1,1,29,0,0.301206," ","integrate(x^2*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{7} \, B b x^{7} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{3} \, A a x^{3}"," ",0,"1/7*B*b*x^7 + 1/5*B*a*x^5 + 1/5*A*b*x^5 + 1/3*A*a*x^3","A",0
2,1,29,0,0.384148," ","integrate(x*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{6} \, B b x^{6} + \frac{1}{4} \, B a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{2} \, A a x^{2}"," ",0,"1/6*B*b*x^6 + 1/4*B*a*x^4 + 1/4*A*b*x^4 + 1/2*A*a*x^2","A",0
3,1,26,0,0.410384," ","integrate((b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{5} \, B b x^{5} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + A a x"," ",0,"1/5*B*b*x^5 + 1/3*B*a*x^3 + 1/3*A*b*x^3 + A*a*x","A",0
4,1,30,0,0.306616," ","integrate((b*x^2+a)*(B*x^2+A)/x,x, algorithm=""giac"")","\frac{1}{4} \, B b x^{4} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} + \frac{1}{2} \, A a \log\left(x^{2}\right)"," ",0,"1/4*B*b*x^4 + 1/2*B*a*x^2 + 1/2*A*b*x^2 + 1/2*A*a*log(x^2)","A",0
5,1,23,0,0.279998," ","integrate((b*x^2+a)*(B*x^2+A)/x^2,x, algorithm=""giac"")","\frac{1}{3} \, B b x^{3} + B a x + A b x - \frac{A a}{x}"," ",0,"1/3*B*b*x^3 + B*a*x + A*b*x - A*a/x","A",0
6,1,42,0,0.411612," ","integrate((b*x^2+a)*(B*x^2+A)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, B b x^{2} + \frac{1}{2} \, {\left(B a + A b\right)} \log\left(x^{2}\right) - \frac{B a x^{2} + A b x^{2} + A a}{2 \, x^{2}}"," ",0,"1/2*B*b*x^2 + 1/2*(B*a + A*b)*log(x^2) - 1/2*(B*a*x^2 + A*b*x^2 + A*a)/x^2","A",0
7,1,28,0,0.318400," ","integrate((b*x^2+a)*(B*x^2+A)/x^4,x, algorithm=""giac"")","B b x - \frac{3 \, B a x^{2} + 3 \, A b x^{2} + A a}{3 \, x^{3}}"," ",0,"B*b*x - 1/3*(3*B*a*x^2 + 3*A*b*x^2 + A*a)/x^3","A",0
8,1,39,0,0.320063," ","integrate((b*x^2+a)*(B*x^2+A)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, B b \log\left(x^{2}\right) - \frac{3 \, B b x^{4} + 2 \, B a x^{2} + 2 \, A b x^{2} + A a}{4 \, x^{4}}"," ",0,"1/2*B*b*log(x^2) - 1/4*(3*B*b*x^4 + 2*B*a*x^2 + 2*A*b*x^2 + A*a)/x^4","A",0
9,1,31,0,0.290868," ","integrate((b*x^2+a)*(B*x^2+A)/x^6,x, algorithm=""giac"")","-\frac{15 \, B b x^{4} + 5 \, B a x^{2} + 5 \, A b x^{2} + 3 \, A a}{15 \, x^{5}}"," ",0,"-1/15*(15*B*b*x^4 + 5*B*a*x^2 + 5*A*b*x^2 + 3*A*a)/x^5","A",0
10,1,31,0,0.334510," ","integrate((b*x^2+a)*(B*x^2+A)/x^7,x, algorithm=""giac"")","-\frac{6 \, B b x^{4} + 3 \, B a x^{2} + 3 \, A b x^{2} + 2 \, A a}{12 \, x^{6}}"," ",0,"-1/12*(6*B*b*x^4 + 3*B*a*x^2 + 3*A*b*x^2 + 2*A*a)/x^6","A",0
11,1,53,0,0.311671," ","integrate(x^2*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{9} \, B b^{2} x^{9} + \frac{2}{7} \, B a b x^{7} + \frac{1}{7} \, A b^{2} x^{7} + \frac{1}{5} \, B a^{2} x^{5} + \frac{2}{5} \, A a b x^{5} + \frac{1}{3} \, A a^{2} x^{3}"," ",0,"1/9*B*b^2*x^9 + 2/7*B*a*b*x^7 + 1/7*A*b^2*x^7 + 1/5*B*a^2*x^5 + 2/5*A*a*b*x^5 + 1/3*A*a^2*x^3","A",0
12,1,53,0,0.284912," ","integrate(x*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{8} \, B b^{2} x^{8} + \frac{1}{3} \, B a b x^{6} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{4} \, B a^{2} x^{4} + \frac{1}{2} \, A a b x^{4} + \frac{1}{2} \, A a^{2} x^{2}"," ",0,"1/8*B*b^2*x^8 + 1/3*B*a*b*x^6 + 1/6*A*b^2*x^6 + 1/4*B*a^2*x^4 + 1/2*A*a*b*x^4 + 1/2*A*a^2*x^2","A",0
13,1,50,0,0.282193," ","integrate((b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{7} \, B b^{2} x^{7} + \frac{2}{5} \, B a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{1}{3} \, B a^{2} x^{3} + \frac{2}{3} \, A a b x^{3} + A a^{2} x"," ",0,"1/7*B*b^2*x^7 + 2/5*B*a*b*x^5 + 1/5*A*b^2*x^5 + 1/3*B*a^2*x^3 + 2/3*A*a*b*x^3 + A*a^2*x","A",0
14,1,53,0,0.308376," ","integrate((b*x^2+a)^2*(B*x^2+A)/x,x, algorithm=""giac"")","\frac{1}{6} \, B b^{2} x^{6} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} + \frac{1}{2} \, A a^{2} \log\left(x^{2}\right)"," ",0,"1/6*B*b^2*x^6 + 1/2*B*a*b*x^4 + 1/4*A*b^2*x^4 + 1/2*B*a^2*x^2 + A*a*b*x^2 + 1/2*A*a^2*log(x^2)","A",0
15,1,48,0,0.372831," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, B b^{2} x^{5} + \frac{2}{3} \, B a b x^{3} + \frac{1}{3} \, A b^{2} x^{3} + B a^{2} x + 2 \, A a b x - \frac{A a^{2}}{x}"," ",0,"1/5*B*b^2*x^5 + 2/3*B*a*b*x^3 + 1/3*A*b^2*x^3 + B*a^2*x + 2*A*a*b*x - A*a^2/x","A",0
16,1,70,0,0.329635," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, B b^{2} x^{4} + B a b x^{2} + \frac{1}{2} \, A b^{2} x^{2} + \frac{1}{2} \, {\left(B a^{2} + 2 \, A a b\right)} \log\left(x^{2}\right) - \frac{B a^{2} x^{2} + 2 \, A a b x^{2} + A a^{2}}{2 \, x^{2}}"," ",0,"1/4*B*b^2*x^4 + B*a*b*x^2 + 1/2*A*b^2*x^2 + 1/2*(B*a^2 + 2*A*a*b)*log(x^2) - 1/2*(B*a^2*x^2 + 2*A*a*b*x^2 + A*a^2)/x^2","A",0
17,1,50,0,0.352856," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, B b^{2} x^{3} + 2 \, B a b x + A b^{2} x - \frac{3 \, B a^{2} x^{2} + 6 \, A a b x^{2} + A a^{2}}{3 \, x^{3}}"," ",0,"1/3*B*b^2*x^3 + 2*B*a*b*x + A*b^2*x - 1/3*(3*B*a^2*x^2 + 6*A*a*b*x^2 + A*a^2)/x^3","A",0
18,1,72,0,0.342485," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^5,x, algorithm=""giac"")","\frac{1}{2} \, B b^{2} x^{2} + \frac{1}{2} \, {\left(2 \, B a b + A b^{2}\right)} \log\left(x^{2}\right) - \frac{6 \, B a b x^{4} + 3 \, A b^{2} x^{4} + 2 \, B a^{2} x^{2} + 4 \, A a b x^{2} + A a^{2}}{4 \, x^{4}}"," ",0,"1/2*B*b^2*x^2 + 1/2*(2*B*a*b + A*b^2)*log(x^2) - 1/4*(6*B*a*b*x^4 + 3*A*b^2*x^4 + 2*B*a^2*x^2 + 4*A*a*b*x^2 + A*a^2)/x^4","A",0
19,1,53,0,0.409522," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^6,x, algorithm=""giac"")","B b^{2} x - \frac{30 \, B a b x^{4} + 15 \, A b^{2} x^{4} + 5 \, B a^{2} x^{2} + 10 \, A a b x^{2} + 3 \, A a^{2}}{15 \, x^{5}}"," ",0,"B*b^2*x - 1/15*(30*B*a*b*x^4 + 15*A*b^2*x^4 + 5*B*a^2*x^2 + 10*A*a*b*x^2 + 3*A*a^2)/x^5","A",0
20,1,66,0,0.320911," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^7,x, algorithm=""giac"")","\frac{1}{2} \, B b^{2} \log\left(x^{2}\right) - \frac{11 \, B b^{2} x^{6} + 12 \, B a b x^{4} + 6 \, A b^{2} x^{4} + 3 \, B a^{2} x^{2} + 6 \, A a b x^{2} + 2 \, A a^{2}}{12 \, x^{6}}"," ",0,"1/2*B*b^2*log(x^2) - 1/12*(11*B*b^2*x^6 + 12*B*a*b*x^4 + 6*A*b^2*x^4 + 3*B*a^2*x^2 + 6*A*a*b*x^2 + 2*A*a^2)/x^6","A",0
21,1,55,0,0.372985," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^8,x, algorithm=""giac"")","-\frac{105 \, B b^{2} x^{6} + 70 \, B a b x^{4} + 35 \, A b^{2} x^{4} + 21 \, B a^{2} x^{2} + 42 \, A a b x^{2} + 15 \, A a^{2}}{105 \, x^{7}}"," ",0,"-1/105*(105*B*b^2*x^6 + 70*B*a*b*x^4 + 35*A*b^2*x^4 + 21*B*a^2*x^2 + 42*A*a*b*x^2 + 15*A*a^2)/x^7","A",0
22,1,55,0,0.375358," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^9,x, algorithm=""giac"")","-\frac{12 \, B b^{2} x^{6} + 12 \, B a b x^{4} + 6 \, A b^{2} x^{4} + 4 \, B a^{2} x^{2} + 8 \, A a b x^{2} + 3 \, A a^{2}}{24 \, x^{8}}"," ",0,"-1/24*(12*B*b^2*x^6 + 12*B*a*b*x^4 + 6*A*b^2*x^4 + 4*B*a^2*x^2 + 8*A*a*b*x^2 + 3*A*a^2)/x^8","A",0
23,1,125,0,0.365149," ","integrate(x^9*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{22} \, B b^{5} x^{22} + \frac{1}{4} \, B a b^{4} x^{20} + \frac{1}{20} \, A b^{5} x^{20} + \frac{5}{9} \, B a^{2} b^{3} x^{18} + \frac{5}{18} \, A a b^{4} x^{18} + \frac{5}{8} \, B a^{3} b^{2} x^{16} + \frac{5}{8} \, A a^{2} b^{3} x^{16} + \frac{5}{14} \, B a^{4} b x^{14} + \frac{5}{7} \, A a^{3} b^{2} x^{14} + \frac{1}{12} \, B a^{5} x^{12} + \frac{5}{12} \, A a^{4} b x^{12} + \frac{1}{10} \, A a^{5} x^{10}"," ",0,"1/22*B*b^5*x^22 + 1/4*B*a*b^4*x^20 + 1/20*A*b^5*x^20 + 5/9*B*a^2*b^3*x^18 + 5/18*A*a*b^4*x^18 + 5/8*B*a^3*b^2*x^16 + 5/8*A*a^2*b^3*x^16 + 5/14*B*a^4*b*x^14 + 5/7*A*a^3*b^2*x^14 + 1/12*B*a^5*x^12 + 5/12*A*a^4*b*x^12 + 1/10*A*a^5*x^10","A",0
24,1,125,0,0.330814," ","integrate(x^8*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{21} \, B b^{5} x^{21} + \frac{5}{19} \, B a b^{4} x^{19} + \frac{1}{19} \, A b^{5} x^{19} + \frac{10}{17} \, B a^{2} b^{3} x^{17} + \frac{5}{17} \, A a b^{4} x^{17} + \frac{2}{3} \, B a^{3} b^{2} x^{15} + \frac{2}{3} \, A a^{2} b^{3} x^{15} + \frac{5}{13} \, B a^{4} b x^{13} + \frac{10}{13} \, A a^{3} b^{2} x^{13} + \frac{1}{11} \, B a^{5} x^{11} + \frac{5}{11} \, A a^{4} b x^{11} + \frac{1}{9} \, A a^{5} x^{9}"," ",0,"1/21*B*b^5*x^21 + 5/19*B*a*b^4*x^19 + 1/19*A*b^5*x^19 + 10/17*B*a^2*b^3*x^17 + 5/17*A*a*b^4*x^17 + 2/3*B*a^3*b^2*x^15 + 2/3*A*a^2*b^3*x^15 + 5/13*B*a^4*b*x^13 + 10/13*A*a^3*b^2*x^13 + 1/11*B*a^5*x^11 + 5/11*A*a^4*b*x^11 + 1/9*A*a^5*x^9","A",0
25,1,125,0,0.336844," ","integrate(x^7*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{20} \, B b^{5} x^{20} + \frac{5}{18} \, B a b^{4} x^{18} + \frac{1}{18} \, A b^{5} x^{18} + \frac{5}{8} \, B a^{2} b^{3} x^{16} + \frac{5}{16} \, A a b^{4} x^{16} + \frac{5}{7} \, B a^{3} b^{2} x^{14} + \frac{5}{7} \, A a^{2} b^{3} x^{14} + \frac{5}{12} \, B a^{4} b x^{12} + \frac{5}{6} \, A a^{3} b^{2} x^{12} + \frac{1}{10} \, B a^{5} x^{10} + \frac{1}{2} \, A a^{4} b x^{10} + \frac{1}{8} \, A a^{5} x^{8}"," ",0,"1/20*B*b^5*x^20 + 5/18*B*a*b^4*x^18 + 1/18*A*b^5*x^18 + 5/8*B*a^2*b^3*x^16 + 5/16*A*a*b^4*x^16 + 5/7*B*a^3*b^2*x^14 + 5/7*A*a^2*b^3*x^14 + 5/12*B*a^4*b*x^12 + 5/6*A*a^3*b^2*x^12 + 1/10*B*a^5*x^10 + 1/2*A*a^4*b*x^10 + 1/8*A*a^5*x^8","A",0
26,1,125,0,0.368817," ","integrate(x^6*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{19} \, B b^{5} x^{19} + \frac{5}{17} \, B a b^{4} x^{17} + \frac{1}{17} \, A b^{5} x^{17} + \frac{2}{3} \, B a^{2} b^{3} x^{15} + \frac{1}{3} \, A a b^{4} x^{15} + \frac{10}{13} \, B a^{3} b^{2} x^{13} + \frac{10}{13} \, A a^{2} b^{3} x^{13} + \frac{5}{11} \, B a^{4} b x^{11} + \frac{10}{11} \, A a^{3} b^{2} x^{11} + \frac{1}{9} \, B a^{5} x^{9} + \frac{5}{9} \, A a^{4} b x^{9} + \frac{1}{7} \, A a^{5} x^{7}"," ",0,"1/19*B*b^5*x^19 + 5/17*B*a*b^4*x^17 + 1/17*A*b^5*x^17 + 2/3*B*a^2*b^3*x^15 + 1/3*A*a*b^4*x^15 + 10/13*B*a^3*b^2*x^13 + 10/13*A*a^2*b^3*x^13 + 5/11*B*a^4*b*x^11 + 10/11*A*a^3*b^2*x^11 + 1/9*B*a^5*x^9 + 5/9*A*a^4*b*x^9 + 1/7*A*a^5*x^7","A",0
27,1,124,0,0.306108," ","integrate(x^5*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{18} \, B b^{5} x^{18} + \frac{5}{16} \, B a b^{4} x^{16} + \frac{1}{16} \, A b^{5} x^{16} + \frac{5}{7} \, B a^{2} b^{3} x^{14} + \frac{5}{14} \, A a b^{4} x^{14} + \frac{5}{6} \, B a^{3} b^{2} x^{12} + \frac{5}{6} \, A a^{2} b^{3} x^{12} + \frac{1}{2} \, B a^{4} b x^{10} + A a^{3} b^{2} x^{10} + \frac{1}{8} \, B a^{5} x^{8} + \frac{5}{8} \, A a^{4} b x^{8} + \frac{1}{6} \, A a^{5} x^{6}"," ",0,"1/18*B*b^5*x^18 + 5/16*B*a*b^4*x^16 + 1/16*A*b^5*x^16 + 5/7*B*a^2*b^3*x^14 + 5/14*A*a*b^4*x^14 + 5/6*B*a^3*b^2*x^12 + 5/6*A*a^2*b^3*x^12 + 1/2*B*a^4*b*x^10 + A*a^3*b^2*x^10 + 1/8*B*a^5*x^8 + 5/8*A*a^4*b*x^8 + 1/6*A*a^5*x^6","A",0
28,1,125,0,0.310967," ","integrate(x^4*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{17} \, B b^{5} x^{17} + \frac{1}{3} \, B a b^{4} x^{15} + \frac{1}{15} \, A b^{5} x^{15} + \frac{10}{13} \, B a^{2} b^{3} x^{13} + \frac{5}{13} \, A a b^{4} x^{13} + \frac{10}{11} \, B a^{3} b^{2} x^{11} + \frac{10}{11} \, A a^{2} b^{3} x^{11} + \frac{5}{9} \, B a^{4} b x^{9} + \frac{10}{9} \, A a^{3} b^{2} x^{9} + \frac{1}{7} \, B a^{5} x^{7} + \frac{5}{7} \, A a^{4} b x^{7} + \frac{1}{5} \, A a^{5} x^{5}"," ",0,"1/17*B*b^5*x^17 + 1/3*B*a*b^4*x^15 + 1/15*A*b^5*x^15 + 10/13*B*a^2*b^3*x^13 + 5/13*A*a*b^4*x^13 + 10/11*B*a^3*b^2*x^11 + 10/11*A*a^2*b^3*x^11 + 5/9*B*a^4*b*x^9 + 10/9*A*a^3*b^2*x^9 + 1/7*B*a^5*x^7 + 5/7*A*a^4*b*x^7 + 1/5*A*a^5*x^5","A",0
29,1,123,0,0.437137," ","integrate(x^3*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{16} \, B b^{5} x^{16} + \frac{5}{14} \, B a b^{4} x^{14} + \frac{1}{14} \, A b^{5} x^{14} + \frac{5}{6} \, B a^{2} b^{3} x^{12} + \frac{5}{12} \, A a b^{4} x^{12} + B a^{3} b^{2} x^{10} + A a^{2} b^{3} x^{10} + \frac{5}{8} \, B a^{4} b x^{8} + \frac{5}{4} \, A a^{3} b^{2} x^{8} + \frac{1}{6} \, B a^{5} x^{6} + \frac{5}{6} \, A a^{4} b x^{6} + \frac{1}{4} \, A a^{5} x^{4}"," ",0,"1/16*B*b^5*x^16 + 5/14*B*a*b^4*x^14 + 1/14*A*b^5*x^14 + 5/6*B*a^2*b^3*x^12 + 5/12*A*a*b^4*x^12 + B*a^3*b^2*x^10 + A*a^2*b^3*x^10 + 5/8*B*a^4*b*x^8 + 5/4*A*a^3*b^2*x^8 + 1/6*B*a^5*x^6 + 5/6*A*a^4*b*x^6 + 1/4*A*a^5*x^4","A",0
30,1,124,0,0.361089," ","integrate(x^2*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{15} \, B b^{5} x^{15} + \frac{5}{13} \, B a b^{4} x^{13} + \frac{1}{13} \, A b^{5} x^{13} + \frac{10}{11} \, B a^{2} b^{3} x^{11} + \frac{5}{11} \, A a b^{4} x^{11} + \frac{10}{9} \, B a^{3} b^{2} x^{9} + \frac{10}{9} \, A a^{2} b^{3} x^{9} + \frac{5}{7} \, B a^{4} b x^{7} + \frac{10}{7} \, A a^{3} b^{2} x^{7} + \frac{1}{5} \, B a^{5} x^{5} + A a^{4} b x^{5} + \frac{1}{3} \, A a^{5} x^{3}"," ",0,"1/15*B*b^5*x^15 + 5/13*B*a*b^4*x^13 + 1/13*A*b^5*x^13 + 10/11*B*a^2*b^3*x^11 + 5/11*A*a*b^4*x^11 + 10/9*B*a^3*b^2*x^9 + 10/9*A*a^2*b^3*x^9 + 5/7*B*a^4*b*x^7 + 10/7*A*a^3*b^2*x^7 + 1/5*B*a^5*x^5 + A*a^4*b*x^5 + 1/3*A*a^5*x^3","A",0
31,1,124,0,0.344924," ","integrate(x*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{14} \, B b^{5} x^{14} + \frac{5}{12} \, B a b^{4} x^{12} + \frac{1}{12} \, A b^{5} x^{12} + B a^{2} b^{3} x^{10} + \frac{1}{2} \, A a b^{4} x^{10} + \frac{5}{4} \, B a^{3} b^{2} x^{8} + \frac{5}{4} \, A a^{2} b^{3} x^{8} + \frac{5}{6} \, B a^{4} b x^{6} + \frac{5}{3} \, A a^{3} b^{2} x^{6} + \frac{1}{4} \, B a^{5} x^{4} + \frac{5}{4} \, A a^{4} b x^{4} + \frac{1}{2} \, A a^{5} x^{2}"," ",0,"1/14*B*b^5*x^14 + 5/12*B*a*b^4*x^12 + 1/12*A*b^5*x^12 + B*a^2*b^3*x^10 + 1/2*A*a*b^4*x^10 + 5/4*B*a^3*b^2*x^8 + 5/4*A*a^2*b^3*x^8 + 5/6*B*a^4*b*x^6 + 5/3*A*a^3*b^2*x^6 + 1/4*B*a^5*x^4 + 5/4*A*a^4*b*x^4 + 1/2*A*a^5*x^2","B",0
32,1,121,0,0.330251," ","integrate((b*x^2+a)^5*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{13} \, B b^{5} x^{13} + \frac{5}{11} \, B a b^{4} x^{11} + \frac{1}{11} \, A b^{5} x^{11} + \frac{10}{9} \, B a^{2} b^{3} x^{9} + \frac{5}{9} \, A a b^{4} x^{9} + \frac{10}{7} \, B a^{3} b^{2} x^{7} + \frac{10}{7} \, A a^{2} b^{3} x^{7} + B a^{4} b x^{5} + 2 \, A a^{3} b^{2} x^{5} + \frac{1}{3} \, B a^{5} x^{3} + \frac{5}{3} \, A a^{4} b x^{3} + A a^{5} x"," ",0,"1/13*B*b^5*x^13 + 5/11*B*a*b^4*x^11 + 1/11*A*b^5*x^11 + 10/9*B*a^2*b^3*x^9 + 5/9*A*a*b^4*x^9 + 10/7*B*a^3*b^2*x^7 + 10/7*A*a^2*b^3*x^7 + B*a^4*b*x^5 + 2*A*a^3*b^2*x^5 + 1/3*B*a^5*x^3 + 5/3*A*a^4*b*x^3 + A*a^5*x","A",0
33,1,126,0,0.323485," ","integrate((b*x^2+a)^5*(B*x^2+A)/x,x, algorithm=""giac"")","\frac{1}{12} \, B b^{5} x^{12} + \frac{1}{2} \, B a b^{4} x^{10} + \frac{1}{10} \, A b^{5} x^{10} + \frac{5}{4} \, B a^{2} b^{3} x^{8} + \frac{5}{8} \, A a b^{4} x^{8} + \frac{5}{3} \, B a^{3} b^{2} x^{6} + \frac{5}{3} \, A a^{2} b^{3} x^{6} + \frac{5}{4} \, B a^{4} b x^{4} + \frac{5}{2} \, A a^{3} b^{2} x^{4} + \frac{1}{2} \, B a^{5} x^{2} + \frac{5}{2} \, A a^{4} b x^{2} + \frac{1}{2} \, A a^{5} \log\left(x^{2}\right)"," ",0,"1/12*B*b^5*x^12 + 1/2*B*a*b^4*x^10 + 1/10*A*b^5*x^10 + 5/4*B*a^2*b^3*x^8 + 5/8*A*a*b^4*x^8 + 5/3*B*a^3*b^2*x^6 + 5/3*A*a^2*b^3*x^6 + 5/4*B*a^4*b*x^4 + 5/2*A*a^3*b^2*x^4 + 1/2*B*a^5*x^2 + 5/2*A*a^4*b*x^2 + 1/2*A*a^5*log(x^2)","A",0
34,1,120,0,0.306625," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^2,x, algorithm=""giac"")","\frac{1}{11} \, B b^{5} x^{11} + \frac{5}{9} \, B a b^{4} x^{9} + \frac{1}{9} \, A b^{5} x^{9} + \frac{10}{7} \, B a^{2} b^{3} x^{7} + \frac{5}{7} \, A a b^{4} x^{7} + 2 \, B a^{3} b^{2} x^{5} + 2 \, A a^{2} b^{3} x^{5} + \frac{5}{3} \, B a^{4} b x^{3} + \frac{10}{3} \, A a^{3} b^{2} x^{3} + B a^{5} x + 5 \, A a^{4} b x - \frac{A a^{5}}{x}"," ",0,"1/11*B*b^5*x^11 + 5/9*B*a*b^4*x^9 + 1/9*A*b^5*x^9 + 10/7*B*a^2*b^3*x^7 + 5/7*A*a*b^4*x^7 + 2*B*a^3*b^2*x^5 + 2*A*a^2*b^3*x^5 + 5/3*B*a^4*b*x^3 + 10/3*A*a^3*b^2*x^3 + B*a^5*x + 5*A*a^4*b*x - A*a^5/x","A",0
35,1,145,0,0.384472," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^3,x, algorithm=""giac"")","\frac{1}{10} \, B b^{5} x^{10} + \frac{5}{8} \, B a b^{4} x^{8} + \frac{1}{8} \, A b^{5} x^{8} + \frac{5}{3} \, B a^{2} b^{3} x^{6} + \frac{5}{6} \, A a b^{4} x^{6} + \frac{5}{2} \, B a^{3} b^{2} x^{4} + \frac{5}{2} \, A a^{2} b^{3} x^{4} + \frac{5}{2} \, B a^{4} b x^{2} + 5 \, A a^{3} b^{2} x^{2} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} \log\left(x^{2}\right) - \frac{B a^{5} x^{2} + 5 \, A a^{4} b x^{2} + A a^{5}}{2 \, x^{2}}"," ",0,"1/10*B*b^5*x^10 + 5/8*B*a*b^4*x^8 + 1/8*A*b^5*x^8 + 5/3*B*a^2*b^3*x^6 + 5/6*A*a*b^4*x^6 + 5/2*B*a^3*b^2*x^4 + 5/2*A*a^2*b^3*x^4 + 5/2*B*a^4*b*x^2 + 5*A*a^3*b^2*x^2 + 1/2*(B*a^5 + 5*A*a^4*b)*log(x^2) - 1/2*(B*a^5*x^2 + 5*A*a^4*b*x^2 + A*a^5)/x^2","A",0
36,1,122,0,0.371956," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^4,x, algorithm=""giac"")","\frac{1}{9} \, B b^{5} x^{9} + \frac{5}{7} \, B a b^{4} x^{7} + \frac{1}{7} \, A b^{5} x^{7} + 2 \, B a^{2} b^{3} x^{5} + A a b^{4} x^{5} + \frac{10}{3} \, B a^{3} b^{2} x^{3} + \frac{10}{3} \, A a^{2} b^{3} x^{3} + 5 \, B a^{4} b x + 10 \, A a^{3} b^{2} x - \frac{3 \, B a^{5} x^{2} + 15 \, A a^{4} b x^{2} + A a^{5}}{3 \, x^{3}}"," ",0,"1/9*B*b^5*x^9 + 5/7*B*a*b^4*x^7 + 1/7*A*b^5*x^7 + 2*B*a^2*b^3*x^5 + A*a*b^4*x^5 + 10/3*B*a^3*b^2*x^3 + 10/3*A*a^2*b^3*x^3 + 5*B*a^4*b*x + 10*A*a^3*b^2*x - 1/3*(3*B*a^5*x^2 + 15*A*a^4*b*x^2 + A*a^5)/x^3","A",0
37,1,149,0,0.345816," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^5,x, algorithm=""giac"")","\frac{1}{8} \, B b^{5} x^{8} + \frac{5}{6} \, B a b^{4} x^{6} + \frac{1}{6} \, A b^{5} x^{6} + \frac{5}{2} \, B a^{2} b^{3} x^{4} + \frac{5}{4} \, A a b^{4} x^{4} + 5 \, B a^{3} b^{2} x^{2} + 5 \, A a^{2} b^{3} x^{2} + \frac{5}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} \log\left(x^{2}\right) - \frac{15 \, B a^{4} b x^{4} + 30 \, A a^{3} b^{2} x^{4} + 2 \, B a^{5} x^{2} + 10 \, A a^{4} b x^{2} + A a^{5}}{4 \, x^{4}}"," ",0,"1/8*B*b^5*x^8 + 5/6*B*a*b^4*x^6 + 1/6*A*b^5*x^6 + 5/2*B*a^2*b^3*x^4 + 5/4*A*a*b^4*x^4 + 5*B*a^3*b^2*x^2 + 5*A*a^2*b^3*x^2 + 5/2*(B*a^4*b + 2*A*a^3*b^2)*log(x^2) - 1/4*(15*B*a^4*b*x^4 + 30*A*a^3*b^2*x^4 + 2*B*a^5*x^2 + 10*A*a^4*b*x^2 + A*a^5)/x^4","A",0
38,1,123,0,0.365717," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^6,x, algorithm=""giac"")","\frac{1}{7} \, B b^{5} x^{7} + B a b^{4} x^{5} + \frac{1}{5} \, A b^{5} x^{5} + \frac{10}{3} \, B a^{2} b^{3} x^{3} + \frac{5}{3} \, A a b^{4} x^{3} + 10 \, B a^{3} b^{2} x + 10 \, A a^{2} b^{3} x - \frac{75 \, B a^{4} b x^{4} + 150 \, A a^{3} b^{2} x^{4} + 5 \, B a^{5} x^{2} + 25 \, A a^{4} b x^{2} + 3 \, A a^{5}}{15 \, x^{5}}"," ",0,"1/7*B*b^5*x^7 + B*a*b^4*x^5 + 1/5*A*b^5*x^5 + 10/3*B*a^2*b^3*x^3 + 5/3*A*a*b^4*x^3 + 10*B*a^3*b^2*x + 10*A*a^2*b^3*x - 1/15*(75*B*a^4*b*x^4 + 150*A*a^3*b^2*x^4 + 5*B*a^5*x^2 + 25*A*a^4*b*x^2 + 3*A*a^5)/x^5","A",0
39,1,151,0,0.339994," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^7,x, algorithm=""giac"")","\frac{1}{6} \, B b^{5} x^{6} + \frac{5}{4} \, B a b^{4} x^{4} + \frac{1}{4} \, A b^{5} x^{4} + 5 \, B a^{2} b^{3} x^{2} + \frac{5}{2} \, A a b^{4} x^{2} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} \log\left(x^{2}\right) - \frac{110 \, B a^{3} b^{2} x^{6} + 110 \, A a^{2} b^{3} x^{6} + 30 \, B a^{4} b x^{4} + 60 \, A a^{3} b^{2} x^{4} + 3 \, B a^{5} x^{2} + 15 \, A a^{4} b x^{2} + 2 \, A a^{5}}{12 \, x^{6}}"," ",0,"1/6*B*b^5*x^6 + 5/4*B*a*b^4*x^4 + 1/4*A*b^5*x^4 + 5*B*a^2*b^3*x^2 + 5/2*A*a*b^4*x^2 + 5*(B*a^3*b^2 + A*a^2*b^3)*log(x^2) - 1/12*(110*B*a^3*b^2*x^6 + 110*A*a^2*b^3*x^6 + 30*B*a^4*b*x^4 + 60*A*a^3*b^2*x^4 + 3*B*a^5*x^2 + 15*A*a^4*b*x^2 + 2*A*a^5)/x^6","A",0
40,1,124,0,0.316590," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^8,x, algorithm=""giac"")","\frac{1}{5} \, B b^{5} x^{5} + \frac{5}{3} \, B a b^{4} x^{3} + \frac{1}{3} \, A b^{5} x^{3} + 10 \, B a^{2} b^{3} x + 5 \, A a b^{4} x - \frac{1050 \, B a^{3} b^{2} x^{6} + 1050 \, A a^{2} b^{3} x^{6} + 175 \, B a^{4} b x^{4} + 350 \, A a^{3} b^{2} x^{4} + 21 \, B a^{5} x^{2} + 105 \, A a^{4} b x^{2} + 15 \, A a^{5}}{105 \, x^{7}}"," ",0,"1/5*B*b^5*x^5 + 5/3*B*a*b^4*x^3 + 1/3*A*b^5*x^3 + 10*B*a^2*b^3*x + 5*A*a*b^4*x - 1/105*(1050*B*a^3*b^2*x^6 + 1050*A*a^2*b^3*x^6 + 175*B*a^4*b*x^4 + 350*A*a^3*b^2*x^4 + 21*B*a^5*x^2 + 105*A*a^4*b*x^2 + 15*A*a^5)/x^7","A",0
41,1,150,0,0.365992," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^9,x, algorithm=""giac"")","\frac{1}{4} \, B b^{5} x^{4} + \frac{5}{2} \, B a b^{4} x^{2} + \frac{1}{2} \, A b^{5} x^{2} + \frac{5}{2} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} \log\left(x^{2}\right) - \frac{250 \, B a^{2} b^{3} x^{8} + 125 \, A a b^{4} x^{8} + 120 \, B a^{3} b^{2} x^{6} + 120 \, A a^{2} b^{3} x^{6} + 30 \, B a^{4} b x^{4} + 60 \, A a^{3} b^{2} x^{4} + 4 \, B a^{5} x^{2} + 20 \, A a^{4} b x^{2} + 3 \, A a^{5}}{24 \, x^{8}}"," ",0,"1/4*B*b^5*x^4 + 5/2*B*a*b^4*x^2 + 1/2*A*b^5*x^2 + 5/2*(2*B*a^2*b^3 + A*a*b^4)*log(x^2) - 1/24*(250*B*a^2*b^3*x^8 + 125*A*a*b^4*x^8 + 120*B*a^3*b^2*x^6 + 120*A*a^2*b^3*x^6 + 30*B*a^4*b*x^4 + 60*A*a^3*b^2*x^4 + 4*B*a^5*x^2 + 20*A*a^4*b*x^2 + 3*A*a^5)/x^8","A",0
42,1,123,0,0.368139," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^10,x, algorithm=""giac"")","\frac{1}{3} \, B b^{5} x^{3} + 5 \, B a b^{4} x + A b^{5} x - \frac{630 \, B a^{2} b^{3} x^{8} + 315 \, A a b^{4} x^{8} + 210 \, B a^{3} b^{2} x^{6} + 210 \, A a^{2} b^{3} x^{6} + 63 \, B a^{4} b x^{4} + 126 \, A a^{3} b^{2} x^{4} + 9 \, B a^{5} x^{2} + 45 \, A a^{4} b x^{2} + 7 \, A a^{5}}{63 \, x^{9}}"," ",0,"1/3*B*b^5*x^3 + 5*B*a*b^4*x + A*b^5*x - 1/63*(630*B*a^2*b^3*x^8 + 315*A*a*b^4*x^8 + 210*B*a^3*b^2*x^6 + 210*A*a^2*b^3*x^6 + 63*B*a^4*b*x^4 + 126*A*a^3*b^2*x^4 + 9*B*a^5*x^2 + 45*A*a^4*b*x^2 + 7*A*a^5)/x^9","A",0
43,1,147,0,0.430094," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^11,x, algorithm=""giac"")","\frac{1}{2} \, B b^{5} x^{2} + \frac{1}{2} \, {\left(5 \, B a b^{4} + A b^{5}\right)} \log\left(x^{2}\right) - \frac{685 \, B a b^{4} x^{10} + 137 \, A b^{5} x^{10} + 600 \, B a^{2} b^{3} x^{8} + 300 \, A a b^{4} x^{8} + 300 \, B a^{3} b^{2} x^{6} + 300 \, A a^{2} b^{3} x^{6} + 100 \, B a^{4} b x^{4} + 200 \, A a^{3} b^{2} x^{4} + 15 \, B a^{5} x^{2} + 75 \, A a^{4} b x^{2} + 12 \, A a^{5}}{120 \, x^{10}}"," ",0,"1/2*B*b^5*x^2 + 1/2*(5*B*a*b^4 + A*b^5)*log(x^2) - 1/120*(685*B*a*b^4*x^10 + 137*A*b^5*x^10 + 600*B*a^2*b^3*x^8 + 300*A*a*b^4*x^8 + 300*B*a^3*b^2*x^6 + 300*A*a^2*b^3*x^6 + 100*B*a^4*b*x^4 + 200*A*a^3*b^2*x^4 + 15*B*a^5*x^2 + 75*A*a^4*b*x^2 + 12*A*a^5)/x^10","A",0
44,1,125,0,0.362529," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^12,x, algorithm=""giac"")","B b^{5} x - \frac{3465 \, B a b^{4} x^{10} + 693 \, A b^{5} x^{10} + 2310 \, B a^{2} b^{3} x^{8} + 1155 \, A a b^{4} x^{8} + 1386 \, B a^{3} b^{2} x^{6} + 1386 \, A a^{2} b^{3} x^{6} + 495 \, B a^{4} b x^{4} + 990 \, A a^{3} b^{2} x^{4} + 77 \, B a^{5} x^{2} + 385 \, A a^{4} b x^{2} + 63 \, A a^{5}}{693 \, x^{11}}"," ",0,"B*b^5*x - 1/693*(3465*B*a*b^4*x^10 + 693*A*b^5*x^10 + 2310*B*a^2*b^3*x^8 + 1155*A*a*b^4*x^8 + 1386*B*a^3*b^2*x^6 + 1386*A*a^2*b^3*x^6 + 495*B*a^4*b*x^4 + 990*A*a^3*b^2*x^4 + 77*B*a^5*x^2 + 385*A*a^4*b*x^2 + 63*A*a^5)/x^11","A",0
45,1,138,0,0.402533," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^13,x, algorithm=""giac"")","\frac{1}{2} \, B b^{5} \log\left(x^{2}\right) - \frac{147 \, B b^{5} x^{12} + 300 \, B a b^{4} x^{10} + 60 \, A b^{5} x^{10} + 300 \, B a^{2} b^{3} x^{8} + 150 \, A a b^{4} x^{8} + 200 \, B a^{3} b^{2} x^{6} + 200 \, A a^{2} b^{3} x^{6} + 75 \, B a^{4} b x^{4} + 150 \, A a^{3} b^{2} x^{4} + 12 \, B a^{5} x^{2} + 60 \, A a^{4} b x^{2} + 10 \, A a^{5}}{120 \, x^{12}}"," ",0,"1/2*B*b^5*log(x^2) - 1/120*(147*B*b^5*x^12 + 300*B*a*b^4*x^10 + 60*A*b^5*x^10 + 300*B*a^2*b^3*x^8 + 150*A*a*b^4*x^8 + 200*B*a^3*b^2*x^6 + 200*A*a^2*b^3*x^6 + 75*B*a^4*b*x^4 + 150*A*a^3*b^2*x^4 + 12*B*a^5*x^2 + 60*A*a^4*b*x^2 + 10*A*a^5)/x^12","A",0
46,1,127,0,0.270309," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^14,x, algorithm=""giac"")","-\frac{9009 \, B b^{5} x^{12} + 15015 \, B a b^{4} x^{10} + 3003 \, A b^{5} x^{10} + 18018 \, B a^{2} b^{3} x^{8} + 9009 \, A a b^{4} x^{8} + 12870 \, B a^{3} b^{2} x^{6} + 12870 \, A a^{2} b^{3} x^{6} + 5005 \, B a^{4} b x^{4} + 10010 \, A a^{3} b^{2} x^{4} + 819 \, B a^{5} x^{2} + 4095 \, A a^{4} b x^{2} + 693 \, A a^{5}}{9009 \, x^{13}}"," ",0,"-1/9009*(9009*B*b^5*x^12 + 15015*B*a*b^4*x^10 + 3003*A*b^5*x^10 + 18018*B*a^2*b^3*x^8 + 9009*A*a*b^4*x^8 + 12870*B*a^3*b^2*x^6 + 12870*A*a^2*b^3*x^6 + 5005*B*a^4*b*x^4 + 10010*A*a^3*b^2*x^4 + 819*B*a^5*x^2 + 4095*A*a^4*b*x^2 + 693*A*a^5)/x^13","A",0
47,1,127,0,0.404521," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^15,x, algorithm=""giac"")","-\frac{42 \, B b^{5} x^{12} + 105 \, B a b^{4} x^{10} + 21 \, A b^{5} x^{10} + 140 \, B a^{2} b^{3} x^{8} + 70 \, A a b^{4} x^{8} + 105 \, B a^{3} b^{2} x^{6} + 105 \, A a^{2} b^{3} x^{6} + 42 \, B a^{4} b x^{4} + 84 \, A a^{3} b^{2} x^{4} + 7 \, B a^{5} x^{2} + 35 \, A a^{4} b x^{2} + 6 \, A a^{5}}{84 \, x^{14}}"," ",0,"-1/84*(42*B*b^5*x^12 + 105*B*a*b^4*x^10 + 21*A*b^5*x^10 + 140*B*a^2*b^3*x^8 + 70*A*a*b^4*x^8 + 105*B*a^3*b^2*x^6 + 105*A*a^2*b^3*x^6 + 42*B*a^4*b*x^4 + 84*A*a^3*b^2*x^4 + 7*B*a^5*x^2 + 35*A*a^4*b*x^2 + 6*A*a^5)/x^14","B",0
48,1,127,0,0.301602," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^16,x, algorithm=""giac"")","-\frac{15015 \, B b^{5} x^{12} + 45045 \, B a b^{4} x^{10} + 9009 \, A b^{5} x^{10} + 64350 \, B a^{2} b^{3} x^{8} + 32175 \, A a b^{4} x^{8} + 50050 \, B a^{3} b^{2} x^{6} + 50050 \, A a^{2} b^{3} x^{6} + 20475 \, B a^{4} b x^{4} + 40950 \, A a^{3} b^{2} x^{4} + 3465 \, B a^{5} x^{2} + 17325 \, A a^{4} b x^{2} + 3003 \, A a^{5}}{45045 \, x^{15}}"," ",0,"-1/45045*(15015*B*b^5*x^12 + 45045*B*a*b^4*x^10 + 9009*A*b^5*x^10 + 64350*B*a^2*b^3*x^8 + 32175*A*a*b^4*x^8 + 50050*B*a^3*b^2*x^6 + 50050*A*a^2*b^3*x^6 + 20475*B*a^4*b*x^4 + 40950*A*a^3*b^2*x^4 + 3465*B*a^5*x^2 + 17325*A*a^4*b*x^2 + 3003*A*a^5)/x^15","A",0
49,1,127,0,0.316947," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^17,x, algorithm=""giac"")","-\frac{84 \, B b^{5} x^{12} + 280 \, B a b^{4} x^{10} + 56 \, A b^{5} x^{10} + 420 \, B a^{2} b^{3} x^{8} + 210 \, A a b^{4} x^{8} + 336 \, B a^{3} b^{2} x^{6} + 336 \, A a^{2} b^{3} x^{6} + 140 \, B a^{4} b x^{4} + 280 \, A a^{3} b^{2} x^{4} + 24 \, B a^{5} x^{2} + 120 \, A a^{4} b x^{2} + 21 \, A a^{5}}{336 \, x^{16}}"," ",0,"-1/336*(84*B*b^5*x^12 + 280*B*a*b^4*x^10 + 56*A*b^5*x^10 + 420*B*a^2*b^3*x^8 + 210*A*a*b^4*x^8 + 336*B*a^3*b^2*x^6 + 336*A*a^2*b^3*x^6 + 140*B*a^4*b*x^4 + 280*A*a^3*b^2*x^4 + 24*B*a^5*x^2 + 120*A*a^4*b*x^2 + 21*A*a^5)/x^16","A",0
50,1,127,0,0.304767," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^18,x, algorithm=""giac"")","-\frac{153153 \, B b^{5} x^{12} + 546975 \, B a b^{4} x^{10} + 109395 \, A b^{5} x^{10} + 850850 \, B a^{2} b^{3} x^{8} + 425425 \, A a b^{4} x^{8} + 696150 \, B a^{3} b^{2} x^{6} + 696150 \, A a^{2} b^{3} x^{6} + 294525 \, B a^{4} b x^{4} + 589050 \, A a^{3} b^{2} x^{4} + 51051 \, B a^{5} x^{2} + 255255 \, A a^{4} b x^{2} + 45045 \, A a^{5}}{765765 \, x^{17}}"," ",0,"-1/765765*(153153*B*b^5*x^12 + 546975*B*a*b^4*x^10 + 109395*A*b^5*x^10 + 850850*B*a^2*b^3*x^8 + 425425*A*a*b^4*x^8 + 696150*B*a^3*b^2*x^6 + 696150*A*a^2*b^3*x^6 + 294525*B*a^4*b*x^4 + 589050*A*a^3*b^2*x^4 + 51051*B*a^5*x^2 + 255255*A*a^4*b*x^2 + 45045*A*a^5)/x^17","A",0
51,1,127,0,0.336430," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^19,x, algorithm=""giac"")","-\frac{168 \, B b^{5} x^{12} + 630 \, B a b^{4} x^{10} + 126 \, A b^{5} x^{10} + 1008 \, B a^{2} b^{3} x^{8} + 504 \, A a b^{4} x^{8} + 840 \, B a^{3} b^{2} x^{6} + 840 \, A a^{2} b^{3} x^{6} + 360 \, B a^{4} b x^{4} + 720 \, A a^{3} b^{2} x^{4} + 63 \, B a^{5} x^{2} + 315 \, A a^{4} b x^{2} + 56 \, A a^{5}}{1008 \, x^{18}}"," ",0,"-1/1008*(168*B*b^5*x^12 + 630*B*a*b^4*x^10 + 126*A*b^5*x^10 + 1008*B*a^2*b^3*x^8 + 504*A*a*b^4*x^8 + 840*B*a^3*b^2*x^6 + 840*A*a^2*b^3*x^6 + 360*B*a^4*b*x^4 + 720*A*a^3*b^2*x^4 + 63*B*a^5*x^2 + 315*A*a^4*b*x^2 + 56*A*a^5)/x^18","A",0
52,1,127,0,0.421738," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^20,x, algorithm=""giac"")","-\frac{415701 \, B b^{5} x^{12} + 1616615 \, B a b^{4} x^{10} + 323323 \, A b^{5} x^{10} + 2645370 \, B a^{2} b^{3} x^{8} + 1322685 \, A a b^{4} x^{8} + 2238390 \, B a^{3} b^{2} x^{6} + 2238390 \, A a^{2} b^{3} x^{6} + 969969 \, B a^{4} b x^{4} + 1939938 \, A a^{3} b^{2} x^{4} + 171171 \, B a^{5} x^{2} + 855855 \, A a^{4} b x^{2} + 153153 \, A a^{5}}{2909907 \, x^{19}}"," ",0,"-1/2909907*(415701*B*b^5*x^12 + 1616615*B*a*b^4*x^10 + 323323*A*b^5*x^10 + 2645370*B*a^2*b^3*x^8 + 1322685*A*a*b^4*x^8 + 2238390*B*a^3*b^2*x^6 + 2238390*A*a^2*b^3*x^6 + 969969*B*a^4*b*x^4 + 1939938*A*a^3*b^2*x^4 + 171171*B*a^5*x^2 + 855855*A*a^4*b*x^2 + 153153*A*a^5)/x^19","A",0
53,1,127,0,0.344148," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^21,x, algorithm=""giac"")","-\frac{630 \, B b^{5} x^{12} + 2520 \, B a b^{4} x^{10} + 504 \, A b^{5} x^{10} + 4200 \, B a^{2} b^{3} x^{8} + 2100 \, A a b^{4} x^{8} + 3600 \, B a^{3} b^{2} x^{6} + 3600 \, A a^{2} b^{3} x^{6} + 1575 \, B a^{4} b x^{4} + 3150 \, A a^{3} b^{2} x^{4} + 280 \, B a^{5} x^{2} + 1400 \, A a^{4} b x^{2} + 252 \, A a^{5}}{5040 \, x^{20}}"," ",0,"-1/5040*(630*B*b^5*x^12 + 2520*B*a*b^4*x^10 + 504*A*b^5*x^10 + 4200*B*a^2*b^3*x^8 + 2100*A*a*b^4*x^8 + 3600*B*a^3*b^2*x^6 + 3600*A*a^2*b^3*x^6 + 1575*B*a^4*b*x^4 + 3150*A*a^3*b^2*x^4 + 280*B*a^5*x^2 + 1400*A*a^4*b*x^2 + 252*A*a^5)/x^20","A",0
54,1,127,0,0.284734," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^22,x, algorithm=""giac"")","-\frac{323323 \, B b^{5} x^{12} + 1322685 \, B a b^{4} x^{10} + 264537 \, A b^{5} x^{10} + 2238390 \, B a^{2} b^{3} x^{8} + 1119195 \, A a b^{4} x^{8} + 1939938 \, B a^{3} b^{2} x^{6} + 1939938 \, A a^{2} b^{3} x^{6} + 855855 \, B a^{4} b x^{4} + 1711710 \, A a^{3} b^{2} x^{4} + 153153 \, B a^{5} x^{2} + 765765 \, A a^{4} b x^{2} + 138567 \, A a^{5}}{2909907 \, x^{21}}"," ",0,"-1/2909907*(323323*B*b^5*x^12 + 1322685*B*a*b^4*x^10 + 264537*A*b^5*x^10 + 2238390*B*a^2*b^3*x^8 + 1119195*A*a*b^4*x^8 + 1939938*B*a^3*b^2*x^6 + 1939938*A*a^2*b^3*x^6 + 855855*B*a^4*b*x^4 + 1711710*A*a^3*b^2*x^4 + 153153*B*a^5*x^2 + 765765*A*a^4*b*x^2 + 138567*A*a^5)/x^21","A",0
55,1,127,0,0.452438," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^23,x, algorithm=""giac"")","-\frac{2772 \, B b^{5} x^{12} + 11550 \, B a b^{4} x^{10} + 2310 \, A b^{5} x^{10} + 19800 \, B a^{2} b^{3} x^{8} + 9900 \, A a b^{4} x^{8} + 17325 \, B a^{3} b^{2} x^{6} + 17325 \, A a^{2} b^{3} x^{6} + 7700 \, B a^{4} b x^{4} + 15400 \, A a^{3} b^{2} x^{4} + 1386 \, B a^{5} x^{2} + 6930 \, A a^{4} b x^{2} + 1260 \, A a^{5}}{27720 \, x^{22}}"," ",0,"-1/27720*(2772*B*b^5*x^12 + 11550*B*a*b^4*x^10 + 2310*A*b^5*x^10 + 19800*B*a^2*b^3*x^8 + 9900*A*a*b^4*x^8 + 17325*B*a^3*b^2*x^6 + 17325*A*a^2*b^3*x^6 + 7700*B*a^4*b*x^4 + 15400*A*a^3*b^2*x^4 + 1386*B*a^5*x^2 + 6930*A*a^4*b*x^2 + 1260*A*a^5)/x^22","A",0
56,1,108,0,0.333311," ","integrate(x^6*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a^{4} - A a^{3} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, B b^{6} x^{7} - 21 \, B a b^{5} x^{5} + 21 \, A b^{6} x^{5} + 35 \, B a^{2} b^{4} x^{3} - 35 \, A a b^{5} x^{3} - 105 \, B a^{3} b^{3} x + 105 \, A a^{2} b^{4} x}{105 \, b^{7}}"," ",0,"(B*a^4 - A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*B*b^6*x^7 - 21*B*a*b^5*x^5 + 21*A*b^6*x^5 + 35*B*a^2*b^4*x^3 - 35*A*a*b^5*x^3 - 105*B*a^3*b^3*x + 105*A*a^2*b^4*x)/b^7","A",0
57,1,77,0,0.308423," ","integrate(x^5*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, B b^{2} x^{6} - 3 \, B a b x^{4} + 3 \, A b^{2} x^{4} + 6 \, B a^{2} x^{2} - 6 \, A a b x^{2}}{12 \, b^{3}} - \frac{{\left(B a^{3} - A a^{2} b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}}"," ",0,"1/12*(2*B*b^2*x^6 - 3*B*a*b*x^4 + 3*A*b^2*x^4 + 6*B*a^2*x^2 - 6*A*a*b*x^2)/b^3 - 1/2*(B*a^3 - A*a^2*b)*log(abs(b*x^2 + a))/b^4","A",0
58,1,85,0,0.325307," ","integrate(x^4*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a^{3} - A a^{2} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, B b^{4} x^{5} - 5 \, B a b^{3} x^{3} + 5 \, A b^{4} x^{3} + 15 \, B a^{2} b^{2} x - 15 \, A a b^{3} x}{15 \, b^{5}}"," ",0,"-(B*a^3 - A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*B*b^4*x^5 - 5*B*a*b^3*x^3 + 5*A*b^4*x^3 + 15*B*a^2*b^2*x - 15*A*a*b^3*x)/b^5","A",0
59,1,52,0,0.267148," ","integrate(x^3*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{B b x^{4} - 2 \, B a x^{2} + 2 \, A b x^{2}}{4 \, b^{2}} + \frac{{\left(B a^{2} - A a b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{3}}"," ",0,"1/4*(B*b*x^4 - 2*B*a*x^2 + 2*A*b*x^2)/b^2 + 1/2*(B*a^2 - A*a*b)*log(abs(b*x^2 + a))/b^3","A",0
60,1,57,0,0.393286," ","integrate(x^2*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a^{2} - A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{B b^{2} x^{3} - 3 \, B a b x + 3 \, A b^{2} x}{3 \, b^{3}}"," ",0,"(B*a^2 - A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(B*b^2*x^3 - 3*B*a*b*x + 3*A*b^2*x)/b^3","A",0
61,1,32,0,0.344757," ","integrate(x*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{B x^{2}}{2 \, b} - \frac{{\left(B a - A b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{2}}"," ",0,"1/2*B*x^2/b - 1/2*(B*a - A*b)*log(abs(b*x^2 + a))/b^2","A",0
62,1,34,0,0.278476," ","integrate((B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{B x}{b} - \frac{{\left(B a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"B*x/b - (B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
63,1,36,0,0.290369," ","integrate((B*x^2+A)/x/(b*x^2+a),x, algorithm=""giac"")","\frac{A \log\left(x^{2}\right)}{2 \, a} + \frac{{\left(B a - A b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a b}"," ",0,"1/2*A*log(x^2)/a + 1/2*(B*a - A*b)*log(abs(b*x^2 + a))/(a*b)","A",0
64,1,36,0,0.300022," ","integrate((B*x^2+A)/x^2/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{A}{a x}"," ",0,"(B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - A/(a*x)","A",0
65,1,71,0,0.324708," ","integrate((B*x^2+A)/x^3/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a - A b\right)} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{{\left(B a b - A b^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b} - \frac{B a x^{2} - A b x^{2} + A a}{2 \, a^{2} x^{2}}"," ",0,"1/2*(B*a - A*b)*log(x^2)/a^2 - 1/2*(B*a*b - A*b^2)*log(abs(b*x^2 + a))/(a^2*b) - 1/2*(B*a*x^2 - A*b*x^2 + A*a)/(a^2*x^2)","A",0
66,1,57,0,0.323364," ","integrate((B*x^2+A)/x^4/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a b - A b^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} - \frac{3 \, B a x^{2} - 3 \, A b x^{2} + A a}{3 \, a^{2} x^{3}}"," ",0,"-(B*a*b - A*b^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/3*(3*B*a*x^2 - 3*A*b*x^2 + A*a)/(a^2*x^3)","A",0
67,1,100,0,0.362267," ","integrate((B*x^2+A)/x^5/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a b - A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{3}} + \frac{{\left(B a b^{2} - A b^{3}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} b} + \frac{3 \, B a b x^{4} - 3 \, A b^{2} x^{4} - 2 \, B a^{2} x^{2} + 2 \, A a b x^{2} - A a^{2}}{4 \, a^{3} x^{4}}"," ",0,"-1/2*(B*a*b - A*b^2)*log(x^2)/a^3 + 1/2*(B*a*b^2 - A*b^3)*log(abs(b*x^2 + a))/(a^3*b) + 1/4*(3*B*a*b*x^4 - 3*A*b^2*x^4 - 2*B*a^2*x^2 + 2*A*a*b*x^2 - A*a^2)/(a^3*x^4)","A",0
68,1,81,0,0.302245," ","integrate((B*x^2+A)/x^6/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a b^{2} - A b^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{3}} + \frac{15 \, B a b x^{4} - 15 \, A b^{2} x^{4} - 5 \, B a^{2} x^{2} + 5 \, A a b x^{2} - 3 \, A a^{2}}{15 \, a^{3} x^{5}}"," ",0,"(B*a*b^2 - A*b^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/15*(15*B*a*b*x^4 - 15*A*b^2*x^4 - 5*B*a^2*x^2 + 5*A*a*b*x^2 - 3*A*a^2)/(a^3*x^5)","A",0
69,1,126,0,0.275851," ","integrate((B*x^2+A)/x^7/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(B a b^{2} - A b^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{4}} - \frac{{\left(B a b^{3} - A b^{4}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4} b} - \frac{11 \, B a b^{2} x^{6} - 11 \, A b^{3} x^{6} - 6 \, B a^{2} b x^{4} + 6 \, A a b^{2} x^{4} + 3 \, B a^{3} x^{2} - 3 \, A a^{2} b x^{2} + 2 \, A a^{3}}{12 \, a^{4} x^{6}}"," ",0,"1/2*(B*a*b^2 - A*b^3)*log(x^2)/a^4 - 1/2*(B*a*b^3 - A*b^4)*log(abs(b*x^2 + a))/(a^4*b) - 1/12*(11*B*a*b^2*x^6 - 11*A*b^3*x^6 - 6*B*a^2*b*x^4 + 6*A*a*b^2*x^4 + 3*B*a^3*x^2 - 3*A*a^2*b*x^2 + 2*A*a^3)/(a^4*x^6)","A",0
70,1,106,0,0.372489," ","integrate((B*x^2+A)/x^8/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(B a b^{3} - A b^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{4}} - \frac{105 \, B a b^{2} x^{6} - 105 \, A b^{3} x^{6} - 35 \, B a^{2} b x^{4} + 35 \, A a b^{2} x^{4} + 21 \, B a^{3} x^{2} - 21 \, A a^{2} b x^{2} + 15 \, A a^{3}}{105 \, a^{4} x^{7}}"," ",0,"-(B*a*b^3 - A*b^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/105*(105*B*a*b^2*x^6 - 105*A*b^3*x^6 - 35*B*a^2*b*x^4 + 35*A*a*b^2*x^4 + 21*B*a^3*x^2 - 21*A*a^2*b*x^2 + 15*A*a^3)/(a^4*x^7)","A",0
71,1,159,0,0.349210," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B a^{4} - 4 \, A a^{3} b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{6}} - \frac{5 \, B a^{4} b x^{2} - 4 \, A a^{3} b^{2} x^{2} + 4 \, B a^{5} - 3 \, A a^{4} b}{2 \, {\left(b x^{2} + a\right)} b^{6}} + \frac{3 \, B b^{6} x^{8} - 8 \, B a b^{5} x^{6} + 4 \, A b^{6} x^{6} + 18 \, B a^{2} b^{4} x^{4} - 12 \, A a b^{5} x^{4} - 48 \, B a^{3} b^{3} x^{2} + 36 \, A a^{2} b^{4} x^{2}}{24 \, b^{8}}"," ",0,"1/2*(5*B*a^4 - 4*A*a^3*b)*log(abs(b*x^2 + a))/b^6 - 1/2*(5*B*a^4*b*x^2 - 4*A*a^3*b^2*x^2 + 4*B*a^5 - 3*A*a^4*b)/((b*x^2 + a)*b^6) + 1/24*(3*B*b^6*x^8 - 8*B*a*b^5*x^6 + 4*A*b^6*x^6 + 18*B*a^2*b^4*x^4 - 12*A*a*b^5*x^4 - 48*B*a^3*b^3*x^2 + 36*A*a^2*b^4*x^2)/b^8","A",0
72,1,139,0,0.418850," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} - \frac{B a^{4} x - A a^{3} b x}{2 \, {\left(b x^{2} + a\right)} b^{5}} + \frac{15 \, B b^{12} x^{7} - 42 \, B a b^{11} x^{5} + 21 \, A b^{12} x^{5} + 105 \, B a^{2} b^{10} x^{3} - 70 \, A a b^{11} x^{3} - 420 \, B a^{3} b^{9} x + 315 \, A a^{2} b^{10} x}{105 \, b^{14}}"," ",0,"1/2*(9*B*a^4 - 7*A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) - 1/2*(B*a^4*x - A*a^3*b*x)/((b*x^2 + a)*b^5) + 1/105*(15*B*b^12*x^7 - 42*B*a*b^11*x^5 + 21*A*b^12*x^5 + 105*B*a^2*b^10*x^3 - 70*A*a*b^11*x^3 - 420*B*a^3*b^9*x + 315*A*a^2*b^10*x)/b^14","A",0
73,1,135,0,0.320365," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, B a^{3} - 3 \, A a^{2} b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{5}} + \frac{2 \, B b^{4} x^{6} - 6 \, B a b^{3} x^{4} + 3 \, A b^{4} x^{4} + 18 \, B a^{2} b^{2} x^{2} - 12 \, A a b^{3} x^{2}}{12 \, b^{6}} + \frac{4 \, B a^{3} b x^{2} - 3 \, A a^{2} b^{2} x^{2} + 3 \, B a^{4} - 2 \, A a^{3} b}{2 \, {\left(b x^{2} + a\right)} b^{5}}"," ",0,"-1/2*(4*B*a^3 - 3*A*a^2*b)*log(abs(b*x^2 + a))/b^5 + 1/12*(2*B*b^4*x^6 - 6*B*a*b^3*x^4 + 3*A*b^4*x^4 + 18*B*a^2*b^2*x^2 - 12*A*a*b^3*x^2)/b^6 + 1/2*(4*B*a^3*b*x^2 - 3*A*a^2*b^2*x^2 + 3*B*a^4 - 2*A*a^3*b)/((b*x^2 + a)*b^5)","A",0
74,1,115,0,0.265371," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} + \frac{B a^{3} x - A a^{2} b x}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, B b^{8} x^{5} - 10 \, B a b^{7} x^{3} + 5 \, A b^{8} x^{3} + 45 \, B a^{2} b^{6} x - 30 \, A a b^{7} x}{15 \, b^{10}}"," ",0,"-1/2*(7*B*a^3 - 5*A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/2*(B*a^3*x - A*a^2*b*x)/((b*x^2 + a)*b^4) + 1/15*(3*B*b^8*x^5 - 10*B*a*b^7*x^3 + 5*A*b^8*x^3 + 45*B*a^2*b^6*x - 30*A*a*b^7*x)/b^10","A",0
75,1,106,0,0.276548," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, B a^{2} - 2 \, A a b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}} + \frac{B b^{2} x^{4} - 4 \, B a b x^{2} + 2 \, A b^{2} x^{2}}{4 \, b^{4}} - \frac{3 \, B a^{2} b x^{2} - 2 \, A a b^{2} x^{2} + 2 \, B a^{3} - A a^{2} b}{2 \, {\left(b x^{2} + a\right)} b^{4}}"," ",0,"1/2*(3*B*a^2 - 2*A*a*b)*log(abs(b*x^2 + a))/b^4 + 1/4*(B*b^2*x^4 - 4*B*a*b*x^2 + 2*A*b^2*x^2)/b^4 - 1/2*(3*B*a^2*b*x^2 - 2*A*a*b^2*x^2 + 2*B*a^3 - A*a^2*b)/((b*x^2 + a)*b^4)","A",0
76,1,88,0,0.301196," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} - \frac{B a^{2} x - A a b x}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{B b^{4} x^{3} - 6 \, B a b^{3} x + 3 \, A b^{4} x}{3 \, b^{6}}"," ",0,"1/2*(5*B*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/2*(B*a^2*x - A*a*b*x)/((b*x^2 + a)*b^3) + 1/3*(B*b^4*x^3 - 6*B*a*b^3*x + 3*A*b^4*x)/b^6","A",0
77,1,91,0,0.338979," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\frac{{\left(b x^{2} + a\right)} B}{b^{2}} + \frac{{\left(2 \, B a - A b\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b^{2}} - \frac{\frac{B a^{2} b}{b x^{2} + a} - \frac{A a b^{2}}{b x^{2} + a}}{b^{3}}}{2 \, b}"," ",0,"1/2*((b*x^2 + a)*B/b^2 + (2*B*a - A*b)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^2 - (B*a^2*b/(b*x^2 + a) - A*a*b^2/(b*x^2 + a))/b^3)/b","A",0
78,1,59,0,0.341802," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{B x}{b^{2}} - \frac{{\left(3 \, B a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} + \frac{B a x - A b x}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"B*x/b^2 - 1/2*(3*B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/2*(B*a*x - A*b*x)/((b*x^2 + a)*b^2)","A",0
79,1,65,0,0.245993," ","integrate(x*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B {\left(\frac{\log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{2} + a\right)} b}\right)}}{2 \, b} - \frac{A}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"-1/2*B*(log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b - a/((b*x^2 + a)*b))/b - 1/2*A/((b*x^2 + a)*b)","A",0
80,1,57,0,0.293759," ","integrate((B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(B a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b} - \frac{B a x - A b x}{2 \, {\left(b x^{2} + a\right)} a b}"," ",0,"1/2*(B*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b) - 1/2*(B*a*x - A*b*x)/((b*x^2 + a)*a*b)","A",0
81,1,63,0,0.325796," ","integrate((B*x^2+A)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{A \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{A \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2}} + \frac{A b^{2} x^{2} - B a^{2} + 2 \, A a b}{2 \, {\left(b x^{2} + a\right)} a^{2} b}"," ",0,"1/2*A*log(x^2)/a^2 - 1/2*A*log(abs(b*x^2 + a))/a^2 + 1/2*(A*b^2*x^2 - B*a^2 + 2*A*a*b)/((b*x^2 + a)*a^2*b)","A",0
82,1,62,0,0.405221," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(B a - 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} + \frac{B a x^{2} - 3 \, A b x^{2} - 2 \, A a}{2 \, {\left(b x^{3} + a x\right)} a^{2}}"," ",0,"1/2*(B*a - 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/2*(B*a*x^2 - 3*A*b*x^2 - 2*A*a)/((b*x^3 + a*x)*a^2)","A",0
83,1,82,0,0.295244," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(B a - 2 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{3}} + \frac{B a x^{2} - 2 \, A b x^{2} - A a}{2 \, {\left(b x^{4} + a x^{2}\right)} a^{2}} - \frac{{\left(B a b - 2 \, A b^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} b}"," ",0,"1/2*(B*a - 2*A*b)*log(x^2)/a^3 + 1/2*(B*a*x^2 - 2*A*b*x^2 - A*a)/((b*x^4 + a*x^2)*a^2) - 1/2*(B*a*b - 2*A*b^2)*log(abs(b*x^2 + a))/(a^3*b)","A",0
84,1,85,0,0.431599," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, B a b - 5 \, A b^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}} - \frac{B a b x - A b^{2} x}{2 \, {\left(b x^{2} + a\right)} a^{3}} - \frac{3 \, B a x^{2} - 6 \, A b x^{2} + A a}{3 \, a^{3} x^{3}}"," ",0,"-1/2*(3*B*a*b - 5*A*b^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) - 1/2*(B*a*b*x - A*b^2*x)/((b*x^2 + a)*a^3) - 1/3*(3*B*a*x^2 - 6*A*b*x^2 + A*a)/(a^3*x^3)","A",0
85,1,150,0,0.392152," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, B a b - 3 \, A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{4}} + \frac{{\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4} b} - \frac{2 \, B a b^{2} x^{2} - 3 \, A b^{3} x^{2} + 3 \, B a^{2} b - 4 \, A a b^{2}}{2 \, {\left(b x^{2} + a\right)} a^{4}} + \frac{6 \, B a b x^{4} - 9 \, A b^{2} x^{4} - 2 \, B a^{2} x^{2} + 4 \, A a b x^{2} - A a^{2}}{4 \, a^{4} x^{4}}"," ",0,"-1/2*(2*B*a*b - 3*A*b^2)*log(x^2)/a^4 + 1/2*(2*B*a*b^2 - 3*A*b^3)*log(abs(b*x^2 + a))/(a^4*b) - 1/2*(2*B*a*b^2*x^2 - 3*A*b^3*x^2 + 3*B*a^2*b - 4*A*a*b^2)/((b*x^2 + a)*a^4) + 1/4*(6*B*a*b*x^4 - 9*A*b^2*x^4 - 2*B*a^2*x^2 + 4*A*a*b*x^2 - A*a^2)/(a^4*x^4)","A",0
86,1,112,0,0.304149," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{4}} + \frac{B a b^{2} x - A b^{3} x}{2 \, {\left(b x^{2} + a\right)} a^{4}} + \frac{30 \, B a b x^{4} - 45 \, A b^{2} x^{4} - 5 \, B a^{2} x^{2} + 10 \, A a b x^{2} - 3 \, A a^{2}}{15 \, a^{4} x^{5}}"," ",0,"1/2*(5*B*a*b^2 - 7*A*b^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) + 1/2*(B*a*b^2*x - A*b^3*x)/((b*x^2 + a)*a^4) + 1/15*(30*B*a*b*x^4 - 45*A*b^2*x^4 - 5*B*a^2*x^2 + 10*A*a*b*x^2 - 3*A*a^2)/(a^4*x^5)","A",0
87,1,178,0,0.386055," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, B a b^{2} - 4 \, A b^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{5}} - \frac{{\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{5} b} + \frac{3 \, B a b^{3} x^{2} - 4 \, A b^{4} x^{2} + 4 \, B a^{2} b^{2} - 5 \, A a b^{3}}{2 \, {\left(b x^{2} + a\right)} a^{5}} - \frac{33 \, B a b^{2} x^{6} - 44 \, A b^{3} x^{6} - 12 \, B a^{2} b x^{4} + 18 \, A a b^{2} x^{4} + 3 \, B a^{3} x^{2} - 6 \, A a^{2} b x^{2} + 2 \, A a^{3}}{12 \, a^{5} x^{6}}"," ",0,"1/2*(3*B*a*b^2 - 4*A*b^3)*log(x^2)/a^5 - 1/2*(3*B*a*b^3 - 4*A*b^4)*log(abs(b*x^2 + a))/(a^5*b) + 1/2*(3*B*a*b^3*x^2 - 4*A*b^4*x^2 + 4*B*a^2*b^2 - 5*A*a*b^3)/((b*x^2 + a)*a^5) - 1/12*(33*B*a*b^2*x^6 - 44*A*b^3*x^6 - 12*B*a^2*b*x^4 + 18*A*a*b^2*x^4 + 3*B*a^3*x^2 - 6*A*a^2*b*x^2 + 2*A*a^3)/(a^5*x^6)","A",0
88,1,183,0,0.399627," ","integrate(x^11*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{5 \, {\left(3 \, B a^{4} - 2 \, A a^{3} b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{7}} - \frac{45 \, B a^{4} b^{2} x^{4} - 30 \, A a^{3} b^{3} x^{4} + 78 \, B a^{5} b x^{2} - 50 \, A a^{4} b^{2} x^{2} + 34 \, B a^{6} - 21 \, A a^{5} b}{4 \, {\left(b x^{2} + a\right)}^{2} b^{7}} + \frac{3 \, B b^{9} x^{8} - 12 \, B a b^{8} x^{6} + 4 \, A b^{9} x^{6} + 36 \, B a^{2} b^{7} x^{4} - 18 \, A a b^{8} x^{4} - 120 \, B a^{3} b^{6} x^{2} + 72 \, A a^{2} b^{7} x^{2}}{24 \, b^{12}}"," ",0,"5/2*(3*B*a^4 - 2*A*a^3*b)*log(abs(b*x^2 + a))/b^7 - 1/4*(45*B*a^4*b^2*x^4 - 30*A*a^3*b^3*x^4 + 78*B*a^5*b*x^2 - 50*A*a^4*b^2*x^2 + 34*B*a^6 - 21*A*a^5*b)/((b*x^2 + a)^2*b^7) + 1/24*(3*B*b^9*x^8 - 12*B*a*b^8*x^6 + 4*A*b^9*x^6 + 36*B*a^2*b^7*x^4 - 18*A*a*b^8*x^4 - 120*B*a^3*b^6*x^2 + 72*A*a^2*b^7*x^2)/b^12","A",0
89,1,159,0,0.327992," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{b^{6}} + \frac{30 \, B a^{3} b^{2} x^{4} - 18 \, A a^{2} b^{3} x^{4} + 50 \, B a^{4} b x^{2} - 28 \, A a^{3} b^{2} x^{2} + 21 \, B a^{5} - 11 \, A a^{4} b}{4 \, {\left(b x^{2} + a\right)}^{2} b^{6}} + \frac{2 \, B b^{6} x^{6} - 9 \, B a b^{5} x^{4} + 3 \, A b^{6} x^{4} + 36 \, B a^{2} b^{4} x^{2} - 18 \, A a b^{5} x^{2}}{12 \, b^{9}}"," ",0,"-(5*B*a^3 - 3*A*a^2*b)*log(abs(b*x^2 + a))/b^6 + 1/4*(30*B*a^3*b^2*x^4 - 18*A*a^2*b^3*x^4 + 50*B*a^4*b*x^2 - 28*A*a^3*b^2*x^2 + 21*B*a^5 - 11*A*a^4*b)/((b*x^2 + a)^2*b^6) + 1/12*(2*B*b^6*x^6 - 9*B*a*b^5*x^4 + 3*A*b^6*x^4 + 36*B*a^2*b^4*x^2 - 18*A*a*b^5*x^2)/b^9","A",0
90,1,132,0,0.362778," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, B a^{2} - A a b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{5}} + \frac{B b^{3} x^{4} - 6 \, B a b^{2} x^{2} + 2 \, A b^{3} x^{2}}{4 \, b^{6}} - \frac{18 \, B a^{2} b^{2} x^{4} - 9 \, A a b^{3} x^{4} + 28 \, B a^{3} b x^{2} - 12 \, A a^{2} b^{2} x^{2} + 11 \, B a^{4} - 4 \, A a^{3} b}{4 \, {\left(b x^{2} + a\right)}^{2} b^{5}}"," ",0,"3/2*(2*B*a^2 - A*a*b)*log(abs(b*x^2 + a))/b^5 + 1/4*(B*b^3*x^4 - 6*B*a*b^2*x^2 + 2*A*b^3*x^2)/b^6 - 1/4*(18*B*a^2*b^2*x^4 - 9*A*a*b^3*x^4 + 28*B*a^3*b*x^2 - 12*A*a^2*b^2*x^2 + 11*B*a^4 - 4*A*a^3*b)/((b*x^2 + a)^2*b^5)","A",0
91,1,93,0,0.362229," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{B x^{2}}{2 \, b^{3}} - \frac{{\left(3 \, B a - A b\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}} + \frac{9 \, B a b^{2} x^{4} - 3 \, A b^{3} x^{4} + 12 \, B a^{2} b x^{2} - 2 \, A a b^{2} x^{2} + 4 \, B a^{3}}{4 \, {\left(b x^{2} + a\right)}^{2} b^{4}}"," ",0,"1/2*B*x^2/b^3 - 1/2*(3*B*a - A*b)*log(abs(b*x^2 + a))/b^4 + 1/4*(9*B*a*b^2*x^4 - 3*A*b^3*x^4 + 12*B*a^2*b*x^2 - 2*A*a*b^2*x^2 + 4*B*a^3)/((b*x^2 + a)^2*b^4)","A",0
92,1,61,0,0.410963," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{B \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{3}} + \frac{2 \, {\left(2 \, B a - A b\right)} x^{2} + \frac{3 \, B a^{2} - A a b}{b}}{4 \, {\left(b x^{2} + a\right)}^{2} b^{2}}"," ",0,"1/2*B*log(abs(b*x^2 + a))/b^3 + 1/4*(2*(2*B*a - A*b)*x^2 + (3*B*a^2 - A*a*b)/b)/((b*x^2 + a)^2*b^2)","A",0
93,1,28,0,0.362160," ","integrate(x*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{2 \, B b x^{2} + B a + A b}{4 \, {\left(b x^{2} + a\right)}^{2} b^{2}}"," ",0,"-1/4*(2*B*b*x^2 + B*a + A*b)/((b*x^2 + a)^2*b^2)","A",0
94,1,76,0,0.381918," ","integrate((B*x^2+A)/x/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{A \log\left(x^{2}\right)}{2 \, a^{3}} - \frac{A \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3}} + \frac{3 \, A b^{3} x^{4} + 8 \, A a b^{2} x^{2} - B a^{3} + 6 \, A a^{2} b}{4 \, {\left(b x^{2} + a\right)}^{2} a^{3} b}"," ",0,"1/2*A*log(x^2)/a^3 - 1/2*A*log(abs(b*x^2 + a))/a^3 + 1/4*(3*A*b^3*x^4 + 8*A*a*b^2*x^2 - B*a^3 + 6*A*a^2*b)/((b*x^2 + a)^2*a^3*b)","A",0
95,1,138,0,0.359444," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(B a - 3 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{4}} - \frac{{\left(B a b - 3 \, A b^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{4} b} + \frac{3 \, B a b^{2} x^{4} - 9 \, A b^{3} x^{4} + 8 \, B a^{2} b x^{2} - 22 \, A a b^{2} x^{2} + 6 \, B a^{3} - 14 \, A a^{2} b}{4 \, {\left(b x^{2} + a\right)}^{2} a^{4}} - \frac{B a x^{2} - 3 \, A b x^{2} + A a}{2 \, a^{4} x^{2}}"," ",0,"1/2*(B*a - 3*A*b)*log(x^2)/a^4 - 1/2*(B*a*b - 3*A*b^2)*log(abs(b*x^2 + a))/(a^4*b) + 1/4*(3*B*a*b^2*x^4 - 9*A*b^3*x^4 + 8*B*a^2*b*x^2 - 22*A*a*b^2*x^2 + 6*B*a^3 - 14*A*a^2*b)/((b*x^2 + a)^2*a^4) - 1/2*(B*a*x^2 - 3*A*b*x^2 + A*a)/(a^4*x^2)","A",0
96,1,133,0,0.352246," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(B a b - 2 \, A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{5}} + \frac{3 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{5} b} - \frac{6 \, B a b^{2} x^{6} - 12 \, A b^{3} x^{6} + 9 \, B a^{2} b x^{4} - 18 \, A a b^{2} x^{4} + 2 \, B a^{3} x^{2} - 4 \, A a^{2} b x^{2} + A a^{3}}{4 \, {\left(b x^{4} + a x^{2}\right)}^{2} a^{4}}"," ",0,"-3/2*(B*a*b - 2*A*b^2)*log(x^2)/a^5 + 3/2*(B*a*b^2 - 2*A*b^3)*log(abs(b*x^2 + a))/(a^5*b) - 1/4*(6*B*a*b^2*x^6 - 12*A*b^3*x^6 + 9*B*a^2*b*x^4 - 18*A*a*b^2*x^4 + 2*B*a^3*x^2 - 4*A*a^2*b*x^2 + A*a^3)/((b*x^4 + a*x^2)^2*a^4)","A",0
97,1,201,0,0.395278," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B a b^{2} - 5 \, A b^{3}\right)} \log\left(x^{2}\right)}{a^{6}} - \frac{{\left(3 \, B a b^{3} - 5 \, A b^{4}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{a^{6} b} + \frac{18 \, B a b^{4} x^{4} - 30 \, A b^{5} x^{4} + 42 \, B a^{2} b^{3} x^{2} - 68 \, A a b^{4} x^{2} + 25 \, B a^{3} b^{2} - 39 \, A a^{2} b^{3}}{4 \, {\left(b x^{2} + a\right)}^{2} a^{6}} - \frac{66 \, B a b^{2} x^{6} - 110 \, A b^{3} x^{6} - 18 \, B a^{2} b x^{4} + 36 \, A a b^{2} x^{4} + 3 \, B a^{3} x^{2} - 9 \, A a^{2} b x^{2} + 2 \, A a^{3}}{12 \, a^{6} x^{6}}"," ",0,"(3*B*a*b^2 - 5*A*b^3)*log(x^2)/a^6 - (3*B*a*b^3 - 5*A*b^4)*log(abs(b*x^2 + a))/(a^6*b) + 1/4*(18*B*a*b^4*x^4 - 30*A*b^5*x^4 + 42*B*a^2*b^3*x^2 - 68*A*a*b^4*x^2 + 25*B*a^3*b^2 - 39*A*a^2*b^3)/((b*x^2 + a)^2*a^6) - 1/12*(66*B*a*b^2*x^6 - 110*A*b^3*x^6 - 18*B*a^2*b*x^4 + 36*A*a*b^2*x^4 + 3*B*a^3*x^2 - 9*A*a^2*b*x^2 + 2*A*a^3)/(a^6*x^6)","A",0
98,1,162,0,0.483387," ","integrate(x^10*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{9 \, {\left(11 \, B a^{4} - 7 \, A a^{3} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{6}} - \frac{21 \, B a^{4} b x^{3} - 17 \, A a^{3} b^{2} x^{3} + 19 \, B a^{5} x - 15 \, A a^{4} b x}{8 \, {\left(b x^{2} + a\right)}^{2} b^{6}} + \frac{5 \, B b^{18} x^{7} - 21 \, B a b^{17} x^{5} + 7 \, A b^{18} x^{5} + 70 \, B a^{2} b^{16} x^{3} - 35 \, A a b^{17} x^{3} - 350 \, B a^{3} b^{15} x + 210 \, A a^{2} b^{16} x}{35 \, b^{21}}"," ",0,"9/8*(11*B*a^4 - 7*A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) - 1/8*(21*B*a^4*b*x^3 - 17*A*a^3*b^2*x^3 + 19*B*a^5*x - 15*A*a^4*b*x)/((b*x^2 + a)^2*b^6) + 1/35*(5*B*b^18*x^7 - 21*B*a*b^17*x^5 + 7*A*b^18*x^5 + 70*B*a^2*b^16*x^3 - 35*A*a*b^17*x^3 - 350*B*a^3*b^15*x + 210*A*a^2*b^16*x)/b^21","A",0
99,1,138,0,0.360161," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{7 \, {\left(9 \, B a^{3} - 5 \, A a^{2} b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{5}} + \frac{17 \, B a^{3} b x^{3} - 13 \, A a^{2} b^{2} x^{3} + 15 \, B a^{4} x - 11 \, A a^{3} b x}{8 \, {\left(b x^{2} + a\right)}^{2} b^{5}} + \frac{3 \, B b^{12} x^{5} - 15 \, B a b^{11} x^{3} + 5 \, A b^{12} x^{3} + 90 \, B a^{2} b^{10} x - 45 \, A a b^{11} x}{15 \, b^{15}}"," ",0,"-7/8*(9*B*a^3 - 5*A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/8*(17*B*a^3*b*x^3 - 13*A*a^2*b^2*x^3 + 15*B*a^4*x - 11*A*a^3*b*x)/((b*x^2 + a)^2*b^5) + 1/15*(3*B*b^12*x^5 - 15*B*a*b^11*x^3 + 5*A*b^12*x^3 + 90*B*a^2*b^10*x - 45*A*a*b^11*x)/b^15","A",0
100,1,111,0,0.382315," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{5 \, {\left(7 \, B a^{2} - 3 \, A a b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{4}} - \frac{13 \, B a^{2} b x^{3} - 9 \, A a b^{2} x^{3} + 11 \, B a^{3} x - 7 \, A a^{2} b x}{8 \, {\left(b x^{2} + a\right)}^{2} b^{4}} + \frac{B b^{6} x^{3} - 9 \, B a b^{5} x + 3 \, A b^{6} x}{3 \, b^{9}}"," ",0,"5/8*(7*B*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) - 1/8*(13*B*a^2*b*x^3 - 9*A*a*b^2*x^3 + 11*B*a^3*x - 7*A*a^2*b*x)/((b*x^2 + a)^2*b^4) + 1/3*(B*b^6*x^3 - 9*B*a*b^5*x + 3*A*b^6*x)/b^9","A",0
101,1,80,0,0.412488," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{B x}{b^{3}} - \frac{3 \, {\left(5 \, B a - A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} b^{3}} + \frac{9 \, B a b x^{3} - 5 \, A b^{2} x^{3} + 7 \, B a^{2} x - 3 \, A a b x}{8 \, {\left(b x^{2} + a\right)}^{2} b^{3}}"," ",0,"B*x/b^3 - 3/8*(5*B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/8*(9*B*a*b*x^3 - 5*A*b^2*x^3 + 7*B*a^2*x - 3*A*a*b*x)/((b*x^2 + a)^2*b^3)","A",0
102,1,78,0,0.336128," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, B a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{2}} - \frac{5 \, B a b x^{3} - A b^{2} x^{3} + 3 \, B a^{2} x + A a b x}{8 \, {\left(b x^{2} + a\right)}^{2} a b^{2}}"," ",0,"1/8*(3*B*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) - 1/8*(5*B*a*b*x^3 - A*b^2*x^3 + 3*B*a^2*x + A*a*b*x)/((b*x^2 + a)^2*a*b^2)","A",0
103,1,78,0,0.341060," ","integrate((B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(B a + 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b} + \frac{B a b x^{3} + 3 \, A b^{2} x^{3} - B a^{2} x + 5 \, A a b x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b}"," ",0,"1/8*(B*a + 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/8*(B*a*b*x^3 + 3*A*b^2*x^3 - B*a^2*x + 5*A*a*b*x)/((b*x^2 + a)^2*a^2*b)","A",0
104,1,82,0,0.298232," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(B a - 5 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}} - \frac{A}{a^{3} x} + \frac{3 \, B a b x^{3} - 7 \, A b^{2} x^{3} + 5 \, B a^{2} x - 9 \, A a b x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{3}}"," ",0,"3/8*(B*a - 5*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) - A/(a^3*x) + 1/8*(3*B*a*b*x^3 - 7*A*b^2*x^3 + 5*B*a^2*x - 9*A*a*b*x)/((b*x^2 + a)^2*a^3)","A",0
105,1,108,0,0.324711," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(3 \, B a b - 7 \, A b^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{4}} - \frac{7 \, B a b^{2} x^{3} - 11 \, A b^{3} x^{3} + 9 \, B a^{2} b x - 13 \, A a b^{2} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{4}} - \frac{3 \, B a x^{2} - 9 \, A b x^{2} + A a}{3 \, a^{4} x^{3}}"," ",0,"-5/8*(3*B*a*b - 7*A*b^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4) - 1/8*(7*B*a*b^2*x^3 - 11*A*b^3*x^3 + 9*B*a^2*b*x - 13*A*a*b^2*x)/((b*x^2 + a)^2*a^4) - 1/3*(3*B*a*x^2 - 9*A*b*x^2 + A*a)/(a^4*x^3)","A",0
106,1,135,0,0.356410," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{7 \, {\left(5 \, B a b^{2} - 9 \, A b^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{5}} + \frac{11 \, B a b^{3} x^{3} - 15 \, A b^{4} x^{3} + 13 \, B a^{2} b^{2} x - 17 \, A a b^{3} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{5}} + \frac{45 \, B a b x^{4} - 90 \, A b^{2} x^{4} - 5 \, B a^{2} x^{2} + 15 \, A a b x^{2} - 3 \, A a^{2}}{15 \, a^{5} x^{5}}"," ",0,"7/8*(5*B*a*b^2 - 9*A*b^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5) + 1/8*(11*B*a*b^3*x^3 - 15*A*b^4*x^3 + 13*B*a^2*b^2*x - 17*A*a*b^3*x)/((b*x^2 + a)^2*a^5) + 1/15*(45*B*a*b*x^4 - 90*A*b^2*x^4 - 5*B*a^2*x^2 + 15*A*a*b*x^2 - 3*A*a^2)/(a^5*x^5)","A",0
107,1,12,0,0.347625," ","integrate((b*x^2+a)/(x^2+1),x, algorithm=""giac"")","b x + {\left(a - b\right)} \arctan\left(x\right)"," ",0,"b*x + (a - b)*arctan(x)","A",0
108,1,25,0,0.363800," ","integrate((b*x^2+a)/(-x^2+1),x, algorithm=""giac"")","-b x + \frac{1}{2} \, {\left(a + b\right)} \log\left({\left| x + 1 \right|}\right) - \frac{1}{2} \, {\left(a + b\right)} \log\left({\left| x - 1 \right|}\right)"," ",0,"-b*x + 1/2*(a + b)*log(abs(x + 1)) - 1/2*(a + b)*log(abs(x - 1))","B",0
109,1,11,0,0.426843," ","integrate((x^2+1)/(x^2-1)^2,x, algorithm=""giac"")","-\frac{1}{x - \frac{1}{x}}"," ",0,"-1/(x - 1/x)","A",0
110,1,7,0,0.348704," ","integrate((-x^2+1)/(x^2+1)^2,x, algorithm=""giac"")","\frac{1}{x + \frac{1}{x}}"," ",0,"1/(x + 1/x)","A",0
111,1,15,0,0.292485," ","integrate((2*x^2+3)/(x^2+1)^2,x, algorithm=""giac"")","\frac{x}{2 \, {\left(x^{2} + 1\right)}} + \frac{5}{2} \, \arctan\left(x\right)"," ",0,"1/2*x/(x^2 + 1) + 5/2*arctan(x)","A",0
112,1,15,0,0.312497," ","integrate((x^2-2)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{3 \, x}{2 \, {\left(x^{2} + 1\right)}} - \frac{1}{2} \, \arctan\left(x\right)"," ",0,"-3/2*x/(x^2 + 1) - 1/2*arctan(x)","A",0
113,1,14,0,0.342900," ","integrate((x^2+3)/(x^2+1)^2,x, algorithm=""giac"")","\frac{x}{x^{2} + 1} + 2 \, \arctan\left(x\right)"," ",0,"x/(x^2 + 1) + 2*arctan(x)","A",0
114,1,14,0,0.321726," ","integrate((b*x^2+a)/(b*x^2-a)^2,x, algorithm=""giac"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
115,1,14,0,0.348622," ","integrate((b*x^2+a)/(-b*x^2+a)^2,x, algorithm=""giac"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
116,1,36,0,0.292641," ","integrate((B*x^2+A)/(-b*x^2+a),x, algorithm=""giac"")","-\frac{B x}{b} - \frac{{\left(B a + A b\right)} \arctan\left(\frac{b x}{\sqrt{-a b}}\right)}{\sqrt{-a b} b}"," ",0,"-B*x/b - (B*a + A*b)*arctan(b*x/sqrt(-a*b))/(sqrt(-a*b)*b)","A",0
117,1,25,0,0.409064," ","integrate((x^2+1)/(x^2+16)^3,x, algorithm=""giac"")","\frac{19 \, x^{3} - 176 \, x}{2048 \, {\left(x^{2} + 16\right)}^{2}} + \frac{19}{8192} \, \arctan\left(\frac{1}{4} \, x\right)"," ",0,"1/2048*(19*x^3 - 176*x)/(x^2 + 16)^2 + 19/8192*arctan(1/4*x)","A",0
118,1,11,0,0.269493," ","integrate((2*x^2+1)/x^5/(x^2+1)^3,x, algorithm=""giac"")","-\frac{1}{4 \, {\left(x^{4} + x^{2}\right)}^{2}}"," ",0,"-1/4/(x^4 + x^2)^2","A",0
119,1,1,0,0.303102," ","integrate((-x^2+1)^2/(x^2-1)^2,x, algorithm=""giac"")","x"," ",0,"x","A",0
120,1,6,0,0.325423," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4}"," ",0,"1/4*c*x^4","A",0
121,1,6,0,0.335666," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""giac"")","\frac{1}{3} \, c x^{3}"," ",0,"1/3*c*x^3","A",0
122,1,6,0,0.315700," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""giac"")","\frac{1}{2} \, c x^{2}"," ",0,"1/2*c*x^2","A",0
123,1,3,0,0.294327," ","integrate((b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""giac"")","c x"," ",0,"c*x","A",0
124,1,5,0,0.267541," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a),x, algorithm=""giac"")","c \log\left({\left| x \right|}\right)"," ",0,"c*log(abs(x))","A",0
125,1,6,0,0.321937," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a),x, algorithm=""giac"")","-\frac{c}{x}"," ",0,"-c/x","A",0
126,1,6,0,0.372082," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{c}{2 \, x^{2}}"," ",0,"-1/2*c/x^2","A",0
127,1,47,0,0.381026," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\frac{a c \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b} + \frac{{\left(b x^{2} + a\right)} c}{b}}{2 \, b}"," ",0,"1/2*(a*c*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b + (b*x^2 + a)*c/b)/b","A",0
128,1,28,0,0.271689," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{a c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{c x}{b}"," ",0,"-a*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) + c*x/b","A",0
129,1,63,0,0.300470," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{1}{2} \, c {\left(\frac{\log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{2} + a\right)} b}\right)} - \frac{a c}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"-1/2*c*(log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b - a/((b*x^2 + a)*b)) - 1/2*a*c/((b*x^2 + a)*b)","B",0
130,1,16,0,0.329065," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"c*arctan(b*x/sqrt(a*b))/sqrt(a*b)","A",0
131,1,26,0,0.269259," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c \log\left(x^{2}\right)}{2 \, a} - \frac{c \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a}"," ",0,"1/2*c*log(x^2)/a - 1/2*c*log(abs(b*x^2 + a))/a","A",0
132,1,31,0,0.350724," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{b c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{c}{a x}"," ",0,"-b*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - c/(a*x)","A",0
133,1,47,0,0.409623," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{b c \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{b c \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2}} + \frac{b c x^{2} - a c}{2 \, a^{2} x^{2}}"," ",0,"-1/2*b*c*log(x^2)/a^2 + 1/2*b*c*log(abs(b*x^2 + a))/a^2 + 1/2*(b*c*x^2 - a*c)/(a^2*x^2)","A",0
134,1,32,0,0.349582," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{c \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{2}} + \frac{a c}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"1/2*c*log(abs(b*x^2 + a))/b^2 + 1/2*a*c/((b*x^2 + a)*b^2)","A",0
135,1,37,0,0.349525," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b} - \frac{c x}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"1/2*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) - 1/2*c*x/((b*x^2 + a)*b)","A",0
136,1,15,0,0.433071," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{c}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"-1/2*c/((b*x^2 + a)*b)","A",0
137,1,37,0,0.384221," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a} + \frac{c x}{2 \, {\left(b x^{2} + a\right)} a}"," ",0,"1/2*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) + 1/2*c*x/((b*x^2 + a)*a)","A",0
138,1,51,0,0.372506," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{c \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{c \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2}} + \frac{b c x^{2} + 2 \, a c}{2 \, {\left(b x^{2} + a\right)} a^{2}}"," ",0,"1/2*c*log(x^2)/a^2 - 1/2*c*log(abs(b*x^2 + a))/a^2 + 1/2*(b*c*x^2 + 2*a*c)/((b*x^2 + a)*a^2)","A",0
139,1,50,0,0.331127," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, b c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} - \frac{3 \, b c x^{2} + 2 \, a c}{2 \, {\left(b x^{3} + a x\right)} a^{2}}"," ",0,"-3/2*b*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/2*(3*b*c*x^2 + 2*a*c)/((b*x^3 + a*x)*a^2)","A",0
140,1,56,0,0.299633," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{b c \log\left(x^{2}\right)}{a^{3}} + \frac{b c \log\left({\left| b x^{2} + a \right|}\right)}{a^{3}} - \frac{2 \, b c x^{2} + a c}{2 \, {\left(b x^{4} + a x^{2}\right)} a^{2}}"," ",0,"-b*c*log(x^2)/a^3 + b*c*log(abs(b*x^2 + a))/a^3 - 1/2*(2*b*c*x^2 + a*c)/((b*x^4 + a*x^2)*a^2)","A",0
141,1,53,0,0.296232," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{11} \, b^{2} d x^{11} + \frac{1}{9} \, b^{2} c x^{9} + \frac{2}{9} \, a b d x^{9} + \frac{2}{7} \, a b c x^{7} + \frac{1}{7} \, a^{2} d x^{7} + \frac{1}{5} \, a^{2} c x^{5}"," ",0,"1/11*b^2*d*x^11 + 1/9*b^2*c*x^9 + 2/9*a*b*d*x^9 + 2/7*a*b*c*x^7 + 1/7*a^2*d*x^7 + 1/5*a^2*c*x^5","A",0
142,1,53,0,0.315300," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d x^{10} + \frac{1}{8} \, b^{2} c x^{8} + \frac{1}{4} \, a b d x^{8} + \frac{1}{3} \, a b c x^{6} + \frac{1}{6} \, a^{2} d x^{6} + \frac{1}{4} \, a^{2} c x^{4}"," ",0,"1/10*b^2*d*x^10 + 1/8*b^2*c*x^8 + 1/4*a*b*d*x^8 + 1/3*a*b*c*x^6 + 1/6*a^2*d*x^6 + 1/4*a^2*c*x^4","A",0
143,1,53,0,0.434445," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{9} \, b^{2} d x^{9} + \frac{1}{7} \, b^{2} c x^{7} + \frac{2}{7} \, a b d x^{7} + \frac{2}{5} \, a b c x^{5} + \frac{1}{5} \, a^{2} d x^{5} + \frac{1}{3} \, a^{2} c x^{3}"," ",0,"1/9*b^2*d*x^9 + 1/7*b^2*c*x^7 + 2/7*a*b*d*x^7 + 2/5*a*b*c*x^5 + 1/5*a^2*d*x^5 + 1/3*a^2*c*x^3","A",0
144,1,53,0,0.426002," ","integrate(x*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{8} \, b^{2} d x^{8} + \frac{1}{6} \, b^{2} c x^{6} + \frac{1}{3} \, a b d x^{6} + \frac{1}{2} \, a b c x^{4} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{2} \, a^{2} c x^{2}"," ",0,"1/8*b^2*d*x^8 + 1/6*b^2*c*x^6 + 1/3*a*b*d*x^6 + 1/2*a*b*c*x^4 + 1/4*a^2*d*x^4 + 1/2*a^2*c*x^2","A",0
145,1,50,0,0.242423," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{7} \, b^{2} d x^{7} + \frac{1}{5} \, b^{2} c x^{5} + \frac{2}{5} \, a b d x^{5} + \frac{2}{3} \, a b c x^{3} + \frac{1}{3} \, a^{2} d x^{3} + a^{2} c x"," ",0,"1/7*b^2*d*x^7 + 1/5*b^2*c*x^5 + 2/5*a*b*d*x^5 + 2/3*a*b*c*x^3 + 1/3*a^2*d*x^3 + a^2*c*x","A",0
146,1,53,0,0.353430," ","integrate((b*x^2+a)^2*(d*x^2+c)/x,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} d x^{6} + \frac{1}{4} \, b^{2} c x^{4} + \frac{1}{2} \, a b d x^{4} + a b c x^{2} + \frac{1}{2} \, a^{2} d x^{2} + \frac{1}{2} \, a^{2} c \log\left(x^{2}\right)"," ",0,"1/6*b^2*d*x^6 + 1/4*b^2*c*x^4 + 1/2*a*b*d*x^4 + a*b*c*x^2 + 1/2*a^2*d*x^2 + 1/2*a^2*c*log(x^2)","A",0
147,1,48,0,0.334095," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} d x^{5} + \frac{1}{3} \, b^{2} c x^{3} + \frac{2}{3} \, a b d x^{3} + 2 \, a b c x + a^{2} d x - \frac{a^{2} c}{x}"," ",0,"1/5*b^2*d*x^5 + 1/3*b^2*c*x^3 + 2/3*a*b*d*x^3 + 2*a*b*c*x + a^2*d*x - a^2*c/x","A",0
148,1,70,0,0.398759," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, b^{2} d x^{4} + \frac{1}{2} \, b^{2} c x^{2} + a b d x^{2} + \frac{1}{2} \, {\left(2 \, a b c + a^{2} d\right)} \log\left(x^{2}\right) - \frac{2 \, a b c x^{2} + a^{2} d x^{2} + a^{2} c}{2 \, x^{2}}"," ",0,"1/4*b^2*d*x^4 + 1/2*b^2*c*x^2 + a*b*d*x^2 + 1/2*(2*a*b*c + a^2*d)*log(x^2) - 1/2*(2*a*b*c*x^2 + a^2*d*x^2 + a^2*c)/x^2","A",0
149,1,50,0,0.419346," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^4,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} d x^{3} + b^{2} c x + 2 \, a b d x - \frac{6 \, a b c x^{2} + 3 \, a^{2} d x^{2} + a^{2} c}{3 \, x^{3}}"," ",0,"1/3*b^2*d*x^3 + b^2*c*x + 2*a*b*d*x - 1/3*(6*a*b*c*x^2 + 3*a^2*d*x^2 + a^2*c)/x^3","A",0
150,1,94,0,0.430631," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{13} \, b^{2} d^{2} x^{13} + \frac{2}{11} \, b^{2} c d x^{11} + \frac{2}{11} \, a b d^{2} x^{11} + \frac{1}{9} \, b^{2} c^{2} x^{9} + \frac{4}{9} \, a b c d x^{9} + \frac{1}{9} \, a^{2} d^{2} x^{9} + \frac{2}{7} \, a b c^{2} x^{7} + \frac{2}{7} \, a^{2} c d x^{7} + \frac{1}{5} \, a^{2} c^{2} x^{5}"," ",0,"1/13*b^2*d^2*x^13 + 2/11*b^2*c*d*x^11 + 2/11*a*b*d^2*x^11 + 1/9*b^2*c^2*x^9 + 4/9*a*b*c*d*x^9 + 1/9*a^2*d^2*x^9 + 2/7*a*b*c^2*x^7 + 2/7*a^2*c*d*x^7 + 1/5*a^2*c^2*x^5","A",0
151,1,94,0,0.410310," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{12} \, b^{2} d^{2} x^{12} + \frac{1}{5} \, b^{2} c d x^{10} + \frac{1}{5} \, a b d^{2} x^{10} + \frac{1}{8} \, b^{2} c^{2} x^{8} + \frac{1}{2} \, a b c d x^{8} + \frac{1}{8} \, a^{2} d^{2} x^{8} + \frac{1}{3} \, a b c^{2} x^{6} + \frac{1}{3} \, a^{2} c d x^{6} + \frac{1}{4} \, a^{2} c^{2} x^{4}"," ",0,"1/12*b^2*d^2*x^12 + 1/5*b^2*c*d*x^10 + 1/5*a*b*d^2*x^10 + 1/8*b^2*c^2*x^8 + 1/2*a*b*c*d*x^8 + 1/8*a^2*d^2*x^8 + 1/3*a*b*c^2*x^6 + 1/3*a^2*c*d*x^6 + 1/4*a^2*c^2*x^4","A",0
152,1,94,0,0.261601," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} d^{2} x^{11} + \frac{2}{9} \, b^{2} c d x^{9} + \frac{2}{9} \, a b d^{2} x^{9} + \frac{1}{7} \, b^{2} c^{2} x^{7} + \frac{4}{7} \, a b c d x^{7} + \frac{1}{7} \, a^{2} d^{2} x^{7} + \frac{2}{5} \, a b c^{2} x^{5} + \frac{2}{5} \, a^{2} c d x^{5} + \frac{1}{3} \, a^{2} c^{2} x^{3}"," ",0,"1/11*b^2*d^2*x^11 + 2/9*b^2*c*d*x^9 + 2/9*a*b*d^2*x^9 + 1/7*b^2*c^2*x^7 + 4/7*a*b*c*d*x^7 + 1/7*a^2*d^2*x^7 + 2/5*a*b*c^2*x^5 + 2/5*a^2*c*d*x^5 + 1/3*a^2*c^2*x^3","A",0
153,1,94,0,0.313359," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d^{2} x^{10} + \frac{1}{4} \, b^{2} c d x^{8} + \frac{1}{4} \, a b d^{2} x^{8} + \frac{1}{6} \, b^{2} c^{2} x^{6} + \frac{2}{3} \, a b c d x^{6} + \frac{1}{6} \, a^{2} d^{2} x^{6} + \frac{1}{2} \, a b c^{2} x^{4} + \frac{1}{2} \, a^{2} c d x^{4} + \frac{1}{2} \, a^{2} c^{2} x^{2}"," ",0,"1/10*b^2*d^2*x^10 + 1/4*b^2*c*d*x^8 + 1/4*a*b*d^2*x^8 + 1/6*b^2*c^2*x^6 + 2/3*a*b*c*d*x^6 + 1/6*a^2*d^2*x^6 + 1/2*a*b*c^2*x^4 + 1/2*a^2*c*d*x^4 + 1/2*a^2*c^2*x^2","A",0
154,1,91,0,0.426220," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} d^{2} x^{9} + \frac{2}{7} \, b^{2} c d x^{7} + \frac{2}{7} \, a b d^{2} x^{7} + \frac{1}{5} \, b^{2} c^{2} x^{5} + \frac{4}{5} \, a b c d x^{5} + \frac{1}{5} \, a^{2} d^{2} x^{5} + \frac{2}{3} \, a b c^{2} x^{3} + \frac{2}{3} \, a^{2} c d x^{3} + a^{2} c^{2} x"," ",0,"1/9*b^2*d^2*x^9 + 2/7*b^2*c*d*x^7 + 2/7*a*b*d^2*x^7 + 1/5*b^2*c^2*x^5 + 4/5*a*b*c*d*x^5 + 1/5*a^2*d^2*x^5 + 2/3*a*b*c^2*x^3 + 2/3*a^2*c*d*x^3 + a^2*c^2*x","A",0
155,1,92,0,0.445831," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} d^{2} x^{8} + \frac{1}{3} \, b^{2} c d x^{6} + \frac{1}{3} \, a b d^{2} x^{6} + \frac{1}{4} \, b^{2} c^{2} x^{4} + a b c d x^{4} + \frac{1}{4} \, a^{2} d^{2} x^{4} + a b c^{2} x^{2} + a^{2} c d x^{2} + \frac{1}{2} \, a^{2} c^{2} \log\left(x^{2}\right)"," ",0,"1/8*b^2*d^2*x^8 + 1/3*b^2*c*d*x^6 + 1/3*a*b*d^2*x^6 + 1/4*b^2*c^2*x^4 + a*b*c*d*x^4 + 1/4*a^2*d^2*x^4 + a*b*c^2*x^2 + a^2*c*d*x^2 + 1/2*a^2*c^2*log(x^2)","A",0
156,1,90,0,0.273455," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} d^{2} x^{7} + \frac{2}{5} \, b^{2} c d x^{5} + \frac{2}{5} \, a b d^{2} x^{5} + \frac{1}{3} \, b^{2} c^{2} x^{3} + \frac{4}{3} \, a b c d x^{3} + \frac{1}{3} \, a^{2} d^{2} x^{3} + 2 \, a b c^{2} x + 2 \, a^{2} c d x - \frac{a^{2} c^{2}}{x}"," ",0,"1/7*b^2*d^2*x^7 + 2/5*b^2*c*d*x^5 + 2/5*a*b*d^2*x^5 + 1/3*b^2*c^2*x^3 + 4/3*a*b*c*d*x^3 + 1/3*a^2*d^2*x^3 + 2*a*b*c^2*x + 2*a^2*c*d*x - a^2*c^2/x","A",0
157,1,114,0,0.291432," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^3,x, algorithm=""giac"")","\frac{1}{6} \, b^{2} d^{2} x^{6} + \frac{1}{2} \, b^{2} c d x^{4} + \frac{1}{2} \, a b d^{2} x^{4} + \frac{1}{2} \, b^{2} c^{2} x^{2} + 2 \, a b c d x^{2} + \frac{1}{2} \, a^{2} d^{2} x^{2} + {\left(a b c^{2} + a^{2} c d\right)} \log\left(x^{2}\right) - \frac{2 \, a b c^{2} x^{2} + 2 \, a^{2} c d x^{2} + a^{2} c^{2}}{2 \, x^{2}}"," ",0,"1/6*b^2*d^2*x^6 + 1/2*b^2*c*d*x^4 + 1/2*a*b*d^2*x^4 + 1/2*b^2*c^2*x^2 + 2*a*b*c*d*x^2 + 1/2*a^2*d^2*x^2 + (a*b*c^2 + a^2*c*d)*log(x^2) - 1/2*(2*a*b*c^2*x^2 + 2*a^2*c*d*x^2 + a^2*c^2)/x^2","A",0
158,1,88,0,0.323435," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^4,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} d^{2} x^{5} + \frac{2}{3} \, b^{2} c d x^{3} + \frac{2}{3} \, a b d^{2} x^{3} + b^{2} c^{2} x + 4 \, a b c d x + a^{2} d^{2} x - \frac{6 \, a b c^{2} x^{2} + 6 \, a^{2} c d x^{2} + a^{2} c^{2}}{3 \, x^{3}}"," ",0,"1/5*b^2*d^2*x^5 + 2/3*b^2*c*d*x^3 + 2/3*a*b*d^2*x^3 + b^2*c^2*x + 4*a*b*c*d*x + a^2*d^2*x - 1/3*(6*a*b*c^2*x^2 + 6*a^2*c*d*x^2 + a^2*c^2)/x^3","A",0
159,1,135,0,0.353096," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{15} \, b^{2} d^{3} x^{15} + \frac{3}{13} \, b^{2} c d^{2} x^{13} + \frac{2}{13} \, a b d^{3} x^{13} + \frac{3}{11} \, b^{2} c^{2} d x^{11} + \frac{6}{11} \, a b c d^{2} x^{11} + \frac{1}{11} \, a^{2} d^{3} x^{11} + \frac{1}{9} \, b^{2} c^{3} x^{9} + \frac{2}{3} \, a b c^{2} d x^{9} + \frac{1}{3} \, a^{2} c d^{2} x^{9} + \frac{2}{7} \, a b c^{3} x^{7} + \frac{3}{7} \, a^{2} c^{2} d x^{7} + \frac{1}{5} \, a^{2} c^{3} x^{5}"," ",0,"1/15*b^2*d^3*x^15 + 3/13*b^2*c*d^2*x^13 + 2/13*a*b*d^3*x^13 + 3/11*b^2*c^2*d*x^11 + 6/11*a*b*c*d^2*x^11 + 1/11*a^2*d^3*x^11 + 1/9*b^2*c^3*x^9 + 2/3*a*b*c^2*d*x^9 + 1/3*a^2*c*d^2*x^9 + 2/7*a*b*c^3*x^7 + 3/7*a^2*c^2*d*x^7 + 1/5*a^2*c^3*x^5","A",0
160,1,135,0,0.382582," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{2} d^{3} x^{14} + \frac{1}{4} \, b^{2} c d^{2} x^{12} + \frac{1}{6} \, a b d^{3} x^{12} + \frac{3}{10} \, b^{2} c^{2} d x^{10} + \frac{3}{5} \, a b c d^{2} x^{10} + \frac{1}{10} \, a^{2} d^{3} x^{10} + \frac{1}{8} \, b^{2} c^{3} x^{8} + \frac{3}{4} \, a b c^{2} d x^{8} + \frac{3}{8} \, a^{2} c d^{2} x^{8} + \frac{1}{3} \, a b c^{3} x^{6} + \frac{1}{2} \, a^{2} c^{2} d x^{6} + \frac{1}{4} \, a^{2} c^{3} x^{4}"," ",0,"1/14*b^2*d^3*x^14 + 1/4*b^2*c*d^2*x^12 + 1/6*a*b*d^3*x^12 + 3/10*b^2*c^2*d*x^10 + 3/5*a*b*c*d^2*x^10 + 1/10*a^2*d^3*x^10 + 1/8*b^2*c^3*x^8 + 3/4*a*b*c^2*d*x^8 + 3/8*a^2*c*d^2*x^8 + 1/3*a*b*c^3*x^6 + 1/2*a^2*c^2*d*x^6 + 1/4*a^2*c^3*x^4","A",0
161,1,135,0,0.371025," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{2} d^{3} x^{13} + \frac{3}{11} \, b^{2} c d^{2} x^{11} + \frac{2}{11} \, a b d^{3} x^{11} + \frac{1}{3} \, b^{2} c^{2} d x^{9} + \frac{2}{3} \, a b c d^{2} x^{9} + \frac{1}{9} \, a^{2} d^{3} x^{9} + \frac{1}{7} \, b^{2} c^{3} x^{7} + \frac{6}{7} \, a b c^{2} d x^{7} + \frac{3}{7} \, a^{2} c d^{2} x^{7} + \frac{2}{5} \, a b c^{3} x^{5} + \frac{3}{5} \, a^{2} c^{2} d x^{5} + \frac{1}{3} \, a^{2} c^{3} x^{3}"," ",0,"1/13*b^2*d^3*x^13 + 3/11*b^2*c*d^2*x^11 + 2/11*a*b*d^3*x^11 + 1/3*b^2*c^2*d*x^9 + 2/3*a*b*c*d^2*x^9 + 1/9*a^2*d^3*x^9 + 1/7*b^2*c^3*x^7 + 6/7*a*b*c^2*d*x^7 + 3/7*a^2*c*d^2*x^7 + 2/5*a*b*c^3*x^5 + 3/5*a^2*c^2*d*x^5 + 1/3*a^2*c^3*x^3","A",0
162,1,134,0,0.322283," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{2} d^{3} x^{12} + \frac{3}{10} \, b^{2} c d^{2} x^{10} + \frac{1}{5} \, a b d^{3} x^{10} + \frac{3}{8} \, b^{2} c^{2} d x^{8} + \frac{3}{4} \, a b c d^{2} x^{8} + \frac{1}{8} \, a^{2} d^{3} x^{8} + \frac{1}{6} \, b^{2} c^{3} x^{6} + a b c^{2} d x^{6} + \frac{1}{2} \, a^{2} c d^{2} x^{6} + \frac{1}{2} \, a b c^{3} x^{4} + \frac{3}{4} \, a^{2} c^{2} d x^{4} + \frac{1}{2} \, a^{2} c^{3} x^{2}"," ",0,"1/12*b^2*d^3*x^12 + 3/10*b^2*c*d^2*x^10 + 1/5*a*b*d^3*x^10 + 3/8*b^2*c^2*d*x^8 + 3/4*a*b*c*d^2*x^8 + 1/8*a^2*d^3*x^8 + 1/6*b^2*c^3*x^6 + a*b*c^2*d*x^6 + 1/2*a^2*c*d^2*x^6 + 1/2*a*b*c^3*x^4 + 3/4*a^2*c^2*d*x^4 + 1/2*a^2*c^3*x^2","B",0
163,1,131,0,0.341375," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} d^{3} x^{11} + \frac{1}{3} \, b^{2} c d^{2} x^{9} + \frac{2}{9} \, a b d^{3} x^{9} + \frac{3}{7} \, b^{2} c^{2} d x^{7} + \frac{6}{7} \, a b c d^{2} x^{7} + \frac{1}{7} \, a^{2} d^{3} x^{7} + \frac{1}{5} \, b^{2} c^{3} x^{5} + \frac{6}{5} \, a b c^{2} d x^{5} + \frac{3}{5} \, a^{2} c d^{2} x^{5} + \frac{2}{3} \, a b c^{3} x^{3} + a^{2} c^{2} d x^{3} + a^{2} c^{3} x"," ",0,"1/11*b^2*d^3*x^11 + 1/3*b^2*c*d^2*x^9 + 2/9*a*b*d^3*x^9 + 3/7*b^2*c^2*d*x^7 + 6/7*a*b*c*d^2*x^7 + 1/7*a^2*d^3*x^7 + 1/5*b^2*c^3*x^5 + 6/5*a*b*c^2*d*x^5 + 3/5*a^2*c*d^2*x^5 + 2/3*a*b*c^3*x^3 + a^2*c^2*d*x^3 + a^2*c^3*x","A",0
164,1,134,0,0.417282," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x,x, algorithm=""giac"")","\frac{1}{10} \, b^{2} d^{3} x^{10} + \frac{3}{8} \, b^{2} c d^{2} x^{8} + \frac{1}{4} \, a b d^{3} x^{8} + \frac{1}{2} \, b^{2} c^{2} d x^{6} + a b c d^{2} x^{6} + \frac{1}{6} \, a^{2} d^{3} x^{6} + \frac{1}{4} \, b^{2} c^{3} x^{4} + \frac{3}{2} \, a b c^{2} d x^{4} + \frac{3}{4} \, a^{2} c d^{2} x^{4} + a b c^{3} x^{2} + \frac{3}{2} \, a^{2} c^{2} d x^{2} + \frac{1}{2} \, a^{2} c^{3} \log\left(x^{2}\right)"," ",0,"1/10*b^2*d^3*x^10 + 3/8*b^2*c*d^2*x^8 + 1/4*a*b*d^3*x^8 + 1/2*b^2*c^2*d*x^6 + a*b*c*d^2*x^6 + 1/6*a^2*d^3*x^6 + 1/4*b^2*c^3*x^4 + 3/2*a*b*c^2*d*x^4 + 3/4*a^2*c*d^2*x^4 + a*b*c^3*x^2 + 3/2*a^2*c^2*d*x^2 + 1/2*a^2*c^3*log(x^2)","A",0
165,1,130,0,0.383583," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} d^{3} x^{9} + \frac{3}{7} \, b^{2} c d^{2} x^{7} + \frac{2}{7} \, a b d^{3} x^{7} + \frac{3}{5} \, b^{2} c^{2} d x^{5} + \frac{6}{5} \, a b c d^{2} x^{5} + \frac{1}{5} \, a^{2} d^{3} x^{5} + \frac{1}{3} \, b^{2} c^{3} x^{3} + 2 \, a b c^{2} d x^{3} + a^{2} c d^{2} x^{3} + 2 \, a b c^{3} x + 3 \, a^{2} c^{2} d x - \frac{a^{2} c^{3}}{x}"," ",0,"1/9*b^2*d^3*x^9 + 3/7*b^2*c*d^2*x^7 + 2/7*a*b*d^3*x^7 + 3/5*b^2*c^2*d*x^5 + 6/5*a*b*c*d^2*x^5 + 1/5*a^2*d^3*x^5 + 1/3*b^2*c^3*x^3 + 2*a*b*c^2*d*x^3 + a^2*c*d^2*x^3 + 2*a*b*c^3*x + 3*a^2*c^2*d*x - a^2*c^3/x","A",0
166,1,160,0,0.316742," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^3,x, algorithm=""giac"")","\frac{1}{8} \, b^{2} d^{3} x^{8} + \frac{1}{2} \, b^{2} c d^{2} x^{6} + \frac{1}{3} \, a b d^{3} x^{6} + \frac{3}{4} \, b^{2} c^{2} d x^{4} + \frac{3}{2} \, a b c d^{2} x^{4} + \frac{1}{4} \, a^{2} d^{3} x^{4} + \frac{1}{2} \, b^{2} c^{3} x^{2} + 3 \, a b c^{2} d x^{2} + \frac{3}{2} \, a^{2} c d^{2} x^{2} + \frac{1}{2} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} \log\left(x^{2}\right) - \frac{2 \, a b c^{3} x^{2} + 3 \, a^{2} c^{2} d x^{2} + a^{2} c^{3}}{2 \, x^{2}}"," ",0,"1/8*b^2*d^3*x^8 + 1/2*b^2*c*d^2*x^6 + 1/3*a*b*d^3*x^6 + 3/4*b^2*c^2*d*x^4 + 3/2*a*b*c*d^2*x^4 + 1/4*a^2*d^3*x^4 + 1/2*b^2*c^3*x^2 + 3*a*b*c^2*d*x^2 + 3/2*a^2*c*d^2*x^2 + 1/2*(2*a*b*c^3 + 3*a^2*c^2*d)*log(x^2) - 1/2*(2*a*b*c^3*x^2 + 3*a^2*c^2*d*x^2 + a^2*c^3)/x^2","A",0
167,1,129,0,0.275573," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^4,x, algorithm=""giac"")","\frac{1}{7} \, b^{2} d^{3} x^{7} + \frac{3}{5} \, b^{2} c d^{2} x^{5} + \frac{2}{5} \, a b d^{3} x^{5} + b^{2} c^{2} d x^{3} + 2 \, a b c d^{2} x^{3} + \frac{1}{3} \, a^{2} d^{3} x^{3} + b^{2} c^{3} x + 6 \, a b c^{2} d x + 3 \, a^{2} c d^{2} x - \frac{6 \, a b c^{3} x^{2} + 9 \, a^{2} c^{2} d x^{2} + a^{2} c^{3}}{3 \, x^{3}}"," ",0,"1/7*b^2*d^3*x^7 + 3/5*b^2*c*d^2*x^5 + 2/5*a*b*d^3*x^5 + b^2*c^2*d*x^3 + 2*a*b*c*d^2*x^3 + 1/3*a^2*d^3*x^3 + b^2*c^3*x + 6*a*b*c^2*d*x + 3*a^2*c*d^2*x - 1/3*(6*a*b*c^3*x^2 + 9*a^2*c^2*d*x^2 + a^2*c^3)/x^3","A",0
168,1,153,0,0.310115," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{4}} + \frac{15 \, b^{2} d^{6} x^{7} - 21 \, b^{2} c d^{5} x^{5} + 42 \, a b d^{6} x^{5} + 35 \, b^{2} c^{2} d^{4} x^{3} - 70 \, a b c d^{5} x^{3} + 35 \, a^{2} d^{6} x^{3} - 105 \, b^{2} c^{3} d^{3} x + 210 \, a b c^{2} d^{4} x - 105 \, a^{2} c d^{5} x}{105 \, d^{7}}"," ",0,"(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^4) + 1/105*(15*b^2*d^6*x^7 - 21*b^2*c*d^5*x^5 + 42*a*b*d^6*x^5 + 35*b^2*c^2*d^4*x^3 - 70*a*b*c*d^5*x^3 + 35*a^2*d^6*x^3 - 105*b^2*c^3*d^3*x + 210*a*b*c^2*d^4*x - 105*a^2*c*d^5*x)/d^7","A",0
169,1,107,0,0.336575," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{2 \, b^{2} d^{2} x^{6} - 3 \, b^{2} c d x^{4} + 6 \, a b d^{2} x^{4} + 6 \, b^{2} c^{2} x^{2} - 12 \, a b c d x^{2} + 6 \, a^{2} d^{2} x^{2}}{12 \, d^{3}} - \frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, d^{4}}"," ",0,"1/12*(2*b^2*d^2*x^6 - 3*b^2*c*d*x^4 + 6*a*b*d^2*x^4 + 6*b^2*c^2*x^2 - 12*a*b*c*d*x^2 + 6*a^2*d^2*x^2)/d^3 - 1/2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*log(abs(d*x^2 + c))/d^4","A",0
170,1,113,0,0.259153," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{3}} + \frac{3 \, b^{2} d^{4} x^{5} - 5 \, b^{2} c d^{3} x^{3} + 10 \, a b d^{4} x^{3} + 15 \, b^{2} c^{2} d^{2} x - 30 \, a b c d^{3} x + 15 \, a^{2} d^{4} x}{15 \, d^{5}}"," ",0,"-(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^3) + 1/15*(3*b^2*d^4*x^5 - 5*b^2*c*d^3*x^3 + 10*a*b*d^4*x^3 + 15*b^2*c^2*d^2*x - 30*a*b*c*d^3*x + 15*a^2*d^4*x)/d^5","A",0
171,1,67,0,0.324205," ","integrate(x*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{2} d x^{4} - 2 \, b^{2} c x^{2} + 4 \, a b d x^{2}}{4 \, d^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, d^{3}}"," ",0,"1/4*(b^2*d*x^4 - 2*b^2*c*x^2 + 4*a*b*d*x^2)/d^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*x^2 + c))/d^3","A",0
172,1,72,0,0.277077," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{2}} + \frac{b^{2} d^{2} x^{3} - 3 \, b^{2} c d x + 6 \, a b d^{2} x}{3 \, d^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^2) + 1/3*(b^2*d^2*x^3 - 3*b^2*c*d*x + 6*a*b*d^2*x)/d^3","A",0
173,1,62,0,0.324987," ","integrate((b*x^2+a)^2/x/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{2} x^{2}}{2 \, d} + \frac{a^{2} \log\left(x^{2}\right)}{2 \, c} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c d^{2}}"," ",0,"1/2*b^2*x^2/d + 1/2*a^2*log(x^2)/c - 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*x^2 + c))/(c*d^2)","A",0
174,1,63,0,0.339689," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{2} x}{d} - \frac{a^{2}}{c x} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c d}"," ",0,"b^2*x/d - a^2/(c*x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d)","A",0
175,1,91,0,0.398623," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(2 \, a b c - a^{2} d\right)} \log\left(x^{2}\right)}{2 \, c^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{2} d} - \frac{2 \, a b c x^{2} - a^{2} d x^{2} + a^{2} c}{2 \, c^{2} x^{2}}"," ",0,"1/2*(2*a*b*c - a^2*d)*log(x^2)/c^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*x^2 + c))/(c^2*d) - 1/2*(2*a*b*c*x^2 - a^2*d*x^2 + a^2*c)/(c^2*x^2)","A",0
176,1,71,0,0.325207," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c^{2}} - \frac{6 \, a b c x^{2} - 3 \, a^{2} d x^{2} + a^{2} c}{3 \, c^{2} x^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2) - 1/3*(6*a*b*c*x^2 - 3*a^2*d*x^2 + a^2*c)/(c^2*x^3)","A",0
177,1,139,0,0.327360," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2}\right)}{2 \, c^{3}} - \frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{3} d} - \frac{3 \, b^{2} c^{2} x^{4} - 6 \, a b c d x^{4} + 3 \, a^{2} d^{2} x^{4} + 4 \, a b c^{2} x^{2} - 2 \, a^{2} c d x^{2} + a^{2} c^{2}}{4 \, c^{3} x^{4}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2)/c^3 - 1/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(abs(d*x^2 + c))/(c^3*d) - 1/4*(3*b^2*c^2*x^4 - 6*a*b*c*d*x^4 + 3*a^2*d^2*x^4 + 4*a*b*c^2*x^2 - 2*a^2*c*d*x^2 + a^2*c^2)/(c^3*x^4)","B",0
178,1,112,0,0.318199," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c^{3}} - \frac{15 \, b^{2} c^{2} x^{4} - 30 \, a b c d x^{4} + 15 \, a^{2} d^{2} x^{4} + 10 \, a b c^{2} x^{2} - 5 \, a^{2} c d x^{2} + 3 \, a^{2} c^{2}}{15 \, c^{3} x^{5}}"," ",0,"-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^3) - 1/15*(15*b^2*c^2*x^4 - 30*a*b*c*d*x^4 + 15*a^2*d^2*x^4 + 10*a*b*c^2*x^2 - 5*a^2*c*d*x^2 + 3*a^2*c^2)/(c^3*x^5)","A",0
179,1,184,0,0.322731," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(x^{2}\right)}{2 \, c^{4}} + \frac{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{4} d} + \frac{11 \, b^{2} c^{2} d x^{6} - 22 \, a b c d^{2} x^{6} + 11 \, a^{2} d^{3} x^{6} - 6 \, b^{2} c^{3} x^{4} + 12 \, a b c^{2} d x^{4} - 6 \, a^{2} c d^{2} x^{4} - 6 \, a b c^{3} x^{2} + 3 \, a^{2} c^{2} d x^{2} - 2 \, a^{2} c^{3}}{12 \, c^{4} x^{6}}"," ",0,"-1/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(x^2)/c^4 + 1/2*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*log(abs(d*x^2 + c))/(c^4*d) + 1/12*(11*b^2*c^2*d*x^6 - 22*a*b*c*d^2*x^6 + 11*a^2*d^3*x^6 - 6*b^2*c^3*x^4 + 12*a*b*c^2*d*x^4 - 6*a^2*c*d^2*x^4 - 6*a*b*c^3*x^2 + 3*a^2*c^2*d*x^2 - 2*a^2*c^3)/(c^4*x^6)","B",0
180,1,156,0,0.373605," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, b^{2} c^{3} - 10 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} d^{4}} + \frac{b^{2} c^{3} x - 2 \, a b c^{2} d x + a^{2} c d^{2} x}{2 \, {\left(d x^{2} + c\right)} d^{4}} + \frac{3 \, b^{2} d^{8} x^{5} - 10 \, b^{2} c d^{7} x^{3} + 10 \, a b d^{8} x^{3} + 45 \, b^{2} c^{2} d^{6} x - 60 \, a b c d^{7} x + 15 \, a^{2} d^{8} x}{15 \, d^{10}}"," ",0,"-1/2*(7*b^2*c^3 - 10*a*b*c^2*d + 3*a^2*c*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^4) + 1/2*(b^2*c^3*x - 2*a*b*c^2*d*x + a^2*c*d^2*x)/((d*x^2 + c)*d^4) + 1/15*(3*b^2*d^8*x^5 - 10*b^2*c*d^7*x^3 + 10*a*b*d^8*x^3 + 45*b^2*c^2*d^6*x - 60*a*b*c*d^7*x + 15*a^2*d^8*x)/d^10","A",0
181,1,163,0,0.345333," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\frac{{\left(d x^{2} + c\right)}^{2} {\left(b^{2} - \frac{2 \, {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)}}{{\left(d x^{2} + c\right)} d}\right)}}{d^{3}} - \frac{2 \, {\left(3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2}\right)} \log\left(\frac{{\left| d x^{2} + c \right|}}{{\left(d x^{2} + c\right)}^{2} {\left| d \right|}}\right)}{d^{3}} + \frac{2 \, {\left(\frac{b^{2} c^{3} d^{2}}{d x^{2} + c} - \frac{2 \, a b c^{2} d^{3}}{d x^{2} + c} + \frac{a^{2} c d^{4}}{d x^{2} + c}\right)}}{d^{5}}}{4 \, d}"," ",0,"1/4*((d*x^2 + c)^2*(b^2 - 2*(3*b^2*c*d - 2*a*b*d^2)/((d*x^2 + c)*d))/d^3 - 2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*log(abs(d*x^2 + c)/((d*x^2 + c)^2*abs(d)))/d^3 + 2*(b^2*c^3*d^2/(d*x^2 + c) - 2*a*b*c^2*d^3/(d*x^2 + c) + a^2*c*d^4/(d*x^2 + c))/d^5)/d","A",0
182,1,114,0,0.299589," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} d^{3}} - \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(d x^{2} + c\right)} d^{3}} + \frac{b^{2} d^{4} x^{3} - 6 \, b^{2} c d^{3} x + 6 \, a b d^{4} x}{3 \, d^{6}}"," ",0,"1/2*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^3) - 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^2 + c)*d^3) + 1/3*(b^2*d^4*x^3 - 6*b^2*c*d^3*x + 6*a*b*d^4*x)/d^6","A",0
183,1,110,0,0.327418," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(d x^{2} + c\right)} b^{2}}{2 \, d^{3}} + \frac{{\left(b^{2} c - a b d\right)} \log\left(\frac{{\left| d x^{2} + c \right|}}{{\left(d x^{2} + c\right)}^{2} {\left| d \right|}}\right)}{d^{3}} - \frac{\frac{b^{2} c^{2} d}{d x^{2} + c} - \frac{2 \, a b c d^{2}}{d x^{2} + c} + \frac{a^{2} d^{3}}{d x^{2} + c}}{2 \, d^{4}}"," ",0,"1/2*(d*x^2 + c)*b^2/d^3 + (b^2*c - a*b*d)*log(abs(d*x^2 + c)/((d*x^2 + c)^2*abs(d)))/d^3 - 1/2*(b^2*c^2*d/(d*x^2 + c) - 2*a*b*c*d^2/(d*x^2 + c) + a^2*d^3/(d*x^2 + c))/d^4","A",0
184,1,95,0,0.355858," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} x}{d^{2}} - \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(d x^{2} + c\right)} c d^{2}}"," ",0,"b^2*x/d^2 - 1/2*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^2) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^2 + c)*c*d^2)","A",0
185,1,99,0,0.317274," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{a^{2} \log\left(x^{2}\right)}{2 \, c^{2}} + \frac{{\left(b^{2} c^{2} - a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{2} d^{2}} - \frac{b^{2} c^{2} x^{2} - a^{2} d^{2} x^{2} + 2 \, a b c^{2} - 2 \, a^{2} c d}{2 \, {\left(d x^{2} + c\right)} c^{2} d}"," ",0,"1/2*a^2*log(x^2)/c^2 + 1/2*(b^2*c^2 - a^2*d^2)*log(abs(d*x^2 + c))/(c^2*d^2) - 1/2*(b^2*c^2*x^2 - a^2*d^2*x^2 + 2*a*b*c^2 - 2*a^2*c*d)/((d*x^2 + c)*c^2*d)","A",0
186,1,102,0,0.322643," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c^{2} d} - \frac{b^{2} c^{2} x^{2} - 2 \, a b c d x^{2} + 3 \, a^{2} d^{2} x^{2} + 2 \, a^{2} c d}{2 \, {\left(d x^{3} + c x\right)} c^{2} d}"," ",0,"1/2*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d) - 1/2*(b^2*c^2*x^2 - 2*a*b*c*d*x^2 + 3*a^2*d^2*x^2 + 2*a^2*c*d)/((d*x^3 + c*x)*c^2*d)","A",0
187,1,109,0,0.301770," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(a b c - a^{2} d\right)} \log\left(x^{2}\right)}{c^{3}} - \frac{{\left(a b c d - a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{c^{3} d} - \frac{b^{2} c^{2} x^{2} - 2 \, a b c d x^{2} + 2 \, a^{2} d^{2} x^{2} + a^{2} c d}{2 \, {\left(d x^{4} + c x^{2}\right)} c^{2} d}"," ",0,"(a*b*c - a^2*d)*log(x^2)/c^3 - (a*b*c*d - a^2*d^2)*log(abs(d*x^2 + c))/(c^3*d) - 1/2*(b^2*c^2*x^2 - 2*a*b*c*d*x^2 + 2*a^2*d^2*x^2 + a^2*c*d)/((d*x^4 + c*x^2)*c^2*d)","A",0
188,1,111,0,0.387280," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 6 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c^{3}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(d x^{2} + c\right)} c^{3}} - \frac{6 \, a b c x^{2} - 6 \, a^{2} d x^{2} + a^{2} c}{3 \, c^{3} x^{3}}"," ",0,"1/2*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^3) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^2 + c)*c^3) - 1/3*(6*a*b*c*x^2 - 6*a^2*d*x^2 + a^2*c)/(c^3*x^3)","A",0
189,1,154,0,0.345627," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(35 \, b^{2} c^{2} - 30 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} d^{4}} - \frac{13 \, b^{2} c^{2} d x^{3} - 18 \, a b c d^{2} x^{3} + 5 \, a^{2} d^{3} x^{3} + 11 \, b^{2} c^{3} x - 14 \, a b c^{2} d x + 3 \, a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} d^{4}} + \frac{b^{2} d^{6} x^{3} - 9 \, b^{2} c d^{5} x + 6 \, a b d^{6} x}{3 \, d^{9}}"," ",0,"1/8*(35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^4) - 1/8*(13*b^2*c^2*d*x^3 - 18*a*b*c*d^2*x^3 + 5*a^2*d^3*x^3 + 11*b^2*c^3*x - 14*a*b*c^2*d*x + 3*a^2*c*d^2*x)/((d*x^2 + c)^2*d^4) + 1/3*(b^2*d^6*x^3 - 9*b^2*c*d^5*x + 6*a*b*d^6*x)/d^9","A",0
190,1,107,0,0.338315," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{2} x^{2}}{2 \, d^{3}} - \frac{{\left(3 \, b^{2} c - 2 \, a b d\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, d^{4}} - \frac{5 \, b^{2} c^{3} - 6 \, a b c^{2} d + a^{2} c d^{2} + 2 \, {\left(3 \, b^{2} c^{2} d - 4 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}}{4 \, {\left(d x^{2} + c\right)}^{2} d^{4}}"," ",0,"1/2*b^2*x^2/d^3 - 1/2*(3*b^2*c - 2*a*b*d)*log(abs(d*x^2 + c))/d^4 - 1/4*(5*b^2*c^3 - 6*a*b*c^2*d + a^2*c*d^2 + 2*(3*b^2*c^2*d - 4*a*b*c*d^2 + a^2*d^3)*x^2)/((d*x^2 + c)^2*d^4)","A",0
191,1,133,0,0.394638," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{2} x}{d^{3}} - \frac{{\left(15 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c d^{3}} + \frac{9 \, b^{2} c^{2} d x^{3} - 10 \, a b c d^{2} x^{3} + a^{2} d^{3} x^{3} + 7 \, b^{2} c^{3} x - 6 \, a b c^{2} d x - a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} c d^{3}}"," ",0,"b^2*x/d^3 - 1/8*(15*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^3) + 1/8*(9*b^2*c^2*d*x^3 - 10*a*b*c*d^2*x^3 + a^2*d^3*x^3 + 7*b^2*c^3*x - 6*a*b*c^2*d*x - a^2*c*d^2*x)/((d*x^2 + c)^2*c*d^3)","A",0
192,1,76,0,0.438699," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, d^{3}} + \frac{4 \, {\left(b^{2} c - a b d\right)} x^{2} + \frac{3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}}{d}}{4 \, {\left(d x^{2} + c\right)}^{2} d^{2}}"," ",0,"1/2*b^2*log(abs(d*x^2 + c))/d^3 + 1/4*(4*(b^2*c - a*b*d)*x^2 + (3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)/d)/((d*x^2 + c)^2*d^2)","A",0
193,1,126,0,0.308796," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d^{2}} - \frac{5 \, b^{2} c^{2} d x^{3} - 2 \, a b c d^{2} x^{3} - 3 \, a^{2} d^{3} x^{3} + 3 \, b^{2} c^{3} x + 2 \, a b c^{2} d x - 5 \, a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{2} d^{2}}"," ",0,"1/8*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d^2) - 1/8*(5*b^2*c^2*d*x^3 - 2*a*b*c*d^2*x^3 - 3*a^2*d^3*x^3 + 3*b^2*c^3*x + 2*a*b*c^2*d*x - 5*a^2*c*d^2*x)/((d*x^2 + c)^2*c^2*d^2)","A",0
194,1,110,0,0.412513," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{a^{2} \log\left(x^{2}\right)}{2 \, c^{3}} - \frac{a^{2} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{3}} + \frac{3 \, a^{2} d^{4} x^{4} - 2 \, b^{2} c^{3} d x^{2} + 8 \, a^{2} c d^{3} x^{2} - b^{2} c^{4} - 2 \, a b c^{3} d + 6 \, a^{2} c^{2} d^{2}}{4 \, {\left(d x^{2} + c\right)}^{2} c^{3} d^{2}}"," ",0,"1/2*a^2*log(x^2)/c^3 - 1/2*a^2*log(abs(d*x^2 + c))/c^3 + 1/4*(3*a^2*d^4*x^4 - 2*b^2*c^3*d*x^2 + 8*a^2*c*d^3*x^2 - b^2*c^4 - 2*a*b*c^3*d + 6*a^2*c^2*d^2)/((d*x^2 + c)^2*c^3*d^2)","A",0
195,1,135,0,0.307752," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{a^{2}}{c^{3} x} + \frac{{\left(b^{2} c^{2} + 6 \, a b c d - 15 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{3} d} + \frac{b^{2} c^{2} d x^{3} + 6 \, a b c d^{2} x^{3} - 7 \, a^{2} d^{3} x^{3} - b^{2} c^{3} x + 10 \, a b c^{2} d x - 9 \, a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{3} d}"," ",0,"-a^2/(c^3*x) + 1/8*(b^2*c^2 + 6*a*b*c*d - 15*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^3*d) + 1/8*(b^2*c^2*d*x^3 + 6*a*b*c*d^2*x^3 - 7*a^2*d^3*x^3 - b^2*c^3*x + 10*a*b*c^2*d*x - 9*a^2*c*d^2*x)/((d*x^2 + c)^2*c^3*d)","A",0
196,1,177,0,0.385224," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(2 \, a b c - 3 \, a^{2} d\right)} \log\left(x^{2}\right)}{2 \, c^{4}} - \frac{{\left(2 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, c^{4} d} - \frac{2 \, a b c x^{2} - 3 \, a^{2} d x^{2} + a^{2} c}{2 \, c^{4} x^{2}} + \frac{6 \, a b c d^{3} x^{4} - 9 \, a^{2} d^{4} x^{4} + 16 \, a b c^{2} d^{2} x^{2} - 22 \, a^{2} c d^{3} x^{2} - b^{2} c^{4} + 12 \, a b c^{3} d - 14 \, a^{2} c^{2} d^{2}}{4 \, {\left(d x^{2} + c\right)}^{2} c^{4} d}"," ",0,"1/2*(2*a*b*c - 3*a^2*d)*log(x^2)/c^4 - 1/2*(2*a*b*c*d - 3*a^2*d^2)*log(abs(d*x^2 + c))/(c^4*d) - 1/2*(2*a*b*c*x^2 - 3*a^2*d*x^2 + a^2*c)/(c^4*x^2) + 1/4*(6*a*b*c*d^3*x^4 - 9*a^2*d^4*x^4 + 16*a*b*c^2*d^2*x^2 - 22*a^2*c*d^3*x^2 - b^2*c^4 + 12*a*b*c^3*d - 14*a^2*c^2*d^2)/((d*x^2 + c)^2*c^4*d)","A",0
197,1,151,0,0.374132," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c^{2} - 30 \, a b c d + 35 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{4}} + \frac{3 \, b^{2} c^{2} d x^{3} - 14 \, a b c d^{2} x^{3} + 11 \, a^{2} d^{3} x^{3} + 5 \, b^{2} c^{3} x - 18 \, a b c^{2} d x + 13 \, a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{4}} - \frac{6 \, a b c x^{2} - 9 \, a^{2} d x^{2} + a^{2} c}{3 \, c^{4} x^{3}}"," ",0,"1/8*(3*b^2*c^2 - 30*a*b*c*d + 35*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^4) + 1/8*(3*b^2*c^2*d*x^3 - 14*a*b*c*d^2*x^3 + 11*a^2*d^3*x^3 + 5*b^2*c^3*x - 18*a*b*c^2*d*x + 13*a^2*c*d^2*x)/((d*x^2 + c)^2*c^4) - 1/3*(6*a*b*c*x^2 - 9*a^2*d*x^2 + a^2*c)/(c^4*x^3)","A",0
198,1,77,0,0.320096," ","integrate(x^5*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, b^{2} d x^{6} + 3 \, b^{2} c x^{4} - 3 \, a b d x^{4} - 6 \, a b c x^{2} + 6 \, a^{2} d x^{2}}{12 \, b^{3}} + \frac{{\left(a^{2} b c - a^{3} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d*x^6 + 3*b^2*c*x^4 - 3*a*b*d*x^4 - 6*a*b*c*x^2 + 6*a^2*d*x^2)/b^3 + 1/2*(a^2*b*c - a^3*d)*log(abs(b*x^2 + a))/b^4","A",0
199,1,84,0,0.393913," ","integrate(x^4*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(a^{2} b c - a^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{4} d x^{5} + 5 \, b^{4} c x^{3} - 5 \, a b^{3} d x^{3} - 15 \, a b^{3} c x + 15 \, a^{2} b^{2} d x}{15 \, b^{5}}"," ",0,"(a^2*b*c - a^3*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^4*d*x^5 + 5*b^4*c*x^3 - 5*a*b^3*d*x^3 - 15*a*b^3*c*x + 15*a^2*b^2*d*x)/b^5","A",0
200,1,52,0,0.331726," ","integrate(x^3*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{b d x^{4} + 2 \, b c x^{2} - 2 \, a d x^{2}}{4 \, b^{2}} - \frac{{\left(a b c - a^{2} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{3}}"," ",0,"1/4*(b*d*x^4 + 2*b*c*x^2 - 2*a*d*x^2)/b^2 - 1/2*(a*b*c - a^2*d)*log(abs(b*x^2 + a))/b^3","A",0
201,1,58,0,0.436540," ","integrate(x^2*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a b c - a^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b^{2} d x^{3} + 3 \, b^{2} c x - 3 \, a b d x}{3 \, b^{3}}"," ",0,"-(a*b*c - a^2*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b^2*d*x^3 + 3*b^2*c*x - 3*a*b*d*x)/b^3","A",0
202,1,32,0,0.273854," ","integrate(x*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{d x^{2}}{2 \, b} + \frac{{\left(b c - a d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{2}}"," ",0,"1/2*d*x^2/b + 1/2*(b*c - a*d)*log(abs(b*x^2 + a))/b^2","A",0
203,1,33,0,0.344287," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{d x}{b} + \frac{{\left(b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"d*x/b + (b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
204,1,36,0,0.302951," ","integrate((d*x^2+c)/x/(b*x^2+a),x, algorithm=""giac"")","\frac{c \log\left(x^{2}\right)}{2 \, a} - \frac{{\left(b c - a d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a b}"," ",0,"1/2*c*log(x^2)/a - 1/2*(b*c - a*d)*log(abs(b*x^2 + a))/(a*b)","A",0
205,1,37,0,0.267568," ","integrate((d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{c}{a x}"," ",0,"-(b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) - c/(a*x)","A",0
206,1,72,0,0.331764," ","integrate((d*x^2+c)/x^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b c - a d\right)} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} c - a b d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b} + \frac{b c x^{2} - a d x^{2} - a c}{2 \, a^{2} x^{2}}"," ",0,"-1/2*(b*c - a*d)*log(x^2)/a^2 + 1/2*(b^2*c - a*b*d)*log(abs(b*x^2 + a))/(a^2*b) + 1/2*(b*c*x^2 - a*d*x^2 - a*c)/(a^2*x^2)","A",0
207,1,57,0,0.305247," ","integrate((d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c - a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, b c x^{2} - 3 \, a d x^{2} - a c}{3 \, a^{2} x^{3}}"," ",0,"(b^2*c - a*b*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/3*(3*b*c*x^2 - 3*a*d*x^2 - a*c)/(a^2*x^3)","A",0
208,1,148,0,0.318033," ","integrate(x^5*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{3 \, b^{3} d^{2} x^{8} + 8 \, b^{3} c d x^{6} - 4 \, a b^{2} d^{2} x^{6} + 6 \, b^{3} c^{2} x^{4} - 12 \, a b^{2} c d x^{4} + 6 \, a^{2} b d^{2} x^{4} - 12 \, a b^{2} c^{2} x^{2} + 24 \, a^{2} b c d x^{2} - 12 \, a^{3} d^{2} x^{2}}{24 \, b^{4}} + \frac{{\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{5}}"," ",0,"1/24*(3*b^3*d^2*x^8 + 8*b^3*c*d*x^6 - 4*a*b^2*d^2*x^6 + 6*b^3*c^2*x^4 - 12*a*b^2*c*d*x^4 + 6*a^2*b*d^2*x^4 - 12*a*b^2*c^2*x^2 + 24*a^2*b*c*d*x^2 - 12*a^3*d^2*x^2)/b^4 + 1/2*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*log(abs(b*x^2 + a))/b^5","A",0
209,1,153,0,0.410932," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{6} d^{2} x^{7} + 42 \, b^{6} c d x^{5} - 21 \, a b^{5} d^{2} x^{5} + 35 \, b^{6} c^{2} x^{3} - 70 \, a b^{5} c d x^{3} + 35 \, a^{2} b^{4} d^{2} x^{3} - 105 \, a b^{5} c^{2} x + 210 \, a^{2} b^{4} c d x - 105 \, a^{3} b^{3} d^{2} x}{105 \, b^{7}}"," ",0,"(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^6*d^2*x^7 + 42*b^6*c*d*x^5 - 21*a*b^5*d^2*x^5 + 35*b^6*c^2*x^3 - 70*a*b^5*c*d*x^3 + 35*a^2*b^4*d^2*x^3 - 105*a*b^5*c^2*x + 210*a^2*b^4*c*d*x - 105*a^3*b^3*d^2*x)/b^7","A",0
210,1,107,0,0.352356," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, b^{2} d^{2} x^{6} + 6 \, b^{2} c d x^{4} - 3 \, a b d^{2} x^{4} + 6 \, b^{2} c^{2} x^{2} - 12 \, a b c d x^{2} + 6 \, a^{2} d^{2} x^{2}}{12 \, b^{3}} - \frac{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d^2*x^6 + 6*b^2*c*d*x^4 - 3*a*b*d^2*x^4 + 6*b^2*c^2*x^2 - 12*a*b*c*d*x^2 + 6*a^2*d^2*x^2)/b^3 - 1/2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*log(abs(b*x^2 + a))/b^4","A",0
211,1,113,0,0.301822," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{4} d^{2} x^{5} + 10 \, b^{4} c d x^{3} - 5 \, a b^{3} d^{2} x^{3} + 15 \, b^{4} c^{2} x - 30 \, a b^{3} c d x + 15 \, a^{2} b^{2} d^{2} x}{15 \, b^{5}}"," ",0,"-(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^4*d^2*x^5 + 10*b^4*c*d*x^3 - 5*a*b^3*d^2*x^3 + 15*b^4*c^2*x - 30*a*b^3*c*d*x + 15*a^2*b^2*d^2*x)/b^5","A",0
212,1,67,0,0.376689," ","integrate(x*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{b d^{2} x^{4} + 4 \, b c d x^{2} - 2 \, a d^{2} x^{2}}{4 \, b^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{3}}"," ",0,"1/4*(b*d^2*x^4 + 4*b*c*d*x^2 - 2*a*d^2*x^2)/b^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(b*x^2 + a))/b^3","A",0
213,1,72,0,0.322947," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b^{2} d^{2} x^{3} + 6 \, b^{2} c d x - 3 \, a b d^{2} x}{3 \, b^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b^2*d^2*x^3 + 6*b^2*c*d*x - 3*a*b*d^2*x)/b^3","A",0
214,1,62,0,0.325129," ","integrate((d*x^2+c)^2/x/(b*x^2+a),x, algorithm=""giac"")","\frac{d^{2} x^{2}}{2 \, b} + \frac{c^{2} \log\left(x^{2}\right)}{2 \, a} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a b^{2}}"," ",0,"1/2*d^2*x^2/b + 1/2*c^2*log(x^2)/a - 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(b*x^2 + a))/(a*b^2)","A",0
215,1,63,0,0.295176," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a),x, algorithm=""giac"")","\frac{d^{2} x}{b} - \frac{c^{2}}{a x} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a b}"," ",0,"d^2*x/b - c^2/(a*x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
216,1,90,0,0.341175," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b c^{2} - 2 \, a c d\right)} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b} + \frac{b c^{2} x^{2} - 2 \, a c d x^{2} - a c^{2}}{2 \, a^{2} x^{2}}"," ",0,"-1/2*(b*c^2 - 2*a*c*d)*log(x^2)/a^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(b*x^2 + a))/(a^2*b) + 1/2*(b*c^2*x^2 - 2*a*c*d*x^2 - a*c^2)/(a^2*x^2)","A",0
217,1,72,0,0.328966," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, b c^{2} x^{2} - 6 \, a c d x^{2} - a c^{2}}{3 \, a^{2} x^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + 1/3*(3*b*c^2*x^2 - 6*a*c*d*x^2 - a*c^2)/(a^2*x^3)","A",0
218,1,238,0,0.322412," ","integrate(x^5*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\frac{12 \, b^{4} d^{3} x^{10} + 45 \, b^{4} c d^{2} x^{8} - 15 \, a b^{3} d^{3} x^{8} + 60 \, b^{4} c^{2} d x^{6} - 60 \, a b^{3} c d^{2} x^{6} + 20 \, a^{2} b^{2} d^{3} x^{6} + 30 \, b^{4} c^{3} x^{4} - 90 \, a b^{3} c^{2} d x^{4} + 90 \, a^{2} b^{2} c d^{2} x^{4} - 30 \, a^{3} b d^{3} x^{4} - 60 \, a b^{3} c^{3} x^{2} + 180 \, a^{2} b^{2} c^{2} d x^{2} - 180 \, a^{3} b c d^{2} x^{2} + 60 \, a^{4} d^{3} x^{2}}{120 \, b^{5}} + \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)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{6}}"," ",0,"1/120*(12*b^4*d^3*x^10 + 45*b^4*c*d^2*x^8 - 15*a*b^3*d^3*x^8 + 60*b^4*c^2*d*x^6 - 60*a*b^3*c*d^2*x^6 + 20*a^2*b^2*d^3*x^6 + 30*b^4*c^3*x^4 - 90*a*b^3*c^2*d*x^4 + 90*a^2*b^2*c*d^2*x^4 - 30*a^3*b*d^3*x^4 - 60*a*b^3*c^3*x^2 + 180*a^2*b^2*c^2*d*x^2 - 180*a^3*b*c*d^2*x^2 + 60*a^4*d^3*x^2)/b^5 + 1/2*(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(abs(b*x^2 + a))/b^6","A",0
219,1,241,0,0.297446," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{5}} + \frac{35 \, b^{8} d^{3} x^{9} + 135 \, b^{8} c d^{2} x^{7} - 45 \, a b^{7} d^{3} x^{7} + 189 \, b^{8} c^{2} d x^{5} - 189 \, a b^{7} c d^{2} x^{5} + 63 \, a^{2} b^{6} d^{3} x^{5} + 105 \, b^{8} c^{3} x^{3} - 315 \, a b^{7} c^{2} d x^{3} + 315 \, a^{2} b^{6} c d^{2} x^{3} - 105 \, a^{3} b^{5} d^{3} x^{3} - 315 \, a b^{7} c^{3} x + 945 \, a^{2} b^{6} c^{2} d x - 945 \, a^{3} b^{5} c d^{2} x + 315 \, a^{4} b^{4} d^{3} x}{315 \, b^{9}}"," ",0,"(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)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/315*(35*b^8*d^3*x^9 + 135*b^8*c*d^2*x^7 - 45*a*b^7*d^3*x^7 + 189*b^8*c^2*d*x^5 - 189*a*b^7*c*d^2*x^5 + 63*a^2*b^6*d^3*x^5 + 105*b^8*c^3*x^3 - 315*a*b^7*c^2*d*x^3 + 315*a^2*b^6*c*d^2*x^3 - 105*a^3*b^5*d^3*x^3 - 315*a*b^7*c^3*x + 945*a^2*b^6*c^2*d*x - 945*a^3*b^5*c*d^2*x + 315*a^4*b^4*d^3*x)/b^9","A",0
220,1,180,0,0.393465," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\frac{3 \, b^{3} d^{3} x^{8} + 12 \, b^{3} c d^{2} x^{6} - 4 \, a b^{2} d^{3} x^{6} + 18 \, b^{3} c^{2} d x^{4} - 18 \, a b^{2} c d^{2} x^{4} + 6 \, a^{2} b d^{3} x^{4} + 12 \, b^{3} c^{3} x^{2} - 36 \, a b^{2} c^{2} d x^{2} + 36 \, a^{2} b c d^{2} x^{2} - 12 \, a^{3} d^{3} x^{2}}{24 \, b^{4}} - \frac{{\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({\left| b x^{2} + a \right|}\right)}{2 \, b^{5}}"," ",0,"1/24*(3*b^3*d^3*x^8 + 12*b^3*c*d^2*x^6 - 4*a*b^2*d^3*x^6 + 18*b^3*c^2*d*x^4 - 18*a*b^2*c*d^2*x^4 + 6*a^2*b*d^3*x^4 + 12*b^3*c^3*x^2 - 36*a*b^2*c^2*d*x^2 + 36*a^2*b*c*d^2*x^2 - 12*a^3*d^3*x^2)/b^4 - 1/2*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*log(abs(b*x^2 + a))/b^5","A",0
221,1,184,0,0.450667," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{6} d^{3} x^{7} + 63 \, b^{6} c d^{2} x^{5} - 21 \, a b^{5} d^{3} x^{5} + 105 \, b^{6} c^{2} d x^{3} - 105 \, a b^{5} c d^{2} x^{3} + 35 \, a^{2} b^{4} d^{3} x^{3} + 105 \, b^{6} c^{3} x - 315 \, a b^{5} c^{2} d x + 315 \, a^{2} b^{4} c d^{2} x - 105 \, a^{3} b^{3} d^{3} x}{105 \, b^{7}}"," ",0,"-(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^6*d^3*x^7 + 63*b^6*c*d^2*x^5 - 21*a*b^5*d^3*x^5 + 105*b^6*c^2*d*x^3 - 105*a*b^5*c*d^2*x^3 + 35*a^2*b^4*d^3*x^3 + 105*b^6*c^3*x - 315*a*b^5*c^2*d*x + 315*a^2*b^4*c*d^2*x - 105*a^3*b^3*d^3*x)/b^7","A",0
222,1,124,0,0.288148," ","integrate(x*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, b^{2} d^{3} x^{6} + 9 \, b^{2} c d^{2} x^{4} - 3 \, a b d^{3} x^{4} + 18 \, b^{2} c^{2} d x^{2} - 18 \, a b c d^{2} x^{2} + 6 \, a^{2} d^{3} x^{2}}{12 \, b^{3}} + \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)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d^3*x^6 + 9*b^2*c*d^2*x^4 - 3*a*b*d^3*x^4 + 18*b^2*c^2*d*x^2 - 18*a*b*c*d^2*x^2 + 6*a^2*d^3*x^2)/b^3 + 1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(b*x^2 + a))/b^4","A",0
223,1,129,0,0.357574," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{4} d^{3} x^{5} + 15 \, b^{4} c d^{2} x^{3} - 5 \, a b^{3} d^{3} x^{3} + 45 \, b^{4} c^{2} d x - 45 \, a b^{3} c d^{2} x + 15 \, a^{2} b^{2} d^{3} x}{15 \, b^{5}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^4*d^3*x^5 + 15*b^4*c*d^2*x^3 - 5*a*b^3*d^3*x^3 + 45*b^4*c^2*d*x - 45*a*b^3*c*d^2*x + 15*a^2*b^2*d^3*x)/b^5","A",0
224,1,99,0,0.355971," ","integrate((d*x^2+c)^3/x/(b*x^2+a),x, algorithm=""giac"")","\frac{c^{3} \log\left(x^{2}\right)}{2 \, a} + \frac{b d^{3} x^{4} + 6 \, b c d^{2} x^{2} - 2 \, a d^{3} x^{2}}{4 \, b^{2}} - \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)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a b^{3}}"," ",0,"1/2*c^3*log(x^2)/a + 1/4*(b*d^3*x^4 + 6*b*c*d^2*x^2 - 2*a*d^3*x^2)/b^2 - 1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(b*x^2 + a))/(a*b^3)","A",0
225,1,104,0,0.359955," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a),x, algorithm=""giac"")","-\frac{c^{3}}{a x} - \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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{2}} + \frac{b^{2} d^{3} x^{3} + 9 \, b^{2} c d^{2} x - 3 \, a b d^{3} x}{3 \, b^{3}}"," ",0,"-c^3/(a*x) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) + 1/3*(b^2*d^3*x^3 + 9*b^2*c*d^2*x - 3*a*b*d^3*x)/b^3","A",0
226,1,120,0,0.308148," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a),x, algorithm=""giac"")","\frac{d^{3} x^{2}}{2 \, b} - \frac{{\left(b c^{3} - 3 \, a c^{2} d\right)} \log\left(x^{2}\right)}{2 \, a^{2}} + \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)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b^{2}} + \frac{b c^{3} x^{2} - 3 \, a c^{2} d x^{2} - a c^{3}}{2 \, a^{2} x^{2}}"," ",0,"1/2*d^3*x^2/b - 1/2*(b*c^3 - 3*a*c^2*d)*log(x^2)/a^2 + 1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(b*x^2 + a))/(a^2*b^2) + 1/2*(b*c^3*x^2 - 3*a*c^2*d*x^2 - a*c^3)/(a^2*x^2)","A",0
227,1,100,0,0.367825," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a),x, algorithm=""giac"")","\frac{d^{3} x}{b} + \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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2} b} + \frac{3 \, b c^{3} x^{2} - 9 \, a c^{2} d x^{2} - a c^{3}}{3 \, a^{2} x^{3}}"," ",0,"d^3*x/b + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/3*(3*b*c^3*x^2 - 9*a*c^2*d*x^2 - a*c^3)/(a^2*x^3)","A",0
228,1,70,0,0.366559," ","integrate(x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(b^{3} c - a b^{2} d\right)}} - \frac{c^{2} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c d^{2} - a d^{3}\right)}} + \frac{x^{2}}{2 \, b d}"," ",0,"1/2*a^2*log(abs(b*x^2 + a))/(b^3*c - a*b^2*d) - 1/2*c^2*log(abs(d*x^2 + c))/(b*c*d^2 - a*d^3) + 1/2*x^2/(b*d)","A",0
229,1,72,0,0.378885," ","integrate(x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c - a b d\right)} \sqrt{a b}} - \frac{c^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c d - a d^{2}\right)} \sqrt{c d}} + \frac{x}{b d}"," ",0,"a^2*arctan(b*x/sqrt(a*b))/((b^2*c - a*b*d)*sqrt(a*b)) - c^2*arctan(d*x/sqrt(c*d))/((b*c*d - a*d^2)*sqrt(c*d)) + x/(b*d)","A",0
230,1,51,0,0.300114," ","integrate(x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{a \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(b^{2} c - a b d\right)}} + \frac{c \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c d - a d^{2}\right)}}"," ",0,"-1/2*a*log(abs(b*x^2 + a))/(b^2*c - a*b*d) + 1/2*c*log(abs(d*x^2 + c))/(b*c*d - a*d^2)","A",0
231,1,54,0,0.338553," ","integrate(x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(b c - a d\right)}} + \frac{c \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c - a d\right)} \sqrt{c d}}"," ",0,"-a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*(b*c - a*d)) + c*arctan(d*x/sqrt(c*d))/((b*c - a*d)*sqrt(c*d))","A",0
232,1,51,0,0.371009," ","integrate(x/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(b^{2} c - a b d\right)}} - \frac{d \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c d - a d^{2}\right)}}"," ",0,"1/2*b*log(abs(b*x^2 + a))/(b^2*c - a*b*d) - 1/2*d*log(abs(d*x^2 + c))/(b*c*d - a*d^2)","A",0
233,1,54,0,0.388589," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(b c - a d\right)}} - \frac{d \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c - a d\right)} \sqrt{c d}}"," ",0,"b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*(b*c - a*d)) - d*arctan(d*x/sqrt(c*d))/((b*c - a*d)*sqrt(c*d))","A",0
234,1,73,0,0.305676," ","integrate(1/x/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a b^{2} c - a^{2} b d\right)}} + \frac{d^{2} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c^{2} d - a c d^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a c}"," ",0,"-1/2*b^2*log(abs(b*x^2 + a))/(a*b^2*c - a^2*b*d) + 1/2*d^2*log(abs(d*x^2 + c))/(b*c^2*d - a*c*d^2) + 1/2*log(x^2)/(a*c)","A",0
235,1,75,0,0.353618," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(a b c - a^{2} d\right)} \sqrt{a b}} + \frac{d^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c^{2} - a c d\right)} \sqrt{c d}} - \frac{1}{a c x}"," ",0,"-b^2*arctan(b*x/sqrt(a*b))/((a*b*c - a^2*d)*sqrt(a*b)) + d^2*arctan(d*x/sqrt(c*d))/((b*c^2 - a*c*d)*sqrt(c*d)) - 1/(a*c*x)","A",0
236,1,112,0,0.356461," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{2} b^{2} c - a^{3} b d\right)}} - \frac{d^{3} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c^{3} d - a c^{2} d^{2}\right)}} - \frac{{\left(b c + a d\right)} \log\left(x^{2}\right)}{2 \, a^{2} c^{2}} + \frac{b c x^{2} + a d x^{2} - a c}{2 \, a^{2} c^{2} x^{2}}"," ",0,"1/2*b^3*log(abs(b*x^2 + a))/(a^2*b^2*c - a^3*b*d) - 1/2*d^3*log(abs(d*x^2 + c))/(b*c^3*d - a*c^2*d^2) - 1/2*(b*c + a*d)*log(x^2)/(a^2*c^2) + 1/2*(b*c*x^2 + a*d*x^2 - a*c)/(a^2*c^2*x^2)","A",0
237,1,98,0,0.351624," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(a^{2} b c - a^{3} d\right)} \sqrt{a b}} - \frac{d^{3} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c^{3} - a c^{2} d\right)} \sqrt{c d}} + \frac{3 \, b c x^{2} + 3 \, a d x^{2} - a c}{3 \, a^{2} c^{2} x^{3}}"," ",0,"b^3*arctan(b*x/sqrt(a*b))/((a^2*b*c - a^3*d)*sqrt(a*b)) - d^3*arctan(d*x/sqrt(c*d))/((b*c^3 - a*c^2*d)*sqrt(c*d)) + 1/3*(3*b*c*x^2 + 3*a*d*x^2 - a*c)/(a^2*c^2*x^3)","A",0
238,1,167,0,0.311057," ","integrate(1/x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{b^{4} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{3} b^{2} c - a^{4} b d\right)}} + \frac{d^{4} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c^{4} d - a c^{3} d^{2}\right)}} + \frac{{\left(b^{2} c^{2} + a b c d + a^{2} d^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{3} c^{3}} - \frac{3 \, b^{2} c^{2} x^{4} + 3 \, a b c d x^{4} + 3 \, a^{2} d^{2} x^{4} - 2 \, a b c^{2} x^{2} - 2 \, a^{2} c d x^{2} + a^{2} c^{2}}{4 \, a^{3} c^{3} x^{4}}"," ",0,"-1/2*b^4*log(abs(b*x^2 + a))/(a^3*b^2*c - a^4*b*d) + 1/2*d^4*log(abs(d*x^2 + c))/(b*c^4*d - a*c^3*d^2) + 1/2*(b^2*c^2 + a*b*c*d + a^2*d^2)*log(x^2)/(a^3*c^3) - 1/4*(3*b^2*c^2*x^4 + 3*a*b*c*d*x^4 + 3*a^2*d^2*x^4 - 2*a*b*c^2*x^2 - 2*a^2*c*d*x^2 + a^2*c^2)/(a^3*c^3*x^4)","A",0
239,1,139,0,0.330000," ","integrate(1/x^6/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{b^{4} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(a^{3} b c - a^{4} d\right)} \sqrt{a b}} + \frac{d^{4} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c^{4} - a c^{3} d\right)} \sqrt{c d}} - \frac{15 \, b^{2} c^{2} x^{4} + 15 \, a b c d x^{4} + 15 \, a^{2} d^{2} x^{4} - 5 \, a b c^{2} x^{2} - 5 \, a^{2} c d x^{2} + 3 \, a^{2} c^{2}}{15 \, a^{3} c^{3} x^{5}}"," ",0,"-b^4*arctan(b*x/sqrt(a*b))/((a^3*b*c - a^4*d)*sqrt(a*b)) + d^4*arctan(d*x/sqrt(c*d))/((b*c^4 - a*c^3*d)*sqrt(c*d)) - 1/15*(15*b^2*c^2*x^4 + 15*a*b*c*d*x^4 + 15*a^2*d^2*x^4 - 5*a*b*c^2*x^2 - 5*a^2*c*d*x^2 + 3*a^2*c^2)/(a^3*c^3*x^5)","A",0
240,1,239,0,0.309273," ","integrate(1/x^7/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b^{5} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{4} b^{2} c - a^{5} b d\right)}} - \frac{d^{5} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b c^{5} d - a c^{4} d^{2}\right)}} - \frac{{\left(b^{3} c^{3} + a b^{2} c^{2} d + a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{4} c^{4}} + \frac{11 \, b^{3} c^{3} x^{6} + 11 \, a b^{2} c^{2} d x^{6} + 11 \, a^{2} b c d^{2} x^{6} + 11 \, a^{3} d^{3} x^{6} - 6 \, a b^{2} c^{3} x^{4} - 6 \, a^{2} b c^{2} d x^{4} - 6 \, a^{3} c d^{2} x^{4} + 3 \, a^{2} b c^{3} x^{2} + 3 \, a^{3} c^{2} d x^{2} - 2 \, a^{3} c^{3}}{12 \, a^{4} c^{4} x^{6}}"," ",0,"1/2*b^5*log(abs(b*x^2 + a))/(a^4*b^2*c - a^5*b*d) - 1/2*d^5*log(abs(d*x^2 + c))/(b*c^5*d - a*c^4*d^2) - 1/2*(b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2 + a^3*d^3)*log(x^2)/(a^4*c^4) + 1/12*(11*b^3*c^3*x^6 + 11*a*b^2*c^2*d*x^6 + 11*a^2*b*c*d^2*x^6 + 11*a^3*d^3*x^6 - 6*a*b^2*c^3*x^4 - 6*a^2*b*c^2*d*x^4 - 6*a^3*c*d^2*x^4 + 3*a^2*b*c^3*x^2 + 3*a^3*c^2*d*x^2 - 2*a^3*c^3)/(a^4*c^4*x^6)","A",0
241,1,152,0,0.278950," ","integrate(x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{c^{2} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}} - \frac{{\left(2 \, a b c - a^{2} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)}} + \frac{2 \, a b c x^{2} - a^{2} d x^{2} + a^{2} c}{2 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} {\left(b x^{2} + a\right)}}"," ",0,"1/2*c^2*log(abs(d*x^2 + c))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) - 1/2*(2*a*b*c - a^2*d)*log(abs(b*x^2 + a))/(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2) + 1/2*(2*a*b*c*x^2 - a^2*d*x^2 + a^2*c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*(b*x^2 + a))","A",0
242,1,121,0,0.344664," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} + \frac{{\left(b c^{2} - 3 \, a c d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{c d}} - \frac{c x}{2 \, {\left(b c d - a d^{2}\right)} {\left(d x^{2} + c\right)}}"," ",0,"a^2*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) + 1/2*(b*c^2 - 3*a*c*d)*arctan(d*x/sqrt(c*d))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(c*d)) - 1/2*c*x/((b*c*d - a*d^2)*(d*x^2 + c))","A",0
243,1,91,0,0.373537," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{\frac{a d^{2} \log\left({\left| b - \frac{b c}{d x^{2} + c} + \frac{a d}{d x^{2} + c} \right|}\right)}{b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}} + \frac{c d}{{\left(b c d - a d^{2}\right)} {\left(d x^{2} + c\right)}}}{2 \, d}"," ",0,"-1/2*(a*d^2*log(abs(b - b*c/(d*x^2 + c) + a*d/(d*x^2 + c)))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) + c*d/((b*c*d - a*d^2)*(d*x^2 + c)))/d","A",0
244,1,110,0,0.321353," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{a b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} + \frac{{\left(b c + a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} + \frac{x}{2 \, {\left(d x^{2} + c\right)} {\left(b c - a d\right)}}"," ",0,"-a*b*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) + 1/2*(b*c + a*d)*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) + 1/2*x/((d*x^2 + c)*(b*c - a*d))","A",0
245,1,85,0,0.339855," ","integrate(x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b d \log\left({\left| b - \frac{b c}{d x^{2} + c} + \frac{a d}{d x^{2} + c} \right|}\right)}{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}} + \frac{d}{2 \, {\left(b c d - a d^{2}\right)} {\left(d x^{2} + c\right)}}"," ",0,"1/2*b*d*log(abs(b - b*c/(d*x^2 + c) + a*d/(d*x^2 + c)))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) + 1/2*d/((b*c*d - a*d^2)*(d*x^2 + c))","A",0
246,1,122,0,0.357897," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} - \frac{{\left(3 \, b c d - a d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{c d}} - \frac{d x}{2 \, {\left(b c^{2} - a c d\right)} {\left(d x^{2} + c\right)}}"," ",0,"b^2*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) - 1/2*(3*b*c*d - a*d^2)*arctan(d*x/sqrt(c*d))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(c*d)) - 1/2*d*x/((b*c^2 - a*c*d)*(d*x^2 + c))","A",0
247,1,185,0,0.386817," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{b^{3} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)}} + \frac{{\left(2 \, b c d^{2} - a d^{3}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)}} - \frac{2 \, b c d^{2} x^{2} - a d^{3} x^{2} + 3 \, b c^{2} d - 2 \, a c d^{2}}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a c^{2}}"," ",0,"-1/2*b^3*log(abs(b*x^2 + a))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2) + 1/2*(2*b*c*d^2 - a*d^3)*log(abs(d*x^2 + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3) - 1/2*(2*b*c*d^2*x^2 - a*d^3*x^2 + 3*b*c^2*d - 2*a*c*d^2)/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)) + 1/2*log(x^2)/(a*c^2)","A",0
248,1,164,0,0.384179," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b}} + \frac{{\left(5 \, b c d^{2} - 3 \, a d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{c d}} - \frac{2 \, b c d x^{2} - 3 \, a d^{2} x^{2} + 2 \, b c^{2} - 2 \, a c d}{2 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} {\left(d x^{3} + c x\right)}}"," ",0,"-b^3*arctan(b*x/sqrt(a*b))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b)) + 1/2*(5*b*c*d^2 - 3*a*d^3)*arctan(d*x/sqrt(c*d))/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(c*d)) - 1/2*(2*b*c*d*x^2 - 3*a*d^2*x^2 + 2*b*c^2 - 2*a*c*d)/((a*b*c^3 - a^2*c^2*d)*(d*x^3 + c*x))","A",0
249,1,257,0,0.349435," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{4} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)}} - \frac{{\left(3 \, b c d^{3} - 2 \, a d^{4}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)}} + \frac{b^{3} c^{2} d x^{4} + b^{3} c^{3} x^{2} - 2 \, a b^{2} c^{2} d x^{2} + 6 \, a^{2} b c d^{2} x^{2} - 4 \, a^{3} d^{3} x^{2} - 2 \, a b^{2} c^{3} + 4 \, a^{2} b c^{2} d - 2 \, a^{3} c d^{2}}{4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(d x^{4} + c x^{2}\right)}} - \frac{{\left(b c + 2 \, a d\right)} \log\left(x^{2}\right)}{2 \, a^{2} c^{3}}"," ",0,"1/2*b^4*log(abs(b*x^2 + a))/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2) - 1/2*(3*b*c*d^3 - 2*a*d^4)*log(abs(d*x^2 + c))/(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3) + 1/4*(b^3*c^2*d*x^4 + b^3*c^3*x^2 - 2*a*b^2*c^2*d*x^2 + 6*a^2*b*c*d^2*x^2 - 4*a^3*d^3*x^2 - 2*a*b^2*c^3 + 4*a^2*b*c^2*d - 2*a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(d*x^4 + c*x^2)) - 1/2*(b*c + 2*a*d)*log(x^2)/(a^2*c^3)","B",0
250,1,165,0,0.342091," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{4} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{a b}} - \frac{d^{3} x}{2 \, {\left(b c^{4} - a c^{3} d\right)} {\left(d x^{2} + c\right)}} - \frac{{\left(7 \, b c d^{3} - 5 \, a d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} \sqrt{c d}} + \frac{3 \, b c x^{2} + 6 \, a d x^{2} - a c}{3 \, a^{2} c^{3} x^{3}}"," ",0,"b^4*arctan(b*x/sqrt(a*b))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(a*b)) - 1/2*d^3*x/((b*c^4 - a*c^3*d)*(d*x^2 + c)) - 1/2*(7*b*c*d^3 - 5*a*d^4)*arctan(d*x/sqrt(c*d))/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*sqrt(c*d)) + 1/3*(3*b*c*x^2 + 6*a*d*x^2 - a*c)/(a^2*c^3*x^3)","A",0
251,1,232,0,0.333971," ","integrate(x^5/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""giac"")","\frac{b c^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} - \frac{c^{2} d \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\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)}} - \frac{3 \, b^{4} c^{2} x^{4} + 2 \, a b^{3} c^{2} x^{2} + 6 \, a^{2} b^{2} c d x^{2} - 2 \, a^{3} b d^{2} x^{2} + 4 \, a^{3} b c d - a^{4} d^{2}}{4 \, {\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(b x^{2} + a\right)}^{2}}"," ",0,"1/2*b*c^2*log(abs(b*x^2 + a))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - 1/2*c^2*d*log(abs(d*x^2 + c))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4) - 1/4*(3*b^4*c^2*x^4 + 2*a*b^3*c^2*x^2 + 6*a^2*b^2*c*d*x^2 - 2*a^3*b*d^2*x^2 + 4*a^3*b*c*d - a^4*d^2)/((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)*(b*x^2 + a)^2)","B",0
252,1,204,0,0.327904," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{a^{2} b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\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}} + \frac{{\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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{c d}} + \frac{b c d x^{3} - 5 \, a d^{2} x^{3} - b c^{2} x - 3 \, a c d x}{8 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"a^2*b*arctan(b*x/sqrt(a*b))/((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)) + 1/8*(b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/((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(c*d)) + 1/8*(b*c*d*x^3 - 5*a*d^2*x^3 - b*c^2*x - 3*a*c*d*x)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(d*x^2 + c)^2)","A",0
253,1,174,0,0.433749," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{a b^{2} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} + \frac{a b d \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\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)}} - \frac{b^{2} c^{3} - a^{2} c d^{2} + 2 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} x^{2}}{4 \, {\left(d x^{2} + c\right)}^{2} {\left(b c - a d\right)}^{3} d}"," ",0,"-1/2*a*b^2*log(abs(b*x^2 + a))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) + 1/2*a*b*d*log(abs(d*x^2 + c))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4) - 1/4*(b^2*c^3 - a^2*c*d^2 + 2*(a*b*c*d^2 - a^2*d^3)*x^2)/((d*x^2 + c)^2*(b*c - a*d)^3*d)","A",0
254,1,206,0,0.373045," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{a b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\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}} + \frac{{\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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)} \sqrt{c d}} + \frac{3 \, b c d x^{3} + a d^{2} x^{3} + 5 \, b c^{2} x - a c d x}{8 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"-a*b^2*arctan(b*x/sqrt(a*b))/((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)) + 1/8*(3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*arctan(d*x/sqrt(c*d))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*sqrt(c*d)) + 1/8*(3*b*c*d*x^3 + a*d^2*x^3 + 5*b*c^2*x - a*c*d*x)/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(d*x^2 + c)^2)","A",0
255,1,174,0,0.383369," ","integrate(x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} - \frac{b^{2} d \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\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)}} + \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}}{4 \, {\left(d x^{2} + c\right)}^{2} {\left(b c - a d\right)}^{3}}"," ",0,"1/2*b^3*log(abs(b*x^2 + a))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - 1/2*b^2*d*log(abs(d*x^2 + c))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4) + 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)/((d*x^2 + c)^2*(b*c - a*d)^3)","A",0
256,1,217,0,0.367345," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\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}} - \frac{{\left(15 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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{c d}} - \frac{7 \, b c d^{2} x^{3} - 3 \, a d^{3} x^{3} + 9 \, b c^{2} d x - 5 \, a c d^{2} x}{8 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"b^3*arctan(b*x/sqrt(a*b))/((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)) - 1/8*(15*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*arctan(d*x/sqrt(c*d))/((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(c*d)) - 1/8*(7*b*c*d^2*x^3 - 3*a*d^3*x^3 + 9*b*c^2*d*x - 5*a*c*d^2*x)/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)^2)","A",0
257,1,315,0,0.427469," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{4} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} + \frac{{\left(3 \, b^{2} c^{2} d^{2} - 3 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{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)}} - \frac{9 \, b^{2} c^{2} d^{3} x^{4} - 9 \, a b c d^{4} x^{4} + 3 \, a^{2} d^{5} x^{4} + 22 \, b^{2} c^{3} d^{2} x^{2} - 24 \, a b c^{2} d^{3} x^{2} + 8 \, a^{2} c d^{4} x^{2} + 14 \, b^{2} c^{4} d - 17 \, a b c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}}{4 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}} + \frac{\log\left(x^{2}\right)}{2 \, a c^{3}}"," ",0,"-1/2*b^4*log(abs(b*x^2 + a))/(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) + 1/2*(3*b^2*c^2*d^2 - 3*a*b*c*d^3 + a^2*d^4)*log(abs(d*x^2 + c))/(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) - 1/4*(9*b^2*c^2*d^3*x^4 - 9*a*b*c*d^4*x^4 + 3*a^2*d^5*x^4 + 22*b^2*c^3*d^2*x^2 - 24*a*b*c^2*d^3*x^2 + 8*a^2*c*d^4*x^2 + 14*b^2*c^4*d - 17*a*b*c^3*d^2 + 6*a^2*c^2*d^3)/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*(d*x^2 + c)^2) + 1/2*log(x^2)/(a*c^3)","B",0
258,1,236,0,0.332156," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{4} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\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{a b}} + \frac{{\left(35 \, b^{2} c^{2} d^{2} - 42 \, a b c d^{3} + 15 \, a^{2} d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} \sqrt{c d}} + \frac{11 \, b c d^{3} x^{3} - 7 \, a d^{4} x^{3} + 13 \, b c^{2} d^{2} x - 9 \, a c d^{3} x}{8 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}} - \frac{1}{a c^{3} x}"," ",0,"-b^4*arctan(b*x/sqrt(a*b))/((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)) + 1/8*(35*b^2*c^2*d^2 - 42*a*b*c*d^3 + 15*a^2*d^4)*arctan(d*x/sqrt(c*d))/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*sqrt(c*d)) + 1/8*(11*b*c*d^3*x^3 - 7*a*d^4*x^3 + 13*b*c^2*d^2*x - 9*a*c*d^3*x)/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*(d*x^2 + c)^2) - 1/(a*c^3*x)","A",0
259,1,357,0,0.338184," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{5} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} - \frac{{\left(6 \, b^{2} c^{2} d^{3} - 8 \, a b c d^{4} + 3 \, a^{2} d^{5}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\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}\right)}} + \frac{18 \, b^{2} c^{2} d^{4} x^{4} - 24 \, a b c d^{5} x^{4} + 9 \, a^{2} d^{6} x^{4} + 42 \, b^{2} c^{3} d^{3} x^{2} - 58 \, a b c^{2} d^{4} x^{2} + 22 \, a^{2} c d^{5} x^{2} + 25 \, b^{2} c^{4} d^{2} - 36 \, a b c^{3} d^{3} + 14 \, a^{2} c^{2} d^{4}}{4 \, {\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(d x^{2} + c\right)}^{2}} - \frac{{\left(b c + 3 \, a d\right)} \log\left(x^{2}\right)}{2 \, a^{2} c^{4}} + \frac{b c x^{2} + 3 \, a d x^{2} - a c}{2 \, a^{2} c^{4} x^{2}}"," ",0,"1/2*b^5*log(abs(b*x^2 + a))/(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) - 1/2*(6*b^2*c^2*d^3 - 8*a*b*c*d^4 + 3*a^2*d^5)*log(abs(d*x^2 + c))/(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) + 1/4*(18*b^2*c^2*d^4*x^4 - 24*a*b*c*d^5*x^4 + 9*a^2*d^6*x^4 + 42*b^2*c^3*d^3*x^2 - 58*a*b*c^2*d^4*x^2 + 22*a^2*c*d^5*x^2 + 25*b^2*c^4*d^2 - 36*a*b*c^3*d^3 + 14*a^2*c^2*d^4)/((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*x^2 + c)^2) - 1/2*(b*c + 3*a*d)*log(x^2)/(a^2*c^4) + 1/2*(b*c*x^2 + 3*a*d*x^2 - a*c)/(a^2*c^4*x^2)","B",0
260,1,256,0,0.314264," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{5} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\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{a b}} - \frac{{\left(63 \, b^{2} c^{2} d^{3} - 90 \, a b c d^{4} + 35 \, a^{2} d^{5}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{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}\right)} \sqrt{c d}} - \frac{15 \, b c d^{4} x^{3} - 11 \, a d^{5} x^{3} + 17 \, b c^{2} d^{3} x - 13 \, a c d^{4} x}{8 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}} + \frac{3 \, b c x^{2} + 9 \, a d x^{2} - a c}{3 \, a^{2} c^{4} x^{3}}"," ",0,"b^5*arctan(b*x/sqrt(a*b))/((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(a*b)) - 1/8*(63*b^2*c^2*d^3 - 90*a*b*c*d^4 + 35*a^2*d^5)*arctan(d*x/sqrt(c*d))/((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)*sqrt(c*d)) - 1/8*(15*b*c*d^4*x^3 - 11*a*d^5*x^3 + 17*b*c^2*d^3*x - 13*a*c*d^4*x)/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2)*(d*x^2 + c)^2) + 1/3*(3*b*c*x^2 + 9*a*d*x^2 - a*c)/(a^2*c^4*x^3)","A",0
261,1,17,0,0.281509," ","integrate(x/(x^2+1)/(x^2+4),x, algorithm=""giac"")","-\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
262,1,88,0,0.392277," ","integrate(x^4*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a b c - 5 \, a^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} + \frac{a b c x - a^{2} d x}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{b^{4} d x^{3} + 3 \, b^{4} c x - 6 \, a b^{3} d x}{3 \, b^{6}}"," ",0,"-1/2*(3*a*b*c - 5*a^2*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/2*(a*b*c*x - a^2*d*x)/((b*x^2 + a)*b^3) + 1/3*(b^4*d*x^3 + 3*b^4*c*x - 6*a*b^3*d*x)/b^6","A",0
263,1,90,0,0.309522," ","integrate(x^3*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\frac{{\left(b x^{2} + a\right)} d}{b^{2}} - \frac{{\left(b c - 2 \, a d\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b^{2}} + \frac{\frac{a b^{2} c}{b x^{2} + a} - \frac{a^{2} b d}{b x^{2} + a}}{b^{3}}}{2 \, b}"," ",0,"1/2*((b*x^2 + a)*d/b^2 - (b*c - 2*a*d)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^2 + (a*b^2*c/(b*x^2 + a) - a^2*b*d/(b*x^2 + a))/b^3)/b","A",0
264,1,58,0,0.298287," ","integrate(x^2*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d x}{b^{2}} + \frac{{\left(b c - 3 \, a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{2}} - \frac{b c x - a d x}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"d*x/b^2 + 1/2*(b*c - 3*a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) - 1/2*(b*c*x - a*d*x)/((b*x^2 + a)*b^2)","A",0
265,1,65,0,0.337457," ","integrate(x*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{d {\left(\frac{\log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x^{2} + a\right)} b}\right)}}{2 \, b} - \frac{c}{2 \, {\left(b x^{2} + a\right)} b}"," ",0,"-1/2*d*(log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b - a/((b*x^2 + a)*b))/b - 1/2*c/((b*x^2 + a)*b)","A",0
266,1,57,0,0.398802," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b} + \frac{b c x - a d x}{2 \, {\left(b x^{2} + a\right)} a b}"," ",0,"1/2*(b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b) + 1/2*(b*c*x - a*d*x)/((b*x^2 + a)*a*b)","A",0
267,1,63,0,0.316557," ","integrate((d*x^2+c)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{c \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2}} + \frac{b^{2} c x^{2} + 2 \, a b c - a^{2} d}{2 \, {\left(b x^{2} + a\right)} a^{2} b}"," ",0,"1/2*c*log(x^2)/a^2 - 1/2*c*log(abs(b*x^2 + a))/a^2 + 1/2*(b^2*c*x^2 + 2*a*b*c - a^2*d)/((b*x^2 + a)*a^2*b)","A",0
268,1,64,0,0.354923," ","integrate((d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}} - \frac{3 \, b c x^{2} - a d x^{2} + 2 \, a c}{2 \, {\left(b x^{3} + a x\right)} a^{2}}"," ",0,"-1/2*(3*b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) - 1/2*(3*b*c*x^2 - a*d*x^2 + 2*a*c)/((b*x^3 + a*x)*a^2)","A",0
269,1,84,0,0.285182," ","integrate((d*x^2+c)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b c - a d\right)} \log\left(x^{2}\right)}{2 \, a^{3}} - \frac{2 \, b c x^{2} - a d x^{2} + a c}{2 \, {\left(b x^{4} + a x^{2}\right)} a^{2}} + \frac{{\left(2 \, b^{2} c - a b d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} b}"," ",0,"-1/2*(2*b*c - a*d)*log(x^2)/a^3 - 1/2*(2*b*c*x^2 - a*d*x^2 + a*c)/((b*x^4 + a*x^2)*a^2) + 1/2*(2*b^2*c - a*b*d)*log(abs(b*x^2 + a))/(a^3*b)","A",0
270,1,86,0,0.349315," ","integrate((d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}} + \frac{b^{2} c x - a b d x}{2 \, {\left(b x^{2} + a\right)} a^{3}} + \frac{6 \, b c x^{2} - 3 \, a d x^{2} - a c}{3 \, a^{3} x^{3}}"," ",0,"1/2*(5*b^2*c - 3*a*b*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/2*(b^2*c*x - a*b*d*x)/((b*x^2 + a)*a^3) + 1/3*(6*b*c*x^2 - 3*a*d*x^2 - a*c)/(a^3*x^3)","A",0
271,1,156,0,0.449381," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a b^{2} c^{2} - 10 \, a^{2} b c d + 7 \, a^{3} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} + \frac{a b^{2} c^{2} x - 2 \, a^{2} b c d x + a^{3} d^{2} x}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, b^{8} d^{2} x^{5} + 10 \, b^{8} c d x^{3} - 10 \, a b^{7} d^{2} x^{3} + 15 \, b^{8} c^{2} x - 60 \, a b^{7} c d x + 45 \, a^{2} b^{6} d^{2} x}{15 \, b^{10}}"," ",0,"-1/2*(3*a*b^2*c^2 - 10*a^2*b*c*d + 7*a^3*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/2*(a*b^2*c^2*x - 2*a^2*b*c*d*x + a^3*d^2*x)/((b*x^2 + a)*b^4) + 1/15*(3*b^8*d^2*x^5 + 10*b^8*c*d*x^3 - 10*a*b^7*d^2*x^3 + 15*b^8*c^2*x - 60*a*b^7*c*d*x + 45*a^2*b^6*d^2*x)/b^10","A",0
272,1,163,0,0.282682," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\frac{{\left(b x^{2} + a\right)}^{2} {\left(d^{2} + \frac{2 \, {\left(2 \, b^{2} c d - 3 \, a b d^{2}\right)}}{{\left(b x^{2} + a\right)} b}\right)}}{b^{3}} - \frac{2 \, {\left(b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} + \frac{2 \, {\left(\frac{a b^{4} c^{2}}{b x^{2} + a} - \frac{2 \, a^{2} b^{3} c d}{b x^{2} + a} + \frac{a^{3} b^{2} d^{2}}{b x^{2} + a}\right)}}{b^{5}}}{4 \, b}"," ",0,"1/4*((b*x^2 + a)^2*(d^2 + 2*(2*b^2*c*d - 3*a*b*d^2)/((b*x^2 + a)*b))/b^3 - 2*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^3 + 2*(a*b^4*c^2/(b*x^2 + a) - 2*a^2*b^3*c*d/(b*x^2 + a) + a^3*b^2*d^2/(b*x^2 + a))/b^5)/b","A",0
273,1,114,0,0.364560," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 6 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{3}} - \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{b^{4} d^{2} x^{3} + 6 \, b^{4} c d x - 6 \, a b^{3} d^{2} x}{3 \, b^{6}}"," ",0,"1/2*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^2 + a)*b^3) + 1/3*(b^4*d^2*x^3 + 6*b^4*c*d*x - 6*a*b^3*d^2*x)/b^6","A",0
274,1,111,0,0.340768," ","integrate(x*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b x^{2} + a\right)} d^{2}}{2 \, b^{3}} - \frac{{\left(b c d - a d^{2}\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} - \frac{\frac{b^{3} c^{2}}{b x^{2} + a} - \frac{2 \, a b^{2} c d}{b x^{2} + a} + \frac{a^{2} b d^{2}}{b x^{2} + a}}{2 \, b^{4}}"," ",0,"1/2*(b*x^2 + a)*d^2/b^3 - (b*c*d - a*d^2)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^3 - 1/2*(b^3*c^2/(b*x^2 + a) - 2*a*b^2*c*d/(b*x^2 + a) + a^2*b*d^2/(b*x^2 + a))/b^4","A",0
275,1,94,0,0.287742," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d^{2} x}{b^{2}} + \frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(b x^{2} + a\right)} a b^{2}}"," ",0,"d^2*x/b^2 + 1/2*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^2 + a)*a*b^2)","A",0
276,1,99,0,0.340281," ","integrate((d*x^2+c)^2/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c^{2} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{{\left(b^{2} c^{2} - a^{2} d^{2}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b^{2}} + \frac{b^{2} c^{2} x^{2} - a^{2} d^{2} x^{2} + 2 \, a b c^{2} - 2 \, a^{2} c d}{2 \, {\left(b x^{2} + a\right)} a^{2} b}"," ",0,"1/2*c^2*log(x^2)/a^2 - 1/2*(b^2*c^2 - a^2*d^2)*log(abs(b*x^2 + a))/(a^2*b^2) + 1/2*(b^2*c^2*x^2 - a^2*d^2*x^2 + 2*a*b*c^2 - 2*a^2*c*d)/((b*x^2 + a)*a^2*b)","A",0
277,1,103,0,0.325293," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2} b} - \frac{3 \, b^{2} c^{2} x^{2} - 2 \, a b c d x^{2} + a^{2} d^{2} x^{2} + 2 \, a b c^{2}}{2 \, {\left(b x^{3} + a x\right)} a^{2} b}"," ",0,"-1/2*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) - 1/2*(3*b^2*c^2*x^2 - 2*a*b*c*d*x^2 + a^2*d^2*x^2 + 2*a*b*c^2)/((b*x^3 + a*x)*a^2*b)","A",0
278,1,109,0,0.336783," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b c^{2} - a c d\right)} \log\left(x^{2}\right)}{a^{3}} + \frac{{\left(b^{2} c^{2} - a b c d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{a^{3} b} - \frac{2 \, b^{2} c^{2} x^{2} - 2 \, a b c d x^{2} + a^{2} d^{2} x^{2} + a b c^{2}}{2 \, {\left(b x^{4} + a x^{2}\right)} a^{2} b}"," ",0,"-(b*c^2 - a*c*d)*log(x^2)/a^3 + (b^2*c^2 - a*b*c*d)*log(abs(b*x^2 + a))/(a^3*b) - 1/2*(2*b^2*c^2*x^2 - 2*a*b*c*d*x^2 + a^2*d^2*x^2 + a*b*c^2)/((b*x^4 + a*x^2)*a^2*b)","A",0
279,1,112,0,0.410503," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(b x^{2} + a\right)} a^{3}} + \frac{6 \, b c^{2} x^{2} - 6 \, a c d x^{2} - a c^{2}}{3 \, a^{3} x^{3}}"," ",0,"1/2*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^2 + a)*a^3) + 1/3*(6*b*c^2*x^2 - 6*a*c*d*x^2 - a*c^2)/(a^3*x^3)","A",0
280,1,241,0,0.391235," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{3 \, {\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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{5}} + \frac{a b^{3} c^{3} x - 3 \, a^{2} b^{2} c^{2} d x + 3 \, a^{3} b c d^{2} x - a^{4} d^{3} x}{2 \, {\left(b x^{2} + a\right)} b^{5}} + \frac{5 \, b^{12} d^{3} x^{7} + 21 \, b^{12} c d^{2} x^{5} - 14 \, a b^{11} d^{3} x^{5} + 35 \, b^{12} c^{2} d x^{3} - 70 \, a b^{11} c d^{2} x^{3} + 35 \, a^{2} b^{10} d^{3} x^{3} + 35 \, b^{12} c^{3} x - 210 \, a b^{11} c^{2} d x + 315 \, a^{2} b^{10} c d^{2} x - 140 \, a^{3} b^{9} d^{3} x}{35 \, b^{14}}"," ",0,"-3/2*(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)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/2*(a*b^3*c^3*x - 3*a^2*b^2*c^2*d*x + 3*a^3*b*c*d^2*x - a^4*d^3*x)/((b*x^2 + a)*b^5) + 1/35*(5*b^12*d^3*x^7 + 21*b^12*c*d^2*x^5 - 14*a*b^11*d^3*x^5 + 35*b^12*c^2*d*x^3 - 70*a*b^11*c*d^2*x^3 + 35*a^2*b^10*d^3*x^3 + 35*b^12*c^3*x - 210*a*b^11*c^2*d*x + 315*a^2*b^10*c*d^2*x - 140*a^3*b^9*d^3*x)/b^14","A",0
281,1,249,0,0.372049," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\frac{{\left(2 \, d^{3} + \frac{3 \, {\left(3 \, b^{2} c d^{2} - 4 \, a b d^{3}\right)}}{{\left(b x^{2} + a\right)} b} + \frac{18 \, {\left(b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)}}{{\left(b x^{2} + a\right)}^{2} b^{2}}\right)} {\left(b x^{2} + a\right)}^{3}}{b^{4}} - \frac{6 \, {\left(b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3}\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{b^{4}} + \frac{6 \, {\left(\frac{a b^{6} c^{3}}{b x^{2} + a} - \frac{3 \, a^{2} b^{5} c^{2} d}{b x^{2} + a} + \frac{3 \, a^{3} b^{4} c d^{2}}{b x^{2} + a} - \frac{a^{4} b^{3} d^{3}}{b x^{2} + a}\right)}}{b^{7}}}{12 \, b}"," ",0,"1/12*((2*d^3 + 3*(3*b^2*c*d^2 - 4*a*b*d^3)/((b*x^2 + a)*b) + 18*(b^4*c^2*d - 3*a*b^3*c*d^2 + 2*a^2*b^2*d^3)/((b*x^2 + a)^2*b^2))*(b*x^2 + a)^3/b^4 - 6*(b^3*c^3 - 6*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 4*a^3*d^3)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^4 + 6*(a*b^6*c^3/(b*x^2 + a) - 3*a^2*b^5*c^2*d/(b*x^2 + a) + 3*a^3*b^4*c*d^2/(b*x^2 + a) - a^4*b^3*d^3/(b*x^2 + a))/b^7)/b","B",0
282,1,184,0,0.358059," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 7 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b^{4}} - \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, b^{8} d^{3} x^{5} + 15 \, b^{8} c d^{2} x^{3} - 10 \, a b^{7} d^{3} x^{3} + 45 \, b^{8} c^{2} d x - 90 \, a b^{7} c d^{2} x + 45 \, a^{2} b^{6} d^{3} x}{15 \, b^{10}}"," ",0,"1/2*(b^3*c^3 - 9*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 7*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) - 1/2*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^2 + a)*b^4) + 1/15*(3*b^8*d^3*x^5 + 15*b^8*c*d^2*x^3 - 10*a*b^7*d^3*x^3 + 45*b^8*c^2*d*x - 90*a*b^7*c*d^2*x + 45*a^2*b^6*d^3*x)/b^10","A",0
283,1,183,0,0.473546," ","integrate(x*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(d^{3} + \frac{6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)}}{{\left(b x^{2} + a\right)} b}\right)} {\left(b x^{2} + a\right)}^{2}}{4 \, b^{4}} - \frac{3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(\frac{{\left| b x^{2} + a \right|}}{{\left(b x^{2} + a\right)}^{2} {\left| b \right|}}\right)}{2 \, b^{4}} - \frac{\frac{b^{5} c^{3}}{b x^{2} + a} - \frac{3 \, a b^{4} c^{2} d}{b x^{2} + a} + \frac{3 \, a^{2} b^{3} c d^{2}}{b x^{2} + a} - \frac{a^{3} b^{2} d^{3}}{b x^{2} + a}}{2 \, b^{6}}"," ",0,"1/4*(d^3 + 6*(b^2*c*d^2 - a*b*d^3)/((b*x^2 + a)*b))*(b*x^2 + a)^2/b^4 - 3/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(abs(b*x^2 + a)/((b*x^2 + a)^2*abs(b)))/b^4 - 1/2*(b^5*c^3/(b*x^2 + a) - 3*a*b^4*c^2*d/(b*x^2 + a) + 3*a^2*b^3*c*d^2/(b*x^2 + a) - a^3*b^2*d^3/(b*x^2 + a))/b^6","B",0
284,1,152,0,0.357876," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{3}} + \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{2 \, {\left(b x^{2} + a\right)} a b^{3}} + \frac{b^{4} d^{3} x^{3} + 9 \, b^{4} c d^{2} x - 6 \, a b^{3} d^{3} x}{3 \, b^{6}}"," ",0,"1/2*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3) + 1/2*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^2 + a)*a*b^3) + 1/3*(b^4*d^3*x^3 + 9*b^4*c*d^2*x - 6*a*b^3*d^3*x)/b^6","A",0
285,1,150,0,0.413956," ","integrate((d*x^2+c)^3/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d^{3} x^{2}}{2 \, b^{2}} + \frac{c^{3} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{{\left(b^{3} c^{3} - 3 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{2} b^{3}} + \frac{b^{4} c^{3} x^{2} - 3 \, a^{2} b^{2} c d^{2} x^{2} + 2 \, a^{3} b d^{3} x^{2} + 2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + a^{4} d^{3}}{2 \, {\left(b x^{2} + a\right)} a^{2} b^{3}}"," ",0,"1/2*d^3*x^2/b^2 + 1/2*c^3*log(x^2)/a^2 - 1/2*(b^3*c^3 - 3*a^2*b*c*d^2 + 2*a^3*d^3)*log(abs(b*x^2 + a))/(a^2*b^3) + 1/2*(b^4*c^3*x^2 - 3*a^2*b^2*c*d^2*x^2 + 2*a^3*b*d^3*x^2 + 2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + a^4*d^3)/((b*x^2 + a)*a^2*b^3)","A",0
286,1,143,0,0.343605," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d^{3} x}{b^{2}} - \frac{3 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2} b^{2}} - \frac{3 \, b^{3} c^{3} x^{2} - 3 \, a b^{2} c^{2} d x^{2} + 3 \, a^{2} b c d^{2} x^{2} - a^{3} d^{3} x^{2} + 2 \, a b^{2} c^{3}}{2 \, {\left(b x^{3} + a x\right)} a^{2} b^{2}}"," ",0,"d^3*x/b^2 - 3/2*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2) - 1/2*(3*b^3*c^3*x^2 - 3*a*b^2*c^2*d*x^2 + 3*a^2*b*c*d^2*x^2 - a^3*d^3*x^2 + 2*a*b^2*c^3)/((b*x^3 + a*x)*a^2*b^2)","A",0
287,1,157,0,0.292964," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b c^{3} - 3 \, a c^{2} d\right)} \log\left(x^{2}\right)}{2 \, a^{3}} + \frac{{\left(2 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + a^{3} d^{3}\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, a^{3} b^{2}} - \frac{a^{2} b d^{3} x^{4} + 4 \, b^{3} c^{3} x^{2} - 6 \, a b^{2} c^{2} d x^{2} + 6 \, a^{2} b c d^{2} x^{2} - a^{3} d^{3} x^{2} + 2 \, a b^{2} c^{3}}{4 \, {\left(b x^{4} + a x^{2}\right)} a^{2} b^{2}}"," ",0,"-1/2*(2*b*c^3 - 3*a*c^2*d)*log(x^2)/a^3 + 1/2*(2*b^3*c^3 - 3*a*b^2*c^2*d + a^3*d^3)*log(abs(b*x^2 + a))/(a^3*b^2) - 1/4*(a^2*b*d^3*x^4 + 4*b^3*c^3*x^2 - 6*a*b^2*c^2*d*x^2 + 6*a^2*b*c*d^2*x^2 - a^3*d^3*x^2 + 2*a*b^2*c^3)/((b*x^4 + a*x^2)*a^2*b^2)","A",0
288,1,150,0,0.298573," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{3} b} + \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{2 \, {\left(b x^{2} + a\right)} a^{3} b} + \frac{6 \, b c^{3} x^{2} - 9 \, a c^{2} d x^{2} - a c^{3}}{3 \, a^{3} x^{3}}"," ",0,"1/2*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3*b) + 1/2*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^2 + a)*a^3*b) + 1/3*(6*b*c^3*x^2 - 9*a*c^2*d*x^2 - a*c^3)/(a^3*x^3)","A",0
289,1,122,0,0.300199," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{c^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} - \frac{{\left(3 \, a b c - a^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} \sqrt{a b}} + \frac{a x}{2 \, {\left(b^{2} c - a b d\right)} {\left(b x^{2} + a\right)}}"," ",0,"c^2*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) - 1/2*(3*a*b*c - a^2*d)*arctan(b*x/sqrt(a*b))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*sqrt(a*b)) + 1/2*a*x/((b^2*c - a*b*d)*(b*x^2 + a))","A",0
290,1,92,0,0.378949," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{\frac{b^{2} c \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{a b}{{\left(b^{2} c - a b d\right)} {\left(b x^{2} + a\right)}}}{2 \, b}"," ",0,"-1/2*(b^2*c*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - a*b/((b^2*c - a*b*d)*(b*x^2 + a)))/b","A",0
291,1,110,0,0.426304," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{c d \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} + \frac{{\left(b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} - \frac{x}{2 \, {\left(b x^{2} + a\right)} {\left(b c - a d\right)}}"," ",0,"-c*d*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) + 1/2*(b*c + a*d)*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) - 1/2*x/((b*x^2 + a)*(b*c - a*d))","A",0
292,1,85,0,0.312694," ","integrate(x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{b d \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{2 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)}} - \frac{b}{2 \, {\left(b^{2} c - a b d\right)} {\left(b x^{2} + a\right)}}"," ",0,"1/2*b*d*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 1/2*b/((b^2*c - a*b*d)*(b*x^2 + a))","A",0
293,1,121,0,0.378778," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{d^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} + \frac{{\left(b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b}} + \frac{b x}{2 \, {\left(a b c - a^{2} d\right)} {\left(b x^{2} + a\right)}}"," ",0,"d^2*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) + 1/2*(b^2*c - 3*a*b*d)*arctan(b*x/sqrt(a*b))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b)) + 1/2*b*x/((a*b*c - a^2*d)*(b*x^2 + a))","A",0
294,1,183,0,0.301512," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{d^{3} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)}} - \frac{{\left(b^{3} c - 2 \, a b^{2} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)}} + \frac{b^{3} c x^{2} - 2 \, a b^{2} d x^{2} + 2 \, a b^{2} c - 3 \, a^{2} b d}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} {\left(b x^{2} + a\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c}"," ",0,"-1/2*d^3*log(abs(d*x^2 + c))/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3) - 1/2*(b^3*c - 2*a*b^2*d)*log(abs(b*x^2 + a))/(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2) + 1/2*(b^3*c*x^2 - 2*a*b^2*d*x^2 + 2*a*b^2*c - 3*a^2*b*d)/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*(b*x^2 + a)) + 1/2*log(x^2)/(a^2*c)","A",0
295,1,164,0,0.368382," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{d^{3} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{c d}} - \frac{{\left(3 \, b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{a b}} - \frac{3 \, b^{2} c x^{2} - 2 \, a b d x^{2} + 2 \, a b c - 2 \, a^{2} d}{2 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} {\left(b x^{3} + a x\right)}}"," ",0,"-d^3*arctan(d*x/sqrt(c*d))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(c*d)) - 1/2*(3*b^3*c - 5*a*b^2*d)*arctan(b*x/sqrt(a*b))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(a*b)) - 1/2*(3*b^2*c*x^2 - 2*a*b*d*x^2 + 2*a*b*c - 2*a^2*d)/((a^2*b*c^2 - a^3*c*d)*(b*x^3 + a*x))","A",0
296,1,257,0,0.346749," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)}} + \frac{{\left(2 \, b^{4} c - 3 \, a b^{3} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)}} + \frac{a^{2} b d^{3} x^{4} - 4 \, b^{3} c^{3} x^{2} + 6 \, a b^{2} c^{2} d x^{2} - 2 \, a^{2} b c d^{2} x^{2} + a^{3} d^{3} x^{2} - 2 \, a b^{2} c^{3} + 4 \, a^{2} b c^{2} d - 2 \, a^{3} c d^{2}}{4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b x^{4} + a x^{2}\right)}} - \frac{{\left(2 \, b c + a d\right)} \log\left(x^{2}\right)}{2 \, a^{3} c^{2}}"," ",0,"1/2*d^4*log(abs(d*x^2 + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3) + 1/2*(2*b^4*c - 3*a*b^3*d)*log(abs(b*x^2 + a))/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2) + 1/4*(a^2*b*d^3*x^4 - 4*b^3*c^3*x^2 + 6*a*b^2*c^2*d*x^2 - 2*a^2*b*c*d^2*x^2 + a^3*d^3*x^2 - 2*a*b^2*c^3 + 4*a^2*b*c^2*d - 2*a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*x^4 + a*x^2)) - 1/2*(2*b*c + a*d)*log(x^2)/(a^3*c^2)","B",0
297,1,165,0,0.378378," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{d^{4} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{c d}} + \frac{b^{3} x}{2 \, {\left(a^{3} b c - a^{4} d\right)} {\left(b x^{2} + a\right)}} + \frac{{\left(5 \, b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} \sqrt{a b}} + \frac{6 \, b c x^{2} + 3 \, a d x^{2} - a c}{3 \, a^{3} c^{2} x^{3}}"," ",0,"d^4*arctan(d*x/sqrt(c*d))/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(c*d)) + 1/2*b^3*x/((a^3*b*c - a^4*d)*(b*x^2 + a)) + 1/2*(5*b^4*c - 7*a*b^3*d)*arctan(b*x/sqrt(a*b))/((a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*sqrt(a*b)) + 1/3*(6*b*c*x^2 + 3*a*d*x^2 - a*c)/(a^3*c^2*x^3)","A",0
298,1,281,0,0.387646," ","integrate(1/x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{d^{5} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)}} - \frac{{\left(3 \, b^{5} c - 4 \, a b^{4} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{4} b^{3} c^{2} - 2 \, a^{5} b^{2} c d + a^{6} b d^{2}\right)}} + \frac{3 \, b^{5} c x^{2} - 4 \, a b^{4} d x^{2} + 4 \, a b^{4} c - 5 \, a^{2} b^{3} d}{2 \, {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2}\right)} {\left(b x^{2} + a\right)}} + \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{4} c^{3}} - \frac{9 \, b^{2} c^{2} x^{4} + 6 \, a b c d x^{4} + 3 \, a^{2} d^{2} x^{4} - 4 \, a b c^{2} x^{2} - 2 \, a^{2} c d x^{2} + a^{2} c^{2}}{4 \, a^{4} c^{3} x^{4}}"," ",0,"-1/2*d^5*log(abs(d*x^2 + c))/(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3) - 1/2*(3*b^5*c - 4*a*b^4*d)*log(abs(b*x^2 + a))/(a^4*b^3*c^2 - 2*a^5*b^2*c*d + a^6*b*d^2) + 1/2*(3*b^5*c*x^2 - 4*a*b^4*d*x^2 + 4*a*b^4*c - 5*a^2*b^3*d)/((a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2)*(b*x^2 + a)) + 1/2*(3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*log(x^2)/(a^4*c^3) - 1/4*(9*b^2*c^2*x^4 + 6*a*b*c*d*x^4 + 3*a^2*d^2*x^4 - 4*a*b*c^2*x^2 - 2*a^2*c*d*x^2 + a^2*c^2)/(a^4*c^3*x^4)","A",0
299,1,207,0,0.393078," ","integrate(1/x^6/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{d^{5} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} \sqrt{c d}} - \frac{b^{4} x}{2 \, {\left(a^{4} b c - a^{5} d\right)} {\left(b x^{2} + a\right)}} - \frac{{\left(7 \, b^{5} c - 9 \, a b^{4} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2}\right)} \sqrt{a b}} - \frac{45 \, b^{2} c^{2} x^{4} + 30 \, a b c d x^{4} + 15 \, a^{2} d^{2} x^{4} - 10 \, a b c^{2} x^{2} - 5 \, a^{2} c d x^{2} + 3 \, a^{2} c^{2}}{15 \, a^{4} c^{3} x^{5}}"," ",0,"-d^5*arctan(d*x/sqrt(c*d))/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*sqrt(c*d)) - 1/2*b^4*x/((a^4*b*c - a^5*d)*(b*x^2 + a)) - 1/2*(7*b^5*c - 9*a*b^4*d)*arctan(b*x/sqrt(a*b))/((a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2)*sqrt(a*b)) - 1/15*(45*b^2*c^2*x^4 + 30*a*b*c*d*x^4 + 15*a^2*d^2*x^4 - 10*a*b*c^2*x^2 - 5*a^2*c*d*x^2 + 3*a^2*c^2)/(a^4*c^3*x^5)","A",0
300,1,354,0,0.396278," ","integrate(1/x^7/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{d^{6} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{2} c^{6} d - 2 \, a b c^{5} d^{2} + a^{2} c^{4} d^{3}\right)}} + \frac{{\left(4 \, b^{6} c - 5 \, a b^{5} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{5} b^{3} c^{2} - 2 \, a^{6} b^{2} c d + a^{7} b d^{2}\right)}} - \frac{4 \, b^{6} c x^{2} - 5 \, a b^{5} d x^{2} + 5 \, a b^{5} c - 6 \, a^{2} b^{4} d}{2 \, {\left(a^{5} b^{2} c^{2} - 2 \, a^{6} b c d + a^{7} d^{2}\right)} {\left(b x^{2} + a\right)}} - \frac{{\left(4 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{5} c^{4}} + \frac{44 \, b^{3} c^{3} x^{6} + 33 \, a b^{2} c^{2} d x^{6} + 22 \, a^{2} b c d^{2} x^{6} + 11 \, a^{3} d^{3} x^{6} - 18 \, a b^{2} c^{3} x^{4} - 12 \, a^{2} b c^{2} d x^{4} - 6 \, a^{3} c d^{2} x^{4} + 6 \, a^{2} b c^{3} x^{2} + 3 \, a^{3} c^{2} d x^{2} - 2 \, a^{3} c^{3}}{12 \, a^{5} c^{4} x^{6}}"," ",0,"1/2*d^6*log(abs(d*x^2 + c))/(b^2*c^6*d - 2*a*b*c^5*d^2 + a^2*c^4*d^3) + 1/2*(4*b^6*c - 5*a*b^5*d)*log(abs(b*x^2 + a))/(a^5*b^3*c^2 - 2*a^6*b^2*c*d + a^7*b*d^2) - 1/2*(4*b^6*c*x^2 - 5*a*b^5*d*x^2 + 5*a*b^5*c - 6*a^2*b^4*d)/((a^5*b^2*c^2 - 2*a^6*b*c*d + a^7*d^2)*(b*x^2 + a)) - 1/2*(4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2 + a^3*d^3)*log(x^2)/(a^5*c^4) + 1/12*(44*b^3*c^3*x^6 + 33*a*b^2*c^2*d*x^6 + 22*a^2*b*c*d^2*x^6 + 11*a^3*d^3*x^6 - 18*a*b^2*c^3*x^4 - 12*a^2*b*c^2*d*x^4 - 6*a^3*c*d^2*x^4 + 6*a^2*b*c^3*x^2 + 3*a^3*c^2*d*x^2 - 2*a^3*c^3)/(a^5*c^4*x^6)","A",0
301,1,198,0,0.337833," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, a b c + a^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{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)} \sqrt{a b}} + \frac{{\left(b c^{2} + 3 \, a c d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{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)} \sqrt{c d}} + \frac{b c x^{3} + a d x^{3} + 2 \, a c x}{2 \, {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"-1/2*(3*a*b*c + a^2*d)*arctan(b*x/sqrt(a*b))/((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)) + 1/2*(b*c^2 + 3*a*c*d)*arctan(d*x/sqrt(c*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d)) + 1/2*(b*c*x^3 + a*d*x^3 + 2*a*c*x)/((b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","A",0
302,1,178,0,0.394012," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\frac{a b^{3}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} {\left(b x^{2} + a\right)}} - \frac{{\left(b^{3} c + a b^{2} d\right)} \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{b^{2} c d}{{\left(b c - a d\right)}^{3} {\left(\frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d\right)}}}{2 \, b}"," ",0,"1/2*(a*b^3/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*(b*x^2 + a)) - (b^3*c + a*b^2*d)*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - b^2*c*d/((b*c - a*d)^3*(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d)))/b","A",0
303,1,196,0,0.360405," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{2} c + 3 \, a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{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)} \sqrt{a b}} - \frac{{\left(3 \, b c d + a d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{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)} \sqrt{c d}} - \frac{2 \, b d x^{3} + b c x + a d x}{2 \, {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"1/2*(b^2*c + 3*a*b*d)*arctan(b*x/sqrt(a*b))/((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)) - 1/2*(3*b*c*d + a*d^2)*arctan(d*x/sqrt(c*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d)) - 1/2*(2*b*d*x^3 + b*c*x + a*d*x)/((b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","A",0
304,1,163,0,0.368432," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} d \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{b^{3}}{2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} {\left(b x^{2} + a\right)}} + \frac{b d^{2}}{2 \, {\left(b c - a d\right)}^{3} {\left(\frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d\right)}}"," ",0,"b^2*d*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - 1/2*b^3/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*(b*x^2 + a)) + 1/2*b*d^2/((b*c - a*d)^3*(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))","A",0
305,1,232,0,0.445386," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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{a b}} + \frac{{\left(5 \, b c d^{2} - a d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\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)} \sqrt{c d}} + \frac{b^{2} c d x^{3} + a b d^{2} x^{3} + b^{2} c^{2} x + a^{2} d^{2} x}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}}"," ",0,"1/2*(b^3*c - 5*a*b^2*d)*arctan(b*x/sqrt(a*b))/((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)) + 1/2*(5*b*c*d^2 - a*d^3)*arctan(d*x/sqrt(c*d))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*sqrt(c*d)) + 1/2*(b^2*c*d*x^3 + a*b*d^2*x^3 + b^2*c^2*x + a^2*d^2*x)/((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c))","A",0
306,1,321,0,0.391238," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(b^{4} c - 3 \, a b^{3} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} - \frac{{\left(3 \, b c d^{3} - a d^{4}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\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)}} + \frac{b^{3} c^{2} d x^{4} - 2 \, a b^{2} c d^{2} x^{4} + a^{2} b d^{3} x^{4} + b^{3} c^{3} x^{2} + a b^{2} c^{2} d x^{2} + a^{2} b c d^{2} x^{2} + a^{3} d^{3} x^{2} + 3 \, a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}}{4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c^{2}}"," ",0,"-1/2*(b^4*c - 3*a*b^3*d)*log(abs(b*x^2 + a))/(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) - 1/2*(3*b*c*d^3 - a*d^4)*log(abs(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) + 1/4*(b^3*c^2*d*x^4 - 2*a*b^2*c*d^2*x^4 + a^2*b*d^3*x^4 + b^3*c^3*x^2 + a*b^2*c^2*d*x^2 + a^2*b*c*d^2*x^2 + a^3*d^3*x^2 + 3*a*b^2*c^3 - 2*a^2*b*c^2*d + 3*a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)) + 1/2*log(x^2)/(a^2*c^2)","B",0
307,1,321,0,0.414663," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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{a b}} - \frac{{\left(7 \, b c d^{3} - 3 \, a d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\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{c d}} - \frac{3 \, b^{3} c^{2} d x^{4} - 4 \, a b^{2} c d^{2} x^{4} + 3 \, a^{2} b d^{3} x^{4} + 3 \, b^{3} c^{3} x^{2} - 2 \, a b^{2} c^{2} d x^{2} - 2 \, a^{2} b c d^{2} x^{2} + 3 \, a^{3} d^{3} x^{2} + 2 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d + 2 \, a^{3} c d^{2}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b d x^{5} + b c x^{3} + a d x^{3} + a c x\right)}}"," ",0,"-1/2*(3*b^4*c - 7*a*b^3*d)*arctan(b*x/sqrt(a*b))/((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(a*b)) - 1/2*(7*b*c*d^3 - 3*a*d^4)*arctan(d*x/sqrt(c*d))/((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(c*d)) - 1/2*(3*b^3*c^2*d*x^4 - 4*a*b^2*c*d^2*x^4 + 3*a^2*b*d^3*x^4 + 3*b^3*c^3*x^2 - 2*a*b^2*c^2*d*x^2 - 2*a^2*b*c*d^2*x^2 + 3*a^3*d^3*x^2 + 2*a*b^2*c^3 - 4*a^2*b*c^2*d + 2*a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*d*x^5 + b*c*x^3 + a*d*x^3 + a*c*x))","A",0
308,1,333,0,0.390298," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{5} c - 2 \, a b^{4} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3}} + \frac{{\left(2 \, b c d^{4} - a d^{5}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{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}} - \frac{2 \, b^{3} c^{2} d x^{4} - 2 \, a b^{2} c d^{2} x^{4} + 2 \, a^{2} b d^{3} x^{4} + 2 \, b^{3} c^{3} x^{2} - a b^{2} c^{2} d x^{2} - a^{2} b c d^{2} x^{2} + 2 \, a^{3} d^{3} x^{2} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b d x^{6} + b c x^{4} + a d x^{4} + a c x^{2}\right)}} - \frac{{\left(b c + a d\right)} \log\left(x^{2}\right)}{a^{3} c^{3}}"," ",0,"(b^5*c - 2*a*b^4*d)*log(abs(b*x^2 + a))/(a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3) + (2*b*c*d^4 - a*d^5)*log(abs(d*x^2 + c))/(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) - 1/2*(2*b^3*c^2*d*x^4 - 2*a*b^2*c*d^2*x^4 + 2*a^2*b*d^3*x^4 + 2*b^3*c^3*x^2 - a*b^2*c^2*d*x^2 - a^2*b*c*d^2*x^2 + 2*a^3*d^3*x^2 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*d*x^6 + b*c*x^4 + a*d*x^4 + a*c*x^2)) - (b*c + a*d)*log(x^2)/(a^3*c^3)","B",0
309,1,275,0,0.351662," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{5} c - 9 \, a b^{4} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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}\right)} \sqrt{a b}} + \frac{{\left(9 \, b c d^{4} - 5 \, a d^{5}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} \sqrt{c d}} + \frac{b^{4} c^{3} d x^{3} + a^{3} b d^{4} x^{3} + b^{4} c^{4} x + a^{4} d^{4} x}{2 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}} + \frac{6 \, b c x^{2} + 6 \, a d x^{2} - a c}{3 \, a^{3} c^{3} x^{3}}"," ",0,"1/2*(5*b^5*c - 9*a*b^4*d)*arctan(b*x/sqrt(a*b))/((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)*sqrt(a*b)) + 1/2*(9*b*c*d^4 - 5*a*d^5)*arctan(d*x/sqrt(c*d))/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*sqrt(c*d)) + 1/2*(b^4*c^3*d*x^3 + a^3*b*d^4*x^3 + b^4*c^4*x + a^4*d^4*x)/((a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)) + 1/3*(6*b*c*x^2 + 6*a*d*x^2 - a*c)/(a^3*c^3*x^3)","A",0
310,1,301,0,0.407382," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{a b x}{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)} {\left(b x^{2} + a\right)}} - \frac{3 \, {\left(a b^{2} c + a^{2} b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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{a b}} + \frac{3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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{c d}} + \frac{3 \, b c d x^{3} + 5 \, a d^{2} x^{3} + 5 \, b c^{2} x + 3 \, a c d x}{8 \, {\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(d x^{2} + c\right)}^{2}}"," ",0,"1/2*a*b*x/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) - 3/2*(a*b^2*c + a^2*b*d)*arctan(b*x/sqrt(a*b))/((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)) + 3/8*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*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)*sqrt(c*d)) + 1/8*(3*b*c*d*x^3 + 5*a*d^2*x^3 + 5*b*c^2*x + 3*a*c*d*x)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(d*x^2 + c)^2)","A",0
311,1,267,0,0.485458," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{\frac{2 \, a b^{5}}{{\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)} {\left(b x^{2} + a\right)}} - \frac{2 \, {\left(b^{4} c + 2 \, a b^{3} d\right)} \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{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}} - \frac{3 \, b^{3} c d^{2} + 2 \, a b^{2} d^{3} + \frac{2 \, {\left(2 \, b^{5} c^{2} d - a b^{4} c d^{2} - a^{2} b^{3} d^{3}\right)}}{{\left(b x^{2} + a\right)} b}}{{\left(b c - a d\right)}^{4} {\left(\frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d\right)}^{2}}}{4 \, b}"," ",0,"1/4*(2*a*b^5/((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)*(b*x^2 + a)) - 2*(b^4*c + 2*a*b^3*d)*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(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*b^3*c*d^2 + 2*a*b^2*d^3 + 2*(2*b^5*c^2*d - a*b^4*c*d^2 - a^2*b^3*d^3)/((b*x^2 + a)*b))/((b*c - a*d)^4*(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d)^2))/b","B",0
312,1,317,0,0.359958," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{2} x}{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)} {\left(b x^{2} + a\right)}} + \frac{{\left(b^{3} c + 5 \, a b^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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{a b}} - \frac{{\left(15 \, b^{2} c^{2} d + 10 \, a b c d^{2} - a^{2} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(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)} \sqrt{c d}} - \frac{7 \, b c d^{2} x^{3} + a d^{3} x^{3} + 9 \, b c^{2} d x - a c d^{2} x}{8 \, {\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(d x^{2} + c\right)}^{2}}"," ",0,"-1/2*b^2*x/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) + 1/2*(b^3*c + 5*a*b^2*d)*arctan(b*x/sqrt(a*b))/((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)) - 1/8*(15*b^2*c^2*d + 10*a*b*c*d^2 - a^2*d^3)*arctan(d*x/sqrt(c*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)*sqrt(c*d)) - 1/8*(7*b*c*d^2*x^3 + a*d^3*x^3 + 9*b*c^2*d*x - a*c*d^2*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)*(d*x^2 + c)^2)","A",0
313,1,229,0,0.432686," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{3 \, b^{3} d \log\left({\left| \frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d \right|}\right)}{2 \, {\left(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{b^{5}}{2 \, {\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)} {\left(b x^{2} + a\right)}} + \frac{5 \, b^{2} d^{3} + \frac{6 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}{{\left(b x^{2} + a\right)} b}}{4 \, {\left(b c - a d\right)}^{4} {\left(\frac{b c}{b x^{2} + a} - \frac{a d}{b x^{2} + a} + d\right)}^{2}}"," ",0,"3/2*b^3*d*log(abs(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d))/(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) - 1/2*b^5/((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)*(b*x^2 + a)) + 1/4*(5*b^2*d^3 + 6*(b^4*c*d^2 - a*b^3*d^3)/((b*x^2 + a)*b))/((b*c - a*d)^4*(b*c/(b*x^2 + a) - a*d/(b*x^2 + a) + d)^2)","A",0
314,1,332,0,0.444781," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} x}{2 \, {\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(b x^{2} + a\right)}} + \frac{{\left(b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(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)} \sqrt{a b}} + \frac{{\left(35 \, b^{2} c^{2} d^{2} - 14 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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{c d}} + \frac{11 \, b c d^{3} x^{3} - 3 \, a d^{4} x^{3} + 13 \, b c^{2} d^{2} x - 5 \, a c d^{3} x}{8 \, {\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)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"1/2*b^3*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*x^2 + a)) + 1/2*(b^4*c - 7*a*b^3*d)*arctan(b*x/sqrt(a*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)*sqrt(a*b)) + 1/8*(35*b^2*c^2*d^2 - 14*a*b*c*d^3 + 3*a^2*d^4)*arctan(d*x/sqrt(c*d))/((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(c*d)) + 1/8*(11*b*c*d^3*x^3 - 3*a*d^4*x^3 + 13*b*c^2*d^2*x - 5*a*c*d^3*x)/((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)*(d*x^2 + c)^2)","A",0
315,1,470,0,0.360507," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(b^{5} c - 4 \, a b^{4} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)}} - \frac{{\left(6 \, b^{2} c^{2} d^{3} - 4 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{4} c^{7} d - 4 \, a b^{3} c^{6} d^{2} + 6 \, a^{2} b^{2} c^{5} d^{3} - 4 \, a^{3} b c^{4} d^{4} + a^{4} c^{3} d^{5}\right)}} + \frac{b^{5} c x^{2} - 4 \, a b^{4} d x^{2} + 2 \, a b^{4} c - 5 \, a^{2} b^{3} d}{2 \, {\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)} {\left(b x^{2} + a\right)}} + \frac{18 \, b^{2} c^{2} d^{4} x^{4} - 12 \, a b c d^{5} x^{4} + 3 \, a^{2} d^{6} x^{4} + 42 \, b^{2} c^{3} d^{3} x^{2} - 32 \, a b c^{2} d^{4} x^{2} + 8 \, a^{2} c d^{5} x^{2} + 25 \, b^{2} c^{4} d^{2} - 22 \, a b c^{3} d^{3} + 6 \, a^{2} c^{2} d^{4}}{4 \, {\left(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)} {\left(d x^{2} + c\right)}^{2}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c^{3}}"," ",0,"-1/2*(b^5*c - 4*a*b^4*d)*log(abs(b*x^2 + a))/(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4) - 1/2*(6*b^2*c^2*d^3 - 4*a*b*c*d^4 + a^2*d^5)*log(abs(d*x^2 + c))/(b^4*c^7*d - 4*a*b^3*c^6*d^2 + 6*a^2*b^2*c^5*d^3 - 4*a^3*b*c^4*d^4 + a^4*c^3*d^5) + 1/2*(b^5*c*x^2 - 4*a*b^4*d*x^2 + 2*a*b^4*c - 5*a^2*b^3*d)/((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)*(b*x^2 + a)) + 1/4*(18*b^2*c^2*d^4*x^4 - 12*a*b*c*d^5*x^4 + 3*a^2*d^6*x^4 + 42*b^2*c^3*d^3*x^2 - 32*a*b*c^2*d^4*x^2 + 8*a^2*c*d^5*x^2 + 25*b^2*c^4*d^2 - 22*a*b*c^3*d^3 + 6*a^2*c^2*d^4)/((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*x^2 + c)^2) + 1/2*log(x^2)/(a^2*c^3)","B",0
316,1,430,0,0.502665," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(b^{5} c - 3 \, a b^{4} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\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{a b}} - \frac{3 \, {\left(21 \, b^{2} c^{2} d^{3} - 18 \, a b c d^{4} + 5 \, a^{2} d^{5}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(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)} \sqrt{c d}} - \frac{3 \, b^{4} c^{3} x^{2} - 6 \, a b^{3} c^{2} d x^{2} + 6 \, a^{2} b^{2} c d^{2} x^{2} - 2 \, a^{3} b d^{3} x^{2} + 2 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - 2 \, a^{4} d^{3}}{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}\right)} {\left(b x^{3} + a x\right)}} - \frac{15 \, b c d^{4} x^{3} - 7 \, a d^{5} x^{3} + 17 \, b c^{2} d^{3} x - 9 \, a c d^{4} x}{8 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"-3/2*(b^5*c - 3*a*b^4*d)*arctan(b*x/sqrt(a*b))/((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(a*b)) - 3/8*(21*b^2*c^2*d^3 - 18*a*b*c*d^4 + 5*a^2*d^5)*arctan(d*x/sqrt(c*d))/((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)*sqrt(c*d)) - 1/2*(3*b^4*c^3*x^2 - 6*a*b^3*c^2*d*x^2 + 6*a^2*b^2*c*d^2*x^2 - 2*a^3*b*d^3*x^2 + 2*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - 2*a^4*d^3)/((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)*(b*x^3 + a*x)) - 1/8*(15*b*c*d^4*x^3 - 7*a*d^5*x^3 + 17*b*c^2*d^3*x - 9*a*c*d^4*x)/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*(d*x^2 + c)^2)","A",0
317,1,638,0,0.451965," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(2 \, b^{6} c - 5 \, a b^{5} d\right)} \log\left({\left| b x^{2} + a \right|}\right)}{2 \, {\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)}} + \frac{{\left(10 \, b^{2} c^{2} d^{4} - 10 \, a b c d^{5} + 3 \, a^{2} d^{6}\right)} \log\left({\left| d x^{2} + c \right|}\right)}{2 \, {\left(b^{4} c^{8} d - 4 \, a b^{3} c^{7} d^{2} + 6 \, a^{2} b^{2} c^{6} d^{3} - 4 \, a^{3} b c^{5} d^{4} + a^{4} c^{4} d^{5}\right)}} + \frac{10 \, a^{2} b^{3} c^{2} d^{3} x^{4} - 10 \, a^{3} b^{2} c d^{4} x^{4} + 3 \, a^{4} b d^{5} x^{4} - 4 \, b^{5} c^{5} x^{2} + 10 \, a b^{4} c^{4} d x^{2} - 12 \, a^{2} b^{3} c^{3} d^{2} x^{2} + 18 \, a^{3} b^{2} c^{2} d^{3} x^{2} - 12 \, a^{4} b c d^{4} x^{2} + 3 \, a^{5} d^{5} x^{2} - 2 \, a b^{4} c^{5} + 8 \, a^{2} b^{3} c^{4} d - 12 \, a^{3} b^{2} c^{3} d^{2} + 8 \, a^{4} b c^{2} d^{3} - 2 \, a^{5} c d^{4}}{4 \, {\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}\right)} {\left(b x^{4} + a x^{2}\right)}} - \frac{30 \, b^{2} c^{2} d^{5} x^{4} - 30 \, a b c d^{6} x^{4} + 9 \, a^{2} d^{7} x^{4} + 68 \, b^{2} c^{3} d^{4} x^{2} - 72 \, a b c^{2} d^{5} x^{2} + 22 \, a^{2} c d^{6} x^{2} + 39 \, b^{2} c^{4} d^{3} - 44 \, a b c^{3} d^{4} + 14 \, a^{2} c^{2} d^{5}}{4 \, {\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)} {\left(d x^{2} + c\right)}^{2}} - \frac{{\left(2 \, b c + 3 \, a d\right)} \log\left(x^{2}\right)}{2 \, a^{3} c^{4}}"," ",0,"1/2*(2*b^6*c - 5*a*b^5*d)*log(abs(b*x^2 + a))/(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) + 1/2*(10*b^2*c^2*d^4 - 10*a*b*c*d^5 + 3*a^2*d^6)*log(abs(d*x^2 + c))/(b^4*c^8*d - 4*a*b^3*c^7*d^2 + 6*a^2*b^2*c^6*d^3 - 4*a^3*b*c^5*d^4 + a^4*c^4*d^5) + 1/4*(10*a^2*b^3*c^2*d^3*x^4 - 10*a^3*b^2*c*d^4*x^4 + 3*a^4*b*d^5*x^4 - 4*b^5*c^5*x^2 + 10*a*b^4*c^4*d*x^2 - 12*a^2*b^3*c^3*d^2*x^2 + 18*a^3*b^2*c^2*d^3*x^2 - 12*a^4*b*c*d^4*x^2 + 3*a^5*d^5*x^2 - 2*a*b^4*c^5 + 8*a^2*b^3*c^4*d - 12*a^3*b^2*c^3*d^2 + 8*a^4*b*c^2*d^3 - 2*a^5*c*d^4)/((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)*(b*x^4 + a*x^2)) - 1/4*(30*b^2*c^2*d^5*x^4 - 30*a*b*c*d^6*x^4 + 9*a^2*d^7*x^4 + 68*b^2*c^3*d^4*x^2 - 72*a*b*c^2*d^5*x^2 + 22*a^2*c*d^6*x^2 + 39*b^2*c^4*d^3 - 44*a*b*c^3*d^4 + 14*a^2*c^2*d^5)/((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)*(d*x^2 + c)^2) - 1/2*(2*b*c + 3*a*d)*log(x^2)/(a^3*c^4)","B",0
318,1,367,0,0.410580," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{5} x}{2 \, {\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}\right)} {\left(b x^{2} + a\right)}} + \frac{{\left(5 \, b^{6} c - 11 \, a b^{5} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(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)} \sqrt{a b}} + \frac{{\left(99 \, b^{2} c^{2} d^{4} - 110 \, a b c d^{5} + 35 \, a^{2} d^{6}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\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{c d}} + \frac{19 \, b c d^{5} x^{3} - 11 \, a d^{6} x^{3} + 21 \, b c^{2} d^{4} x - 13 \, a c d^{5} 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}\right)} {\left(d x^{2} + c\right)}^{2}} + \frac{6 \, b c x^{2} + 9 \, a d x^{2} - a c}{3 \, a^{3} c^{4} x^{3}}"," ",0,"1/2*b^5*x/((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*x^2 + a)) + 1/2*(5*b^6*c - 11*a*b^5*d)*arctan(b*x/sqrt(a*b))/((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)*sqrt(a*b)) + 1/8*(99*b^2*c^2*d^4 - 110*a*b*c*d^5 + 35*a^2*d^6)*arctan(d*x/sqrt(c*d))/((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(c*d)) + 1/8*(19*b*c*d^5*x^3 - 11*a*d^6*x^3 + 21*b*c^2*d^4*x - 13*a*c*d^5*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*x^2 + c)^2) + 1/3*(6*b*c*x^2 + 9*a*d*x^2 - a*c)/(a^3*c^4*x^3)","A",0
319,1,593,0,0.440603," ","integrate(x^m*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""giac"")","\frac{B b^{3} m^{4} x^{9} x^{m} + 16 \, B b^{3} m^{3} x^{9} x^{m} + 3 \, B a b^{2} m^{4} x^{7} x^{m} + A b^{3} m^{4} x^{7} x^{m} + 86 \, B b^{3} m^{2} x^{9} x^{m} + 54 \, B a b^{2} m^{3} x^{7} x^{m} + 18 \, A b^{3} m^{3} x^{7} x^{m} + 176 \, B b^{3} m x^{9} x^{m} + 3 \, B a^{2} b m^{4} x^{5} x^{m} + 3 \, A a b^{2} m^{4} x^{5} x^{m} + 312 \, B a b^{2} m^{2} x^{7} x^{m} + 104 \, A b^{3} m^{2} x^{7} x^{m} + 105 \, B b^{3} x^{9} x^{m} + 60 \, B a^{2} b m^{3} x^{5} x^{m} + 60 \, A a b^{2} m^{3} x^{5} x^{m} + 666 \, B a b^{2} m x^{7} x^{m} + 222 \, A b^{3} m x^{7} x^{m} + B a^{3} m^{4} x^{3} x^{m} + 3 \, A a^{2} b m^{4} x^{3} x^{m} + 390 \, B a^{2} b m^{2} x^{5} x^{m} + 390 \, A a b^{2} m^{2} x^{5} x^{m} + 405 \, B a b^{2} x^{7} x^{m} + 135 \, A b^{3} x^{7} x^{m} + 22 \, B a^{3} m^{3} x^{3} x^{m} + 66 \, A a^{2} b m^{3} x^{3} x^{m} + 900 \, B a^{2} b m x^{5} x^{m} + 900 \, A a b^{2} m x^{5} x^{m} + A a^{3} m^{4} x x^{m} + 164 \, B a^{3} m^{2} x^{3} x^{m} + 492 \, A a^{2} b m^{2} x^{3} x^{m} + 567 \, B a^{2} b x^{5} x^{m} + 567 \, A a b^{2} x^{5} x^{m} + 24 \, A a^{3} m^{3} x x^{m} + 458 \, B a^{3} m x^{3} x^{m} + 1374 \, A a^{2} b m x^{3} x^{m} + 206 \, A a^{3} m^{2} x x^{m} + 315 \, B a^{3} x^{3} x^{m} + 945 \, A a^{2} b x^{3} x^{m} + 744 \, A a^{3} m x x^{m} + 945 \, A a^{3} x x^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"(B*b^3*m^4*x^9*x^m + 16*B*b^3*m^3*x^9*x^m + 3*B*a*b^2*m^4*x^7*x^m + A*b^3*m^4*x^7*x^m + 86*B*b^3*m^2*x^9*x^m + 54*B*a*b^2*m^3*x^7*x^m + 18*A*b^3*m^3*x^7*x^m + 176*B*b^3*m*x^9*x^m + 3*B*a^2*b*m^4*x^5*x^m + 3*A*a*b^2*m^4*x^5*x^m + 312*B*a*b^2*m^2*x^7*x^m + 104*A*b^3*m^2*x^7*x^m + 105*B*b^3*x^9*x^m + 60*B*a^2*b*m^3*x^5*x^m + 60*A*a*b^2*m^3*x^5*x^m + 666*B*a*b^2*m*x^7*x^m + 222*A*b^3*m*x^7*x^m + B*a^3*m^4*x^3*x^m + 3*A*a^2*b*m^4*x^3*x^m + 390*B*a^2*b*m^2*x^5*x^m + 390*A*a*b^2*m^2*x^5*x^m + 405*B*a*b^2*x^7*x^m + 135*A*b^3*x^7*x^m + 22*B*a^3*m^3*x^3*x^m + 66*A*a^2*b*m^3*x^3*x^m + 900*B*a^2*b*m*x^5*x^m + 900*A*a*b^2*m*x^5*x^m + A*a^3*m^4*x*x^m + 164*B*a^3*m^2*x^3*x^m + 492*A*a^2*b*m^2*x^3*x^m + 567*B*a^2*b*x^5*x^m + 567*A*a*b^2*x^5*x^m + 24*A*a^3*m^3*x*x^m + 458*B*a^3*m*x^3*x^m + 1374*A*a^2*b*m*x^3*x^m + 206*A*a^3*m^2*x*x^m + 315*B*a^3*x^3*x^m + 945*A*a^2*b*x^3*x^m + 744*A*a^3*m*x*x^m + 945*A*a^3*x*x^m)/(m^5 + 25*m^4 + 230*m^3 + 950*m^2 + 1689*m + 945)","B",0
320,1,332,0,0.445361," ","integrate(x^m*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{B b^{2} m^{3} x^{7} x^{m} + 9 \, B b^{2} m^{2} x^{7} x^{m} + 2 \, B a b m^{3} x^{5} x^{m} + A b^{2} m^{3} x^{5} x^{m} + 23 \, B b^{2} m x^{7} x^{m} + 22 \, B a b m^{2} x^{5} x^{m} + 11 \, A b^{2} m^{2} x^{5} x^{m} + 15 \, B b^{2} x^{7} x^{m} + B a^{2} m^{3} x^{3} x^{m} + 2 \, A a b m^{3} x^{3} x^{m} + 62 \, B a b m x^{5} x^{m} + 31 \, A b^{2} m x^{5} x^{m} + 13 \, B a^{2} m^{2} x^{3} x^{m} + 26 \, A a b m^{2} x^{3} x^{m} + 42 \, B a b x^{5} x^{m} + 21 \, A b^{2} x^{5} x^{m} + A a^{2} m^{3} x x^{m} + 47 \, B a^{2} m x^{3} x^{m} + 94 \, A a b m x^{3} x^{m} + 15 \, A a^{2} m^{2} x x^{m} + 35 \, B a^{2} x^{3} x^{m} + 70 \, A a b x^{3} x^{m} + 71 \, A a^{2} m x x^{m} + 105 \, A a^{2} x x^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"(B*b^2*m^3*x^7*x^m + 9*B*b^2*m^2*x^7*x^m + 2*B*a*b*m^3*x^5*x^m + A*b^2*m^3*x^5*x^m + 23*B*b^2*m*x^7*x^m + 22*B*a*b*m^2*x^5*x^m + 11*A*b^2*m^2*x^5*x^m + 15*B*b^2*x^7*x^m + B*a^2*m^3*x^3*x^m + 2*A*a*b*m^3*x^3*x^m + 62*B*a*b*m*x^5*x^m + 31*A*b^2*m*x^5*x^m + 13*B*a^2*m^2*x^3*x^m + 26*A*a*b*m^2*x^3*x^m + 42*B*a*b*x^5*x^m + 21*A*b^2*x^5*x^m + A*a^2*m^3*x*x^m + 47*B*a^2*m*x^3*x^m + 94*A*a*b*m*x^3*x^m + 15*A*a^2*m^2*x*x^m + 35*B*a^2*x^3*x^m + 70*A*a*b*x^3*x^m + 71*A*a^2*m*x*x^m + 105*A*a^2*x*x^m)/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
321,1,143,0,0.363910," ","integrate(x^m*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{B b m^{2} x^{5} x^{m} + 4 \, B b m x^{5} x^{m} + B a m^{2} x^{3} x^{m} + A b m^{2} x^{3} x^{m} + 3 \, B b x^{5} x^{m} + 6 \, B a m x^{3} x^{m} + 6 \, A b m x^{3} x^{m} + A a m^{2} x x^{m} + 5 \, B a x^{3} x^{m} + 5 \, A b x^{3} x^{m} + 8 \, A a m x x^{m} + 15 \, A a x x^{m}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"(B*b*m^2*x^5*x^m + 4*B*b*m*x^5*x^m + B*a*m^2*x^3*x^m + A*b*m^2*x^3*x^m + 3*B*b*x^5*x^m + 6*B*a*m*x^3*x^m + 6*A*b*m*x^3*x^m + A*a*m^2*x*x^m + 5*B*a*x^3*x^m + 5*A*b*x^3*x^m + 8*A*a*m*x*x^m + 15*A*a*x*x^m)/(m^3 + 9*m^2 + 23*m + 15)","B",0
322,0,0,0,0.000000," ","integrate(x^m*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} x^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((B*x^2 + A)*x^m/(b*x^2 + a), x)","F",0
323,0,0,0,0.000000," ","integrate(x^m*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} x^{m}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*x^2 + A)*x^m/(b*x^2 + a)^2, x)","F",0
324,0,0,0,0.000000," ","integrate(x^m*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} x^{m}}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*x^2 + A)*x^m/(b*x^2 + a)^3, x)","F",0
325,1,1192,0,0.587341," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{2} d^{3} m^{5} x^{11} x^{m} + 25 \, b^{2} d^{3} m^{4} x^{11} x^{m} + 3 \, b^{2} c d^{2} m^{5} x^{9} x^{m} + 2 \, a b d^{3} m^{5} x^{9} x^{m} + 230 \, b^{2} d^{3} m^{3} x^{11} x^{m} + 81 \, b^{2} c d^{2} m^{4} x^{9} x^{m} + 54 \, a b d^{3} m^{4} x^{9} x^{m} + 950 \, b^{2} d^{3} m^{2} x^{11} x^{m} + 3 \, b^{2} c^{2} d m^{5} x^{7} x^{m} + 6 \, a b c d^{2} m^{5} x^{7} x^{m} + a^{2} d^{3} m^{5} x^{7} x^{m} + 786 \, b^{2} c d^{2} m^{3} x^{9} x^{m} + 524 \, a b d^{3} m^{3} x^{9} x^{m} + 1689 \, b^{2} d^{3} m x^{11} x^{m} + 87 \, b^{2} c^{2} d m^{4} x^{7} x^{m} + 174 \, a b c d^{2} m^{4} x^{7} x^{m} + 29 \, a^{2} d^{3} m^{4} x^{7} x^{m} + 3366 \, b^{2} c d^{2} m^{2} x^{9} x^{m} + 2244 \, a b d^{3} m^{2} x^{9} x^{m} + 945 \, b^{2} d^{3} x^{11} x^{m} + b^{2} c^{3} m^{5} x^{5} x^{m} + 6 \, a b c^{2} d m^{5} x^{5} x^{m} + 3 \, a^{2} c d^{2} m^{5} x^{5} x^{m} + 906 \, b^{2} c^{2} d m^{3} x^{7} x^{m} + 1812 \, a b c d^{2} m^{3} x^{7} x^{m} + 302 \, a^{2} d^{3} m^{3} x^{7} x^{m} + 6123 \, b^{2} c d^{2} m x^{9} x^{m} + 4082 \, a b d^{3} m x^{9} x^{m} + 31 \, b^{2} c^{3} m^{4} x^{5} x^{m} + 186 \, a b c^{2} d m^{4} x^{5} x^{m} + 93 \, a^{2} c d^{2} m^{4} x^{5} x^{m} + 4098 \, b^{2} c^{2} d m^{2} x^{7} x^{m} + 8196 \, a b c d^{2} m^{2} x^{7} x^{m} + 1366 \, a^{2} d^{3} m^{2} x^{7} x^{m} + 3465 \, b^{2} c d^{2} x^{9} x^{m} + 2310 \, a b d^{3} x^{9} x^{m} + 2 \, a b c^{3} m^{5} x^{3} x^{m} + 3 \, a^{2} c^{2} d m^{5} x^{3} x^{m} + 350 \, b^{2} c^{3} m^{3} x^{5} x^{m} + 2100 \, a b c^{2} d m^{3} x^{5} x^{m} + 1050 \, a^{2} c d^{2} m^{3} x^{5} x^{m} + 7731 \, b^{2} c^{2} d m x^{7} x^{m} + 15462 \, a b c d^{2} m x^{7} x^{m} + 2577 \, a^{2} d^{3} m x^{7} x^{m} + 66 \, a b c^{3} m^{4} x^{3} x^{m} + 99 \, a^{2} c^{2} d m^{4} x^{3} x^{m} + 1730 \, b^{2} c^{3} m^{2} x^{5} x^{m} + 10380 \, a b c^{2} d m^{2} x^{5} x^{m} + 5190 \, a^{2} c d^{2} m^{2} x^{5} x^{m} + 4455 \, b^{2} c^{2} d x^{7} x^{m} + 8910 \, a b c d^{2} x^{7} x^{m} + 1485 \, a^{2} d^{3} x^{7} x^{m} + a^{2} c^{3} m^{5} x x^{m} + 812 \, a b c^{3} m^{3} x^{3} x^{m} + 1218 \, a^{2} c^{2} d m^{3} x^{3} x^{m} + 3489 \, b^{2} c^{3} m x^{5} x^{m} + 20934 \, a b c^{2} d m x^{5} x^{m} + 10467 \, a^{2} c d^{2} m x^{5} x^{m} + 35 \, a^{2} c^{3} m^{4} x x^{m} + 4524 \, a b c^{3} m^{2} x^{3} x^{m} + 6786 \, a^{2} c^{2} d m^{2} x^{3} x^{m} + 2079 \, b^{2} c^{3} x^{5} x^{m} + 12474 \, a b c^{2} d x^{5} x^{m} + 6237 \, a^{2} c d^{2} x^{5} x^{m} + 470 \, a^{2} c^{3} m^{3} x x^{m} + 10706 \, a b c^{3} m x^{3} x^{m} + 16059 \, a^{2} c^{2} d m x^{3} x^{m} + 3010 \, a^{2} c^{3} m^{2} x x^{m} + 6930 \, a b c^{3} x^{3} x^{m} + 10395 \, a^{2} c^{2} d x^{3} x^{m} + 9129 \, a^{2} c^{3} m x x^{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}"," ",0,"(b^2*d^3*m^5*x^11*x^m + 25*b^2*d^3*m^4*x^11*x^m + 3*b^2*c*d^2*m^5*x^9*x^m + 2*a*b*d^3*m^5*x^9*x^m + 230*b^2*d^3*m^3*x^11*x^m + 81*b^2*c*d^2*m^4*x^9*x^m + 54*a*b*d^3*m^4*x^9*x^m + 950*b^2*d^3*m^2*x^11*x^m + 3*b^2*c^2*d*m^5*x^7*x^m + 6*a*b*c*d^2*m^5*x^7*x^m + a^2*d^3*m^5*x^7*x^m + 786*b^2*c*d^2*m^3*x^9*x^m + 524*a*b*d^3*m^3*x^9*x^m + 1689*b^2*d^3*m*x^11*x^m + 87*b^2*c^2*d*m^4*x^7*x^m + 174*a*b*c*d^2*m^4*x^7*x^m + 29*a^2*d^3*m^4*x^7*x^m + 3366*b^2*c*d^2*m^2*x^9*x^m + 2244*a*b*d^3*m^2*x^9*x^m + 945*b^2*d^3*x^11*x^m + b^2*c^3*m^5*x^5*x^m + 6*a*b*c^2*d*m^5*x^5*x^m + 3*a^2*c*d^2*m^5*x^5*x^m + 906*b^2*c^2*d*m^3*x^7*x^m + 1812*a*b*c*d^2*m^3*x^7*x^m + 302*a^2*d^3*m^3*x^7*x^m + 6123*b^2*c*d^2*m*x^9*x^m + 4082*a*b*d^3*m*x^9*x^m + 31*b^2*c^3*m^4*x^5*x^m + 186*a*b*c^2*d*m^4*x^5*x^m + 93*a^2*c*d^2*m^4*x^5*x^m + 4098*b^2*c^2*d*m^2*x^7*x^m + 8196*a*b*c*d^2*m^2*x^7*x^m + 1366*a^2*d^3*m^2*x^7*x^m + 3465*b^2*c*d^2*x^9*x^m + 2310*a*b*d^3*x^9*x^m + 2*a*b*c^3*m^5*x^3*x^m + 3*a^2*c^2*d*m^5*x^3*x^m + 350*b^2*c^3*m^3*x^5*x^m + 2100*a*b*c^2*d*m^3*x^5*x^m + 1050*a^2*c*d^2*m^3*x^5*x^m + 7731*b^2*c^2*d*m*x^7*x^m + 15462*a*b*c*d^2*m*x^7*x^m + 2577*a^2*d^3*m*x^7*x^m + 66*a*b*c^3*m^4*x^3*x^m + 99*a^2*c^2*d*m^4*x^3*x^m + 1730*b^2*c^3*m^2*x^5*x^m + 10380*a*b*c^2*d*m^2*x^5*x^m + 5190*a^2*c*d^2*m^2*x^5*x^m + 4455*b^2*c^2*d*x^7*x^m + 8910*a*b*c*d^2*x^7*x^m + 1485*a^2*d^3*x^7*x^m + a^2*c^3*m^5*x*x^m + 812*a*b*c^3*m^3*x^3*x^m + 1218*a^2*c^2*d*m^3*x^3*x^m + 3489*b^2*c^3*m*x^5*x^m + 20934*a*b*c^2*d*m*x^5*x^m + 10467*a^2*c*d^2*m*x^5*x^m + 35*a^2*c^3*m^4*x*x^m + 4524*a*b*c^3*m^2*x^3*x^m + 6786*a^2*c^2*d*m^2*x^3*x^m + 2079*b^2*c^3*x^5*x^m + 12474*a*b*c^2*d*x^5*x^m + 6237*a^2*c*d^2*x^5*x^m + 470*a^2*c^3*m^3*x*x^m + 10706*a*b*c^3*m*x^3*x^m + 16059*a^2*c^2*d*m*x^3*x^m + 3010*a^2*c^3*m^2*x*x^m + 6930*a*b*c^3*x^3*x^m + 10395*a^2*c^2*d*x^3*x^m + 9129*a^2*c^3*m*x*x^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
326,1,703,0,0.382712," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} d^{2} m^{4} x^{9} x^{m} + 16 \, b^{2} d^{2} m^{3} x^{9} x^{m} + 2 \, b^{2} c d m^{4} x^{7} x^{m} + 2 \, a b d^{2} m^{4} x^{7} x^{m} + 86 \, b^{2} d^{2} m^{2} x^{9} x^{m} + 36 \, b^{2} c d m^{3} x^{7} x^{m} + 36 \, a b d^{2} m^{3} x^{7} x^{m} + 176 \, b^{2} d^{2} m x^{9} x^{m} + b^{2} c^{2} m^{4} x^{5} x^{m} + 4 \, a b c d m^{4} x^{5} x^{m} + a^{2} d^{2} m^{4} x^{5} x^{m} + 208 \, b^{2} c d m^{2} x^{7} x^{m} + 208 \, a b d^{2} m^{2} x^{7} x^{m} + 105 \, b^{2} d^{2} x^{9} x^{m} + 20 \, b^{2} c^{2} m^{3} x^{5} x^{m} + 80 \, a b c d m^{3} x^{5} x^{m} + 20 \, a^{2} d^{2} m^{3} x^{5} x^{m} + 444 \, b^{2} c d m x^{7} x^{m} + 444 \, a b d^{2} m x^{7} x^{m} + 2 \, a b c^{2} m^{4} x^{3} x^{m} + 2 \, a^{2} c d m^{4} x^{3} x^{m} + 130 \, b^{2} c^{2} m^{2} x^{5} x^{m} + 520 \, a b c d m^{2} x^{5} x^{m} + 130 \, a^{2} d^{2} m^{2} x^{5} x^{m} + 270 \, b^{2} c d x^{7} x^{m} + 270 \, a b d^{2} x^{7} x^{m} + 44 \, a b c^{2} m^{3} x^{3} x^{m} + 44 \, a^{2} c d m^{3} x^{3} x^{m} + 300 \, b^{2} c^{2} m x^{5} x^{m} + 1200 \, a b c d m x^{5} x^{m} + 300 \, a^{2} d^{2} m x^{5} x^{m} + a^{2} c^{2} m^{4} x x^{m} + 328 \, a b c^{2} m^{2} x^{3} x^{m} + 328 \, a^{2} c d m^{2} x^{3} x^{m} + 189 \, b^{2} c^{2} x^{5} x^{m} + 756 \, a b c d x^{5} x^{m} + 189 \, a^{2} d^{2} x^{5} x^{m} + 24 \, a^{2} c^{2} m^{3} x x^{m} + 916 \, a b c^{2} m x^{3} x^{m} + 916 \, a^{2} c d m x^{3} x^{m} + 206 \, a^{2} c^{2} m^{2} x x^{m} + 630 \, a b c^{2} x^{3} x^{m} + 630 \, a^{2} c d x^{3} x^{m} + 744 \, a^{2} c^{2} m x x^{m} + 945 \, a^{2} c^{2} x x^{m}}{m^{5} + 25 \, m^{4} + 230 \, m^{3} + 950 \, m^{2} + 1689 \, m + 945}"," ",0,"(b^2*d^2*m^4*x^9*x^m + 16*b^2*d^2*m^3*x^9*x^m + 2*b^2*c*d*m^4*x^7*x^m + 2*a*b*d^2*m^4*x^7*x^m + 86*b^2*d^2*m^2*x^9*x^m + 36*b^2*c*d*m^3*x^7*x^m + 36*a*b*d^2*m^3*x^7*x^m + 176*b^2*d^2*m*x^9*x^m + b^2*c^2*m^4*x^5*x^m + 4*a*b*c*d*m^4*x^5*x^m + a^2*d^2*m^4*x^5*x^m + 208*b^2*c*d*m^2*x^7*x^m + 208*a*b*d^2*m^2*x^7*x^m + 105*b^2*d^2*x^9*x^m + 20*b^2*c^2*m^3*x^5*x^m + 80*a*b*c*d*m^3*x^5*x^m + 20*a^2*d^2*m^3*x^5*x^m + 444*b^2*c*d*m*x^7*x^m + 444*a*b*d^2*m*x^7*x^m + 2*a*b*c^2*m^4*x^3*x^m + 2*a^2*c*d*m^4*x^3*x^m + 130*b^2*c^2*m^2*x^5*x^m + 520*a*b*c*d*m^2*x^5*x^m + 130*a^2*d^2*m^2*x^5*x^m + 270*b^2*c*d*x^7*x^m + 270*a*b*d^2*x^7*x^m + 44*a*b*c^2*m^3*x^3*x^m + 44*a^2*c*d*m^3*x^3*x^m + 300*b^2*c^2*m*x^5*x^m + 1200*a*b*c*d*m*x^5*x^m + 300*a^2*d^2*m*x^5*x^m + a^2*c^2*m^4*x*x^m + 328*a*b*c^2*m^2*x^3*x^m + 328*a^2*c*d*m^2*x^3*x^m + 189*b^2*c^2*x^5*x^m + 756*a*b*c*d*x^5*x^m + 189*a^2*d^2*x^5*x^m + 24*a^2*c^2*m^3*x*x^m + 916*a*b*c^2*m*x^3*x^m + 916*a^2*c*d*m*x^3*x^m + 206*a^2*c^2*m^2*x*x^m + 630*a*b*c^2*x^3*x^m + 630*a^2*c*d*x^3*x^m + 744*a^2*c^2*m*x*x^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
327,1,332,0,0.425554," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{b^{2} d m^{3} x^{7} x^{m} + 9 \, b^{2} d m^{2} x^{7} x^{m} + b^{2} c m^{3} x^{5} x^{m} + 2 \, a b d m^{3} x^{5} x^{m} + 23 \, b^{2} d m x^{7} x^{m} + 11 \, b^{2} c m^{2} x^{5} x^{m} + 22 \, a b d m^{2} x^{5} x^{m} + 15 \, b^{2} d x^{7} x^{m} + 2 \, a b c m^{3} x^{3} x^{m} + a^{2} d m^{3} x^{3} x^{m} + 31 \, b^{2} c m x^{5} x^{m} + 62 \, a b d m x^{5} x^{m} + 26 \, a b c m^{2} x^{3} x^{m} + 13 \, a^{2} d m^{2} x^{3} x^{m} + 21 \, b^{2} c x^{5} x^{m} + 42 \, a b d x^{5} x^{m} + a^{2} c m^{3} x x^{m} + 94 \, a b c m x^{3} x^{m} + 47 \, a^{2} d m x^{3} x^{m} + 15 \, a^{2} c m^{2} x x^{m} + 70 \, a b c x^{3} x^{m} + 35 \, a^{2} d x^{3} x^{m} + 71 \, a^{2} c m x x^{m} + 105 \, a^{2} c x x^{m}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"(b^2*d*m^3*x^7*x^m + 9*b^2*d*m^2*x^7*x^m + b^2*c*m^3*x^5*x^m + 2*a*b*d*m^3*x^5*x^m + 23*b^2*d*m*x^7*x^m + 11*b^2*c*m^2*x^5*x^m + 22*a*b*d*m^2*x^5*x^m + 15*b^2*d*x^7*x^m + 2*a*b*c*m^3*x^3*x^m + a^2*d*m^3*x^3*x^m + 31*b^2*c*m*x^5*x^m + 62*a*b*d*m*x^5*x^m + 26*a*b*c*m^2*x^3*x^m + 13*a^2*d*m^2*x^3*x^m + 21*b^2*c*x^5*x^m + 42*a*b*d*x^5*x^m + a^2*c*m^3*x*x^m + 94*a*b*c*m*x^3*x^m + 47*a^2*d*m*x^3*x^m + 15*a^2*c*m^2*x*x^m + 70*a*b*c*x^3*x^m + 35*a^2*d*x^3*x^m + 71*a^2*c*m*x*x^m + 105*a^2*c*x*x^m)/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","B",0
328,0,0,0,0.000000," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} x^{m}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*x^m/(d*x^2 + c), x)","F",0
329,0,0,0,0.000000," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} x^{m}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*x^m/(d*x^2 + c)^2, x)","F",0
330,0,0,0,0.000000," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} x^{m}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*x^m/(d*x^2 + c)^3, x)","F",0
331,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{3} x^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^3*x^m/(b*x^2 + a), x)","F",0
332,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{2} x^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^2*x^m/(b*x^2 + a), x)","F",0
333,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} x^{m}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)*x^m/(b*x^2 + a), x)","F",0
334,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)*(d*x^2 + c)), x)","F",0
335,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)^2*(d*x^2 + c)), x)","F",0
336,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)}^{3} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)^3*(d*x^2 + c)), x)","F",0
337,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{3} x^{m}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^3*x^m/(b*x^2 + a)^2, x)","F",0
338,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{2} x^{m}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^2*x^m/(b*x^2 + a)^2, x)","F",0
339,0,0,0,0.000000," ","integrate(x^m*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} x^{m}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)*x^m/(b*x^2 + a)^2, x)","F",0
340,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)^2*(d*x^2 + c)), x)","F",0
341,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)^2*(d*x^2 + c)^2), x)","F",0
342,0,0,0,0.000000," ","integrate(x^m/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\int \frac{x^{m}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate(x^m/((b*x^2 + a)^2*(d*x^2 + c)^3), x)","F",0
343,1,29,0,0.354817," ","integrate(x^(7/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{17} \, B b x^{\frac{17}{2}} + \frac{2}{13} \, B a x^{\frac{13}{2}} + \frac{2}{13} \, A b x^{\frac{13}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}}"," ",0,"2/17*B*b*x^(17/2) + 2/13*B*a*x^(13/2) + 2/13*A*b*x^(13/2) + 2/9*A*a*x^(9/2)","A",0
344,1,29,0,0.317052," ","integrate(x^(5/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{15} \, B b x^{\frac{15}{2}} + \frac{2}{11} \, B a x^{\frac{11}{2}} + \frac{2}{11} \, A b x^{\frac{11}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}}"," ",0,"2/15*B*b*x^(15/2) + 2/11*B*a*x^(11/2) + 2/11*A*b*x^(11/2) + 2/7*A*a*x^(7/2)","A",0
345,1,29,0,0.344034," ","integrate(x^(3/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}}"," ",0,"2/13*B*b*x^(13/2) + 2/9*B*a*x^(9/2) + 2/9*A*b*x^(9/2) + 2/5*A*a*x^(5/2)","A",0
346,1,29,0,0.296360," ","integrate((b*x^2+a)*(B*x^2+A)*x^(1/2),x, algorithm=""giac"")","\frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}}"," ",0,"2/11*B*b*x^(11/2) + 2/7*B*a*x^(7/2) + 2/7*A*b*x^(7/2) + 2/3*A*a*x^(3/2)","A",0
347,1,29,0,0.306896," ","integrate((b*x^2+a)*(B*x^2+A)/x^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} + 2 \, A a \sqrt{x}"," ",0,"2/9*B*b*x^(9/2) + 2/5*B*a*x^(5/2) + 2/5*A*b*x^(5/2) + 2*A*a*sqrt(x)","A",0
348,1,29,0,0.348080," ","integrate((b*x^2+a)*(B*x^2+A)/x^(3/2),x, algorithm=""giac"")","\frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{3} \, B a x^{\frac{3}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} - \frac{2 \, A a}{\sqrt{x}}"," ",0,"2/7*B*b*x^(7/2) + 2/3*B*a*x^(3/2) + 2/3*A*b*x^(3/2) - 2*A*a/sqrt(x)","A",0
349,1,29,0,0.332573," ","integrate((b*x^2+a)*(B*x^2+A)/x^(5/2),x, algorithm=""giac"")","\frac{2}{5} \, B b x^{\frac{5}{2}} + 2 \, B a \sqrt{x} + 2 \, A b \sqrt{x} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*B*b*x^(5/2) + 2*B*a*sqrt(x) + 2*A*b*sqrt(x) - 2/3*A*a/x^(3/2)","A",0
350,1,31,0,0.370881," ","integrate((b*x^2+a)*(B*x^2+A)/x^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, B b x^{\frac{3}{2}} - \frac{2 \, {\left(5 \, B a x^{2} + 5 \, A b x^{2} + A a\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/3*B*b*x^(3/2) - 2/5*(5*B*a*x^2 + 5*A*b*x^2 + A*a)/x^(5/2)","A",0
351,1,53,0,0.275247," ","integrate(x^(7/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{21} \, B b^{2} x^{\frac{21}{2}} + \frac{4}{17} \, B a b x^{\frac{17}{2}} + \frac{2}{17} \, A b^{2} x^{\frac{17}{2}} + \frac{2}{13} \, B a^{2} x^{\frac{13}{2}} + \frac{4}{13} \, A a b x^{\frac{13}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}}"," ",0,"2/21*B*b^2*x^(21/2) + 4/17*B*a*b*x^(17/2) + 2/17*A*b^2*x^(17/2) + 2/13*B*a^2*x^(13/2) + 4/13*A*a*b*x^(13/2) + 2/9*A*a^2*x^(9/2)","A",0
352,1,53,0,0.294151," ","integrate(x^(5/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{19} \, B b^{2} x^{\frac{19}{2}} + \frac{4}{15} \, B a b x^{\frac{15}{2}} + \frac{2}{15} \, A b^{2} x^{\frac{15}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a b x^{\frac{11}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}}"," ",0,"2/19*B*b^2*x^(19/2) + 4/15*B*a*b*x^(15/2) + 2/15*A*b^2*x^(15/2) + 2/11*B*a^2*x^(11/2) + 4/11*A*a*b*x^(11/2) + 2/7*A*a^2*x^(7/2)","A",0
353,1,53,0,0.314648," ","integrate(x^(3/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{4}{13} \, B a b x^{\frac{13}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a b x^{\frac{9}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}}"," ",0,"2/17*B*b^2*x^(17/2) + 4/13*B*a*b*x^(13/2) + 2/13*A*b^2*x^(13/2) + 2/9*B*a^2*x^(9/2) + 4/9*A*a*b*x^(9/2) + 2/5*A*a^2*x^(5/2)","A",0
354,1,53,0,0.310015," ","integrate((b*x^2+a)^2*(B*x^2+A)*x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{2}{7} \, B a^{2} x^{\frac{7}{2}} + \frac{4}{7} \, A a b x^{\frac{7}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}}"," ",0,"2/15*B*b^2*x^(15/2) + 4/11*B*a*b*x^(11/2) + 2/11*A*b^2*x^(11/2) + 2/7*B*a^2*x^(7/2) + 4/7*A*a*b*x^(7/2) + 2/3*A*a^2*x^(3/2)","A",0
355,1,53,0,0.263829," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{9} \, B a b x^{\frac{9}{2}} + \frac{2}{9} \, A b^{2} x^{\frac{9}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a b x^{\frac{5}{2}} + 2 \, A a^{2} \sqrt{x}"," ",0,"2/13*B*b^2*x^(13/2) + 4/9*B*a*b*x^(9/2) + 2/9*A*b^2*x^(9/2) + 2/5*B*a^2*x^(5/2) + 4/5*A*a*b*x^(5/2) + 2*A*a^2*sqrt(x)","A",0
356,1,53,0,0.364169," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(3/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{2} x^{\frac{11}{2}} + \frac{4}{7} \, B a b x^{\frac{7}{2}} + \frac{2}{7} \, A b^{2} x^{\frac{7}{2}} + \frac{2}{3} \, B a^{2} x^{\frac{3}{2}} + \frac{4}{3} \, A a b x^{\frac{3}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}}"," ",0,"2/11*B*b^2*x^(11/2) + 4/7*B*a*b*x^(7/2) + 2/7*A*b^2*x^(7/2) + 2/3*B*a^2*x^(3/2) + 4/3*A*a*b*x^(3/2) - 2*A*a^2/sqrt(x)","A",0
357,1,53,0,0.411279," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(5/2),x, algorithm=""giac"")","\frac{2}{9} \, B b^{2} x^{\frac{9}{2}} + \frac{4}{5} \, B a b x^{\frac{5}{2}} + \frac{2}{5} \, A b^{2} x^{\frac{5}{2}} + 2 \, B a^{2} \sqrt{x} + 4 \, A a b \sqrt{x} - \frac{2 \, A a^{2}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/9*B*b^2*x^(9/2) + 4/5*B*a*b*x^(5/2) + 2/5*A*b^2*x^(5/2) + 2*B*a^2*sqrt(x) + 4*A*a*b*sqrt(x) - 2/3*A*a^2/x^(3/2)","A",0
358,1,55,0,0.396033," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(7/2),x, algorithm=""giac"")","\frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{4}{3} \, B a b x^{\frac{3}{2}} + \frac{2}{3} \, A b^{2} x^{\frac{3}{2}} - \frac{2 \, {\left(5 \, B a^{2} x^{2} + 10 \, A a b x^{2} + A a^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/7*B*b^2*x^(7/2) + 4/3*B*a*b*x^(3/2) + 2/3*A*b^2*x^(3/2) - 2/5*(5*B*a^2*x^2 + 10*A*a*b*x^2 + A*a^2)/x^(5/2)","A",0
359,1,77,0,0.373499," ","integrate(x^(7/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{25} \, B b^{3} x^{\frac{25}{2}} + \frac{2}{7} \, B a b^{2} x^{\frac{21}{2}} + \frac{2}{21} \, A b^{3} x^{\frac{21}{2}} + \frac{6}{17} \, B a^{2} b x^{\frac{17}{2}} + \frac{6}{17} \, A a b^{2} x^{\frac{17}{2}} + \frac{2}{13} \, B a^{3} x^{\frac{13}{2}} + \frac{6}{13} \, A a^{2} b x^{\frac{13}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}}"," ",0,"2/25*B*b^3*x^(25/2) + 2/7*B*a*b^2*x^(21/2) + 2/21*A*b^3*x^(21/2) + 6/17*B*a^2*b*x^(17/2) + 6/17*A*a*b^2*x^(17/2) + 2/13*B*a^3*x^(13/2) + 6/13*A*a^2*b*x^(13/2) + 2/9*A*a^3*x^(9/2)","A",0
360,1,77,0,0.357568," ","integrate(x^(5/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{23} \, B b^{3} x^{\frac{23}{2}} + \frac{6}{19} \, B a b^{2} x^{\frac{19}{2}} + \frac{2}{19} \, A b^{3} x^{\frac{19}{2}} + \frac{2}{5} \, B a^{2} b x^{\frac{15}{2}} + \frac{2}{5} \, A a b^{2} x^{\frac{15}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{6}{11} \, A a^{2} b x^{\frac{11}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}}"," ",0,"2/23*B*b^3*x^(23/2) + 6/19*B*a*b^2*x^(19/2) + 2/19*A*b^3*x^(19/2) + 2/5*B*a^2*b*x^(15/2) + 2/5*A*a*b^2*x^(15/2) + 2/11*B*a^3*x^(11/2) + 6/11*A*a^2*b*x^(11/2) + 2/7*A*a^3*x^(7/2)","A",0
361,1,77,0,0.377993," ","integrate(x^(3/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""giac"")","\frac{2}{21} \, B b^{3} x^{\frac{21}{2}} + \frac{6}{17} \, B a b^{2} x^{\frac{17}{2}} + \frac{2}{17} \, A b^{3} x^{\frac{17}{2}} + \frac{6}{13} \, B a^{2} b x^{\frac{13}{2}} + \frac{6}{13} \, A a b^{2} x^{\frac{13}{2}} + \frac{2}{9} \, B a^{3} x^{\frac{9}{2}} + \frac{2}{3} \, A a^{2} b x^{\frac{9}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}}"," ",0,"2/21*B*b^3*x^(21/2) + 6/17*B*a*b^2*x^(17/2) + 2/17*A*b^3*x^(17/2) + 6/13*B*a^2*b*x^(13/2) + 6/13*A*a*b^2*x^(13/2) + 2/9*B*a^3*x^(9/2) + 2/3*A*a^2*b*x^(9/2) + 2/5*A*a^3*x^(5/2)","A",0
362,1,77,0,0.396950," ","integrate((b*x^2+a)^3*(B*x^2+A)*x^(1/2),x, algorithm=""giac"")","\frac{2}{19} \, B b^{3} x^{\frac{19}{2}} + \frac{2}{5} \, B a b^{2} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{3} x^{\frac{15}{2}} + \frac{6}{11} \, B a^{2} b x^{\frac{11}{2}} + \frac{6}{11} \, A a b^{2} x^{\frac{11}{2}} + \frac{2}{7} \, B a^{3} x^{\frac{7}{2}} + \frac{6}{7} \, A a^{2} b x^{\frac{7}{2}} + \frac{2}{3} \, A a^{3} x^{\frac{3}{2}}"," ",0,"2/19*B*b^3*x^(19/2) + 2/5*B*a*b^2*x^(15/2) + 2/15*A*b^3*x^(15/2) + 6/11*B*a^2*b*x^(11/2) + 6/11*A*a*b^2*x^(11/2) + 2/7*B*a^3*x^(7/2) + 6/7*A*a^2*b*x^(7/2) + 2/3*A*a^3*x^(3/2)","A",0
363,1,77,0,0.246907," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, B b^{3} x^{\frac{17}{2}} + \frac{6}{13} \, B a b^{2} x^{\frac{13}{2}} + \frac{2}{13} \, A b^{3} x^{\frac{13}{2}} + \frac{2}{3} \, B a^{2} b x^{\frac{9}{2}} + \frac{2}{3} \, A a b^{2} x^{\frac{9}{2}} + \frac{2}{5} \, B a^{3} x^{\frac{5}{2}} + \frac{6}{5} \, A a^{2} b x^{\frac{5}{2}} + 2 \, A a^{3} \sqrt{x}"," ",0,"2/17*B*b^3*x^(17/2) + 6/13*B*a*b^2*x^(13/2) + 2/13*A*b^3*x^(13/2) + 2/3*B*a^2*b*x^(9/2) + 2/3*A*a*b^2*x^(9/2) + 2/5*B*a^3*x^(5/2) + 6/5*A*a^2*b*x^(5/2) + 2*A*a^3*sqrt(x)","A",0
364,1,77,0,0.297826," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, B b^{3} x^{\frac{15}{2}} + \frac{6}{11} \, B a b^{2} x^{\frac{11}{2}} + \frac{2}{11} \, A b^{3} x^{\frac{11}{2}} + \frac{6}{7} \, B a^{2} b x^{\frac{7}{2}} + \frac{6}{7} \, A a b^{2} x^{\frac{7}{2}} + \frac{2}{3} \, B a^{3} x^{\frac{3}{2}} + 2 \, A a^{2} b x^{\frac{3}{2}} - \frac{2 \, A a^{3}}{\sqrt{x}}"," ",0,"2/15*B*b^3*x^(15/2) + 6/11*B*a*b^2*x^(11/2) + 2/11*A*b^3*x^(11/2) + 6/7*B*a^2*b*x^(7/2) + 6/7*A*a*b^2*x^(7/2) + 2/3*B*a^3*x^(3/2) + 2*A*a^2*b*x^(3/2) - 2*A*a^3/sqrt(x)","A",0
365,1,77,0,0.408549," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(5/2),x, algorithm=""giac"")","\frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{2}{3} \, B a b^{2} x^{\frac{9}{2}} + \frac{2}{9} \, A b^{3} x^{\frac{9}{2}} + \frac{6}{5} \, B a^{2} b x^{\frac{5}{2}} + \frac{6}{5} \, A a b^{2} x^{\frac{5}{2}} + 2 \, B a^{3} \sqrt{x} + 6 \, A a^{2} b \sqrt{x} - \frac{2 \, A a^{3}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/13*B*b^3*x^(13/2) + 2/3*B*a*b^2*x^(9/2) + 2/9*A*b^3*x^(9/2) + 6/5*B*a^2*b*x^(5/2) + 6/5*A*a*b^2*x^(5/2) + 2*B*a^3*sqrt(x) + 6*A*a^2*b*sqrt(x) - 2/3*A*a^3/x^(3/2)","A",0
366,1,79,0,0.285004," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(7/2),x, algorithm=""giac"")","\frac{2}{11} \, B b^{3} x^{\frac{11}{2}} + \frac{6}{7} \, B a b^{2} x^{\frac{7}{2}} + \frac{2}{7} \, A b^{3} x^{\frac{7}{2}} + 2 \, B a^{2} b x^{\frac{3}{2}} + 2 \, A a b^{2} x^{\frac{3}{2}} - \frac{2 \, {\left(5 \, B a^{3} x^{2} + 15 \, A a^{2} b x^{2} + A a^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*B*b^3*x^(11/2) + 6/7*B*a*b^2*x^(7/2) + 2/7*A*b^3*x^(7/2) + 2*B*a^2*b*x^(3/2) + 2*A*a*b^2*x^(3/2) - 2/5*(5*B*a^3*x^2 + 15*A*a^2*b*x^2 + A*a^3)/x^(5/2)","A",0
367,1,298,0,0.371385," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a^{2} - \left(a b^{3}\right)^{\frac{1}{4}} A a b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a^{2} - \left(a b^{3}\right)^{\frac{1}{4}} A a b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a^{2} - \left(a b^{3}\right)^{\frac{1}{4}} A a b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a^{2} - \left(a b^{3}\right)^{\frac{1}{4}} A a b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{4}} + \frac{2 \, {\left(5 \, B b^{8} x^{\frac{9}{2}} - 9 \, B a b^{7} x^{\frac{5}{2}} + 9 \, A b^{8} x^{\frac{5}{2}} + 45 \, B a^{2} b^{6} \sqrt{x} - 45 \, A a b^{7} \sqrt{x}\right)}}{45 \, b^{9}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(1/4)*B*a^2 - (a*b^3)^(1/4)*A*a*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^4 - 1/2*sqrt(2)*((a*b^3)^(1/4)*B*a^2 - (a*b^3)^(1/4)*A*a*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^4 - 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a^2 - (a*b^3)^(1/4)*A*a*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^4 + 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a^2 - (a*b^3)^(1/4)*A*a*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^4 + 2/45*(5*B*b^8*x^(9/2) - 9*B*a*b^7*x^(5/2) + 9*A*b^8*x^(5/2) + 45*B*a^2*b^6*sqrt(x) - 45*A*a*b^7*sqrt(x))/b^9","A",0
368,1,264,0,0.325380," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{5}} + \frac{2 \, {\left(3 \, B b^{6} x^{\frac{7}{2}} - 7 \, B a b^{5} x^{\frac{3}{2}} + 7 \, A b^{6} x^{\frac{3}{2}}\right)}}{21 \, b^{7}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^5 + 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^5 - 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^5 + 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^5 + 2/21*(3*B*b^6*x^(7/2) - 7*B*a*b^5*x^(3/2) + 7*A*b^6*x^(3/2))/b^7","A",0
369,1,263,0,0.407772," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{3}} + \frac{2 \, {\left(B b^{4} x^{\frac{5}{2}} - 5 \, B a b^{3} \sqrt{x} + 5 \, A b^{4} \sqrt{x}\right)}}{5 \, b^{5}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^3 + 1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^3 + 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^3 - 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^3 + 2/5*(B*b^4*x^(5/2) - 5*B*a*b^3*sqrt(x) + 5*A*b^4*sqrt(x))/b^5","A",0
370,1,251,0,0.416884," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, B x^{\frac{3}{2}}}{3 \, b} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{4}}"," ",0,"2/3*B*x^(3/2)/b - 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) - 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) + 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4) - 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4)","A",0
371,1,251,0,0.417237," ","integrate((B*x^2+A)/(b*x^2+a)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{2}}"," ",0,"2*B*sqrt(x)/b - 1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^2) - 1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^2) - 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^2) + 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^2)","A",0
372,1,251,0,0.370376," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{2 \, A}{a \sqrt{x}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{3}}"," ",0,"-2*A/(a*sqrt(x)) + 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) + 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) - 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3) + 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3)","A",0
373,1,251,0,0.363506," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b} - \frac{2 \, A}{3 \, a x^{\frac{3}{2}}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b) + 1/2*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b) + 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b) - 1/4*sqrt(2)*((a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b) - 2/3*A/(a*x^(3/2))","A",0
374,1,268,0,0.348397," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{2}} - \frac{2 \, {\left(5 \, B a x^{2} - 5 \, A b x^{2} + A a\right)}}{5 \, a^{2} x^{\frac{5}{2}}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) - 1/2*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) + 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) - 1/4*sqrt(2)*((a*b^3)^(3/4)*B*a - (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) - 2/5*(5*B*a*x^2 - 5*A*b*x^2 + A*a)/(a^2*x^(5/2))","A",0
375,1,298,0,0.509680," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4}} + \frac{\sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{4}} + \frac{\sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, b^{4}} - \frac{\sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, b^{4}} - \frac{B a^{2} \sqrt{x} - A a b \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} b^{3}} + \frac{2 \, {\left(B b^{8} x^{\frac{5}{2}} - 10 \, B a b^{7} \sqrt{x} + 5 \, A b^{8} \sqrt{x}\right)}}{5 \, b^{10}}"," ",0,"1/8*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - 5*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^4 + 1/8*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - 5*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^4 + 1/16*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - 5*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^4 - 1/16*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - 5*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^4 - 1/2*(B*a^2*sqrt(x) - A*a*b*sqrt(x))/((b*x^2 + a)*b^3) + 2/5*(B*b^8*x^(5/2) - 10*B*a*b^7*sqrt(x) + 5*A*b^8*sqrt(x))/b^10","A",0
376,1,283,0,0.418628," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, B x^{\frac{3}{2}}}{3 \, b^{2}} + \frac{B a x^{\frac{3}{2}} - A b x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} b^{2}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{5}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{5}} + \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{5}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{5}}"," ",0,"2/3*B*x^(3/2)/b^2 + 1/2*(B*a*x^(3/2) - A*b*x^(3/2))/((b*x^2 + a)*b^2) - 1/8*sqrt(2)*(7*(a*b^3)^(3/4)*B*a - 3*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^5) - 1/8*sqrt(2)*(7*(a*b^3)^(3/4)*B*a - 3*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^5) + 1/16*sqrt(2)*(7*(a*b^3)^(3/4)*B*a - 3*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^5) - 1/16*sqrt(2)*(7*(a*b^3)^(3/4)*B*a - 3*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^5)","A",0
377,1,283,0,0.434342," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{2}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{3}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{3}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{3}} + \frac{B a \sqrt{x} - A b \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} b^{2}}"," ",0,"2*B*sqrt(x)/b^2 - 1/8*sqrt(2)*(5*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^3) - 1/8*sqrt(2)*(5*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^3) - 1/16*sqrt(2)*(5*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^3) + 1/16*sqrt(2)*(5*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^3) + 1/2*(B*a*sqrt(x) - A*b*sqrt(x))/((b*x^2 + a)*b^2)","A",0
378,1,273,0,0.365355," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B a x^{\frac{3}{2}} - A b x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} a b} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{4}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{4}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{4}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{4}}"," ",0,"-1/2*(B*a*x^(3/2) - A*b*x^(3/2))/((b*x^2 + a)*a*b) + 1/8*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^4) + 1/8*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^4) - 1/16*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^4) + 1/16*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^4)","A",0
379,1,273,0,0.378161," ","integrate((B*x^2+A)/(b*x^2+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{2}} - \frac{B a \sqrt{x} - A b \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} a b}"," ",0,"1/8*sqrt(2)*((a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^2) + 1/8*sqrt(2)*((a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^2) + 1/16*sqrt(2)*((a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^2) - 1/16*sqrt(2)*((a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^2) - 1/2*(B*a*sqrt(x) - A*b*sqrt(x))/((b*x^2 + a)*a*b)","A",0
380,1,278,0,0.463520," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{B a x^{2} - 5 \, A b x^{2} - 4 \, A a}{2 \, {\left(b x^{\frac{5}{2}} + a \sqrt{x}\right)} a^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{3}}"," ",0,"1/2*(B*a*x^2 - 5*A*b*x^2 - 4*A*a)/((b*x^(5/2) + a*sqrt(x))*a^2) + 1/8*sqrt(2)*((a*b^3)^(3/4)*B*a - 5*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^3) + 1/8*sqrt(2)*((a*b^3)^(3/4)*B*a - 5*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^3) - 1/16*sqrt(2)*((a*b^3)^(3/4)*B*a - 5*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^3) + 1/16*sqrt(2)*((a*b^3)^(3/4)*B*a - 5*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^3)","A",0
381,1,283,0,0.496570," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b} + \frac{B a \sqrt{x} - A b \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} a^{2}} - \frac{2 \, A}{3 \, a^{2} x^{\frac{3}{2}}}"," ",0,"1/8*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 7*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b) + 1/8*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 7*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b) + 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 7*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b) - 1/16*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 7*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b) + 1/2*(B*a*sqrt(x) - A*b*sqrt(x))/((b*x^2 + a)*a^2) - 2/3*A/(a^2*x^(3/2))","A",0
382,1,303,0,0.536819," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{B a b x^{\frac{3}{2}} - A b^{2} x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} a^{3}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{2}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{2}} - \frac{2 \, {\left(5 \, B a x^{2} - 10 \, A b x^{2} + A a\right)}}{5 \, a^{3} x^{\frac{5}{2}}}"," ",0,"-1/2*(B*a*b*x^(3/2) - A*b^2*x^(3/2))/((b*x^2 + a)*a^3) - 1/8*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) - 1/8*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) + 1/16*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) - 1/16*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) - 2/5*(5*B*a*x^2 - 10*A*b*x^2 + A*a)/(a^3*x^(5/2))","A",0
383,1,304,0,0.406365," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{2 \, B \sqrt{x}}{b^{3}} - \frac{5 \, \sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a b^{4}} - \frac{5 \, \sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a b^{4}} - \frac{5 \, \sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a b^{4}} + \frac{5 \, \sqrt{2} {\left(9 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a b^{4}} + \frac{17 \, B a b x^{\frac{5}{2}} - 9 \, A b^{2} x^{\frac{5}{2}} + 13 \, B a^{2} \sqrt{x} - 5 \, A a b \sqrt{x}}{16 \, {\left(b x^{2} + a\right)}^{2} b^{3}}"," ",0,"2*B*sqrt(x)/b^3 - 5/64*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) - 5/64*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) - 5/128*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4) + 5/128*sqrt(2)*(9*(a*b^3)^(1/4)*B*a - (a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4) + 1/16*(17*B*a*b*x^(5/2) - 9*A*b^2*x^(5/2) + 13*B*a^2*sqrt(x) - 5*A*a*b*sqrt(x))/((b*x^2 + a)^2*b^3)","A",0
384,1,293,0,0.467011," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{11 \, B a b x^{\frac{7}{2}} - 3 \, A b^{2} x^{\frac{7}{2}} + 7 \, B a^{2} x^{\frac{3}{2}} + A a b x^{\frac{3}{2}}}{16 \, {\left(b x^{2} + a\right)}^{2} a b^{2}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} b^{5}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} b^{5}} - \frac{3 \, \sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{2} b^{5}} + \frac{3 \, \sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{2} b^{5}}"," ",0,"-1/16*(11*B*a*b*x^(7/2) - 3*A*b^2*x^(7/2) + 7*B*a^2*x^(3/2) + A*a*b*x^(3/2))/((b*x^2 + a)^2*a*b^2) + 3/64*sqrt(2)*(7*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^5) + 3/64*sqrt(2)*(7*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^5) - 3/128*sqrt(2)*(7*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^5) + 3/128*sqrt(2)*(7*(a*b^3)^(3/4)*B*a + (a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^5)","A",0
385,1,298,0,0.518904," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} B a + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{2} b^{3}} - \frac{9 \, B a b x^{\frac{5}{2}} - A b^{2} x^{\frac{5}{2}} + 5 \, B a^{2} \sqrt{x} + 3 \, A a b \sqrt{x}}{16 \, {\left(b x^{2} + a\right)}^{2} a b^{2}}"," ",0,"1/64*sqrt(2)*(5*(a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) + 1/64*sqrt(2)*(5*(a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) + 1/128*sqrt(2)*(5*(a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3) - 1/128*sqrt(2)*(5*(a*b^3)^(1/4)*B*a + 3*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3) - 1/16*(9*B*a*b*x^(5/2) - A*b^2*x^(5/2) + 5*B*a^2*sqrt(x) + 3*A*a*b*sqrt(x))/((b*x^2 + a)^2*a*b^2)","A",0
386,1,298,0,0.521948," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, B a b x^{\frac{7}{2}} + 5 \, A b^{2} x^{\frac{7}{2}} - B a^{2} x^{\frac{3}{2}} + 9 \, A a b x^{\frac{3}{2}}}{16 \, {\left(b x^{2} + a\right)}^{2} a^{2} b} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b^{4}} - \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} B a + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{3} b^{4}}"," ",0,"1/16*(3*B*a*b*x^(7/2) + 5*A*b^2*x^(7/2) - B*a^2*x^(3/2) + 9*A*a*b*x^(3/2))/((b*x^2 + a)^2*a^2*b) + 1/64*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + 5*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^4) + 1/64*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + 5*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^4) - 1/128*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + 5*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^4) + 1/128*sqrt(2)*(3*(a*b^3)^(3/4)*B*a + 5*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^4)","A",0
387,1,293,0,0.439038," ","integrate((B*x^2+A)/(b*x^2+a)^3/x^(1/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b^{2}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{3} b^{2}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{3} b^{2}} - \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} B a + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{3} b^{2}} + \frac{B a b x^{\frac{5}{2}} + 7 \, A b^{2} x^{\frac{5}{2}} - 3 \, B a^{2} \sqrt{x} + 11 \, A a b \sqrt{x}}{16 \, {\left(b x^{2} + a\right)}^{2} a^{2} b}"," ",0,"3/64*sqrt(2)*((a*b^3)^(1/4)*B*a + 7*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) + 3/64*sqrt(2)*((a*b^3)^(1/4)*B*a + 7*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) + 3/128*sqrt(2)*((a*b^3)^(1/4)*B*a + 7*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) - 3/128*sqrt(2)*((a*b^3)^(1/4)*B*a + 7*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) + 1/16*(B*a*b*x^(5/2) + 7*A*b^2*x^(5/2) - 3*B*a^2*sqrt(x) + 11*A*a*b*sqrt(x))/((b*x^2 + a)^2*a^2*b)","A",0
388,1,300,0,0.409122," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{2 \, A}{a^{3} \sqrt{x}} + \frac{5 \, B a b x^{\frac{7}{2}} - 13 \, A b^{2} x^{\frac{7}{2}} + 9 \, B a^{2} x^{\frac{3}{2}} - 17 \, A a b x^{\frac{3}{2}}}{16 \, {\left(b x^{2} + a\right)}^{2} a^{3}} + \frac{5 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} b^{3}} + \frac{5 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} b^{3}} - \frac{5 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{4} b^{3}} + \frac{5 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} B a - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{4} b^{3}}"," ",0,"-2*A/(a^3*sqrt(x)) + 1/16*(5*B*a*b*x^(7/2) - 13*A*b^2*x^(7/2) + 9*B*a^2*x^(3/2) - 17*A*a*b*x^(3/2))/((b*x^2 + a)^2*a^3) + 5/64*sqrt(2)*((a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^3) + 5/64*sqrt(2)*((a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^3) - 5/128*sqrt(2)*((a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^3) + 5/128*sqrt(2)*((a*b^3)^(3/4)*B*a - 9*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^3)","A",0
389,1,304,0,0.445158," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{7 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} b} + \frac{7 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{4} b} + \frac{7 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{4} b} - \frac{7 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} B a - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{4} b} - \frac{2 \, A}{3 \, a^{3} x^{\frac{3}{2}}} + \frac{7 \, B a b x^{\frac{5}{2}} - 15 \, A b^{2} x^{\frac{5}{2}} + 11 \, B a^{2} \sqrt{x} - 19 \, A a b \sqrt{x}}{16 \, {\left(b x^{2} + a\right)}^{2} a^{3}}"," ",0,"7/64*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 11*(a*b^3)^(1/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b) + 7/64*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 11*(a*b^3)^(1/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b) + 7/128*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 11*(a*b^3)^(1/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b) - 7/128*sqrt(2)*(3*(a*b^3)^(1/4)*B*a - 11*(a*b^3)^(1/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b) - 2/3*A/(a^3*x^(3/2)) + 1/16*(7*B*a*b*x^(5/2) - 15*A*b^2*x^(5/2) + 11*B*a^2*sqrt(x) - 19*A*a*b*sqrt(x))/((b*x^2 + a)^2*a^3)","A",0
390,1,326,0,0.540542," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{9 \, \sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{5} b^{2}} - \frac{9 \, \sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \, a^{5} b^{2}} + \frac{9 \, \sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{5} b^{2}} - \frac{9 \, \sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} B a - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} A b\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{128 \, a^{5} b^{2}} - \frac{13 \, B a b^{2} x^{\frac{7}{2}} - 21 \, A b^{3} x^{\frac{7}{2}} + 17 \, B a^{2} b x^{\frac{3}{2}} - 25 \, A a b^{2} x^{\frac{3}{2}}}{16 \, {\left(b x^{2} + a\right)}^{2} a^{4}} - \frac{2 \, {\left(5 \, B a x^{2} - 15 \, A b x^{2} + A a\right)}}{5 \, a^{4} x^{\frac{5}{2}}}"," ",0,"-9/64*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 13*(a*b^3)^(3/4)*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^5*b^2) - 9/64*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 13*(a*b^3)^(3/4)*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^5*b^2) + 9/128*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 13*(a*b^3)^(3/4)*A*b)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^5*b^2) - 9/128*sqrt(2)*(5*(a*b^3)^(3/4)*B*a - 13*(a*b^3)^(3/4)*A*b)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^5*b^2) - 1/16*(13*B*a*b^2*x^(7/2) - 21*A*b^3*x^(7/2) + 17*B*a^2*b*x^(3/2) - 25*A*a*b^2*x^(3/2))/((b*x^2 + a)^2*a^4) - 2/5*(5*B*a*x^2 - 15*A*b*x^2 + A*a)/(a^4*x^(5/2))","A",0
391,1,53,0,0.399187," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{2}{21} \, b^{2} d x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} c x^{\frac{17}{2}} + \frac{4}{17} \, a b d x^{\frac{17}{2}} + \frac{4}{13} \, a b c x^{\frac{13}{2}} + \frac{2}{13} \, a^{2} d x^{\frac{13}{2}} + \frac{2}{9} \, a^{2} c x^{\frac{9}{2}}"," ",0,"2/21*b^2*d*x^(21/2) + 2/17*b^2*c*x^(17/2) + 4/17*a*b*d*x^(17/2) + 4/13*a*b*c*x^(13/2) + 2/13*a^2*d*x^(13/2) + 2/9*a^2*c*x^(9/2)","A",0
392,1,53,0,0.362872," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{2}{19} \, b^{2} d x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} c x^{\frac{15}{2}} + \frac{4}{15} \, a b d x^{\frac{15}{2}} + \frac{4}{11} \, a b c x^{\frac{11}{2}} + \frac{2}{11} \, a^{2} d x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} c x^{\frac{7}{2}}"," ",0,"2/19*b^2*d*x^(19/2) + 2/15*b^2*c*x^(15/2) + 4/15*a*b*d*x^(15/2) + 4/11*a*b*c*x^(11/2) + 2/11*a^2*d*x^(11/2) + 2/7*a^2*c*x^(7/2)","A",0
393,1,53,0,0.317558," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{2}{17} \, b^{2} d x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} c x^{\frac{13}{2}} + \frac{4}{13} \, a b d x^{\frac{13}{2}} + \frac{4}{9} \, a b c x^{\frac{9}{2}} + \frac{2}{9} \, a^{2} d x^{\frac{9}{2}} + \frac{2}{5} \, a^{2} c x^{\frac{5}{2}}"," ",0,"2/17*b^2*d*x^(17/2) + 2/13*b^2*c*x^(13/2) + 4/13*a*b*d*x^(13/2) + 4/9*a*b*c*x^(9/2) + 2/9*a^2*d*x^(9/2) + 2/5*a^2*c*x^(5/2)","A",0
394,1,53,0,0.330616," ","integrate((b*x^2+a)^2*(d*x^2+c)*x^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, b^{2} d x^{\frac{15}{2}} + \frac{2}{11} \, b^{2} c x^{\frac{11}{2}} + \frac{4}{11} \, a b d x^{\frac{11}{2}} + \frac{4}{7} \, a b c x^{\frac{7}{2}} + \frac{2}{7} \, a^{2} d x^{\frac{7}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{3}{2}}"," ",0,"2/15*b^2*d*x^(15/2) + 2/11*b^2*c*x^(11/2) + 4/11*a*b*d*x^(11/2) + 4/7*a*b*c*x^(7/2) + 2/7*a^2*d*x^(7/2) + 2/3*a^2*c*x^(3/2)","A",0
395,1,53,0,0.282007," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(1/2),x, algorithm=""giac"")","\frac{2}{13} \, b^{2} d x^{\frac{13}{2}} + \frac{2}{9} \, b^{2} c x^{\frac{9}{2}} + \frac{4}{9} \, a b d x^{\frac{9}{2}} + \frac{4}{5} \, a b c x^{\frac{5}{2}} + \frac{2}{5} \, a^{2} d x^{\frac{5}{2}} + 2 \, a^{2} c \sqrt{x}"," ",0,"2/13*b^2*d*x^(13/2) + 2/9*b^2*c*x^(9/2) + 4/9*a*b*d*x^(9/2) + 4/5*a*b*c*x^(5/2) + 2/5*a^2*d*x^(5/2) + 2*a^2*c*sqrt(x)","A",0
396,1,53,0,0.270504," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(3/2),x, algorithm=""giac"")","\frac{2}{11} \, b^{2} d x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} c x^{\frac{7}{2}} + \frac{4}{7} \, a b d x^{\frac{7}{2}} + \frac{4}{3} \, a b c x^{\frac{3}{2}} + \frac{2}{3} \, a^{2} d x^{\frac{3}{2}} - \frac{2 \, a^{2} c}{\sqrt{x}}"," ",0,"2/11*b^2*d*x^(11/2) + 2/7*b^2*c*x^(7/2) + 4/7*a*b*d*x^(7/2) + 4/3*a*b*c*x^(3/2) + 2/3*a^2*d*x^(3/2) - 2*a^2*c/sqrt(x)","A",0
397,1,53,0,0.329244," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(5/2),x, algorithm=""giac"")","\frac{2}{9} \, b^{2} d x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} c x^{\frac{5}{2}} + \frac{4}{5} \, a b d x^{\frac{5}{2}} + 4 \, a b c \sqrt{x} + 2 \, a^{2} d \sqrt{x} - \frac{2 \, a^{2} c}{3 \, x^{\frac{3}{2}}}"," ",0,"2/9*b^2*d*x^(9/2) + 2/5*b^2*c*x^(5/2) + 4/5*a*b*d*x^(5/2) + 4*a*b*c*sqrt(x) + 2*a^2*d*sqrt(x) - 2/3*a^2*c/x^(3/2)","A",0
398,1,55,0,0.345476," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(7/2),x, algorithm=""giac"")","\frac{2}{7} \, b^{2} d x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} c x^{\frac{3}{2}} + \frac{4}{3} \, a b d x^{\frac{3}{2}} - \frac{2 \, {\left(10 \, a b c x^{2} + 5 \, a^{2} d x^{2} + a^{2} c\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/7*b^2*d*x^(7/2) + 2/3*b^2*c*x^(3/2) + 4/3*a*b*d*x^(3/2) - 2/5*(10*a*b*c*x^2 + 5*a^2*d*x^2 + a^2*c)/x^(5/2)","A",0
399,1,94,0,0.341681," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{2}{25} \, b^{2} d^{2} x^{\frac{25}{2}} + \frac{4}{21} \, b^{2} c d x^{\frac{21}{2}} + \frac{4}{21} \, a b d^{2} x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} c^{2} x^{\frac{17}{2}} + \frac{8}{17} \, a b c d x^{\frac{17}{2}} + \frac{2}{17} \, a^{2} d^{2} x^{\frac{17}{2}} + \frac{4}{13} \, a b c^{2} x^{\frac{13}{2}} + \frac{4}{13} \, a^{2} c d x^{\frac{13}{2}} + \frac{2}{9} \, a^{2} c^{2} x^{\frac{9}{2}}"," ",0,"2/25*b^2*d^2*x^(25/2) + 4/21*b^2*c*d*x^(21/2) + 4/21*a*b*d^2*x^(21/2) + 2/17*b^2*c^2*x^(17/2) + 8/17*a*b*c*d*x^(17/2) + 2/17*a^2*d^2*x^(17/2) + 4/13*a*b*c^2*x^(13/2) + 4/13*a^2*c*d*x^(13/2) + 2/9*a^2*c^2*x^(9/2)","A",0
400,1,94,0,0.360633," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{2}{23} \, b^{2} d^{2} x^{\frac{23}{2}} + \frac{4}{19} \, b^{2} c d x^{\frac{19}{2}} + \frac{4}{19} \, a b d^{2} x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} c^{2} x^{\frac{15}{2}} + \frac{8}{15} \, a b c d x^{\frac{15}{2}} + \frac{2}{15} \, a^{2} d^{2} x^{\frac{15}{2}} + \frac{4}{11} \, a b c^{2} x^{\frac{11}{2}} + \frac{4}{11} \, a^{2} c d x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} c^{2} x^{\frac{7}{2}}"," ",0,"2/23*b^2*d^2*x^(23/2) + 4/19*b^2*c*d*x^(19/2) + 4/19*a*b*d^2*x^(19/2) + 2/15*b^2*c^2*x^(15/2) + 8/15*a*b*c*d*x^(15/2) + 2/15*a^2*d^2*x^(15/2) + 4/11*a*b*c^2*x^(11/2) + 4/11*a^2*c*d*x^(11/2) + 2/7*a^2*c^2*x^(7/2)","A",0
401,1,94,0,0.440375," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{2}{21} \, b^{2} d^{2} x^{\frac{21}{2}} + \frac{4}{17} \, b^{2} c d x^{\frac{17}{2}} + \frac{4}{17} \, a b d^{2} x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} c^{2} x^{\frac{13}{2}} + \frac{8}{13} \, a b c d x^{\frac{13}{2}} + \frac{2}{13} \, a^{2} d^{2} x^{\frac{13}{2}} + \frac{4}{9} \, a b c^{2} x^{\frac{9}{2}} + \frac{4}{9} \, a^{2} c d x^{\frac{9}{2}} + \frac{2}{5} \, a^{2} c^{2} x^{\frac{5}{2}}"," ",0,"2/21*b^2*d^2*x^(21/2) + 4/17*b^2*c*d*x^(17/2) + 4/17*a*b*d^2*x^(17/2) + 2/13*b^2*c^2*x^(13/2) + 8/13*a*b*c*d*x^(13/2) + 2/13*a^2*d^2*x^(13/2) + 4/9*a*b*c^2*x^(9/2) + 4/9*a^2*c*d*x^(9/2) + 2/5*a^2*c^2*x^(5/2)","A",0
402,1,94,0,0.417955," ","integrate((b*x^2+a)^2*(d*x^2+c)^2*x^(1/2),x, algorithm=""giac"")","\frac{2}{19} \, b^{2} d^{2} x^{\frac{19}{2}} + \frac{4}{15} \, b^{2} c d x^{\frac{15}{2}} + \frac{4}{15} \, a b d^{2} x^{\frac{15}{2}} + \frac{2}{11} \, b^{2} c^{2} x^{\frac{11}{2}} + \frac{8}{11} \, a b c d x^{\frac{11}{2}} + \frac{2}{11} \, a^{2} d^{2} x^{\frac{11}{2}} + \frac{4}{7} \, a b c^{2} x^{\frac{7}{2}} + \frac{4}{7} \, a^{2} c d x^{\frac{7}{2}} + \frac{2}{3} \, a^{2} c^{2} x^{\frac{3}{2}}"," ",0,"2/19*b^2*d^2*x^(19/2) + 4/15*b^2*c*d*x^(15/2) + 4/15*a*b*d^2*x^(15/2) + 2/11*b^2*c^2*x^(11/2) + 8/11*a*b*c*d*x^(11/2) + 2/11*a^2*d^2*x^(11/2) + 4/7*a*b*c^2*x^(7/2) + 4/7*a^2*c*d*x^(7/2) + 2/3*a^2*c^2*x^(3/2)","A",0
403,1,94,0,0.307801," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(1/2),x, algorithm=""giac"")","\frac{2}{17} \, b^{2} d^{2} x^{\frac{17}{2}} + \frac{4}{13} \, b^{2} c d x^{\frac{13}{2}} + \frac{4}{13} \, a b d^{2} x^{\frac{13}{2}} + \frac{2}{9} \, b^{2} c^{2} x^{\frac{9}{2}} + \frac{8}{9} \, a b c d x^{\frac{9}{2}} + \frac{2}{9} \, a^{2} d^{2} x^{\frac{9}{2}} + \frac{4}{5} \, a b c^{2} x^{\frac{5}{2}} + \frac{4}{5} \, a^{2} c d x^{\frac{5}{2}} + 2 \, a^{2} c^{2} \sqrt{x}"," ",0,"2/17*b^2*d^2*x^(17/2) + 4/13*b^2*c*d*x^(13/2) + 4/13*a*b*d^2*x^(13/2) + 2/9*b^2*c^2*x^(9/2) + 8/9*a*b*c*d*x^(9/2) + 2/9*a^2*d^2*x^(9/2) + 4/5*a*b*c^2*x^(5/2) + 4/5*a^2*c*d*x^(5/2) + 2*a^2*c^2*sqrt(x)","A",0
404,1,94,0,0.391798," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, b^{2} d^{2} x^{\frac{15}{2}} + \frac{4}{11} \, b^{2} c d x^{\frac{11}{2}} + \frac{4}{11} \, a b d^{2} x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} c^{2} x^{\frac{7}{2}} + \frac{8}{7} \, a b c d x^{\frac{7}{2}} + \frac{2}{7} \, a^{2} d^{2} x^{\frac{7}{2}} + \frac{4}{3} \, a b c^{2} x^{\frac{3}{2}} + \frac{4}{3} \, a^{2} c d x^{\frac{3}{2}} - \frac{2 \, a^{2} c^{2}}{\sqrt{x}}"," ",0,"2/15*b^2*d^2*x^(15/2) + 4/11*b^2*c*d*x^(11/2) + 4/11*a*b*d^2*x^(11/2) + 2/7*b^2*c^2*x^(7/2) + 8/7*a*b*c*d*x^(7/2) + 2/7*a^2*d^2*x^(7/2) + 4/3*a*b*c^2*x^(3/2) + 4/3*a^2*c*d*x^(3/2) - 2*a^2*c^2/sqrt(x)","A",0
405,1,94,0,0.368230," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(5/2),x, algorithm=""giac"")","\frac{2}{13} \, b^{2} d^{2} x^{\frac{13}{2}} + \frac{4}{9} \, b^{2} c d x^{\frac{9}{2}} + \frac{4}{9} \, a b d^{2} x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} c^{2} x^{\frac{5}{2}} + \frac{8}{5} \, a b c d x^{\frac{5}{2}} + \frac{2}{5} \, a^{2} d^{2} x^{\frac{5}{2}} + 4 \, a b c^{2} \sqrt{x} + 4 \, a^{2} c d \sqrt{x} - \frac{2 \, a^{2} c^{2}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/13*b^2*d^2*x^(13/2) + 4/9*b^2*c*d*x^(9/2) + 4/9*a*b*d^2*x^(9/2) + 2/5*b^2*c^2*x^(5/2) + 8/5*a*b*c*d*x^(5/2) + 2/5*a^2*d^2*x^(5/2) + 4*a*b*c^2*sqrt(x) + 4*a^2*c*d*sqrt(x) - 2/3*a^2*c^2/x^(3/2)","A",0
406,1,96,0,0.431797," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(7/2),x, algorithm=""giac"")","\frac{2}{11} \, b^{2} d^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b^{2} c d x^{\frac{7}{2}} + \frac{4}{7} \, a b d^{2} x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} c^{2} x^{\frac{3}{2}} + \frac{8}{3} \, a b c d x^{\frac{3}{2}} + \frac{2}{3} \, a^{2} d^{2} x^{\frac{3}{2}} - \frac{2 \, {\left(10 \, a b c^{2} x^{2} + 10 \, a^{2} c d x^{2} + a^{2} c^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*b^2*d^2*x^(11/2) + 4/7*b^2*c*d*x^(7/2) + 4/7*a*b*d^2*x^(7/2) + 2/3*b^2*c^2*x^(3/2) + 8/3*a*b*c*d*x^(3/2) + 2/3*a^2*d^2*x^(3/2) - 2/5*(10*a*b*c^2*x^2 + 10*a^2*c*d*x^2 + a^2*c^2)/x^(5/2)","A",0
407,1,135,0,0.348019," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{2}{29} \, b^{2} d^{3} x^{\frac{29}{2}} + \frac{6}{25} \, b^{2} c d^{2} x^{\frac{25}{2}} + \frac{4}{25} \, a b d^{3} x^{\frac{25}{2}} + \frac{2}{7} \, b^{2} c^{2} d x^{\frac{21}{2}} + \frac{4}{7} \, a b c d^{2} x^{\frac{21}{2}} + \frac{2}{21} \, a^{2} d^{3} x^{\frac{21}{2}} + \frac{2}{17} \, b^{2} c^{3} x^{\frac{17}{2}} + \frac{12}{17} \, a b c^{2} d x^{\frac{17}{2}} + \frac{6}{17} \, a^{2} c d^{2} x^{\frac{17}{2}} + \frac{4}{13} \, a b c^{3} x^{\frac{13}{2}} + \frac{6}{13} \, a^{2} c^{2} d x^{\frac{13}{2}} + \frac{2}{9} \, a^{2} c^{3} x^{\frac{9}{2}}"," ",0,"2/29*b^2*d^3*x^(29/2) + 6/25*b^2*c*d^2*x^(25/2) + 4/25*a*b*d^3*x^(25/2) + 2/7*b^2*c^2*d*x^(21/2) + 4/7*a*b*c*d^2*x^(21/2) + 2/21*a^2*d^3*x^(21/2) + 2/17*b^2*c^3*x^(17/2) + 12/17*a*b*c^2*d*x^(17/2) + 6/17*a^2*c*d^2*x^(17/2) + 4/13*a*b*c^3*x^(13/2) + 6/13*a^2*c^2*d*x^(13/2) + 2/9*a^2*c^3*x^(9/2)","A",0
408,1,135,0,0.443219," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{2}{27} \, b^{2} d^{3} x^{\frac{27}{2}} + \frac{6}{23} \, b^{2} c d^{2} x^{\frac{23}{2}} + \frac{4}{23} \, a b d^{3} x^{\frac{23}{2}} + \frac{6}{19} \, b^{2} c^{2} d x^{\frac{19}{2}} + \frac{12}{19} \, a b c d^{2} x^{\frac{19}{2}} + \frac{2}{19} \, a^{2} d^{3} x^{\frac{19}{2}} + \frac{2}{15} \, b^{2} c^{3} x^{\frac{15}{2}} + \frac{4}{5} \, a b c^{2} d x^{\frac{15}{2}} + \frac{2}{5} \, a^{2} c d^{2} x^{\frac{15}{2}} + \frac{4}{11} \, a b c^{3} x^{\frac{11}{2}} + \frac{6}{11} \, a^{2} c^{2} d x^{\frac{11}{2}} + \frac{2}{7} \, a^{2} c^{3} x^{\frac{7}{2}}"," ",0,"2/27*b^2*d^3*x^(27/2) + 6/23*b^2*c*d^2*x^(23/2) + 4/23*a*b*d^3*x^(23/2) + 6/19*b^2*c^2*d*x^(19/2) + 12/19*a*b*c*d^2*x^(19/2) + 2/19*a^2*d^3*x^(19/2) + 2/15*b^2*c^3*x^(15/2) + 4/5*a*b*c^2*d*x^(15/2) + 2/5*a^2*c*d^2*x^(15/2) + 4/11*a*b*c^3*x^(11/2) + 6/11*a^2*c^2*d*x^(11/2) + 2/7*a^2*c^3*x^(7/2)","A",0
409,1,135,0,0.307246," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{2}{25} \, b^{2} d^{3} x^{\frac{25}{2}} + \frac{2}{7} \, b^{2} c d^{2} x^{\frac{21}{2}} + \frac{4}{21} \, a b d^{3} x^{\frac{21}{2}} + \frac{6}{17} \, b^{2} c^{2} d x^{\frac{17}{2}} + \frac{12}{17} \, a b c d^{2} x^{\frac{17}{2}} + \frac{2}{17} \, a^{2} d^{3} x^{\frac{17}{2}} + \frac{2}{13} \, b^{2} c^{3} x^{\frac{13}{2}} + \frac{12}{13} \, a b c^{2} d x^{\frac{13}{2}} + \frac{6}{13} \, a^{2} c d^{2} x^{\frac{13}{2}} + \frac{4}{9} \, a b c^{3} x^{\frac{9}{2}} + \frac{2}{3} \, a^{2} c^{2} d x^{\frac{9}{2}} + \frac{2}{5} \, a^{2} c^{3} x^{\frac{5}{2}}"," ",0,"2/25*b^2*d^3*x^(25/2) + 2/7*b^2*c*d^2*x^(21/2) + 4/21*a*b*d^3*x^(21/2) + 6/17*b^2*c^2*d*x^(17/2) + 12/17*a*b*c*d^2*x^(17/2) + 2/17*a^2*d^3*x^(17/2) + 2/13*b^2*c^3*x^(13/2) + 12/13*a*b*c^2*d*x^(13/2) + 6/13*a^2*c*d^2*x^(13/2) + 4/9*a*b*c^3*x^(9/2) + 2/3*a^2*c^2*d*x^(9/2) + 2/5*a^2*c^3*x^(5/2)","A",0
410,1,135,0,0.384502," ","integrate((b*x^2+a)^2*(d*x^2+c)^3*x^(1/2),x, algorithm=""giac"")","\frac{2}{23} \, b^{2} d^{3} x^{\frac{23}{2}} + \frac{6}{19} \, b^{2} c d^{2} x^{\frac{19}{2}} + \frac{4}{19} \, a b d^{3} x^{\frac{19}{2}} + \frac{2}{5} \, b^{2} c^{2} d x^{\frac{15}{2}} + \frac{4}{5} \, a b c d^{2} x^{\frac{15}{2}} + \frac{2}{15} \, a^{2} d^{3} x^{\frac{15}{2}} + \frac{2}{11} \, b^{2} c^{3} x^{\frac{11}{2}} + \frac{12}{11} \, a b c^{2} d x^{\frac{11}{2}} + \frac{6}{11} \, a^{2} c d^{2} x^{\frac{11}{2}} + \frac{4}{7} \, a b c^{3} x^{\frac{7}{2}} + \frac{6}{7} \, a^{2} c^{2} d x^{\frac{7}{2}} + \frac{2}{3} \, a^{2} c^{3} x^{\frac{3}{2}}"," ",0,"2/23*b^2*d^3*x^(23/2) + 6/19*b^2*c*d^2*x^(19/2) + 4/19*a*b*d^3*x^(19/2) + 2/5*b^2*c^2*d*x^(15/2) + 4/5*a*b*c*d^2*x^(15/2) + 2/15*a^2*d^3*x^(15/2) + 2/11*b^2*c^3*x^(11/2) + 12/11*a*b*c^2*d*x^(11/2) + 6/11*a^2*c*d^2*x^(11/2) + 4/7*a*b*c^3*x^(7/2) + 6/7*a^2*c^2*d*x^(7/2) + 2/3*a^2*c^3*x^(3/2)","A",0
411,1,135,0,0.289140," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(1/2),x, algorithm=""giac"")","\frac{2}{21} \, b^{2} d^{3} x^{\frac{21}{2}} + \frac{6}{17} \, b^{2} c d^{2} x^{\frac{17}{2}} + \frac{4}{17} \, a b d^{3} x^{\frac{17}{2}} + \frac{6}{13} \, b^{2} c^{2} d x^{\frac{13}{2}} + \frac{12}{13} \, a b c d^{2} x^{\frac{13}{2}} + \frac{2}{13} \, a^{2} d^{3} x^{\frac{13}{2}} + \frac{2}{9} \, b^{2} c^{3} x^{\frac{9}{2}} + \frac{4}{3} \, a b c^{2} d x^{\frac{9}{2}} + \frac{2}{3} \, a^{2} c d^{2} x^{\frac{9}{2}} + \frac{4}{5} \, a b c^{3} x^{\frac{5}{2}} + \frac{6}{5} \, a^{2} c^{2} d x^{\frac{5}{2}} + 2 \, a^{2} c^{3} \sqrt{x}"," ",0,"2/21*b^2*d^3*x^(21/2) + 6/17*b^2*c*d^2*x^(17/2) + 4/17*a*b*d^3*x^(17/2) + 6/13*b^2*c^2*d*x^(13/2) + 12/13*a*b*c*d^2*x^(13/2) + 2/13*a^2*d^3*x^(13/2) + 2/9*b^2*c^3*x^(9/2) + 4/3*a*b*c^2*d*x^(9/2) + 2/3*a^2*c*d^2*x^(9/2) + 4/5*a*b*c^3*x^(5/2) + 6/5*a^2*c^2*d*x^(5/2) + 2*a^2*c^3*sqrt(x)","A",0
412,1,135,0,0.306536," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(3/2),x, algorithm=""giac"")","\frac{2}{19} \, b^{2} d^{3} x^{\frac{19}{2}} + \frac{2}{5} \, b^{2} c d^{2} x^{\frac{15}{2}} + \frac{4}{15} \, a b d^{3} x^{\frac{15}{2}} + \frac{6}{11} \, b^{2} c^{2} d x^{\frac{11}{2}} + \frac{12}{11} \, a b c d^{2} x^{\frac{11}{2}} + \frac{2}{11} \, a^{2} d^{3} x^{\frac{11}{2}} + \frac{2}{7} \, b^{2} c^{3} x^{\frac{7}{2}} + \frac{12}{7} \, a b c^{2} d x^{\frac{7}{2}} + \frac{6}{7} \, a^{2} c d^{2} x^{\frac{7}{2}} + \frac{4}{3} \, a b c^{3} x^{\frac{3}{2}} + 2 \, a^{2} c^{2} d x^{\frac{3}{2}} - \frac{2 \, a^{2} c^{3}}{\sqrt{x}}"," ",0,"2/19*b^2*d^3*x^(19/2) + 2/5*b^2*c*d^2*x^(15/2) + 4/15*a*b*d^3*x^(15/2) + 6/11*b^2*c^2*d*x^(11/2) + 12/11*a*b*c*d^2*x^(11/2) + 2/11*a^2*d^3*x^(11/2) + 2/7*b^2*c^3*x^(7/2) + 12/7*a*b*c^2*d*x^(7/2) + 6/7*a^2*c*d^2*x^(7/2) + 4/3*a*b*c^3*x^(3/2) + 2*a^2*c^2*d*x^(3/2) - 2*a^2*c^3/sqrt(x)","A",0
413,1,135,0,0.445209," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(5/2),x, algorithm=""giac"")","\frac{2}{17} \, b^{2} d^{3} x^{\frac{17}{2}} + \frac{6}{13} \, b^{2} c d^{2} x^{\frac{13}{2}} + \frac{4}{13} \, a b d^{3} x^{\frac{13}{2}} + \frac{2}{3} \, b^{2} c^{2} d x^{\frac{9}{2}} + \frac{4}{3} \, a b c d^{2} x^{\frac{9}{2}} + \frac{2}{9} \, a^{2} d^{3} x^{\frac{9}{2}} + \frac{2}{5} \, b^{2} c^{3} x^{\frac{5}{2}} + \frac{12}{5} \, a b c^{2} d x^{\frac{5}{2}} + \frac{6}{5} \, a^{2} c d^{2} x^{\frac{5}{2}} + 4 \, a b c^{3} \sqrt{x} + 6 \, a^{2} c^{2} d \sqrt{x} - \frac{2 \, a^{2} c^{3}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/17*b^2*d^3*x^(17/2) + 6/13*b^2*c*d^2*x^(13/2) + 4/13*a*b*d^3*x^(13/2) + 2/3*b^2*c^2*d*x^(9/2) + 4/3*a*b*c*d^2*x^(9/2) + 2/9*a^2*d^3*x^(9/2) + 2/5*b^2*c^3*x^(5/2) + 12/5*a*b*c^2*d*x^(5/2) + 6/5*a^2*c*d^2*x^(5/2) + 4*a*b*c^3*sqrt(x) + 6*a^2*c^2*d*sqrt(x) - 2/3*a^2*c^3/x^(3/2)","A",0
414,1,137,0,0.336700," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, b^{2} d^{3} x^{\frac{15}{2}} + \frac{6}{11} \, b^{2} c d^{2} x^{\frac{11}{2}} + \frac{4}{11} \, a b d^{3} x^{\frac{11}{2}} + \frac{6}{7} \, b^{2} c^{2} d x^{\frac{7}{2}} + \frac{12}{7} \, a b c d^{2} x^{\frac{7}{2}} + \frac{2}{7} \, a^{2} d^{3} x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} c^{3} x^{\frac{3}{2}} + 4 \, a b c^{2} d x^{\frac{3}{2}} + 2 \, a^{2} c d^{2} x^{\frac{3}{2}} - \frac{2 \, {\left(10 \, a b c^{3} x^{2} + 15 \, a^{2} c^{2} d x^{2} + a^{2} c^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/15*b^2*d^3*x^(15/2) + 6/11*b^2*c*d^2*x^(11/2) + 4/11*a*b*d^3*x^(11/2) + 6/7*b^2*c^2*d*x^(7/2) + 12/7*a*b*c*d^2*x^(7/2) + 2/7*a^2*d^3*x^(7/2) + 2/3*b^2*c^3*x^(3/2) + 4*a*b*c^2*d*x^(3/2) + 2*a^2*c*d^2*x^(3/2) - 2/5*(10*a*b*c^3*x^2 + 15*a^2*c^2*d*x^2 + a^2*c^3)/x^(5/2)","A",0
415,1,436,0,0.458738," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{3} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c^{2} d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} c d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{5}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{3} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c^{2} d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} c d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{5}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{3} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c^{2} d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} c d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{5}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{3} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c^{2} d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} c d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{5}} + \frac{2 \, {\left(45 \, b^{2} d^{12} x^{\frac{13}{2}} - 65 \, b^{2} c d^{11} x^{\frac{9}{2}} + 130 \, a b d^{12} x^{\frac{9}{2}} + 117 \, b^{2} c^{2} d^{10} x^{\frac{5}{2}} - 234 \, a b c d^{11} x^{\frac{5}{2}} + 117 \, a^{2} d^{12} x^{\frac{5}{2}} - 585 \, b^{2} c^{3} d^{9} \sqrt{x} + 1170 \, a b c^{2} d^{10} \sqrt{x} - 585 \, a^{2} c d^{11} \sqrt{x}\right)}}{585 \, d^{13}}"," ",0,"1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^3 - 2*(c*d^3)^(1/4)*a*b*c^2*d + (c*d^3)^(1/4)*a^2*c*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/d^5 + 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^3 - 2*(c*d^3)^(1/4)*a*b*c^2*d + (c*d^3)^(1/4)*a^2*c*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/d^5 + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^3 - 2*(c*d^3)^(1/4)*a*b*c^2*d + (c*d^3)^(1/4)*a^2*c*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^5 - 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^3 - 2*(c*d^3)^(1/4)*a*b*c^2*d + (c*d^3)^(1/4)*a^2*c*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^5 + 2/585*(45*b^2*d^12*x^(13/2) - 65*b^2*c*d^11*x^(9/2) + 130*a*b*d^12*x^(9/2) + 117*b^2*c^2*d^10*x^(5/2) - 234*a*b*c*d^11*x^(5/2) + 117*a^2*d^12*x^(5/2) - 585*b^2*c^3*d^9*sqrt(x) + 1170*a*b*c^2*d^10*sqrt(x) - 585*a^2*c*d^11*sqrt(x))/d^13","A",0
416,1,385,0,0.458172," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{6}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{6}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{6}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{6}} + \frac{2 \, {\left(21 \, b^{2} d^{10} x^{\frac{11}{2}} - 33 \, b^{2} c d^{9} x^{\frac{7}{2}} + 66 \, a b d^{10} x^{\frac{7}{2}} + 77 \, b^{2} c^{2} d^{8} x^{\frac{3}{2}} - 154 \, a b c d^{9} x^{\frac{3}{2}} + 77 \, a^{2} d^{10} x^{\frac{3}{2}}\right)}}{231 \, d^{11}}"," ",0,"-1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/d^6 - 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/d^6 + 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^6 - 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^6 + 2/231*(21*b^2*d^10*x^(11/2) - 33*b^2*c*d^9*x^(7/2) + 66*a*b*d^10*x^(7/2) + 77*b^2*c^2*d^8*x^(3/2) - 154*a*b*c*d^9*x^(3/2) + 77*a^2*d^10*x^(3/2))/d^11","A",0
417,1,385,0,0.460455," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{4}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, d^{4}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{4}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, d^{4}} + \frac{2 \, {\left(5 \, b^{2} d^{8} x^{\frac{9}{2}} - 9 \, b^{2} c d^{7} x^{\frac{5}{2}} + 18 \, a b d^{8} x^{\frac{5}{2}} + 45 \, b^{2} c^{2} d^{6} \sqrt{x} - 90 \, a b c d^{7} \sqrt{x} + 45 \, a^{2} d^{8} \sqrt{x}\right)}}{45 \, d^{9}}"," ",0,"-1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/d^4 - 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/d^4 - 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^4 + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^4 + 2/45*(5*b^2*d^8*x^(9/2) - 9*b^2*c*d^7*x^(5/2) + 18*a*b*d^8*x^(5/2) + 45*b^2*c^2*d^6*sqrt(x) - 90*a*b*c*d^7*sqrt(x) + 45*a^2*d^8*sqrt(x))/d^9","A",0
418,1,361,0,0.539716," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c d^{5}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c d^{5}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c d^{5}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c d^{5}} + \frac{2 \, {\left(3 \, b^{2} d^{6} x^{\frac{7}{2}} - 7 \, b^{2} c d^{5} x^{\frac{3}{2}} + 14 \, a b d^{6} x^{\frac{3}{2}}\right)}}{21 \, d^{7}}"," ",0,"1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c*d^5) + 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c*d^5) - 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^5) + 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^5) + 2/21*(3*b^2*d^6*x^(7/2) - 7*b^2*c*d^5*x^(3/2) + 14*a*b*d^6*x^(3/2))/d^7","A",0
419,1,360,0,0.398535," ","integrate((b*x^2+a)^2/(d*x^2+c)/x^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c d^{3}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c d^{3}} + \frac{2 \, {\left(b^{2} d^{4} x^{\frac{5}{2}} - 5 \, b^{2} c d^{3} \sqrt{x} + 10 \, a b d^{4} \sqrt{x}\right)}}{5 \, d^{5}}"," ",0,"1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c*d^3) + 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c*d^3) + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^3) - 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^3) + 2/5*(b^2*d^4*x^(5/2) - 5*b^2*c*d^3*sqrt(x) + 10*a*b*d^4*sqrt(x))/d^5","A",0
420,1,344,0,0.479557," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c),x, algorithm=""giac"")","\frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d} - \frac{2 \, a^{2}}{c \sqrt{x}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2} d^{4}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2} d^{4}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{2} d^{4}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{2} d^{4}}"," ",0,"2/3*b^2*x^(3/2)/d - 2*a^2/(c*sqrt(x)) - 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^4) - 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^4) + 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^4) - 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^4)","A",0
421,1,344,0,0.404829," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c),x, algorithm=""giac"")","\frac{2 \, b^{2} \sqrt{x}}{d} - \frac{2 \, a^{2}}{3 \, c x^{\frac{3}{2}}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2} d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{2} d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{2} d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{2} d^{2}}"," ",0,"2*b^2*sqrt(x)/d - 2/3*a^2/(c*x^(3/2)) - 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^2) - 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^2) - 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^2) + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^2)","A",0
422,1,353,0,0.471896," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c),x, algorithm=""giac"")","-\frac{2 \, {\left(10 \, a b c x^{2} - 5 \, a^{2} d x^{2} + a^{2} c\right)}}{5 \, c^{2} x^{\frac{5}{2}}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3} d^{3}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{3} d^{3}}"," ",0,"-2/5*(10*a*b*c*x^2 - 5*a^2*d*x^2 + a^2*c)/(c^2*x^(5/2)) + 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^3) + 1/2*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^3) - 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^3) + 1/4*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 2*(c*d^3)^(3/4)*a*b*c*d + (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^3)","A",0
423,1,354,0,0.478244," ","integrate((b*x^2+a)^2/x^(9/2)/(d*x^2+c),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3} d} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{2 \, c^{3} d} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{3} d} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{4 \, c^{3} d} - \frac{2 \, {\left(14 \, a b c x^{2} - 7 \, a^{2} d x^{2} + 3 \, a^{2} c\right)}}{21 \, c^{2} x^{\frac{7}{2}}}"," ",0,"1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d) + 1/2*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d) + 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d) - 1/4*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d) - 2/21*(14*a*b*c*x^2 - 7*a^2*d*x^2 + 3*a^2*c)/(c^2*x^(7/2))","A",0
424,1,390,0,0.473656," ","integrate((d*x^2+c)^2/x^(11/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{3}{4}} a b c d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{3}{4}} a b c d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{3}{4}} a b c d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 2 \, \left(a b^{3}\right)^{\frac{3}{4}} a b c d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b^{2}} - \frac{2 \, {\left(45 \, b^{2} c^{2} x^{4} - 90 \, a b c d x^{4} + 45 \, a^{2} d^{2} x^{4} - 9 \, a b c^{2} x^{2} + 18 \, a^{2} c d x^{2} + 5 \, a^{2} c^{2}\right)}}{45 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(3/4)*b^2*c^2 - 2*(a*b^3)^(3/4)*a*b*c*d + (a*b^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) - 1/2*sqrt(2)*((a*b^3)^(3/4)*b^2*c^2 - 2*(a*b^3)^(3/4)*a*b*c*d + (a*b^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^2*c^2 - 2*(a*b^3)^(3/4)*a*b*c*d + (a*b^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^2*c^2 - 2*(a*b^3)^(3/4)*a*b*c*d + (a*b^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) - 2/45*(45*b^2*c^2*x^4 - 90*a*b*c*d*x^4 + 45*a^2*d^2*x^4 - 9*a*b*c^2*x^2 + 18*a^2*c*d*x^2 + 5*a^2*c^2)/(a^3*x^(9/2))","A",0
425,1,440,0,0.394019," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(13 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, d^{5}} - \frac{\sqrt{2} {\left(13 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, d^{5}} - \frac{\sqrt{2} {\left(13 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, d^{5}} + \frac{\sqrt{2} {\left(13 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, d^{5}} + \frac{b^{2} c^{3} \sqrt{x} - 2 \, a b c^{2} d \sqrt{x} + a^{2} c d^{2} \sqrt{x}}{2 \, {\left(d x^{2} + c\right)} d^{4}} + \frac{2 \, {\left(5 \, b^{2} d^{16} x^{\frac{9}{2}} - 18 \, b^{2} c d^{15} x^{\frac{5}{2}} + 18 \, a b d^{16} x^{\frac{5}{2}} + 135 \, b^{2} c^{2} d^{14} \sqrt{x} - 180 \, a b c d^{15} \sqrt{x} + 45 \, a^{2} d^{16} \sqrt{x}\right)}}{45 \, d^{18}}"," ",0,"-1/8*sqrt(2)*(13*(c*d^3)^(1/4)*b^2*c^2 - 18*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/d^5 - 1/8*sqrt(2)*(13*(c*d^3)^(1/4)*b^2*c^2 - 18*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/d^5 - 1/16*sqrt(2)*(13*(c*d^3)^(1/4)*b^2*c^2 - 18*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^5 + 1/16*sqrt(2)*(13*(c*d^3)^(1/4)*b^2*c^2 - 18*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/d^5 + 1/2*(b^2*c^3*sqrt(x) - 2*a*b*c^2*d*sqrt(x) + a^2*c*d^2*sqrt(x))/((d*x^2 + c)*d^4) + 2/45*(5*b^2*d^16*x^(9/2) - 18*b^2*c*d^15*x^(5/2) + 18*a*b*d^16*x^(5/2) + 135*b^2*c^2*d^14*sqrt(x) - 180*a*b*c*d^15*sqrt(x) + 45*a^2*d^16*sqrt(x))/d^18","A",0
426,1,413,0,0.479830," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{b^{2} c^{2} x^{\frac{3}{2}} - 2 \, a b c d x^{\frac{3}{2}} + a^{2} d^{2} x^{\frac{3}{2}}}{2 \, {\left(d x^{2} + c\right)} d^{3}} + \frac{\sqrt{2} {\left(11 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 14 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c d^{6}} + \frac{\sqrt{2} {\left(11 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 14 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c d^{6}} - \frac{\sqrt{2} {\left(11 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 14 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c d^{6}} + \frac{\sqrt{2} {\left(11 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 14 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c d^{6}} + \frac{2 \, {\left(3 \, b^{2} d^{12} x^{\frac{7}{2}} - 14 \, b^{2} c d^{11} x^{\frac{3}{2}} + 14 \, a b d^{12} x^{\frac{3}{2}}\right)}}{21 \, d^{14}}"," ",0,"-1/2*(b^2*c^2*x^(3/2) - 2*a*b*c*d*x^(3/2) + a^2*d^2*x^(3/2))/((d*x^2 + c)*d^3) + 1/8*sqrt(2)*(11*(c*d^3)^(3/4)*b^2*c^2 - 14*(c*d^3)^(3/4)*a*b*c*d + 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c*d^6) + 1/8*sqrt(2)*(11*(c*d^3)^(3/4)*b^2*c^2 - 14*(c*d^3)^(3/4)*a*b*c*d + 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c*d^6) - 1/16*sqrt(2)*(11*(c*d^3)^(3/4)*b^2*c^2 - 14*(c*d^3)^(3/4)*a*b*c*d + 3*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^6) + 1/16*sqrt(2)*(11*(c*d^3)^(3/4)*b^2*c^2 - 14*(c*d^3)^(3/4)*a*b*c*d + 3*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^6) + 2/21*(3*b^2*d^12*x^(7/2) - 14*b^2*c*d^11*x^(3/2) + 14*a*b*d^12*x^(3/2))/d^14","A",0
427,1,408,0,0.468703," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(9 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c d^{4}} + \frac{\sqrt{2} {\left(9 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c d^{4}} + \frac{\sqrt{2} {\left(9 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c d^{4}} - \frac{\sqrt{2} {\left(9 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c d^{4}} - \frac{b^{2} c^{2} \sqrt{x} - 2 \, a b c d \sqrt{x} + a^{2} d^{2} \sqrt{x}}{2 \, {\left(d x^{2} + c\right)} d^{3}} + \frac{2 \, {\left(b^{2} d^{8} x^{\frac{5}{2}} - 10 \, b^{2} c d^{7} \sqrt{x} + 10 \, a b d^{8} \sqrt{x}\right)}}{5 \, d^{10}}"," ",0,"1/8*sqrt(2)*(9*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c*d^4) + 1/8*sqrt(2)*(9*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c*d^4) + 1/16*sqrt(2)*(9*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^4) - 1/16*sqrt(2)*(9*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d + (c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^4) - 1/2*(b^2*c^2*sqrt(x) - 2*a*b*c*d*sqrt(x) + a^2*d^2*sqrt(x))/((d*x^2 + c)*d^3) + 2/5*(b^2*d^8*x^(5/2) - 10*b^2*c*d^7*sqrt(x) + 10*a*b*d^8*sqrt(x))/d^10","A",0
428,1,388,0,0.459580," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d^{2}} + \frac{b^{2} c^{2} x^{\frac{3}{2}} - 2 \, a b c d x^{\frac{3}{2}} + a^{2} d^{2} x^{\frac{3}{2}}}{2 \, {\left(d x^{2} + c\right)} c d^{2}} - \frac{\sqrt{2} {\left(7 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{2} d^{5}} - \frac{\sqrt{2} {\left(7 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{2} d^{5}} + \frac{\sqrt{2} {\left(7 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{2} d^{5}} - \frac{\sqrt{2} {\left(7 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{2} d^{5}}"," ",0,"2/3*b^2*x^(3/2)/d^2 + 1/2*(b^2*c^2*x^(3/2) - 2*a*b*c*d*x^(3/2) + a^2*d^2*x^(3/2))/((d*x^2 + c)*c*d^2) - 1/8*sqrt(2)*(7*(c*d^3)^(3/4)*b^2*c^2 - 6*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^5) - 1/8*sqrt(2)*(7*(c*d^3)^(3/4)*b^2*c^2 - 6*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^5) + 1/16*sqrt(2)*(7*(c*d^3)^(3/4)*b^2*c^2 - 6*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^5) - 1/16*sqrt(2)*(7*(c*d^3)^(3/4)*b^2*c^2 - 6*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^5)","A",0
429,1,388,0,0.495273," ","integrate((b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""giac"")","\frac{2 \, b^{2} \sqrt{x}}{d^{2}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{2} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{2} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{2} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 2 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{2} d^{3}} + \frac{b^{2} c^{2} \sqrt{x} - 2 \, a b c d \sqrt{x} + a^{2} d^{2} \sqrt{x}}{2 \, {\left(d x^{2} + c\right)} c d^{2}}"," ",0,"2*b^2*sqrt(x)/d^2 - 1/8*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^3) - 1/8*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^3) - 1/16*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^3) + 1/16*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 - 2*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^3) + 1/2*(b^2*c^2*sqrt(x) - 2*a*b*c*d*sqrt(x) + a^2*d^2*sqrt(x))/((d*x^2 + c)*c*d^2)","A",0
430,1,389,0,0.533667," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{b^{2} c^{2} x^{2} - 2 \, a b c d x^{2} + 5 \, a^{2} d^{2} x^{2} + 4 \, a^{2} c d}{2 \, {\left(d x^{\frac{5}{2}} + c \sqrt{x}\right)} c^{2} d} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3} d^{4}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3} d^{4}} - \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{3} d^{4}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 2 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{3} d^{4}}"," ",0,"-1/2*(b^2*c^2*x^2 - 2*a*b*c*d*x^2 + 5*a^2*d^2*x^2 + 4*a^2*c*d)/((d*x^(5/2) + c*sqrt(x))*c^2*d) + 1/8*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 2*(c*d^3)^(3/4)*a*b*c*d - 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^4) + 1/8*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 2*(c*d^3)^(3/4)*a*b*c*d - 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^4) - 1/16*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 2*(c*d^3)^(3/4)*a*b*c*d - 5*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^4) + 1/16*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 2*(c*d^3)^(3/4)*a*b*c*d - 5*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^4)","A",0
431,1,384,0,0.444419," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{2 \, a^{2}}{3 \, c^{2} x^{\frac{3}{2}}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3} d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{3} d^{2}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{3} d^{2}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{3} d^{2}} - \frac{b^{2} c^{2} \sqrt{x} - 2 \, a b c d \sqrt{x} + a^{2} d^{2} \sqrt{x}}{2 \, {\left(d x^{2} + c\right)} c^{2} d}"," ",0,"-2/3*a^2/(c^2*x^(3/2)) + 1/8*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d - 7*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^2) + 1/8*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d - 7*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^2) + 1/16*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d - 7*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^2) - 1/16*sqrt(2)*((c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d - 7*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^2) - 1/2*(b^2*c^2*sqrt(x) - 2*a*b*c*d*sqrt(x) + a^2*d^2*sqrt(x))/((d*x^2 + c)*c^2*d)","A",0
432,1,401,0,0.499999," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} c^{2} x^{\frac{3}{2}} - 2 \, a b c d x^{\frac{3}{2}} + a^{2} d^{2} x^{\frac{3}{2}}}{2 \, {\left(d x^{2} + c\right)} c^{3}} - \frac{2 \, {\left(10 \, a b c x^{2} - 10 \, a^{2} d x^{2} + a^{2} c\right)}}{5 \, c^{3} x^{\frac{5}{2}}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{4} d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{8 \, c^{4} d^{3}} - \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{4} d^{3}} + \frac{\sqrt{2} {\left(\left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{16 \, c^{4} d^{3}}"," ",0,"1/2*(b^2*c^2*x^(3/2) - 2*a*b*c*d*x^(3/2) + a^2*d^2*x^(3/2))/((d*x^2 + c)*c^3) - 2/5*(10*a*b*c*x^2 - 10*a^2*d*x^2 + a^2*c)/(c^3*x^(5/2)) + 1/8*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 10*(c*d^3)^(3/4)*a*b*c*d + 9*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^3) + 1/8*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 10*(c*d^3)^(3/4)*a*b*c*d + 9*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^3) - 1/16*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 10*(c*d^3)^(3/4)*a*b*c*d + 9*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^3) + 1/16*sqrt(2)*((c*d^3)^(3/4)*b^2*c^2 - 10*(c*d^3)^(3/4)*a*b*c*d + 9*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^3)","A",0
433,1,451,0,0.443530," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(117 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c d^{5}} + \frac{\sqrt{2} {\left(117 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c d^{5}} + \frac{\sqrt{2} {\left(117 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c d^{5}} - \frac{\sqrt{2} {\left(117 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c d^{5}} - \frac{25 \, b^{2} c^{2} d x^{\frac{5}{2}} - 34 \, a b c d^{2} x^{\frac{5}{2}} + 9 \, a^{2} d^{3} x^{\frac{5}{2}} + 21 \, b^{2} c^{3} \sqrt{x} - 26 \, a b c^{2} d \sqrt{x} + 5 \, a^{2} c d^{2} \sqrt{x}}{16 \, {\left(d x^{2} + c\right)}^{2} d^{4}} + \frac{2 \, {\left(b^{2} d^{12} x^{\frac{5}{2}} - 15 \, b^{2} c d^{11} \sqrt{x} + 10 \, a b d^{12} \sqrt{x}\right)}}{5 \, d^{15}}"," ",0,"1/64*sqrt(2)*(117*(c*d^3)^(1/4)*b^2*c^2 - 90*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c*d^5) + 1/64*sqrt(2)*(117*(c*d^3)^(1/4)*b^2*c^2 - 90*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c*d^5) + 1/128*sqrt(2)*(117*(c*d^3)^(1/4)*b^2*c^2 - 90*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^5) - 1/128*sqrt(2)*(117*(c*d^3)^(1/4)*b^2*c^2 - 90*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c*d^5) - 1/16*(25*b^2*c^2*d*x^(5/2) - 34*a*b*c*d^2*x^(5/2) + 9*a^2*d^3*x^(5/2) + 21*b^2*c^3*sqrt(x) - 26*a*b*c^2*d*sqrt(x) + 5*a^2*c*d^2*sqrt(x))/((d*x^2 + c)^2*d^4) + 2/5*(b^2*d^12*x^(5/2) - 15*b^2*c*d^11*sqrt(x) + 10*a*b*d^12*sqrt(x))/d^15","A",0
434,1,427,0,0.473398," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d^{3}} + \frac{19 \, b^{2} c^{2} d x^{\frac{7}{2}} - 22 \, a b c d^{2} x^{\frac{7}{2}} + 3 \, a^{2} d^{3} x^{\frac{7}{2}} + 15 \, b^{2} c^{3} x^{\frac{3}{2}} - 14 \, a b c^{2} d x^{\frac{3}{2}} - a^{2} c d^{2} x^{\frac{3}{2}}}{16 \, {\left(d x^{2} + c\right)}^{2} c d^{3}} - \frac{\sqrt{2} {\left(77 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 42 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{2} d^{6}} - \frac{\sqrt{2} {\left(77 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 42 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{2} d^{6}} + \frac{\sqrt{2} {\left(77 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 42 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{2} d^{6}} - \frac{\sqrt{2} {\left(77 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 42 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{2} d^{6}}"," ",0,"2/3*b^2*x^(3/2)/d^3 + 1/16*(19*b^2*c^2*d*x^(7/2) - 22*a*b*c*d^2*x^(7/2) + 3*a^2*d^3*x^(7/2) + 15*b^2*c^3*x^(3/2) - 14*a*b*c^2*d*x^(3/2) - a^2*c*d^2*x^(3/2))/((d*x^2 + c)^2*c*d^3) - 1/64*sqrt(2)*(77*(c*d^3)^(3/4)*b^2*c^2 - 42*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^6) - 1/64*sqrt(2)*(77*(c*d^3)^(3/4)*b^2*c^2 - 42*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^6) + 1/128*sqrt(2)*(77*(c*d^3)^(3/4)*b^2*c^2 - 42*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^6) - 1/128*sqrt(2)*(77*(c*d^3)^(3/4)*b^2*c^2 - 42*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^6)","A",0
435,1,426,0,0.426136," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{2 \, b^{2} \sqrt{x}}{d^{3}} - \frac{\sqrt{2} {\left(45 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{2} d^{4}} - \frac{\sqrt{2} {\left(45 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{2} d^{4}} - \frac{\sqrt{2} {\left(45 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{2} d^{4}} + \frac{\sqrt{2} {\left(45 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 10 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{2} d^{4}} + \frac{17 \, b^{2} c^{2} d x^{\frac{5}{2}} - 18 \, a b c d^{2} x^{\frac{5}{2}} + a^{2} d^{3} x^{\frac{5}{2}} + 13 \, b^{2} c^{3} \sqrt{x} - 10 \, a b c^{2} d \sqrt{x} - 3 \, a^{2} c d^{2} \sqrt{x}}{16 \, {\left(d x^{2} + c\right)}^{2} c d^{3}}"," ",0,"2*b^2*sqrt(x)/d^3 - 1/64*sqrt(2)*(45*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^4) - 1/64*sqrt(2)*(45*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^2*d^4) - 1/128*sqrt(2)*(45*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^4) + 1/128*sqrt(2)*(45*(c*d^3)^(1/4)*b^2*c^2 - 10*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^2*d^4) + 1/16*(17*b^2*c^2*d*x^(5/2) - 18*a*b*c*d^2*x^(5/2) + a^2*d^3*x^(5/2) + 13*b^2*c^3*sqrt(x) - 10*a*b*c^2*d*sqrt(x) - 3*a^2*c*d^2*sqrt(x))/((d*x^2 + c)^2*c*d^3)","A",0
436,1,416,0,0.521216," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{11 \, b^{2} c^{2} d x^{\frac{7}{2}} - 6 \, a b c d^{2} x^{\frac{7}{2}} - 5 \, a^{2} d^{3} x^{\frac{7}{2}} + 7 \, b^{2} c^{3} x^{\frac{3}{2}} + 2 \, a b c^{2} d x^{\frac{3}{2}} - 9 \, a^{2} c d^{2} x^{\frac{3}{2}}}{16 \, {\left(d x^{2} + c\right)}^{2} c^{2} d^{2}} + \frac{\sqrt{2} {\left(21 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{3} d^{5}} + \frac{\sqrt{2} {\left(21 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{3} d^{5}} - \frac{\sqrt{2} {\left(21 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{3} d^{5}} + \frac{\sqrt{2} {\left(21 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{3} d^{5}}"," ",0,"-1/16*(11*b^2*c^2*d*x^(7/2) - 6*a*b*c*d^2*x^(7/2) - 5*a^2*d^3*x^(7/2) + 7*b^2*c^3*x^(3/2) + 2*a*b*c^2*d*x^(3/2) - 9*a^2*c*d^2*x^(3/2))/((d*x^2 + c)^2*c^2*d^2) + 1/64*sqrt(2)*(21*(c*d^3)^(3/4)*b^2*c^2 + 6*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^5) + 1/64*sqrt(2)*(21*(c*d^3)^(3/4)*b^2*c^2 + 6*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^5) - 1/128*sqrt(2)*(21*(c*d^3)^(3/4)*b^2*c^2 + 6*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^5) + 1/128*sqrt(2)*(21*(c*d^3)^(3/4)*b^2*c^2 + 6*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^5)","A",0
437,1,416,0,0.529737," ","integrate((b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{3} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{3} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 6 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{3} d^{3}} - \frac{9 \, b^{2} c^{2} d x^{\frac{5}{2}} - 2 \, a b c d^{2} x^{\frac{5}{2}} - 7 \, a^{2} d^{3} x^{\frac{5}{2}} + 5 \, b^{2} c^{3} \sqrt{x} + 6 \, a b c^{2} d \sqrt{x} - 11 \, a^{2} c d^{2} \sqrt{x}}{16 \, {\left(d x^{2} + c\right)}^{2} c^{2} d^{2}}"," ",0,"1/64*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^3) + 1/64*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^3*d^3) + 1/128*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^3) - 1/128*sqrt(2)*(5*(c*d^3)^(1/4)*b^2*c^2 + 6*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^3*d^3) - 1/16*(9*b^2*c^2*d*x^(5/2) - 2*a*b*c*d^2*x^(5/2) - 7*a^2*d^3*x^(5/2) + 5*b^2*c^3*sqrt(x) + 6*a*b*c^2*d*sqrt(x) - 11*a^2*c*d^2*sqrt(x))/((d*x^2 + c)^2*c^2*d^2)","A",0
438,1,427,0,0.535684," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{2 \, a^{2}}{c^{3} \sqrt{x}} + \frac{3 \, b^{2} c^{2} d x^{\frac{7}{2}} + 10 \, a b c d^{2} x^{\frac{7}{2}} - 13 \, a^{2} d^{3} x^{\frac{7}{2}} - b^{2} c^{3} x^{\frac{3}{2}} + 18 \, a b c^{2} d x^{\frac{3}{2}} - 17 \, a^{2} c d^{2} x^{\frac{3}{2}}}{16 \, {\left(d x^{2} + c\right)}^{2} c^{3} d} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4} d^{4}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4} d^{4}} - \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{4} d^{4}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 10 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{4} d^{4}}"," ",0,"-2*a^2/(c^3*sqrt(x)) + 1/16*(3*b^2*c^2*d*x^(7/2) + 10*a*b*c*d^2*x^(7/2) - 13*a^2*d^3*x^(7/2) - b^2*c^3*x^(3/2) + 18*a*b*c^2*d*x^(3/2) - 17*a^2*c*d^2*x^(3/2))/((d*x^2 + c)^2*c^3*d) + 1/64*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 10*(c*d^3)^(3/4)*a*b*c*d - 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^4) + 1/64*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 10*(c*d^3)^(3/4)*a*b*c*d - 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^4) - 1/128*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 10*(c*d^3)^(3/4)*a*b*c*d - 45*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^4) + 1/128*sqrt(2)*(3*(c*d^3)^(3/4)*b^2*c^2 + 10*(c*d^3)^(3/4)*a*b*c*d - 45*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^4)","A",0
439,1,426,0,0.493414," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{2 \, a^{2}}{3 \, c^{3} x^{\frac{3}{2}}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 42 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4} d^{2}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 42 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{4} d^{2}} + \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 42 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{4} d^{2}} - \frac{\sqrt{2} {\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 42 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{4} d^{2}} + \frac{b^{2} c^{2} d x^{\frac{5}{2}} + 14 \, a b c d^{2} x^{\frac{5}{2}} - 15 \, a^{2} d^{3} x^{\frac{5}{2}} - 3 \, b^{2} c^{3} \sqrt{x} + 22 \, a b c^{2} d \sqrt{x} - 19 \, a^{2} c d^{2} \sqrt{x}}{16 \, {\left(d x^{2} + c\right)}^{2} c^{3} d}"," ",0,"-2/3*a^2/(c^3*x^(3/2)) + 1/64*sqrt(2)*(3*(c*d^3)^(1/4)*b^2*c^2 + 42*(c*d^3)^(1/4)*a*b*c*d - 77*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^2) + 1/64*sqrt(2)*(3*(c*d^3)^(1/4)*b^2*c^2 + 42*(c*d^3)^(1/4)*a*b*c*d - 77*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^4*d^2) + 1/128*sqrt(2)*(3*(c*d^3)^(1/4)*b^2*c^2 + 42*(c*d^3)^(1/4)*a*b*c*d - 77*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^2) - 1/128*sqrt(2)*(3*(c*d^3)^(1/4)*b^2*c^2 + 42*(c*d^3)^(1/4)*a*b*c*d - 77*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^4*d^2) + 1/16*(b^2*c^2*d*x^(5/2) + 14*a*b*c*d^2*x^(5/2) - 15*a^2*d^3*x^(5/2) - 3*b^2*c^3*sqrt(x) + 22*a*b*c^2*d*sqrt(x) - 19*a^2*c*d^2*sqrt(x))/((d*x^2 + c)^2*c^3*d)","A",0
440,1,444,0,0.526709," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{5 \, b^{2} c^{2} d x^{\frac{7}{2}} - 26 \, a b c d^{2} x^{\frac{7}{2}} + 21 \, a^{2} d^{3} x^{\frac{7}{2}} + 9 \, b^{2} c^{3} x^{\frac{3}{2}} - 34 \, a b c^{2} d x^{\frac{3}{2}} + 25 \, a^{2} c d^{2} x^{\frac{3}{2}}}{16 \, {\left(d x^{2} + c\right)}^{2} c^{4}} - \frac{2 \, {\left(10 \, a b c x^{2} - 15 \, a^{2} d x^{2} + a^{2} c\right)}}{5 \, c^{4} x^{\frac{5}{2}}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{5} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{64 \, c^{5} d^{3}} - \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{5} d^{3}} + \frac{\sqrt{2} {\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 90 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{128 \, c^{5} d^{3}}"," ",0,"1/16*(5*b^2*c^2*d*x^(7/2) - 26*a*b*c*d^2*x^(7/2) + 21*a^2*d^3*x^(7/2) + 9*b^2*c^3*x^(3/2) - 34*a*b*c^2*d*x^(3/2) + 25*a^2*c*d^2*x^(3/2))/((d*x^2 + c)^2*c^4) - 2/5*(10*a*b*c*x^2 - 15*a^2*d*x^2 + a^2*c)/(c^4*x^(5/2)) + 1/64*sqrt(2)*(5*(c*d^3)^(3/4)*b^2*c^2 - 90*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(c^5*d^3) + 1/64*sqrt(2)*(5*(c*d^3)^(3/4)*b^2*c^2 - 90*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(c^5*d^3) - 1/128*sqrt(2)*(5*(c*d^3)^(3/4)*b^2*c^2 - 90*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^5*d^3) + 1/128*sqrt(2)*(5*(c*d^3)^(3/4)*b^2*c^2 - 90*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(c^5*d^3)","A",0
441,1,531,0,0.523478," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{7}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{7}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{7}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{7}} + \frac{2 \, {\left(77 \, b^{14} d^{3} x^{\frac{15}{2}} + 315 \, b^{14} c d^{2} x^{\frac{11}{2}} - 105 \, a b^{13} d^{3} x^{\frac{11}{2}} + 495 \, b^{14} c^{2} d x^{\frac{7}{2}} - 495 \, a b^{13} c d^{2} x^{\frac{7}{2}} + 165 \, a^{2} b^{12} d^{3} x^{\frac{7}{2}} + 385 \, b^{14} c^{3} x^{\frac{3}{2}} - 1155 \, a b^{13} c^{2} d x^{\frac{3}{2}} + 1155 \, a^{2} b^{12} c d^{2} x^{\frac{3}{2}} - 385 \, a^{3} b^{11} d^{3} x^{\frac{3}{2}}\right)}}{1155 \, b^{15}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^7 - 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^7 + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^7 - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^7 + 2/1155*(77*b^14*d^3*x^(15/2) + 315*b^14*c*d^2*x^(11/2) - 105*a*b^13*d^3*x^(11/2) + 495*b^14*c^2*d*x^(7/2) - 495*a*b^13*c*d^2*x^(7/2) + 165*a^2*b^12*d^3*x^(7/2) + 385*b^14*c^3*x^(3/2) - 1155*a*b^13*c^2*d*x^(3/2) + 1155*a^2*b^12*c*d^2*x^(3/2) - 385*a^3*b^11*d^3*x^(3/2))/b^15","B",0
442,1,531,0,0.446033," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, b^{5}} + \frac{2 \, {\left(45 \, b^{12} d^{3} x^{\frac{13}{2}} + 195 \, b^{12} c d^{2} x^{\frac{9}{2}} - 65 \, a b^{11} d^{3} x^{\frac{9}{2}} + 351 \, b^{12} c^{2} d x^{\frac{5}{2}} - 351 \, a b^{11} c d^{2} x^{\frac{5}{2}} + 117 \, a^{2} b^{10} d^{3} x^{\frac{5}{2}} + 585 \, b^{12} c^{3} \sqrt{x} - 1755 \, a b^{11} c^{2} d \sqrt{x} + 1755 \, a^{2} b^{10} c d^{2} \sqrt{x} - 585 \, a^{3} b^{9} d^{3} \sqrt{x}\right)}}{585 \, b^{13}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^5 - 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^5 - 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^5 + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^5 + 2/585*(45*b^12*d^3*x^(13/2) + 195*b^12*c*d^2*x^(9/2) - 65*a*b^11*d^3*x^(9/2) + 351*b^12*c^2*d*x^(5/2) - 351*a*b^11*c*d^2*x^(5/2) + 117*a^2*b^10*d^3*x^(5/2) + 585*b^12*c^3*sqrt(x) - 1755*a*b^11*c^2*d*sqrt(x) + 1755*a^2*b^10*c*d^2*sqrt(x) - 585*a^3*b^9*d^3*sqrt(x))/b^13","B",0
443,1,490,0,0.485727," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{6}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{6}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{6}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{6}} + \frac{2 \, {\left(21 \, b^{10} d^{3} x^{\frac{11}{2}} + 99 \, b^{10} c d^{2} x^{\frac{7}{2}} - 33 \, a b^{9} d^{3} x^{\frac{7}{2}} + 231 \, b^{10} c^{2} d x^{\frac{3}{2}} - 231 \, a b^{9} c d^{2} x^{\frac{3}{2}} + 77 \, a^{2} b^{8} d^{3} x^{\frac{3}{2}}\right)}}{231 \, b^{11}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^6) + 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^6) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^6) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^6) + 2/231*(21*b^10*d^3*x^(11/2) + 99*b^10*c*d^2*x^(7/2) - 33*a*b^9*d^3*x^(7/2) + 231*b^10*c^2*d*x^(3/2) - 231*a*b^9*c*d^2*x^(3/2) + 77*a^2*b^8*d^3*x^(3/2))/b^11","B",0
444,1,490,0,0.426254," ","integrate((d*x^2+c)^3/(b*x^2+a)/x^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a b^{4}} + \frac{2 \, {\left(5 \, b^{8} d^{3} x^{\frac{9}{2}} + 27 \, b^{8} c d^{2} x^{\frac{5}{2}} - 9 \, a b^{7} d^{3} x^{\frac{5}{2}} + 135 \, b^{8} c^{2} d \sqrt{x} - 135 \, a b^{7} c d^{2} \sqrt{x} + 45 \, a^{2} b^{6} d^{3} \sqrt{x}\right)}}{45 \, b^{9}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) + 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^4) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4) - 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^4) + 2/45*(5*b^8*d^3*x^(9/2) + 27*b^8*c*d^2*x^(5/2) - 9*a*b^7*d^3*x^(5/2) + 135*b^8*c^2*d*sqrt(x) - 135*a*b^7*c*d^2*sqrt(x) + 45*a^2*b^6*d^3*sqrt(x))/b^9","B",0
445,1,462,0,0.455144," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{2 \, c^{3}}{a \sqrt{x}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{5}} + \frac{2 \, {\left(3 \, b^{6} d^{3} x^{\frac{7}{2}} + 21 \, b^{6} c d^{2} x^{\frac{3}{2}} - 7 \, a b^{5} d^{3} x^{\frac{3}{2}}\right)}}{21 \, b^{7}}"," ",0,"-2*c^3/(a*sqrt(x)) - 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^5) - 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^5) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^5) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^5) + 2/21*(3*b^6*d^3*x^(7/2) + 21*b^6*c*d^2*x^(3/2) - 7*a*b^5*d^3*x^(3/2))/b^7","B",0
446,1,461,0,0.449592," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{2 \, c^{3}}{3 \, a x^{\frac{3}{2}}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{2} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{2} b^{3}} + \frac{2 \, {\left(b^{4} d^{3} x^{\frac{5}{2}} + 15 \, b^{4} c d^{2} \sqrt{x} - 5 \, a b^{3} d^{3} \sqrt{x}\right)}}{5 \, b^{5}}"," ",0,"-2/3*c^3/(a*x^(3/2)) - 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) - 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^3) - 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^3) + 2/5*(b^4*d^3*x^(5/2) + 15*b^4*c*d^2*sqrt(x) - 5*a*b^3*d^3*sqrt(x))/b^5","B",0
447,1,455,0,0.434874," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, d^{3} x^{\frac{3}{2}}}{3 \, b} + \frac{2 \, {\left(5 \, b c^{3} x^{2} - 15 \, a c^{2} d x^{2} - a c^{3}\right)}}{5 \, a^{2} x^{\frac{5}{2}}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{4}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{4}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{4}}"," ",0,"2/3*d^3*x^(3/2)/b + 2/5*(5*b*c^3*x^2 - 15*a*c^2*d*x^2 - a*c^3)/(a^2*x^(5/2)) + 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^4) + 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^4) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^4) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^4)","B",0
448,1,455,0,0.445314," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{2 \, d^{3} \sqrt{x}}{b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{3} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{3} b^{2}} + \frac{2 \, {\left(7 \, b c^{3} x^{2} - 21 \, a c^{2} d x^{2} - 3 \, a c^{3}\right)}}{21 \, a^{2} x^{\frac{7}{2}}}"," ",0,"2*d^3*sqrt(x)/b + 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) + 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^2) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) - 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^2) + 2/21*(7*b*c^3*x^2 - 21*a*c^2*d*x^2 - 3*a*c^3)/(a^2*x^(7/2))","B",0
449,1,483,0,0.471062," ","integrate((d*x^2+c)^3/x^(11/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b^{3}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b^{3}} - \frac{2 \, {\left(45 \, b^{2} c^{3} x^{4} - 135 \, a b c^{2} d x^{4} + 135 \, a^{2} c d^{2} x^{4} - 9 \, a b c^{3} x^{2} + 27 \, a^{2} c^{2} d x^{2} + 5 \, a^{2} c^{3}\right)}}{45 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^3) - 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^3) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^3) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^3) - 2/45*(45*b^2*c^3*x^4 - 135*a*b*c^2*d*x^4 + 135*a^2*c*d^2*x^4 - 9*a*b*c^3*x^2 + 27*a^2*c^2*d*x^2 + 5*a^2*c^3)/(a^3*x^(9/2))","B",0
450,1,483,0,0.505353," ","integrate((d*x^2+c)^3/x^(13/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{4} b} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{4} b} - \frac{2 \, {\left(77 \, b^{2} c^{3} x^{4} - 231 \, a b c^{2} d x^{4} + 231 \, a^{2} c d^{2} x^{4} - 33 \, a b c^{3} x^{2} + 99 \, a^{2} c^{2} d x^{2} + 21 \, a^{2} c^{3}\right)}}{231 \, a^{3} x^{\frac{11}{2}}}"," ",0,"-1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b) - 1/2*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b) - 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b) + 1/4*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 3*(a*b^3)^(1/4)*a*b^2*c^2*d + 3*(a*b^3)^(1/4)*a^2*b*c*d^2 - (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b) - 2/231*(77*b^2*c^3*x^4 - 231*a*b*c^2*d*x^4 + 231*a^2*c*d^2*x^4 - 33*a*b*c^3*x^2 + 99*a^2*c^2*d*x^2 + 21*a^2*c^3)/(a^3*x^(11/2))","B",0
451,1,536,0,0.446695," ","integrate((d*x^2+c)^3/x^(15/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{5} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \, a^{5} b^{2}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{5} b^{2}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{4 \, a^{5} b^{2}} + \frac{2 \, {\left(585 \, b^{3} c^{3} x^{6} - 1755 \, a b^{2} c^{2} d x^{6} + 1755 \, a^{2} b c d^{2} x^{6} - 585 \, a^{3} d^{3} x^{6} - 117 \, a b^{2} c^{3} x^{4} + 351 \, a^{2} b c^{2} d x^{4} - 351 \, a^{3} c d^{2} x^{4} + 65 \, a^{2} b c^{3} x^{2} - 195 \, a^{3} c^{2} d x^{2} - 45 \, a^{3} c^{3}\right)}}{585 \, a^{4} x^{\frac{13}{2}}}"," ",0,"1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^5*b^2) + 1/2*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^5*b^2) - 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^5*b^2) + 1/4*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d + 3*(a*b^3)^(3/4)*a^2*b*c*d^2 - (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^5*b^2) + 2/585*(585*b^3*c^3*x^6 - 1755*a*b^2*c^2*d*x^6 + 1755*a^2*b*c*d^2*x^6 - 585*a^3*d^3*x^6 - 117*a*b^2*c^3*x^4 + 351*a^2*b*c^2*d*x^4 - 351*a^3*c*d^2*x^4 + 65*a^2*b*c^3*x^2 - 195*a^3*c^2*d*x^2 - 45*a^3*c^3)/(a^4*x^(13/2))","B",0
452,1,600,0,0.493851," ","integrate(x^(7/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 39 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{6}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 39 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, b^{6}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 39 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, b^{6}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 39 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 17 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, b^{6}} + \frac{a b^{3} c^{3} \sqrt{x} - 3 \, a^{2} b^{2} c^{2} d \sqrt{x} + 3 \, a^{3} b c d^{2} \sqrt{x} - a^{4} d^{3} \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} b^{5}} + \frac{2 \, {\left(45 \, b^{24} d^{3} x^{\frac{13}{2}} + 195 \, b^{24} c d^{2} x^{\frac{9}{2}} - 130 \, a b^{23} d^{3} x^{\frac{9}{2}} + 351 \, b^{24} c^{2} d x^{\frac{5}{2}} - 702 \, a b^{23} c d^{2} x^{\frac{5}{2}} + 351 \, a^{2} b^{22} d^{3} x^{\frac{5}{2}} + 585 \, b^{24} c^{3} \sqrt{x} - 3510 \, a b^{23} c^{2} d \sqrt{x} + 5265 \, a^{2} b^{22} c d^{2} \sqrt{x} - 2340 \, a^{3} b^{21} d^{3} \sqrt{x}\right)}}{585 \, b^{26}}"," ",0,"-1/8*sqrt(2)*(5*(a*b^3)^(1/4)*b^3*c^3 - 27*(a*b^3)^(1/4)*a*b^2*c^2*d + 39*(a*b^3)^(1/4)*a^2*b*c*d^2 - 17*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/b^6 - 1/8*sqrt(2)*(5*(a*b^3)^(1/4)*b^3*c^3 - 27*(a*b^3)^(1/4)*a*b^2*c^2*d + 39*(a*b^3)^(1/4)*a^2*b*c*d^2 - 17*(a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/b^6 - 1/16*sqrt(2)*(5*(a*b^3)^(1/4)*b^3*c^3 - 27*(a*b^3)^(1/4)*a*b^2*c^2*d + 39*(a*b^3)^(1/4)*a^2*b*c*d^2 - 17*(a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^6 + 1/16*sqrt(2)*(5*(a*b^3)^(1/4)*b^3*c^3 - 27*(a*b^3)^(1/4)*a*b^2*c^2*d + 39*(a*b^3)^(1/4)*a^2*b*c*d^2 - 17*(a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/b^6 + 1/2*(a*b^3*c^3*sqrt(x) - 3*a^2*b^2*c^2*d*sqrt(x) + 3*a^3*b*c*d^2*sqrt(x) - a^4*d^3*sqrt(x))/((b*x^2 + a)*b^5) + 2/585*(45*b^24*d^3*x^(13/2) + 195*b^24*c*d^2*x^(9/2) - 130*a*b^23*d^3*x^(9/2) + 351*b^24*c^2*d*x^(5/2) - 702*a*b^23*c*d^2*x^(5/2) + 351*a^2*b^22*d^3*x^(5/2) + 585*b^24*c^3*sqrt(x) - 3510*a*b^23*c^2*d*sqrt(x) + 5265*a^2*b^22*c*d^2*sqrt(x) - 2340*a^3*b^21*d^3*sqrt(x))/b^26","A",0
453,1,552,0,0.598742," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{b^{3} c^{3} x^{\frac{3}{2}} - 3 \, a b^{2} c^{2} d x^{\frac{3}{2}} + 3 \, a^{2} b c d^{2} x^{\frac{3}{2}} - a^{3} d^{3} x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{7}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{7}} - \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{7}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{7}} + \frac{2 \, {\left(7 \, b^{20} d^{3} x^{\frac{11}{2}} + 33 \, b^{20} c d^{2} x^{\frac{7}{2}} - 22 \, a b^{19} d^{3} x^{\frac{7}{2}} + 77 \, b^{20} c^{2} d x^{\frac{3}{2}} - 154 \, a b^{19} c d^{2} x^{\frac{3}{2}} + 77 \, a^{2} b^{18} d^{3} x^{\frac{3}{2}}\right)}}{77 \, b^{22}}"," ",0,"-1/2*(b^3*c^3*x^(3/2) - 3*a*b^2*c^2*d*x^(3/2) + 3*a^2*b*c*d^2*x^(3/2) - a^3*d^3*x^(3/2))/((b*x^2 + a)*b^4) + 3/8*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 7*(a*b^3)^(3/4)*a*b^2*c^2*d + 11*(a*b^3)^(3/4)*a^2*b*c*d^2 - 5*(a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^7) + 3/8*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 7*(a*b^3)^(3/4)*a*b^2*c^2*d + 11*(a*b^3)^(3/4)*a^2*b*c*d^2 - 5*(a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^7) - 3/16*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 7*(a*b^3)^(3/4)*a*b^2*c^2*d + 11*(a*b^3)^(3/4)*a^2*b*c*d^2 - 5*(a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^7) + 3/16*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 - 7*(a*b^3)^(3/4)*a*b^2*c^2*d + 11*(a*b^3)^(3/4)*a^2*b*c*d^2 - 5*(a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^7) + 2/77*(7*b^20*d^3*x^(11/2) + 33*b^20*c*d^2*x^(7/2) - 22*a*b^19*d^3*x^(7/2) + 77*b^20*c^2*d*x^(3/2) - 154*a*b^19*c*d^2*x^(3/2) + 77*a^2*b^18*d^3*x^(3/2))/b^22","A",0
454,1,552,0,0.502438," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a b^{5}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{5}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 27 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} - 13 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a b^{5}} - \frac{b^{3} c^{3} \sqrt{x} - 3 \, a b^{2} c^{2} d \sqrt{x} + 3 \, a^{2} b c d^{2} \sqrt{x} - a^{3} d^{3} \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} b^{4}} + \frac{2 \, {\left(5 \, b^{16} d^{3} x^{\frac{9}{2}} + 27 \, b^{16} c d^{2} x^{\frac{5}{2}} - 18 \, a b^{15} d^{3} x^{\frac{5}{2}} + 135 \, b^{16} c^{2} d \sqrt{x} - 270 \, a b^{15} c d^{2} \sqrt{x} + 135 \, a^{2} b^{14} d^{3} \sqrt{x}\right)}}{45 \, b^{18}}"," ",0,"1/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 15*(a*b^3)^(1/4)*a*b^2*c^2*d + 27*(a*b^3)^(1/4)*a^2*b*c*d^2 - 13*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a*b^5) + 1/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 15*(a*b^3)^(1/4)*a*b^2*c^2*d + 27*(a*b^3)^(1/4)*a^2*b*c*d^2 - 13*(a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a*b^5) + 1/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 15*(a*b^3)^(1/4)*a*b^2*c^2*d + 27*(a*b^3)^(1/4)*a^2*b*c*d^2 - 13*(a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^5) - 1/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 - 15*(a*b^3)^(1/4)*a*b^2*c^2*d + 27*(a*b^3)^(1/4)*a^2*b*c*d^2 - 13*(a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a*b^5) - 1/2*(b^3*c^3*sqrt(x) - 3*a*b^2*c^2*d*sqrt(x) + 3*a^2*b*c*d^2*sqrt(x) - a^3*d^3*sqrt(x))/((b*x^2 + a)*b^4) + 2/45*(5*b^16*d^3*x^(9/2) + 27*b^16*c*d^2*x^(5/2) - 18*a*b^15*d^3*x^(5/2) + 135*b^16*c^2*d*sqrt(x) - 270*a*b^15*c*d^2*sqrt(x) + 135*a^2*b^14*d^3*sqrt(x))/b^18","A",0
455,1,516,0,0.498258," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{b^{3} c^{3} x^{\frac{3}{2}} - 3 \, a b^{2} c^{2} d x^{\frac{3}{2}} + 3 \, a^{2} b c d^{2} x^{\frac{3}{2}} - a^{3} d^{3} x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} a b^{3}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} + 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 21 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{6}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} + 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 21 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{6}} - \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} + 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 21 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{6}} + \frac{\sqrt{2} {\left(\left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} + 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 21 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 11 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{6}} + \frac{2 \, {\left(3 \, b^{12} d^{3} x^{\frac{7}{2}} + 21 \, b^{12} c d^{2} x^{\frac{3}{2}} - 14 \, a b^{11} d^{3} x^{\frac{3}{2}}\right)}}{21 \, b^{14}}"," ",0,"1/2*(b^3*c^3*x^(3/2) - 3*a*b^2*c^2*d*x^(3/2) + 3*a^2*b*c*d^2*x^(3/2) - a^3*d^3*x^(3/2))/((b*x^2 + a)*a*b^3) + 1/8*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 + 9*(a*b^3)^(3/4)*a*b^2*c^2*d - 21*(a*b^3)^(3/4)*a^2*b*c*d^2 + 11*(a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^6) + 1/8*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 + 9*(a*b^3)^(3/4)*a*b^2*c^2*d - 21*(a*b^3)^(3/4)*a^2*b*c*d^2 + 11*(a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^6) - 1/16*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 + 9*(a*b^3)^(3/4)*a*b^2*c^2*d - 21*(a*b^3)^(3/4)*a^2*b*c*d^2 + 11*(a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^6) + 1/16*sqrt(2)*((a*b^3)^(3/4)*b^3*c^3 + 9*(a*b^3)^(3/4)*a*b^2*c^2*d - 21*(a*b^3)^(3/4)*a^2*b*c*d^2 + 11*(a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^6) + 2/21*(3*b^12*d^3*x^(7/2) + 21*b^12*c*d^2*x^(3/2) - 14*a*b^11*d^3*x^(3/2))/b^14","A",0
456,1,511,0,0.426517," ","integrate((d*x^2+c)^3/(b*x^2+a)^2/x^(1/2),x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{2} b^{4}} + \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{4}} - \frac{3 \, \sqrt{2} {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} + \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{2} b^{4}} + \frac{b^{3} c^{3} \sqrt{x} - 3 \, a b^{2} c^{2} d \sqrt{x} + 3 \, a^{2} b c d^{2} \sqrt{x} - a^{3} d^{3} \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} a b^{3}} + \frac{2 \, {\left(b^{8} d^{3} x^{\frac{5}{2}} + 15 \, b^{8} c d^{2} \sqrt{x} - 10 \, a b^{7} d^{3} \sqrt{x}\right)}}{5 \, b^{10}}"," ",0,"3/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^4) + 3/8*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^2*b^4) + 3/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^4) - 3/16*sqrt(2)*((a*b^3)^(1/4)*b^3*c^3 + (a*b^3)^(1/4)*a*b^2*c^2*d - 5*(a*b^3)^(1/4)*a^2*b*c*d^2 + 3*(a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^2*b^4) + 1/2*(b^3*c^3*sqrt(x) - 3*a*b^2*c^2*d*sqrt(x) + 3*a^2*b*c*d^2*sqrt(x) - a^3*d^3*sqrt(x))/((b*x^2 + a)*a*b^3) + 2/5*(b^8*d^3*x^(5/2) + 15*b^8*c*d^2*sqrt(x) - 10*a*b^7*d^3*sqrt(x))/b^10","A",0
457,1,504,0,0.503176," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, d^{3} x^{\frac{3}{2}}}{3 \, b^{2}} - \frac{5 \, b^{3} c^{3} x^{2} - 3 \, a b^{2} c^{2} d x^{2} + 3 \, a^{2} b c d^{2} x^{2} - a^{3} d^{3} x^{2} + 4 \, a b^{2} c^{3}}{2 \, {\left(b x^{\frac{5}{2}} + a \sqrt{x}\right)} a^{2} b^{2}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{5}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{5}} + \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{5}} - \frac{\sqrt{2} {\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{5}}"," ",0,"2/3*d^3*x^(3/2)/b^2 - 1/2*(5*b^3*c^3*x^2 - 3*a*b^2*c^2*d*x^2 + 3*a^2*b*c*d^2*x^2 - a^3*d^3*x^2 + 4*a*b^2*c^3)/((b*x^(5/2) + a*sqrt(x))*a^2*b^2) - 1/8*sqrt(2)*(5*(a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d - 9*(a*b^3)^(3/4)*a^2*b*c*d^2 + 7*(a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^5) - 1/8*sqrt(2)*(5*(a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d - 9*(a*b^3)^(3/4)*a^2*b*c*d^2 + 7*(a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^5) + 1/16*sqrt(2)*(5*(a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d - 9*(a*b^3)^(3/4)*a^2*b*c*d^2 + 7*(a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^5) - 1/16*sqrt(2)*(5*(a*b^3)^(3/4)*b^3*c^3 - 3*(a*b^3)^(3/4)*a*b^2*c^2*d - 9*(a*b^3)^(3/4)*a^2*b*c*d^2 + 7*(a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^5)","A",0
458,1,501,0,0.483817," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, d^{3} \sqrt{x}}{b^{2}} - \frac{2 \, c^{3}}{3 \, a^{2} x^{\frac{3}{2}}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{3} b^{3}} - \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{3}} + \frac{\sqrt{2} {\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d - 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{3} b^{3}} - \frac{b^{3} c^{3} \sqrt{x} - 3 \, a b^{2} c^{2} d \sqrt{x} + 3 \, a^{2} b c d^{2} \sqrt{x} - a^{3} d^{3} \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} a^{2} b^{2}}"," ",0,"2*d^3*sqrt(x)/b^2 - 2/3*c^3/(a^2*x^(3/2)) - 1/8*sqrt(2)*(7*(a*b^3)^(1/4)*b^3*c^3 - 9*(a*b^3)^(1/4)*a*b^2*c^2*d - 3*(a*b^3)^(1/4)*a^2*b*c*d^2 + 5*(a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^3) - 1/8*sqrt(2)*(7*(a*b^3)^(1/4)*b^3*c^3 - 9*(a*b^3)^(1/4)*a*b^2*c^2*d - 3*(a*b^3)^(1/4)*a^2*b*c*d^2 + 5*(a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^3*b^3) - 1/16*sqrt(2)*(7*(a*b^3)^(1/4)*b^3*c^3 - 9*(a*b^3)^(1/4)*a*b^2*c^2*d - 3*(a*b^3)^(1/4)*a^2*b*c*d^2 + 5*(a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^3) + 1/16*sqrt(2)*(7*(a*b^3)^(1/4)*b^3*c^3 - 9*(a*b^3)^(1/4)*a*b^2*c^2*d - 3*(a*b^3)^(1/4)*a^2*b*c*d^2 + 5*(a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^3*b^3) - 1/2*(b^3*c^3*sqrt(x) - 3*a*b^2*c^2*d*sqrt(x) + 3*a^2*b*c*d^2*sqrt(x) - a^3*d^3*sqrt(x))/((b*x^2 + a)*a^2*b^2)","A",0
459,1,505,0,0.573137," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{b^{3} c^{3} x^{\frac{3}{2}} - 3 \, a b^{2} c^{2} d x^{\frac{3}{2}} + 3 \, a^{2} b c d^{2} x^{\frac{3}{2}} - a^{3} d^{3} x^{\frac{3}{2}}}{2 \, {\left(b x^{2} + a\right)} a^{3} b} + \frac{2 \, {\left(10 \, b c^{3} x^{2} - 15 \, a c^{2} d x^{2} - a c^{3}\right)}}{5 \, a^{3} x^{\frac{5}{2}}} + \frac{3 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{4}} + \frac{3 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{4}} - \frac{3 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{4}} + \frac{3 \, \sqrt{2} {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c^{3} - 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} c^{2} d + \left(a b^{3}\right)^{\frac{3}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{3}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{4}}"," ",0,"1/2*(b^3*c^3*x^(3/2) - 3*a*b^2*c^2*d*x^(3/2) + 3*a^2*b*c*d^2*x^(3/2) - a^3*d^3*x^(3/2))/((b*x^2 + a)*a^3*b) + 2/5*(10*b*c^3*x^2 - 15*a*c^2*d*x^2 - a*c^3)/(a^3*x^(5/2)) + 3/8*sqrt(2)*(3*(a*b^3)^(3/4)*b^3*c^3 - 5*(a*b^3)^(3/4)*a*b^2*c^2*d + (a*b^3)^(3/4)*a^2*b*c*d^2 + (a*b^3)^(3/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^4) + 3/8*sqrt(2)*(3*(a*b^3)^(3/4)*b^3*c^3 - 5*(a*b^3)^(3/4)*a*b^2*c^2*d + (a*b^3)^(3/4)*a^2*b*c*d^2 + (a*b^3)^(3/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^4) - 3/16*sqrt(2)*(3*(a*b^3)^(3/4)*b^3*c^3 - 5*(a*b^3)^(3/4)*a*b^2*c^2*d + (a*b^3)^(3/4)*a^2*b*c*d^2 + (a*b^3)^(3/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^4) + 3/16*sqrt(2)*(3*(a*b^3)^(3/4)*b^3*c^3 - 5*(a*b^3)^(3/4)*a*b^2*c^2*d + (a*b^3)^(3/4)*a^2*b*c*d^2 + (a*b^3)^(3/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^4)","A",0
460,1,509,0,0.462322," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(11 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 21 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{2}} + \frac{\sqrt{2} {\left(11 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 21 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \, a^{4} b^{2}} + \frac{\sqrt{2} {\left(11 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 21 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{2}} - \frac{\sqrt{2} {\left(11 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c^{3} - 21 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} c^{2} d + 9 \, \left(a b^{3}\right)^{\frac{1}{4}} a^{2} b c d^{2} + \left(a b^{3}\right)^{\frac{1}{4}} a^{3} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{16 \, a^{4} b^{2}} + \frac{b^{3} c^{3} \sqrt{x} - 3 \, a b^{2} c^{2} d \sqrt{x} + 3 \, a^{2} b c d^{2} \sqrt{x} - a^{3} d^{3} \sqrt{x}}{2 \, {\left(b x^{2} + a\right)} a^{3} b} + \frac{2 \, {\left(14 \, b c^{3} x^{2} - 21 \, a c^{2} d x^{2} - 3 \, a c^{3}\right)}}{21 \, a^{3} x^{\frac{7}{2}}}"," ",0,"1/8*sqrt(2)*(11*(a*b^3)^(1/4)*b^3*c^3 - 21*(a*b^3)^(1/4)*a*b^2*c^2*d + 9*(a*b^3)^(1/4)*a^2*b*c*d^2 + (a*b^3)^(1/4)*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) + 1/8*sqrt(2)*(11*(a*b^3)^(1/4)*b^3*c^3 - 21*(a*b^3)^(1/4)*a*b^2*c^2*d + 9*(a*b^3)^(1/4)*a^2*b*c*d^2 + (a*b^3)^(1/4)*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(a^4*b^2) + 1/16*sqrt(2)*(11*(a*b^3)^(1/4)*b^3*c^3 - 21*(a*b^3)^(1/4)*a*b^2*c^2*d + 9*(a*b^3)^(1/4)*a^2*b*c*d^2 + (a*b^3)^(1/4)*a^3*d^3)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) - 1/16*sqrt(2)*(11*(a*b^3)^(1/4)*b^3*c^3 - 21*(a*b^3)^(1/4)*a*b^2*c^2*d + 9*(a*b^3)^(1/4)*a^2*b*c*d^2 + (a*b^3)^(1/4)*a^3*d^3)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(a^4*b^2) + 1/2*(b^3*c^3*sqrt(x) - 3*a*b^2*c^2*d*sqrt(x) + 3*a^2*b*c*d^2*sqrt(x) - a^3*d^3*sqrt(x))/((b*x^2 + a)*a^3*b) + 2/21*(14*b*c^3*x^2 - 21*a*c^2*d*x^2 - 3*a*c^3)/(a^3*x^(7/2))","A",0
461,1,476,0,0.762664," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{3}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{5} c - \sqrt{2} a b^{4} d} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{5} c - \sqrt{2} a b^{4} d} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{4} - \sqrt{2} a d^{5}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{4} - \sqrt{2} a d^{5}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{5} c - \sqrt{2} a b^{4} d\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{5} c - \sqrt{2} a b^{4} d\right)}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} c \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{4} - \sqrt{2} a d^{5}\right)}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} c \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{4} - \sqrt{2} a d^{5}\right)}} + \frac{2 \, x^{\frac{3}{2}}}{3 \, b d}"," ",0,"(a*b^3)^(3/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^5*c - sqrt(2)*a*b^4*d) + (a*b^3)^(3/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^5*c - sqrt(2)*a*b^4*d) - (c*d^3)^(3/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^4 - sqrt(2)*a*d^5) - (c*d^3)^(3/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^4 - sqrt(2)*a*d^5) - 1/2*(a*b^3)^(3/4)*a*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^5*c - sqrt(2)*a*b^4*d) + 1/2*(a*b^3)^(3/4)*a*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^5*c - sqrt(2)*a*b^4*d) + 1/2*(c*d^3)^(3/4)*c*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^4 - sqrt(2)*a*d^5) - 1/2*(c*d^3)^(3/4)*c*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^4 - sqrt(2)*a*d^5) + 2/3*x^(3/2)/(b*d)","A",0
462,1,476,0,0.757343," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c - \sqrt{2} a b^{2} d} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c - \sqrt{2} a b^{2} d} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{2} - \sqrt{2} a d^{3}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{2} - \sqrt{2} a d^{3}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c - \sqrt{2} a b^{2} d\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c - \sqrt{2} a b^{2} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} c \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{2} - \sqrt{2} a d^{3}\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} c \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{2} - \sqrt{2} a d^{3}\right)}} + \frac{2 \, \sqrt{x}}{b d}"," ",0,"(a*b^3)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c - sqrt(2)*a*b^2*d) + (a*b^3)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c - sqrt(2)*a*b^2*d) - (c*d^3)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^2 - sqrt(2)*a*d^3) - (c*d^3)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^2 - sqrt(2)*a*d^3) + 1/2*(a*b^3)^(1/4)*a*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c - sqrt(2)*a*b^2*d) - 1/2*(a*b^3)^(1/4)*a*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c - sqrt(2)*a*b^2*d) - 1/2*(c*d^3)^(1/4)*c*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^2 - sqrt(2)*a*d^3) + 1/2*(c*d^3)^(1/4)*c*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^2 - sqrt(2)*a*d^3) + 2*sqrt(x)/(b*d)","A",0
463,1,457,0,0.687152," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c - \sqrt{2} a b^{3} d} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c - \sqrt{2} a b^{3} d} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{3} - \sqrt{2} a d^{4}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d^{3} - \sqrt{2} a d^{4}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c - \sqrt{2} a b^{3} d\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c - \sqrt{2} a b^{3} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{3} - \sqrt{2} a d^{4}\right)}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d^{3} - \sqrt{2} a d^{4}\right)}}"," ",0,"-(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c - sqrt(2)*a*b^3*d) - (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c - sqrt(2)*a*b^3*d) + (c*d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^3 - sqrt(2)*a*d^4) + (c*d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d^3 - sqrt(2)*a*d^4) + 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c - sqrt(2)*a*b^3*d) - 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c - sqrt(2)*a*b^3*d) - 1/2*(c*d^3)^(3/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^3 - sqrt(2)*a*d^4) + 1/2*(c*d^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d^3 - sqrt(2)*a*d^4)","A",0
464,1,441,0,0.644627," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} c - \sqrt{2} a b d} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} c - \sqrt{2} a b d} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d - \sqrt{2} a d^{2}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c d - \sqrt{2} a d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{2} c - \sqrt{2} a b d\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{2} c - \sqrt{2} a b d\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d - \sqrt{2} a d^{2}\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c d - \sqrt{2} a d^{2}\right)}}"," ",0,"-(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^2*c - sqrt(2)*a*b*d) - (a*b^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^2*c - sqrt(2)*a*b*d) + (c*d^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d - sqrt(2)*a*d^2) + (c*d^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c*d - sqrt(2)*a*d^2) - 1/2*(a*b^3)^(1/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^2*c - sqrt(2)*a*b*d) + 1/2*(a*b^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^2*c - sqrt(2)*a*b*d) + 1/2*(c*d^3)^(1/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d - sqrt(2)*a*d^2) - 1/2*(c*d^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c*d - sqrt(2)*a*d^2)","A",0
465,1,481,0,0.767478," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c - \sqrt{2} a^{2} b^{2} d} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c - \sqrt{2} a^{2} b^{2} d} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{2} d^{2} - \sqrt{2} a c d^{3}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{2} d^{2} - \sqrt{2} a c d^{3}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c - \sqrt{2} a^{2} b^{2} d\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c - \sqrt{2} a^{2} b^{2} d\right)}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{2} d^{2} - \sqrt{2} a c d^{3}\right)}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{2} d^{2} - \sqrt{2} a c d^{3}\right)}}"," ",0,"(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c - sqrt(2)*a^2*b^2*d) + (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c - sqrt(2)*a^2*b^2*d) - (c*d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^2*d^2 - sqrt(2)*a*c*d^3) - (c*d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^2*d^2 - sqrt(2)*a*c*d^3) - 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c - sqrt(2)*a^2*b^2*d) + 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c - sqrt(2)*a^2*b^2*d) + 1/2*(c*d^3)^(3/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^2*d^2 - sqrt(2)*a*c*d^3) - 1/2*(c*d^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^2*d^2 - sqrt(2)*a*c*d^3)","A",0
466,1,441,0,0.650435," ","integrate(1/(b*x^2+a)/(d*x^2+c)/x^(1/2),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b c - \sqrt{2} a^{2} d} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b c - \sqrt{2} a^{2} d} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{2} - \sqrt{2} a c d} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{2} - \sqrt{2} a c d} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b c - \sqrt{2} a^{2} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{2} - \sqrt{2} a c d\right)}}"," ",0,"(a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) + (a*b^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - (c*d^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) - (c*d^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) + 1/2*(a*b^3)^(1/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - 1/2*(a*b^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b*c - sqrt(2)*a^2*d) - 1/2*(c*d^3)^(1/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d) + 1/2*(c*d^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^2 - sqrt(2)*a*c*d)","A",0
467,1,492,0,0.858023," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c - \sqrt{2} a^{3} b d} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c - \sqrt{2} a^{3} b d} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{3} d - \sqrt{2} a c^{2} d^{2}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{3} d - \sqrt{2} a c^{2} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c - \sqrt{2} a^{3} b d\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c - \sqrt{2} a^{3} b d\right)}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{3} d - \sqrt{2} a c^{2} d^{2}\right)}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{3} d - \sqrt{2} a c^{2} d^{2}\right)}} - \frac{2}{a c \sqrt{x}}"," ",0,"-(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c - sqrt(2)*a^3*b*d) - (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c - sqrt(2)*a^3*b*d) + (c*d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^3*d - sqrt(2)*a*c^2*d^2) + (c*d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^3*d - sqrt(2)*a*c^2*d^2) + 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c - sqrt(2)*a^3*b*d) - 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c - sqrt(2)*a^3*b*d) - 1/2*(c*d^3)^(3/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^3*d - sqrt(2)*a*c^2*d^2) + 1/2*(c*d^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^3*d - sqrt(2)*a*c^2*d^2) - 2/(a*c*sqrt(x))","A",0
468,1,476,0,0.704795," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b c - \sqrt{2} a^{3} d} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b c - \sqrt{2} a^{3} d} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{3} - \sqrt{2} a c^{2} d} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{3} - \sqrt{2} a c^{2} d} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b c - \sqrt{2} a^{3} d\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b c - \sqrt{2} a^{3} d\right)}} + \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{3} - \sqrt{2} a c^{2} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{1}{4}} d \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{3} - \sqrt{2} a c^{2} d\right)}} - \frac{2}{3 \, a c x^{\frac{3}{2}}}"," ",0,"-(a*b^3)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b*c - sqrt(2)*a^3*d) - (a*b^3)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b*c - sqrt(2)*a^3*d) + (c*d^3)^(1/4)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^3 - sqrt(2)*a*c^2*d) + (c*d^3)^(1/4)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^3 - sqrt(2)*a*c^2*d) - 1/2*(a*b^3)^(1/4)*b*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b*c - sqrt(2)*a^3*d) + 1/2*(a*b^3)^(1/4)*b*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b*c - sqrt(2)*a^3*d) + 1/2*(c*d^3)^(1/4)*d*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^3 - sqrt(2)*a*c^2*d) - 1/2*(c*d^3)^(1/4)*d*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^3 - sqrt(2)*a*c^2*d) - 2/3/(a*c*x^(3/2))","A",0
469,1,487,0,0.740491," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b c - \sqrt{2} a^{4} d} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b c - \sqrt{2} a^{4} d} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{4} - \sqrt{2} a c^{3} d} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b c^{4} - \sqrt{2} a c^{3} d} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b c - \sqrt{2} a^{4} d\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b c - \sqrt{2} a^{4} d\right)}} + \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{4} - \sqrt{2} a c^{3} d\right)}} - \frac{\left(c d^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{2 \, {\left(\sqrt{2} b c^{4} - \sqrt{2} a c^{3} d\right)}} + \frac{2 \, {\left(5 \, b c x^{2} + 5 \, a d x^{2} - a c\right)}}{5 \, a^{2} c^{2} x^{\frac{5}{2}}}"," ",0,"(a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b*c - sqrt(2)*a^4*d) + (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b*c - sqrt(2)*a^4*d) - (c*d^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^4 - sqrt(2)*a*c^3*d) - (c*d^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b*c^4 - sqrt(2)*a*c^3*d) - 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b*c - sqrt(2)*a^4*d) + 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b*c - sqrt(2)*a^4*d) + 1/2*(c*d^3)^(3/4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^4 - sqrt(2)*a*c^3*d) - 1/2*(c*d^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b*c^4 - sqrt(2)*a*c^3*d) + 2/5*(5*b*c*x^2 + 5*a*d*x^2 - a*c)/(a^2*c^2*x^(5/2))","A",0
470,1,718,0,1.108440," ","integrate(x^(11/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} a^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} a^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} a^{2} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a^{2} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b c^{2} - 9 \, \left(c d^{3}\right)^{\frac{1}{4}} a c d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{3} - 2 \, \sqrt{2} a b c d^{4} + \sqrt{2} a^{2} d^{5}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b c^{2} - 9 \, \left(c d^{3}\right)^{\frac{1}{4}} a c d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{3} - 2 \, \sqrt{2} a b c d^{4} + \sqrt{2} a^{2} d^{5}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b c^{2} - 9 \, \left(c d^{3}\right)^{\frac{1}{4}} a c d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{3} - 2 \, \sqrt{2} a b c d^{4} + \sqrt{2} a^{2} d^{5}\right)}} + \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{1}{4}} b c^{2} - 9 \, \left(c d^{3}\right)^{\frac{1}{4}} a c d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{3} - 2 \, \sqrt{2} a b c d^{4} + \sqrt{2} a^{2} d^{5}\right)}} + \frac{c^{2} \sqrt{x}}{2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(d x^{2} + c\right)}} + \frac{2 \, \sqrt{x}}{b d^{2}}"," ",0,"-(a*b^3)^(1/4)*a^2*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) - (a*b^3)^(1/4)*a^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) - 1/2*(a*b^3)^(1/4)*a^2*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) + 1/2*(a*b^3)^(1/4)*a^2*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) - 1/4*(5*(c*d^3)^(1/4)*b*c^2 - 9*(c*d^3)^(1/4)*a*c*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^3 - 2*sqrt(2)*a*b*c*d^4 + sqrt(2)*a^2*d^5) - 1/4*(5*(c*d^3)^(1/4)*b*c^2 - 9*(c*d^3)^(1/4)*a*c*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^3 - 2*sqrt(2)*a*b*c*d^4 + sqrt(2)*a^2*d^5) - 1/8*(5*(c*d^3)^(1/4)*b*c^2 - 9*(c*d^3)^(1/4)*a*c*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^3 - 2*sqrt(2)*a*b*c*d^4 + sqrt(2)*a^2*d^5) + 1/8*(5*(c*d^3)^(1/4)*b*c^2 - 9*(c*d^3)^(1/4)*a*c*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^3 - 2*sqrt(2)*a*b*c*d^4 + sqrt(2)*a^2*d^5) + 1/2*c^2*sqrt(x)/((b*c*d^2 - a*d^3)*(d*x^2 + c)) + 2*sqrt(x)/(b*d^2)","A",0
471,1,681,0,1.244879," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{3}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{5} c^{2} - 2 \, \sqrt{2} a b^{4} c d + \sqrt{2} a^{2} b^{3} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{5} c^{2} - 2 \, \sqrt{2} a b^{4} c d + \sqrt{2} a^{2} b^{3} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{5} c^{2} - 2 \, \sqrt{2} a b^{4} c d + \sqrt{2} a^{2} b^{3} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} a \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{5} c^{2} - 2 \, \sqrt{2} a b^{4} c d + \sqrt{2} a^{2} b^{3} d^{2}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 7 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{4} - 2 \, \sqrt{2} a b c d^{5} + \sqrt{2} a^{2} d^{6}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 7 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{4} - 2 \, \sqrt{2} a b c d^{5} + \sqrt{2} a^{2} d^{6}\right)}} - \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 7 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{4} - 2 \, \sqrt{2} a b c d^{5} + \sqrt{2} a^{2} d^{6}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 7 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{4} - 2 \, \sqrt{2} a b c d^{5} + \sqrt{2} a^{2} d^{6}\right)}} - \frac{c x^{\frac{3}{2}}}{2 \, {\left(b c d - a d^{2}\right)} {\left(d x^{2} + c\right)}}"," ",0,"(a*b^3)^(3/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^5*c^2 - 2*sqrt(2)*a*b^4*c*d + sqrt(2)*a^2*b^3*d^2) + (a*b^3)^(3/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^5*c^2 - 2*sqrt(2)*a*b^4*c*d + sqrt(2)*a^2*b^3*d^2) - 1/2*(a*b^3)^(3/4)*a*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^5*c^2 - 2*sqrt(2)*a*b^4*c*d + sqrt(2)*a^2*b^3*d^2) + 1/2*(a*b^3)^(3/4)*a*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^5*c^2 - 2*sqrt(2)*a*b^4*c*d + sqrt(2)*a^2*b^3*d^2) + 1/4*(3*(c*d^3)^(3/4)*b*c - 7*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^4 - 2*sqrt(2)*a*b*c*d^5 + sqrt(2)*a^2*d^6) + 1/4*(3*(c*d^3)^(3/4)*b*c - 7*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^4 - 2*sqrt(2)*a*b*c*d^5 + sqrt(2)*a^2*d^6) - 1/8*(3*(c*d^3)^(3/4)*b*c - 7*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^4 - 2*sqrt(2)*a*b*c*d^5 + sqrt(2)*a^2*d^6) + 1/8*(3*(c*d^3)^(3/4)*b*c - 7*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^4 - 2*sqrt(2)*a*b*c*d^5 + sqrt(2)*a^2*d^6) - 1/2*c*x^(3/2)/((b*c*d - a*d^2)*(d*x^2 + c))","A",0
472,1,669,0,0.976691," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{2} - 2 \, \sqrt{2} a b^{2} c d + \sqrt{2} a^{2} b d^{2}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{2} - 2 \, \sqrt{2} a b^{2} c d + \sqrt{2} a^{2} b d^{2}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{2} - 2 \, \sqrt{2} a b^{2} c d + \sqrt{2} a^{2} b d^{2}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{2} - 2 \, \sqrt{2} a b^{2} c d + \sqrt{2} a^{2} b d^{2}\right)}} + \frac{{\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{2} - 2 \, \sqrt{2} a b c d^{3} + \sqrt{2} a^{2} d^{4}\right)}} + \frac{{\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{2} d^{2} - 2 \, \sqrt{2} a b c d^{3} + \sqrt{2} a^{2} d^{4}\right)}} + \frac{{\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{2} - 2 \, \sqrt{2} a b c d^{3} + \sqrt{2} a^{2} d^{4}\right)}} - \frac{{\left(\left(c d^{3}\right)^{\frac{1}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{2} d^{2} - 2 \, \sqrt{2} a b c d^{3} + \sqrt{2} a^{2} d^{4}\right)}} - \frac{c \sqrt{x}}{2 \, {\left(b c d - a d^{2}\right)} {\left(d x^{2} + c\right)}}"," ",0,"(a*b^3)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^2 - 2*sqrt(2)*a*b^2*c*d + sqrt(2)*a^2*b*d^2) + (a*b^3)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^2 - 2*sqrt(2)*a*b^2*c*d + sqrt(2)*a^2*b*d^2) + 1/2*(a*b^3)^(1/4)*a*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^2 - 2*sqrt(2)*a*b^2*c*d + sqrt(2)*a^2*b*d^2) - 1/2*(a*b^3)^(1/4)*a*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^2 - 2*sqrt(2)*a*b^2*c*d + sqrt(2)*a^2*b*d^2) + 1/4*((c*d^3)^(1/4)*b*c - 5*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^2 - 2*sqrt(2)*a*b*c*d^3 + sqrt(2)*a^2*d^4) + 1/4*((c*d^3)^(1/4)*b*c - 5*(c*d^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^2*d^2 - 2*sqrt(2)*a*b*c*d^3 + sqrt(2)*a^2*d^4) + 1/8*((c*d^3)^(1/4)*b*c - 5*(c*d^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^2 - 2*sqrt(2)*a*b*c*d^3 + sqrt(2)*a^2*d^4) - 1/8*((c*d^3)^(1/4)*b*c - 5*(c*d^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^2*d^2 - 2*sqrt(2)*a*b*c*d^3 + sqrt(2)*a^2*d^4) - 1/2*c*sqrt(x)/((b*c*d - a*d^2)*(d*x^2 + c))","A",0
473,1,683,0,0.934369," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(\left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} d^{3} - 2 \, \sqrt{2} a b c^{2} d^{4} + \sqrt{2} a^{2} c d^{5}\right)}} + \frac{{\left(\left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} d^{3} - 2 \, \sqrt{2} a b c^{2} d^{4} + \sqrt{2} a^{2} c d^{5}\right)}} - \frac{{\left(\left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{3} d^{3} - 2 \, \sqrt{2} a b c^{2} d^{4} + \sqrt{2} a^{2} c d^{5}\right)}} + \frac{{\left(\left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{3} d^{3} - 2 \, \sqrt{2} a b c^{2} d^{4} + \sqrt{2} a^{2} c d^{5}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{2} - 2 \, \sqrt{2} a b^{3} c d + \sqrt{2} a^{2} b^{2} d^{2}\right)}} + \frac{x^{\frac{3}{2}}}{2 \, {\left(d x^{2} + c\right)} {\left(b c - a d\right)}}"," ",0,"1/4*((c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3*d^3 - 2*sqrt(2)*a*b*c^2*d^4 + sqrt(2)*a^2*c*d^5) + 1/4*((c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3*d^3 - 2*sqrt(2)*a*b*c^2*d^4 + sqrt(2)*a^2*c*d^5) - 1/8*((c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^3*d^3 - 2*sqrt(2)*a*b*c^2*d^4 + sqrt(2)*a^2*c*d^5) + 1/8*((c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^3*d^3 - 2*sqrt(2)*a*b*c^2*d^4 + sqrt(2)*a^2*c*d^5) - (a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) - (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) + 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) - 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^2 - 2*sqrt(2)*a*b^3*c*d + sqrt(2)*a^2*b^2*d^2) + 1/2*x^(3/2)/((d*x^2 + c)*(b*c - a*d))","A",0
474,1,655,0,1.128485," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} d - 2 \, \sqrt{2} a b c^{2} d^{2} + \sqrt{2} a^{2} c d^{3}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{3} d - 2 \, \sqrt{2} a b c^{2} d^{2} + \sqrt{2} a^{2} c d^{3}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{3} d - 2 \, \sqrt{2} a b c^{2} d^{2} + \sqrt{2} a^{2} c d^{3}\right)}} - \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{3} d - 2 \, \sqrt{2} a b c^{2} d^{2} + \sqrt{2} a^{2} c d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} c^{2} - 2 \, \sqrt{2} a b c d + \sqrt{2} a^{2} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} c^{2} - 2 \, \sqrt{2} a b c d + \sqrt{2} a^{2} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{2} c^{2} - 2 \, \sqrt{2} a b c d + \sqrt{2} a^{2} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{2} c^{2} - 2 \, \sqrt{2} a b c d + \sqrt{2} a^{2} d^{2}\right)}} + \frac{\sqrt{x}}{2 \, {\left(d x^{2} + c\right)} {\left(b c - a d\right)}}"," ",0,"1/4*(3*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3*d - 2*sqrt(2)*a*b*c^2*d^2 + sqrt(2)*a^2*c*d^3) + 1/4*(3*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^3*d - 2*sqrt(2)*a*b*c^2*d^2 + sqrt(2)*a^2*c*d^3) + 1/8*(3*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^3*d - 2*sqrt(2)*a*b*c^2*d^2 + sqrt(2)*a^2*c*d^3) - 1/8*(3*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^3*d - 2*sqrt(2)*a*b*c^2*d^2 + sqrt(2)*a^2*c*d^3) - (a*b^3)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^2*c^2 - 2*sqrt(2)*a*b*c*d + sqrt(2)*a^2*d^2) - (a*b^3)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^2*c^2 - 2*sqrt(2)*a*b*c*d + sqrt(2)*a^2*d^2) - 1/2*(a*b^3)^(1/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^2*c^2 - 2*sqrt(2)*a*b*c*d + sqrt(2)*a^2*d^2) + 1/2*(a*b^3)^(1/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^2*c^2 - 2*sqrt(2)*a*b*c*d + sqrt(2)*a^2*d^2) + 1/2*sqrt(x)/((d*x^2 + c)*(b*c - a*d))","A",0
475,1,701,0,1.283537," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{4} d^{2} - 2 \, \sqrt{2} a b c^{3} d^{3} + \sqrt{2} a^{2} c^{2} d^{4}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{4} d^{2} - 2 \, \sqrt{2} a b c^{3} d^{3} + \sqrt{2} a^{2} c^{2} d^{4}\right)}} + \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} d^{2} - 2 \, \sqrt{2} a b c^{3} d^{3} + \sqrt{2} a^{2} c^{2} d^{4}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} d^{2} - 2 \, \sqrt{2} a b c^{3} d^{3} + \sqrt{2} a^{2} c^{2} d^{4}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{2} - 2 \, \sqrt{2} a^{2} b^{2} c d + \sqrt{2} a^{3} b d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{2} - 2 \, \sqrt{2} a^{2} b^{2} c d + \sqrt{2} a^{3} b d^{2}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{2} - 2 \, \sqrt{2} a^{2} b^{2} c d + \sqrt{2} a^{3} b d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{2} - 2 \, \sqrt{2} a^{2} b^{2} c d + \sqrt{2} a^{3} b d^{2}\right)}} - \frac{d x^{\frac{3}{2}}}{2 \, {\left(b c^{2} - a c d\right)} {\left(d x^{2} + c\right)}}"," ",0,"-1/4*(5*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4*d^2 - 2*sqrt(2)*a*b*c^3*d^3 + sqrt(2)*a^2*c^2*d^4) - 1/4*(5*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4*d^2 - 2*sqrt(2)*a*b*c^3*d^3 + sqrt(2)*a^2*c^2*d^4) + 1/8*(5*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^4*d^2 - 2*sqrt(2)*a*b*c^3*d^3 + sqrt(2)*a^2*c^2*d^4) - 1/8*(5*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^4*d^2 - 2*sqrt(2)*a*b*c^3*d^3 + sqrt(2)*a^2*c^2*d^4) + (a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^2 - 2*sqrt(2)*a^2*b^2*c*d + sqrt(2)*a^3*b*d^2) + (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^2 - 2*sqrt(2)*a^2*b^2*c*d + sqrt(2)*a^3*b*d^2) - 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^2 - 2*sqrt(2)*a^2*b^2*c*d + sqrt(2)*a^3*b*d^2) + 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^2 - 2*sqrt(2)*a^2*b^2*c*d + sqrt(2)*a^3*b*d^2) - 1/2*d*x^(3/2)/((b*c^2 - a*c*d)*(d*x^2 + c))","A",0
476,1,673,0,0.970457," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2/x^(1/2),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{2} c^{2} - 2 \, \sqrt{2} a^{2} b c d + \sqrt{2} a^{3} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} + \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{4} - 2 \, \sqrt{2} a b c^{3} d + \sqrt{2} a^{2} c^{2} d^{2}\right)}} - \frac{d \sqrt{x}}{2 \, {\left(b c^{2} - a c d\right)} {\left(d x^{2} + c\right)}}"," ",0,"(a*b^3)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) + (a*b^3)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) + 1/2*(a*b^3)^(1/4)*b*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) - 1/2*(a*b^3)^(1/4)*b*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^2*c^2 - 2*sqrt(2)*a^2*b*c*d + sqrt(2)*a^3*d^2) - 1/4*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/4*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/8*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) + 1/8*(7*(c*d^3)^(1/4)*b*c - 3*(c*d^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^4 - 2*sqrt(2)*a*b*c^3*d + sqrt(2)*a^2*c^2*d^2) - 1/2*d*sqrt(x)/((b*c^2 - a*c*d)*(d*x^2 + c))","A",0
477,1,725,0,1.168862," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{5} d - 2 \, \sqrt{2} a b c^{4} d^{2} + \sqrt{2} a^{2} c^{3} d^{3}\right)}} + \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{5} d - 2 \, \sqrt{2} a b c^{4} d^{2} + \sqrt{2} a^{2} c^{3} d^{3}\right)}} - \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{5} d - 2 \, \sqrt{2} a b c^{4} d^{2} + \sqrt{2} a^{2} c^{3} d^{3}\right)}} + \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{5} d - 2 \, \sqrt{2} a b c^{4} d^{2} + \sqrt{2} a^{2} c^{3} d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} - \frac{4 \, b c d x^{2} - 5 \, a d^{2} x^{2} + 4 \, b c^{2} - 4 \, a c d}{2 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} {\left(d x^{\frac{5}{2}} + c \sqrt{x}\right)}}"," ",0,"1/4*(9*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^5*d - 2*sqrt(2)*a*b*c^4*d^2 + sqrt(2)*a^2*c^3*d^3) + 1/4*(9*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^5*d - 2*sqrt(2)*a*b*c^4*d^2 + sqrt(2)*a^2*c^3*d^3) - 1/8*(9*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^5*d - 2*sqrt(2)*a*b*c^4*d^2 + sqrt(2)*a^2*c^3*d^3) + 1/8*(9*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^5*d - 2*sqrt(2)*a*b*c^4*d^2 + sqrt(2)*a^2*c^3*d^3) - (a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - 1/2*(4*b*c*d*x^2 - 5*a*d^2*x^2 + 4*b*c^2 - 4*a*c*d)/((a*b*c^3 - a^2*c^2*d)*(d*x^(5/2) + c*sqrt(x)))","A",0
478,1,718,0,1.151191," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{2} c^{2} - 2 \, \sqrt{2} a^{3} b c d + \sqrt{2} a^{4} d^{2}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{5} - 2 \, \sqrt{2} a b c^{4} d + \sqrt{2} a^{2} c^{3} d^{2}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{5} - 2 \, \sqrt{2} a b c^{4} d + \sqrt{2} a^{2} c^{3} d^{2}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{5} - 2 \, \sqrt{2} a b c^{4} d + \sqrt{2} a^{2} c^{3} d^{2}\right)}} - \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{5} - 2 \, \sqrt{2} a b c^{4} d + \sqrt{2} a^{2} c^{3} d^{2}\right)}} + \frac{d^{2} \sqrt{x}}{2 \, {\left(b c^{3} - a c^{2} d\right)} {\left(d x^{2} + c\right)}} - \frac{2}{3 \, a c^{2} x^{\frac{3}{2}}}"," ",0,"-(a*b^3)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - (a*b^3)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) - 1/2*(a*b^3)^(1/4)*b^2*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/2*(a*b^3)^(1/4)*b^2*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^2*c^2 - 2*sqrt(2)*a^3*b*c*d + sqrt(2)*a^4*d^2) + 1/4*(11*(c*d^3)^(1/4)*b*c*d - 7*(c*d^3)^(1/4)*a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^5 - 2*sqrt(2)*a*b*c^4*d + sqrt(2)*a^2*c^3*d^2) + 1/4*(11*(c*d^3)^(1/4)*b*c*d - 7*(c*d^3)^(1/4)*a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^5 - 2*sqrt(2)*a*b*c^4*d + sqrt(2)*a^2*c^3*d^2) + 1/8*(11*(c*d^3)^(1/4)*b*c*d - 7*(c*d^3)^(1/4)*a*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^5 - 2*sqrt(2)*a*b*c^4*d + sqrt(2)*a^2*c^3*d^2) - 1/8*(11*(c*d^3)^(1/4)*b*c*d - 7*(c*d^3)^(1/4)*a*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^5 - 2*sqrt(2)*a*b*c^4*d + sqrt(2)*a^2*c^3*d^2) + 1/2*d^2*sqrt(x)/((b*c^3 - a*c^2*d)*(d*x^2 + c)) - 2/3/(a*c^2*x^(3/2))","A",0
479,1,715,0,1.230875," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{d^{3} x^{\frac{3}{2}}}{2 \, {\left(b c^{4} - a c^{3} d\right)} {\left(d x^{2} + c\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} a^{4} b c d + \sqrt{2} a^{5} d^{2}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} a^{4} b c d + \sqrt{2} a^{5} d^{2}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} a^{4} b c d + \sqrt{2} a^{5} d^{2}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b^{2} c^{2} - 2 \, \sqrt{2} a^{4} b c d + \sqrt{2} a^{5} d^{2}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{6} - 2 \, \sqrt{2} a b c^{5} d + \sqrt{2} a^{2} c^{4} d^{2}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{2} c^{6} - 2 \, \sqrt{2} a b c^{5} d + \sqrt{2} a^{2} c^{4} d^{2}\right)}} + \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{6} - 2 \, \sqrt{2} a b c^{5} d + \sqrt{2} a^{2} c^{4} d^{2}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{2} c^{6} - 2 \, \sqrt{2} a b c^{5} d + \sqrt{2} a^{2} c^{4} d^{2}\right)}} + \frac{2 \, {\left(5 \, b c x^{2} + 10 \, a d x^{2} - a c\right)}}{5 \, a^{2} c^{3} x^{\frac{5}{2}}}"," ",0,"-1/2*d^3*x^(3/2)/((b*c^4 - a*c^3*d)*(d*x^2 + c)) + (a*b^3)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^2*c^2 - 2*sqrt(2)*a^4*b*c*d + sqrt(2)*a^5*d^2) + (a*b^3)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^2*c^2 - 2*sqrt(2)*a^4*b*c*d + sqrt(2)*a^5*d^2) - 1/2*(a*b^3)^(3/4)*b*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^2*c^2 - 2*sqrt(2)*a^4*b*c*d + sqrt(2)*a^5*d^2) + 1/2*(a*b^3)^(3/4)*b*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^2*c^2 - 2*sqrt(2)*a^4*b*c*d + sqrt(2)*a^5*d^2) - 1/4*(13*(c*d^3)^(3/4)*b*c - 9*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^6 - 2*sqrt(2)*a*b*c^5*d + sqrt(2)*a^2*c^4*d^2) - 1/4*(13*(c*d^3)^(3/4)*b*c - 9*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^2*c^6 - 2*sqrt(2)*a*b*c^5*d + sqrt(2)*a^2*c^4*d^2) + 1/8*(13*(c*d^3)^(3/4)*b*c - 9*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^6 - 2*sqrt(2)*a*b*c^5*d + sqrt(2)*a^2*c^4*d^2) - 1/8*(13*(c*d^3)^(3/4)*b*c - 9*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^2*c^6 - 2*sqrt(2)*a*b*c^5*d + sqrt(2)*a^2*c^4*d^2) + 2/5*(5*b*c*x^2 + 10*a*d*x^2 - a*c)/(a^2*c^3*x^(5/2))","A",0
480,1,944,0,1.567287," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} a \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} - \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} + \frac{b c d x^{\frac{5}{2}} - 9 \, a d^{2} x^{\frac{5}{2}} - 3 \, b c^{2} \sqrt{x} - 5 \, a c d \sqrt{x}}{16 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"(a*b^3)^(1/4)*a*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) + (a*b^3)^(1/4)*a*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) + 1/2*(a*b^3)^(1/4)*a*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) - 1/2*(a*b^3)^(1/4)*a*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) + 1/32*(3*(c*d^3)^(1/4)*b^2*c^2 - 30*(c*d^3)^(1/4)*a*b*c*d - 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) + 1/32*(3*(c*d^3)^(1/4)*b^2*c^2 - 30*(c*d^3)^(1/4)*a*b*c*d - 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) + 1/64*(3*(c*d^3)^(1/4)*b^2*c^2 - 30*(c*d^3)^(1/4)*a*b*c*d - 5*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) - 1/64*(3*(c*d^3)^(1/4)*b^2*c^2 - 30*(c*d^3)^(1/4)*a*b*c*d - 5*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) + 1/16*(b*c*d*x^(5/2) - 9*a*d^2*x^(5/2) - 3*b*c^2*sqrt(x) - 5*a*c*d*sqrt(x))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(d*x^2 + c)^2)","A",0
481,1,963,0,1.648421," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 30 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{5} d^{3} - 3 \, \sqrt{2} a b^{2} c^{4} d^{4} + 3 \, \sqrt{2} a^{2} b c^{3} d^{5} - \sqrt{2} a^{3} c^{2} d^{6}\right)}} + \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 30 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{5} d^{3} - 3 \, \sqrt{2} a b^{2} c^{4} d^{4} + 3 \, \sqrt{2} a^{2} b c^{3} d^{5} - \sqrt{2} a^{3} c^{2} d^{6}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 30 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{5} d^{3} - 3 \, \sqrt{2} a b^{2} c^{4} d^{4} + 3 \, \sqrt{2} a^{2} b c^{3} d^{5} - \sqrt{2} a^{3} c^{2} d^{6}\right)}} + \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 30 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{5} d^{3} - 3 \, \sqrt{2} a b^{2} c^{4} d^{4} + 3 \, \sqrt{2} a^{2} b c^{3} d^{5} - \sqrt{2} a^{3} c^{2} d^{6}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} + \frac{5 \, b c d x^{\frac{7}{2}} + 3 \, a d^{2} x^{\frac{7}{2}} + 9 \, b c^{2} x^{\frac{3}{2}} - a c d x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"1/32*(5*(c*d^3)^(3/4)*b^2*c^2 + 30*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d^3 - 3*sqrt(2)*a*b^2*c^4*d^4 + 3*sqrt(2)*a^2*b*c^3*d^5 - sqrt(2)*a^3*c^2*d^6) + 1/32*(5*(c*d^3)^(3/4)*b^2*c^2 + 30*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d^3 - 3*sqrt(2)*a*b^2*c^4*d^4 + 3*sqrt(2)*a^2*b*c^3*d^5 - sqrt(2)*a^3*c^2*d^6) - 1/64*(5*(c*d^3)^(3/4)*b^2*c^2 + 30*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d^3 - 3*sqrt(2)*a*b^2*c^4*d^4 + 3*sqrt(2)*a^2*b*c^3*d^5 - sqrt(2)*a^3*c^2*d^6) + 1/64*(5*(c*d^3)^(3/4)*b^2*c^2 + 30*(c*d^3)^(3/4)*a*b*c*d - 3*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d^3 - 3*sqrt(2)*a*b^2*c^4*d^4 + 3*sqrt(2)*a^2*b*c^3*d^5 - sqrt(2)*a^3*c^2*d^6) - (a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) - (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) + 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) - 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) + 1/16*(5*b*c*d*x^(7/2) + 3*a*d^2*x^(7/2) + 9*b*c^2*x^(3/2) - a*c*d*x^(3/2))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(d*x^2 + c)^2)","B",0
482,1,946,0,1.400983," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} b^{3} c^{3} - 3 \, \sqrt{2} a b^{2} c^{2} d + 3 \, \sqrt{2} a^{2} b c d^{2} - \sqrt{2} a^{3} d^{3}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 14 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 14 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 14 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} - \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 14 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{7 \, b c d x^{\frac{5}{2}} + a d^{2} x^{\frac{5}{2}} + 11 \, b c^{2} \sqrt{x} - 3 \, a c d \sqrt{x}}{16 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"-(a*b^3)^(1/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) - (a*b^3)^(1/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) - 1/2*(a*b^3)^(1/4)*b*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) + 1/2*(a*b^3)^(1/4)*b*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^3*c^3 - 3*sqrt(2)*a*b^2*c^2*d + 3*sqrt(2)*a^2*b*c*d^2 - sqrt(2)*a^3*d^3) + 1/32*(21*(c*d^3)^(1/4)*b^2*c^2 + 14*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/32*(21*(c*d^3)^(1/4)*b^2*c^2 + 14*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/64*(21*(c*d^3)^(1/4)*b^2*c^2 + 14*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) - 1/64*(21*(c*d^3)^(1/4)*b^2*c^2 + 14*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/16*(7*b*c*d*x^(5/2) + a*d^2*x^(5/2) + 11*b*c^2*sqrt(x) - 3*a*c*d*sqrt(x))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(d*x^2 + c)^2)","A",0
483,1,968,0,1.608265," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(45 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{6} d^{2} - 3 \, \sqrt{2} a b^{2} c^{5} d^{3} + 3 \, \sqrt{2} a^{2} b c^{4} d^{4} - \sqrt{2} a^{3} c^{3} d^{5}\right)}} - \frac{{\left(45 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{6} d^{2} - 3 \, \sqrt{2} a b^{2} c^{5} d^{3} + 3 \, \sqrt{2} a^{2} b c^{4} d^{4} - \sqrt{2} a^{3} c^{3} d^{5}\right)}} + \frac{{\left(45 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{6} d^{2} - 3 \, \sqrt{2} a b^{2} c^{5} d^{3} + 3 \, \sqrt{2} a^{2} b c^{4} d^{4} - \sqrt{2} a^{3} c^{3} d^{5}\right)}} - \frac{{\left(45 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{6} d^{2} - 3 \, \sqrt{2} a b^{2} c^{5} d^{3} + 3 \, \sqrt{2} a^{2} b c^{4} d^{4} - \sqrt{2} a^{3} c^{3} d^{5}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{13 \, b c d^{2} x^{\frac{7}{2}} - 5 \, a d^{3} x^{\frac{7}{2}} + 17 \, b c^{2} d x^{\frac{3}{2}} - 9 \, a c d^{2} x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"-1/32*(45*(c*d^3)^(3/4)*b^2*c^2 - 18*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6*d^2 - 3*sqrt(2)*a*b^2*c^5*d^3 + 3*sqrt(2)*a^2*b*c^4*d^4 - sqrt(2)*a^3*c^3*d^5) - 1/32*(45*(c*d^3)^(3/4)*b^2*c^2 - 18*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6*d^2 - 3*sqrt(2)*a*b^2*c^5*d^3 + 3*sqrt(2)*a^2*b*c^4*d^4 - sqrt(2)*a^3*c^3*d^5) + 1/64*(45*(c*d^3)^(3/4)*b^2*c^2 - 18*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6*d^2 - 3*sqrt(2)*a*b^2*c^5*d^3 + 3*sqrt(2)*a^2*b*c^4*d^4 - sqrt(2)*a^3*c^3*d^5) - 1/64*(45*(c*d^3)^(3/4)*b^2*c^2 - 18*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6*d^2 - 3*sqrt(2)*a*b^2*c^5*d^3 + 3*sqrt(2)*a^2*b*c^4*d^4 - sqrt(2)*a^3*c^3*d^5) + (a*b^3)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) + (a*b^3)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/2*(a*b^3)^(3/4)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) + 1/2*(a*b^3)^(3/4)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/16*(13*b*c*d^2*x^(7/2) - 5*a*d^3*x^(7/2) + 17*b*c^2*d*x^(3/2) - 9*a*c*d^2*x^(3/2))/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)^2)","A",0
484,1,960,0,1.455563," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3/x^(1/2),x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{2} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 66 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 66 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 66 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} + \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} - 66 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 21 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{15 \, b c d^{2} x^{\frac{5}{2}} - 7 \, a d^{3} x^{\frac{5}{2}} + 19 \, b c^{2} d \sqrt{x} - 11 \, a c d^{2} \sqrt{x}}{16 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"(a*b^3)^(1/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) + (a*b^3)^(1/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) + 1/2*(a*b^3)^(1/4)*b^2*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/2*(a*b^3)^(1/4)*b^2*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/32*(77*(c*d^3)^(1/4)*b^2*c^2 - 66*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/32*(77*(c*d^3)^(1/4)*b^2*c^2 - 66*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 - 66*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) + 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 - 66*(c*d^3)^(1/4)*a*b*c*d + 21*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/16*(15*b*c*d^2*x^(5/2) - 7*a*d^3*x^(5/2) + 19*b*c^2*d*sqrt(x) - 11*a*c*d^2*sqrt(x))/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)^2)","A",0
485,1,987,0,1.441003," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} b \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 130 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{7} d - 3 \, \sqrt{2} a b^{2} c^{6} d^{2} + 3 \, \sqrt{2} a^{2} b c^{5} d^{3} - \sqrt{2} a^{3} c^{4} d^{4}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 130 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{7} d - 3 \, \sqrt{2} a b^{2} c^{6} d^{2} + 3 \, \sqrt{2} a^{2} b c^{5} d^{3} - \sqrt{2} a^{3} c^{4} d^{4}\right)}} - \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 130 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{7} d - 3 \, \sqrt{2} a b^{2} c^{6} d^{2} + 3 \, \sqrt{2} a^{2} b c^{5} d^{3} - \sqrt{2} a^{3} c^{4} d^{4}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 130 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{7} d - 3 \, \sqrt{2} a b^{2} c^{6} d^{2} + 3 \, \sqrt{2} a^{2} b c^{5} d^{3} - \sqrt{2} a^{3} c^{4} d^{4}\right)}} + \frac{21 \, b c d^{3} x^{\frac{7}{2}} - 13 \, a d^{4} x^{\frac{7}{2}} + 25 \, b c^{2} d^{2} x^{\frac{3}{2}} - 17 \, a c d^{3} x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}} - \frac{2}{a c^{3} \sqrt{x}}"," ",0,"-(a*b^3)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - (a*b^3)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/2*(a*b^3)^(3/4)*b*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - 1/2*(a*b^3)^(3/4)*b*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 130*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7*d - 3*sqrt(2)*a*b^2*c^6*d^2 + 3*sqrt(2)*a^2*b*c^5*d^3 - sqrt(2)*a^3*c^4*d^4) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 130*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7*d - 3*sqrt(2)*a*b^2*c^6*d^2 + 3*sqrt(2)*a^2*b*c^5*d^3 - sqrt(2)*a^3*c^4*d^4) - 1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 130*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7*d - 3*sqrt(2)*a*b^2*c^6*d^2 + 3*sqrt(2)*a^2*b*c^5*d^3 - sqrt(2)*a^3*c^4*d^4) + 1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 130*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7*d - 3*sqrt(2)*a*b^2*c^6*d^2 + 3*sqrt(2)*a^2*b*c^5*d^3 - sqrt(2)*a^3*c^4*d^4) + 1/16*(21*b*c*d^3*x^(7/2) - 13*a*d^4*x^(7/2) + 25*b*c^2*d^2*x^(3/2) - 17*a*c*d^3*x^(3/2))/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*(d*x^2 + c)^2) - 2/(a*c^3*sqrt(x))","A",0
486,1,995,0,1.714717," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{3} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{\left(a b^{3}\right)^{\frac{1}{4}} b^{3} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(165 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 210 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{{\left(165 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 210 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{{\left(165 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 210 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} - \frac{{\left(165 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 210 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{23 \, b c d^{3} x^{\frac{5}{2}} - 15 \, a d^{4} x^{\frac{5}{2}} + 27 \, b c^{2} d^{2} \sqrt{x} - 19 \, a c d^{3} \sqrt{x}}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}} - \frac{2}{3 \, a c^{3} x^{\frac{3}{2}}}"," ",0,"-(a*b^3)^(1/4)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - (a*b^3)^(1/4)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - 1/2*(a*b^3)^(1/4)*b^3*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/2*(a*b^3)^(1/4)*b^3*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/32*(165*(c*d^3)^(1/4)*b^2*c^2*d - 210*(c*d^3)^(1/4)*a*b*c*d^2 + 77*(c*d^3)^(1/4)*a^2*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/32*(165*(c*d^3)^(1/4)*b^2*c^2*d - 210*(c*d^3)^(1/4)*a*b*c*d^2 + 77*(c*d^3)^(1/4)*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/64*(165*(c*d^3)^(1/4)*b^2*c^2*d - 210*(c*d^3)^(1/4)*a*b*c*d^2 + 77*(c*d^3)^(1/4)*a^2*d^3)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) - 1/64*(165*(c*d^3)^(1/4)*b^2*c^2*d - 210*(c*d^3)^(1/4)*a*b*c*d^2 + 77*(c*d^3)^(1/4)*a^2*d^3)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/16*(23*b*c*d^3*x^(5/2) - 15*a*d^4*x^(5/2) + 27*b*c^2*d^2*sqrt(x) - 19*a*c*d^3*sqrt(x))/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*(d*x^2 + c)^2) - 2/3/(a*c^3*x^(3/2))","A",0
487,1,1000,0,1.860178," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{\left(a b^{3}\right)^{\frac{3}{4}} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}} - \frac{\left(a b^{3}\right)^{\frac{3}{4}} b^{2} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} + \frac{\left(a b^{3}\right)^{\frac{3}{4}} b^{2} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{2 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 306 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{8} - 3 \, \sqrt{2} a b^{2} c^{7} d + 3 \, \sqrt{2} a^{2} b c^{6} d^{2} - \sqrt{2} a^{3} c^{5} d^{3}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 306 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{3} c^{8} - 3 \, \sqrt{2} a b^{2} c^{7} d + 3 \, \sqrt{2} a^{2} b c^{6} d^{2} - \sqrt{2} a^{3} c^{5} d^{3}\right)}} + \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 306 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{8} - 3 \, \sqrt{2} a b^{2} c^{7} d + 3 \, \sqrt{2} a^{2} b c^{6} d^{2} - \sqrt{2} a^{3} c^{5} d^{3}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 306 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 117 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{3} c^{8} - 3 \, \sqrt{2} a b^{2} c^{7} d + 3 \, \sqrt{2} a^{2} b c^{6} d^{2} - \sqrt{2} a^{3} c^{5} d^{3}\right)}} - \frac{29 \, b c d^{4} x^{\frac{7}{2}} - 21 \, a d^{5} x^{\frac{7}{2}} + 33 \, b c^{2} d^{3} x^{\frac{3}{2}} - 25 \, a c d^{4} x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}} + \frac{2 \, {\left(5 \, b c x^{2} + 15 \, a d x^{2} - a c\right)}}{5 \, a^{2} c^{4} x^{\frac{5}{2}}}"," ",0,"(a*b^3)^(3/4)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + (a*b^3)^(3/4)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/2*(a*b^3)^(3/4)*b^2*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + 1/2*(a*b^3)^(3/4)*b^2*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) + 1/64*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/64*(221*(c*d^3)^(3/4)*b^2*c^2 - 306*(c*d^3)^(3/4)*a*b*c*d + 117*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^8 - 3*sqrt(2)*a*b^2*c^7*d + 3*sqrt(2)*a^2*b*c^6*d^2 - sqrt(2)*a^3*c^5*d^3) - 1/16*(29*b*c*d^4*x^(7/2) - 21*a*d^5*x^(7/2) + 33*b*c^2*d^3*x^(3/2) - 25*a*c*d^4*x^(3/2))/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2)*(d*x^2 + c)^2) + 2/5*(5*b*c*x^2 + 15*a*d*x^2 - a*c)/(a^2*c^4*x^(5/2))","A",0
488,1,912,0,1.297934," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{3} d - 3 \, \sqrt{2} a b^{2} c^{2} d^{2} + 3 \, \sqrt{2} a^{2} b c d^{3} - \sqrt{2} a^{3} d^{4}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{3} d - 3 \, \sqrt{2} a b^{2} c^{2} d^{2} + 3 \, \sqrt{2} a^{2} b c d^{3} - \sqrt{2} a^{3} d^{4}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} + \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} b^{4} c^{3} - 3 \, \sqrt{2} a b^{3} c^{2} d + 3 \, \sqrt{2} a^{2} b^{2} c d^{2} - \sqrt{2} a^{3} b d^{3}\right)}} + \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{3} d - 3 \, \sqrt{2} a b^{2} c^{2} d^{2} + 3 \, \sqrt{2} a^{2} b c d^{3} - \sqrt{2} a^{3} d^{4}\right)}} - \frac{{\left(3 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{3} d - 3 \, \sqrt{2} a b^{2} c^{2} d^{2} + 3 \, \sqrt{2} a^{2} b c d^{3} - \sqrt{2} a^{3} d^{4}\right)}} + \frac{b c x^{\frac{5}{2}} + a d x^{\frac{5}{2}} + 2 \, a c \sqrt{x}}{2 \, {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"-1/4*(5*(a*b^3)^(1/4)*b*c + 3*(a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) - 1/4*(5*(a*b^3)^(1/4)*b*c + 3*(a*b^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) + 1/4*(3*(c*d^3)^(1/4)*b*c + 5*(c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^3*d - 3*sqrt(2)*a*b^2*c^2*d^2 + 3*sqrt(2)*a^2*b*c*d^3 - sqrt(2)*a^3*d^4) + 1/4*(3*(c*d^3)^(1/4)*b*c + 5*(c*d^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^3*d - 3*sqrt(2)*a*b^2*c^2*d^2 + 3*sqrt(2)*a^2*b*c*d^3 - sqrt(2)*a^3*d^4) - 1/8*(5*(a*b^3)^(1/4)*b*c + 3*(a*b^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) + 1/8*(5*(a*b^3)^(1/4)*b*c + 3*(a*b^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^3 - 3*sqrt(2)*a*b^3*c^2*d + 3*sqrt(2)*a^2*b^2*c*d^2 - sqrt(2)*a^3*b*d^3) + 1/8*(3*(c*d^3)^(1/4)*b*c + 5*(c*d^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^3*d - 3*sqrt(2)*a*b^2*c^2*d^2 + 3*sqrt(2)*a^2*b*c*d^3 - sqrt(2)*a^3*d^4) - 1/8*(3*(c*d^3)^(1/4)*b*c + 5*(c*d^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^3*d - 3*sqrt(2)*a*b^2*c^2*d^2 + 3*sqrt(2)*a^2*b*c*d^3 - sqrt(2)*a^3*d^4) + 1/2*(b*c*x^(5/2) + a*d*x^(5/2) + 2*a*c*sqrt(x))/((b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","A",0
489,1,952,0,1.757078," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{5} c^{3} - 3 \, \sqrt{2} a^{2} b^{4} c^{2} d + 3 \, \sqrt{2} a^{3} b^{3} c d^{2} - \sqrt{2} a^{4} b^{2} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{5} c^{3} - 3 \, \sqrt{2} a^{2} b^{4} c^{2} d + 3 \, \sqrt{2} a^{3} b^{3} c d^{2} - \sqrt{2} a^{4} b^{2} d^{3}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} - \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{5} c^{3} - 3 \, \sqrt{2} a^{2} b^{4} c^{2} d + 3 \, \sqrt{2} a^{3} b^{3} c d^{2} - \sqrt{2} a^{4} b^{2} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b c + 5 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{5} c^{3} - 3 \, \sqrt{2} a^{2} b^{4} c^{2} d + 3 \, \sqrt{2} a^{3} b^{3} c d^{2} - \sqrt{2} a^{4} b^{2} d^{3}\right)}} + \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} - \frac{{\left(5 \, \left(c d^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{4} d^{2} - 3 \, \sqrt{2} a b^{2} c^{3} d^{3} + 3 \, \sqrt{2} a^{2} b c^{2} d^{4} - \sqrt{2} a^{3} c d^{5}\right)}} - \frac{2 \, b d x^{\frac{7}{2}} + b c x^{\frac{3}{2}} + a d x^{\frac{3}{2}}}{2 \, {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"1/4*(3*(a*b^3)^(3/4)*b*c + 5*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^5*c^3 - 3*sqrt(2)*a^2*b^4*c^2*d + 3*sqrt(2)*a^3*b^3*c*d^2 - sqrt(2)*a^4*b^2*d^3) + 1/4*(3*(a*b^3)^(3/4)*b*c + 5*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^5*c^3 - 3*sqrt(2)*a^2*b^4*c^2*d + 3*sqrt(2)*a^3*b^3*c*d^2 - sqrt(2)*a^4*b^2*d^3) - 1/4*(5*(c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) - 1/4*(5*(c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) - 1/8*(3*(a*b^3)^(3/4)*b*c + 5*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^5*c^3 - 3*sqrt(2)*a^2*b^4*c^2*d + 3*sqrt(2)*a^3*b^3*c*d^2 - sqrt(2)*a^4*b^2*d^3) + 1/8*(3*(a*b^3)^(3/4)*b*c + 5*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^5*c^3 - 3*sqrt(2)*a^2*b^4*c^2*d + 3*sqrt(2)*a^3*b^3*c*d^2 - sqrt(2)*a^4*b^2*d^3) + 1/8*(5*(c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) - 1/8*(5*(c*d^3)^(3/4)*b*c + 3*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4*d^2 - 3*sqrt(2)*a*b^2*c^3*d^3 + 3*sqrt(2)*a^2*b*c^2*d^4 - sqrt(2)*a^3*c*d^5) - 1/2*(2*b*d*x^(7/2) + b*c*x^(3/2) + a*d*x^(3/2))/((b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","B",0
490,1,904,0,1.731380," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{4} - 3 \, \sqrt{2} a b^{2} c^{3} d + 3 \, \sqrt{2} a^{2} b c^{2} d^{2} - \sqrt{2} a^{3} c d^{3}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{4} - 3 \, \sqrt{2} a b^{2} c^{3} d + 3 \, \sqrt{2} a^{2} b c^{2} d^{2} - \sqrt{2} a^{3} c d^{3}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{3} c^{3} - 3 \, \sqrt{2} a^{2} b^{2} c^{2} d + 3 \, \sqrt{2} a^{3} b c d^{2} - \sqrt{2} a^{4} d^{3}\right)}} - \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{4} - 3 \, \sqrt{2} a b^{2} c^{3} d + 3 \, \sqrt{2} a^{2} b c^{2} d^{2} - \sqrt{2} a^{3} c d^{3}\right)}} + \frac{{\left(7 \, \left(c d^{3}\right)^{\frac{1}{4}} b c + \left(c d^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{4} - 3 \, \sqrt{2} a b^{2} c^{3} d + 3 \, \sqrt{2} a^{2} b c^{2} d^{2} - \sqrt{2} a^{3} c d^{3}\right)}} - \frac{2 \, b d x^{\frac{5}{2}} + b c \sqrt{x} + a d \sqrt{x}}{2 \, {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"1/4*((a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) + 1/4*((a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/4*(7*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4 - 3*sqrt(2)*a*b^2*c^3*d + 3*sqrt(2)*a^2*b*c^2*d^2 - sqrt(2)*a^3*c*d^3) - 1/4*(7*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^4 - 3*sqrt(2)*a*b^2*c^3*d + 3*sqrt(2)*a^2*b*c^2*d^2 - sqrt(2)*a^3*c*d^3) + 1/8*((a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/8*((a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^3*c^3 - 3*sqrt(2)*a^2*b^2*c^2*d + 3*sqrt(2)*a^3*b*c*d^2 - sqrt(2)*a^4*d^3) - 1/8*(7*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4 - 3*sqrt(2)*a*b^2*c^3*d + 3*sqrt(2)*a^2*b*c^2*d^2 - sqrt(2)*a^3*c*d^3) + 1/8*(7*(c*d^3)^(1/4)*b*c + (c*d^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^4 - 3*sqrt(2)*a*b^2*c^3*d + 3*sqrt(2)*a^2*b*c^2*d^2 - sqrt(2)*a^3*c*d^3) - 1/2*(2*b*d*x^(5/2) + b*c*sqrt(x) + a*d*sqrt(x))/((b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","B",0
491,1,973,0,1.642341," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{3} - 3 \, \sqrt{2} a^{3} b^{3} c^{2} d + 3 \, \sqrt{2} a^{4} b^{2} c d^{2} - \sqrt{2} a^{5} b d^{3}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{3} - 3 \, \sqrt{2} a^{3} b^{3} c^{2} d + 3 \, \sqrt{2} a^{4} b^{2} c d^{2} - \sqrt{2} a^{5} b d^{3}\right)}} + \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} - \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{3} - 3 \, \sqrt{2} a^{3} b^{3} c^{2} d + 3 \, \sqrt{2} a^{4} b^{2} c d^{2} - \sqrt{2} a^{5} b d^{3}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 9 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{3} - 3 \, \sqrt{2} a^{3} b^{3} c^{2} d + 3 \, \sqrt{2} a^{4} b^{2} c d^{2} - \sqrt{2} a^{5} b d^{3}\right)}} - \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{{\left(9 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} d - 3 \, \sqrt{2} a b^{2} c^{4} d^{2} + 3 \, \sqrt{2} a^{2} b c^{3} d^{3} - \sqrt{2} a^{3} c^{2} d^{4}\right)}} + \frac{b^{2} c d x^{\frac{7}{2}} + a b d^{2} x^{\frac{7}{2}} + b^{2} c^{2} x^{\frac{3}{2}} + a^{2} d^{2} x^{\frac{3}{2}}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}}"," ",0,"1/4*((a*b^3)^(3/4)*b*c - 9*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^3 - 3*sqrt(2)*a^3*b^3*c^2*d + 3*sqrt(2)*a^4*b^2*c*d^2 - sqrt(2)*a^5*b*d^3) + 1/4*((a*b^3)^(3/4)*b*c - 9*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^3 - 3*sqrt(2)*a^3*b^3*c^2*d + 3*sqrt(2)*a^4*b^2*c*d^2 - sqrt(2)*a^5*b*d^3) + 1/4*(9*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/4*(9*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) - 1/8*((a*b^3)^(3/4)*b*c - 9*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^3 - 3*sqrt(2)*a^3*b^3*c^2*d + 3*sqrt(2)*a^4*b^2*c*d^2 - sqrt(2)*a^5*b*d^3) + 1/8*((a*b^3)^(3/4)*b*c - 9*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^3 - 3*sqrt(2)*a^3*b^3*c^2*d + 3*sqrt(2)*a^4*b^2*c*d^2 - sqrt(2)*a^5*b*d^3) - 1/8*(9*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/8*(9*(c*d^3)^(3/4)*b*c - (c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5*d - 3*sqrt(2)*a*b^2*c^4*d^2 + 3*sqrt(2)*a^2*b*c^3*d^3 - sqrt(2)*a^3*c^2*d^4) + 1/2*(b^2*c*d*x^(7/2) + a*b*d^2*x^(7/2) + b^2*c^2*x^(3/2) + a^2*d^2*x^(3/2))/((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c))","B",0
492,1,977,0,1.285851," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""giac"")","\frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} - \frac{{\left(3 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{2} c - 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{3} c^{3} - 3 \, \sqrt{2} a^{3} b^{2} c^{2} d + 3 \, \sqrt{2} a^{4} b c d^{2} - \sqrt{2} a^{5} d^{3}\right)}} + \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} - \frac{{\left(11 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{5} - 3 \, \sqrt{2} a b^{2} c^{4} d + 3 \, \sqrt{2} a^{2} b c^{3} d^{2} - \sqrt{2} a^{3} c^{2} d^{3}\right)}} + \frac{b^{2} c d x^{\frac{5}{2}} + a b d^{2} x^{\frac{5}{2}} + b^{2} c^{2} \sqrt{x} + a^{2} d^{2} \sqrt{x}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}}"," ",0,"1/4*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/4*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/4*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/4*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/8*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) - 1/8*(3*(a*b^3)^(1/4)*b^2*c - 11*(a*b^3)^(1/4)*a*b*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^3*c^3 - 3*sqrt(2)*a^3*b^2*c^2*d + 3*sqrt(2)*a^4*b*c*d^2 - sqrt(2)*a^5*d^3) + 1/8*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) - 1/8*(11*(c*d^3)^(1/4)*b*c*d - 3*(c*d^3)^(1/4)*a*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^5 - 3*sqrt(2)*a*b^2*c^4*d + 3*sqrt(2)*a^2*b*c^3*d^2 - sqrt(2)*a^3*c^2*d^3) + 1/2*(b^2*c*d*x^(5/2) + a*b*d^2*x^(5/2) + b^2*c^2*sqrt(x) + a^2*d^2*sqrt(x))/((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c))","B",0
493,1,1035,0,1.560046," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} + \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} + \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(13 \, \left(c d^{3}\right)^{\frac{3}{4}} b c - 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{5 \, b^{3} c^{2} d x^{4} - 8 \, a b^{2} c d^{2} x^{4} + 5 \, a^{2} b d^{3} x^{4} + 5 \, b^{3} c^{3} x^{2} - 4 \, a b^{2} c^{2} d x^{2} - 4 \, a^{2} b c d^{2} x^{2} + 5 \, a^{3} d^{3} x^{2} + 4 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b d x^{\frac{9}{2}} + b c x^{\frac{5}{2}} + a d x^{\frac{5}{2}} + a c \sqrt{x}\right)}}"," ",0,"-1/4*(5*(a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(5*(a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(13*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/4*(13*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) + 1/8*(5*(a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/8*(5*(a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + 1/8*(13*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/8*(13*(c*d^3)^(3/4)*b*c - 5*(c*d^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/2*(5*b^3*c^2*d*x^4 - 8*a*b^2*c*d^2*x^4 + 5*a^2*b*d^3*x^4 + 5*b^3*c^3*x^2 - 4*a*b^2*c^2*d*x^2 - 4*a^2*b*c*d^2*x^2 + 5*a^3*d^3*x^2 + 4*a*b^2*c^3 - 8*a^2*b*c^2*d + 4*a^3*c*d^2)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*d*x^(9/2) + b*c*x^(5/2) + a*d*x^(5/2) + a*c*sqrt(x)))","A",0
494,1,1012,0,2.032060," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(15 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d^{2} - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(15 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d^{2} - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} + \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 15 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{3} c^{3} - 3 \, \sqrt{2} a^{4} b^{2} c^{2} d + 3 \, \sqrt{2} a^{5} b c d^{2} - \sqrt{2} a^{6} d^{3}\right)}} - \frac{{\left(15 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d^{2} - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} + \frac{{\left(15 \, \left(c d^{3}\right)^{\frac{1}{4}} b c d^{2} - 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{6} - 3 \, \sqrt{2} a b^{2} c^{5} d + 3 \, \sqrt{2} a^{2} b c^{4} d^{2} - \sqrt{2} a^{3} c^{3} d^{3}\right)}} - \frac{b^{3} c^{2} d x^{\frac{5}{2}} + a^{2} b d^{3} x^{\frac{5}{2}} + b^{3} c^{3} \sqrt{x} + a^{3} d^{3} \sqrt{x}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}} - \frac{2}{3 \, a^{2} c^{2} x^{\frac{3}{2}}}"," ",0,"-1/4*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/4*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/4*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/8*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) + 1/8*(7*(a*b^3)^(1/4)*b^3*c - 15*(a*b^3)^(1/4)*a*b^2*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^3*c^3 - 3*sqrt(2)*a^4*b^2*c^2*d + 3*sqrt(2)*a^5*b*c*d^2 - sqrt(2)*a^6*d^3) - 1/8*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) + 1/8*(15*(c*d^3)^(1/4)*b*c*d^2 - 7*(c*d^3)^(1/4)*a*d^3)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^6 - 3*sqrt(2)*a*b^2*c^5*d + 3*sqrt(2)*a^2*b*c^4*d^2 - sqrt(2)*a^3*c^3*d^3) - 1/2*(b^3*c^2*d*x^(5/2) + a^2*b*d^3*x^(5/2) + b^3*c^3*sqrt(x) + a^3*d^3*sqrt(x))/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)) - 2/3/(a^2*c^2*x^(3/2))","A",0
495,1,1015,0,1.961368," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(9 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{4} b^{3} c^{3} - 3 \, \sqrt{2} a^{5} b^{2} c^{2} d + 3 \, \sqrt{2} a^{6} b c d^{2} - \sqrt{2} a^{7} d^{3}\right)}} + \frac{{\left(9 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{4} b^{3} c^{3} - 3 \, \sqrt{2} a^{5} b^{2} c^{2} d + 3 \, \sqrt{2} a^{6} b c d^{2} - \sqrt{2} a^{7} d^{3}\right)}} + \frac{{\left(17 \, \left(c d^{3}\right)^{\frac{3}{4}} b c d - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{{\left(17 \, \left(c d^{3}\right)^{\frac{3}{4}} b c d - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} - \frac{{\left(9 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{4} b^{3} c^{3} - 3 \, \sqrt{2} a^{5} b^{2} c^{2} d + 3 \, \sqrt{2} a^{6} b c d^{2} - \sqrt{2} a^{7} d^{3}\right)}} + \frac{{\left(9 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{4} b^{3} c^{3} - 3 \, \sqrt{2} a^{5} b^{2} c^{2} d + 3 \, \sqrt{2} a^{6} b c d^{2} - \sqrt{2} a^{7} d^{3}\right)}} - \frac{{\left(17 \, \left(c d^{3}\right)^{\frac{3}{4}} b c d - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{{\left(17 \, \left(c d^{3}\right)^{\frac{3}{4}} b c d - 9 \, \left(c d^{3}\right)^{\frac{3}{4}} a d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{8 \, {\left(\sqrt{2} b^{3} c^{7} - 3 \, \sqrt{2} a b^{2} c^{6} d + 3 \, \sqrt{2} a^{2} b c^{5} d^{2} - \sqrt{2} a^{3} c^{4} d^{3}\right)}} + \frac{b^{4} c^{3} d x^{\frac{7}{2}} + a^{3} b d^{4} x^{\frac{7}{2}} + b^{4} c^{4} x^{\frac{3}{2}} + a^{4} d^{4} x^{\frac{3}{2}}}{2 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}} + \frac{2 \, {\left(10 \, b c x^{2} + 10 \, a d x^{2} - a c\right)}}{5 \, a^{3} c^{3} x^{\frac{5}{2}}}"," ",0,"1/4*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/4*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/4*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/4*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) - 1/8*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) + 1/8*(9*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^3*c^3 - 3*sqrt(2)*a^5*b^2*c^2*d + 3*sqrt(2)*a^6*b*c*d^2 - sqrt(2)*a^7*d^3) - 1/8*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/8*(17*(c*d^3)^(3/4)*b*c*d - 9*(c*d^3)^(3/4)*a*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^3*c^7 - 3*sqrt(2)*a*b^2*c^6*d + 3*sqrt(2)*a^2*b*c^5*d^2 - sqrt(2)*a^3*c^4*d^3) + 1/2*(b^4*c^3*d*x^(7/2) + a^3*b*d^4*x^(7/2) + b^4*c^4*x^(3/2) + a^4*d^4*x^(3/2))/((a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)) + 2/5*(10*b*c*x^2 + 10*a*d*x^2 - a*c)/(a^3*c^3*x^(5/2))","A",0
496,1,1193,0,2.212973," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{4} c^{4} - 4 \, \sqrt{2} a b^{3} c^{3} d + 6 \, \sqrt{2} a^{2} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{3} b c d^{3} + \sqrt{2} a^{4} d^{4}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} b^{4} c^{4} - 4 \, \sqrt{2} a b^{3} c^{3} d + 6 \, \sqrt{2} a^{2} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{3} b c d^{3} + \sqrt{2} a^{4} d^{4}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 70 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{5} d - 4 \, \sqrt{2} a b^{3} c^{4} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{3} d^{3} - 4 \, \sqrt{2} a^{3} b c^{2} d^{4} + \sqrt{2} a^{4} c d^{5}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 70 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{5} d - 4 \, \sqrt{2} a b^{3} c^{4} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{3} d^{3} - 4 \, \sqrt{2} a^{3} b c^{2} d^{4} + \sqrt{2} a^{4} c d^{5}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} b^{4} c^{4} - 4 \, \sqrt{2} a b^{3} c^{3} d + 6 \, \sqrt{2} a^{2} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{3} b c d^{3} + \sqrt{2} a^{4} d^{4}\right)}} + \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{1}{4}} b c + 7 \, \left(a b^{3}\right)^{\frac{1}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} b^{4} c^{4} - 4 \, \sqrt{2} a b^{3} c^{3} d + 6 \, \sqrt{2} a^{2} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{3} b c d^{3} + \sqrt{2} a^{4} d^{4}\right)}} + \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 70 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{5} d - 4 \, \sqrt{2} a b^{3} c^{4} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{3} d^{3} - 4 \, \sqrt{2} a^{3} b c^{2} d^{4} + \sqrt{2} a^{4} c d^{5}\right)}} - \frac{{\left(21 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 70 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{5} d - 4 \, \sqrt{2} a b^{3} c^{4} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{3} d^{3} - 4 \, \sqrt{2} a^{3} b c^{2} d^{4} + \sqrt{2} a^{4} c d^{5}\right)}} + \frac{a b \sqrt{x}}{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)} {\left(b x^{2} + a\right)}} + \frac{7 \, b c d x^{\frac{5}{2}} + 9 \, a d^{2} x^{\frac{5}{2}} + 11 \, b c^{2} \sqrt{x} + 5 \, a c d \sqrt{x}}{16 \, {\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(d x^{2} + c\right)}^{2}}"," ",0,"-1/4*(5*(a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^4 - 4*sqrt(2)*a*b^3*c^3*d + 6*sqrt(2)*a^2*b^2*c^2*d^2 - 4*sqrt(2)*a^3*b*c*d^3 + sqrt(2)*a^4*d^4) - 1/4*(5*(a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*b^4*c^4 - 4*sqrt(2)*a*b^3*c^3*d + 6*sqrt(2)*a^2*b^2*c^2*d^2 - 4*sqrt(2)*a^3*b*c*d^3 + sqrt(2)*a^4*d^4) + 1/32*(21*(c*d^3)^(1/4)*b^2*c^2 + 70*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^5*d - 4*sqrt(2)*a*b^3*c^4*d^2 + 6*sqrt(2)*a^2*b^2*c^3*d^3 - 4*sqrt(2)*a^3*b*c^2*d^4 + sqrt(2)*a^4*c*d^5) + 1/32*(21*(c*d^3)^(1/4)*b^2*c^2 + 70*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^5*d - 4*sqrt(2)*a*b^3*c^4*d^2 + 6*sqrt(2)*a^2*b^2*c^3*d^3 - 4*sqrt(2)*a^3*b*c^2*d^4 + sqrt(2)*a^4*c*d^5) - 1/8*(5*(a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^4 - 4*sqrt(2)*a*b^3*c^3*d + 6*sqrt(2)*a^2*b^2*c^2*d^2 - 4*sqrt(2)*a^3*b*c*d^3 + sqrt(2)*a^4*d^4) + 1/8*(5*(a*b^3)^(1/4)*b*c + 7*(a*b^3)^(1/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*b^4*c^4 - 4*sqrt(2)*a*b^3*c^3*d + 6*sqrt(2)*a^2*b^2*c^2*d^2 - 4*sqrt(2)*a^3*b*c*d^3 + sqrt(2)*a^4*d^4) + 1/64*(21*(c*d^3)^(1/4)*b^2*c^2 + 70*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^5*d - 4*sqrt(2)*a*b^3*c^4*d^2 + 6*sqrt(2)*a^2*b^2*c^3*d^3 - 4*sqrt(2)*a^3*b*c^2*d^4 + sqrt(2)*a^4*c*d^5) - 1/64*(21*(c*d^3)^(1/4)*b^2*c^2 + 70*(c*d^3)^(1/4)*a*b*c*d + 5*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^5*d - 4*sqrt(2)*a*b^3*c^4*d^2 + 6*sqrt(2)*a^2*b^2*c^3*d^3 - 4*sqrt(2)*a^3*b*c^2*d^4 + sqrt(2)*a^4*c*d^5) + 1/2*a*b*sqrt(x)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) + 1/16*(7*b*c*d*x^(5/2) + 9*a*d^2*x^(5/2) + 11*b*c^2*sqrt(x) + 5*a*c*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)*(d*x^2 + c)^2)","B",0
497,1,1238,0,2.572709," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{2} x^{\frac{3}{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)} {\left(b x^{2} + a\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{5} c^{4} - 4 \, \sqrt{2} a^{2} b^{4} c^{3} d + 6 \, \sqrt{2} a^{3} b^{3} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b^{2} c d^{3} + \sqrt{2} a^{5} b d^{4}\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{5} c^{4} - 4 \, \sqrt{2} a^{2} b^{4} c^{3} d + 6 \, \sqrt{2} a^{3} b^{3} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b^{2} c d^{3} + \sqrt{2} a^{5} b d^{4}\right)}} - \frac{3 \, {\left(15 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{6} d^{2} - 4 \, \sqrt{2} a b^{3} c^{5} d^{3} + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{4} - 4 \, \sqrt{2} a^{3} b c^{3} d^{5} + \sqrt{2} a^{4} c^{2} d^{6}\right)}} - \frac{3 \, {\left(15 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{6} d^{2} - 4 \, \sqrt{2} a b^{3} c^{5} d^{3} + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{4} - 4 \, \sqrt{2} a^{3} b c^{3} d^{5} + \sqrt{2} a^{4} c^{2} d^{6}\right)}} - \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{5} c^{4} - 4 \, \sqrt{2} a^{2} b^{4} c^{3} d + 6 \, \sqrt{2} a^{3} b^{3} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b^{2} c d^{3} + \sqrt{2} a^{5} b d^{4}\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{3}{4}} b c + 3 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{5} c^{4} - 4 \, \sqrt{2} a^{2} b^{4} c^{3} d + 6 \, \sqrt{2} a^{3} b^{3} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b^{2} c d^{3} + \sqrt{2} a^{5} b d^{4}\right)}} + \frac{3 \, {\left(15 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{6} d^{2} - 4 \, \sqrt{2} a b^{3} c^{5} d^{3} + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{4} - 4 \, \sqrt{2} a^{3} b c^{3} d^{5} + \sqrt{2} a^{4} c^{2} d^{6}\right)}} - \frac{3 \, {\left(15 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} + 18 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d - \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{6} d^{2} - 4 \, \sqrt{2} a b^{3} c^{5} d^{3} + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{4} - 4 \, \sqrt{2} a^{3} b c^{3} d^{5} + \sqrt{2} a^{4} c^{2} d^{6}\right)}} - \frac{13 \, b c d^{2} x^{\frac{7}{2}} + 3 \, a d^{3} x^{\frac{7}{2}} + 17 \, b c^{2} d x^{\frac{3}{2}} - a c d^{2} x^{\frac{3}{2}}}{16 \, {\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(d x^{2} + c\right)}^{2}}"," ",0,"-1/2*b^2*x^(3/2)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) + 3/4*((a*b^3)^(3/4)*b*c + 3*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^5*c^4 - 4*sqrt(2)*a^2*b^4*c^3*d + 6*sqrt(2)*a^3*b^3*c^2*d^2 - 4*sqrt(2)*a^4*b^2*c*d^3 + sqrt(2)*a^5*b*d^4) + 3/4*((a*b^3)^(3/4)*b*c + 3*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^5*c^4 - 4*sqrt(2)*a^2*b^4*c^3*d + 6*sqrt(2)*a^3*b^3*c^2*d^2 - 4*sqrt(2)*a^4*b^2*c*d^3 + sqrt(2)*a^5*b*d^4) - 3/32*(15*(c*d^3)^(3/4)*b^2*c^2 + 18*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^6*d^2 - 4*sqrt(2)*a*b^3*c^5*d^3 + 6*sqrt(2)*a^2*b^2*c^4*d^4 - 4*sqrt(2)*a^3*b*c^3*d^5 + sqrt(2)*a^4*c^2*d^6) - 3/32*(15*(c*d^3)^(3/4)*b^2*c^2 + 18*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^6*d^2 - 4*sqrt(2)*a*b^3*c^5*d^3 + 6*sqrt(2)*a^2*b^2*c^4*d^4 - 4*sqrt(2)*a^3*b*c^3*d^5 + sqrt(2)*a^4*c^2*d^6) - 3/8*((a*b^3)^(3/4)*b*c + 3*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^5*c^4 - 4*sqrt(2)*a^2*b^4*c^3*d + 6*sqrt(2)*a^3*b^3*c^2*d^2 - 4*sqrt(2)*a^4*b^2*c*d^3 + sqrt(2)*a^5*b*d^4) + 3/8*((a*b^3)^(3/4)*b*c + 3*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^5*c^4 - 4*sqrt(2)*a^2*b^4*c^3*d + 6*sqrt(2)*a^3*b^3*c^2*d^2 - 4*sqrt(2)*a^4*b^2*c*d^3 + sqrt(2)*a^5*b*d^4) + 3/64*(15*(c*d^3)^(3/4)*b^2*c^2 + 18*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6*d^2 - 4*sqrt(2)*a*b^3*c^5*d^3 + 6*sqrt(2)*a^2*b^2*c^4*d^4 - 4*sqrt(2)*a^3*b*c^3*d^5 + sqrt(2)*a^4*c^2*d^6) - 3/64*(15*(c*d^3)^(3/4)*b^2*c^2 + 18*(c*d^3)^(3/4)*a*b*c*d - (c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6*d^2 - 4*sqrt(2)*a*b^3*c^5*d^3 + 6*sqrt(2)*a^2*b^2*c^4*d^4 - 4*sqrt(2)*a^3*b*c^3*d^5 + sqrt(2)*a^4*c^2*d^6) - 1/16*(13*b*c*d^2*x^(7/2) + 3*a*d^3*x^(7/2) + 17*b*c^2*d*x^(3/2) - a*c*d^2*x^(3/2))/((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*x^2 + c)^2)","B",0
498,1,1217,0,2.322127," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{4} c^{4} - 4 \, \sqrt{2} a^{2} b^{3} c^{3} d + 6 \, \sqrt{2} a^{3} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b c d^{3} + \sqrt{2} a^{5} d^{4}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a b^{4} c^{4} - 4 \, \sqrt{2} a^{2} b^{3} c^{3} d + 6 \, \sqrt{2} a^{3} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b c d^{3} + \sqrt{2} a^{5} d^{4}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 22 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{6} - 4 \, \sqrt{2} a b^{3} c^{5} d + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{2} - 4 \, \sqrt{2} a^{3} b c^{3} d^{3} + \sqrt{2} a^{4} c^{2} d^{4}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 22 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{6} - 4 \, \sqrt{2} a b^{3} c^{5} d + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{2} - 4 \, \sqrt{2} a^{3} b c^{3} d^{3} + \sqrt{2} a^{4} c^{2} d^{4}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{4} c^{4} - 4 \, \sqrt{2} a^{2} b^{3} c^{3} d + 6 \, \sqrt{2} a^{3} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b c d^{3} + \sqrt{2} a^{5} d^{4}\right)}} - \frac{{\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{2} c + 11 \, \left(a b^{3}\right)^{\frac{1}{4}} a b d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a b^{4} c^{4} - 4 \, \sqrt{2} a^{2} b^{3} c^{3} d + 6 \, \sqrt{2} a^{3} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{4} b c d^{3} + \sqrt{2} a^{5} d^{4}\right)}} - \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 22 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{6} - 4 \, \sqrt{2} a b^{3} c^{5} d + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{2} - 4 \, \sqrt{2} a^{3} b c^{3} d^{3} + \sqrt{2} a^{4} c^{2} d^{4}\right)}} + \frac{{\left(77 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} + 22 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d - 3 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{6} - 4 \, \sqrt{2} a b^{3} c^{5} d + 6 \, \sqrt{2} a^{2} b^{2} c^{4} d^{2} - 4 \, \sqrt{2} a^{3} b c^{3} d^{3} + \sqrt{2} a^{4} c^{2} d^{4}\right)}} - \frac{b^{2} \sqrt{x}}{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)} {\left(b x^{2} + a\right)}} - \frac{15 \, b c d^{2} x^{\frac{5}{2}} + a d^{3} x^{\frac{5}{2}} + 19 \, b c^{2} d \sqrt{x} - 3 \, a c d^{2} \sqrt{x}}{16 \, {\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(d x^{2} + c\right)}^{2}}"," ",0,"1/4*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3 + sqrt(2)*a^5*d^4) + 1/4*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3 + sqrt(2)*a^5*d^4) - 1/32*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) - 1/32*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) + 1/8*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3 + sqrt(2)*a^5*d^4) - 1/8*((a*b^3)^(1/4)*b^2*c + 11*(a*b^3)^(1/4)*a*b*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a*b^4*c^4 - 4*sqrt(2)*a^2*b^3*c^3*d + 6*sqrt(2)*a^3*b^2*c^2*d^2 - 4*sqrt(2)*a^4*b*c*d^3 + sqrt(2)*a^5*d^4) - 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) + 1/64*(77*(c*d^3)^(1/4)*b^2*c^2 + 22*(c*d^3)^(1/4)*a*b*c*d - 3*(c*d^3)^(1/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^6 - 4*sqrt(2)*a*b^3*c^5*d + 6*sqrt(2)*a^2*b^2*c^4*d^2 - 4*sqrt(2)*a^3*b*c^3*d^3 + sqrt(2)*a^4*c^2*d^4) - 1/2*b^2*sqrt(x)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(b*x^2 + a)) - 1/16*(15*b*c*d^2*x^(5/2) + a*d^3*x^(5/2) + 19*b*c^2*d*sqrt(x) - 3*a*c*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)*(d*x^2 + c)^2)","B",0
499,1,1233,0,2.587742," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} x^{\frac{3}{2}}}{2 \, {\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(b x^{2} + a\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 26 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{7} d - 4 \, \sqrt{2} a b^{3} c^{6} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{3} - 4 \, \sqrt{2} a^{3} b c^{4} d^{4} + \sqrt{2} a^{4} c^{3} d^{5}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 26 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{7} d - 4 \, \sqrt{2} a b^{3} c^{6} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{3} - 4 \, \sqrt{2} a^{3} b c^{4} d^{4} + \sqrt{2} a^{4} c^{3} d^{5}\right)}} - \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{{\left(\left(a b^{3}\right)^{\frac{3}{4}} b c - 13 \, \left(a b^{3}\right)^{\frac{3}{4}} a d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} - \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 26 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{7} d - 4 \, \sqrt{2} a b^{3} c^{6} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{3} - 4 \, \sqrt{2} a^{3} b c^{4} d^{4} + \sqrt{2} a^{4} c^{3} d^{5}\right)}} + \frac{{\left(117 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 26 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 5 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{7} d - 4 \, \sqrt{2} a b^{3} c^{6} d^{2} + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{3} - 4 \, \sqrt{2} a^{3} b c^{4} d^{4} + \sqrt{2} a^{4} c^{3} d^{5}\right)}} + \frac{21 \, b c d^{3} x^{\frac{7}{2}} - 5 \, a d^{4} x^{\frac{7}{2}} + 25 \, b c^{2} d^{2} x^{\frac{3}{2}} - 9 \, a c d^{3} x^{\frac{3}{2}}}{16 \, {\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)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"1/2*b^3*x^(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)*(b*x^2 + a)) + 1/4*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 1/4*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/32*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) - 1/8*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 1/8*((a*b^3)^(3/4)*b*c - 13*(a*b^3)^(3/4)*a*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) - 1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/64*(117*(c*d^3)^(3/4)*b^2*c^2 - 26*(c*d^3)^(3/4)*a*b*c*d + 5*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7*d - 4*sqrt(2)*a*b^3*c^6*d^2 + 6*sqrt(2)*a^2*b^2*c^5*d^3 - 4*sqrt(2)*a^3*b*c^4*d^4 + sqrt(2)*a^4*c^3*d^5) + 1/16*(21*b*c*d^3*x^(7/2) - 5*a*d^4*x^(7/2) + 25*b*c^2*d^2*x^(3/2) - 9*a*c*d^3*x^(3/2))/((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)*(d*x^2 + c)^2)","B",0
500,1,1253,0,2.534532," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""giac"")","\frac{b^{3} \sqrt{x}}{2 \, {\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(b x^{2} + a\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{3 \, {\left(55 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{7} - 4 \, \sqrt{2} a b^{3} c^{6} d + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{2} - 4 \, \sqrt{2} a^{3} b c^{4} d^{3} + \sqrt{2} a^{4} c^{3} d^{4}\right)}} + \frac{3 \, {\left(55 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{7} - 4 \, \sqrt{2} a b^{3} c^{6} d + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{2} - 4 \, \sqrt{2} a^{3} b c^{4} d^{3} + \sqrt{2} a^{4} c^{3} d^{4}\right)}} + \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} - \frac{3 \, {\left(\left(a b^{3}\right)^{\frac{1}{4}} b^{3} c - 5 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{2} d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{2} b^{4} c^{4} - 4 \, \sqrt{2} a^{3} b^{3} c^{3} d + 6 \, \sqrt{2} a^{4} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{5} b c d^{3} + \sqrt{2} a^{6} d^{4}\right)}} + \frac{3 \, {\left(55 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{7} - 4 \, \sqrt{2} a b^{3} c^{6} d + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{2} - 4 \, \sqrt{2} a^{3} b c^{4} d^{3} + \sqrt{2} a^{4} c^{3} d^{4}\right)}} - \frac{3 \, {\left(55 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d - 30 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{2} + 7 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{7} - 4 \, \sqrt{2} a b^{3} c^{6} d + 6 \, \sqrt{2} a^{2} b^{2} c^{5} d^{2} - 4 \, \sqrt{2} a^{3} b c^{4} d^{3} + \sqrt{2} a^{4} c^{3} d^{4}\right)}} + \frac{23 \, b c d^{3} x^{\frac{5}{2}} - 7 \, a d^{4} x^{\frac{5}{2}} + 27 \, b c^{2} d^{2} \sqrt{x} - 11 \, a c d^{3} \sqrt{x}}{16 \, {\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)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"1/2*b^3*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*x^2 + a)) + 3/4*((a*b^3)^(1/4)*b^3*c - 5*(a*b^3)^(1/4)*a*b^2*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 3/4*((a*b^3)^(1/4)*b^3*c - 5*(a*b^3)^(1/4)*a*b^2*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 3/32*(55*(c*d^3)^(1/4)*b^2*c^2*d - 30*(c*d^3)^(1/4)*a*b*c*d^2 + 7*(c*d^3)^(1/4)*a^2*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^7 - 4*sqrt(2)*a*b^3*c^6*d + 6*sqrt(2)*a^2*b^2*c^5*d^2 - 4*sqrt(2)*a^3*b*c^4*d^3 + sqrt(2)*a^4*c^3*d^4) + 3/32*(55*(c*d^3)^(1/4)*b^2*c^2*d - 30*(c*d^3)^(1/4)*a*b*c*d^2 + 7*(c*d^3)^(1/4)*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^7 - 4*sqrt(2)*a*b^3*c^6*d + 6*sqrt(2)*a^2*b^2*c^5*d^2 - 4*sqrt(2)*a^3*b*c^4*d^3 + sqrt(2)*a^4*c^3*d^4) + 3/8*((a*b^3)^(1/4)*b^3*c - 5*(a*b^3)^(1/4)*a*b^2*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) - 3/8*((a*b^3)^(1/4)*b^3*c - 5*(a*b^3)^(1/4)*a*b^2*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^2*b^4*c^4 - 4*sqrt(2)*a^3*b^3*c^3*d + 6*sqrt(2)*a^4*b^2*c^2*d^2 - 4*sqrt(2)*a^5*b*c*d^3 + sqrt(2)*a^6*d^4) + 3/64*(55*(c*d^3)^(1/4)*b^2*c^2*d - 30*(c*d^3)^(1/4)*a*b*c*d^2 + 7*(c*d^3)^(1/4)*a^2*d^3)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7 - 4*sqrt(2)*a*b^3*c^6*d + 6*sqrt(2)*a^2*b^2*c^5*d^2 - 4*sqrt(2)*a^3*b*c^4*d^3 + sqrt(2)*a^4*c^3*d^4) - 3/64*(55*(c*d^3)^(1/4)*b^2*c^2*d - 30*(c*d^3)^(1/4)*a*b*c*d^2 + 7*(c*d^3)^(1/4)*a^2*d^3)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^7 - 4*sqrt(2)*a*b^3*c^6*d + 6*sqrt(2)*a^2*b^2*c^5*d^2 - 4*sqrt(2)*a^3*b*c^4*d^3 + sqrt(2)*a^4*c^3*d^4) + 1/16*(23*b*c*d^3*x^(5/2) - 7*a*d^4*x^(5/2) + 27*b*c^2*d^2*sqrt(x) - 11*a*c*d^3*sqrt(x))/((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)*(d*x^2 + c)^2)","B",0
501,1,1333,0,3.046602," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 170 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 170 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} + \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(5 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{2} c - 17 \, \left(a b^{3}\right)^{\frac{3}{4}} a b d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} + \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 170 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{{\left(221 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} - 170 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d + 45 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{2}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{5 \, b^{4} c^{3} x^{2} - 12 \, a b^{3} c^{2} d x^{2} + 12 \, a^{2} b^{2} c d^{2} x^{2} - 4 \, a^{3} b d^{3} x^{2} + 4 \, a b^{3} c^{3} - 12 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} - 4 \, a^{4} d^{3}}{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}\right)} {\left(b x^{\frac{5}{2}} + a \sqrt{x}\right)}} - \frac{29 \, b c d^{4} x^{\frac{7}{2}} - 13 \, a d^{5} x^{\frac{7}{2}} + 33 \, b c^{2} d^{3} x^{\frac{3}{2}} - 17 \, a c d^{4} x^{\frac{3}{2}}}{16 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"-1/4*(5*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/4*(5*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 170*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/32*(221*(c*d^3)^(3/4)*b^2*c^2 - 170*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) + 1/8*(5*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/8*(5*(a*b^3)^(3/4)*b^2*c - 17*(a*b^3)^(3/4)*a*b*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) + 1/64*(221*(c*d^3)^(3/4)*b^2*c^2 - 170*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/64*(221*(c*d^3)^(3/4)*b^2*c^2 - 170*(c*d^3)^(3/4)*a*b*c*d + 45*(c*d^3)^(3/4)*a^2*d^2)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/2*(5*b^4*c^3*x^2 - 12*a*b^3*c^2*d*x^2 + 12*a^2*b^2*c*d^2*x^2 - 4*a^3*b*d^3*x^2 + 4*a*b^3*c^3 - 12*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 - 4*a^4*d^3)/((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)*(b*x^(5/2) + a*sqrt(x))) - 1/16*(29*b*c*d^4*x^(7/2) - 13*a*d^5*x^(7/2) + 33*b*c^2*d^3*x^(3/2) - 17*a*c*d^4*x^(3/2))/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*(d*x^2 + c)^2)","B",0
502,1,1278,0,2.534828," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{4} \sqrt{x}}{2 \, {\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)} {\left(b x^{2} + a\right)}} - \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c - 19 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c - 19 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(285 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d^{2} - 266 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{3} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{{\left(285 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d^{2} - 266 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{3} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{4}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c - 19 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} + \frac{{\left(7 \, \left(a b^{3}\right)^{\frac{1}{4}} b^{4} c - 19 \, \left(a b^{3}\right)^{\frac{1}{4}} a b^{3} d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{3} b^{4} c^{4} - 4 \, \sqrt{2} a^{4} b^{3} c^{3} d + 6 \, \sqrt{2} a^{5} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{6} b c d^{3} + \sqrt{2} a^{7} d^{4}\right)}} - \frac{{\left(285 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d^{2} - 266 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{3} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{4}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} + \frac{{\left(285 \, \left(c d^{3}\right)^{\frac{1}{4}} b^{2} c^{2} d^{2} - 266 \, \left(c d^{3}\right)^{\frac{1}{4}} a b c d^{3} + 77 \, \left(c d^{3}\right)^{\frac{1}{4}} a^{2} d^{4}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{8} - 4 \, \sqrt{2} a b^{3} c^{7} d + 6 \, \sqrt{2} a^{2} b^{2} c^{6} d^{2} - 4 \, \sqrt{2} a^{3} b c^{5} d^{3} + \sqrt{2} a^{4} c^{4} d^{4}\right)}} - \frac{31 \, b c d^{4} x^{\frac{5}{2}} - 15 \, a d^{5} x^{\frac{5}{2}} + 35 \, b c^{2} d^{3} \sqrt{x} - 19 \, a c d^{4} \sqrt{x}}{16 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}} - \frac{2}{3 \, a^{2} c^{3} x^{\frac{3}{2}}}"," ",0,"-1/2*b^4*sqrt(x)/((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)*(b*x^2 + a)) - 1/4*(7*(a*b^3)^(1/4)*b^4*c - 19*(a*b^3)^(1/4)*a*b^3*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/4*(7*(a*b^3)^(1/4)*b^4*c - 19*(a*b^3)^(1/4)*a*b^3*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/32*(285*(c*d^3)^(1/4)*b^2*c^2*d^2 - 266*(c*d^3)^(1/4)*a*b*c*d^3 + 77*(c*d^3)^(1/4)*a^2*d^4)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/32*(285*(c*d^3)^(1/4)*b^2*c^2*d^2 - 266*(c*d^3)^(1/4)*a*b*c*d^3 + 77*(c*d^3)^(1/4)*a^2*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/8*(7*(a*b^3)^(1/4)*b^4*c - 19*(a*b^3)^(1/4)*a*b^3*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) + 1/8*(7*(a*b^3)^(1/4)*b^4*c - 19*(a*b^3)^(1/4)*a*b^3*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^3*b^4*c^4 - 4*sqrt(2)*a^4*b^3*c^3*d + 6*sqrt(2)*a^5*b^2*c^2*d^2 - 4*sqrt(2)*a^6*b*c*d^3 + sqrt(2)*a^7*d^4) - 1/64*(285*(c*d^3)^(1/4)*b^2*c^2*d^2 - 266*(c*d^3)^(1/4)*a*b*c*d^3 + 77*(c*d^3)^(1/4)*a^2*d^4)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) + 1/64*(285*(c*d^3)^(1/4)*b^2*c^2*d^2 - 266*(c*d^3)^(1/4)*a*b*c*d^3 + 77*(c*d^3)^(1/4)*a^2*d^4)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^8 - 4*sqrt(2)*a*b^3*c^7*d + 6*sqrt(2)*a^2*b^2*c^6*d^2 - 4*sqrt(2)*a^3*b*c^5*d^3 + sqrt(2)*a^4*c^4*d^4) - 1/16*(31*b*c*d^4*x^(5/2) - 15*a*d^5*x^(5/2) + 35*b*c^2*d^3*sqrt(x) - 19*a*c*d^4*sqrt(x))/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*(d*x^2 + c)^2) - 2/3/(a^2*c^3*x^(3/2))","A",0
503,1,1289,0,2.728623," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{5} x^{\frac{3}{2}}}{2 \, {\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}\right)} {\left(b x^{2} + a\right)}} + \frac{3 \, {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{4} b^{4} c^{4} - 4 \, \sqrt{2} a^{5} b^{3} c^{3} d + 6 \, \sqrt{2} a^{6} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{7} b c d^{3} + \sqrt{2} a^{8} d^{4}\right)}} + \frac{3 \, {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \, {\left(\sqrt{2} a^{4} b^{4} c^{4} - 4 \, \sqrt{2} a^{5} b^{3} c^{3} d + 6 \, \sqrt{2} a^{6} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{7} b c d^{3} + \sqrt{2} a^{8} d^{4}\right)}} + \frac{3 \, {\left(119 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} d - 126 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d^{2} + 39 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} + 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{9} - 4 \, \sqrt{2} a b^{3} c^{8} d + 6 \, \sqrt{2} a^{2} b^{2} c^{7} d^{2} - 4 \, \sqrt{2} a^{3} b c^{6} d^{3} + \sqrt{2} a^{4} c^{5} d^{4}\right)}} + \frac{3 \, {\left(119 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} d - 126 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d^{2} + 39 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{c}{d}\right)^{\frac{1}{4}} - 2 \, \sqrt{x}\right)}}{2 \, \left(\frac{c}{d}\right)^{\frac{1}{4}}}\right)}{32 \, {\left(\sqrt{2} b^{4} c^{9} - 4 \, \sqrt{2} a b^{3} c^{8} d + 6 \, \sqrt{2} a^{2} b^{2} c^{7} d^{2} - 4 \, \sqrt{2} a^{3} b c^{6} d^{3} + \sqrt{2} a^{4} c^{5} d^{4}\right)}} - \frac{3 \, {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} d\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{4} b^{4} c^{4} - 4 \, \sqrt{2} a^{5} b^{3} c^{3} d + 6 \, \sqrt{2} a^{6} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{7} b c d^{3} + \sqrt{2} a^{8} d^{4}\right)}} + \frac{3 \, {\left(3 \, \left(a b^{3}\right)^{\frac{3}{4}} b^{3} c - 7 \, \left(a b^{3}\right)^{\frac{3}{4}} a b^{2} d\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{a}{b}\right)^{\frac{1}{4}} + x + \sqrt{\frac{a}{b}}\right)}{8 \, {\left(\sqrt{2} a^{4} b^{4} c^{4} - 4 \, \sqrt{2} a^{5} b^{3} c^{3} d + 6 \, \sqrt{2} a^{6} b^{2} c^{2} d^{2} - 4 \, \sqrt{2} a^{7} b c d^{3} + \sqrt{2} a^{8} d^{4}\right)}} - \frac{3 \, {\left(119 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} d - 126 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d^{2} + 39 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{3}\right)} \log\left(\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{9} - 4 \, \sqrt{2} a b^{3} c^{8} d + 6 \, \sqrt{2} a^{2} b^{2} c^{7} d^{2} - 4 \, \sqrt{2} a^{3} b c^{6} d^{3} + \sqrt{2} a^{4} c^{5} d^{4}\right)}} + \frac{3 \, {\left(119 \, \left(c d^{3}\right)^{\frac{3}{4}} b^{2} c^{2} d - 126 \, \left(c d^{3}\right)^{\frac{3}{4}} a b c d^{2} + 39 \, \left(c d^{3}\right)^{\frac{3}{4}} a^{2} d^{3}\right)} \log\left(-\sqrt{2} \sqrt{x} \left(\frac{c}{d}\right)^{\frac{1}{4}} + x + \sqrt{\frac{c}{d}}\right)}{64 \, {\left(\sqrt{2} b^{4} c^{9} - 4 \, \sqrt{2} a b^{3} c^{8} d + 6 \, \sqrt{2} a^{2} b^{2} c^{7} d^{2} - 4 \, \sqrt{2} a^{3} b c^{6} d^{3} + \sqrt{2} a^{4} c^{5} d^{4}\right)}} + \frac{37 \, b c d^{5} x^{\frac{7}{2}} - 21 \, a d^{6} x^{\frac{7}{2}} + 41 \, b c^{2} d^{4} x^{\frac{3}{2}} - 25 \, a c d^{5} x^{\frac{3}{2}}}{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}\right)} {\left(d x^{2} + c\right)}^{2}} + \frac{2 \, {\left(10 \, b c x^{2} + 15 \, a d x^{2} - a c\right)}}{5 \, a^{3} c^{4} x^{\frac{5}{2}}}"," ",0,"1/2*b^5*x^(3/2)/((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*x^2 + a)) + 3/4*(3*(a*b^3)^(3/4)*b^3*c - 7*(a*b^3)^(3/4)*a*b^2*d)*arctan(1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) + 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^4*b^4*c^4 - 4*sqrt(2)*a^5*b^3*c^3*d + 6*sqrt(2)*a^6*b^2*c^2*d^2 - 4*sqrt(2)*a^7*b*c*d^3 + sqrt(2)*a^8*d^4) + 3/4*(3*(a*b^3)^(3/4)*b^3*c - 7*(a*b^3)^(3/4)*a*b^2*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*(a/b)^(1/4) - 2*sqrt(x))/(a/b)^(1/4))/(sqrt(2)*a^4*b^4*c^4 - 4*sqrt(2)*a^5*b^3*c^3*d + 6*sqrt(2)*a^6*b^2*c^2*d^2 - 4*sqrt(2)*a^7*b*c*d^3 + sqrt(2)*a^8*d^4) + 3/32*(119*(c*d^3)^(3/4)*b^2*c^2*d - 126*(c*d^3)^(3/4)*a*b*c*d^2 + 39*(c*d^3)^(3/4)*a^2*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) + 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^9 - 4*sqrt(2)*a*b^3*c^8*d + 6*sqrt(2)*a^2*b^2*c^7*d^2 - 4*sqrt(2)*a^3*b*c^6*d^3 + sqrt(2)*a^4*c^5*d^4) + 3/32*(119*(c*d^3)^(3/4)*b^2*c^2*d - 126*(c*d^3)^(3/4)*a*b*c*d^2 + 39*(c*d^3)^(3/4)*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(c/d)^(1/4) - 2*sqrt(x))/(c/d)^(1/4))/(sqrt(2)*b^4*c^9 - 4*sqrt(2)*a*b^3*c^8*d + 6*sqrt(2)*a^2*b^2*c^7*d^2 - 4*sqrt(2)*a^3*b*c^6*d^3 + sqrt(2)*a^4*c^5*d^4) - 3/8*(3*(a*b^3)^(3/4)*b^3*c - 7*(a*b^3)^(3/4)*a*b^2*d)*log(sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^4*c^4 - 4*sqrt(2)*a^5*b^3*c^3*d + 6*sqrt(2)*a^6*b^2*c^2*d^2 - 4*sqrt(2)*a^7*b*c*d^3 + sqrt(2)*a^8*d^4) + 3/8*(3*(a*b^3)^(3/4)*b^3*c - 7*(a*b^3)^(3/4)*a*b^2*d)*log(-sqrt(2)*sqrt(x)*(a/b)^(1/4) + x + sqrt(a/b))/(sqrt(2)*a^4*b^4*c^4 - 4*sqrt(2)*a^5*b^3*c^3*d + 6*sqrt(2)*a^6*b^2*c^2*d^2 - 4*sqrt(2)*a^7*b*c*d^3 + sqrt(2)*a^8*d^4) - 3/64*(119*(c*d^3)^(3/4)*b^2*c^2*d - 126*(c*d^3)^(3/4)*a*b*c*d^2 + 39*(c*d^3)^(3/4)*a^2*d^3)*log(sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^9 - 4*sqrt(2)*a*b^3*c^8*d + 6*sqrt(2)*a^2*b^2*c^7*d^2 - 4*sqrt(2)*a^3*b*c^6*d^3 + sqrt(2)*a^4*c^5*d^4) + 3/64*(119*(c*d^3)^(3/4)*b^2*c^2*d - 126*(c*d^3)^(3/4)*a*b*c*d^2 + 39*(c*d^3)^(3/4)*a^2*d^3)*log(-sqrt(2)*sqrt(x)*(c/d)^(1/4) + x + sqrt(c/d))/(sqrt(2)*b^4*c^9 - 4*sqrt(2)*a*b^3*c^8*d + 6*sqrt(2)*a^2*b^2*c^7*d^2 - 4*sqrt(2)*a^3*b*c^6*d^3 + sqrt(2)*a^4*c^5*d^4) + 1/16*(37*b*c*d^5*x^(7/2) - 21*a*d^6*x^(7/2) + 41*b*c^2*d^4*x^(3/2) - 25*a*c*d^5*x^(3/2))/((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*x^2 + c)^2) + 2/5*(10*b*c*x^2 + 15*a*d*x^2 - a*c)/(a^3*c^4*x^(5/2))","A",0
504,1,104,0,0.311994," ","integrate(x^5*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{35 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B - 135 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a + 189 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} - 105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} + 45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b - 126 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a b + 105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} b}{315 \, b^{4}}"," ",0,"1/315*(35*(b*x^2 + a)^(9/2)*B - 135*(b*x^2 + a)^(7/2)*B*a + 189*(b*x^2 + a)^(5/2)*B*a^2 - 105*(b*x^2 + a)^(3/2)*B*a^3 + 45*(b*x^2 + a)^(7/2)*A*b - 126*(b*x^2 + a)^(5/2)*A*a*b + 105*(b*x^2 + a)^(3/2)*A*a^2*b)/b^4","A",0
505,1,132,0,0.386958," ","integrate(x^4*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, B x^{2} + \frac{B a b^{5} + 8 \, A b^{6}}{b^{6}}\right)} x^{2} - \frac{5 \, B a^{2} b^{4} - 8 \, A a b^{5}}{b^{6}}\right)} x^{2} + \frac{3 \, {\left(5 \, B a^{3} b^{3} - 8 \, A a^{2} b^{4}\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{7}{2}}}"," ",0,"1/384*(2*(4*(6*B*x^2 + (B*a*b^5 + 8*A*b^6)/b^6)*x^2 - (5*B*a^2*b^4 - 8*A*a*b^5)/b^6)*x^2 + 3*(5*B*a^3*b^3 - 8*A*a^2*b^4)/b^6)*sqrt(b*x^2 + a)*x + 1/128*(5*B*a^4 - 8*A*a^3*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
506,1,73,0,0.296548," ","integrate(x^3*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B - 42 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a + 35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} + 21 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b - 35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b}{105 \, b^{3}}"," ",0,"1/105*(15*(b*x^2 + a)^(7/2)*B - 42*(b*x^2 + a)^(5/2)*B*a + 35*(b*x^2 + a)^(3/2)*B*a^2 + 21*(b*x^2 + a)^(5/2)*A*b - 35*(b*x^2 + a)^(3/2)*A*a*b)/b^3","A",0
507,1,100,0,0.398343," ","integrate(x^2*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, B x^{2} + \frac{B a b^{3} + 6 \, A b^{4}}{b^{4}}\right)} x^{2} - \frac{3 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)}}{b^{4}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(B a^{3} - 2 \, A a^{2} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{5}{2}}}"," ",0,"1/48*(2*(4*B*x^2 + (B*a*b^3 + 6*A*b^4)/b^4)*x^2 - 3*(B*a^2*b^2 - 2*A*a*b^3)/b^4)*sqrt(b*x^2 + a)*x - 1/16*(B*a^3 - 2*A*a^2*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
508,1,44,0,0.310594," ","integrate(x*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B - 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{15 \, b^{2}}"," ",0,"1/15*(3*(b*x^2 + a)^(5/2)*B - 5*(b*x^2 + a)^(3/2)*B*a + 5*(b*x^2 + a)^(3/2)*A*b)/b^2","A",0
509,1,69,0,0.494282," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, B x^{2} + \frac{B a b + 4 \, A b^{2}}{b^{2}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(B a^{2} - 4 \, A a b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{3}{2}}}"," ",0,"1/8*(2*B*x^2 + (B*a*b + 4*A*b^2)/b^2)*sqrt(b*x^2 + a)*x + 1/8*(B*a^2 - 4*A*a*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
510,1,60,0,0.406851," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""giac"")","\frac{A a \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2} + 3 \, \sqrt{b x^{2} + a} A b^{3}}{3 \, b^{3}}"," ",0,"A*a*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) + 1/3*((b*x^2 + a)^(3/2)*B*b^2 + 3*sqrt(b*x^2 + a)*A*b^3)/b^3","A",0
511,1,84,0,0.421049," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b x^{2} + a} B x + \frac{2 \, A a \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} - \frac{{\left(B a \sqrt{b} + 2 \, A b^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{4 \, b}"," ",0,"1/2*sqrt(b*x^2 + a)*B*x + 2*A*a*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) - 1/4*(B*a*sqrt(b) + 2*A*b^(3/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/b","A",0
512,1,68,0,0.360749," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, \sqrt{b x^{2} + a} B b + \frac{{\left(2 \, B a b + A b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{b x^{2} + a} A b}{x^{2}}}{2 \, b}"," ",0,"1/2*(2*sqrt(b*x^2 + a)*B*b + (2*B*a*b + A*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) - sqrt(b*x^2 + a)*A*b/x^2)/b","A",0
513,1,151,0,0.521306," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^4,x, algorithm=""giac"")","-\frac{1}{2} \, B \sqrt{b} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a \sqrt{b} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} \sqrt{b} + 3 \, B a^{3} \sqrt{b} + A a^{2} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"-1/2*B*sqrt(b)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a*sqrt(b) + 3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*sqrt(b) + 3*B*a^3*sqrt(b) + A*a^2*b^(3/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","B",0
514,1,120,0,0.348662," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^5,x, algorithm=""giac"")","\frac{\frac{{\left(4 \, B a b^{2} - A b^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b^{2} - 4 \, \sqrt{b x^{2} + a} B a^{2} b^{2} + {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3} + \sqrt{b x^{2} + a} A a b^{3}}{a b^{2} x^{4}}}{8 \, b}"," ",0,"1/8*((4*B*a*b^2 - A*b^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - (4*(b*x^2 + a)^(3/2)*B*a*b^2 - 4*sqrt(b*x^2 + a)*B*a^2*b^2 + (b*x^2 + a)^(3/2)*A*b^3 + sqrt(b*x^2 + a)*A*a*b^3)/(a*b^2*x^4))/b","A",0
515,1,232,0,0.425373," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B b^{\frac{3}{2}} - 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a b^{\frac{3}{2}} + 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A b^{\frac{5}{2}} + 20 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{2} b^{\frac{3}{2}} + 10 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a b^{\frac{5}{2}} - 10 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{3} b^{\frac{3}{2}} + 10 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{2} b^{\frac{5}{2}} + 5 \, B a^{4} b^{\frac{3}{2}} - 2 \, A a^{3} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"2/15*(15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*b^(3/2) - 30*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a*b^(3/2) + 30*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*b^(5/2) + 20*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^2*b^(3/2) + 10*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a*b^(5/2) - 10*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^3*b^(3/2) + 10*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^2*b^(5/2) + 5*B*a^4*b^(3/2) - 2*A*a^3*b^(5/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5","B",0
516,1,140,0,0.311861," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^7,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(2 \, B a b^{3} - A b^{4}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{6 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a b^{3} - 6 \, \sqrt{b x^{2} + a} B a^{3} b^{3} - 3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4} + 8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{4} + 3 \, \sqrt{b x^{2} + a} A a^{2} b^{4}}{a^{2} b^{3} x^{6}}}{48 \, b}"," ",0,"-1/48*(3*(2*B*a*b^3 - A*b^4)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (6*(b*x^2 + a)^(5/2)*B*a*b^3 - 6*sqrt(b*x^2 + a)*B*a^3*b^3 - 3*(b*x^2 + a)^(5/2)*A*b^4 + 8*(b*x^2 + a)^(3/2)*A*a*b^4 + 3*sqrt(b*x^2 + a)*A*a^2*b^4)/(a^2*b^3*x^6))/b","A",0
517,1,288,0,0.464749," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^8,x, algorithm=""giac"")","\frac{4 \, {\left(105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B b^{\frac{5}{2}} - 175 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a b^{\frac{5}{2}} + 280 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A b^{\frac{7}{2}} + 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{2} b^{\frac{5}{2}} + 140 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a b^{\frac{7}{2}} - 42 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} b^{\frac{5}{2}} + 84 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{7}{2}} + 49 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} b^{\frac{5}{2}} - 28 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{3} b^{\frac{7}{2}} - 7 \, B a^{5} b^{\frac{5}{2}} + 4 \, A a^{4} b^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"4/105*(105*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*b^(5/2) - 175*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a*b^(5/2) + 280*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*b^(7/2) + 70*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^2*b^(5/2) + 140*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a*b^(7/2) - 42*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*b^(5/2) + 84*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(7/2) + 49*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*b^(5/2) - 28*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^3*b^(7/2) - 7*B*a^5*b^(5/2) + 4*A*a^4*b^(7/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7","B",0
518,1,194,0,0.452007," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^9,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, B a b^{4} - 5 \, A b^{5}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{24 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a b^{4} - 88 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} b^{4} + 40 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} b^{4} + 24 \, \sqrt{b x^{2} + a} B a^{4} b^{4} - 15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{5} + 55 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a b^{5} - 73 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} b^{5} - 15 \, \sqrt{b x^{2} + a} A a^{3} b^{5}}{a^{3} b^{4} x^{8}}}{384 \, b}"," ",0,"1/384*(3*(8*B*a*b^4 - 5*A*b^5)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) + (24*(b*x^2 + a)^(7/2)*B*a*b^4 - 88*(b*x^2 + a)^(5/2)*B*a^2*b^4 + 40*(b*x^2 + a)^(3/2)*B*a^3*b^4 + 24*sqrt(b*x^2 + a)*B*a^4*b^4 - 15*(b*x^2 + a)^(7/2)*A*b^5 + 55*(b*x^2 + a)^(5/2)*A*a*b^5 - 73*(b*x^2 + a)^(3/2)*A*a^2*b^5 - 15*sqrt(b*x^2 + a)*A*a^3*b^5)/(a^3*b^4*x^8))/b","A",0
519,1,344,0,0.420923," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^10,x, algorithm=""giac"")","\frac{16 \, {\left(210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B b^{\frac{7}{2}} - 315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a b^{\frac{7}{2}} + 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A b^{\frac{9}{2}} + 63 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{2} b^{\frac{7}{2}} + 378 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a b^{\frac{9}{2}} - 42 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{3} b^{\frac{7}{2}} + 168 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{2} b^{\frac{9}{2}} + 108 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{4} b^{\frac{7}{2}} - 72 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{3} b^{\frac{9}{2}} - 27 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{5} b^{\frac{7}{2}} + 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{4} b^{\frac{9}{2}} + 3 \, B a^{6} b^{\frac{7}{2}} - 2 \, A a^{5} b^{\frac{9}{2}}\right)}}{315 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{9}}"," ",0,"16/315*(210*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*b^(7/2) - 315*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a*b^(7/2) + 630*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*b^(9/2) + 63*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^2*b^(7/2) + 378*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a*b^(9/2) - 42*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^3*b^(7/2) + 168*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^2*b^(9/2) + 108*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^4*b^(7/2) - 72*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^3*b^(9/2) - 27*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^5*b^(7/2) + 18*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^4*b^(9/2) + 3*B*a^6*b^(7/2) - 2*A*a^5*b^(9/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^9","B",0
520,1,230,0,0.335184," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^11,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(10 \, B a b^{5} - 7 \, A b^{6}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{4}} + \frac{150 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a b^{5} - 700 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} b^{5} + 1280 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{3} b^{5} - 580 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{4} b^{5} - 150 \, \sqrt{b x^{2} + a} B a^{5} b^{5} - 105 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A b^{6} + 490 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a b^{6} - 896 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2} b^{6} + 790 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{3} b^{6} + 105 \, \sqrt{b x^{2} + a} A a^{4} b^{6}}{a^{4} b^{5} x^{10}}}{3840 \, b}"," ",0,"-1/3840*(15*(10*B*a*b^5 - 7*A*b^6)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^4) + (150*(b*x^2 + a)^(9/2)*B*a*b^5 - 700*(b*x^2 + a)^(7/2)*B*a^2*b^5 + 1280*(b*x^2 + a)^(5/2)*B*a^3*b^5 - 580*(b*x^2 + a)^(3/2)*B*a^4*b^5 - 150*sqrt(b*x^2 + a)*B*a^5*b^5 - 105*(b*x^2 + a)^(9/2)*A*b^6 + 490*(b*x^2 + a)^(7/2)*A*a*b^6 - 896*(b*x^2 + a)^(5/2)*A*a^2*b^6 + 790*(b*x^2 + a)^(3/2)*A*a^3*b^6 + 105*sqrt(b*x^2 + a)*A*a^4*b^6)/(a^4*b^5*x^10))/b","A",0
521,1,104,0,0.426239," ","integrate(x^5*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{315 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} B - 1155 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a + 1485 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} - 693 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{3} + 385 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A b - 990 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a b + 693 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2} b}{3465 \, b^{4}}"," ",0,"1/3465*(315*(b*x^2 + a)^(11/2)*B - 1155*(b*x^2 + a)^(9/2)*B*a + 1485*(b*x^2 + a)^(7/2)*B*a^2 - 693*(b*x^2 + a)^(5/2)*B*a^3 + 385*(b*x^2 + a)^(9/2)*A*b - 990*(b*x^2 + a)^(7/2)*A*a*b + 693*(b*x^2 + a)^(5/2)*A*a^2*b)/b^4","A",0
522,1,159,0,0.415480," ","integrate(x^4*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{1280} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, B b x^{2} + \frac{11 \, B a b^{8} + 10 \, A b^{9}}{b^{8}}\right)} x^{2} + \frac{B a^{2} b^{7} + 30 \, A a b^{8}}{b^{8}}\right)} x^{2} - \frac{5 \, {\left(B a^{3} b^{6} - 2 \, A a^{2} b^{7}\right)}}{b^{8}}\right)} x^{2} + \frac{15 \, {\left(B a^{4} b^{5} - 2 \, A a^{3} b^{6}\right)}}{b^{8}}\right)} \sqrt{b x^{2} + a} x + \frac{3 \, {\left(B a^{5} - 2 \, A a^{4} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{7}{2}}}"," ",0,"1/1280*(2*(4*(2*(8*B*b*x^2 + (11*B*a*b^8 + 10*A*b^9)/b^8)*x^2 + (B*a^2*b^7 + 30*A*a*b^8)/b^8)*x^2 - 5*(B*a^3*b^6 - 2*A*a^2*b^7)/b^8)*x^2 + 15*(B*a^4*b^5 - 2*A*a^3*b^6)/b^8)*sqrt(b*x^2 + a)*x + 3/256*(B*a^5 - 2*A*a^4*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
523,1,73,0,0.280687," ","integrate(x^3*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{35 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B - 90 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a + 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} + 45 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b - 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a b}{315 \, b^{3}}"," ",0,"1/315*(35*(b*x^2 + a)^(9/2)*B - 90*(b*x^2 + a)^(7/2)*B*a + 63*(b*x^2 + a)^(5/2)*B*a^2 + 45*(b*x^2 + a)^(7/2)*A*b - 63*(b*x^2 + a)^(5/2)*A*a*b)/b^3","A",0
524,1,133,0,0.375674," ","integrate(x^2*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, B b x^{2} + \frac{9 \, B a b^{6} + 8 \, A b^{7}}{b^{6}}\right)} x^{2} + \frac{3 \, B a^{2} b^{5} + 56 \, A a b^{6}}{b^{6}}\right)} x^{2} - \frac{3 \, {\left(3 \, B a^{3} b^{4} - 8 \, A a^{2} b^{5}\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{5}{2}}}"," ",0,"1/384*(2*(4*(6*B*b*x^2 + (9*B*a*b^6 + 8*A*b^7)/b^6)*x^2 + (3*B*a^2*b^5 + 56*A*a*b^6)/b^6)*x^2 - 3*(3*B*a^3*b^4 - 8*A*a^2*b^5)/b^6)*sqrt(b*x^2 + a)*x - 1/128*(3*B*a^4 - 8*A*a^3*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
525,1,44,0,0.426133," ","integrate(x*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{5 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B - 7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a + 7 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{35 \, b^{2}}"," ",0,"1/35*(5*(b*x^2 + a)^(7/2)*B - 7*(b*x^2 + a)^(5/2)*B*a + 7*(b*x^2 + a)^(5/2)*A*b)/b^2","A",0
526,1,102,0,0.415928," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, B b x^{2} + \frac{7 \, B a b^{4} + 6 \, A b^{5}}{b^{4}}\right)} x^{2} + \frac{3 \, {\left(B a^{2} b^{3} + 10 \, A a b^{4}\right)}}{b^{4}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(B a^{3} - 6 \, A a^{2} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{3}{2}}}"," ",0,"1/48*(2*(4*B*b*x^2 + (7*B*a*b^4 + 6*A*b^5)/b^4)*x^2 + 3*(B*a^2*b^3 + 10*A*a*b^4)/b^4)*sqrt(b*x^2 + a)*x + 1/16*(B*a^3 - 6*A*a^2*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
527,1,79,0,0.354171," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x,x, algorithm=""giac"")","\frac{A a^{2} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{4} + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{5} + 15 \, \sqrt{b x^{2} + a} A a b^{5}}{15 \, b^{5}}"," ",0,"A*a^2*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) + 1/15*(3*(b*x^2 + a)^(5/2)*B*b^4 + 5*(b*x^2 + a)^(3/2)*A*b^5 + 15*sqrt(b*x^2 + a)*A*a*b^5)/b^5","A",0
528,1,114,0,0.436157," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^2,x, algorithm=""giac"")","\frac{2 \, A a^{2} \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} + \frac{1}{8} \, {\left(2 \, B b x^{2} + \frac{5 \, B a b^{2} + 4 \, A b^{3}}{b^{2}}\right)} \sqrt{b x^{2} + a} x - \frac{3 \, {\left(B a^{2} \sqrt{b} + 4 \, A a b^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{16 \, b}"," ",0,"2*A*a^2*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) + 1/8*(2*B*b*x^2 + (5*B*a*b^2 + 4*A*b^3)/b^2)*sqrt(b*x^2 + a)*x - 3/16*(B*a^2*sqrt(b) + 4*A*a*b^(3/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/b","A",0
529,1,103,0,0.406063," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b + 6 \, \sqrt{b x^{2} + a} B a b + 6 \, \sqrt{b x^{2} + a} A b^{2} - \frac{3 \, \sqrt{b x^{2} + a} A a b}{x^{2}} + \frac{3 \, {\left(2 \, B a^{2} b + 3 \, A a b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}}{6 \, b}"," ",0,"1/6*(2*(b*x^2 + a)^(3/2)*B*b + 6*sqrt(b*x^2 + a)*B*a*b + 6*sqrt(b*x^2 + a)*A*b^2 - 3*sqrt(b*x^2 + a)*A*a*b/x^2 + 3*(2*B*a^2*b + 3*A*a*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a))/b","A",0
530,1,207,0,0.521837," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^4,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b x^{2} + a} B b x - \frac{1}{4} \, {\left(3 \, B a \sqrt{b} + 2 \, A b^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{2} \sqrt{b} + 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{3} \sqrt{b} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{2} b^{\frac{3}{2}} + 3 \, B a^{4} \sqrt{b} + 4 \, A a^{3} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"1/2*sqrt(b*x^2 + a)*B*b*x - 1/4*(3*B*a*sqrt(b) + 2*A*b^(3/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^2*sqrt(b) + 6*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^3*sqrt(b) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^2*b^(3/2) + 3*B*a^4*sqrt(b) + 4*A*a^3*b^(3/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","B",0
531,1,131,0,0.470872," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^5,x, algorithm=""giac"")","\frac{8 \, \sqrt{b x^{2} + a} B b^{2} + \frac{3 \, {\left(4 \, B a b^{2} + A b^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b^{2} - 4 \, \sqrt{b x^{2} + a} B a^{2} b^{2} + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3} - 3 \, \sqrt{b x^{2} + a} A a b^{3}}{b^{2} x^{4}}}{8 \, b}"," ",0,"1/8*(8*sqrt(b*x^2 + a)*B*b^2 + 3*(4*B*a*b^2 + A*b^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) - (4*(b*x^2 + a)^(3/2)*B*a*b^2 - 4*sqrt(b*x^2 + a)*B*a^2*b^2 + 5*(b*x^2 + a)^(3/2)*A*b^3 - 3*sqrt(b*x^2 + a)*A*a*b^3)/(b^2*x^4))/b","A",0
532,1,236,0,0.442986," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^6,x, algorithm=""giac"")","-\frac{1}{2} \, B b^{\frac{3}{2}} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a b^{\frac{3}{2}} + 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A b^{\frac{5}{2}} - 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{2} b^{\frac{3}{2}} + 110 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} b^{\frac{3}{2}} + 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{5}{2}} - 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} b^{\frac{3}{2}} + 20 \, B a^{5} b^{\frac{3}{2}} + 3 \, A a^{4} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"-1/2*B*b^(3/2)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/15*(30*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a*b^(3/2) + 15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*b^(5/2) - 90*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^2*b^(3/2) + 110*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*b^(3/2) + 30*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(5/2) - 70*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*b^(3/2) + 20*B*a^5*b^(3/2) + 3*A*a^4*b^(5/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5","B",0
533,1,159,0,0.334839," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^7,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(6 \, B a b^{3} - A b^{4}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{30 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a b^{3} - 48 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} b^{3} + 18 \, \sqrt{b x^{2} + a} B a^{3} b^{3} + 3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4} + 8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{4} - 3 \, \sqrt{b x^{2} + a} A a^{2} b^{4}}{a b^{3} x^{6}}}{48 \, b}"," ",0,"1/48*(3*(6*B*a*b^3 - A*b^4)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - (30*(b*x^2 + a)^(5/2)*B*a*b^3 - 48*(b*x^2 + a)^(3/2)*B*a^2*b^3 + 18*sqrt(b*x^2 + a)*B*a^3*b^3 + 3*(b*x^2 + a)^(5/2)*A*b^4 + 8*(b*x^2 + a)^(3/2)*A*a*b^4 - 3*sqrt(b*x^2 + a)*A*a^2*b^4)/(a*b^3*x^6))/b","A",0
534,1,344,0,0.466287," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B b^{\frac{5}{2}} - 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a b^{\frac{5}{2}} + 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A b^{\frac{7}{2}} + 105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{2} b^{\frac{5}{2}} + 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a b^{\frac{7}{2}} - 140 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{3} b^{\frac{5}{2}} + 140 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{2} b^{\frac{7}{2}} + 77 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{4} b^{\frac{5}{2}} + 28 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{3} b^{\frac{7}{2}} - 14 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{5} b^{\frac{5}{2}} + 14 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{4} b^{\frac{7}{2}} + 7 \, B a^{6} b^{\frac{5}{2}} - 2 \, A a^{5} b^{\frac{7}{2}}\right)}}{35 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"2/35*(35*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*b^(5/2) - 70*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a*b^(5/2) + 70*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*b^(7/2) + 105*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^2*b^(5/2) + 70*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a*b^(7/2) - 140*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^3*b^(5/2) + 140*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^2*b^(7/2) + 77*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^4*b^(5/2) + 28*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^3*b^(7/2) - 14*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^5*b^(5/2) + 14*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^4*b^(7/2) + 7*B*a^6*b^(5/2) - 2*A*a^5*b^(7/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7","B",0
535,1,194,0,0.414318," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^9,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, B a b^{4} - 3 \, A b^{5}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{24 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a b^{4} + 40 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} b^{4} - 88 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} b^{4} + 24 \, \sqrt{b x^{2} + a} B a^{4} b^{4} - 9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{5} + 33 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a b^{5} + 33 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} b^{5} - 9 \, \sqrt{b x^{2} + a} A a^{3} b^{5}}{a^{2} b^{4} x^{8}}}{384 \, b}"," ",0,"-1/384*(3*(8*B*a*b^4 - 3*A*b^5)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (24*(b*x^2 + a)^(7/2)*B*a*b^4 + 40*(b*x^2 + a)^(5/2)*B*a^2*b^4 - 88*(b*x^2 + a)^(3/2)*B*a^3*b^4 + 24*sqrt(b*x^2 + a)*B*a^4*b^4 - 9*(b*x^2 + a)^(7/2)*A*b^5 + 33*(b*x^2 + a)^(5/2)*A*a*b^5 + 33*(b*x^2 + a)^(3/2)*A*a^2*b^5 - 9*sqrt(b*x^2 + a)*A*a^3*b^5)/(a^2*b^4*x^8))/b","A",0
536,1,400,0,0.494790," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^10,x, algorithm=""giac"")","\frac{4 \, {\left(315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} B b^{\frac{7}{2}} - 315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a b^{\frac{7}{2}} + 840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A b^{\frac{9}{2}} + 315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{2} b^{\frac{7}{2}} + 1260 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A a b^{\frac{9}{2}} - 819 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{3} b^{\frac{7}{2}} + 1764 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{2} b^{\frac{9}{2}} + 441 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{4} b^{\frac{7}{2}} + 504 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{3} b^{\frac{9}{2}} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{5} b^{\frac{7}{2}} + 144 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{4} b^{\frac{9}{2}} + 81 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{6} b^{\frac{7}{2}} - 36 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{5} b^{\frac{9}{2}} - 9 \, B a^{7} b^{\frac{7}{2}} + 4 \, A a^{6} b^{\frac{9}{2}}\right)}}{315 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{9}}"," ",0,"4/315*(315*(sqrt(b)*x - sqrt(b*x^2 + a))^14*B*b^(7/2) - 315*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a*b^(7/2) + 840*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*b^(9/2) + 315*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^2*b^(7/2) + 1260*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*a*b^(9/2) - 819*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^3*b^(7/2) + 1764*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^2*b^(9/2) + 441*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^4*b^(7/2) + 504*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^3*b^(9/2) - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^5*b^(7/2) + 144*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^4*b^(9/2) + 81*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^6*b^(7/2) - 36*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^5*b^(9/2) - 9*B*a^7*b^(7/2) + 4*A*a^6*b^(9/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^9","B",0
537,1,212,0,0.480494," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^11,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(2 \, B a b^{5} - A b^{6}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{30 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a b^{5} - 140 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} b^{5} + 140 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{4} b^{5} - 30 \, \sqrt{b x^{2} + a} B a^{5} b^{5} - 15 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A b^{6} + 70 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a b^{6} - 128 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2} b^{6} - 70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{3} b^{6} + 15 \, \sqrt{b x^{2} + a} A a^{4} b^{6}}{a^{3} b^{5} x^{10}}}{1280 \, b}"," ",0,"1/1280*(15*(2*B*a*b^5 - A*b^6)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) + (30*(b*x^2 + a)^(9/2)*B*a*b^5 - 140*(b*x^2 + a)^(7/2)*B*a^2*b^5 + 140*(b*x^2 + a)^(3/2)*B*a^4*b^5 - 30*sqrt(b*x^2 + a)*B*a^5*b^5 - 15*(b*x^2 + a)^(9/2)*A*b^6 + 70*(b*x^2 + a)^(7/2)*A*a*b^6 - 128*(b*x^2 + a)^(5/2)*A*a^2*b^6 - 70*(b*x^2 + a)^(3/2)*A*a^3*b^6 + 15*sqrt(b*x^2 + a)*A*a^4*b^6)/(a^3*b^5*x^10))/b","A",0
538,1,104,0,0.342076," ","integrate(x^5*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{693 \, {\left(b x^{2} + a\right)}^{\frac{13}{2}} B - 2457 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} B a + 3003 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a^{2} - 1287 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{3} + 819 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} A b - 2002 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A a b + 1287 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a^{2} b}{9009 \, b^{4}}"," ",0,"1/9009*(693*(b*x^2 + a)^(13/2)*B - 2457*(b*x^2 + a)^(11/2)*B*a + 3003*(b*x^2 + a)^(9/2)*B*a^2 - 1287*(b*x^2 + a)^(7/2)*B*a^3 + 819*(b*x^2 + a)^(11/2)*A*b - 2002*(b*x^2 + a)^(9/2)*A*a*b + 1287*(b*x^2 + a)^(7/2)*A*a^2*b)/b^4","A",0
539,1,195,0,0.352197," ","integrate(x^4*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{15360} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, B b^{2} x^{2} + \frac{25 \, B a b^{11} + 12 \, A b^{12}}{b^{10}}\right)} x^{2} + \frac{9 \, {\left(15 \, B a^{2} b^{10} + 28 \, A a b^{11}\right)}}{b^{10}}\right)} x^{2} + \frac{5 \, B a^{3} b^{9} + 372 \, A a^{2} b^{10}}{b^{10}}\right)} x^{2} - \frac{5 \, {\left(5 \, B a^{4} b^{8} - 12 \, A a^{3} b^{9}\right)}}{b^{10}}\right)} x^{2} + \frac{15 \, {\left(5 \, B a^{5} b^{7} - 12 \, A a^{4} b^{8}\right)}}{b^{10}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{1024 \, b^{\frac{7}{2}}}"," ",0,"1/15360*(2*(4*(2*(8*(10*B*b^2*x^2 + (25*B*a*b^11 + 12*A*b^12)/b^10)*x^2 + 9*(15*B*a^2*b^10 + 28*A*a*b^11)/b^10)*x^2 + (5*B*a^3*b^9 + 372*A*a^2*b^10)/b^10)*x^2 - 5*(5*B*a^4*b^8 - 12*A*a^3*b^9)/b^10)*x^2 + 15*(5*B*a^5*b^7 - 12*A*a^4*b^8)/b^10)*sqrt(b*x^2 + a)*x + 1/1024*(5*B*a^6 - 12*A*a^5*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
540,1,73,0,0.406736," ","integrate(x^3*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{63 \, {\left(b x^{2} + a\right)}^{\frac{11}{2}} B - 154 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a + 99 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} + 77 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A b - 99 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a b}{693 \, b^{3}}"," ",0,"1/693*(63*(b*x^2 + a)^(11/2)*B - 154*(b*x^2 + a)^(9/2)*B*a + 99*(b*x^2 + a)^(7/2)*B*a^2 + 77*(b*x^2 + a)^(9/2)*A*b - 99*(b*x^2 + a)^(7/2)*A*a*b)/b^3","A",0
541,1,165,0,0.405750," ","integrate(x^2*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, B b^{2} x^{2} + \frac{21 \, B a b^{9} + 10 \, A b^{10}}{b^{8}}\right)} x^{2} + \frac{93 \, B a^{2} b^{8} + 170 \, A a b^{9}}{b^{8}}\right)} x^{2} + \frac{5 \, {\left(3 \, B a^{3} b^{7} + 118 \, A a^{2} b^{8}\right)}}{b^{8}}\right)} x^{2} - \frac{15 \, {\left(3 \, B a^{4} b^{6} - 10 \, A a^{3} b^{7}\right)}}{b^{8}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{5}{2}}}"," ",0,"1/3840*(2*(4*(6*(8*B*b^2*x^2 + (21*B*a*b^9 + 10*A*b^10)/b^8)*x^2 + (93*B*a^2*b^8 + 170*A*a*b^9)/b^8)*x^2 + 5*(3*B*a^3*b^7 + 118*A*a^2*b^8)/b^8)*x^2 - 15*(3*B*a^4*b^6 - 10*A*a^3*b^7)/b^8)*sqrt(b*x^2 + a)*x - 1/256*(3*B*a^5 - 10*A*a^4*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
542,1,44,0,0.461263," ","integrate(x*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{7 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B - 9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a + 9 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{63 \, b^{2}}"," ",0,"1/63*(7*(b*x^2 + a)^(9/2)*B - 9*(b*x^2 + a)^(7/2)*B*a + 9*(b*x^2 + a)^(7/2)*A*b)/b^2","A",0
543,1,134,0,0.507691," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, B b^{2} x^{2} + \frac{17 \, B a b^{7} + 8 \, A b^{8}}{b^{6}}\right)} x^{2} + \frac{59 \, B a^{2} b^{6} + 104 \, A a b^{7}}{b^{6}}\right)} x^{2} + \frac{3 \, {\left(5 \, B a^{3} b^{5} + 88 \, A a^{2} b^{6}\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x + \frac{5 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{3}{2}}}"," ",0,"1/384*(2*(4*(6*B*b^2*x^2 + (17*B*a*b^7 + 8*A*b^8)/b^6)*x^2 + (59*B*a^2*b^6 + 104*A*a*b^7)/b^6)*x^2 + 3*(5*B*a^3*b^5 + 88*A*a^2*b^6)/b^6)*sqrt(b*x^2 + a)*x + 5/128*(B*a^4 - 8*A*a^3*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
544,1,97,0,0.368329," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x,x, algorithm=""giac"")","\frac{A a^{3} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B b^{6} + 21 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{7} + 35 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{7} + 105 \, \sqrt{b x^{2} + a} A a^{2} b^{7}}{105 \, b^{7}}"," ",0,"A*a^3*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) + 1/105*(15*(b*x^2 + a)^(7/2)*B*b^6 + 21*(b*x^2 + a)^(5/2)*A*b^7 + 35*(b*x^2 + a)^(3/2)*A*a*b^7 + 105*sqrt(b*x^2 + a)*A*a^2*b^7)/b^7","A",0
545,1,146,0,0.541806," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^2,x, algorithm=""giac"")","\frac{2 \, A a^{3} \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a} + \frac{1}{48} \, {\left(2 \, {\left(4 \, B b^{2} x^{2} + \frac{13 \, B a b^{5} + 6 \, A b^{6}}{b^{4}}\right)} x^{2} + \frac{3 \, {\left(11 \, B a^{2} b^{4} + 18 \, A a b^{5}\right)}}{b^{4}}\right)} \sqrt{b x^{2} + a} x - \frac{5 \, {\left(B a^{3} \sqrt{b} + 6 \, A a^{2} b^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{32 \, b}"," ",0,"2*A*a^3*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a) + 1/48*(2*(4*B*b^2*x^2 + (13*B*a*b^5 + 6*A*b^6)/b^4)*x^2 + 3*(11*B*a^2*b^4 + 18*A*a*b^5)/b^4)*sqrt(b*x^2 + a)*x - 5/32*(B*a^3*sqrt(b) + 6*A*a^2*b^(3/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/b","A",0
546,1,139,0,0.368574," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^3,x, algorithm=""giac"")","\frac{6 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b + 10 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b + 30 \, \sqrt{b x^{2} + a} B a^{2} b + 10 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2} + 60 \, \sqrt{b x^{2} + a} A a b^{2} - \frac{15 \, \sqrt{b x^{2} + a} A a^{2} b}{x^{2}} + \frac{15 \, {\left(2 \, B a^{3} b + 5 \, A a^{2} b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}}}{30 \, b}"," ",0,"1/30*(6*(b*x^2 + a)^(5/2)*B*b + 10*(b*x^2 + a)^(3/2)*B*a*b + 30*sqrt(b*x^2 + a)*B*a^2*b + 10*(b*x^2 + a)^(3/2)*A*b^2 + 60*sqrt(b*x^2 + a)*A*a*b^2 - 15*sqrt(b*x^2 + a)*A*a^2*b/x^2 + 15*(2*B*a^3*b + 5*A*a^2*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a))/b","A",0
547,1,238,0,0.471311," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^4,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, B b^{2} x^{2} + \frac{9 \, B a b^{3} + 4 \, A b^{4}}{b^{2}}\right)} \sqrt{b x^{2} + a} x - \frac{5}{16} \, {\left(3 \, B a^{2} \sqrt{b} + 4 \, A a b^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} \sqrt{b} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} \sqrt{b} - 12 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{3} b^{\frac{3}{2}} + 3 \, B a^{5} \sqrt{b} + 7 \, A a^{4} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"1/8*(2*B*b^2*x^2 + (9*B*a*b^3 + 4*A*b^4)/b^2)*sqrt(b*x^2 + a)*x - 5/16*(3*B*a^2*sqrt(b) + 4*A*a*b^(3/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*sqrt(b) + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*sqrt(b) - 12*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^3*b^(3/2) + 3*B*a^5*sqrt(b) + 7*A*a^4*b^(3/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","A",0
548,1,171,0,0.351757," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^5,x, algorithm=""giac"")","\frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2} + 48 \, \sqrt{b x^{2} + a} B a b^{2} + 24 \, \sqrt{b x^{2} + a} A b^{3} + \frac{15 \, {\left(4 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{3 \, {\left(4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} b^{2} - 4 \, \sqrt{b x^{2} + a} B a^{3} b^{2} + 9 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{3} - 7 \, \sqrt{b x^{2} + a} A a^{2} b^{3}\right)}}{b^{2} x^{4}}}{24 \, b}"," ",0,"1/24*(8*(b*x^2 + a)^(3/2)*B*b^2 + 48*sqrt(b*x^2 + a)*B*a*b^2 + 24*sqrt(b*x^2 + a)*A*b^3 + 15*(4*B*a^2*b^2 + 3*A*a*b^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) - 3*(4*(b*x^2 + a)^(3/2)*B*a^2*b^2 - 4*sqrt(b*x^2 + a)*B*a^3*b^2 + 9*(b*x^2 + a)^(3/2)*A*a*b^3 - 7*sqrt(b*x^2 + a)*A*a^2*b^3)/(b^2*x^4))/b","A",0
549,1,321,0,0.571778," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^6,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b x^{2} + a} B b^{2} x - \frac{1}{4} \, {\left(5 \, B a b^{\frac{3}{2}} + 2 \, A b^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(45 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{2} b^{\frac{3}{2}} + 45 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a b^{\frac{5}{2}} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{3} b^{\frac{3}{2}} - 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{2} b^{\frac{5}{2}} + 200 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{4} b^{\frac{3}{2}} + 140 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{3} b^{\frac{5}{2}} - 130 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{5} b^{\frac{3}{2}} - 70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{4} b^{\frac{5}{2}} + 35 \, B a^{6} b^{\frac{3}{2}} + 23 \, A a^{5} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"1/2*sqrt(b*x^2 + a)*B*b^2*x - 1/4*(5*B*a*b^(3/2) + 2*A*b^(5/2))*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/15*(45*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^2*b^(3/2) + 45*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a*b^(5/2) - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^3*b^(3/2) - 90*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^2*b^(5/2) + 200*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^4*b^(3/2) + 140*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^3*b^(5/2) - 130*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^5*b^(3/2) - 70*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^4*b^(5/2) + 35*B*a^6*b^(3/2) + 23*A*a^5*b^(5/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5","B",0
550,1,167,0,0.363449," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^7,x, algorithm=""giac"")","\frac{48 \, \sqrt{b x^{2} + a} B b^{3} + \frac{15 \, {\left(6 \, B a b^{3} + A b^{4}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{54 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a b^{3} - 96 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} b^{3} + 42 \, \sqrt{b x^{2} + a} B a^{3} b^{3} + 33 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4} - 40 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{4} + 15 \, \sqrt{b x^{2} + a} A a^{2} b^{4}}{b^{3} x^{6}}}{48 \, b}"," ",0,"1/48*(48*sqrt(b*x^2 + a)*B*b^3 + 15*(6*B*a*b^3 + A*b^4)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) - (54*(b*x^2 + a)^(5/2)*B*a*b^3 - 96*(b*x^2 + a)^(3/2)*B*a^2*b^3 + 42*sqrt(b*x^2 + a)*B*a^3*b^3 + 33*(b*x^2 + a)^(5/2)*A*b^4 - 40*(b*x^2 + a)^(3/2)*A*a*b^4 + 15*sqrt(b*x^2 + a)*A*a^2*b^4)/(b^3*x^6))/b","A",0
551,1,320,0,0.576030," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^8,x, algorithm=""giac"")","-\frac{1}{2} \, B b^{\frac{5}{2}} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right) + \frac{2 \, {\left(315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a b^{\frac{5}{2}} + 105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A b^{\frac{7}{2}} - 1260 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{2} b^{\frac{5}{2}} + 2555 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{3} b^{\frac{5}{2}} + 525 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{2} b^{\frac{7}{2}} - 3080 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{4} b^{\frac{5}{2}} + 2121 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{5} b^{\frac{5}{2}} + 315 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{4} b^{\frac{7}{2}} - 812 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{6} b^{\frac{5}{2}} + 161 \, B a^{7} b^{\frac{5}{2}} + 15 \, A a^{6} b^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"-1/2*B*b^(5/2)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2) + 2/105*(315*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a*b^(5/2) + 105*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*b^(7/2) - 1260*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^2*b^(5/2) + 2555*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^3*b^(5/2) + 525*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^2*b^(7/2) - 3080*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^4*b^(5/2) + 2121*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^5*b^(5/2) + 315*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^4*b^(7/2) - 812*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^6*b^(5/2) + 161*B*a^7*b^(5/2) + 15*A*a^6*b^(7/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7","B",0
552,1,195,0,0.443568," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(8 \, B a b^{4} - A b^{5}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{264 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a b^{4} - 584 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} b^{4} + 440 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} b^{4} - 120 \, \sqrt{b x^{2} + a} B a^{4} b^{4} + 15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{5} + 73 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a b^{5} - 55 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} b^{5} + 15 \, \sqrt{b x^{2} + a} A a^{3} b^{5}}{a b^{4} x^{8}}}{384 \, b}"," ",0,"1/384*(15*(8*B*a*b^4 - A*b^5)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - (264*(b*x^2 + a)^(7/2)*B*a*b^4 - 584*(b*x^2 + a)^(5/2)*B*a^2*b^4 + 440*(b*x^2 + a)^(3/2)*B*a^3*b^4 - 120*sqrt(b*x^2 + a)*B*a^4*b^4 + 15*(b*x^2 + a)^(7/2)*A*b^5 + 73*(b*x^2 + a)^(5/2)*A*a*b^5 - 55*(b*x^2 + a)^(3/2)*A*a^2*b^5 + 15*sqrt(b*x^2 + a)*A*a^3*b^5)/(a*b^4*x^8))/b","A",0
553,1,456,0,0.472750," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^10,x, algorithm=""giac"")","\frac{2 \, {\left(63 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{16} B b^{\frac{7}{2}} - 126 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} B a b^{\frac{7}{2}} + 126 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} A b^{\frac{9}{2}} + 378 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a^{2} b^{\frac{7}{2}} + 210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A a b^{\frac{9}{2}} - 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{3} b^{\frac{7}{2}} + 630 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A a^{2} b^{\frac{9}{2}} + 504 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{4} b^{\frac{7}{2}} + 378 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{3} b^{\frac{9}{2}} - 378 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{5} b^{\frac{7}{2}} + 378 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{4} b^{\frac{9}{2}} + 198 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{6} b^{\frac{7}{2}} + 54 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{5} b^{\frac{9}{2}} - 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{7} b^{\frac{7}{2}} + 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{6} b^{\frac{9}{2}} + 9 \, B a^{8} b^{\frac{7}{2}} - 2 \, A a^{7} b^{\frac{9}{2}}\right)}}{63 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{9}}"," ",0,"2/63*(63*(sqrt(b)*x - sqrt(b*x^2 + a))^16*B*b^(7/2) - 126*(sqrt(b)*x - sqrt(b*x^2 + a))^14*B*a*b^(7/2) + 126*(sqrt(b)*x - sqrt(b*x^2 + a))^14*A*b^(9/2) + 378*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a^2*b^(7/2) + 210*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*a*b^(9/2) - 630*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^3*b^(7/2) + 630*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*a^2*b^(9/2) + 504*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^4*b^(7/2) + 378*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^3*b^(9/2) - 378*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^5*b^(7/2) + 378*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^4*b^(9/2) + 198*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^6*b^(7/2) + 54*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^5*b^(9/2) - 18*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^7*b^(7/2) + 18*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^6*b^(9/2) + 9*B*a^8*b^(7/2) - 2*A*a^7*b^(9/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^9","B",0
554,1,230,0,0.348208," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^11,x, algorithm=""giac"")","-\frac{\frac{15 \, {\left(10 \, B a b^{5} - 3 \, A b^{6}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{150 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} B a b^{5} + 580 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} b^{5} - 1280 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{3} b^{5} + 700 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{4} b^{5} - 150 \, \sqrt{b x^{2} + a} B a^{5} b^{5} - 45 \, {\left(b x^{2} + a\right)}^{\frac{9}{2}} A b^{6} + 210 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a b^{6} + 384 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2} b^{6} - 210 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{3} b^{6} + 45 \, \sqrt{b x^{2} + a} A a^{4} b^{6}}{a^{2} b^{5} x^{10}}}{3840 \, b}"," ",0,"-1/3840*(15*(10*B*a*b^5 - 3*A*b^6)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (150*(b*x^2 + a)^(9/2)*B*a*b^5 + 580*(b*x^2 + a)^(7/2)*B*a^2*b^5 - 1280*(b*x^2 + a)^(5/2)*B*a^3*b^5 + 700*(b*x^2 + a)^(3/2)*B*a^4*b^5 - 150*sqrt(b*x^2 + a)*B*a^5*b^5 - 45*(b*x^2 + a)^(9/2)*A*b^6 + 210*(b*x^2 + a)^(7/2)*A*a*b^6 + 384*(b*x^2 + a)^(5/2)*A*a^2*b^6 - 210*(b*x^2 + a)^(3/2)*A*a^3*b^6 + 45*sqrt(b*x^2 + a)*A*a^4*b^6)/(a^2*b^5*x^10))/b","A",0
555,1,101,0,0.305228," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{{\left(B a^{3} - A a^{2} b\right)} \sqrt{b x^{2} + a}}{b^{4}} + \frac{15 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B - 63 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a + 105 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} + 21 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b - 70 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b}{105 \, b^{4}}"," ",0,"-(B*a^3 - A*a^2*b)*sqrt(b*x^2 + a)/b^4 + 1/105*(15*(b*x^2 + a)^(7/2)*B - 63*(b*x^2 + a)^(5/2)*B*a + 105*(b*x^2 + a)^(3/2)*B*a^2 + 21*(b*x^2 + a)^(5/2)*A*b - 70*(b*x^2 + a)^(3/2)*A*a*b)/b^4","A",0
556,1,107,0,0.453004," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(\frac{4 \, B x^{2}}{b} - \frac{5 \, B a b^{3} - 6 \, A b^{4}}{b^{5}}\right)} x^{2} + \frac{3 \, {\left(5 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)}}{b^{5}}\right)} \sqrt{b x^{2} + a} x + \frac{{\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{7}{2}}}"," ",0,"1/48*(2*(4*B*x^2/b - (5*B*a*b^3 - 6*A*b^4)/b^5)*x^2 + 3*(5*B*a^2*b^2 - 6*A*a*b^3)/b^5)*sqrt(b*x^2 + a)*x + 1/16*(5*B*a^3 - 6*A*a^2*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
557,1,69,0,0.333601," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(B a^{2} - A a b\right)} \sqrt{b x^{2} + a}}{b^{3}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B - 10 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{15 \, b^{3}}"," ",0,"(B*a^2 - A*a*b)*sqrt(b*x^2 + a)/b^3 + 1/15*(3*(b*x^2 + a)^(5/2)*B - 10*(b*x^2 + a)^(3/2)*B*a + 5*(b*x^2 + a)^(3/2)*A*b)/b^3","A",0
558,1,75,0,0.359473," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{b x^{2} + a} {\left(\frac{2 \, B x^{2}}{b} - \frac{3 \, B a b - 4 \, A b^{2}}{b^{3}}\right)} x - \frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/8*sqrt(b*x^2 + a)*(2*B*x^2/b - (3*B*a*b - 4*A*b^2)/b^3)*x - 1/8*(3*B*a^2 - 4*A*a*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
559,1,38,0,0.305286," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{3 \, b^{2}} - \frac{\sqrt{b x^{2} + a} {\left(B a - A b\right)}}{b^{2}}"," ",0,"1/3*(b*x^2 + a)^(3/2)*B/b^2 - sqrt(b*x^2 + a)*(B*a - A*b)/b^2","A",0
560,1,48,0,0.398246," ","integrate((B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} B x}{2 \, b} + \frac{{\left(B a - 2 \, A b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*B*x/b + 1/2*(B*a - 2*A*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
561,1,38,0,0.365510," ","integrate((B*x^2+A)/x/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{A \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} + \frac{\sqrt{b x^{2} + a} B}{b}"," ",0,"A*arctan(sqrt(b*x^2 + a)/sqrt(-a))/sqrt(-a) + sqrt(b*x^2 + a)*B/b","A",0
562,1,58,0,0.413785," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{B \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{2 \, \sqrt{b}} + \frac{2 \, A \sqrt{b}}{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a}"," ",0,"-1/2*B*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/sqrt(b) + 2*A*sqrt(b)/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)","A",0
563,1,62,0,0.372723," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, B a b - A b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{\sqrt{b x^{2} + a} A b}{a x^{2}}}{2 \, b}"," ",0,"1/2*((2*B*a*b - A*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - sqrt(b*x^2 + a)*A*b/(a*x^2))/b","A",0
564,1,120,0,0.432544," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B \sqrt{b} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a \sqrt{b} + 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A b^{\frac{3}{2}} + 3 \, B a^{2} \sqrt{b} - 2 \, A a b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3}}"," ",0,"2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*sqrt(b) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a*sqrt(b) + 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*b^(3/2) + 3*B*a^2*sqrt(b) - 2*A*a*b^(3/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3","B",0
565,1,121,0,0.341462," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\frac{{\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} + \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b^{2} - 4 \, \sqrt{b x^{2} + a} B a^{2} b^{2} - 3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3} + 5 \, \sqrt{b x^{2} + a} A a b^{3}}{a^{2} b^{2} x^{4}}}{8 \, b}"," ",0,"-1/8*((4*B*a*b^2 - 3*A*b^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + (4*(b*x^2 + a)^(3/2)*B*a*b^2 - 4*sqrt(b*x^2 + a)*B*a^2*b^2 - 3*(b*x^2 + a)^(3/2)*A*b^3 + 5*sqrt(b*x^2 + a)*A*a*b^3)/(a^2*b^2*x^4))/b","A",0
566,1,176,0,0.419562," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B b^{\frac{3}{2}} - 35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a b^{\frac{3}{2}} + 40 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A b^{\frac{5}{2}} + 25 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} b^{\frac{3}{2}} - 20 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a b^{\frac{5}{2}} - 5 \, B a^{3} b^{\frac{3}{2}} + 4 \, A a^{2} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5}}"," ",0,"4/15*(15*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*b^(3/2) - 35*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a*b^(3/2) + 40*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*b^(5/2) + 25*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*b^(3/2) - 20*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a*b^(5/2) - 5*B*a^3*b^(3/2) + 4*A*a^2*b^(5/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5","B",0
567,1,158,0,0.377604," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, {\left(6 \, B a b^{3} - 5 \, A b^{4}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{3}} + \frac{18 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a b^{3} - 48 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} b^{3} + 30 \, \sqrt{b x^{2} + a} B a^{3} b^{3} - 15 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4} + 40 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{4} - 33 \, \sqrt{b x^{2} + a} A a^{2} b^{4}}{a^{3} b^{3} x^{6}}}{48 \, b}"," ",0,"1/48*(3*(6*B*a*b^3 - 5*A*b^4)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) + (18*(b*x^2 + a)^(5/2)*B*a*b^3 - 48*(b*x^2 + a)^(3/2)*B*a^2*b^3 + 30*sqrt(b*x^2 + a)*B*a^3*b^3 - 15*(b*x^2 + a)^(5/2)*A*b^4 + 40*(b*x^2 + a)^(3/2)*A*a*b^4 - 33*sqrt(b*x^2 + a)*A*a^2*b^4)/(a^3*b^3*x^6))/b","A",0
568,1,232,0,0.416122," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{16 \, {\left(70 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B b^{\frac{5}{2}} - 175 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a b^{\frac{5}{2}} + 210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A b^{\frac{7}{2}} + 147 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{2} b^{\frac{5}{2}} - 126 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a b^{\frac{7}{2}} - 49 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{3} b^{\frac{5}{2}} + 42 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{2} b^{\frac{7}{2}} + 7 \, B a^{4} b^{\frac{5}{2}} - 6 \, A a^{3} b^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7}}"," ",0,"16/105*(70*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*b^(5/2) - 175*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a*b^(5/2) + 210*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*b^(7/2) + 147*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^2*b^(5/2) - 126*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a*b^(7/2) - 49*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^3*b^(5/2) + 42*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^2*b^(7/2) + 7*B*a^4*b^(5/2) - 6*A*a^3*b^(7/2))/((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7","B",0
569,1,136,0,0.369589," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, B x^{2}}{b} - \frac{7 \, B a b^{5} - 6 \, A b^{6}}{b^{7}}\right)} x^{2} + \frac{5 \, {\left(7 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)}}{b^{7}}\right)} x^{2} + \frac{15 \, {\left(7 \, B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)}}{b^{7}}\right)} x}{48 \, \sqrt{b x^{2} + a}} + \frac{5 \, {\left(7 \, B a^{3} - 6 \, A a^{2} b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{9}{2}}}"," ",0,"1/48*((2*(4*B*x^2/b - (7*B*a*b^5 - 6*A*b^6)/b^7)*x^2 + 5*(7*B*a^2*b^4 - 6*A*a*b^5)/b^7)*x^2 + 15*(7*B*a^3*b^3 - 6*A*a^2*b^4)/b^7)*x/sqrt(b*x^2 + a) + 5/16*(7*B*a^3 - 6*A*a^2*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
570,1,113,0,0.344482," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{B a^{3} - A a^{2} b}{\sqrt{b x^{2} + a} b^{4}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{16} - 15 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b^{16} + 45 \, \sqrt{b x^{2} + a} B a^{2} b^{16} + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{17} - 30 \, \sqrt{b x^{2} + a} A a b^{17}}{15 \, b^{20}}"," ",0,"(B*a^3 - A*a^2*b)/(sqrt(b*x^2 + a)*b^4) + 1/15*(3*(b*x^2 + a)^(5/2)*B*b^16 - 15*(b*x^2 + a)^(3/2)*B*a*b^16 + 45*sqrt(b*x^2 + a)*B*a^2*b^16 + 5*(b*x^2 + a)^(3/2)*A*b^17 - 30*sqrt(b*x^2 + a)*A*a*b^17)/b^20","A",0
571,1,104,0,0.373179," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, B x^{2}}{b} - \frac{5 \, B a b^{3} - 4 \, A b^{4}}{b^{5}}\right)} x^{2} - \frac{3 \, {\left(5 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)}}{b^{5}}\right)} x}{8 \, \sqrt{b x^{2} + a}} - \frac{3 \, {\left(5 \, B a^{2} - 4 \, A a b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{7}{2}}}"," ",0,"1/8*((2*B*x^2/b - (5*B*a*b^3 - 4*A*b^4)/b^5)*x^2 - 3*(5*B*a^2*b^2 - 4*A*a*b^3)/b^5)*x/sqrt(b*x^2 + a) - 3/8*(5*B*a^2 - 4*A*a*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
572,1,77,0,0.377511," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{B a^{2} - A a b}{\sqrt{b x^{2} + a} b^{3}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{6} - 6 \, \sqrt{b x^{2} + a} B a b^{6} + 3 \, \sqrt{b x^{2} + a} A b^{7}}{3 \, b^{9}}"," ",0,"-(B*a^2 - A*a*b)/(sqrt(b*x^2 + a)*b^3) + 1/3*((b*x^2 + a)^(3/2)*B*b^6 - 6*sqrt(b*x^2 + a)*B*a*b^6 + 3*sqrt(b*x^2 + a)*A*b^7)/b^9","A",0
573,1,70,0,0.467340," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{B x^{2}}{b} + \frac{3 \, B a b - 2 \, A b^{2}}{b^{3}}\right)} x}{2 \, \sqrt{b x^{2} + a}} + \frac{{\left(3 \, B a - 2 \, A b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{5}{2}}}"," ",0,"1/2*(B*x^2/b + (3*B*a*b - 2*A*b^2)/b^3)*x/sqrt(b*x^2 + a) + 1/2*(3*B*a - 2*A*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
574,1,36,0,0.431643," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} B}{b^{2}} + \frac{B a - A b}{\sqrt{b x^{2} + a} b^{2}}"," ",0,"sqrt(b*x^2 + a)*B/b^2 + (B*a - A*b)/(sqrt(b*x^2 + a)*b^2)","A",0
575,1,51,0,0.439018," ","integrate((B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{3}{2}}} - \frac{{\left(B a - A b\right)} x}{\sqrt{b x^{2} + a} a b}"," ",0,"-B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) - (B*a - A*b)*x/(sqrt(b*x^2 + a)*a*b)","A",0
576,1,52,0,0.289023," ","integrate((B*x^2+A)/x/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{A \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a} - \frac{B a - A b}{\sqrt{b x^{2} + a} a b}"," ",0,"A*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - (B*a - A*b)/(sqrt(b*x^2 + a)*a*b)","A",0
577,1,57,0,0.506063," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a} + \frac{{\left(B a - A b\right)} x}{\sqrt{b x^{2} + a} a^{2}}"," ",0,"2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a) + (B*a - A*b)*x/(sqrt(b*x^2 + a)*a^2)","A",0
578,1,99,0,0.353694," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(2 \, B a - 3 \, A b\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a^{2}} + \frac{2 \, {\left(b x^{2} + a\right)} B a - 2 \, B a^{2} - 3 \, {\left(b x^{2} + a\right)} A b + 2 \, A a b}{2 \, {\left({\left(b x^{2} + a\right)}^{\frac{3}{2}} - \sqrt{b x^{2} + a} a\right)} a^{2}}"," ",0,"1/2*(2*B*a - 3*A*b)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) + 1/2*(2*(b*x^2 + a)*B*a - 2*B*a^2 - 3*(b*x^2 + a)*A*b + 2*A*a*b)/(((b*x^2 + a)^(3/2) - sqrt(b*x^2 + a)*a)*a^2)","A",0
579,1,181,0,0.571576," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{{\left(B a b - A b^{2}\right)} x}{\sqrt{b x^{2} + a} a^{3}} + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a \sqrt{b} - 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} \sqrt{b} + 12 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a b^{\frac{3}{2}} + 3 \, B a^{3} \sqrt{b} - 5 \, A a^{2} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{2}}"," ",0,"-(B*a*b - A*b^2)*x/(sqrt(b*x^2 + a)*a^3) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a*sqrt(b) - 3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*sqrt(b) + 12*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a*b^(3/2) + 3*B*a^3*sqrt(b) - 5*A*a^2*b^(3/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3*a^2)","B",0
580,1,137,0,0.371017," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{3}} - \frac{B a b - A b^{2}}{\sqrt{b x^{2} + a} a^{3}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b - 4 \, \sqrt{b x^{2} + a} B a^{2} b - 7 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2} + 9 \, \sqrt{b x^{2} + a} A a b^{2}}{8 \, a^{3} b^{2} x^{4}}"," ",0,"-3/8*(4*B*a*b - 5*A*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) - (B*a*b - A*b^2)/(sqrt(b*x^2 + a)*a^3) - 1/8*(4*(b*x^2 + a)^(3/2)*B*a*b - 4*sqrt(b*x^2 + a)*B*a^2*b - 7*(b*x^2 + a)^(3/2)*A*b^2 + 9*sqrt(b*x^2 + a)*A*a*b^2)/(a^3*b^2*x^4)","A",0
581,1,294,0,0.474006," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(B a b^{2} - A b^{3}\right)} x}{\sqrt{b x^{2} + a} a^{4}} - \frac{2 \, {\left(15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a b^{\frac{3}{2}} - 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A b^{\frac{5}{2}} - 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{2} b^{\frac{3}{2}} + 90 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a b^{\frac{5}{2}} + 160 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} b^{\frac{3}{2}} - 240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{5}{2}} - 110 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} b^{\frac{3}{2}} + 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{3} b^{\frac{5}{2}} + 25 \, B a^{5} b^{\frac{3}{2}} - 33 \, A a^{4} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5} a^{3}}"," ",0,"(B*a*b^2 - A*b^3)*x/(sqrt(b*x^2 + a)*a^4) - 2/15*(15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a*b^(3/2) - 15*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*b^(5/2) - 90*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^2*b^(3/2) + 90*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a*b^(5/2) + 160*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*b^(3/2) - 240*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(5/2) - 110*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*b^(3/2) + 150*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^3*b^(5/2) + 25*B*a^5*b^(3/2) - 33*A*a^4*b^(5/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5*a^3)","B",0
582,1,180,0,0.379752," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{5 \, {\left(6 \, B a b^{2} - 7 \, A b^{3}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{16 \, \sqrt{-a} a^{4}} + \frac{B a b^{2} - A b^{3}}{\sqrt{b x^{2} + a} a^{4}} + \frac{42 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a b^{2} - 96 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} b^{2} + 54 \, \sqrt{b x^{2} + a} B a^{3} b^{2} - 57 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{3} + 136 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a b^{3} - 87 \, \sqrt{b x^{2} + a} A a^{2} b^{3}}{48 \, a^{4} b^{3} x^{6}}"," ",0,"5/16*(6*B*a*b^2 - 7*A*b^3)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^4) + (B*a*b^2 - A*b^3)/(sqrt(b*x^2 + a)*a^4) + 1/48*(42*(b*x^2 + a)^(5/2)*B*a*b^2 - 96*(b*x^2 + a)^(3/2)*B*a^2*b^2 + 54*sqrt(b*x^2 + a)*B*a^3*b^2 - 57*(b*x^2 + a)^(5/2)*A*b^3 + 136*(b*x^2 + a)^(3/2)*A*a*b^3 - 87*sqrt(b*x^2 + a)*A*a^2*b^3)/(a^4*b^3*x^6)","A",0
583,1,407,0,0.540741," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{{\left(B a b^{3} - A b^{4}\right)} x}{\sqrt{b x^{2} + a} a^{5}} + \frac{2 \, {\left(35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} B a b^{\frac{5}{2}} - 35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} A b^{\frac{7}{2}} - 280 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} B a^{2} b^{\frac{5}{2}} + 280 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} A a b^{\frac{7}{2}} + 1015 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a^{3} b^{\frac{5}{2}} - 1015 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A a^{2} b^{\frac{7}{2}} - 1680 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{4} b^{\frac{5}{2}} + 2240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a^{3} b^{\frac{7}{2}} + 1337 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{5} b^{\frac{5}{2}} - 1673 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{4} b^{\frac{7}{2}} - 504 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{6} b^{\frac{5}{2}} + 616 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{5} b^{\frac{7}{2}} + 77 \, B a^{7} b^{\frac{5}{2}} - 93 \, A a^{6} b^{\frac{7}{2}}\right)}}{35 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{7} a^{4}}"," ",0,"-(B*a*b^3 - A*b^4)*x/(sqrt(b*x^2 + a)*a^5) + 2/35*(35*(sqrt(b)*x - sqrt(b*x^2 + a))^12*B*a*b^(5/2) - 35*(sqrt(b)*x - sqrt(b*x^2 + a))^12*A*b^(7/2) - 280*(sqrt(b)*x - sqrt(b*x^2 + a))^10*B*a^2*b^(5/2) + 280*(sqrt(b)*x - sqrt(b*x^2 + a))^10*A*a*b^(7/2) + 1015*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a^3*b^(5/2) - 1015*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*a^2*b^(7/2) - 1680*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^4*b^(5/2) + 2240*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a^3*b^(7/2) + 1337*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^5*b^(5/2) - 1673*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^4*b^(7/2) - 504*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^6*b^(5/2) + 616*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^5*b^(7/2) + 77*B*a^7*b^(5/2) - 93*A*a^6*b^(7/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^7*a^4)","B",0
584,1,141,0,0.363879," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{12 \, {\left(b x^{2} + a\right)} B a^{3} - B a^{4} - 9 \, {\left(b x^{2} + a\right)} A a^{2} b + A a^{3} b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{20} - 20 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b^{20} + 90 \, \sqrt{b x^{2} + a} B a^{2} b^{20} + 5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{21} - 45 \, \sqrt{b x^{2} + a} A a b^{21}}{15 \, b^{25}}"," ",0,"1/3*(12*(b*x^2 + a)*B*a^3 - B*a^4 - 9*(b*x^2 + a)*A*a^2*b + A*a^3*b)/((b*x^2 + a)^(3/2)*b^5) + 1/15*(3*(b*x^2 + a)^(5/2)*B*b^20 - 20*(b*x^2 + a)^(3/2)*B*a*b^20 + 90*sqrt(b*x^2 + a)*B*a^2*b^20 + 5*(b*x^2 + a)^(3/2)*A*b^21 - 45*sqrt(b*x^2 + a)*A*a*b^21)/b^25","A",0
585,1,148,0,0.577553," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, {\left(\frac{2 \, B x^{2}}{b} - \frac{7 \, B a^{2} b^{5} - 4 \, A a b^{6}}{a b^{7}}\right)} x^{2} - \frac{20 \, {\left(7 \, B a^{3} b^{4} - 4 \, A a^{2} b^{5}\right)}}{a b^{7}}\right)} x^{2} - \frac{15 \, {\left(7 \, B a^{4} b^{3} - 4 \, A a^{3} b^{4}\right)}}{a b^{7}}\right)} x}{24 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{5 \, {\left(7 \, B a^{2} - 4 \, A a b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{9}{2}}}"," ",0,"1/24*((3*(2*B*x^2/b - (7*B*a^2*b^5 - 4*A*a*b^6)/(a*b^7))*x^2 - 20*(7*B*a^3*b^4 - 4*A*a^2*b^5)/(a*b^7))*x^2 - 15*(7*B*a^4*b^3 - 4*A*a^3*b^4)/(a*b^7))*x/(b*x^2 + a)^(3/2) - 5/8*(7*B*a^2 - 4*A*a*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
586,1,104,0,0.446245," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{9 \, {\left(b x^{2} + a\right)} B a^{2} - B a^{3} - 6 \, {\left(b x^{2} + a\right)} A a b + A a^{2} b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{8} - 9 \, \sqrt{b x^{2} + a} B a b^{8} + 3 \, \sqrt{b x^{2} + a} A b^{9}}{3 \, b^{12}}"," ",0,"-1/3*(9*(b*x^2 + a)*B*a^2 - B*a^3 - 6*(b*x^2 + a)*A*a*b + A*a^2*b)/((b*x^2 + a)^(3/2)*b^4) + 1/3*((b*x^2 + a)^(3/2)*B*b^8 - 9*sqrt(b*x^2 + a)*B*a*b^8 + 3*sqrt(b*x^2 + a)*A*b^9)/b^12","A",0
587,1,112,0,0.500881," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{3 \, B x^{2}}{b} + \frac{4 \, {\left(5 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)}}{a b^{5}}\right)} x^{2} + \frac{3 \, {\left(5 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)}}{a b^{5}}\right)} x}{6 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{{\left(5 \, B a - 2 \, A b\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{7}{2}}}"," ",0,"1/6*((3*B*x^2/b + 4*(5*B*a^2*b^3 - 2*A*a*b^4)/(a*b^5))*x^2 + 3*(5*B*a^3*b^2 - 2*A*a^2*b^3)/(a*b^5))*x/(b*x^2 + a)^(3/2) + 1/2*(5*B*a - 2*A*b)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
588,1,62,0,0.336760," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} B}{b^{3}} + \frac{6 \, {\left(b x^{2} + a\right)} B a - B a^{2} - 3 \, {\left(b x^{2} + a\right)} A b + A a b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}}"," ",0,"sqrt(b*x^2 + a)*B/b^3 + 1/3*(6*(b*x^2 + a)*B*a - B*a^2 - 3*(b*x^2 + a)*A*b + A*a*b)/((b*x^2 + a)^(3/2)*b^3)","A",0
589,1,69,0,0.382932," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{x {\left(\frac{3 \, B a}{b^{2}} + \frac{{\left(4 \, B a b^{2} - A b^{3}\right)} x^{2}}{a b^{3}}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{B \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*x*(3*B*a/b^2 + (4*B*a*b^2 - A*b^3)*x^2/(a*b^3))/(b*x^2 + a)^(3/2) - B*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
590,1,32,0,0.339864," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{3 \, {\left(b x^{2} + a\right)} B - B a + A b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}"," ",0,"-1/3*(3*(b*x^2 + a)*B - B*a + A*b)/((b*x^2 + a)^(3/2)*b^2)","A",0
591,1,40,0,0.402355," ","integrate((B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{3 \, A}{a} + \frac{{\left(B a b + 2 \, A b^{2}\right)} x^{2}}{a^{2} b}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*x*(3*A/a + (B*a*b + 2*A*b^2)*x^2/(a^2*b))/(b*x^2 + a)^(3/2)","A",0
592,1,66,0,0.310145," ","integrate((B*x^2+A)/x/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{A \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} a^{2}} - \frac{B a^{2} - 3 \, {\left(b x^{2} + a\right)} A b - A a b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} b}"," ",0,"A*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^2) - 1/3*(B*a^2 - 3*(b*x^2 + a)*A*b - A*a*b)/((b*x^2 + a)^(3/2)*a^2*b)","A",0
593,1,101,0,0.421056," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{{\left(2 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{2}}{a^{5} b} + \frac{3 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)}}{a^{5} b}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, A \sqrt{b}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)} a^{2}}"," ",0,"1/3*x*((2*B*a^3*b^2 - 5*A*a^2*b^3)*x^2/(a^5*b) + 3*(B*a^4*b - 2*A*a^3*b^2)/(a^5*b))/(b*x^2 + a)^(3/2) + 2*A*sqrt(b)/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)*a^2)","A",0
594,1,101,0,0.358355," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(2 \, B a - 5 \, A b\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{2 \, \sqrt{-a} a^{3}} + \frac{3 \, {\left(b x^{2} + a\right)} B a + B a^{2} - 6 \, {\left(b x^{2} + a\right)} A b - A a b}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} - \frac{\sqrt{b x^{2} + a} A}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*B*a - 5*A*b)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^3) + 1/3*(3*(b*x^2 + a)*B*a + B*a^2 - 6*(b*x^2 + a)*A*b - A*a*b)/((b*x^2 + a)^(3/2)*a^3) - 1/2*sqrt(b*x^2 + a)*A/(a^3*x^2)","A",0
595,1,224,0,0.467837," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{x {\left(\frac{{\left(5 \, B a^{4} b^{3} - 8 \, A a^{3} b^{4}\right)} x^{2}}{a^{7} b} + \frac{3 \, {\left(2 \, B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)}}{a^{7} b}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a \sqrt{b} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A b^{\frac{3}{2}} - 6 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{2} \sqrt{b} + 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a b^{\frac{3}{2}} + 3 \, B a^{3} \sqrt{b} - 8 \, A a^{2} b^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{3} a^{3}}"," ",0,"-1/3*x*((5*B*a^4*b^3 - 8*A*a^3*b^4)*x^2/(a^7*b) + 3*(2*B*a^5*b^2 - 3*A*a^4*b^3)/(a^7*b))/(b*x^2 + a)^(3/2) + 2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a*sqrt(b) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*b^(3/2) - 6*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^2*sqrt(b) + 18*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a*b^(3/2) + 3*B*a^3*sqrt(b) - 8*A*a^2*b^(3/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^3*a^3)","B",0
596,1,165,0,0.411038," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, {\left(4 \, B a b - 7 \, A b^{2}\right)} \arctan\left(\frac{\sqrt{b x^{2} + a}}{\sqrt{-a}}\right)}{8 \, \sqrt{-a} a^{4}} - \frac{6 \, {\left(b x^{2} + a\right)} B a b + B a^{2} b - 9 \, {\left(b x^{2} + a\right)} A b^{2} - A a b^{2}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a b - 4 \, \sqrt{b x^{2} + a} B a^{2} b - 11 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2} + 13 \, \sqrt{b x^{2} + a} A a b^{2}}{8 \, a^{4} b^{2} x^{4}}"," ",0,"-5/8*(4*B*a*b - 7*A*b^2)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a^4) - 1/3*(6*(b*x^2 + a)*B*a*b + B*a^2*b - 9*(b*x^2 + a)*A*b^2 - A*a*b^2)/((b*x^2 + a)^(3/2)*a^4) - 1/8*(4*(b*x^2 + a)^(3/2)*B*a*b - 4*sqrt(b*x^2 + a)*B*a^2*b - 11*(b*x^2 + a)^(3/2)*A*b^2 + 13*sqrt(b*x^2 + a)*A*a*b^2)/(a^4*b^2*x^4)","A",0
597,1,336,0,0.577573," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{{\left(8 \, B a^{5} b^{4} - 11 \, A a^{4} b^{5}\right)} x^{2}}{a^{9} b} + \frac{3 \, {\left(3 \, B a^{6} b^{3} - 4 \, A a^{5} b^{4}\right)}}{a^{9} b}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} B a b^{\frac{3}{2}} - 45 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} A b^{\frac{5}{2}} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} B a^{2} b^{\frac{3}{2}} + 240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} A a b^{\frac{5}{2}} + 250 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} B a^{3} b^{\frac{3}{2}} - 490 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} A a^{2} b^{\frac{5}{2}} - 170 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} B a^{4} b^{\frac{3}{2}} + 320 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} A a^{3} b^{\frac{5}{2}} + 40 \, B a^{5} b^{\frac{3}{2}} - 73 \, A a^{4} b^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} - a\right)}^{5} a^{4}}"," ",0,"1/3*x*((8*B*a^5*b^4 - 11*A*a^4*b^5)*x^2/(a^9*b) + 3*(3*B*a^6*b^3 - 4*A*a^5*b^4)/(a^9*b))/(b*x^2 + a)^(3/2) - 2/15*(30*(sqrt(b)*x - sqrt(b*x^2 + a))^8*B*a*b^(3/2) - 45*(sqrt(b)*x - sqrt(b*x^2 + a))^8*A*b^(5/2) - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^6*B*a^2*b^(3/2) + 240*(sqrt(b)*x - sqrt(b*x^2 + a))^6*A*a*b^(5/2) + 250*(sqrt(b)*x - sqrt(b*x^2 + a))^4*B*a^3*b^(3/2) - 490*(sqrt(b)*x - sqrt(b*x^2 + a))^4*A*a^2*b^(5/2) - 170*(sqrt(b)*x - sqrt(b*x^2 + a))^2*B*a^4*b^(3/2) + 320*(sqrt(b)*x - sqrt(b*x^2 + a))^2*A*a^3*b^(5/2) + 40*B*a^5*b^(3/2) - 73*A*a^4*b^(5/2))/(((sqrt(b)*x - sqrt(b*x^2 + a))^2 - a)^5*a^4)","B",0
598,1,204,0,0.286880," ","integrate(x^5*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{315 \, {\left(d x^{2} + c\right)}^{\frac{11}{2}} b^{2} - 1540 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} c + 2970 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2} - 2772 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{3} + 1155 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{4} + 770 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} a b d - 2970 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c d + 4158 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c^{2} d - 2310 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{3} d + 495 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d^{2} - 1386 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} c d^{2} + 1155 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c^{2} d^{2}}{3465 \, d^{5}}"," ",0,"1/3465*(315*(d*x^2 + c)^(11/2)*b^2 - 1540*(d*x^2 + c)^(9/2)*b^2*c + 2970*(d*x^2 + c)^(7/2)*b^2*c^2 - 2772*(d*x^2 + c)^(5/2)*b^2*c^3 + 1155*(d*x^2 + c)^(3/2)*b^2*c^4 + 770*(d*x^2 + c)^(9/2)*a*b*d - 2970*(d*x^2 + c)^(7/2)*a*b*c*d + 4158*(d*x^2 + c)^(5/2)*a*b*c^2*d - 2310*(d*x^2 + c)^(3/2)*a*b*c^3*d + 495*(d*x^2 + c)^(7/2)*a^2*d^2 - 1386*(d*x^2 + c)^(5/2)*a^2*c*d^2 + 1155*(d*x^2 + c)^(3/2)*a^2*c^2*d^2)/d^5","A",0
599,1,150,0,0.352808," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{35 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} - 135 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c + 189 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} - 105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} + 90 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b d - 252 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d + 210 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d + 63 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{2} - 105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{2}}{315 \, d^{4}}"," ",0,"1/315*(35*(d*x^2 + c)^(9/2)*b^2 - 135*(d*x^2 + c)^(7/2)*b^2*c + 189*(d*x^2 + c)^(5/2)*b^2*c^2 - 105*(d*x^2 + c)^(3/2)*b^2*c^3 + 90*(d*x^2 + c)^(7/2)*a*b*d - 252*(d*x^2 + c)^(5/2)*a*b*c*d + 210*(d*x^2 + c)^(3/2)*a*b*c^2*d + 63*(d*x^2 + c)^(5/2)*a^2*d^2 - 105*(d*x^2 + c)^(3/2)*a^2*c*d^2)/d^4","A",0
600,1,98,0,0.292111," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{15 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} - 42 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c + 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} + 42 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d - 70 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d + 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{105 \, d^{3}}"," ",0,"1/105*(15*(d*x^2 + c)^(7/2)*b^2 - 42*(d*x^2 + c)^(5/2)*b^2*c + 35*(d*x^2 + c)^(3/2)*b^2*c^2 + 42*(d*x^2 + c)^(5/2)*a*b*d - 70*(d*x^2 + c)^(3/2)*a*b*c*d + 35*(d*x^2 + c)^(3/2)*a^2*d^2)/d^3","A",0
601,1,101,0,0.315718," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\frac{a^{2} c \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} d^{8} - 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c d^{8} + 10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{9} + 15 \, \sqrt{d x^{2} + c} a^{2} d^{10}}{15 \, d^{10}}"," ",0,"a^2*c*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) + 1/15*(3*(d*x^2 + c)^(5/2)*b^2*d^8 - 5*(d*x^2 + c)^(3/2)*b^2*c*d^8 + 10*(d*x^2 + c)^(3/2)*a*b*d^9 + 15*sqrt(d*x^2 + c)*a^2*d^10)/d^10","A",0
602,1,89,0,0.380093," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} + 12 \, \sqrt{d x^{2} + c} a b d - \frac{3 \, \sqrt{d x^{2} + c} a^{2} d}{x^{2}} + \frac{3 \, {\left(4 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}}}{6 \, d}"," ",0,"1/6*(2*(d*x^2 + c)^(3/2)*b^2 + 12*sqrt(d*x^2 + c)*a*b*d - 3*sqrt(d*x^2 + c)*a^2*d/x^2 + 3*(4*a*b*c*d + a^2*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c))/d","A",0
603,1,153,0,0.355070," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^5,x, algorithm=""giac"")","\frac{8 \, \sqrt{d x^{2} + c} b^{2} d + \frac{{\left(8 \, b^{2} c^{2} d + 8 \, a b c d^{2} - a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d^{2} - 8 \, \sqrt{d x^{2} + c} a b c^{2} d^{2} + {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3} + \sqrt{d x^{2} + c} a^{2} c d^{3}}{c d^{2} x^{4}}}{8 \, d}"," ",0,"1/8*(8*sqrt(d*x^2 + c)*b^2*d + (8*b^2*c^2*d + 8*a*b*c*d^2 - a^2*d^3)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c) - (8*(d*x^2 + c)^(3/2)*a*b*c*d^2 - 8*sqrt(d*x^2 + c)*a*b*c^2*d^2 + (d*x^2 + c)^(3/2)*a^2*d^3 + sqrt(d*x^2 + c)*a^2*c*d^3)/(c*d^2*x^4))/d","A",0
604,1,222,0,0.484964," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^7,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(8 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2}} - \frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} - 48 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} d^{2} + 24 \, \sqrt{d x^{2} + c} b^{2} c^{4} d^{2} + 12 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d^{3} - 12 \, \sqrt{d x^{2} + c} a b c^{3} d^{3} - 3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{4} + 8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{4} + 3 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{4}}{c^{2} d^{3} x^{6}}}{48 \, d}"," ",0,"1/48*(3*(8*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^2) - (24*(d*x^2 + c)^(5/2)*b^2*c^2*d^2 - 48*(d*x^2 + c)^(3/2)*b^2*c^3*d^2 + 24*sqrt(d*x^2 + c)*b^2*c^4*d^2 + 12*(d*x^2 + c)^(5/2)*a*b*c*d^3 - 12*sqrt(d*x^2 + c)*a*b*c^3*d^3 - 3*(d*x^2 + c)^(5/2)*a^2*d^4 + 8*(d*x^2 + c)^(3/2)*a^2*c*d^4 + 3*sqrt(d*x^2 + c)*a^2*c^2*d^4)/(c^2*d^3*x^6))/d","A",0
605,1,174,0,0.491500," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, b^{2} x^{2} + \frac{b^{2} c d^{5} + 16 \, a b d^{6}}{d^{6}}\right)} x^{2} - \frac{5 \, b^{2} c^{2} d^{4} - 16 \, a b c d^{5} - 48 \, a^{2} d^{6}}{d^{6}}\right)} x^{2} + \frac{3 \, {\left(5 \, b^{2} c^{3} d^{3} - 16 \, a b c^{2} d^{4} + 16 \, a^{2} c d^{5}\right)}}{d^{6}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(5 \, b^{2} c^{4} - 16 \, a b c^{3} d + 16 \, a^{2} c^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{128 \, d^{\frac{7}{2}}}"," ",0,"1/384*(2*(4*(6*b^2*x^2 + (b^2*c*d^5 + 16*a*b*d^6)/d^6)*x^2 - (5*b^2*c^2*d^4 - 16*a*b*c*d^5 - 48*a^2*d^6)/d^6)*x^2 + 3*(5*b^2*c^3*d^3 - 16*a*b*c^2*d^4 + 16*a^2*c*d^5)/d^6)*sqrt(d*x^2 + c)*x + 1/128*(5*b^2*c^4 - 16*a*b*c^3*d + 16*a^2*c^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
606,1,128,0,0.384609," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, b^{2} x^{2} + \frac{b^{2} c d^{3} + 12 \, a b d^{4}}{d^{4}}\right)} x^{2} - \frac{3 \, {\left(b^{2} c^{2} d^{2} - 4 \, a b c d^{3} - 8 \, a^{2} d^{4}\right)}}{d^{4}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(b^{2} c^{3} - 4 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{16 \, d^{\frac{5}{2}}}"," ",0,"1/48*(2*(4*b^2*x^2 + (b^2*c*d^3 + 12*a*b*d^4)/d^4)*x^2 - 3*(b^2*c^2*d^2 - 4*a*b*c*d^3 - 8*a^2*d^4)/d^4)*sqrt(d*x^2 + c)*x - 1/16*(b^2*c^3 - 4*a*b*c^2*d + 8*a^2*c*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
607,1,126,0,0.470672," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, a^{2} c \sqrt{d}}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c} + \frac{1}{8} \, {\left(2 \, b^{2} x^{2} + \frac{b^{2} c d + 8 \, a b d^{2}}{d^{2}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(b^{2} c^{2} \sqrt{d} - 8 \, a b c d^{\frac{3}{2}} - 8 \, a^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{16 \, d^{2}}"," ",0,"2*a^2*c*sqrt(d)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c) + 1/8*(2*b^2*x^2 + (b^2*c*d + 8*a*b*d^2)/d^2)*sqrt(d*x^2 + c)*x + 1/16*(b^2*c^2*sqrt(d) - 8*a*b*c*d^(3/2) - 8*a^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d^2","A",0
608,1,188,0,0.456728," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^4,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{d x^{2} + c} b^{2} x - \frac{{\left(b^{2} c \sqrt{d} + 4 \, a b d^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, d} + \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{2} \sqrt{d} + 6 \, a b c^{3} \sqrt{d} + a^{2} c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"1/2*sqrt(d*x^2 + c)*b^2*x - 1/4*(b^2*c*sqrt(d) + 4*a*b*d^(3/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d + 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^2*sqrt(d) + 6*a*b*c^3*sqrt(d) + a^2*c^2*d^(3/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3","B",0
609,1,403,0,0.465690," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^6,x, algorithm=""giac"")","-\frac{1}{2} \, b^{2} \sqrt{d} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right) + \frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c \sqrt{d} + 30 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b d^{\frac{3}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{2} \sqrt{d} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c d^{\frac{3}{2}} + 30 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} d^{\frac{5}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{3} \sqrt{d} + 40 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{2} d^{\frac{3}{2}} + 10 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{4} \sqrt{d} - 20 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{3} d^{\frac{3}{2}} + 10 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{2} d^{\frac{5}{2}} + 15 \, b^{2} c^{5} \sqrt{d} + 10 \, a b c^{4} d^{\frac{3}{2}} - 2 \, a^{2} c^{3} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5}}"," ",0,"-1/2*b^2*sqrt(d)*log((sqrt(d)*x - sqrt(d*x^2 + c))^2) + 2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c*sqrt(d) + 30*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*d^(3/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^2*sqrt(d) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c*d^(3/2) + 30*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*d^(5/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^3*sqrt(d) + 40*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^2*d^(3/2) + 10*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^4*sqrt(d) - 20*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^3*d^(3/2) + 10*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^2*d^(5/2) + 15*b^2*c^5*sqrt(d) + 10*a*b*c^4*d^(3/2) - 2*a^2*c^3*d^(5/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5","B",0
610,1,490,0,0.444152," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(105 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} b^{2} d^{\frac{3}{2}} - 420 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} b^{2} c d^{\frac{3}{2}} + 420 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a b d^{\frac{5}{2}} + 665 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{2} d^{\frac{3}{2}} - 700 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c d^{\frac{5}{2}} + 560 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} d^{\frac{7}{2}} - 560 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{3} d^{\frac{3}{2}} + 280 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{2} d^{\frac{5}{2}} + 280 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c d^{\frac{7}{2}} + 315 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{4} d^{\frac{3}{2}} - 168 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{3} d^{\frac{5}{2}} + 168 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{2} d^{\frac{7}{2}} - 140 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{5} d^{\frac{3}{2}} + 196 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{4} d^{\frac{5}{2}} - 56 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{3} d^{\frac{7}{2}} + 35 \, b^{2} c^{6} d^{\frac{3}{2}} - 28 \, a b c^{5} d^{\frac{5}{2}} + 8 \, a^{2} c^{4} d^{\frac{7}{2}}\right)}}{105 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{7}}"," ",0,"2/105*(105*(sqrt(d)*x - sqrt(d*x^2 + c))^12*b^2*d^(3/2) - 420*(sqrt(d)*x - sqrt(d*x^2 + c))^10*b^2*c*d^(3/2) + 420*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a*b*d^(5/2) + 665*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^2*d^(3/2) - 700*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c*d^(5/2) + 560*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*d^(7/2) - 560*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^3*d^(3/2) + 280*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^2*d^(5/2) + 280*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c*d^(7/2) + 315*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^4*d^(3/2) - 168*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^3*d^(5/2) + 168*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^2*d^(7/2) - 140*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^5*d^(3/2) + 196*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^4*d^(5/2) - 56*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^3*d^(7/2) + 35*b^2*c^6*d^(3/2) - 28*a*b*c^5*d^(5/2) + 8*a^2*c^4*d^(7/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^7","B",0
611,1,579,0,0.437862," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^10,x, algorithm=""giac"")","\frac{4 \, {\left(315 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{14} b^{2} d^{\frac{5}{2}} - 1155 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} b^{2} c d^{\frac{5}{2}} + 1680 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} a b d^{\frac{7}{2}} + 1575 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} b^{2} c^{2} d^{\frac{5}{2}} - 2520 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a b c d^{\frac{7}{2}} + 2520 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a^{2} d^{\frac{9}{2}} - 1071 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{3} d^{\frac{5}{2}} + 504 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c^{2} d^{\frac{7}{2}} + 1512 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} c d^{\frac{9}{2}} + 609 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{4} d^{\frac{5}{2}} - 336 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{3} d^{\frac{7}{2}} + 672 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c^{2} d^{\frac{9}{2}} - 441 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{5} d^{\frac{5}{2}} + 864 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{4} d^{\frac{7}{2}} - 288 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{3} d^{\frac{9}{2}} + 189 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{6} d^{\frac{5}{2}} - 216 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{5} d^{\frac{7}{2}} + 72 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{4} d^{\frac{9}{2}} - 21 \, b^{2} c^{7} d^{\frac{5}{2}} + 24 \, a b c^{6} d^{\frac{7}{2}} - 8 \, a^{2} c^{5} d^{\frac{9}{2}}\right)}}{315 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{9}}"," ",0,"4/315*(315*(sqrt(d)*x - sqrt(d*x^2 + c))^14*b^2*d^(5/2) - 1155*(sqrt(d)*x - sqrt(d*x^2 + c))^12*b^2*c*d^(5/2) + 1680*(sqrt(d)*x - sqrt(d*x^2 + c))^12*a*b*d^(7/2) + 1575*(sqrt(d)*x - sqrt(d*x^2 + c))^10*b^2*c^2*d^(5/2) - 2520*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a*b*c*d^(7/2) + 2520*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a^2*d^(9/2) - 1071*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^3*d^(5/2) + 504*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c^2*d^(7/2) + 1512*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*c*d^(9/2) + 609*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^4*d^(5/2) - 336*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^3*d^(7/2) + 672*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c^2*d^(9/2) - 441*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^5*d^(5/2) + 864*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^4*d^(7/2) - 288*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^3*d^(9/2) + 189*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^6*d^(5/2) - 216*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^5*d^(7/2) + 72*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^4*d^(9/2) - 21*b^2*c^7*d^(5/2) + 24*a*b*c^6*d^(7/2) - 8*a^2*c^5*d^(9/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^9","B",0
612,1,668,0,0.421413," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^12,x, algorithm=""giac"")","\frac{16 \, {\left(2310 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{16} b^{2} d^{\frac{7}{2}} - 8085 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{14} b^{2} c d^{\frac{7}{2}} + 13860 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{14} a b d^{\frac{9}{2}} + 9933 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} b^{2} c^{2} d^{\frac{7}{2}} - 19404 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} a b c d^{\frac{9}{2}} + 22176 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{12} a^{2} d^{\frac{11}{2}} - 5313 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} b^{2} c^{3} d^{\frac{7}{2}} + 924 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a b c^{2} d^{\frac{9}{2}} + 14784 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a^{2} c d^{\frac{11}{2}} + 2805 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{4} d^{\frac{7}{2}} - 660 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c^{3} d^{\frac{9}{2}} + 5280 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} c^{2} d^{\frac{11}{2}} - 3135 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{5} d^{\frac{7}{2}} + 7260 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{4} d^{\frac{9}{2}} - 2640 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c^{3} d^{\frac{11}{2}} + 1815 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{6} d^{\frac{7}{2}} - 2420 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{5} d^{\frac{9}{2}} + 880 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{4} d^{\frac{11}{2}} - 363 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{7} d^{\frac{7}{2}} + 484 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{6} d^{\frac{9}{2}} - 176 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{5} d^{\frac{11}{2}} + 33 \, b^{2} c^{8} d^{\frac{7}{2}} - 44 \, a b c^{7} d^{\frac{9}{2}} + 16 \, a^{2} c^{6} d^{\frac{11}{2}}\right)}}{3465 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{11}}"," ",0,"16/3465*(2310*(sqrt(d)*x - sqrt(d*x^2 + c))^16*b^2*d^(7/2) - 8085*(sqrt(d)*x - sqrt(d*x^2 + c))^14*b^2*c*d^(7/2) + 13860*(sqrt(d)*x - sqrt(d*x^2 + c))^14*a*b*d^(9/2) + 9933*(sqrt(d)*x - sqrt(d*x^2 + c))^12*b^2*c^2*d^(7/2) - 19404*(sqrt(d)*x - sqrt(d*x^2 + c))^12*a*b*c*d^(9/2) + 22176*(sqrt(d)*x - sqrt(d*x^2 + c))^12*a^2*d^(11/2) - 5313*(sqrt(d)*x - sqrt(d*x^2 + c))^10*b^2*c^3*d^(7/2) + 924*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a*b*c^2*d^(9/2) + 14784*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a^2*c*d^(11/2) + 2805*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^4*d^(7/2) - 660*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c^3*d^(9/2) + 5280*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*c^2*d^(11/2) - 3135*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^5*d^(7/2) + 7260*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^4*d^(9/2) - 2640*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c^3*d^(11/2) + 1815*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^6*d^(7/2) - 2420*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^5*d^(9/2) + 880*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^4*d^(11/2) - 363*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^7*d^(7/2) + 484*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^6*d^(9/2) - 176*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^5*d^(11/2) + 33*b^2*c^8*d^(7/2) - 44*a*b*c^7*d^(9/2) + 16*a^2*c^6*d^(11/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^11","B",0
613,1,263,0,0.494260," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{15360} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, b^{2} d x^{2} + \frac{13 \, b^{2} c d^{10} + 24 \, a b d^{11}}{d^{10}}\right)} x^{2} + \frac{3 \, {\left(b^{2} c^{2} d^{9} + 88 \, a b c d^{10} + 40 \, a^{2} d^{11}\right)}}{d^{10}}\right)} x^{2} - \frac{7 \, b^{2} c^{3} d^{8} - 24 \, a b c^{2} d^{9} - 360 \, a^{2} c d^{10}}{d^{10}}\right)} x^{2} + \frac{5 \, {\left(7 \, b^{2} c^{4} d^{7} - 24 \, a b c^{3} d^{8} + 24 \, a^{2} c^{2} d^{9}\right)}}{d^{10}}\right)} x^{2} - \frac{15 \, {\left(7 \, b^{2} c^{5} d^{6} - 24 \, a b c^{4} d^{7} + 24 \, a^{2} c^{3} d^{8}\right)}}{d^{10}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(7 \, b^{2} c^{6} - 24 \, a b c^{5} d + 24 \, a^{2} c^{4} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{1024 \, d^{\frac{9}{2}}}"," ",0,"1/15360*(2*(4*(2*(8*(10*b^2*d*x^2 + (13*b^2*c*d^10 + 24*a*b*d^11)/d^10)*x^2 + 3*(b^2*c^2*d^9 + 88*a*b*c*d^10 + 40*a^2*d^11)/d^10)*x^2 - (7*b^2*c^3*d^8 - 24*a*b*c^2*d^9 - 360*a^2*c*d^10)/d^10)*x^2 + 5*(7*b^2*c^4*d^7 - 24*a*b*c^3*d^8 + 24*a^2*c^2*d^9)/d^10)*x^2 - 15*(7*b^2*c^5*d^6 - 24*a*b*c^4*d^7 + 24*a^2*c^3*d^8)/d^10)*sqrt(d*x^2 + c)*x - 1/1024*(7*b^2*c^6 - 24*a*b*c^5*d + 24*a^2*c^4*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(9/2)","A",0
614,1,150,0,0.374026," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{315 \, {\left(d x^{2} + c\right)}^{\frac{11}{2}} b^{2} - 1155 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} c + 1485 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2} - 693 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{3} + 770 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} a b d - 1980 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c d + 1386 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c^{2} d + 495 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d^{2} - 693 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} c d^{2}}{3465 \, d^{4}}"," ",0,"1/3465*(315*(d*x^2 + c)^(11/2)*b^2 - 1155*(d*x^2 + c)^(9/2)*b^2*c + 1485*(d*x^2 + c)^(7/2)*b^2*c^2 - 693*(d*x^2 + c)^(5/2)*b^2*c^3 + 770*(d*x^2 + c)^(9/2)*a*b*d - 1980*(d*x^2 + c)^(7/2)*a*b*c*d + 1386*(d*x^2 + c)^(5/2)*a*b*c^2*d + 495*(d*x^2 + c)^(7/2)*a^2*d^2 - 693*(d*x^2 + c)^(5/2)*a^2*c*d^2)/d^4","A",0
615,1,219,0,0.431126," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, b^{2} d x^{2} + \frac{11 \, b^{2} c d^{8} + 20 \, a b d^{9}}{d^{8}}\right)} x^{2} + \frac{3 \, b^{2} c^{2} d^{7} + 180 \, a b c d^{8} + 80 \, a^{2} d^{9}}{d^{8}}\right)} x^{2} - \frac{5 \, {\left(3 \, b^{2} c^{3} d^{6} - 12 \, a b c^{2} d^{7} - 112 \, a^{2} c d^{8}\right)}}{d^{8}}\right)} x^{2} + \frac{15 \, {\left(3 \, b^{2} c^{4} d^{5} - 12 \, a b c^{3} d^{6} + 16 \, a^{2} c^{2} d^{7}\right)}}{d^{8}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(3 \, b^{2} c^{5} - 12 \, a b c^{4} d + 16 \, a^{2} c^{3} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{256 \, d^{\frac{7}{2}}}"," ",0,"1/3840*(2*(4*(6*(8*b^2*d*x^2 + (11*b^2*c*d^8 + 20*a*b*d^9)/d^8)*x^2 + (3*b^2*c^2*d^7 + 180*a*b*c*d^8 + 80*a^2*d^9)/d^8)*x^2 - 5*(3*b^2*c^3*d^6 - 12*a*b*c^2*d^7 - 112*a^2*c*d^8)/d^8)*x^2 + 15*(3*b^2*c^4*d^5 - 12*a*b*c^3*d^6 + 16*a^2*c^2*d^7)/d^8)*sqrt(d*x^2 + c)*x + 1/256*(3*b^2*c^5 - 12*a*b*c^4*d + 16*a^2*c^3*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
616,1,98,0,0.319151," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{35 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} - 90 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c + 63 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} + 90 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b d - 126 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d + 63 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{2}}{315 \, d^{3}}"," ",0,"1/315*(35*(d*x^2 + c)^(9/2)*b^2 - 90*(d*x^2 + c)^(7/2)*b^2*c + 63*(d*x^2 + c)^(5/2)*b^2*c^2 + 90*(d*x^2 + c)^(7/2)*a*b*d - 126*(d*x^2 + c)^(5/2)*a*b*c*d + 63*(d*x^2 + c)^(5/2)*a^2*d^2)/d^3","A",0
617,1,175,0,0.462024," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, b^{2} d x^{2} + \frac{9 \, b^{2} c d^{6} + 16 \, a b d^{7}}{d^{6}}\right)} x^{2} + \frac{3 \, b^{2} c^{2} d^{5} + 112 \, a b c d^{6} + 48 \, a^{2} d^{7}}{d^{6}}\right)} x^{2} - \frac{3 \, {\left(3 \, b^{2} c^{3} d^{4} - 16 \, a b c^{2} d^{5} - 80 \, a^{2} c d^{6}\right)}}{d^{6}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(3 \, b^{2} c^{4} - 16 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{128 \, d^{\frac{5}{2}}}"," ",0,"1/384*(2*(4*(6*b^2*d*x^2 + (9*b^2*c*d^6 + 16*a*b*d^7)/d^6)*x^2 + (3*b^2*c^2*d^5 + 112*a*b*c*d^6 + 48*a^2*d^7)/d^6)*x^2 - 3*(3*b^2*c^3*d^4 - 16*a*b*c^2*d^5 - 80*a^2*c*d^6)/d^6)*sqrt(d*x^2 + c)*x - 1/128*(3*b^2*c^4 - 16*a*b*c^3*d + 48*a^2*c^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
618,1,121,0,0.381627," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x,x, algorithm=""giac"")","\frac{a^{2} c^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{15 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} d^{12} - 21 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c d^{12} + 42 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d^{13} + 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{14} + 105 \, \sqrt{d x^{2} + c} a^{2} c d^{14}}{105 \, d^{14}}"," ",0,"a^2*c^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) + 1/105*(15*(d*x^2 + c)^(7/2)*b^2*d^12 - 21*(d*x^2 + c)^(5/2)*b^2*c*d^12 + 42*(d*x^2 + c)^(5/2)*a*b*d^13 + 35*(d*x^2 + c)^(3/2)*a^2*d^14 + 105*sqrt(d*x^2 + c)*a^2*c*d^14)/d^14","A",0
619,1,173,0,0.495849," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^2,x, algorithm=""giac"")","\frac{2 \, a^{2} c^{2} \sqrt{d}}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c} + \frac{1}{48} \, {\left(2 \, {\left(4 \, b^{2} d x^{2} + \frac{7 \, b^{2} c d^{4} + 12 \, a b d^{5}}{d^{4}}\right)} x^{2} + \frac{3 \, {\left(b^{2} c^{2} d^{3} + 20 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)}}{d^{4}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(b^{2} c^{3} \sqrt{d} - 12 \, a b c^{2} d^{\frac{3}{2}} - 24 \, a^{2} c d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{32 \, d^{2}}"," ",0,"2*a^2*c^2*sqrt(d)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c) + 1/48*(2*(4*b^2*d*x^2 + (7*b^2*c*d^4 + 12*a*b*d^5)/d^4)*x^2 + 3*(b^2*c^2*d^3 + 20*a*b*c*d^4 + 8*a^2*d^5)/d^4)*sqrt(d*x^2 + c)*x + 1/32*(b^2*c^3*sqrt(d) - 12*a*b*c^2*d^(3/2) - 24*a^2*c*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d^2","A",0
620,1,126,0,0.365407," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^3,x, algorithm=""giac"")","\frac{6 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} + 20 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d + 60 \, \sqrt{d x^{2} + c} a b c d + 30 \, \sqrt{d x^{2} + c} a^{2} d^{2} - \frac{15 \, \sqrt{d x^{2} + c} a^{2} c d}{x^{2}} + \frac{15 \, {\left(4 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}}}{30 \, d}"," ",0,"1/30*(6*(d*x^2 + c)^(5/2)*b^2 + 20*(d*x^2 + c)^(3/2)*a*b*d + 60*sqrt(d*x^2 + c)*a*b*c*d + 30*sqrt(d*x^2 + c)*a^2*d^2 - 15*sqrt(d*x^2 + c)*a^2*c*d/x^2 + 15*(4*a*b*c^2*d + 3*a^2*c*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c))/d","A",0
621,1,262,0,0.462525," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^4,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b^{2} d x^{2} + \frac{5 \, b^{2} c d^{2} + 8 \, a b d^{3}}{d^{2}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(3 \, b^{2} c^{2} \sqrt{d} + 24 \, a b c d^{\frac{3}{2}} + 8 \, a^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{16 \, d} + \frac{4 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{2} \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{3} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{2} d^{\frac{3}{2}} + 3 \, a b c^{4} \sqrt{d} + 2 \, a^{2} c^{3} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"1/8*(2*b^2*d*x^2 + (5*b^2*c*d^2 + 8*a*b*d^3)/d^2)*sqrt(d*x^2 + c)*x - 1/16*(3*b^2*c^2*sqrt(d) + 24*a*b*c*d^(3/2) + 8*a^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d + 4/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^2*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^3*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^2*d^(3/2) + 3*a*b*c^4*sqrt(d) + 2*a^2*c^3*d^(3/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3","A",0
622,1,182,0,0.345677," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^5,x, algorithm=""giac"")","\frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d + 24 \, \sqrt{d x^{2} + c} b^{2} c d + 48 \, \sqrt{d x^{2} + c} a b d^{2} + \frac{3 \, {\left(8 \, b^{2} c^{2} d + 24 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{3 \, {\left(8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d^{2} - 8 \, \sqrt{d x^{2} + c} a b c^{2} d^{2} + 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3} - 3 \, \sqrt{d x^{2} + c} a^{2} c d^{3}\right)}}{d^{2} x^{4}}}{24 \, d}"," ",0,"1/24*(8*(d*x^2 + c)^(3/2)*b^2*d + 24*sqrt(d*x^2 + c)*b^2*c*d + 48*sqrt(d*x^2 + c)*a*b*d^2 + 3*(8*b^2*c^2*d + 24*a*b*c*d^2 + 3*a^2*d^3)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) - 3*(8*(d*x^2 + c)^(3/2)*a*b*c*d^2 - 8*sqrt(d*x^2 + c)*a*b*c^2*d^2 + 5*(d*x^2 + c)^(3/2)*a^2*d^3 - 3*sqrt(d*x^2 + c)*a^2*c*d^3)/(d^2*x^4))/d","A",0
623,1,407,0,0.531895," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^6,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{d x^{2} + c} b^{2} d x - \frac{1}{4} \, {\left(3 \, b^{2} c \sqrt{d} + 4 \, a b d^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right) + \frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{2} \sqrt{d} + 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c d^{\frac{3}{2}} + 15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{3} \sqrt{d} - 180 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{2} d^{\frac{3}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{4} \sqrt{d} + 220 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{3} d^{\frac{3}{2}} + 30 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{5} \sqrt{d} - 140 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{4} d^{\frac{3}{2}} + 15 \, b^{2} c^{6} \sqrt{d} + 40 \, a b c^{5} d^{\frac{3}{2}} + 3 \, a^{2} c^{4} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5}}"," ",0,"1/2*sqrt(d*x^2 + c)*b^2*d*x - 1/4*(3*b^2*c*sqrt(d) + 4*a*b*d^(3/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2) + 2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^2*sqrt(d) + 60*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c*d^(3/2) + 15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^3*sqrt(d) - 180*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^2*d^(3/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^4*sqrt(d) + 220*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^3*d^(3/2) + 30*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^5*sqrt(d) - 140*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^4*d^(3/2) + 15*b^2*c^6*sqrt(d) + 40*a*b*c^5*d^(3/2) + 3*a^2*c^4*d^(5/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5","B",0
624,1,259,0,0.322272," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^7,x, algorithm=""giac"")","\frac{48 \, \sqrt{d x^{2} + c} b^{2} d^{2} + \frac{3 \, {\left(24 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} - \frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} - 48 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} d^{2} + 24 \, \sqrt{d x^{2} + c} b^{2} c^{4} d^{2} + 60 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d^{3} - 96 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d^{3} + 36 \, \sqrt{d x^{2} + c} a b c^{3} d^{3} + 3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{4} + 8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{4} - 3 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{4}}{c d^{3} x^{6}}}{48 \, d}"," ",0,"1/48*(48*sqrt(d*x^2 + c)*b^2*d^2 + 3*(24*b^2*c^2*d^2 + 12*a*b*c*d^3 - a^2*d^4)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c) - (24*(d*x^2 + c)^(5/2)*b^2*c^2*d^2 - 48*(d*x^2 + c)^(3/2)*b^2*c^3*d^2 + 24*sqrt(d*x^2 + c)*b^2*c^4*d^2 + 60*(d*x^2 + c)^(5/2)*a*b*c*d^3 - 96*(d*x^2 + c)^(3/2)*a*b*c^2*d^3 + 36*sqrt(d*x^2 + c)*a*b*c^3*d^3 + 3*(d*x^2 + c)^(5/2)*a^2*d^4 + 8*(d*x^2 + c)^(3/2)*a^2*c*d^4 - 3*sqrt(d*x^2 + c)*a^2*c^2*d^4)/(c*d^3*x^6))/d","A",0
625,1,150,0,0.272131," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{693 \, {\left(d x^{2} + c\right)}^{\frac{13}{2}} b^{2} - 2457 \, {\left(d x^{2} + c\right)}^{\frac{11}{2}} b^{2} c + 3003 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} c^{2} - 1287 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{3} + 1638 \, {\left(d x^{2} + c\right)}^{\frac{11}{2}} a b d - 4004 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} a b c d + 2574 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c^{2} d + 1001 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} a^{2} d^{2} - 1287 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} c d^{2}}{9009 \, d^{4}}"," ",0,"1/9009*(693*(d*x^2 + c)^(13/2)*b^2 - 2457*(d*x^2 + c)^(11/2)*b^2*c + 3003*(d*x^2 + c)^(9/2)*b^2*c^2 - 1287*(d*x^2 + c)^(7/2)*b^2*c^3 + 1638*(d*x^2 + c)^(11/2)*a*b*d - 4004*(d*x^2 + c)^(9/2)*a*b*c*d + 2574*(d*x^2 + c)^(7/2)*a*b*c^2*d + 1001*(d*x^2 + c)^(9/2)*a^2*d^2 - 1287*(d*x^2 + c)^(7/2)*a^2*c*d^2)/d^4","A",0
626,1,265,0,0.486441," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{15360} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, b^{2} d^{2} x^{2} + \frac{25 \, b^{2} c d^{11} + 24 \, a b d^{12}}{d^{10}}\right)} x^{2} + \frac{3 \, {\left(45 \, b^{2} c^{2} d^{10} + 168 \, a b c d^{11} + 40 \, a^{2} d^{12}\right)}}{d^{10}}\right)} x^{2} + \frac{5 \, b^{2} c^{3} d^{9} + 744 \, a b c^{2} d^{10} + 680 \, a^{2} c d^{11}}{d^{10}}\right)} x^{2} - \frac{5 \, {\left(5 \, b^{2} c^{4} d^{8} - 24 \, a b c^{3} d^{9} - 472 \, a^{2} c^{2} d^{10}\right)}}{d^{10}}\right)} x^{2} + \frac{15 \, {\left(5 \, b^{2} c^{5} d^{7} - 24 \, a b c^{4} d^{8} + 40 \, a^{2} c^{3} d^{9}\right)}}{d^{10}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(5 \, b^{2} c^{6} - 24 \, a b c^{5} d + 40 \, a^{2} c^{4} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{1024 \, d^{\frac{7}{2}}}"," ",0,"1/15360*(2*(4*(2*(8*(10*b^2*d^2*x^2 + (25*b^2*c*d^11 + 24*a*b*d^12)/d^10)*x^2 + 3*(45*b^2*c^2*d^10 + 168*a*b*c*d^11 + 40*a^2*d^12)/d^10)*x^2 + (5*b^2*c^3*d^9 + 744*a*b*c^2*d^10 + 680*a^2*c*d^11)/d^10)*x^2 - 5*(5*b^2*c^4*d^8 - 24*a*b*c^3*d^9 - 472*a^2*c^2*d^10)/d^10)*x^2 + 15*(5*b^2*c^5*d^7 - 24*a*b*c^4*d^8 + 40*a^2*c^3*d^9)/d^10)*sqrt(d*x^2 + c)*x + 1/1024*(5*b^2*c^6 - 24*a*b*c^5*d + 40*a^2*c^4*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
627,1,98,0,0.323103," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{63 \, {\left(d x^{2} + c\right)}^{\frac{11}{2}} b^{2} - 154 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} c + 99 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2} + 154 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} a b d - 198 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c d + 99 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d^{2}}{693 \, d^{3}}"," ",0,"1/693*(63*(d*x^2 + c)^(11/2)*b^2 - 154*(d*x^2 + c)^(9/2)*b^2*c + 99*(d*x^2 + c)^(7/2)*b^2*c^2 + 154*(d*x^2 + c)^(9/2)*a*b*d - 198*(d*x^2 + c)^(7/2)*a*b*c*d + 99*(d*x^2 + c)^(7/2)*a^2*d^2)/d^3","A",0
628,1,221,0,0.507121," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, b^{2} d^{2} x^{2} + \frac{21 \, b^{2} c d^{9} + 20 \, a b d^{10}}{d^{8}}\right)} x^{2} + \frac{93 \, b^{2} c^{2} d^{8} + 340 \, a b c d^{9} + 80 \, a^{2} d^{10}}{d^{8}}\right)} x^{2} + \frac{5 \, {\left(3 \, b^{2} c^{3} d^{7} + 236 \, a b c^{2} d^{8} + 208 \, a^{2} c d^{9}\right)}}{d^{8}}\right)} x^{2} - \frac{15 \, {\left(3 \, b^{2} c^{4} d^{6} - 20 \, a b c^{3} d^{7} - 176 \, a^{2} c^{2} d^{8}\right)}}{d^{8}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(3 \, b^{2} c^{5} - 20 \, a b c^{4} d + 80 \, a^{2} c^{3} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{256 \, d^{\frac{5}{2}}}"," ",0,"1/3840*(2*(4*(6*(8*b^2*d^2*x^2 + (21*b^2*c*d^9 + 20*a*b*d^10)/d^8)*x^2 + (93*b^2*c^2*d^8 + 340*a*b*c*d^9 + 80*a^2*d^10)/d^8)*x^2 + 5*(3*b^2*c^3*d^7 + 236*a*b*c^2*d^8 + 208*a^2*c*d^9)/d^8)*x^2 - 15*(3*b^2*c^4*d^6 - 20*a*b*c^3*d^7 - 176*a^2*c^2*d^8)/d^8)*sqrt(d*x^2 + c)*x - 1/256*(3*b^2*c^5 - 20*a*b*c^4*d + 80*a^2*c^3*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
629,1,141,0,0.442965," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x,x, algorithm=""giac"")","\frac{a^{2} c^{3} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{35 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}} b^{2} d^{16} - 45 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c d^{16} + 90 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b d^{17} + 63 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{18} + 105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{18} + 315 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{18}}{315 \, d^{18}}"," ",0,"a^2*c^3*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) + 1/315*(35*(d*x^2 + c)^(9/2)*b^2*d^16 - 45*(d*x^2 + c)^(7/2)*b^2*c*d^16 + 90*(d*x^2 + c)^(7/2)*a*b*d^17 + 63*(d*x^2 + c)^(5/2)*a^2*d^18 + 105*(d*x^2 + c)^(3/2)*a^2*c*d^18 + 315*sqrt(d*x^2 + c)*a^2*c^2*d^18)/d^18","A",0
630,1,219,0,0.564103," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^2,x, algorithm=""giac"")","\frac{2 \, a^{2} c^{3} \sqrt{d}}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c} + \frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, b^{2} d^{2} x^{2} + \frac{17 \, b^{2} c d^{7} + 16 \, a b d^{8}}{d^{6}}\right)} x^{2} + \frac{59 \, b^{2} c^{2} d^{6} + 208 \, a b c d^{7} + 48 \, a^{2} d^{8}}{d^{6}}\right)} x^{2} + \frac{3 \, {\left(5 \, b^{2} c^{3} d^{5} + 176 \, a b c^{2} d^{6} + 144 \, a^{2} c d^{7}\right)}}{d^{6}}\right)} \sqrt{d x^{2} + c} x + \frac{5 \, {\left(b^{2} c^{4} \sqrt{d} - 16 \, a b c^{3} d^{\frac{3}{2}} - 48 \, a^{2} c^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{256 \, d^{2}}"," ",0,"2*a^2*c^3*sqrt(d)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c) + 1/384*(2*(4*(6*b^2*d^2*x^2 + (17*b^2*c*d^7 + 16*a*b*d^8)/d^6)*x^2 + (59*b^2*c^2*d^6 + 208*a*b*c*d^7 + 48*a^2*d^8)/d^6)*x^2 + 3*(5*b^2*c^3*d^5 + 176*a*b*c^2*d^6 + 144*a^2*c*d^7)/d^6)*sqrt(d*x^2 + c)*x + 5/256*(b^2*c^4*sqrt(d) - 16*a*b*c^3*d^(3/2) - 48*a^2*c^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d^2","A",0
631,1,165,0,0.503467," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^3,x, algorithm=""giac"")","\frac{30 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} + 84 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d + 140 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d + 420 \, \sqrt{d x^{2} + c} a b c^{2} d + 70 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2} + 420 \, \sqrt{d x^{2} + c} a^{2} c d^{2} - \frac{105 \, \sqrt{d x^{2} + c} a^{2} c^{2} d}{x^{2}} + \frac{105 \, {\left(4 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}}}{210 \, d}"," ",0,"1/210*(30*(d*x^2 + c)^(7/2)*b^2 + 84*(d*x^2 + c)^(5/2)*a*b*d + 140*(d*x^2 + c)^(3/2)*a*b*c*d + 420*sqrt(d*x^2 + c)*a*b*c^2*d + 70*(d*x^2 + c)^(3/2)*a^2*d^2 + 420*sqrt(d*x^2 + c)*a^2*c*d^2 - 105*sqrt(d*x^2 + c)*a^2*c^2*d/x^2 + 105*(4*a*b*c^3*d + 5*a^2*c^2*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c))/d","A",0
632,1,307,0,0.599694," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, b^{2} d^{2} x^{2} + \frac{13 \, b^{2} c d^{5} + 12 \, a b d^{6}}{d^{4}}\right)} x^{2} + \frac{3 \, {\left(11 \, b^{2} c^{2} d^{4} + 36 \, a b c d^{5} + 8 \, a^{2} d^{6}\right)}}{d^{4}}\right)} \sqrt{d x^{2} + c} x - \frac{5 \, {\left(b^{2} c^{3} \sqrt{d} + 12 \, a b c^{2} d^{\frac{3}{2}} + 8 \, a^{2} c d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{32 \, d} + \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{3} \sqrt{d} + 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{2} d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{4} \sqrt{d} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{3} d^{\frac{3}{2}} + 6 \, a b c^{5} \sqrt{d} + 7 \, a^{2} c^{4} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"1/48*(2*(4*b^2*d^2*x^2 + (13*b^2*c*d^5 + 12*a*b*d^6)/d^4)*x^2 + 3*(11*b^2*c^2*d^4 + 36*a*b*c*d^5 + 8*a^2*d^6)/d^4)*sqrt(d*x^2 + c)*x - 5/32*(b^2*c^3*sqrt(d) + 12*a*b*c^2*d^(3/2) + 8*a^2*c*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d + 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^3*sqrt(d) + 9*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^2*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^4*sqrt(d) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^3*d^(3/2) + 6*a*b*c^5*sqrt(d) + 7*a^2*c^4*d^(3/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3","A",0
633,1,242,0,0.526250," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^5,x, algorithm=""giac"")","\frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} d + 40 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c d + 120 \, \sqrt{d x^{2} + c} b^{2} c^{2} d + 80 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2} + 480 \, \sqrt{d x^{2} + c} a b c d^{2} + 120 \, \sqrt{d x^{2} + c} a^{2} d^{3} + \frac{15 \, {\left(8 \, b^{2} c^{3} d + 40 \, a b c^{2} d^{2} + 15 \, a^{2} c d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{15 \, {\left(8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d^{2} - 8 \, \sqrt{d x^{2} + c} a b c^{3} d^{2} + 9 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{3} - 7 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{3}\right)}}{d^{2} x^{4}}}{120 \, d}"," ",0,"1/120*(24*(d*x^2 + c)^(5/2)*b^2*d + 40*(d*x^2 + c)^(3/2)*b^2*c*d + 120*sqrt(d*x^2 + c)*b^2*c^2*d + 80*(d*x^2 + c)^(3/2)*a*b*d^2 + 480*sqrt(d*x^2 + c)*a*b*c*d^2 + 120*sqrt(d*x^2 + c)*a^2*d^3 + 15*(8*b^2*c^3*d + 40*a*b*c^2*d^2 + 15*a^2*c*d^3)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) - 15*(8*(d*x^2 + c)^(3/2)*a*b*c^2*d^2 - 8*sqrt(d*x^2 + c)*a*b*c^3*d^2 + 9*(d*x^2 + c)^(3/2)*a^2*c*d^3 - 7*sqrt(d*x^2 + c)*a^2*c^2*d^3)/(d^2*x^4))/d","A",0
634,1,510,0,0.544453," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^6,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b^{2} d^{2} x^{2} + \frac{9 \, b^{2} c d^{3} + 8 \, a b d^{4}}{d^{2}}\right)} \sqrt{d x^{2} + c} x - \frac{1}{16} \, {\left(15 \, b^{2} c^{2} \sqrt{d} + 40 \, a b c d^{\frac{3}{2}} + 8 \, a^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right) + \frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{3} \sqrt{d} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c^{2} d^{\frac{3}{2}} + 45 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} c d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{4} \sqrt{d} - 300 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{3} d^{\frac{3}{2}} - 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c^{2} d^{\frac{5}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{5} \sqrt{d} + 400 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{4} d^{\frac{3}{2}} + 140 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{3} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{6} \sqrt{d} - 260 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{5} d^{\frac{3}{2}} - 70 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{4} d^{\frac{5}{2}} + 15 \, b^{2} c^{7} \sqrt{d} + 70 \, a b c^{6} d^{\frac{3}{2}} + 23 \, a^{2} c^{5} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5}}"," ",0,"1/8*(2*b^2*d^2*x^2 + (9*b^2*c*d^3 + 8*a*b*d^4)/d^2)*sqrt(d*x^2 + c)*x - 1/16*(15*b^2*c^2*sqrt(d) + 40*a*b*c*d^(3/2) + 8*a^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2) + 2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^3*sqrt(d) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c^2*d^(3/2) + 45*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*c*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^4*sqrt(d) - 300*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^3*d^(3/2) - 90*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c^2*d^(5/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^5*sqrt(d) + 400*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^4*d^(3/2) + 140*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^3*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^6*sqrt(d) - 260*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^5*d^(3/2) - 70*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^4*d^(5/2) + 15*b^2*c^7*sqrt(d) + 70*a*b*c^6*d^(3/2) + 23*a^2*c^5*d^(5/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5","B",0
635,1,286,0,0.469436," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^7,x, algorithm=""giac"")","\frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{2} + 96 \, \sqrt{d x^{2} + c} b^{2} c d^{2} + 96 \, \sqrt{d x^{2} + c} a b d^{3} + \frac{15 \, {\left(8 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} + a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} - \frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} - 48 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} d^{2} + 24 \, \sqrt{d x^{2} + c} b^{2} c^{4} d^{2} + 108 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d^{3} - 192 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d^{3} + 84 \, \sqrt{d x^{2} + c} a b c^{3} d^{3} + 33 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{4} - 40 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{4} + 15 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{4}}{d^{3} x^{6}}}{48 \, d}"," ",0,"1/48*(16*(d*x^2 + c)^(3/2)*b^2*d^2 + 96*sqrt(d*x^2 + c)*b^2*c*d^2 + 96*sqrt(d*x^2 + c)*a*b*d^3 + 15*(8*b^2*c^2*d^2 + 12*a*b*c*d^3 + a^2*d^4)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) - (24*(d*x^2 + c)^(5/2)*b^2*c^2*d^2 - 48*(d*x^2 + c)^(3/2)*b^2*c^3*d^2 + 24*sqrt(d*x^2 + c)*b^2*c^4*d^2 + 108*(d*x^2 + c)^(5/2)*a*b*c*d^3 - 192*(d*x^2 + c)^(3/2)*a*b*c^2*d^3 + 84*sqrt(d*x^2 + c)*a*b*c^3*d^3 + 33*(d*x^2 + c)^(5/2)*a^2*d^4 - 40*(d*x^2 + c)^(3/2)*a^2*c*d^4 + 15*sqrt(d*x^2 + c)*a^2*c^2*d^4)/(d^3*x^6))/d","A",0
636,1,178,0,0.414349," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(\frac{6 \, b^{2} x^{2}}{d} - \frac{7 \, b^{2} c d^{5} - 16 \, a b d^{6}}{d^{7}}\right)} x^{2} + \frac{35 \, b^{2} c^{2} d^{4} - 80 \, a b c d^{5} + 48 \, a^{2} d^{6}}{d^{7}}\right)} x^{2} - \frac{3 \, {\left(35 \, b^{2} c^{3} d^{3} - 80 \, a b c^{2} d^{4} + 48 \, a^{2} c d^{5}\right)}}{d^{7}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(35 \, b^{2} c^{4} - 80 \, a b c^{3} d + 48 \, a^{2} c^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{128 \, d^{\frac{9}{2}}}"," ",0,"1/384*(2*(4*(6*b^2*x^2/d - (7*b^2*c*d^5 - 16*a*b*d^6)/d^7)*x^2 + (35*b^2*c^2*d^4 - 80*a*b*c*d^5 + 48*a^2*d^6)/d^7)*x^2 - 3*(35*b^2*c^3*d^3 - 80*a*b*c^2*d^4 + 48*a^2*c*d^5)/d^7)*sqrt(d*x^2 + c)*x - 1/128*(35*b^2*c^4 - 80*a*b*c^3*d + 48*a^2*c^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(9/2)","A",0
637,1,137,0,0.358176," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{d x^{2} + c}}{d^{4}} + \frac{15 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} - 63 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c + 105 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} + 42 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d - 140 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d + 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{105 \, d^{4}}"," ",0,"-(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(d*x^2 + c)/d^4 + 1/105*(15*(d*x^2 + c)^(7/2)*b^2 - 63*(d*x^2 + c)^(5/2)*b^2*c + 105*(d*x^2 + c)^(3/2)*b^2*c^2 + 42*(d*x^2 + c)^(5/2)*a*b*d - 140*(d*x^2 + c)^(3/2)*a*b*c*d + 35*(d*x^2 + c)^(3/2)*a^2*d^2)/d^4","A",0
638,1,135,0,0.371620," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(\frac{4 \, b^{2} x^{2}}{d} - \frac{5 \, b^{2} c d^{3} - 12 \, a b d^{4}}{d^{5}}\right)} x^{2} + \frac{3 \, {\left(5 \, b^{2} c^{2} d^{2} - 12 \, a b c d^{3} + 8 \, a^{2} d^{4}\right)}}{d^{5}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(5 \, b^{2} c^{3} - 12 \, a b c^{2} d + 8 \, a^{2} c d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{16 \, d^{\frac{7}{2}}}"," ",0,"1/48*(2*(4*b^2*x^2/d - (5*b^2*c*d^3 - 12*a*b*d^4)/d^5)*x^2 + 3*(5*b^2*c^2*d^2 - 12*a*b*c*d^3 + 8*a^2*d^4)/d^5)*sqrt(d*x^2 + c)*x + 1/16*(5*b^2*c^3 - 12*a*b*c^2*d + 8*a^2*c*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
639,1,84,0,0.333017," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{d x^{2} + c}}{d^{3}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} - 10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c + 10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{15 \, d^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(d*x^2 + c)/d^3 + 1/15*(3*(d*x^2 + c)^(5/2)*b^2 - 10*(d*x^2 + c)^(3/2)*b^2*c + 10*(d*x^2 + c)^(3/2)*a*b*d)/d^3","A",0
640,1,91,0,0.492773," ","integrate((b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{2 \, b^{2} x^{2}}{d} - \frac{3 \, b^{2} c d - 8 \, a b d^{2}}{d^{3}}\right)} \sqrt{d x^{2} + c} x - \frac{{\left(3 \, b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{8 \, d^{\frac{5}{2}}}"," ",0,"1/8*(2*b^2*x^2/d - (3*b^2*c*d - 8*a*b*d^2)/d^3)*sqrt(d*x^2 + c)*x - 1/8*(3*b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
641,1,82,0,0.294901," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{4} - 3 \, \sqrt{d x^{2} + c} b^{2} c d^{4} + 6 \, \sqrt{d x^{2} + c} a b d^{5}}{3 \, d^{6}}"," ",0,"a^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/sqrt(-c) + 1/3*((d*x^2 + c)^(3/2)*b^2*d^4 - 3*sqrt(d*x^2 + c)*b^2*c*d^4 + 6*sqrt(d*x^2 + c)*a*b*d^5)/d^6","A",0
642,1,93,0,0.462597," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} b^{2} x}{2 \, d} + \frac{2 \, a^{2} \sqrt{d}}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c} + \frac{{\left(b^{2} c \sqrt{d} - 4 \, a b d^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, d^{2}}"," ",0,"1/2*sqrt(d*x^2 + c)*b^2*x/d + 2*a^2*sqrt(d)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c) + 1/4*(b^2*c*sqrt(d) - 4*a*b*d^(3/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d^2","A",0
643,1,81,0,0.492459," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{d x^{2} + c} b^{2} - \frac{\sqrt{d x^{2} + c} a^{2} d}{c x^{2}} + \frac{{\left(4 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c}}{2 \, d}"," ",0,"1/2*(2*sqrt(d*x^2 + c)*b^2 - sqrt(d*x^2 + c)*a^2*d/(c*x^2) + (4*a*b*c*d - a^2*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c))/d","A",0
644,1,156,0,0.459490," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{2 \, \sqrt{d}} + \frac{4 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b \sqrt{d} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{3}{2}} + 3 \, a b c^{2} \sqrt{d} - a^{2} c d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3}}"," ",0,"-1/2*b^2*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/sqrt(d) + 4/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*sqrt(d) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(3/2) + 3*a*b*c^2*sqrt(d) - a^2*c*d^(3/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3","B",0
645,1,140,0,0.385049," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(8 \, b^{2} c^{2} d - 8 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d^{2} - 8 \, \sqrt{d x^{2} + c} a b c^{2} d^{2} - 3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3} + 5 \, \sqrt{d x^{2} + c} a^{2} c d^{3}}{c^{2} d^{2} x^{4}}}{8 \, d}"," ",0,"1/8*((8*b^2*c^2*d - 8*a*b*c*d^2 + 3*a^2*d^3)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^2) - (8*(d*x^2 + c)^(3/2)*a*b*c*d^2 - 8*sqrt(d*x^2 + c)*a*b*c^2*d^2 - 3*(d*x^2 + c)^(3/2)*a^2*d^3 + 5*sqrt(d*x^2 + c)*a^2*c*d^3)/(c^2*d^2*x^4))/d","A",0
646,1,312,0,0.457785," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} \sqrt{d} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c \sqrt{d} + 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b d^{\frac{3}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{2} \sqrt{d} - 140 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c d^{\frac{3}{2}} + 80 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{3} \sqrt{d} + 100 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{2} d^{\frac{3}{2}} - 40 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c d^{\frac{5}{2}} + 15 \, b^{2} c^{4} \sqrt{d} - 20 \, a b c^{3} d^{\frac{3}{2}} + 8 \, a^{2} c^{2} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5}}"," ",0,"2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*sqrt(d) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c*sqrt(d) + 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*d^(3/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^2*sqrt(d) - 140*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c*d^(3/2) + 80*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^3*sqrt(d) + 100*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^2*d^(3/2) - 40*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c*d^(5/2) + 15*b^2*c^4*sqrt(d) - 20*a*b*c^3*d^(3/2) + 8*a^2*c^2*d^(5/2))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5","B",0
647,1,241,0,0.341413," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(8 \, b^{2} c^{2} d^{2} - 12 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{3}} + \frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} - 48 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} d^{2} + 24 \, \sqrt{d x^{2} + c} b^{2} c^{4} d^{2} - 36 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d^{3} + 96 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d^{3} - 60 \, \sqrt{d x^{2} + c} a b c^{3} d^{3} + 15 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{4} - 40 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{4} + 33 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{4}}{c^{3} d^{3} x^{6}}}{48 \, d}"," ",0,"-1/48*(3*(8*b^2*c^2*d^2 - 12*a*b*c*d^3 + 5*a^2*d^4)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^3) + (24*(d*x^2 + c)^(5/2)*b^2*c^2*d^2 - 48*(d*x^2 + c)^(3/2)*b^2*c^3*d^2 + 24*sqrt(d*x^2 + c)*b^2*c^4*d^2 - 36*(d*x^2 + c)^(5/2)*a*b*c*d^3 + 96*(d*x^2 + c)^(3/2)*a*b*c^2*d^3 - 60*sqrt(d*x^2 + c)*a*b*c^3*d^3 + 15*(d*x^2 + c)^(5/2)*a^2*d^4 - 40*(d*x^2 + c)^(3/2)*a^2*c*d^4 + 33*sqrt(d*x^2 + c)*a^2*c^2*d^4)/(c^3*d^3*x^6))/d","A",0
648,1,175,0,0.475778," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, b^{2} x^{2}}{d} - \frac{7 \, b^{2} c d^{5} - 12 \, a b d^{6}}{d^{7}}\right)} x^{2} + \frac{35 \, b^{2} c^{2} d^{4} - 60 \, a b c d^{5} + 24 \, a^{2} d^{6}}{d^{7}}\right)} x^{2} + \frac{3 \, {\left(35 \, b^{2} c^{3} d^{3} - 60 \, a b c^{2} d^{4} + 24 \, a^{2} c d^{5}\right)}}{d^{7}}\right)} x}{48 \, \sqrt{d x^{2} + c}} + \frac{{\left(35 \, b^{2} c^{3} - 60 \, a b c^{2} d + 24 \, a^{2} c d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{16 \, d^{\frac{9}{2}}}"," ",0,"1/48*((2*(4*b^2*x^2/d - (7*b^2*c*d^5 - 12*a*b*d^6)/d^7)*x^2 + (35*b^2*c^2*d^4 - 60*a*b*c*d^5 + 24*a^2*d^6)/d^7)*x^2 + 3*(35*b^2*c^3*d^3 - 60*a*b*c^2*d^4 + 24*a^2*c*d^5)/d^7)*x/sqrt(d*x^2 + c) + 1/16*(35*b^2*c^3 - 60*a*b*c^2*d + 24*a^2*c*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(9/2)","A",0
649,1,149,0,0.407286," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}}{\sqrt{d x^{2} + c} d^{4}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} d^{16} - 15 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c d^{16} + 45 \, \sqrt{d x^{2} + c} b^{2} c^{2} d^{16} + 10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{17} - 60 \, \sqrt{d x^{2} + c} a b c d^{17} + 15 \, \sqrt{d x^{2} + c} a^{2} d^{18}}{15 \, d^{20}}"," ",0,"(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)/(sqrt(d*x^2 + c)*d^4) + 1/15*(3*(d*x^2 + c)^(5/2)*b^2*d^16 - 15*(d*x^2 + c)^(3/2)*b^2*c*d^16 + 45*sqrt(d*x^2 + c)*b^2*c^2*d^16 + 10*(d*x^2 + c)^(3/2)*a*b*d^17 - 60*sqrt(d*x^2 + c)*a*b*c*d^17 + 15*sqrt(d*x^2 + c)*a^2*d^18)/d^20","A",0
650,1,131,0,0.425978," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, b^{2} x^{2}}{d} - \frac{5 \, b^{2} c d^{3} - 8 \, a b d^{4}}{d^{5}}\right)} x^{2} - \frac{15 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 8 \, a^{2} d^{4}}{d^{5}}\right)} x}{8 \, \sqrt{d x^{2} + c}} - \frac{{\left(15 \, b^{2} c^{2} - 24 \, a b c d + 8 \, a^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{8 \, d^{\frac{7}{2}}}"," ",0,"1/8*((2*b^2*x^2/d - (5*b^2*c*d^3 - 8*a*b*d^4)/d^5)*x^2 - (15*b^2*c^2*d^2 - 24*a*b*c*d^3 + 8*a^2*d^4)/d^5)*x/sqrt(d*x^2 + c) - 1/8*(15*b^2*c^2 - 24*a*b*c*d + 8*a^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
651,1,92,0,0.447528," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{\sqrt{d x^{2} + c} d^{3}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{6} - 6 \, \sqrt{d x^{2} + c} b^{2} c d^{6} + 6 \, \sqrt{d x^{2} + c} a b d^{7}}{3 \, d^{9}}"," ",0,"-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(sqrt(d*x^2 + c)*d^3) + 1/3*((d*x^2 + c)^(3/2)*b^2*d^6 - 6*sqrt(d*x^2 + c)*b^2*c*d^6 + 6*sqrt(d*x^2 + c)*a*b*d^7)/d^9","A",0
652,1,92,0,0.458399," ","integrate((b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{b^{2} x^{2}}{d} + \frac{3 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, a^{2} d^{3}}{c d^{3}}\right)} x}{2 \, \sqrt{d x^{2} + c}} + \frac{{\left(3 \, b^{2} c - 4 \, a b d\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{2 \, d^{\frac{5}{2}}}"," ",0,"1/2*(b^2*x^2/d + (3*b^2*c^2*d - 4*a*b*c*d^2 + 2*a^2*d^3)/(c*d^3))*x/sqrt(d*x^2 + c) + 1/2*(3*b^2*c - 4*a*b*d)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
653,1,82,0,0.327322," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c} + \frac{\sqrt{d x^{2} + c} b^{2}}{d^{2}} + \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{\sqrt{d x^{2} + c} c d^{2}}"," ",0,"a^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c) + sqrt(d*x^2 + c)*b^2/d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(sqrt(d*x^2 + c)*c*d^2)","A",0
654,1,104,0,0.467132," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{b^{2} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{2 \, d^{\frac{3}{2}}} + \frac{2 \, a^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} c} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{\sqrt{d x^{2} + c} c^{2} d}"," ",0,"-1/2*b^2*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/d^(3/2) + 2*a^2*sqrt(d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*c) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(sqrt(d*x^2 + c)*c^2*d)","A",0
655,1,140,0,0.388587," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(4 \, a b c - 3 \, a^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, \sqrt{-c} c^{2}} - \frac{2 \, {\left(d x^{2} + c\right)} b^{2} c^{2} - 2 \, b^{2} c^{3} - 4 \, {\left(d x^{2} + c\right)} a b c d + 4 \, a b c^{2} d + 3 \, {\left(d x^{2} + c\right)} a^{2} d^{2} - 2 \, a^{2} c d^{2}}{2 \, {\left({\left(d x^{2} + c\right)}^{\frac{3}{2}} - \sqrt{d x^{2} + c} c\right)} c^{2} d}"," ",0,"1/2*(4*a*b*c - 3*a^2*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^2) - 1/2*(2*(d*x^2 + c)*b^2*c^2 - 2*b^2*c^3 - 4*(d*x^2 + c)*a*b*c*d + 4*a*b*c^2*d + 3*(d*x^2 + c)*a^2*d^2 - 2*a^2*c*d^2)/(((d*x^2 + c)^(3/2) - sqrt(d*x^2 + c)*c)*c^2*d)","A",0
656,1,199,0,0.445927," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{\sqrt{d x^{2} + c} c^{3}} + \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{2} \sqrt{d} + 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c d^{\frac{3}{2}} + 6 \, a b c^{3} \sqrt{d} - 5 \, a^{2} c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} c^{2}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(sqrt(d*x^2 + c)*c^3) + 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^2*sqrt(d) + 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c*d^(3/2) + 6*a*b*c^3*sqrt(d) - 5*a^2*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*c^2)","B",0
657,1,163,0,0.349781," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(8 \, b^{2} c^{2} - 24 \, a b c d + 15 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{8 \, \sqrt{-c} c^{3}} + \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{\sqrt{d x^{2} + c} c^{3}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d - 8 \, \sqrt{d x^{2} + c} a b c^{2} d - 7 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2} + 9 \, \sqrt{d x^{2} + c} a^{2} c d^{2}}{8 \, c^{3} d^{2} x^{4}}"," ",0,"1/8*(8*b^2*c^2 - 24*a*b*c*d + 15*a^2*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^3) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(sqrt(d*x^2 + c)*c^3) - 1/8*(8*(d*x^2 + c)^(3/2)*a*b*c*d - 8*sqrt(d*x^2 + c)*a*b*c^2*d - 7*(d*x^2 + c)^(3/2)*a^2*d^2 + 9*sqrt(d*x^2 + c)*a^2*c*d^2)/(c^3*d^2*x^4)","A",0
658,1,452,0,0.502631," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x}{\sqrt{d x^{2} + c} c^{4}} + \frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{2} \sqrt{d} - 30 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c d^{\frac{3}{2}} + 15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{3} \sqrt{d} + 180 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{2} d^{\frac{3}{2}} - 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c d^{\frac{5}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{4} \sqrt{d} - 320 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{3} d^{\frac{3}{2}} + 240 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{5} \sqrt{d} + 220 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{4} d^{\frac{3}{2}} - 150 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{3} d^{\frac{5}{2}} + 15 \, b^{2} c^{6} \sqrt{d} - 50 \, a b c^{5} d^{\frac{3}{2}} + 33 \, a^{2} c^{4} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5} c^{3}}"," ",0,"-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x/(sqrt(d*x^2 + c)*c^4) + 2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^2*sqrt(d) - 30*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c*d^(3/2) + 15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^3*sqrt(d) + 180*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^2*d^(3/2) - 90*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c*d^(5/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^4*sqrt(d) - 320*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^3*d^(3/2) + 240*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^5*sqrt(d) + 220*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^4*d^(3/2) - 150*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^3*d^(5/2) + 15*b^2*c^6*sqrt(d) - 50*a*b*c^5*d^(3/2) + 33*a^2*c^4*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5*c^3)","B",0
659,1,267,0,0.403210," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(24 \, b^{2} c^{2} d - 60 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{16 \, \sqrt{-c} c^{4}} - \frac{b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}}{\sqrt{d x^{2} + c} c^{4}} - \frac{24 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} d - 48 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} d + 24 \, \sqrt{d x^{2} + c} b^{2} c^{4} d - 84 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c d^{2} + 192 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} d^{2} - 108 \, \sqrt{d x^{2} + c} a b c^{3} d^{2} + 57 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{3} - 136 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c d^{3} + 87 \, \sqrt{d x^{2} + c} a^{2} c^{2} d^{3}}{48 \, c^{4} d^{3} x^{6}}"," ",0,"-1/16*(24*b^2*c^2*d - 60*a*b*c*d^2 + 35*a^2*d^3)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^4) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)/(sqrt(d*x^2 + c)*c^4) - 1/48*(24*(d*x^2 + c)^(5/2)*b^2*c^2*d - 48*(d*x^2 + c)^(3/2)*b^2*c^3*d + 24*sqrt(d*x^2 + c)*b^2*c^4*d - 84*(d*x^2 + c)^(5/2)*a*b*c*d^2 + 192*(d*x^2 + c)^(3/2)*a*b*c^2*d^2 - 108*sqrt(d*x^2 + c)*a*b*c^3*d^2 + 57*(d*x^2 + c)^(5/2)*a^2*d^3 - 136*(d*x^2 + c)^(3/2)*a^2*c*d^3 + 87*sqrt(d*x^2 + c)*a^2*c^2*d^3)/(c^4*d^3*x^6)","A",0
660,1,190,0,0.506594," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, {\left(\frac{2 \, b^{2} x^{2}}{d} - \frac{7 \, b^{2} c^{2} d^{5} - 8 \, a b c d^{6}}{c d^{7}}\right)} x^{2} - \frac{4 \, {\left(35 \, b^{2} c^{3} d^{4} - 40 \, a b c^{2} d^{5} + 8 \, a^{2} c d^{6}\right)}}{c d^{7}}\right)} x^{2} - \frac{3 \, {\left(35 \, b^{2} c^{4} d^{3} - 40 \, a b c^{3} d^{4} + 8 \, a^{2} c^{2} d^{5}\right)}}{c d^{7}}\right)} x}{24 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{{\left(35 \, b^{2} c^{2} - 40 \, a b c d + 8 \, a^{2} d^{2}\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{8 \, d^{\frac{9}{2}}}"," ",0,"1/24*((3*(2*b^2*x^2/d - (7*b^2*c^2*d^5 - 8*a*b*c*d^6)/(c*d^7))*x^2 - 4*(35*b^2*c^3*d^4 - 40*a*b*c^2*d^5 + 8*a^2*c*d^6)/(c*d^7))*x^2 - 3*(35*b^2*c^4*d^3 - 40*a*b*c^3*d^4 + 8*a^2*c^2*d^5)/(c*d^7))*x/(d*x^2 + c)^(3/2) - 1/8*(35*b^2*c^2 - 40*a*b*c*d + 8*a^2*d^2)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(9/2)","A",0
661,1,140,0,0.392658," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{9 \, {\left(d x^{2} + c\right)} b^{2} c^{2} - b^{2} c^{3} - 12 \, {\left(d x^{2} + c\right)} a b c d + 2 \, a b c^{2} d + 3 \, {\left(d x^{2} + c\right)} a^{2} d^{2} - a^{2} c d^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{4}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{8} - 9 \, \sqrt{d x^{2} + c} b^{2} c d^{8} + 6 \, \sqrt{d x^{2} + c} a b d^{9}}{3 \, d^{12}}"," ",0,"-1/3*(9*(d*x^2 + c)*b^2*c^2 - b^2*c^3 - 12*(d*x^2 + c)*a*b*c*d + 2*a*b*c^2*d + 3*(d*x^2 + c)*a^2*d^2 - a^2*c*d^2)/((d*x^2 + c)^(3/2)*d^4) + 1/3*((d*x^2 + c)^(3/2)*b^2*d^8 - 9*sqrt(d*x^2 + c)*b^2*c*d^8 + 6*sqrt(d*x^2 + c)*a*b*d^9)/d^12","A",0
662,1,130,0,0.469395," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{3 \, b^{2} x^{2}}{d} + \frac{2 \, {\left(10 \, b^{2} c^{2} d^{3} - 8 \, a b c d^{4} + a^{2} d^{5}\right)}}{c d^{5}}\right)} x^{2} + \frac{3 \, {\left(5 \, b^{2} c^{3} d^{2} - 4 \, a b c^{2} d^{3}\right)}}{c d^{5}}\right)} x}{6 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{{\left(5 \, b^{2} c - 4 \, a b d\right)} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{2 \, d^{\frac{7}{2}}}"," ",0,"1/6*((3*b^2*x^2/d + 2*(10*b^2*c^2*d^3 - 8*a*b*c*d^4 + a^2*d^5)/(c*d^5))*x^2 + 3*(5*b^2*c^3*d^2 - 4*a*b*c^2*d^3)/(c*d^5))*x/(d*x^2 + c)^(3/2) + 1/2*(5*b^2*c - 4*a*b*d)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(7/2)","A",0
663,1,79,0,0.456287," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} b^{2}}{d^{3}} + \frac{6 \, {\left(d x^{2} + c\right)} b^{2} c - b^{2} c^{2} - 6 \, {\left(d x^{2} + c\right)} a b d + 2 \, a b c d - a^{2} d^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{3}}"," ",0,"sqrt(d*x^2 + c)*b^2/d^3 + 1/3*(6*(d*x^2 + c)*b^2*c - b^2*c^2 - 6*(d*x^2 + c)*a*b*d + 2*a*b*c*d - a^2*d^2)/((d*x^2 + c)^(3/2)*d^3)","A",0
664,1,105,0,0.521199," ","integrate((b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{x {\left(\frac{2 \, {\left(2 \, b^{2} c^{2} d^{2} - a b c d^{3} - a^{2} d^{4}\right)} x^{2}}{c^{2} d^{3}} + \frac{3 \, {\left(b^{2} c^{3} d - a^{2} c d^{3}\right)}}{c^{2} d^{3}}\right)}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{b^{2} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right)}{d^{\frac{5}{2}}}"," ",0,"-1/3*x*(2*(2*b^2*c^2*d^2 - a*b*c*d^3 - a^2*d^4)*x^2/(c^2*d^3) + 3*(b^2*c^3*d - a^2*c*d^3)/(c^2*d^3))/(d*x^2 + c)^(3/2) - b^2*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))/d^(5/2)","A",0
665,1,102,0,0.436779," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2}} - \frac{3 \, {\left(d x^{2} + c\right)} b^{2} c^{2} - b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, {\left(d x^{2} + c\right)} a^{2} d^{2} - a^{2} c d^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"a^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^2) - 1/3*(3*(d*x^2 + c)*b^2*c^2 - b^2*c^3 + 2*a*b*c^2*d - 3*(d*x^2 + c)*a^2*d^2 - a^2*c*d^2)/((d*x^2 + c)^(3/2)*c^2*d^2)","A",0
666,1,117,0,0.430615," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{{\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3}\right)} x^{2}}{c^{5} d} + \frac{6 \, {\left(a b c^{4} d - a^{2} c^{3} d^{2}\right)}}{c^{5} d}\right)}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{2 \, a^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} c^{2}}"," ",0,"1/3*x*((b^2*c^4*d + 4*a*b*c^3*d^2 - 5*a^2*c^2*d^3)*x^2/(c^5*d) + 6*(a*b*c^4*d - a^2*c^3*d^2)/(c^5*d))/(d*x^2 + c)^(3/2) + 2*a^2*sqrt(d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*c^2)","A",0
667,1,128,0,0.371609," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(4 \, a b c - 5 \, a^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, \sqrt{-c} c^{3}} - \frac{\sqrt{d x^{2} + c} a^{2}}{2 \, c^{3} x^{2}} - \frac{b^{2} c^{3} - 6 \, {\left(d x^{2} + c\right)} a b c d - 2 \, a b c^{2} d + 6 \, {\left(d x^{2} + c\right)} a^{2} d^{2} + a^{2} c d^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3} d}"," ",0,"1/2*(4*a*b*c - 5*a^2*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^3) - 1/2*sqrt(d*x^2 + c)*a^2/(c^3*x^2) - 1/3*(b^2*c^3 - 6*(d*x^2 + c)*a*b*c*d - 2*a*b*c^2*d + 6*(d*x^2 + c)*a^2*d^2 + a^2*c*d^2)/((d*x^2 + c)^(3/2)*c^3*d)","A",0
668,1,258,0,0.445382," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{2 \, {\left(b^{2} c^{5} d^{2} - 5 \, a b c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4}\right)} x^{2}}{c^{7} d} + \frac{3 \, {\left(b^{2} c^{6} d - 4 \, a b c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3}\right)}}{c^{7} d}\right)}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{4 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{2} \sqrt{d} + 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c d^{\frac{3}{2}} + 3 \, a b c^{3} \sqrt{d} - 4 \, a^{2} c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} c^{3}}"," ",0,"1/3*x*(2*(b^2*c^5*d^2 - 5*a*b*c^4*d^3 + 4*a^2*c^3*d^4)*x^2/(c^7*d) + 3*(b^2*c^6*d - 4*a*b*c^5*d^2 + 3*a^2*c^4*d^3)/(c^7*d))/(d*x^2 + c)^(3/2) + 4/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^2*sqrt(d) + 9*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c*d^(3/2) + 3*a*b*c^3*sqrt(d) - 4*a^2*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*c^3)","B",0
669,1,210,0,0.402526," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(8 \, b^{2} c^{2} - 40 \, a b c d + 35 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{8 \, \sqrt{-c} c^{4}} + \frac{3 \, {\left(d x^{2} + c\right)} b^{2} c^{2} + b^{2} c^{3} - 12 \, {\left(d x^{2} + c\right)} a b c d - 2 \, a b c^{2} d + 9 \, {\left(d x^{2} + c\right)} a^{2} d^{2} + a^{2} c d^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{4}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d - 8 \, \sqrt{d x^{2} + c} a b c^{2} d - 11 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2} + 13 \, \sqrt{d x^{2} + c} a^{2} c d^{2}}{8 \, c^{4} d^{2} x^{4}}"," ",0,"1/8*(8*b^2*c^2 - 40*a*b*c*d + 35*a^2*d^2)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(sqrt(-c)*c^4) + 1/3*(3*(d*x^2 + c)*b^2*c^2 + b^2*c^3 - 12*(d*x^2 + c)*a*b*c*d - 2*a*b*c^2*d + 9*(d*x^2 + c)*a^2*d^2 + a^2*c*d^2)/((d*x^2 + c)^(3/2)*c^4) - 1/8*(8*(d*x^2 + c)^(3/2)*a*b*c*d - 8*sqrt(d*x^2 + c)*a*b*c^2*d - 11*(d*x^2 + c)^(3/2)*a^2*d^2 + 13*sqrt(d*x^2 + c)*a^2*c*d^2)/(c^4*d^2*x^4)","A",0
670,1,509,0,0.539935," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{x {\left(\frac{{\left(5 \, b^{2} c^{6} d^{3} - 16 \, a b c^{5} d^{4} + 11 \, a^{2} c^{4} d^{5}\right)} x^{2}}{c^{9} d} + \frac{6 \, {\left(b^{2} c^{7} d^{2} - 3 \, a b c^{6} d^{3} + 2 \, a^{2} c^{5} d^{4}\right)}}{c^{9} d}\right)}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{2} c^{2} \sqrt{d} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b c d^{\frac{3}{2}} + 45 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{2} c^{3} \sqrt{d} + 300 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b c^{2} d^{\frac{3}{2}} - 240 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} c d^{\frac{5}{2}} + 90 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{4} \sqrt{d} - 500 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c^{3} d^{\frac{3}{2}} + 490 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} c^{2} d^{\frac{5}{2}} - 60 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{5} \sqrt{d} + 340 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{4} d^{\frac{3}{2}} - 320 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c^{3} d^{\frac{5}{2}} + 15 \, b^{2} c^{6} \sqrt{d} - 80 \, a b c^{5} d^{\frac{3}{2}} + 73 \, a^{2} c^{4} d^{\frac{5}{2}}\right)}}{15 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{5} c^{4}}"," ",0,"-1/3*x*((5*b^2*c^6*d^3 - 16*a*b*c^5*d^4 + 11*a^2*c^4*d^5)*x^2/(c^9*d) + 6*(b^2*c^7*d^2 - 3*a*b*c^6*d^3 + 2*a^2*c^5*d^4)/(c^9*d))/(d*x^2 + c)^(3/2) + 2/15*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^2*c^2*sqrt(d) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b*c*d^(3/2) + 45*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^2*c^3*sqrt(d) + 300*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b*c^2*d^(3/2) - 240*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*c*d^(5/2) + 90*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^4*sqrt(d) - 500*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c^3*d^(3/2) + 490*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*c^2*d^(5/2) - 60*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^5*sqrt(d) + 340*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^4*d^(3/2) - 320*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c^3*d^(5/2) + 15*b^2*c^6*sqrt(d) - 80*a*b*c^5*d^(3/2) + 73*a^2*c^4*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^5*c^4)","B",0
671,1,70,0,0.408834," ","integrate(x^5/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} b^{2}} + \frac{\sqrt{d x^{2}} b^{2} d^{5} x^{2} - 3 \, \sqrt{d x^{2}} a b d^{5}}{3 \, b^{3} d^{6}}"," ",0,"a^2*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*b^2) + 1/3*(sqrt(d*x^2)*b^2*d^5*x^2 - 3*sqrt(d*x^2)*a*b*d^5)/(b^3*d^6)","A",0
672,1,46,0,0.430159," ","integrate(x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\frac{a d \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} b} - \frac{\sqrt{d x^{2}}}{b}}{d}"," ",0,"-(a*d*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*b) - sqrt(d*x^2)/b)/d","A",0
673,1,23,0,0.357639," ","integrate(x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d}}"," ",0,"arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/sqrt(a*b*d)","A",0
674,1,41,0,0.282851," ","integrate(1/x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} a} - \frac{1}{\sqrt{d x^{2}} a}"," ",0,"-b*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*a) - 1/(sqrt(d*x^2)*a)","A",0
675,1,60,0,0.308657," ","integrate(1/x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} a^{2}} + \frac{3 \, b d x^{2} - a d}{3 \, \sqrt{d x^{2}} a^{2} d x^{2}}"," ",0,"b^2*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*a^2) + 1/3*(3*b*d*x^2 - a*d)/(sqrt(d*x^2)*a^2*d*x^2)","A",0
676,-2,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
677,1,96,0,0.317017," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a b c - a^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{2} - 3 \, \sqrt{d x^{2} + c} a b d^{3}}{3 \, b^{3} d^{3}}"," ",0,"-(a*b*c - a^2*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^2) + 1/3*((d*x^2 + c)^(3/2)*b^2*d^2 - 3*sqrt(d*x^2 + c)*a*b*d^3)/(b^3*d^3)","A",0
678,-2,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
679,1,64,0,0.301272," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b c - a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b} + \frac{\sqrt{d x^{2} + c}}{b}"," ",0,"(b*c - a*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b) + sqrt(d*x^2 + c)/b","A",0
680,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
681,1,78,0,0.387662," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b c - a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a} + \frac{c \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c}}"," ",0,"-(b*c - a*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a) + c*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c))","A",0
682,1,117,0,3.646248," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b c \sqrt{d} - a d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} a} + \frac{2 \, c \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} a}"," ",0,"(b*c*sqrt(d) - a*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a) + 2*c*sqrt(d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*a)","B",0
683,1,106,0,0.467479," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c - a b d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a^{2}} - \frac{{\left(2 \, b c - a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c}} - \frac{\sqrt{d x^{2} + c}}{2 \, a x^{2}}"," ",0,"(b^2*c - a*b*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2) - 1/2*(2*b*c - a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)) - 1/2*sqrt(d*x^2 + c)/(a*x^2)","A",0
684,1,215,0,5.430057," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} c \sqrt{d} - a b d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} a^{2}} - \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} + 3 \, b c^{3} \sqrt{d} - a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{2}}"," ",0,"-(b^2*c*sqrt(d) - a*b*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^2) - 2/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) + 3*b*c^3*sqrt(d) - a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^2)","B",0
685,-2,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
686,1,151,0,0.368253," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{3}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{4} d^{4} - 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b^{3} d^{5} - 15 \, \sqrt{d x^{2} + c} a b^{3} c d^{5} + 15 \, \sqrt{d x^{2} + c} a^{2} b^{2} d^{6}}{15 \, b^{5} d^{5}}"," ",0,"-(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^3) + 1/15*(3*(d*x^2 + c)^(5/2)*b^4*d^4 - 5*(d*x^2 + c)^(3/2)*a*b^3*d^5 - 15*sqrt(d*x^2 + c)*a*b^3*c*d^5 + 15*sqrt(d*x^2 + c)*a^2*b^2*d^6)/(b^5*d^5)","A",0
687,-2,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
688,1,112,0,0.376091," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} + 3 \, \sqrt{d x^{2} + c} b^{2} c - 3 \, \sqrt{d x^{2} + c} a b d}{3 \, b^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^2) + 1/3*((d*x^2 + c)^(3/2)*b^2 + 3*sqrt(d*x^2 + c)*b^2*c - 3*sqrt(d*x^2 + c)*a*b*d)/b^3","A",0
689,-2,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
690,1,110,0,0.374597," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a),x, algorithm=""giac"")","\frac{c^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c}} + \frac{\sqrt{d x^{2} + c} d}{b} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a b}"," ",0,"c^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c)) + sqrt(d*x^2 + c)*d/b - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a*b)","A",0
691,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
692,1,120,0,0.412297," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a^{2}} - \frac{{\left(2 \, b c^{2} - 3 \, a c d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c}} - \frac{\sqrt{d x^{2} + c} c}{2 \, a x^{2}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2) - 1/2*(2*b*c^2 - 3*a*c*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)) - 1/2*sqrt(d*x^2 + c)*c/(a*x^2)","A",0
693,1,256,0,5.349888," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\left(b^{2} c^{2} \sqrt{d} - 2 \, a b c d^{\frac{3}{2}} + a^{2} d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} a^{2}} - \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c^{2} \sqrt{d} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a c d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{3} \sqrt{d} + 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c^{2} d^{\frac{3}{2}} + 3 \, b c^{4} \sqrt{d} - 4 \, a c^{3} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{2}}"," ",0,"-(b^2*c^2*sqrt(d) - 2*a*b*c*d^(3/2) + a^2*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^2) - 2/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c^2*sqrt(d) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*c*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^3*sqrt(d) + 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c^2*d^(3/2) + 3*b*c^4*sqrt(d) - 4*a*c^3*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^2)","B",0
694,-2,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
695,1,228,0,0.467000," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""giac"")","-\frac{{\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)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{4}} + \frac{15 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{6} d^{6} - 21 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b^{5} d^{7} - 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b^{5} c d^{7} - 105 \, \sqrt{d x^{2} + c} a b^{5} c^{2} d^{7} + 35 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} b^{4} d^{8} + 210 \, \sqrt{d x^{2} + c} a^{2} b^{4} c d^{8} - 105 \, \sqrt{d x^{2} + c} a^{3} b^{3} d^{9}}{105 \, b^{7} d^{7}}"," ",0,"-(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^4) + 1/105*(15*(d*x^2 + c)^(7/2)*b^6*d^6 - 21*(d*x^2 + c)^(5/2)*a*b^5*d^7 - 35*(d*x^2 + c)^(3/2)*a*b^5*c*d^7 - 105*sqrt(d*x^2 + c)*a*b^5*c^2*d^7 + 35*(d*x^2 + c)^(3/2)*a^2*b^4*d^8 + 210*sqrt(d*x^2 + c)*a^2*b^4*c*d^8 - 105*sqrt(d*x^2 + c)*a^3*b^3*d^9)/(b^7*d^7)","A",0
696,-2,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
697,1,184,0,0.435143," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""giac"")","\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)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{3}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{4} + 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{4} c + 15 \, \sqrt{d x^{2} + c} b^{4} c^{2} - 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b^{3} d - 30 \, \sqrt{d x^{2} + c} a b^{3} c d + 15 \, \sqrt{d x^{2} + c} a^{2} b^{2} d^{2}}{15 \, b^{5}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^3) + 1/15*(3*(d*x^2 + c)^(5/2)*b^4 + 5*(d*x^2 + c)^(3/2)*b^4*c + 15*sqrt(d*x^2 + c)*b^4*c^2 - 5*(d*x^2 + c)^(3/2)*a*b^3*d - 30*sqrt(d*x^2 + c)*a*b^3*c*d + 15*sqrt(d*x^2 + c)*a^2*b^2*d^2)/b^5","A",0
698,-2,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
699,1,163,0,0.382773," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a),x, algorithm=""giac"")","\frac{c^{3} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c}} - \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)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a b^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d + 6 \, \sqrt{d x^{2} + c} b^{2} c d - 3 \, \sqrt{d x^{2} + c} a b d^{2}}{3 \, b^{3}}"," ",0,"c^3*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c)) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a*b^2) + 1/3*((d*x^2 + c)^(3/2)*b^2*d + 6*sqrt(d*x^2 + c)*b^2*c*d - 3*sqrt(d*x^2 + c)*a*b*d^2)/b^3","A",0
700,-2,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
701,1,158,0,0.386162," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} d^{2}}{b} - \frac{\sqrt{d x^{2} + c} c^{2}}{2 \, a x^{2}} - \frac{{\left(2 \, b c^{3} - 5 \, a c^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c}} + \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)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a^{2} b}"," ",0,"sqrt(d*x^2 + c)*d^2/b - 1/2*sqrt(d*x^2 + c)*c^2/(a*x^2) - 1/2*(2*b*c^3 - 5*a*c^2*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2*b)","A",0
702,-2,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
703,1,105,0,0.380195," ","integrate(x^5/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{4} - 3 \, \sqrt{d x^{2} + c} b^{2} c d^{4} - 3 \, \sqrt{d x^{2} + c} a b d^{5}}{3 \, b^{3} d^{6}}"," ",0,"a^2*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^2) + 1/3*((d*x^2 + c)^(3/2)*b^2*d^4 - 3*sqrt(d*x^2 + c)*b^2*c*d^4 - 3*sqrt(d*x^2 + c)*a*b*d^5)/(b^3*d^6)","A",0
704,1,64,0,0.344777," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{a d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} b} - \frac{\sqrt{d x^{2} + c}}{b}}{d}"," ",0,"-(a*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b) - sqrt(d*x^2 + c)/b)/d","A",0
705,1,39,0,0.324552," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d}}"," ",0,"arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/sqrt(-b^2*c + a*b*d)","A",0
706,1,70,0,0.298793," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c}}"," ",0,"-b*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c))","A",0
707,1,103,0,0.351296," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} a^{2}} - \frac{{\left(2 \, b c + a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c} c} - \frac{\sqrt{d x^{2} + c}}{2 \, a c x^{2}}"," ",0,"b^2*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2) - 1/2*(2*b*c + a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)*c) - 1/2*sqrt(d*x^2 + c)/(a*c*x^2)","A",0
708,-2,0,0,0.000000," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
709,-2,0,0,0.000000," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
710,1,70,0,0.326536," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}}}"," ",0,"-sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/sqrt(a*b*c*d - a^2*d^2)","A",0
711,1,111,0,0.319694," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","d^{\frac{3}{2}} {\left(\frac{b \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} a d} + \frac{2}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} a d}\right)}"," ",0,"d^(3/2)*(b*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a*d) + 2/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*a*d))","A",0
712,1,195,0,5.362013," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, d^{\frac{5}{2}} {\left(\frac{3 \, b^{2} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} a^{2} d^{2}} + \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + 3 \, b c^{2} + 2 \, a c d\right)}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{2} d^{2}}\right)}"," ",0,"-1/3*d^(5/2)*(3*b^2*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^2*d^2) + 2*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + 3*b*c^2 + 2*a*c*d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^2*d^2))","B",0
713,-2,0,0,0.000000," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
714,1,78,0,0.466036," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{\frac{a d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} {\left(b c - a d\right)}} + \frac{c}{\sqrt{d x^{2} + c} {\left(b c - a d\right)}}}{d}"," ",0,"-(a*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*(b*c - a*d)) + c/(sqrt(d*x^2 + c)*(b*c - a*d)))/d","A",0
715,1,103,0,0.464356," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{a \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} {\left(b c - a d\right)}} + \frac{x}{\sqrt{d x^{2} + c} {\left(b c - a d\right)}}"," ",0,"-a*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*(b*c - a*d)) + x/(sqrt(d*x^2 + c)*(b*c - a*d))","A",0
716,1,71,0,0.365819," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{\sqrt{-b^{2} c + a b d} {\left(b c - a d\right)}} + \frac{1}{\sqrt{d x^{2} + c} {\left(b c - a d\right)}}"," ",0,"b*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*(b*c - a*d)) + 1/(sqrt(d*x^2 + c)*(b*c - a*d))","A",0
717,1,107,0,0.305527," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} {\left(b c - a d\right)}} - \frac{d x}{{\left(b c^{2} - a c d\right)} \sqrt{d x^{2} + c}}"," ",0,"b*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*(b*c - a*d)) - d*x/((b*c^2 - a*c*d)*sqrt(d*x^2 + c))","A",0
718,1,110,0,0.364143," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{b^{2} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d}} - \frac{d}{{\left(b c^{2} - a c d\right)} \sqrt{d x^{2} + c}} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c} c}"," ",0,"-b^2*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)) - d/((b*c^2 - a*c*d)*sqrt(d*x^2 + c)) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c)*c)","A",0
719,1,152,0,3.563112," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{b^{2} \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} {\left(a b c - a^{2} d\right)}} + \frac{d^{2} x}{{\left(b c^{3} - a c^{2} d\right)} \sqrt{d x^{2} + c}} + \frac{2 \, \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} a c}"," ",0,"-b^2*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*(a*b*c - a^2*d)) + d^2*x/((b*c^3 - a*c^2*d)*sqrt(d*x^2 + c)) + 2*sqrt(d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*a*c)","A",0
720,1,172,0,0.449991," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b^{3} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(a^{2} b c - a^{3} d\right)} \sqrt{-b^{2} c + a b d}} - \frac{{\left(d x^{2} + c\right)} b c d - 3 \, {\left(d x^{2} + c\right)} a d^{2} + 2 \, a c d^{2}}{2 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} {\left({\left(d x^{2} + c\right)}^{\frac{3}{2}} - \sqrt{d x^{2} + c} c\right)}} - \frac{{\left(2 \, b c + 3 \, a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c} c^{2}}"," ",0,"b^3*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^2*b*c - a^3*d)*sqrt(-b^2*c + a*b*d)) - 1/2*((d*x^2 + c)*b*c*d - 3*(d*x^2 + c)*a*d^2 + 2*a*c*d^2)/((a*b*c^3 - a^2*c^2*d)*((d*x^2 + c)^(3/2) - sqrt(d*x^2 + c)*c)) - 1/2*(2*b*c + 3*a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)*c^2)","A",0
721,1,275,0,3.615348," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b^{3} \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a^{2} b c - a^{3} d\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{d^{3} x}{{\left(b c^{4} - a c^{3} d\right)} \sqrt{d x^{2} + c}} - \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d^{\frac{3}{2}} + 3 \, b c^{3} \sqrt{d} + 5 \, a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{2} c^{2}}"," ",0,"b^3*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^2*b*c - a^3*d)*sqrt(a*b*c*d - a^2*d^2)) - d^3*x/((b*c^4 - a*c^3*d)*sqrt(d*x^2 + c)) - 2/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d^(3/2) + 3*b*c^3*sqrt(d) + 5*a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^2*c^2)","A",0
722,1,304,0,0.450509," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{a^{2} \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{{\left(\frac{{\left(b^{3} c^{4} d - 6 \, a b^{2} c^{3} d^{2} + 9 \, a^{2} b c^{2} d^{3} - 4 \, a^{3} c d^{4}\right)} x^{2}}{b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3} - 4 \, a^{3} b c^{2} d^{4} + a^{4} c d^{5}} - \frac{3 \, {\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)}}{b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3} - 4 \, a^{3} b c^{2} d^{4} + a^{4} c d^{5}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"-a^2*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b*c*d - a^2*d^2)) + 1/3*((b^3*c^4*d - 6*a*b^2*c^3*d^2 + 9*a^2*b*c^2*d^3 - 4*a^3*c*d^4)*x^2/(b^4*c^5*d - 4*a*b^3*c^4*d^2 + 6*a^2*b^2*c^3*d^3 - 4*a^3*b*c^2*d^4 + a^4*c*d^5) - 3*(a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)/(b^4*c^5*d - 4*a*b^3*c^4*d^2 + 6*a^2*b^2*c^3*d^3 - 4*a^3*b*c^2*d^4 + a^4*c*d^5))*x/(d*x^2 + c)^(3/2)","B",0
723,1,127,0,0.317466," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{\frac{3 \, a b d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{b c^{2} + 3 \, {\left(d x^{2} + c\right)} a d - a c d}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}}{3 \, d}"," ",0,"-1/3*(3*a*b*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b^2*c + a*b*d)) + (b*c^2 + 3*(d*x^2 + c)*a*d - a*c*d)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(d*x^2 + c)^(3/2)))/d","A",0
724,1,291,0,0.454010," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{a b \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{{\left(\frac{{\left(2 \, b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + a^{3} d^{5}\right)} x^{2}}{b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3} - 4 \, a^{3} b c^{2} d^{4} + a^{4} c d^{5}} + \frac{3 \, {\left(b^{3} c^{4} d - 2 \, a b^{2} c^{3} d^{2} + a^{2} b c^{2} d^{3}\right)}}{b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3} - 4 \, a^{3} b c^{2} d^{4} + a^{4} c d^{5}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"a*b*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b*c*d - a^2*d^2)) + 1/3*((2*b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + a^3*d^5)*x^2/(b^4*c^5*d - 4*a*b^3*c^4*d^2 + 6*a^2*b^2*c^3*d^3 - 4*a^3*b*c^2*d^4 + a^4*c*d^5) + 3*(b^3*c^4*d - 2*a*b^2*c^3*d^2 + a^2*b*c^2*d^3)/(b^4*c^5*d - 4*a*b^3*c^4*d^2 + 6*a^2*b^2*c^3*d^3 - 4*a^3*b*c^2*d^4 + a^4*c*d^5))*x/(d*x^2 + c)^(3/2)","B",0
725,1,118,0,0.346289," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{3 \, {\left(d x^{2} + c\right)} b + b c - a d}{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"b^2*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b^2*c + a*b*d)) + 1/3*(3*(d*x^2 + c)*b + b*c - a*d)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(d*x^2 + c)^(3/2))","A",0
726,1,321,0,0.513199," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{b^{2} \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\frac{{\left(5 \, b^{3} c^{3} d^{3} - 12 \, a b^{2} c^{2} d^{4} + 9 \, a^{2} b c d^{5} - 2 \, a^{3} d^{6}\right)} x^{2}}{b^{4} c^{6} d - 4 \, a b^{3} c^{5} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{3} - 4 \, a^{3} b c^{3} d^{4} + a^{4} c^{2} d^{5}} + \frac{3 \, {\left(2 \, b^{3} c^{4} d^{2} - 5 \, a b^{2} c^{3} d^{3} + 4 \, a^{2} b c^{2} d^{4} - a^{3} c d^{5}\right)}}{b^{4} c^{6} d - 4 \, a b^{3} c^{5} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{3} - 4 \, a^{3} b c^{3} d^{4} + a^{4} c^{2} d^{5}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"-b^2*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b*c*d - a^2*d^2)) - 1/3*((5*b^3*c^3*d^3 - 12*a*b^2*c^2*d^4 + 9*a^2*b*c*d^5 - 2*a^3*d^6)*x^2/(b^4*c^6*d - 4*a*b^3*c^5*d^2 + 6*a^2*b^2*c^4*d^3 - 4*a^3*b*c^3*d^4 + a^4*c^2*d^5) + 3*(2*b^3*c^4*d^2 - 5*a*b^2*c^3*d^3 + 4*a^2*b*c^2*d^4 - a^3*c*d^5)/(b^4*c^6*d - 4*a*b^3*c^5*d^2 + 6*a^2*b^2*c^4*d^3 - 4*a^3*b*c^3*d^4 + a^4*c^2*d^5))*x/(d*x^2 + c)^(3/2)","B",0
727,1,176,0,0.343322," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{b^{3} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{-b^{2} c + a b d}} - \frac{6 \, {\left(d x^{2} + c\right)} b c d + b c^{2} d - 3 \, {\left(d x^{2} + c\right)} a d^{2} - a c d^{2}}{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a \sqrt{-c} c^{2}}"," ",0,"-b^3*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(-b^2*c + a*b*d)) - 1/3*(6*(d*x^2 + c)*b*c*d + b*c^2*d - 3*(d*x^2 + c)*a*d^2 - a*c*d^2)/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)^(3/2)) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a*sqrt(-c)*c^2)","A",0
728,1,366,0,3.801542," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{b^{3} \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{{\left(\frac{{\left(8 \, b^{3} c^{5} d^{4} - 21 \, a b^{2} c^{4} d^{5} + 18 \, a^{2} b c^{3} d^{6} - 5 \, a^{3} c^{2} d^{7}\right)} x^{2}}{b^{4} c^{9} d - 4 \, a b^{3} c^{8} d^{2} + 6 \, a^{2} b^{2} c^{7} d^{3} - 4 \, a^{3} b c^{6} d^{4} + a^{4} c^{5} d^{5}} + \frac{3 \, {\left(3 \, b^{3} c^{6} d^{3} - 8 \, a b^{2} c^{5} d^{4} + 7 \, a^{2} b c^{4} d^{5} - 2 \, a^{3} c^{3} d^{6}\right)}}{b^{4} c^{9} d - 4 \, a b^{3} c^{8} d^{2} + 6 \, a^{2} b^{2} c^{7} d^{3} - 4 \, a^{3} b c^{6} d^{4} + a^{4} c^{5} d^{5}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{2 \, \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)} a c^{2}}"," ",0,"b^3*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b*c*d - a^2*d^2)) + 1/3*((8*b^3*c^5*d^4 - 21*a*b^2*c^4*d^5 + 18*a^2*b*c^3*d^6 - 5*a^3*c^2*d^7)*x^2/(b^4*c^9*d - 4*a*b^3*c^8*d^2 + 6*a^2*b^2*c^7*d^3 - 4*a^3*b*c^6*d^4 + a^4*c^5*d^5) + 3*(3*b^3*c^6*d^3 - 8*a*b^2*c^5*d^4 + 7*a^2*b*c^4*d^5 - 2*a^3*c^3*d^6)/(b^4*c^9*d - 4*a*b^3*c^8*d^2 + 6*a^2*b^2*c^7*d^3 - 4*a^3*b*c^6*d^4 + a^4*c^5*d^5))*x/(d*x^2 + c)^(3/2) + 2*sqrt(d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)*a*c^2)","B",0
729,1,211,0,0.361537," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{b^{4} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{9 \, {\left(d x^{2} + c\right)} b c d^{2} + b c^{2} d^{2} - 6 \, {\left(d x^{2} + c\right)} a d^{3} - a c d^{3}}{3 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{{\left(2 \, b c + 5 \, a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{2} \sqrt{-c} c^{3}} - \frac{\sqrt{d x^{2} + c}}{2 \, a c^{3} x^{2}}"," ",0,"b^4*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b^2*c + a*b*d)) + 1/3*(9*(d*x^2 + c)*b*c*d^2 + b*c^2*d^2 - 6*(d*x^2 + c)*a*d^3 - a*c*d^3)/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*(d*x^2 + c)^(3/2)) - 1/2*(2*b*c + 5*a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)*c^3) - 1/2*sqrt(d*x^2 + c)/(a*c^3*x^2)","A",0
730,1,490,0,4.332777," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{b^{4} \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\frac{{\left(11 \, b^{3} c^{6} d^{5} - 30 \, a b^{2} c^{5} d^{6} + 27 \, a^{2} b c^{4} d^{7} - 8 \, a^{3} c^{3} d^{8}\right)} x^{2}}{b^{4} c^{11} d - 4 \, a b^{3} c^{10} d^{2} + 6 \, a^{2} b^{2} c^{9} d^{3} - 4 \, a^{3} b c^{8} d^{4} + a^{4} c^{7} d^{5}} + \frac{3 \, {\left(4 \, b^{3} c^{7} d^{4} - 11 \, a b^{2} c^{6} d^{5} + 10 \, a^{2} b c^{5} d^{6} - 3 \, a^{3} c^{4} d^{7}\right)}}{b^{4} c^{11} d - 4 \, a b^{3} c^{10} d^{2} + 6 \, a^{2} b^{2} c^{9} d^{3} - 4 \, a^{3} b c^{8} d^{4} + a^{4} c^{7} d^{5}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} + 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} - 18 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d^{\frac{3}{2}} + 3 \, b c^{3} \sqrt{d} + 8 \, a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{2} c^{3}}"," ",0,"-b^4*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(a*b*c*d - a^2*d^2)) - 1/3*((11*b^3*c^6*d^5 - 30*a*b^2*c^5*d^6 + 27*a^2*b*c^4*d^7 - 8*a^3*c^3*d^8)*x^2/(b^4*c^11*d - 4*a*b^3*c^10*d^2 + 6*a^2*b^2*c^9*d^3 - 4*a^3*b*c^8*d^4 + a^4*c^7*d^5) + 3*(4*b^3*c^7*d^4 - 11*a*b^2*c^6*d^5 + 10*a^2*b*c^5*d^6 - 3*a^3*c^4*d^7)/(b^4*c^11*d - 4*a*b^3*c^10*d^2 + 6*a^2*b^2*c^9*d^3 - 4*a^3*b*c^8*d^4 + a^4*c^7*d^5))*x/(d*x^2 + c)^(3/2) - 2/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) + 6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) - 18*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d^(3/2) + 3*b*c^3*sqrt(d) + 8*a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^2*c^3)","B",0
731,1,288,0,0.603143," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} x}{2 \, b^{2}} + \frac{{\left(3 \, a b c \sqrt{d} - 4 \, a^{2} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{3}} - \frac{{\left(b c \sqrt{d} - 4 \, a d^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, b^{3} d} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{3}{2}} - a b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{3}}"," ",0,"1/2*sqrt(d*x^2 + c)*x/b^2 + 1/2*(3*a*b*c*sqrt(d) - 4*a^2*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^3) - 1/4*(b*c*sqrt(d) - 4*a*d^(3/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/(b^3*d) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(3/2) - a*b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^3)","B",0
732,1,101,0,0.318554," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} a d}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b^{2}} + \frac{{\left(2 \, b c - 3 \, a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b^{2}} + \frac{\sqrt{d x^{2} + c}}{b^{2}}"," ",0,"1/2*sqrt(d*x^2 + c)*a*d/(((d*x^2 + c)*b - b*c + a*d)*b^2) + 1/2*(2*b*c - 3*a*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^2) + sqrt(d*x^2 + c)/b^2","A",0
733,1,251,0,0.490017," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(b c \sqrt{d} - 2 \, a d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{2}} - \frac{\sqrt{d} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{2 \, b^{2}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d^{\frac{3}{2}} - b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{2}}"," ",0,"-1/2*(b*c*sqrt(d) - 2*a*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^2) - 1/2*sqrt(d)*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/b^2 + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d^(3/2) - b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^2)","B",0
734,1,79,0,0.396081," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b} - \frac{\sqrt{d x^{2} + c} d}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b}"," ",0,"1/2*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b) - 1/2*sqrt(d*x^2 + c)*d/(((d*x^2 + c)*b - b*c + a*d)*b)","A",0
735,1,218,0,3.788911," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{c \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d^{\frac{3}{2}} - b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a b}"," ",0,"-1/2*c*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d^(3/2) - b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a*b)","B",0
736,1,113,0,0.355751," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} d}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} a} - \frac{{\left(2 \, b c - a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{2}} + \frac{c \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}}"," ",0,"1/2*sqrt(d*x^2 + c)*d/(((d*x^2 + c)*b - b*c + a*d)*a) - 1/2*(2*b*c - a*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2) + c*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c))","A",0
737,1,329,0,4.065668," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(3 \, b c \sqrt{d} - 2 \, a d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a^{2}} + \frac{3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} + 10 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d^{\frac{3}{2}} + 3 \, b c^{3} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d - b c^{3}\right)} a^{2}}"," ",0,"1/2*(3*b*c*sqrt(d) - 2*a*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^2) + (3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) + 10*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d^(3/2) + 3*b*c^3*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^6*b - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2 - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d - b*c^3)*a^2)","B",0
738,1,183,0,0.359846," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(4 \, b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{3}} - \frac{{\left(4 \, b c - a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b d - 2 \, \sqrt{d x^{2} + c} b c d + \sqrt{d x^{2} + c} a d^{2}}{2 \, {\left({\left(d x^{2} + c\right)}^{2} b - 2 \, {\left(d x^{2} + c\right)} b c + b c^{2} + {\left(d x^{2} + c\right)} a d - a c d\right)} a^{2}}"," ",0,"1/2*(4*b^2*c - 3*a*b*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^3) - 1/2*(4*b*c - a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)) - 1/2*(2*(d*x^2 + c)^(3/2)*b*d - 2*sqrt(d*x^2 + c)*b*c*d + sqrt(d*x^2 + c)*a*d^2)/(((d*x^2 + c)^2*b - 2*(d*x^2 + c)*b*c + b*c^2 + (d*x^2 + c)*a*d - a*c*d)*a^2)","A",0
739,1,361,0,4.516362," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(5 \, b^{2} c \sqrt{d} - 4 \, a b d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a^{3}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b d^{\frac{3}{2}} - b^{2} c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a^{3}} - \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} + 6 \, b c^{3} \sqrt{d} - a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3}}"," ",0,"-1/2*(5*b^2*c*sqrt(d) - 4*a*b*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^3) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*d^(3/2) - b^2*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a^3) - 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) + 6*b*c^3*sqrt(d) - a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3)","B",0
740,1,394,0,0.540917," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{d x^{2} + c} x {\left(\frac{2 \, d x^{2}}{b^{2}} + \frac{5 \, b^{7} c d^{2} - 8 \, a b^{6} d^{3}}{b^{9} d^{2}}\right)} + \frac{3 \, {\left(a b^{2} c^{2} \sqrt{d} - 3 \, a^{2} b c d^{\frac{3}{2}} + 2 \, a^{3} d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{4}} - \frac{3 \, {\left(b^{2} c^{2} \sqrt{d} - 8 \, a b c d^{\frac{3}{2}} + 8 \, a^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{16 \, b^{4} d} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} d^{\frac{5}{2}} - a b^{2} c^{3} \sqrt{d} + a^{2} b c^{2} d^{\frac{3}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{4}}"," ",0,"1/8*sqrt(d*x^2 + c)*x*(2*d*x^2/b^2 + (5*b^7*c*d^2 - 8*a*b^6*d^3)/(b^9*d^2)) + 3/2*(a*b^2*c^2*sqrt(d) - 3*a^2*b*c*d^(3/2) + 2*a^3*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^4) - 3/16*(b^2*c^2*sqrt(d) - 8*a*b*c*d^(3/2) + 8*a^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/(b^4*d) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*d^(5/2) - a*b^2*c^3*sqrt(d) + a^2*b*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^4)","B",0
741,1,173,0,0.356254," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{2} c^{2} - 7 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b^{3}} + \frac{\sqrt{d x^{2} + c} a b c d - \sqrt{d x^{2} + c} a^{2} d^{2}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b^{3}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{4} + 3 \, \sqrt{d x^{2} + c} b^{4} c - 6 \, \sqrt{d x^{2} + c} a b^{3} d}{3 \, b^{6}}"," ",0,"1/2*(2*b^2*c^2 - 7*a*b*c*d + 5*a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^3) + 1/2*(sqrt(d*x^2 + c)*a*b*c*d - sqrt(d*x^2 + c)*a^2*d^2)/(((d*x^2 + c)*b - b*c + a*d)*b^3) + 1/3*((d*x^2 + c)^(3/2)*b^4 + 3*sqrt(d*x^2 + c)*b^4*c - 6*sqrt(d*x^2 + c)*a*b^3*d)/b^6","A",0
742,1,336,0,0.512732," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} d x}{2 \, b^{2}} - \frac{{\left(3 \, b c \sqrt{d} - 4 \, a d^{\frac{3}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, b^{3}} - \frac{{\left(b^{2} c^{2} \sqrt{d} - 5 \, a b c d^{\frac{3}{2}} + 4 \, a^{2} d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{3}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{5}{2}} - b^{2} c^{3} \sqrt{d} + a b c^{2} d^{\frac{3}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{3}}"," ",0,"1/2*sqrt(d*x^2 + c)*d*x/b^2 - 1/4*(3*b*c*sqrt(d) - 4*a*d^(3/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/b^3 - 1/2*(b^2*c^2*sqrt(d) - 5*a*b*c*d^(3/2) + 4*a^2*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^3) + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(5/2) - b^2*c^3*sqrt(d) + a*b*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^3)","B",0
743,1,122,0,0.429442," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} d}{b^{2}} + \frac{3 \, {\left(b c d - a d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b^{2}} - \frac{\sqrt{d x^{2} + c} b c d - \sqrt{d x^{2} + c} a d^{2}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b^{2}}"," ",0,"sqrt(d*x^2 + c)*d/b^2 + 3/2*(b*c*d - a*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^2) - 1/2*(sqrt(d*x^2 + c)*b*c*d - sqrt(d*x^2 + c)*a*d^2)/(((d*x^2 + c)*b - b*c + a*d)*b^2)","A",0
744,1,315,0,0.488377," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{d^{\frac{3}{2}} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{2 \, b^{2}} - \frac{{\left(b^{2} c^{2} \sqrt{d} + a b c d^{\frac{3}{2}} - 2 \, a^{2} d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a b^{2}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{5}{2}} - b^{2} c^{3} \sqrt{d} + a b c^{2} d^{\frac{3}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a b^{2}}"," ",0,"-1/2*d^(3/2)*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/b^2 - 1/2*(b^2*c^2*sqrt(d) + a*b*c*d^(3/2) - 2*a^2*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a*b^2) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(5/2) - b^2*c^3*sqrt(d) + a*b*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a*b^2)","B",0
745,1,154,0,0.286899," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c^{2} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}} - \frac{{\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{2} b} + \frac{\sqrt{d x^{2} + c} b c d - \sqrt{d x^{2} + c} a d^{2}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} a b}"," ",0,"c^2*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)) - 1/2*(2*b^2*c^2 - a*b*c*d - a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2*b) + 1/2*(sqrt(d*x^2 + c)*b*c*d - sqrt(d*x^2 + c)*a*d^2)/(((d*x^2 + c)*b - b*c + a*d)*a*b)","A",0
746,1,412,0,3.488986," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{3 \, {\left(b c^{2} \sqrt{d} - a c d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a^{2}} + \frac{3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} d^{\frac{5}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{3} \sqrt{d} + 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c^{2} d^{\frac{3}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} c d^{\frac{5}{2}} + 3 \, b^{2} c^{4} \sqrt{d} - a b c^{3} d^{\frac{3}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d - b c^{3}\right)} a^{2} b}"," ",0,"3/2*(b*c^2*sqrt(d) - a*c*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^2) + (3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*d^(5/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^3*sqrt(d) + 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c^2*d^(3/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*c*d^(5/2) + 3*b^2*c^4*sqrt(d) - a*b*c^3*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^6*b - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2 - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d - b*c^3)*a^2*b)","B",0
747,1,216,0,0.438950," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(4 \, b^{2} c^{2} - 5 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{3}} - \frac{{\left(4 \, b c^{2} - 3 \, a c d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b c d - 2 \, \sqrt{d x^{2} + c} b c^{2} d - {\left(d x^{2} + c\right)}^{\frac{3}{2}} a d^{2} + 2 \, \sqrt{d x^{2} + c} a c d^{2}}{2 \, {\left({\left(d x^{2} + c\right)}^{2} b - 2 \, {\left(d x^{2} + c\right)} b c + b c^{2} + {\left(d x^{2} + c\right)} a d - a c d\right)} a^{2}}"," ",0,"1/2*(4*b^2*c^2 - 5*a*b*c*d + a^2*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^3) - 1/2*(4*b*c^2 - 3*a*c*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)) - 1/2*(2*(d*x^2 + c)^(3/2)*b*c*d - 2*sqrt(d*x^2 + c)*b*c^2*d - (d*x^2 + c)^(3/2)*a*d^2 + 2*sqrt(d*x^2 + c)*a*c*d^2)/(((d*x^2 + c)^2*b - 2*(d*x^2 + c)*b*c + b*c^2 + (d*x^2 + c)*a*d - a*c*d)*a^2)","A",0
748,1,442,0,4.269908," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(5 \, b^{2} c^{2} \sqrt{d} - 7 \, a b c d^{\frac{3}{2}} + 2 \, a^{2} d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a^{3}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{5}{2}} - b^{2} c^{3} \sqrt{d} + a b c^{2} d^{\frac{3}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a^{3}} - \frac{4 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c^{2} \sqrt{d} - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a c d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{3} \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c^{2} d^{\frac{3}{2}} + 3 \, b c^{4} \sqrt{d} - 2 \, a c^{3} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3}}"," ",0,"-1/2*(5*b^2*c^2*sqrt(d) - 7*a*b*c*d^(3/2) + 2*a^2*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^3) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(5/2) - b^2*c^3*sqrt(d) + a*b*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a^3) - 4/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c^2*sqrt(d) - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*c*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^3*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c^2*d^(3/2) + 3*b*c^4*sqrt(d) - 2*a*c^3*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3)","B",0
749,1,521,0,0.601886," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(\frac{4 \, d^{2} x^{2}}{b^{2}} + \frac{13 \, b^{12} c d^{5} - 12 \, a b^{11} d^{6}}{b^{14} d^{4}}\right)} x^{2} + \frac{3 \, {\left(11 \, b^{12} c^{2} d^{4} - 36 \, a b^{11} c d^{5} + 24 \, a^{2} b^{10} d^{6}\right)}}{b^{14} d^{4}}\right)} \sqrt{d x^{2} + c} x + \frac{{\left(3 \, a b^{3} c^{3} \sqrt{d} - 14 \, a^{2} b^{2} c^{2} d^{\frac{3}{2}} + 19 \, a^{3} b c d^{\frac{5}{2}} - 8 \, a^{4} d^{\frac{7}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{5}} - \frac{{\left(5 \, b^{3} c^{3} \sqrt{d} - 60 \, a b^{2} c^{2} d^{\frac{3}{2}} + 120 \, a^{2} b c d^{\frac{5}{2}} - 64 \, a^{3} d^{\frac{7}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{32 \, b^{5} d} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{3} c^{3} \sqrt{d} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b^{2} c^{2} d^{\frac{3}{2}} + 5 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} b c d^{\frac{5}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{4} d^{\frac{7}{2}} - a b^{3} c^{4} \sqrt{d} + 2 \, a^{2} b^{2} c^{3} d^{\frac{3}{2}} - a^{3} b c^{2} d^{\frac{5}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{5}}"," ",0,"1/48*(2*(4*d^2*x^2/b^2 + (13*b^12*c*d^5 - 12*a*b^11*d^6)/(b^14*d^4))*x^2 + 3*(11*b^12*c^2*d^4 - 36*a*b^11*c*d^5 + 24*a^2*b^10*d^6)/(b^14*d^4))*sqrt(d*x^2 + c)*x + 1/2*(3*a*b^3*c^3*sqrt(d) - 14*a^2*b^2*c^2*d^(3/2) + 19*a^3*b*c*d^(5/2) - 8*a^4*d^(7/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^5) - 1/32*(5*b^3*c^3*sqrt(d) - 60*a*b^2*c^2*d^(3/2) + 120*a^2*b*c*d^(5/2) - 64*a^3*d^(7/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/(b^5*d) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^3*c^3*sqrt(d) - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b^2*c^2*d^(3/2) + 5*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*b*c*d^(5/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^4*d^(7/2) - a*b^3*c^4*sqrt(d) + 2*a^2*b^2*c^3*d^(3/2) - a^3*b*c^2*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^5)","B",0
750,1,264,0,0.397987," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{3} c^{3} - 11 \, a b^{2} c^{2} d + 16 \, a^{2} b c d^{2} - 7 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b^{4}} + \frac{\sqrt{d x^{2} + c} a b^{2} c^{2} d - 2 \, \sqrt{d x^{2} + c} a^{2} b c d^{2} + \sqrt{d x^{2} + c} a^{3} d^{3}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b^{4}} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{8} + 5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{8} c + 15 \, \sqrt{d x^{2} + c} b^{8} c^{2} - 10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b^{7} d - 60 \, \sqrt{d x^{2} + c} a b^{7} c d + 45 \, \sqrt{d x^{2} + c} a^{2} b^{6} d^{2}}{15 \, b^{10}}"," ",0,"1/2*(2*b^3*c^3 - 11*a*b^2*c^2*d + 16*a^2*b*c*d^2 - 7*a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^4) + 1/2*(sqrt(d*x^2 + c)*a*b^2*c^2*d - 2*sqrt(d*x^2 + c)*a^2*b*c*d^2 + sqrt(d*x^2 + c)*a^3*d^3)/(((d*x^2 + c)*b - b*c + a*d)*b^4) + 1/15*(3*(d*x^2 + c)^(5/2)*b^8 + 5*(d*x^2 + c)^(3/2)*b^8*c + 15*sqrt(d*x^2 + c)*b^8*c^2 - 10*(d*x^2 + c)^(3/2)*a*b^7*d - 60*sqrt(d*x^2 + c)*a*b^7*c*d + 45*sqrt(d*x^2 + c)*a^2*b^6*d^2)/b^10","A",0
751,1,446,0,0.572022," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{d x^{2} + c} {\left(\frac{2 \, d^{2} x^{2}}{b^{2}} + \frac{9 \, b^{7} c d^{3} - 8 \, a b^{6} d^{4}}{b^{9} d^{2}}\right)} x - \frac{{\left(15 \, b^{2} c^{2} \sqrt{d} - 40 \, a b c d^{\frac{3}{2}} + 24 \, a^{2} d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{16 \, b^{4}} - \frac{{\left(b^{3} c^{3} \sqrt{d} - 8 \, a b^{2} c^{2} d^{\frac{3}{2}} + 13 \, a^{2} b c d^{\frac{5}{2}} - 6 \, a^{3} d^{\frac{7}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} b^{4}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c^{3} \sqrt{d} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{2} d^{\frac{3}{2}} + 5 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c d^{\frac{5}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} d^{\frac{7}{2}} - b^{3} c^{4} \sqrt{d} + 2 \, a b^{2} c^{3} d^{\frac{3}{2}} - a^{2} b c^{2} d^{\frac{5}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} b^{4}}"," ",0,"1/8*sqrt(d*x^2 + c)*(2*d^2*x^2/b^2 + (9*b^7*c*d^3 - 8*a*b^6*d^4)/(b^9*d^2))*x - 1/16*(15*b^2*c^2*sqrt(d) - 40*a*b*c*d^(3/2) + 24*a^2*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/b^4 - 1/2*(b^3*c^3*sqrt(d) - 8*a*b^2*c^2*d^(3/2) + 13*a^2*b*c*d^(5/2) - 6*a^3*d^(7/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*b^4) + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c^3*sqrt(d) - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^2*d^(3/2) + 5*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c*d^(5/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*d^(7/2) - b^3*c^4*sqrt(d) + 2*a*b^2*c^3*d^(3/2) - a^2*b*c^2*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*b^4)","B",0
752,1,197,0,0.397171," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{5 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} b^{3}} - \frac{\sqrt{d x^{2} + c} b^{2} c^{2} d - 2 \, \sqrt{d x^{2} + c} a b c d^{2} + \sqrt{d x^{2} + c} a^{2} d^{3}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} b^{3}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{4} d + 6 \, \sqrt{d x^{2} + c} b^{4} c d - 6 \, \sqrt{d x^{2} + c} a b^{3} d^{2}}{3 \, b^{6}}"," ",0,"5/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*b^3) - 1/2*(sqrt(d*x^2 + c)*b^2*c^2*d - 2*sqrt(d*x^2 + c)*a*b*c*d^2 + sqrt(d*x^2 + c)*a^2*d^3)/(((d*x^2 + c)*b - b*c + a*d)*b^3) + 1/3*((d*x^2 + c)^(3/2)*b^4*d + 6*sqrt(d*x^2 + c)*b^4*c*d - 6*sqrt(d*x^2 + c)*a*b^3*d^2)/b^6","A",0
753,1,407,0,0.610315," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} d^{2} x}{2 \, b^{2}} - \frac{{\left(5 \, b c d^{\frac{3}{2}} - 4 \, a d^{\frac{5}{2}}\right)} \log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{4 \, b^{3}} - \frac{{\left(b^{3} c^{3} \sqrt{d} + 2 \, a b^{2} c^{2} d^{\frac{3}{2}} - 7 \, a^{2} b c d^{\frac{5}{2}} + 4 \, a^{3} d^{\frac{7}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a b^{3}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c^{3} \sqrt{d} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{2} d^{\frac{3}{2}} + 5 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c d^{\frac{5}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} d^{\frac{7}{2}} - b^{3} c^{4} \sqrt{d} + 2 \, a b^{2} c^{3} d^{\frac{3}{2}} - a^{2} b c^{2} d^{\frac{5}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a b^{3}}"," ",0,"1/2*sqrt(d*x^2 + c)*d^2*x/b^2 - 1/4*(5*b*c*d^(3/2) - 4*a*d^(5/2))*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/b^3 - 1/2*(b^3*c^3*sqrt(d) + 2*a*b^2*c^2*d^(3/2) - 7*a^2*b*c*d^(5/2) + 4*a^3*d^(7/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a*b^3) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c^3*sqrt(d) - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^2*d^(3/2) + 5*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c*d^(5/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*d^(7/2) - b^3*c^4*sqrt(d) + 2*a*b^2*c^3*d^(3/2) - a^2*b*c^2*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a*b^3)","B",0
754,1,206,0,0.344994," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{c^{3} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}} + \frac{\sqrt{d x^{2} + c} d^{2}}{b^{2}} - \frac{{\left(2 \, b^{3} c^{3} - a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{2} b^{2}} + \frac{\sqrt{d x^{2} + c} b^{2} c^{2} d - 2 \, \sqrt{d x^{2} + c} a b c d^{2} + \sqrt{d x^{2} + c} a^{2} d^{3}}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} a b^{2}}"," ",0,"c^3*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)) + sqrt(d*x^2 + c)*d^2/b^2 - 1/2*(2*b^3*c^3 - a*b^2*c^2*d - 4*a^2*b*c*d^2 + 3*a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^2*b^2) + 1/2*(sqrt(d*x^2 + c)*b^2*c^2*d - 2*sqrt(d*x^2 + c)*a*b*c*d^2 + sqrt(d*x^2 + c)*a^2*d^3)/(((d*x^2 + c)*b - b*c + a*d)*a*b^2)","A",0
755,-2,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
756,1,283,0,0.347664," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, b c^{3} - 5 \, a c^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c}} + \frac{{\left(4 \, b^{3} c^{3} - 7 \, a b^{2} c^{2} d + 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} a^{3} b} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} d - 2 \, \sqrt{d x^{2} + c} b^{2} c^{3} d - 2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c d^{2} + 3 \, \sqrt{d x^{2} + c} a b c^{2} d^{2} + {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3} - \sqrt{d x^{2} + c} a^{2} c d^{3}}{2 \, {\left({\left(d x^{2} + c\right)}^{2} b - 2 \, {\left(d x^{2} + c\right)} b c + b c^{2} + {\left(d x^{2} + c\right)} a d - a c d\right)} a^{2} b}"," ",0,"-1/2*(4*b*c^3 - 5*a*c^2*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)) + 1/2*(4*b^3*c^3 - 7*a*b^2*c^2*d + 2*a^2*b*c*d^2 + a^3*d^3)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*a^3*b) - 1/2*(2*(d*x^2 + c)^(3/2)*b^2*c^2*d - 2*sqrt(d*x^2 + c)*b^2*c^3*d - 2*(d*x^2 + c)^(3/2)*a*b*c*d^2 + 3*sqrt(d*x^2 + c)*a*b*c^2*d^2 + (d*x^2 + c)^(3/2)*a^2*d^3 - sqrt(d*x^2 + c)*a^2*c*d^3)/(((d*x^2 + c)^2*b - 2*(d*x^2 + c)*b*c + b*c^2 + (d*x^2 + c)*a*d - a*c*d)*a^2*b)","A",0
757,1,496,0,4.941996," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a)^2,x, algorithm=""giac"")","-\frac{5 \, {\left(b^{2} c^{3} \sqrt{d} - 2 \, a b c^{2} d^{\frac{3}{2}} + a^{2} c d^{\frac{5}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} a^{3}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c^{3} \sqrt{d} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{2} d^{\frac{3}{2}} + 5 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c d^{\frac{5}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} d^{\frac{7}{2}} - b^{3} c^{4} \sqrt{d} + 2 \, a b^{2} c^{3} d^{\frac{3}{2}} - a^{2} b c^{2} d^{\frac{5}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} a^{3} b} - \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c^{3} \sqrt{d} - 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a c^{2} d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{4} \sqrt{d} + 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c^{3} d^{\frac{3}{2}} + 6 \, b c^{5} \sqrt{d} - 7 \, a c^{4} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3}}"," ",0,"-5/2*(b^2*c^3*sqrt(d) - 2*a*b*c^2*d^(3/2) + a^2*c*d^(5/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*a^3) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c^3*sqrt(d) - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^2*d^(3/2) + 5*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c*d^(5/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*d^(7/2) - b^3*c^4*sqrt(d) + 2*a*b^2*c^3*d^(3/2) - a^2*b*c^2*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*a^3*b) - 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c^3*sqrt(d) - 9*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*c^2*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^4*sqrt(d) + 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c^3*d^(3/2) + 6*b*c^5*sqrt(d) - 7*a*c^4*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3)","B",0
758,1,284,0,0.574622," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(3 \, a b c \sqrt{d} - 2 \, a^{2} d^{\frac{3}{2}}\right)} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(b^{3} c - a b^{2} d\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{3}{2}} - a b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(b^{3} c - a b^{2} d\right)}} - \frac{\log\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2}\right)}{2 \, b^{2} \sqrt{d}}"," ",0,"-1/2*(3*a*b*c*sqrt(d) - 2*a^2*d^(3/2))*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^3*c - a*b^2*d)*sqrt(a*b*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(3/2) - a*b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(b^3*c - a*b^2*d)) - 1/2*log((sqrt(d)*x - sqrt(d*x^2 + c))^2)/(b^2*sqrt(d))","B",0
759,1,116,0,0.333533," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{d x^{2} + c} a d^{2}}{{\left(b^{2} c - a b d\right)} {\left({\left(d x^{2} + c\right)} b - b c + a d\right)}} + \frac{{\left(2 \, b c d - a d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{2} c - a b d\right)} \sqrt{-b^{2} c + a b d}}}{2 \, d}"," ",0,"1/2*(sqrt(d*x^2 + c)*a*d^2/((b^2*c - a*b*d)*((d*x^2 + c)*b - b*c + a*d)) + (2*b*c*d - a*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^2*c - a*b*d)*sqrt(-b^2*c + a*b*d)))/d","A",0
760,1,231,0,3.834707," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{c \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, \sqrt{a b c d - a^{2} d^{2}} {\left(b c - a d\right)}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d^{\frac{3}{2}} - b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(b^{2} c - a b d\right)}}"," ",0,"1/2*c*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*(b*c - a*d)) + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d^(3/2) - b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(b^2*c - a*b*d))","B",0
761,1,93,0,0.280959," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, \sqrt{-b^{2} c + a b d} {\left(b c - a d\right)}} - \frac{\sqrt{d x^{2} + c} d}{2 \, {\left({\left(d x^{2} + c\right)} b - b c + a d\right)} {\left(b c - a d\right)}}"," ",0,"-1/2*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/(sqrt(-b^2*c + a*b*d)*(b*c - a*d)) - 1/2*sqrt(d*x^2 + c)*d/(((d*x^2 + c)*b - b*c + a*d)*(b*c - a*d))","A",0
762,1,225,0,0.545484," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, d^{\frac{3}{2}} {\left(\frac{{\left(b c - 2 \, a d\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a b c d - a^{2} d^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d - b c^{2}\right)}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(a b c d - a^{2} d^{2}\right)}}\right)}"," ",0,"-1/2*d^(3/2)*((b*c - 2*a*d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(a*b*c*d - a^2*d^2)^(3/2) + 2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d - b*c^2)/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(a*b*c*d - a^2*d^2)))","B",0
763,1,138,0,0.311545," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} b d}{2 \, {\left(a b c - a^{2} d\right)} {\left({\left(d x^{2} + c\right)} b - b c + a d\right)}} - \frac{{\left(2 \, b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\left(a^{2} b c - a^{3} d\right)} \sqrt{-b^{2} c + a b d}} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c}}"," ",0,"1/2*sqrt(d*x^2 + c)*b*d/((a*b*c - a^2*d)*((d*x^2 + c)*b - b*c + a*d)) - 1/2*(2*b^2*c - 3*a*b*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^2*b*c - a^3*d)*sqrt(-b^2*c + a*b*d)) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c))","A",0
764,1,396,0,3.941410," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, d^{\frac{5}{2}} {\left(\frac{{\left(3 \, b^{2} c - 4 \, a b d\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{2 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{2} c - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b d - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c^{2} + 14 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c d - 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{2} + 3 \, b^{2} c^{3} - 2 \, a b c^{2} d\right)}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d - b c^{3}\right)} {\left(a^{2} b c d^{2} - a^{3} d^{3}\right)}}\right)}"," ",0,"1/2*d^(5/2)*((3*b^2*c - 4*a*b*d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b*c*d - a^2*d^2)) + 2*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^2*c - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b*d - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c^2 + 14*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*d - 8*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^2 + 3*b^2*c^3 - 2*a*b*c^2*d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^6*b - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2 - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d - b*c^3)*(a^2*b*c*d^2 - a^3*d^3)))","B",0
765,1,257,0,0.335676," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(4 \, b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\left(a^{3} b c - a^{4} d\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c d - 2 \, \sqrt{d x^{2} + c} b^{2} c^{2} d - {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2} + 2 \, \sqrt{d x^{2} + c} a b c d^{2} - \sqrt{d x^{2} + c} a^{2} d^{3}}{2 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} {\left({\left(d x^{2} + c\right)}^{2} b - 2 \, {\left(d x^{2} + c\right)} b c + b c^{2} + {\left(d x^{2} + c\right)} a d - a c d\right)}} - \frac{{\left(4 \, b c + a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c} c}"," ",0,"1/2*(4*b^3*c - 5*a*b^2*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^3*b*c - a^4*d)*sqrt(-b^2*c + a*b*d)) - 1/2*(2*(d*x^2 + c)^(3/2)*b^2*c*d - 2*sqrt(d*x^2 + c)*b^2*c^2*d - (d*x^2 + c)^(3/2)*a*b*d^2 + 2*sqrt(d*x^2 + c)*a*b*c*d^2 - sqrt(d*x^2 + c)*a^2*d^3)/((a^2*b*c^2 - a^3*c*d)*((d*x^2 + c)^2*b - 2*(d*x^2 + c)*b*c + b*c^2 + (d*x^2 + c)*a*d - a*c*d)) - 1/2*(4*b*c + a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)*c)","A",0
766,1,375,0,4.747782," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, d^{\frac{7}{2}} {\left(\frac{3 \, {\left(5 \, b^{3} c - 6 \, a b^{2} d\right)} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{6 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} d - b^{3} c^{2}\right)}}{{\left(a^{3} b c d^{3} - a^{4} d^{4}\right)} {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}} - \frac{8 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + 3 \, b c^{2} + a c d\right)}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3} d^{3}}\right)}"," ",0,"1/6*d^(7/2)*(3*(5*b^3*c - 6*a*b^2*d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^3*b*c*d^3 - a^4*d^4)*sqrt(a*b*c*d - a^2*d^2)) - 6*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*d - b^3*c^2)/((a^3*b*c*d^3 - a^4*d^4)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)) - 8*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + 3*b*c^2 + a*c*d)/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3*d^3))","B",0
767,1,298,0,4.327105," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{3 \, a c \sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{c x}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{d x^{2} + c}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{3}{2}} - a b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)}}"," ",0,"3/2*a*c*sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b*c*d - a^2*d^2)) + c*x/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(d*x^2 + c)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(3/2) - a*b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2))","B",0
768,1,181,0,0.391052," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(2 \, b c d + a d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{2 \, {\left(d x^{2} + c\right)} b c d - 2 \, b c^{2} d + {\left(d x^{2} + c\right)} a d^{2} + 2 \, a c d^{2}}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left({\left(d x^{2} + c\right)}^{\frac{3}{2}} b - \sqrt{d x^{2} + c} b c + \sqrt{d x^{2} + c} a d\right)}}}{2 \, d}"," ",0,"1/2*((2*b*c*d + a*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b^2*c + a*b*d)) + (2*(d*x^2 + c)*b*c*d - 2*b*c^2*d + (d*x^2 + c)*a*d^2 + 2*a*c*d^2)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*((d*x^2 + c)^(3/2)*b - sqrt(d*x^2 + c)*b*c + sqrt(d*x^2 + c)*a*d)))/d","A",0
769,1,299,0,4.449640," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{d x}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{d x^{2} + c}} - \frac{{\left(b c \sqrt{d} + 2 \, a d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d^{\frac{3}{2}} - b c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"-d*x/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(d*x^2 + c)) - 1/2*(b*c*sqrt(d) + 2*a*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b*c*d - a^2*d^2)) + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d^(3/2) - b*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2))","B",0
770,1,153,0,0.391604," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b^{2} c + a b d}} - \frac{3 \, {\left(d x^{2} + c\right)} b d - 2 \, b c d + 2 \, a d^{2}}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left({\left(d x^{2} + c\right)}^{\frac{3}{2}} b - \sqrt{d x^{2} + c} b c + \sqrt{d x^{2} + c} a d\right)}}"," ",0,"-3/2*b*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b^2*c + a*b*d)) - 1/2*(3*(d*x^2 + c)*b*d - 2*b*c*d + 2*a*d^2)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*((d*x^2 + c)^(3/2)*b - sqrt(d*x^2 + c)*b*c + sqrt(d*x^2 + c)*a*d))","A",0
771,1,318,0,4.531527," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{d^{2} x}{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{d x^{2} + c}} - \frac{{\left(b^{2} c \sqrt{d} - 4 \, a b d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b d^{\frac{3}{2}} - b^{2} c^{2} \sqrt{d}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}}"," ",0,"d^2*x/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(d*x^2 + c)) - 1/2*(b^2*c*sqrt(d) - 4*a*b*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*d^(3/2) - b^2*c^2*sqrt(d))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2))","B",0
772,1,225,0,0.347820," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{{\left(2 \, b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-b^{2} c + a b d}} + \frac{{\left(d x^{2} + c\right)} b^{2} c d + 2 \, {\left(d x^{2} + c\right)} a b d^{2} - 2 \, a b c d^{2} + 2 \, a^{2} d^{3}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} {\left({\left(d x^{2} + c\right)}^{\frac{3}{2}} b - \sqrt{d x^{2} + c} b c + \sqrt{d x^{2} + c} a d\right)}} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c}"," ",0,"-1/2*(2*b^3*c - 5*a*b^2*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b^2*c + a*b*d)) + 1/2*((d*x^2 + c)*b^2*c*d + 2*(d*x^2 + c)*a*b*d^2 - 2*a*b*c*d^2 + 2*a^2*d^3)/((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*((d*x^2 + c)^(3/2)*b - sqrt(d*x^2 + c)*b*c + sqrt(d*x^2 + c)*a*d)) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)*c)","A",0
773,1,554,0,4.766226," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","-\frac{d^{3} x}{{\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{d x^{2} + c}} + \frac{3 \, {\left(b^{3} c \sqrt{d} - 2 \, a b^{2} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{3} c^{2} \sqrt{d} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b^{2} c d^{\frac{3}{2}} + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} b d^{\frac{5}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c^{3} \sqrt{d} + 18 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{2} d^{\frac{3}{2}} - 20 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c d^{\frac{5}{2}} + 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} d^{\frac{7}{2}} + 3 \, b^{3} c^{4} \sqrt{d} - 4 \, a b^{2} c^{3} d^{\frac{3}{2}} + 2 \, a^{2} b c^{2} d^{\frac{5}{2}}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d - b c^{3}\right)} {\left(a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)}}"," ",0,"-d^3*x/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(d*x^2 + c)) + 3/2*(b^3*c*sqrt(d) - 2*a*b^2*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(a*b*c*d - a^2*d^2)) + (3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^3*c^2*sqrt(d) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b^2*c*d^(3/2) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*b*d^(5/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c^3*sqrt(d) + 18*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^2*d^(3/2) - 20*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c*d^(5/2) + 8*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*d^(7/2) + 3*b^3*c^4*sqrt(d) - 4*a*b^2*c^3*d^(3/2) + 2*a^2*b*c^2*d^(5/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^6*b - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2 - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d - b*c^3)*(a^2*b^2*c^3 - 2*a^3*b*c^2*d + a^4*c*d^2))","B",0
774,1,367,0,0.363375," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{{\left(4 \, b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(d x^{2} + c\right)}^{2} b^{3} c^{2} d - 2 \, {\left(d x^{2} + c\right)} b^{3} c^{3} d - 2 \, {\left(d x^{2} + c\right)}^{2} a b^{2} c d^{2} + 3 \, {\left(d x^{2} + c\right)} a b^{2} c^{2} d^{2} + 3 \, {\left(d x^{2} + c\right)}^{2} a^{2} b d^{3} - 7 \, {\left(d x^{2} + c\right)} a^{2} b c d^{3} + 2 \, a^{2} b c^{2} d^{3} + 3 \, {\left(d x^{2} + c\right)} a^{3} d^{4} - 2 \, a^{3} c d^{4}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} {\left({\left(d x^{2} + c\right)}^{\frac{5}{2}} b - 2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b c + \sqrt{d x^{2} + c} b c^{2} + {\left(d x^{2} + c\right)}^{\frac{3}{2}} a d - \sqrt{d x^{2} + c} a c d\right)}} - \frac{{\left(4 \, b c + 3 \, a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c} c^{2}}"," ",0,"1/2*(4*b^4*c - 7*a*b^3*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*sqrt(-b^2*c + a*b*d)) - 1/2*(2*(d*x^2 + c)^2*b^3*c^2*d - 2*(d*x^2 + c)*b^3*c^3*d - 2*(d*x^2 + c)^2*a*b^2*c*d^2 + 3*(d*x^2 + c)*a*b^2*c^2*d^2 + 3*(d*x^2 + c)^2*a^2*b*d^3 - 7*(d*x^2 + c)*a^2*b*c*d^3 + 2*a^2*b*c^2*d^3 + 3*(d*x^2 + c)*a^3*d^4 - 2*a^3*c*d^4)/((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*((d*x^2 + c)^(5/2)*b - 2*(d*x^2 + c)^(3/2)*b*c + sqrt(d*x^2 + c)*b*c^2 + (d*x^2 + c)^(3/2)*a*d - sqrt(d*x^2 + c)*a*c*d)) - 1/2*(4*b*c + 3*a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)*c^2)","A",0
775,1,486,0,5.810029," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{d^{4} x}{{\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} \sqrt{d x^{2} + c}} - \frac{{\left(5 \, b^{4} c \sqrt{d} - 8 \, a b^{3} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{4} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{3} d^{\frac{3}{2}} - b^{4} c^{2} \sqrt{d}}{{\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}} - \frac{2 \, {\left(6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} - 12 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d^{\frac{3}{2}} + 6 \, b c^{3} \sqrt{d} + 5 \, a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3} c^{2}}"," ",0,"d^4*x/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*sqrt(d*x^2 + c)) - 1/2*(5*b^4*c*sqrt(d) - 8*a*b^3*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*sqrt(a*b*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^4*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^3*d^(3/2) - b^4*c^2*sqrt(d))/((a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)) - 2/3*(6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) - 12*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d^(3/2) + 6*b*c^3*sqrt(d) + 5*a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3*c^2)","A",0
776,1,594,0,4.489335," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, {\left(b^{4} c^{5} d^{2} - a b^{3} c^{4} d^{3} - 3 \, a^{2} b^{2} c^{3} d^{4} + 5 \, a^{3} b c^{2} d^{5} - 2 \, a^{4} c d^{6}\right)} x^{2}}{b^{6} c^{7} d - 6 \, a b^{5} c^{6} d^{2} + 15 \, a^{2} b^{4} c^{5} d^{3} - 20 \, a^{3} b^{3} c^{4} d^{4} + 15 \, a^{4} b^{2} c^{3} d^{5} - 6 \, a^{5} b c^{2} d^{6} + a^{6} c d^{7}} + \frac{3 \, {\left(b^{4} c^{6} d - 2 \, a b^{3} c^{5} d^{2} + 2 \, a^{3} b c^{3} d^{4} - a^{4} c^{2} d^{5}\right)}}{b^{6} c^{7} d - 6 \, a b^{5} c^{6} d^{2} + 15 \, a^{2} b^{4} c^{5} d^{3} - 20 \, a^{3} b^{3} c^{4} d^{4} + 15 \, a^{4} b^{2} c^{3} d^{5} - 6 \, a^{5} b c^{2} d^{6} + a^{6} c d^{7}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{{\left(3 \, a b c \sqrt{d} + 2 \, a^{2} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{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)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} d^{\frac{3}{2}} - a b c^{2} \sqrt{d}}{{\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({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}}"," ",0,"1/3*(2*(b^4*c^5*d^2 - a*b^3*c^4*d^3 - 3*a^2*b^2*c^3*d^4 + 5*a^3*b*c^2*d^5 - 2*a^4*c*d^6)*x^2/(b^6*c^7*d - 6*a*b^5*c^6*d^2 + 15*a^2*b^4*c^5*d^3 - 20*a^3*b^3*c^4*d^4 + 15*a^4*b^2*c^3*d^5 - 6*a^5*b*c^2*d^6 + a^6*c*d^7) + 3*(b^4*c^6*d - 2*a*b^3*c^5*d^2 + 2*a^3*b*c^3*d^4 - a^4*c^2*d^5)/(b^6*c^7*d - 6*a*b^5*c^6*d^2 + 15*a^2*b^4*c^5*d^3 - 20*a^3*b^3*c^4*d^4 + 15*a^4*b^2*c^3*d^5 - 6*a^5*b*c^2*d^6 + a^6*c*d^7))*x/(d*x^2 + c)^(3/2) + 1/2*(3*a*b*c*sqrt(d) + 2*a^2*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((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*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*d^(3/2) - a*b*c^2*sqrt(d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2))","B",0
777,1,260,0,0.363727," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{d x^{2} + c} a b d^{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)} {\left({\left(d x^{2} + c\right)} b - b c + a d\right)}} + \frac{3 \, {\left(2 \, b^{2} c d + 3 \, a b d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{{\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^{2} c + a b d}} + \frac{2 \, {\left(3 \, {\left(d x^{2} + c\right)} b c d + b c^{2} d + 3 \, {\left(d x^{2} + c\right)} a d^{2} - a c d^{2}\right)}}{{\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(d x^{2} + c\right)}^{\frac{3}{2}}}}{6 \, d}"," ",0,"1/6*(3*sqrt(d*x^2 + c)*a*b*d^2/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*((d*x^2 + c)*b - b*c + a*d)) + 3*(2*b^2*c*d + 3*a*b*d^2)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b^2*c + a*b*d)) + 2*(3*(d*x^2 + c)*b*c*d + b*c^2*d + 3*(d*x^2 + c)*a*d^2 - a*c*d^2)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(d*x^2 + c)^(3/2)))/d","A",0
778,1,595,0,4.518342," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{{\left(\frac{{\left(5 \, b^{4} c^{4} d^{3} - 14 \, a b^{3} c^{3} d^{4} + 12 \, a^{2} b^{2} c^{2} d^{5} - 2 \, a^{3} b c d^{6} - a^{4} d^{7}\right)} x^{2}}{b^{6} c^{7} d - 6 \, a b^{5} c^{6} d^{2} + 15 \, a^{2} b^{4} c^{5} d^{3} - 20 \, a^{3} b^{3} c^{4} d^{4} + 15 \, a^{4} b^{2} c^{3} d^{5} - 6 \, a^{5} b c^{2} d^{6} + a^{6} c d^{7}} + \frac{6 \, {\left(b^{4} c^{5} d^{2} - 3 \, a b^{3} c^{4} d^{3} + 3 \, a^{2} b^{2} c^{3} d^{4} - a^{3} b c^{2} d^{5}\right)}}{b^{6} c^{7} d - 6 \, a b^{5} c^{6} d^{2} + 15 \, a^{2} b^{4} c^{5} d^{3} - 20 \, a^{3} b^{3} c^{4} d^{4} + 15 \, a^{4} b^{2} c^{3} d^{5} - 6 \, a^{5} b c^{2} d^{6} + a^{6} c d^{7}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{{\left(b^{2} c \sqrt{d} + 4 \, a b d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{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)} \sqrt{a b c d - a^{2} d^{2}}} + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{2} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b d^{\frac{3}{2}} - b^{2} c^{2} \sqrt{d}}{{\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({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}}"," ",0,"-1/3*((5*b^4*c^4*d^3 - 14*a*b^3*c^3*d^4 + 12*a^2*b^2*c^2*d^5 - 2*a^3*b*c*d^6 - a^4*d^7)*x^2/(b^6*c^7*d - 6*a*b^5*c^6*d^2 + 15*a^2*b^4*c^5*d^3 - 20*a^3*b^3*c^4*d^4 + 15*a^4*b^2*c^3*d^5 - 6*a^5*b*c^2*d^6 + a^6*c*d^7) + 6*(b^4*c^5*d^2 - 3*a*b^3*c^4*d^3 + 3*a^2*b^2*c^3*d^4 - a^3*b*c^2*d^5)/(b^6*c^7*d - 6*a*b^5*c^6*d^2 + 15*a^2*b^4*c^5*d^3 - 20*a^3*b^3*c^4*d^4 + 15*a^4*b^2*c^3*d^5 - 6*a^5*b*c^2*d^6 + a^6*c*d^7))*x/(d*x^2 + c)^(3/2) - 1/2*(b^2*c*sqrt(d) + 4*a*b*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((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*c*d - a^2*d^2)) + ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^2*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b*d^(3/2) - b^2*c^2*sqrt(d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2))","B",0
779,1,226,0,0.564669," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{5 \, b^{2} d \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{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)} \sqrt{-b^{2} c + a b d}} - \frac{\sqrt{d x^{2} + c} b^{2} d}{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)} {\left({\left(d x^{2} + c\right)} b - b c + a d\right)}} - \frac{6 \, {\left(d x^{2} + c\right)} b d + b c d - a d^{2}}{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)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"-5/2*b^2*d*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b^2*c + a*b*d)) - 1/2*sqrt(d*x^2 + c)*b^2*d/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*((d*x^2 + c)*b - b*c + a*d)) - 1/3*(6*(d*x^2 + c)*b*d + b*c*d - a*d^2)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(d*x^2 + c)^(3/2))","A",0
780,1,619,0,4.906854," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, {\left(4 \, b^{4} c^{4} d^{4} - 13 \, a b^{3} c^{3} d^{5} + 15 \, a^{2} b^{2} c^{2} d^{6} - 7 \, a^{3} b c d^{7} + a^{4} d^{8}\right)} x^{2}}{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}} + \frac{3 \, {\left(3 \, b^{4} c^{5} d^{3} - 10 \, a b^{3} c^{4} d^{4} + 12 \, a^{2} b^{2} c^{3} d^{5} - 6 \, a^{3} b c^{2} d^{6} + a^{4} c d^{7}\right)}}{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)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{{\left(b^{3} c \sqrt{d} - 6 \, a b^{2} d^{\frac{3}{2}}\right)} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\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{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} d^{\frac{3}{2}} - b^{3} c^{2} \sqrt{d}}{{\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({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}}"," ",0,"1/3*(2*(4*b^4*c^4*d^4 - 13*a*b^3*c^3*d^5 + 15*a^2*b^2*c^2*d^6 - 7*a^3*b*c*d^7 + a^4*d^8)*x^2/(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) + 3*(3*b^4*c^5*d^3 - 10*a*b^3*c^4*d^4 + 12*a^2*b^2*c^3*d^5 - 6*a^3*b*c^2*d^6 + a^4*c*d^7)/(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))*x/(d*x^2 + c)^(3/2) + 1/2*(b^3*c*sqrt(d) - 6*a*b^2*d^(3/2))*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^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)*sqrt(a*b*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*d^(3/2) - b^3*c^2*sqrt(d))/((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(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2))","B",0
781,1,298,0,0.422111," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{d x^{2} + c} b^{3} d}{2 \, {\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({\left(d x^{2} + c\right)} b - b c + a d\right)}} - \frac{{\left(2 \, b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\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} c + a b d}} + \frac{9 \, {\left(d x^{2} + c\right)} b c d^{2} + b c^{2} d^{2} - 3 \, {\left(d x^{2} + c\right)} a d^{3} - a c d^{3}}{3 \, {\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)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{a^{2} \sqrt{-c} c^{2}}"," ",0,"1/2*sqrt(d*x^2 + c)*b^3*d/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*((d*x^2 + c)*b - b*c + a*d)) - 1/2*(2*b^4*c - 7*a*b^3*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((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*c + a*b*d)) + 1/3*(9*(d*x^2 + c)*b*c*d^2 + b*c^2*d^2 - 3*(d*x^2 + c)*a*d^3 - a*c*d^3)/((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)*(d*x^2 + c)^(3/2)) + arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^2*sqrt(-c)*c^2)","A",0
782,1,938,0,5.335249," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","-\frac{{\left(\frac{{\left(11 \, b^{4} c^{6} d^{5} - 38 \, a b^{3} c^{5} d^{6} + 48 \, a^{2} b^{2} c^{4} d^{7} - 26 \, a^{3} b c^{3} d^{8} + 5 \, a^{4} c^{2} d^{9}\right)} x^{2}}{b^{6} c^{11} d - 6 \, a b^{5} c^{10} d^{2} + 15 \, a^{2} b^{4} c^{9} d^{3} - 20 \, a^{3} b^{3} c^{8} d^{4} + 15 \, a^{4} b^{2} c^{7} d^{5} - 6 \, a^{5} b c^{6} d^{6} + a^{6} c^{5} d^{7}} + \frac{6 \, {\left(2 \, b^{4} c^{7} d^{4} - 7 \, a b^{3} c^{6} d^{5} + 9 \, a^{2} b^{2} c^{5} d^{6} - 5 \, a^{3} b c^{4} d^{7} + a^{4} c^{3} d^{8}\right)}}{b^{6} c^{11} d - 6 \, a b^{5} c^{10} d^{2} + 15 \, a^{2} b^{4} c^{9} d^{3} - 20 \, a^{3} b^{3} c^{8} d^{4} + 15 \, a^{4} b^{2} c^{7} d^{5} - 6 \, a^{5} b c^{6} d^{6} + a^{6} c^{5} d^{7}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} + \frac{{\left(3 \, b^{4} c \sqrt{d} - 8 \, a b^{3} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\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{a b c d - a^{2} d^{2}}} + \frac{3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{4} c^{3} \sqrt{d} - 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b^{3} c^{2} d^{\frac{3}{2}} + 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} b^{2} c d^{\frac{5}{2}} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{3} b d^{\frac{7}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{4} c^{4} \sqrt{d} + 22 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{3} c^{3} d^{\frac{3}{2}} - 36 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b^{2} c^{2} d^{\frac{5}{2}} + 28 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} b c d^{\frac{7}{2}} - 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{4} d^{\frac{9}{2}} + 3 \, b^{4} c^{5} \sqrt{d} - 6 \, a b^{3} c^{4} d^{\frac{3}{2}} + 6 \, a^{2} b^{2} c^{3} d^{\frac{5}{2}} - 2 \, a^{3} b c^{2} d^{\frac{7}{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}\right)} {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b - 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d - b c^{3}\right)}}"," ",0,"-1/3*((11*b^4*c^6*d^5 - 38*a*b^3*c^5*d^6 + 48*a^2*b^2*c^4*d^7 - 26*a^3*b*c^3*d^8 + 5*a^4*c^2*d^9)*x^2/(b^6*c^11*d - 6*a*b^5*c^10*d^2 + 15*a^2*b^4*c^9*d^3 - 20*a^3*b^3*c^8*d^4 + 15*a^4*b^2*c^7*d^5 - 6*a^5*b*c^6*d^6 + a^6*c^5*d^7) + 6*(2*b^4*c^7*d^4 - 7*a*b^3*c^6*d^5 + 9*a^2*b^2*c^5*d^6 - 5*a^3*b*c^4*d^7 + a^4*c^3*d^8)/(b^6*c^11*d - 6*a*b^5*c^10*d^2 + 15*a^2*b^4*c^9*d^3 - 20*a^3*b^3*c^8*d^4 + 15*a^4*b^2*c^7*d^5 - 6*a^5*b*c^6*d^6 + a^6*c^5*d^7))*x/(d*x^2 + c)^(3/2) + 1/2*(3*b^4*c*sqrt(d) - 8*a*b^3*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((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(a*b*c*d - a^2*d^2)) + (3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^4*c^3*sqrt(d) - 8*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b^3*c^2*d^(3/2) + 6*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*b^2*c*d^(5/2) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^3*b*d^(7/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^4*c^4*sqrt(d) + 22*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^3*c^3*d^(3/2) - 36*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b^2*c^2*d^(5/2) + 28*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*b*c*d^(7/2) - 8*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^4*d^(9/2) + 3*b^4*c^5*sqrt(d) - 6*a*b^3*c^4*d^(3/2) + 6*a^2*b^2*c^3*d^(5/2) - 2*a^3*b*c^2*d^(7/2))/((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)*((sqrt(d)*x - sqrt(d*x^2 + c))^6*b - 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2 - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d - b*c^3))","B",0
783,1,505,0,0.424973," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(4 \, b^{5} c - 9 \, a b^{4} d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} b}{\sqrt{-b^{2} c + a b d}}\right)}{2 \, {\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}\right)} \sqrt{-b^{2} c + a b d}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{4} c^{3} d - 2 \, \sqrt{d x^{2} + c} b^{4} c^{4} d - 3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b^{3} c^{2} d^{2} + 4 \, \sqrt{d x^{2} + c} a b^{3} c^{3} d^{2} + 3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} b^{2} c d^{3} - 6 \, \sqrt{d x^{2} + c} a^{2} b^{2} c^{2} d^{3} - {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{3} b d^{4} + 4 \, \sqrt{d x^{2} + c} a^{3} b c d^{4} - \sqrt{d x^{2} + c} a^{4} d^{5}}{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}\right)} {\left({\left(d x^{2} + c\right)}^{2} b - 2 \, {\left(d x^{2} + c\right)} b c + b c^{2} + {\left(d x^{2} + c\right)} a d - a c d\right)}} - \frac{12 \, {\left(d x^{2} + c\right)} b c d^{3} + b c^{2} d^{3} - 6 \, {\left(d x^{2} + c\right)} a d^{4} - a c d^{4}}{3 \, {\left(b^{3} c^{6} - 3 \, a b^{2} c^{5} d + 3 \, a^{2} b c^{4} d^{2} - a^{3} c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{{\left(4 \, b c + 5 \, a d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c}}{\sqrt{-c}}\right)}{2 \, a^{3} \sqrt{-c} c^{3}}"," ",0,"1/2*(4*b^5*c - 9*a*b^4*d)*arctan(sqrt(d*x^2 + c)*b/sqrt(-b^2*c + a*b*d))/((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)*sqrt(-b^2*c + a*b*d)) - 1/2*(2*(d*x^2 + c)^(3/2)*b^4*c^3*d - 2*sqrt(d*x^2 + c)*b^4*c^4*d - 3*(d*x^2 + c)^(3/2)*a*b^3*c^2*d^2 + 4*sqrt(d*x^2 + c)*a*b^3*c^3*d^2 + 3*(d*x^2 + c)^(3/2)*a^2*b^2*c*d^3 - 6*sqrt(d*x^2 + c)*a^2*b^2*c^2*d^3 - (d*x^2 + c)^(3/2)*a^3*b*d^4 + 4*sqrt(d*x^2 + c)*a^3*b*c*d^4 - sqrt(d*x^2 + c)*a^4*d^5)/((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)*((d*x^2 + c)^2*b - 2*(d*x^2 + c)*b*c + b*c^2 + (d*x^2 + c)*a*d - a*c*d)) - 1/3*(12*(d*x^2 + c)*b*c*d^3 + b*c^2*d^3 - 6*(d*x^2 + c)*a*d^4 - a*c*d^4)/((b^3*c^6 - 3*a*b^2*c^5*d + 3*a^2*b*c^4*d^2 - a^3*c^3*d^3)*(d*x^2 + c)^(3/2)) - 1/2*(4*b*c + 5*a*d)*arctan(sqrt(d*x^2 + c)/sqrt(-c))/(a^3*sqrt(-c)*c^3)","A",0
784,1,789,0,6.410233," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, {\left(7 \, b^{4} c^{7} d^{6} - 25 \, a b^{3} c^{6} d^{7} + 33 \, a^{2} b^{2} c^{5} d^{8} - 19 \, a^{3} b c^{4} d^{9} + 4 \, a^{4} c^{3} d^{10}\right)} x^{2}}{b^{6} c^{13} d - 6 \, a b^{5} c^{12} d^{2} + 15 \, a^{2} b^{4} c^{11} d^{3} - 20 \, a^{3} b^{3} c^{10} d^{4} + 15 \, a^{4} b^{2} c^{9} d^{5} - 6 \, a^{5} b c^{8} d^{6} + a^{6} c^{7} d^{7}} + \frac{3 \, {\left(5 \, b^{4} c^{8} d^{5} - 18 \, a b^{3} c^{7} d^{6} + 24 \, a^{2} b^{2} c^{6} d^{7} - 14 \, a^{3} b c^{5} d^{8} + 3 \, a^{4} c^{4} d^{9}\right)}}{b^{6} c^{13} d - 6 \, a b^{5} c^{12} d^{2} + 15 \, a^{2} b^{4} c^{11} d^{3} - 20 \, a^{3} b^{3} c^{10} d^{4} + 15 \, a^{4} b^{2} c^{9} d^{5} - 6 \, a^{5} b c^{8} d^{6} + a^{6} c^{7} d^{7}}\right)} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}} - \frac{5 \, {\left(b^{5} c \sqrt{d} - 2 \, a b^{4} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{2 \, {\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}\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{5} c \sqrt{d} - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{4} d^{\frac{3}{2}} - b^{5} c^{2} \sqrt{d}}{{\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}\right)} {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}} - \frac{4 \, {\left(3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b c \sqrt{d} + 3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a d^{\frac{3}{2}} - 6 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c^{2} \sqrt{d} - 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a c d^{\frac{3}{2}} + 3 \, b c^{3} \sqrt{d} + 4 \, a c^{2} d^{\frac{3}{2}}\right)}}{3 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{3} a^{3} c^{3}}"," ",0,"1/3*(2*(7*b^4*c^7*d^6 - 25*a*b^3*c^6*d^7 + 33*a^2*b^2*c^5*d^8 - 19*a^3*b*c^4*d^9 + 4*a^4*c^3*d^10)*x^2/(b^6*c^13*d - 6*a*b^5*c^12*d^2 + 15*a^2*b^4*c^11*d^3 - 20*a^3*b^3*c^10*d^4 + 15*a^4*b^2*c^9*d^5 - 6*a^5*b*c^8*d^6 + a^6*c^7*d^7) + 3*(5*b^4*c^8*d^5 - 18*a*b^3*c^7*d^6 + 24*a^2*b^2*c^6*d^7 - 14*a^3*b*c^5*d^8 + 3*a^4*c^4*d^9)/(b^6*c^13*d - 6*a*b^5*c^12*d^2 + 15*a^2*b^4*c^11*d^3 - 20*a^3*b^3*c^10*d^4 + 15*a^4*b^2*c^9*d^5 - 6*a^5*b*c^8*d^6 + a^6*c^7*d^7))*x/(d*x^2 + c)^(3/2) - 5/2*(b^5*c*sqrt(d) - 2*a*b^4*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((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)*sqrt(a*b*c*d - a^2*d^2)) - ((sqrt(d)*x - sqrt(d*x^2 + c))^2*b^5*c*sqrt(d) - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^4*d^(3/2) - b^5*c^2*sqrt(d))/((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)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)) - 4/3*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b*c*sqrt(d) + 3*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*d^(3/2) - 6*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c^2*sqrt(d) - 9*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*c*d^(3/2) + 3*b*c^3*sqrt(d) + 4*a*c^2*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^3*a^3*c^3)","B",0
785,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int {\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)*(e*x)^(3/2), x)","F",0
786,0,0,0,0.000000," ","integrate((B*x^2+A)*(e*x)^(1/2)*(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int {\left(B x^{2} + A\right)} \sqrt{b x^{2} + a} \sqrt{e x}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)*sqrt(e*x), x)","F",0
787,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/sqrt(e*x), x)","F",0
788,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/(e*x)^(3/2), x)","F",0
789,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/(e*x)^(5/2), x)","F",0
790,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/(e*x)^(7/2), x)","F",0
791,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(9/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/x^(9/2), x)","F",0
792,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(11/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/x^(11/2), x)","F",0
793,0,0,0,0.000000," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^(13/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{b x^{2} + a}}{x^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(b*x^2 + a)/x^(13/2), x)","F",0
794,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""giac"")","\int {\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)*(e*x)^(3/2), x)","F",0
795,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)*(e*x)^(1/2),x, algorithm=""giac"")","\int {\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)*sqrt(e*x), x)","F",0
796,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)/sqrt(e*x), x)","F",0
797,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)/(e*x)^(3/2), x)","F",0
798,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)/(e*x)^(5/2), x)","F",0
799,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} {\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(b*x^2 + a)^(3/2)/(e*x)^(7/2), x)","F",0
800,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{5}{2}}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(5/2)/sqrt(b*x^2 + a), x)","F",0
801,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{3}{2}}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(3/2)/sqrt(b*x^2 + a), x)","F",0
802,0,0,0,0.000000," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{e x}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(e*x)/sqrt(b*x^2 + a), x)","F",0
803,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{b x^{2} + a} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(b*x^2 + a)*sqrt(e*x)), x)","F",0
804,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{b x^{2} + a} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(b*x^2 + a)*(e*x)^(3/2)), x)","F",0
805,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{b x^{2} + a} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(b*x^2 + a)*(e*x)^(5/2)), x)","F",0
806,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{\sqrt{b x^{2} + a} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/(sqrt(b*x^2 + a)*(e*x)^(7/2)), x)","F",0
807,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(7/2)/(b*x^2 + a)^(3/2), x)","F",0
808,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(5/2)/(b*x^2 + a)^(3/2), x)","F",0
809,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(3/2)/(b*x^2 + a)^(3/2), x)","F",0
810,0,0,0,0.000000," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(e*x)/(b*x^2 + a)^(3/2), x)","F",0
811,0,0,0,0.000000," ","integrate((B*x^2+A)/(b*x^2+a)^(3/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(3/2)*sqrt(e*x)), x)","F",0
812,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(3/2)*(e*x)^(3/2)), x)","F",0
813,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(3/2)*(e*x)^(5/2)), x)","F",0
814,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(7/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(3/2)*(e*x)^(7/2)), x)","F",0
815,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(7/2)/(b*x^2 + a)^(5/2), x)","F",0
816,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(5/2)/(b*x^2 + a)^(5/2), x)","F",0
817,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*(e*x)^(3/2)/(b*x^2 + a)^(5/2), x)","F",0
818,0,0,0,0.000000," ","integrate((B*x^2+A)*(e*x)^(1/2)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(B x^{2} + A\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)*sqrt(e*x)/(b*x^2 + a)^(5/2), x)","F",0
819,0,0,0,0.000000," ","integrate((B*x^2+A)/(b*x^2+a)^(5/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(5/2)*sqrt(e*x)), x)","F",0
820,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(3/2)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(5/2)*(e*x)^(3/2)), x)","F",0
821,0,0,0,0.000000," ","integrate((B*x^2+A)/(e*x)^(5/2)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{B x^{2} + A}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*x^2 + A)/((b*x^2 + a)^(5/2)*(e*x)^(5/2)), x)","F",0
822,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)*(e*x)^(3/2), x)","F",0
823,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(e*x)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} \sqrt{e x}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)*sqrt(e*x), x)","F",0
824,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/sqrt(e*x), x)","F",0
825,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/(e*x)^(3/2), x)","F",0
826,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/(e*x)^(5/2), x)","F",0
827,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/(e*x)^(7/2), x)","F",0
828,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{x^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/x^(9/2), x)","F",0
829,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(11/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{x^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/x^(11/2), x)","F",0
830,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(13/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{x^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/x^(13/2), x)","F",0
831,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^(15/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}{x^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(d*x^2 + c)/x^(15/2), x)","F",0
832,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*(e*x)^(5/2), x)","F",0
833,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*(e*x)^(3/2), x)","F",0
834,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)*(e*x)^(1/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*sqrt(e*x), x)","F",0
835,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)/sqrt(e*x), x)","F",0
836,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)/(e*x)^(3/2), x)","F",0
837,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)/(e*x)^(5/2), x)","F",0
838,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/(e*x)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(d*x^2 + c)^(3/2)/(e*x)^(7/2), x)","F",0
839,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{5}{2}}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(5/2)/sqrt(d*x^2 + c), x)","F",0
840,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{3}{2}}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(3/2)/sqrt(d*x^2 + c), x)","F",0
841,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{e x}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(e*x)/sqrt(d*x^2 + c), x)","F",0
842,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*sqrt(e*x)), x)","F",0
843,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(3/2)), x)","F",0
844,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(5/2)), x)","F",0
845,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(7/2)), x)","F",0
846,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(9/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(9/2)), x)","F",0
847,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(11/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(11/2)), x)","F",0
848,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(13/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{\sqrt{d x^{2} + c} \left(e x\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/(sqrt(d*x^2 + c)*(e*x)^(13/2)), x)","F",0
849,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{7}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(7/2)/(d*x^2 + c)^(3/2), x)","F",0
850,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(5/2)/(d*x^2 + c)^(3/2), x)","F",0
851,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(3/2)/(d*x^2 + c)^(3/2), x)","F",0
852,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{e x}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(e*x)/(d*x^2 + c)^(3/2), x)","F",0
853,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(3/2)*sqrt(e*x)), x)","F",0
854,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(3/2)*(e*x)^(3/2)), x)","F",0
855,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(3/2)*(e*x)^(5/2)), x)","F",0
856,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(3/2)*(e*x)^(7/2)), x)","F",0
857,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{7}{2}}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(7/2)/(d*x^2 + c)^(5/2), x)","F",0
858,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(5/2)/(d*x^2 + c)^(5/2), x)","F",0
859,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \left(e x\right)^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*(e*x)^(3/2)/(d*x^2 + c)^(5/2), x)","F",0
860,0,0,0,0.000000," ","integrate((b*x^2+a)^2*(e*x)^(1/2)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2} \sqrt{e x}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2*sqrt(e*x)/(d*x^2 + c)^(5/2), x)","F",0
861,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(d*x^2+c)^(5/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(5/2)*sqrt(e*x)), x)","F",0
862,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(3/2)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(5/2)*(e*x)^(3/2)), x)","F",0
863,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(5/2)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(5/2)*(e*x)^(5/2)), x)","F",0
864,0,0,0,0.000000," ","integrate((b*x^2+a)^2/(e*x)^(7/2)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{2}}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^2/((d*x^2 + c)^(5/2)*(e*x)^(7/2)), x)","F",0
865,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{7}{2}}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)*(e*x)^(7/2)/(b*x^2 - a), x)","F",0
866,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{5}{2}}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)*(e*x)^(5/2)/(b*x^2 - a), x)","F",0
867,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{3}{2}}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)*(e*x)^(3/2)/(b*x^2 - a), x)","F",0
868,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c} \sqrt{e x}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)*sqrt(e*x)/(b*x^2 - a), x)","F",0
869,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2+a)/(e*x)^(1/2),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)} \sqrt{e x}}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)/((b*x^2 - a)*sqrt(e*x)), x)","F",0
870,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)/((b*x^2 - a)*(e*x)^(3/2)), x)","F",0
871,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)/((b*x^2 - a)*(e*x)^(5/2)), x)","F",0
872,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(7/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-sqrt(-d*x^2 + c)/((b*x^2 - a)*(e*x)^(7/2)), x)","F",0
873,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)*(e*x)^(5/2)/(b*x^2 - a), x)","F",0
874,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)*(e*x)^(3/2)/(b*x^2 - a), x)","F",0
875,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)*(e*x)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}}{b x^{2} - a}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)*sqrt(e*x)/(b*x^2 - a), x)","F",0
876,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(-b*x^2+a)/(e*x)^(1/2),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} \sqrt{e x}}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)/((b*x^2 - a)*sqrt(e*x)), x)","F",0
877,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)/((b*x^2 - a)*(e*x)^(3/2)), x)","F",0
878,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(5/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)/((b*x^2 - a)*(e*x)^(5/2)), x)","F",0
879,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(7/2)/(-b*x^2+a),x, algorithm=""giac"")","\int -\frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-(-d*x^2 + c)^(3/2)/((b*x^2 - a)*(e*x)^(7/2)), x)","F",0
880,0,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(-(e*x)^(7/2)/((b*x^2 - a)*sqrt(-d*x^2 + c)), x)","F",0
881,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(-(e*x)^(5/2)/((b*x^2 - a)*sqrt(-d*x^2 + c)), x)","F",0
882,0,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(-(e*x)^(3/2)/((b*x^2 - a)*sqrt(-d*x^2 + c)), x)","F",0
883,0,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{\sqrt{e x}}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(-sqrt(e*x)/((b*x^2 - a)*sqrt(-d*x^2 + c)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)/(e*x)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c} \sqrt{e x}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*sqrt(-d*x^2 + c)*sqrt(e*x)), x)","F",0
885,0,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*sqrt(-d*x^2 + c)*(e*x)^(3/2)), x)","F",0
886,0,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*sqrt(-d*x^2 + c)*(e*x)^(5/2)), x)","F",0
887,0,0,0,0.000000," ","integrate(1/(e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} \sqrt{-d x^{2} + c} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*sqrt(-d*x^2 + c)*(e*x)^(7/2)), x)","F",0
888,0,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(e*x)^(9/2)/((b*x^2 - a)*(-d*x^2 + c)^(3/2)), x)","F",0
889,0,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(e*x)^(7/2)/((b*x^2 - a)*(-d*x^2 + c)^(3/2)), x)","F",0
890,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(e*x)^(5/2)/((b*x^2 - a)*(-d*x^2 + c)^(3/2)), x)","F",0
891,0,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{\left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-(e*x)^(3/2)/((b*x^2 - a)*(-d*x^2 + c)^(3/2)), x)","F",0
892,0,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{\sqrt{e x}}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-sqrt(e*x)/((b*x^2 - a)*(-d*x^2 + c)^(3/2)), x)","F",0
893,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)/(-d*x^2+c)^(3/2)/(e*x)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*(-d*x^2 + c)^(3/2)*sqrt(e*x)), x)","F",0
894,0,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*(-d*x^2 + c)^(3/2)*(e*x)^(3/2)), x)","F",0
895,0,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - a\right)} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - a)*(-d*x^2 + c)^(3/2)*(e*x)^(5/2)), x)","F",0
896,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)*(e*x)^(7/2)/(b*x^2 - a)^2, x)","F",0
897,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)*(e*x)^(5/2)/(b*x^2 - a)^2, x)","F",0
898,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)*(e*x)^(3/2)/(b*x^2 - a)^2, x)","F",0
899,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c} \sqrt{e x}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)*sqrt(e*x)/(b*x^2 - a)^2, x)","F",0
900,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)}^{2} \sqrt{e x}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/((b*x^2 - a)^2*sqrt(e*x)), x)","F",0
901,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)}^{2} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/((b*x^2 - a)^2*(e*x)^(3/2)), x)","F",0
902,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(e*x)^(5/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{{\left(b x^{2} - a\right)}^{2} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/((b*x^2 - a)^2*(e*x)^(5/2)), x)","F",0
903,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)*(e*x)^(7/2)/(b*x^2 - a)^2, x)","F",0
904,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)*(e*x)^(5/2)/(b*x^2 - a)^2, x)","F",0
905,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)*(e*x)^(3/2)/(b*x^2 - a)^2, x)","F",0
906,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(-d*x^2+c)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}}{{\left(b x^{2} - a\right)}^{2}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)*sqrt(e*x)/(b*x^2 - a)^2, x)","F",0
907,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(1/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2} \sqrt{e x}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)/((b*x^2 - a)^2*sqrt(e*x)), x)","F",0
908,0,0,0,0.000000," ","integrate((-d*x^2+c)^(3/2)/(e*x)^(3/2)/(-b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-d*x^2 + c)^(3/2)/((b*x^2 - a)^2*(e*x)^(3/2)), x)","F",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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,0,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate((e*x)^(9/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)","F",0
911,0,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate((e*x)^(7/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)","F",0
912,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate((e*x)^(5/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)","F",0
913,0,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate((e*x)^(3/2)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)","F",0
914,0,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x}}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(e*x)/((b*x^2 - a)^2*sqrt(-d*x^2 + c)), x)","F",0
915,0,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c} \sqrt{e x}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*sqrt(-d*x^2 + c)*sqrt(e*x)), x)","F",0
916,0,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} \sqrt{-d x^{2} + c} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*sqrt(-d*x^2 + c)*(e*x)^(3/2)), x)","F",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=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,0,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x)^(9/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)), x)","F",0
919,0,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x)^(7/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)), x)","F",0
920,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x)^(5/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)), x)","F",0
921,0,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x)^(3/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)), x)","F",0
922,0,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x)/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)), x)","F",0
923,0,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)*sqrt(e*x)), x)","F",0
924,0,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)*(e*x)^(3/2)), x)","F",0
925,0,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{3}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(3/2)*(e*x)^(5/2)), x)","F",0
926,0,0,0,0.000000," ","integrate((e*x)^(9/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x)^(9/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)), x)","F",0
927,0,0,0,0.000000," ","integrate((e*x)^(7/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x)^(7/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)), x)","F",0
928,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x)^(5/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)), x)","F",0
929,0,0,0,0.000000," ","integrate((e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x)^(3/2)/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)), x)","F",0
930,0,0,0,0.000000," ","integrate((e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x}}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x)/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)), x)","F",0
931,0,0,0,0.000000," ","integrate(1/(e*x)^(1/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}} \sqrt{e x}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)*sqrt(e*x)), x)","F",0
932,0,0,0,0.000000," ","integrate(1/(e*x)^(3/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)*(e*x)^(3/2)), x)","F",0
933,0,0,0,0.000000," ","integrate(1/(e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{2} {\left(-d x^{2} + c\right)}^{\frac{5}{2}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^2*(-d*x^2 + c)^(5/2)*(e*x)^(5/2)), x)","F",0
934,1,226,0,0.479797," ","integrate(x^5*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(\frac{4 \, {\left(b x^{2} + a\right)}}{b^{3} d} - \frac{5 \, b^{7} c d^{3} + 7 \, a b^{6} d^{4}}{b^{9} d^{5}}\right)} + \frac{3 \, {\left(5 \, b^{8} c^{2} d^{2} + 2 \, a b^{7} c d^{3} + a^{2} b^{6} d^{4}\right)}}{b^{9} d^{5}}\right)} + \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b^{2} d^{3}}\right)} b}{48 \, {\left| b \right|}}"," ",0,"1/48*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)/(b^3*d) - (5*b^7*c*d^3 + 7*a*b^6*d^4)/(b^9*d^5)) + 3*(5*b^8*c^2*d^2 + 2*a*b^7*c*d^3 + a^2*b^6*d^4)/(b^9*d^5)) + 3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b^2*d^3))*b/abs(b)","A",0
935,1,159,0,0.564057," ","integrate(x^3*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(\frac{2 \, {\left(b x^{2} + a\right)}}{b^{2} d} - \frac{3 \, b^{3} c d + a b^{2} d^{2}}{b^{4} d^{3}}\right)} - \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b d^{2}}\right)} b}{8 \, {\left| b \right|}}"," ",0,"1/8*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)/(b^2*d) - (3*b^3*c*d + a*b^2*d^2)/(b^4*d^3)) - (3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b*d^2))*b/abs(b)","A",0
936,1,106,0,0.549881," ","integrate(x*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b {\left(\frac{{\left(b c - a d\right)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} d} + \frac{\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a}}{b d}\right)}}{2 \, {\left| b \right|}}"," ",0,"1/2*b*((b*c - a*d)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)/(b*d))/abs(b)","A",0
937,-2,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
938,1,434,0,2.102049," ","integrate((b*x^2+a)^(1/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{b {\left(\frac{{\left(\sqrt{b d} b^{2} c - \sqrt{b d} a b d\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} b c} + \frac{2 \, {\left(\sqrt{b d} b^{4} c^{2} - 2 \, \sqrt{b d} a b^{3} c d + \sqrt{b d} a^{2} b^{2} d^{2} - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)} c}\right)}}{2 \, {\left| b \right|}}"," ",0,"-1/2*b*((sqrt(b*d)*b^2*c - sqrt(b*d)*a*b*d)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*b*c) + 2*(sqrt(b*d)*b^4*c^2 - 2*sqrt(b*d)*a*b^3*c*d + sqrt(b*d)*a^2*b^2*d^2 - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)*c))/abs(b)","B",0
939,1,1107,0,2.273563," ","integrate((b*x^2+a)^(1/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b {\left(\frac{{\left(\sqrt{b d} b^{3} c^{2} + 2 \, \sqrt{b d} a b^{2} c d - 3 \, \sqrt{b d} a^{2} b d^{2}\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} a b c^{2}} - \frac{2 \, {\left(\sqrt{b d} b^{9} c^{5} - 7 \, \sqrt{b d} a b^{8} c^{4} d + 18 \, \sqrt{b d} a^{2} b^{7} c^{3} d^{2} - 22 \, \sqrt{b d} a^{3} b^{6} c^{2} d^{3} + 13 \, \sqrt{b d} a^{4} b^{5} c d^{4} - 3 \, \sqrt{b d} a^{5} b^{4} d^{5} - 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{7} c^{4} + 16 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{6} c^{3} d - 14 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{5} c^{2} d^{2} - 8 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b^{4} c d^{3} + 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{4} b^{3} d^{4} + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{5} c^{3} - 7 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{4} c^{2} d - 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{3} c d^{2} - 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{3} b^{2} d^{3} - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{3} c^{2} - 2 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a b^{2} c d + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{2} b d^{2}\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)}^{2} a c^{2}}\right)}}{8 \, {\left| b \right|}}"," ",0,"1/8*b*((sqrt(b*d)*b^3*c^2 + 2*sqrt(b*d)*a*b^2*c*d - 3*sqrt(b*d)*a^2*b*d^2)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*a*b*c^2) - 2*(sqrt(b*d)*b^9*c^5 - 7*sqrt(b*d)*a*b^8*c^4*d + 18*sqrt(b*d)*a^2*b^7*c^3*d^2 - 22*sqrt(b*d)*a^3*b^6*c^2*d^3 + 13*sqrt(b*d)*a^4*b^5*c*d^4 - 3*sqrt(b*d)*a^5*b^4*d^5 - 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^7*c^4 + 16*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^6*c^3*d - 14*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^5*c^2*d^2 - 8*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b^4*c*d^3 + 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^4*b^3*d^4 + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^5*c^3 - 7*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^4*c^2*d - 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^3*c*d^2 - 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^3*b^2*d^3 - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^3*c^2 - 2*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a*b^2*c*d + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^2*b*d^2)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)^2*a*c^2))/abs(b)","B",0
940,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a} x^{4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*x^4/sqrt(d*x^2 + c), x)","F",0
941,0,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a} x^{2}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*x^2/sqrt(d*x^2 + c), x)","F",0
942,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(sqrt(d*x^2 + c)*x^2), x)","F",0
943,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(sqrt(d*x^2 + c)*x^4), x)","F",0
944,1,305,0,0.653590," ","integrate(x^5*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(4 \, {\left(b x^{2} + a\right)} {\left(\frac{6 \, {\left(b x^{2} + a\right)}}{b^{3} d} - \frac{7 \, b^{7} c d^{5} + 9 \, a b^{6} d^{6}}{b^{9} d^{7}}\right)} + \frac{35 \, b^{8} c^{2} d^{4} + 10 \, a b^{7} c d^{5} + 3 \, a^{2} b^{6} d^{6}}{b^{9} d^{7}}\right)} - \frac{3 \, {\left(35 \, b^{9} c^{3} d^{3} - 25 \, a b^{8} c^{2} d^{4} - 7 \, a^{2} b^{7} c d^{5} - 3 \, a^{3} b^{6} d^{6}\right)}}{b^{9} d^{7}}\right)} - \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b^{2} d^{4}}\right)} b}{384 \, {\left| b \right|}}"," ",0,"1/384*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)*(6*(b*x^2 + a)/(b^3*d) - (7*b^7*c*d^5 + 9*a*b^6*d^6)/(b^9*d^7)) + (35*b^8*c^2*d^4 + 10*a*b^7*c*d^5 + 3*a^2*b^6*d^6)/(b^9*d^7)) - 3*(35*b^9*c^3*d^3 - 25*a*b^8*c^2*d^4 - 7*a^2*b^7*c*d^5 - 3*a^3*b^6*d^6)/(b^9*d^7)) - 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)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b^2*d^4))*b/abs(b)","A",0
945,1,225,0,0.496860," ","integrate(x^3*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(\frac{4 \, {\left(b x^{2} + a\right)}}{b^{2} d} - \frac{5 \, b^{3} c d^{3} + a b^{2} d^{4}}{b^{4} d^{5}}\right)} + \frac{3 \, {\left(5 \, b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3} - a^{2} b^{2} d^{4}\right)}}{b^{4} d^{5}}\right)} + \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b d^{3}}\right)} b}{48 \, {\left| b \right|}}"," ",0,"1/48*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)/(b^2*d) - (5*b^3*c*d^3 + a*b^2*d^4)/(b^4*d^5)) + 3*(5*b^4*c^2*d^2 - 4*a*b^3*c*d^3 - a^2*b^2*d^4)/(b^4*d^5)) + 3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b*d^3))*b/abs(b)","A",0
946,1,149,0,0.515293," ","integrate(x*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(\frac{2 \, {\left(b x^{2} + a\right)}}{b d} - \frac{3 \, {\left(b c d - a d^{2}\right)}}{b d^{3}}\right)} - \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} d^{2}}\right)} b}{8 \, {\left| b \right|}}"," ",0,"1/8*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)/(b*d) - 3*(b*c*d - a*d^2)/(b*d^3)) - 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*d^2))*b/abs(b)","A",0
947,-2,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
948,1,498,0,0.754724," ","integrate((b*x^2+a)^(3/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(\frac{\sqrt{b d} b \log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{d} + \frac{{\left(3 \, \sqrt{b d} a b^{2} c - \sqrt{b d} a^{2} b d\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} b c} + \frac{2 \, {\left(\sqrt{b d} a b^{4} c^{2} - 2 \, \sqrt{b d} a^{2} b^{3} c d + \sqrt{b d} a^{3} b^{2} d^{2} - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{2} c - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b d\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)} c}\right)} b}{2 \, {\left| b \right|}}"," ",0,"-1/2*(sqrt(b*d)*b*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/d + (3*sqrt(b*d)*a*b^2*c - sqrt(b*d)*a^2*b*d)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*b*c) + 2*(sqrt(b*d)*a*b^4*c^2 - 2*sqrt(b*d)*a^2*b^3*c*d + sqrt(b*d)*a^3*b^2*d^2 - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^2*c - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)*c))*b/abs(b)","B",0
949,1,1101,0,2.288023," ","integrate((b*x^2+a)^(3/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{b {\left(\frac{3 \, {\left(\sqrt{b d} b^{3} c^{2} - 2 \, \sqrt{b d} a b^{2} c d + \sqrt{b d} a^{2} b d^{2}\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} b c^{2}} + \frac{2 \, {\left(5 \, \sqrt{b d} b^{9} c^{5} - 23 \, \sqrt{b d} a b^{8} c^{4} d + 42 \, \sqrt{b d} a^{2} b^{7} c^{3} d^{2} - 38 \, \sqrt{b d} a^{3} b^{6} c^{2} d^{3} + 17 \, \sqrt{b d} a^{4} b^{5} c d^{4} - 3 \, \sqrt{b d} a^{5} b^{4} d^{5} - 15 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{7} c^{4} + 28 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{6} c^{3} d - 2 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{5} c^{2} d^{2} - 20 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b^{4} c d^{3} + 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{4} b^{3} d^{4} + 15 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{5} c^{3} + \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{4} c^{2} d + 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{3} c d^{2} - 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{3} b^{2} d^{3} - 5 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{3} c^{2} - 6 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a b^{2} c d + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{2} b d^{2}\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)}^{2} c^{2}}\right)}}{8 \, {\left| b \right|}}"," ",0,"-1/8*b*(3*(sqrt(b*d)*b^3*c^2 - 2*sqrt(b*d)*a*b^2*c*d + sqrt(b*d)*a^2*b*d^2)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*b*c^2) + 2*(5*sqrt(b*d)*b^9*c^5 - 23*sqrt(b*d)*a*b^8*c^4*d + 42*sqrt(b*d)*a^2*b^7*c^3*d^2 - 38*sqrt(b*d)*a^3*b^6*c^2*d^3 + 17*sqrt(b*d)*a^4*b^5*c*d^4 - 3*sqrt(b*d)*a^5*b^4*d^5 - 15*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^7*c^4 + 28*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^6*c^3*d - 2*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^5*c^2*d^2 - 20*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b^4*c*d^3 + 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^4*b^3*d^4 + 15*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^5*c^3 + sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^4*c^2*d + 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^3*c*d^2 - 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^3*b^2*d^3 - 5*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^3*c^2 - 6*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a*b^2*c*d + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^2*b*d^2)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)^2*c^2))/abs(b)","B",0
950,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} x^{4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*x^4/sqrt(d*x^2 + c), x)","F",0
951,0,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} x^{2}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*x^2/sqrt(d*x^2 + c), x)","F",0
952,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(sqrt(d*x^2 + c)*x^2), x)","F",0
953,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(sqrt(d*x^2 + c)*x^4), x)","F",0
954,1,398,0,0.684051," ","integrate(x^5*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(4 \, {\left(b x^{2} + a\right)} {\left(6 \, {\left(b x^{2} + a\right)} {\left(\frac{8 \, {\left(b x^{2} + a\right)}}{b^{3} d} - \frac{9 \, b^{7} c d^{7} + 11 \, a b^{6} d^{8}}{b^{9} d^{9}}\right)} + \frac{63 \, b^{8} c^{2} d^{6} + 14 \, a b^{7} c d^{7} + 3 \, a^{2} b^{6} d^{8}}{b^{9} d^{9}}\right)} - \frac{5 \, {\left(63 \, b^{9} c^{3} d^{5} - 49 \, a b^{8} c^{2} d^{6} - 11 \, a^{2} b^{7} c d^{7} - 3 \, a^{3} b^{6} d^{8}\right)}}{b^{9} d^{9}}\right)} + \frac{15 \, {\left(63 \, b^{10} c^{4} d^{4} - 112 \, a b^{9} c^{3} d^{5} + 38 \, a^{2} b^{8} c^{2} d^{6} + 8 \, a^{3} b^{7} c d^{7} + 3 \, a^{4} b^{6} d^{8}\right)}}{b^{9} d^{9}}\right)} + \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b^{2} d^{5}}\right)} b}{3840 \, {\left| b \right|}}"," ",0,"1/3840*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)*(6*(b*x^2 + a)*(8*(b*x^2 + a)/(b^3*d) - (9*b^7*c*d^7 + 11*a*b^6*d^8)/(b^9*d^9)) + (63*b^8*c^2*d^6 + 14*a*b^7*c*d^7 + 3*a^2*b^6*d^8)/(b^9*d^9)) - 5*(63*b^9*c^3*d^5 - 49*a*b^8*c^2*d^6 - 11*a^2*b^7*c*d^7 - 3*a^3*b^6*d^8)/(b^9*d^9)) + 15*(63*b^10*c^4*d^4 - 112*a*b^9*c^3*d^5 + 38*a^2*b^8*c^2*d^6 + 8*a^3*b^7*c*d^7 + 3*a^4*b^6*d^8)/(b^9*d^9)) + 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)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b^2*d^5))*b/abs(b)","A",0
955,1,304,0,0.571115," ","integrate(x^3*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(4 \, {\left(b x^{2} + a\right)} {\left(\frac{6 \, {\left(b x^{2} + a\right)}}{b^{2} d} - \frac{7 \, b^{3} c d^{5} + a b^{2} d^{6}}{b^{4} d^{7}}\right)} + \frac{5 \, {\left(7 \, b^{4} c^{2} d^{4} - 6 \, a b^{3} c d^{5} - a^{2} b^{2} d^{6}\right)}}{b^{4} d^{7}}\right)} - \frac{15 \, {\left(7 \, b^{5} c^{3} d^{3} - 13 \, a b^{4} c^{2} d^{4} + 5 \, a^{2} b^{3} c d^{5} + a^{3} b^{2} d^{6}\right)}}{b^{4} d^{7}}\right)} - \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b d^{4}}\right)} b}{384 \, {\left| b \right|}}"," ",0,"1/384*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)*(6*(b*x^2 + a)/(b^2*d) - (7*b^3*c*d^5 + a*b^2*d^6)/(b^4*d^7)) + 5*(7*b^4*c^2*d^4 - 6*a*b^3*c*d^5 - a^2*b^2*d^6)/(b^4*d^7)) - 15*(7*b^5*c^3*d^3 - 13*a*b^4*c^2*d^4 + 5*a^2*b^3*c*d^5 + a^3*b^2*d^6)/(b^4*d^7)) - 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)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b*d^4))*b/abs(b)","A",0
956,1,210,0,0.496575," ","integrate(x*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(2 \, {\left(b x^{2} + a\right)} {\left(\frac{4 \, {\left(b x^{2} + a\right)}}{b d} - \frac{5 \, {\left(b c d^{3} - a d^{4}\right)}}{b d^{5}}\right)} + \frac{15 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)}}{b d^{5}}\right)} + \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)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} d^{3}}\right)} b}{48 \, {\left| b \right|}}"," ",0,"1/48*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)*(4*(b*x^2 + a)/(b*d) - 5*(b*c*d^3 - a*d^4)/(b*d^5)) + 15*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)/(b*d^5)) + 15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*d^3))*b/abs(b)","A",0
957,-2,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
958,1,558,0,0.867324," ","integrate((b*x^2+a)^(5/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b {\left(\frac{2 \, \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} b}{d} + \frac{{\left(\sqrt{b d} b^{2} c - 5 \, \sqrt{b d} a b d\right)} \log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{d^{2}} - \frac{2 \, {\left(5 \, \sqrt{b d} a^{2} b^{2} c - \sqrt{b d} a^{3} b d\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} b c} - \frac{4 \, {\left(\sqrt{b d} a^{2} b^{4} c^{2} - 2 \, \sqrt{b d} a^{3} b^{3} c d + \sqrt{b d} a^{4} b^{2} d^{2} - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{2} c - \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b d\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)} c}\right)}}{4 \, {\left| b \right|}}"," ",0,"1/4*b*(2*sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*b/d + (sqrt(b*d)*b^2*c - 5*sqrt(b*d)*a*b*d)*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/d^2 - 2*(5*sqrt(b*d)*a^2*b^2*c - sqrt(b*d)*a^3*b*d)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*b*c) - 4*(sqrt(b*d)*a^2*b^4*c^2 - 2*sqrt(b*d)*a^3*b^3*c*d + sqrt(b*d)*a^4*b^2*d^2 - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^2*c - sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)*c))/abs(b)","B",0
959,1,1175,0,1.178695," ","integrate((b*x^2+a)^(5/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{{\left(\frac{4 \, \sqrt{b d} b^{2} \log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{d} + \frac{{\left(15 \, \sqrt{b d} a b^{3} c^{2} - 10 \, \sqrt{b d} a^{2} b^{2} c d + 3 \, \sqrt{b d} a^{3} b d^{2}\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} b c^{2}} + \frac{2 \, {\left(9 \, \sqrt{b d} a b^{9} c^{5} - 39 \, \sqrt{b d} a^{2} b^{8} c^{4} d + 66 \, \sqrt{b d} a^{3} b^{7} c^{3} d^{2} - 54 \, \sqrt{b d} a^{4} b^{6} c^{2} d^{3} + 21 \, \sqrt{b d} a^{5} b^{5} c d^{4} - 3 \, \sqrt{b d} a^{6} b^{4} d^{5} - 27 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{7} c^{4} + 40 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{6} c^{3} d + 10 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b^{5} c^{2} d^{2} - 32 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{4} b^{4} c d^{3} + 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{5} b^{3} d^{4} + 27 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{5} c^{3} + 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{4} c^{2} d + 21 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{3} b^{3} c d^{2} - 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{4} b^{2} d^{3} - 9 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a b^{3} c^{2} - 10 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{2} b^{2} c d + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{3} b d^{2}\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)}^{2} c^{2}}\right)} b}{8 \, {\left| b \right|}}"," ",0,"-1/8*(4*sqrt(b*d)*b^2*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/d + (15*sqrt(b*d)*a*b^3*c^2 - 10*sqrt(b*d)*a^2*b^2*c*d + 3*sqrt(b*d)*a^3*b*d^2)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*b*c^2) + 2*(9*sqrt(b*d)*a*b^9*c^5 - 39*sqrt(b*d)*a^2*b^8*c^4*d + 66*sqrt(b*d)*a^3*b^7*c^3*d^2 - 54*sqrt(b*d)*a^4*b^6*c^2*d^3 + 21*sqrt(b*d)*a^5*b^5*c*d^4 - 3*sqrt(b*d)*a^6*b^4*d^5 - 27*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^7*c^4 + 40*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^6*c^3*d + 10*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b^5*c^2*d^2 - 32*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^4*b^4*c*d^3 + 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^5*b^3*d^4 + 27*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^5*c^3 + 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^4*c^2*d + 21*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^3*b^3*c*d^2 - 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^4*b^2*d^3 - 9*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a*b^3*c^2 - 10*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^2*b^2*c*d + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^3*b*d^2)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)^2*c^2))*b/abs(b)","B",0
960,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} x^{4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)*x^4/sqrt(d*x^2 + c), x)","F",0
961,0,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} x^{2}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)*x^2/sqrt(d*x^2 + c), x)","F",0
962,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(sqrt(d*x^2 + c)*x^2), x)","F",0
963,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x^4/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(sqrt(d*x^2 + c)*x^4), x)","F",0
964,0,0,0,0.000000," ","integrate(x^4*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{3 \, x^{2} - 1} x^{4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(3*x^2 - 1)*x^4/sqrt(-3*x^2 + 2), x)","F",0
965,1,40,0,0.380974," ","integrate(x^3*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{72} \, {\left(6 \, x^{2} + 5\right)} \sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} + \frac{7}{72} \, \arcsin\left(\sqrt{3 \, x^{2} - 1}\right)"," ",0,"-1/72*(6*x^2 + 5)*sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2) + 7/72*arcsin(sqrt(3*x^2 - 1))","A",0
966,0,0,0,0.000000," ","integrate(x^2*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{3 \, x^{2} - 1} x^{2}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(3*x^2 - 1)*x^2/sqrt(-3*x^2 + 2), x)","F",0
967,1,33,0,0.452295," ","integrate(x*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3 \, x^{2} - 1} \sqrt{-3 \, x^{2} + 2} + \frac{1}{6} \, \arcsin\left(\sqrt{3 \, x^{2} - 1}\right)"," ",0,"-1/6*sqrt(3*x^2 - 1)*sqrt(-3*x^2 + 2) + 1/6*arcsin(sqrt(3*x^2 - 1))","A",0
968,0,0,0,0.000000," ","integrate(x^2*(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + 2} x^{2}}{\sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + 2)*x^2/sqrt(d*x^2 + 3), x)","F",0
969,1,160,0,0.547254," ","integrate(x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{{\left(\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left(\frac{2 \, {\left(b x^{2} + a\right)}}{b^{3} d} - \frac{3 \, b^{6} c d + 5 \, a b^{5} d^{2}}{b^{8} d^{3}}\right)} - \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} b^{2} d^{2}}\right)} b}{8 \, {\left| b \right|}}"," ",0,"1/8*(sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*(2*(b*x^2 + a)/(b^3*d) - (3*b^6*c*d + 5*a*b^5*d^2)/(b^8*d^3)) - (3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*b^2*d^2))*b/abs(b)","A",0
970,1,104,0,0.396188," ","integrate(x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{{\left(b c + a d\right)} \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} d} + \frac{\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a}}{b d}}{2 \, {\left| b \right|}}"," ",0,"1/2*((b*c + a*d)*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)/(b*d))/abs(b)","A",0
971,1,54,0,0.415540," ","integrate(x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{b \log\left({\left| -\sqrt{b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} {\left| b \right|}}"," ",0,"-b*log(abs(-sqrt(b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)))/(sqrt(b*d)*abs(b))","A",0
972,1,89,0,0.428922," ","integrate(1/x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b d} b \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} {\left| b \right|}}"," ",0,"-sqrt(b*d)*b*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*abs(b))","B",0
973,1,413,0,0.482941," ","integrate(1/x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b d} b^{4} d {\left(\frac{{\left(b c + a d\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} a b^{3} c d} - \frac{2 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2} - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b c - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a d\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)} a b^{2} c d}\right)}}{2 \, {\left| b \right|}}"," ",0,"1/2*sqrt(b*d)*b^4*d*((b*c + a*d)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*a*b^3*c*d) - 2*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2 - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b*c - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)*a*b^2*c*d))/abs(b)","B",0
974,1,1015,0,1.971253," ","integrate(1/x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{b d} b^{6} d^{2} {\left(\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(-\frac{b^{2} c + a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}}{2 \, \sqrt{-a b c d} b}\right)}{\sqrt{-a b c d} a^{2} b^{5} c^{2} d^{2}} - \frac{2 \, {\left(3 \, b^{8} c^{5} - 9 \, a b^{7} c^{4} d + 6 \, a^{2} b^{6} c^{3} d^{2} + 6 \, a^{3} b^{5} c^{2} d^{3} - 9 \, a^{4} b^{4} c d^{4} + 3 \, a^{5} b^{3} d^{5} - 9 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{6} c^{4} - 4 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{5} c^{3} d + 26 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{4} c^{2} d^{2} - 4 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b^{3} c d^{3} - 9 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{4} b^{2} d^{4} + 9 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{4} c^{3} + 15 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{3} c^{2} d + 15 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{2} c d^{2} + 9 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{3} b d^{3} - 3 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{2} c^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a b c d - 3 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{2} d^{2}\right)}}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c - 2 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)}^{2} a^{2} b^{4} c^{2} d^{2}}\right)}}{8 \, {\left| b \right|}}"," ",0,"-1/8*sqrt(b*d)*b^6*d^2*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(-1/2*(b^2*c + a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(-a*b*c*d)*b))/(sqrt(-a*b*c*d)*a^2*b^5*c^2*d^2) - 2*(3*b^8*c^5 - 9*a*b^7*c^4*d + 6*a^2*b^6*c^3*d^2 + 6*a^3*b^5*c^2*d^3 - 9*a^4*b^4*c*d^4 + 3*a^5*b^3*d^5 - 9*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^6*c^4 - 4*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^5*c^3*d + 26*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^4*c^2*d^2 - 4*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b^3*c*d^3 - 9*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^4*b^2*d^4 + 9*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^4*c^3 + 15*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^3*c^2*d + 15*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^2*c*d^2 + 9*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^3*b*d^3 - 3*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^2*c^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a*b*c*d - 3*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^2*d^2)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c - 2*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)^2*a^2*b^4*c^2*d^2))/abs(b)","B",0
975,0,0,0,0.000000," ","integrate(x^6/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{6}}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^6/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
976,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^4/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
977,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^2/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
978,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x^2), x)","F",0
979,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)*x^4), x)","F",0
980,1,192,0,0.540358," ","integrate(x^5/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b d} a^{2}}{{\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)} b {\left| b \right|}} + \frac{\sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d} \sqrt{b x^{2} + a} {\left| b \right|}}{2 \, b^{4} d} + \frac{{\left(\sqrt{b d} b c + 3 \, \sqrt{b d} a d\right)} \log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{4 \, b^{2} d^{2} {\left| b \right|}}"," ",0,"-2*sqrt(b*d)*a^2/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)*b*abs(b)) + 1/2*sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d)*sqrt(b*x^2 + a)*abs(b)/(b^4*d) + 1/4*(sqrt(b*d)*b*c + 3*sqrt(b*d)*a*d)*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(b^2*d^2*abs(b))","A",0
981,1,135,0,0.479562," ","integrate(x^3/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{\frac{4 \, \sqrt{b d} a b}{{\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)} {\left| b \right|}} - \frac{\sqrt{b d} \log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{d {\left| b \right|}}}{2 \, b}"," ",0,"1/2*(4*sqrt(b*d)*a*b/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)*abs(b)) - sqrt(b*d)*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(d*abs(b)))/b","B",0
982,1,70,0,0.486162," ","integrate(x/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{b d} b}{{\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)} {\left| b \right|}}"," ",0,"-2*sqrt(b*d)*b/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)*abs(b))","B",0
983,1,333,0,0.861104," ","integrate(x^5/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}{2 \, \sqrt{b d} b {\left| b \right|}} + \frac{4 \, {\left(3 \, \sqrt{b d} a b^{4} c^{2} - 5 \, \sqrt{b d} a^{2} b^{3} c d + 2 \, \sqrt{b d} a^{3} b^{2} d^{2} - 6 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{2} c + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b d + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a\right)}}{3 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{3} b {\left| b \right|}}"," ",0,"-1/2*log((sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)/(sqrt(b*d)*b*abs(b)) + 4/3*(3*sqrt(b*d)*a*b^4*c^2 - 5*sqrt(b*d)*a^2*b^3*c*d + 2*sqrt(b*d)*a^3*b^2*d^2 - 6*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^2*c + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b*d + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a)/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^3*b*abs(b))","B",0
984,1,214,0,0.633296," ","integrate(x^3/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, \sqrt{b d} b^{5} c^{2} - 4 \, \sqrt{b d} a b^{4} c d + \sqrt{b d} a^{2} b^{3} d^{2} - 6 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{3} c + 3 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b\right)}}{3 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{3} b {\left| b \right|}}"," ",0,"-2/3*(3*sqrt(b*d)*b^5*c^2 - 4*sqrt(b*d)*a*b^4*c*d + sqrt(b*d)*a^2*b^3*d^2 - 6*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^3*c + 3*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b)/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^3*b*abs(b))","B",0
985,1,129,0,0.447336," ","integrate(x/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(b^{2} c - a b d - 3 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)} \sqrt{b d} b^{2} d}{3 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{3} {\left| b \right|}}"," ",0,"4/3*(b^2*c - a*b*d - 3*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)*sqrt(b*d)*b^2*d/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^3*abs(b))","B",0
986,1,597,0,0.873902," ","integrate(x^5/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, \sqrt{b d} b^{8} c^{4} - 40 \, \sqrt{b d} a b^{7} c^{3} d + 38 \, \sqrt{b d} a^{2} b^{6} c^{2} d^{2} - 16 \, \sqrt{b d} a^{3} b^{5} c d^{3} + 3 \, \sqrt{b d} a^{4} b^{4} d^{4} - 60 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{6} c^{3} + 80 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{5} c^{2} d - 20 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{4} c d^{2} + 90 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{4} c^{2} - 40 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{3} c d + 30 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{2} d^{2} - 60 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{2} c + 15 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{8}\right)}}{15 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{5} b {\left| b \right|}}"," ",0,"-2/15*(15*sqrt(b*d)*b^8*c^4 - 40*sqrt(b*d)*a*b^7*c^3*d + 38*sqrt(b*d)*a^2*b^6*c^2*d^2 - 16*sqrt(b*d)*a^3*b^5*c*d^3 + 3*sqrt(b*d)*a^4*b^4*d^4 - 60*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^6*c^3 + 80*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^5*c^2*d - 20*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^4*c*d^2 + 90*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^4*c^2 - 40*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^3*c*d + 30*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^2*d^2 - 60*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^2*c + 15*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^8)/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^5*b*abs(b))","B",0
987,1,472,0,0.914801," ","integrate(x^3/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(5 \, \sqrt{b d} b^{8} c^{3} d - 11 \, \sqrt{b d} a b^{7} c^{2} d^{2} + 7 \, \sqrt{b d} a^{2} b^{6} c d^{3} - \sqrt{b d} a^{3} b^{5} d^{4} - 25 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{6} c^{2} d + 30 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{5} c d^{2} - 5 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{4} d^{3} + 35 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{4} c d + 5 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{3} d^{2} - 15 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{2} d\right)}}{15 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{5} b {\left| b \right|}}"," ",0,"4/15*(5*sqrt(b*d)*b^8*c^3*d - 11*sqrt(b*d)*a*b^7*c^2*d^2 + 7*sqrt(b*d)*a^2*b^6*c*d^3 - sqrt(b*d)*a^3*b^5*d^4 - 25*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^6*c^2*d + 30*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^5*c*d^2 - 5*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^4*d^3 + 35*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^4*c*d + 5*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^3*d^2 - 15*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^2*d)/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^5*b*abs(b))","B",0
988,1,243,0,0.480001," ","integrate(x/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{16 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2} - 5 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{2} c + 5 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b d + 10 \, {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4}\right)} \sqrt{b d} b^{3} d^{2}}{15 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{5} {\left| b \right|}}"," ",0,"-16/15*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2 - 5*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^2*c + 5*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b*d + 10*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4)*sqrt(b*d)*b^3*d^2/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^5*abs(b))","B",0
989,1,1036,0,1.240313," ","integrate(x^5/(b*x^2+a)^(9/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(35 \, \sqrt{b d} b^{10} c^{5} d - 119 \, \sqrt{b d} a b^{9} c^{4} d^{2} + 150 \, \sqrt{b d} a^{2} b^{8} c^{3} d^{3} - 86 \, \sqrt{b d} a^{3} b^{7} c^{2} d^{4} + 23 \, \sqrt{b d} a^{4} b^{6} c d^{5} - 3 \, \sqrt{b d} a^{5} b^{5} d^{6} - 245 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} b^{8} c^{4} d + 588 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a b^{7} c^{3} d^{2} - 462 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{2} b^{6} c^{2} d^{3} + 140 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{3} b^{5} c d^{4} - 21 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2} a^{4} b^{4} d^{5} + 630 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} b^{6} c^{3} d - 714 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a b^{5} c^{2} d^{2} + 42 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{2} b^{4} c d^{3} + 42 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{4} a^{3} b^{3} d^{4} - 770 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} b^{4} c^{2} d + 140 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a b^{3} c d^{2} - 210 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{6} a^{2} b^{2} d^{3} + 455 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{8} b^{2} c d + 105 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{8} a b d^{2} - 105 \, \sqrt{b d} {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{10} d\right)}}{105 \, {\left(b^{2} c - a b d - {\left(\sqrt{b x^{2} + a} \sqrt{b d} - \sqrt{b^{2} c + {\left(b x^{2} + a\right)} b d - a b d}\right)}^{2}\right)}^{7} {\left| b \right|}}"," ",0,"4/105*(35*sqrt(b*d)*b^10*c^5*d - 119*sqrt(b*d)*a*b^9*c^4*d^2 + 150*sqrt(b*d)*a^2*b^8*c^3*d^3 - 86*sqrt(b*d)*a^3*b^7*c^2*d^4 + 23*sqrt(b*d)*a^4*b^6*c*d^5 - 3*sqrt(b*d)*a^5*b^5*d^6 - 245*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*b^8*c^4*d + 588*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a*b^7*c^3*d^2 - 462*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^2*b^6*c^2*d^3 + 140*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^3*b^5*c*d^4 - 21*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2*a^4*b^4*d^5 + 630*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*b^6*c^3*d - 714*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a*b^5*c^2*d^2 + 42*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^2*b^4*c*d^3 + 42*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^4*a^3*b^3*d^4 - 770*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*b^4*c^2*d + 140*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a*b^3*c*d^2 - 210*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^6*a^2*b^2*d^3 + 455*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^8*b^2*c*d + 105*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^8*a*b*d^2 - 105*sqrt(b*d)*(sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^10*d)/((b^2*c - a*b*d - (sqrt(b*x^2 + a)*sqrt(b*d) - sqrt(b^2*c + (b*x^2 + a)*b*d - a*b*d))^2)^7*abs(b))","B",0
990,1,57,0,0.425647," ","integrate(x/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -\sqrt{-b x^{2} + a} \sqrt{-b d} + \sqrt{b^{2} c + {\left(b x^{2} - a\right)} b d + a b d} \right|}\right)}{\sqrt{-b d} {\left| b \right|}}"," ",0,"b*log(abs(-sqrt(-b*x^2 + a)*sqrt(-b*d) + sqrt(b^2*c + (b*x^2 - a)*b*d + a*b*d)))/(sqrt(-b*d)*abs(b))","A",0
991,1,57,0,0.382128," ","integrate(x/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -\sqrt{-b x^{2} + a} \sqrt{b d} + \sqrt{b^{2} c - {\left(b x^{2} - a\right)} b d - a b d} \right|}\right)}{\sqrt{b d} {\left| b \right|}}"," ",0,"b*log(abs(-sqrt(-b*x^2 + a)*sqrt(b*d) + sqrt(b^2*c - (b*x^2 - a)*b*d - a*b*d)))/(sqrt(b*d)*abs(b))","A",0
992,0,0,0,0.000000," ","integrate(x^2/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(x^2/(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3)), x)","F",0
993,0,0,0,0.000000," ","integrate(x^2/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{d x^{2} + c} \sqrt{-x^{2} + 4}}\,{d x}"," ",0,"integrate(x^2/(sqrt(d*x^2 + c)*sqrt(-x^2 + 4)), x)","F",0
994,0,0,0,0.000000," ","integrate(x^2/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{d x^{2} + c} \sqrt{x^{2} + 4}}\,{d x}"," ",0,"integrate(x^2/(sqrt(d*x^2 + c)*sqrt(x^2 + 4)), x)","F",0
995,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
996,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)), x)","F",0
997,0,0,0,0.000000," ","integrate(x^2/(-x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 4}}\,{d x}"," ",0,"integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 4)), x)","F",0
998,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/2)/(-x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-x^2 + 4)*sqrt(-3*x^2 + 2)), x)","F",0
999,0,0,0,0.000000," ","integrate(x^2/(-4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-4 \, x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-4*x^2 + 1)), x)","F",0
1000,0,0,0,0.000000," ","integrate(x^2/(-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-3 \, x^{2} + 2} \sqrt{-4 \, x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-3*x^2 + 2)*sqrt(-4*x^2 + 1)), x)","F",0
1001,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(x^2 + 1)*sqrt(-3*x^2 + 2)), x)","F",0
1002,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/2)/(x^2+4)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)), x)","F",0
1003,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{4 \, x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(4*x^2 + 1)*sqrt(-3*x^2 + 2)), x)","F",0
1004,0,0,0,0.000000," ","integrate(x^2/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(x^2 + 1)), x)","F",0
1005,0,0,0,0.000000," ","integrate(x^2/(x^2+4)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 4}}\,{d x}"," ",0,"integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(x^2 + 4)), x)","F",0
1006,0,0,0,0.000000," ","integrate(x^2/(3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{4 \, x^{2} + 1} \sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(x^2/(sqrt(4*x^2 + 1)*sqrt(3*x^2 + 2)), x)","F",0
1007,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{2 \, x^{2} - 1} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2/(sqrt(2*x^2 - 1)*sqrt(-x^2 + 1)), x)","F",0
1008,1,108,0,0.423092," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\frac{9}{8} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{3}{10} \, {\left(-x^{2} + 1\right)}^{\frac{5}{3}} - \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) + \frac{3}{2} \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}"," ",0,"9/8*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 3/10*(-x^2 + 1)^(5/3) - 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)) + 3/2*(-x^2 + 1)^(2/3)","A",0
1009,1,97,0,0.511295," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","-\frac{3}{8} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{3}{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{3}{8} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{3}{4} \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}"," ",0,"-3/8*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 3/16*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 3/8*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) - 3/4*(-x^2 + 1)^(2/3)","A",0
1010,1,86,0,0.465390," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\frac{1}{8} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \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,"1/8*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*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
1011,1,149,0,0.411191," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","-\frac{1}{24} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{48} \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}{24} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\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,"-1/24*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 1/48*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 1/24*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 1/6*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-x^2 + 1)^(1/3) + 1)) - 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
1012,1,100,0,0.370041," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\frac{1}{72} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{144} \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}{72} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{6 \, x^{2}}"," ",0,"1/72*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 1/144*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 1/72*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) - 1/6*(-x^2 + 1)^(2/3)/x^2","A",0
1013,1,177,0,0.452306," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","-\frac{1}{216} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{1}{432} \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}{216} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{27} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{2 \, {\left(-x^{2} + 1\right)}^{\frac{5}{3}} - 5 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{36 \, x^{4}} - \frac{1}{54} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{27} \, \log\left(-{\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"-1/216*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 1/432*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 1/216*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 1/27*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-x^2 + 1)^(1/3) + 1)) + 1/36*(2*(-x^2 + 1)^(5/3) - 5*(-x^2 + 1)^(2/3))/x^4 - 1/54*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) + 1/27*log(-(-x^2 + 1)^(1/3) + 1)","A",0
1014,0,0,0,0.000000," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^4/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
1015,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^2/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
1016,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
1017,0,0,0,0.000000," ","integrate(1/x^2/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)*x^2), x)","F",0
1018,0,0,0,0.000000," ","integrate(1/x^4/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)*x^4), x)","F",0
1019,1,126,0,0.480886," ","integrate(x^7/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\frac{99}{32} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{3}{10} \, {\left(-x^{2} + 1\right)}^{\frac{5}{3}} - \frac{99}{64} \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{99}{32} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{15}{4} \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + \frac{27 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{8 \, {\left(x^{2} + 3\right)}}"," ",0,"99/32*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 3/10*(-x^2 + 1)^(5/3) - 99/64*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 99/32*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 15/4*(-x^2 + 1)^(2/3) + 27/8*(-x^2 + 1)^(2/3)/(x^2 + 3)","A",0
1020,1,115,0,0.424927," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","-\frac{21}{32} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{21}{64} \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{21}{32} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{3}{4} \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} - \frac{9 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{8 \, {\left(x^{2} + 3\right)}}"," ",0,"-21/32*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 21/64*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 21/32*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) - 3/4*(-x^2 + 1)^(2/3) - 9/8*(-x^2 + 1)^(2/3)/(x^2 + 3)","A",0
1021,1,104,0,0.410546," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\frac{3}{32} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{3}{64} \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{3}{32} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{3 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{8 \, {\left(x^{2} + 3\right)}}"," ",0,"3/32*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 3/64*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 3/32*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 3/8*(-x^2 + 1)^(2/3)/(x^2 + 3)","A",0
1022,1,104,0,0.387620," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\frac{1}{96} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{192} \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}{96} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{8 \, {\left(x^{2} + 3\right)}}"," ",0,"1/96*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 1/192*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 1/96*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) - 1/8*(-x^2 + 1)^(2/3)/(x^2 + 3)","A",0
1023,1,167,0,0.546264," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","-\frac{5}{288} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{5}{576} \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{5}{288} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{18} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{24 \, {\left(x^{2} + 3\right)}} - \frac{1}{36} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{18} \, \log\left(-{\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"-5/288*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 5/576*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 5/288*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 1/18*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-x^2 + 1)^(1/3) + 1)) + 1/24*(-x^2 + 1)^(2/3)/(x^2 + 3) - 1/36*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) + 1/18*log(-(-x^2 + 1)^(1/3) + 1)","A",0
1024,1,190,0,0.419667," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\frac{1}{96} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{192} \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}{96} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{5 \, {\left(-x^{2} + 1\right)}^{\frac{5}{3}} - 17 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{72 \, {\left({\left(x^{2} - 1\right)}^{2} + 5 \, x^{2} - 1\right)}} + \frac{1}{108} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{54} \, \log\left(-{\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"1/96*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) - 1/192*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) + 1/96*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) - 1/54*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-x^2 + 1)^(1/3) + 1)) + 1/72*(5*(-x^2 + 1)^(5/3) - 17*(-x^2 + 1)^(2/3))/((x^2 - 1)^2 + 5*x^2 - 1) + 1/108*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) - 1/54*log(-(-x^2 + 1)^(1/3) + 1)","A",0
1025,1,181,0,0.451190," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","-\frac{13}{2592} \cdot 4^{\frac{2}{3}} \sqrt{3} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(4^{\frac{1}{3}} + 2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right)}\right) + \frac{13}{5184} \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{13}{2592} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{1}{3}} - {\left(-x^{2} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{54} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)}\right) + \frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{216 \, {\left(x^{2} + 3\right)}} - \frac{{\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{36 \, x^{4}} - \frac{1}{108} \, \log\left({\left(-x^{2} + 1\right)}^{\frac{2}{3}} + {\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{54} \, \log\left(-{\left(-x^{2} + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"-13/2592*4^(2/3)*sqrt(3)*arctan(1/12*4^(2/3)*sqrt(3)*(4^(1/3) + 2*(-x^2 + 1)^(1/3))) + 13/5184*4^(2/3)*log(4^(2/3) + 4^(1/3)*(-x^2 + 1)^(1/3) + (-x^2 + 1)^(2/3)) - 13/2592*4^(2/3)*log(4^(1/3) - (-x^2 + 1)^(1/3)) + 1/54*sqrt(3)*arctan(1/3*sqrt(3)*(2*(-x^2 + 1)^(1/3) + 1)) + 1/216*(-x^2 + 1)^(2/3)/(x^2 + 3) - 1/36*(-x^2 + 1)^(2/3)/x^4 - 1/108*log((-x^2 + 1)^(2/3) + (-x^2 + 1)^(1/3) + 1) + 1/54*log(-(-x^2 + 1)^(1/3) + 1)","A",0
1026,0,0,0,0.000000," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^4/((x^2 + 3)^2*(-x^2 + 1)^(1/3)), x)","F",0
1027,0,0,0,0.000000," ","integrate(x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(x^2/((x^2 + 3)^2*(-x^2 + 1)^(1/3)), x)","F",0
1028,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)), x)","F",0
1029,0,0,0,0.000000," ","integrate(1/x^2/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{2}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)*x^2), x)","F",0
1030,0,0,0,0.000000," ","integrate(1/x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{4}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)*x^4), x)","F",0
1031,1,160,0,0.446551," ","integrate(x^7/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\frac{2}{891} \, {\left(3 \, x^{2} - 2\right)}^{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} - \frac{16}{567} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{7}{4}} - \frac{32}{81} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{32}{81} \cdot 2^{\frac{1}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{16}{81} \cdot 2^{\frac{1}{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{16}{81} \cdot 2^{\frac{1}{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{56}{243} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}"," ",0,"2/891*(3*x^2 - 2)^2*(-3*x^2 + 2)^(3/4) - 16/567*(-3*x^2 + 2)^(7/4) - 32/81*2^(1/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 32/81*2^(1/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) + 16/81*2^(1/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 16/81*2^(1/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 56/243*(-3*x^2 + 2)^(3/4)","A",0
1032,1,140,0,0.519911," ","integrate(x^5/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{2}{189} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{7}{4}} - \frac{2}{27} \cdot 8^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{2}{27} \cdot 8^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{4}{27} \cdot 2^{\frac{1}{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{4}{27} \cdot 2^{\frac{1}{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{4}{27} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}"," ",0,"-2/189*(-3*x^2 + 2)^(7/4) - 2/27*8^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 2/27*8^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) + 4/27*2^(1/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 4/27*2^(1/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 4/27*(-3*x^2 + 2)^(3/4)","A",0
1033,1,129,0,0.432101," ","integrate(x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{2}{9} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{2}{9} \cdot 2^{\frac{1}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{9} \cdot 2^{\frac{1}{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}{9} \cdot 2^{\frac{1}{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} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}"," ",0,"-2/9*2^(1/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 2/9*2^(1/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) + 1/9*2^(1/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 1/9*2^(1/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 2/27*(-3*x^2 + 2)^(3/4)","A",0
1034,1,118,0,0.367224," ","integrate(x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{1}{6} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{6} \cdot 2^{\frac{1}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{12} \cdot 2^{\frac{1}{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}{12} \cdot 2^{\frac{1}{4}} \log\left(-2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{2} + \sqrt{-3 \, x^{2} + 2}\right)"," ",0,"-1/6*2^(1/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 1/6*2^(1/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) + 1/12*2^(1/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 1/12*2^(1/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2))","A",0
1035,1,216,0,0.420691," ","integrate(1/x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{1}{16} \cdot 4^{\frac{3}{8}} \sqrt{2} \arctan\left(\frac{1}{8} \cdot 4^{\frac{7}{8}} \sqrt{2} {\left(4^{\frac{1}{8}} \sqrt{2} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{16} \cdot 4^{\frac{3}{8}} \sqrt{2} \arctan\left(-\frac{1}{8} \cdot 4^{\frac{7}{8}} \sqrt{2} {\left(4^{\frac{1}{8}} \sqrt{2} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{32} \cdot 4^{\frac{3}{8}} \sqrt{2} \log\left(4^{\frac{1}{8}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{-3 \, x^{2} + 2} + 4^{\frac{1}{4}}\right) - \frac{1}{32} \cdot 4^{\frac{3}{8}} \sqrt{2} \log\left(-4^{\frac{1}{8}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{-3 \, x^{2} + 2} + 4^{\frac{1}{4}}\right) + \frac{1}{8} \cdot 4^{\frac{1}{8}} \sqrt{2} \arctan\left(\frac{1}{4} \cdot 4^{\frac{7}{8}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{1}{16} \cdot 4^{\frac{1}{8}} \sqrt{2} \log\left(-{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4^{\frac{1}{8}}\right) - \frac{1}{16} \cdot 4^{\frac{3}{8}} \log\left({\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4^{\frac{1}{8}}\right)"," ",0,"-1/16*4^(3/8)*sqrt(2)*arctan(1/8*4^(7/8)*sqrt(2)*(4^(1/8)*sqrt(2) + 2*(-3*x^2 + 2)^(1/4))) - 1/16*4^(3/8)*sqrt(2)*arctan(-1/8*4^(7/8)*sqrt(2)*(4^(1/8)*sqrt(2) - 2*(-3*x^2 + 2)^(1/4))) + 1/32*4^(3/8)*sqrt(2)*log(4^(1/8)*sqrt(2)*(-3*x^2 + 2)^(1/4) + sqrt(-3*x^2 + 2) + 4^(1/4)) - 1/32*4^(3/8)*sqrt(2)*log(-4^(1/8)*sqrt(2)*(-3*x^2 + 2)^(1/4) + sqrt(-3*x^2 + 2) + 4^(1/4)) + 1/8*4^(1/8)*sqrt(2)*arctan(1/4*4^(7/8)*(-3*x^2 + 2)^(1/4)) + 1/16*4^(1/8)*sqrt(2)*log(-(-3*x^2 + 2)^(1/4) + 4^(1/8)) - 1/16*4^(3/8)*log((-3*x^2 + 2)^(1/4) + 4^(1/8))","A",0
1036,1,192,0,0.586154," ","integrate(1/x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\frac{9}{64} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{9}{128} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{9}{128} \cdot 2^{\frac{3}{4}} \log\left(2^{\frac{1}{4}} - {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{3}{32} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{3}{32} \cdot 2^{\frac{1}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) + \frac{3}{64} \cdot 2^{\frac{1}{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{3}{64} \cdot 2^{\frac{1}{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{{\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}{16 \, x^{2}}"," ",0,"9/64*2^(3/4)*arctan(1/2*2^(3/4)*(-3*x^2 + 2)^(1/4)) - 9/128*2^(3/4)*log(2^(1/4) + (-3*x^2 + 2)^(1/4)) + 9/128*2^(3/4)*log(2^(1/4) - (-3*x^2 + 2)^(1/4)) - 3/32*2^(1/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 3/32*2^(1/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) + 3/64*2^(1/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 3/64*2^(1/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 1/16*(-3*x^2 + 2)^(3/4)/x^2","A",0
1037,0,0,0,0.000000," ","integrate(x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{4}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-x^4/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)), x)","F",0
1038,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)), x)","F",0
1039,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)), x)","F",0
1040,0,0,0,0.000000," ","integrate(1/x^2/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{2}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)*x^2), x)","F",0
1041,0,0,0,0.000000," ","integrate(1/x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{4}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)*x^4), x)","F",0
1042,1,75,0,0.307348," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\frac{2}{891} \, {\left(3 \, x^{2} - 1\right)}^{\frac{11}{4}} + \frac{8}{567} \, {\left(3 \, x^{2} - 1\right)}^{\frac{7}{4}} + \frac{14}{243} \, {\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2/891*(3*x^2 - 1)^(11/4) + 8/567*(3*x^2 - 1)^(7/4) + 14/243*(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(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1043,1,64,0,0.495221," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\frac{2}{189} \, {\left(3 \, x^{2} - 1\right)}^{\frac{7}{4}} + \frac{2}{27} \, {\left(3 \, x^{2} - 1\right)}^{\frac{3}{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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2/189*(3*x^2 - 1)^(7/4) + 2/27*(3*x^2 - 1)^(3/4) + 4/27*arctan((3*x^2 - 1)^(1/4)) - 2/27*log((3*x^2 - 1)^(1/4) + 1) + 2/27*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1044,1,53,0,0.481080," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\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(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1045,1,42,0,0.358530," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1046,1,155,0,0.356640," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{1}{8} \, \sqrt{2} \log\left(\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(-\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(3*x^2 - 1)^(1/4))) - 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(3*x^2 - 1)^(1/4))) + 1/8*sqrt(2)*log(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - 1/8*sqrt(2)*log(-sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) + 1/2*arctan((3*x^2 - 1)^(1/4)) - 1/4*log((3*x^2 - 1)^(1/4) + 1) + 1/4*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1047,1,169,0,0.502874," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","-\frac{9}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{9}{16} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) + \frac{9}{32} \, \sqrt{2} \log\left(\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) - \frac{9}{32} \, \sqrt{2} \log\left(-\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) - \frac{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}}}{4 \, x^{2}} + \frac{3}{4} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{3}{8} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{3}{8} \, \log\left({\left| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-9/16*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(3*x^2 - 1)^(1/4))) - 9/16*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(3*x^2 - 1)^(1/4))) + 9/32*sqrt(2)*log(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - 9/32*sqrt(2)*log(-sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - 1/4*(3*x^2 - 1)^(3/4)/x^2 + 3/4*arctan((3*x^2 - 1)^(1/4)) - 3/8*log((3*x^2 - 1)^(1/4) + 1) + 3/8*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1048,0,0,0,0.000000," ","integrate(x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^4/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F",0
1049,0,0,0,0.000000," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F",0
1050,0,0,0,0.000000," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F",0
1051,0,0,0,0.000000," ","integrate(1/x^2/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)*x^2), x)","F",0
1052,0,0,0,0.000000," ","integrate(1/x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)} x^{4}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)*x^4), x)","F",0
1053,0,0,0,0.000000," ","integrate(x^2/(3*x^2+2)^(3/4)/(3*x^2+4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} + 4\right)} {\left(3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 + 4)*(3*x^2 + 2)^(3/4)), x)","F",0
1054,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)), x)","F",0
1055,0,0,0,0.000000," ","integrate(x^2/(b*x^2+2)^(3/4)/(b*x^2+4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{2} + 4\right)} {\left(b x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + 4)*(b*x^2 + 2)^(3/4)), x)","F",0
1056,0,0,0,0.000000," ","integrate(x^2/(-b*x^2+2)^(3/4)/(-b*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(b x^{2} - 4\right)} {\left(-b x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((b*x^2 - 4)*(-b*x^2 + 2)^(3/4)), x)","F",0
1057,0,0,0,0.000000," ","integrate(x^2/(3*x^2+a)^(3/4)/(3*x^2+2*a),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(3 \, x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 + 2*a)*(3*x^2 + a)^(3/4)), x)","F",0
1058,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+a)^(3/4)/(-3*x^2+2*a),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} - 2 \, a\right)} {\left(-3 \, x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 - 2*a)*(-3*x^2 + a)^(3/4)), x)","F",0
1059,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)^(3/4)/(b*x^2+2*a),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{2} + 2 \, a\right)} {\left(b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + 2*a)*(b*x^2 + a)^(3/4)), x)","F",0
1060,0,0,0,0.000000," ","integrate(x^2/(-b*x^2+a)^(3/4)/(-b*x^2+2*a),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(b x^{2} - 2 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((b*x^2 - 2*a)*(-b*x^2 + a)^(3/4)), x)","F",0
1061,1,160,0,0.347309," ","integrate(x^7/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\frac{2}{729} \, {\left(3 \, x^{2} - 2\right)}^{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} - \frac{16}{81} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{16}{81} \cdot 2^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\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{16}{405} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{5}{4}} + \frac{56}{81} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}"," ",0,"2/729*(3*x^2 - 2)^2*(-3*x^2 + 2)^(1/4) - 16/81*2^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 16/81*2^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) - 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)) - 16/405*(-3*x^2 + 2)^(5/4) + 56/81*(-3*x^2 + 2)^(1/4)","A",0
1062,1,140,0,0.416320," ","integrate(x^5/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{4}{27} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{4}{27} \cdot 2^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\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} + 2\right)}^{\frac{5}{4}} + \frac{4}{9} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}"," ",0,"-4/27*2^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 4/27*2^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) - 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 + 2)^(5/4) + 4/9*(-3*x^2 + 2)^(1/4)","A",0
1063,1,129,0,0.456348," ","integrate(x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{1}{9} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{9} \cdot 2^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\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,"-1/9*2^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 1/9*2^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) - 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
1064,1,118,0,0.379251," ","integrate(x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{1}{12} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{24} \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}{24} \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)"," ",0,"-1/12*2^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 1/12*2^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) - 1/24*2^(3/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 1/24*2^(3/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2))","A",0
1065,1,210,0,0.504942," ","integrate(1/x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{1}{16} \cdot 4^{\frac{1}{8}} \sqrt{2} \arctan\left(\frac{1}{8} \cdot 4^{\frac{7}{8}} \sqrt{2} {\left(4^{\frac{1}{8}} \sqrt{2} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{16} \cdot 4^{\frac{1}{8}} \sqrt{2} \arctan\left(-\frac{1}{8} \cdot 4^{\frac{7}{8}} \sqrt{2} {\left(4^{\frac{1}{8}} \sqrt{2} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{32} \cdot 4^{\frac{1}{8}} \sqrt{2} \log\left(4^{\frac{1}{8}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{-3 \, x^{2} + 2} + 4^{\frac{1}{4}}\right) + \frac{1}{32} \cdot 4^{\frac{1}{8}} \sqrt{2} \log\left(-4^{\frac{1}{8}} \sqrt{2} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + \sqrt{-3 \, x^{2} + 2} + 4^{\frac{1}{4}}\right) - \frac{1}{8} \cdot 4^{\frac{1}{8}} \arctan\left(\frac{1}{4} \cdot 4^{\frac{7}{8}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{1}{16} \cdot 4^{\frac{1}{8}} \log\left({\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4^{\frac{1}{8}}\right) + \frac{1}{16} \cdot 4^{\frac{1}{8}} \log\left(-{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} + 4^{\frac{1}{8}}\right)"," ",0,"-1/16*4^(1/8)*sqrt(2)*arctan(1/8*4^(7/8)*sqrt(2)*(4^(1/8)*sqrt(2) + 2*(-3*x^2 + 2)^(1/4))) - 1/16*4^(1/8)*sqrt(2)*arctan(-1/8*4^(7/8)*sqrt(2)*(4^(1/8)*sqrt(2) - 2*(-3*x^2 + 2)^(1/4))) - 1/32*4^(1/8)*sqrt(2)*log(4^(1/8)*sqrt(2)*(-3*x^2 + 2)^(1/4) + sqrt(-3*x^2 + 2) + 4^(1/4)) + 1/32*4^(1/8)*sqrt(2)*log(-4^(1/8)*sqrt(2)*(-3*x^2 + 2)^(1/4) + sqrt(-3*x^2 + 2) + 4^(1/4)) - 1/8*4^(1/8)*arctan(1/4*4^(7/8)*(-3*x^2 + 2)^(1/4)) - 1/16*4^(1/8)*log((-3*x^2 + 2)^(1/4) + 4^(1/8)) + 1/16*4^(1/8)*log(-(-3*x^2 + 2)^(1/4) + 4^(1/8))","A",0
1066,1,192,0,0.575372," ","integrate(1/x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","-\frac{3}{64} \cdot 2^{\frac{3}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} + 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{3}{64} \cdot 2^{\frac{3}{4}} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{1}{4}} {\left(2^{\frac{3}{4}} - 2 \, {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right)}\right) - \frac{3}{128} \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{3}{128} \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{15}{64} \cdot 2^{\frac{1}{4}} \arctan\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{15}{128} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} + {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) + \frac{15}{128} \cdot 2^{\frac{1}{4}} \log\left(2^{\frac{1}{4}} - {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}\right) - \frac{{\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}{16 \, x^{2}}"," ",0,"-3/64*2^(3/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 3/64*2^(3/4)*arctan(-1/2*2^(1/4)*(2^(3/4) - 2*(-3*x^2 + 2)^(1/4))) - 3/128*2^(3/4)*log(2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) + 3/128*2^(3/4)*log(-2^(3/4)*(-3*x^2 + 2)^(1/4) + sqrt(2) + sqrt(-3*x^2 + 2)) - 15/64*2^(1/4)*arctan(1/2*2^(3/4)*(-3*x^2 + 2)^(1/4)) - 15/128*2^(1/4)*log(2^(1/4) + (-3*x^2 + 2)^(1/4)) + 15/128*2^(1/4)*log(2^(1/4) - (-3*x^2 + 2)^(1/4)) - 1/16*(-3*x^2 + 2)^(1/4)/x^2","A",0
1067,0,0,0,0.000000," ","integrate(x^6/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{6}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^6/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)), x)","F",0
1068,0,0,0,0.000000," ","integrate(x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{4}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^4/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)), x)","F",0
1069,0,0,0,0.000000," ","integrate(x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)), x)","F",0
1070,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)), x)","F",0
1071,0,0,0,0.000000," ","integrate(1/x^2/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x^{2}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)*x^2), x)","F",0
1072,0,0,0,0.000000," ","integrate(1/x^4/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x^{4}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)*x^4), x)","F",0
1073,0,0,0,0.000000," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F",0
1074,0,0,0,0.000000," ","integrate(x^2/(-3*x^2-2)/(-3*x^2-1)^(3/4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} + 2\right)} {\left(-3 \, x^{2} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 + 2)*(-3*x^2 - 1)^(3/4)), x)","F",0
1075,0,0,0,0.000000," ","integrate(x^2/(b*x^2-2)/(b*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{2} - 1\right)}^{\frac{3}{4}} {\left(b x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 - 1)^(3/4)*(b*x^2 - 2)), x)","F",0
1076,0,0,0,0.000000," ","integrate(x^2/(-b*x^2-2)/(-b*x^2-1)^(3/4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(b x^{2} + 2\right)} {\left(-b x^{2} - 1\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((b*x^2 + 2)*(-b*x^2 - 1)^(3/4)), x)","F",0
1077,0,0,0,0.000000," ","integrate(x^2/(3*x^2-2*a)/(3*x^2-a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} - a\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 - a)^(3/4)*(3*x^2 - 2*a)), x)","F",0
1078,0,0,0,0.000000," ","integrate(x^2/(-3*x^2-2*a)/(-3*x^2-a)^(3/4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(-3 \, x^{2} - a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((3*x^2 + 2*a)*(-3*x^2 - a)^(3/4)), x)","F",0
1079,0,0,0,0.000000," ","integrate(x^2/(b*x^2-2*a)/(b*x^2-a)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(b x^{2} - a\right)}^{\frac{3}{4}} {\left(b x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 - a)^(3/4)*(b*x^2 - 2*a)), x)","F",0
1080,0,0,0,0.000000," ","integrate(x^2/(-b*x^2-2*a)/(-b*x^2-a)^(3/4),x, algorithm=""giac"")","\int -\frac{x^{2}}{{\left(b x^{2} + 2 \, a\right)} {\left(-b x^{2} - a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate(-x^2/((b*x^2 + 2*a)*(-b*x^2 - a)^(3/4)), x)","F",0
1081,1,75,0,0.283209," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\frac{2}{729} \, {\left(3 \, x^{2} - 1\right)}^{\frac{9}{4}} + \frac{8}{405} \, {\left(3 \, x^{2} - 1\right)}^{\frac{5}{4}} + \frac{14}{81} \, {\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2/729*(3*x^2 - 1)^(9/4) + 8/405*(3*x^2 - 1)^(5/4) + 14/81*(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(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1082,1,64,0,0.443153," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\frac{2}{135} \, {\left(3 \, x^{2} - 1\right)}^{\frac{5}{4}} + \frac{2}{9} \, {\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"2/135*(3*x^2 - 1)^(5/4) + 2/9*(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(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1083,1,53,0,0.405617," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\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(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1084,1,42,0,0.423606," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","-\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1085,1,155,0,0.409295," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{1}{8} \, \sqrt{2} \log\left(\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(-\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\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| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(3*x^2 - 1)^(1/4))) - 1/4*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(3*x^2 - 1)^(1/4))) - 1/8*sqrt(2)*log(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) + 1/8*sqrt(2)*log(-sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - 1/2*arctan((3*x^2 - 1)^(1/4)) - 1/4*log((3*x^2 - 1)^(1/4) + 1) + 1/4*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1086,1,169,0,0.499207," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","-\frac{15}{16} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{15}{16} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right)}\right) - \frac{15}{32} \, \sqrt{2} \log\left(\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) + \frac{15}{32} \, \sqrt{2} \log\left(-\sqrt{2} {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + \sqrt{3 \, x^{2} - 1} + 1\right) - \frac{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}}{4 \, x^{2}} - \frac{3}{4} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{3}{8} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{3}{8} \, \log\left({\left| {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1 \right|}\right)"," ",0,"-15/16*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(3*x^2 - 1)^(1/4))) - 15/16*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(3*x^2 - 1)^(1/4))) - 15/32*sqrt(2)*log(sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) + 15/32*sqrt(2)*log(-sqrt(2)*(3*x^2 - 1)^(1/4) + sqrt(3*x^2 - 1) + 1) - 1/4*(3*x^2 - 1)^(1/4)/x^2 - 3/4*arctan((3*x^2 - 1)^(1/4)) - 3/8*log((3*x^2 - 1)^(1/4) + 1) + 3/8*log(abs((3*x^2 - 1)^(1/4) - 1))","A",0
1087,0,0,0,0.000000," ","integrate(x^6/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{6}}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^6/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F",0
1088,0,0,0,0.000000," ","integrate(x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{4}}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^4/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F",0
1089,0,0,0,0.000000," ","integrate(x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F",0
1090,0,0,0,0.000000," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F",0
1091,0,0,0,0.000000," ","integrate(1/x^2/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)*x^2), x)","F",0
1092,0,0,0,0.000000," ","integrate(1/x^4/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)} x^{4}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)*x^4), x)","F",0
1093,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(5/2)/(b*x^2 + a)^(3/4), x)","F",0
1094,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*sqrt(e*x)/(b*x^2 + a)^(3/4), x)","F",0
1095,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(3/2)), x)","F",0
1096,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(7/2)), x)","F",0
1097,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(11/2)), x)","F",0
1098,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(15/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(15/2)), x)","F",0
1099,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(7/2)/(b*x^2 + a)^(3/4), x)","F",0
1100,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(3/2)/(b*x^2 + a)^(3/4), x)","F",0
1101,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*sqrt(e*x)), x)","F",0
1102,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(5/2)), x)","F",0
1103,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(9/2)), x)","F",0
1104,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(3/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} \left(e x\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(3/4)*(e*x)^(13/2)), x)","F",0
1105,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(3/2)/(b*x^2 + a)^(5/4), x)","F",0
1106,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \sqrt{e x}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*sqrt(e*x)), x)","F",0
1107,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(5/2)), x)","F",0
1108,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(9/2)), x)","F",0
1109,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(13/2)), x)","F",0
1110,0,0,0,0.000000," ","integrate((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(9/2)/(b*x^2 + a)^(5/4), x)","F",0
1111,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(5/2)/(b*x^2 + a)^(5/4), x)","F",0
1112,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*sqrt(e*x)/(b*x^2 + a)^(5/4), x)","F",0
1113,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(3/2)), x)","F",0
1114,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(7/2)), x)","F",0
1115,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(5/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} \left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(5/4)*(e*x)^(11/2)), x)","F",0
1116,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(5/2)/(b*x^2 + a)^(7/4), x)","F",0
1117,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*sqrt(e*x)/(b*x^2 + a)^(7/4), x)","F",0
1118,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*(e*x)^(3/2)), x)","F",0
1119,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*(e*x)^(7/2)), x)","F",0
1120,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*(e*x)^(11/2)), x)","F",0
1121,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(7/2)/(b*x^2 + a)^(7/4), x)","F",0
1122,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(3/2)/(b*x^2 + a)^(7/4), x)","F",0
1123,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \sqrt{e x}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*sqrt(e*x)), x)","F",0
1124,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*(e*x)^(5/2)), x)","F",0
1125,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(7/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} \left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(7/4)*(e*x)^(9/2)), x)","F",0
1126,0,0,0,0.000000," ","integrate((e*x)^(7/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{7}{2}}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(7/2)/(b*x^2 + a)^(9/4), x)","F",0
1127,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(3/2)/(b*x^2 + a)^(9/4), x)","F",0
1128,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(1/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \sqrt{e x}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*sqrt(e*x)), x)","F",0
1129,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(5/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(5/2)), x)","F",0
1130,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(9/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(9/2)), x)","F",0
1131,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(13/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(13/2)), x)","F",0
1132,0,0,0,0.000000," ","integrate((e*x)^(13/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{13}{2}}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(13/2)/(b*x^2 + a)^(9/4), x)","F",0
1133,0,0,0,0.000000," ","integrate((e*x)^(9/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{9}{2}}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(9/2)/(b*x^2 + a)^(9/4), x)","F",0
1134,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \left(e x\right)^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*(e*x)^(5/2)/(b*x^2 + a)^(9/4), x)","F",0
1135,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^2+c)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)} \sqrt{e x}}{{\left(b x^{2} + a\right)}^{\frac{9}{4}}}\,{d x}"," ",0,"integrate((d*x^2 + c)*sqrt(e*x)/(b*x^2 + a)^(9/4), x)","F",0
1136,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(3/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(3/2)), x)","F",0
1137,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(7/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(7/2)), x)","F",0
1138,0,0,0,0.000000," ","integrate((d*x^2+c)/(e*x)^(11/2)/(b*x^2+a)^(9/4),x, algorithm=""giac"")","\int \frac{d x^{2} + c}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} \left(e x\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)/((b*x^2 + a)^(9/4)*(e*x)^(11/2)), x)","F",0
1139,0,0,0,0.000000," ","integrate((e*x)^m*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} \left(e x\right)^{m}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*(e*x)^m, x)","F",0
1140,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{4}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*x^4, x)","F",0
1141,0,0,0,0.000000," ","integrate(x^2*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{2}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*x^2, x)","F",0
1142,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1143,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/x^2, x)","F",0
1144,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^4,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{4}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/x^4, x)","F",0
1145,0,0,0,0.000000," ","integrate(x^5*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{5}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*x^5, x)","F",0
1146,0,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x^{3}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*x^3, x)","F",0
1147,0,0,0,0.000000," ","integrate(x*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q} x\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q*x, x)","F",0
1148,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/x, x)","F",0
1149,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/x^3, x)","F",0
1150,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/x^5,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{x^{5}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/x^5, x)","F",0
1151,0,0,0,0.000000," ","integrate((e*x)^(5/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int \left(e x\right)^{\frac{5}{2}} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((e*x)^(5/2)*(b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1152,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int \left(e x\right)^{\frac{3}{2}} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((e*x)^(3/2)*(b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1153,0,0,0,0.000000," ","integrate((e*x)^(1/2)*(b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int \sqrt{e x} {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate(sqrt(e*x)*(b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
1154,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{\sqrt{e x}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/sqrt(e*x), x)","F",0
1155,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{\left(e x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/(e*x)^(3/2), x)","F",0
1156,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q/(e*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}}{\left(e x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q/(e*x)^(5/2), x)","F",0
