*B*a^4*b + A*a^3*b^2)*x^4 - 16*(10*B*a^5 + 11*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^10)]","A",0
538,1,147,0,0.678705," ","integrate(x^5*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(693 \, B b^{6} x^{12} + 63 \, {\left(27 \, B a b^{5} + 13 \, A b^{6}\right)} x^{10} + 7 \, {\left(159 \, B a^{2} b^{4} + 299 \, A a b^{5}\right)} x^{8} - 48 \, B a^{6} + 104 \, A a^{5} b + {\left(15 \, B a^{3} b^{3} + 1469 \, A a^{2} b^{4}\right)} x^{6} - 3 \, {\left(6 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{4} + 4 \, {\left(6 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{9009 \, b^{4}}"," ",0,"1/9009*(693*B*b^6*x^12 + 63*(27*B*a*b^5 + 13*A*b^6)*x^10 + 7*(159*B*a^2*b^4 + 299*A*a*b^5)*x^8 - 48*B*a^6 + 104*A*a^5*b + (15*B*a^3*b^3 + 1469*A*a^2*b^4)*x^6 - 3*(6*B*a^4*b^2 - 13*A*a^3*b^3)*x^4 + 4*(6*B*a^5*b - 13*A*a^4*b^2)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
539,1,355,0,1.057107," ","integrate(x^4*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(1280 \, B b^{6} x^{11} + 128 \, {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} x^{9} + 144 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} x^{7} + 8 \, {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} x^{5} - 10 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x^{3} + 15 \, {\left(5 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{30720 \, b^{4}}, \frac{15 \, {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(1280 \, B b^{6} x^{11} + 128 \, {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} x^{9} + 144 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} x^{7} + 8 \, {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} x^{5} - 10 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x^{3} + 15 \, {\left(5 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{15360 \, b^{4}}\right]"," ",0,"[-1/30720*(15*(5*B*a^6 - 12*A*a^5*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(1280*B*b^6*x^11 + 128*(25*B*a*b^5 + 12*A*b^6)*x^9 + 144*(15*B*a^2*b^4 + 28*A*a*b^5)*x^7 + 8*(5*B*a^3*b^3 + 372*A*a^2*b^4)*x^5 - 10*(5*B*a^4*b^2 - 12*A*a^3*b^3)*x^3 + 15*(5*B*a^5*b - 12*A*a^4*b^2)*x)*sqrt(b*x^2 + a))/b^4, 1/15360*(15*(5*B*a^6 - 12*A*a^5*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (1280*B*b^6*x^11 + 128*(25*B*a*b^5 + 12*A*b^6)*x^9 + 144*(15*B*a^2*b^4 + 28*A*a*b^5)*x^7 + 8*(5*B*a^3*b^3 + 372*A*a^2*b^4)*x^5 - 10*(5*B*a^4*b^2 - 12*A*a^3*b^3)*x^3 + 15*(5*B*a^5*b - 12*A*a^4*b^2)*x)*sqrt(b*x^2 + a))/b^4]","A",0
540,1,122,0,0.724420," ","integrate(x^3*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(63 \, B b^{5} x^{10} + 7 \, {\left(23 \, B a b^{4} + 11 \, A b^{5}\right)} x^{8} + {\left(113 \, B a^{2} b^{3} + 209 \, A a b^{4}\right)} x^{6} + 8 \, B a^{5} - 22 \, A a^{4} b + 3 \, {\left(B a^{3} b^{2} + 55 \, A a^{2} b^{3}\right)} x^{4} - {\left(4 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{693 \, b^{3}}"," ",0,"1/693*(63*B*b^5*x^10 + 7*(23*B*a*b^4 + 11*A*b^5)*x^8 + (113*B*a^2*b^3 + 209*A*a*b^4)*x^6 + 8*B*a^5 - 22*A*a^4*b + 3*(B*a^3*b^2 + 55*A*a^2*b^3)*x^4 - (4*B*a^4*b - 11*A*a^3*b^2)*x^2)*sqrt(b*x^2 + a)/b^3","A",0
541,1,308,0,1.137008," ","integrate(x^2*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(384 \, B b^{5} x^{9} + 48 \, {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} x^{7} + 8 \, {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} x^{5} + 10 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} x^{3} - 15 \, {\left(3 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{7680 \, b^{3}}, -\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(384 \, B b^{5} x^{9} + 48 \, {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} x^{7} + 8 \, {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} x^{5} + 10 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} x^{3} - 15 \, {\left(3 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{3840 \, b^{3}}\right]"," ",0,"[-1/7680*(15*(3*B*a^5 - 10*A*a^4*b)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(384*B*b^5*x^9 + 48*(21*B*a*b^4 + 10*A*b^5)*x^7 + 8*(93*B*a^2*b^3 + 170*A*a*b^4)*x^5 + 10*(3*B*a^3*b^2 + 118*A*a^2*b^3)*x^3 - 15*(3*B*a^4*b - 10*A*a^3*b^2)*x)*sqrt(b*x^2 + a))/b^3, -1/3840*(15*(3*B*a^5 - 10*A*a^4*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (384*B*b^5*x^9 + 48*(21*B*a*b^4 + 10*A*b^5)*x^7 + 8*(93*B*a^2*b^3 + 170*A*a*b^4)*x^5 + 10*(3*B*a^3*b^2 + 118*A*a^2*b^3)*x^3 - 15*(3*B*a^4*b - 10*A*a^3*b^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
542,1,97,0,0.913193," ","integrate(x*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\frac{{\left(7 \, B b^{4} x^{8} + {\left(19 \, B a b^{3} + 9 \, A b^{4}\right)} x^{6} - 2 \, B a^{4} + 9 \, A a^{3} b + 3 \, {\left(5 \, B a^{2} b^{2} + 9 \, A a b^{3}\right)} x^{4} + {\left(B a^{3} b + 27 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{63 \, b^{2}}"," ",0,"1/63*(7*B*b^4*x^8 + (19*B*a*b^3 + 9*A*b^4)*x^6 - 2*B*a^4 + 9*A*a^3*b + 3*(5*B*a^2*b^2 + 9*A*a*b^3)*x^4 + (B*a^3*b + 27*A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/b^2","B",0
543,1,257,0,1.091095," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(48 \, B b^{4} x^{7} + 8 \, {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} x^{5} + 2 \, {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} b + 88 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{768 \, b^{2}}, \frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(48 \, B b^{4} x^{7} + 8 \, {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} x^{5} + 2 \, {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{3} b + 88 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{384 \, b^{2}}\right]"," ",0,"[-1/768*(15*(B*a^4 - 8*A*a^3*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(48*B*b^4*x^7 + 8*(17*B*a*b^3 + 8*A*b^4)*x^5 + 2*(59*B*a^2*b^2 + 104*A*a*b^3)*x^3 + 3*(5*B*a^3*b + 88*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^2, 1/384*(15*(B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (48*B*b^4*x^7 + 8*(17*B*a*b^3 + 8*A*b^4)*x^5 + 2*(59*B*a^2*b^2 + 104*A*a*b^3)*x^3 + 3*(5*B*a^3*b + 88*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/b^2]","A",0
544,1,220,0,1.105072," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x,x, algorithm=""fricas"")","\left[\frac{105 \, A a^{\frac{5}{2}} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(15 \, B b^{3} x^{6} + 3 \, {\left(15 \, B a b^{2} + 7 \, A b^{3}\right)} x^{4} + 15 \, B a^{3} + 161 \, A a^{2} b + {\left(45 \, B a^{2} b + 77 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{210 \, b}, \frac{105 \, A \sqrt{-a} a^{2} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, B b^{3} x^{6} + 3 \, {\left(15 \, B a b^{2} + 7 \, A b^{3}\right)} x^{4} + 15 \, B a^{3} + 161 \, A a^{2} b + {\left(45 \, B a^{2} b + 77 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, b}\right]"," ",0,"[1/210*(105*A*a^(5/2)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(15*B*b^3*x^6 + 3*(15*B*a*b^2 + 7*A*b^3)*x^4 + 15*B*a^3 + 161*A*a^2*b + (45*B*a^2*b + 77*A*a*b^2)*x^2)*sqrt(b*x^2 + a))/b, 1/105*(105*A*sqrt(-a)*a^2*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*B*b^3*x^6 + 3*(15*B*a*b^2 + 7*A*b^3)*x^4 + 15*B*a^3 + 161*A*a^2*b + (45*B*a^2*b + 77*A*a*b^2)*x^2)*sqrt(b*x^2 + a))/b]","A",0
545,1,236,0,1.128042," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(8 \, B b^{3} x^{6} + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{4} - 48 \, A a^{2} b + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, b x}, -\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(8 \, B b^{3} x^{6} + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{4} - 48 \, A a^{2} b + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, b x}\right]"," ",0,"[1/96*(15*(B*a^3 + 6*A*a^2*b)*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(8*B*b^3*x^6 + 2*(13*B*a*b^2 + 6*A*b^3)*x^4 - 48*A*a^2*b + 3*(11*B*a^2*b + 18*A*a*b^2)*x^2)*sqrt(b*x^2 + a))/(b*x), -1/48*(15*(B*a^3 + 6*A*a^2*b)*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (8*B*b^3*x^6 + 2*(13*B*a*b^2 + 6*A*b^3)*x^4 - 48*A*a^2*b + 3*(11*B*a^2*b + 18*A*a*b^2)*x^2)*sqrt(b*x^2 + a))/(b*x)]","A",0
546,1,221,0,1.196657," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(6 \, B b^{2} x^{6} + 2 \, {\left(11 \, B a b + 5 \, A b^{2}\right)} x^{4} - 15 \, A a^{2} + 2 \, {\left(23 \, B a^{2} + 35 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{60 \, x^{2}}, \frac{15 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(6 \, B b^{2} x^{6} + 2 \, {\left(11 \, B a b + 5 \, A b^{2}\right)} x^{4} - 15 \, A a^{2} + 2 \, {\left(23 \, B a^{2} + 35 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, x^{2}}\right]"," ",0,"[1/60*(15*(2*B*a^2 + 5*A*a*b)*sqrt(a)*x^2*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(6*B*b^2*x^6 + 2*(11*B*a*b + 5*A*b^2)*x^4 - 15*A*a^2 + 2*(23*B*a^2 + 35*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^2, 1/30*(15*(2*B*a^2 + 5*A*a*b)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (6*B*b^2*x^6 + 2*(11*B*a*b + 5*A*b^2)*x^4 - 15*A*a^2 + 2*(23*B*a^2 + 35*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^2]","A",0
547,1,220,0,0.883461," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, B a^{2} + 4 \, A a b\right)} \sqrt{b} x^{3} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(6 \, B b^{2} x^{6} + 3 \, {\left(9 \, B a b + 4 \, A b^{2}\right)} x^{4} - 8 \, A a^{2} - 8 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, x^{3}}, -\frac{15 \, {\left(3 \, B a^{2} + 4 \, A a b\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, B b^{2} x^{6} + 3 \, {\left(9 \, B a b + 4 \, A b^{2}\right)} x^{4} - 8 \, A a^{2} - 8 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{24 \, x^{3}}\right]"," ",0,"[1/48*(15*(3*B*a^2 + 4*A*a*b)*sqrt(b)*x^3*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(6*B*b^2*x^6 + 3*(9*B*a*b + 4*A*b^2)*x^4 - 8*A*a^2 - 8*(3*B*a^2 + 7*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^3, -1/24*(15*(3*B*a^2 + 4*A*a*b)*sqrt(-b)*x^3*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (6*B*b^2*x^6 + 3*(9*B*a*b + 4*A*b^2)*x^4 - 8*A*a^2 - 8*(3*B*a^2 + 7*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^3]","A",0
548,1,221,0,0.941137," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} \sqrt{a} x^{4} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(8 \, B b^{2} x^{6} + 8 \, {\left(7 \, B a b + 3 \, A b^{2}\right)} x^{4} - 6 \, A a^{2} - 3 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, x^{4}}, \frac{15 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, B b^{2} x^{6} + 8 \, {\left(7 \, B a b + 3 \, A b^{2}\right)} x^{4} - 6 \, A a^{2} - 3 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{24 \, x^{4}}\right]"," ",0,"[1/48*(15*(4*B*a*b + 3*A*b^2)*sqrt(a)*x^4*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(8*B*b^2*x^6 + 8*(7*B*a*b + 3*A*b^2)*x^4 - 6*A*a^2 - 3*(4*B*a^2 + 9*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^4, 1/24*(15*(4*B*a*b + 3*A*b^2)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (8*B*b^2*x^6 + 8*(7*B*a*b + 3*A*b^2)*x^4 - 6*A*a^2 - 3*(4*B*a^2 + 9*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^4]","A",0
549,1,220,0,1.118392," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} \sqrt{b} x^{5} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) + 2 \, {\left(15 \, B b^{2} x^{6} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} x^{4} - 6 \, A a^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{60 \, x^{5}}, -\frac{15 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} \sqrt{-b} x^{5} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(15 \, B b^{2} x^{6} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} x^{4} - 6 \, A a^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{30 \, x^{5}}\right]"," ",0,"[1/60*(15*(5*B*a*b + 2*A*b^2)*sqrt(b)*x^5*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) + 2*(15*B*b^2*x^6 - 2*(35*B*a*b + 23*A*b^2)*x^4 - 6*A*a^2 - 2*(5*B*a^2 + 11*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^5, -1/30*(15*(5*B*a*b + 2*A*b^2)*sqrt(-b)*x^5*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (15*B*b^2*x^6 - 2*(35*B*a*b + 23*A*b^2)*x^4 - 6*A*a^2 - 2*(5*B*a^2 + 11*A*a*b)*x^2)*sqrt(b*x^2 + a))/x^5]","A",0
550,1,241,0,1.031683," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(6 \, B a b^{2} + A b^{3}\right)} \sqrt{a} x^{6} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(48 \, B a b^{2} x^{6} - 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, a x^{6}}, \frac{15 \, {\left(6 \, B a b^{2} + A b^{3}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(48 \, B a b^{2} x^{6} - 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, a x^{6}}\right]"," ",0,"[1/96*(15*(6*B*a*b^2 + A*b^3)*sqrt(a)*x^6*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(48*B*a*b^2*x^6 - 3*(18*B*a^2*b + 11*A*a*b^2)*x^4 - 8*A*a^3 - 2*(6*B*a^3 + 13*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a*x^6), 1/48*(15*(6*B*a*b^2 + A*b^3)*sqrt(-a)*x^6*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (48*B*a*b^2*x^6 - 3*(18*B*a^2*b + 11*A*a*b^2)*x^4 - 8*A*a^3 - 2*(6*B*a^3 + 13*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a*x^6)]","A",0
551,1,234,0,0.853913," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^8,x, algorithm=""fricas"")","\left[\frac{105 \, B a b^{\frac{5}{2}} x^{7} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left({\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} x^{6} + {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} x^{4} + 15 \, A a^{3} + 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{210 \, a x^{7}}, -\frac{105 \, B a \sqrt{-b} b^{2} x^{7} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left({\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} x^{6} + {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} x^{4} + 15 \, A a^{3} + 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, a x^{7}}\right]"," ",0,"[1/210*(105*B*a*b^(5/2)*x^7*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*((161*B*a*b^2 + 15*A*b^3)*x^6 + (77*B*a^2*b + 45*A*a*b^2)*x^4 + 15*A*a^3 + 3*(7*B*a^3 + 15*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a*x^7), -1/105*(105*B*a*sqrt(-b)*b^2*x^7*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + ((161*B*a*b^2 + 15*A*b^3)*x^6 + (77*B*a^2*b + 45*A*a*b^2)*x^4 + 15*A*a^3 + 3*(7*B*a^3 + 15*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a*x^7)]","A",0
552,1,272,0,0.938710," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, B a b^{3} - A b^{4}\right)} \sqrt{a} x^{8} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{6} + 48 \, A a^{4} + 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right)} x^{4} + 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{768 \, a^{2} x^{8}}, \frac{15 \, {\left(8 \, B a b^{3} - A b^{4}\right)} \sqrt{-a} x^{8} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(3 \, {\left(88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{6} + 48 \, A a^{4} + 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right)} x^{4} + 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{384 \, a^{2} x^{8}}\right]"," ",0,"[-1/768*(15*(8*B*a*b^3 - A*b^4)*sqrt(a)*x^8*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(88*B*a^2*b^2 + 5*A*a*b^3)*x^6 + 48*A*a^4 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 17*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^8), 1/384*(15*(8*B*a*b^3 - A*b^4)*sqrt(-a)*x^8*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (3*(88*B*a^2*b^2 + 5*A*a*b^3)*x^6 + 48*A*a^4 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 17*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^2*x^8)]","A",0
553,1,102,0,1.114039," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^10,x, algorithm=""fricas"")","-\frac{{\left({\left(9 \, B a b^{3} - 2 \, A b^{4}\right)} x^{8} + {\left(27 \, B a^{2} b^{2} + A a b^{3}\right)} x^{6} + 7 \, A a^{4} + 3 \, {\left(9 \, B a^{3} b + 5 \, A a^{2} b^{2}\right)} x^{4} + {\left(9 \, B a^{4} + 19 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{63 \, a^{2} x^{9}}"," ",0,"-1/63*((9*B*a*b^3 - 2*A*b^4)*x^8 + (27*B*a^2*b^2 + A*a*b^3)*x^6 + 7*A*a^4 + 3*(9*B*a^3*b + 5*A*a^2*b^2)*x^4 + (9*B*a^4 + 19*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^2*x^9)","B",0
554,1,319,0,0.977105," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^11,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5}\right)} \sqrt{a} x^{10} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(15 \, {\left(10 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{8} + 10 \, {\left(118 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{6} + 384 \, A a^{5} + 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2}\right)} x^{4} + 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{7680 \, a^{3} x^{10}}, -\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5}\right)} \sqrt{-a} x^{10} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, {\left(10 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{8} + 10 \, {\left(118 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{6} + 384 \, A a^{5} + 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2}\right)} x^{4} + 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3840 \, a^{3} x^{10}}\right]"," ",0,"[-1/7680*(15*(10*B*a*b^4 - 3*A*b^5)*sqrt(a)*x^10*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(15*(10*B*a^2*b^3 - 3*A*a*b^4)*x^8 + 10*(118*B*a^3*b^2 + 3*A*a^2*b^3)*x^6 + 384*A*a^5 + 8*(170*B*a^4*b + 93*A*a^3*b^2)*x^4 + 48*(10*B*a^5 + 21*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^10), -1/3840*(15*(10*B*a*b^4 - 3*A*b^5)*sqrt(-a)*x^10*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*(10*B*a^2*b^3 - 3*A*a*b^4)*x^8 + 10*(118*B*a^3*b^2 + 3*A*a^2*b^3)*x^6 + 384*A*a^5 + 8*(170*B*a^4*b + 93*A*a^3*b^2)*x^4 + 48*(10*B*a^5 + 21*A*a^4*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^10)]","A",0
555,1,76,0,1.021339," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, B b^{3} x^{6} - 3 \, {\left(6 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} - 48 \, B a^{3} + 56 \, A a^{2} b + 4 \, {\left(6 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, b^{4}}"," ",0,"1/105*(15*B*b^3*x^6 - 3*(6*B*a*b^2 - 7*A*b^3)*x^4 - 48*B*a^3 + 56*A*a^2*b + 4*(6*B*a^2*b - 7*A*a*b^2)*x^2)*sqrt(b*x^2 + a)/b^4","A",0
556,1,211,0,0.988815," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, B b^{3} x^{5} - 2 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, b^{4}}, \frac{3 \, {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, B b^{3} x^{5} - 2 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, b^{4}}\right]"," ",0,"[-1/96*(3*(5*B*a^3 - 6*A*a^2*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*B*b^3*x^5 - 2*(5*B*a*b^2 - 6*A*b^3)*x^3 + 3*(5*B*a^2*b - 6*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^4, 1/48*(3*(5*B*a^3 - 6*A*a^2*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (8*B*b^3*x^5 - 2*(5*B*a*b^2 - 6*A*b^3)*x^3 + 3*(5*B*a^2*b - 6*A*a*b^2)*x)*sqrt(b*x^2 + a))/b^4]","A",0
557,1,52,0,0.845033," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B b^{2} x^{4} + 8 \, B a^{2} - 10 \, A a b - {\left(4 \, B a b - 5 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, b^{3}}"," ",0,"1/15*(3*B*b^2*x^4 + 8*B*a^2 - 10*A*a*b - (4*B*a*b - 5*A*b^2)*x^2)*sqrt(b*x^2 + a)/b^3","A",0
558,1,162,0,0.706667," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(2 \, B b^{2} x^{3} - {\left(3 \, B a b - 4 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, b^{3}}, -\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, B b^{2} x^{3} - {\left(3 \, B a b - 4 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, b^{3}}\right]"," ",0,"[-1/16*((3*B*a^2 - 4*A*a*b)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(2*B*b^2*x^3 - (3*B*a*b - 4*A*b^2)*x)*sqrt(b*x^2 + a))/b^3, -1/8*((3*B*a^2 - 4*A*a*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*B*b^2*x^3 - (3*B*a*b - 4*A*b^2)*x)*sqrt(b*x^2 + a))/b^3]","A",0
559,1,29,0,0.830100," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(B b x^{2} - 2 \, B a + 3 \, A b\right)} \sqrt{b x^{2} + a}}{3 \, b^{2}}"," ",0,"1/3*(B*b*x^2 - 2*B*a + 3*A*b)*sqrt(b*x^2 + a)/b^2","A",0
560,1,110,0,1.120046," ","integrate((B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x^{2} + a} B b x - {\left(B a - 2 \, A b\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{4 \, b^{2}}, \frac{\sqrt{b x^{2} + a} B b x + {\left(B a - 2 \, A b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*sqrt(b*x^2 + a)*B*b*x - (B*a - 2*A*b)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/b^2, 1/2*(sqrt(b*x^2 + a)*B*b*x + (B*a - 2*A*b)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/b^2]","A",0
561,1,102,0,0.966092," ","integrate((B*x^2+A)/x/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{a} b \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, \sqrt{b x^{2} + a} B a}{2 \, a b}, \frac{A \sqrt{-a} b \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + \sqrt{b x^{2} + a} B a}{a b}\right]"," ",0,"[1/2*(A*sqrt(a)*b*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*sqrt(b*x^2 + a)*B*a)/(a*b), (A*sqrt(-a)*b*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + sqrt(b*x^2 + a)*B*a)/(a*b)]","A",0
562,1,109,0,0.672039," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{b} x \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, \sqrt{b x^{2} + a} A b}{2 \, a b x}, -\frac{B a \sqrt{-b} x \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + \sqrt{b x^{2} + a} A b}{a b x}\right]"," ",0,"[1/2*(B*a*sqrt(b)*x*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*sqrt(b*x^2 + a)*A*b)/(a*b*x), -(B*a*sqrt(-b)*x*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + sqrt(b*x^2 + a)*A*b)/(a*b*x)]","A",0
563,1,124,0,0.888100," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{a} x^{2} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, \sqrt{b x^{2} + a} A a}{4 \, a^{2} x^{2}}, \frac{{\left(2 \, B a - A b\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - \sqrt{b x^{2} + a} A a}{2 \, a^{2} x^{2}}\right]"," ",0,"[-1/4*((2*B*a - A*b)*sqrt(a)*x^2*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*sqrt(b*x^2 + a)*A*a)/(a^2*x^2), 1/2*((2*B*a - A*b)*sqrt(-a)*x^2*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - sqrt(b*x^2 + a)*A*a)/(a^2*x^2)]","A",0
564,1,34,0,0.990240," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(3 \, B a - 2 \, A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a}}{3 \, a^{2} x^{3}}"," ",0,"-1/3*((3*B*a - 2*A*b)*x^2 + A*a)*sqrt(b*x^2 + a)/(a^2*x^3)","A",0
565,1,171,0,1.079353," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{a} x^{4} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, a^{3} x^{4}}, -\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, a^{3} x^{4}}\right]"," ",0,"[-1/16*((4*B*a*b - 3*A*b^2)*sqrt(a)*x^4*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^4), -1/8*((4*B*a*b - 3*A*b^2)*sqrt(-a)*x^4*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^3*x^4)]","A",0
566,1,58,0,1.163503," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(5 \, B a b - 4 \, A b^{2}\right)} x^{4} - 3 \, A a^{2} - {\left(5 \, B a^{2} - 4 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, a^{3} x^{5}}"," ",0,"1/15*(2*(5*B*a*b - 4*A*b^2)*x^4 - 3*A*a^2 - (5*B*a^2 - 4*A*a*b)*x^2)*sqrt(b*x^2 + a)/(a^3*x^5)","A",0
567,1,223,0,0.740403," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} \sqrt{a} x^{6} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(3 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, a^{4} x^{6}}, \frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} - 8 \, A a^{3} - 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, a^{4} x^{6}}\right]"," ",0,"[-1/96*(3*(6*B*a*b^2 - 5*A*b^3)*sqrt(a)*x^6*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(3*(6*B*a^2*b - 5*A*a*b^2)*x^4 - 8*A*a^3 - 2*(6*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^6), 1/48*(3*(6*B*a*b^2 - 5*A*b^3)*sqrt(-a)*x^6*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(6*B*a^2*b - 5*A*a*b^2)*x^4 - 8*A*a^3 - 2*(6*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*x^6)]","A",0
568,1,82,0,1.062368," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(7 \, B a b^{2} - 6 \, A b^{3}\right)} x^{6} - 4 \, {\left(7 \, B a^{2} b - 6 \, A a b^{2}\right)} x^{4} + 15 \, A a^{3} + 3 \, {\left(7 \, B a^{3} - 6 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{105 \, a^{4} x^{7}}"," ",0,"-1/105*(8*(7*B*a*b^2 - 6*A*b^3)*x^6 - 4*(7*B*a^2*b - 6*A*a*b^2)*x^4 + 15*A*a^3 + 3*(7*B*a^3 - 6*A*a^2*b)*x^2)*sqrt(b*x^2 + a)/(a^4*x^7)","A",0
569,1,325,0,1.152230," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{4} - 6 \, A a^{3} b + {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(8 \, B b^{4} x^{7} - 2 \, {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} x^{5} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} x^{3} + 15 \, {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{96 \, {\left(b^{6} x^{2} + a b^{5}\right)}}, \frac{15 \, {\left(7 \, B a^{4} - 6 \, A a^{3} b + {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(8 \, B b^{4} x^{7} - 2 \, {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} x^{5} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} x^{3} + 15 \, {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, {\left(b^{6} x^{2} + a b^{5}\right)}}\right]"," ",0,"[-1/96*(15*(7*B*a^4 - 6*A*a^3*b + (7*B*a^3*b - 6*A*a^2*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(8*B*b^4*x^7 - 2*(7*B*a*b^3 - 6*A*b^4)*x^5 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*x^3 + 15*(7*B*a^3*b - 6*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/(b^6*x^2 + a*b^5), 1/48*(15*(7*B*a^4 - 6*A*a^3*b + (7*B*a^3*b - 6*A*a^2*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (8*B*b^4*x^7 - 2*(7*B*a*b^3 - 6*A*b^4)*x^5 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*x^3 + 15*(7*B*a^3*b - 6*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/(b^6*x^2 + a*b^5)]","A",0
570,1,88,0,0.714616," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B b^{3} x^{6} - {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} x^{4} + 48 \, B a^{3} - 40 \, A a^{2} b + 4 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, {\left(b^{5} x^{2} + a b^{4}\right)}}"," ",0,"1/15*(3*B*b^3*x^6 - (6*B*a*b^2 - 5*A*b^3)*x^4 + 48*B*a^3 - 40*A*a^2*b + 4*(6*B*a^2*b - 5*A*a*b^2)*x^2)*sqrt(b*x^2 + a)/(b^5*x^2 + a*b^4)","A",0
571,1,274,0,1.079075," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{3} - 4 \, A a^{2} b + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(2 \, B b^{3} x^{5} - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} x^{3} - 3 \, {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, -\frac{3 \, {\left(5 \, B a^{3} - 4 \, A a^{2} b + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(2 \, B b^{3} x^{5} - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} x^{3} - 3 \, {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{8 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[-1/16*(3*(5*B*a^3 - 4*A*a^2*b + (5*B*a^2*b - 4*A*a*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(2*B*b^3*x^5 - (5*B*a*b^2 - 4*A*b^3)*x^3 - 3*(5*B*a^2*b - 4*A*a*b^2)*x)*sqrt(b*x^2 + a))/(b^5*x^2 + a*b^4), -1/8*(3*(5*B*a^3 - 4*A*a^2*b + (5*B*a^2*b - 4*A*a*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (2*B*b^3*x^5 - (5*B*a*b^2 - 4*A*b^3)*x^3 - 3*(5*B*a^2*b - 4*A*a*b^2)*x)*sqrt(b*x^2 + a))/(b^5*x^2 + a*b^4)]","A",0
572,1,63,0,0.872121," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(B b^{2} x^{4} - 8 \, B a^{2} + 6 \, A a b - {\left(4 \, B a b - 3 \, A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(b^{4} x^{2} + a b^{3}\right)}}"," ",0,"1/3*(B*b^2*x^4 - 8*B*a^2 + 6*A*a*b - (4*B*a*b - 3*A*b^2)*x^2)*sqrt(b*x^2 + a)/(b^4*x^2 + a*b^3)","A",0
573,1,213,0,0.713082," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{2} - 2 \, A a b + {\left(3 \, B a b - 2 \, A b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(B b^{2} x^{3} + {\left(3 \, B a b - 2 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{4 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{{\left(3 \, B a^{2} - 2 \, A a b + {\left(3 \, B a b - 2 \, A b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(B b^{2} x^{3} + {\left(3 \, B a b - 2 \, A b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[-1/4*((3*B*a^2 - 2*A*a*b + (3*B*a*b - 2*A*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(B*b^2*x^3 + (3*B*a*b - 2*A*b^2)*x)*sqrt(b*x^2 + a))/(b^4*x^2 + a*b^3), 1/2*((3*B*a^2 - 2*A*a*b + (3*B*a*b - 2*A*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (B*b^2*x^3 + (3*B*a*b - 2*A*b^2)*x)*sqrt(b*x^2 + a))/(b^4*x^2 + a*b^3)]","A",0
574,1,40,0,1.062965," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(B b x^{2} + 2 \, B a - A b\right)} \sqrt{b x^{2} + a}}{b^{3} x^{2} + a b^{2}}"," ",0,"(B*b*x^2 + 2*B*a - A*b)*sqrt(b*x^2 + a)/(b^3*x^2 + a*b^2)","A",0
575,1,168,0,1.037669," ","integrate((B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(B a b - A b^{2}\right)} \sqrt{b x^{2} + a} x - {\left(B a b x^{2} + B a^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right)}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, -\frac{{\left(B a b - A b^{2}\right)} \sqrt{b x^{2} + a} x + {\left(B a b x^{2} + B a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right)}{a b^{3} x^{2} + a^{2} b^{2}}\right]"," ",0,"[-1/2*(2*(B*a*b - A*b^2)*sqrt(b*x^2 + a)*x - (B*a*b*x^2 + B*a^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a))/(a*b^3*x^2 + a^2*b^2), -((B*a*b - A*b^2)*sqrt(b*x^2 + a)*x + (B*a*b*x^2 + B*a^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)))/(a*b^3*x^2 + a^2*b^2)]","A",0
576,1,167,0,0.947675," ","integrate((B*x^2+A)/x/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A b^{2} x^{2} + A a b\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(B a^{2} - A a b\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{{\left(A b^{2} x^{2} + A a b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(B a^{2} - A a b\right)} \sqrt{b x^{2} + a}}{a^{2} b^{2} x^{2} + a^{3} b}\right]"," ",0,"[1/2*((A*b^2*x^2 + A*a*b)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(B*a^2 - A*a*b)*sqrt(b*x^2 + a))/(a^2*b^2*x^2 + a^3*b), ((A*b^2*x^2 + A*a*b)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (B*a^2 - A*a*b)*sqrt(b*x^2 + a))/(a^2*b^2*x^2 + a^3*b)]","A",0
577,1,43,0,1.090559," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(B a - 2 \, A b\right)} x^{2} - A a\right)} \sqrt{b x^{2} + a}}{a^{2} b x^{3} + a^{3} x}"," ",0,"((B*a - 2*A*b)*x^2 - A*a)*sqrt(b*x^2 + a)/(a^2*b*x^3 + a^3*x)","A",0
578,1,232,0,1.216877," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{4} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(A a^{2} - {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{4 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}, \frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{4} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) - {\left(A a^{2} - {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{2 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}\right]"," ",0,"[-1/4*(((2*B*a*b - 3*A*b^2)*x^4 + (2*B*a^2 - 3*A*a*b)*x^2)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(A*a^2 - (2*B*a^2 - 3*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^4 + a^4*x^2), 1/2*(((2*B*a*b - 3*A*b^2)*x^4 + (2*B*a^2 - 3*A*a*b)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (A*a^2 - (2*B*a^2 - 3*A*a*b)*x^2)*sqrt(b*x^2 + a))/(a^3*b*x^4 + a^4*x^2)]","A",0
579,1,68,0,0.946908," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(3 \, B a b - 4 \, A b^{2}\right)} x^{4} + A a^{2} + {\left(3 \, B a^{2} - 4 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}"," ",0,"-1/3*(2*(3*B*a*b - 4*A*b^2)*x^4 + A*a^2 + (3*B*a^2 - 4*A*a*b)*x^2)*sqrt(b*x^2 + a)/(a^3*b*x^5 + a^4*x^3)","A",0
580,1,287,0,1.047694," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4}\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} + 2 \, A a^{3} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{16 \, {\left(a^{4} b x^{6} + a^{5} x^{4}\right)}}, -\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} + 2 \, A a^{3} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{8 \, {\left(a^{4} b x^{6} + a^{5} x^{4}\right)}}\right]"," ",0,"[-1/16*(3*((4*B*a*b^2 - 5*A*b^3)*x^6 + (4*B*a^2*b - 5*A*a*b^2)*x^4)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(4*B*a^2*b - 5*A*a*b^2)*x^4 + 2*A*a^3 + (4*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*b*x^6 + a^5*x^4), -1/8*(3*((4*B*a*b^2 - 5*A*b^3)*x^6 + (4*B*a^2*b - 5*A*a*b^2)*x^4)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(4*B*a^2*b - 5*A*a*b^2)*x^4 + 2*A*a^3 + (4*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*b*x^6 + a^5*x^4)]","A",0
581,1,94,0,1.038239," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x^{6} + 4 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} x^{4} - 3 \, A a^{3} - {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}}"," ",0,"1/15*(8*(5*B*a*b^2 - 6*A*b^3)*x^6 + 4*(5*B*a^2*b - 6*A*a*b^2)*x^4 - 3*A*a^3 - (5*B*a^3 - 6*A*a^2*b)*x^2)*sqrt(b*x^2 + a)/(a^4*b*x^7 + a^5*x^5)","A",0
582,1,341,0,0.744982," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(6 \, B a b^{3} - 7 \, A b^{4}\right)} x^{8} + {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(15 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} - 8 \, A a^{4} + 5 \, {\left(6 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4} - 2 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{96 \, {\left(a^{5} b x^{8} + a^{6} x^{6}\right)}}, \frac{15 \, {\left({\left(6 \, B a b^{3} - 7 \, A b^{4}\right)} x^{8} + {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} - 8 \, A a^{4} + 5 \, {\left(6 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4} - 2 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, {\left(a^{5} b x^{8} + a^{6} x^{6}\right)}}\right]"," ",0,"[-1/96*(15*((6*B*a*b^3 - 7*A*b^4)*x^8 + (6*B*a^2*b^2 - 7*A*a*b^3)*x^6)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(15*(6*B*a^2*b^2 - 7*A*a*b^3)*x^6 - 8*A*a^4 + 5*(6*B*a^3*b - 7*A*a^2*b^2)*x^4 - 2*(6*B*a^4 - 7*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b*x^8 + a^6*x^6), 1/48*(15*((6*B*a*b^3 - 7*A*b^4)*x^8 + (6*B*a^2*b^2 - 7*A*a*b^3)*x^6)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*(6*B*a^2*b^2 - 7*A*a*b^3)*x^6 - 8*A*a^4 + 5*(6*B*a^3*b - 7*A*a^2*b^2)*x^4 - 2*(6*B*a^4 - 7*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b*x^8 + a^6*x^6)]","A",0
583,1,117,0,1.159557," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(16 \, {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} x^{8} + 8 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{6} + 5 \, A a^{4} - 2 \, {\left(7 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{4} + {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{35 \, {\left(a^{5} b x^{9} + a^{6} x^{7}\right)}}"," ",0,"-1/35*(16*(7*B*a*b^3 - 8*A*b^4)*x^8 + 8*(7*B*a^2*b^2 - 8*A*a*b^3)*x^6 + 5*A*a^4 - 2*(7*B*a^3*b - 8*A*a^2*b^2)*x^4 + (7*B*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^5*b*x^9 + a^6*x^7)","A",0
584,1,123,0,1.200497," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B b^{4} x^{8} - {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} x^{6} + 128 \, B a^{4} - 80 \, A a^{3} b + 6 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{4} + 24 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}"," ",0,"1/15*(3*B*b^4*x^8 - (8*B*a*b^3 - 5*A*b^4)*x^6 + 128*B*a^4 - 80*A*a^3*b + 6*(8*B*a^2*b^2 - 5*A*a*b^3)*x^4 + 24*(8*B*a^3*b - 5*A*a^2*b^2)*x^2)*sqrt(b*x^2 + a)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5)","A",0
585,1,392,0,1.294457," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{4} - 4 \, A a^{3} b + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{4} + 2 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(6 \, B b^{4} x^{7} - 3 \, {\left(7 \, B a b^{3} - 4 \, A b^{4}\right)} x^{5} - 20 \, {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} - 15 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{48 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}, -\frac{15 \, {\left(7 \, B a^{4} - 4 \, A a^{3} b + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{4} + 2 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) - {\left(6 \, B b^{4} x^{7} - 3 \, {\left(7 \, B a b^{3} - 4 \, A b^{4}\right)} x^{5} - 20 \, {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} - 15 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{24 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/48*(15*(7*B*a^4 - 4*A*a^3*b + (7*B*a^2*b^2 - 4*A*a*b^3)*x^4 + 2*(7*B*a^3*b - 4*A*a^2*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(6*B*b^4*x^7 - 3*(7*B*a*b^3 - 4*A*b^4)*x^5 - 20*(7*B*a^2*b^2 - 4*A*a*b^3)*x^3 - 15*(7*B*a^3*b - 4*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5), -1/24*(15*(7*B*a^4 - 4*A*a^3*b + (7*B*a^2*b^2 - 4*A*a*b^3)*x^4 + 2*(7*B*a^3*b - 4*A*a^2*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) - (6*B*b^4*x^7 - 3*(7*B*a*b^3 - 4*A*b^4)*x^5 - 20*(7*B*a^2*b^2 - 4*A*a*b^3)*x^3 - 15*(7*B*a^3*b - 4*A*a^2*b^2)*x)*sqrt(b*x^2 + a))/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5)]","A",0
586,1,98,0,0.858590," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(B b^{3} x^{6} - 3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} x^{4} - 16 \, B a^{3} + 8 \, A a^{2} b - 12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}"," ",0,"1/3*(B*b^3*x^6 - 3*(2*B*a*b^2 - A*b^3)*x^4 - 16*B*a^3 + 8*A*a^2*b - 12*(2*B*a^2*b - A*a*b^2)*x^2)*sqrt(b*x^2 + a)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)","A",0
587,1,333,0,0.702648," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{4} + 5 \, B a^{3} - 2 \, A a^{2} b + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(3 \, B b^{3} x^{5} + 4 \, {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{12 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}, \frac{3 \, {\left({\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{4} + 5 \, B a^{3} - 2 \, A a^{2} b + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, B b^{3} x^{5} + 4 \, {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{b x^{2} + a}}{6 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/12*(3*((5*B*a*b^2 - 2*A*b^3)*x^4 + 5*B*a^3 - 2*A*a^2*b + 2*(5*B*a^2*b - 2*A*a*b^2)*x^2)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(3*B*b^3*x^5 + 4*(5*B*a*b^2 - 2*A*b^3)*x^3 + 3*(5*B*a^2*b - 2*A*a*b^2)*x)*sqrt(b*x^2 + a))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4), 1/6*(3*((5*B*a*b^2 - 2*A*b^3)*x^4 + 5*B*a^3 - 2*A*a^2*b + 2*(5*B*a^2*b - 2*A*a*b^2)*x^2)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (3*B*b^3*x^5 + 4*(5*B*a*b^2 - 2*A*b^3)*x^3 + 3*(5*B*a^2*b - 2*A*a*b^2)*x)*sqrt(b*x^2 + a))/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4)]","A",0
588,1,75,0,0.865000," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B b^{2} x^{4} + 8 \, B a^{2} - 2 \, A a b + 3 \, {\left(4 \, B a b - A b^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/3*(3*B*b^2*x^4 + 8*B*a^2 - 2*A*a*b + 3*(4*B*a*b - A*b^2)*x^2)*sqrt(b*x^2 + a)/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","A",0
589,1,245,0,0.945594," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b^{2} x^{4} + 2 \, B a^{2} b x^{2} + B a^{3}\right)} \sqrt{b} \log\left(-2 \, b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{b} x - a\right) - 2 \, {\left(3 \, B a^{2} b x + {\left(4 \, B a b^{2} - A b^{3}\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}, -\frac{3 \, {\left(B a b^{2} x^{4} + 2 \, B a^{2} b x^{2} + B a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} x}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, B a^{2} b x + {\left(4 \, B a b^{2} - A b^{3}\right)} x^{3}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}\right]"," ",0,"[1/6*(3*(B*a*b^2*x^4 + 2*B*a^2*b*x^2 + B*a^3)*sqrt(b)*log(-2*b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(b)*x - a) - 2*(3*B*a^2*b*x + (4*B*a*b^2 - A*b^3)*x^3)*sqrt(b*x^2 + a))/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3), -1/3*(3*(B*a*b^2*x^4 + 2*B*a^2*b*x^2 + B*a^3)*sqrt(-b)*arctan(sqrt(-b)*x/sqrt(b*x^2 + a)) + (3*B*a^2*b*x + (4*B*a*b^2 - A*b^3)*x^3)*sqrt(b*x^2 + a))/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3)]","A",0
590,1,52,0,1.030272," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, B b x^{2} + 2 \, B a + A b\right)} \sqrt{b x^{2} + a}}{3 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/3*(3*B*b*x^2 + 2*B*a + A*b)*sqrt(b*x^2 + a)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
591,1,54,0,1.038875," ","integrate((B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(B a + 2 \, A b\right)} x^{3} + 3 \, A a x\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{2} b^{2} x^{4} + 2 \, a^{3} b x^{2} + a^{4}\right)}}"," ",0,"1/3*((B*a + 2*A*b)*x^3 + 3*A*a*x)*sqrt(b*x^2 + a)/(a^2*b^2*x^4 + 2*a^3*b*x^2 + a^4)","A",0
592,1,241,0,1.128911," ","integrate((B*x^2+A)/x/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{3} x^{4} + 2 \, A a b^{2} x^{2} + A a^{2} b\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(3 \, A a b^{2} x^{2} - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}, \frac{3 \, {\left(A b^{3} x^{4} + 2 \, A a b^{2} x^{2} + A a^{2} b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, A a b^{2} x^{2} - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}\right]"," ",0,"[1/6*(3*(A*b^3*x^4 + 2*A*a*b^2*x^2 + A*a^2*b)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*A*a*b^2*x^2 - B*a^3 + 4*A*a^2*b)*sqrt(b*x^2 + a))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b), 1/3*(3*(A*b^3*x^4 + 2*A*a*b^2*x^2 + A*a^2*b)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*A*a*b^2*x^2 - B*a^3 + 4*A*a^2*b)*sqrt(b*x^2 + a))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)]","A",0
593,1,77,0,0.950598," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(B a b - 4 \, A b^{2}\right)} x^{4} - 3 \, A a^{2} + 3 \, {\left(B a^{2} - 4 \, A a b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}}"," ",0,"1/3*(2*(B*a*b - 4*A*b^2)*x^4 - 3*A*a^2 + 3*(B*a^2 - 4*A*a*b)*x^2)*sqrt(b*x^2 + a)/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x)","A",0
594,1,349,0,1.078651," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{a} \log\left(-\frac{b x^{2} + 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) - 2 \, {\left(3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} - 3 \, A a^{3} + 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{12 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}, \frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{4} - 3 \, A a^{3} + 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{6 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}\right]"," ",0,"[-1/12*(3*((2*B*a*b^2 - 5*A*b^3)*x^6 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^4 + (2*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(a)*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) - 2*(3*(2*B*a^2*b - 5*A*a*b^2)*x^4 - 3*A*a^3 + 4*(2*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2), 1/6*(3*((2*B*a*b^2 - 5*A*b^3)*x^6 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^4 + (2*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (3*(2*B*a^2*b - 5*A*a*b^2)*x^4 - 3*A*a^3 + 4*(2*B*a^3 - 5*A*a^2*b)*x^2)*sqrt(b*x^2 + a))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)]","A",0
595,1,101,0,0.723212," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 12 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} x^{4} + A a^{3} + 3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{3 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}}"," ",0,"-1/3*(8*(B*a*b^2 - 2*A*b^3)*x^6 + 12*(B*a^2*b - 2*A*a*b^2)*x^4 + A*a^3 + 3*(B*a^3 - 2*A*a^2*b)*x^2)*sqrt(b*x^2 + a)/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3)","A",0
596,1,407,0,1.061393," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, B a b^{3} - 7 \, A b^{4}\right)} x^{8} + 2 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4}\right)} \sqrt{a} \log\left(-\frac{b x^{2} - 2 \, \sqrt{b x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right) + 2 \, {\left(15 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} + 6 \, A a^{4} + 20 \, {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4} + 3 \, {\left(4 \, B a^{4} - 7 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{48 \, {\left(a^{5} b^{2} x^{8} + 2 \, a^{6} b x^{6} + a^{7} x^{4}\right)}}, -\frac{15 \, {\left({\left(4 \, B a b^{3} - 7 \, A b^{4}\right)} x^{8} + 2 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{b x^{2} + a}}\right) + {\left(15 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{6} + 6 \, A a^{4} + 20 \, {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{4} + 3 \, {\left(4 \, B a^{4} - 7 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{24 \, {\left(a^{5} b^{2} x^{8} + 2 \, a^{6} b x^{6} + a^{7} x^{4}\right)}}\right]"," ",0,"[-1/48*(15*((4*B*a*b^3 - 7*A*b^4)*x^8 + 2*(4*B*a^2*b^2 - 7*A*a*b^3)*x^6 + (4*B*a^3*b - 7*A*a^2*b^2)*x^4)*sqrt(a)*log(-(b*x^2 - 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(15*(4*B*a^2*b^2 - 7*A*a*b^3)*x^6 + 6*A*a^4 + 20*(4*B*a^3*b - 7*A*a^2*b^2)*x^4 + 3*(4*B*a^4 - 7*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b^2*x^8 + 2*a^6*b*x^6 + a^7*x^4), -1/24*(15*((4*B*a*b^3 - 7*A*b^4)*x^8 + 2*(4*B*a^2*b^2 - 7*A*a*b^3)*x^6 + (4*B*a^3*b - 7*A*a^2*b^2)*x^4)*sqrt(-a)*arctan(sqrt(-a)/sqrt(b*x^2 + a)) + (15*(4*B*a^2*b^2 - 7*A*a*b^3)*x^6 + 6*A*a^4 + 20*(4*B*a^3*b - 7*A*a^2*b^2)*x^4 + 3*(4*B*a^4 - 7*A*a^3*b)*x^2)*sqrt(b*x^2 + a))/(a^5*b^2*x^8 + 2*a^6*b*x^6 + a^7*x^4)]","A",0
597,1,129,0,1.229843," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(5 \, B a b^{3} - 8 \, A b^{4}\right)} x^{8} + 24 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{6} - 3 \, A a^{4} + 6 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{4} - {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} x^{2}\right)} \sqrt{b x^{2} + a}}{15 \, {\left(a^{5} b^{2} x^{9} + 2 \, a^{6} b x^{7} + a^{7} x^{5}\right)}}"," ",0,"1/15*(16*(5*B*a*b^3 - 8*A*b^4)*x^8 + 24*(5*B*a^2*b^2 - 8*A*a*b^3)*x^6 - 3*A*a^4 + 6*(5*B*a^3*b - 8*A*a^2*b^2)*x^4 - (5*B*a^4 - 8*A*a^3*b)*x^2)*sqrt(b*x^2 + a)/(a^5*b^2*x^9 + 2*a^6*b*x^7 + a^7*x^5)","A",0
598,1,179,0,1.534383," ","integrate(x^5*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(315 \, b^{2} d^{5} x^{10} + 35 \, {\left(b^{2} c d^{4} + 22 \, a b d^{5}\right)} x^{8} + 128 \, b^{2} c^{5} - 352 \, a b c^{4} d + 264 \, a^{2} c^{3} d^{2} - 5 \, {\left(8 \, b^{2} c^{2} d^{3} - 22 \, a b c d^{4} - 99 \, a^{2} d^{5}\right)} x^{6} + 3 \, {\left(16 \, b^{2} c^{3} d^{2} - 44 \, a b c^{2} d^{3} + 33 \, a^{2} c d^{4}\right)} x^{4} - 4 \, {\left(16 \, b^{2} c^{4} d - 44 \, a b c^{3} d^{2} + 33 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3465 \, d^{5}}"," ",0,"1/3465*(315*b^2*d^5*x^10 + 35*(b^2*c*d^4 + 22*a*b*d^5)*x^8 + 128*b^2*c^5 - 352*a*b*c^4*d + 264*a^2*c^3*d^2 - 5*(8*b^2*c^2*d^3 - 22*a*b*c*d^4 - 99*a^2*d^5)*x^6 + 3*(16*b^2*c^3*d^2 - 44*a*b*c^2*d^3 + 33*a^2*c*d^4)*x^4 - 4*(16*b^2*c^4*d - 44*a*b*c^3*d^2 + 33*a^2*c^2*d^3)*x^2)*sqrt(d*x^2 + c)/d^5","A",0
599,1,140,0,1.137867," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b^{2} d^{4} x^{8} + 5 \, {\left(b^{2} c d^{3} + 18 \, a b d^{4}\right)} x^{6} - 16 \, b^{2} c^{4} + 48 \, a b c^{3} d - 42 \, a^{2} c^{2} d^{2} - 3 \, {\left(2 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} - 21 \, a^{2} d^{4}\right)} x^{4} + {\left(8 \, b^{2} c^{3} d - 24 \, a b c^{2} d^{2} + 21 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{315 \, d^{4}}"," ",0,"1/315*(35*b^2*d^4*x^8 + 5*(b^2*c*d^3 + 18*a*b*d^4)*x^6 - 16*b^2*c^4 + 48*a*b*c^3*d - 42*a^2*c^2*d^2 - 3*(2*b^2*c^2*d^2 - 6*a*b*c*d^3 - 21*a^2*d^4)*x^4 + (8*b^2*c^3*d - 24*a*b*c^2*d^2 + 21*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c)/d^4","A",0
600,1,103,0,0.959230," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{2} d^{3} x^{6} + 8 \, b^{2} c^{3} - 28 \, a b c^{2} d + 35 \, a^{2} c d^{2} + 3 \, {\left(b^{2} c d^{2} + 14 \, a b d^{3}\right)} x^{4} - {\left(4 \, b^{2} c^{2} d - 14 \, a b c d^{2} - 35 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{105 \, d^{3}}"," ",0,"1/105*(15*b^2*d^3*x^6 + 8*b^2*c^3 - 28*a*b*c^2*d + 35*a^2*c*d^2 + 3*(b^2*c*d^2 + 14*a*b*d^3)*x^4 - (4*b^2*c^2*d - 14*a*b*c*d^2 - 35*a^2*d^3)*x^2)*sqrt(d*x^2 + c)/d^3","A",0
601,1,207,0,0.864318," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{c} d^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{4} - 2 \, b^{2} c^{2} + 10 \, a b c d + 15 \, a^{2} d^{2} + {\left(b^{2} c d + 10 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, d^{2}}, \frac{15 \, a^{2} \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, b^{2} d^{2} x^{4} - 2 \, b^{2} c^{2} + 10 \, a b c d + 15 \, a^{2} d^{2} + {\left(b^{2} c d + 10 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, d^{2}}\right]"," ",0,"[1/30*(15*a^2*sqrt(c)*d^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(3*b^2*d^2*x^4 - 2*b^2*c^2 + 10*a*b*c*d + 15*a^2*d^2 + (b^2*c*d + 10*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/d^2, 1/15*(15*a^2*sqrt(-c)*d^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (3*b^2*d^2*x^4 - 2*b^2*c^2 + 10*a*b*c*d + 15*a^2*d^2 + (b^2*c*d + 10*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/d^2]","A",0
602,1,211,0,1.601737," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a b c d + a^{2} d^{2}\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, b^{2} c d x^{4} - 3 \, a^{2} c d + 2 \, {\left(b^{2} c^{2} + 6 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, c d x^{2}}, \frac{3 \, {\left(4 \, a b c d + a^{2} d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b^{2} c d x^{4} - 3 \, a^{2} c d + 2 \, {\left(b^{2} c^{2} + 6 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, c d x^{2}}\right]"," ",0,"[1/12*(3*(4*a*b*c*d + a^2*d^2)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(2*b^2*c*d*x^4 - 3*a^2*c*d + 2*(b^2*c^2 + 6*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(c*d*x^2), 1/6*(3*(4*a*b*c*d + a^2*d^2)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*b^2*c*d*x^4 - 3*a^2*c*d + 2*(b^2*c^2 + 6*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(c*d*x^2)]","A",0
603,1,225,0,1.267705," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, b^{2} c^{2} + 8 \, a b c d - a^{2} d^{2}\right)} \sqrt{c} x^{4} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(8 \, b^{2} c^{2} x^{4} - 2 \, a^{2} c^{2} - {\left(8 \, a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{16 \, c^{2} x^{4}}, \frac{{\left(8 \, b^{2} c^{2} + 8 \, a b c d - a^{2} d^{2}\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{2} c^{2} x^{4} - 2 \, a^{2} c^{2} - {\left(8 \, a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, c^{2} x^{4}}\right]"," ",0,"[-1/16*((8*b^2*c^2 + 8*a*b*c*d - a^2*d^2)*sqrt(c)*x^4*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(8*b^2*c^2*x^4 - 2*a^2*c^2 - (8*a*b*c^2 + a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^4), 1/8*((8*b^2*c^2 + 8*a*b*c*d - a^2*d^2)*sqrt(-c)*x^4*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (8*b^2*c^2*x^4 - 2*a^2*c^2 - (8*a*b*c^2 + a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^4)]","A",0
604,1,276,0,1.812335," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, b^{2} c^{2} d - 4 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{c} x^{6} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(8 \, a^{2} c^{3} + 3 \, {\left(8 \, b^{2} c^{3} + 4 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{3} + a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, c^{3} x^{6}}, \frac{3 \, {\left(8 \, b^{2} c^{2} d - 4 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, a^{2} c^{3} + 3 \, {\left(8 \, b^{2} c^{3} + 4 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{3} + a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, c^{3} x^{6}}\right]"," ",0,"[1/96*(3*(8*b^2*c^2*d - 4*a*b*c*d^2 + a^2*d^3)*sqrt(c)*x^6*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(8*a^2*c^3 + 3*(8*b^2*c^3 + 4*a*b*c^2*d - a^2*c*d^2)*x^4 + 2*(12*a*b*c^3 + a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^3*x^6), 1/48*(3*(8*b^2*c^2*d - 4*a*b*c*d^2 + a^2*d^3)*sqrt(-c)*x^6*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (8*a^2*c^3 + 3*(8*b^2*c^3 + 4*a*b*c^2*d - a^2*c*d^2)*x^4 + 2*(12*a*b*c^3 + a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^3*x^6)]","A",0
605,1,341,0,1.660807," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{2} c^{4} - 16 \, a b c^{3} d + 16 \, a^{2} c^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(48 \, b^{2} d^{4} x^{7} + 8 \, {\left(b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{5} - 2 \, {\left(5 \, b^{2} c^{2} d^{2} - 16 \, a b c d^{3} - 48 \, a^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{3} d - 16 \, a b c^{2} d^{2} + 16 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{768 \, d^{4}}, \frac{3 \, {\left(5 \, b^{2} c^{4} - 16 \, a b c^{3} d + 16 \, a^{2} c^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(48 \, b^{2} d^{4} x^{7} + 8 \, {\left(b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{5} - 2 \, {\left(5 \, b^{2} c^{2} d^{2} - 16 \, a b c d^{3} - 48 \, a^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{3} d - 16 \, a b c^{2} d^{2} + 16 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{384 \, d^{4}}\right]"," ",0,"[1/768*(3*(5*b^2*c^4 - 16*a*b*c^3*d + 16*a^2*c^2*d^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(48*b^2*d^4*x^7 + 8*(b^2*c*d^3 + 16*a*b*d^4)*x^5 - 2*(5*b^2*c^2*d^2 - 16*a*b*c*d^3 - 48*a^2*d^4)*x^3 + 3*(5*b^2*c^3*d - 16*a*b*c^2*d^2 + 16*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^4, 1/384*(3*(5*b^2*c^4 - 16*a*b*c^3*d + 16*a^2*c^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (48*b^2*d^4*x^7 + 8*(b^2*c*d^3 + 16*a*b*d^4)*x^5 - 2*(5*b^2*c^2*d^2 - 16*a*b*c*d^3 - 48*a^2*d^4)*x^3 + 3*(5*b^2*c^3*d - 16*a*b*c^2*d^2 + 16*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^4]","A",0
606,1,262,0,1.769286," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(8 \, b^{2} d^{3} x^{5} + 2 \, {\left(b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{3} - 3 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2} - 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, d^{3}}, -\frac{3 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, b^{2} d^{3} x^{5} + 2 \, {\left(b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{3} - 3 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2} - 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, d^{3}}\right]"," ",0,"[1/96*(3*(b^2*c^3 - 4*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(8*b^2*d^3*x^5 + 2*(b^2*c*d^2 + 12*a*b*d^3)*x^3 - 3*(b^2*c^2*d - 4*a*b*c*d^2 - 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/d^3, -1/48*(3*(b^2*c^3 - 4*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (8*b^2*d^3*x^5 + 2*(b^2*c*d^2 + 12*a*b*d^3)*x^3 - 3*(b^2*c^2*d - 4*a*b*c*d^2 - 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/d^3]","A",0
607,1,215,0,1.425371," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 8 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{4} - 8 \, a^{2} d^{2} + {\left(b^{2} c d + 8 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{16 \, d^{2} x}, \frac{{\left(b^{2} c^{2} - 8 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b^{2} d^{2} x^{4} - 8 \, a^{2} d^{2} + {\left(b^{2} c d + 8 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, d^{2} x}\right]"," ",0,"[-1/16*((b^2*c^2 - 8*a*b*c*d - 8*a^2*d^2)*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(2*b^2*d^2*x^4 - 8*a^2*d^2 + (b^2*c*d + 8*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(d^2*x), 1/8*((b^2*c^2 - 8*a*b*c*d - 8*a^2*d^2)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (2*b^2*d^2*x^4 - 8*a^2*d^2 + (b^2*c*d + 8*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(d^2*x)]","A",0
608,1,210,0,1.637510," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{d} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(3 \, b^{2} c d x^{4} - 2 \, a^{2} c d - 2 \, {\left(6 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, c d x^{3}}, -\frac{3 \, {\left(b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(3 \, b^{2} c d x^{4} - 2 \, a^{2} c d - 2 \, {\left(6 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, c d x^{3}}\right]"," ",0,"[1/12*(3*(b^2*c^2 + 4*a*b*c*d)*sqrt(d)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(3*b^2*c*d*x^4 - 2*a^2*c*d - 2*(6*a*b*c*d + a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c*d*x^3), -1/6*(3*(b^2*c^2 + 4*a*b*c*d)*sqrt(-d)*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (3*b^2*c*d*x^4 - 2*a^2*c*d - 2*(6*a*b*c*d + a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c*d*x^3)]","A",0
609,1,221,0,1.518554," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, b^{2} c^{2} \sqrt{d} x^{5} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left({\left(15 \, b^{2} c^{2} + 10 \, a b c d - 2 \, a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} + {\left(10 \, a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, c^{2} x^{5}}, -\frac{15 \, b^{2} c^{2} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left({\left(15 \, b^{2} c^{2} + 10 \, a b c d - 2 \, a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} + {\left(10 \, a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, c^{2} x^{5}}\right]"," ",0,"[1/30*(15*b^2*c^2*sqrt(d)*x^5*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*((15*b^2*c^2 + 10*a*b*c*d - 2*a^2*d^2)*x^4 + 3*a^2*c^2 + (10*a*b*c^2 + a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^5), -1/15*(15*b^2*c^2*sqrt(-d)*x^5*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + ((15*b^2*c^2 + 10*a*b*c*d - 2*a^2*d^2)*x^4 + 3*a^2*c^2 + (10*a*b*c^2 + a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^5)]","A",0
610,1,107,0,1.430162," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^8,x, algorithm=""fricas"")","-\frac{{\left({\left(35 \, b^{2} c^{2} d - 28 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{6} + 15 \, a^{2} c^{3} + {\left(35 \, b^{2} c^{3} + 14 \, a b c^{2} d - 4 \, a^{2} c d^{2}\right)} x^{4} + 3 \, {\left(14 \, a b c^{3} + a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{105 \, c^{3} x^{7}}"," ",0,"-1/105*((35*b^2*c^2*d - 28*a*b*c*d^2 + 8*a^2*d^3)*x^6 + 15*a^2*c^3 + (35*b^2*c^3 + 14*a*b*c^2*d - 4*a^2*c*d^2)*x^4 + 3*(14*a*b*c^3 + a^2*c^2*d)*x^2)*sqrt(d*x^2 + c)/(c^3*x^7)","A",0
611,1,147,0,2.038310," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^10,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(21 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)} x^{8} - {\left(21 \, b^{2} c^{3} d - 24 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x^{6} - 35 \, a^{2} c^{4} - 3 \, {\left(21 \, b^{2} c^{4} + 6 \, a b c^{3} d - 2 \, a^{2} c^{2} d^{2}\right)} x^{4} - 5 \, {\left(18 \, a b c^{4} + a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{315 \, c^{4} x^{9}}"," ",0,"1/315*(2*(21*b^2*c^2*d^2 - 24*a*b*c*d^3 + 8*a^2*d^4)*x^8 - (21*b^2*c^3*d - 24*a*b*c^2*d^2 + 8*a^2*c*d^3)*x^6 - 35*a^2*c^4 - 3*(21*b^2*c^4 + 6*a*b*c^3*d - 2*a^2*c^2*d^2)*x^4 - 5*(18*a*b*c^4 + a^2*c^3*d)*x^2)*sqrt(d*x^2 + c)/(c^4*x^9)","A",0
612,1,185,0,2.328810," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^12,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(33 \, b^{2} c^{2} d^{3} - 44 \, a b c d^{4} + 16 \, a^{2} d^{5}\right)} x^{10} - 4 \, {\left(33 \, b^{2} c^{3} d^{2} - 44 \, a b c^{2} d^{3} + 16 \, a^{2} c d^{4}\right)} x^{8} + 315 \, a^{2} c^{5} + 3 \, {\left(33 \, b^{2} c^{4} d - 44 \, a b c^{3} d^{2} + 16 \, a^{2} c^{2} d^{3}\right)} x^{6} + 5 \, {\left(99 \, b^{2} c^{5} + 22 \, a b c^{4} d - 8 \, a^{2} c^{3} d^{2}\right)} x^{4} + 35 \, {\left(22 \, a b c^{5} + a^{2} c^{4} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3465 \, c^{5} x^{11}}"," ",0,"-1/3465*(8*(33*b^2*c^2*d^3 - 44*a*b*c*d^4 + 16*a^2*d^5)*x^10 - 4*(33*b^2*c^3*d^2 - 44*a*b*c^2*d^3 + 16*a^2*c*d^4)*x^8 + 315*a^2*c^5 + 3*(33*b^2*c^4*d - 44*a*b*c^3*d^2 + 16*a^2*c^2*d^3)*x^6 + 5*(99*b^2*c^5 + 22*a*b*c^4*d - 8*a^2*c^3*d^2)*x^4 + 35*(22*a*b*c^5 + a^2*c^4*d)*x^2)*sqrt(d*x^2 + c)/(c^5*x^11)","A",0
613,1,494,0,2.505933," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{2} c^{6} - 24 \, a b c^{5} d + 24 \, a^{2} c^{4} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(1280 \, b^{2} d^{6} x^{11} + 128 \, {\left(13 \, b^{2} c d^{5} + 24 \, a b d^{6}\right)} x^{9} + 48 \, {\left(b^{2} c^{2} d^{4} + 88 \, a b c d^{5} + 40 \, a^{2} d^{6}\right)} x^{7} - 8 \, {\left(7 \, b^{2} c^{3} d^{3} - 24 \, a b c^{2} d^{4} - 360 \, a^{2} c d^{5}\right)} x^{5} + 10 \, {\left(7 \, b^{2} c^{4} d^{2} - 24 \, a b c^{3} d^{3} + 24 \, a^{2} c^{2} d^{4}\right)} x^{3} - 15 \, {\left(7 \, b^{2} c^{5} d - 24 \, a b c^{4} d^{2} + 24 \, a^{2} c^{3} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{30720 \, d^{5}}, -\frac{15 \, {\left(7 \, b^{2} c^{6} - 24 \, a b c^{5} d + 24 \, a^{2} c^{4} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(1280 \, b^{2} d^{6} x^{11} + 128 \, {\left(13 \, b^{2} c d^{5} + 24 \, a b d^{6}\right)} x^{9} + 48 \, {\left(b^{2} c^{2} d^{4} + 88 \, a b c d^{5} + 40 \, a^{2} d^{6}\right)} x^{7} - 8 \, {\left(7 \, b^{2} c^{3} d^{3} - 24 \, a b c^{2} d^{4} - 360 \, a^{2} c d^{5}\right)} x^{5} + 10 \, {\left(7 \, b^{2} c^{4} d^{2} - 24 \, a b c^{3} d^{3} + 24 \, a^{2} c^{2} d^{4}\right)} x^{3} - 15 \, {\left(7 \, b^{2} c^{5} d - 24 \, a b c^{4} d^{2} + 24 \, a^{2} c^{3} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{15360 \, d^{5}}\right]"," ",0,"[1/30720*(15*(7*b^2*c^6 - 24*a*b*c^5*d + 24*a^2*c^4*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(1280*b^2*d^6*x^11 + 128*(13*b^2*c*d^5 + 24*a*b*d^6)*x^9 + 48*(b^2*c^2*d^4 + 88*a*b*c*d^5 + 40*a^2*d^6)*x^7 - 8*(7*b^2*c^3*d^3 - 24*a*b*c^2*d^4 - 360*a^2*c*d^5)*x^5 + 10*(7*b^2*c^4*d^2 - 24*a*b*c^3*d^3 + 24*a^2*c^2*d^4)*x^3 - 15*(7*b^2*c^5*d - 24*a*b*c^4*d^2 + 24*a^2*c^3*d^3)*x)*sqrt(d*x^2 + c))/d^5, -1/15360*(15*(7*b^2*c^6 - 24*a*b*c^5*d + 24*a^2*c^4*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (1280*b^2*d^6*x^11 + 128*(13*b^2*c*d^5 + 24*a*b*d^6)*x^9 + 48*(b^2*c^2*d^4 + 88*a*b*c*d^5 + 40*a^2*d^6)*x^7 - 8*(7*b^2*c^3*d^3 - 24*a*b*c^2*d^4 - 360*a^2*c*d^5)*x^5 + 10*(7*b^2*c^4*d^2 - 24*a*b*c^3*d^3 + 24*a^2*c^2*d^4)*x^3 - 15*(7*b^2*c^5*d - 24*a*b*c^4*d^2 + 24*a^2*c^3*d^3)*x)*sqrt(d*x^2 + c))/d^5]","A",0
614,1,179,0,1.195839," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(315 \, b^{2} d^{5} x^{10} + 70 \, {\left(6 \, b^{2} c d^{4} + 11 \, a b d^{5}\right)} x^{8} - 48 \, b^{2} c^{5} + 176 \, a b c^{4} d - 198 \, a^{2} c^{3} d^{2} + 5 \, {\left(3 \, b^{2} c^{2} d^{3} + 220 \, a b c d^{4} + 99 \, a^{2} d^{5}\right)} x^{6} - 6 \, {\left(3 \, b^{2} c^{3} d^{2} - 11 \, a b c^{2} d^{3} - 132 \, a^{2} c d^{4}\right)} x^{4} + {\left(24 \, b^{2} c^{4} d - 88 \, a b c^{3} d^{2} + 99 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3465 \, d^{4}}"," ",0,"1/3465*(315*b^2*d^5*x^10 + 70*(6*b^2*c*d^4 + 11*a*b*d^5)*x^8 - 48*b^2*c^5 + 176*a*b*c^4*d - 198*a^2*c^3*d^2 + 5*(3*b^2*c^2*d^3 + 220*a*b*c*d^4 + 99*a^2*d^5)*x^6 - 6*(3*b^2*c^3*d^2 - 11*a*b*c^2*d^3 - 132*a^2*c*d^4)*x^4 + (24*b^2*c^4*d - 88*a*b*c^3*d^2 + 99*a^2*c^2*d^3)*x^2)*sqrt(d*x^2 + c)/d^4","A",0
615,1,419,0,1.874482," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{2} c^{5} - 12 \, a b c^{4} d + 16 \, a^{2} c^{3} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(384 \, b^{2} d^{5} x^{9} + 48 \, {\left(11 \, b^{2} c d^{4} + 20 \, a b d^{5}\right)} x^{7} + 8 \, {\left(3 \, b^{2} c^{2} d^{3} + 180 \, a b c d^{4} + 80 \, a^{2} d^{5}\right)} x^{5} - 10 \, {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} - 112 \, a^{2} c d^{4}\right)} x^{3} + 15 \, {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 16 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{7680 \, d^{4}}, \frac{15 \, {\left(3 \, b^{2} c^{5} - 12 \, a b c^{4} d + 16 \, a^{2} c^{3} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(384 \, b^{2} d^{5} x^{9} + 48 \, {\left(11 \, b^{2} c d^{4} + 20 \, a b d^{5}\right)} x^{7} + 8 \, {\left(3 \, b^{2} c^{2} d^{3} + 180 \, a b c d^{4} + 80 \, a^{2} d^{5}\right)} x^{5} - 10 \, {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} - 112 \, a^{2} c d^{4}\right)} x^{3} + 15 \, {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 16 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{3840 \, d^{4}}\right]"," ",0,"[1/7680*(15*(3*b^2*c^5 - 12*a*b*c^4*d + 16*a^2*c^3*d^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(384*b^2*d^5*x^9 + 48*(11*b^2*c*d^4 + 20*a*b*d^5)*x^7 + 8*(3*b^2*c^2*d^3 + 180*a*b*c*d^4 + 80*a^2*d^5)*x^5 - 10*(3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 - 112*a^2*c*d^4)*x^3 + 15*(3*b^2*c^4*d - 12*a*b*c^3*d^2 + 16*a^2*c^2*d^3)*x)*sqrt(d*x^2 + c))/d^4, 1/3840*(15*(3*b^2*c^5 - 12*a*b*c^4*d + 16*a^2*c^3*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (384*b^2*d^5*x^9 + 48*(11*b^2*c*d^4 + 20*a*b*d^5)*x^7 + 8*(3*b^2*c^2*d^3 + 180*a*b*c*d^4 + 80*a^2*d^5)*x^5 - 10*(3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 - 112*a^2*c*d^4)*x^3 + 15*(3*b^2*c^4*d - 12*a*b*c^3*d^2 + 16*a^2*c^2*d^3)*x)*sqrt(d*x^2 + c))/d^4]","A",0
616,1,141,0,1.402079," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(35 \, b^{2} d^{4} x^{8} + 10 \, {\left(5 \, b^{2} c d^{3} + 9 \, a b d^{4}\right)} x^{6} + 8 \, b^{2} c^{4} - 36 \, a b c^{3} d + 63 \, a^{2} c^{2} d^{2} + 3 \, {\left(b^{2} c^{2} d^{2} + 48 \, a b c d^{3} + 21 \, a^{2} d^{4}\right)} x^{4} - 2 \, {\left(2 \, b^{2} c^{3} d - 9 \, a b c^{2} d^{2} - 63 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{315 \, d^{3}}"," ",0,"1/315*(35*b^2*d^4*x^8 + 10*(5*b^2*c*d^3 + 9*a*b*d^4)*x^6 + 8*b^2*c^4 - 36*a*b*c^3*d + 63*a^2*c^2*d^2 + 3*(b^2*c^2*d^2 + 48*a*b*c*d^3 + 21*a^2*d^4)*x^4 - 2*(2*b^2*c^3*d - 9*a*b*c^2*d^2 - 63*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c)/d^3","B",0
617,1,344,0,1.308306," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b^{2} c^{4} - 16 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(48 \, b^{2} d^{4} x^{7} + 8 \, {\left(9 \, b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{5} + 2 \, {\left(3 \, b^{2} c^{2} d^{2} + 112 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(3 \, b^{2} c^{3} d - 16 \, a b c^{2} d^{2} - 80 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{768 \, d^{3}}, -\frac{3 \, {\left(3 \, b^{2} c^{4} - 16 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(48 \, b^{2} d^{4} x^{7} + 8 \, {\left(9 \, b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{5} + 2 \, {\left(3 \, b^{2} c^{2} d^{2} + 112 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(3 \, b^{2} c^{3} d - 16 \, a b c^{2} d^{2} - 80 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{384 \, d^{3}}\right]"," ",0,"[1/768*(3*(3*b^2*c^4 - 16*a*b*c^3*d + 48*a^2*c^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(48*b^2*d^4*x^7 + 8*(9*b^2*c*d^3 + 16*a*b*d^4)*x^5 + 2*(3*b^2*c^2*d^2 + 112*a*b*c*d^3 + 48*a^2*d^4)*x^3 - 3*(3*b^2*c^3*d - 16*a*b*c^2*d^2 - 80*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^3, -1/384*(3*(3*b^2*c^4 - 16*a*b*c^3*d + 48*a^2*c^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (48*b^2*d^4*x^7 + 8*(9*b^2*c*d^3 + 16*a*b*d^4)*x^5 + 2*(3*b^2*c^2*d^2 + 112*a*b*c*d^3 + 48*a^2*d^4)*x^3 - 3*(3*b^2*c^3*d - 16*a*b*c^2*d^2 - 80*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^3]","A",0
618,1,282,0,1.407032," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{105 \, a^{2} c^{\frac{3}{2}} d^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(15 \, b^{2} d^{3} x^{6} - 6 \, b^{2} c^{3} + 42 \, a b c^{2} d + 140 \, a^{2} c d^{2} + 6 \, {\left(4 \, b^{2} c d^{2} + 7 \, a b d^{3}\right)} x^{4} + {\left(3 \, b^{2} c^{2} d + 84 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{210 \, d^{2}}, \frac{105 \, a^{2} \sqrt{-c} c d^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(15 \, b^{2} d^{3} x^{6} - 6 \, b^{2} c^{3} + 42 \, a b c^{2} d + 140 \, a^{2} c d^{2} + 6 \, {\left(4 \, b^{2} c d^{2} + 7 \, a b d^{3}\right)} x^{4} + {\left(3 \, b^{2} c^{2} d + 84 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{105 \, d^{2}}\right]"," ",0,"[1/210*(105*a^2*c^(3/2)*d^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(15*b^2*d^3*x^6 - 6*b^2*c^3 + 42*a*b*c^2*d + 140*a^2*c*d^2 + 6*(4*b^2*c*d^2 + 7*a*b*d^3)*x^4 + (3*b^2*c^2*d + 84*a*b*c*d^2 + 35*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/d^2, 1/105*(105*a^2*sqrt(-c)*c*d^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (15*b^2*d^3*x^6 - 6*b^2*c^3 + 42*a*b*c^2*d + 140*a^2*c*d^2 + 6*(4*b^2*c*d^2 + 7*a*b*d^3)*x^4 + (3*b^2*c^2*d + 84*a*b*c*d^2 + 35*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/d^2]","A",0
619,1,293,0,1.362376," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} c^{3} - 12 \, a b c^{2} d - 24 \, a^{2} c d^{2}\right)} \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(8 \, b^{2} d^{3} x^{6} - 48 \, a^{2} c d^{2} + 2 \, {\left(7 \, b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{4} + 3 \, {\left(b^{2} c^{2} d + 20 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, d^{2} x}, \frac{3 \, {\left(b^{2} c^{3} - 12 \, a b c^{2} d - 24 \, a^{2} c d^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{2} d^{3} x^{6} - 48 \, a^{2} c d^{2} + 2 \, {\left(7 \, b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{4} + 3 \, {\left(b^{2} c^{2} d + 20 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, d^{2} x}\right]"," ",0,"[-1/96*(3*(b^2*c^3 - 12*a*b*c^2*d - 24*a^2*c*d^2)*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(8*b^2*d^3*x^6 - 48*a^2*c*d^2 + 2*(7*b^2*c*d^2 + 12*a*b*d^3)*x^4 + 3*(b^2*c^2*d + 20*a*b*c*d^2 + 8*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/(d^2*x), 1/48*(3*(b^2*c^3 - 12*a*b*c^2*d - 24*a^2*c*d^2)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (8*b^2*d^3*x^6 - 48*a^2*c*d^2 + 2*(7*b^2*c*d^2 + 12*a*b*d^3)*x^4 + 3*(b^2*c^2*d + 20*a*b*c*d^2 + 8*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/(d^2*x)]","A",0
620,1,267,0,1.626789," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(6 \, b^{2} d^{2} x^{6} + 4 \, {\left(3 \, b^{2} c d + 5 \, a b d^{2}\right)} x^{4} - 15 \, a^{2} c d + 2 \, {\left(3 \, b^{2} c^{2} + 40 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{60 \, d x^{2}}, \frac{15 \, {\left(4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(6 \, b^{2} d^{2} x^{6} + 4 \, {\left(3 \, b^{2} c d + 5 \, a b d^{2}\right)} x^{4} - 15 \, a^{2} c d + 2 \, {\left(3 \, b^{2} c^{2} + 40 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, d x^{2}}\right]"," ",0,"[1/60*(15*(4*a*b*c*d + 3*a^2*d^2)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(6*b^2*d^2*x^6 + 4*(3*b^2*c*d + 5*a*b*d^2)*x^4 - 15*a^2*c*d + 2*(3*b^2*c^2 + 40*a*b*c*d + 15*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^2), 1/30*(15*(4*a*b*c*d + 3*a^2*d^2)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (6*b^2*d^2*x^6 + 4*(3*b^2*c*d + 5*a*b*d^2)*x^4 - 15*a^2*c*d + 2*(3*b^2*c^2 + 40*a*b*c*d + 15*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^2)]","A",0
621,1,266,0,1.575765," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b^{2} c^{2} + 24 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(6 \, b^{2} d^{2} x^{6} + 3 \, {\left(5 \, b^{2} c d + 8 \, a b d^{2}\right)} x^{4} - 8 \, a^{2} c d - 16 \, {\left(3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, d x^{3}}, -\frac{3 \, {\left(3 \, b^{2} c^{2} + 24 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(6 \, b^{2} d^{2} x^{6} + 3 \, {\left(5 \, b^{2} c d + 8 \, a b d^{2}\right)} x^{4} - 8 \, a^{2} c d - 16 \, {\left(3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, d x^{3}}\right]"," ",0,"[1/48*(3*(3*b^2*c^2 + 24*a*b*c*d + 8*a^2*d^2)*sqrt(d)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(6*b^2*d^2*x^6 + 3*(5*b^2*c*d + 8*a*b*d^2)*x^4 - 8*a^2*c*d - 16*(3*a*b*c*d + 2*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^3), -1/24*(3*(3*b^2*c^2 + 24*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (6*b^2*d^2*x^6 + 3*(5*b^2*c*d + 8*a*b*d^2)*x^4 - 8*a^2*c*d - 16*(3*a*b*c*d + 2*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^3)]","A",0
622,1,267,0,1.473622," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, b^{2} c^{2} + 24 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{c} x^{4} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(8 \, b^{2} c d x^{6} + 16 \, {\left(2 \, b^{2} c^{2} + 3 \, a b c d\right)} x^{4} - 6 \, a^{2} c^{2} - 3 \, {\left(8 \, a b c^{2} + 5 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, c x^{4}}, \frac{3 \, {\left(8 \, b^{2} c^{2} + 24 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{2} c d x^{6} + 16 \, {\left(2 \, b^{2} c^{2} + 3 \, a b c d\right)} x^{4} - 6 \, a^{2} c^{2} - 3 \, {\left(8 \, a b c^{2} + 5 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, c x^{4}}\right]"," ",0,"[1/48*(3*(8*b^2*c^2 + 24*a*b*c*d + 3*a^2*d^2)*sqrt(c)*x^4*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(8*b^2*c*d*x^6 + 16*(2*b^2*c^2 + 3*a*b*c*d)*x^4 - 6*a^2*c^2 - 3*(8*a*b*c^2 + 5*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c*x^4), 1/24*(3*(8*b^2*c^2 + 24*a*b*c*d + 3*a^2*d^2)*sqrt(-c)*x^4*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (8*b^2*c*d*x^6 + 16*(2*b^2*c^2 + 3*a*b*c*d)*x^4 - 6*a^2*c^2 - 3*(8*a*b*c^2 + 5*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c*x^4)]","A",0
623,1,266,0,1.560270," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{d} x^{5} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(15 \, b^{2} c d x^{6} - 2 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} - 6 \, a^{2} c^{2} - 4 \, {\left(5 \, a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{60 \, c x^{5}}, -\frac{15 \, {\left(3 \, b^{2} c^{2} + 4 \, a b c d\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(15 \, b^{2} c d x^{6} - 2 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} - 6 \, a^{2} c^{2} - 4 \, {\left(5 \, a b c^{2} + 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, c x^{5}}\right]"," ",0,"[1/60*(15*(3*b^2*c^2 + 4*a*b*c*d)*sqrt(d)*x^5*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(15*b^2*c*d*x^6 - 2*(15*b^2*c^2 + 40*a*b*c*d + 3*a^2*d^2)*x^4 - 6*a^2*c^2 - 4*(5*a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c*x^5), -1/30*(15*(3*b^2*c^2 + 4*a*b*c*d)*sqrt(-d)*x^5*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (15*b^2*c*d*x^6 - 2*(15*b^2*c^2 + 40*a*b*c*d + 3*a^2*d^2)*x^4 - 6*a^2*c^2 - 4*(5*a*b*c^2 + 3*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c*x^5)]","A",0
624,1,301,0,1.691248," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(24 \, b^{2} c^{2} d + 12 \, a b c d^{2} - a^{2} d^{3}\right)} \sqrt{c} x^{6} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(48 \, b^{2} c^{2} d x^{6} - 8 \, a^{2} c^{3} - 3 \, {\left(8 \, b^{2} c^{3} + 20 \, a b c^{2} d + a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(12 \, a b c^{3} + 7 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, c^{2} x^{6}}, \frac{3 \, {\left(24 \, b^{2} c^{2} d + 12 \, a b c d^{2} - a^{2} d^{3}\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(48 \, b^{2} c^{2} d x^{6} - 8 \, a^{2} c^{3} - 3 \, {\left(8 \, b^{2} c^{3} + 20 \, a b c^{2} d + a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(12 \, a b c^{3} + 7 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, c^{2} x^{6}}\right]"," ",0,"[-1/96*(3*(24*b^2*c^2*d + 12*a*b*c*d^2 - a^2*d^3)*sqrt(c)*x^6*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(48*b^2*c^2*d*x^6 - 8*a^2*c^3 - 3*(8*b^2*c^3 + 20*a*b*c^2*d + a^2*c*d^2)*x^4 - 2*(12*a*b*c^3 + 7*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^6), 1/48*(3*(24*b^2*c^2*d + 12*a*b*c*d^2 - a^2*d^3)*sqrt(-c)*x^6*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (48*b^2*c^2*d*x^6 - 8*a^2*c^3 - 3*(8*b^2*c^3 + 20*a*b*c^2*d + a^2*c*d^2)*x^4 - 2*(12*a*b*c^3 + 7*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^2*x^6)]","A",0
625,1,216,0,1.520617," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(693 \, b^{2} d^{6} x^{12} + 63 \, {\left(27 \, b^{2} c d^{5} + 26 \, a b d^{6}\right)} x^{10} + 7 \, {\left(159 \, b^{2} c^{2} d^{4} + 598 \, a b c d^{5} + 143 \, a^{2} d^{6}\right)} x^{8} - 48 \, b^{2} c^{6} + 208 \, a b c^{5} d - 286 \, a^{2} c^{4} d^{2} + {\left(15 \, b^{2} c^{3} d^{3} + 2938 \, a b c^{2} d^{4} + 2717 \, a^{2} c d^{5}\right)} x^{6} - 3 \, {\left(6 \, b^{2} c^{4} d^{2} - 26 \, a b c^{3} d^{3} - 715 \, a^{2} c^{2} d^{4}\right)} x^{4} + {\left(24 \, b^{2} c^{5} d - 104 \, a b c^{4} d^{2} + 143 \, a^{2} c^{3} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{9009 \, d^{4}}"," ",0,"1/9009*(693*b^2*d^6*x^12 + 63*(27*b^2*c*d^5 + 26*a*b*d^6)*x^10 + 7*(159*b^2*c^2*d^4 + 598*a*b*c*d^5 + 143*a^2*d^6)*x^8 - 48*b^2*c^6 + 208*a*b*c^5*d - 286*a^2*c^4*d^2 + (15*b^2*c^3*d^3 + 2938*a*b*c^2*d^4 + 2717*a^2*c*d^5)*x^6 - 3*(6*b^2*c^4*d^2 - 26*a*b*c^3*d^3 - 715*a^2*c^2*d^4)*x^4 + (24*b^2*c^5*d - 104*a*b*c^4*d^2 + 143*a^2*c^3*d^3)*x^2)*sqrt(d*x^2 + c)/d^4","B",0
626,1,495,0,2.124104," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, b^{2} c^{6} - 24 \, a b c^{5} d + 40 \, a^{2} c^{4} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(1280 \, b^{2} d^{6} x^{11} + 128 \, {\left(25 \, b^{2} c d^{5} + 24 \, a b d^{6}\right)} x^{9} + 48 \, {\left(45 \, b^{2} c^{2} d^{4} + 168 \, a b c d^{5} + 40 \, a^{2} d^{6}\right)} x^{7} + 8 \, {\left(5 \, b^{2} c^{3} d^{3} + 744 \, a b c^{2} d^{4} + 680 \, a^{2} c d^{5}\right)} x^{5} - 10 \, {\left(5 \, b^{2} c^{4} d^{2} - 24 \, a b c^{3} d^{3} - 472 \, a^{2} c^{2} d^{4}\right)} x^{3} + 15 \, {\left(5 \, b^{2} c^{5} d - 24 \, a b c^{4} d^{2} + 40 \, a^{2} c^{3} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{30720 \, d^{4}}, \frac{15 \, {\left(5 \, b^{2} c^{6} - 24 \, a b c^{5} d + 40 \, a^{2} c^{4} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(1280 \, b^{2} d^{6} x^{11} + 128 \, {\left(25 \, b^{2} c d^{5} + 24 \, a b d^{6}\right)} x^{9} + 48 \, {\left(45 \, b^{2} c^{2} d^{4} + 168 \, a b c d^{5} + 40 \, a^{2} d^{6}\right)} x^{7} + 8 \, {\left(5 \, b^{2} c^{3} d^{3} + 744 \, a b c^{2} d^{4} + 680 \, a^{2} c d^{5}\right)} x^{5} - 10 \, {\left(5 \, b^{2} c^{4} d^{2} - 24 \, a b c^{3} d^{3} - 472 \, a^{2} c^{2} d^{4}\right)} x^{3} + 15 \, {\left(5 \, b^{2} c^{5} d - 24 \, a b c^{4} d^{2} + 40 \, a^{2} c^{3} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{15360 \, d^{4}}\right]"," ",0,"[1/30720*(15*(5*b^2*c^6 - 24*a*b*c^5*d + 40*a^2*c^4*d^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(1280*b^2*d^6*x^11 + 128*(25*b^2*c*d^5 + 24*a*b*d^6)*x^9 + 48*(45*b^2*c^2*d^4 + 168*a*b*c*d^5 + 40*a^2*d^6)*x^7 + 8*(5*b^2*c^3*d^3 + 744*a*b*c^2*d^4 + 680*a^2*c*d^5)*x^5 - 10*(5*b^2*c^4*d^2 - 24*a*b*c^3*d^3 - 472*a^2*c^2*d^4)*x^3 + 15*(5*b^2*c^5*d - 24*a*b*c^4*d^2 + 40*a^2*c^3*d^3)*x)*sqrt(d*x^2 + c))/d^4, 1/15360*(15*(5*b^2*c^6 - 24*a*b*c^5*d + 40*a^2*c^4*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (1280*b^2*d^6*x^11 + 128*(25*b^2*c*d^5 + 24*a*b*d^6)*x^9 + 48*(45*b^2*c^2*d^4 + 168*a*b*c*d^5 + 40*a^2*d^6)*x^7 + 8*(5*b^2*c^3*d^3 + 744*a*b*c^2*d^4 + 680*a^2*c*d^5)*x^5 - 10*(5*b^2*c^4*d^2 - 24*a*b*c^3*d^3 - 472*a^2*c^2*d^4)*x^3 + 15*(5*b^2*c^5*d - 24*a*b*c^4*d^2 + 40*a^2*c^3*d^3)*x)*sqrt(d*x^2 + c))/d^4]","A",0
627,1,178,0,1.457338," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(63 \, b^{2} d^{5} x^{10} + 7 \, {\left(23 \, b^{2} c d^{4} + 22 \, a b d^{5}\right)} x^{8} + 8 \, b^{2} c^{5} - 44 \, a b c^{4} d + 99 \, a^{2} c^{3} d^{2} + {\left(113 \, b^{2} c^{2} d^{3} + 418 \, a b c d^{4} + 99 \, a^{2} d^{5}\right)} x^{6} + 3 \, {\left(b^{2} c^{3} d^{2} + 110 \, a b c^{2} d^{3} + 99 \, a^{2} c d^{4}\right)} x^{4} - {\left(4 \, b^{2} c^{4} d - 22 \, a b c^{3} d^{2} - 297 \, a^{2} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{693 \, d^{3}}"," ",0,"1/693*(63*b^2*d^5*x^10 + 7*(23*b^2*c*d^4 + 22*a*b*d^5)*x^8 + 8*b^2*c^5 - 44*a*b*c^4*d + 99*a^2*c^3*d^2 + (113*b^2*c^2*d^3 + 418*a*b*c*d^4 + 99*a^2*d^5)*x^6 + 3*(b^2*c^3*d^2 + 110*a*b*c^2*d^3 + 99*a^2*c*d^4)*x^4 - (4*b^2*c^4*d - 22*a*b*c^3*d^2 - 297*a^2*c^2*d^3)*x^2)*sqrt(d*x^2 + c)/d^3","B",0
628,1,420,0,1.883891," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{2} c^{5} - 20 \, a b c^{4} d + 80 \, a^{2} c^{3} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(384 \, b^{2} d^{5} x^{9} + 48 \, {\left(21 \, b^{2} c d^{4} + 20 \, a b d^{5}\right)} x^{7} + 8 \, {\left(93 \, b^{2} c^{2} d^{3} + 340 \, a b c d^{4} + 80 \, a^{2} d^{5}\right)} x^{5} + 10 \, {\left(3 \, b^{2} c^{3} d^{2} + 236 \, a b c^{2} d^{3} + 208 \, a^{2} c d^{4}\right)} x^{3} - 15 \, {\left(3 \, b^{2} c^{4} d - 20 \, a b c^{3} d^{2} - 176 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{7680 \, d^{3}}, -\frac{15 \, {\left(3 \, b^{2} c^{5} - 20 \, a b c^{4} d + 80 \, a^{2} c^{3} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(384 \, b^{2} d^{5} x^{9} + 48 \, {\left(21 \, b^{2} c d^{4} + 20 \, a b d^{5}\right)} x^{7} + 8 \, {\left(93 \, b^{2} c^{2} d^{3} + 340 \, a b c d^{4} + 80 \, a^{2} d^{5}\right)} x^{5} + 10 \, {\left(3 \, b^{2} c^{3} d^{2} + 236 \, a b c^{2} d^{3} + 208 \, a^{2} c d^{4}\right)} x^{3} - 15 \, {\left(3 \, b^{2} c^{4} d - 20 \, a b c^{3} d^{2} - 176 \, a^{2} c^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{3840 \, d^{3}}\right]"," ",0,"[1/7680*(15*(3*b^2*c^5 - 20*a*b*c^4*d + 80*a^2*c^3*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(384*b^2*d^5*x^9 + 48*(21*b^2*c*d^4 + 20*a*b*d^5)*x^7 + 8*(93*b^2*c^2*d^3 + 340*a*b*c*d^4 + 80*a^2*d^5)*x^5 + 10*(3*b^2*c^3*d^2 + 236*a*b*c^2*d^3 + 208*a^2*c*d^4)*x^3 - 15*(3*b^2*c^4*d - 20*a*b*c^3*d^2 - 176*a^2*c^2*d^3)*x)*sqrt(d*x^2 + c))/d^3, -1/3840*(15*(3*b^2*c^5 - 20*a*b*c^4*d + 80*a^2*c^3*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (384*b^2*d^5*x^9 + 48*(21*b^2*c*d^4 + 20*a*b*d^5)*x^7 + 8*(93*b^2*c^2*d^3 + 340*a*b*c*d^4 + 80*a^2*d^5)*x^5 + 10*(3*b^2*c^3*d^2 + 236*a*b*c^2*d^3 + 208*a^2*c*d^4)*x^3 - 15*(3*b^2*c^4*d - 20*a*b*c^3*d^2 - 176*a^2*c^2*d^3)*x)*sqrt(d*x^2 + c))/d^3]","A",0
629,1,360,0,1.642879," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{315 \, a^{2} c^{\frac{5}{2}} d^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(35 \, b^{2} d^{4} x^{8} + 5 \, {\left(19 \, b^{2} c d^{3} + 18 \, a b d^{4}\right)} x^{6} - 10 \, b^{2} c^{4} + 90 \, a b c^{3} d + 483 \, a^{2} c^{2} d^{2} + 3 \, {\left(25 \, b^{2} c^{2} d^{2} + 90 \, a b c d^{3} + 21 \, a^{2} d^{4}\right)} x^{4} + {\left(5 \, b^{2} c^{3} d + 270 \, a b c^{2} d^{2} + 231 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{630 \, d^{2}}, \frac{315 \, a^{2} \sqrt{-c} c^{2} d^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(35 \, b^{2} d^{4} x^{8} + 5 \, {\left(19 \, b^{2} c d^{3} + 18 \, a b d^{4}\right)} x^{6} - 10 \, b^{2} c^{4} + 90 \, a b c^{3} d + 483 \, a^{2} c^{2} d^{2} + 3 \, {\left(25 \, b^{2} c^{2} d^{2} + 90 \, a b c d^{3} + 21 \, a^{2} d^{4}\right)} x^{4} + {\left(5 \, b^{2} c^{3} d + 270 \, a b c^{2} d^{2} + 231 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{315 \, d^{2}}\right]"," ",0,"[1/630*(315*a^2*c^(5/2)*d^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(35*b^2*d^4*x^8 + 5*(19*b^2*c*d^3 + 18*a*b*d^4)*x^6 - 10*b^2*c^4 + 90*a*b*c^3*d + 483*a^2*c^2*d^2 + 3*(25*b^2*c^2*d^2 + 90*a*b*c*d^3 + 21*a^2*d^4)*x^4 + (5*b^2*c^3*d + 270*a*b*c^2*d^2 + 231*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/d^2, 1/315*(315*a^2*sqrt(-c)*c^2*d^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (35*b^2*d^4*x^8 + 5*(19*b^2*c*d^3 + 18*a*b*d^4)*x^6 - 10*b^2*c^4 + 90*a*b*c^3*d + 483*a^2*c^2*d^2 + 3*(25*b^2*c^2*d^2 + 90*a*b*c*d^3 + 21*a^2*d^4)*x^4 + (5*b^2*c^3*d + 270*a*b*c^2*d^2 + 231*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/d^2]","A",0
630,1,375,0,1.692100," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} c^{4} - 16 \, a b c^{3} d - 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(48 \, b^{2} d^{4} x^{8} + 8 \, {\left(17 \, b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{6} - 384 \, a^{2} c^{2} d^{2} + 2 \, {\left(59 \, b^{2} c^{2} d^{2} + 208 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{4} + 3 \, {\left(5 \, b^{2} c^{3} d + 176 \, a b c^{2} d^{2} + 144 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{768 \, d^{2} x}, \frac{15 \, {\left(b^{2} c^{4} - 16 \, a b c^{3} d - 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(48 \, b^{2} d^{4} x^{8} + 8 \, {\left(17 \, b^{2} c d^{3} + 16 \, a b d^{4}\right)} x^{6} - 384 \, a^{2} c^{2} d^{2} + 2 \, {\left(59 \, b^{2} c^{2} d^{2} + 208 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{4} + 3 \, {\left(5 \, b^{2} c^{3} d + 176 \, a b c^{2} d^{2} + 144 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{384 \, d^{2} x}\right]"," ",0,"[-1/768*(15*(b^2*c^4 - 16*a*b*c^3*d - 48*a^2*c^2*d^2)*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(48*b^2*d^4*x^8 + 8*(17*b^2*c*d^3 + 16*a*b*d^4)*x^6 - 384*a^2*c^2*d^2 + 2*(59*b^2*c^2*d^2 + 208*a*b*c*d^3 + 48*a^2*d^4)*x^4 + 3*(5*b^2*c^3*d + 176*a*b*c^2*d^2 + 144*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(d^2*x), 1/384*(15*(b^2*c^4 - 16*a*b*c^3*d - 48*a^2*c^2*d^2)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (48*b^2*d^4*x^8 + 8*(17*b^2*c*d^3 + 16*a*b*d^4)*x^6 - 384*a^2*c^2*d^2 + 2*(59*b^2*c^2*d^2 + 208*a*b*c*d^3 + 48*a^2*d^4)*x^4 + 3*(5*b^2*c^3*d + 176*a*b*c^2*d^2 + 144*a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(d^2*x)]","A",0
631,1,349,0,1.575394," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(30 \, b^{2} d^{3} x^{8} + 6 \, {\left(15 \, b^{2} c d^{2} + 14 \, a b d^{3}\right)} x^{6} - 105 \, a^{2} c^{2} d + 2 \, {\left(45 \, b^{2} c^{2} d + 154 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} + 322 \, a b c^{2} d + 245 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{420 \, d x^{2}}, \frac{105 \, {\left(4 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(30 \, b^{2} d^{3} x^{8} + 6 \, {\left(15 \, b^{2} c d^{2} + 14 \, a b d^{3}\right)} x^{6} - 105 \, a^{2} c^{2} d + 2 \, {\left(45 \, b^{2} c^{2} d + 154 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{4} + 2 \, {\left(15 \, b^{2} c^{3} + 322 \, a b c^{2} d + 245 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{210 \, d x^{2}}\right]"," ",0,"[1/420*(105*(4*a*b*c^2*d + 5*a^2*c*d^2)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(30*b^2*d^3*x^8 + 6*(15*b^2*c*d^2 + 14*a*b*d^3)*x^6 - 105*a^2*c^2*d + 2*(45*b^2*c^2*d + 154*a*b*c*d^2 + 35*a^2*d^3)*x^4 + 2*(15*b^2*c^3 + 322*a*b*c^2*d + 245*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^2), 1/210*(105*(4*a*b*c^2*d + 5*a^2*c*d^2)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (30*b^2*d^3*x^8 + 6*(15*b^2*c*d^2 + 14*a*b*d^3)*x^6 - 105*a^2*c^2*d + 2*(45*b^2*c^2*d + 154*a*b*c*d^2 + 35*a^2*d^3)*x^4 + 2*(15*b^2*c^3 + 322*a*b*c^2*d + 245*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^2)]","A",0
632,1,346,0,1.584260," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{3} + 12 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{d} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(8 \, b^{2} d^{3} x^{8} + 2 \, {\left(13 \, b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{6} - 16 \, a^{2} c^{2} d + 3 \, {\left(11 \, b^{2} c^{2} d + 36 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{4} - 16 \, {\left(6 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, d x^{3}}, -\frac{15 \, {\left(b^{2} c^{3} + 12 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, b^{2} d^{3} x^{8} + 2 \, {\left(13 \, b^{2} c d^{2} + 12 \, a b d^{3}\right)} x^{6} - 16 \, a^{2} c^{2} d + 3 \, {\left(11 \, b^{2} c^{2} d + 36 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{4} - 16 \, {\left(6 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, d x^{3}}\right]"," ",0,"[1/96*(15*(b^2*c^3 + 12*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(d)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(8*b^2*d^3*x^8 + 2*(13*b^2*c*d^2 + 12*a*b*d^3)*x^6 - 16*a^2*c^2*d + 3*(11*b^2*c^2*d + 36*a*b*c*d^2 + 8*a^2*d^3)*x^4 - 16*(6*a*b*c^2*d + 7*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^3), -1/48*(15*(b^2*c^3 + 12*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(-d)*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (8*b^2*d^3*x^8 + 2*(13*b^2*c*d^2 + 12*a*b*d^3)*x^6 - 16*a^2*c^2*d + 3*(11*b^2*c^2*d + 36*a*b*c*d^2 + 8*a^2*d^3)*x^4 - 16*(6*a*b*c^2*d + 7*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(d*x^3)]","A",0
633,1,319,0,1.496704," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, b^{2} c^{2} + 40 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{c} x^{4} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(24 \, b^{2} d^{2} x^{8} + 8 \, {\left(11 \, b^{2} c d + 10 \, a b d^{2}\right)} x^{6} + 8 \, {\left(23 \, b^{2} c^{2} + 70 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{4} - 30 \, a^{2} c^{2} - 15 \, {\left(8 \, a b c^{2} + 9 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{240 \, x^{4}}, \frac{15 \, {\left(8 \, b^{2} c^{2} + 40 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(24 \, b^{2} d^{2} x^{8} + 8 \, {\left(11 \, b^{2} c d + 10 \, a b d^{2}\right)} x^{6} + 8 \, {\left(23 \, b^{2} c^{2} + 70 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{4} - 30 \, a^{2} c^{2} - 15 \, {\left(8 \, a b c^{2} + 9 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{120 \, x^{4}}\right]"," ",0,"[1/240*(15*(8*b^2*c^2 + 40*a*b*c*d + 15*a^2*d^2)*sqrt(c)*x^4*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(24*b^2*d^2*x^8 + 8*(11*b^2*c*d + 10*a*b*d^2)*x^6 + 8*(23*b^2*c^2 + 70*a*b*c*d + 15*a^2*d^2)*x^4 - 30*a^2*c^2 - 15*(8*a*b*c^2 + 9*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/x^4, 1/120*(15*(8*b^2*c^2 + 40*a*b*c*d + 15*a^2*d^2)*sqrt(-c)*x^4*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (24*b^2*d^2*x^8 + 8*(11*b^2*c*d + 10*a*b*d^2)*x^6 + 8*(23*b^2*c^2 + 70*a*b*c*d + 15*a^2*d^2)*x^4 - 30*a^2*c^2 - 15*(8*a*b*c^2 + 9*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/x^4]","A",0
634,1,318,0,1.051262," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} x^{5} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(30 \, b^{2} d^{2} x^{8} + 15 \, {\left(9 \, b^{2} c d + 8 \, a b d^{2}\right)} x^{6} - 8 \, {\left(15 \, b^{2} c^{2} + 70 \, a b c d + 23 \, a^{2} d^{2}\right)} x^{4} - 24 \, a^{2} c^{2} - 8 \, {\left(10 \, a b c^{2} + 11 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{240 \, x^{5}}, -\frac{15 \, {\left(15 \, b^{2} c^{2} + 40 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(30 \, b^{2} d^{2} x^{8} + 15 \, {\left(9 \, b^{2} c d + 8 \, a b d^{2}\right)} x^{6} - 8 \, {\left(15 \, b^{2} c^{2} + 70 \, a b c d + 23 \, a^{2} d^{2}\right)} x^{4} - 24 \, a^{2} c^{2} - 8 \, {\left(10 \, a b c^{2} + 11 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{120 \, x^{5}}\right]"," ",0,"[1/240*(15*(15*b^2*c^2 + 40*a*b*c*d + 8*a^2*d^2)*sqrt(d)*x^5*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(30*b^2*d^2*x^8 + 15*(9*b^2*c*d + 8*a*b*d^2)*x^6 - 8*(15*b^2*c^2 + 70*a*b*c*d + 23*a^2*d^2)*x^4 - 24*a^2*c^2 - 8*(10*a*b*c^2 + 11*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/x^5, -1/120*(15*(15*b^2*c^2 + 40*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*x^5*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (30*b^2*d^2*x^8 + 15*(9*b^2*c*d + 8*a*b*d^2)*x^6 - 8*(15*b^2*c^2 + 70*a*b*c*d + 23*a^2*d^2)*x^4 - 24*a^2*c^2 - 8*(10*a*b*c^2 + 11*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/x^5]","A",0
635,1,347,0,1.695778," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, b^{2} c^{2} d + 12 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{c} x^{6} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(16 \, b^{2} c d^{2} x^{8} + 16 \, {\left(7 \, b^{2} c^{2} d + 6 \, a b c d^{2}\right)} x^{6} - 8 \, a^{2} c^{3} - 3 \, {\left(8 \, b^{2} c^{3} + 36 \, a b c^{2} d + 11 \, a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(12 \, a b c^{3} + 13 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, c x^{6}}, \frac{15 \, {\left(8 \, b^{2} c^{2} d + 12 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(16 \, b^{2} c d^{2} x^{8} + 16 \, {\left(7 \, b^{2} c^{2} d + 6 \, a b c d^{2}\right)} x^{6} - 8 \, a^{2} c^{3} - 3 \, {\left(8 \, b^{2} c^{3} + 36 \, a b c^{2} d + 11 \, a^{2} c d^{2}\right)} x^{4} - 2 \, {\left(12 \, a b c^{3} + 13 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, c x^{6}}\right]"," ",0,"[1/96*(15*(8*b^2*c^2*d + 12*a*b*c*d^2 + a^2*d^3)*sqrt(c)*x^6*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(16*b^2*c*d^2*x^8 + 16*(7*b^2*c^2*d + 6*a*b*c*d^2)*x^6 - 8*a^2*c^3 - 3*(8*b^2*c^3 + 36*a*b*c^2*d + 11*a^2*c*d^2)*x^4 - 2*(12*a*b*c^3 + 13*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c*x^6), 1/48*(15*(8*b^2*c^2*d + 12*a*b*c*d^2 + a^2*d^3)*sqrt(-c)*x^6*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (16*b^2*c*d^2*x^8 + 16*(7*b^2*c^2*d + 6*a*b*c*d^2)*x^6 - 8*a^2*c^3 - 3*(8*b^2*c^3 + 36*a*b*c^2*d + 11*a^2*c*d^2)*x^4 - 2*(12*a*b*c^3 + 13*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c*x^6)]","A",0
636,1,344,0,1.173962," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{2} c^{4} - 80 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(48 \, b^{2} d^{4} x^{7} - 8 \, {\left(7 \, b^{2} c d^{3} - 16 \, a b d^{4}\right)} x^{5} + 2 \, {\left(35 \, b^{2} c^{2} d^{2} - 80 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(35 \, b^{2} c^{3} d - 80 \, a b c^{2} d^{2} + 48 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{768 \, d^{5}}, -\frac{3 \, {\left(35 \, b^{2} c^{4} - 80 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(48 \, b^{2} d^{4} x^{7} - 8 \, {\left(7 \, b^{2} c d^{3} - 16 \, a b d^{4}\right)} x^{5} + 2 \, {\left(35 \, b^{2} c^{2} d^{2} - 80 \, a b c d^{3} + 48 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(35 \, b^{2} c^{3} d - 80 \, a b c^{2} d^{2} + 48 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{384 \, d^{5}}\right]"," ",0,"[1/768*(3*(35*b^2*c^4 - 80*a*b*c^3*d + 48*a^2*c^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(48*b^2*d^4*x^7 - 8*(7*b^2*c*d^3 - 16*a*b*d^4)*x^5 + 2*(35*b^2*c^2*d^2 - 80*a*b*c*d^3 + 48*a^2*d^4)*x^3 - 3*(35*b^2*c^3*d - 80*a*b*c^2*d^2 + 48*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^5, -1/384*(3*(35*b^2*c^4 - 80*a*b*c^3*d + 48*a^2*c^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (48*b^2*d^4*x^7 - 8*(7*b^2*c*d^3 - 16*a*b*d^4)*x^5 + 2*(35*b^2*c^2*d^2 - 80*a*b*c*d^3 + 48*a^2*d^4)*x^3 - 3*(35*b^2*c^3*d - 80*a*b*c^2*d^2 + 48*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/d^5]","A",0
637,1,103,0,1.404129," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, b^{2} d^{3} x^{6} - 48 \, b^{2} c^{3} + 112 \, a b c^{2} d - 70 \, a^{2} c d^{2} - 6 \, {\left(3 \, b^{2} c d^{2} - 7 \, a b d^{3}\right)} x^{4} + {\left(24 \, b^{2} c^{2} d - 56 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{105 \, d^{4}}"," ",0,"1/105*(15*b^2*d^3*x^6 - 48*b^2*c^3 + 112*a*b*c^2*d - 70*a^2*c*d^2 - 6*(3*b^2*c*d^2 - 7*a*b*d^3)*x^4 + (24*b^2*c^2*d - 56*a*b*c*d^2 + 35*a^2*d^3)*x^2)*sqrt(d*x^2 + c)/d^4","A",0
638,1,267,0,0.917825," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{2} c^{3} - 12 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(8 \, b^{2} d^{3} x^{5} - 2 \, {\left(5 \, b^{2} c d^{2} - 12 \, a b d^{3}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, d^{4}}, \frac{3 \, {\left(5 \, b^{2} c^{3} - 12 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{2} d^{3} x^{5} - 2 \, {\left(5 \, b^{2} c d^{2} - 12 \, a b d^{3}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, d^{4}}\right]"," ",0,"[1/96*(3*(5*b^2*c^3 - 12*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(8*b^2*d^3*x^5 - 2*(5*b^2*c*d^2 - 12*a*b*d^3)*x^3 + 3*(5*b^2*c^2*d - 12*a*b*c*d^2 + 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/d^4, 1/48*(3*(5*b^2*c^3 - 12*a*b*c^2*d + 8*a^2*c*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (8*b^2*d^3*x^5 - 2*(5*b^2*c*d^2 - 12*a*b*d^3)*x^3 + 3*(5*b^2*c^2*d - 12*a*b*c*d^2 + 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/d^4]","A",0
639,1,68,0,1.475832," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2} - 2 \, {\left(2 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, d^{3}}"," ",0,"1/15*(3*b^2*d^2*x^4 + 8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 - 2*(2*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c)/d^3","A",0
640,1,194,0,1.428531," ","integrate((b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} - {\left(3 \, b^{2} c d - 8 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, d^{3}}, -\frac{{\left(3 \, b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b^{2} d^{2} x^{3} - {\left(3 \, b^{2} c d - 8 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, d^{3}}\right]"," ",0,"[1/16*((3*b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^2*d^2*x^3 - (3*b^2*c*d - 8*a*b*d^2)*x)*sqrt(d*x^2 + c))/d^3, -1/8*((3*b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (2*b^2*d^2*x^3 - (3*b^2*c*d - 8*a*b*d^2)*x)*sqrt(d*x^2 + c))/d^3]","A",0
641,1,157,0,1.661981," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{c} d^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(b^{2} c d x^{2} - 2 \, b^{2} c^{2} + 6 \, a b c d\right)} \sqrt{d x^{2} + c}}{6 \, c d^{2}}, \frac{3 \, a^{2} \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c d x^{2} - 2 \, b^{2} c^{2} + 6 \, a b c d\right)} \sqrt{d x^{2} + c}}{3 \, c d^{2}}\right]"," ",0,"[1/6*(3*a^2*sqrt(c)*d^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(b^2*c*d*x^2 - 2*b^2*c^2 + 6*a*b*c*d)*sqrt(d*x^2 + c))/(c*d^2), 1/3*(3*a^2*sqrt(-c)*d^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b^2*c*d*x^2 - 2*b^2*c^2 + 6*a*b*c*d)*sqrt(d*x^2 + c))/(c*d^2)]","A",0
642,1,165,0,0.970346," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 4 \, a b c d\right)} \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(b^{2} c d x^{2} - 2 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{4 \, c d^{2} x}, \frac{{\left(b^{2} c^{2} - 4 \, a b c d\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c d x^{2} - 2 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{2 \, c d^{2} x}\right]"," ",0,"[-1/4*((b^2*c^2 - 4*a*b*c*d)*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(b^2*c*d*x^2 - 2*a^2*d^2)*sqrt(d*x^2 + c))/(c*d^2*x), 1/2*((b^2*c^2 - 4*a*b*c*d)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b^2*c*d*x^2 - 2*a^2*d^2)*sqrt(d*x^2 + c))/(c*d^2*x)]","A",0
643,1,175,0,1.540130," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a b c d - a^{2} d^{2}\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, b^{2} c^{2} x^{2} - a^{2} c d\right)} \sqrt{d x^{2} + c}}{4 \, c^{2} d x^{2}}, \frac{{\left(4 \, a b c d - a^{2} d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b^{2} c^{2} x^{2} - a^{2} c d\right)} \sqrt{d x^{2} + c}}{2 \, c^{2} d x^{2}}\right]"," ",0,"[-1/4*((4*a*b*c*d - a^2*d^2)*sqrt(c)*x^2*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*b^2*c^2*x^2 - a^2*c*d)*sqrt(d*x^2 + c))/(c^2*d*x^2), 1/2*((4*a*b*c*d - a^2*d^2)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*b^2*c^2*x^2 - a^2*c*d)*sqrt(d*x^2 + c))/(c^2*d*x^2)]","A",0
644,1,173,0,1.538585," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} c^{2} \sqrt{d} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(a^{2} c d + 2 \, {\left(3 \, a b c d - a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, c^{2} d x^{3}}, -\frac{3 \, b^{2} c^{2} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a^{2} c d + 2 \, {\left(3 \, a b c d - a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, c^{2} d x^{3}}\right]"," ",0,"[1/6*(3*b^2*c^2*sqrt(d)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(a^2*c*d + 2*(3*a*b*c*d - a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c^2*d*x^3), -1/3*(3*b^2*c^2*sqrt(-d)*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a^2*c*d + 2*(3*a*b*c*d - a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c^2*d*x^3)]","A",0
645,1,204,0,0.819734," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{c} x^{4} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, a^{2} c^{2} + {\left(8 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{16 \, c^{3} x^{4}}, \frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a^{2} c^{2} + {\left(8 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, c^{3} x^{4}}\right]"," ",0,"[1/16*((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*sqrt(c)*x^4*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*a^2*c^2 + (8*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^3*x^4), 1/8*((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*sqrt(-c)*x^4*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a^2*c^2 + (8*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(c^3*x^4)]","A",0
646,1,73,0,1.307844," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(15 \, b^{2} c^{2} - 20 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} + 2 \, {\left(5 \, a b c^{2} - 2 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, c^{3} x^{5}}"," ",0,"-1/15*((15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*x^4 + 3*a^2*c^2 + 2*(5*a*b*c^2 - 2*a^2*c*d)*x^2)*sqrt(d*x^2 + c)/(c^3*x^5)","A",0
647,1,279,0,1.428314," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} \sqrt{c} x^{6} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(8 \, a^{2} c^{3} + 3 \, {\left(8 \, b^{2} c^{3} - 12 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{3} - 5 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, c^{4} x^{6}}, -\frac{3 \, {\left(8 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, a^{2} c^{3} + 3 \, {\left(8 \, b^{2} c^{3} - 12 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{3} - 5 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, c^{4} x^{6}}\right]"," ",0,"[1/96*(3*(8*b^2*c^2*d - 12*a*b*c*d^2 + 5*a^2*d^3)*sqrt(c)*x^6*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(8*a^2*c^3 + 3*(8*b^2*c^3 - 12*a*b*c^2*d + 5*a^2*c*d^2)*x^4 + 2*(12*a*b*c^3 - 5*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^4*x^6), -1/48*(3*(8*b^2*c^2*d - 12*a*b*c*d^2 + 5*a^2*d^3)*sqrt(-c)*x^6*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (8*a^2*c^3 + 3*(8*b^2*c^3 - 12*a*b*c^2*d + 5*a^2*c*d^2)*x^4 + 2*(12*a*b*c^3 - 5*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^4*x^6)]","A",0
648,1,431,0,1.440691," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{2} c^{4} - 60 \, a b c^{3} d + 24 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 24 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(8 \, b^{2} d^{4} x^{7} - 2 \, {\left(7 \, b^{2} c d^{3} - 12 \, a b d^{4}\right)} x^{5} + {\left(35 \, b^{2} c^{2} d^{2} - 60 \, a b c d^{3} + 24 \, a^{2} d^{4}\right)} x^{3} + 3 \, {\left(35 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, {\left(d^{6} x^{2} + c d^{5}\right)}}, \frac{3 \, {\left(35 \, b^{2} c^{4} - 60 \, a b c^{3} d + 24 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 24 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{2} d^{4} x^{7} - 2 \, {\left(7 \, b^{2} c d^{3} - 12 \, a b d^{4}\right)} x^{5} + {\left(35 \, b^{2} c^{2} d^{2} - 60 \, a b c d^{3} + 24 \, a^{2} d^{4}\right)} x^{3} + 3 \, {\left(35 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 24 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, {\left(d^{6} x^{2} + c d^{5}\right)}}\right]"," ",0,"[1/96*(3*(35*b^2*c^4 - 60*a*b*c^3*d + 24*a^2*c^2*d^2 + (35*b^2*c^3*d - 60*a*b*c^2*d^2 + 24*a^2*c*d^3)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(8*b^2*d^4*x^7 - 2*(7*b^2*c*d^3 - 12*a*b*d^4)*x^5 + (35*b^2*c^2*d^2 - 60*a*b*c*d^3 + 24*a^2*d^4)*x^3 + 3*(35*b^2*c^3*d - 60*a*b*c^2*d^2 + 24*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(d^6*x^2 + c*d^5), 1/48*(3*(35*b^2*c^4 - 60*a*b*c^3*d + 24*a^2*c^2*d^2 + (35*b^2*c^3*d - 60*a*b*c^2*d^2 + 24*a^2*c*d^3)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (8*b^2*d^4*x^7 - 2*(7*b^2*c*d^3 - 12*a*b*d^4)*x^5 + (35*b^2*c^2*d^2 - 60*a*b*c*d^3 + 24*a^2*d^4)*x^3 + 3*(35*b^2*c^3*d - 60*a*b*c^2*d^2 + 24*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(d^6*x^2 + c*d^5)]","A",0
649,1,115,0,0.751461," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} d^{3} x^{6} + 48 \, b^{2} c^{3} - 80 \, a b c^{2} d + 30 \, a^{2} c d^{2} - 2 \, {\left(3 \, b^{2} c d^{2} - 5 \, a b d^{3}\right)} x^{4} + {\left(24 \, b^{2} c^{2} d - 40 \, a b c d^{2} + 15 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, {\left(d^{5} x^{2} + c d^{4}\right)}}"," ",0,"1/15*(3*b^2*d^3*x^6 + 48*b^2*c^3 - 80*a*b*c^2*d + 30*a^2*c*d^2 - 2*(3*b^2*c*d^2 - 5*a*b*d^3)*x^4 + (24*b^2*c^2*d - 40*a*b*c*d^2 + 15*a^2*d^3)*x^2)*sqrt(d*x^2 + c)/(d^5*x^2 + c*d^4)","A",0
650,1,350,0,1.715837," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, b^{2} c^{3} - 24 \, a b c^{2} d + 8 \, a^{2} c d^{2} + {\left(15 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{2} d^{3} x^{5} - {\left(5 \, b^{2} c d^{2} - 8 \, a b d^{3}\right)} x^{3} - {\left(15 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(d^{5} x^{2} + c d^{4}\right)}}, -\frac{{\left(15 \, b^{2} c^{3} - 24 \, a b c^{2} d + 8 \, a^{2} c d^{2} + {\left(15 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b^{2} d^{3} x^{5} - {\left(5 \, b^{2} c d^{2} - 8 \, a b d^{3}\right)} x^{3} - {\left(15 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(d^{5} x^{2} + c d^{4}\right)}}\right]"," ",0,"[1/16*((15*b^2*c^3 - 24*a*b*c^2*d + 8*a^2*c*d^2 + (15*b^2*c^2*d - 24*a*b*c*d^2 + 8*a^2*d^3)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^2*d^3*x^5 - (5*b^2*c*d^2 - 8*a*b*d^3)*x^3 - (15*b^2*c^2*d - 24*a*b*c*d^2 + 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/(d^5*x^2 + c*d^4), -1/8*((15*b^2*c^3 - 24*a*b*c^2*d + 8*a^2*c*d^2 + (15*b^2*c^2*d - 24*a*b*c*d^2 + 8*a^2*d^3)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (2*b^2*d^3*x^5 - (5*b^2*c*d^2 - 8*a*b*d^3)*x^3 - (15*b^2*c^2*d - 24*a*b*c*d^2 + 8*a^2*d^3)*x)*sqrt(d*x^2 + c))/(d^5*x^2 + c*d^4)]","A",0
651,1,79,0,1.561911," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} d^{2} x^{4} - 8 \, b^{2} c^{2} + 12 \, a b c d - 3 \, a^{2} d^{2} - 2 \, {\left(2 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(d^{4} x^{2} + c d^{3}\right)}}"," ",0,"1/3*(b^2*d^2*x^4 - 8*b^2*c^2 + 12*a*b*c*d - 3*a^2*d^2 - 2*(2*b^2*c*d - 3*a*b*d^2)*x^2)*sqrt(d*x^2 + c)/(d^4*x^2 + c*d^3)","A",0
652,1,275,0,1.380160," ","integrate((b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(b^{2} c d^{2} x^{3} + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}, \frac{{\left(3 \, b^{2} c^{3} - 4 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c d^{2} x^{3} + {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{2 \, {\left(c d^{4} x^{2} + c^{2} d^{3}\right)}}\right]"," ",0,"[-1/4*((3*b^2*c^3 - 4*a*b*c^2*d + (3*b^2*c^2*d - 4*a*b*c*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(b^2*c*d^2*x^3 + (3*b^2*c^2*d - 4*a*b*c*d^2 + 2*a^2*d^3)*x)*sqrt(d*x^2 + c))/(c*d^4*x^2 + c^2*d^3), 1/2*((3*b^2*c^3 - 4*a*b*c^2*d + (3*b^2*c^2*d - 4*a*b*c*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b^2*c*d^2*x^3 + (3*b^2*c^2*d - 4*a*b*c*d^2 + 2*a^2*d^3)*x)*sqrt(d*x^2 + c))/(c*d^4*x^2 + c^2*d^3)]","A",0
653,1,232,0,1.535897," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} d^{3} x^{2} + a^{2} c d^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(b^{2} c^{2} d x^{2} + 2 \, b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{d x^{2} + c}}{2 \, {\left(c^{2} d^{3} x^{2} + c^{3} d^{2}\right)}}, \frac{{\left(a^{2} d^{3} x^{2} + a^{2} c d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c^{2} d x^{2} + 2 \, b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{d x^{2} + c}}{c^{2} d^{3} x^{2} + c^{3} d^{2}}\right]"," ",0,"[1/2*((a^2*d^3*x^2 + a^2*c*d^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(b^2*c^2*d*x^2 + 2*b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(d*x^2 + c))/(c^2*d^3*x^2 + c^3*d^2), ((a^2*d^3*x^2 + a^2*c*d^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b^2*c^2*d*x^2 + 2*b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(d*x^2 + c))/(c^2*d^3*x^2 + c^3*d^2)]","A",0
654,1,239,0,1.549073," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{2 \, {\left(c^{2} d^{3} x^{3} + c^{3} d^{2} x\right)}}, -\frac{{\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{c^{2} d^{3} x^{3} + c^{3} d^{2} x}\right]"," ",0,"[1/2*((b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + 2*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/(c^2*d^3*x^3 + c^3*d^2*x), -((b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + 2*a^2*d^3)*x^2)*sqrt(d*x^2 + c))/(c^2*d^3*x^3 + c^3*d^2*x)]","A",0
655,1,292,0,1.190560," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(4 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a^{2} c^{2} d + {\left(2 \, b^{2} c^{3} - 4 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(c^{3} d^{2} x^{4} + c^{4} d x^{2}\right)}}, \frac{{\left({\left(4 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(4 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(a^{2} c^{2} d + {\left(2 \, b^{2} c^{3} - 4 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{2 \, {\left(c^{3} d^{2} x^{4} + c^{4} d x^{2}\right)}}\right]"," ",0,"[-1/4*(((4*a*b*c*d^2 - 3*a^2*d^3)*x^4 + (4*a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a^2*c^2*d + (2*b^2*c^3 - 4*a*b*c^2*d + 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(c^3*d^2*x^4 + c^4*d*x^2), 1/2*(((4*a*b*c*d^2 - 3*a^2*d^3)*x^4 + (4*a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (a^2*c^2*d + (2*b^2*c^3 - 4*a*b*c^2*d + 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/(c^3*d^2*x^4 + c^4*d*x^2)]","A",0
656,1,85,0,1.361829," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, b^{2} c^{2} - 12 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} - a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 2 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)}}"," ",0,"1/3*((3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*x^4 - a^2*c^2 - 2*(3*a*b*c^2 - 2*a^2*c*d)*x^2)*sqrt(d*x^2 + c)/(c^3*d*x^5 + c^4*x^3)","A",0
657,1,364,0,0.997741," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 15 \, a^{2} d^{3}\right)} x^{6} + {\left(8 \, b^{2} c^{3} - 24 \, a b c^{2} d + 15 \, a^{2} c d^{2}\right)} x^{4}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, a^{2} c^{3} - {\left(8 \, b^{2} c^{3} - 24 \, a b c^{2} d + 15 \, a^{2} c d^{2}\right)} x^{4} + {\left(8 \, a b c^{3} - 5 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{16 \, {\left(c^{4} d x^{6} + c^{5} x^{4}\right)}}, \frac{{\left({\left(8 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 15 \, a^{2} d^{3}\right)} x^{6} + {\left(8 \, b^{2} c^{3} - 24 \, a b c^{2} d + 15 \, a^{2} c d^{2}\right)} x^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a^{2} c^{3} - {\left(8 \, b^{2} c^{3} - 24 \, a b c^{2} d + 15 \, a^{2} c d^{2}\right)} x^{4} + {\left(8 \, a b c^{3} - 5 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(c^{4} d x^{6} + c^{5} x^{4}\right)}}\right]"," ",0,"[1/16*(((8*b^2*c^2*d - 24*a*b*c*d^2 + 15*a^2*d^3)*x^6 + (8*b^2*c^3 - 24*a*b*c^2*d + 15*a^2*c*d^2)*x^4)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*a^2*c^3 - (8*b^2*c^3 - 24*a*b*c^2*d + 15*a^2*c*d^2)*x^4 + (8*a*b*c^3 - 5*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^4*d*x^6 + c^5*x^4), 1/8*(((8*b^2*c^2*d - 24*a*b*c*d^2 + 15*a^2*d^3)*x^6 + (8*b^2*c^3 - 24*a*b*c^2*d + 15*a^2*c*d^2)*x^4)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a^2*c^3 - (8*b^2*c^3 - 24*a*b*c^2*d + 15*a^2*c*d^2)*x^4 + (8*a*b*c^3 - 5*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c))/(c^4*d*x^6 + c^5*x^4)]","A",0
658,1,121,0,1.671139," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(15 \, b^{2} c^{2} d - 40 \, a b c d^{2} + 24 \, a^{2} d^{3}\right)} x^{6} + 3 \, a^{2} c^{3} + {\left(15 \, b^{2} c^{3} - 40 \, a b c^{2} d + 24 \, a^{2} c d^{2}\right)} x^{4} + 2 \, {\left(5 \, a b c^{3} - 3 \, a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, {\left(c^{4} d x^{7} + c^{5} x^{5}\right)}}"," ",0,"-1/15*(2*(15*b^2*c^2*d - 40*a*b*c*d^2 + 24*a^2*d^3)*x^6 + 3*a^2*c^3 + (15*b^2*c^3 - 40*a*b*c^2*d + 24*a^2*c*d^2)*x^4 + 2*(5*a*b*c^3 - 3*a^2*c^2*d)*x^2)*sqrt(d*x^2 + c)/(c^4*d*x^7 + c^5*x^5)","A",0
659,1,447,0,1.641854," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(24 \, b^{2} c^{2} d^{2} - 60 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{8} + {\left(24 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(3 \, {\left(24 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} + 8 \, a^{2} c^{4} + {\left(24 \, b^{2} c^{4} - 60 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{96 \, {\left(c^{5} d x^{8} + c^{6} x^{6}\right)}}, -\frac{3 \, {\left({\left(24 \, b^{2} c^{2} d^{2} - 60 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{8} + {\left(24 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, {\left(24 \, b^{2} c^{3} d - 60 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} + 8 \, a^{2} c^{4} + {\left(24 \, b^{2} c^{4} - 60 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4} + 2 \, {\left(12 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, {\left(c^{5} d x^{8} + c^{6} x^{6}\right)}}\right]"," ",0,"[1/96*(3*((24*b^2*c^2*d^2 - 60*a*b*c*d^3 + 35*a^2*d^4)*x^8 + (24*b^2*c^3*d - 60*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(3*(24*b^2*c^3*d - 60*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 + 8*a^2*c^4 + (24*b^2*c^4 - 60*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4 + 2*(12*a*b*c^4 - 7*a^2*c^3*d)*x^2)*sqrt(d*x^2 + c))/(c^5*d*x^8 + c^6*x^6), -1/48*(3*((24*b^2*c^2*d^2 - 60*a*b*c*d^3 + 35*a^2*d^4)*x^8 + (24*b^2*c^3*d - 60*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (3*(24*b^2*c^3*d - 60*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 + 8*a^2*c^4 + (24*b^2*c^4 - 60*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4 + 2*(12*a*b*c^4 - 7*a^2*c^3*d)*x^2)*sqrt(d*x^2 + c))/(c^5*d*x^8 + c^6*x^6)]","A",0
660,1,522,0,1.356337," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{2} c^{4} - 40 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(6 \, b^{2} d^{4} x^{7} - 3 \, {\left(7 \, b^{2} c d^{3} - 8 \, a b d^{4}\right)} x^{5} - 4 \, {\left(35 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(35 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, {\left(d^{7} x^{4} + 2 \, c d^{6} x^{2} + c^{2} d^{5}\right)}}, -\frac{3 \, {\left(35 \, b^{2} c^{4} - 40 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(6 \, b^{2} d^{4} x^{7} - 3 \, {\left(7 \, b^{2} c d^{3} - 8 \, a b d^{4}\right)} x^{5} - 4 \, {\left(35 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)} x^{3} - 3 \, {\left(35 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 8 \, a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{24 \, {\left(d^{7} x^{4} + 2 \, c d^{6} x^{2} + c^{2} d^{5}\right)}}\right]"," ",0,"[1/48*(3*(35*b^2*c^4 - 40*a*b*c^3*d + 8*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 40*a*b*c*d^3 + 8*a^2*d^4)*x^4 + 2*(35*b^2*c^3*d - 40*a*b*c^2*d^2 + 8*a^2*c*d^3)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(6*b^2*d^4*x^7 - 3*(7*b^2*c*d^3 - 8*a*b*d^4)*x^5 - 4*(35*b^2*c^2*d^2 - 40*a*b*c*d^3 + 8*a^2*d^4)*x^3 - 3*(35*b^2*c^3*d - 40*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(d^7*x^4 + 2*c*d^6*x^2 + c^2*d^5), -1/24*(3*(35*b^2*c^4 - 40*a*b*c^3*d + 8*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 40*a*b*c*d^3 + 8*a^2*d^4)*x^4 + 2*(35*b^2*c^3*d - 40*a*b*c^2*d^2 + 8*a^2*c*d^3)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (6*b^2*d^4*x^7 - 3*(7*b^2*c*d^3 - 8*a*b*d^4)*x^5 - 4*(35*b^2*c^2*d^2 - 40*a*b*c*d^3 + 8*a^2*d^4)*x^3 - 3*(35*b^2*c^3*d - 40*a*b*c^2*d^2 + 8*a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(d^7*x^4 + 2*c*d^6*x^2 + c^2*d^5)]","A",0
661,1,124,0,1.515077," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(b^{2} d^{3} x^{6} - 16 \, b^{2} c^{3} + 16 \, a b c^{2} d - 2 \, a^{2} c d^{2} - 6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{4} - 3 \, {\left(8 \, b^{2} c^{2} d - 8 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}}"," ",0,"1/3*(b^2*d^3*x^6 - 16*b^2*c^3 + 16*a*b*c^2*d - 2*a^2*c*d^2 - 6*(b^2*c*d^2 - a*b*d^3)*x^4 - 3*(8*b^2*c^2*d - 8*a*b*c*d^2 + a^2*d^3)*x^2)*sqrt(d*x^2 + c)/(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4)","A",0
662,1,409,0,1.227956," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{2} c^{4} - 4 \, a b c^{3} d + {\left(5 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3}\right)} x^{4} + 2 \, {\left(5 \, b^{2} c^{3} d - 4 \, a b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(3 \, b^{2} c d^{3} x^{5} + 2 \, {\left(10 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + a^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{3} d - 4 \, a b c^{2} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(c d^{6} x^{4} + 2 \, c^{2} d^{5} x^{2} + c^{3} d^{4}\right)}}, \frac{3 \, {\left(5 \, b^{2} c^{4} - 4 \, a b c^{3} d + {\left(5 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3}\right)} x^{4} + 2 \, {\left(5 \, b^{2} c^{3} d - 4 \, a b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, b^{2} c d^{3} x^{5} + 2 \, {\left(10 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + a^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{2} c^{3} d - 4 \, a b c^{2} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{6 \, {\left(c d^{6} x^{4} + 2 \, c^{2} d^{5} x^{2} + c^{3} d^{4}\right)}}\right]"," ",0,"[-1/12*(3*(5*b^2*c^4 - 4*a*b*c^3*d + (5*b^2*c^2*d^2 - 4*a*b*c*d^3)*x^4 + 2*(5*b^2*c^3*d - 4*a*b*c^2*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(3*b^2*c*d^3*x^5 + 2*(10*b^2*c^2*d^2 - 8*a*b*c*d^3 + a^2*d^4)*x^3 + 3*(5*b^2*c^3*d - 4*a*b*c^2*d^2)*x)*sqrt(d*x^2 + c))/(c*d^6*x^4 + 2*c^2*d^5*x^2 + c^3*d^4), 1/6*(3*(5*b^2*c^4 - 4*a*b*c^3*d + (5*b^2*c^2*d^2 - 4*a*b*c*d^3)*x^4 + 2*(5*b^2*c^3*d - 4*a*b*c^2*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (3*b^2*c*d^3*x^5 + 2*(10*b^2*c^2*d^2 - 8*a*b*c*d^3 + a^2*d^4)*x^3 + 3*(5*b^2*c^3*d - 4*a*b*c^2*d^2)*x)*sqrt(d*x^2 + c))/(c*d^6*x^4 + 2*c^2*d^5*x^2 + c^3*d^4)]","A",0
663,1,91,0,1.116336," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 4 \, a b c d - a^{2} d^{2} + 6 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(d^{5} x^{4} + 2 \, c d^{4} x^{2} + c^{2} d^{3}\right)}}"," ",0,"1/3*(3*b^2*d^2*x^4 + 8*b^2*c^2 - 4*a*b*c*d - a^2*d^2 + 6*(2*b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)/(d^5*x^4 + 2*c*d^4*x^2 + c^2*d^3)","A",0
664,1,321,0,1.391672," ","integrate((b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(2 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + 3 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{6 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}, -\frac{3 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{3} + 3 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{2} d^{5} x^{4} + 2 \, c^{3} d^{4} x^{2} + c^{4} d^{3}\right)}}\right]"," ",0,"[1/6*(3*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(2*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + 3*(b^2*c^3*d - a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3), -1/3*(3*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (2*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^3 + 3*(b^2*c^3*d - a^2*c*d^3)*x)*sqrt(d*x^2 + c))/(c^2*d^5*x^4 + 2*c^3*d^4*x^2 + c^4*d^3)]","A",0
665,1,316,0,1.168234," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} d^{4} x^{4} + 2 \, a^{2} c d^{3} x^{2} + a^{2} c^{2} d^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, b^{2} c^{4} + 2 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(c^{3} d^{4} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{5} d^{2}\right)}}, \frac{3 \, {\left(a^{2} d^{4} x^{4} + 2 \, a^{2} c d^{3} x^{2} + a^{2} c^{2} d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b^{2} c^{4} + 2 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{3} d^{4} x^{4} + 2 \, c^{4} d^{3} x^{2} + c^{5} d^{2}\right)}}\right]"," ",0,"[1/6*(3*(a^2*d^4*x^4 + 2*a^2*c*d^3*x^2 + a^2*c^2*d^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*b^2*c^4 + 2*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(b^2*c^3*d - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(c^3*d^4*x^4 + 2*c^4*d^3*x^2 + c^5*d^2), 1/3*(3*(a^2*d^4*x^4 + 2*a^2*c*d^3*x^2 + a^2*c^2*d^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*b^2*c^4 + 2*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(b^2*c^3*d - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(c^3*d^4*x^4 + 2*c^4*d^3*x^2 + c^5*d^2)]","A",0
666,1,92,0,0.987512," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} c^{2} + 4 \, a b c d - 8 \, a^{2} d^{2}\right)} x^{4} - 3 \, a^{2} c^{2} + 6 \, {\left(a b c^{2} - 2 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{3} d^{2} x^{5} + 2 \, c^{4} d x^{3} + c^{5} x\right)}}"," ",0,"1/3*((b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*x^4 - 3*a^2*c^2 + 6*(a*b*c^2 - 2*a^2*c*d)*x^2)*sqrt(d*x^2 + c)/(c^3*d^2*x^5 + 2*c^4*d*x^3 + c^5*x)","A",0
667,1,426,0,1.100344," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, a b c d^{3} - 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, {\left(4 \, a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x^{4} + {\left(4 \, a b c^{3} d - 5 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(3 \, a^{2} c^{3} d - 3 \, {\left(4 \, a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 10 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(c^{4} d^{3} x^{6} + 2 \, c^{5} d^{2} x^{4} + c^{6} d x^{2}\right)}}, \frac{3 \, {\left({\left(4 \, a b c d^{3} - 5 \, a^{2} d^{4}\right)} x^{6} + 2 \, {\left(4 \, a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x^{4} + {\left(4 \, a b c^{3} d - 5 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(3 \, a^{2} c^{3} d - 3 \, {\left(4 \, a b c^{2} d^{2} - 5 \, a^{2} c d^{3}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} - 8 \, a b c^{3} d + 10 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(c^{4} d^{3} x^{6} + 2 \, c^{5} d^{2} x^{4} + c^{6} d x^{2}\right)}}\right]"," ",0,"[-1/12*(3*((4*a*b*c*d^3 - 5*a^2*d^4)*x^6 + 2*(4*a*b*c^2*d^2 - 5*a^2*c*d^3)*x^4 + (4*a*b*c^3*d - 5*a^2*c^2*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(3*a^2*c^3*d - 3*(4*a*b*c^2*d^2 - 5*a^2*c*d^3)*x^4 + 2*(b^2*c^4 - 8*a*b*c^3*d + 10*a^2*c^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c^4*d^3*x^6 + 2*c^5*d^2*x^4 + c^6*d*x^2), 1/6*(3*((4*a*b*c*d^3 - 5*a^2*d^4)*x^6 + 2*(4*a*b*c^2*d^2 - 5*a^2*c*d^3)*x^4 + (4*a*b*c^3*d - 5*a^2*c^2*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (3*a^2*c^3*d - 3*(4*a*b*c^2*d^2 - 5*a^2*c*d^3)*x^4 + 2*(b^2*c^4 - 8*a*b*c^3*d + 10*a^2*c^2*d^2)*x^2)*sqrt(d*x^2 + c))/(c^4*d^3*x^6 + 2*c^5*d^2*x^4 + c^6*d*x^2)]","A",0
668,1,130,0,1.340268," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(b^{2} c^{2} d - 8 \, a b c d^{2} + 8 \, a^{2} d^{3}\right)} x^{6} - a^{2} c^{3} + 3 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} x^{4} - 6 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{3 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)}}"," ",0,"1/3*(2*(b^2*c^2*d - 8*a*b*c*d^2 + 8*a^2*d^3)*x^6 - a^2*c^3 + 3*(b^2*c^3 - 8*a*b*c^2*d + 8*a^2*c*d^2)*x^4 - 6*(a*b*c^3 - a^2*c^2*d)*x^2)*sqrt(d*x^2 + c)/(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3)","A",0
669,1,537,0,1.332091," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{8} + 2 \, {\left(8 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} + {\left(8 \, b^{2} c^{4} - 40 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(3 \, {\left(8 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} - 6 \, a^{2} c^{4} + 4 \, {\left(8 \, b^{2} c^{4} - 40 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4} - 3 \, {\left(8 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{48 \, {\left(c^{5} d^{2} x^{8} + 2 \, c^{6} d x^{6} + c^{7} x^{4}\right)}}, \frac{3 \, {\left({\left(8 \, b^{2} c^{2} d^{2} - 40 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{8} + 2 \, {\left(8 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} + {\left(8 \, b^{2} c^{4} - 40 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, {\left(8 \, b^{2} c^{3} d - 40 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{6} - 6 \, a^{2} c^{4} + 4 \, {\left(8 \, b^{2} c^{4} - 40 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{4} - 3 \, {\left(8 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(c^{5} d^{2} x^{8} + 2 \, c^{6} d x^{6} + c^{7} x^{4}\right)}}\right]"," ",0,"[1/48*(3*((8*b^2*c^2*d^2 - 40*a*b*c*d^3 + 35*a^2*d^4)*x^8 + 2*(8*b^2*c^3*d - 40*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 + (8*b^2*c^4 - 40*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(3*(8*b^2*c^3*d - 40*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 - 6*a^2*c^4 + 4*(8*b^2*c^4 - 40*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4 - 3*(8*a*b*c^4 - 7*a^2*c^3*d)*x^2)*sqrt(d*x^2 + c))/(c^5*d^2*x^8 + 2*c^6*d*x^6 + c^7*x^4), 1/24*(3*((8*b^2*c^2*d^2 - 40*a*b*c*d^3 + 35*a^2*d^4)*x^8 + 2*(8*b^2*c^3*d - 40*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 + (8*b^2*c^4 - 40*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (3*(8*b^2*c^3*d - 40*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^6 - 6*a^2*c^4 + 4*(8*b^2*c^4 - 40*a*b*c^3*d + 35*a^2*c^2*d^2)*x^4 - 3*(8*a*b*c^4 - 7*a^2*c^3*d)*x^2)*sqrt(d*x^2 + c))/(c^5*d^2*x^8 + 2*c^6*d*x^6 + c^7*x^4)]","A",0
670,1,171,0,1.276604," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(5 \, b^{2} c^{2} d^{2} - 20 \, a b c d^{3} + 16 \, a^{2} d^{4}\right)} x^{8} + 12 \, {\left(5 \, b^{2} c^{3} d - 20 \, a b c^{2} d^{2} + 16 \, a^{2} c d^{3}\right)} x^{6} + 3 \, a^{2} c^{4} + 3 \, {\left(5 \, b^{2} c^{4} - 20 \, a b c^{3} d + 16 \, a^{2} c^{2} d^{2}\right)} x^{4} + 2 \, {\left(5 \, a b c^{4} - 4 \, a^{2} c^{3} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{15 \, {\left(c^{5} d^{2} x^{9} + 2 \, c^{6} d x^{7} + c^{7} x^{5}\right)}}"," ",0,"-1/15*(8*(5*b^2*c^2*d^2 - 20*a*b*c*d^3 + 16*a^2*d^4)*x^8 + 12*(5*b^2*c^3*d - 20*a*b*c^2*d^2 + 16*a^2*c*d^3)*x^6 + 3*a^2*c^4 + 3*(5*b^2*c^4 - 20*a*b*c^3*d + 16*a^2*c^2*d^2)*x^4 + 2*(5*a*b*c^4 - 4*a^2*c^3*d)*x^2)*sqrt(d*x^2 + c)/(c^5*d^2*x^9 + 2*c^6*d*x^7 + c^7*x^5)","A",0
671,1,147,0,1.260099," ","integrate(x^5/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a d \sqrt{-\frac{a}{b d}} \log\left(\frac{b x^{2} + 2 \, \sqrt{d x^{2}} b \sqrt{-\frac{a}{b d}} - a}{b x^{2} + a}\right) + 2 \, {\left(b x^{2} - 3 \, a\right)} \sqrt{d x^{2}}}{6 \, b^{2} d}, \frac{3 \, a d \sqrt{\frac{a}{b d}} \arctan\left(\frac{\sqrt{d x^{2}} b \sqrt{\frac{a}{b d}}}{a}\right) + {\left(b x^{2} - 3 \, a\right)} \sqrt{d x^{2}}}{3 \, b^{2} d}\right]"," ",0,"[1/6*(3*a*d*sqrt(-a/(b*d))*log((b*x^2 + 2*sqrt(d*x^2)*b*sqrt(-a/(b*d)) - a)/(b*x^2 + a)) + 2*(b*x^2 - 3*a)*sqrt(d*x^2))/(b^2*d), 1/3*(3*a*d*sqrt(a/(b*d))*arctan(sqrt(d*x^2)*b*sqrt(a/(b*d))/a) + (b*x^2 - 3*a)*sqrt(d*x^2))/(b^2*d)]","A",0
672,1,126,0,1.234928," ","integrate(x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{b d}} \log\left(\frac{b x^{2} - 2 \, \sqrt{d x^{2}} b \sqrt{-\frac{a}{b d}} - a}{b x^{2} + a}\right) + 2 \, \sqrt{d x^{2}}}{2 \, b d}, -\frac{d \sqrt{\frac{a}{b d}} \arctan\left(\frac{\sqrt{d x^{2}} b \sqrt{\frac{a}{b d}}}{a}\right) - \sqrt{d x^{2}}}{b d}\right]"," ",0,"[1/2*(d*sqrt(-a/(b*d))*log((b*x^2 - 2*sqrt(d*x^2)*b*sqrt(-a/(b*d)) - a)/(b*x^2 + a)) + 2*sqrt(d*x^2))/(b*d), -(d*sqrt(a/(b*d))*arctan(sqrt(d*x^2)*b*sqrt(a/(b*d))/a) - sqrt(d*x^2))/(b*d)]","A",0
673,1,94,0,1.245756," ","integrate(x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b d} \log\left(\frac{b d x^{2} - a d - 2 \, \sqrt{-a b d} \sqrt{d x^{2}}}{b x^{2} + a}\right)}{2 \, a b d}, \frac{\sqrt{a b d} \arctan\left(\frac{\sqrt{a b d} \sqrt{d x^{2}}}{a d}\right)}{a b d}\right]"," ",0,"[-1/2*sqrt(-a*b*d)*log((b*d*x^2 - a*d - 2*sqrt(-a*b*d)*sqrt(d*x^2))/(b*x^2 + a))/(a*b*d), sqrt(a*b*d)*arctan(sqrt(a*b*d)*sqrt(d*x^2)/(a*d))/(a*b*d)]","A",0
674,1,132,0,0.791299," ","integrate(1/x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{d x^{2} \sqrt{-\frac{b}{a d}} \log\left(\frac{b x^{2} - 2 \, \sqrt{d x^{2}} a \sqrt{-\frac{b}{a d}} - a}{b x^{2} + a}\right) - 2 \, \sqrt{d x^{2}}}{2 \, a d x^{2}}, -\frac{d x^{2} \sqrt{\frac{b}{a d}} \arctan\left(\sqrt{d x^{2}} \sqrt{\frac{b}{a d}}\right) + \sqrt{d x^{2}}}{a d x^{2}}\right]"," ",0,"[1/2*(d*x^2*sqrt(-b/(a*d))*log((b*x^2 - 2*sqrt(d*x^2)*a*sqrt(-b/(a*d)) - a)/(b*x^2 + a)) - 2*sqrt(d*x^2))/(a*d*x^2), -(d*x^2*sqrt(b/(a*d))*arctan(sqrt(d*x^2)*sqrt(b/(a*d))) + sqrt(d*x^2))/(a*d*x^2)]","A",0
675,1,157,0,1.369798," ","integrate(1/x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b d x^{4} \sqrt{-\frac{b}{a d}} \log\left(\frac{b x^{2} + 2 \, \sqrt{d x^{2}} a \sqrt{-\frac{b}{a d}} - a}{b x^{2} + a}\right) + 2 \, {\left(3 \, b x^{2} - a\right)} \sqrt{d x^{2}}}{6 \, a^{2} d x^{4}}, \frac{3 \, b d x^{4} \sqrt{\frac{b}{a d}} \arctan\left(\sqrt{d x^{2}} \sqrt{\frac{b}{a d}}\right) + {\left(3 \, b x^{2} - a\right)} \sqrt{d x^{2}}}{3 \, a^{2} d x^{4}}\right]"," ",0,"[1/6*(3*b*d*x^4*sqrt(-b/(a*d))*log((b*x^2 + 2*sqrt(d*x^2)*a*sqrt(-b/(a*d)) - a)/(b*x^2 + a)) + 2*(3*b*x^2 - a)*sqrt(d*x^2))/(a^2*d*x^4), 1/3*(3*b*d*x^4*sqrt(b/(a*d))*arctan(sqrt(d*x^2)*sqrt(b/(a*d))) + (3*b*x^2 - a)*sqrt(d*x^2))/(a^2*d*x^4)]","A",0
676,1,857,0,1.880367," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-a b c + a^{2} d} a d^{2} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(b^{2} c^{2} + 4 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3} d^{2}}, \frac{2 \, \sqrt{-a b c + a^{2} d} a d^{2} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + {\left(b^{2} c^{2} + 4 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b^{2} d^{2} x^{3} + {\left(b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3} d^{2}}, \frac{8 \, \sqrt{a b c - a^{2} d} a d^{2} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - {\left(b^{2} c^{2} + 4 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3} d^{2}}, \frac{4 \, \sqrt{a b c - a^{2} d} a d^{2} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + {\left(b^{2} c^{2} + 4 \, a b c d - 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b^{2} d^{2} x^{3} + {\left(b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3} d^{2}}\right]"," ",0,"[1/16*(4*sqrt(-a*b*c + a^2*d)*a*d^2*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^2*d^2*x^3 + (b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d^2), 1/8*(2*sqrt(-a*b*c + a^2*d)*a*d^2*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + (b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (2*b^2*d^2*x^3 + (b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d^2), 1/16*(8*sqrt(a*b*c - a^2*d)*a*d^2*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - (b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^2*d^2*x^3 + (b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d^2), 1/8*(4*sqrt(a*b*c - a^2*d)*a*d^2*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + (b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (2*b^2*d^2*x^3 + (b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d^2)]","A",0
677,1,295,0,1.428946," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, a d \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(b d x^{2} + b c - 3 \, a d\right)} \sqrt{d x^{2} + c}}{12 \, b^{2} d}, \frac{3 \, a d \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b d x^{2} + b c - 3 \, a d\right)} \sqrt{d x^{2} + c}}{6 \, b^{2} d}\right]"," ",0,"[1/12*(3*a*d*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(b*d*x^2 + b*c - 3*a*d)*sqrt(d*x^2 + c))/(b^2*d), 1/6*(3*a*d*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(b*d*x^2 + b*c - 3*a*d)*sqrt(d*x^2 + c))/(b^2*d)]","A",0
678,1,690,0,1.181308," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{2} + c} b d x - {\left(b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + \sqrt{-a b c + a^{2} d} d \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b^{2} d}, \frac{2 \, \sqrt{d x^{2} + c} b d x - 2 \, {\left(b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + \sqrt{-a b c + a^{2} d} d \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b^{2} d}, \frac{2 \, \sqrt{d x^{2} + c} b d x - 2 \, \sqrt{a b c - a^{2} d} d \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - {\left(b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, b^{2} d}, \frac{\sqrt{d x^{2} + c} b d x - \sqrt{a b c - a^{2} d} d \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - {\left(b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{2 \, b^{2} d}\right]"," ",0,"[1/4*(2*sqrt(d*x^2 + c)*b*d*x - (b*c - 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + sqrt(-a*b*c + a^2*d)*d*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(b^2*d), 1/4*(2*sqrt(d*x^2 + c)*b*d*x - 2*(b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + sqrt(-a*b*c + a^2*d)*d*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(b^2*d), 1/4*(2*sqrt(d*x^2 + c)*b*d*x - 2*sqrt(a*b*c - a^2*d)*d*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - (b*c - 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b^2*d), 1/2*(sqrt(d*x^2 + c)*b*d*x - sqrt(a*b*c - a^2*d)*d*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - (b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(b^2*d)]","A",0
679,1,255,0,1.369574," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, \sqrt{d x^{2} + c}}{4 \, b}, -\frac{\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, \sqrt{d x^{2} + c}}{2 \, b}\right]"," ",0,"[1/4*(sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*sqrt(d*x^2 + c))/b, -1/2*(sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*sqrt(d*x^2 + c))/b]","A",0
680,1,596,0,0.963706," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b}, -\frac{4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b}, \frac{\sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{2 \, b}, -\frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right)}{2 \, b}\right]"," ",0,"[1/4*(2*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/b, -1/4*(4*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/b, 1/2*(sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/b, -1/2*(2*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)))/b]","A",0
681,1,578,0,1.530163," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{4 \, a}, \frac{4 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, a}, \frac{\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{2 \, a}, \frac{\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right)}{2 \, a}\right]"," ",0,"[1/4*(sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/a, 1/4*(4*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/a, 1/2*(sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/a, 1/2*(sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)))/a]","A",0
682,1,273,0,1.208589," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{d x^{2} + c}}{4 \, a x}, -\frac{x \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, \sqrt{d x^{2} + c}}{2 \, a x}\right]"," ",0,"[1/4*(x*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(d*x^2 + c))/(a*x), -1/2*(x*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*sqrt(d*x^2 + c))/(a*x)]","A",0
683,1,708,0,1.637953," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} c x^{2} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b c - a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c x^{2}}, -\frac{2 \, {\left(2 \, b c - a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - \sqrt{b^{2} c - a b d} c x^{2} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c x^{2}}, -\frac{2 \, \sqrt{-b^{2} c + a b d} c x^{2} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c - a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c x^{2}}, -\frac{\sqrt{-b^{2} c + a b d} c x^{2} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c - a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + \sqrt{d x^{2} + c} a c}{2 \, a^{2} c x^{2}}\right]"," ",0,"[1/4*(sqrt(b^2*c - a*b*d)*c*x^2*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b*c - a*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(d*x^2 + c)*a*c)/(a^2*c*x^2), -1/4*(2*(2*b*c - a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - sqrt(b^2*c - a*b*d)*c*x^2*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(d*x^2 + c)*a*c)/(a^2*c*x^2), -1/4*(2*sqrt(-b^2*c + a*b*d)*c*x^2*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + (2*b*c - a*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*sqrt(d*x^2 + c)*a*c)/(a^2*c*x^2), -1/2*(sqrt(-b^2*c + a*b*d)*c*x^2*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + (2*b*c - a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + sqrt(d*x^2 + c)*a*c)/(a^2*c*x^2)]","A",0
684,1,325,0,1.430976," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, b c x^{3} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left({\left(3 \, b c - a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{12 \, a^{2} c x^{3}}, \frac{3 \, b c x^{3} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left({\left(3 \, b c - a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{6 \, a^{2} c x^{3}}\right]"," ",0,"[1/12*(3*b*c*x^3*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*((3*b*c - a*d)*x^2 - a*c)*sqrt(d*x^2 + c))/(a^2*c*x^3), 1/6*(3*b*c*x^3*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*((3*b*c - a*d)*x^2 - a*c)*sqrt(d*x^2 + c))/(a^2*c*x^3)]","A",0
685,1,1119,0,7.624360," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + 16 \, a^{3} d^{3}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 24 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(7 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} d - 10 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, b^{4} d^{2}}, \frac{3 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + 16 \, a^{3} d^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 12 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(7 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} d - 10 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, b^{4} d^{2}}, \frac{48 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + 16 \, a^{3} d^{3}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(7 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} d - 10 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, b^{4} d^{2}}, \frac{24 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + 16 \, a^{3} d^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(7 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} d - 10 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, b^{4} d^{2}}\right]"," ",0,"[1/96*(3*(b^3*c^3 + 6*a*b^2*c^2*d - 24*a^2*b*c*d^2 + 16*a^3*d^3)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 24*(a*b*c*d^2 - a^2*d^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(8*b^3*d^3*x^5 + 2*(7*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(b^3*c^2*d - 10*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d^2), 1/48*(3*(b^3*c^3 + 6*a*b^2*c^2*d - 24*a^2*b*c*d^2 + 16*a^3*d^3)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 12*(a*b*c*d^2 - a^2*d^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + (8*b^3*d^3*x^5 + 2*(7*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(b^3*c^2*d - 10*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d^2), 1/96*(48*(a*b*c*d^2 - a^2*d^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(b^3*c^3 + 6*a*b^2*c^2*d - 24*a^2*b*c*d^2 + 16*a^3*d^3)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(8*b^3*d^3*x^5 + 2*(7*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(b^3*c^2*d - 10*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d^2), 1/48*(24*(a*b*c*d^2 - a^2*d^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(b^3*c^3 + 6*a*b^2*c^2*d - 24*a^2*b*c*d^2 + 16*a^3*d^3)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (8*b^3*d^3*x^5 + 2*(7*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(b^3*c^2*d - 10*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d^2)]","A",0
686,1,397,0,1.378568," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(3 \, b^{2} d^{2} x^{4} + 3 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2} + {\left(6 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{60 \, b^{3} d}, \frac{15 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{4} + 3 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2} + {\left(6 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, b^{3} d}\right]"," ",0,"[-1/60*(15*(a*b*c*d - a^2*d^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(3*b^2*d^2*x^4 + 3*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 + (6*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^3*d), 1/30*(15*(a*b*c*d - a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(3*b^2*d^2*x^4 + 3*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 + (6*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^3*d)]","A",0
687,1,894,0,2.992573," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} - 12 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 4 \, \sqrt{-a b c + a^{2} d} {\left(b c d - a d^{2}\right)} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(5 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3} d}, -\frac{{\left(3 \, b^{2} c^{2} - 12 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + 2 \, \sqrt{-a b c + a^{2} d} {\left(b c d - a d^{2}\right)} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b^{2} d^{2} x^{3} + {\left(5 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3} d}, -\frac{8 \, \sqrt{a b c - a^{2} d} {\left(b c d - a d^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} - 12 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(5 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3} d}, -\frac{4 \, \sqrt{a b c - a^{2} d} {\left(b c d - a d^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + {\left(3 \, b^{2} c^{2} - 12 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b^{2} d^{2} x^{3} + {\left(5 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3} d}\right]"," ",0,"[1/16*((3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 4*sqrt(-a*b*c + a^2*d)*(b*c*d - a*d^2)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(2*b^2*d^2*x^3 + (5*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d), -1/8*((3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + 2*sqrt(-a*b*c + a^2*d)*(b*c*d - a*d^2)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b^2*d^2*x^3 + (5*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d), -1/16*(8*sqrt(a*b*c - a^2*d)*(b*c*d - a*d^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - (3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(2*b^2*d^2*x^3 + (5*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d), -1/8*(4*sqrt(a*b*c - a^2*d)*(b*c*d - a*d^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + (3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (2*b^2*d^2*x^3 + (5*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/(b^3*d)]","A",0
688,1,303,0,1.619039," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b d x^{2} + 4 \, b c - 3 \, a d\right)} \sqrt{d x^{2} + c}}{12 \, b^{2}}, -\frac{3 \, {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b d x^{2} + 4 \, b c - 3 \, a d\right)} \sqrt{d x^{2} + c}}{6 \, b^{2}}\right]"," ",0,"[-1/12*(3*(b*c - a*d)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b*d*x^2 + 4*b*c - 3*a*d)*sqrt(d*x^2 + c))/b^2, -1/6*(3*(b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(b*d*x^2 + 4*b*c - 3*a*d)*sqrt(d*x^2 + c))/b^2]","A",0
689,1,721,0,1.556868," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{2} + c} b d x - {\left(3 \, b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b^{2}}, \frac{2 \, \sqrt{d x^{2} + c} b d x - 2 \, {\left(3 \, b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, b^{2}}, \frac{2 \, \sqrt{d x^{2} + c} b d x + 2 \, {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(3 \, b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, b^{2}}, \frac{\sqrt{d x^{2} + c} b d x - {\left(3 \, b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right)}{2 \, b^{2}}\right]"," ",0,"[1/4*(2*sqrt(d*x^2 + c)*b*d*x - (3*b*c - 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (b*c - a*d)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/b^2, 1/4*(2*sqrt(d*x^2 + c)*b*d*x - 2*(3*b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (b*c - a*d)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/b^2, 1/4*(2*sqrt(d*x^2 + c)*b*d*x + 2*(b*c - a*d)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (3*b*c - 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/b^2, 1/2*(sqrt(d*x^2 + c)*b*d*x - (3*b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b*c - a*d)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)))/b^2]","A",0
690,1,682,0,2.424850," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{\frac{3}{2}} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, \sqrt{d x^{2} + c} a d - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, a b}, \frac{4 \, b \sqrt{-c} c \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 4 \, \sqrt{d x^{2} + c} a d - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, a b}, \frac{b c^{\frac{3}{2}} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a d + {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right)}{2 \, a b}, \frac{2 \, b \sqrt{-c} c \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, \sqrt{d x^{2} + c} a d + {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right)}{2 \, a b}\right]"," ",0,"[1/4*(2*b*c^(3/2)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*sqrt(d*x^2 + c)*a*d - (b*c - a*d)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b), 1/4*(4*b*sqrt(-c)*c*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 4*sqrt(d*x^2 + c)*a*d - (b*c - a*d)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b), 1/2*(b*c^(3/2)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*sqrt(d*x^2 + c)*a*d + (b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)))/(a*b), 1/2*(2*b*sqrt(-c)*c*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*sqrt(d*x^2 + c)*a*d + (b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)))/(a*b)]","A",0
691,1,718,0,1.948579," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a d^{\frac{3}{2}} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(b c - a d\right)} x \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{d x^{2} + c} b c}{4 \, a b x}, -\frac{4 \, a \sqrt{-d} d x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b c - a d\right)} x \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, \sqrt{d x^{2} + c} b c}{4 \, a b x}, \frac{a d^{\frac{3}{2}} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(b c - a d\right)} x \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - 2 \, \sqrt{d x^{2} + c} b c}{2 \, a b x}, -\frac{2 \, a \sqrt{-d} d x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b c - a d\right)} x \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, \sqrt{d x^{2} + c} b c}{2 \, a b x}\right]"," ",0,"[1/4*(2*a*d^(3/2)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (b*c - a*d)*x*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(d*x^2 + c)*b*c)/(a*b*x), -1/4*(4*a*sqrt(-d)*d*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b*c - a*d)*x*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*sqrt(d*x^2 + c)*b*c)/(a*b*x), 1/2*(a*d^(3/2)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (b*c - a*d)*x*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - 2*sqrt(d*x^2 + c)*b*c)/(a*b*x), -1/2*(2*a*sqrt(-d)*d*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b*c - a*d)*x*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*sqrt(d*x^2 + c)*b*c)/(a*b*x)]","A",0
692,1,732,0,3.186754," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b c - a d\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} x^{2}}, -\frac{2 \, {\left(2 \, b c - 3 \, a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b c - a d\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} x^{2}}, -\frac{2 \, {\left(b c - a d\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} x^{2}}, -\frac{{\left(b c - a d\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + \sqrt{d x^{2} + c} a c}{2 \, a^{2} x^{2}}\right]"," ",0,"[-1/4*((b*c - a*d)*x^2*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + (2*b*c - 3*a*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*sqrt(d*x^2 + c)*a*c)/(a^2*x^2), -1/4*(2*(2*b*c - 3*a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b*c - a*d)*x^2*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(d*x^2 + c)*a*c)/(a^2*x^2), -1/4*(2*(b*c - a*d)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + (2*b*c - 3*a*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*sqrt(d*x^2 + c)*a*c)/(a^2*x^2), -1/2*((b*c - a*d)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + (2*b*c - 3*a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + sqrt(d*x^2 + c)*a*c)/(a^2*x^2)]","A",0
693,1,331,0,2.056347," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} x^{3} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(3 \, b c - 4 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{12 \, a^{2} x^{3}}, \frac{3 \, {\left(b c - a d\right)} x^{3} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left({\left(3 \, b c - 4 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{6 \, a^{2} x^{3}}\right]"," ",0,"[-1/12*(3*(b*c - a*d)*x^3*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((3*b*c - 4*a*d)*x^2 - a*c)*sqrt(d*x^2 + c))/(a^2*x^3), 1/6*(3*(b*c - a*d)*x^3*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*((3*b*c - 4*a*d)*x^2 - a*c)*sqrt(d*x^2 + c))/(a^2*x^3)]","A",0
694,1,1443,0,21.592431," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{4} c^{4} + 40 \, a b^{3} c^{3} d - 240 \, a^{2} b^{2} c^{2} d^{2} + 320 \, a^{3} b c d^{3} - 128 \, a^{4} d^{4}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 192 \, {\left(a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{7} + 8 \, {\left(17 \, b^{4} c d^{3} - 8 \, a b^{3} d^{4}\right)} x^{5} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 104 \, a b^{3} c d^{3} + 48 \, a^{2} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{4} c^{3} d - 88 \, a b^{3} c^{2} d^{2} + 144 \, a^{2} b^{2} c d^{3} - 64 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{768 \, b^{5} d^{2}}, \frac{3 \, {\left(5 \, b^{4} c^{4} + 40 \, a b^{3} c^{3} d - 240 \, a^{2} b^{2} c^{2} d^{2} + 320 \, a^{3} b c d^{3} - 128 \, a^{4} d^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + 96 \, {\left(a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + {\left(48 \, b^{4} d^{4} x^{7} + 8 \, {\left(17 \, b^{4} c d^{3} - 8 \, a b^{3} d^{4}\right)} x^{5} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 104 \, a b^{3} c d^{3} + 48 \, a^{2} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{4} c^{3} d - 88 \, a b^{3} c^{2} d^{2} + 144 \, a^{2} b^{2} c d^{3} - 64 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{384 \, b^{5} d^{2}}, \frac{384 \, {\left(a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{4} c^{4} + 40 \, a b^{3} c^{3} d - 240 \, a^{2} b^{2} c^{2} d^{2} + 320 \, a^{3} b c d^{3} - 128 \, a^{4} d^{4}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{7} + 8 \, {\left(17 \, b^{4} c d^{3} - 8 \, a b^{3} d^{4}\right)} x^{5} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 104 \, a b^{3} c d^{3} + 48 \, a^{2} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{4} c^{3} d - 88 \, a b^{3} c^{2} d^{2} + 144 \, a^{2} b^{2} c d^{3} - 64 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{768 \, b^{5} d^{2}}, \frac{192 \, {\left(a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{4} c^{4} + 40 \, a b^{3} c^{3} d - 240 \, a^{2} b^{2} c^{2} d^{2} + 320 \, a^{3} b c d^{3} - 128 \, a^{4} d^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(48 \, b^{4} d^{4} x^{7} + 8 \, {\left(17 \, b^{4} c d^{3} - 8 \, a b^{3} d^{4}\right)} x^{5} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 104 \, a b^{3} c d^{3} + 48 \, a^{2} b^{2} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{4} c^{3} d - 88 \, a b^{3} c^{2} d^{2} + 144 \, a^{2} b^{2} c d^{3} - 64 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{384 \, b^{5} d^{2}}\right]"," ",0,"[-1/768*(3*(5*b^4*c^4 + 40*a*b^3*c^3*d - 240*a^2*b^2*c^2*d^2 + 320*a^3*b*c*d^3 - 128*a^4*d^4)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 192*(a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + a^3*d^4)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(48*b^4*d^4*x^7 + 8*(17*b^4*c*d^3 - 8*a*b^3*d^4)*x^5 + 2*(59*b^4*c^2*d^2 - 104*a*b^3*c*d^3 + 48*a^2*b^2*d^4)*x^3 + 3*(5*b^4*c^3*d - 88*a*b^3*c^2*d^2 + 144*a^2*b^2*c*d^3 - 64*a^3*b*d^4)*x)*sqrt(d*x^2 + c))/(b^5*d^2), 1/384*(3*(5*b^4*c^4 + 40*a*b^3*c^3*d - 240*a^2*b^2*c^2*d^2 + 320*a^3*b*c*d^3 - 128*a^4*d^4)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + 96*(a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + a^3*d^4)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + (48*b^4*d^4*x^7 + 8*(17*b^4*c*d^3 - 8*a*b^3*d^4)*x^5 + 2*(59*b^4*c^2*d^2 - 104*a*b^3*c*d^3 + 48*a^2*b^2*d^4)*x^3 + 3*(5*b^4*c^3*d - 88*a*b^3*c^2*d^2 + 144*a^2*b^2*c*d^3 - 64*a^3*b*d^4)*x)*sqrt(d*x^2 + c))/(b^5*d^2), 1/768*(384*(a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + a^3*d^4)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 3*(5*b^4*c^4 + 40*a*b^3*c^3*d - 240*a^2*b^2*c^2*d^2 + 320*a^3*b*c*d^3 - 128*a^4*d^4)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(48*b^4*d^4*x^7 + 8*(17*b^4*c*d^3 - 8*a*b^3*d^4)*x^5 + 2*(59*b^4*c^2*d^2 - 104*a*b^3*c*d^3 + 48*a^2*b^2*d^4)*x^3 + 3*(5*b^4*c^3*d - 88*a*b^3*c^2*d^2 + 144*a^2*b^2*c*d^3 - 64*a^3*b*d^4)*x)*sqrt(d*x^2 + c))/(b^5*d^2), 1/384*(192*(a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + a^3*d^4)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(5*b^4*c^4 + 40*a*b^3*c^3*d - 240*a^2*b^2*c^2*d^2 + 320*a^3*b*c*d^3 - 128*a^4*d^4)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (48*b^4*d^4*x^7 + 8*(17*b^4*c*d^3 - 8*a*b^3*d^4)*x^5 + 2*(59*b^4*c^2*d^2 - 104*a*b^3*c*d^3 + 48*a^2*b^2*d^4)*x^3 + 3*(5*b^4*c^3*d - 88*a*b^3*c^2*d^2 + 144*a^2*b^2*c*d^3 - 64*a^3*b*d^4)*x)*sqrt(d*x^2 + c))/(b^5*d^2)]","A",0
695,1,527,0,1.164770," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(15 \, b^{3} d^{3} x^{6} + 15 \, b^{3} c^{3} - 161 \, a b^{2} c^{2} d + 245 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + 3 \, {\left(15 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{4} + {\left(45 \, b^{3} c^{2} d - 77 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{420 \, b^{4} d}, \frac{105 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(15 \, b^{3} d^{3} x^{6} + 15 \, b^{3} c^{3} - 161 \, a b^{2} c^{2} d + 245 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + 3 \, {\left(15 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{4} + {\left(45 \, b^{3} c^{2} d - 77 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{210 \, b^{4} d}\right]"," ",0,"[1/420*(105*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(15*b^3*d^3*x^6 + 15*b^3*c^3 - 161*a*b^2*c^2*d + 245*a^2*b*c*d^2 - 105*a^3*d^3 + 3*(15*b^3*c*d^2 - 7*a*b^2*d^3)*x^4 + (45*b^3*c^2*d - 77*a*b^2*c*d^2 + 35*a^2*b*d^3)*x^2)*sqrt(d*x^2 + c))/(b^4*d), 1/210*(105*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(15*b^3*d^3*x^6 + 15*b^3*c^3 - 161*a*b^2*c^2*d + 245*a^2*b*c*d^2 - 105*a^3*d^3 + 3*(15*b^3*c*d^2 - 7*a*b^2*d^3)*x^4 + (45*b^3*c^2*d - 77*a*b^2*c*d^2 + 35*a^2*b*d^3)*x^2)*sqrt(d*x^2 + c))/(b^4*d)]","A",0
696,1,1161,0,7.142089," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} - 30 \, a b^{2} c^{2} d + 40 \, a^{2} b c d^{2} - 16 \, a^{3} d^{3}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 24 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(13 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, b^{4} d}, -\frac{3 \, {\left(5 \, b^{3} c^{3} - 30 \, a b^{2} c^{2} d + 40 \, a^{2} b c d^{2} - 16 \, a^{3} d^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(13 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, b^{4} d}, -\frac{48 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{3} c^{3} - 30 \, a b^{2} c^{2} d + 40 \, a^{2} b c d^{2} - 16 \, a^{3} d^{3}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(13 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, b^{4} d}, -\frac{24 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{3} c^{3} - 30 \, a b^{2} c^{2} d + 40 \, a^{2} b c d^{2} - 16 \, a^{3} d^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, b^{3} d^{3} x^{5} + 2 \, {\left(13 \, b^{3} c d^{2} - 6 \, a b^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{3} c^{2} d - 18 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, b^{4} d}\right]"," ",0,"[-1/96*(3*(5*b^3*c^3 - 30*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 24*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(8*b^3*d^3*x^5 + 2*(13*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(11*b^3*c^2*d - 18*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d), -1/48*(3*(5*b^3*c^3 - 30*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 12*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (8*b^3*d^3*x^5 + 2*(13*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(11*b^3*c^2*d - 18*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d), -1/96*(48*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(5*b^3*c^3 - 30*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(8*b^3*d^3*x^5 + 2*(13*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(11*b^3*c^2*d - 18*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d), -1/48*(24*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(5*b^3*c^3 - 30*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (8*b^3*d^3*x^5 + 2*(13*b^3*c*d^2 - 6*a*b^2*d^3)*x^3 + 3*(11*b^3*c^2*d - 18*a*b^2*c*d^2 + 8*a^2*b*d^3)*x)*sqrt(d*x^2 + c))/(b^4*d)]","A",0
697,1,405,0,0.933729," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, b^{2} d^{2} x^{4} + 23 \, b^{2} c^{2} - 35 \, a b c d + 15 \, a^{2} d^{2} + {\left(11 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{60 \, b^{3}}, -\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{4} + 23 \, b^{2} c^{2} - 35 \, a b c d + 15 \, a^{2} d^{2} + {\left(11 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{30 \, b^{3}}\right]"," ",0,"[1/60*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*b^2*d^2*x^4 + 23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + (11*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/b^3, -1/30*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(3*b^2*d^2*x^4 + 23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + (11*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/b^3]","A",0
698,1,931,0,3.574055," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, b^{2} c^{2} - 20 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(9 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3}}, -\frac{{\left(15 \, b^{2} c^{2} - 20 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b^{2} d^{2} x^{3} + {\left(9 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3}}, \frac{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + {\left(15 \, b^{2} c^{2} - 20 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{3} + {\left(9 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, b^{3}}, -\frac{{\left(15 \, b^{2} c^{2} - 20 \, a b c d + 8 \, a^{2} d^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(2 \, b^{2} d^{2} x^{3} + {\left(9 \, b^{2} c d - 4 \, a b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, b^{3}}\right]"," ",0,"[1/16*((15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(2*b^2*d^2*x^3 + (9*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/b^3, -1/8*((15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b^2*d^2*x^3 + (9*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/b^3, 1/16*(8*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + (15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^2*d^2*x^3 + (9*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/b^3, -1/8*((15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (2*b^2*d^2*x^3 + (9*b^2*c*d - 4*a*b*d^2)*x)*sqrt(d*x^2 + c))/b^3]","A",0
699,1,837,0,3.470204," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, b^{2} c^{\frac{5}{2}} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b d^{2} x^{2} + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{12 \, a b^{2}}, \frac{12 \, b^{2} \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b d^{2} x^{2} + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{12 \, a b^{2}}, \frac{3 \, b^{2} c^{\frac{5}{2}} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(a b d^{2} x^{2} + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{6 \, a b^{2}}, \frac{6 \, b^{2} \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(a b d^{2} x^{2} + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{6 \, a b^{2}}\right]"," ",0,"[1/12*(6*b^2*c^(5/2)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*d^2*x^2 + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x^2 + c))/(a*b^2), 1/12*(12*b^2*sqrt(-c)*c^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*d^2*x^2 + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x^2 + c))/(a*b^2), 1/6*(3*b^2*c^(5/2)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(a*b*d^2*x^2 + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x^2 + c))/(a*b^2), 1/6*(6*b^2*sqrt(-c)*c^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(a*b*d^2*x^2 + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x^2 + c))/(a*b^2)]","A",0
700,1,887,0,2.501855," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\left[-\frac{{\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{d} x \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(a b d^{2} x^{2} - 2 \, b^{2} c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a b^{2} x}, -\frac{2 \, {\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(a b d^{2} x^{2} - 2 \, b^{2} c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a b^{2} x}, -\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + {\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{d} x \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(a b d^{2} x^{2} - 2 \, b^{2} c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a b^{2} x}, -\frac{{\left(5 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(a b d^{2} x^{2} - 2 \, b^{2} c^{2}\right)} \sqrt{d x^{2} + c}}{2 \, a b^{2} x}\right]"," ",0,"[-1/4*((5*a*b*c*d - 2*a^2*d^2)*sqrt(d)*x*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(a*b*d^2*x^2 - 2*b^2*c^2)*sqrt(d*x^2 + c))/(a*b^2*x), -1/4*(2*(5*a*b*c*d - 2*a^2*d^2)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(a*b*d^2*x^2 - 2*b^2*c^2)*sqrt(d*x^2 + c))/(a*b^2*x), -1/4*(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + (5*a*b*c*d - 2*a^2*d^2)*sqrt(d)*x*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(a*b*d^2*x^2 - 2*b^2*c^2)*sqrt(d*x^2 + c))/(a*b^2*x), -1/2*((5*a*b*c*d - 2*a^2*d^2)*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (a*b*d^2*x^2 - 2*b^2*c^2)*sqrt(d*x^2 + c))/(a*b^2*x)]","A",0
701,1,891,0,4.393419," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, a^{2} d^{2} x^{2} - a b c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a^{2} b x^{2}}, -\frac{2 \, {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(2 \, a^{2} d^{2} x^{2} - a b c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a^{2} b x^{2}}, -\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, a^{2} d^{2} x^{2} - a b c^{2}\right)} \sqrt{d x^{2} + c}}{4 \, a^{2} b x^{2}}, -\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a^{2} d^{2} x^{2} - a b c^{2}\right)} \sqrt{d x^{2} + c}}{2 \, a^{2} b x^{2}}\right]"," ",0,"[1/4*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b^2*c^2 - 5*a*b*c*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(2*a^2*d^2*x^2 - a*b*c^2)*sqrt(d*x^2 + c))/(a^2*b*x^2), -1/4*(2*(2*b^2*c^2 - 5*a*b*c*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(2*a^2*d^2*x^2 - a*b*c^2)*sqrt(d*x^2 + c))/(a^2*b*x^2), -1/4*(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + (2*b^2*c^2 - 5*a*b*c*d)*sqrt(c)*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*a^2*d^2*x^2 - a*b*c^2)*sqrt(d*x^2 + c))/(a^2*b*x^2), -1/2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + (2*b^2*c^2 - 5*a*b*c*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a^2*d^2*x^2 - a*b*c^2)*sqrt(d*x^2 + c))/(a^2*b*x^2)]","A",0
702,1,901,0,2.052382," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a),x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} d^{\frac{5}{2}} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{3} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b c^{2} - {\left(3 \, b^{2} c^{2} - 7 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, a^{2} b x^{3}}, -\frac{12 \, a^{2} \sqrt{-d} d^{2} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{3} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b c^{2} - {\left(3 \, b^{2} c^{2} - 7 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, a^{2} b x^{3}}, \frac{3 \, a^{2} d^{\frac{5}{2}} x^{3} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{3} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - 2 \, {\left(a b c^{2} - {\left(3 \, b^{2} c^{2} - 7 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, a^{2} b x^{3}}, -\frac{6 \, a^{2} \sqrt{-d} d^{2} x^{3} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{3} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left(a b c^{2} - {\left(3 \, b^{2} c^{2} - 7 \, a b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, a^{2} b x^{3}}\right]"," ",0,"[1/12*(6*a^2*d^(5/2)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^3*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b*c^2 - (3*b^2*c^2 - 7*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(a^2*b*x^3), -1/12*(12*a^2*sqrt(-d)*d^2*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^3*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*c^2 - (3*b^2*c^2 - 7*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(a^2*b*x^3), 1/6*(3*a^2*d^(5/2)*x^3*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^3*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - 2*(a*b*c^2 - (3*b^2*c^2 - 7*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(a^2*b*x^3), -1/6*(6*a^2*sqrt(-d)*d^2*x^3*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^3*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*(a*b*c^2 - (3*b^2*c^2 - 7*a*b*c*d)*x^2)*sqrt(d*x^2 + c))/(a^2*b*x^3)]","A",0
703,1,390,0,1.271981," ","integrate(x^5/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} c - a b d} a^{2} d^{2} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}, -\frac{3 \, \sqrt{-b^{2} c + a b d} a^{2} d^{2} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}\right]"," ",0,"[1/12*(3*sqrt(b^2*c - a*b*d)*a^2*d^2*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^2)*sqrt(d*x^2 + c))/(b^4*c*d^2 - a*b^3*d^3), -1/6*(3*sqrt(-b^2*c + a*b*d)*a^2*d^2*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + 2*(2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^2)*sqrt(d*x^2 + c))/(b^4*c*d^2 - a*b^3*d^3)]","B",0
704,1,306,0,1.095172," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} a d \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}, \frac{\sqrt{-b^{2} c + a b d} a d \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{2 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(b^2*c - a*b*d)*a*d*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^3*c*d - a*b^2*d^2), 1/2*(sqrt(-b^2*c + a*b*d)*a*d*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + 2*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^3*c*d - a*b^2*d^2)]","B",0
705,1,231,0,1.202110," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, \sqrt{b^{2} c - a b d}}, -\frac{\sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(b^{2} c - a b d\right)}}\right]"," ",0,"[1/4*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2))/sqrt(b^2*c - a*b*d), -1/2*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2))/(b^2*c - a*b*d)]","B",0
706,1,603,0,1.226617," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{4 \, a c}, \frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right)}{4 \, a c}, -\frac{c \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{2 \, a c}, -\frac{c \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right)}{2 \, a c}\right]"," ",0,"[1/4*(c*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a*c), 1/4*(c*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)))/(a*c), -1/2*(c*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a*c), -1/2*(c*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)))/(a*c)]","A",0
707,1,734,0,1.386880," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{b c^{2} x^{2} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c^{2} x^{2}}, \frac{b c^{2} x^{2} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(2 \, b c + a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c^{2} x^{2}}, \frac{2 \, b c^{2} x^{2} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{2} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{d x^{2} + c} a c}{4 \, a^{2} c^{2} x^{2}}, \frac{b c^{2} x^{2} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - {\left(2 \, b c + a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - \sqrt{d x^{2} + c} a c}{2 \, a^{2} c^{2} x^{2}}\right]"," ",0,"[1/4*(b*c^2*x^2*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + (2*b*c + a*d)*sqrt(c)*x^2*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2), 1/4*(b*c^2*x^2*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(2*b*c + a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2), 1/4*(2*b*c^2*x^2*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + (2*b*c + a*d)*sqrt(c)*x^2*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2), 1/2*(b*c^2*x^2*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - (2*b*c + a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2)]","A",0
708,1,717,0,1.098382," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{d x^{2} + c} b d x + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, b^{2} d^{2}}, \frac{a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{d x^{2} + c} b d x + 2 \, {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{4 \, b^{2} d^{2}}, -\frac{2 \, a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - 2 \, \sqrt{d x^{2} + c} b d x - {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, b^{2} d^{2}}, -\frac{a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - \sqrt{d x^{2} + c} b d x - {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{2 \, b^{2} d^{2}}\right]"," ",0,"[1/4*(a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(d*x^2 + c)*b*d*x + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b^2*d^2), 1/4*(a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(d*x^2 + c)*b*d*x + 2*(b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(b^2*d^2), -1/4*(2*a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - 2*sqrt(d*x^2 + c)*b*d*x - (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b^2*d^2), -1/2*(a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - sqrt(d*x^2 + c)*b*d*x - (b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(b^2*d^2)]","A",0
709,1,616,0,1.257803," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, b d}, \frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{4 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{2 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - 2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{2 \, b d}\right]"," ",0,"[1/4*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b*d), 1/4*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(b*d), 1/2*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b*d), 1/2*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - 2*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(b*d)]","A",0
710,1,241,0,1.017853," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(a b c - a^{2} d\right)}}, \frac{\arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, \sqrt{a b c - a^{2} d}}\right]"," ",0,"[-1/4*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2))/(a*b*c - a^2*d), 1/2*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x))/sqrt(a*b*c - a^2*d)]","B",0
711,1,324,0,1.306725," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} b c x \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x}, -\frac{\sqrt{a b c - a^{2} d} b c x \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{2 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x}\right]"," ",0,"[-1/4*(sqrt(-a*b*c + a^2*d)*b*c*x*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/((a^2*b*c^2 - a^3*c*d)*x), -1/2*(sqrt(a*b*c - a^2*d)*b*c*x*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/((a^2*b*c^2 - a^3*c*d)*x)]","B",0
712,1,414,0,1.449559," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a b c + a^{2} d} b^{2} c^{2} x^{3} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} b c^{2} - a^{3} c d - {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{3}}, \frac{3 \, \sqrt{a b c - a^{2} d} b^{2} c^{2} x^{3} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d - {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{3}}\right]"," ",0,"[-1/12*(3*sqrt(-a*b*c + a^2*d)*b^2*c^2*x^3*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*b*c^2 - a^3*c*d - (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^2)*sqrt(d*x^2 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^3), 1/6*(3*sqrt(a*b*c - a^2*d)*b^2*c^2*x^3*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(a^2*b*c^2 - a^3*c*d - (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^2)*sqrt(d*x^2 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^3)]","B",0
713,1,977,0,1.736735," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{d x^{2} + c} b c d x - 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(a d^{3} x^{2} + a c d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)}}, -\frac{4 \, \sqrt{d x^{2} + c} b c d x + 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a d^{3} x^{2} + a c d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)}}, -\frac{2 \, \sqrt{d x^{2} + c} b c d x + {\left(a d^{3} x^{2} + a c d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{2 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)}}, -\frac{2 \, \sqrt{d x^{2} + c} b c d x + 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a d^{3} x^{2} + a c d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right)}{2 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*sqrt(d*x^2 + c)*b*c*d*x - 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (a*d^3*x^2 + a*c*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2), -1/4*(4*sqrt(d*x^2 + c)*b*c*d*x + 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*d^3*x^2 + a*c*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2), -1/2*(2*sqrt(d*x^2 + c)*b*c*d*x + (a*d^3*x^2 + a*c*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2), -1/2*(2*sqrt(d*x^2 + c)*b*c*d*x + 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*d^3*x^2 + a*c*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x^2)]","B",0
714,1,428,0,1.137855," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a d^{2} x^{2} + a c d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(b^{2} c^{2} - a b c d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{3} c^{3} d - 2 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{2}\right)}}, \frac{{\left(a d^{2} x^{2} + a c d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b^{2} c^{2} - a b c d\right)} \sqrt{d x^{2} + c}}{2 \, {\left(b^{3} c^{3} d - 2 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((a*d^2*x^2 + a*c*d)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(b^2*c^2 - a*b*c*d)*sqrt(d*x^2 + c))/(b^3*c^3*d - 2*a*b^2*c^2*d^2 + a^2*b*c*d^3 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^2), 1/2*((a*d^2*x^2 + a*c*d)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) - 2*(b^2*c^2 - a*b*c*d)*sqrt(d*x^2 + c))/(b^3*c^3*d - 2*a*b^2*c^2*d^2 + a^2*b*c*d^3 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^2)]","B",0
715,1,334,0,1.220222," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(d x^{2} + c\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{d x^{2} + c} x}{4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}, \frac{{\left(d x^{2} + c\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + 2 \, \sqrt{d x^{2} + c} x}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((d*x^2 + c)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(d*x^2 + c)*x)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2), 1/2*((d*x^2 + c)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + 2*sqrt(d*x^2 + c)*x)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)]","A",0
716,1,323,0,1.124093," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(d x^{2} + c\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{d x^{2} + c}}{4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}, \frac{{\left(d x^{2} + c\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, \sqrt{d x^{2} + c}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((d*x^2 + c)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(d*x^2 + c))/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2), 1/2*((d*x^2 + c)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*sqrt(d*x^2 + c))/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)]","A",0
717,1,442,0,1.170754," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{d x^{2} + c} x - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x^{2}\right)}}, -\frac{2 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{d x^{2} + c} x - {\left(b c d x^{2} + b c^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{2 \, {\left(a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*(a*b*c*d - a^2*d^2)*sqrt(d*x^2 + c)*x - (b*c*d*x^2 + b*c^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 2*a^2*b*c^2*d^2 + a^3*c*d^3)*x^2), -1/2*(2*(a*b*c*d - a^2*d^2)*sqrt(d*x^2 + c)*x - (b*c*d*x^2 + b*c^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 2*a^2*b*c^2*d^2 + a^3*c*d^3)*x^2)]","B",0
718,1,959,0,2.021311," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{d x^{2} + c} a c d + {\left(b c^{2} d x^{2} + b c^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{4 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{2}\right)}}, -\frac{4 \, \sqrt{d x^{2} + c} a c d - 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b c^{2} d x^{2} + b c^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{2}\right)}}, -\frac{2 \, \sqrt{d x^{2} + c} a c d + {\left(b c^{2} d x^{2} + b c^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{2 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{2}\right)}}, -\frac{2 \, \sqrt{d x^{2} + c} a c d + {\left(b c^{2} d x^{2} + b c^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right)}{2 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*sqrt(d*x^2 + c)*a*c*d + (b*c^2*d*x^2 + b*c^3)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^2), -1/4*(4*sqrt(d*x^2 + c)*a*c*d - 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b*c^2*d*x^2 + b*c^3)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^2), -1/2*(2*sqrt(d*x^2 + c)*a*c*d + (b*c^2*d*x^2 + b*c^3)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^2), -1/2*(2*sqrt(d*x^2 + c)*a*c*d + (b*c^2*d*x^2 + b*c^3)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^2)]","B",0
719,1,560,0,1.439731," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{2} b^{2} c^{4} d - 2 \, a^{3} b c^{3} d^{2} + a^{4} c^{2} d^{3}\right)} x^{3} + {\left(a^{2} b^{2} c^{5} - 2 \, a^{3} b c^{4} d + a^{4} c^{3} d^{2}\right)} x\right)}}, -\frac{{\left(b^{2} c^{2} d x^{3} + b^{2} c^{3} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a^{2} b^{2} c^{4} d - 2 \, a^{3} b c^{3} d^{2} + a^{4} c^{2} d^{3}\right)} x^{3} + {\left(a^{2} b^{2} c^{5} - 2 \, a^{3} b c^{4} d + a^{4} c^{3} d^{2}\right)} x\right)}}\right]"," ",0,"[1/4*((b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (a*b^2*c^2*d - 3*a^2*b*c*d^2 + 2*a^3*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^4*d - 2*a^3*b*c^3*d^2 + a^4*c^2*d^3)*x^3 + (a^2*b^2*c^5 - 2*a^3*b*c^4*d + a^4*c^3*d^2)*x), -1/2*((b^2*c^2*d*x^3 + b^2*c^3*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (a*b^2*c^2*d - 3*a^2*b*c*d^2 + 2*a^3*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^4*d - 2*a^3*b*c^3*d^2 + a^4*c^2*d^3)*x^3 + (a^2*b^2*c^5 - 2*a^3*b*c^4*d + a^4*c^3*d^2)*x)]","B",0
720,1,1291,0,2.656281," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{3} d x^{4} + b^{2} c^{4} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{4} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{2}\right)}}, -\frac{2 \, {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(b^{2} c^{3} d x^{4} + b^{2} c^{4} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{4} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{2}\right)}}, \frac{2 \, {\left(b^{2} c^{3} d x^{4} + b^{2} c^{4} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{4} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{2}\right)}}, \frac{{\left(b^{2} c^{3} d x^{4} + b^{2} c^{4} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{4} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*((b^2*c^3*d*x^4 + b^2*c^4*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^4 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^4 + (a^2*b*c^5 - a^3*c^4*d)*x^2), -1/4*(2*((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^4 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (b^2*c^3*d*x^4 + b^2*c^4*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^4 + (a^2*b*c^5 - a^3*c^4*d)*x^2), 1/4*(2*(b^2*c^3*d*x^4 + b^2*c^4*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^4 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^4 + (a^2*b*c^5 - a^3*c^4*d)*x^2), 1/2*((b^2*c^3*d*x^4 + b^2*c^4*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^4 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^2)*sqrt(d*x^2 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^4 + (a^2*b*c^5 - a^3*c^4*d)*x^2)]","B",0
721,1,706,0,1.751328," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} - {\left(3 \, a b^{3} c^{3} d - a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 8 \, a^{4} d^{4}\right)} x^{4} - {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{3} b^{2} c^{5} d - 2 \, a^{4} b c^{4} d^{2} + a^{5} c^{3} d^{3}\right)} x^{5} + {\left(a^{3} b^{2} c^{6} - 2 \, a^{4} b c^{5} d + a^{5} c^{4} d^{2}\right)} x^{3}\right)}}, \frac{3 \, {\left(b^{3} c^{3} d x^{5} + b^{3} c^{4} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} - {\left(3 \, a b^{3} c^{3} d - a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 8 \, a^{4} d^{4}\right)} x^{4} - {\left(3 \, a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d - 5 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left({\left(a^{3} b^{2} c^{5} d - 2 \, a^{4} b c^{4} d^{2} + a^{5} c^{3} d^{3}\right)} x^{5} + {\left(a^{3} b^{2} c^{6} - 2 \, a^{4} b c^{5} d + a^{5} c^{4} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[1/12*(3*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 - (3*a*b^3*c^3*d - a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 8*a^4*d^4)*x^4 - (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^5*d - 2*a^4*b*c^4*d^2 + a^5*c^3*d^3)*x^5 + (a^3*b^2*c^6 - 2*a^4*b*c^5*d + a^5*c^4*d^2)*x^3), 1/6*(3*(b^3*c^3*d*x^5 + b^3*c^4*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 - (3*a*b^3*c^3*d - a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 8*a^4*d^4)*x^4 - (3*a*b^3*c^4 - 2*a^2*b^2*c^3*d - 5*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^5*d - 2*a^4*b*c^4*d^2 + a^5*c^3*d^3)*x^5 + (a^3*b^2*c^6 - 2*a^4*b*c^5*d + a^5*c^4*d^2)*x^3)]","B",0
722,1,524,0,1.943296," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a d^{2} x^{4} + 2 \, a c d x^{2} + a c^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left({\left(b c - 4 \, a d\right)} x^{3} - 3 \, a c x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a d^{2} x^{4} + 2 \, a c d x^{2} + a c^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - 2 \, {\left({\left(b c - 4 \, a d\right)} x^{3} - 3 \, a c x\right)} \sqrt{d x^{2} + c}}{6 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(a*d^2*x^4 + 2*a*c*d*x^2 + a*c^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*((b*c - 4*a*d)*x^3 - 3*a*c*x)*sqrt(d*x^2 + c))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2), -1/6*(3*(a*d^2*x^4 + 2*a*c*d*x^2 + a*c^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - 2*((b*c - 4*a*d)*x^3 - 3*a*c*x)*sqrt(d*x^2 + c))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)]","B",0
723,1,535,0,1.087936," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a d^{3} x^{4} + 2 \, a c d^{2} x^{2} + a c^{2} d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(3 \, a d^{2} x^{2} + b c^{2} + 2 \, a c d\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a d^{3} x^{4} + 2 \, a c d^{2} x^{2} + a c^{2} d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(3 \, a d^{2} x^{2} + b c^{2} + 2 \, a c d\right)} \sqrt{d x^{2} + c}}{6 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(a*d^3*x^4 + 2*a*c*d^2*x^2 + a*c^2*d)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(3*a*d^2*x^2 + b*c^2 + 2*a*c*d)*sqrt(d*x^2 + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*x^4 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2), -1/6*(3*(a*d^3*x^4 + 2*a*c*d^2*x^2 + a*c^2*d)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(3*a*d^2*x^2 + b*c^2 + 2*a*c*d)*sqrt(d*x^2 + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*x^4 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2)]","B",0
724,1,550,0,1.791884," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c d^{2} x^{4} + 2 \, b c^{2} d x^{2} + b c^{3}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, b c^{2} x + {\left(2 \, b c d + a d^{2}\right)} x^{3}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left(b c d^{2} x^{4} + 2 \, b c^{2} d x^{2} + b c^{3}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + 2 \, {\left(3 \, b c^{2} x + {\left(2 \, b c d + a d^{2}\right)} x^{3}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b*c*d^2*x^4 + 2*b*c^2*d*x^2 + b*c^3)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*b*c^2*x + (2*b*c*d + a*d^2)*x^3)*sqrt(d*x^2 + c))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2), 1/6*(3*(b*c*d^2*x^4 + 2*b*c^2*d*x^2 + b*c^3)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + 2*(3*b*c^2*x + (2*b*c*d + a*d^2)*x^3)*sqrt(d*x^2 + c))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2)]","B",0
725,1,511,0,1.146170," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d^{2} x^{4} + 2 \, b c d x^{2} + b c^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, b d x^{2} + 4 \, b c - a d\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left(b d^{2} x^{4} + 2 \, b c d x^{2} + b c^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(3 \, b d x^{2} + 4 \, b c - a d\right)} \sqrt{d x^{2} + c}}{6 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b*d^2*x^4 + 2*b*c*d*x^2 + b*c^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*b*d*x^2 + 4*b*c - a*d)*sqrt(d*x^2 + c))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2), 1/6*(3*(b*d^2*x^4 + 2*b*c*d*x^2 + b*c^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(3*b*d*x^2 + 4*b*c - a*d)*sqrt(d*x^2 + c))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)]","B",0
726,1,764,0,1.608975," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left({\left(5 \, a b^{2} c^{2} d^{2} - 7 \, a^{2} b c d^{3} + 2 \, a^{3} d^{4}\right)} x^{3} + 3 \, {\left(2 \, a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{3} c^{7} - 3 \, a^{2} b^{2} c^{6} d + 3 \, a^{3} b c^{5} d^{2} - a^{4} c^{4} d^{3} + {\left(a b^{3} c^{5} d^{2} - 3 \, a^{2} b^{2} c^{4} d^{3} + 3 \, a^{3} b c^{3} d^{4} - a^{4} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(a b^{3} c^{6} d - 3 \, a^{2} b^{2} c^{5} d^{2} + 3 \, a^{3} b c^{4} d^{3} - a^{4} c^{3} d^{4}\right)} x^{2}\right)}}, \frac{3 \, {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c^{3} d x^{2} + b^{2} c^{4}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(5 \, a b^{2} c^{2} d^{2} - 7 \, a^{2} b c d^{3} + 2 \, a^{3} d^{4}\right)} x^{3} + 3 \, {\left(2 \, a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a b^{3} c^{7} - 3 \, a^{2} b^{2} c^{6} d + 3 \, a^{3} b c^{5} d^{2} - a^{4} c^{4} d^{3} + {\left(a b^{3} c^{5} d^{2} - 3 \, a^{2} b^{2} c^{4} d^{3} + 3 \, a^{3} b c^{3} d^{4} - a^{4} c^{2} d^{5}\right)} x^{4} + 2 \, {\left(a b^{3} c^{6} d - 3 \, a^{2} b^{2} c^{5} d^{2} + 3 \, a^{3} b c^{4} d^{3} - a^{4} c^{3} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/12*(3*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*((5*a*b^2*c^2*d^2 - 7*a^2*b*c*d^3 + 2*a^3*d^4)*x^3 + 3*(2*a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + a^3*c*d^3)*x)*sqrt(d*x^2 + c))/(a*b^3*c^7 - 3*a^2*b^2*c^6*d + 3*a^3*b*c^5*d^2 - a^4*c^4*d^3 + (a*b^3*c^5*d^2 - 3*a^2*b^2*c^4*d^3 + 3*a^3*b*c^3*d^4 - a^4*c^2*d^5)*x^4 + 2*(a*b^3*c^6*d - 3*a^2*b^2*c^5*d^2 + 3*a^3*b*c^4*d^3 - a^4*c^3*d^4)*x^2), 1/6*(3*(b^2*c^2*d^2*x^4 + 2*b^2*c^3*d*x^2 + b^2*c^4)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((5*a*b^2*c^2*d^2 - 7*a^2*b*c*d^3 + 2*a^3*d^4)*x^3 + 3*(2*a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + a^3*c*d^3)*x)*sqrt(d*x^2 + c))/(a*b^3*c^7 - 3*a^2*b^2*c^6*d + 3*a^3*b*c^5*d^2 - a^4*c^4*d^3 + (a*b^3*c^5*d^2 - 3*a^2*b^2*c^4*d^3 + 3*a^3*b*c^3*d^4 - a^4*c^2*d^5)*x^4 + 2*(a*b^3*c^6*d - 3*a^2*b^2*c^5*d^2 + 3*a^3*b*c^4*d^3 - a^4*c^3*d^4)*x^2)]","B",0
727,1,1711,0,3.201065," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{3} d^{2} x^{4} + 2 \, b^{2} c^{4} d x^{2} + b^{2} c^{5}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 6 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(7 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(2 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{2}\right)}}, \frac{12 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 3 \, {\left(b^{2} c^{3} d^{2} x^{4} + 2 \, b^{2} c^{4} d x^{2} + b^{2} c^{5}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(7 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(2 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b^{2} c^{3} d^{2} x^{4} + 2 \, b^{2} c^{4} d x^{2} + b^{2} c^{5}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(7 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(2 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b^{2} c^{3} d^{2} x^{4} + 2 \, b^{2} c^{4} d x^{2} + b^{2} c^{5}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 6 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(7 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + 3 \, {\left(2 \, a b c^{2} d^{2} - a^{2} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b^2*c^3*d^2*x^4 + 2*b^2*c^4*d*x^2 + b^2*c^5)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 6*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(7*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(2*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^4 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^2), 1/12*(12*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 3*(b^2*c^3*d^2*x^4 + 2*b^2*c^4*d*x^2 + b^2*c^5)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(7*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(2*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^4 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^2), -1/6*(3*(b^2*c^3*d^2*x^4 + 2*b^2*c^4*d*x^2 + b^2*c^5)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 3*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(7*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(2*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^4 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^2), -1/6*(3*(b^2*c^3*d^2*x^4 + 2*b^2*c^4*d*x^2 + b^2*c^5)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 6*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(7*a*b*c^3*d - 4*a^2*c^2*d^2 + 3*(2*a*b*c^2*d^2 - a^2*c*d^3)*x^2)*sqrt(d*x^2 + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^4 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^2)]","B",0
728,1,934,0,2.170150," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, a b^{3} c^{5} - 9 \, a^{2} b^{2} c^{4} d + 9 \, a^{3} b c^{3} d^{2} - 3 \, a^{4} c^{2} d^{3} + {\left(3 \, a b^{3} c^{3} d^{2} - 17 \, a^{2} b^{2} c^{2} d^{3} + 22 \, a^{3} b c d^{4} - 8 \, a^{4} d^{5}\right)} x^{4} + 3 \, {\left(2 \, a b^{3} c^{4} d - 9 \, a^{2} b^{2} c^{3} d^{2} + 11 \, a^{3} b c^{2} d^{3} - 4 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{2} b^{3} c^{6} d^{2} - 3 \, a^{3} b^{2} c^{5} d^{3} + 3 \, a^{4} b c^{4} d^{4} - a^{5} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a^{2} b^{3} c^{7} d - 3 \, a^{3} b^{2} c^{6} d^{2} + 3 \, a^{4} b c^{5} d^{3} - a^{5} c^{4} d^{4}\right)} x^{3} + {\left(a^{2} b^{3} c^{8} - 3 \, a^{3} b^{2} c^{7} d + 3 \, a^{4} b c^{6} d^{2} - a^{5} c^{5} d^{3}\right)} x\right)}}, -\frac{3 \, {\left(b^{3} c^{3} d^{2} x^{5} + 2 \, b^{3} c^{4} d x^{3} + b^{3} c^{5} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a b^{3} c^{5} - 9 \, a^{2} b^{2} c^{4} d + 9 \, a^{3} b c^{3} d^{2} - 3 \, a^{4} c^{2} d^{3} + {\left(3 \, a b^{3} c^{3} d^{2} - 17 \, a^{2} b^{2} c^{2} d^{3} + 22 \, a^{3} b c d^{4} - 8 \, a^{4} d^{5}\right)} x^{4} + 3 \, {\left(2 \, a b^{3} c^{4} d - 9 \, a^{2} b^{2} c^{3} d^{2} + 11 \, a^{3} b c^{2} d^{3} - 4 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left({\left(a^{2} b^{3} c^{6} d^{2} - 3 \, a^{3} b^{2} c^{5} d^{3} + 3 \, a^{4} b c^{4} d^{4} - a^{5} c^{3} d^{5}\right)} x^{5} + 2 \, {\left(a^{2} b^{3} c^{7} d - 3 \, a^{3} b^{2} c^{6} d^{2} + 3 \, a^{4} b c^{5} d^{3} - a^{5} c^{4} d^{4}\right)} x^{3} + {\left(a^{2} b^{3} c^{8} - 3 \, a^{3} b^{2} c^{7} d + 3 \, a^{4} b c^{6} d^{2} - a^{5} c^{5} d^{3}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*a*b^3*c^5 - 9*a^2*b^2*c^4*d + 9*a^3*b*c^3*d^2 - 3*a^4*c^2*d^3 + (3*a*b^3*c^3*d^2 - 17*a^2*b^2*c^2*d^3 + 22*a^3*b*c*d^4 - 8*a^4*d^5)*x^4 + 3*(2*a*b^3*c^4*d - 9*a^2*b^2*c^3*d^2 + 11*a^3*b*c^2*d^3 - 4*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/((a^2*b^3*c^6*d^2 - 3*a^3*b^2*c^5*d^3 + 3*a^4*b*c^4*d^4 - a^5*c^3*d^5)*x^5 + 2*(a^2*b^3*c^7*d - 3*a^3*b^2*c^6*d^2 + 3*a^4*b*c^5*d^3 - a^5*c^4*d^4)*x^3 + (a^2*b^3*c^8 - 3*a^3*b^2*c^7*d + 3*a^4*b*c^6*d^2 - a^5*c^5*d^3)*x), -1/6*(3*(b^3*c^3*d^2*x^5 + 2*b^3*c^4*d*x^3 + b^3*c^5*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(3*a*b^3*c^5 - 9*a^2*b^2*c^4*d + 9*a^3*b*c^3*d^2 - 3*a^4*c^2*d^3 + (3*a*b^3*c^3*d^2 - 17*a^2*b^2*c^2*d^3 + 22*a^3*b*c*d^4 - 8*a^4*d^5)*x^4 + 3*(2*a*b^3*c^4*d - 9*a^2*b^2*c^3*d^2 + 11*a^3*b*c^2*d^3 - 4*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/((a^2*b^3*c^6*d^2 - 3*a^3*b^2*c^5*d^3 + 3*a^4*b*c^4*d^4 - a^5*c^3*d^5)*x^5 + 2*(a^2*b^3*c^7*d - 3*a^3*b^2*c^6*d^2 + 3*a^4*b*c^5*d^3 - a^5*c^4*d^4)*x^3 + (a^2*b^3*c^8 - 3*a^3*b^2*c^7*d + 3*a^4*b*c^6*d^2 - a^5*c^5*d^3)*x)]","B",0
729,1,2219,0,6.035376," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{4} d^{2} x^{6} + 2 \, b^{3} c^{5} d x^{4} + b^{3} c^{6} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 3 \, {\left({\left(2 \, b^{3} c^{3} d^{2} + a b^{2} c^{2} d^{3} - 8 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{3} c^{4} d + a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + {\left(2 \, b^{3} c^{5} + a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + 3 \, {\left(a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{4} d - 16 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{6} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2}\right)}}, -\frac{6 \, {\left({\left(2 \, b^{3} c^{3} d^{2} + a b^{2} c^{2} d^{3} - 8 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{3} c^{4} d + a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + {\left(2 \, b^{3} c^{5} + a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 3 \, {\left(b^{3} c^{4} d^{2} x^{6} + 2 \, b^{3} c^{5} d x^{4} + b^{3} c^{6} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + 3 \, {\left(a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{4} d - 16 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{6} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2}\right)}}, \frac{6 \, {\left(b^{3} c^{4} d^{2} x^{6} + 2 \, b^{3} c^{5} d x^{4} + b^{3} c^{6} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 3 \, {\left({\left(2 \, b^{3} c^{3} d^{2} + a b^{2} c^{2} d^{3} - 8 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{3} c^{4} d + a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + {\left(2 \, b^{3} c^{5} + a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + 3 \, {\left(a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{4} d - 16 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{6} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2}\right)}}, \frac{3 \, {\left(b^{3} c^{4} d^{2} x^{6} + 2 \, b^{3} c^{5} d x^{4} + b^{3} c^{6} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 3 \, {\left({\left(2 \, b^{3} c^{3} d^{2} + a b^{2} c^{2} d^{3} - 8 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{3} c^{4} d + a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + {\left(2 \, b^{3} c^{5} + a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + 3 \, {\left(a b^{2} c^{3} d^{2} - 8 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{2} c^{4} d - 16 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{6} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{4} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(b^3*c^4*d^2*x^6 + 2*b^3*c^5*d*x^4 + b^3*c^6*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 3*((2*b^3*c^3*d^2 + a*b^2*c^2*d^3 - 8*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 2*(2*b^3*c^4*d + a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + (2*b^3*c^5 + a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + 3*(a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 2*(3*a*b^2*c^4*d - 16*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^6 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2), -1/12*(6*((2*b^3*c^3*d^2 + a*b^2*c^2*d^3 - 8*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 2*(2*b^3*c^4*d + a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + (2*b^3*c^5 + a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 3*(b^3*c^4*d^2*x^6 + 2*b^3*c^5*d*x^4 + b^3*c^6*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + 3*(a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 2*(3*a*b^2*c^4*d - 16*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^6 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2), 1/12*(6*(b^3*c^4*d^2*x^6 + 2*b^3*c^5*d*x^4 + b^3*c^6*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 3*((2*b^3*c^3*d^2 + a*b^2*c^2*d^3 - 8*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 2*(2*b^3*c^4*d + a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + (2*b^3*c^5 + a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + 3*(a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 2*(3*a*b^2*c^4*d - 16*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^6 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2), 1/6*(3*(b^3*c^4*d^2*x^6 + 2*b^3*c^5*d*x^4 + b^3*c^6*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 3*((2*b^3*c^3*d^2 + a*b^2*c^2*d^3 - 8*a^2*b*c*d^4 + 5*a^3*d^5)*x^6 + 2*(2*b^3*c^4*d + a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + (2*b^3*c^5 + a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + 3*(a*b^2*c^3*d^2 - 8*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^4 + 2*(3*a*b^2*c^4*d - 16*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x^2)*sqrt(d*x^2 + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^6 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^4 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^2)]","B",0
730,1,1128,0,3.409658," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3} - {\left(3 \, a b^{4} c^{4} d^{2} - a^{2} b^{3} c^{3} d^{3} - 26 \, a^{3} b^{2} c^{2} d^{4} + 40 \, a^{4} b c d^{5} - 16 \, a^{5} d^{6}\right)} x^{6} - 3 \, {\left(2 \, a b^{4} c^{5} d - a^{2} b^{3} c^{4} d^{2} - 13 \, a^{3} b^{2} c^{3} d^{3} + 20 \, a^{4} b c^{2} d^{4} - 8 \, a^{5} c d^{5}\right)} x^{4} - 3 \, {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{3} b^{3} c^{7} d^{2} - 3 \, a^{4} b^{2} c^{6} d^{3} + 3 \, a^{5} b c^{5} d^{4} - a^{6} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{3} b^{3} c^{8} d - 3 \, a^{4} b^{2} c^{7} d^{2} + 3 \, a^{5} b c^{6} d^{3} - a^{6} c^{5} d^{4}\right)} x^{5} + {\left(a^{3} b^{3} c^{9} - 3 \, a^{4} b^{2} c^{8} d + 3 \, a^{5} b c^{7} d^{2} - a^{6} c^{6} d^{3}\right)} x^{3}\right)}}, \frac{3 \, {\left(b^{4} c^{4} d^{2} x^{7} + 2 \, b^{4} c^{5} d x^{5} + b^{4} c^{6} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(a^{2} b^{3} c^{6} - 3 \, a^{3} b^{2} c^{5} d + 3 \, a^{4} b c^{4} d^{2} - a^{5} c^{3} d^{3} - {\left(3 \, a b^{4} c^{4} d^{2} - a^{2} b^{3} c^{3} d^{3} - 26 \, a^{3} b^{2} c^{2} d^{4} + 40 \, a^{4} b c d^{5} - 16 \, a^{5} d^{6}\right)} x^{6} - 3 \, {\left(2 \, a b^{4} c^{5} d - a^{2} b^{3} c^{4} d^{2} - 13 \, a^{3} b^{2} c^{3} d^{3} + 20 \, a^{4} b c^{2} d^{4} - 8 \, a^{5} c d^{5}\right)} x^{4} - 3 \, {\left(a b^{4} c^{6} - a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 5 \, a^{4} b c^{3} d^{3} - 2 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{6 \, {\left({\left(a^{3} b^{3} c^{7} d^{2} - 3 \, a^{4} b^{2} c^{6} d^{3} + 3 \, a^{5} b c^{5} d^{4} - a^{6} c^{4} d^{5}\right)} x^{7} + 2 \, {\left(a^{3} b^{3} c^{8} d - 3 \, a^{4} b^{2} c^{7} d^{2} + 3 \, a^{5} b c^{6} d^{3} - a^{6} c^{5} d^{4}\right)} x^{5} + {\left(a^{3} b^{3} c^{9} - 3 \, a^{4} b^{2} c^{8} d + 3 \, a^{5} b c^{7} d^{2} - a^{6} c^{6} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[-1/12*(3*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3 - (3*a*b^4*c^4*d^2 - a^2*b^3*c^3*d^3 - 26*a^3*b^2*c^2*d^4 + 40*a^4*b*c*d^5 - 16*a^5*d^6)*x^6 - 3*(2*a*b^4*c^5*d - a^2*b^3*c^4*d^2 - 13*a^3*b^2*c^3*d^3 + 20*a^4*b*c^2*d^4 - 8*a^5*c*d^5)*x^4 - 3*(a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^7*d^2 - 3*a^4*b^2*c^6*d^3 + 3*a^5*b*c^5*d^4 - a^6*c^4*d^5)*x^7 + 2*(a^3*b^3*c^8*d - 3*a^4*b^2*c^7*d^2 + 3*a^5*b*c^6*d^3 - a^6*c^5*d^4)*x^5 + (a^3*b^3*c^9 - 3*a^4*b^2*c^8*d + 3*a^5*b*c^7*d^2 - a^6*c^6*d^3)*x^3), 1/6*(3*(b^4*c^4*d^2*x^7 + 2*b^4*c^5*d*x^5 + b^4*c^6*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(a^2*b^3*c^6 - 3*a^3*b^2*c^5*d + 3*a^4*b*c^4*d^2 - a^5*c^3*d^3 - (3*a*b^4*c^4*d^2 - a^2*b^3*c^3*d^3 - 26*a^3*b^2*c^2*d^4 + 40*a^4*b*c*d^5 - 16*a^5*d^6)*x^6 - 3*(2*a*b^4*c^5*d - a^2*b^3*c^4*d^2 - 13*a^3*b^2*c^3*d^3 + 20*a^4*b*c^2*d^4 - 8*a^5*c*d^5)*x^4 - 3*(a*b^4*c^6 - a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 5*a^4*b*c^3*d^3 - 2*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^7*d^2 - 3*a^4*b^2*c^6*d^3 + 3*a^5*b*c^5*d^4 - a^6*c^4*d^5)*x^7 + 2*(a^3*b^3*c^8*d - 3*a^4*b^2*c^7*d^2 + 3*a^5*b*c^6*d^3 - a^6*c^5*d^4)*x^5 + (a^3*b^3*c^9 - 3*a^4*b^2*c^8*d + 3*a^5*b*c^7*d^2 - a^6*c^6*d^3)*x^3)]","B",0
731,1,1002,0,1.946796," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 4 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{2} d x^{3} + 2 \, a b d x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{4} d x^{2} + a b^{3} d\right)}}, -\frac{4 \, {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 4 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{2} d x^{3} + 2 \, a b d x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{4} d x^{2} + a b^{3} d\right)}}, \frac{{\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 4 \, a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(b^{2} d x^{3} + 2 \, a b d x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{4} d x^{2} + a b^{3} d\right)}}, -\frac{2 \, {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(3 \, a b c d - 4 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 4 \, a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) - 2 \, {\left(b^{2} d x^{3} + 2 \, a b d x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{4} d x^{2} + a b^{3} d\right)}}\right]"," ",0,"[-1/8*(2*(a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (3*a*b*c*d - 4*a^2*d^2 + (3*b^2*c*d - 4*a*b*d^2)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^2*d*x^3 + 2*a*b*d*x)*sqrt(d*x^2 + c))/(b^4*d*x^2 + a*b^3*d), -1/8*(4*(a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (3*a*b*c*d - 4*a^2*d^2 + (3*b^2*c*d - 4*a*b*d^2)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^2*d*x^3 + 2*a*b*d*x)*sqrt(d*x^2 + c))/(b^4*d*x^2 + a*b^3*d), 1/4*((3*a*b*c*d - 4*a^2*d^2 + (3*b^2*c*d - 4*a*b*d^2)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - (a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(b^2*d*x^3 + 2*a*b*d*x)*sqrt(d*x^2 + c))/(b^4*d*x^2 + a*b^3*d), -1/4*(2*(a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (3*a*b*c*d - 4*a^2*d^2 + (3*b^2*c*d - 4*a*b*d^2)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) - 2*(b^2*d*x^3 + 2*a*b*d*x)*sqrt(d*x^2 + c))/(b^4*d*x^2 + a*b^3*d)]","A",0
732,1,436,0,0.965698," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b c - 3 \, a^{2} d + {\left(2 \, b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(3 \, a b^{2} c - 3 \, a^{2} b d + 2 \, {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} c - a^{2} b^{3} d + {\left(b^{5} c - a b^{4} d\right)} x^{2}\right)}}, -\frac{{\left(2 \, a b c - 3 \, a^{2} d + {\left(2 \, b^{2} c - 3 \, a b d\right)} x^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(3 \, a b^{2} c - 3 \, a^{2} b d + 2 \, {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} c - a^{2} b^{3} d + {\left(b^{5} c - a b^{4} d\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*((2*a*b*c - 3*a^2*d + (2*b^2*c - 3*a*b*d)*x^2)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(3*a*b^2*c - 3*a^2*b*d + 2*(b^3*c - a*b^2*d)*x^2)*sqrt(d*x^2 + c))/(a*b^4*c - a^2*b^3*d + (b^5*c - a*b^4*d)*x^2), -1/4*((2*a*b*c - 3*a^2*d + (2*b^2*c - 3*a*b*d)*x^2)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) - 2*(3*a*b^2*c - 3*a^2*b*d + 2*(b^3*c - a*b^2*d)*x^2)*sqrt(d*x^2 + c))/(a*b^4*c - a^2*b^3*d + (b^5*c - a*b^4*d)*x^2)]","A",0
733,1,1069,0,1.109715," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x - 4 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + {\left(a b^{4} c - a^{2} b^{3} d\right)} x^{2}\right)}}, -\frac{4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x + 8 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + {\left(a b^{4} c - a^{2} b^{3} d\right)} x^{2}\right)}}, -\frac{2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x - \sqrt{a b c - a^{2} d} {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + {\left(a b^{4} c - a^{2} b^{3} d\right)} x^{2}\right)}}, -\frac{2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x - \sqrt{a b c - a^{2} d} {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 4 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right)}{4 \, {\left(a^{2} b^{3} c - a^{3} b^{2} d + {\left(a b^{4} c - a^{2} b^{3} d\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x - 4*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^2*b^3*c - a^3*b^2*d + (a*b^4*c - a^2*b^3*d)*x^2), -1/8*(4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x + 8*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^2*b^3*c - a^3*b^2*d + (a*b^4*c - a^2*b^3*d)*x^2), -1/4*(2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x - sqrt(a*b*c - a^2*d)*(a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(a^2*b^3*c - a^3*b^2*d + (a*b^4*c - a^2*b^3*d)*x^2), -1/4*(2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x - sqrt(a*b*c - a^2*d)*(a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 4*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)))/(a^2*b^3*c - a^3*b^2*d + (a*b^4*c - a^2*b^3*d)*x^2)]","B",0
734,1,356,0,1.107456," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b d x^{2} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{3} c - a^{2} b^{2} d + {\left(b^{4} c - a b^{3} d\right)} x^{2}\right)}}, -\frac{{\left(b d x^{2} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{3} c - a^{2} b^{2} d + {\left(b^{4} c - a b^{3} d\right)} x^{2}\right)}}\right]"," ",0,"[1/8*((b*d*x^2 + a*d)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(a*b^3*c - a^2*b^2*d + (b^4*c - a*b^3*d)*x^2), -1/4*((b*d*x^2 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + 2*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(a*b^3*c - a^2*b^2*d + (b^4*c - a*b^3*d)*x^2)]","B",0
735,1,369,0,1.115160," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c} x - {\left(b c x^{2} + a c\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{3} b c - a^{4} d + {\left(a^{2} b^{2} c - a^{3} b d\right)} x^{2}\right)}}, \frac{2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c} x + {\left(b c x^{2} + a c\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(a^{3} b c - a^{4} d + {\left(a^{2} b^{2} c - a^{3} b d\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*(a*b*c - a^2*d)*sqrt(d*x^2 + c)*x - (b*c*x^2 + a*c)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^3*b*c - a^4*d + (a^2*b^2*c - a^3*b*d)*x^2), 1/4*(2*(a*b*c - a^2*d)*sqrt(d*x^2 + c)*x + (b*c*x^2 + a*c)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a^3*b*c - a^4*d + (a^2*b^2*c - a^3*b*d)*x^2)]","B",0
736,1,1054,0,1.505669," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{2}\right)}}, \frac{8 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{2}\right)}}, \frac{{\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{2}\right)}}, \frac{{\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) + 4 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*((2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^2), 1/8*(8*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^2), 1/4*((2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + 2*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^2), 1/4*((2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) + 4*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^2)]","B",0
737,1,458,0,1.127506," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, b^{2} c - 2 \, a b d\right)} x^{3} + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, a^{2} b c - 2 \, a^{3} d + 3 \, {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{2} c - a^{4} b d\right)} x^{3} + {\left(a^{4} b c - a^{5} d\right)} x\right)}}, -\frac{{\left({\left(3 \, b^{2} c - 2 \, a b d\right)} x^{3} + {\left(3 \, a b c - 2 \, a^{2} d\right)} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} b c - 2 \, a^{3} d + 3 \, {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{2} c - a^{4} b d\right)} x^{3} + {\left(a^{4} b c - a^{5} d\right)} x\right)}}\right]"," ",0,"[1/8*(((3*b^2*c - 2*a*b*d)*x^3 + (3*a*b*c - 2*a^2*d)*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*a^2*b*c - 2*a^3*d + 3*(a*b^2*c - a^2*b*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c - a^4*b*d)*x^3 + (a^4*b*c - a^5*d)*x), -1/4*(((3*b^2*c - 2*a*b*d)*x^3 + (3*a*b*c - 2*a^2*d)*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(2*a^2*b*c - 2*a^3*d + 3*(a*b^2*c - a^2*b*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c - a^4*b*d)*x^3 + (a^4*b*c - a^5*d)*x)]","B",0
738,1,1043,0,1.638907," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(2 \, a b c x^{2} + a^{2} c\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b c x^{4} + a^{4} c x^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a b c x^{2} + a^{2} c\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b c x^{4} + a^{4} c x^{2}\right)}}, \frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - {\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, a b c x^{2} + a^{2} c\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b c x^{4} + a^{4} c x^{2}\right)}}, \frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(2 \, a b c x^{2} + a^{2} c\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b c x^{4} + a^{4} c x^{2}\right)}}\right]"," ",0,"[-1/8*(((4*b^2*c^2 - 3*a*b*c*d)*x^4 + (4*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(2*a*b*c*x^2 + a^2*c)*sqrt(d*x^2 + c))/(a^3*b*c*x^4 + a^4*c*x^2), -1/8*(4*((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + ((4*b^2*c^2 - 3*a*b*c*d)*x^4 + (4*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a*b*c*x^2 + a^2*c)*sqrt(d*x^2 + c))/(a^3*b*c*x^4 + a^4*c*x^2), 1/4*(((4*b^2*c^2 - 3*a*b*c*d)*x^4 + (4*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - ((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*a*b*c*x^2 + a^2*c)*sqrt(d*x^2 + c))/(a^3*b*c*x^4 + a^4*c*x^2), 1/4*(((4*b^2*c^2 - 3*a*b*c*d)*x^4 + (4*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(2*a*b*c*x^2 + a^2*c)*sqrt(d*x^2 + c))/(a^3*b*c*x^4 + a^4*c*x^2)]","A",0
739,1,602,0,1.316212," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{5} + {\left(5 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, a^{3} b c^{2} - 2 \, a^{4} c d - {\left(15 \, a b^{3} c^{2} - 17 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{4} b^{2} c^{2} - a^{5} b c d\right)} x^{5} + {\left(a^{5} b c^{2} - a^{6} c d\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{5} + {\left(5 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b c^{2} - 2 \, a^{4} c d - {\left(15 \, a b^{3} c^{2} - 17 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{2} c^{2} - 6 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{4} b^{2} c^{2} - a^{5} b c d\right)} x^{5} + {\left(a^{5} b c^{2} - a^{6} c d\right)} x^{3}\right)}}\right]"," ",0,"[1/24*(3*((5*b^3*c^2 - 4*a*b^2*c*d)*x^5 + (5*a*b^2*c^2 - 4*a^2*b*c*d)*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*a^3*b*c^2 - 2*a^4*c*d - (15*a*b^3*c^2 - 17*a^2*b^2*c*d + 2*a^3*b*d^2)*x^4 - 2*(5*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*x^2)*sqrt(d*x^2 + c))/((a^4*b^2*c^2 - a^5*b*c*d)*x^5 + (a^5*b*c^2 - a^6*c*d)*x^3), 1/12*(3*((5*b^3*c^2 - 4*a*b^2*c*d)*x^5 + (5*a*b^2*c^2 - 4*a^2*b*c*d)*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(2*a^3*b*c^2 - 2*a^4*c*d - (15*a*b^3*c^2 - 17*a^2*b^2*c*d + 2*a^3*b*d^2)*x^4 - 2*(5*a^2*b^2*c^2 - 6*a^3*b*c*d + a^4*d^2)*x^2)*sqrt(d*x^2 + c))/((a^4*b^2*c^2 - a^5*b*c*d)*x^5 + (a^5*b*c^2 - a^6*c*d)*x^3)]","B",0
740,1,1249,0,1.835653," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{2} c^{2} - 8 \, a^{2} b c d + 8 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 8 \, a b^{2} c d + 8 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 6 \, {\left(a b c d - 2 \, a^{2} d^{2} + {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(2 \, b^{3} d^{2} x^{5} + {\left(5 \, b^{3} c d - 6 \, a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(b^{5} d x^{2} + a b^{4} d\right)}}, -\frac{3 \, {\left(a b^{2} c^{2} - 8 \, a^{2} b c d + 8 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 8 \, a b^{2} c d + 8 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + 3 \, {\left(a b c d - 2 \, a^{2} d^{2} + {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b^{3} d^{2} x^{5} + {\left(5 \, b^{3} c d - 6 \, a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{5} d x^{2} + a b^{4} d\right)}}, -\frac{12 \, {\left(a b c d - 2 \, a^{2} d^{2} + {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(a b^{2} c^{2} - 8 \, a^{2} b c d + 8 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 8 \, a b^{2} c d + 8 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(2 \, b^{3} d^{2} x^{5} + {\left(5 \, b^{3} c d - 6 \, a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(b^{5} d x^{2} + a b^{4} d\right)}}, -\frac{6 \, {\left(a b c d - 2 \, a^{2} d^{2} + {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(a b^{2} c^{2} - 8 \, a^{2} b c d + 8 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 8 \, a b^{2} c d + 8 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b^{3} d^{2} x^{5} + {\left(5 \, b^{3} c d - 6 \, a b^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{5} d x^{2} + a b^{4} d\right)}}\right]"," ",0,"[1/16*(3*(a*b^2*c^2 - 8*a^2*b*c*d + 8*a^3*d^2 + (b^3*c^2 - 8*a*b^2*c*d + 8*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 6*(a*b*c*d - 2*a^2*d^2 + (b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(2*b^3*d^2*x^5 + (5*b^3*c*d - 6*a*b^2*d^2)*x^3 + 3*(3*a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*d*x^2 + a*b^4*d), -1/8*(3*(a*b^2*c^2 - 8*a^2*b*c*d + 8*a^3*d^2 + (b^3*c^2 - 8*a*b^2*c*d + 8*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + 3*(a*b*c*d - 2*a^2*d^2 + (b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b^3*d^2*x^5 + (5*b^3*c*d - 6*a*b^2*d^2)*x^3 + 3*(3*a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*d*x^2 + a*b^4*d), -1/16*(12*(a*b*c*d - 2*a^2*d^2 + (b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 3*(a*b^2*c^2 - 8*a^2*b*c*d + 8*a^3*d^2 + (b^3*c^2 - 8*a*b^2*c*d + 8*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(2*b^3*d^2*x^5 + (5*b^3*c*d - 6*a*b^2*d^2)*x^3 + 3*(3*a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*d*x^2 + a*b^4*d), -1/8*(6*(a*b*c*d - 2*a^2*d^2 + (b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(a*b^2*c^2 - 8*a^2*b*c*d + 8*a^3*d^2 + (b^3*c^2 - 8*a*b^2*c*d + 8*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (2*b^3*d^2*x^5 + (5*b^3*c*d - 6*a*b^2*d^2)*x^3 + 3*(3*a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*d*x^2 + a*b^4*d)]","A",0
741,1,413,0,0.939368," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, a b c - 5 \, a^{2} d + {\left(2 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, b^{2} d x^{4} + 11 \, a b c - 15 \, a^{2} d + 2 \, {\left(4 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, -\frac{3 \, {\left(2 \, a b c - 5 \, a^{2} d + {\left(2 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b^{2} d x^{4} + 11 \, a b c - 15 \, a^{2} d + 2 \, {\left(4 \, b^{2} c - 5 \, a b d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[-1/24*(3*(2*a*b*c - 5*a^2*d + (2*b^2*c - 5*a*b*d)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*b^2*d*x^4 + 11*a*b*c - 15*a^2*d + 2*(4*b^2*c - 5*a*b*d)*x^2)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3), -1/12*(3*(2*a*b*c - 5*a^2*d + (2*b^2*c - 5*a*b*d)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(2*b^2*d*x^4 + 11*a*b*c - 15*a^2*d + 2*(4*b^2*c - 5*a*b*d)*x^2)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3)]","A",0
742,1,996,0,1.503293," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(3 \, a b c - 4 \, a^{2} d + {\left(3 \, b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{2} d x^{3} - {\left(b^{2} c - 2 \, a b d\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, -\frac{4 \, {\left(3 \, a b c - 4 \, a^{2} d + {\left(3 \, b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{2} d x^{3} - {\left(b^{2} c - 2 \, a b d\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, \frac{{\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(3 \, a b c - 4 \, a^{2} d + {\left(3 \, b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(b^{2} d x^{3} - {\left(b^{2} c - 2 \, a b d\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, -\frac{2 \, {\left(3 \, a b c - 4 \, a^{2} d + {\left(3 \, b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(a b c - 4 \, a^{2} d + {\left(b^{2} c - 4 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - 2 \, {\left(b^{2} d x^{3} - {\left(b^{2} c - 2 \, a b d\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[-1/8*(2*(3*a*b*c - 4*a^2*d + (3*b^2*c - 4*a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^2*d*x^3 - (b^2*c - 2*a*b*d)*x)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3), -1/8*(4*(3*a*b*c - 4*a^2*d + (3*b^2*c - 4*a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^2*d*x^3 - (b^2*c - 2*a*b*d)*x)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3), 1/4*((a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (3*a*b*c - 4*a^2*d + (3*b^2*c - 4*a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(b^2*d*x^3 - (b^2*c - 2*a*b*d)*x)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3), -1/4*(2*(3*a*b*c - 4*a^2*d + (3*b^2*c - 4*a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (a*b*c - 4*a^2*d + (b^2*c - 4*a*b*d)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - 2*(b^2*d*x^3 - (b^2*c - 2*a*b*d)*x)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3)]","A",0
743,1,333,0,1.305335," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d x^{2} + a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, b d x^{2} - b c + 3 \, a d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{3} x^{2} + a b^{2}\right)}}, -\frac{3 \, {\left(b d x^{2} + a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b d x^{2} - b c + 3 \, a d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(b^{3} x^{2} + a b^{2}\right)}}\right]"," ",0,"[1/8*(3*(b*d*x^2 + a*d)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*b*d*x^2 - b*c + 3*a*d)*sqrt(d*x^2 + c))/(b^3*x^2 + a*b^2), -1/4*(3*(b*d*x^2 + a*d)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(2*b*d*x^2 - b*c + 3*a*d)*sqrt(d*x^2 + c))/(b^3*x^2 + a*b^2)]","A",0
744,1,903,0,1.682418," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c} x + 4 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(a b c + 2 \, a^{2} d + {\left(b^{2} c + 2 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, \frac{4 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c} x - 8 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a b c + 2 \, a^{2} d + {\left(b^{2} c + 2 \, a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, \frac{2 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c} x + {\left(a b c + 2 \, a^{2} d + {\left(b^{2} c + 2 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}, \frac{2 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c} x - 4 \, {\left(a b d x^{2} + a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a b c + 2 \, a^{2} d + {\left(b^{2} c + 2 \, a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right)}{4 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}}\right]"," ",0,"[1/8*(4*(b^2*c - a*b*d)*sqrt(d*x^2 + c)*x + 4*(a*b*d*x^2 + a^2*d)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (a*b*c + 2*a^2*d + (b^2*c + 2*a*b*d)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^3*x^2 + a^2*b^2), 1/8*(4*(b^2*c - a*b*d)*sqrt(d*x^2 + c)*x - 8*(a*b*d*x^2 + a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*b*c + 2*a^2*d + (b^2*c + 2*a*b*d)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^3*x^2 + a^2*b^2), 1/4*(2*(b^2*c - a*b*d)*sqrt(d*x^2 + c)*x + (a*b*c + 2*a^2*d + (b^2*c + 2*a*b*d)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*(a*b*d*x^2 + a^2*d)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(a*b^3*x^2 + a^2*b^2), 1/4*(2*(b^2*c - a*b*d)*sqrt(d*x^2 + c)*x - 4*(a*b*d*x^2 + a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*b*c + 2*a^2*d + (b^2*c + 2*a*b*d)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)))/(a*b^3*x^2 + a^2*b^2)]","A",0
745,1,883,0,1.639524," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{8 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}, \frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 4 \, {\left(b^{2} c x^{2} + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b\right)}}\right]"," ",0,"[1/8*((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(b^2*c*x^2 + a*b*c)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/(a^2*b^2*x^2 + a^3*b), 1/8*(8*(b^2*c*x^2 + a*b*c)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/(a^2*b^2*x^2 + a^3*b), 1/4*((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(b^2*c*x^2 + a*b*c)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/(a^2*b^2*x^2 + a^3*b), 1/4*((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 4*(b^2*c*x^2 + a*b*c)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(a*b*c - a^2*d)*sqrt(d*x^2 + c))/(a^2*b^2*x^2 + a^3*b)]","A",0
746,1,351,0,0.986666," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c x^{3} + a c x\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(3 \, b c - a d\right)} x^{2} + 2 \, a c\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}, -\frac{3 \, {\left(b c x^{3} + a c x\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left({\left(3 \, b c - a d\right)} x^{2} + 2 \, a c\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b x^{3} + a^{3} x\right)}}\right]"," ",0,"[1/8*(3*(b*c*x^3 + a*c*x)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((3*b*c - a*d)*x^2 + 2*a*c)*sqrt(d*x^2 + c))/(a^2*b*x^3 + a^3*x), -1/4*(3*(b*c*x^3 + a*c*x)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*((3*b*c - a*d)*x^2 + 2*a*c)*sqrt(d*x^2 + c))/(a^2*b*x^3 + a^3*x)]","A",0
747,1,1034,0,1.555423," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{4} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{4} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}, -\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{4} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}, -\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{4} + {\left(4 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{4} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b x^{4} + a^{4} x^{2}\right)}}\right]"," ",0,"[-1/8*(((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*((4*b^2*c - 3*a*b*d)*x^4 + (4*a*b*c - 3*a^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(a^2*c + (2*a*b*c - a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^4 + a^4*x^2), -1/8*(4*((4*b^2*c - 3*a*b*d)*x^4 + (4*a*b*c - 3*a^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + ((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*c + (2*a*b*c - a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^4 + a^4*x^2), -1/4*(((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + ((4*b^2*c - 3*a*b*d)*x^4 + (4*a*b*c - 3*a^2*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a^2*c + (2*a*b*c - a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^4 + a^4*x^2), -1/4*(((4*b^2*c - a*b*d)*x^4 + (4*a*b*c - a^2*d)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*((4*b^2*c - 3*a*b*d)*x^4 + (4*a*b*c - 3*a^2*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(a^2*c + (2*a*b*c - a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^4 + a^4*x^2)]","A",0
748,1,443,0,1.153722," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{2} c - 2 \, a b d\right)} x^{5} + {\left(5 \, a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(15 \, b^{2} c - 11 \, a b d\right)} x^{4} - 2 \, a^{2} c + 2 \, {\left(5 \, a b c - 4 \, a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b^{2} c - 2 \, a b d\right)} x^{5} + {\left(5 \, a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left({\left(15 \, b^{2} c - 11 \, a b d\right)} x^{4} - 2 \, a^{2} c + 2 \, {\left(5 \, a b c - 4 \, a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[-1/24*(3*((5*b^2*c - 2*a*b*d)*x^5 + (5*a*b*c - 2*a^2*d)*x^3)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((15*b^2*c - 11*a*b*d)*x^4 - 2*a^2*c + 2*(5*a*b*c - 4*a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^5 + a^4*x^3), 1/12*(3*((5*b^2*c - 2*a*b*d)*x^5 + (5*a*b*c - 2*a^2*d)*x^3)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*((15*b^2*c - 11*a*b*d)*x^4 - 2*a^2*c + 2*(5*a*b*c - 4*a^2*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^5 + a^4*x^3)]","A",0
749,1,1697,0,6.211709," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, a b^{3} c^{3} - 60 \, a^{2} b^{2} c^{2} d + 120 \, a^{3} b c d^{2} - 64 \, a^{4} d^{3} + {\left(5 \, b^{4} c^{3} - 60 \, a b^{3} c^{2} d + 120 \, a^{2} b^{2} c d^{2} - 64 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 12 \, {\left(3 \, a b^{2} c^{2} d - 11 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left(8 \, b^{4} d^{3} x^{7} + 2 \, {\left(13 \, b^{4} c d^{2} - 8 \, a b^{3} d^{3}\right)} x^{5} + {\left(33 \, b^{4} c^{2} d - 82 \, a b^{3} c d^{2} + 48 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(19 \, a b^{3} c^{2} d - 52 \, a^{2} b^{2} c d^{2} + 32 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, {\left(b^{6} d x^{2} + a b^{5} d\right)}}, -\frac{3 \, {\left(5 \, a b^{3} c^{3} - 60 \, a^{2} b^{2} c^{2} d + 120 \, a^{3} b c d^{2} - 64 \, a^{4} d^{3} + {\left(5 \, b^{4} c^{3} - 60 \, a b^{3} c^{2} d + 120 \, a^{2} b^{2} c d^{2} - 64 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 6 \, {\left(3 \, a b^{2} c^{2} d - 11 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(8 \, b^{4} d^{3} x^{7} + 2 \, {\left(13 \, b^{4} c d^{2} - 8 \, a b^{3} d^{3}\right)} x^{5} + {\left(33 \, b^{4} c^{2} d - 82 \, a b^{3} c d^{2} + 48 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(19 \, a b^{3} c^{2} d - 52 \, a^{2} b^{2} c d^{2} + 32 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, {\left(b^{6} d x^{2} + a b^{5} d\right)}}, -\frac{24 \, {\left(3 \, a b^{2} c^{2} d - 11 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, a b^{3} c^{3} - 60 \, a^{2} b^{2} c^{2} d + 120 \, a^{3} b c d^{2} - 64 \, a^{4} d^{3} + {\left(5 \, b^{4} c^{3} - 60 \, a b^{3} c^{2} d + 120 \, a^{2} b^{2} c d^{2} - 64 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - 2 \, {\left(8 \, b^{4} d^{3} x^{7} + 2 \, {\left(13 \, b^{4} c d^{2} - 8 \, a b^{3} d^{3}\right)} x^{5} + {\left(33 \, b^{4} c^{2} d - 82 \, a b^{3} c d^{2} + 48 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(19 \, a b^{3} c^{2} d - 52 \, a^{2} b^{2} c d^{2} + 32 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{96 \, {\left(b^{6} d x^{2} + a b^{5} d\right)}}, -\frac{12 \, {\left(3 \, a b^{2} c^{2} d - 11 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} + 8 \, a^{2} b d^{3}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, a b^{3} c^{3} - 60 \, a^{2} b^{2} c^{2} d + 120 \, a^{3} b c d^{2} - 64 \, a^{4} d^{3} + {\left(5 \, b^{4} c^{3} - 60 \, a b^{3} c^{2} d + 120 \, a^{2} b^{2} c d^{2} - 64 \, a^{3} b d^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(8 \, b^{4} d^{3} x^{7} + 2 \, {\left(13 \, b^{4} c d^{2} - 8 \, a b^{3} d^{3}\right)} x^{5} + {\left(33 \, b^{4} c^{2} d - 82 \, a b^{3} c d^{2} + 48 \, a^{2} b^{2} d^{3}\right)} x^{3} + 3 \, {\left(19 \, a b^{3} c^{2} d - 52 \, a^{2} b^{2} c d^{2} + 32 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{48 \, {\left(b^{6} d x^{2} + a b^{5} d\right)}}\right]"," ",0,"[-1/96*(3*(5*a*b^3*c^3 - 60*a^2*b^2*c^2*d + 120*a^3*b*c*d^2 - 64*a^4*d^3 + (5*b^4*c^3 - 60*a*b^3*c^2*d + 120*a^2*b^2*c*d^2 - 64*a^3*b*d^3)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 12*(3*a*b^2*c^2*d - 11*a^2*b*c*d^2 + 8*a^3*d^3 + (3*b^3*c^2*d - 11*a*b^2*c*d^2 + 8*a^2*b*d^3)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*(8*b^4*d^3*x^7 + 2*(13*b^4*c*d^2 - 8*a*b^3*d^3)*x^5 + (33*b^4*c^2*d - 82*a*b^3*c*d^2 + 48*a^2*b^2*d^3)*x^3 + 3*(19*a*b^3*c^2*d - 52*a^2*b^2*c*d^2 + 32*a^3*b*d^3)*x)*sqrt(d*x^2 + c))/(b^6*d*x^2 + a*b^5*d), -1/48*(3*(5*a*b^3*c^3 - 60*a^2*b^2*c^2*d + 120*a^3*b*c*d^2 - 64*a^4*d^3 + (5*b^4*c^3 - 60*a*b^3*c^2*d + 120*a^2*b^2*c*d^2 - 64*a^3*b*d^3)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 6*(3*a*b^2*c^2*d - 11*a^2*b*c*d^2 + 8*a^3*d^3 + (3*b^3*c^2*d - 11*a*b^2*c*d^2 + 8*a^2*b*d^3)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (8*b^4*d^3*x^7 + 2*(13*b^4*c*d^2 - 8*a*b^3*d^3)*x^5 + (33*b^4*c^2*d - 82*a*b^3*c*d^2 + 48*a^2*b^2*d^3)*x^3 + 3*(19*a*b^3*c^2*d - 52*a^2*b^2*c*d^2 + 32*a^3*b*d^3)*x)*sqrt(d*x^2 + c))/(b^6*d*x^2 + a*b^5*d), -1/96*(24*(3*a*b^2*c^2*d - 11*a^2*b*c*d^2 + 8*a^3*d^3 + (3*b^3*c^2*d - 11*a*b^2*c*d^2 + 8*a^2*b*d^3)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(5*a*b^3*c^3 - 60*a^2*b^2*c^2*d + 120*a^3*b*c*d^2 - 64*a^4*d^3 + (5*b^4*c^3 - 60*a*b^3*c^2*d + 120*a^2*b^2*c*d^2 - 64*a^3*b*d^3)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - 2*(8*b^4*d^3*x^7 + 2*(13*b^4*c*d^2 - 8*a*b^3*d^3)*x^5 + (33*b^4*c^2*d - 82*a*b^3*c*d^2 + 48*a^2*b^2*d^3)*x^3 + 3*(19*a*b^3*c^2*d - 52*a^2*b^2*c*d^2 + 32*a^3*b*d^3)*x)*sqrt(d*x^2 + c))/(b^6*d*x^2 + a*b^5*d), -1/48*(12*(3*a*b^2*c^2*d - 11*a^2*b*c*d^2 + 8*a^3*d^3 + (3*b^3*c^2*d - 11*a*b^2*c*d^2 + 8*a^2*b*d^3)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 3*(5*a*b^3*c^3 - 60*a^2*b^2*c^2*d + 120*a^3*b*c*d^2 - 64*a^4*d^3 + (5*b^4*c^3 - 60*a*b^3*c^2*d + 120*a^2*b^2*c*d^2 - 64*a^3*b*d^3)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (8*b^4*d^3*x^7 + 2*(13*b^4*c*d^2 - 8*a*b^3*d^3)*x^5 + (33*b^4*c^2*d - 82*a*b^3*c*d^2 + 48*a^2*b^2*d^3)*x^3 + 3*(19*a*b^3*c^2*d - 52*a^2*b^2*c*d^2 + 32*a^3*b*d^3)*x)*sqrt(d*x^2 + c))/(b^6*d*x^2 + a*b^5*d)]","A",0
750,1,573,0,0.877302," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} - 9 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(6 \, b^{3} d^{2} x^{6} + 61 \, a b^{2} c^{2} - 170 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(11 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{4} + 2 \, {\left(23 \, b^{3} c^{2} - 59 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{120 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, -\frac{15 \, {\left(2 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} - 9 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(6 \, b^{3} d^{2} x^{6} + 61 \, a b^{2} c^{2} - 170 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(11 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{4} + 2 \, {\left(23 \, b^{3} c^{2} - 59 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{60 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/120*(15*(2*a*b^2*c^2 - 9*a^2*b*c*d + 7*a^3*d^2 + (2*b^3*c^2 - 9*a*b^2*c*d + 7*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(6*b^3*d^2*x^6 + 61*a*b^2*c^2 - 170*a^2*b*c*d + 105*a^3*d^2 + 2*(11*b^3*c*d - 7*a*b^2*d^2)*x^4 + 2*(23*b^3*c^2 - 59*a*b^2*c*d + 35*a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4), -1/60*(15*(2*a*b^2*c^2 - 9*a^2*b*c*d + 7*a^3*d^2 + (2*b^3*c^2 - 9*a*b^2*c*d + 7*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(6*b^3*d^2*x^6 + 61*a*b^2*c^2 - 170*a^2*b*c*d + 105*a^3*d^2 + 2*(11*b^3*c*d - 7*a*b^2*d^2)*x^4 + 2*(23*b^3*c^2 - 59*a*b^2*c*d + 35*a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4)]","A",0
751,1,1379,0,3.139180," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(15 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 24 \, a^{3} d^{2} + {\left(15 \, b^{3} c^{2} - 40 \, a b^{2} c d + 24 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(a b^{2} c^{2} - 7 \, a^{2} b c d + 6 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 7 \, a b^{2} c d + 6 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left(2 \, b^{3} d^{2} x^{5} + 3 \, {\left(3 \, b^{3} c d - 2 \, a b^{2} d^{2}\right)} x^{3} - {\left(4 \, b^{3} c^{2} - 17 \, a b^{2} c d + 12 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, -\frac{{\left(15 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 24 \, a^{3} d^{2} + {\left(15 \, b^{3} c^{2} - 40 \, a b^{2} c d + 24 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(a b^{2} c^{2} - 7 \, a^{2} b c d + 6 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 7 \, a b^{2} c d + 6 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - {\left(2 \, b^{3} d^{2} x^{5} + 3 \, {\left(3 \, b^{3} c d - 2 \, a b^{2} d^{2}\right)} x^{3} - {\left(4 \, b^{3} c^{2} - 17 \, a b^{2} c d + 12 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, \frac{4 \, {\left(a b^{2} c^{2} - 7 \, a^{2} b c d + 6 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 7 \, a b^{2} c d + 6 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + {\left(15 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 24 \, a^{3} d^{2} + {\left(15 \, b^{3} c^{2} - 40 \, a b^{2} c d + 24 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b^{3} d^{2} x^{5} + 3 \, {\left(3 \, b^{3} c d - 2 \, a b^{2} d^{2}\right)} x^{3} - {\left(4 \, b^{3} c^{2} - 17 \, a b^{2} c d + 12 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{16 \, {\left(b^{5} x^{2} + a b^{4}\right)}}, -\frac{{\left(15 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 24 \, a^{3} d^{2} + {\left(15 \, b^{3} c^{2} - 40 \, a b^{2} c d + 24 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(a b^{2} c^{2} - 7 \, a^{2} b c d + 6 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 7 \, a b^{2} c d + 6 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(2 \, b^{3} d^{2} x^{5} + 3 \, {\left(3 \, b^{3} c d - 2 \, a b^{2} d^{2}\right)} x^{3} - {\left(4 \, b^{3} c^{2} - 17 \, a b^{2} c d + 12 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(b^{5} x^{2} + a b^{4}\right)}}\right]"," ",0,"[1/16*((15*a*b^2*c^2 - 40*a^2*b*c*d + 24*a^3*d^2 + (15*b^3*c^2 - 40*a*b^2*c*d + 24*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(a*b^2*c^2 - 7*a^2*b*c*d + 6*a^3*d^2 + (b^3*c^2 - 7*a*b^2*c*d + 6*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*(2*b^3*d^2*x^5 + 3*(3*b^3*c*d - 2*a*b^2*d^2)*x^3 - (4*b^3*c^2 - 17*a*b^2*c*d + 12*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4), -1/8*((15*a*b^2*c^2 - 40*a^2*b*c*d + 24*a^3*d^2 + (15*b^3*c^2 - 40*a*b^2*c*d + 24*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (a*b^2*c^2 - 7*a^2*b*c*d + 6*a^3*d^2 + (b^3*c^2 - 7*a*b^2*c*d + 6*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - (2*b^3*d^2*x^5 + 3*(3*b^3*c*d - 2*a*b^2*d^2)*x^3 - (4*b^3*c^2 - 17*a*b^2*c*d + 12*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4), 1/16*(4*(a*b^2*c^2 - 7*a^2*b*c*d + 6*a^3*d^2 + (b^3*c^2 - 7*a*b^2*c*d + 6*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + (15*a*b^2*c^2 - 40*a^2*b*c*d + 24*a^3*d^2 + (15*b^3*c^2 - 40*a*b^2*c*d + 24*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b^3*d^2*x^5 + 3*(3*b^3*c*d - 2*a*b^2*d^2)*x^3 - (4*b^3*c^2 - 17*a*b^2*c*d + 12*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4), -1/8*((15*a*b^2*c^2 - 40*a^2*b*c*d + 24*a^3*d^2 + (15*b^3*c^2 - 40*a*b^2*c*d + 24*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 2*(a*b^2*c^2 - 7*a^2*b*c*d + 6*a^3*d^2 + (b^3*c^2 - 7*a*b^2*c*d + 6*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (2*b^3*d^2*x^5 + 3*(3*b^3*c*d - 2*a*b^2*d^2)*x^3 - (4*b^3*c^2 - 17*a*b^2*c*d + 12*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(b^5*x^2 + a*b^4)]","A",0
752,1,453,0,0.946593," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, b^{2} d^{2} x^{4} - 3 \, b^{2} c^{2} + 20 \, a b c d - 15 \, a^{2} d^{2} + 2 \, {\left(7 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(b^{4} x^{2} + a b^{3}\right)}}, -\frac{15 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{4} - 3 \, b^{2} c^{2} + 20 \, a b c d - 15 \, a^{2} d^{2} + 2 \, {\left(7 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(b^{4} x^{2} + a b^{3}\right)}}\right]"," ",0,"[-1/24*(15*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*b^2*d^2*x^4 - 3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 2*(7*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3), -1/12*(15*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) - 2*(2*b^2*d^2*x^4 - 3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 2*(7*b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(b^4*x^2 + a*b^3)]","A",0
753,1,1228,0,2.374524," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b^{2} d^{2} x^{3} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, -\frac{4 \, {\left(5 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b^{2} d^{2} x^{3} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, \frac{{\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - {\left(5 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(a b^{2} d^{2} x^{3} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}, -\frac{2 \, {\left(5 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - 2 \, {\left(a b^{2} d^{2} x^{3} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/8*(2*(5*a^2*b*c*d - 4*a^3*d^2 + (5*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b^2*d^2*x^3 + (b^3*c^2 - 2*a*b^2*c*d + 2*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(a*b^4*x^2 + a^2*b^3), -1/8*(4*(5*a^2*b*c*d - 4*a^3*d^2 + (5*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b^2*d^2*x^3 + (b^3*c^2 - 2*a*b^2*c*d + 2*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(a*b^4*x^2 + a^2*b^3), 1/4*((a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - (5*a^2*b*c*d - 4*a^3*d^2 + (5*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(a*b^2*d^2*x^3 + (b^3*c^2 - 2*a*b^2*c*d + 2*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(a*b^4*x^2 + a^2*b^3), -1/4*(2*(5*a^2*b*c*d - 4*a^3*d^2 + (5*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - 2*(a*b^2*d^2*x^3 + (b^3*c^2 - 2*a*b^2*c*d + 2*a^2*b*d^2)*x)*sqrt(d*x^2 + c))/(a*b^4*x^2 + a^2*b^3)]","A",0
754,1,1132,0,3.480609," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} b d^{2} x^{2} + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{8 \, {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a^{2} b d^{2} x^{2} + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, a^{2} b d^{2} x^{2} + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}, \frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 4 \, {\left(b^{3} c^{2} x^{2} + a b^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(2 \, a^{2} b d^{2} x^{2} + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/8*((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(b^3*c^2*x^2 + a*b^2*c^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(2*a^2*b*d^2*x^2 + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^2 + a^3*b^2), 1/8*(8*(b^3*c^2*x^2 + a*b^2*c^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a^2*b*d^2*x^2 + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^2 + a^3*b^2), 1/4*((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*(b^3*c^2*x^2 + a*b^2*c^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(2*a^2*b*d^2*x^2 + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^2 + a^3*b^2), 1/4*((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 4*(b^3*c^2*x^2 + a*b^2*c^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(2*a^2*b*d^2*x^2 + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^2 + a^3*b^2)]","A",0
755,1,1184,0,1.845857," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left({\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, a b^{2} c^{2} + {\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}}, -\frac{8 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left({\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a b^{2} c^{2} + {\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) - 2 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, a b^{2} c^{2} + {\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}}, -\frac{4 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left({\left(3 \, b^{3} c^{2} - a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a b^{2} c^{2} + {\left(3 \, b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}}\right]"," ",0,"[1/8*(4*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - ((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*a*b^2*c^2 + (3*b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^3 + a^3*b^2*x), -1/8*(8*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + ((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a*b^2*c^2 + (3*b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^3 + a^3*b^2*x), -1/4*(((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) - 2*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*a*b^2*c^2 + (3*b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^3 + a^3*b^2*x), -1/4*(4*(a^2*b*d^2*x^3 + a^3*d^2*x)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + ((3*b^3*c^2 - a*b^2*c*d - 2*a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*(2*a*b^2*c^2 + (3*b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a^2*b^3*x^3 + a^3*b^2*x)]","A",0
756,1,1266,0,3.824600," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(b^{2} d x^{2} + 2 \, b^{2} c - a b d\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{b}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{b}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 2 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} x^{4} + a^{4} b x^{2}\right)}}\right]"," ",0,"[-1/8*(((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*((4*b^3*c^2 - 5*a*b^2*c*d)*x^4 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*x^4 + a^4*b*x^2), -1/8*(4*((4*b^3*c^2 - 5*a*b^2*c*d)*x^4 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(b^2*d*x^2 + 2*b^2*c - a*b*d)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/b))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*x^4 + a^4*b*x^2), -1/4*(((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + ((4*b^3*c^2 - 5*a*b^2*c*d)*x^4 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*x^4 + a^4*b*x^2), -1/4*(((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/b)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)) + 2*((4*b^3*c^2 - 5*a*b^2*c*d)*x^4 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*x^4 + a^4*b*x^2)]","A",0
757,1,483,0,1.174524," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{5} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left(a^{2} c x - {\left(a b c - 2 \, a^{2} d\right)} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(15 \, b^{2} c^{2} - 20 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} - 2 \, a^{2} c^{2} + 2 \, {\left(5 \, a b c^{2} - 7 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}, \frac{15 \, {\left({\left(b^{2} c^{2} - a b c d\right)} x^{5} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + {\left(b c^{2} - a c d\right)} x\right)}}\right) + 2 \, {\left({\left(15 \, b^{2} c^{2} - 20 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} - 2 \, a^{2} c^{2} + 2 \, {\left(5 \, a b c^{2} - 7 \, a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}}\right]"," ",0,"[-1/24*(15*((b^2*c^2 - a*b*c*d)*x^5 + (a*b*c^2 - a^2*c*d)*x^3)*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*(a^2*c*x - (a*b*c - 2*a^2*d)*x^3)*sqrt(d*x^2 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((15*b^2*c^2 - 20*a*b*c*d + 3*a^2*d^2)*x^4 - 2*a^2*c^2 + 2*(5*a*b*c^2 - 7*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^5 + a^4*x^3), 1/12*(15*((b^2*c^2 - a*b*c*d)*x^5 + (a*b*c^2 - a^2*c*d)*x^3)*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^3 + (b*c^2 - a*c*d)*x)) + 2*((15*b^2*c^2 - 20*a*b*c*d + 3*a^2*d^2)*x^4 - 2*a^2*c^2 + 2*(5*a*b*c^2 - 7*a^2*c*d)*x^2)*sqrt(d*x^2 + c))/(a^3*b*x^5 + a^4*x^3)]","A",0
758,1,1053,0,1.650787," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{2} + c} a b d x + 4 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + {\left(3 \, a b c d - 2 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}, \frac{4 \, \sqrt{d x^{2} + c} a b d x - 8 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, a b c d - 2 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}, \frac{2 \, \sqrt{d x^{2} + c} a b d x + {\left(3 \, a b c d - 2 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + 2 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right)}{4 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}, \frac{2 \, \sqrt{d x^{2} + c} a b d x - 4 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(3 \, a b c d - 2 \, a^{2} d^{2} + {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right)}{4 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*sqrt(d*x^2 + c)*a*b*d*x + 4*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + (3*a*b*c*d - 2*a^2*d^2 + (3*b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2), 1/8*(4*sqrt(d*x^2 + c)*a*b*d*x - 8*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (3*a*b*c*d - 2*a^2*d^2 + (3*b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2), 1/4*(2*sqrt(d*x^2 + c)*a*b*d*x + (3*a*b*c*d - 2*a^2*d^2 + (3*b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + 2*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2), 1/4*(2*sqrt(d*x^2 + c)*a*b*d*x - 4*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (3*a*b*c*d - 2*a^2*d^2 + (3*b^2*c*d - 2*a*b*d^2)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2)]","A",0
759,1,450,0,0.915406," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2}\right)}}, -\frac{{\left(2 \, a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*((2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2), -1/4*((2*a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) - 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2)]","B",0
760,1,418,0,1.016630," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c} x - {\left(b c x^{2} + a c\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}, -\frac{2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x^{2} + c} x - {\left(b c x^{2} + a c\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(4*(a*b*c - a^2*d)*sqrt(d*x^2 + c)*x - (b*c*x^2 + a*c)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2), -1/4*(2*(a*b*c - a^2*d)*sqrt(d*x^2 + c)*x - (b*c*x^2 + a*c)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)]","B",0
761,1,404,0,0.847287," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b d x^{2} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}, \frac{{\left(b d x^{2} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(b^{2} c - a b d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*((b*d*x^2 + a*d)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2), 1/4*((b*d*x^2 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) - 2*(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2)]","B",0
762,1,459,0,0.946216," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x - {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{2}\right)}}, \frac{2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{2} + c} x + \sqrt{a b c - a^{2} d} {\left(a b c - 2 \, a^{2} d + {\left(b^{2} c - 2 \, a b d\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right)}{4 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x - (a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^2), 1/4*(2*(a*b^2*c - a^2*b*d)*sqrt(d*x^2 + c)*x + sqrt(a*b*c - a^2*d)*(a*b*c - 2*a^2*d + (b^2*c - 2*a*b*d)*x^2)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^2)]","B",0
763,1,1037,0,1.864702," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{2} + c} a b c + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{8 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{2}\right)}}, \frac{4 \, \sqrt{d x^{2} + c} a b c + 8 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{8 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{2}\right)}}, \frac{2 \, \sqrt{d x^{2} + c} a b c - {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right)}{4 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{2}\right)}}, \frac{2 \, \sqrt{d x^{2} + c} a b c - {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 4 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right)}{4 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(4*sqrt(d*x^2 + c)*a*b*c + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^2), 1/8*(4*sqrt(d*x^2 + c)*a*b*c + 8*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^2), 1/4*(2*sqrt(d*x^2 + c)*a*b*c - (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^2), 1/4*(2*sqrt(d*x^2 + c)*a*b*c - (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 4*(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^2)]","A",0
764,1,600,0,1.110569," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2} + {\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{3} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2} + {\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{3} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x\right)}}\right]"," ",0,"[-1/8*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2 + (3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^3 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x), -1/4*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^3 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2 + (3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^3 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x)]","B",0
765,1,1407,0,2.768823," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{4} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{4} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{4} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{4} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{2}\right)}}, \frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{4} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{4} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{2}\right)}}, \frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{4} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{4} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{4} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^4 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^4 + (a^4*b*c^3 - a^5*c^2*d)*x^2), -1/8*(4*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^4 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^4 + (a^4*b*c^3 - a^5*c^2*d)*x^2), 1/4*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^4 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^4 + (a^4*b*c^3 - a^5*c^2*d)*x^2), 1/4*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^4 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^4 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^2)*sqrt(d*x^2 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^4 + (a^4*b*c^3 - a^5*c^2*d)*x^2)]","A",0
766,1,758,0,1.637662," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a^{3} b^{2} c^{3} - 4 \, a^{4} b c^{2} d + 2 \, a^{5} c d^{2} - {\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{5} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{5} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b^{2} c^{3} - 4 \, a^{4} b c^{2} d + 2 \, a^{5} c d^{2} - {\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{5} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/24*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a^3*b^2*c^3 - 4*a^4*b*c^2*d + 2*a^5*c*d^2 - (15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^4 - 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2)*sqrt(d*x^2 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^5 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^3), 1/12*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^5 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(2*a^3*b^2*c^3 - 4*a^4*b*c^2*d + 2*a^5*c*d^2 - (15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^4 - 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^2)*sqrt(d*x^2 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^5 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^3)]","A",0
767,1,552,0,1.571824," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c d x^{4} + a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left({\left(2 \, b c + a d\right)} x^{3} + 3 \, a c x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left(b c d x^{4} + a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + 2 \, {\left({\left(2 \, b c + a d\right)} x^{3} + 3 \, a c x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*(b*c*d*x^4 + a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*((2*b*c + a*d)*x^3 + 3*a*c*x)*sqrt(d*x^2 + c))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2), 1/4*(3*(b*c*d*x^4 + a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + 2*((2*b*c + a*d)*x^3 + 3*a*c*x)*sqrt(d*x^2 + c))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)]","B",0
768,1,732,0,1.179002," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c d + a b d^{2}\right)} x^{4} + 2 \, a b c^{2} + a^{2} c d + {\left(2 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{b^{2} c - a b d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, a b^{2} c^{2} - 3 \, a^{2} b c d + {\left(2 \, b^{3} c^{2} - a b^{2} c d - a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} c^{4} - 3 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} - a^{4} b c d^{3} + {\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{4} + {\left(b^{5} c^{4} - 2 \, a b^{4} c^{3} d + 2 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{2}\right)}}, -\frac{{\left({\left(2 \, b^{2} c d + a b d^{2}\right)} x^{4} + 2 \, a b c^{2} + a^{2} c d + {\left(2 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(-\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{-b^{2} c + a b d} \sqrt{d x^{2} + c}}{2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(3 \, a b^{2} c^{2} - 3 \, a^{2} b c d + {\left(2 \, b^{3} c^{2} - a b^{2} c d - a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} c^{4} - 3 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} - a^{4} b c d^{3} + {\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{4} + {\left(b^{5} c^{4} - 2 \, a b^{4} c^{3} d + 2 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(((2*b^2*c*d + a*b*d^2)*x^4 + 2*a*b*c^2 + a^2*c*d + (2*b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^2)*sqrt(b^2*c - a*b*d)*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(b*d*x^2 + 2*b*c - a*d)*sqrt(b^2*c - a*b*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*a*b^2*c^2 - 3*a^2*b*c*d + (2*b^3*c^2 - a*b^2*c*d - a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^4*c^4 - 3*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 - a^4*b*c*d^3 + (b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^4 + (b^5*c^4 - 2*a*b^4*c^3*d + 2*a^3*b^2*c*d^3 - a^4*b*d^4)*x^2), -1/4*(((2*b^2*c*d + a*b*d^2)*x^4 + 2*a*b*c^2 + a^2*c*d + (2*b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^2)*sqrt(-b^2*c + a*b*d)*arctan(-1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(-b^2*c + a*b*d)*sqrt(d*x^2 + c)/(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2)) - 2*(3*a*b^2*c^2 - 3*a^2*b*c*d + (2*b^3*c^2 - a*b^2*c*d - a^2*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^4*c^4 - 3*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 - a^4*b*c*d^3 + (b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^4 + (b^5*c^4 - 2*a*b^4*c^3*d + 2*a^3*b^2*c*d^3 - a^4*b*d^4)*x^2)]","B",0
769,1,744,0,1.725950," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b^{2} c d + 2 \, a b d^{2}\right)} x^{4} + a b c^{2} + 2 \, a^{2} c d + {\left(b^{2} c^{2} + 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x^{3} + {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 3 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{4} + {\left(a b^{4} c^{4} - 2 \, a^{2} b^{3} c^{3} d + 2 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)}}, \frac{{\left({\left(b^{2} c d + 2 \, a b d^{2}\right)} x^{4} + a b c^{2} + 2 \, a^{2} c d + {\left(b^{2} c^{2} + 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(3 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x^{3} + {\left(a b^{2} c^{2} + a^{2} b c d - 2 \, a^{3} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3} + {\left(a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 3 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{4} + {\left(a b^{4} c^{4} - 2 \, a^{2} b^{3} c^{3} d + 2 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(((b^2*c*d + 2*a*b*d^2)*x^4 + a*b*c^2 + 2*a^2*c*d + (b^2*c^2 + 3*a*b*c*d + 2*a^2*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*(a*b^2*c*d - a^2*b*d^2)*x^3 + (a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(d*x^2 + c))/(a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3 + (a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 3*a^3*b^2*c*d^3 - a^4*b*d^4)*x^4 + (a*b^4*c^4 - 2*a^2*b^3*c^3*d + 2*a^4*b*c*d^3 - a^5*d^4)*x^2), 1/4*(((b^2*c*d + 2*a*b*d^2)*x^4 + a*b*c^2 + 2*a^2*c*d + (b^2*c^2 + 3*a*b*c*d + 2*a^2*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(3*(a*b^2*c*d - a^2*b*d^2)*x^3 + (a*b^2*c^2 + a^2*b*c*d - 2*a^3*d^2)*x)*sqrt(d*x^2 + c))/(a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3 + (a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 3*a^3*b^2*c*d^3 - a^4*b*d^4)*x^4 + (a*b^4*c^4 - 2*a^2*b^3*c^3*d + 2*a^4*b*c*d^3 - a^5*d^4)*x^2)]","B",0
770,1,537,0,0.997194," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d^{2} x^{4} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(3 \, b d x^{2} + b c + 2 \, a d\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b d^{2} x^{4} + a c d + {\left(b c d + a d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(3 \, b d x^{2} + b c + 2 \, a d\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*(b*d^2*x^4 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(3*b*d*x^2 + b*c + 2*a*d)*sqrt(d*x^2 + c))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2), -1/4*(3*(b*d^2*x^4 + a*c*d + (b*c*d + a*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(3*b*d*x^2 + b*c + 2*a*d)*sqrt(d*x^2 + c))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)]","B",0
771,1,854,0,1.747925," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} c^{3} - 4 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 4 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left({\left(a b^{3} c^{2} d + a^{2} b^{2} c d^{2} - 2 \, a^{3} b d^{3}\right)} x^{3} + {\left(a b^{3} c^{3} - a^{2} b^{2} c^{2} d + 2 \, a^{3} b c d^{2} - 2 \, a^{4} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3} + {\left(a^{2} b^{4} c^{4} d - 3 \, a^{3} b^{3} c^{3} d^{2} + 3 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4}\right)} x^{4} + {\left(a^{2} b^{4} c^{5} - 2 \, a^{3} b^{3} c^{4} d + 2 \, a^{5} b c^{2} d^{3} - a^{6} c d^{4}\right)} x^{2}\right)}}, \frac{{\left(a b^{2} c^{3} - 4 \, a^{2} b c^{2} d + {\left(b^{3} c^{2} d - 4 \, a b^{2} c d^{2}\right)} x^{4} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(a b^{3} c^{2} d + a^{2} b^{2} c d^{2} - 2 \, a^{3} b d^{3}\right)} x^{3} + {\left(a b^{3} c^{3} - a^{2} b^{2} c^{2} d + 2 \, a^{3} b c d^{2} - 2 \, a^{4} d^{3}\right)} x\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{3} c^{5} - 3 \, a^{4} b^{2} c^{4} d + 3 \, a^{5} b c^{3} d^{2} - a^{6} c^{2} d^{3} + {\left(a^{2} b^{4} c^{4} d - 3 \, a^{3} b^{3} c^{3} d^{2} + 3 \, a^{4} b^{2} c^{2} d^{3} - a^{5} b c d^{4}\right)} x^{4} + {\left(a^{2} b^{4} c^{5} - 2 \, a^{3} b^{3} c^{4} d + 2 \, a^{5} b c^{2} d^{3} - a^{6} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*((a*b^2*c^3 - 4*a^2*b*c^2*d + (b^3*c^2*d - 4*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 3*a*b^2*c^2*d - 4*a^2*b*c*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*((a*b^3*c^2*d + a^2*b^2*c*d^2 - 2*a^3*b*d^3)*x^3 + (a*b^3*c^3 - a^2*b^2*c^2*d + 2*a^3*b*c*d^2 - 2*a^4*d^3)*x)*sqrt(d*x^2 + c))/(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3 + (a^2*b^4*c^4*d - 3*a^3*b^3*c^3*d^2 + 3*a^4*b^2*c^2*d^3 - a^5*b*c*d^4)*x^4 + (a^2*b^4*c^5 - 2*a^3*b^3*c^4*d + 2*a^5*b*c^2*d^3 - a^6*c*d^4)*x^2), 1/4*((a*b^2*c^3 - 4*a^2*b*c^2*d + (b^3*c^2*d - 4*a*b^2*c*d^2)*x^4 + (b^3*c^3 - 3*a*b^2*c^2*d - 4*a^2*b*c*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((a*b^3*c^2*d + a^2*b^2*c*d^2 - 2*a^3*b*d^3)*x^3 + (a*b^3*c^3 - a^2*b^2*c^2*d + 2*a^3*b*c*d^2 - 2*a^4*d^3)*x)*sqrt(d*x^2 + c))/(a^3*b^3*c^5 - 3*a^4*b^2*c^4*d + 3*a^5*b*c^3*d^2 - a^6*c^2*d^3 + (a^2*b^4*c^4*d - 3*a^3*b^3*c^3*d^2 + 3*a^4*b^2*c^2*d^3 - a^5*b*c*d^4)*x^4 + (a^2*b^4*c^5 - 2*a^3*b^3*c^4*d + 2*a^5*b*c^2*d^3 - a^6*c*d^4)*x^2)]","B",0
772,1,1992,0,5.882099," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{4} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{4} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{2}\right)}}, \frac{8 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{4} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{4} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{2}\right)}}, -\frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{4} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{4} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{2}\right)}}, -\frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{4} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 4 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{4} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^4 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^4 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^2), 1/8*(8*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^4 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^4 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^2), -1/4*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^4 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^4 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^2), -1/4*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^4 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 4*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^2)*sqrt(d*x^2 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^4 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^2)]","B",0
773,1,1018,0,1.826711," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(b^{4} c^{4} - a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, a^{2} b^{3} c^{4} - 6 \, a^{3} b^{2} c^{3} d + 6 \, a^{4} b c^{2} d^{2} - 2 \, a^{5} c d^{3} + {\left(3 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 8 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4}\right)} x^{4} + {\left(3 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 6 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{4} c^{5} d - 3 \, a^{4} b^{3} c^{4} d^{2} + 3 \, a^{5} b^{2} c^{3} d^{3} - a^{6} b c^{2} d^{4}\right)} x^{5} + {\left(a^{3} b^{4} c^{6} - 2 \, a^{4} b^{3} c^{5} d + 2 \, a^{6} b c^{3} d^{3} - a^{7} c^{2} d^{4}\right)} x^{3} + {\left(a^{4} b^{3} c^{6} - 3 \, a^{5} b^{2} c^{5} d + 3 \, a^{6} b c^{4} d^{2} - a^{7} c^{3} d^{3}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2}\right)} x^{5} + {\left(b^{4} c^{4} - a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b^{3} c^{4} - 2 \, a^{2} b^{2} c^{3} d\right)} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} b^{3} c^{4} - 6 \, a^{3} b^{2} c^{3} d + 6 \, a^{4} b c^{2} d^{2} - 2 \, a^{5} c d^{3} + {\left(3 \, a b^{4} c^{3} d - 7 \, a^{2} b^{3} c^{2} d^{2} + 8 \, a^{3} b^{2} c d^{3} - 4 \, a^{4} b d^{4}\right)} x^{4} + {\left(3 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 6 \, a^{4} b c d^{3} - 4 \, a^{5} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{4} c^{5} d - 3 \, a^{4} b^{3} c^{4} d^{2} + 3 \, a^{5} b^{2} c^{3} d^{3} - a^{6} b c^{2} d^{4}\right)} x^{5} + {\left(a^{3} b^{4} c^{6} - 2 \, a^{4} b^{3} c^{5} d + 2 \, a^{6} b c^{3} d^{3} - a^{7} c^{2} d^{4}\right)} x^{3} + {\left(a^{4} b^{3} c^{6} - 3 \, a^{5} b^{2} c^{5} d + 3 \, a^{6} b c^{4} d^{2} - a^{7} c^{3} d^{3}\right)} x\right)}}\right]"," ",0,"[1/8*(3*((b^4*c^3*d - 2*a*b^3*c^2*d^2)*x^5 + (b^4*c^4 - a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2)*x^3 + (a*b^3*c^4 - 2*a^2*b^2*c^3*d)*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*a^2*b^3*c^4 - 6*a^3*b^2*c^3*d + 6*a^4*b*c^2*d^2 - 2*a^5*c*d^3 + (3*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 8*a^3*b^2*c*d^3 - 4*a^4*b*d^4)*x^4 + (3*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 6*a^4*b*c*d^3 - 4*a^5*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^5*d - 3*a^4*b^3*c^4*d^2 + 3*a^5*b^2*c^3*d^3 - a^6*b*c^2*d^4)*x^5 + (a^3*b^4*c^6 - 2*a^4*b^3*c^5*d + 2*a^6*b*c^3*d^3 - a^7*c^2*d^4)*x^3 + (a^4*b^3*c^6 - 3*a^5*b^2*c^5*d + 3*a^6*b*c^4*d^2 - a^7*c^3*d^3)*x), -1/4*(3*((b^4*c^3*d - 2*a*b^3*c^2*d^2)*x^5 + (b^4*c^4 - a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2)*x^3 + (a*b^3*c^4 - 2*a^2*b^2*c^3*d)*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(2*a^2*b^3*c^4 - 6*a^3*b^2*c^3*d + 6*a^4*b*c^2*d^2 - 2*a^5*c*d^3 + (3*a*b^4*c^3*d - 7*a^2*b^3*c^2*d^2 + 8*a^3*b^2*c*d^3 - 4*a^4*b*d^4)*x^4 + (3*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 6*a^4*b*c*d^3 - 4*a^5*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^5*d - 3*a^4*b^3*c^4*d^2 + 3*a^5*b^2*c^3*d^3 - a^6*b*c^2*d^4)*x^5 + (a^3*b^4*c^6 - 2*a^4*b^3*c^5*d + 2*a^6*b*c^3*d^3 - a^7*c^2*d^4)*x^3 + (a^4*b^3*c^6 - 3*a^5*b^2*c^5*d + 3*a^6*b*c^4*d^2 - a^7*c^3*d^3)*x)]","B",0
774,1,2554,0,11.546128," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{6} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{4} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 2 \, {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{6} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{4} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{6} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{4} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2}\right)}}, -\frac{4 \, {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{6} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{4} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{6} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{4} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{8 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{6} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{4} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2}\right)}}, \frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{6} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{4} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{6} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{4} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{6} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{4} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2}\right)}}, \frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{6} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{4} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 2 \, {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{6} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{4} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{4} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{4 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{6} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{4} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^6 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^4 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 2*((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^6 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^4 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^4 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^6 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^4 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2), -1/8*(4*((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^6 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^4 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + ((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^6 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^4 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^4 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^6 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^4 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2), 1/4*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^6 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^4 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + ((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^6 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^4 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^4 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^6 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^4 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2), 1/4*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^6 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^4 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 2*((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^6 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^4 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^4 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^2)*sqrt(d*x^2 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^6 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^4 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^2)]","B",0
775,1,1252,0,3.019975," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, b^{5} c^{4} d - 8 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 8 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 8 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(2 \, a^{3} b^{3} c^{5} - 6 \, a^{4} b^{2} c^{4} d + 6 \, a^{5} b c^{3} d^{2} - 2 \, a^{6} c^{2} d^{3} - {\left(15 \, a b^{5} c^{4} d - 29 \, a^{2} b^{4} c^{3} d^{2} + 6 \, a^{3} b^{3} c^{2} d^{3} + 24 \, a^{4} b^{2} c d^{4} - 16 \, a^{5} b d^{5}\right)} x^{6} - {\left(15 \, a b^{5} c^{5} - 19 \, a^{2} b^{4} c^{4} d - 14 \, a^{3} b^{3} c^{3} d^{2} + 18 \, a^{4} b^{2} c^{2} d^{3} + 16 \, a^{5} b c d^{4} - 16 \, a^{6} d^{5}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{4} b^{4} c^{6} d - 3 \, a^{5} b^{3} c^{5} d^{2} + 3 \, a^{6} b^{2} c^{4} d^{3} - a^{7} b c^{3} d^{4}\right)} x^{7} + {\left(a^{4} b^{4} c^{7} - 2 \, a^{5} b^{3} c^{6} d + 2 \, a^{7} b c^{4} d^{3} - a^{8} c^{3} d^{4}\right)} x^{5} + {\left(a^{5} b^{3} c^{7} - 3 \, a^{6} b^{2} c^{6} d + 3 \, a^{7} b c^{5} d^{2} - a^{8} c^{4} d^{3}\right)} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b^{5} c^{4} d - 8 \, a b^{4} c^{3} d^{2}\right)} x^{7} + {\left(5 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 8 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{5} - 8 \, a^{2} b^{3} c^{4} d\right)} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b^{3} c^{5} - 6 \, a^{4} b^{2} c^{4} d + 6 \, a^{5} b c^{3} d^{2} - 2 \, a^{6} c^{2} d^{3} - {\left(15 \, a b^{5} c^{4} d - 29 \, a^{2} b^{4} c^{3} d^{2} + 6 \, a^{3} b^{3} c^{2} d^{3} + 24 \, a^{4} b^{2} c d^{4} - 16 \, a^{5} b d^{5}\right)} x^{6} - {\left(15 \, a b^{5} c^{5} - 19 \, a^{2} b^{4} c^{4} d - 14 \, a^{3} b^{3} c^{3} d^{2} + 18 \, a^{4} b^{2} c^{2} d^{3} + 16 \, a^{5} b c d^{4} - 16 \, a^{6} d^{5}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{4} c^{5} - 11 \, a^{3} b^{3} c^{4} d + 3 \, a^{4} b^{2} c^{3} d^{2} + 7 \, a^{5} b c^{2} d^{3} - 4 \, a^{6} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{4} b^{4} c^{6} d - 3 \, a^{5} b^{3} c^{5} d^{2} + 3 \, a^{6} b^{2} c^{4} d^{3} - a^{7} b c^{3} d^{4}\right)} x^{7} + {\left(a^{4} b^{4} c^{7} - 2 \, a^{5} b^{3} c^{6} d + 2 \, a^{7} b c^{4} d^{3} - a^{8} c^{3} d^{4}\right)} x^{5} + {\left(a^{5} b^{3} c^{7} - 3 \, a^{6} b^{2} c^{6} d + 3 \, a^{7} b c^{5} d^{2} - a^{8} c^{4} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[1/24*(3*((5*b^5*c^4*d - 8*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 3*a*b^4*c^4*d - 8*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 8*a^2*b^3*c^4*d)*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(2*a^3*b^3*c^5 - 6*a^4*b^2*c^4*d + 6*a^5*b*c^3*d^2 - 2*a^6*c^2*d^3 - (15*a*b^5*c^4*d - 29*a^2*b^4*c^3*d^2 + 6*a^3*b^3*c^2*d^3 + 24*a^4*b^2*c*d^4 - 16*a^5*b*d^5)*x^6 - (15*a*b^5*c^5 - 19*a^2*b^4*c^4*d - 14*a^3*b^3*c^3*d^2 + 18*a^4*b^2*c^2*d^3 + 16*a^5*b*c*d^4 - 16*a^6*d^5)*x^4 - 2*(5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^2)*sqrt(d*x^2 + c))/((a^4*b^4*c^6*d - 3*a^5*b^3*c^5*d^2 + 3*a^6*b^2*c^4*d^3 - a^7*b*c^3*d^4)*x^7 + (a^4*b^4*c^7 - 2*a^5*b^3*c^6*d + 2*a^7*b*c^4*d^3 - a^8*c^3*d^4)*x^5 + (a^5*b^3*c^7 - 3*a^6*b^2*c^6*d + 3*a^7*b*c^5*d^2 - a^8*c^4*d^3)*x^3), 1/12*(3*((5*b^5*c^4*d - 8*a*b^4*c^3*d^2)*x^7 + (5*b^5*c^5 - 3*a*b^4*c^4*d - 8*a^2*b^3*c^3*d^2)*x^5 + (5*a*b^4*c^5 - 8*a^2*b^3*c^4*d)*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(2*a^3*b^3*c^5 - 6*a^4*b^2*c^4*d + 6*a^5*b*c^3*d^2 - 2*a^6*c^2*d^3 - (15*a*b^5*c^4*d - 29*a^2*b^4*c^3*d^2 + 6*a^3*b^3*c^2*d^3 + 24*a^4*b^2*c*d^4 - 16*a^5*b*d^5)*x^6 - (15*a*b^5*c^5 - 19*a^2*b^4*c^4*d - 14*a^3*b^3*c^3*d^2 + 18*a^4*b^2*c^2*d^3 + 16*a^5*b*c*d^4 - 16*a^6*d^5)*x^4 - 2*(5*a^2*b^4*c^5 - 11*a^3*b^3*c^4*d + 3*a^4*b^2*c^3*d^2 + 7*a^5*b*c^2*d^3 - 4*a^6*c*d^4)*x^2)*sqrt(d*x^2 + c))/((a^4*b^4*c^6*d - 3*a^5*b^3*c^5*d^2 + 3*a^6*b^2*c^4*d^3 - a^7*b*c^3*d^4)*x^7 + (a^4*b^4*c^7 - 2*a^5*b^3*c^6*d + 2*a^7*b*c^4*d^3 - a^8*c^3*d^4)*x^5 + (a^5*b^3*c^7 - 3*a^6*b^2*c^6*d + 3*a^7*b*c^5*d^2 - a^8*c^4*d^3)*x^3)]","B",0
776,1,1008,0,2.590440," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{6} + 3 \, a b c^{3} + 2 \, a^{2} c^{2} d + {\left(6 \, b^{2} c^{2} d + 7 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x^{4} + {\left(3 \, b^{2} c^{3} + 8 \, a b c^{2} d + 4 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(4 \, b^{2} c d + 11 \, a b d^{2}\right)} x^{5} + 2 \, {\left(3 \, b^{2} c^{2} + 8 \, a b c d + 4 \, a^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b c^{2} + 2 \, a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{6} + 3 \, a b c^{3} + 2 \, a^{2} c^{2} d + {\left(6 \, b^{2} c^{2} d + 7 \, a b c d^{2} + 2 \, a^{2} d^{3}\right)} x^{4} + {\left(3 \, b^{2} c^{3} + 8 \, a b c^{2} d + 4 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{3} + a c x\right)}}\right) + 2 \, {\left({\left(4 \, b^{2} c d + 11 \, a b d^{2}\right)} x^{5} + 2 \, {\left(3 \, b^{2} c^{2} + 8 \, a b c d + 4 \, a^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b c^{2} + 2 \, a^{2} c d\right)} x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/24*(3*((3*b^2*c*d^2 + 2*a*b*d^3)*x^6 + 3*a*b*c^3 + 2*a^2*c^2*d + (6*b^2*c^2*d + 7*a*b*c*d^2 + 2*a^2*d^3)*x^4 + (3*b^2*c^3 + 8*a*b*c^2*d + 4*a^2*c*d^2)*x^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^3 - (a*b*c^2 - a^2*c*d)*x)*sqrt(d*x^2 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((4*b^2*c*d + 11*a*b*d^2)*x^5 + 2*(3*b^2*c^2 + 8*a*b*c*d + 4*a^2*d^2)*x^3 + 3*(3*a*b*c^2 + 2*a^2*c*d)*x)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2), 1/12*(3*((3*b^2*c*d^2 + 2*a*b*d^3)*x^6 + 3*a*b*c^3 + 2*a^2*c^2*d + (6*b^2*c^2*d + 7*a*b*c*d^2 + 2*a^2*d^3)*x^4 + (3*b^2*c^3 + 8*a*b*c^2*d + 4*a^2*c*d^2)*x^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)*sqrt(a/(b*c - a*d))/(a*d*x^3 + a*c*x)) + 2*((4*b^2*c*d + 11*a*b*d^2)*x^5 + 2*(3*b^2*c^2 + 8*a*b*c*d + 4*a^2*d^2)*x^3 + 3*(3*a*b*c^2 + 2*a^2*c*d)*x)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)]","B",0
777,1,993,0,1.537018," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, b^{2} c d^{2} + 3 \, a b d^{3}\right)} x^{6} + 2 \, a b c^{3} + 3 \, a^{2} c^{2} d + {\left(4 \, b^{2} c^{2} d + 8 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + 7 \, a b c^{2} d + 6 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left(3 \, {\left(2 \, b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + 11 \, a b c^{2} + 4 \, a^{2} c d + 2 \, {\left(4 \, b^{2} c^{2} + 8 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(2 \, b^{2} c d^{2} + 3 \, a b d^{3}\right)} x^{6} + 2 \, a b c^{3} + 3 \, a^{2} c^{2} d + {\left(4 \, b^{2} c^{2} d + 8 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{4} + {\left(2 \, b^{2} c^{3} + 7 \, a b c^{2} d + 6 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(3 \, {\left(2 \, b^{2} c d + 3 \, a b d^{2}\right)} x^{4} + 11 \, a b c^{2} + 4 \, a^{2} c d + 2 \, {\left(4 \, b^{2} c^{2} + 8 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/24*(3*((2*b^2*c*d^2 + 3*a*b*d^3)*x^6 + 2*a*b*c^3 + 3*a^2*c^2*d + (4*b^2*c^2*d + 8*a*b*c*d^2 + 3*a^2*d^3)*x^4 + (2*b^2*c^3 + 7*a*b*c^2*d + 6*a^2*c*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*(3*(2*b^2*c*d + 3*a*b*d^2)*x^4 + 11*a*b*c^2 + 4*a^2*c*d + 2*(4*b^2*c^2 + 8*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2), 1/12*(3*((2*b^2*c*d^2 + 3*a*b*d^3)*x^6 + 2*a*b*c^3 + 3*a^2*c^2*d + (4*b^2*c^2*d + 8*a*b*c*d^2 + 3*a^2*d^3)*x^4 + (2*b^2*c^3 + 7*a*b*c^2*d + 6*a^2*c*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(3*(2*b^2*c*d + 3*a*b*d^2)*x^4 + 11*a*b*c^2 + 4*a^2*c*d + 2*(4*b^2*c^2 + 8*a*b*c*d + 3*a^2*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)]","B",0
778,1,1292,0,2.928021," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 9 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d + 8 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(13 \, a b^{3} c^{2} d^{2} - 11 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} x^{5} + 2 \, {\left(9 \, a b^{3} c^{3} d - 4 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{2} b^{4} c^{7} - 4 \, a^{3} b^{3} c^{6} d + 6 \, a^{4} b^{2} c^{5} d^{2} - 4 \, a^{5} b c^{4} d^{3} + a^{6} c^{3} d^{4} + {\left(a b^{5} c^{5} d^{2} - 4 \, a^{2} b^{4} c^{4} d^{3} + 6 \, a^{3} b^{3} c^{3} d^{4} - 4 \, a^{4} b^{2} c^{2} d^{5} + a^{5} b c d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{6} d - 7 \, a^{2} b^{4} c^{5} d^{2} + 8 \, a^{3} b^{3} c^{4} d^{3} - 2 \, a^{4} b^{2} c^{3} d^{4} - 2 \, a^{5} b c^{2} d^{5} + a^{6} c d^{6}\right)} x^{4} + {\left(a b^{5} c^{7} - 2 \, a^{2} b^{4} c^{6} d - 2 \, a^{3} b^{3} c^{5} d^{2} + 8 \, a^{4} b^{2} c^{4} d^{3} - 7 \, a^{5} b c^{3} d^{4} + 2 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + {\left(b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3}\right)} x^{6} + {\left(2 \, b^{3} c^{3} d + 9 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3}\right)} x^{4} + {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d + 8 \, a^{2} b c^{2} d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left({\left(13 \, a b^{3} c^{2} d^{2} - 11 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} x^{5} + 2 \, {\left(9 \, a b^{3} c^{3} d - 4 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2}\right)} x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{2} b^{4} c^{7} - 4 \, a^{3} b^{3} c^{6} d + 6 \, a^{4} b^{2} c^{5} d^{2} - 4 \, a^{5} b c^{4} d^{3} + a^{6} c^{3} d^{4} + {\left(a b^{5} c^{5} d^{2} - 4 \, a^{2} b^{4} c^{4} d^{3} + 6 \, a^{3} b^{3} c^{3} d^{4} - 4 \, a^{4} b^{2} c^{2} d^{5} + a^{5} b c d^{6}\right)} x^{6} + {\left(2 \, a b^{5} c^{6} d - 7 \, a^{2} b^{4} c^{5} d^{2} + 8 \, a^{3} b^{3} c^{4} d^{3} - 2 \, a^{4} b^{2} c^{3} d^{4} - 2 \, a^{5} b c^{2} d^{5} + a^{6} c d^{6}\right)} x^{4} + {\left(a b^{5} c^{7} - 2 \, a^{2} b^{4} c^{6} d - 2 \, a^{3} b^{3} c^{5} d^{2} + 8 \, a^{4} b^{2} c^{4} d^{3} - 7 \, a^{5} b c^{3} d^{4} + 2 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/24*(3*(a*b^2*c^4 + 4*a^2*b*c^3*d + (b^3*c^2*d^2 + 4*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 9*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 6*a*b^2*c^3*d + 8*a^2*b*c^2*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((13*a*b^3*c^2*d^2 - 11*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*x^5 + 2*(9*a*b^3*c^3*d - 4*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*x^3 + 3*(a*b^3*c^4 + 3*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2)*x)*sqrt(d*x^2 + c))/(a^2*b^4*c^7 - 4*a^3*b^3*c^6*d + 6*a^4*b^2*c^5*d^2 - 4*a^5*b*c^4*d^3 + a^6*c^3*d^4 + (a*b^5*c^5*d^2 - 4*a^2*b^4*c^4*d^3 + 6*a^3*b^3*c^3*d^4 - 4*a^4*b^2*c^2*d^5 + a^5*b*c*d^6)*x^6 + (2*a*b^5*c^6*d - 7*a^2*b^4*c^5*d^2 + 8*a^3*b^3*c^4*d^3 - 2*a^4*b^2*c^3*d^4 - 2*a^5*b*c^2*d^5 + a^6*c*d^6)*x^4 + (a*b^5*c^7 - 2*a^2*b^4*c^6*d - 2*a^3*b^3*c^5*d^2 + 8*a^4*b^2*c^4*d^3 - 7*a^5*b*c^3*d^4 + 2*a^6*c^2*d^5)*x^2), 1/12*(3*(a*b^2*c^4 + 4*a^2*b*c^3*d + (b^3*c^2*d^2 + 4*a*b^2*c*d^3)*x^6 + (2*b^3*c^3*d + 9*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3)*x^4 + (b^3*c^4 + 6*a*b^2*c^3*d + 8*a^2*b*c^2*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*((13*a*b^3*c^2*d^2 - 11*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*x^5 + 2*(9*a*b^3*c^3*d - 4*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*x^3 + 3*(a*b^3*c^4 + 3*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2)*x)*sqrt(d*x^2 + c))/(a^2*b^4*c^7 - 4*a^3*b^3*c^6*d + 6*a^4*b^2*c^5*d^2 - 4*a^5*b*c^4*d^3 + a^6*c^3*d^4 + (a*b^5*c^5*d^2 - 4*a^2*b^4*c^4*d^3 + 6*a^3*b^3*c^3*d^4 - 4*a^4*b^2*c^2*d^5 + a^5*b*c*d^6)*x^6 + (2*a*b^5*c^6*d - 7*a^2*b^4*c^5*d^2 + 8*a^3*b^3*c^4*d^3 - 2*a^4*b^2*c^3*d^4 - 2*a^5*b*c^2*d^5 + a^6*c*d^6)*x^4 + (a*b^5*c^7 - 2*a^2*b^4*c^6*d - 2*a^3*b^3*c^5*d^2 + 8*a^4*b^2*c^4*d^3 - 7*a^5*b*c^3*d^4 + 2*a^6*c^2*d^5)*x^2)]","B",0
779,1,895,0,1.137980," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} d^{3} x^{6} + a b c^{2} d + {\left(2 \, b^{2} c d^{2} + a b d^{3}\right)} x^{4} + {\left(b^{2} c^{2} d + 2 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(15 \, b^{2} d^{2} x^{4} + 3 \, b^{2} c^{2} + 14 \, a b c d - 2 \, a^{2} d^{2} + 10 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}, -\frac{15 \, {\left(b^{2} d^{3} x^{6} + a b c^{2} d + {\left(2 \, b^{2} c d^{2} + a b d^{3}\right)} x^{4} + {\left(b^{2} c^{2} d + 2 \, a b c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 2 \, {\left(15 \, b^{2} d^{2} x^{4} + 3 \, b^{2} c^{2} + 14 \, a b c d - 2 \, a^{2} d^{2} + 10 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/24*(15*(b^2*d^3*x^6 + a*b*c^2*d + (2*b^2*c*d^2 + a*b*d^3)*x^4 + (b^2*c^2*d + 2*a*b*c*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(15*b^2*d^2*x^4 + 3*b^2*c^2 + 14*a*b*c*d - 2*a^2*d^2 + 10*(2*b^2*c*d + a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2), -1/12*(15*(b^2*d^3*x^6 + a*b*c^2*d + (2*b^2*c*d^2 + a*b*d^3)*x^4 + (b^2*c^2*d + 2*a*b*c*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 2*(15*b^2*d^2*x^4 + 3*b^2*c^2 + 14*a*b*c*d - 2*a^2*d^2 + 10*(2*b^2*c*d + a*b*d^2)*x^2)*sqrt(d*x^2 + c))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)]","B",0
780,1,1434,0,3.219064," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a b^{3} c^{5} - 6 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 6 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 11 \, a b^{3} c^{3} d^{2} - 6 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 4 \, a b^{3} c^{4} d - 12 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, {\left({\left(3 \, a b^{4} c^{3} d^{2} + 13 \, a^{2} b^{3} c^{2} d^{3} - 20 \, a^{3} b^{2} c d^{4} + 4 \, a^{4} b d^{5}\right)} x^{5} + 2 \, {\left(3 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} - 4 \, a^{3} b^{2} c^{2} d^{3} - 7 \, a^{4} b c d^{4} + 2 \, a^{5} d^{5}\right)} x^{3} + 3 \, {\left(a b^{4} c^{5} - a^{2} b^{3} c^{4} d + 6 \, a^{3} b^{2} c^{3} d^{2} - 8 \, a^{4} b c^{2} d^{3} + 2 \, a^{5} c d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{3} b^{4} c^{8} - 4 \, a^{4} b^{3} c^{7} d + 6 \, a^{5} b^{2} c^{6} d^{2} - 4 \, a^{6} b c^{5} d^{3} + a^{7} c^{4} d^{4} + {\left(a^{2} b^{5} c^{6} d^{2} - 4 \, a^{3} b^{4} c^{5} d^{3} + 6 \, a^{4} b^{3} c^{4} d^{4} - 4 \, a^{5} b^{2} c^{3} d^{5} + a^{6} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a^{2} b^{5} c^{7} d - 7 \, a^{3} b^{4} c^{6} d^{2} + 8 \, a^{4} b^{3} c^{5} d^{3} - 2 \, a^{5} b^{2} c^{4} d^{4} - 2 \, a^{6} b c^{3} d^{5} + a^{7} c^{2} d^{6}\right)} x^{4} + {\left(a^{2} b^{5} c^{8} - 2 \, a^{3} b^{4} c^{7} d - 2 \, a^{4} b^{3} c^{6} d^{2} + 8 \, a^{5} b^{2} c^{5} d^{3} - 7 \, a^{6} b c^{4} d^{4} + 2 \, a^{7} c^{3} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(a b^{3} c^{5} - 6 \, a^{2} b^{2} c^{4} d + {\left(b^{4} c^{3} d^{2} - 6 \, a b^{3} c^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 11 \, a b^{3} c^{3} d^{2} - 6 \, a^{2} b^{2} c^{2} d^{3}\right)} x^{4} + {\left(b^{4} c^{5} - 4 \, a b^{3} c^{4} d - 12 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left({\left(3 \, a b^{4} c^{3} d^{2} + 13 \, a^{2} b^{3} c^{2} d^{3} - 20 \, a^{3} b^{2} c d^{4} + 4 \, a^{4} b d^{5}\right)} x^{5} + 2 \, {\left(3 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} - 4 \, a^{3} b^{2} c^{2} d^{3} - 7 \, a^{4} b c d^{4} + 2 \, a^{5} d^{5}\right)} x^{3} + 3 \, {\left(a b^{4} c^{5} - a^{2} b^{3} c^{4} d + 6 \, a^{3} b^{2} c^{3} d^{2} - 8 \, a^{4} b c^{2} d^{3} + 2 \, a^{5} c d^{4}\right)} x\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b^{4} c^{8} - 4 \, a^{4} b^{3} c^{7} d + 6 \, a^{5} b^{2} c^{6} d^{2} - 4 \, a^{6} b c^{5} d^{3} + a^{7} c^{4} d^{4} + {\left(a^{2} b^{5} c^{6} d^{2} - 4 \, a^{3} b^{4} c^{5} d^{3} + 6 \, a^{4} b^{3} c^{4} d^{4} - 4 \, a^{5} b^{2} c^{3} d^{5} + a^{6} b c^{2} d^{6}\right)} x^{6} + {\left(2 \, a^{2} b^{5} c^{7} d - 7 \, a^{3} b^{4} c^{6} d^{2} + 8 \, a^{4} b^{3} c^{5} d^{3} - 2 \, a^{5} b^{2} c^{4} d^{4} - 2 \, a^{6} b c^{3} d^{5} + a^{7} c^{2} d^{6}\right)} x^{4} + {\left(a^{2} b^{5} c^{8} - 2 \, a^{3} b^{4} c^{7} d - 2 \, a^{4} b^{3} c^{6} d^{2} + 8 \, a^{5} b^{2} c^{5} d^{3} - 7 \, a^{6} b c^{4} d^{4} + 2 \, a^{7} c^{3} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/24*(3*(a*b^3*c^5 - 6*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 6*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 11*a*b^3*c^3*d^2 - 6*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 4*a*b^3*c^4*d - 12*a^2*b^2*c^3*d^2)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*((3*a*b^4*c^3*d^2 + 13*a^2*b^3*c^2*d^3 - 20*a^3*b^2*c*d^4 + 4*a^4*b*d^5)*x^5 + 2*(3*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 - 4*a^3*b^2*c^2*d^3 - 7*a^4*b*c*d^4 + 2*a^5*d^5)*x^3 + 3*(a*b^4*c^5 - a^2*b^3*c^4*d + 6*a^3*b^2*c^3*d^2 - 8*a^4*b*c^2*d^3 + 2*a^5*c*d^4)*x)*sqrt(d*x^2 + c))/(a^3*b^4*c^8 - 4*a^4*b^3*c^7*d + 6*a^5*b^2*c^6*d^2 - 4*a^6*b*c^5*d^3 + a^7*c^4*d^4 + (a^2*b^5*c^6*d^2 - 4*a^3*b^4*c^5*d^3 + 6*a^4*b^3*c^4*d^4 - 4*a^5*b^2*c^3*d^5 + a^6*b*c^2*d^6)*x^6 + (2*a^2*b^5*c^7*d - 7*a^3*b^4*c^6*d^2 + 8*a^4*b^3*c^5*d^3 - 2*a^5*b^2*c^4*d^4 - 2*a^6*b*c^3*d^5 + a^7*c^2*d^6)*x^4 + (a^2*b^5*c^8 - 2*a^3*b^4*c^7*d - 2*a^4*b^3*c^6*d^2 + 8*a^5*b^2*c^5*d^3 - 7*a^6*b*c^4*d^4 + 2*a^7*c^3*d^5)*x^2), 1/12*(3*(a*b^3*c^5 - 6*a^2*b^2*c^4*d + (b^4*c^3*d^2 - 6*a*b^3*c^2*d^3)*x^6 + (2*b^4*c^4*d - 11*a*b^3*c^3*d^2 - 6*a^2*b^2*c^2*d^3)*x^4 + (b^4*c^5 - 4*a*b^3*c^4*d - 12*a^2*b^2*c^3*d^2)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*((3*a*b^4*c^3*d^2 + 13*a^2*b^3*c^2*d^3 - 20*a^3*b^2*c*d^4 + 4*a^4*b*d^5)*x^5 + 2*(3*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 - 4*a^3*b^2*c^2*d^3 - 7*a^4*b*c*d^4 + 2*a^5*d^5)*x^3 + 3*(a*b^4*c^5 - a^2*b^3*c^4*d + 6*a^3*b^2*c^3*d^2 - 8*a^4*b*c^2*d^3 + 2*a^5*c*d^4)*x)*sqrt(d*x^2 + c))/(a^3*b^4*c^8 - 4*a^4*b^3*c^7*d + 6*a^5*b^2*c^6*d^2 - 4*a^6*b*c^5*d^3 + a^7*c^4*d^4 + (a^2*b^5*c^6*d^2 - 4*a^3*b^4*c^5*d^3 + 6*a^4*b^3*c^4*d^4 - 4*a^5*b^2*c^3*d^5 + a^6*b*c^2*d^6)*x^6 + (2*a^2*b^5*c^7*d - 7*a^3*b^4*c^6*d^2 + 8*a^4*b^3*c^5*d^3 - 2*a^5*b^2*c^4*d^4 - 2*a^6*b*c^3*d^5 + a^7*c^2*d^6)*x^4 + (a^2*b^5*c^8 - 2*a^3*b^4*c^7*d - 2*a^4*b^3*c^6*d^2 + 8*a^5*b^2*c^5*d^3 - 7*a^6*b*c^4*d^4 + 2*a^7*c^3*d^5)*x^2)]","B",0
781,1,3403,0,15.720000," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, a b^{3} c^{6} - 7 \, a^{2} b^{2} c^{5} d + {\left(2 \, b^{4} c^{4} d^{2} - 7 \, a b^{3} c^{3} d^{3}\right)} x^{6} + {\left(4 \, b^{4} c^{5} d - 12 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3}\right)} x^{4} + {\left(2 \, b^{4} c^{6} - 3 \, a b^{3} c^{5} d - 14 \, a^{2} b^{2} c^{4} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 12 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 4 \, {\left(3 \, a b^{3} c^{5} + 20 \, a^{3} b c^{3} d^{2} - 8 \, a^{4} c^{2} d^{3} + 3 \, {\left(a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 2 \, a^{3} b c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{4} d + 10 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{6} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{4} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{2}\right)}}, \frac{24 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + 3 \, {\left(2 \, a b^{3} c^{6} - 7 \, a^{2} b^{2} c^{5} d + {\left(2 \, b^{4} c^{4} d^{2} - 7 \, a b^{3} c^{3} d^{3}\right)} x^{6} + {\left(4 \, b^{4} c^{5} d - 12 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3}\right)} x^{4} + {\left(2 \, b^{4} c^{6} - 3 \, a b^{3} c^{5} d - 14 \, a^{2} b^{2} c^{4} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, a b^{3} c^{5} + 20 \, a^{3} b c^{3} d^{2} - 8 \, a^{4} c^{2} d^{3} + 3 \, {\left(a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 2 \, a^{3} b c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{4} d + 10 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{6} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{4} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left(2 \, a b^{3} c^{6} - 7 \, a^{2} b^{2} c^{5} d + {\left(2 \, b^{4} c^{4} d^{2} - 7 \, a b^{3} c^{3} d^{3}\right)} x^{6} + {\left(4 \, b^{4} c^{5} d - 12 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3}\right)} x^{4} + {\left(2 \, b^{4} c^{6} - 3 \, a b^{3} c^{5} d - 14 \, a^{2} b^{2} c^{4} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 6 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(3 \, a b^{3} c^{5} + 20 \, a^{3} b c^{3} d^{2} - 8 \, a^{4} c^{2} d^{3} + 3 \, {\left(a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 2 \, a^{3} b c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{4} d + 10 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{6} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{4} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{2}\right)}}, -\frac{3 \, {\left(2 \, a b^{3} c^{6} - 7 \, a^{2} b^{2} c^{5} d + {\left(2 \, b^{4} c^{4} d^{2} - 7 \, a b^{3} c^{3} d^{3}\right)} x^{6} + {\left(4 \, b^{4} c^{5} d - 12 \, a b^{3} c^{4} d^{2} - 7 \, a^{2} b^{2} c^{3} d^{3}\right)} x^{4} + {\left(2 \, b^{4} c^{6} - 3 \, a b^{3} c^{5} d - 14 \, a^{2} b^{2} c^{4} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 12 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(3 \, a b^{3} c^{5} + 20 \, a^{3} b c^{3} d^{2} - 8 \, a^{4} c^{2} d^{3} + 3 \, {\left(a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 2 \, a^{3} b c d^{4}\right)} x^{4} + 2 \, {\left(3 \, a b^{3} c^{4} d + 10 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{6} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{4} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/24*(3*(2*a*b^3*c^6 - 7*a^2*b^2*c^5*d + (2*b^4*c^4*d^2 - 7*a*b^3*c^3*d^3)*x^6 + (4*b^4*c^5*d - 12*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3)*x^4 + (2*b^4*c^6 - 3*a*b^3*c^5*d - 14*a^2*b^2*c^4*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 12*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 4*(3*a*b^3*c^5 + 20*a^3*b*c^3*d^2 - 8*a^4*c^2*d^3 + 3*(a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 2*a^3*b*c*d^4)*x^4 + 2*(3*a*b^3*c^4*d + 10*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^6 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^4 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^2), 1/24*(24*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + 3*(2*a*b^3*c^6 - 7*a^2*b^2*c^5*d + (2*b^4*c^4*d^2 - 7*a*b^3*c^3*d^3)*x^6 + (4*b^4*c^5*d - 12*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3)*x^4 + (2*b^4*c^6 - 3*a*b^3*c^5*d - 14*a^2*b^2*c^4*d^2)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 + 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*a*b^3*c^5 + 20*a^3*b*c^3*d^2 - 8*a^4*c^2*d^3 + 3*(a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 2*a^3*b*c*d^4)*x^4 + 2*(3*a*b^3*c^4*d + 10*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^6 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^4 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^2), -1/12*(3*(2*a*b^3*c^6 - 7*a^2*b^2*c^5*d + (2*b^4*c^4*d^2 - 7*a*b^3*c^3*d^3)*x^6 + (4*b^4*c^5*d - 12*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3)*x^4 + (2*b^4*c^6 - 3*a*b^3*c^5*d - 14*a^2*b^2*c^4*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 6*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)*sqrt(c)*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(3*a*b^3*c^5 + 20*a^3*b*c^3*d^2 - 8*a^4*c^2*d^3 + 3*(a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 2*a^3*b*c*d^4)*x^4 + 2*(3*a*b^3*c^4*d + 10*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^6 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^4 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^2), -1/12*(3*(2*a*b^3*c^6 - 7*a^2*b^2*c^5*d + (2*b^4*c^4*d^2 - 7*a*b^3*c^3*d^3)*x^6 + (4*b^4*c^5*d - 12*a*b^3*c^4*d^2 - 7*a^2*b^2*c^3*d^3)*x^4 + (2*b^4*c^6 - 3*a*b^3*c^5*d - 14*a^2*b^2*c^4*d^2)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 12*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(3*a*b^3*c^5 + 20*a^3*b*c^3*d^2 - 8*a^4*c^2*d^3 + 3*(a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 2*a^3*b*c*d^4)*x^4 + 2*(3*a*b^3*c^4*d + 10*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x^2)*sqrt(d*x^2 + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^6 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^4 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^2)]","B",0
782,1,1662,0,3.962948," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, b^{5} c^{4} d^{2} - 8 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(6 \, b^{5} c^{5} d - 13 \, a b^{4} c^{4} d^{2} - 8 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(3 \, b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(3 \, a b^{4} c^{6} - 8 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(6 \, a^{2} b^{4} c^{6} - 24 \, a^{3} b^{3} c^{5} d + 36 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 6 \, a^{6} c^{2} d^{4} + {\left(9 \, a b^{5} c^{4} d^{2} - 27 \, a^{2} b^{4} c^{3} d^{3} + 58 \, a^{3} b^{3} c^{2} d^{4} - 56 \, a^{4} b^{2} c d^{5} + 16 \, a^{5} b d^{6}\right)} x^{6} + 2 \, {\left(9 \, a b^{5} c^{5} d - 24 \, a^{2} b^{4} c^{4} d^{2} + 36 \, a^{3} b^{3} c^{3} d^{3} - 13 \, a^{4} b^{2} c^{2} d^{4} - 16 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x^{4} + 3 \, {\left(3 \, a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d - 4 \, a^{3} b^{3} c^{4} d^{2} + 24 \, a^{4} b^{2} c^{3} d^{3} - 26 \, a^{5} b c^{2} d^{4} + 8 \, a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{3} b^{5} c^{7} d^{2} - 4 \, a^{4} b^{4} c^{6} d^{3} + 6 \, a^{5} b^{3} c^{5} d^{4} - 4 \, a^{6} b^{2} c^{4} d^{5} + a^{7} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{3} b^{5} c^{8} d - 7 \, a^{4} b^{4} c^{7} d^{2} + 8 \, a^{5} b^{3} c^{6} d^{3} - 2 \, a^{6} b^{2} c^{5} d^{4} - 2 \, a^{7} b c^{4} d^{5} + a^{8} c^{3} d^{6}\right)} x^{5} + {\left(a^{3} b^{5} c^{9} - 2 \, a^{4} b^{4} c^{8} d - 2 \, a^{5} b^{3} c^{7} d^{2} + 8 \, a^{6} b^{2} c^{6} d^{3} - 7 \, a^{7} b c^{5} d^{4} + 2 \, a^{8} c^{4} d^{5}\right)} x^{3} + {\left(a^{4} b^{4} c^{9} - 4 \, a^{5} b^{3} c^{8} d + 6 \, a^{6} b^{2} c^{7} d^{2} - 4 \, a^{7} b c^{6} d^{3} + a^{8} c^{5} d^{4}\right)} x\right)}}, -\frac{3 \, {\left({\left(3 \, b^{5} c^{4} d^{2} - 8 \, a b^{4} c^{3} d^{3}\right)} x^{7} + {\left(6 \, b^{5} c^{5} d - 13 \, a b^{4} c^{4} d^{2} - 8 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{5} + {\left(3 \, b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 16 \, a^{2} b^{3} c^{4} d^{2}\right)} x^{3} + {\left(3 \, a b^{4} c^{6} - 8 \, a^{2} b^{3} c^{5} d\right)} x\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(6 \, a^{2} b^{4} c^{6} - 24 \, a^{3} b^{3} c^{5} d + 36 \, a^{4} b^{2} c^{4} d^{2} - 24 \, a^{5} b c^{3} d^{3} + 6 \, a^{6} c^{2} d^{4} + {\left(9 \, a b^{5} c^{4} d^{2} - 27 \, a^{2} b^{4} c^{3} d^{3} + 58 \, a^{3} b^{3} c^{2} d^{4} - 56 \, a^{4} b^{2} c d^{5} + 16 \, a^{5} b d^{6}\right)} x^{6} + 2 \, {\left(9 \, a b^{5} c^{5} d - 24 \, a^{2} b^{4} c^{4} d^{2} + 36 \, a^{3} b^{3} c^{3} d^{3} - 13 \, a^{4} b^{2} c^{2} d^{4} - 16 \, a^{5} b c d^{5} + 8 \, a^{6} d^{6}\right)} x^{4} + 3 \, {\left(3 \, a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d - 4 \, a^{3} b^{3} c^{4} d^{2} + 24 \, a^{4} b^{2} c^{3} d^{3} - 26 \, a^{5} b c^{2} d^{4} + 8 \, a^{6} c d^{5}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{3} b^{5} c^{7} d^{2} - 4 \, a^{4} b^{4} c^{6} d^{3} + 6 \, a^{5} b^{3} c^{5} d^{4} - 4 \, a^{6} b^{2} c^{4} d^{5} + a^{7} b c^{3} d^{6}\right)} x^{7} + {\left(2 \, a^{3} b^{5} c^{8} d - 7 \, a^{4} b^{4} c^{7} d^{2} + 8 \, a^{5} b^{3} c^{6} d^{3} - 2 \, a^{6} b^{2} c^{5} d^{4} - 2 \, a^{7} b c^{4} d^{5} + a^{8} c^{3} d^{6}\right)} x^{5} + {\left(a^{3} b^{5} c^{9} - 2 \, a^{4} b^{4} c^{8} d - 2 \, a^{5} b^{3} c^{7} d^{2} + 8 \, a^{6} b^{2} c^{6} d^{3} - 7 \, a^{7} b c^{5} d^{4} + 2 \, a^{8} c^{4} d^{5}\right)} x^{3} + {\left(a^{4} b^{4} c^{9} - 4 \, a^{5} b^{3} c^{8} d + 6 \, a^{6} b^{2} c^{7} d^{2} - 4 \, a^{7} b c^{6} d^{3} + a^{8} c^{5} d^{4}\right)} x\right)}}\right]"," ",0,"[-1/24*(3*((3*b^5*c^4*d^2 - 8*a*b^4*c^3*d^3)*x^7 + (6*b^5*c^5*d - 13*a*b^4*c^4*d^2 - 8*a^2*b^3*c^3*d^3)*x^5 + (3*b^5*c^6 - 2*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2)*x^3 + (3*a*b^4*c^6 - 8*a^2*b^3*c^5*d)*x)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 + 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(6*a^2*b^4*c^6 - 24*a^3*b^3*c^5*d + 36*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 6*a^6*c^2*d^4 + (9*a*b^5*c^4*d^2 - 27*a^2*b^4*c^3*d^3 + 58*a^3*b^3*c^2*d^4 - 56*a^4*b^2*c*d^5 + 16*a^5*b*d^6)*x^6 + 2*(9*a*b^5*c^5*d - 24*a^2*b^4*c^4*d^2 + 36*a^3*b^3*c^3*d^3 - 13*a^4*b^2*c^2*d^4 - 16*a^5*b*c*d^5 + 8*a^6*d^6)*x^4 + 3*(3*a*b^5*c^6 - 5*a^2*b^4*c^5*d - 4*a^3*b^3*c^4*d^2 + 24*a^4*b^2*c^3*d^3 - 26*a^5*b*c^2*d^4 + 8*a^6*c*d^5)*x^2)*sqrt(d*x^2 + c))/((a^3*b^5*c^7*d^2 - 4*a^4*b^4*c^6*d^3 + 6*a^5*b^3*c^5*d^4 - 4*a^6*b^2*c^4*d^5 + a^7*b*c^3*d^6)*x^7 + (2*a^3*b^5*c^8*d - 7*a^4*b^4*c^7*d^2 + 8*a^5*b^3*c^6*d^3 - 2*a^6*b^2*c^5*d^4 - 2*a^7*b*c^4*d^5 + a^8*c^3*d^6)*x^5 + (a^3*b^5*c^9 - 2*a^4*b^4*c^8*d - 2*a^5*b^3*c^7*d^2 + 8*a^6*b^2*c^6*d^3 - 7*a^7*b*c^5*d^4 + 2*a^8*c^4*d^5)*x^3 + (a^4*b^4*c^9 - 4*a^5*b^3*c^8*d + 6*a^6*b^2*c^7*d^2 - 4*a^7*b*c^6*d^3 + a^8*c^5*d^4)*x), -1/12*(3*((3*b^5*c^4*d^2 - 8*a*b^4*c^3*d^3)*x^7 + (6*b^5*c^5*d - 13*a*b^4*c^4*d^2 - 8*a^2*b^3*c^3*d^3)*x^5 + (3*b^5*c^6 - 2*a*b^4*c^5*d - 16*a^2*b^3*c^4*d^2)*x^3 + (3*a*b^4*c^6 - 8*a^2*b^3*c^5*d)*x)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) + 2*(6*a^2*b^4*c^6 - 24*a^3*b^3*c^5*d + 36*a^4*b^2*c^4*d^2 - 24*a^5*b*c^3*d^3 + 6*a^6*c^2*d^4 + (9*a*b^5*c^4*d^2 - 27*a^2*b^4*c^3*d^3 + 58*a^3*b^3*c^2*d^4 - 56*a^4*b^2*c*d^5 + 16*a^5*b*d^6)*x^6 + 2*(9*a*b^5*c^5*d - 24*a^2*b^4*c^4*d^2 + 36*a^3*b^3*c^3*d^3 - 13*a^4*b^2*c^2*d^4 - 16*a^5*b*c*d^5 + 8*a^6*d^6)*x^4 + 3*(3*a*b^5*c^6 - 5*a^2*b^4*c^5*d - 4*a^3*b^3*c^4*d^2 + 24*a^4*b^2*c^3*d^3 - 26*a^5*b*c^2*d^4 + 8*a^6*c*d^5)*x^2)*sqrt(d*x^2 + c))/((a^3*b^5*c^7*d^2 - 4*a^4*b^4*c^6*d^3 + 6*a^5*b^3*c^5*d^4 - 4*a^6*b^2*c^4*d^5 + a^7*b*c^3*d^6)*x^7 + (2*a^3*b^5*c^8*d - 7*a^4*b^4*c^7*d^2 + 8*a^5*b^3*c^6*d^3 - 2*a^6*b^2*c^5*d^4 - 2*a^7*b*c^4*d^5 + a^8*c^3*d^6)*x^5 + (a^3*b^5*c^9 - 2*a^4*b^4*c^8*d - 2*a^5*b^3*c^7*d^2 + 8*a^6*b^2*c^6*d^3 - 7*a^7*b*c^5*d^4 + 2*a^8*c^4*d^5)*x^3 + (a^4*b^4*c^9 - 4*a^5*b^3*c^8*d + 6*a^6*b^2*c^7*d^2 - 4*a^7*b*c^6*d^3 + a^8*c^5*d^4)*x)]","B",0
783,1,4115,0,29.743048," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{8} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{6} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{4} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 6 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{8} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{6} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{4} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 4 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{6} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{4} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{8} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{6} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{4} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{2}\right)}}, -\frac{12 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{8} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{6} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{4} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{8} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{6} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{4} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x^{2}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b^{2} d^{2} x^{4} + 8 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(4 \, b^{2} c d - 3 \, a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} c^{2} - 3 \, a b c d + a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{\frac{b}{b c - a d}}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{6} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{4} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{8} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{6} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{4} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{8} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{6} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{4} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) + 3 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{8} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{6} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{4} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-\frac{d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{6} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{4} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{8} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{6} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{4} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{8} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{6} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{4} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x^{2}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(\frac{{\left(b d x^{2} + 2 \, b c - a d\right)} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{b c - a d}}}{2 \, {\left(b d x^{2} + b c\right)}}\right) - 6 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{8} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{6} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{4} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{6} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{4} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{8} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{6} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{4} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/24*(3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^8 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^6 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^4 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 6*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^8 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^6 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^4 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 4*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^6 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^4 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^8 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^6 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^4 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^2), -1/24*(12*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^8 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^6 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^4 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^8 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^6 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^4 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x^2)*sqrt(b/(b*c - a*d))*log((b^2*d^2*x^4 + 8*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(4*b^2*c*d - 3*a*b*d^2)*x^2 - 4*(2*b^2*c^2 - 3*a*b*c*d + a^2*d^2 + (b^2*c*d - a*b*d^2)*x^2)*sqrt(d*x^2 + c)*sqrt(b/(b*c - a*d)))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^6 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^4 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^8 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^6 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^4 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^2), 1/12*(3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^8 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^6 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^4 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) + 3*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^8 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^6 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^4 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x^2)*sqrt(c)*log(-(d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^6 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^4 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^8 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^6 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^4 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^2), 1/12*(3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^8 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^6 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^4 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x^2)*sqrt(-b/(b*c - a*d))*arctan(1/2*(b*d*x^2 + 2*b*c - a*d)*sqrt(d*x^2 + c)*sqrt(-b/(b*c - a*d))/(b*d*x^2 + b*c)) - 6*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^8 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^6 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^4 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^6 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^4 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x^2)*sqrt(d*x^2 + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^8 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^6 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^4 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^2)]","B",0
784,1,1890,0,5.631042," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{6} c^{5} d^{2} - 2 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(2 \, b^{6} c^{6} d - 3 \, a b^{5} c^{5} d^{2} - 2 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(b^{6} c^{7} - 4 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(a b^{5} c^{7} - 2 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{4} + a^{2} c^{2} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{3} - a c x\right)} \sqrt{-a b c + a^{2} d} \sqrt{d x^{2} + c}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) + 4 \, {\left(2 \, a^{3} b^{4} c^{7} - 8 \, a^{4} b^{3} c^{6} d + 12 \, a^{5} b^{2} c^{5} d^{2} - 8 \, a^{6} b c^{4} d^{3} + 2 \, a^{7} c^{3} d^{4} - {\left(15 \, a b^{6} c^{5} d^{2} - 35 \, a^{2} b^{5} c^{4} d^{3} + 8 \, a^{3} b^{4} c^{3} d^{4} + 76 \, a^{4} b^{3} c^{2} d^{5} - 96 \, a^{5} b^{2} c d^{6} + 32 \, a^{6} b d^{7}\right)} x^{8} - 2 \, {\left(15 \, a b^{6} c^{6} d - 30 \, a^{2} b^{5} c^{5} d^{2} - 4 \, a^{3} b^{4} c^{4} d^{3} + 61 \, a^{4} b^{3} c^{3} d^{4} - 34 \, a^{5} b^{2} c^{2} d^{5} - 24 \, a^{6} b c d^{6} + 16 \, a^{7} d^{7}\right)} x^{6} - 3 \, {\left(5 \, a b^{6} c^{7} - 5 \, a^{2} b^{5} c^{6} d - 14 \, a^{3} b^{4} c^{5} d^{2} + 16 \, a^{4} b^{3} c^{4} d^{3} + 26 \, a^{5} b^{2} c^{3} d^{4} - 44 \, a^{6} b c^{2} d^{5} + 16 \, a^{7} c d^{6}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{24 \, {\left({\left(a^{4} b^{5} c^{8} d^{2} - 4 \, a^{5} b^{4} c^{7} d^{3} + 6 \, a^{6} b^{3} c^{6} d^{4} - 4 \, a^{7} b^{2} c^{5} d^{5} + a^{8} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{4} b^{5} c^{9} d - 7 \, a^{5} b^{4} c^{8} d^{2} + 8 \, a^{6} b^{3} c^{7} d^{3} - 2 \, a^{7} b^{2} c^{6} d^{4} - 2 \, a^{8} b c^{5} d^{5} + a^{9} c^{4} d^{6}\right)} x^{7} + {\left(a^{4} b^{5} c^{10} - 2 \, a^{5} b^{4} c^{9} d - 2 \, a^{6} b^{3} c^{8} d^{2} + 8 \, a^{7} b^{2} c^{7} d^{3} - 7 \, a^{8} b c^{6} d^{4} + 2 \, a^{9} c^{5} d^{5}\right)} x^{5} + {\left(a^{5} b^{4} c^{10} - 4 \, a^{6} b^{3} c^{9} d + 6 \, a^{7} b^{2} c^{8} d^{2} - 4 \, a^{8} b c^{7} d^{3} + a^{9} c^{6} d^{4}\right)} x^{3}\right)}}, \frac{15 \, {\left({\left(b^{6} c^{5} d^{2} - 2 \, a b^{5} c^{4} d^{3}\right)} x^{9} + {\left(2 \, b^{6} c^{6} d - 3 \, a b^{5} c^{5} d^{2} - 2 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{7} + {\left(b^{6} c^{7} - 4 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{5} + {\left(a b^{5} c^{7} - 2 \, a^{2} b^{4} c^{6} d\right)} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{\sqrt{a b c - a^{2} d} {\left({\left(b c - 2 \, a d\right)} x^{2} - a c\right)} \sqrt{d x^{2} + c}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{3} + {\left(a b c^{2} - a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b^{4} c^{7} - 8 \, a^{4} b^{3} c^{6} d + 12 \, a^{5} b^{2} c^{5} d^{2} - 8 \, a^{6} b c^{4} d^{3} + 2 \, a^{7} c^{3} d^{4} - {\left(15 \, a b^{6} c^{5} d^{2} - 35 \, a^{2} b^{5} c^{4} d^{3} + 8 \, a^{3} b^{4} c^{3} d^{4} + 76 \, a^{4} b^{3} c^{2} d^{5} - 96 \, a^{5} b^{2} c d^{6} + 32 \, a^{6} b d^{7}\right)} x^{8} - 2 \, {\left(15 \, a b^{6} c^{6} d - 30 \, a^{2} b^{5} c^{5} d^{2} - 4 \, a^{3} b^{4} c^{4} d^{3} + 61 \, a^{4} b^{3} c^{3} d^{4} - 34 \, a^{5} b^{2} c^{2} d^{5} - 24 \, a^{6} b c d^{6} + 16 \, a^{7} d^{7}\right)} x^{6} - 3 \, {\left(5 \, a b^{6} c^{7} - 5 \, a^{2} b^{5} c^{6} d - 14 \, a^{3} b^{4} c^{5} d^{2} + 16 \, a^{4} b^{3} c^{4} d^{3} + 26 \, a^{5} b^{2} c^{3} d^{4} - 44 \, a^{6} b c^{2} d^{5} + 16 \, a^{7} c d^{6}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{5} c^{7} - 14 \, a^{3} b^{4} c^{6} d + 6 \, a^{4} b^{3} c^{5} d^{2} + 16 \, a^{5} b^{2} c^{4} d^{3} - 19 \, a^{6} b c^{3} d^{4} + 6 \, a^{7} c^{2} d^{5}\right)} x^{2}\right)} \sqrt{d x^{2} + c}}{12 \, {\left({\left(a^{4} b^{5} c^{8} d^{2} - 4 \, a^{5} b^{4} c^{7} d^{3} + 6 \, a^{6} b^{3} c^{6} d^{4} - 4 \, a^{7} b^{2} c^{5} d^{5} + a^{8} b c^{4} d^{6}\right)} x^{9} + {\left(2 \, a^{4} b^{5} c^{9} d - 7 \, a^{5} b^{4} c^{8} d^{2} + 8 \, a^{6} b^{3} c^{7} d^{3} - 2 \, a^{7} b^{2} c^{6} d^{4} - 2 \, a^{8} b c^{5} d^{5} + a^{9} c^{4} d^{6}\right)} x^{7} + {\left(a^{4} b^{5} c^{10} - 2 \, a^{5} b^{4} c^{9} d - 2 \, a^{6} b^{3} c^{8} d^{2} + 8 \, a^{7} b^{2} c^{7} d^{3} - 7 \, a^{8} b c^{6} d^{4} + 2 \, a^{9} c^{5} d^{5}\right)} x^{5} + {\left(a^{5} b^{4} c^{10} - 4 \, a^{6} b^{3} c^{9} d + 6 \, a^{7} b^{2} c^{8} d^{2} - 4 \, a^{8} b c^{7} d^{3} + a^{9} c^{6} d^{4}\right)} x^{3}\right)}}\right]"," ",0,"[-1/24*(15*((b^6*c^5*d^2 - 2*a*b^5*c^4*d^3)*x^9 + (2*b^6*c^6*d - 3*a*b^5*c^5*d^2 - 2*a^2*b^4*c^4*d^3)*x^7 + (b^6*c^7 - 4*a^2*b^4*c^5*d^2)*x^5 + (a*b^5*c^7 - 2*a^2*b^4*c^6*d)*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^4 + a^2*c^2 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^2 - 4*((b*c - 2*a*d)*x^3 - a*c*x)*sqrt(-a*b*c + a^2*d)*sqrt(d*x^2 + c))/(b^2*x^4 + 2*a*b*x^2 + a^2)) + 4*(2*a^3*b^4*c^7 - 8*a^4*b^3*c^6*d + 12*a^5*b^2*c^5*d^2 - 8*a^6*b*c^4*d^3 + 2*a^7*c^3*d^4 - (15*a*b^6*c^5*d^2 - 35*a^2*b^5*c^4*d^3 + 8*a^3*b^4*c^3*d^4 + 76*a^4*b^3*c^2*d^5 - 96*a^5*b^2*c*d^6 + 32*a^6*b*d^7)*x^8 - 2*(15*a*b^6*c^6*d - 30*a^2*b^5*c^5*d^2 - 4*a^3*b^4*c^4*d^3 + 61*a^4*b^3*c^3*d^4 - 34*a^5*b^2*c^2*d^5 - 24*a^6*b*c*d^6 + 16*a^7*d^7)*x^6 - 3*(5*a*b^6*c^7 - 5*a^2*b^5*c^6*d - 14*a^3*b^4*c^5*d^2 + 16*a^4*b^3*c^4*d^3 + 26*a^5*b^2*c^3*d^4 - 44*a^6*b*c^2*d^5 + 16*a^7*c*d^6)*x^4 - 2*(5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^2)*sqrt(d*x^2 + c))/((a^4*b^5*c^8*d^2 - 4*a^5*b^4*c^7*d^3 + 6*a^6*b^3*c^6*d^4 - 4*a^7*b^2*c^5*d^5 + a^8*b*c^4*d^6)*x^9 + (2*a^4*b^5*c^9*d - 7*a^5*b^4*c^8*d^2 + 8*a^6*b^3*c^7*d^3 - 2*a^7*b^2*c^6*d^4 - 2*a^8*b*c^5*d^5 + a^9*c^4*d^6)*x^7 + (a^4*b^5*c^10 - 2*a^5*b^4*c^9*d - 2*a^6*b^3*c^8*d^2 + 8*a^7*b^2*c^7*d^3 - 7*a^8*b*c^6*d^4 + 2*a^9*c^5*d^5)*x^5 + (a^5*b^4*c^10 - 4*a^6*b^3*c^9*d + 6*a^7*b^2*c^8*d^2 - 4*a^8*b*c^7*d^3 + a^9*c^6*d^4)*x^3), 1/12*(15*((b^6*c^5*d^2 - 2*a*b^5*c^4*d^3)*x^9 + (2*b^6*c^6*d - 3*a*b^5*c^5*d^2 - 2*a^2*b^4*c^4*d^3)*x^7 + (b^6*c^7 - 4*a^2*b^4*c^5*d^2)*x^5 + (a*b^5*c^7 - 2*a^2*b^4*c^6*d)*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*sqrt(a*b*c - a^2*d)*((b*c - 2*a*d)*x^2 - a*c)*sqrt(d*x^2 + c)/((a*b*c*d - a^2*d^2)*x^3 + (a*b*c^2 - a^2*c*d)*x)) - 2*(2*a^3*b^4*c^7 - 8*a^4*b^3*c^6*d + 12*a^5*b^2*c^5*d^2 - 8*a^6*b*c^4*d^3 + 2*a^7*c^3*d^4 - (15*a*b^6*c^5*d^2 - 35*a^2*b^5*c^4*d^3 + 8*a^3*b^4*c^3*d^4 + 76*a^4*b^3*c^2*d^5 - 96*a^5*b^2*c*d^6 + 32*a^6*b*d^7)*x^8 - 2*(15*a*b^6*c^6*d - 30*a^2*b^5*c^5*d^2 - 4*a^3*b^4*c^4*d^3 + 61*a^4*b^3*c^3*d^4 - 34*a^5*b^2*c^2*d^5 - 24*a^6*b*c*d^6 + 16*a^7*d^7)*x^6 - 3*(5*a*b^6*c^7 - 5*a^2*b^5*c^6*d - 14*a^3*b^4*c^5*d^2 + 16*a^4*b^3*c^4*d^3 + 26*a^5*b^2*c^3*d^4 - 44*a^6*b*c^2*d^5 + 16*a^7*c*d^6)*x^4 - 2*(5*a^2*b^5*c^7 - 14*a^3*b^4*c^6*d + 6*a^4*b^3*c^5*d^2 + 16*a^5*b^2*c^4*d^3 - 19*a^6*b*c^3*d^4 + 6*a^7*c^2*d^5)*x^2)*sqrt(d*x^2 + c))/((a^4*b^5*c^8*d^2 - 4*a^5*b^4*c^7*d^3 + 6*a^6*b^3*c^6*d^4 - 4*a^7*b^2*c^5*d^5 + a^8*b*c^4*d^6)*x^9 + (2*a^4*b^5*c^9*d - 7*a^5*b^4*c^8*d^2 + 8*a^6*b^3*c^7*d^3 - 2*a^7*b^2*c^6*d^4 - 2*a^8*b*c^5*d^5 + a^9*c^4*d^6)*x^7 + (a^4*b^5*c^10 - 2*a^5*b^4*c^9*d - 2*a^6*b^3*c^8*d^2 + 8*a^7*b^2*c^7*d^3 - 7*a^8*b*c^6*d^4 + 2*a^9*c^5*d^5)*x^5 + (a^5*b^4*c^10 - 4*a^6*b^3*c^9*d + 6*a^7*b^2*c^8*d^2 - 4*a^8*b*c^7*d^3 + a^9*c^6*d^4)*x^3)]","B",0
785,0,0,0,0.837251," ","integrate((e*x)^(3/2)*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e x^{3} + A e x\right)} \sqrt{b x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e*x^3 + A*e*x)*sqrt(b*x^2 + a)*sqrt(e*x), x)","F",0
786,0,0,0,0.849040," ","integrate((B*x^2+A)*(e*x)^(1/2)*(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x), x)","F",0
787,0,0,0,0.759224," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(e*x), x)","F",0
788,0,0,0,1.245540," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
789,0,0,0,1.500681," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^3*x^3), x)","F",0
790,0,0,0,1.093613," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
791,0,0,0,1.099308," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)/x^(9/2), x)","F",0
792,0,0,0,1.174742," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)/x^(11/2), x)","F",0
793,0,0,0,1.098054," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)/x^(13/2), x)","F",0
794,0,0,0,1.006420," ","integrate((e*x)^(3/2)*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b e x^{5} + {\left(B a + A b\right)} e x^{3} + A a e x\right)} \sqrt{b x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b*e*x^5 + (B*a + A*b)*e*x^3 + A*a*e*x)*sqrt(b*x^2 + a)*sqrt(e*x), x)","F",0
795,0,0,0,0.800196," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)*(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a)*sqrt(e*x), x)","F",0
796,0,0,0,0.912963," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a)*sqrt(e*x)/(e*x), x)","F",0
797,0,0,0,0.990000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
798,0,0,0,0.984652," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^3*x^3), x)","F",0
799,0,0,0,1.006166," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{4} + {\left(B a + A b\right)} x^{2} + A a\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*b*x^4 + (B*a + A*b)*x^2 + A*a)*sqrt(b*x^2 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
800,0,0,0,0.841486," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{4} + A e^{2} x^{2}\right)} \sqrt{e x}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral((B*e^2*x^4 + A*e^2*x^2)*sqrt(e*x)/sqrt(b*x^2 + a), x)","F",0
801,0,0,0,0.871499," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{3} + A e x\right)} \sqrt{e x}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral((B*e*x^3 + A*e*x)*sqrt(e*x)/sqrt(b*x^2 + a), x)","F",0
802,0,0,0,0.814502," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{e x}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(e*x)/sqrt(b*x^2 + a), x)","F",0
803,0,0,0,1.061431," ","integrate((B*x^2+A)/(e*x)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b e x^{3} + a e x}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b*e*x^3 + a*e*x), x)","F",0
804,0,0,0,0.775769," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b e^{2} x^{4} + a e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b*e^2*x^4 + a*e^2*x^2), x)","F",0
805,0,0,0,0.706768," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b e^{3} x^{5} + a e^{3} x^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b*e^3*x^5 + a*e^3*x^3), x)","F",0
806,0,0,0,0.872905," ","integrate((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b e^{4} x^{6} + a e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b*e^4*x^6 + a*e^4*x^4), x)","F",0
807,0,0,0,1.104586," ","integrate((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{5} + A e^{3} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^3*x^5 + A*e^3*x^3)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
808,0,0,0,1.108927," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{4} + A e^{2} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^4 + A*e^2*x^2)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
809,0,0,0,0.859058," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{3} + A e x\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e*x^3 + A*e*x)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
810,0,0,0,0.985332," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
811,0,0,0,0.967056," ","integrate((B*x^2+A)/(b*x^2+a)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x), x)","F",0
812,0,0,0,0.905271," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2), x)","F",0
813,0,0,0,1.126026," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} e^{3} x^{7} + 2 \, a b e^{3} x^{5} + a^{2} e^{3} x^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*e^3*x^7 + 2*a*b*e^3*x^5 + a^2*e^3*x^3), x)","F",0
814,0,0,0,0.773563," ","integrate((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{2} e^{4} x^{8} + 2 \, a b e^{4} x^{6} + a^{2} e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^2*e^4*x^8 + 2*a*b*e^4*x^6 + a^2*e^4*x^4), x)","F",0
815,0,0,0,0.905196," ","integrate((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{5} + A e^{3} x^{3}\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^3*x^5 + A*e^3*x^3)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
816,0,0,0,0.849264," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{4} + A e^{2} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e^2*x^4 + A*e^2*x^2)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
817,0,0,0,0.871051," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{3} + A e x\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*e*x^3 + A*e*x)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
818,0,0,0,0.818969," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
819,0,0,0,0.718556," ","integrate((B*x^2+A)/(b*x^2+a)^(5/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} e x^{7} + 3 \, a b^{2} e x^{5} + 3 \, a^{2} b e x^{3} + a^{3} e x}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*e*x^7 + 3*a*b^2*e*x^5 + 3*a^2*b*e*x^3 + a^3*e*x), x)","F",0
820,0,0,0,0.881005," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} e^{2} x^{8} + 3 \, a b^{2} e^{2} x^{6} + 3 \, a^{2} b e^{2} x^{4} + a^{3} e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*e^2*x^8 + 3*a*b^2*e^2*x^6 + 3*a^2*b*e^2*x^4 + a^3*e^2*x^2), x)","F",0
821,0,0,0,0.849349," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}}{b^{3} e^{3} x^{9} + 3 \, a b^{2} e^{3} x^{7} + 3 \, a^{2} b e^{3} x^{5} + a^{3} e^{3} x^{3}}, x\right)"," ",0,"integral((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x)/(b^3*e^3*x^9 + 3*a*b^2*e^3*x^7 + 3*a^2*b*e^3*x^5 + a^3*e^3*x^3), x)","F",0
822,0,0,0,0.616316," ","integrate((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x\right)} \sqrt{d x^{2} + c} \sqrt{e x}, x\right)"," ",0,"integral((b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x)*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
823,0,0,0,1.003876," ","integrate((b*x^2+a)^2*(e*x)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
824,0,0,0,0.858167," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e*x), x)","F",0
825,0,0,0,0.772078," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^2*x^2), x)","F",0
826,0,0,0,0.773330," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^3*x^3), x)","F",0
827,0,0,0,0.892776," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^4*x^4), x)","F",0
828,0,0,0,1.223926," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)/x^(9/2), x)","F",0
829,0,0,0,1.413867," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c}}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)/x^(11/2), x)","F",0
830,0,0,0,0.970920," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)/x^(13/2), x)","F",0
831,0,0,0,1.083760," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c}}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)/x^(15/2), x)","F",0
832,0,0,0,1.167870," ","integrate((e*x)^(5/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d e^{2} x^{8} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} x^{6} + a^{2} c e^{2} x^{2} + {\left(2 \, a b c + a^{2} d\right)} e^{2} x^{4}\right)} \sqrt{d x^{2} + c} \sqrt{e x}, x\right)"," ",0,"integral((b^2*d*e^2*x^8 + (b^2*c + 2*a*b*d)*e^2*x^6 + a^2*c*e^2*x^2 + (2*a*b*c + a^2*d)*e^2*x^4)*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
833,0,0,0,1.026396," ","integrate((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d e x^{7} + {\left(b^{2} c + 2 \, a b d\right)} e x^{5} + a^{2} c e x + {\left(2 \, a b c + a^{2} d\right)} e x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{e x}, x\right)"," ",0,"integral((b^2*d*e*x^7 + (b^2*c + 2*a*b*d)*e*x^5 + a^2*c*e*x + (2*a*b*c + a^2*d)*e*x^3)*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
834,0,0,0,0.912567," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)*(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}, x\right)"," ",0,"integral((b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2)*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
835,0,0,0,0.771362," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e*x), x)","F",0
836,0,0,0,0.962137," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^2*x^2), x)","F",0
837,0,0,0,0.990539," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{3} x^{3}}, x\right)"," ",0,"integral((b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^3*x^3), x)","F",0
838,0,0,0,0.930200," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} d x^{6} + {\left(b^{2} c + 2 \, a b d\right)} x^{4} + a^{2} c + {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((b^2*d*x^6 + (b^2*c + 2*a*b*d)*x^4 + a^2*c + (2*a*b*c + a^2*d)*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(e^4*x^4), x)","F",0
839,0,0,0,1.042766," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}\right)} \sqrt{e x}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2)*sqrt(e*x)/sqrt(d*x^2 + c), x)","F",0
840,0,0,0,0.915694," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x\right)} \sqrt{e x}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x)*sqrt(e*x)/sqrt(d*x^2 + c), x)","F",0
841,0,0,0,0.961360," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{e x}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(e*x)/sqrt(d*x^2 + c), x)","F",0
842,0,0,0,0.833624," ","integrate((b*x^2+a)^2/(e*x)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e x^{3} + c e x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e*x^3 + c*e*x), x)","F",0
843,0,0,0,0.783963," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{2} x^{4} + c e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^2*x^4 + c*e^2*x^2), x)","F",0
844,0,0,0,0.917875," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{3} x^{5} + c e^{3} x^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^3*x^5 + c*e^3*x^3), x)","F",0
845,0,0,0,1.059277," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{4} x^{6} + c e^{4} x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^4*x^6 + c*e^4*x^4), x)","F",0
846,0,0,0,0.810214," ","integrate((b*x^2+a)^2/(e*x)^(9/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{5} x^{7} + c e^{5} x^{5}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^5*x^7 + c*e^5*x^5), x)","F",0
847,0,0,0,0.984602," ","integrate((b*x^2+a)^2/(e*x)^(11/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{6} x^{8} + c e^{6} x^{6}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^6*x^8 + c*e^6*x^6), x)","F",0
848,0,0,0,0.929478," ","integrate((b*x^2+a)^2/(e*x)^(13/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d e^{7} x^{9} + c e^{7} x^{7}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d*e^7*x^9 + c*e^7*x^7), x)","F",0
849,0,0,0,1.180093," ","integrate((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e^{3} x^{7} + 2 \, a b e^{3} x^{5} + a^{2} e^{3} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*e^3*x^7 + 2*a*b*e^3*x^5 + a^2*e^3*x^3)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
850,0,0,0,0.958733," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
851,0,0,0,0.871396," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
852,0,0,0,1.073193," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
853,0,0,0,0.482188," ","integrate((b*x^2+a)^2/(d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} e x^{5} + 2 \, c d e x^{3} + c^{2} e x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*e*x^5 + 2*c*d*e*x^3 + c^2*e*x), x)","F",0
854,0,0,0,1.006682," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} e^{2} x^{6} + 2 \, c d e^{2} x^{4} + c^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*e^2*x^6 + 2*c*d*e^2*x^4 + c^2*e^2*x^2), x)","F",0
855,0,0,0,0.882180," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} e^{3} x^{7} + 2 \, c d e^{3} x^{5} + c^{2} e^{3} x^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*e^3*x^7 + 2*c*d*e^3*x^5 + c^2*e^3*x^3), x)","F",0
856,0,0,0,0.916647," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{2} e^{4} x^{8} + 2 \, c d e^{4} x^{6} + c^{2} e^{4} x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^2*e^4*x^8 + 2*c*d*e^4*x^6 + c^2*e^4*x^4), x)","F",0
857,0,0,0,1.007991," ","integrate((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e^{3} x^{7} + 2 \, a b e^{3} x^{5} + a^{2} e^{3} x^{3}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b^2*e^3*x^7 + 2*a*b*e^3*x^5 + a^2*e^3*x^3)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
858,0,0,0,0.940292," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
859,0,0,0,0.999275," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
860,0,0,0,0.833806," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
861,0,0,0,0.922774," ","integrate((b*x^2+a)^2/(d*x^2+c)^(5/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} e x^{7} + 3 \, c d^{2} e x^{5} + 3 \, c^{2} d e x^{3} + c^{3} e x}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*e*x^7 + 3*c*d^2*e*x^5 + 3*c^2*d*e*x^3 + c^3*e*x), x)","F",0
862,0,0,0,0.959522," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} e^{2} x^{8} + 3 \, c d^{2} e^{2} x^{6} + 3 \, c^{2} d e^{2} x^{4} + c^{3} e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*e^2*x^8 + 3*c*d^2*e^2*x^6 + 3*c^2*d*e^2*x^4 + c^3*e^2*x^2), x)","F",0
863,0,0,0,0.905824," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} e^{3} x^{9} + 3 \, c d^{2} e^{3} x^{7} + 3 \, c^{2} d e^{3} x^{5} + c^{3} e^{3} x^{3}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*e^3*x^9 + 3*c*d^2*e^3*x^7 + 3*c^2*d*e^3*x^5 + c^3*e^3*x^3), x)","F",0
864,0,0,0,0.997044," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{d x^{2} + c} \sqrt{e x}}{d^{3} e^{4} x^{10} + 3 \, c d^{2} e^{4} x^{8} + 3 \, c^{2} d e^{4} x^{6} + c^{3} e^{4} x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(d*x^2 + c)*sqrt(e*x)/(d^3*e^4*x^10 + 3*c*d^2*e^4*x^8 + 3*c^2*d*e^4*x^6 + c^3*e^4*x^4), x)","F",0
865,-1,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2+a)/(e*x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(7/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)*(e*x)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(-b*x^2+a)/(e*x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(5/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(7/2)/(-b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)/(e*x)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate(1/(e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,-1,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
890,-1,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate(1/(-b*x^2+a)/(-d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(5/2)/(-b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,-1,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,-1,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
914,-1,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
915,-1,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
916,-1,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
917,-1,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,-1,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,-1,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
924,-1,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,-1,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
928,-1,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
929,-1,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
930,-1,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
931,-1,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
932,-1,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
933,-1,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
934,1,442,0,1.960283," ","integrate(x^5*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{192 \, b^{3} d^{4}}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{96 \, b^{3} d^{4}}\right]"," ",0,"[-1/192*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) - 4*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 4*a*b^2*c*d^2 - 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^4), 1/96*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) + 2*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 4*a*b^2*c*d^2 - 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^4)]","A",0
935,1,334,0,1.419183," ","integrate(x^3*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) - 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, b^{2} d^{3}}, -\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, b^{2} d^{3}}\right]"," ",0,"[-1/32*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) - 4*(2*b^2*d^2*x^2 - 3*b^2*c*d + a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^3), -1/16*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(2*b^2*d^2*x^2 - 3*b^2*c*d + a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^3)]","A",0
936,1,259,0,1.623733," ","integrate(x*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b d - {\left(b c - a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right)}{8 \, b d^{2}}, \frac{2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b d + {\left(b c - a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{4 \, b d^{2}}\right]"," ",0,"[1/8*(4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b*d - (b*c - a*d)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)))/(b*d^2), 1/4*(2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b*d + (b*c - a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)))/(b*d^2)]","A",0
937,1,777,0,1.879341," ","integrate((b*x^2+a)^(1/2)/x/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + \frac{1}{4} \, \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right), -\frac{1}{2} \, \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right), \frac{1}{2} \, \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + \frac{1}{4} \, \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right), \frac{1}{2} \, \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - \frac{1}{2} \, \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right)\right]"," ",0,"[1/4*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 1/4*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4), -1/2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 1/4*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4), 1/2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + 1/4*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)), 1/2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - 1/2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2))]","B",0
938,1,280,0,1.640375," ","integrate((b*x^2+a)^(1/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a c} {\left(b c - a d\right)} x^{2} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right) + 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a c}{8 \, a c^{2} x^{2}}, \frac{\sqrt{-a c} {\left(b c - a d\right)} x^{2} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right) - 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a c}{4 \, a c^{2} x^{2}}\right]"," ",0,"[-1/8*(sqrt(a*c)*(b*c - a*d)*x^2*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4) + 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*c)/(a*c^2*x^2), 1/4*(sqrt(-a*c)*(b*c - a*d)*x^2*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2)) - 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*c)/(a*c^2*x^2)]","A",0
939,1,358,0,1.855002," ","integrate((b*x^2+a)^(1/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{4} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right) + 4 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, a^{2} c^{3} x^{4}}, -\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, a^{2} c^{3} x^{4}}\right]"," ",0,"[-1/32*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(a*c)*x^4*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4) + 4*(2*a^2*c^2 + (a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^2*c^3*x^4), -1/16*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(-a*c)*x^4*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2)) + 2*(2*a^2*c^2 + (a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^2*c^3*x^4)]","A",0
940,0,0,0,1.149790," ","integrate(x^4*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} x^{4}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*x^4/sqrt(d*x^2 + c), x)","F",0
941,0,0,0,1.275890," ","integrate(x^2*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} x^{2}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*x^2/sqrt(d*x^2 + c), x)","F",0
942,0,0,0,1.045928," ","integrate((b*x^2+a)^(1/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d x^{4} + c x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d*x^4 + c*x^2), x)","F",0
943,0,0,0,1.361737," ","integrate((b*x^2+a)^(1/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d x^{6} + c x^{4}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d*x^6 + c*x^4), x)","F",0
944,1,574,0,1.034851," ","integrate(x^5*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{6} - 105 \, b^{4} c^{3} d + 145 \, a b^{3} c^{2} d^{2} - 15 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{1536 \, b^{3} d^{5}}, -\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{6} - 105 \, b^{4} c^{3} d + 145 \, a b^{3} c^{2} d^{2} - 15 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{768 \, b^{3} d^{5}}\right]"," ",0,"[1/1536*(3*(35*b^4*c^4 - 60*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + 3*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(48*b^4*d^4*x^6 - 105*b^4*c^3*d + 145*a*b^3*c^2*d^2 - 15*a^2*b^2*c*d^3 - 9*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 9*a*b^3*d^4)*x^4 + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^5), -1/768*(3*(35*b^4*c^4 - 60*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + 3*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(48*b^4*d^4*x^6 - 105*b^4*c^3*d + 145*a*b^3*c^2*d^2 - 15*a^2*b^2*c*d^3 - 9*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 9*a*b^3*d^4)*x^4 + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^5)]","A",0
945,1,440,0,1.532821," ","integrate(x^3*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{192 \, b^{2} d^{4}}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{96 \, b^{2} d^{4}}\right]"," ",0,"[1/192*(3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 22*a*b^2*c*d^2 + 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 7*a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^4), 1/96*(3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) + 2*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 22*a*b^2*c*d^2 + 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 7*a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^4)]","A",0
946,1,334,0,0.982771," ","integrate(x*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, b d^{3}}, -\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, b d^{3}}\right]"," ",0,"[1/32*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(2*b^2*d^2*x^2 - 3*b^2*c*d + 5*a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b*d^3), -1/16*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(2*b^2*d^2*x^2 - 3*b^2*c*d + 5*a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b*d^3)]","A",0
947,1,918,0,3.094134," ","integrate((b*x^2+a)^(3/2)/x/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a d \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) - {\left(b c - 3 \, a d\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b}{8 \, d}, \frac{a d \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) + {\left(b c - 3 \, a d\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b}{4 \, d}, \frac{4 \, a d \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - {\left(b c - 3 \, a d\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b}{8 \, d}, \frac{2 \, a d \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + {\left(b c - 3 \, a d\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b}{4 \, d}\right]"," ",0,"[1/8*(2*a*d*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) - (b*c - 3*a*d)*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b)/d, 1/4*(a*d*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) + (b*c - 3*a*d)*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b)/d, 1/8*(4*a*d*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - (b*c - 3*a*d)*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b)/d, 1/4*(2*a*d*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + (b*c - 3*a*d)*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b)/d]","A",0
948,1,958,0,3.082888," ","integrate((b*x^2+a)^(3/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) - {\left(3 \, b c - a d\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) - 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a}{8 \, c x^{2}}, -\frac{4 \, b c x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + {\left(3 \, b c - a d\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) + 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a}{8 \, c x^{2}}, \frac{b c x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + {\left(3 \, b c - a d\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a}{4 \, c x^{2}}, -\frac{2 \, b c x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) - {\left(3 \, b c - a d\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a}{4 \, c x^{2}}\right]"," ",0,"[1/8*(2*b*c*x^2*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) - (3*b*c - a*d)*x^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) - 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a)/(c*x^2), -1/8*(4*b*c*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + (3*b*c - a*d)*x^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) + 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a)/(c*x^2), 1/4*(b*c*x^2*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + (3*b*c - a*d)*x^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a)/(c*x^2), -1/4*(2*b*c*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) - (3*b*c - a*d)*x^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a)/(c*x^2)]","B",0
949,1,360,0,2.130688," ","integrate((b*x^2+a)^(3/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{4} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, a c^{3} x^{4}}, \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, a c^{3} x^{4}}\right]"," ",0,"[1/32*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^4*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4) - 4*(2*a^2*c^2 + (5*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a*c^3*x^4), 1/16*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^4*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2)) - 2*(2*a^2*c^2 + (5*a*b*c^2 - 3*a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a*c^3*x^4)]","A",0
950,0,0,0,1.360180," ","integrate(x^4*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{6} + a x^{4}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b*x^6 + a*x^4)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
951,0,0,0,1.505945," ","integrate(x^2*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a x^{2}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b*x^4 + a*x^2)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
952,0,0,0,1.667666," ","integrate((b*x^2+a)^(3/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}}{d x^{4} + c x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c)/(d*x^4 + c*x^2), x)","F",0
953,0,0,0,1.256516," ","integrate((b*x^2+a)^(3/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}}{d x^{6} + c x^{4}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c)/(d*x^6 + c*x^4), x)","F",0
954,1,734,0,1.048131," ","integrate(x^5*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{8} + 945 \, b^{5} c^{4} d - 2310 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 90 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} - 144 \, {\left(3 \, b^{5} c d^{4} - 7 \, a b^{4} d^{5}\right)} x^{6} + 8 \, {\left(63 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{4} - 2 \, {\left(315 \, b^{5} c^{3} d^{2} - 749 \, a b^{4} c^{2} d^{3} + 481 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{15360 \, b^{3} d^{6}}, \frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{8} + 945 \, b^{5} c^{4} d - 2310 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 90 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} - 144 \, {\left(3 \, b^{5} c d^{4} - 7 \, a b^{4} d^{5}\right)} x^{6} + 8 \, {\left(63 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{4} - 2 \, {\left(315 \, b^{5} c^{3} d^{2} - 749 \, a b^{4} c^{2} d^{3} + 481 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{7680 \, b^{3} d^{6}}\right]"," ",0,"[-1/15360*(15*(63*b^5*c^5 - 175*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) - 4*(384*b^5*d^5*x^8 + 945*b^5*c^4*d - 2310*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 90*a^3*b^2*c*d^4 - 45*a^4*b*d^5 - 144*(3*b^5*c*d^4 - 7*a*b^4*d^5)*x^6 + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^4 - 2*(315*b^5*c^3*d^2 - 749*a*b^4*c^2*d^3 + 481*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^6), 1/7680*(15*(63*b^5*c^5 - 175*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) + 2*(384*b^5*d^5*x^8 + 945*b^5*c^4*d - 2310*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 90*a^3*b^2*c*d^4 - 45*a^4*b*d^5 - 144*(3*b^5*c*d^4 - 7*a*b^4*d^5)*x^6 + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^4 - 2*(315*b^5*c^3*d^2 - 749*a*b^4*c^2*d^3 + 481*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^6)]","A",0
955,1,574,0,1.349384," ","integrate(x^3*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{6} - 105 \, b^{4} c^{3} d + 265 \, a b^{3} c^{2} d^{2} - 191 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 17 \, a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{1536 \, b^{2} d^{5}}, -\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{6} - 105 \, b^{4} c^{3} d + 265 \, a b^{3} c^{2} d^{2} - 191 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 17 \, a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{768 \, b^{2} d^{5}}\right]"," ",0,"[-1/1536*(15*(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) - 4*(48*b^4*d^4*x^6 - 105*b^4*c^3*d + 265*a*b^3*c^2*d^2 - 191*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 17*a*b^3*d^4)*x^4 + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^5), -1/768*(15*(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(48*b^4*d^4*x^6 - 105*b^4*c^3*d + 265*a*b^3*c^2*d^2 - 191*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 17*a*b^3*d^4)*x^4 + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^2*d^5)]","A",0
956,1,440,0,1.491338," ","integrate(x*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 13 \, a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{192 \, b d^{4}}, \frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{4} + 15 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 13 \, a b^{2} d^{3}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{96 \, b d^{4}}\right]"," ",0,"[-1/192*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) - 4*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 40*a*b^2*c*d^2 + 33*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 13*a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b*d^4), 1/96*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) + 2*(8*b^3*d^3*x^4 + 15*b^3*c^2*d - 40*a*b^2*c*d^2 + 33*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 13*a*b^2*d^3)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b*d^4)]","A",0
957,1,1075,0,10.418750," ","integrate((b*x^2+a)^(5/2)/x/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} d^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + 4 \, {\left(2 \, b^{2} d x^{2} - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, d^{2}}, \frac{4 \, a^{2} d^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, b^{2} d x^{2} - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, d^{2}}, \frac{16 \, a^{2} d^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + 4 \, {\left(2 \, b^{2} d x^{2} - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, d^{2}}, \frac{8 \, a^{2} d^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, b^{2} d x^{2} - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, d^{2}}\right]"," ",0,"[1/32*(8*a^2*d^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 4*(2*b^2*d*x^2 - 3*b^2*c + 9*a*b*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/d^2, 1/16*(4*a^2*d^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 2*(2*b^2*d*x^2 - 3*b^2*c + 9*a*b*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/d^2, 1/32*(16*a^2*d^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 4*(2*b^2*d*x^2 - 3*b^2*c + 9*a*b*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/d^2, 1/16*(8*a^2*d^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 2*(2*b^2*d*x^2 - 3*b^2*c + 9*a*b*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/d^2]","A",0
958,1,1097,0,8.105178," ","integrate((b*x^2+a)^(5/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 5 \, a b c d\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + {\left(5 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) - 4 \, {\left(b^{2} c x^{2} - a^{2} d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{8 \, c d x^{2}}, \frac{2 \, {\left(b^{2} c^{2} - 5 \, a b c d\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) - {\left(5 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) + 4 \, {\left(b^{2} c x^{2} - a^{2} d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{8 \, c d x^{2}}, \frac{2 \, {\left(5 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - {\left(b^{2} c^{2} - 5 \, a b c d\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + 4 \, {\left(b^{2} c x^{2} - a^{2} d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{8 \, c d x^{2}}, \frac{{\left(5 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + {\left(b^{2} c^{2} - 5 \, a b c d\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) + 2 \, {\left(b^{2} c x^{2} - a^{2} d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{4 \, c d x^{2}}\right]"," ",0,"[-1/8*((b^2*c^2 - 5*a*b*c*d)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + (5*a*b*c*d - a^2*d^2)*x^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) - 4*(b^2*c*x^2 - a^2*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c*d*x^2), 1/8*(2*(b^2*c^2 - 5*a*b*c*d)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) - (5*a*b*c*d - a^2*d^2)*x^2*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) + 4*(b^2*c*x^2 - a^2*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c*d*x^2), 1/8*(2*(5*a*b*c*d - a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - (b^2*c^2 - 5*a*b*c*d)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + 4*(b^2*c*x^2 - a^2*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c*d*x^2), 1/4*((5*a*b*c*d - a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + (b^2*c^2 - 5*a*b*c*d)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) + 2*(b^2*c*x^2 - a^2*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c*d*x^2)]","A",0
959,1,1123,0,6.706449," ","integrate((b*x^2+a)^(5/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, b^{2} c^{2} x^{4} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, c^{2} x^{4}}, -\frac{16 \, b^{2} c^{2} x^{4} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{\frac{a}{c}} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{a}{c}}}{x^{4}}\right) + 4 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, c^{2} x^{4}}, \frac{4 \, b^{2} c^{2} x^{4} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d^{2} x^{2} + b c d + a d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{\frac{b}{d}}\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, c^{2} x^{4}}, -\frac{8 \, b^{2} c^{2} x^{4} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{4} + a b c + {\left(b^{2} c + a b d\right)} x^{2}\right)}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{4} + a^{2} c + {\left(a b c + a^{2} d\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, c^{2} x^{4}}\right]"," ",0,"[1/32*(8*b^2*c^2*x^4*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) - 4*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c^2*x^4), -1/32*(16*b^2*c^2*x^4*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4*sqrt(a/c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a/c))/x^4) + 4*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c^2*x^4), 1/16*(4*b^2*c^2*x^4*sqrt(b/d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d^2*x^2 + b*c*d + a*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b/d)) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) - 2*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c^2*x^4), -1/16*(8*b^2*c^2*x^4*sqrt(-b/d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b/d)/(b^2*d*x^4 + a*b*c + (b^2*c + a*b*d)*x^2)) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4*sqrt(-a/c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a/c)/(a*b*d*x^4 + a^2*c + (a*b*c + a^2*d)*x^2)) + 2*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(c^2*x^4)]","A",0
960,0,0,0,1.258977," ","integrate(x^4*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{8} + 2 \, a b x^{6} + a^{2} x^{4}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*x^8 + 2*a*b*x^6 + a^2*x^4)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
961,0,0,0,1.394050," ","integrate(x^2*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{6} + 2 \, a b x^{4} + a^{2} x^{2}\right)} \sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral((b^2*x^6 + 2*a*b*x^4 + a^2*x^2)*sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
962,0,0,0,1.588675," ","integrate((b*x^2+a)^(5/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d x^{4} + c x^{2}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d*x^4 + c*x^2), x)","F",0
963,0,0,0,1.607305," ","integrate((b*x^2+a)^(5/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{d x^{6} + c x^{4}}, x\right)"," ",0,"integral((b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(d*x^6 + c*x^4), x)","F",0
964,0,0,0,1.300934," ","integrate(x^4*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} x^{4}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2)*x^4/(3*x^2 - 2), x)","F",0
965,1,72,0,0.709432," ","integrate(x^3*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{72} \, {\left(6 \, x^{2} + 5\right)} \sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} - \frac{7}{144} \, \arctan\left(\frac{3 \, \sqrt{3 \, x^{2} - 1} {\left(2 \, x^{2} - 1\right)} \sqrt{-3 \, x^{2} + 2}}{2 \, {\left(9 \, x^{4} - 9 \, x^{2} + 2\right)}}\right)"," ",0,"-1/72*(6*x^2 + 5)*sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2) - 7/144*arctan(3/2*sqrt(3*x^2 - 1)*(2*x^2 - 1)*sqrt(-3*x^2 + 2)/(9*x^4 - 9*x^2 + 2))","A",0
966,0,0,0,1.240250," ","integrate(x^2*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} x^{2}}{3 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2)*x^2/(3*x^2 - 2), x)","F",0
967,1,65,0,1.253630," ","integrate(x*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} - \frac{1}{12} \, \arctan\left(\frac{3 \, \sqrt{3 \, x^{2} - 1} {\left(2 \, x^{2} - 1\right)} \sqrt{-3 \, x^{2} + 2}}{2 \, {\left(9 \, x^{4} - 9 \, x^{2} + 2\right)}}\right)"," ",0,"-1/6*sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2) - 1/12*arctan(3/2*sqrt(3*x^2 - 1)*(2*x^2 - 1)*sqrt(-3*x^2 + 2)/(9*x^4 - 9*x^2 + 2))","B",0
968,0,0,0,1.232319," ","integrate(x^2*(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + 2} x^{2}}{\sqrt{d x^{2} + 3}}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)*x^2/sqrt(d*x^2 + 3), x)","F",0
969,1,336,0,1.540358," ","integrate(x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, b^{3} d^{3}}, -\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, b^{3} d^{3}}\right]"," ",0,"[1/32*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(2*b^2*d^2*x^2 - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^3), -1/16*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(2*b^2*d^2*x^2 - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(b^3*d^3)]","A",0
970,1,256,0,1.199226," ","integrate(x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right)}{8 \, b^{2} d^{2}}, \frac{2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} b d + {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{4 \, b^{2} d^{2}}\right]"," ",0,"[1/8*(4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)))/(b^2*d^2), 1/4*(2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*b*d + (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)))/(b^2*d^2)]","A",0
971,1,194,0,1.240760," ","integrate(x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right)}{4 \, b d}, -\frac{\sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, b d}\right]"," ",0,"[1/4*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d))/(b*d), -1/2*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2))/(b*d)]","B",0
972,1,204,0,1.219064," ","integrate(1/x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right)}{4 \, a c}, \frac{\sqrt{-a c} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right)}{2 \, a c}\right]"," ",0,"[1/4*sqrt(a*c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4)/(a*c), 1/2*sqrt(-a*c)*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2))/(a*c)]","B",0
973,1,278,0,1.382291," ","integrate(1/x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} {\left(b c + a d\right)} x^{2} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} + 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right) - 4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a c}{8 \, a^{2} c^{2} x^{2}}, -\frac{\sqrt{-a c} {\left(b c + a d\right)} x^{2} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a c}{4 \, a^{2} c^{2} x^{2}}\right]"," ",0,"[1/8*(sqrt(a*c)*(b*c + a*d)*x^2*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 + 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4) - 4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2), -1/4*(sqrt(-a*c)*(b*c + a*d)*x^2*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2)) + 2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*c)/(a^2*c^2*x^2)]","A",0
974,1,360,0,2.036417," ","integrate(1/x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{4} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2} - 4 \, {\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{a c}}{x^{4}}\right) - 4 \, {\left(2 \, a^{2} c^{2} - 3 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{32 \, a^{3} c^{3} x^{4}}, \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{4} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - 3 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{16 \, a^{3} c^{3} x^{4}}\right]"," ",0,"[1/32*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(a*c)*x^4*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^2 - 4*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(a*c))/x^4) - 4*(2*a^2*c^2 - 3*(a*b*c^2 + a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^3*c^3*x^4), 1/16*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(-a*c)*x^4*arctan(1/2*((b*c + a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-a*c)/(a*b*c*d*x^4 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^2)) - 2*(2*a^2*c^2 - 3*(a*b*c^2 + a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^3*c^3*x^4)]","A",0
975,0,0,0,1.197033," ","integrate(x^6/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x^{6}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x^6/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
976,0,0,0,1.314861," ","integrate(x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x^{4}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x^4/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
977,0,0,0,1.215184," ","integrate(x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x^{2}}{b d x^{4} + {\left(b c + a d\right)} x^{2} + a c}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x^2/(b*d*x^4 + (b*c + a*d)*x^2 + a*c), x)","F",0
978,0,0,0,1.290984," ","integrate(1/x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b d x^{6} + {\left(b c + a d\right)} x^{4} + a c x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b*d*x^6 + (b*c + a*d)*x^4 + a*c*x^2), x)","F",0
979,0,0,0,1.294616," ","integrate(1/x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{b d x^{8} + {\left(b c + a d\right)} x^{6} + a c x^{4}}, x\right)"," ",0,"integral(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(b*d*x^8 + (b*c + a*d)*x^6 + a*c*x^4), x)","F",0
980,1,498,0,1.448043," ","integrate(x^5/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(a b^{2} c d - 3 \, a^{2} b d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{8 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{2}\right)}}, \frac{{\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(a b^{2} c d - 3 \, a^{2} b d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{4 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*((a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(a*b^2*c*d - 3*a^2*b*d^2 + (b^3*c*d - a*b^2*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^2), 1/4*((a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2 + (b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*x^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) + 2*(a*b^2*c*d - 3*a^2*b*d^2 + (b^3*c*d - a*b^2*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^2)]","B",0
981,1,367,0,1.435685," ","integrate(x^3/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a b d + {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right)}{4 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}, \frac{2 \, \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} a b d - {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(4*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*b*d + (a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2), 1/2*(2*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*a*b*d - (a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^2)]","B",0
982,1,48,0,1.179143," ","integrate(x/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}}"," ",0,"-sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)","A",0
983,1,706,0,1.706230," ","integrate(x^5/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}\right) + 4 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{12 \, {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3} + {\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} x^{4} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c + a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{6 \, {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3} + {\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} x^{4} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)) + 4*(5*a^2*b^2*c*d - 3*a^3*b*d^2 + 2*(3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3 + (b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*x^4 + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*x^2), -1/6*(3*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 + b*c + a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^2)) - 2*(5*a^2*b^2*c*d - 3*a^3*b*d^2 + 2*(3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c))/(a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3 + (b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*x^4 + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*x^2)]","B",0
984,1,128,0,1.549749," ","integrate(x^3/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(3 \, b c - a d\right)} x^{2} + 2 \, a c\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}"," ",0,"-1/3*((3*b*c - a*d)*x^2 + 2*a*c)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)","A",0
985,1,126,0,1.433563," ","integrate(x/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, b d x^{2} - b c + 3 \, a d\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{2}\right)}}"," ",0,"1/3*(2*b*d*x^2 - b*c + 3*a*d)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^2)","B",0
986,1,262,0,1.578439," ","integrate(x^5/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{4} + 8 \, a^{2} c^{2} + 4 \, {\left(5 \, a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{15 \, {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3} + {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{6} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{4} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} x^{2}\right)}}"," ",0,"-1/15*((15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^4 + 8*a^2*c^2 + 4*(5*a*b*c^2 - a^2*c*d)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3 + (b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^6 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^4 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*x^2)","A",0
987,1,269,0,2.092543," ","integrate(x^3/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(5 \, b^{2} c d - a b d^{2}\right)} x^{4} - 2 \, a b c^{2} + 10 \, a^{2} c d - {\left(5 \, b^{2} c^{2} - 26 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{15 \, {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3} + {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{6} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{4} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} x^{2}\right)}}"," ",0,"1/15*(2*(5*b^2*c*d - a*b*d^2)*x^4 - 2*a*b*c^2 + 10*a^2*c*d - (5*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3 + (b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^6 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^4 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*x^2)","B",0
988,1,259,0,2.085326," ","integrate(x/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, b^{2} d^{2} x^{4} + 3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2} - 4 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{15 \, {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3} + {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{6} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{4} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} x^{2}\right)}}"," ",0,"-1/15*(8*b^2*d^2*x^4 + 3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2 - 4*(b^2*c*d - 5*a*b*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3 + (b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^6 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^4 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*x^2)","B",0
989,1,451,0,3.459651," ","integrate(x^5/(b*x^2+a)^(9/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(35 \, b^{3} c^{2} d - 14 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x^{6} - 8 \, a^{2} b c^{3} + 56 \, a^{3} c^{2} d - {\left(35 \, b^{3} c^{3} - 259 \, a b^{2} c^{2} d + 101 \, a^{2} b c d^{2} - 21 \, a^{3} d^{3}\right)} x^{4} - 4 \, {\left(7 \, a b^{2} c^{3} - 50 \, a^{2} b c^{2} d + 7 \, a^{3} c d^{2}\right)} x^{2}\right)} \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}{105 \, {\left(a^{4} b^{4} c^{4} - 4 \, a^{5} b^{3} c^{3} d + 6 \, a^{6} b^{2} c^{2} d^{2} - 4 \, a^{7} b c d^{3} + a^{8} d^{4} + {\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} x^{8} + 4 \, {\left(a b^{7} c^{4} - 4 \, a^{2} b^{6} c^{3} d + 6 \, a^{3} b^{5} c^{2} d^{2} - 4 \, a^{4} b^{4} c d^{3} + a^{5} b^{3} d^{4}\right)} x^{6} + 6 \, {\left(a^{2} b^{6} c^{4} - 4 \, a^{3} b^{5} c^{3} d + 6 \, a^{4} b^{4} c^{2} d^{2} - 4 \, a^{5} b^{3} c d^{3} + a^{6} b^{2} d^{4}\right)} x^{4} + 4 \, {\left(a^{3} b^{5} c^{4} - 4 \, a^{4} b^{4} c^{3} d + 6 \, a^{5} b^{3} c^{2} d^{2} - 4 \, a^{6} b^{2} c d^{3} + a^{7} b d^{4}\right)} x^{2}\right)}}"," ",0,"1/105*(2*(35*b^3*c^2*d - 14*a*b^2*c*d^2 + 3*a^2*b*d^3)*x^6 - 8*a^2*b*c^3 + 56*a^3*c^2*d - (35*b^3*c^3 - 259*a*b^2*c^2*d + 101*a^2*b*c*d^2 - 21*a^3*d^3)*x^4 - 4*(7*a*b^2*c^3 - 50*a^2*b*c^2*d + 7*a^3*c*d^2)*x^2)*sqrt(b*x^2 + a)*sqrt(d*x^2 + c)/(a^4*b^4*c^4 - 4*a^5*b^3*c^3*d + 6*a^6*b^2*c^2*d^2 - 4*a^7*b*c*d^3 + a^8*d^4 + (b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*x^8 + 4*(a*b^7*c^4 - 4*a^2*b^6*c^3*d + 6*a^3*b^5*c^2*d^2 - 4*a^4*b^4*c*d^3 + a^5*b^3*d^4)*x^6 + 6*(a^2*b^6*c^4 - 4*a^3*b^5*c^3*d + 6*a^4*b^4*c^2*d^2 - 4*a^5*b^3*c*d^3 + a^6*b^2*d^4)*x^4 + 4*(a^3*b^5*c^4 - 4*a^4*b^4*c^3*d + 6*a^5*b^3*c^2*d^2 - 4*a^6*b^2*c*d^3 + a^7*b*d^4)*x^2)","B",0
990,1,201,0,1.386910," ","integrate(x/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d - a b d^{2}\right)} x^{2} - 4 \, {\left(2 \, b d x^{2} + b c - a d\right)} \sqrt{-b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{-b d}\right)}{4 \, b d}, -\frac{\sqrt{b d} \arctan\left(\frac{{\left(2 \, b d x^{2} + b c - a d\right)} \sqrt{-b x^{2} + a} \sqrt{d x^{2} + c} \sqrt{b d}}{2 \, {\left(b^{2} d^{2} x^{4} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, b d}\right]"," ",0,"[-1/4*sqrt(-b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 - 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d - a*b*d^2)*x^2 - 4*(2*b*d*x^2 + b*c - a*d)*sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(-b*d))/(b*d), -1/2*sqrt(b*d)*arctan(1/2*(2*b*d*x^2 + b*c - a*d)*sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)*sqrt(b*d)/(b^2*d^2*x^4 - a*b*c*d + (b^2*c*d - a*b*d^2)*x^2))/(b*d)]","B",0
991,1,203,0,1.457358," ","integrate(x/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{4} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{2} + 4 \, {\left(2 \, b d x^{2} - b c - a d\right)} \sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c} \sqrt{b d}\right)}{4 \, b d}, -\frac{\sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{2} - b c - a d\right)} \sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{4} + a b c d - {\left(b^{2} c d + a b d^{2}\right)} x^{2}\right)}}\right)}{2 \, b d}\right]"," ",0,"[1/4*sqrt(b*d)*log(8*b^2*d^2*x^4 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 8*(b^2*c*d + a*b*d^2)*x^2 + 4*(2*b*d*x^2 - b*c - a*d)*sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)*sqrt(b*d))/(b*d), -1/2*sqrt(-b*d)*arctan(1/2*(2*b*d*x^2 - b*c - a*d)*sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)*sqrt(-b*d)/(b^2*d^2*x^4 + a*b*c*d - (b^2*c*d + a*b*d^2)*x^2))/(b*d)]","B",0
992,0,0,0,1.409790," ","integrate(x^2/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3} x^{2}}{b d x^{4} + {\left(3 \, b + 2 \, d\right)} x^{2} + 6}, x\right)"," ",0,"integral(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3)*x^2/(b*d*x^4 + (3*b + 2*d)*x^2 + 6), x)","F",0
993,0,0,0,1.470722," ","integrate(x^2/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{2} + c} \sqrt{-x^{2} + 4} x^{2}}{d x^{4} + {\left(c - 4 \, d\right)} x^{2} - 4 \, c}, x\right)"," ",0,"integral(-sqrt(d*x^2 + c)*sqrt(-x^2 + 4)*x^2/(d*x^4 + (c - 4*d)*x^2 - 4*c), x)","F",0
994,0,0,0,1.425280," ","integrate(x^2/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{2} + c} \sqrt{x^{2} + 4} x^{2}}{d x^{4} + {\left(c + 4 \, d\right)} x^{2} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^2 + c)*sqrt(x^2 + 4)*x^2/(d*x^4 + (c + 4*d)*x^2 + 4*c), x)","F",0
995,0,0,0,1.432336," ","integrate(x^2/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1} x^{2}}{3 \, x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)*x^2/(3*x^4 - x^2 - 2), x)","F",0
996,0,0,0,1.251984," ","integrate(x^2/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2} x^{2}}{3 \, x^{4} - 5 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)*x^2/(3*x^4 - 5*x^2 + 2), x)","F",0
997,0,0,0,1.280713," ","integrate(x^2/(-x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 4} x^{2}}{3 \, x^{4} - 10 \, x^{2} - 8}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 2)*sqrt(-x^2 + 4)*x^2/(3*x^4 - 10*x^2 - 8), x)","F",0
998,0,0,0,0.890446," ","integrate(x^2/(-3*x^2+2)^(1/2)/(-x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 4} \sqrt{-3 \, x^{2} + 2} x^{2}}{3 \, x^{4} - 14 \, x^{2} + 8}, x\right)"," ",0,"integral(sqrt(-x^2 + 4)*sqrt(-3*x^2 + 2)*x^2/(3*x^4 - 14*x^2 + 8), x)","F",0
999,0,0,0,1.437716," ","integrate(x^2/(-4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x^{2} + 2} \sqrt{-4 \, x^{2} + 1} x^{2}}{12 \, x^{4} + 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(3*x^2 + 2)*sqrt(-4*x^2 + 1)*x^2/(12*x^4 + 5*x^2 - 2), x)","F",0
1000,0,0,0,0.910029," ","integrate(x^2/(-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-3 \, x^{2} + 2} \sqrt{-4 \, x^{2} + 1} x^{2}}{12 \, x^{4} - 11 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-3*x^2 + 2)*sqrt(-4*x^2 + 1)*x^2/(12*x^4 - 11*x^2 + 2), x)","F",0
1001,0,0,0,1.360363," ","integrate(x^2/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 1} \sqrt{-3 \, x^{2} + 2} x^{2}}{3 \, x^{4} + x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(x^2 + 1)*sqrt(-3*x^2 + 2)*x^2/(3*x^4 + x^2 - 2), x)","F",0
1002,0,0,0,1.551324," ","integrate(x^2/(-3*x^2+2)^(1/2)/(x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2} x^{2}}{3 \, x^{4} + 10 \, x^{2} - 8}, x\right)"," ",0,"integral(-sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)*x^2/(3*x^4 + 10*x^2 - 8), x)","F",0
1003,0,0,0,1.263939," ","integrate(x^2/(-3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x^{2} + 1} \sqrt{-3 \, x^{2} + 2} x^{2}}{12 \, x^{4} - 5 \, x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(4*x^2 + 1)*sqrt(-3*x^2 + 2)*x^2/(12*x^4 - 5*x^2 - 2), x)","F",0
1004,0,0,0,1.207183," ","integrate(x^2/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 1} x^{2}}{3 \, x^{4} + 5 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(3*x^2 + 2)*sqrt(x^2 + 1)*x^2/(3*x^4 + 5*x^2 + 2), x)","F",0
1005,0,0,0,1.435876," ","integrate(x^2/(x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 4} x^{2}}{3 \, x^{4} + 14 \, x^{2} + 8}, x\right)"," ",0,"integral(sqrt(3*x^2 + 2)*sqrt(x^2 + 4)*x^2/(3*x^4 + 14*x^2 + 8), x)","F",0
1006,0,0,0,1.463203," ","integrate(x^2/(3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x^{2} + 1} \sqrt{3 \, x^{2} + 2} x^{2}}{12 \, x^{4} + 11 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(4*x^2 + 1)*sqrt(3*x^2 + 2)*x^2/(12*x^4 + 11*x^2 + 2), x)","F",0
1007,0,0,0,1.440073," ","integrate(x^2/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{2 \, x^{2} - 1} \sqrt{-x^{2} + 1} x^{2}}{2 \, x^{4} - 3 \, x^{2} + 1}, x\right)"," ",0,"integral(-sqrt(2*x^2 - 1)*sqrt(-x^2 + 1)*x^2/(2*x^4 - 3*x^2 + 1), x)","F",0
1008,1,102,0,0.919633," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{3}{10} \, {\left(x^{2} - 6\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + \frac{9}{4} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{9}{16} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + \frac{9}{8} \cdot 4^{\frac{2}{3}} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"-3/10*(x^2 - 6)*(-x^2 + 1)^(2/3) + 9/4*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 9/16*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 9/8*4^(2/3)*log(-4^(1/3) + (-x^2 + 1)^(1/3))","A",0
1009,1,122,0,1.317765," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{3}{4} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(2 \, \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}}\right)}\right) - \frac{3}{16} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + \frac{3}{8} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{3}{4} \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/4*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*sqrt(3)*(2*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3))) - 3/16*4^(2/3)*(-1)^(1/3)*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) + 3/8*4^(2/3)*(-1)^(1/3)*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) - 3/4*(-x^2 + 1)^(2/3)","A",0
1010,1,86,0,1.404835," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","\frac{1}{4} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{16} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{8} \cdot 4^{\frac{2}{3}} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"1/4*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 1/16*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 1/8*4^(2/3)*log(-4^(1/3) + (-x^2 + 1)^(1/3))","A",0
1011,1,177,0,1.372546," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{1}{12} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(2 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{48} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{12} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{6} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/12*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*(2*sqrt(3)*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3)*sqrt(3))) - 1/48*4^(2/3)*(-1)^(1/3)*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) + 1/24*4^(2/3)*(-1)^(1/3)*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) + 1/6*sqrt(3)*arctan(2/3*sqrt(3)*(-x^2 + 1)^(1/3) + 1/3*sqrt(3)) - 1/12*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) + 1/6*log((-x^2 + 1)^(1/3) - 1)","A",0
1012,1,115,0,1.132939," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} x^{2} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{1}{3}} \sqrt{3} + 2 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - 4^{\frac{2}{3}} x^{2} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + 2 \cdot 4^{\frac{2}{3}} x^{2} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 24 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{144 \, x^{2}}"," ",0,"1/144*(4*4^(1/6)*sqrt(3)*x^2*arctan(1/6*4^(1/6)*(4^(1/3)*sqrt(3) + 2*sqrt(3)*(-x^2 + 1)^(1/3))) - 4^(2/3)*x^2*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 2*4^(2/3)*x^2*log(-4^(1/3) + (-x^2 + 1)^(1/3)) - 24*(-x^2 + 1)^(2/3))/x^2","A",0
1013,1,217,0,1.174063," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} x^{4} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(2 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}} \sqrt{3}\right)}\right) + 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{4} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) - 2 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{4} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 16 \, \sqrt{3} x^{4} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 8 \, x^{4} \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - 16 \, x^{4} \log\left({\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 1\right) + 12 \, {\left(2 \, x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{432 \, x^{4}}"," ",0,"-1/432*(4*4^(1/6)*sqrt(3)*(-1)^(1/3)*x^4*arctan(1/6*4^(1/6)*(2*sqrt(3)*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3)*sqrt(3))) + 4^(2/3)*(-1)^(1/3)*x^4*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) - 2*4^(2/3)*(-1)^(1/3)*x^4*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) - 16*sqrt(3)*x^4*arctan(2/3*sqrt(3)*(-x^2 + 1)^(1/3) + 1/3*sqrt(3)) + 8*x^4*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) - 16*x^4*log((-x^2 + 1)^(1/3) - 1) + 12*(2*x^2 + 3)*(-x^2 + 1)^(2/3))/x^4","A",0
1014,0,0,0,5.816962," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}} x^{4}}{x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)*x^4/(x^4 + 2*x^2 - 3), x)","F",0
1015,0,0,0,4.392819," ","integrate(x^2/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}} x^{2}}{x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)*x^2/(x^4 + 2*x^2 - 3), x)","F",0
1016,1,1943,0,4.820131," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","-\frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{10368 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) - \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{2592 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) + \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{10368 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) + \frac{1}{20736} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{2592 \, {\left(6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}\right) - \frac{1}{1296} \cdot 432^{\frac{5}{6}} \arctan\left(\frac{432^{\frac{5}{6}} {\left(x^{5} - 18 \, x^{3} + 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \sqrt{3} 2^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{4} + 9 \, x^{2}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 288 \, \sqrt{3} {\left(2 \, x^{4} - 3 \, x^{2}\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 6 \cdot 432^{\frac{1}{6}} {\left(x^{6} + 141 \, x^{4} - 153 \, x^{2} + 27\right)}\right)} - 648 \cdot 432^{\frac{1}{6}} {\left(3 \, x^{3} - x\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, \sqrt{3} {\left(7 \, x^{5} + 6 \, x^{3} - 9 \, x\right)}}{36 \, {\left(x^{6} - 225 \, x^{4} + 243 \, x^{2} - 27\right)}}\right) - \frac{1}{2592} \cdot 432^{\frac{5}{6}} \arctan\left(-\frac{\sqrt{2} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(29 \, x^{11} + 879 \, x^{9} - 12078 \, x^{7} + 10638 \, x^{5} - 3807 \, x^{3} + 243 \, x\right)} - 2 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{10} + 153 \, x^{8} - 1701 \, x^{6} + 459 \, x^{4}\right)} - 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(31 \, x^{9} - 297 \, x^{7} - 27 \, x^{5} - 27 \, x^{3}\right)}\right)} - 36 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} {\left(x^{11} + 1167 \, x^{9} - 13158 \, x^{7} + 17550 \, x^{5} - 4779 \, x^{3} + 243 \, x\right)} - 8 \, \sqrt{3} {\left(13 \, x^{10} - 6 \, x^{8} - 1404 \, x^{6} + 1350 \, x^{4} - 81 \, x^{2}\right)}\right)} - 3 \cdot 432^{\frac{1}{6}} {\left(x^{12} + 7620 \, x^{10} - 92115 \, x^{8} + 169776 \, x^{6} - 109269 \, x^{4} + 16524 \, x^{2} - 729\right)}\right)} \sqrt{\frac{6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} + 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} + {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} + 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 72 \, {\left(x^{5} + 18 \, x^{4} + 24 \, x^{3} - 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}} - 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 144 \, x^{8} - 918 \, x^{6} + 2808 \, x^{4} - 243 \, x^{2}\right)} - 3 \cdot 432^{\frac{1}{6}} {\left(31 \, x^{9} - 568 \, x^{7} + 1710 \, x^{5} - 432 \, x^{3} + 27 \, x\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 18 \, \sqrt{3} {\left(x^{12} - 366 \, x^{10} + 14535 \, x^{8} - 42660 \, x^{6} + 58239 \, x^{4} - 14094 \, x^{2} + 729\right)} + 144 \, \sqrt{3} {\left(11 \, x^{11} - 807 \, x^{9} + 4518 \, x^{7} - 5238 \, x^{5} + 3807 \, x^{3} - 243 \, x\right)} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{11} - 1215 \, x^{9} + 11754 \, x^{7} - 21006 \, x^{5} + 5589 \, x^{3} - 243 \, x\right)} - 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{10} - 120 \, x^{8} + 1242 \, x^{6} - 1728 \, x^{4} + 81 \, x^{2}\right)}\right)}}{18 \, {\left(x^{12} - 8334 \, x^{10} + 110727 \, x^{8} - 301860 \, x^{6} + 187839 \, x^{4} - 21870 \, x^{2} + 729\right)}}\right) - \frac{1}{2592} \cdot 432^{\frac{5}{6}} \arctan\left(\frac{\sqrt{2} {\left(18 \, \sqrt{3} 2^{\frac{2}{3}} {\left(29 \, x^{11} + 879 \, x^{9} - 12078 \, x^{7} + 10638 \, x^{5} - 3807 \, x^{3} + 243 \, x\right)} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} {\left(432^{\frac{5}{6}} {\left(x^{10} + 153 \, x^{8} - 1701 \, x^{6} + 459 \, x^{4}\right)} + 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(31 \, x^{9} - 297 \, x^{7} - 27 \, x^{5} - 27 \, x^{3}\right)}\right)} - 36 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} {\left(x^{11} + 1167 \, x^{9} - 13158 \, x^{7} + 17550 \, x^{5} - 4779 \, x^{3} + 243 \, x\right)} + 8 \, \sqrt{3} {\left(13 \, x^{10} - 6 \, x^{8} - 1404 \, x^{6} + 1350 \, x^{4} - 81 \, x^{2}\right)}\right)} + 3 \cdot 432^{\frac{1}{6}} {\left(x^{12} + 7620 \, x^{10} - 92115 \, x^{8} + 169776 \, x^{6} - 109269 \, x^{4} + 16524 \, x^{2} - 729\right)}\right)} \sqrt{\frac{6 \cdot 2^{\frac{2}{3}} {\left(x^{6} + 225 \, x^{4} - 189 \, x^{2} + 27\right)} - 144 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(x^{5} - x^{3}\right)} - {\left(432^{\frac{5}{6}} \sqrt{3} {\left(7 \, x^{3} - 3 \, x\right)} - 216 \cdot 2^{\frac{1}{3}} {\left(x^{4} + 3 \, x^{2}\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 72 \, {\left(x^{5} - 18 \, x^{4} + 24 \, x^{3} + 18 \, x^{2} - 9 \, x\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}{x^{6} + 9 \, x^{4} + 27 \, x^{2} + 27}} - 216 \, {\left(\sqrt{3} 2^{\frac{2}{3}} {\left(x^{10} + 144 \, x^{8} - 918 \, x^{6} + 2808 \, x^{4} - 243 \, x^{2}\right)} + 3 \cdot 432^{\frac{1}{6}} {\left(31 \, x^{9} - 568 \, x^{7} + 1710 \, x^{5} - 432 \, x^{3} + 27 \, x\right)}\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - 18 \, \sqrt{3} {\left(x^{12} - 366 \, x^{10} + 14535 \, x^{8} - 42660 \, x^{6} + 58239 \, x^{4} - 14094 \, x^{2} + 729\right)} - 144 \, \sqrt{3} {\left(11 \, x^{11} - 807 \, x^{9} + 4518 \, x^{7} - 5238 \, x^{5} + 3807 \, x^{3} - 243 \, x\right)} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(432^{\frac{5}{6}} {\left(x^{11} - 1215 \, x^{9} + 11754 \, x^{7} - 21006 \, x^{5} + 5589 \, x^{3} - 243 \, x\right)} + 432 \, \sqrt{3} 2^{\frac{1}{3}} {\left(13 \, x^{10} - 120 \, x^{8} + 1242 \, x^{6} - 1728 \, x^{4} + 81 \, x^{2}\right)}\right)}}{18 \, {\left(x^{12} - 8334 \, x^{10} + 110727 \, x^{8} - 301860 \, x^{6} + 187839 \, x^{4} - 21870 \, x^{2} + 729\right)}}\right)"," ",0,"-1/20736*432^(5/6)*sqrt(3)*log(10368*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 1/20736*432^(5/6)*sqrt(3)*log(2592*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) + 1/20736*432^(5/6)*sqrt(3)*log(10368*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) + 1/20736*432^(5/6)*sqrt(3)*log(2592*(6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 1/1296*432^(5/6)*arctan(1/36*(432^(5/6)*(x^5 - 18*x^3 + 9*x)*(-x^2 + 1)^(1/3) + sqrt(3)*2^(1/3)*(432^(5/6)*(x^4 + 9*x^2)*(-x^2 + 1)^(2/3) - 288*sqrt(3)*(2*x^4 - 3*x^2)*(-x^2 + 1)^(1/3) + 6*432^(1/6)*(x^6 + 141*x^4 - 153*x^2 + 27)) - 648*432^(1/6)*(3*x^3 - x)*(-x^2 + 1)^(2/3) - 72*sqrt(3)*(7*x^5 + 6*x^3 - 9*x))/(x^6 - 225*x^4 + 243*x^2 - 27)) - 1/2592*432^(5/6)*arctan(-1/18*(sqrt(2)*(18*sqrt(3)*2^(2/3)*(29*x^11 + 879*x^9 - 12078*x^7 + 10638*x^5 - 3807*x^3 + 243*x) - 2*(-x^2 + 1)^(2/3)*(432^(5/6)*(x^10 + 153*x^8 - 1701*x^6 + 459*x^4) - 216*sqrt(3)*2^(1/3)*(31*x^9 - 297*x^7 - 27*x^5 - 27*x^3)) - 36*(-x^2 + 1)^(1/3)*(sqrt(3)*(x^11 + 1167*x^9 - 13158*x^7 + 17550*x^5 - 4779*x^3 + 243*x) - 8*sqrt(3)*(13*x^10 - 6*x^8 - 1404*x^6 + 1350*x^4 - 81*x^2)) - 3*432^(1/6)*(x^12 + 7620*x^10 - 92115*x^8 + 169776*x^6 - 109269*x^4 + 16524*x^2 - 729))*sqrt((6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) + 144*432^(1/6)*sqrt(3)*(x^5 - x^3) + (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) + 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) - 72*(x^5 + 18*x^4 + 24*x^3 - 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 216*(sqrt(3)*2^(2/3)*(x^10 + 144*x^8 - 918*x^6 + 2808*x^4 - 243*x^2) - 3*432^(1/6)*(31*x^9 - 568*x^7 + 1710*x^5 - 432*x^3 + 27*x))*(-x^2 + 1)^(2/3) - 18*sqrt(3)*(x^12 - 366*x^10 + 14535*x^8 - 42660*x^6 + 58239*x^4 - 14094*x^2 + 729) + 144*sqrt(3)*(11*x^11 - 807*x^9 + 4518*x^7 - 5238*x^5 + 3807*x^3 - 243*x) - (-x^2 + 1)^(1/3)*(432^(5/6)*(x^11 - 1215*x^9 + 11754*x^7 - 21006*x^5 + 5589*x^3 - 243*x) - 432*sqrt(3)*2^(1/3)*(13*x^10 - 120*x^8 + 1242*x^6 - 1728*x^4 + 81*x^2)))/(x^12 - 8334*x^10 + 110727*x^8 - 301860*x^6 + 187839*x^4 - 21870*x^2 + 729)) - 1/2592*432^(5/6)*arctan(1/18*(sqrt(2)*(18*sqrt(3)*2^(2/3)*(29*x^11 + 879*x^9 - 12078*x^7 + 10638*x^5 - 3807*x^3 + 243*x) + 2*(-x^2 + 1)^(2/3)*(432^(5/6)*(x^10 + 153*x^8 - 1701*x^6 + 459*x^4) + 216*sqrt(3)*2^(1/3)*(31*x^9 - 297*x^7 - 27*x^5 - 27*x^3)) - 36*(-x^2 + 1)^(1/3)*(sqrt(3)*(x^11 + 1167*x^9 - 13158*x^7 + 17550*x^5 - 4779*x^3 + 243*x) + 8*sqrt(3)*(13*x^10 - 6*x^8 - 1404*x^6 + 1350*x^4 - 81*x^2)) + 3*432^(1/6)*(x^12 + 7620*x^10 - 92115*x^8 + 169776*x^6 - 109269*x^4 + 16524*x^2 - 729))*sqrt((6*2^(2/3)*(x^6 + 225*x^4 - 189*x^2 + 27) - 144*432^(1/6)*sqrt(3)*(x^5 - x^3) - (432^(5/6)*sqrt(3)*(7*x^3 - 3*x) - 216*2^(1/3)*(x^4 + 3*x^2))*(-x^2 + 1)^(2/3) + 72*(x^5 - 18*x^4 + 24*x^3 + 18*x^2 - 9*x)*(-x^2 + 1)^(1/3))/(x^6 + 9*x^4 + 27*x^2 + 27)) - 216*(sqrt(3)*2^(2/3)*(x^10 + 144*x^8 - 918*x^6 + 2808*x^4 - 243*x^2) + 3*432^(1/6)*(31*x^9 - 568*x^7 + 1710*x^5 - 432*x^3 + 27*x))*(-x^2 + 1)^(2/3) - 18*sqrt(3)*(x^12 - 366*x^10 + 14535*x^8 - 42660*x^6 + 58239*x^4 - 14094*x^2 + 729) - 144*sqrt(3)*(11*x^11 - 807*x^9 + 4518*x^7 - 5238*x^5 + 3807*x^3 - 243*x) + (-x^2 + 1)^(1/3)*(432^(5/6)*(x^11 - 1215*x^9 + 11754*x^7 - 21006*x^5 + 5589*x^3 - 243*x) + 432*sqrt(3)*2^(1/3)*(13*x^10 - 120*x^8 + 1242*x^6 - 1728*x^4 + 81*x^2)))/(x^12 - 8334*x^10 + 110727*x^8 - 301860*x^6 + 187839*x^4 - 21870*x^2 + 729))","B",0
1017,0,0,0,3.674589," ","integrate(1/x^2/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{6} + 2 \, x^{4} - 3 \, x^{2}}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)/(x^6 + 2*x^4 - 3*x^2), x)","F",0
1018,0,0,0,3.844537," ","integrate(1/x^4/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{8} + 2 \, x^{6} - 3 \, x^{4}}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)/(x^8 + 2*x^6 - 3*x^4), x)","F",0
1019,1,133,0,1.031260," ","integrate(x^7/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(660 \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(x^{2} + 3\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - 165 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + 330 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 8 \, {\left(4 \, x^{4} - 42 \, x^{2} - 207\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right)}}{320 \, {\left(x^{2} + 3\right)}}"," ",0,"3/320*(660*4^(1/6)*sqrt(3)*(x^2 + 3)*arctan(1/6*4^(1/6)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 165*4^(2/3)*(x^2 + 3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 330*4^(2/3)*(x^2 + 3)*log(-4^(1/3) + (-x^2 + 1)^(1/3)) - 8*(4*x^4 - 42*x^2 - 207)*(-x^2 + 1)^(2/3))/(x^2 + 3)","A",0
1020,1,153,0,1.147662," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(28 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(2 \, \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}}\right)}\right) + 7 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) - 14 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + 8 \, {\left(2 \, x^{2} + 9\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right)}}{64 \, {\left(x^{2} + 3\right)}}"," ",0,"-3/64*(28*4^(1/6)*sqrt(3)*(-1)^(1/3)*(x^2 + 3)*arctan(1/6*4^(1/6)*sqrt(3)*(2*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3))) + 7*4^(2/3)*(-1)^(1/3)*(x^2 + 3)*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) - 14*4^(2/3)*(-1)^(1/3)*(x^2 + 3)*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) + 8*(2*x^2 + 9)*(-x^2 + 1)^(2/3))/(x^2 + 3)","A",0
1021,1,121,0,1.035810," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(4 \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(x^{2} + 3\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + 2 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + 8 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right)}}{64 \, {\left(x^{2} + 3\right)}}"," ",0,"3/64*(4*4^(1/6)*sqrt(3)*(x^2 + 3)*arctan(1/6*4^(1/6)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 4^(2/3)*(x^2 + 3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 2*4^(2/3)*(x^2 + 3)*log(-4^(1/3) + (-x^2 + 1)^(1/3)) + 8*(-x^2 + 1)^(2/3))/(x^2 + 3)","A",0
1022,1,125,0,0.959774," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(x^{2} + 3\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{1}{3}} \sqrt{3} + 2 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + 2 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 3\right)} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 24 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{192 \, {\left(x^{2} + 3\right)}}"," ",0,"1/192*(4*4^(1/6)*sqrt(3)*(x^2 + 3)*arctan(1/6*4^(1/6)*(4^(1/3)*sqrt(3) + 2*sqrt(3)*(-x^2 + 1)^(1/3))) - 4^(2/3)*(x^2 + 3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 2*4^(2/3)*(x^2 + 3)*log(-4^(1/3) + (-x^2 + 1)^(1/3)) - 24*(-x^2 + 1)^(2/3))/(x^2 + 3)","A",0
1023,1,227,0,1.292277," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","-\frac{20 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(2 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}} \sqrt{3}\right)}\right) + 5 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) - 10 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 32 \, \sqrt{3} {\left(x^{2} + 3\right)} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 16 \, {\left(x^{2} + 3\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - 32 \, {\left(x^{2} + 3\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 1\right) - 24 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{576 \, {\left(x^{2} + 3\right)}}"," ",0,"-1/576*(20*4^(1/6)*sqrt(3)*(-1)^(1/3)*(x^2 + 3)*arctan(1/6*4^(1/6)*(2*sqrt(3)*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3)*sqrt(3))) + 5*4^(2/3)*(-1)^(1/3)*(x^2 + 3)*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) - 10*4^(2/3)*(-1)^(1/3)*(x^2 + 3)*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) - 32*sqrt(3)*(x^2 + 3)*arctan(2/3*sqrt(3)*(-x^2 + 1)^(1/3) + 1/3*sqrt(3)) + 16*(x^2 + 3)*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) - 32*(x^2 + 3)*log((-x^2 + 1)^(1/3) - 1) - 24*(-x^2 + 1)^(2/3))/(x^2 + 3)","A",0
1024,1,238,0,1.170238," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","\frac{36 \cdot 4^{\frac{1}{6}} \sqrt{3} {\left(x^{4} + 3 \, x^{2}\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{1}{3}} \sqrt{3} + 2 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - 9 \cdot 4^{\frac{2}{3}} {\left(x^{4} + 3 \, x^{2}\right)} \log\left(4^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) + 18 \cdot 4^{\frac{2}{3}} {\left(x^{4} + 3 \, x^{2}\right)} \log\left(-4^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 32 \, \sqrt{3} {\left(x^{4} + 3 \, x^{2}\right)} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 16 \, {\left(x^{4} + 3 \, x^{2}\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - 32 \, {\left(x^{4} + 3 \, x^{2}\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 1\right) - 24 \, {\left(5 \, x^{2} + 12\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{1728 \, {\left(x^{4} + 3 \, x^{2}\right)}}"," ",0,"1/1728*(36*4^(1/6)*sqrt(3)*(x^4 + 3*x^2)*arctan(1/6*4^(1/6)*(4^(1/3)*sqrt(3) + 2*sqrt(3)*(-x^2 + 1)^(1/3))) - 9*4^(2/3)*(x^4 + 3*x^2)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 18*4^(2/3)*(x^4 + 3*x^2)*log(-4^(1/3) + (-x^2 + 1)^(1/3)) - 32*sqrt(3)*(x^4 + 3*x^2)*arctan(2/3*sqrt(3)*(-x^2 + 1)^(1/3) + 1/3*sqrt(3)) + 16*(x^4 + 3*x^2)*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) - 32*(x^4 + 3*x^2)*log((-x^2 + 1)^(1/3) - 1) - 24*(5*x^2 + 12)*(-x^2 + 1)^(2/3))/(x^4 + 3*x^2)","A",0
1025,1,265,0,0.702893," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","-\frac{52 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(x^{6} + 3 \, x^{4}\right)} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(2 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}} \sqrt{3}\right)}\right) + 13 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{6} + 3 \, x^{4}\right)} \log\left(4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{2} + 1\right)}^{\frac{2}{3}}\right) - 26 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{6} + 3 \, x^{4}\right)} \log\left(-4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - 96 \, \sqrt{3} {\left(x^{6} + 3 \, x^{4}\right)} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 48 \, {\left(x^{6} + 3 \, x^{4}\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - 96 \, {\left(x^{6} + 3 \, x^{4}\right)} \log\left({\left(-x^{2} + 1\right)}^{\frac{1}{3}} - 1\right) - 24 \, {\left(x^{4} - 6 \, x^{2} - 18\right)} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{5184 \, {\left(x^{6} + 3 \, x^{4}\right)}}"," ",0,"-1/5184*(52*4^(1/6)*sqrt(3)*(-1)^(1/3)*(x^6 + 3*x^4)*arctan(1/6*4^(1/6)*(2*sqrt(3)*(-1)^(1/3)*(-x^2 + 1)^(1/3) - 4^(1/3)*sqrt(3))) + 13*4^(2/3)*(-1)^(1/3)*(x^6 + 3*x^4)*log(4^(1/3)*(-1)^(2/3)*(-x^2 + 1)^(1/3) - 4^(2/3)*(-1)^(1/3) + (-x^2 + 1)^(2/3)) - 26*4^(2/3)*(-1)^(1/3)*(x^6 + 3*x^4)*log(-4^(1/3)*(-1)^(2/3) + (-x^2 + 1)^(1/3)) - 96*sqrt(3)*(x^6 + 3*x^4)*arctan(2/3*sqrt(3)*(-x^2 + 1)^(1/3) + 1/3*sqrt(3)) + 48*(x^6 + 3*x^4)*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) - 96*(x^6 + 3*x^4)*log((-x^2 + 1)^(1/3) - 1) - 24*(x^4 - 6*x^2 - 18)*(-x^2 + 1)^(2/3))/(x^6 + 3*x^4)","A",0
1026,0,0,0,4.783719," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}} x^{4}}{x^{6} + 5 \, x^{4} + 3 \, x^{2} - 9}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)*x^4/(x^6 + 5*x^4 + 3*x^2 - 9), x)","F",0
1027,0,0,0,3.197237," ","integrate(x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}} x^{2}}{x^{6} + 5 \, x^{4} + 3 \, x^{2} - 9}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)*x^2/(x^6 + 5*x^4 + 3*x^2 - 9), x)","F",0
1028,0,0,0,2.836017," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{6} + 5 \, x^{4} + 3 \, x^{2} - 9}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)/(x^6 + 5*x^4 + 3*x^2 - 9), x)","F",0
1029,0,0,0,4.990731," ","integrate(1/x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{8} + 5 \, x^{6} + 3 \, x^{4} - 9 \, x^{2}}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)/(x^8 + 5*x^6 + 3*x^4 - 9*x^2), x)","F",0
1030,0,0,0,6.459475," ","integrate(1/x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{x^{10} + 5 \, x^{8} + 3 \, x^{6} - 9 \, x^{4}}, x\right)"," ",0,"integral(-(-x^2 + 1)^(2/3)/(x^10 + 5*x^8 + 3*x^6 - 9*x^4), x)","F",0
1031,1,253,0,1.283767," ","integrate(x^7/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{2}{18711} \, {\left(189 \, x^{4} + 540 \, x^{2} + 1712\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} + \frac{32}{81} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{32}{81} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) + \frac{8}{81} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right) - \frac{8}{81} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"2/18711*(189*x^4 + 540*x^2 + 1712)*(-3*x^2 + 2)^(3/4) + 32/81*8^(1/4)*sqrt(2)*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 32/81*8^(1/4)*sqrt(2)*arctan(1/8*8^(1/4)*sqrt(2)*sqrt(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) + 8/81*8^(1/4)*sqrt(2)*log(4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 8/81*8^(1/4)*sqrt(2)*log(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2))","B",0
1032,1,246,0,1.166155," ","integrate(x^5/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{2}{63} \, {\left(x^{2} + 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} + \frac{8}{27} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{8}{27} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) + \frac{2}{27} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right) - \frac{2}{27} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"2/63*(x^2 + 4)*(-3*x^2 + 2)^(3/4) + 8/27*8^(1/4)*sqrt(2)*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 8/27*8^(1/4)*sqrt(2)*arctan(1/8*8^(1/4)*sqrt(2)*sqrt(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) + 2/27*8^(1/4)*sqrt(2)*log(4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 2/27*8^(1/4)*sqrt(2)*log(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2))","B",0
1033,1,241,0,1.138432," ","integrate(x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{2}{9} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{2}{9} \cdot 8^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{18} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right) - \frac{1}{18} \cdot 8^{\frac{1}{4}} \sqrt{2} \log\left(-4 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 16 \, \sqrt{2} + 16 \, \sqrt{-3 \, x^{2} + 2}\right) + \frac{2}{27} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}"," ",0,"2/9*8^(1/4)*sqrt(2)*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 2/9*8^(1/4)*sqrt(2)*arctan(1/8*8^(1/4)*sqrt(2)*sqrt(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) + 1/18*8^(1/4)*sqrt(2)*log(4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) - 1/18*8^(1/4)*sqrt(2)*log(-4*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 16*sqrt(2) + 16*sqrt(-3*x^2 + 2)) + 2/27*(-3*x^2 + 2)^(3/4)","B",0
1034,1,189,0,1.395072," ","integrate(x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{3} \cdot 2^{\frac{1}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{3} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{12} \cdot 2^{\frac{1}{4}} \log\left(4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right) - \frac{1}{12} \cdot 2^{\frac{1}{4}} \log\left(-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"1/3*2^(1/4)*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) + 1/3*2^(1/4)*arctan(1/2*2^(1/4)*sqrt(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) + 1/12*2^(1/4)*log(4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/12*2^(1/4)*log(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2))","B",0
1035,1,270,0,1.467673," ","integrate(1/x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","-\frac{1}{4} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{1}{16} \cdot 2^{\frac{3}{4}} \log\left(-2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{4} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{16} \cdot 2^{\frac{1}{4}} \log\left(4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} \log\left(-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"-1/4*2^(3/4)*arctan(1/2*2^(3/4)*sqrt(sqrt(2) + sqrt(-3*x^2 + 2)) - 1/2*2^(3/4)*(-3*x^2 + 2)^(1/4)) - 1/16*2^(3/4)*log(2^(1/4) + (-3*x^2 + 2)^(1/4)) + 1/16*2^(3/4)*log(-2^(1/4) + (-3*x^2 + 2)^(1/4)) + 1/4*2^(1/4)*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) + 1/4*2^(1/4)*arctan(1/2*2^(1/4)*sqrt(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) + 1/16*2^(1/4)*log(4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/16*2^(1/4)*log(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2))","B",0
1036,1,307,0,1.272285," ","integrate(1/x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","-\frac{36 \cdot 2^{\frac{3}{4}} x^{2} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{\sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + 9 \cdot 2^{\frac{3}{4}} x^{2} \log\left(2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - 9 \cdot 2^{\frac{3}{4}} x^{2} \log\left(-2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - 24 \cdot 2^{\frac{1}{4}} x^{2} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) - 24 \cdot 2^{\frac{1}{4}} x^{2} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - 6 \cdot 2^{\frac{1}{4}} x^{2} \log\left(4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right) + 6 \cdot 2^{\frac{1}{4}} x^{2} \log\left(-4 \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}\right) + 8 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}{128 \, x^{2}}"," ",0,"-1/128*(36*2^(3/4)*x^2*arctan(1/2*2^(3/4)*sqrt(sqrt(2) + sqrt(-3*x^2 + 2)) - 1/2*2^(3/4)*(-3*x^2 + 2)^(1/4)) + 9*2^(3/4)*x^2*log(2^(1/4) + (-3*x^2 + 2)^(1/4)) - 9*2^(3/4)*x^2*log(-2^(1/4) + (-3*x^2 + 2)^(1/4)) - 24*2^(1/4)*x^2*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) - 24*2^(1/4)*x^2*arctan(1/2*2^(1/4)*sqrt(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) - 6*2^(1/4)*x^2*log(4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) + 6*2^(1/4)*x^2*log(-4*2^(3/4)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) + 8*(-3*x^2 + 2)^(3/4))/x^2","B",0
1037,0,0,0,6.916135," ","integrate(x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x^{4}}{9 \, x^{4} - 18 \, x^{2} + 8}, x\right)"," ",0,"integral((-3*x^2 + 2)^(3/4)*x^4/(9*x^4 - 18*x^2 + 8), x)","F",0
1038,0,0,0,7.265825," ","integrate(x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x^{2}}{9 \, x^{4} - 18 \, x^{2} + 8}, x\right)"," ",0,"integral((-3*x^2 + 2)^(3/4)*x^2/(9*x^4 - 18*x^2 + 8), x)","F",0
1039,1,553,0,6.600167," ","integrate(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(-\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} + 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x + 12 \, \sqrt{2} {\left(3 \, x^{2} - 4\right)} \sqrt{-3 \, x^{2} + 2} - 72 \, x^{2} + {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} \sqrt{-3 \, x^{2} + 2} - 72 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} - 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} - 48 \, \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{-\frac{3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 4}}}{6 \, {\left(9 \, x^{4} + 24 \, x^{2} - 16\right)}}\right) - \frac{1}{72} \cdot 18^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{6 \cdot 18^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3} - 54 \, x^{4} + 24 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x - 12 \, \sqrt{2} {\left(3 \, x^{2} - 4\right)} \sqrt{-3 \, x^{2} + 2} + 72 \, x^{2} + {\left(18^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{3} + 4 \, x\right)} \sqrt{-3 \, x^{2} + 2} + 72 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2} - 6 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{3} - 4 \, x\right)} + 48 \, \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}\right)} \sqrt{-\frac{3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}}{3 \, x^{2} - 4}}}{6 \, {\left(9 \, x^{4} + 24 \, x^{2} - 16\right)}}\right) + \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{36 \, {\left(3 \, \sqrt{2} x^{2} + 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}\right)}}{3 \, x^{2} - 4}\right) - \frac{1}{288} \cdot 18^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{36 \, {\left(3 \, \sqrt{2} x^{2} - 2 \cdot 18^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 4 \, \sqrt{-3 \, x^{2} + 2}\right)}}{3 \, x^{2} - 4}\right)"," ",0,"1/72*18^(3/4)*sqrt(2)*arctan(-1/6*(6*18^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x^3 + 54*x^4 + 24*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(3/4)*x + 12*sqrt(2)*(3*x^2 - 4)*sqrt(-3*x^2 + 2) - 72*x^2 + (18^(3/4)*sqrt(2)*(3*x^3 + 4*x)*sqrt(-3*x^2 + 2) - 72*(-3*x^2 + 2)^(1/4)*x^2 - 6*18^(1/4)*sqrt(2)*(3*x^3 - 4*x) - 48*sqrt(2)*(-3*x^2 + 2)^(3/4))*sqrt(-(3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)))/(9*x^4 + 24*x^2 - 16)) - 1/72*18^(3/4)*sqrt(2)*arctan(1/6*(6*18^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x^3 - 54*x^4 + 24*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(3/4)*x - 12*sqrt(2)*(3*x^2 - 4)*sqrt(-3*x^2 + 2) + 72*x^2 + (18^(3/4)*sqrt(2)*(3*x^3 + 4*x)*sqrt(-3*x^2 + 2) + 72*(-3*x^2 + 2)^(1/4)*x^2 - 6*18^(1/4)*sqrt(2)*(3*x^3 - 4*x) + 48*sqrt(2)*(-3*x^2 + 2)^(3/4))*sqrt(-(3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)))/(9*x^4 + 24*x^2 - 16)) + 1/288*18^(3/4)*sqrt(2)*log(-36*(3*sqrt(2)*x^2 + 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4)) - 1/288*18^(3/4)*sqrt(2)*log(-36*(3*sqrt(2)*x^2 - 2*18^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 4*sqrt(-3*x^2 + 2))/(3*x^2 - 4))","B",0
1040,0,0,0,7.953691," ","integrate(1/x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}{9 \, x^{6} - 18 \, x^{4} + 8 \, x^{2}}, x\right)"," ",0,"integral((-3*x^2 + 2)^(3/4)/(9*x^6 - 18*x^4 + 8*x^2), x)","F",0
1041,0,0,0,8.869967," ","integrate(1/x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}{9 \, x^{8} - 18 \, x^{6} + 8 \, x^{4}}, x\right)"," ",0,"integral((-3*x^2 + 2)^(3/4)/(9*x^8 - 18*x^6 + 8*x^4), x)","F",0
1042,1,64,0,0.901093," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{2}{18711} \, {\left(189 \, x^{4} + 270 \, x^{2} + 428\right)} {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} + \frac{8}{81} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{4}{81} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{4}{81} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/18711*(189*x^4 + 270*x^2 + 428)*(3*x^2 - 1)^(3/4) + 8/81*arctan((3*x^2 - 1)^(1/4)) - 4/81*log((3*x^2 - 1)^(1/4) + 1) + 4/81*log((3*x^2 - 1)^(1/4) - 1)","A",0
1043,1,57,0,0.913603," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{2}{63} \, {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(x^{2} + 2\right)} + \frac{4}{27} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{2}{27} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{2}{27} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/63*(3*x^2 - 1)^(3/4)*(x^2 + 2) + 4/27*arctan((3*x^2 - 1)^(1/4)) - 2/27*log((3*x^2 - 1)^(1/4) + 1) + 2/27*log((3*x^2 - 1)^(1/4) - 1)","A",0
1044,1,52,0,0.953014," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{2}{27} \, {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} + \frac{2}{9} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/27*(3*x^2 - 1)^(3/4) + 2/9*arctan((3*x^2 - 1)^(1/4)) - 1/9*log((3*x^2 - 1)^(1/4) + 1) + 1/9*log((3*x^2 - 1)^(1/4) - 1)","A",0
1045,1,41,0,0.904964," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{1}{3} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log((3*x^2 - 1)^(1/4) - 1)","A",0
1046,1,215,0,0.774842," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) - \frac{1}{8} \, \sqrt{2} \log\left(-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) + \frac{1}{2} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{4} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - sqrt(2)*(3*x^2 - 1)^(1/4) - 1) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - sqrt(2)*(3*x^2 - 1)^(1/4) + 1) + 1/8*sqrt(2)*log(4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - 1/8*sqrt(2)*log(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) + 1/2*arctan((3*x^2 - 1)^(1/4)) - 1/4*log((3*x^2 - 1)^(1/4) + 1) + 1/4*log((3*x^2 - 1)^(1/4) - 1)","A",0
1047,1,252,0,1.032638," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{36 \, \sqrt{2} x^{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) + 36 \, \sqrt{2} x^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + 9 \, \sqrt{2} x^{2} \log\left(4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) - 9 \, \sqrt{2} x^{2} \log\left(-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) + 24 \, x^{2} \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - 12 \, x^{2} \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + 12 \, x^{2} \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) - 8 \, {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}}}{32 \, x^{2}}"," ",0,"1/32*(36*sqrt(2)*x^2*arctan(sqrt(2)*sqrt(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - sqrt(2)*(3*x^2 - 1)^(1/4) - 1) + 36*sqrt(2)*x^2*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - sqrt(2)*(3*x^2 - 1)^(1/4) + 1) + 9*sqrt(2)*x^2*log(4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - 9*sqrt(2)*x^2*log(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) + 24*x^2*arctan((3*x^2 - 1)^(1/4)) - 12*x^2*log((3*x^2 - 1)^(1/4) + 1) + 12*x^2*log((3*x^2 - 1)^(1/4) - 1) - 8*(3*x^2 - 1)^(3/4))/x^2","A",0
1048,0,0,0,9.107769," ","integrate(x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x^{4}}{9 \, x^{4} - 9 \, x^{2} + 2}, x\right)"," ",0,"integral((3*x^2 - 1)^(3/4)*x^4/(9*x^4 - 9*x^2 + 2), x)","F",0
1049,0,0,0,7.070421," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x^{2}}{9 \, x^{4} - 9 \, x^{2} + 2}, x\right)"," ",0,"integral((3*x^2 - 1)^(3/4)*x^2/(9*x^4 - 9*x^2 + 2), x)","F",0
1050,1,104,0,6.595600," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \arctan\left(\frac{\sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, x}\right) + \frac{1}{24} \, \sqrt{6} \log\left(-\frac{9 \, x^{4} - 6 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{3} + 12 \, \sqrt{3 \, x^{2} - 1} x^{2} - 4 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x + 12 \, x^{2} - 4}{9 \, x^{4} - 12 \, x^{2} + 4}\right)"," ",0,"1/12*sqrt(6)*arctan(1/3*sqrt(6)*(3*x^2 - 1)^(1/4)/x) + 1/24*sqrt(6)*log(-(9*x^4 - 6*sqrt(6)*(3*x^2 - 1)^(1/4)*x^3 + 12*sqrt(3*x^2 - 1)*x^2 - 4*sqrt(6)*(3*x^2 - 1)^(3/4)*x + 12*x^2 - 4)/(9*x^4 - 12*x^2 + 4))","B",0
1051,0,0,0,7.104883," ","integrate(1/x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}}}{9 \, x^{6} - 9 \, x^{4} + 2 \, x^{2}}, x\right)"," ",0,"integral((3*x^2 - 1)^(3/4)/(9*x^6 - 9*x^4 + 2*x^2), x)","F",0
1052,0,0,0,8.932801," ","integrate(1/x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}}}{9 \, x^{8} - 9 \, x^{6} + 2 \, x^{4}}, x\right)"," ",0,"integral((3*x^2 - 1)^(3/4)/(9*x^8 - 9*x^6 + 2*x^4), x)","F",0
1053,1,282,0,1.083335," ","integrate(x^2/(3*x^2+2)^(3/4)/(3*x^2+4),x, algorithm=""fricas"")","\frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{\frac{72^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 36 \, x}{36 \, x}\right) + \frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{-\frac{72^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 36 \, x}{36 \, x}\right) - \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{3 \, x^{2} + 2}\right)}}{x^{2}}\right) + \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{3 \, x^{2} + 2}\right)}}{x^{2}}\right)"," ",0,"1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt((72^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4) - 36*x)/x) + 1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt(-(72^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(3*x^2 + 2)^(1/4) + 36*x)/x) - 1/864*72^(3/4)*sqrt(2)*log(96*(72^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(3*x^2 + 2))/x^2) + 1/864*72^(3/4)*sqrt(2)*log(-96*(72^(3/4)*sqrt(2)*(3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(3*x^2 + 2))/x^2)","B",0
1054,1,282,0,1.083391," ","integrate(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{\frac{72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{-3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 36 \, x}{36 \, x}\right) + \frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{-\frac{72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{-3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 36 \, x}{36 \, x}\right) - \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{-3 \, x^{2} + 2}\right)}}{x^{2}}\right) + \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{-3 \, x^{2} + 2}\right)}}{x^{2}}\right)"," ",0,"1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt((72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(-3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 36*x)/x) + 1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt(-(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(-3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 36*x)/x) - 1/864*72^(3/4)*sqrt(2)*log(96*(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(-3*x^2 + 2))/x^2) + 1/864*72^(3/4)*sqrt(2)*log(-96*(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(-3*x^2 + 2))/x^2)","B",0
1055,1,393,0,1.103678," ","integrate(x^2/(b*x^2+2)^(3/4)/(b*x^2+4),x, algorithm=""fricas"")","\sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \arctan\left(\frac{8 \, \sqrt{2} \sqrt{\frac{1}{2}} \left(\frac{1}{8}\right)^{\frac{3}{4}} b^{4} \sqrt{\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} + 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{b x^{2} + 2}}{x^{2}}} \frac{1}{b^{6}}^{\frac{3}{4}} x - 8 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{4} \frac{1}{b^{6}}^{\frac{3}{4}} - x}{x}\right) + \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \arctan\left(\frac{8 \, \sqrt{2} \sqrt{\frac{1}{2}} \left(\frac{1}{8}\right)^{\frac{3}{4}} b^{4} \sqrt{\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} - 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{b x^{2} + 2}}{x^{2}}} \frac{1}{b^{6}}^{\frac{3}{4}} x - 8 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{4} \frac{1}{b^{6}}^{\frac{3}{4}} + x}{x}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \log\left(\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} + 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{b x^{2} + 2}}{2 \, x^{2}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \log\left(\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} - 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{b x^{2} + 2}}{2 \, x^{2}}\right)"," ",0,"sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*arctan((8*sqrt(2)*sqrt(1/2)*(1/8)^(3/4)*b^4*sqrt((sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 + 2*sqrt(2)*(1/8)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(b*x^2 + 2))/x^2)*(b^(-6))^(3/4)*x - 8*sqrt(2)*(1/8)^(3/4)*(b*x^2 + 2)^(1/4)*b^4*(b^(-6))^(3/4) - x)/x) + sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*arctan((8*sqrt(2)*sqrt(1/2)*(1/8)^(3/4)*b^4*sqrt((sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 - 2*sqrt(2)*(1/8)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(b*x^2 + 2))/x^2)*(b^(-6))^(3/4)*x - 8*sqrt(2)*(1/8)^(3/4)*(b*x^2 + 2)^(1/4)*b^4*(b^(-6))^(3/4) + x)/x) - 1/4*sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*log(1/2*(sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 + 2*sqrt(2)*(1/8)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(b*x^2 + 2))/x^2) + 1/4*sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*log(1/2*(sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 - 2*sqrt(2)*(1/8)^(1/4)*(b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(b*x^2 + 2))/x^2)","B",0
1056,1,403,0,0.945381," ","integrate(x^2/(-b*x^2+2)^(3/4)/(-b*x^2+4),x, algorithm=""fricas"")","\sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \arctan\left(\frac{8 \, \sqrt{2} \sqrt{\frac{1}{2}} \left(\frac{1}{8}\right)^{\frac{3}{4}} b^{4} \sqrt{\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} + 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{-b x^{2} + 2}}{x^{2}}} \frac{1}{b^{6}}^{\frac{3}{4}} x - 8 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{4} \frac{1}{b^{6}}^{\frac{3}{4}} - x}{x}\right) + \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \arctan\left(\frac{8 \, \sqrt{2} \sqrt{\frac{1}{2}} \left(\frac{1}{8}\right)^{\frac{3}{4}} b^{4} \frac{1}{b^{6}}^{\frac{3}{4}} x \sqrt{\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} - 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{-b x^{2} + 2}}{x^{2}}} - 8 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{3}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{4} \frac{1}{b^{6}}^{\frac{3}{4}} + x}{x}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \log\left(\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} + 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{-b x^{2} + 2}}{2 \, x^{2}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} \frac{1}{b^{6}}^{\frac{1}{4}} \log\left(\frac{\sqrt{\frac{1}{2}} b^{4} \sqrt{\frac{1}{b^{6}}} x^{2} - 2 \, \sqrt{2} \left(\frac{1}{8}\right)^{\frac{1}{4}} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}} b^{2} \frac{1}{b^{6}}^{\frac{1}{4}} x + 2 \, \sqrt{-b x^{2} + 2}}{2 \, x^{2}}\right)"," ",0,"sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*arctan((8*sqrt(2)*sqrt(1/2)*(1/8)^(3/4)*b^4*sqrt((sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 + 2*sqrt(2)*(1/8)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(-b*x^2 + 2))/x^2)*(b^(-6))^(3/4)*x - 8*sqrt(2)*(1/8)^(3/4)*(-b*x^2 + 2)^(1/4)*b^4*(b^(-6))^(3/4) - x)/x) + sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*arctan((8*sqrt(2)*sqrt(1/2)*(1/8)^(3/4)*b^4*(b^(-6))^(3/4)*x*sqrt((sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 - 2*sqrt(2)*(1/8)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(-b*x^2 + 2))/x^2) - 8*sqrt(2)*(1/8)^(3/4)*(-b*x^2 + 2)^(1/4)*b^4*(b^(-6))^(3/4) + x)/x) - 1/4*sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*log(1/2*(sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 + 2*sqrt(2)*(1/8)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(-b*x^2 + 2))/x^2) + 1/4*sqrt(2)*(1/8)^(1/4)*(b^(-6))^(1/4)*log(1/2*(sqrt(1/2)*b^4*sqrt(b^(-6))*x^2 - 2*sqrt(2)*(1/8)^(1/4)*(-b*x^2 + 2)^(1/4)*b^2*(b^(-6))^(1/4)*x + 2*sqrt(-b*x^2 + 2))/x^2)","B",0
1057,1,171,0,0.921553," ","integrate(x^2/(3*x^2+a)^(3/4)/(3*x^2+2*a),x, algorithm=""fricas"")","-\frac{2}{3} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \arctan\left(\frac{12 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{36}\right)^{\frac{3}{4}} a x \left(-\frac{1}{a}\right)^{\frac{3}{4}} \sqrt{\frac{3 \, x^{2} \sqrt{-\frac{1}{a}} + 2 \, \sqrt{3 \, x^{2} + a}}{x^{2}}} - \left(\frac{1}{36}\right)^{\frac{3}{4}} {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{6} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \log\left(\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x \left(-\frac{1}{a}\right)^{\frac{1}{4}} + {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{6} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \log\left(-\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x \left(-\frac{1}{a}\right)^{\frac{1}{4}} - {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-2/3*(1/36)^(1/4)*(-1/a)^(1/4)*arctan(12*(sqrt(1/2)*(1/36)^(3/4)*a*x*(-1/a)^(3/4)*sqrt((3*x^2*sqrt(-1/a) + 2*sqrt(3*x^2 + a))/x^2) - (1/36)^(3/4)*(3*x^2 + a)^(1/4)*a*(-1/a)^(3/4))/x) - 1/6*(1/36)^(1/4)*(-1/a)^(1/4)*log((3*(1/36)^(1/4)*x*(-1/a)^(1/4) + (3*x^2 + a)^(1/4))/x) + 1/6*(1/36)^(1/4)*(-1/a)^(1/4)*log(-(3*(1/36)^(1/4)*x*(-1/a)^(1/4) - (3*x^2 + a)^(1/4))/x)","A",0
1058,1,171,0,0.820740," ","integrate(x^2/(-3*x^2+a)^(3/4)/(-3*x^2+2*a),x, algorithm=""fricas"")","-\frac{2}{3} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \arctan\left(\frac{12 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{36}\right)^{\frac{3}{4}} a x \left(-\frac{1}{a}\right)^{\frac{3}{4}} \sqrt{\frac{3 \, x^{2} \sqrt{-\frac{1}{a}} + 2 \, \sqrt{-3 \, x^{2} + a}}{x^{2}}} - \left(\frac{1}{36}\right)^{\frac{3}{4}} {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}} a \left(-\frac{1}{a}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{6} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \log\left(\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x \left(-\frac{1}{a}\right)^{\frac{1}{4}} + {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{6} \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \left(-\frac{1}{a}\right)^{\frac{1}{4}} \log\left(-\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x \left(-\frac{1}{a}\right)^{\frac{1}{4}} - {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-2/3*(1/36)^(1/4)*(-1/a)^(1/4)*arctan(12*(sqrt(1/2)*(1/36)^(3/4)*a*x*(-1/a)^(3/4)*sqrt((3*x^2*sqrt(-1/a) + 2*sqrt(-3*x^2 + a))/x^2) - (1/36)^(3/4)*(-3*x^2 + a)^(1/4)*a*(-1/a)^(3/4))/x) - 1/6*(1/36)^(1/4)*(-1/a)^(1/4)*log((3*(1/36)^(1/4)*x*(-1/a)^(1/4) + (-3*x^2 + a)^(1/4))/x) + 1/6*(1/36)^(1/4)*(-1/a)^(1/4)*log(-(3*(1/36)^(1/4)*x*(-1/a)^(1/4) - (-3*x^2 + a)^(1/4))/x)","A",0
1059,1,207,0,0.907697," ","integrate(x^2/(b*x^2+a)^(3/4)/(b*x^2+2*a),x, algorithm=""fricas"")","-2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{4 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{4}\right)^{\frac{3}{4}} a b^{4} x \sqrt{\frac{b^{4} x^{2} \sqrt{-\frac{1}{a b^{6}}} + 2 \, \sqrt{b x^{2} + a}}{x^{2}}} \left(-\frac{1}{a b^{6}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(b x^{2} + a\right)}^{\frac{1}{4}} a b^{4} \left(-\frac{1}{a b^{6}}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} + {\left(b x^{2} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} - {\left(b x^{2} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*arctan(4*(sqrt(1/2)*(1/4)^(3/4)*a*b^4*x*sqrt((b^4*x^2*sqrt(-1/(a*b^6)) + 2*sqrt(b*x^2 + a))/x^2)*(-1/(a*b^6))^(3/4) - (1/4)^(3/4)*(b*x^2 + a)^(1/4)*a*b^4*(-1/(a*b^6))^(3/4))/x) - 1/2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*log(((1/4)^(1/4)*b^2*x*(-1/(a*b^6))^(1/4) + (b*x^2 + a)^(1/4))/x) + 1/2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*log(-((1/4)^(1/4)*b^2*x*(-1/(a*b^6))^(1/4) - (b*x^2 + a)^(1/4))/x)","B",0
1060,1,211,0,0.964050," ","integrate(x^2/(-b*x^2+a)^(3/4)/(-b*x^2+2*a),x, algorithm=""fricas"")","-2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{4 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{4}\right)^{\frac{3}{4}} a b^{4} x \sqrt{\frac{b^{4} x^{2} \sqrt{-\frac{1}{a b^{6}}} + 2 \, \sqrt{-b x^{2} + a}}{x^{2}}} \left(-\frac{1}{a b^{6}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(-b x^{2} + a\right)}^{\frac{1}{4}} a b^{4} \left(-\frac{1}{a b^{6}}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} + {\left(-b x^{2} + a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(-\frac{1}{a b^{6}}\right)^{\frac{1}{4}} - {\left(-b x^{2} + a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"-2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*arctan(4*(sqrt(1/2)*(1/4)^(3/4)*a*b^4*x*sqrt((b^4*x^2*sqrt(-1/(a*b^6)) + 2*sqrt(-b*x^2 + a))/x^2)*(-1/(a*b^6))^(3/4) - (1/4)^(3/4)*(-b*x^2 + a)^(1/4)*a*b^4*(-1/(a*b^6))^(3/4))/x) - 1/2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*log(((1/4)^(1/4)*b^2*x*(-1/(a*b^6))^(1/4) + (-b*x^2 + a)^(1/4))/x) + 1/2*(1/4)^(1/4)*(-1/(a*b^6))^(1/4)*log(-((1/4)^(1/4)*b^2*x*(-1/(a*b^6))^(1/4) - (-b*x^2 + a)^(1/4))/x)","B",0
1061,1,198,0,0.829175," ","integrate(x^7/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{32}{81} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{32}{81} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - \frac{8}{81} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{8}{81} \cdot 2^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{2}{3645} \, {\left(45 \, x^{4} + 156 \, x^{2} + 1136\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}"," ",0,"32/81*2^(3/4)*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) + 32/81*2^(3/4)*arctan(2^(1/4)*sqrt(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) - 8/81*2^(3/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 8/81*2^(3/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 2/3645*(45*x^4 + 156*x^2 + 1136)*(-3*x^2 + 2)^(1/4)","A",0
1062,1,193,0,1.049035," ","integrate(x^5/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{8}{27} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{8}{27} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - \frac{2}{27} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{2}{27} \cdot 2^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{2}{135} \, {\left(3 \, x^{2} + 28\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}"," ",0,"8/27*2^(3/4)*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) + 8/27*2^(3/4)*arctan(2^(1/4)*sqrt(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) - 2/27*2^(3/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 2/27*2^(3/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 2/135*(3*x^2 + 28)*(-3*x^2 + 2)^(1/4)","A",0
1063,1,186,0,0.973794," ","integrate(x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{2}{9} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{2}{9} \cdot 2^{\frac{3}{4}} \arctan\left(2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - 2^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{18} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{1}{18} \cdot 2^{\frac{3}{4}} \log\left(-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right) + \frac{2}{9} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}"," ",0,"2/9*2^(3/4)*arctan(2^(1/4)*sqrt(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) - 1) + 2/9*2^(3/4)*arctan(2^(1/4)*sqrt(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 2^(1/4)*(-3*x^2 + 2)^(1/4) + 1) - 1/18*2^(3/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 1/18*2^(3/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 2/9*(-3*x^2 + 2)^(1/4)","A",0
1064,1,230,0,1.052449," ","integrate(x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{24} \cdot 8^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{24} \cdot 8^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{16} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{96} \cdot 8^{\frac{3}{4}} \sqrt{2} \log\left(16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right) + \frac{1}{96} \cdot 8^{\frac{3}{4}} \sqrt{2} \log\left(-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"1/24*8^(3/4)*sqrt(2)*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 1/24*8^(3/4)*sqrt(2)*arctan(1/16*8^(1/4)*sqrt(2)*sqrt(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) - 1/96*8^(3/4)*sqrt(2)*log(16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) + 1/96*8^(3/4)*sqrt(2)*log(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2))","B",0
1065,1,315,0,1.012491," ","integrate(1/x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{32} \cdot 8^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{32} \cdot 8^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{16} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{128} \cdot 8^{\frac{3}{4}} \sqrt{2} \log\left(16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right) + \frac{1}{128} \cdot 8^{\frac{3}{4}} \sqrt{2} \log\left(-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right) + \frac{1}{16} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{\sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{1}{64} \cdot 8^{\frac{3}{4}} \log\left(8^{\frac{3}{4}} + 4 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{1}{64} \cdot 8^{\frac{3}{4}} \log\left(-8^{\frac{3}{4}} + 4 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)"," ",0,"1/32*8^(3/4)*sqrt(2)*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 1/32*8^(3/4)*sqrt(2)*arctan(1/16*8^(1/4)*sqrt(2)*sqrt(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) - 1/128*8^(3/4)*sqrt(2)*log(16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) + 1/128*8^(3/4)*sqrt(2)*log(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) + 1/16*8^(3/4)*arctan(1/2*8^(1/4)*sqrt(sqrt(2) + sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*(-3*x^2 + 2)^(1/4)) - 1/64*8^(3/4)*log(8^(3/4) + 4*(-3*x^2 + 2)^(1/4)) + 1/64*8^(3/4)*log(-8^(3/4) + 4*(-3*x^2 + 2)^(1/4))","B",0
1066,1,352,0,0.961219," ","integrate(1/x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{12 \cdot 8^{\frac{3}{4}} \sqrt{2} x^{2} \arctan\left(\frac{1}{4} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4 \, \sqrt{2} + 4 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 1\right) + 12 \cdot 8^{\frac{3}{4}} \sqrt{2} x^{2} \arctan\left(\frac{1}{16} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 1\right) - 3 \cdot 8^{\frac{3}{4}} \sqrt{2} x^{2} \log\left(16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right) + 3 \cdot 8^{\frac{3}{4}} \sqrt{2} x^{2} \log\left(-16 \cdot 8^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 64 \, \sqrt{2} + 64 \, \sqrt{-3 \, x^{2} + 2}\right) + 60 \cdot 8^{\frac{3}{4}} x^{2} \arctan\left(\frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{\sqrt{2} + \sqrt{-3 \, x^{2} + 2}} - \frac{1}{2} \cdot 8^{\frac{1}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - 15 \cdot 8^{\frac{3}{4}} x^{2} \log\left(8^{\frac{3}{4}} + 4 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + 15 \cdot 8^{\frac{3}{4}} x^{2} \log\left(-8^{\frac{3}{4}} + 4 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - 32 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}{512 \, x^{2}}"," ",0,"1/512*(12*8^(3/4)*sqrt(2)*x^2*arctan(1/4*8^(1/4)*sqrt(2)*sqrt(8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 4*sqrt(2) + 4*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 1) + 12*8^(3/4)*sqrt(2)*x^2*arctan(1/16*8^(1/4)*sqrt(2)*sqrt(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 1) - 3*8^(3/4)*sqrt(2)*x^2*log(16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) + 3*8^(3/4)*sqrt(2)*x^2*log(-16*8^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 64*sqrt(2) + 64*sqrt(-3*x^2 + 2)) + 60*8^(3/4)*x^2*arctan(1/2*8^(1/4)*sqrt(sqrt(2) + sqrt(-3*x^2 + 2)) - 1/2*8^(1/4)*(-3*x^2 + 2)^(1/4)) - 15*8^(3/4)*x^2*log(8^(3/4) + 4*(-3*x^2 + 2)^(1/4)) + 15*8^(3/4)*x^2*log(-8^(3/4) + 4*(-3*x^2 + 2)^(1/4)) - 32*(-3*x^2 + 2)^(1/4))/x^2","B",0
1067,0,0,0,3.448366," ","integrate(x^6/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{6}}{9 \, x^{4} - 18 \, x^{2} + 8}, x\right)"," ",0,"integral((-3*x^2 + 2)^(1/4)*x^6/(9*x^4 - 18*x^2 + 8), x)","F",0
1068,0,0,0,3.210989," ","integrate(x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{4}}{9 \, x^{4} - 18 \, x^{2} + 8}, x\right)"," ",0,"integral((-3*x^2 + 2)^(1/4)*x^4/(9*x^4 - 18*x^2 + 8), x)","F",0
1069,1,282,0,1.140613," ","integrate(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","\frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{\frac{72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{-3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - 36 \, x}{36 \, x}\right) + \frac{1}{216} \cdot 72^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{72^{\frac{1}{4}} \sqrt{6} \sqrt{2} x \sqrt{-\frac{72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{-3 \, x^{2} + 2}}{x^{2}}} - 12 \cdot 72^{\frac{1}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 36 \, x}{36 \, x}\right) - \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x + 18 \, \sqrt{2} x^{2} + 24 \, \sqrt{-3 \, x^{2} + 2}\right)}}{x^{2}}\right) + \frac{1}{864} \cdot 72^{\frac{3}{4}} \sqrt{2} \log\left(-\frac{96 \, {\left(72^{\frac{3}{4}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x - 18 \, \sqrt{2} x^{2} - 24 \, \sqrt{-3 \, x^{2} + 2}\right)}}{x^{2}}\right)"," ",0,"1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt((72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(-3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) - 36*x)/x) + 1/216*72^(3/4)*sqrt(2)*arctan(1/36*(72^(1/4)*sqrt(6)*sqrt(2)*x*sqrt(-(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(-3*x^2 + 2))/x^2) - 12*72^(1/4)*sqrt(2)*(-3*x^2 + 2)^(1/4) + 36*x)/x) - 1/864*72^(3/4)*sqrt(2)*log(96*(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x + 18*sqrt(2)*x^2 + 24*sqrt(-3*x^2 + 2))/x^2) + 1/864*72^(3/4)*sqrt(2)*log(-96*(72^(3/4)*sqrt(2)*(-3*x^2 + 2)^(1/4)*x - 18*sqrt(2)*x^2 - 24*sqrt(-3*x^2 + 2))/x^2)","B",0
1070,0,0,0,4.544125," ","integrate(1/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}{9 \, x^{4} - 18 \, x^{2} + 8}, x\right)"," ",0,"integral((-3*x^2 + 2)^(1/4)/(9*x^4 - 18*x^2 + 8), x)","F",0
1071,0,0,0,5.057142," ","integrate(1/x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}{9 \, x^{6} - 18 \, x^{4} + 8 \, x^{2}}, x\right)"," ",0,"integral((-3*x^2 + 2)^(1/4)/(9*x^6 - 18*x^4 + 8*x^2), x)","F",0
1072,0,0,0,6.013962," ","integrate(1/x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}{9 \, x^{8} - 18 \, x^{6} + 8 \, x^{4}}, x\right)"," ",0,"integral((-3*x^2 + 2)^(1/4)/(9*x^8 - 18*x^6 + 8*x^4), x)","F",0
1073,1,104,0,0.866113," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","-\frac{1}{18} \, \sqrt{6} \arctan\left(\frac{\sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, x}\right) + \frac{1}{36} \, \sqrt{6} \log\left(-\frac{9 \, x^{4} - 6 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{3} + 12 \, \sqrt{3 \, x^{2} - 1} x^{2} - 4 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x + 12 \, x^{2} - 4}{9 \, x^{4} - 12 \, x^{2} + 4}\right)"," ",0,"-1/18*sqrt(6)*arctan(1/3*sqrt(6)*(3*x^2 - 1)^(1/4)/x) + 1/36*sqrt(6)*log(-(9*x^4 - 6*sqrt(6)*(3*x^2 - 1)^(1/4)*x^3 + 12*sqrt(3*x^2 - 1)*x^2 - 4*sqrt(6)*(3*x^2 - 1)^(3/4)*x + 12*x^2 - 4)/(9*x^4 - 12*x^2 + 4))","B",0
1074,1,115,0,0.928165," ","integrate(x^2/(-3*x^2-2)/(-3*x^2-1)^(3/4),x, algorithm=""fricas"")","-\frac{1}{36} \, \sqrt{6} \log\left(\frac{\sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right) + \frac{1}{36} \, \sqrt{6} \log\left(-\frac{\sqrt{6} x - 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right) - \frac{1}{36} i \, \sqrt{6} \log\left(\frac{i \, \sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right) + \frac{1}{36} i \, \sqrt{6} \log\left(\frac{-i \, \sqrt{6} x + 2 \, {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{2 \, x}\right)"," ",0,"-1/36*sqrt(6)*log(1/2*(sqrt(6)*x + 2*(-3*x^2 - 1)^(1/4))/x) + 1/36*sqrt(6)*log(-1/2*(sqrt(6)*x - 2*(-3*x^2 - 1)^(1/4))/x) - 1/36*I*sqrt(6)*log(1/2*(I*sqrt(6)*x + 2*(-3*x^2 - 1)^(1/4))/x) + 1/36*I*sqrt(6)*log(1/2*(-I*sqrt(6)*x + 2*(-3*x^2 - 1)^(1/4))/x)","C",0
1075,1,275,0,0.951964," ","integrate(x^2/(b*x^2-2)/(b*x^2-1)^(3/4),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}}}{\sqrt{b} x}\right) - \sqrt{2} \sqrt{b} \log\left(-\frac{b^{2} x^{4} - 2 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} b^{\frac{3}{2}} x^{3} + 4 \, \sqrt{b x^{2} - 1} b x^{2} + 4 \, b x^{2} - 4 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{3}{4}} \sqrt{b} x - 4}{b^{2} x^{4} - 4 \, b x^{2} + 4}\right)}{4 \, b^{2}}, \frac{2 \, \sqrt{2} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b}}{b x}\right) - \sqrt{2} \sqrt{-b} \log\left(-\frac{b^{2} x^{4} - 2 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b} b x^{3} - 4 \, \sqrt{b x^{2} - 1} b x^{2} + 4 \, b x^{2} + 4 \, \sqrt{2} {\left(b x^{2} - 1\right)}^{\frac{3}{4}} \sqrt{-b} x - 4}{b^{2} x^{4} - 4 \, b x^{2} + 4}\right)}{4 \, b^{2}}\right]"," ",0,"[-1/4*(2*sqrt(2)*sqrt(b)*arctan(sqrt(2)*(b*x^2 - 1)^(1/4)/(sqrt(b)*x)) - sqrt(2)*sqrt(b)*log(-(b^2*x^4 - 2*sqrt(2)*(b*x^2 - 1)^(1/4)*b^(3/2)*x^3 + 4*sqrt(b*x^2 - 1)*b*x^2 + 4*b*x^2 - 4*sqrt(2)*(b*x^2 - 1)^(3/4)*sqrt(b)*x - 4)/(b^2*x^4 - 4*b*x^2 + 4)))/b^2, 1/4*(2*sqrt(2)*sqrt(-b)*arctan(sqrt(2)*(b*x^2 - 1)^(1/4)*sqrt(-b)/(b*x)) - sqrt(2)*sqrt(-b)*log(-(b^2*x^4 - 2*sqrt(2)*(b*x^2 - 1)^(1/4)*sqrt(-b)*b*x^3 - 4*sqrt(b*x^2 - 1)*b*x^2 + 4*b*x^2 + 4*sqrt(2)*(b*x^2 - 1)^(3/4)*sqrt(-b)*x - 4)/(b^2*x^4 - 4*b*x^2 + 4)))/b^2]","B",0
1076,1,274,0,0.807810," ","integrate(x^2/(-b*x^2-2)/(-b*x^2-1)^(3/4),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}}}{\sqrt{b} x}\right) - \sqrt{2} \sqrt{b} \log\left(-\frac{b^{2} x^{4} + 4 \, \sqrt{-b x^{2} - 1} b x^{2} - 4 \, b x^{2} - 2 \, \sqrt{2} {\left({\left(-b x^{2} - 1\right)}^{\frac{1}{4}} b x^{3} + 2 \, {\left(-b x^{2} - 1\right)}^{\frac{3}{4}} x\right)} \sqrt{b} - 4}{b^{2} x^{4} + 4 \, b x^{2} + 4}\right)}{4 \, b^{2}}, \frac{2 \, \sqrt{2} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}} \sqrt{-b}}{b x}\right) - \sqrt{2} \sqrt{-b} \log\left(-\frac{b^{2} x^{4} - 4 \, \sqrt{-b x^{2} - 1} b x^{2} - 4 \, b x^{2} - 2 \, \sqrt{2} {\left({\left(-b x^{2} - 1\right)}^{\frac{1}{4}} b x^{3} - 2 \, {\left(-b x^{2} - 1\right)}^{\frac{3}{4}} x\right)} \sqrt{-b} - 4}{b^{2} x^{4} + 4 \, b x^{2} + 4}\right)}{4 \, b^{2}}\right]"," ",0,"[-1/4*(2*sqrt(2)*sqrt(b)*arctan(sqrt(2)*(-b*x^2 - 1)^(1/4)/(sqrt(b)*x)) - sqrt(2)*sqrt(b)*log(-(b^2*x^4 + 4*sqrt(-b*x^2 - 1)*b*x^2 - 4*b*x^2 - 2*sqrt(2)*((-b*x^2 - 1)^(1/4)*b*x^3 + 2*(-b*x^2 - 1)^(3/4)*x)*sqrt(b) - 4)/(b^2*x^4 + 4*b*x^2 + 4)))/b^2, 1/4*(2*sqrt(2)*sqrt(-b)*arctan(sqrt(2)*(-b*x^2 - 1)^(1/4)*sqrt(-b)/(b*x)) - sqrt(2)*sqrt(-b)*log(-(b^2*x^4 - 4*sqrt(-b*x^2 - 1)*b*x^2 - 4*b*x^2 - 2*sqrt(2)*((-b*x^2 - 1)^(1/4)*b*x^3 - 2*(-b*x^2 - 1)^(3/4)*x)*sqrt(-b) - 4)/(b^2*x^4 + 4*b*x^2 + 4)))/b^2]","B",0
1077,1,145,0,0.838357," ","integrate(x^2/(3*x^2-2*a)/(3*x^2-a)^(3/4),x, algorithm=""fricas"")","\frac{2 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \arctan\left(\frac{12 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{\frac{1}{4}} x \sqrt{\frac{\frac{3 \, x^{2}}{\sqrt{a}} + 2 \, \sqrt{3 \, x^{2} - a}}{x^{2}}} - \left(\frac{1}{36}\right)^{\frac{3}{4}} {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{\frac{1}{4}}\right)}}{x}\right)}{3 \, a^{\frac{1}{4}}} - \frac{\left(\frac{1}{36}\right)^{\frac{1}{4}} \log\left(\frac{\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x}{a^{\frac{1}{4}}} + {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)}{6 \, a^{\frac{1}{4}}} + \frac{\left(\frac{1}{36}\right)^{\frac{1}{4}} \log\left(-\frac{\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x}{a^{\frac{1}{4}}} - {\left(3 \, x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)}{6 \, a^{\frac{1}{4}}}"," ",0,"2/3*(1/36)^(1/4)*arctan(12*(sqrt(1/2)*(1/36)^(3/4)*a^(1/4)*x*sqrt((3*x^2/sqrt(a) + 2*sqrt(3*x^2 - a))/x^2) - (1/36)^(3/4)*(3*x^2 - a)^(1/4)*a^(1/4))/x)/a^(1/4) - 1/6*(1/36)^(1/4)*log((3*(1/36)^(1/4)*x/a^(1/4) + (3*x^2 - a)^(1/4))/x)/a^(1/4) + 1/6*(1/36)^(1/4)*log(-(3*(1/36)^(1/4)*x/a^(1/4) - (3*x^2 - a)^(1/4))/x)/a^(1/4)","B",0
1078,1,145,0,0.845166," ","integrate(x^2/(-3*x^2-2*a)/(-3*x^2-a)^(3/4),x, algorithm=""fricas"")","\frac{2 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} \arctan\left(\frac{12 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{36}\right)^{\frac{3}{4}} a^{\frac{1}{4}} x \sqrt{\frac{\frac{3 \, x^{2}}{\sqrt{a}} + 2 \, \sqrt{-3 \, x^{2} - a}}{x^{2}}} - \left(\frac{1}{36}\right)^{\frac{3}{4}} {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}} a^{\frac{1}{4}}\right)}}{x}\right)}{3 \, a^{\frac{1}{4}}} - \frac{\left(\frac{1}{36}\right)^{\frac{1}{4}} \log\left(\frac{\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x}{a^{\frac{1}{4}}} + {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)}{6 \, a^{\frac{1}{4}}} + \frac{\left(\frac{1}{36}\right)^{\frac{1}{4}} \log\left(-\frac{\frac{3 \, \left(\frac{1}{36}\right)^{\frac{1}{4}} x}{a^{\frac{1}{4}}} - {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)}{6 \, a^{\frac{1}{4}}}"," ",0,"2/3*(1/36)^(1/4)*arctan(12*(sqrt(1/2)*(1/36)^(3/4)*a^(1/4)*x*sqrt((3*x^2/sqrt(a) + 2*sqrt(-3*x^2 - a))/x^2) - (1/36)^(3/4)*(-3*x^2 - a)^(1/4)*a^(1/4))/x)/a^(1/4) - 1/6*(1/36)^(1/4)*log((3*(1/36)^(1/4)*x/a^(1/4) + (-3*x^2 - a)^(1/4))/x)/a^(1/4) + 1/6*(1/36)^(1/4)*log(-(3*(1/36)^(1/4)*x/a^(1/4) - (-3*x^2 - a)^(1/4))/x)/a^(1/4)","B",0
1079,1,207,0,0.734628," ","integrate(x^2/(b*x^2-2*a)/(b*x^2-a)^(3/4),x, algorithm=""fricas"")","2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{4 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{4}\right)^{\frac{3}{4}} a b^{4} x \sqrt{\frac{b^{4} x^{2} \sqrt{\frac{1}{a b^{6}}} + 2 \, \sqrt{b x^{2} - a}}{x^{2}}} \left(\frac{1}{a b^{6}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(b x^{2} - a\right)}^{\frac{1}{4}} a b^{4} \left(\frac{1}{a b^{6}}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} + {\left(b x^{2} - a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} - {\left(b x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*arctan(4*(sqrt(1/2)*(1/4)^(3/4)*a*b^4*x*sqrt((b^4*x^2*sqrt(1/(a*b^6)) + 2*sqrt(b*x^2 - a))/x^2)*(1/(a*b^6))^(3/4) - (1/4)^(3/4)*(b*x^2 - a)^(1/4)*a*b^4*(1/(a*b^6))^(3/4))/x) - 1/2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*log(((1/4)^(1/4)*b^2*x*(1/(a*b^6))^(1/4) + (b*x^2 - a)^(1/4))/x) + 1/2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*log(-((1/4)^(1/4)*b^2*x*(1/(a*b^6))^(1/4) - (b*x^2 - a)^(1/4))/x)","B",0
1080,1,211,0,0.960755," ","integrate(x^2/(-b*x^2-2*a)/(-b*x^2-a)^(3/4),x, algorithm=""fricas"")","2 \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{4 \, {\left(\sqrt{\frac{1}{2}} \left(\frac{1}{4}\right)^{\frac{3}{4}} a b^{4} x \sqrt{\frac{b^{4} x^{2} \sqrt{\frac{1}{a b^{6}}} + 2 \, \sqrt{-b x^{2} - a}}{x^{2}}} \left(\frac{1}{a b^{6}}\right)^{\frac{3}{4}} - \left(\frac{1}{4}\right)^{\frac{3}{4}} {\left(-b x^{2} - a\right)}^{\frac{1}{4}} a b^{4} \left(\frac{1}{a b^{6}}\right)^{\frac{3}{4}}\right)}}{x}\right) - \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} + {\left(-b x^{2} - a\right)}^{\frac{1}{4}}}{x}\right) + \frac{1}{2} \, \left(\frac{1}{4}\right)^{\frac{1}{4}} \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} \log\left(-\frac{\left(\frac{1}{4}\right)^{\frac{1}{4}} b^{2} x \left(\frac{1}{a b^{6}}\right)^{\frac{1}{4}} - {\left(-b x^{2} - a\right)}^{\frac{1}{4}}}{x}\right)"," ",0,"2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*arctan(4*(sqrt(1/2)*(1/4)^(3/4)*a*b^4*x*sqrt((b^4*x^2*sqrt(1/(a*b^6)) + 2*sqrt(-b*x^2 - a))/x^2)*(1/(a*b^6))^(3/4) - (1/4)^(3/4)*(-b*x^2 - a)^(1/4)*a*b^4*(1/(a*b^6))^(3/4))/x) - 1/2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*log(((1/4)^(1/4)*b^2*x*(1/(a*b^6))^(1/4) + (-b*x^2 - a)^(1/4))/x) + 1/2*(1/4)^(1/4)*(1/(a*b^6))^(1/4)*log(-((1/4)^(1/4)*b^2*x*(1/(a*b^6))^(1/4) - (-b*x^2 - a)^(1/4))/x)","B",0
1081,1,64,0,0.796548," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","\frac{2}{3645} \, {\left(45 \, x^{4} + 78 \, x^{2} + 284\right)} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - \frac{8}{81} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{4}{81} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{4}{81} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/3645*(45*x^4 + 78*x^2 + 284)*(3*x^2 - 1)^(1/4) - 8/81*arctan((3*x^2 - 1)^(1/4)) - 4/81*log((3*x^2 - 1)^(1/4) + 1) + 4/81*log((3*x^2 - 1)^(1/4) - 1)","A",0
1082,1,59,0,0.941755," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","\frac{2}{135} \, {\left(3 \, x^{2} + 14\right)} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - \frac{4}{27} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{2}{27} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{2}{27} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/135*(3*x^2 + 14)*(3*x^2 - 1)^(1/4) - 4/27*arctan((3*x^2 - 1)^(1/4)) - 2/27*log((3*x^2 - 1)^(1/4) + 1) + 2/27*log((3*x^2 - 1)^(1/4) - 1)","A",0
1083,1,52,0,0.893277," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","\frac{2}{9} \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - \frac{2}{9} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/9*(3*x^2 - 1)^(1/4) - 2/9*arctan((3*x^2 - 1)^(1/4)) - 1/9*log((3*x^2 - 1)^(1/4) + 1) + 1/9*log((3*x^2 - 1)^(1/4) - 1)","A",0
1084,1,41,0,0.740850," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","-\frac{1}{3} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log((3*x^2 - 1)^(1/4) - 1)","A",0
1085,1,215,0,0.819440," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) + \frac{1}{8} \, \sqrt{2} \log\left(-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) - \frac{1}{2} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{4} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{4} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - sqrt(2)*(3*x^2 - 1)^(1/4) - 1) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - sqrt(2)*(3*x^2 - 1)^(1/4) + 1) - 1/8*sqrt(2)*log(4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) + 1/8*sqrt(2)*log(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - 1/2*arctan((3*x^2 - 1)^(1/4)) - 1/4*log((3*x^2 - 1)^(1/4) + 1) + 1/4*log((3*x^2 - 1)^(1/4) - 1)","A",0
1086,1,252,0,0.843204," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","\frac{60 \, \sqrt{2} x^{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) + 60 \, \sqrt{2} x^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4} - \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) - 15 \, \sqrt{2} x^{2} \log\left(4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) + 15 \, \sqrt{2} x^{2} \log\left(-4 \, \sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 4 \, \sqrt{3 \, x^{2} - 1} + 4\right) - 24 \, x^{2} \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - 12 \, x^{2} \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + 12 \, x^{2} \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right) - 8 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{32 \, x^{2}}"," ",0,"1/32*(60*sqrt(2)*x^2*arctan(sqrt(2)*sqrt(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - sqrt(2)*(3*x^2 - 1)^(1/4) - 1) + 60*sqrt(2)*x^2*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - sqrt(2)*(3*x^2 - 1)^(1/4) + 1) - 15*sqrt(2)*x^2*log(4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) + 15*sqrt(2)*x^2*log(-4*sqrt(2)*(3*x^2 - 1)^(1/4) + 4*sqrt(3*x^2 - 1) + 4) - 24*x^2*arctan((3*x^2 - 1)^(1/4)) - 12*x^2*log((3*x^2 - 1)^(1/4) + 1) + 12*x^2*log((3*x^2 - 1)^(1/4) - 1) - 8*(3*x^2 - 1)^(1/4))/x^2","A",0
1087,0,0,0,4.893261," ","integrate(x^6/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{6}}{9 \, x^{4} - 9 \, x^{2} + 2}, x\right)"," ",0,"integral((3*x^2 - 1)^(1/4)*x^6/(9*x^4 - 9*x^2 + 2), x)","F",0
1088,0,0,0,4.121315," ","integrate(x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{4}}{9 \, x^{4} - 9 \, x^{2} + 2}, x\right)"," ",0,"integral((3*x^2 - 1)^(1/4)*x^4/(9*x^4 - 9*x^2 + 2), x)","F",0
1089,1,104,0,0.648961," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","-\frac{1}{18} \, \sqrt{6} \arctan\left(\frac{\sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{3 \, x}\right) + \frac{1}{36} \, \sqrt{6} \log\left(-\frac{9 \, x^{4} - 6 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} x^{3} + 12 \, \sqrt{3 \, x^{2} - 1} x^{2} - 4 \, \sqrt{6} {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} x + 12 \, x^{2} - 4}{9 \, x^{4} - 12 \, x^{2} + 4}\right)"," ",0,"-1/18*sqrt(6)*arctan(1/3*sqrt(6)*(3*x^2 - 1)^(1/4)/x) + 1/36*sqrt(6)*log(-(9*x^4 - 6*sqrt(6)*(3*x^2 - 1)^(1/4)*x^3 + 12*sqrt(3*x^2 - 1)*x^2 - 4*sqrt(6)*(3*x^2 - 1)^(3/4)*x + 12*x^2 - 4)/(9*x^4 - 12*x^2 + 4))","B",0
1090,0,0,0,4.654740," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{9 \, x^{4} - 9 \, x^{2} + 2}, x\right)"," ",0,"integral((3*x^2 - 1)^(1/4)/(9*x^4 - 9*x^2 + 2), x)","F",0
1091,0,0,0,4.947724," ","integrate(1/x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{9 \, x^{6} - 9 \, x^{4} + 2 \, x^{2}}, x\right)"," ",0,"integral((3*x^2 - 1)^(1/4)/(9*x^6 - 9*x^4 + 2*x^2), x)","F",0
1092,0,0,0,5.699831," ","integrate(1/x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{9 \, x^{8} - 9 \, x^{6} + 2 \, x^{4}}, x\right)"," ",0,"integral((3*x^2 - 1)^(1/4)/(9*x^8 - 9*x^6 + 2*x^4), x)","F",0
1093,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1094,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1095,-1,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1096,1,43,0,1.158654," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(4 \, b c - 5 \, a d\right)} x^{2} - a c\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{5 \, a^{2} e^{4} x^{3}}"," ",0,"2/5*((4*b*c - 5*a*d)*x^2 - a*c)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^2*e^4*x^3)","A",0
1097,1,66,0,1.553464," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, {\left(8 \, b^{2} c - 9 \, a b d\right)} x^{4} + 5 \, a^{2} c - {\left(8 \, a b c - 9 \, a^{2} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{45 \, a^{3} e^{6} x^{5}}"," ",0,"-2/45*(4*(8*b^2*c - 9*a*b*d)*x^4 + 5*a^2*c - (8*a*b*c - 9*a^2*d)*x^2)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^3*e^6*x^5)","A",0
1098,1,90,0,0.701601," ","integrate((d*x^2+c)/(e*x)^(15/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","\frac{2 \, {\left(32 \, {\left(12 \, b^{3} c - 13 \, a b^{2} d\right)} x^{6} - 8 \, {\left(12 \, a b^{2} c - 13 \, a^{2} b d\right)} x^{4} - 45 \, a^{3} c + 5 \, {\left(12 \, a^{2} b c - 13 \, a^{3} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{585 \, a^{4} e^{8} x^{7}}"," ",0,"2/585*(32*(12*b^3*c - 13*a*b^2*d)*x^6 - 8*(12*a*b^2*c - 13*a^2*b*d)*x^4 - 45*a^3*c + 5*(12*a^2*b*c - 13*a^3*d)*x^2)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^4*e^8*x^7)","A",0
1099,0,0,0,1.501371," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{3} x^{5} + c e^{3} x^{3}\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((d*e^3*x^5 + c*e^3*x^3)*sqrt(e*x)/(b*x^2 + a)^(3/4), x)","F",0
1100,0,0,0,1.215529," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x^{3} + c e x\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((d*e*x^3 + c*e*x)*sqrt(e*x)/(b*x^2 + a)^(3/4), x)","F",0
1101,0,0,0,1.326623," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b e x^{3} + a e x}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b*e*x^3 + a*e*x), x)","F",0
1102,0,0,0,1.271605," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b e^{3} x^{5} + a e^{3} x^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b*e^3*x^5 + a*e^3*x^3), x)","F",0
1103,0,0,0,0.825912," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b e^{5} x^{7} + a e^{5} x^{5}}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b*e^5*x^7 + a*e^5*x^5), x)","F",0
1104,0,0,0,1.471435," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b e^{7} x^{9} + a e^{7} x^{7}}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b*e^7*x^9 + a*e^7*x^7), x)","F",0
1105,1,916,0,1.102283," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","\frac{4 \, {\left(b d e x^{2} - {\left(4 \, b c - 5 \, a d\right)} e\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} + 4 \, {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(4 \, b^{8} c - 5 \, a b^{7} d\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} e \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{3}{4}} + {\left(b^{8} x^{2} + a b^{7}\right)} \sqrt{\frac{{\left(16 \, b^{2} c^{2} - 40 \, a b c d + 25 \, a^{2} d^{2}\right)} \sqrt{b x^{2} + a} e^{3} x + {\left(b^{5} x^{2} + a b^{4}\right)} \sqrt{\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}}}{b x^{2} + a}} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{3}{4}}}{{\left(256 \, b^{5} c^{4} - 1280 \, a b^{4} c^{3} d + 2400 \, a^{2} b^{3} c^{2} d^{2} - 2000 \, a^{3} b^{2} c d^{3} + 625 \, a^{4} b d^{4}\right)} e^{6} x^{2} + {\left(256 \, a b^{4} c^{4} - 1280 \, a^{2} b^{3} c^{3} d + 2400 \, a^{3} b^{2} c^{2} d^{2} - 2000 \, a^{4} b c d^{3} + 625 \, a^{5} d^{4}\right)} e^{6}}\right) + {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(4 \, b c - 5 \, a d\right)} \sqrt{e x} e + {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right) - {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(4 \, b c - 5 \, a d\right)} \sqrt{e x} e - {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 1280 \, a b^{3} c^{3} d + 2400 \, a^{2} b^{2} c^{2} d^{2} - 2000 \, a^{3} b c d^{3} + 625 \, a^{4} d^{4}\right)} e^{6}}{b^{9}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right)}{8 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/8*(4*(b*d*e*x^2 - (4*b*c - 5*a*d)*e)*(b*x^2 + a)^(3/4)*sqrt(e*x) + 4*(b^3*x^2 + a*b^2)*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(1/4)*arctan(((4*b^8*c - 5*a*b^7*d)*(b*x^2 + a)^(3/4)*sqrt(e*x)*e*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(3/4) + (b^8*x^2 + a*b^7)*sqrt(((16*b^2*c^2 - 40*a*b*c*d + 25*a^2*d^2)*sqrt(b*x^2 + a)*e^3*x + (b^5*x^2 + a*b^4)*sqrt((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9))/(b*x^2 + a))*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(3/4))/((256*b^5*c^4 - 1280*a*b^4*c^3*d + 2400*a^2*b^3*c^2*d^2 - 2000*a^3*b^2*c*d^3 + 625*a^4*b*d^4)*e^6*x^2 + (256*a*b^4*c^4 - 1280*a^2*b^3*c^3*d + 2400*a^3*b^2*c^2*d^2 - 2000*a^4*b*c*d^3 + 625*a^5*d^4)*e^6)) + (b^3*x^2 + a*b^2)*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(1/4)*log(-((b*x^2 + a)^(3/4)*(4*b*c - 5*a*d)*sqrt(e*x)*e + (b^3*x^2 + a*b^2)*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(1/4))/(b*x^2 + a)) - (b^3*x^2 + a*b^2)*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(1/4)*log(-((b*x^2 + a)^(3/4)*(4*b*c - 5*a*d)*sqrt(e*x)*e - (b^3*x^2 + a*b^2)*((256*b^4*c^4 - 1280*a*b^3*c^3*d + 2400*a^2*b^2*c^2*d^2 - 2000*a^3*b*c*d^3 + 625*a^4*d^4)*e^6/b^9)^(1/4))/(b*x^2 + a)))/(b^3*x^2 + a*b^2)","B",0
1106,1,384,0,1.060276," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","\frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(b c - a d\right)} \sqrt{e x} - 4 \, {\left(a b^{2} e x^{2} + a^{2} b e\right)} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} b^{4} d e \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{3}{4}} - {\left(b^{5} e x^{2} + a b^{4} e\right)} \sqrt{\frac{\sqrt{b x^{2} + a} d^{2} e x + {\left(b^{3} e^{2} x^{2} + a b^{2} e^{2}\right)} \sqrt{\frac{d^{4}}{b^{5} e^{2}}}}{b x^{2} + a}} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{3}{4}}}{b d^{4} x^{2} + a d^{4}}\right) + {\left(a b^{2} e x^{2} + a^{2} b e\right)} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} d + {\left(b^{2} e x^{2} + a b e\right)} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right) - {\left(a b^{2} e x^{2} + a^{2} b e\right)} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} d - {\left(b^{2} e x^{2} + a b e\right)} \left(\frac{d^{4}}{b^{5} e^{2}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right)}{2 \, {\left(a b^{2} e x^{2} + a^{2} b e\right)}}"," ",0,"1/2*(4*(b*x^2 + a)^(3/4)*(b*c - a*d)*sqrt(e*x) - 4*(a*b^2*e*x^2 + a^2*b*e)*(d^4/(b^5*e^2))^(1/4)*arctan(-((b*x^2 + a)^(3/4)*sqrt(e*x)*b^4*d*e*(d^4/(b^5*e^2))^(3/4) - (b^5*e*x^2 + a*b^4*e)*sqrt((sqrt(b*x^2 + a)*d^2*e*x + (b^3*e^2*x^2 + a*b^2*e^2)*sqrt(d^4/(b^5*e^2)))/(b*x^2 + a))*(d^4/(b^5*e^2))^(3/4))/(b*d^4*x^2 + a*d^4)) + (a*b^2*e*x^2 + a^2*b*e)*(d^4/(b^5*e^2))^(1/4)*log(((b*x^2 + a)^(3/4)*sqrt(e*x)*d + (b^2*e*x^2 + a*b*e)*(d^4/(b^5*e^2))^(1/4))/(b*x^2 + a)) - (a*b^2*e*x^2 + a^2*b*e)*(d^4/(b^5*e^2))^(1/4)*log(((b*x^2 + a)^(3/4)*sqrt(e*x)*d - (b^2*e*x^2 + a*b*e)*(d^4/(b^5*e^2))^(1/4))/(b*x^2 + a)))/(a*b^2*e*x^2 + a^2*b*e)","B",0
1107,1,57,0,0.821508," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(4 \, b c - 3 \, a d\right)} x^{2} + a c\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{3 \, {\left(a^{2} b e^{3} x^{4} + a^{3} e^{3} x^{2}\right)}}"," ",0,"-2/3*((4*b*c - 3*a*d)*x^2 + a*c)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^2*b*e^3*x^4 + a^3*e^3*x^2)","A",0
1108,1,80,0,1.197650," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, {\left(8 \, b^{2} c - 7 \, a b d\right)} x^{4} - 3 \, a^{2} c + {\left(8 \, a b c - 7 \, a^{2} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{21 \, {\left(a^{3} b e^{5} x^{6} + a^{4} e^{5} x^{4}\right)}}"," ",0,"2/21*(4*(8*b^2*c - 7*a*b*d)*x^4 - 3*a^2*c + (8*a*b*c - 7*a^2*d)*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^3*b*e^5*x^6 + a^4*e^5*x^4)","A",0
1109,1,105,0,1.090480," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, {\left(12 \, b^{3} c - 11 \, a b^{2} d\right)} x^{6} + 8 \, {\left(12 \, a b^{2} c - 11 \, a^{2} b d\right)} x^{4} + 21 \, a^{3} c - 3 \, {\left(12 \, a^{2} b c - 11 \, a^{3} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{231 \, {\left(a^{4} b e^{7} x^{8} + a^{5} e^{7} x^{6}\right)}}"," ",0,"-2/231*(32*(12*b^3*c - 11*a*b^2*d)*x^6 + 8*(12*a*b^2*c - 11*a^2*b*d)*x^4 + 21*a^3*c - 3*(12*a^2*b*c - 11*a^3*d)*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^4*b*e^7*x^8 + a^5*e^7*x^6)","A",0
1110,0,0,0,1.399154," ","integrate((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{4} x^{6} + c e^{4} x^{4}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*e^4*x^6 + c*e^4*x^4)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1111,0,0,0,1.248221," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{2} x^{4} + c e^{2} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*e^2*x^4 + c*e^2*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1112,0,0,0,1.369264," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1113,0,0,0,0.995273," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e^{2} x^{6} + 2 \, a b e^{2} x^{4} + a^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e^2*x^6 + 2*a*b*e^2*x^4 + a^2*e^2*x^2), x)","F",0
1114,0,0,0,1.254719," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e^{4} x^{8} + 2 \, a b e^{4} x^{6} + a^{2} e^{4} x^{4}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e^4*x^8 + 2*a*b*e^4*x^6 + a^2*e^4*x^4), x)","F",0
1115,0,0,0,1.116564," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e^{6} x^{10} + 2 \, a b e^{6} x^{8} + a^{2} e^{6} x^{6}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e^6*x^10 + 2*a*b*e^6*x^8 + a^2*e^6*x^6), x)","F",0
1116,-1,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1117,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1118,1,56,0,1.744023," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(4 \, b c - a d\right)} x^{2} + 3 \, a c\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{3 \, {\left(a^{2} b e^{2} x^{3} + a^{3} e^{2} x\right)}}"," ",0,"-2/3*((4*b*c - a*d)*x^2 + 3*a*c)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^2*b*e^2*x^3 + a^3*e^2*x)","A",0
1119,1,81,0,2.416671," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, {\left(8 \, b^{2} c - 5 \, a b d\right)} x^{4} - 3 \, a^{2} c + 3 \, {\left(8 \, a b c - 5 \, a^{2} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{15 \, {\left(a^{3} b e^{4} x^{5} + a^{4} e^{4} x^{3}\right)}}"," ",0,"2/15*(4*(8*b^2*c - 5*a*b*d)*x^4 - 3*a^2*c + 3*(8*a*b*c - 5*a^2*d)*x^2)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^3*b*e^4*x^5 + a^4*e^4*x^3)","A",0
1120,1,105,0,1.155618," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, {\left(4 \, b^{3} c - 3 \, a b^{2} d\right)} x^{6} + 24 \, {\left(4 \, a b^{2} c - 3 \, a^{2} b d\right)} x^{4} + 5 \, a^{3} c - 3 \, {\left(4 \, a^{2} b c - 3 \, a^{3} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{45 \, {\left(a^{4} b e^{6} x^{7} + a^{5} e^{6} x^{5}\right)}}"," ",0,"-2/45*(32*(4*b^3*c - 3*a*b^2*d)*x^6 + 24*(4*a*b^2*c - 3*a^2*b*d)*x^4 + 5*a^3*c - 3*(4*a^2*b*c - 3*a^3*d)*x^2)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(a^4*b*e^6*x^7 + a^5*e^6*x^5)","A",0
1121,0,0,0,1.313416," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{3} x^{5} + c e^{3} x^{3}\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*e^3*x^5 + c*e^3*x^3)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1122,0,0,0,0.776419," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x^{3} + c e x\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}} \sqrt{e x}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((d*e*x^3 + c*e*x)*(b*x^2 + a)^(1/4)*sqrt(e*x)/(b^2*x^4 + 2*a*b*x^2 + a^2), x)","F",0
1123,0,0,0,1.169232," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e x^{5} + 2 \, a b e x^{3} + a^{2} e x}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e*x^5 + 2*a*b*e*x^3 + a^2*e*x), x)","F",0
1124,0,0,0,1.373170," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e^{3} x^{7} + 2 \, a b e^{3} x^{5} + a^{2} e^{3} x^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e^3*x^7 + 2*a*b*e^3*x^5 + a^2*e^3*x^3), x)","F",0
1125,0,0,0,0.747974," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(7/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{2} e^{5} x^{9} + 2 \, a b e^{5} x^{7} + a^{2} e^{5} x^{5}}, x\right)"," ",0,"integral((b*x^2 + a)^(1/4)*(d*x^2 + c)*sqrt(e*x)/(b^2*e^5*x^9 + 2*a*b*e^5*x^7 + a^2*e^5*x^5), x)","F",0
1126,1,997,0,1.750378," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","\frac{4 \, {\left(5 \, b^{2} d e^{3} x^{4} - 6 \, {\left(4 \, b^{2} c - 9 \, a b d\right)} e^{3} x^{2} - 5 \, {\left(4 \, a b c - 9 \, a^{2} d\right)} e^{3}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} + 20 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(4 \, b^{11} c - 9 \, a b^{10} d\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{3}{4}} \sqrt{e x} e^{3} + {\left(b^{11} x^{2} + a b^{10}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{3}{4}} \sqrt{\frac{{\left(16 \, b^{2} c^{2} - 72 \, a b c d + 81 \, a^{2} d^{2}\right)} \sqrt{b x^{2} + a} e^{7} x + {\left(b^{7} x^{2} + a b^{6}\right)} \sqrt{\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}}}{b x^{2} + a}}}{{\left(256 \, b^{5} c^{4} - 2304 \, a b^{4} c^{3} d + 7776 \, a^{2} b^{3} c^{2} d^{2} - 11664 \, a^{3} b^{2} c d^{3} + 6561 \, a^{4} b d^{4}\right)} e^{14} x^{2} + {\left(256 \, a b^{4} c^{4} - 2304 \, a^{2} b^{3} c^{3} d + 7776 \, a^{3} b^{2} c^{2} d^{2} - 11664 \, a^{4} b c d^{3} + 6561 \, a^{5} d^{4}\right)} e^{14}}\right) + 5 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(4 \, b c - 9 \, a d\right)} \sqrt{e x} e^{3} + {\left(b^{4} x^{2} + a b^{3}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right) - 5 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(4 \, b c - 9 \, a d\right)} \sqrt{e x} e^{3} - {\left(b^{4} x^{2} + a b^{3}\right)} \left(\frac{{\left(256 \, b^{4} c^{4} - 2304 \, a b^{3} c^{3} d + 7776 \, a^{2} b^{2} c^{2} d^{2} - 11664 \, a^{3} b c d^{3} + 6561 \, a^{4} d^{4}\right)} e^{14}}{b^{13}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right)}{40 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}}"," ",0,"1/40*(4*(5*b^2*d*e^3*x^4 - 6*(4*b^2*c - 9*a*b*d)*e^3*x^2 - 5*(4*a*b*c - 9*a^2*d)*e^3)*(b*x^2 + a)^(3/4)*sqrt(e*x) + 20*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(1/4)*arctan(((4*b^11*c - 9*a*b^10*d)*(b*x^2 + a)^(3/4)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(3/4)*sqrt(e*x)*e^3 + (b^11*x^2 + a*b^10)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(3/4)*sqrt(((16*b^2*c^2 - 72*a*b*c*d + 81*a^2*d^2)*sqrt(b*x^2 + a)*e^7*x + (b^7*x^2 + a*b^6)*sqrt((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13))/(b*x^2 + a)))/((256*b^5*c^4 - 2304*a*b^4*c^3*d + 7776*a^2*b^3*c^2*d^2 - 11664*a^3*b^2*c*d^3 + 6561*a^4*b*d^4)*e^14*x^2 + (256*a*b^4*c^4 - 2304*a^2*b^3*c^3*d + 7776*a^3*b^2*c^2*d^2 - 11664*a^4*b*c*d^3 + 6561*a^5*d^4)*e^14)) + 5*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(1/4)*log(-((b*x^2 + a)^(3/4)*(4*b*c - 9*a*d)*sqrt(e*x)*e^3 + (b^4*x^2 + a*b^3)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(1/4))/(b*x^2 + a)) - 5*(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(1/4)*log(-((b*x^2 + a)^(3/4)*(4*b*c - 9*a*d)*sqrt(e*x)*e^3 - (b^4*x^2 + a*b^3)*((256*b^4*c^4 - 2304*a*b^3*c^3*d + 7776*a^2*b^2*c^2*d^2 - 11664*a^3*b*c*d^3 + 6561*a^4*d^4)*e^14/b^13)^(1/4))/(b*x^2 + a)))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3)","B",0
1127,1,448,0,1.530660," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","-\frac{4 \, {\left(5 \, a^{2} d e - {\left(b^{2} c - 6 \, a b d\right)} e x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} + 20 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} b^{7} d e \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{3}{4}} - {\left(b^{8} x^{2} + a b^{7}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{3}{4}} \sqrt{\frac{\sqrt{b x^{2} + a} d^{2} e^{3} x + {\left(b^{5} x^{2} + a b^{4}\right)} \sqrt{\frac{d^{4} e^{6}}{b^{9}}}}{b x^{2} + a}}}{b d^{4} e^{6} x^{2} + a d^{4} e^{6}}\right) - 5 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} d e + {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right) + 5 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x} d e - {\left(b^{3} x^{2} + a b^{2}\right)} \left(\frac{d^{4} e^{6}}{b^{9}}\right)^{\frac{1}{4}}}{b x^{2} + a}\right)}{10 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}}"," ",0,"-1/10*(4*(5*a^2*d*e - (b^2*c - 6*a*b*d)*e*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x) + 20*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(d^4*e^6/b^9)^(1/4)*arctan(-((b*x^2 + a)^(3/4)*sqrt(e*x)*b^7*d*e*(d^4*e^6/b^9)^(3/4) - (b^8*x^2 + a*b^7)*(d^4*e^6/b^9)^(3/4)*sqrt((sqrt(b*x^2 + a)*d^2*e^3*x + (b^5*x^2 + a*b^4)*sqrt(d^4*e^6/b^9))/(b*x^2 + a)))/(b*d^4*e^6*x^2 + a*d^4*e^6)) - 5*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(d^4*e^6/b^9)^(1/4)*log(((b*x^2 + a)^(3/4)*sqrt(e*x)*d*e + (b^3*x^2 + a*b^2)*(d^4*e^6/b^9)^(1/4))/(b*x^2 + a)) + 5*(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)*(d^4*e^6/b^9)^(1/4)*log(((b*x^2 + a)^(3/4)*sqrt(e*x)*d*e - (b^3*x^2 + a*b^2)*(d^4*e^6/b^9)^(1/4))/(b*x^2 + a)))/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2)","B",0
1128,1,62,0,1.326220," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(4 \, b c + a d\right)} x^{2} + 5 \, a c\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{5 \, {\left(a^{2} b^{2} e x^{4} + 2 \, a^{3} b e x^{2} + a^{4} e\right)}}"," ",0,"2/5*((4*b*c + a*d)*x^2 + 5*a*c)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^2*b^2*e*x^4 + 2*a^3*b*e*x^2 + a^4*e)","A",0
1129,1,95,0,1.154886," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, {\left(8 \, b^{2} c - 3 \, a b d\right)} x^{4} + 5 \, a^{2} c + 5 \, {\left(8 \, a b c - 3 \, a^{2} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{15 \, {\left(a^{3} b^{2} e^{3} x^{6} + 2 \, a^{4} b e^{3} x^{4} + a^{5} e^{3} x^{2}\right)}}"," ",0,"-2/15*(4*(8*b^2*c - 3*a*b*d)*x^4 + 5*a^2*c + 5*(8*a*b*c - 3*a^2*d)*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^3*b^2*e^3*x^6 + 2*a^4*b*e^3*x^4 + a^5*e^3*x^2)","A",0
1130,1,119,0,1.257592," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","\frac{2 \, {\left(32 \, {\left(12 \, b^{3} c - 7 \, a b^{2} d\right)} x^{6} + 40 \, {\left(12 \, a b^{2} c - 7 \, a^{2} b d\right)} x^{4} - 15 \, a^{3} c + 5 \, {\left(12 \, a^{2} b c - 7 \, a^{3} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{105 \, {\left(a^{4} b^{2} e^{5} x^{8} + 2 \, a^{5} b e^{5} x^{6} + a^{6} e^{5} x^{4}\right)}}"," ",0,"2/105*(32*(12*b^3*c - 7*a*b^2*d)*x^6 + 40*(12*a*b^2*c - 7*a^2*b*d)*x^4 - 15*a^3*c + 5*(12*a^2*b*c - 7*a^3*d)*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^4*b^2*e^5*x^8 + 2*a^5*b*e^5*x^6 + a^6*e^5*x^4)","A",0
1131,1,143,0,1.083174," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, {\left(16 \, b^{4} c - 11 \, a b^{3} d\right)} x^{8} + 160 \, {\left(16 \, a b^{3} c - 11 \, a^{2} b^{2} d\right)} x^{6} + 35 \, a^{4} c + 20 \, {\left(16 \, a^{2} b^{2} c - 11 \, a^{3} b d\right)} x^{4} - 5 \, {\left(16 \, a^{3} b c - 11 \, a^{4} d\right)} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{385 \, {\left(a^{5} b^{2} e^{7} x^{10} + 2 \, a^{6} b e^{7} x^{8} + a^{7} e^{7} x^{6}\right)}}"," ",0,"-2/385*(128*(16*b^4*c - 11*a*b^3*d)*x^8 + 160*(16*a*b^3*c - 11*a^2*b^2*d)*x^6 + 35*a^4*c + 20*(16*a^2*b^2*c - 11*a^3*b*d)*x^4 - 5*(16*a^3*b*c - 11*a^4*d)*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(a^5*b^2*e^7*x^10 + 2*a^6*b*e^7*x^8 + a^7*e^7*x^6)","A",0
1132,0,0,0,1.071210," ","integrate((e*x)^(13/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{6} x^{8} + c e^{6} x^{6}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((d*e^6*x^8 + c*e^6*x^6)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
1133,0,0,0,1.701355," ","integrate((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{4} x^{6} + c e^{4} x^{4}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((d*e^4*x^6 + c*e^4*x^4)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
1134,0,0,0,1.655214," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e^{2} x^{4} + c e^{2} x^{2}\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((d*e^2*x^4 + c*e^2*x^2)*(b*x^2 + a)^(3/4)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
1135,0,0,0,1.381332," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3), x)","F",0
1136,0,0,0,1.468680," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{3} e^{2} x^{8} + 3 \, a b^{2} e^{2} x^{6} + 3 \, a^{2} b e^{2} x^{4} + a^{3} e^{2} x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^3*e^2*x^8 + 3*a*b^2*e^2*x^6 + 3*a^2*b*e^2*x^4 + a^3*e^2*x^2), x)","F",0
1137,0,0,0,1.185993," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{3} e^{4} x^{10} + 3 \, a b^{2} e^{4} x^{8} + 3 \, a^{2} b e^{4} x^{6} + a^{3} e^{4} x^{4}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^3*e^4*x^10 + 3*a*b^2*e^4*x^8 + 3*a^2*b*e^4*x^6 + a^3*e^4*x^4), x)","F",0
1138,0,0,0,1.471782," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(9/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)} \sqrt{e x}}{b^{3} e^{6} x^{12} + 3 \, a b^{2} e^{6} x^{10} + 3 \, a^{2} b e^{6} x^{8} + a^{3} e^{6} x^{6}}, x\right)"," ",0,"integral((b*x^2 + a)^(3/4)*(d*x^2 + c)*sqrt(e*x)/(b^3*e^6*x^12 + 3*a*b^2*e^6*x^10 + 3*a^2*b*e^6*x^8 + a^3*e^6*x^6), x)","F",0
1139,0,0,0,1.816843," ","integrate((e*x)^m*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} \left(e x\right)^{m}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*(e*x)^m, x)","F",0
1140,0,0,0,1.474690," ","integrate(x^4*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{4}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*x^4, x)","F",0
1141,0,0,0,1.353642," ","integrate(x^2*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{2}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*x^2, x)","F",0
1142,0,0,0,0.837492," ","integrate((b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1143,0,0,0,0.762816," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{2}}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q/x^2, x)","F",0
1144,0,0,0,1.384059," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{4}}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q/x^4, x)","F",0
1145,0,0,0,1.766006," ","integrate(x^5*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{5}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*x^5, x)","F",0
1146,0,0,0,1.489374," ","integrate(x^3*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{3}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*x^3, x)","F",0
1147,0,0,0,0.954753," ","integrate(x*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q*x, x)","F",0
1148,0,0,0,1.530006," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q/x, x)","F",0
1149,0,0,0,1.363241," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{3}}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q/x^3, x)","F",0
1150,0,0,0,1.376348," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{5}}, x\right)"," ",0,"integral((b*x^2 + a)^p*(d*x^2 + c)^q/x^5, x)","F",0
1151,0,0,0,1.503382," ","integrate((e*x)^(5/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} e^{2} x^{2}, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q*e^2*x^2, x)","F",0
1152,0,0,0,1.563697," ","integrate((e*x)^(3/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} e x, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q*e*x, x)","F",0
1153,0,0,0,1.629015," ","integrate((e*x)^(1/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1154,0,0,0,1.640304," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{e x}, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q/(e*x), x)","F",0
1155,0,0,0,2.407814," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q/(e^2*x^2), x)","F",0
1156,0,0,0,1.841501," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q/(e^3*x^3), x)","F",0
