1,1,27,0,1.342144," ","integrate(x^2*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{7} \, B b x^{7} + \frac{1}{5} \, {\left(B a + A b\right)} x^{5} + \frac{1}{3} \, A a x^{3}"," ",0,"1/7*B*b*x^7 + 1/5*(B*a + A*b)*x^5 + 1/3*A*a*x^3","A",0
2,1,27,0,1.350478," ","integrate(x*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{6} \, B b x^{6} + \frac{1}{4} \, {\left(B a + A b\right)} x^{4} + \frac{1}{2} \, A a x^{2}"," ",0,"1/6*B*b*x^6 + 1/4*(B*a + A*b)*x^4 + 1/2*A*a*x^2","A",0
3,1,24,0,1.336484," ","integrate((b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{5} \, B b x^{5} + \frac{1}{3} \, {\left(B a + A b\right)} x^{3} + A a x"," ",0,"1/5*B*b*x^5 + 1/3*(B*a + A*b)*x^3 + A*a*x","A",0
4,1,28,0,1.311317," ","integrate((b*x^2+a)*(B*x^2+A)/x,x, algorithm=""maxima"")","\frac{1}{4} \, B b x^{4} + \frac{1}{2} \, {\left(B a + A b\right)} x^{2} + \frac{1}{2} \, A a \log\left(x^{2}\right)"," ",0,"1/4*B*b*x^4 + 1/2*(B*a + A*b)*x^2 + 1/2*A*a*log(x^2)","A",0
5,1,24,0,1.387622," ","integrate((b*x^2+a)*(B*x^2+A)/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, B b x^{3} + {\left(B a + A b\right)} x - \frac{A a}{x}"," ",0,"1/3*B*b*x^3 + (B*a + A*b)*x - A*a/x","A",0
6,1,28,0,1.349593," ","integrate((b*x^2+a)*(B*x^2+A)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, B b x^{2} + \frac{1}{2} \, {\left(B a + A b\right)} \log\left(x^{2}\right) - \frac{A a}{2 \, x^{2}}"," ",0,"1/2*B*b*x^2 + 1/2*(B*a + A*b)*log(x^2) - 1/2*A*a/x^2","A",0
7,1,26,0,1.375127," ","integrate((b*x^2+a)*(B*x^2+A)/x^4,x, algorithm=""maxima"")","B b x - \frac{3 \, {\left(B a + A b\right)} x^{2} + A a}{3 \, x^{3}}"," ",0,"B*b*x - 1/3*(3*(B*a + A*b)*x^2 + A*a)/x^3","A",0
8,1,30,0,1.385259," ","integrate((b*x^2+a)*(B*x^2+A)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, B b \log\left(x^{2}\right) - \frac{2 \, {\left(B a + A b\right)} x^{2} + A a}{4 \, x^{4}}"," ",0,"1/2*B*b*log(x^2) - 1/4*(2*(B*a + A*b)*x^2 + A*a)/x^4","A",0
9,1,29,0,1.395203," ","integrate((b*x^2+a)*(B*x^2+A)/x^6,x, algorithm=""maxima"")","-\frac{15 \, B b x^{4} + 5 \, {\left(B a + A b\right)} x^{2} + 3 \, A a}{15 \, x^{5}}"," ",0,"-1/15*(15*B*b*x^4 + 5*(B*a + A*b)*x^2 + 3*A*a)/x^5","A",0
10,1,29,0,1.374692," ","integrate((b*x^2+a)*(B*x^2+A)/x^7,x, algorithm=""maxima"")","-\frac{6 \, B b x^{4} + 3 \, {\left(B a + A b\right)} x^{2} + 2 \, A a}{12 \, x^{6}}"," ",0,"-1/12*(6*B*b*x^4 + 3*(B*a + A*b)*x^2 + 2*A*a)/x^6","A",0
11,1,51,0,1.378964," ","integrate(x^2*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{9} \, B b^{2} x^{9} + \frac{1}{7} \, {\left(2 \, B a b + A b^{2}\right)} x^{7} + \frac{1}{3} \, A a^{2} x^{3} + \frac{1}{5} \, {\left(B a^{2} + 2 \, A a b\right)} x^{5}"," ",0,"1/9*B*b^2*x^9 + 1/7*(2*B*a*b + A*b^2)*x^7 + 1/3*A*a^2*x^3 + 1/5*(B*a^2 + 2*A*a*b)*x^5","A",0
12,1,51,0,1.369650," ","integrate(x*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{8} \, B b^{2} x^{8} + \frac{1}{6} \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + \frac{1}{2} \, A a^{2} x^{2} + \frac{1}{4} \, {\left(B a^{2} + 2 \, A a b\right)} x^{4}"," ",0,"1/8*B*b^2*x^8 + 1/6*(2*B*a*b + A*b^2)*x^6 + 1/2*A*a^2*x^2 + 1/4*(B*a^2 + 2*A*a*b)*x^4","A",0
13,1,48,0,1.328685," ","integrate((b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{7} \, B b^{2} x^{7} + \frac{1}{5} \, {\left(2 \, B a b + A b^{2}\right)} x^{5} + A a^{2} x + \frac{1}{3} \, {\left(B a^{2} + 2 \, A a b\right)} x^{3}"," ",0,"1/7*B*b^2*x^7 + 1/5*(2*B*a*b + A*b^2)*x^5 + A*a^2*x + 1/3*(B*a^2 + 2*A*a*b)*x^3","A",0
14,1,52,0,1.302452," ","integrate((b*x^2+a)^2*(B*x^2+A)/x,x, algorithm=""maxima"")","\frac{1}{6} \, B b^{2} x^{6} + \frac{1}{4} \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + \frac{1}{2} \, A a^{2} \log\left(x^{2}\right) + \frac{1}{2} \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}"," ",0,"1/6*B*b^2*x^6 + 1/4*(2*B*a*b + A*b^2)*x^4 + 1/2*A*a^2*log(x^2) + 1/2*(B*a^2 + 2*A*a*b)*x^2","A",0
15,1,48,0,1.308334," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, B b^{2} x^{5} + \frac{1}{3} \, {\left(2 \, B a b + A b^{2}\right)} x^{3} - \frac{A a^{2}}{x} + {\left(B a^{2} + 2 \, A a b\right)} x"," ",0,"1/5*B*b^2*x^5 + 1/3*(2*B*a*b + A*b^2)*x^3 - A*a^2/x + (B*a^2 + 2*A*a*b)*x","A",0
16,1,52,0,1.360663," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, B b^{2} x^{4} + \frac{1}{2} \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + \frac{1}{2} \, {\left(B a^{2} + 2 \, A a b\right)} \log\left(x^{2}\right) - \frac{A a^{2}}{2 \, x^{2}}"," ",0,"1/4*B*b^2*x^4 + 1/2*(2*B*a*b + A*b^2)*x^2 + 1/2*(B*a^2 + 2*A*a*b)*log(x^2) - 1/2*A*a^2/x^2","A",0
17,1,50,0,1.374871," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, B b^{2} x^{3} + {\left(2 \, B a b + A b^{2}\right)} x - \frac{A a^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/3*B*b^2*x^3 + (2*B*a*b + A*b^2)*x - 1/3*(A*a^2 + 3*(B*a^2 + 2*A*a*b)*x^2)/x^3","A",0
18,1,54,0,1.389396," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^5,x, algorithm=""maxima"")","\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{A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} x^{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*(A*a^2 + 2*(B*a^2 + 2*A*a*b)*x^2)/x^4","A",0
19,1,51,0,1.353007," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^6,x, algorithm=""maxima"")","B b^{2} x - \frac{15 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 3 \, A a^{2} + 5 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{15 \, x^{5}}"," ",0,"B*b^2*x - 1/15*(15*(2*B*a*b + A*b^2)*x^4 + 3*A*a^2 + 5*(B*a^2 + 2*A*a*b)*x^2)/x^5","A",0
20,1,55,0,1.010212," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^7,x, algorithm=""maxima"")","\frac{1}{2} \, B b^{2} \log\left(x^{2}\right) - \frac{6 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 2 \, A a^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/2*B*b^2*log(x^2) - 1/12*(6*(2*B*a*b + A*b^2)*x^4 + 2*A*a^2 + 3*(B*a^2 + 2*A*a*b)*x^2)/x^6","A",0
21,1,53,0,0.980977," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^8,x, algorithm=""maxima"")","-\frac{105 \, B b^{2} x^{6} + 35 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 15 \, A a^{2} + 21 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{105 \, x^{7}}"," ",0,"-1/105*(105*B*b^2*x^6 + 35*(2*B*a*b + A*b^2)*x^4 + 15*A*a^2 + 21*(B*a^2 + 2*A*a*b)*x^2)/x^7","A",0
22,1,53,0,1.045563," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^9,x, algorithm=""maxima"")","-\frac{12 \, B b^{2} x^{6} + 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 3 \, A a^{2} + 4 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}}{24 \, x^{8}}"," ",0,"-1/24*(12*B*b^2*x^6 + 6*(2*B*a*b + A*b^2)*x^4 + 3*A*a^2 + 4*(B*a^2 + 2*A*a*b)*x^2)/x^8","A",0
23,1,119,0,0.997241," ","integrate(x^9*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{22} \, B b^{5} x^{22} + \frac{1}{20} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{20} + \frac{5}{18} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{18} + \frac{5}{8} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{16} + \frac{1}{10} \, A a^{5} x^{10} + \frac{5}{14} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{14} + \frac{1}{12} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{12}"," ",0,"1/22*B*b^5*x^22 + 1/20*(5*B*a*b^4 + A*b^5)*x^20 + 5/18*(2*B*a^2*b^3 + A*a*b^4)*x^18 + 5/8*(B*a^3*b^2 + A*a^2*b^3)*x^16 + 1/10*A*a^5*x^10 + 5/14*(B*a^4*b + 2*A*a^3*b^2)*x^14 + 1/12*(B*a^5 + 5*A*a^4*b)*x^12","A",0
24,1,119,0,0.976565," ","integrate(x^8*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{21} \, B b^{5} x^{21} + \frac{1}{19} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{19} + \frac{5}{17} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{17} + \frac{2}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{15} + \frac{1}{9} \, A a^{5} x^{9} + \frac{5}{13} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{13} + \frac{1}{11} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{11}"," ",0,"1/21*B*b^5*x^21 + 1/19*(5*B*a*b^4 + A*b^5)*x^19 + 5/17*(2*B*a^2*b^3 + A*a*b^4)*x^17 + 2/3*(B*a^3*b^2 + A*a^2*b^3)*x^15 + 1/9*A*a^5*x^9 + 5/13*(B*a^4*b + 2*A*a^3*b^2)*x^13 + 1/11*(B*a^5 + 5*A*a^4*b)*x^11","A",0
25,1,119,0,0.997238," ","integrate(x^7*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{20} \, B b^{5} x^{20} + \frac{1}{18} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{18} + \frac{5}{16} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{16} + \frac{5}{7} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{14} + \frac{1}{8} \, A a^{5} x^{8} + \frac{5}{12} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{12} + \frac{1}{10} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{10}"," ",0,"1/20*B*b^5*x^20 + 1/18*(5*B*a*b^4 + A*b^5)*x^18 + 5/16*(2*B*a^2*b^3 + A*a*b^4)*x^16 + 5/7*(B*a^3*b^2 + A*a^2*b^3)*x^14 + 1/8*A*a^5*x^8 + 5/12*(B*a^4*b + 2*A*a^3*b^2)*x^12 + 1/10*(B*a^5 + 5*A*a^4*b)*x^10","A",0
26,1,119,0,1.062076," ","integrate(x^6*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{19} \, B b^{5} x^{19} + \frac{1}{17} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{17} + \frac{1}{3} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{15} + \frac{10}{13} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{13} + \frac{1}{7} \, A a^{5} x^{7} + \frac{5}{11} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{11} + \frac{1}{9} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{9}"," ",0,"1/19*B*b^5*x^19 + 1/17*(5*B*a*b^4 + A*b^5)*x^17 + 1/3*(2*B*a^2*b^3 + A*a*b^4)*x^15 + 10/13*(B*a^3*b^2 + A*a^2*b^3)*x^13 + 1/7*A*a^5*x^7 + 5/11*(B*a^4*b + 2*A*a^3*b^2)*x^11 + 1/9*(B*a^5 + 5*A*a^4*b)*x^9","A",0
27,1,119,0,0.977922," ","integrate(x^5*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{18} \, B b^{5} x^{18} + \frac{1}{16} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{16} + \frac{5}{14} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{14} + \frac{5}{6} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{12} + \frac{1}{6} \, A a^{5} x^{6} + \frac{1}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{10} + \frac{1}{8} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{8}"," ",0,"1/18*B*b^5*x^18 + 1/16*(5*B*a*b^4 + A*b^5)*x^16 + 5/14*(2*B*a^2*b^3 + A*a*b^4)*x^14 + 5/6*(B*a^3*b^2 + A*a^2*b^3)*x^12 + 1/6*A*a^5*x^6 + 1/2*(B*a^4*b + 2*A*a^3*b^2)*x^10 + 1/8*(B*a^5 + 5*A*a^4*b)*x^8","A",0
28,1,119,0,1.105134," ","integrate(x^4*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{17} \, B b^{5} x^{17} + \frac{1}{15} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + \frac{5}{13} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{13} + \frac{10}{11} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{11} + \frac{1}{5} \, A a^{5} x^{5} + \frac{5}{9} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{9} + \frac{1}{7} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{7}"," ",0,"1/17*B*b^5*x^17 + 1/15*(5*B*a*b^4 + A*b^5)*x^15 + 5/13*(2*B*a^2*b^3 + A*a*b^4)*x^13 + 10/11*(B*a^3*b^2 + A*a^2*b^3)*x^11 + 1/5*A*a^5*x^5 + 5/9*(B*a^4*b + 2*A*a^3*b^2)*x^9 + 1/7*(B*a^5 + 5*A*a^4*b)*x^7","A",0
29,1,118,0,1.010777," ","integrate(x^3*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{16} \, B b^{5} x^{16} + \frac{1}{14} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{14} + \frac{5}{12} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{10} + \frac{1}{4} \, A a^{5} x^{4} + \frac{5}{8} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{8} + \frac{1}{6} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{6}"," ",0,"1/16*B*b^5*x^16 + 1/14*(5*B*a*b^4 + A*b^5)*x^14 + 5/12*(2*B*a^2*b^3 + A*a*b^4)*x^12 + (B*a^3*b^2 + A*a^2*b^3)*x^10 + 1/4*A*a^5*x^4 + 5/8*(B*a^4*b + 2*A*a^3*b^2)*x^8 + 1/6*(B*a^5 + 5*A*a^4*b)*x^6","A",0
30,1,119,0,0.978232," ","integrate(x^2*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{15} \, B b^{5} x^{15} + \frac{1}{13} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{13} + \frac{5}{11} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{11} + \frac{10}{9} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + \frac{1}{3} \, A a^{5} x^{3} + \frac{5}{7} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{7} + \frac{1}{5} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{5}"," ",0,"1/15*B*b^5*x^15 + 1/13*(5*B*a*b^4 + A*b^5)*x^13 + 5/11*(2*B*a^2*b^3 + A*a*b^4)*x^11 + 10/9*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 1/3*A*a^5*x^3 + 5/7*(B*a^4*b + 2*A*a^3*b^2)*x^7 + 1/5*(B*a^5 + 5*A*a^4*b)*x^5","A",0
31,1,119,0,1.014968," ","integrate(x*(b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{14} \, B b^{5} x^{14} + \frac{1}{12} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{12} + \frac{1}{2} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{10} + \frac{5}{4} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{8} + \frac{1}{2} \, A a^{5} x^{2} + \frac{5}{6} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + \frac{1}{4} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{4}"," ",0,"1/14*B*b^5*x^14 + 1/12*(5*B*a*b^4 + A*b^5)*x^12 + 1/2*(2*B*a^2*b^3 + A*a*b^4)*x^10 + 5/4*(B*a^3*b^2 + A*a^2*b^3)*x^8 + 1/2*A*a^5*x^2 + 5/6*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 1/4*(B*a^5 + 5*A*a^4*b)*x^4","B",0
32,1,115,0,1.009648," ","integrate((b*x^2+a)^5*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{13} \, B b^{5} x^{13} + \frac{1}{11} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{11} + \frac{5}{9} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{9} + \frac{10}{7} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{7} + A a^{5} x + {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{5} + \frac{1}{3} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}"," ",0,"1/13*B*b^5*x^13 + 1/11*(5*B*a*b^4 + A*b^5)*x^11 + 5/9*(2*B*a^2*b^3 + A*a*b^4)*x^9 + 10/7*(B*a^3*b^2 + A*a^2*b^3)*x^7 + A*a^5*x + (B*a^4*b + 2*A*a^3*b^2)*x^5 + 1/3*(B*a^5 + 5*A*a^4*b)*x^3","A",0
33,1,120,0,1.034253," ","integrate((b*x^2+a)^5*(B*x^2+A)/x,x, algorithm=""maxima"")","\frac{1}{12} \, B b^{5} x^{12} + \frac{1}{10} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + \frac{5}{8} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + \frac{5}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + \frac{1}{2} \, A a^{5} \log\left(x^{2}\right) + \frac{5}{4} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}"," ",0,"1/12*B*b^5*x^12 + 1/10*(5*B*a*b^4 + A*b^5)*x^10 + 5/8*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 5/3*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 1/2*A*a^5*log(x^2) + 5/4*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 1/2*(B*a^5 + 5*A*a^4*b)*x^2","A",0
34,1,116,0,1.129200," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^2,x, algorithm=""maxima"")","\frac{1}{11} \, B b^{5} x^{11} + \frac{1}{9} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{9} + \frac{5}{7} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{7} + 2 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{5} - \frac{A a^{5}}{x} + \frac{5}{3} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{3} + {\left(B a^{5} + 5 \, A a^{4} b\right)} x"," ",0,"1/11*B*b^5*x^11 + 1/9*(5*B*a*b^4 + A*b^5)*x^9 + 5/7*(2*B*a^2*b^3 + A*a*b^4)*x^7 + 2*(B*a^3*b^2 + A*a^2*b^3)*x^5 - A*a^5/x + 5/3*(B*a^4*b + 2*A*a^3*b^2)*x^3 + (B*a^5 + 5*A*a^4*b)*x","A",0
35,1,120,0,1.096507," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^3,x, algorithm=""maxima"")","\frac{1}{10} \, B b^{5} x^{10} + \frac{1}{8} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{8} + \frac{5}{6} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + \frac{5}{2} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{4} - \frac{A a^{5}}{2 \, x^{2}} + \frac{5}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + \frac{1}{2} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} \log\left(x^{2}\right)"," ",0,"1/10*B*b^5*x^10 + 1/8*(5*B*a*b^4 + A*b^5)*x^8 + 5/6*(2*B*a^2*b^3 + A*a*b^4)*x^6 + 5/2*(B*a^3*b^2 + A*a^2*b^3)*x^4 - 1/2*A*a^5/x^2 + 5/2*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 1/2*(B*a^5 + 5*A*a^4*b)*log(x^2)","A",0
36,1,118,0,1.030275," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^4,x, algorithm=""maxima"")","\frac{1}{9} \, B b^{5} x^{9} + \frac{1}{7} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{7} + {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{5} + \frac{10}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 5 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x - \frac{A a^{5} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/9*B*b^5*x^9 + 1/7*(5*B*a*b^4 + A*b^5)*x^7 + (2*B*a^2*b^3 + A*a*b^4)*x^5 + 10/3*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 5*(B*a^4*b + 2*A*a^3*b^2)*x - 1/3*(A*a^5 + 3*(B*a^5 + 5*A*a^4*b)*x^2)/x^3","A",0
37,1,122,0,1.037399," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, B b^{5} x^{8} + \frac{1}{6} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{6} + \frac{5}{4} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{2} + \frac{5}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} \log\left(x^{2}\right) - \frac{A a^{5} + 2 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{4 \, x^{4}}"," ",0,"1/8*B*b^5*x^8 + 1/6*(5*B*a*b^4 + A*b^5)*x^6 + 5/4*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 5*(B*a^3*b^2 + A*a^2*b^3)*x^2 + 5/2*(B*a^4*b + 2*A*a^3*b^2)*log(x^2) - 1/4*(A*a^5 + 2*(B*a^5 + 5*A*a^4*b)*x^2)/x^4","A",0
38,1,120,0,0.947534," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^6,x, algorithm=""maxima"")","\frac{1}{7} \, B b^{5} x^{7} + \frac{1}{5} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + \frac{5}{3} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{3} + 10 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x - \frac{3 \, A a^{5} + 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 5 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{15 \, x^{5}}"," ",0,"1/7*B*b^5*x^7 + 1/5*(5*B*a*b^4 + A*b^5)*x^5 + 5/3*(2*B*a^2*b^3 + A*a*b^4)*x^3 + 10*(B*a^3*b^2 + A*a^2*b^3)*x - 1/15*(3*A*a^5 + 75*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 5*(B*a^5 + 5*A*a^4*b)*x^2)/x^5","A",0
39,1,123,0,1.063411," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^7,x, algorithm=""maxima"")","\frac{1}{6} \, B b^{5} x^{6} + \frac{1}{4} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{4} + \frac{5}{2} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{2} + 5 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} \log\left(x^{2}\right) - \frac{2 \, A a^{5} + 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{12 \, x^{6}}"," ",0,"1/6*B*b^5*x^6 + 1/4*(5*B*a*b^4 + A*b^5)*x^4 + 5/2*(2*B*a^2*b^3 + A*a*b^4)*x^2 + 5*(B*a^3*b^2 + A*a^2*b^3)*log(x^2) - 1/12*(2*A*a^5 + 30*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 3*(B*a^5 + 5*A*a^4*b)*x^2)/x^6","A",0
40,1,120,0,1.016181," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^8,x, algorithm=""maxima"")","\frac{1}{5} \, B b^{5} x^{5} + \frac{1}{3} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{3} + 5 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x - \frac{1050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 15 \, A a^{5} + 175 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 21 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{105 \, x^{7}}"," ",0,"1/5*B*b^5*x^5 + 1/3*(5*B*a*b^4 + A*b^5)*x^3 + 5*(2*B*a^2*b^3 + A*a*b^4)*x - 1/105*(1050*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 15*A*a^5 + 175*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 21*(B*a^5 + 5*A*a^4*b)*x^2)/x^7","A",0
41,1,123,0,0.958499," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^9,x, algorithm=""maxima"")","\frac{1}{4} \, B b^{5} x^{4} + \frac{1}{2} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{2} + \frac{5}{2} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} \log\left(x^{2}\right) - \frac{120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 3 \, A a^{5} + 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{24 \, x^{8}}"," ",0,"1/4*B*b^5*x^4 + 1/2*(5*B*a*b^4 + A*b^5)*x^2 + 5/2*(2*B*a^2*b^3 + A*a*b^4)*log(x^2) - 1/24*(120*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 3*A*a^5 + 30*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 4*(B*a^5 + 5*A*a^4*b)*x^2)/x^8","A",0
42,1,119,0,1.077976," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^10,x, algorithm=""maxima"")","\frac{1}{3} \, B b^{5} x^{3} + {\left(5 \, B a b^{4} + A b^{5}\right)} x - \frac{315 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 210 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 7 \, A a^{5} + 63 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 9 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{63 \, x^{9}}"," ",0,"1/3*B*b^5*x^3 + (5*B*a*b^4 + A*b^5)*x - 1/63*(315*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 210*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 7*A*a^5 + 63*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 9*(B*a^5 + 5*A*a^4*b)*x^2)/x^9","A",0
43,1,123,0,1.023061," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^11,x, algorithm=""maxima"")","\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{300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 12 \, A a^{5} + 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{120 \, x^{10}}"," ",0,"1/2*B*b^5*x^2 + 1/2*(5*B*a*b^4 + A*b^5)*log(x^2) - 1/120*(300*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 300*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 12*A*a^5 + 100*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 15*(B*a^5 + 5*A*a^4*b)*x^2)/x^10","A",0
44,1,119,0,1.022884," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^12,x, algorithm=""maxima"")","B b^{5} x - \frac{693 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 1155 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1386 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 63 \, A a^{5} + 495 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 77 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{693 \, x^{11}}"," ",0,"B*b^5*x - 1/693*(693*(5*B*a*b^4 + A*b^5)*x^10 + 1155*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1386*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 63*A*a^5 + 495*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 77*(B*a^5 + 5*A*a^4*b)*x^2)/x^11","A",0
45,1,123,0,1.093875," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^13,x, algorithm=""maxima"")","\frac{1}{2} \, B b^{5} \log\left(x^{2}\right) - \frac{60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 150 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 10 \, A a^{5} + 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{120 \, x^{12}}"," ",0,"1/2*B*b^5*log(x^2) - 1/120*(60*(5*B*a*b^4 + A*b^5)*x^10 + 150*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 200*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 10*A*a^5 + 75*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 12*(B*a^5 + 5*A*a^4*b)*x^2)/x^12","A",0
46,1,121,0,1.069776," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^14,x, algorithm=""maxima"")","-\frac{9009 \, B b^{5} x^{12} + 3003 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 9009 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 12870 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 693 \, A a^{5} + 5005 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 819 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{9009 \, x^{13}}"," ",0,"-1/9009*(9009*B*b^5*x^12 + 3003*(5*B*a*b^4 + A*b^5)*x^10 + 9009*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 12870*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 693*A*a^5 + 5005*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 819*(B*a^5 + 5*A*a^4*b)*x^2)/x^13","A",0
47,1,121,0,1.059018," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^15,x, algorithm=""maxima"")","-\frac{42 \, B b^{5} x^{12} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 70 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 6 \, A a^{5} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{84 \, x^{14}}"," ",0,"-1/84*(42*B*b^5*x^12 + 21*(5*B*a*b^4 + A*b^5)*x^10 + 70*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 105*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 6*A*a^5 + 42*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 7*(B*a^5 + 5*A*a^4*b)*x^2)/x^14","B",0
48,1,121,0,0.967511," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^16,x, algorithm=""maxima"")","-\frac{15015 \, B b^{5} x^{12} + 9009 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 32175 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 50050 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 3003 \, A a^{5} + 20475 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 3465 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{45045 \, x^{15}}"," ",0,"-1/45045*(15015*B*b^5*x^12 + 9009*(5*B*a*b^4 + A*b^5)*x^10 + 32175*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 50050*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 3003*A*a^5 + 20475*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 3465*(B*a^5 + 5*A*a^4*b)*x^2)/x^15","A",0
49,1,121,0,1.087192," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^17,x, algorithm=""maxima"")","-\frac{84 \, B b^{5} x^{12} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 210 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 336 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 21 \, A a^{5} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 24 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{336 \, x^{16}}"," ",0,"-1/336*(84*B*b^5*x^12 + 56*(5*B*a*b^4 + A*b^5)*x^10 + 210*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 336*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 21*A*a^5 + 140*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 24*(B*a^5 + 5*A*a^4*b)*x^2)/x^16","A",0
50,1,121,0,1.136598," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^18,x, algorithm=""maxima"")","-\frac{153153 \, B b^{5} x^{12} + 109395 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 425425 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 696150 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 45045 \, A a^{5} + 294525 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 51051 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{765765 \, x^{17}}"," ",0,"-1/765765*(153153*B*b^5*x^12 + 109395*(5*B*a*b^4 + A*b^5)*x^10 + 425425*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 696150*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 45045*A*a^5 + 294525*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 51051*(B*a^5 + 5*A*a^4*b)*x^2)/x^17","A",0
51,1,121,0,1.115680," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^19,x, algorithm=""maxima"")","-\frac{168 \, B b^{5} x^{12} + 126 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 504 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 840 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 56 \, A a^{5} + 360 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{1008 \, x^{18}}"," ",0,"-1/1008*(168*B*b^5*x^12 + 126*(5*B*a*b^4 + A*b^5)*x^10 + 504*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 840*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 56*A*a^5 + 360*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 63*(B*a^5 + 5*A*a^4*b)*x^2)/x^18","A",0
52,1,121,0,1.037718," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^20,x, algorithm=""maxima"")","-\frac{415701 \, B b^{5} x^{12} + 323323 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 1322685 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 2238390 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 153153 \, A a^{5} + 969969 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 171171 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{2909907 \, x^{19}}"," ",0,"-1/2909907*(415701*B*b^5*x^12 + 323323*(5*B*a*b^4 + A*b^5)*x^10 + 1322685*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 2238390*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 153153*A*a^5 + 969969*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 171171*(B*a^5 + 5*A*a^4*b)*x^2)/x^19","A",0
53,1,121,0,1.000916," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^21,x, algorithm=""maxima"")","-\frac{630 \, B b^{5} x^{12} + 504 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 2100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 3600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 252 \, A a^{5} + 1575 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 280 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{5040 \, x^{20}}"," ",0,"-1/5040*(630*B*b^5*x^12 + 504*(5*B*a*b^4 + A*b^5)*x^10 + 2100*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 3600*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 252*A*a^5 + 1575*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 280*(B*a^5 + 5*A*a^4*b)*x^2)/x^20","A",0
54,1,121,0,1.033108," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^22,x, algorithm=""maxima"")","-\frac{323323 \, B b^{5} x^{12} + 264537 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 1119195 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 1939938 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 138567 \, A a^{5} + 855855 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 153153 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{2909907 \, x^{21}}"," ",0,"-1/2909907*(323323*B*b^5*x^12 + 264537*(5*B*a*b^4 + A*b^5)*x^10 + 1119195*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 1939938*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 138567*A*a^5 + 855855*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 153153*(B*a^5 + 5*A*a^4*b)*x^2)/x^21","A",0
55,1,121,0,1.008462," ","integrate((b*x^2+a)^5*(B*x^2+A)/x^23,x, algorithm=""maxima"")","-\frac{2772 \, B b^{5} x^{12} + 2310 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{10} + 9900 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{8} + 17325 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{6} + 1260 \, A a^{5} + 7700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{4} + 1386 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{2}}{27720 \, x^{22}}"," ",0,"-1/27720*(2772*B*b^5*x^12 + 2310*(5*B*a*b^4 + A*b^5)*x^10 + 9900*(2*B*a^2*b^3 + A*a*b^4)*x^8 + 17325*(B*a^3*b^2 + A*a^2*b^3)*x^6 + 1260*A*a^5 + 7700*(B*a^4*b + 2*A*a^3*b^2)*x^4 + 1386*(B*a^5 + 5*A*a^4*b)*x^2)/x^22","A",0
56,1,100,0,2.414965," ","integrate(x^6*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\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^{3} x^{7} - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{5} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{3} - 105 \, {\left(B a^{3} - A a^{2} b\right)} x}{105 \, b^{4}}"," ",0,"(B*a^4 - A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*B*b^3*x^7 - 21*(B*a*b^2 - A*b^3)*x^5 + 35*(B*a^2*b - A*a*b^2)*x^3 - 105*(B*a^3 - A*a^2*b)*x)/b^4","A",0
57,1,74,0,1.025649," ","integrate(x^5*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, B b^{2} x^{6} - 3 \, {\left(B a b - A b^{2}\right)} x^{4} + 6 \, {\left(B a^{2} - A a b\right)} x^{2}}{12 \, b^{3}} - \frac{{\left(B a^{3} - A a^{2} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/12*(2*B*b^2*x^6 - 3*(B*a*b - A*b^2)*x^4 + 6*(B*a^2 - A*a*b)*x^2)/b^3 - 1/2*(B*a^3 - A*a^2*b)*log(b*x^2 + a)/b^4","A",0
58,1,78,0,2.462581," ","integrate(x^4*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","-\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^{2} x^{5} - 5 \, {\left(B a b - A b^{2}\right)} x^{3} + 15 \, {\left(B a^{2} - A a b\right)} x}{15 \, b^{3}}"," ",0,"-(B*a^3 - A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*B*b^2*x^5 - 5*(B*a*b - A*b^2)*x^3 + 15*(B*a^2 - A*a*b)*x)/b^3","A",0
59,1,50,0,1.028084," ","integrate(x^3*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{B b x^{4} - 2 \, {\left(B a - A b\right)} x^{2}}{4 \, b^{2}} + \frac{{\left(B a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/4*(B*b*x^4 - 2*(B*a - A*b)*x^2)/b^2 + 1/2*(B*a^2 - A*a*b)*log(b*x^2 + a)/b^3","A",0
60,1,53,0,2.227620," ","integrate(x^2*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\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 x^{3} - 3 \, {\left(B a - A b\right)} x}{3 \, b^{2}}"," ",0,"(B*a^2 - A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(B*b*x^3 - 3*(B*a - A*b)*x)/b^2","A",0
61,1,31,0,1.094470," ","integrate(x*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{B x^{2}}{2 \, b} - \frac{{\left(B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*B*x^2/b - 1/2*(B*a - A*b)*log(b*x^2 + a)/b^2","A",0
62,1,34,0,2.498898," ","integrate((B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\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
63,1,35,0,1.017278," ","integrate((B*x^2+A)/x/(b*x^2+a),x, algorithm=""maxima"")","\frac{A \log\left(x^{2}\right)}{2 \, a} + \frac{{\left(B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"1/2*A*log(x^2)/a + 1/2*(B*a - A*b)*log(b*x^2 + a)/(a*b)","A",0
64,1,36,0,2.358404," ","integrate((B*x^2+A)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\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
65,1,48,0,1.039267," ","integrate((B*x^2+A)/x^3/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{{\left(B a - A b\right)} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{A}{2 \, a x^{2}}"," ",0,"-1/2*(B*a - A*b)*log(b*x^2 + a)/a^2 + 1/2*(B*a - A*b)*log(x^2)/a^2 - 1/2*A/(a*x^2)","A",0
66,1,56,0,2.393973," ","integrate((B*x^2+A)/x^4/(b*x^2+a),x, algorithm=""maxima"")","-\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 \, {\left(B a - A b\right)} 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 - A*b)*x^2 + A*a)/(a^2*x^3)","A",0
67,1,70,0,1.116033," ","integrate((B*x^2+A)/x^5/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B a b - A b^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{3}} - \frac{{\left(B a b - A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{3}} - \frac{2 \, {\left(B a - A b\right)} x^{2} + A a}{4 \, a^{2} x^{4}}"," ",0,"1/2*(B*a*b - A*b^2)*log(b*x^2 + a)/a^3 - 1/2*(B*a*b - A*b^2)*log(x^2)/a^3 - 1/4*(2*(B*a - A*b)*x^2 + A*a)/(a^2*x^4)","A",0
68,1,79,0,2.463966," ","integrate((B*x^2+A)/x^6/(b*x^2+a),x, algorithm=""maxima"")","\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 \, {\left(B a b - A b^{2}\right)} x^{4} - 3 \, A a^{2} - 5 \, {\left(B a^{2} - A a b\right)} x^{2}}{15 \, a^{3} x^{5}}"," ",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 - A*b^2)*x^4 - 3*A*a^2 - 5*(B*a^2 - A*a*b)*x^2)/(a^3*x^5)","A",0
69,1,96,0,0.966130," ","integrate((B*x^2+A)/x^7/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(B a b^{2} - A b^{3}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{4}} + \frac{{\left(B a b^{2} - A b^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{4}} + \frac{6 \, {\left(B a b - A b^{2}\right)} x^{4} - 2 \, A a^{2} - 3 \, {\left(B a^{2} - A a b\right)} x^{2}}{12 \, a^{3} x^{6}}"," ",0,"-1/2*(B*a*b^2 - A*b^3)*log(b*x^2 + a)/a^4 + 1/2*(B*a*b^2 - A*b^3)*log(x^2)/a^4 + 1/12*(6*(B*a*b - A*b^2)*x^4 - 2*A*a^2 - 3*(B*a^2 - A*a*b)*x^2)/(a^3*x^6)","A",0
70,1,103,0,2.479037," ","integrate((B*x^2+A)/x^8/(b*x^2+a),x, algorithm=""maxima"")","-\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 \, {\left(B a b^{2} - A b^{3}\right)} x^{6} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{4} + 15 \, A a^{3} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x^{2}}{105 \, a^{4} x^{7}}"," ",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 - A*b^3)*x^6 - 35*(B*a^2*b - A*a*b^2)*x^4 + 15*A*a^3 + 21*(B*a^3 - A*a^2*b)*x^2)/(a^4*x^7)","A",0
71,1,131,0,1.087956," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B a^{5} - A a^{4} b}{2 \, {\left(b^{7} x^{2} + a b^{6}\right)}} + \frac{3 \, B b^{3} x^{8} - 4 \, {\left(2 \, B a b^{2} - A b^{3}\right)} x^{6} + 6 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{4} - 12 \, {\left(4 \, B a^{3} - 3 \, A a^{2} b\right)} x^{2}}{24 \, b^{5}} + \frac{{\left(5 \, B a^{4} - 4 \, A a^{3} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{6}}"," ",0,"1/2*(B*a^5 - A*a^4*b)/(b^7*x^2 + a*b^6) + 1/24*(3*B*b^3*x^8 - 4*(2*B*a*b^2 - A*b^3)*x^6 + 6*(3*B*a^2*b - 2*A*a*b^2)*x^4 - 12*(4*B*a^3 - 3*A*a^2*b)*x^2)/b^5 + 1/2*(5*B*a^4 - 4*A*a^3*b)*log(b*x^2 + a)/b^6","A",0
72,1,136,0,2.390282," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(B a^{4} - A a^{3} b\right)} x}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} + \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{15 \, B b^{3} x^{7} - 21 \, {\left(2 \, B a b^{2} - A b^{3}\right)} x^{5} + 35 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{3} - 105 \, {\left(4 \, B a^{3} - 3 \, A a^{2} b\right)} x}{105 \, b^{5}}"," ",0,"-1/2*(B*a^4 - A*a^3*b)*x/(b^6*x^2 + a*b^5) + 1/2*(9*B*a^4 - 7*A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/105*(15*B*b^3*x^7 - 21*(2*B*a*b^2 - A*b^3)*x^5 + 35*(3*B*a^2*b - 2*A*a*b^2)*x^3 - 105*(4*B*a^3 - 3*A*a^2*b)*x)/b^5","A",0
73,1,107,0,0.989097," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{B a^{4} - A a^{3} b}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} + \frac{2 \, B b^{2} x^{6} - 3 \, {\left(2 \, B a b - A b^{2}\right)} x^{4} + 6 \, {\left(3 \, B a^{2} - 2 \, A a b\right)} x^{2}}{12 \, b^{4}} - \frac{{\left(4 \, B a^{3} - 3 \, A a^{2} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"-1/2*(B*a^4 - A*a^3*b)/(b^6*x^2 + a*b^5) + 1/12*(2*B*b^2*x^6 - 3*(2*B*a*b - A*b^2)*x^4 + 6*(3*B*a^2 - 2*A*a*b)*x^2)/b^4 - 1/2*(4*B*a^3 - 3*A*a^2*b)*log(b*x^2 + a)/b^5","A",0
74,1,112,0,2.229902," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a^{3} - A a^{2} b\right)} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} - \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{3 \, B b^{2} x^{5} - 5 \, {\left(2 \, B a b - A b^{2}\right)} x^{3} + 15 \, {\left(3 \, B a^{2} - 2 \, A a b\right)} x}{15 \, b^{4}}"," ",0,"1/2*(B*a^3 - A*a^2*b)*x/(b^5*x^2 + a*b^4) - 1/2*(7*B*a^3 - 5*A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/15*(3*B*b^2*x^5 - 5*(2*B*a*b - A*b^2)*x^3 + 15*(3*B*a^2 - 2*A*a*b)*x)/b^4","A",0
75,1,82,0,1.040035," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B a^{3} - A a^{2} b}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{B b x^{4} - 2 \, {\left(2 \, B a - A b\right)} x^{2}}{4 \, b^{3}} + \frac{{\left(3 \, B a^{2} - 2 \, A a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/2*(B*a^3 - A*a^2*b)/(b^5*x^2 + a*b^4) + 1/4*(B*b*x^4 - 2*(2*B*a - A*b)*x^2)/b^3 + 1/2*(3*B*a^2 - 2*A*a*b)*log(b*x^2 + a)/b^4","A",0
76,1,85,0,2.420968," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(B a^{2} - A a b\right)} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \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 b x^{3} - 3 \, {\left(2 \, B a - A b\right)} x}{3 \, b^{3}}"," ",0,"-1/2*(B*a^2 - A*a*b)*x/(b^4*x^2 + a*b^3) + 1/2*(5*B*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/3*(B*b*x^3 - 3*(2*B*a - A*b)*x)/b^3","A",0
77,1,60,0,1.031190," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B x^{2}}{2 \, b^{2}} - \frac{B a^{2} - A a b}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} - \frac{{\left(2 \, B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/2*B*x^2/b^2 - 1/2*(B*a^2 - A*a*b)/(b^4*x^2 + a*b^3) - 1/2*(2*B*a - A*b)*log(b*x^2 + a)/b^3","A",0
78,1,61,0,2.357986," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - A b\right)} x}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \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}}"," ",0,"1/2*(B*a - A*b)*x/(b^3*x^2 + a*b^2) + B*x/b^2 - 1/2*(3*B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2)","A",0
79,1,40,0,1.092250," ","integrate(x*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{B a - A b}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{B \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*(B*a - A*b)/(b^3*x^2 + a*b^2) + 1/2*B*log(b*x^2 + a)/b^2","A",0
80,1,57,0,2.411155," ","integrate((B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(B a - A b\right)} x}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} + \frac{{\left(B a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"-1/2*(B*a - A*b)*x/(a*b^2*x^2 + a^2*b) + 1/2*(B*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
81,1,51,0,1.116452," ","integrate((B*x^2+A)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{B a - A b}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} - \frac{A \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{A \log\left(x^{2}\right)}{2 \, a^{2}}"," ",0,"-1/2*(B*a - A*b)/(a*b^2*x^2 + a^2*b) - 1/2*A*log(b*x^2 + a)/a^2 + 1/2*A*log(x^2)/a^2","A",0
82,1,63,0,2.147846," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - 3 \, A b\right)} x^{2} - 2 \, A a}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}} + \frac{{\left(B a - 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}}"," ",0,"1/2*((B*a - 3*A*b)*x^2 - 2*A*a)/(a^2*b*x^3 + a^3*x) + 1/2*(B*a - 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2)","A",0
83,1,76,0,1.062749," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - 2 \, A b\right)} x^{2} - A a}{2 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}} - \frac{{\left(B a - 2 \, A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{{\left(B a - 2 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"1/2*((B*a - 2*A*b)*x^2 - A*a)/(a^2*b*x^4 + a^3*x^2) - 1/2*(B*a - 2*A*b)*log(b*x^2 + a)/a^3 + 1/2*(B*a - 2*A*b)*log(x^2)/a^3","A",0
84,1,93,0,2.452326," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{4} + 2 \, A a^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2}}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}} - \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}}"," ",0,"-1/6*(3*(3*B*a*b - 5*A*b^2)*x^4 + 2*A*a^2 + 2*(3*B*a^2 - 5*A*a*b)*x^2)/(a^3*b*x^5 + a^4*x^3) - 1/2*(3*B*a*b - 5*A*b^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
85,1,106,0,1.126090," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} x^{4} + A a^{2} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{2}}{4 \, {\left(a^{3} b x^{6} + a^{4} x^{4}\right)}} + \frac{{\left(2 \, B a b - 3 \, A b^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{4}} - \frac{{\left(2 \, B a b - 3 \, A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{4}}"," ",0,"-1/4*(2*(2*B*a*b - 3*A*b^2)*x^4 + A*a^2 + (2*B*a^2 - 3*A*a*b)*x^2)/(a^3*b*x^6 + a^4*x^4) + 1/2*(2*B*a*b - 3*A*b^2)*log(b*x^2 + a)/a^4 - 1/2*(2*B*a*b - 3*A*b^2)*log(x^2)/a^4","A",0
86,1,119,0,2.306315," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} - 6 \, A a^{3} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}}{30 \, {\left(a^{4} b x^{7} + a^{5} x^{5}\right)}} + \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}}"," ",0,"1/30*(15*(5*B*a*b^2 - 7*A*b^3)*x^6 + 10*(5*B*a^2*b - 7*A*a*b^2)*x^4 - 6*A*a^3 - 2*(5*B*a^3 - 7*A*a^2*b)*x^2)/(a^4*b*x^7 + a^5*x^5) + 1/2*(5*B*a*b^2 - 7*A*b^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
87,1,136,0,1.101976," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(3 \, B a b^{2} - 4 \, A b^{3}\right)} x^{6} + 3 \, {\left(3 \, B a^{2} b - 4 \, A a b^{2}\right)} x^{4} - 2 \, A a^{3} - {\left(3 \, B a^{3} - 4 \, A a^{2} b\right)} x^{2}}{12 \, {\left(a^{4} b x^{8} + a^{5} x^{6}\right)}} - \frac{{\left(3 \, B a b^{2} - 4 \, A b^{3}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{5}} + \frac{{\left(3 \, B a b^{2} - 4 \, A b^{3}\right)} \log\left(x^{2}\right)}{2 \, a^{5}}"," ",0,"1/12*(6*(3*B*a*b^2 - 4*A*b^3)*x^6 + 3*(3*B*a^2*b - 4*A*a*b^2)*x^4 - 2*A*a^3 - (3*B*a^3 - 4*A*a^2*b)*x^2)/(a^4*b*x^8 + a^5*x^6) - 1/2*(3*B*a*b^2 - 4*A*b^3)*log(b*x^2 + a)/a^5 + 1/2*(3*B*a*b^2 - 4*A*b^3)*log(x^2)/a^5","A",0
88,1,165,0,1.124851," ","integrate(x^11*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{11 \, B a^{6} - 9 \, A a^{5} b + 2 \, {\left(6 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} x^{2}}{4 \, {\left(b^{9} x^{4} + 2 \, a b^{8} x^{2} + a^{2} b^{7}\right)}} + \frac{3 \, B b^{3} x^{8} - 4 \, {\left(3 \, B a b^{2} - A b^{3}\right)} x^{6} + 18 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{4} - 24 \, {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} x^{2}}{24 \, b^{6}} + \frac{5 \, {\left(3 \, B a^{4} - 2 \, A a^{3} b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{7}}"," ",0,"1/4*(11*B*a^6 - 9*A*a^5*b + 2*(6*B*a^5*b - 5*A*a^4*b^2)*x^2)/(b^9*x^4 + 2*a*b^8*x^2 + a^2*b^7) + 1/24*(3*B*b^3*x^8 - 4*(3*B*a*b^2 - A*b^3)*x^6 + 18*(2*B*a^2*b - A*a*b^2)*x^4 - 24*(5*B*a^3 - 3*A*a^2*b)*x^2)/b^6 + 5/2*(3*B*a^4 - 2*A*a^3*b)*log(b*x^2 + a)/b^7","A",0
89,1,141,0,1.063022," ","integrate(x^9*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{9 \, B a^{5} - 7 \, A a^{4} b + 2 \, {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{2}}{4 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}} + \frac{2 \, B b^{2} x^{6} - 3 \, {\left(3 \, B a b - A b^{2}\right)} x^{4} + 18 \, {\left(2 \, B a^{2} - A a b\right)} x^{2}}{12 \, b^{5}} - \frac{{\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} \log\left(b x^{2} + a\right)}{b^{6}}"," ",0,"-1/4*(9*B*a^5 - 7*A*a^4*b + 2*(5*B*a^4*b - 4*A*a^3*b^2)*x^2)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6) + 1/12*(2*B*b^2*x^6 - 3*(3*B*a*b - A*b^2)*x^4 + 18*(2*B*a^2 - A*a*b)*x^2)/b^5 - (5*B*a^3 - 3*A*a^2*b)*log(b*x^2 + a)/b^6","A",0
90,1,116,0,1.090205," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{7 \, B a^{4} - 5 \, A a^{3} b + 2 \, {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{2}}{4 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}} + \frac{B b x^{4} - 2 \, {\left(3 \, B a - A b\right)} x^{2}}{4 \, b^{4}} + \frac{3 \, {\left(2 \, B a^{2} - A a b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"1/4*(7*B*a^4 - 5*A*a^3*b + 2*(4*B*a^3*b - 3*A*a^2*b^2)*x^2)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5) + 1/4*(B*b*x^4 - 2*(3*B*a - A*b)*x^2)/b^4 + 3/2*(2*B*a^2 - A*a*b)*log(b*x^2 + a)/b^5","A",0
91,1,94,0,1.080936," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{5 \, B a^{3} - 3 \, A a^{2} b + 2 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{2}}{4 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}} + \frac{B x^{2}}{2 \, b^{3}} - \frac{{\left(3 \, B a - A b\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"-1/4*(5*B*a^3 - 3*A*a^2*b + 2*(3*B*a^2*b - 2*A*a*b^2)*x^2)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4) + 1/2*B*x^2/b^3 - 1/2*(3*B*a - A*b)*log(b*x^2 + a)/b^4","A",0
92,1,72,0,1.009120," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, B a^{2} - A a b + 2 \, {\left(2 \, B a b - A b^{2}\right)} x^{2}}{4 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{B \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/4*(3*B*a^2 - A*a*b + 2*(2*B*a*b - A*b^2)*x^2)/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3) + 1/2*B*log(b*x^2 + a)/b^3","A",0
93,1,42,0,1.055784," ","integrate(x*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{2 \, B b x^{2} + B a + A b}{4 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{2} + a^{2} b^{2}\right)}}"," ",0,"-1/4*(2*B*b*x^2 + B*a + A*b)/(b^4*x^4 + 2*a*b^3*x^2 + a^2*b^2)","A",0
94,1,77,0,1.120243," ","integrate((B*x^2+A)/x/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{2 \, A b^{2} x^{2} - B a^{2} + 3 \, A a b}{4 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} - \frac{A \log\left(b x^{2} + a\right)}{2 \, a^{3}} + \frac{A \log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"1/4*(2*A*b^2*x^2 - B*a^2 + 3*A*a*b)/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) - 1/2*A*log(b*x^2 + a)/a^3 + 1/2*A*log(x^2)/a^3","A",0
95,1,109,0,0.999011," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(B a b - 3 \, A b^{2}\right)} x^{4} - 2 \, A a^{2} + 3 \, {\left(B a^{2} - 3 \, A a b\right)} x^{2}}{4 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{4} + a^{5} x^{2}\right)}} - \frac{{\left(B a - 3 \, A b\right)} \log\left(b x^{2} + a\right)}{2 \, a^{4}} + \frac{{\left(B a - 3 \, A b\right)} \log\left(x^{2}\right)}{2 \, a^{4}}"," ",0,"1/4*(2*(B*a*b - 3*A*b^2)*x^4 - 2*A*a^2 + 3*(B*a^2 - 3*A*a*b)*x^2)/(a^3*b^2*x^6 + 2*a^4*b*x^4 + a^5*x^2) - 1/2*(B*a - 3*A*b)*log(b*x^2 + a)/a^4 + 1/2*(B*a - 3*A*b)*log(x^2)/a^4","A",0
96,1,137,0,1.060624," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 9 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} x^{4} + A a^{3} + 2 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} x^{2}}{4 \, {\left(a^{4} b^{2} x^{8} + 2 \, a^{5} b x^{6} + a^{6} x^{4}\right)}} + \frac{3 \, {\left(B a b - 2 \, A b^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{5}} - \frac{3 \, {\left(B a b - 2 \, A b^{2}\right)} \log\left(x^{2}\right)}{2 \, a^{5}}"," ",0,"-1/4*(6*(B*a*b^2 - 2*A*b^3)*x^6 + 9*(B*a^2*b - 2*A*a*b^2)*x^4 + A*a^3 + 2*(B*a^3 - 2*A*a^2*b)*x^2)/(a^4*b^2*x^8 + 2*a^5*b*x^6 + a^6*x^4) + 3/2*(B*a*b - 2*A*b^2)*log(b*x^2 + a)/a^5 - 3/2*(B*a*b - 2*A*b^2)*log(x^2)/a^5","A",0
97,1,170,0,1.028984," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(3 \, B a b^{3} - 5 \, A b^{4}\right)} x^{8} + 18 \, {\left(3 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{6} - 2 \, A a^{4} + 4 \, {\left(3 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{4} - {\left(3 \, B a^{4} - 5 \, A a^{3} b\right)} x^{2}}{12 \, {\left(a^{5} b^{2} x^{10} + 2 \, a^{6} b x^{8} + a^{7} x^{6}\right)}} - \frac{{\left(3 \, B a b^{2} - 5 \, A b^{3}\right)} \log\left(b x^{2} + a\right)}{a^{6}} + \frac{{\left(3 \, B a b^{2} - 5 \, A b^{3}\right)} \log\left(x^{2}\right)}{a^{6}}"," ",0,"1/12*(12*(3*B*a*b^3 - 5*A*b^4)*x^8 + 18*(3*B*a^2*b^2 - 5*A*a*b^3)*x^6 - 2*A*a^4 + 4*(3*B*a^3*b - 5*A*a^2*b^2)*x^4 - (3*B*a^4 - 5*A*a^3*b)*x^2)/(a^5*b^2*x^10 + 2*a^6*b*x^8 + a^7*x^6) - (3*B*a*b^2 - 5*A*b^3)*log(b*x^2 + a)/a^6 + (3*B*a*b^2 - 5*A*b^3)*log(x^2)/a^6","A",0
98,1,171,0,2.346765," ","integrate(x^10*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(21 \, B a^{4} b - 17 \, A a^{3} b^{2}\right)} x^{3} + {\left(19 \, B a^{5} - 15 \, A a^{4} b\right)} x}{8 \, {\left(b^{8} x^{4} + 2 \, a b^{7} x^{2} + a^{2} b^{6}\right)}} + \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{5 \, B b^{3} x^{7} - 7 \, {\left(3 \, B a b^{2} - A b^{3}\right)} x^{5} + 35 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{3} - 70 \, {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} x}{35 \, b^{6}}"," ",0,"-1/8*((21*B*a^4*b - 17*A*a^3*b^2)*x^3 + (19*B*a^5 - 15*A*a^4*b)*x)/(b^8*x^4 + 2*a*b^7*x^2 + a^2*b^6) + 9/8*(11*B*a^4 - 7*A*a^3*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^6) + 1/35*(5*B*b^3*x^7 - 7*(3*B*a*b^2 - A*b^3)*x^5 + 35*(2*B*a^2*b - A*a*b^2)*x^3 - 70*(5*B*a^3 - 3*A*a^2*b)*x)/b^6","A",0
99,1,147,0,2.392483," ","integrate(x^8*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(17 \, B a^{3} b - 13 \, A a^{2} b^{2}\right)} x^{3} + {\left(15 \, B a^{4} - 11 \, A a^{3} b\right)} x}{8 \, {\left(b^{7} x^{4} + 2 \, a b^{6} x^{2} + a^{2} b^{5}\right)}} - \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{3 \, B b^{2} x^{5} - 5 \, {\left(3 \, B a b - A b^{2}\right)} x^{3} + 45 \, {\left(2 \, B a^{2} - A a b\right)} x}{15 \, b^{5}}"," ",0,"1/8*((17*B*a^3*b - 13*A*a^2*b^2)*x^3 + (15*B*a^4 - 11*A*a^3*b)*x)/(b^7*x^4 + 2*a*b^6*x^2 + a^2*b^5) - 7/8*(9*B*a^3 - 5*A*a^2*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^5) + 1/15*(3*B*b^2*x^5 - 5*(3*B*a*b - A*b^2)*x^3 + 45*(2*B*a^2 - A*a*b)*x)/b^5","A",0
100,1,120,0,2.341978," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(13 \, B a^{2} b - 9 \, A a b^{2}\right)} x^{3} + {\left(11 \, B a^{3} - 7 \, A a^{2} b\right)} x}{8 \, {\left(b^{6} x^{4} + 2 \, a b^{5} x^{2} + a^{2} b^{4}\right)}} + \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{B b x^{3} - 3 \, {\left(3 \, B a - A b\right)} x}{3 \, b^{4}}"," ",0,"-1/8*((13*B*a^2*b - 9*A*a*b^2)*x^3 + (11*B*a^3 - 7*A*a^2*b)*x)/(b^6*x^4 + 2*a*b^5*x^2 + a^2*b^4) + 5/8*(7*B*a^2 - 3*A*a*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/3*(B*b*x^3 - 3*(3*B*a - A*b)*x)/b^4","A",0
101,1,94,0,2.293427," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(9 \, B a b - 5 \, A b^{2}\right)} x^{3} + {\left(7 \, B a^{2} - 3 \, A a b\right)} x}{8 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}} + \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}}"," ",0,"1/8*((9*B*a*b - 5*A*b^2)*x^3 + (7*B*a^2 - 3*A*a*b)*x)/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3) + B*x/b^3 - 3/8*(5*B*a - A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3)","A",0
102,1,92,0,2.372714," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, B a b - A b^{2}\right)} x^{3} + {\left(3 \, B a^{2} + A a b\right)} x}{8 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}} + \frac{{\left(3 \, B a + A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a b^{2}}"," ",0,"-1/8*((5*B*a*b - A*b^2)*x^3 + (3*B*a^2 + A*a*b)*x)/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2) + 1/8*(3*B*a + A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2)","A",0
103,1,92,0,2.516040," ","integrate((B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(B a b + 3 \, A b^{2}\right)} x^{3} - {\left(B a^{2} - 5 \, A a b\right)} x}{8 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} + \frac{{\left(B a + 3 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b}"," ",0,"1/8*((B*a*b + 3*A*b^2)*x^3 - (B*a^2 - 5*A*a*b)*x)/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) + 1/8*(B*a + 3*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b)","A",0
104,1,96,0,2.427629," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(B a b - 5 \, A b^{2}\right)} x^{4} - 8 \, A a^{2} + 5 \, {\left(B a^{2} - 5 \, A a b\right)} x^{2}}{8 \, {\left(a^{3} b^{2} x^{5} + 2 \, a^{4} b x^{3} + a^{5} x\right)}} + \frac{3 \, {\left(B a - 5 \, A b\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{3}}"," ",0,"1/8*(3*(B*a*b - 5*A*b^2)*x^4 - 8*A*a^2 + 5*(B*a^2 - 5*A*a*b)*x^2)/(a^3*b^2*x^5 + 2*a^4*b*x^3 + a^5*x) + 3/8*(B*a - 5*A*b)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
105,1,128,0,2.285375," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + 8 \, A a^{3} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}}{24 \, {\left(a^{4} b^{2} x^{7} + 2 \, a^{5} b x^{5} + a^{6} x^{3}\right)}} - \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}}"," ",0,"-1/24*(15*(3*B*a*b^2 - 7*A*b^3)*x^6 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^4 + 8*A*a^3 + 8*(3*B*a^3 - 7*A*a^2*b)*x^2)/(a^4*b^2*x^7 + 2*a^5*b*x^5 + a^6*x^3) - 5/8*(3*B*a*b - 7*A*b^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^4)","A",0
106,1,154,0,2.361139," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{8} + 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{6} - 24 \, A a^{4} + 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{4} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x^{2}}{120 \, {\left(a^{5} b^{2} x^{9} + 2 \, a^{6} b x^{7} + a^{7} x^{5}\right)}} + \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}}"," ",0,"1/120*(105*(5*B*a*b^3 - 9*A*b^4)*x^8 + 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^6 - 24*A*a^4 + 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^4 - 8*(5*B*a^4 - 9*A*a^3*b)*x^2)/(a^5*b^2*x^9 + 2*a^6*b*x^7 + a^7*x^5) + 7/8*(5*B*a*b^2 - 9*A*b^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^5)","A",0
107,1,12,0,2.286882," ","integrate((b*x^2+a)/(x^2+1),x, algorithm=""maxima"")","b x + {\left(a - b\right)} \arctan\left(x\right)"," ",0,"b*x + (a - b)*arctan(x)","A",0
108,1,23,0,0.993320," ","integrate((b*x^2+a)/(-x^2+1),x, algorithm=""maxima"")","-b x + \frac{1}{2} \, {\left(a + b\right)} \log\left(x + 1\right) - \frac{1}{2} \, {\left(a + b\right)} \log\left(x - 1\right)"," ",0,"-b*x + 1/2*(a + b)*log(x + 1) - 1/2*(a + b)*log(x - 1)","B",0
109,1,10,0,1.034331," ","integrate((x^2+1)/(x^2-1)^2,x, algorithm=""maxima"")","-\frac{x}{x^{2} - 1}"," ",0,"-x/(x^2 - 1)","A",0
110,1,9,0,1.021207," ","integrate((-x^2+1)/(x^2+1)^2,x, algorithm=""maxima"")","\frac{x}{x^{2} + 1}"," ",0,"x/(x^2 + 1)","A",0
111,1,15,0,2.300435," ","integrate((2*x^2+3)/(x^2+1)^2,x, algorithm=""maxima"")","\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
112,1,15,0,2.344164," ","integrate((x^2-2)/(x^2+1)^2,x, algorithm=""maxima"")","-\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
113,1,14,0,2.291960," ","integrate((x^2+3)/(x^2+1)^2,x, algorithm=""maxima"")","\frac{x}{x^{2} + 1} + 2 \, \arctan\left(x\right)"," ",0,"x/(x^2 + 1) + 2*arctan(x)","A",0
114,1,14,0,1.001464," ","integrate((b*x^2+a)/(b*x^2-a)^2,x, algorithm=""maxima"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
115,1,14,0,1.052166," ","integrate((b*x^2+a)/(-b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{x}{b x^{2} - a}"," ",0,"-x/(b*x^2 - a)","A",0
116,1,49,0,2.422165," ","integrate((B*x^2+A)/(-b*x^2+a),x, algorithm=""maxima"")","-\frac{B x}{b} - \frac{{\left(B a + A b\right)} \log\left(\frac{b x - \sqrt{a b}}{b x + \sqrt{a b}}\right)}{2 \, \sqrt{a b} b}"," ",0,"-B*x/b - 1/2*(B*a + A*b)*log((b*x - sqrt(a*b))/(b*x + sqrt(a*b)))/(sqrt(a*b)*b)","A",0
117,1,30,0,2.468892," ","integrate((x^2+1)/(x^2+16)^3,x, algorithm=""maxima"")","\frac{19 \, x^{3} - 176 \, x}{2048 \, {\left(x^{4} + 32 \, x^{2} + 256\right)}} + \frac{19}{8192} \, \arctan\left(\frac{1}{4} \, x\right)"," ",0,"1/2048*(19*x^3 - 176*x)/(x^4 + 32*x^2 + 256) + 19/8192*arctan(1/4*x)","A",0
118,1,16,0,1.029037," ","integrate((2*x^2+1)/x^5/(x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{4 \, {\left(x^{8} + 2 \, x^{6} + x^{4}\right)}}"," ",0,"-1/4/(x^8 + 2*x^6 + x^4)","A",0
119,1,1,0,1.048259," ","integrate((-x^2+1)^2/(x^2-1)^2,x, algorithm=""maxima"")","x"," ",0,"x","A",0
120,1,6,0,1.062834," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{1}{4} \, c x^{4}"," ",0,"1/4*c*x^4","A",0
121,1,6,0,0.967520," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{1}{3} \, c x^{3}"," ",0,"1/3*c*x^3","A",0
122,1,6,0,0.980903," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{1}{2} \, c x^{2}"," ",0,"1/2*c*x^2","A",0
123,1,3,0,1.050965," ","integrate((b*c*x^2+a*c)/(b*x^2+a),x, algorithm=""maxima"")","c x"," ",0,"c*x","A",0
124,1,7,0,1.020996," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a),x, algorithm=""maxima"")","\frac{1}{2} \, c \log\left(x^{2}\right)"," ",0,"1/2*c*log(x^2)","A",0
125,1,6,0,1.087768," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a),x, algorithm=""maxima"")","-\frac{c}{x}"," ",0,"-c/x","A",0
126,1,6,0,1.059349," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a),x, algorithm=""maxima"")","-\frac{c}{2 \, x^{2}}"," ",0,"-1/2*c/x^2","A",0
127,1,25,0,1.082272," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{c x^{2}}{2 \, b} - \frac{a c \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*c*x^2/b - 1/2*a*c*log(b*x^2 + a)/b^2","A",0
128,1,28,0,2.575326," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\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
129,1,14,0,1.149700," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{c \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*c*log(b*x^2 + a)/b","A",0
130,1,16,0,2.226986," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\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
131,1,25,0,0.999723," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{c \log\left(b x^{2} + a\right)}{2 \, a} + \frac{c \log\left(x^{2}\right)}{2 \, a}"," ",0,"-1/2*c*log(b*x^2 + a)/a + 1/2*c*log(x^2)/a","A",0
132,1,31,0,2.345648," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\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
133,1,36,0,1.038168," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c \log\left(b x^{2} + a\right)}{2 \, a^{2}} - \frac{b c \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{c}{2 \, a x^{2}}"," ",0,"1/2*b*c*log(b*x^2 + a)/a^2 - 1/2*b*c*log(x^2)/a^2 - 1/2*c/(a*x^2)","A",0
134,1,34,0,1.027416," ","integrate(x^3*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{a c}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{c \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*a*c/(b^3*x^2 + a*b^2) + 1/2*c*log(b*x^2 + a)/b^2","A",0
135,1,38,0,2.387754," ","integrate(x^2*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{c x}{2 \, {\left(b^{2} x^{2} + a b\right)}} + \frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} b}"," ",0,"-1/2*c*x/(b^2*x^2 + a*b) + 1/2*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
136,1,16,0,1.003226," ","integrate(x*(b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{c}{2 \, {\left(b^{2} x^{2} + a b\right)}}"," ",0,"-1/2*c/(b^2*x^2 + a*b)","A",0
137,1,37,0,2.400593," ","integrate((b*c*x^2+a*c)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{c x}{2 \, {\left(a b x^{2} + a^{2}\right)}} + \frac{c \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a}"," ",0,"1/2*c*x/(a*b*x^2 + a^2) + 1/2*c*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a)","A",0
138,1,40,0,1.007926," ","integrate((b*c*x^2+a*c)/x/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{c}{2 \, {\left(a b x^{2} + a^{2}\right)}} - \frac{c \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{c \log\left(x^{2}\right)}{2 \, a^{2}}"," ",0,"1/2*c/(a*b*x^2 + a^2) - 1/2*c*log(b*x^2 + a)/a^2 + 1/2*c*log(x^2)/a^2","A",0
139,1,52,0,2.400059," ","integrate((b*c*x^2+a*c)/x^2/(b*x^2+a)^3,x, algorithm=""maxima"")","-\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(a^{2} b x^{3} + a^{3} x\right)}}"," ",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)/(a^2*b*x^3 + a^3*x)","A",0
140,1,57,0,1.050295," ","integrate((b*c*x^2+a*c)/x^3/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{2 \, b c x^{2} + a c}{2 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}} + \frac{b c \log\left(b x^{2} + a\right)}{a^{3}} - \frac{b c \log\left(x^{2}\right)}{a^{3}}"," ",0,"-1/2*(2*b*c*x^2 + a*c)/(a^2*b*x^4 + a^3*x^2) + b*c*log(b*x^2 + a)/a^3 - b*c*log(x^2)/a^3","A",0
141,1,51,0,1.040226," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} d x^{11} + \frac{1}{9} \, {\left(b^{2} c + 2 \, a b d\right)} x^{9} + \frac{1}{5} \, a^{2} c x^{5} + \frac{1}{7} \, {\left(2 \, a b c + a^{2} d\right)} x^{7}"," ",0,"1/11*b^2*d*x^11 + 1/9*(b^2*c + 2*a*b*d)*x^9 + 1/5*a^2*c*x^5 + 1/7*(2*a*b*c + a^2*d)*x^7","A",0
142,1,51,0,0.988907," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} d x^{10} + \frac{1}{8} \, {\left(b^{2} c + 2 \, a b d\right)} x^{8} + \frac{1}{4} \, a^{2} c x^{4} + \frac{1}{6} \, {\left(2 \, a b c + a^{2} d\right)} x^{6}"," ",0,"1/10*b^2*d*x^10 + 1/8*(b^2*c + 2*a*b*d)*x^8 + 1/4*a^2*c*x^4 + 1/6*(2*a*b*c + a^2*d)*x^6","A",0
143,1,51,0,0.955586," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} d x^{9} + \frac{1}{7} \, {\left(b^{2} c + 2 \, a b d\right)} x^{7} + \frac{1}{3} \, a^{2} c x^{3} + \frac{1}{5} \, {\left(2 \, a b c + a^{2} d\right)} x^{5}"," ",0,"1/9*b^2*d*x^9 + 1/7*(b^2*c + 2*a*b*d)*x^7 + 1/3*a^2*c*x^3 + 1/5*(2*a*b*c + a^2*d)*x^5","A",0
144,1,51,0,1.069384," ","integrate(x*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} d x^{8} + \frac{1}{6} \, {\left(b^{2} c + 2 \, a b d\right)} x^{6} + \frac{1}{2} \, a^{2} c x^{2} + \frac{1}{4} \, {\left(2 \, a b c + a^{2} d\right)} x^{4}"," ",0,"1/8*b^2*d*x^8 + 1/6*(b^2*c + 2*a*b*d)*x^6 + 1/2*a^2*c*x^2 + 1/4*(2*a*b*c + a^2*d)*x^4","A",0
145,1,48,0,1.052860," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} d x^{7} + \frac{1}{5} \, {\left(b^{2} c + 2 \, a b d\right)} x^{5} + a^{2} c x + \frac{1}{3} \, {\left(2 \, a b c + a^{2} d\right)} x^{3}"," ",0,"1/7*b^2*d*x^7 + 1/5*(b^2*c + 2*a*b*d)*x^5 + a^2*c*x + 1/3*(2*a*b*c + a^2*d)*x^3","A",0
146,1,52,0,1.049577," ","integrate((b*x^2+a)^2*(d*x^2+c)/x,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} d x^{6} + \frac{1}{4} \, {\left(b^{2} c + 2 \, a b d\right)} x^{4} + \frac{1}{2} \, a^{2} c \log\left(x^{2}\right) + \frac{1}{2} \, {\left(2 \, a b c + a^{2} d\right)} x^{2}"," ",0,"1/6*b^2*d*x^6 + 1/4*(b^2*c + 2*a*b*d)*x^4 + 1/2*a^2*c*log(x^2) + 1/2*(2*a*b*c + a^2*d)*x^2","A",0
147,1,48,0,1.068723," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} d x^{5} + \frac{1}{3} \, {\left(b^{2} c + 2 \, a b d\right)} x^{3} - \frac{a^{2} c}{x} + {\left(2 \, a b c + a^{2} d\right)} x"," ",0,"1/5*b^2*d*x^5 + 1/3*(b^2*c + 2*a*b*d)*x^3 - a^2*c/x + (2*a*b*c + a^2*d)*x","A",0
148,1,52,0,1.072312," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} d x^{4} + \frac{1}{2} \, {\left(b^{2} c + 2 \, a b d\right)} x^{2} + \frac{1}{2} \, {\left(2 \, a b c + a^{2} d\right)} \log\left(x^{2}\right) - \frac{a^{2} c}{2 \, x^{2}}"," ",0,"1/4*b^2*d*x^4 + 1/2*(b^2*c + 2*a*b*d)*x^2 + 1/2*(2*a*b*c + a^2*d)*log(x^2) - 1/2*a^2*c/x^2","A",0
149,1,50,0,1.044937," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} d x^{3} + {\left(b^{2} c + 2 \, a b d\right)} x - \frac{a^{2} c + 3 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/3*b^2*d*x^3 + (b^2*c + 2*a*b*d)*x - 1/3*(a^2*c + 3*(2*a*b*c + a^2*d)*x^2)/x^3","A",0
150,1,85,0,1.072654," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{13} \, b^{2} d^{2} x^{13} + \frac{2}{11} \, {\left(b^{2} c d + a b d^{2}\right)} x^{11} + \frac{1}{9} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{9} + \frac{1}{5} \, a^{2} c^{2} x^{5} + \frac{2}{7} \, {\left(a b c^{2} + a^{2} c d\right)} x^{7}"," ",0,"1/13*b^2*d^2*x^13 + 2/11*(b^2*c*d + a*b*d^2)*x^11 + 1/9*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^9 + 1/5*a^2*c^2*x^5 + 2/7*(a*b*c^2 + a^2*c*d)*x^7","A",0
151,1,85,0,1.153679," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} d^{2} x^{12} + \frac{1}{5} \, {\left(b^{2} c d + a b d^{2}\right)} x^{10} + \frac{1}{8} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{8} + \frac{1}{4} \, a^{2} c^{2} x^{4} + \frac{1}{3} \, {\left(a b c^{2} + a^{2} c d\right)} x^{6}"," ",0,"1/12*b^2*d^2*x^12 + 1/5*(b^2*c*d + a*b*d^2)*x^10 + 1/8*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^8 + 1/4*a^2*c^2*x^4 + 1/3*(a*b*c^2 + a^2*c*d)*x^6","A",0
152,1,85,0,1.072231," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} d^{2} x^{11} + \frac{2}{9} \, {\left(b^{2} c d + a b d^{2}\right)} x^{9} + \frac{1}{7} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{7} + \frac{1}{3} \, a^{2} c^{2} x^{3} + \frac{2}{5} \, {\left(a b c^{2} + a^{2} c d\right)} x^{5}"," ",0,"1/11*b^2*d^2*x^11 + 2/9*(b^2*c*d + a*b*d^2)*x^9 + 1/7*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^7 + 1/3*a^2*c^2*x^3 + 2/5*(a*b*c^2 + a^2*c*d)*x^5","A",0
153,1,85,0,1.021631," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} d^{2} x^{10} + \frac{1}{4} \, {\left(b^{2} c d + a b d^{2}\right)} x^{8} + \frac{1}{6} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{6} + \frac{1}{2} \, a^{2} c^{2} x^{2} + \frac{1}{2} \, {\left(a b c^{2} + a^{2} c d\right)} x^{4}"," ",0,"1/10*b^2*d^2*x^10 + 1/4*(b^2*c*d + a*b*d^2)*x^8 + 1/6*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^6 + 1/2*a^2*c^2*x^2 + 1/2*(a*b*c^2 + a^2*c*d)*x^4","A",0
154,1,82,0,1.062568," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} d^{2} x^{9} + \frac{2}{7} \, {\left(b^{2} c d + a b d^{2}\right)} x^{7} + \frac{1}{5} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{5} + a^{2} c^{2} x + \frac{2}{3} \, {\left(a b c^{2} + a^{2} c d\right)} x^{3}"," ",0,"1/9*b^2*d^2*x^9 + 2/7*(b^2*c*d + a*b*d^2)*x^7 + 1/5*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^5 + a^2*c^2*x + 2/3*(a*b*c^2 + a^2*c*d)*x^3","A",0
155,1,85,0,1.065546," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} d^{2} x^{8} + \frac{1}{3} \, {\left(b^{2} c d + a b d^{2}\right)} x^{6} + \frac{1}{4} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{4} + \frac{1}{2} \, a^{2} c^{2} \log\left(x^{2}\right) + {\left(a b c^{2} + a^{2} c d\right)} x^{2}"," ",0,"1/8*b^2*d^2*x^8 + 1/3*(b^2*c*d + a*b*d^2)*x^6 + 1/4*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4 + 1/2*a^2*c^2*log(x^2) + (a*b*c^2 + a^2*c*d)*x^2","A",0
156,1,83,0,1.097208," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} d^{2} x^{7} + \frac{2}{5} \, {\left(b^{2} c d + a b d^{2}\right)} x^{5} + \frac{1}{3} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{3} - \frac{a^{2} c^{2}}{x} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x"," ",0,"1/7*b^2*d^2*x^7 + 2/5*(b^2*c*d + a*b*d^2)*x^5 + 1/3*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^3 - a^2*c^2/x + 2*(a*b*c^2 + a^2*c*d)*x","A",0
157,1,85,0,1.049115," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} d^{2} x^{6} + \frac{1}{2} \, {\left(b^{2} c d + a b d^{2}\right)} x^{4} + \frac{1}{2} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{2} - \frac{a^{2} c^{2}}{2 \, x^{2}} + {\left(a b c^{2} + a^{2} c d\right)} \log\left(x^{2}\right)"," ",0,"1/6*b^2*d^2*x^6 + 1/2*(b^2*c*d + a*b*d^2)*x^4 + 1/2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2 - 1/2*a^2*c^2/x^2 + (a*b*c^2 + a^2*c*d)*log(x^2)","A",0
158,1,84,0,1.173884," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^4,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} d^{2} x^{5} + \frac{2}{3} \, {\left(b^{2} c d + a b d^{2}\right)} x^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x - \frac{a^{2} c^{2} + 6 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/5*b^2*d^2*x^5 + 2/3*(b^2*c*d + a*b*d^2)*x^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x - 1/3*(a^2*c^2 + 6*(a*b*c^2 + a^2*c*d)*x^2)/x^3","A",0
159,1,127,0,1.020803," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{15} \, b^{2} d^{3} x^{15} + \frac{1}{13} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{13} + \frac{1}{11} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{11} + \frac{1}{5} \, a^{2} c^{3} x^{5} + \frac{1}{9} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{9} + \frac{1}{7} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{7}"," ",0,"1/15*b^2*d^3*x^15 + 1/13*(3*b^2*c*d^2 + 2*a*b*d^3)*x^13 + 1/11*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^11 + 1/5*a^2*c^3*x^5 + 1/9*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^9 + 1/7*(2*a*b*c^3 + 3*a^2*c^2*d)*x^7","A",0
160,1,127,0,1.023684," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{14} \, b^{2} d^{3} x^{14} + \frac{1}{12} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{12} + \frac{1}{10} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{10} + \frac{1}{4} \, a^{2} c^{3} x^{4} + \frac{1}{8} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{8} + \frac{1}{6} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{6}"," ",0,"1/14*b^2*d^3*x^14 + 1/12*(3*b^2*c*d^2 + 2*a*b*d^3)*x^12 + 1/10*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^10 + 1/4*a^2*c^3*x^4 + 1/8*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^8 + 1/6*(2*a*b*c^3 + 3*a^2*c^2*d)*x^6","A",0
161,1,127,0,1.038157," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{13} \, b^{2} d^{3} x^{13} + \frac{1}{11} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{11} + \frac{1}{9} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{9} + \frac{1}{3} \, a^{2} c^{3} x^{3} + \frac{1}{7} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{7} + \frac{1}{5} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{5}"," ",0,"1/13*b^2*d^3*x^13 + 1/11*(3*b^2*c*d^2 + 2*a*b*d^3)*x^11 + 1/9*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^9 + 1/3*a^2*c^3*x^3 + 1/7*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^7 + 1/5*(2*a*b*c^3 + 3*a^2*c^2*d)*x^5","A",0
162,1,127,0,1.064378," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} d^{3} x^{12} + \frac{1}{10} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{10} + \frac{1}{8} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{8} + \frac{1}{2} \, a^{2} c^{3} x^{2} + \frac{1}{6} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{6} + \frac{1}{4} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{4}"," ",0,"1/12*b^2*d^3*x^12 + 1/10*(3*b^2*c*d^2 + 2*a*b*d^3)*x^10 + 1/8*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^8 + 1/2*a^2*c^3*x^2 + 1/6*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^6 + 1/4*(2*a*b*c^3 + 3*a^2*c^2*d)*x^4","A",0
163,1,124,0,1.012365," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{11} \, b^{2} d^{3} x^{11} + \frac{1}{9} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{9} + \frac{1}{7} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{7} + a^{2} c^{3} x + \frac{1}{5} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{5} + \frac{1}{3} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{3}"," ",0,"1/11*b^2*d^3*x^11 + 1/9*(3*b^2*c*d^2 + 2*a*b*d^3)*x^9 + 1/7*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^7 + a^2*c^3*x + 1/5*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^5 + 1/3*(2*a*b*c^3 + 3*a^2*c^2*d)*x^3","A",0
164,1,128,0,1.102524," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x,x, algorithm=""maxima"")","\frac{1}{10} \, b^{2} d^{3} x^{10} + \frac{1}{8} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{8} + \frac{1}{6} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{6} + \frac{1}{2} \, a^{2} c^{3} \log\left(x^{2}\right) + \frac{1}{4} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} + \frac{1}{2} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}"," ",0,"1/10*b^2*d^3*x^10 + 1/8*(3*b^2*c*d^2 + 2*a*b*d^3)*x^8 + 1/6*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^6 + 1/2*a^2*c^3*log(x^2) + 1/4*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^4 + 1/2*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2","A",0
165,1,124,0,1.003597," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} d^{3} x^{9} + \frac{1}{7} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{7} + \frac{1}{5} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{5} - \frac{a^{2} c^{3}}{x} + \frac{1}{3} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{3} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x"," ",0,"1/9*b^2*d^3*x^9 + 1/7*(3*b^2*c*d^2 + 2*a*b*d^3)*x^7 + 1/5*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^5 - a^2*c^3/x + 1/3*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^3 + (2*a*b*c^3 + 3*a^2*c^2*d)*x","A",0
166,1,128,0,1.059995," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} d^{3} x^{8} + \frac{1}{6} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{6} + \frac{1}{4} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{4} - \frac{a^{2} c^{3}}{2 \, x^{2}} + \frac{1}{2} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{2} + \frac{1}{2} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} \log\left(x^{2}\right)"," ",0,"1/8*b^2*d^3*x^8 + 1/6*(3*b^2*c*d^2 + 2*a*b*d^3)*x^6 + 1/4*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^4 - 1/2*a^2*c^3/x^2 + 1/2*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^2 + 1/2*(2*a*b*c^3 + 3*a^2*c^2*d)*log(x^2)","A",0
167,1,126,0,1.093161," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^4,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} d^{3} x^{7} + \frac{1}{5} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{5} + \frac{1}{3} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x - \frac{a^{2} c^{3} + 3 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}}{3 \, x^{3}}"," ",0,"1/7*b^2*d^3*x^7 + 1/5*(3*b^2*c*d^2 + 2*a*b*d^3)*x^5 + 1/3*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^3 + (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x - 1/3*(a^2*c^3 + 3*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x^3","A",0
168,1,139,0,2.414833," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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^{3} x^{7} - 21 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{5} + 35 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} - 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x}{105 \, d^{4}}"," ",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^3*x^7 - 21*(b^2*c*d^2 - 2*a*b*d^3)*x^5 + 35*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^3 - 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x)/d^4","A",0
169,1,100,0,1.049242," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{2 \, b^{2} d^{2} x^{6} - 3 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{4} + 6 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} 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(d x^{2} + c\right)}{2 \, d^{4}}"," ",0,"1/12*(2*b^2*d^2*x^6 - 3*(b^2*c*d - 2*a*b*d^2)*x^4 + 6*(b^2*c^2 - 2*a*b*c*d + 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(d*x^2 + c)/d^4","A",0
170,1,104,0,2.417564," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\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^{2} x^{5} - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{3} + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{15 \, d^{3}}"," ",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^2*x^5 - 5*(b^2*c*d - 2*a*b*d^2)*x^3 + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/d^3","A",0
171,1,65,0,1.032962," ","integrate(x*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{b^{2} d x^{4} - 2 \, {\left(b^{2} c - 2 \, a b d\right)} x^{2}}{4 \, d^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, d^{3}}"," ",0,"1/4*(b^2*d*x^4 - 2*(b^2*c - 2*a*b*d)*x^2)/d^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x^2 + c)/d^3","A",0
172,1,68,0,2.336963," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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 x^{3} - 3 \, {\left(b^{2} c - 2 \, a b d\right)} x}{3 \, d^{2}}"," ",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*x^3 - 3*(b^2*c - 2*a*b*d)*x)/d^2","A",0
173,1,61,0,1.098841," ","integrate((b*x^2+a)^2/x/(d*x^2+c),x, algorithm=""maxima"")","\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(d x^{2} + c\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(d*x^2 + c)/(c*d^2)","A",0
174,1,63,0,2.389300," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c),x, algorithm=""maxima"")","\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
175,1,70,0,1.044174," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(2 \, a b c - a^{2} d\right)} \log\left(x^{2}\right)}{2 \, c^{2}} - \frac{a^{2}}{2 \, c x^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, c^{2} d}"," ",0,"1/2*(2*a*b*c - a^2*d)*log(x^2)/c^2 - 1/2*a^2/(c*x^2) + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x^2 + c)/(c^2*d)","A",0
176,1,71,0,2.330832," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c),x, algorithm=""maxima"")","\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{a^{2} c + 3 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}}{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*(a^2*c + 3*(2*a*b*c - a^2*d)*x^2)/(c^2*x^3)","A",0
177,1,96,0,0.978175," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c),x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, c^{3}} + \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{a^{2} c + 2 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}}{4 \, c^{2} x^{4}}"," ",0,"-1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x^2 + c)/c^3 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(x^2)/c^3 - 1/4*(a^2*c + 2*(2*a*b*c - a^2*d)*x^2)/(c^2*x^4)","A",0
178,1,107,0,2.440103," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c),x, algorithm=""maxima"")","-\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 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} + 5 \, {\left(2 \, a b c^{2} - a^{2} c d\right)} x^{2}}{15 \, c^{3} x^{5}}"," ",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 - 2*a*b*c*d + a^2*d^2)*x^4 + 3*a^2*c^2 + 5*(2*a*b*c^2 - a^2*c*d)*x^2)/(c^3*x^5)","A",0
179,1,134,0,0.967399," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x^{2} + c\right)}{2 \, c^{4}} - \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{6 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} + 3 \, {\left(2 \, a b c^{2} - a^{2} c d\right)} x^{2}}{12 \, c^{3} x^{6}}"," ",0,"1/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(d*x^2 + c)/c^4 - 1/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(x^2)/c^4 - 1/12*(6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 + 3*(2*a*b*c^2 - a^2*c*d)*x^2)/(c^3*x^6)","A",0
180,1,149,0,2.379306," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x}{2 \, {\left(d^{5} x^{2} + c d^{4}\right)}} - \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{3 \, b^{2} d^{2} x^{5} - 10 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + 15 \, {\left(3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2}\right)} x}{15 \, d^{4}}"," ",0,"1/2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x/(d^5*x^2 + c*d^4) - 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) + 1/15*(3*b^2*d^2*x^5 - 10*(b^2*c*d - a*b*d^2)*x^3 + 15*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*x)/d^4","A",0
181,1,107,0,1.046765," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}}{2 \, {\left(d^{5} x^{2} + c d^{4}\right)}} + \frac{b^{2} d x^{4} - 4 \, {\left(b^{2} c - a b d\right)} x^{2}}{4 \, d^{3}} + \frac{{\left(3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, d^{4}}"," ",0,"1/2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)/(d^5*x^2 + c*d^4) + 1/4*(b^2*d*x^4 - 4*(b^2*c - a*b*d)*x^2)/d^3 + 1/2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*log(d*x^2 + c)/d^4","A",0
182,1,109,0,2.348459," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(d^{4} x^{2} + c d^{3}\right)}} + \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} d x^{3} - 6 \, {\left(b^{2} c - a b d\right)} x}{3 \, d^{3}}"," ",0,"-1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(d^4*x^2 + c*d^3) + 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) + 1/3*(b^2*d*x^3 - 6*(b^2*c - a*b*d)*x)/d^3","A",0
183,1,74,0,1.047536," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{2} x^{2}}{2 \, d^{2}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{2 \, {\left(d^{4} x^{2} + c d^{3}\right)}} - \frac{{\left(b^{2} c - a b d\right)} \log\left(d x^{2} + c\right)}{d^{3}}"," ",0,"1/2*b^2*x^2/d^2 - 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(d^4*x^2 + c*d^3) - (b^2*c - a*b*d)*log(d*x^2 + c)/d^3","A",0
184,1,96,0,2.384816," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}} + \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}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(c*d^3*x^2 + c^2*d^2) + 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)","A",0
185,1,86,0,1.068976," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(x^{2}\right)}{2 \, c^{2}} + \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{2 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}} + \frac{{\left(b^{2} c^{2} - a^{2} d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, c^{2} d^{2}}"," ",0,"1/2*a^2*log(x^2)/c^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(c*d^3*x^2 + c^2*d^2) + 1/2*(b^2*c^2 - a^2*d^2)*log(d*x^2 + c)/(c^2*d^2)","A",0
186,1,100,0,2.494296," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} c d + {\left(b^{2} c^{2} - 2 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2}}{2 \, {\left(c^{2} d^{2} x^{3} + c^{3} d x\right)}} + \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}"," ",0,"-1/2*(2*a^2*c*d + (b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*x^2)/(c^2*d^2*x^3 + c^3*d*x) + 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)","A",0
187,1,100,0,1.069242," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a^{2} c d + {\left(b^{2} c^{2} - 2 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}}{2 \, {\left(c^{2} d^{2} x^{4} + c^{3} d x^{2}\right)}} - \frac{{\left(a b c - a^{2} d\right)} \log\left(d x^{2} + c\right)}{c^{3}} + \frac{{\left(a b c - a^{2} d\right)} \log\left(x^{2}\right)}{c^{3}}"," ",0,"-1/2*(a^2*c*d + (b^2*c^2 - 2*a*b*c*d + 2*a^2*d^2)*x^2)/(c^2*d^2*x^4 + c^3*d*x^2) - (a*b*c - a^2*d)*log(d*x^2 + c)/c^3 + (a*b*c - a^2*d)*log(x^2)/c^3","A",0
188,1,118,0,2.489968," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{2} c^{2} - 6 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(6 \, a b c^{2} - 5 \, a^{2} c d\right)} x^{2}}{6 \, {\left(c^{3} d x^{5} + c^{4} x^{3}\right)}} + \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}}"," ",0,"1/6*(3*(b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*x^4 - 2*a^2*c^2 - 2*(6*a*b*c^2 - 5*a^2*c*d)*x^2)/(c^3*d*x^5 + c^4*x^3) + 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)","A",0
189,1,159,0,2.373075," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(13 \, b^{2} c^{2} d - 18 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{3} + {\left(11 \, b^{2} c^{3} - 14 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x}{8 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}} + \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{b^{2} d x^{3} - 3 \, {\left(3 \, b^{2} c - 2 \, a b d\right)} x}{3 \, d^{4}}"," ",0,"-1/8*((13*b^2*c^2*d - 18*a*b*c*d^2 + 5*a^2*d^3)*x^3 + (11*b^2*c^3 - 14*a*b*c^2*d + 3*a^2*c*d^2)*x)/(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4) + 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) + 1/3*(b^2*d*x^3 - 3*(3*b^2*c - 2*a*b*d)*x)/d^4","A",0
190,1,120,0,1.123574," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{2} x^{2}}{2 \, d^{3}} - \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^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}} - \frac{{\left(3 \, b^{2} c - 2 \, a b d\right)} \log\left(d x^{2} + c\right)}{2 \, d^{4}}"," ",0,"1/2*b^2*x^2/d^3 - 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^6*x^4 + 2*c*d^5*x^2 + c^2*d^4) - 1/2*(3*b^2*c - 2*a*b*d)*log(d*x^2 + c)/d^4","A",0
191,1,143,0,2.398559," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(9 \, b^{2} c^{2} d - 10 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + {\left(7 \, b^{2} c^{3} - 6 \, a b c^{2} d - a^{2} c d^{2}\right)} x}{8 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}} + \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}}"," ",0,"1/8*((9*b^2*c^2*d - 10*a*b*c*d^2 + a^2*d^3)*x^3 + (7*b^2*c^3 - 6*a*b*c^2*d - a^2*c*d^2)*x)/(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3) + 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)","A",0
192,1,87,0,1.022064," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2} + 4 \, {\left(b^{2} c d - a b d^{2}\right)} x^{2}}{4 \, {\left(d^{5} x^{4} + 2 \, c d^{4} x^{2} + c^{2} d^{3}\right)}} + \frac{b^{2} \log\left(d x^{2} + c\right)}{2 \, d^{3}}"," ",0,"1/4*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2 + 4*(b^2*c*d - a*b*d^2)*x^2)/(d^5*x^4 + 2*c*d^4*x^2 + c^2*d^3) + 1/2*b^2*log(d*x^2 + c)/d^3","A",0
193,1,138,0,2.324679," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{3} + 2 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} x}{8 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}} + \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}}"," ",0,"-1/8*((5*b^2*c^2*d - 2*a*b*c*d^2 - 3*a^2*d^3)*x^3 + (3*b^2*c^3 + 2*a*b*c^2*d - 5*a^2*c*d^2)*x)/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2) + 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)","A",0
194,1,109,0,1.005093," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, a^{2} c d^{2} + 2 \, {\left(b^{2} c^{2} d - a^{2} d^{3}\right)} x^{2}}{4 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}} - \frac{a^{2} \log\left(d x^{2} + c\right)}{2 \, c^{3}} + \frac{a^{2} \log\left(x^{2}\right)}{2 \, c^{3}}"," ",0,"-1/4*(b^2*c^3 + 2*a*b*c^2*d - 3*a^2*c*d^2 + 2*(b^2*c^2*d - a^2*d^3)*x^2)/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2) - 1/2*a^2*log(d*x^2 + c)/c^3 + 1/2*a^2*log(x^2)/c^3","A",0
195,1,146,0,2.410730," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{8 \, a^{2} c^{2} d - {\left(b^{2} c^{2} d + 6 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} x^{4} + {\left(b^{2} c^{3} - 10 \, a b c^{2} d + 25 \, a^{2} c d^{2}\right)} x^{2}}{8 \, {\left(c^{3} d^{3} x^{5} + 2 \, c^{4} d^{2} x^{3} + c^{5} d x\right)}} + \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}"," ",0,"-1/8*(8*a^2*c^2*d - (b^2*c^2*d + 6*a*b*c*d^2 - 15*a^2*d^3)*x^4 + (b^2*c^3 - 10*a*b*c^2*d + 25*a^2*c*d^2)*x^2)/(c^3*d^3*x^5 + 2*c^4*d^2*x^3 + c^5*d*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)","A",0
196,1,142,0,1.016909," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{2 \, a^{2} c^{2} d - 2 \, {\left(2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{4} + {\left(b^{2} c^{3} - 6 \, a b c^{2} d + 9 \, a^{2} c d^{2}\right)} x^{2}}{4 \, {\left(c^{3} d^{3} x^{6} + 2 \, c^{4} d^{2} x^{4} + c^{5} d x^{2}\right)}} - \frac{{\left(2 \, a b c - 3 \, a^{2} d\right)} \log\left(d x^{2} + c\right)}{2 \, c^{4}} + \frac{{\left(2 \, a b c - 3 \, a^{2} d\right)} \log\left(x^{2}\right)}{2 \, c^{4}}"," ",0,"-1/4*(2*a^2*c^2*d - 2*(2*a*b*c*d^2 - 3*a^2*d^3)*x^4 + (b^2*c^3 - 6*a*b*c^2*d + 9*a^2*c*d^2)*x^2)/(c^3*d^3*x^6 + 2*c^4*d^2*x^4 + c^5*d*x^2) - 1/2*(2*a*b*c - 3*a^2*d)*log(d*x^2 + c)/c^4 + 1/2*(2*a*b*c - 3*a^2*d)*log(x^2)/c^4","A",0
197,1,167,0,2.300694," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(3 \, b^{2} c^{2} d - 30 \, a b c d^{2} + 35 \, a^{2} d^{3}\right)} x^{6} - 8 \, a^{2} c^{3} + 5 \, {\left(3 \, b^{2} c^{3} - 30 \, a b c^{2} d + 35 \, a^{2} c d^{2}\right)} x^{4} - 8 \, {\left(6 \, a b c^{3} - 7 \, a^{2} c^{2} d\right)} x^{2}}{24 \, {\left(c^{4} d^{2} x^{7} + 2 \, c^{5} d x^{5} + c^{6} x^{3}\right)}} + \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}}"," ",0,"1/24*(3*(3*b^2*c^2*d - 30*a*b*c*d^2 + 35*a^2*d^3)*x^6 - 8*a^2*c^3 + 5*(3*b^2*c^3 - 30*a*b*c^2*d + 35*a^2*c*d^2)*x^4 - 8*(6*a*b*c^3 - 7*a^2*c^2*d)*x^2)/(c^4*d^2*x^7 + 2*c^5*d*x^5 + c^6*x^3) + 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)","A",0
198,1,74,0,1.019647," ","integrate(x^5*(d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, b^{2} d x^{6} + 3 \, {\left(b^{2} c - a b d\right)} x^{4} - 6 \, {\left(a b c - a^{2} d\right)} x^{2}}{12 \, b^{3}} + \frac{{\left(a^{2} b c - a^{3} d\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d*x^6 + 3*(b^2*c - a*b*d)*x^4 - 6*(a*b*c - a^2*d)*x^2)/b^3 + 1/2*(a^2*b*c - a^3*d)*log(b*x^2 + a)/b^4","A",0
199,1,77,0,2.533747," ","integrate(x^4*(d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\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^{2} d x^{5} + 5 \, {\left(b^{2} c - a b d\right)} x^{3} - 15 \, {\left(a b c - a^{2} d\right)} x}{15 \, b^{3}}"," ",0,"(a^2*b*c - a^3*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^2*d*x^5 + 5*(b^2*c - a*b*d)*x^3 - 15*(a*b*c - a^2*d)*x)/b^3","A",0
200,1,50,0,1.050716," ","integrate(x^3*(d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{b d x^{4} + 2 \, {\left(b c - a d\right)} x^{2}}{4 \, b^{2}} - \frac{{\left(a b c - a^{2} d\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/4*(b*d*x^4 + 2*(b*c - a*d)*x^2)/b^2 - 1/2*(a*b*c - a^2*d)*log(b*x^2 + a)/b^3","A",0
201,1,54,0,2.162000," ","integrate(x^2*(d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","-\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 d x^{3} + 3 \, {\left(b c - a d\right)} x}{3 \, b^{2}}"," ",0,"-(a*b*c - a^2*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b*d*x^3 + 3*(b*c - a*d)*x)/b^2","A",0
202,1,31,0,0.983443," ","integrate(x*(d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\frac{d x^{2}}{2 \, b} + \frac{{\left(b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"1/2*d*x^2/b + 1/2*(b*c - a*d)*log(b*x^2 + a)/b^2","A",0
203,1,33,0,2.273769," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""maxima"")","\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
204,1,35,0,1.109256," ","integrate((d*x^2+c)/x/(b*x^2+a),x, algorithm=""maxima"")","\frac{c \log\left(x^{2}\right)}{2 \, a} - \frac{{\left(b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, a b}"," ",0,"1/2*c*log(x^2)/a - 1/2*(b*c - a*d)*log(b*x^2 + a)/(a*b)","A",0
205,1,37,0,2.463082," ","integrate((d*x^2+c)/x^2/(b*x^2+a),x, algorithm=""maxima"")","-\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
206,1,48,0,1.044909," ","integrate((d*x^2+c)/x^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, a^{2}} - \frac{{\left(b c - a d\right)} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{c}{2 \, a x^{2}}"," ",0,"1/2*(b*c - a*d)*log(b*x^2 + a)/a^2 - 1/2*(b*c - a*d)*log(x^2)/a^2 - 1/2*c/(a*x^2)","A",0
207,1,56,0,2.327078," ","integrate((d*x^2+c)/x^4/(b*x^2+a),x, algorithm=""maxima"")","\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 \, {\left(b c - a d\right)} 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 - a*d)*x^2 - a*c)/(a^2*x^3)","A",0
208,1,137,0,1.107343," ","integrate(x^5*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{3 \, b^{3} d^{2} x^{8} + 4 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{6} + 6 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{4} - 12 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} 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(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"1/24*(3*b^3*d^2*x^8 + 4*(2*b^3*c*d - a*b^2*d^2)*x^6 + 6*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^4 - 12*(a*b^2*c^2 - 2*a^2*b*c*d + 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(b*x^2 + a)/b^5","A",0
209,1,140,0,2.402087," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\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^{3} d^{2} x^{7} + 21 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{5} + 35 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} - 105 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x}{105 \, b^{4}}"," ",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^3*d^2*x^7 + 21*(2*b^3*c*d - a*b^2*d^2)*x^5 + 35*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3 - 105*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)/b^4","A",0
210,1,101,0,1.034396," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, b^{2} d^{2} x^{6} + 3 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{4} + 6 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} 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(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d^2*x^6 + 3*(2*b^2*c*d - a*b*d^2)*x^4 + 6*(b^2*c^2 - 2*a*b*c*d + 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(b*x^2 + a)/b^4","A",0
211,1,105,0,2.457087," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","-\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^{2} d^{2} x^{5} + 5 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x^{3} + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{15 \, b^{3}}"," ",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^2*d^2*x^5 + 5*(2*b^2*c*d - a*b*d^2)*x^3 + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x)/b^3","A",0
212,1,66,0,1.120899," ","integrate(x*(d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\frac{b d^{2} x^{4} + 2 \, {\left(2 \, b c d - a d^{2}\right)} x^{2}}{4 \, b^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/4*(b*d^2*x^4 + 2*(2*b*c*d - a*d^2)*x^2)/b^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x^2 + a)/b^3","A",0
213,1,69,0,2.403600," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""maxima"")","\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 d^{2} x^{3} + 3 \, {\left(2 \, b c d - a d^{2}\right)} x}{3 \, b^{2}}"," ",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*d^2*x^3 + 3*(2*b*c*d - a*d^2)*x)/b^2","A",0
214,1,61,0,1.109806," ","integrate((d*x^2+c)^2/x/(b*x^2+a),x, algorithm=""maxima"")","\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(b x^{2} + a\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(b*x^2 + a)/(a*b^2)","A",0
215,1,63,0,2.430535," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a),x, algorithm=""maxima"")","\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
216,1,69,0,1.128075," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(b c^{2} - 2 \, a c d\right)} \log\left(x^{2}\right)}{2 \, a^{2}} - \frac{c^{2}}{2 \, a x^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{2} b}"," ",0,"-1/2*(b*c^2 - 2*a*c*d)*log(x^2)/a^2 - 1/2*c^2/(a*x^2) + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x^2 + a)/(a^2*b)","A",0
217,1,70,0,2.456192," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a),x, algorithm=""maxima"")","\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{a c^{2} - 3 \, {\left(b c^{2} - 2 \, a c d\right)} x^{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*(a*c^2 - 3*(b*c^2 - 2*a*c*d)*x^2)/(a^2*x^3)","A",0
218,1,219,0,1.200798," ","integrate(x^5*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{12 \, b^{4} d^{3} x^{10} + 15 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{8} + 20 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{6} + 30 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} - 60 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{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(b x^{2} + a\right)}{2 \, b^{6}}"," ",0,"1/120*(12*b^4*d^3*x^10 + 15*(3*b^4*c*d^2 - a*b^3*d^3)*x^8 + 20*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^6 + 30*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4 - 60*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x^2)/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(b*x^2 + a)/b^6","A",0
219,1,222,0,2.584446," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\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^{4} d^{3} x^{9} + 45 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{7} + 63 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{5} + 105 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{3} - 315 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x}{315 \, b^{5}}"," ",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^4*d^3*x^9 + 45*(3*b^4*c*d^2 - a*b^3*d^3)*x^7 + 63*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^5 + 105*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^3 - 315*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x)/b^5","A",0
220,1,168,0,1.038914," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{3 \, b^{3} d^{3} x^{8} + 4 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{6} + 6 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + 12 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}}{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(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"1/24*(3*b^3*d^3*x^8 + 4*(3*b^3*c*d^2 - a*b^2*d^3)*x^6 + 6*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + 12*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - 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(b*x^2 + a)/b^5","A",0
221,1,172,0,2.350146," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","-\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^{3} d^{3} x^{7} + 21 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{5} + 35 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} + 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x}{105 \, b^{4}}"," ",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^3*d^3*x^7 + 21*(3*b^3*c*d^2 - a*b^2*d^3)*x^5 + 35*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^3 + 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x)/b^4","A",0
222,1,119,0,1.057669," ","integrate(x*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, b^{2} d^{3} x^{6} + 3 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{4} + 6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} 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(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/12*(2*b^2*d^3*x^6 + 3*(3*b^2*c*d^2 - a*b*d^3)*x^4 + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + 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(b*x^2 + a)/b^4","A",0
223,1,122,0,2.432363," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","\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^{2} d^{3} x^{5} + 5 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{3} + 15 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x}{15 \, b^{3}}"," ",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^2*d^3*x^5 + 5*(3*b^2*c*d^2 - a*b*d^3)*x^3 + 15*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x)/b^3","A",0
224,1,98,0,1.155894," ","integrate((d*x^2+c)^3/x/(b*x^2+a),x, algorithm=""maxima"")","\frac{c^{3} \log\left(x^{2}\right)}{2 \, a} + \frac{b d^{3} x^{4} + 2 \, {\left(3 \, b c d^{2} - a d^{3}\right)} 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(b x^{2} + a\right)}{2 \, a b^{3}}"," ",0,"1/2*c^3*log(x^2)/a + 1/4*(b*d^3*x^4 + 2*(3*b*c*d^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(b*x^2 + a)/(a*b^3)","A",0
225,1,101,0,2.369193," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a),x, algorithm=""maxima"")","-\frac{c^{3}}{a x} + \frac{b d^{3} x^{3} + 3 \, {\left(3 \, b c d^{2} - a d^{3}\right)} x}{3 \, 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)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a b^{2}}"," ",0,"-c^3/(a*x) + 1/3*(b*d^3*x^3 + 3*(3*b*c*d^2 - a*d^3)*x)/b^2 - (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)","A",0
226,1,97,0,1.076763," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a),x, algorithm=""maxima"")","\frac{d^{3} x^{2}}{2 \, b} - \frac{c^{3}}{2 \, a x^{2}} - \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(b x^{2} + a\right)}{2 \, a^{2} b^{2}}"," ",0,"1/2*d^3*x^2/b - 1/2*c^3/(a*x^2) - 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(b*x^2 + a)/(a^2*b^2)","A",0
227,1,98,0,2.440882," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a),x, algorithm=""maxima"")","\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{a c^{3} - 3 \, {\left(b c^{3} - 3 \, a c^{2} d\right)} x^{2}}{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*(a*c^3 - 3*(b*c^3 - 3*a*c^2*d)*x^2)/(a^2*x^3)","A",0
228,1,68,0,1.002498," ","integrate(x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{a^{2} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{3} c - a b^{2} d\right)}} - \frac{c^{2} \log\left(d x^{2} + c\right)}{2 \, {\left(b c d^{2} - a d^{3}\right)}} + \frac{x^{2}}{2 \, b d}"," ",0,"1/2*a^2*log(b*x^2 + a)/(b^3*c - a*b^2*d) - 1/2*c^2*log(d*x^2 + c)/(b*c*d^2 - a*d^3) + 1/2*x^2/(b*d)","A",0
229,1,72,0,2.353234," ","integrate(x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\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
230,1,49,0,1.032125," ","integrate(x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{a \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c - a b d\right)}} + \frac{c \log\left(d x^{2} + c\right)}{2 \, {\left(b c d - a d^{2}\right)}}"," ",0,"-1/2*a*log(b*x^2 + a)/(b^2*c - a*b*d) + 1/2*c*log(d*x^2 + c)/(b*c*d - a*d^2)","A",0
231,1,54,0,2.309513," ","integrate(x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\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
232,1,41,0,1.074964," ","integrate(x/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\log\left(b x^{2} + a\right)}{2 \, {\left(b c - a d\right)}} - \frac{\log\left(d x^{2} + c\right)}{2 \, {\left(b c - a d\right)}}"," ",0,"1/2*log(b*x^2 + a)/(b*c - a*d) - 1/2*log(d*x^2 + c)/(b*c - a*d)","A",0
233,1,54,0,2.314568," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\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
234,1,61,0,1.034827," ","integrate(1/x/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{b \log\left(b x^{2} + a\right)}{2 \, {\left(a b c - a^{2} d\right)}} + \frac{d \log\left(d x^{2} + c\right)}{2 \, {\left(b c^{2} - a c d\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a c}"," ",0,"-1/2*b*log(b*x^2 + a)/(a*b*c - a^2*d) + 1/2*d*log(d*x^2 + c)/(b*c^2 - a*c*d) + 1/2*log(x^2)/(a*c)","A",0
235,1,75,0,2.394702," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\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
236,1,87,0,1.019482," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b^{2} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{2} b c - a^{3} d\right)}} - \frac{d^{2} \log\left(d x^{2} + c\right)}{2 \, {\left(b c^{3} - a c^{2} d\right)}} - \frac{{\left(b c + a d\right)} \log\left(x^{2}\right)}{2 \, a^{2} c^{2}} - \frac{1}{2 \, a c x^{2}}"," ",0,"1/2*b^2*log(b*x^2 + a)/(a^2*b*c - a^3*d) - 1/2*d^2*log(d*x^2 + c)/(b*c^3 - a*c^2*d) - 1/2*(b*c + a*d)*log(x^2)/(a^2*c^2) - 1/2/(a*c*x^2)","A",0
237,1,96,0,2.412073," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\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 \, {\left(b c + a d\right)} 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 + a*d)*x^2 - a*c)/(a^2*c^2*x^3)","A",0
238,1,117,0,1.113269," ","integrate(1/x^5/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{b^{3} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{3} b c - a^{4} d\right)}} + \frac{d^{3} \log\left(d x^{2} + c\right)}{2 \, {\left(b c^{4} - a c^{3} d\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{2 \, {\left(b c + a d\right)} x^{2} - a c}{4 \, a^{2} c^{2} x^{4}}"," ",0,"-1/2*b^3*log(b*x^2 + a)/(a^3*b*c - a^4*d) + 1/2*d^3*log(d*x^2 + c)/(b*c^4 - a*c^3*d) + 1/2*(b^2*c^2 + a*b*c*d + a^2*d^2)*log(x^2)/(a^3*c^3) + 1/4*(2*(b*c + a*d)*x^2 - a*c)/(a^2*c^2*x^4)","A",0
239,1,131,0,2.449054," ","integrate(1/x^6/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\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 \, {\left(b^{2} c^{2} + a b c d + a^{2} d^{2}\right)} x^{4} + 3 \, a^{2} c^{2} - 5 \, {\left(a b c^{2} + a^{2} c d\right)} x^{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 + a*b*c*d + a^2*d^2)*x^4 + 3*a^2*c^2 - 5*(a*b*c^2 + a^2*c*d)*x^2)/(a^3*c^3*x^5)","A",0
240,1,165,0,1.116741," ","integrate(1/x^7/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b^{4} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{4} b c - a^{5} d\right)}} - \frac{d^{4} \log\left(d x^{2} + c\right)}{2 \, {\left(b c^{5} - a c^{4} d\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{6 \, {\left(b^{2} c^{2} + a b c d + a^{2} d^{2}\right)} x^{4} + 2 \, a^{2} c^{2} - 3 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}}{12 \, a^{3} c^{3} x^{6}}"," ",0,"1/2*b^4*log(b*x^2 + a)/(a^4*b*c - a^5*d) - 1/2*d^4*log(d*x^2 + c)/(b*c^5 - a*c^4*d) - 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*(6*(b^2*c^2 + a*b*c*d + a^2*d^2)*x^4 + 2*a^2*c^2 - 3*(a*b*c^2 + a^2*c*d)*x^2)/(a^3*c^3*x^6)","A",0
241,1,130,0,1.063713," ","integrate(x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{c^{2} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}} - \frac{a^{2}}{2 \, {\left(a b^{3} c - a^{2} b^{2} d + {\left(b^{4} c - a b^{3} d\right)} x^{2}\right)}} - \frac{{\left(2 \, a b c - a^{2} d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)}}"," ",0,"1/2*c^2*log(d*x^2 + c)/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) - 1/2*a^2/(a*b^3*c - a^2*b^2*d + (b^4*c - a*b^3*d)*x^2) - 1/2*(2*a*b*c - a^2*d)*log(b*x^2 + a)/(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)","A",0
242,1,132,0,2.488473," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\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{c x}{2 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}} + \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}}"," ",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*c*x/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2) + 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))","A",0
243,1,105,0,1.110460," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{a \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{c}{2 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*a*log(b*x^2 + a)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2*a*log(d*x^2 + c)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2*c/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2)","A",0
244,1,119,0,2.445903," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\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(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\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/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","A",0
245,1,99,0,1.029641," ","integrate(x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{b \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{1}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}"," ",0,"1/2*b*log(b*x^2 + a)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2*b*log(d*x^2 + c)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","A",0
246,1,133,0,2.351023," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\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{d x}{2 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}} - \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}}"," ",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*d*x/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2) - 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))","A",0
247,1,138,0,0.985623," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(b x^{2} + a\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} + \frac{{\left(2 \, b c d - a d^{2}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}} - \frac{d}{2 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a c^{2}}"," ",0,"-1/2*b^2*log(b*x^2 + a)/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) + 1/2*(2*b*c*d - a*d^2)*log(d*x^2 + c)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2) - 1/2*d/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2) + 1/2*log(x^2)/(a*c^2)","A",0
248,1,178,0,2.304147," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\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^{2} - 2 \, a c d + {\left(2 \, b c d - 3 \, a d^{2}\right)} x^{2}}{2 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x\right)}}"," ",0,"-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^2 - 2*a*c*d + (2*b*c*d - 3*a*d^2)*x^2)/((a*b*c^3*d - a^2*c^2*d^2)*x^3 + (a*b*c^4 - a^2*c^3*d)*x)","A",0
249,1,188,0,1.133010," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{3} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}} - \frac{{\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)}} - \frac{b c^{2} - a c d + {\left(b c d - 2 \, a d^{2}\right)} x^{2}}{2 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{4} + {\left(a b c^{4} - a^{2} c^{3} d\right)} 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^3*log(b*x^2 + a)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2) - 1/2*(3*b*c*d^2 - 2*a*d^3)*log(d*x^2 + c)/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2) - 1/2*(b*c^2 - a*c*d + (b*c*d - 2*a*d^2)*x^2)/((a*b*c^3*d - a^2*c^2*d^2)*x^4 + (a*b*c^4 - a^2*c^3*d)*x^2) - 1/2*(b*c + 2*a*d)*log(x^2)/(a^2*c^3)","A",0
250,1,236,0,2.374073," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\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{{\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{2 \, a b c^{3} - 2 \, a^{2} c^{2} d - 3 \, {\left(2 \, b^{2} c^{2} d + 2 \, a b c d^{2} - 5 \, a^{2} d^{3}\right)} x^{4} - 2 \, {\left(3 \, b^{2} c^{3} + 2 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} x^{2}}{6 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{5} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{3}\right)}}"," ",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*(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)) - 1/6*(2*a*b*c^3 - 2*a^2*c^2*d - 3*(2*b^2*c^2*d + 2*a*b*c*d^2 - 5*a^2*d^3)*x^4 - 2*(3*b^2*c^3 + 2*a*b*c^2*d - 5*a^2*c*d^2)*x^2)/((a^2*b*c^4*d - a^3*c^3*d^2)*x^5 + (a^2*b*c^5 - a^3*c^4*d)*x^3)","A",0
251,1,236,0,1.227452," ","integrate(x^5/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""maxima"")","\frac{c^{2} \log\left(b x^{2} + a\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)}} - \frac{c^{2} \log\left(d x^{2} + c\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)}} + \frac{3 \, a^{2} b c - a^{3} d + 2 \, {\left(2 \, a b^{2} c - a^{2} b d\right)} x^{2}}{4 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{4} + 2 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2}\right)}}"," ",0,"1/2*c^2*log(b*x^2 + a)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*c^2*log(d*x^2 + c)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/4*(3*a^2*b*c - a^3*d + 2*(2*a*b^2*c - a^2*b*d)*x^2)/(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^4 + 2*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2)","B",0
252,1,264,0,2.519257," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{{\left(b c d - 5 \, a d^{2}\right)} x^{3} - {\left(b c^{2} + 3 \, a c d\right)} x}{8 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}"," ",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 - 5*a*d^2)*x^3 - (b*c^2 + 3*a*c*d)*x)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*x^4 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2)","A",0
253,1,217,0,1.144150," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{a b \log\left(b x^{2} + a\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)}} + \frac{a b \log\left(d x^{2} + c\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)}} - \frac{2 \, a d^{2} x^{2} + b c^{2} + a c d}{4 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}}"," ",0,"-1/2*a*b*log(b*x^2 + a)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/2*a*b*log(d*x^2 + c)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/4*(2*a*d^2*x^2 + b*c^2 + a*c*d)/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*x^4 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2)","B",0
254,1,266,0,2.300266," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\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{{\left(3 \, b c d + a d^{2}\right)} x^{3} + {\left(5 \, b c^{2} - a c d\right)} x}{8 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}"," ",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 + a*d^2)*x^3 + (5*b*c^2 - a*c*d)*x)/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2)","A",0
255,1,211,0,1.058012," ","integrate(x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{2} \log\left(b x^{2} + a\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)}} - \frac{b^{2} \log\left(d x^{2} + c\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)}} + \frac{2 \, b d x^{2} + 3 \, b c - a d}{4 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{2}\right)}}"," ",0,"1/2*b^2*log(b*x^2 + a)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*b^2*log(d*x^2 + c)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/4*(2*b*d*x^2 + 3*b*c - a*d)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^4 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^2)","B",0
256,1,277,0,2.333906," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{{\left(7 \, b c d^{2} - 3 \, a d^{3}\right)} x^{3} + {\left(9 \, b c^{2} d - 5 \, a c d^{2}\right)} x}{8 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} x^{2}\right)}}"," ",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 - 3*a*d^3)*x^3 + (9*b*c^2*d - 5*a*c*d^2)*x)/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*x^4 + 2*(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*x^2)","B",0
257,1,278,0,1.253214," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{b^{3} \log\left(b x^{2} + a\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)}} + \frac{{\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x^{2} + c\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)}} - \frac{5 \, b c^{2} d - 3 \, a c d^{2} + 2 \, {\left(2 \, b c d^{2} - a d^{3}\right)} x^{2}}{4 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} x^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a c^{3}}"," ",0,"-1/2*b^3*log(b*x^2 + a)/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3) + 1/2*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x^2 + c)/(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) - 1/4*(5*b*c^2*d - 3*a*c*d^2 + 2*(2*b*c*d^2 - a*d^3)*x^2)/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*x^4 + 2*(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*x^2) + 1/2*log(x^2)/(a*c^3)","A",0
258,1,352,0,2.538396," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\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{8 \, b^{2} c^{4} - 16 \, a b c^{3} d + 8 \, a^{2} c^{2} d^{2} + {\left(8 \, b^{2} c^{2} d^{2} - 27 \, a b c d^{3} + 15 \, a^{2} d^{4}\right)} x^{4} + {\left(16 \, b^{2} c^{3} d - 45 \, a b c^{2} d^{2} + 25 \, a^{2} c d^{3}\right)} x^{2}}{8 \, {\left({\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{5} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{3} + {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2}\right)} x\right)}}"," ",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*(8*b^2*c^4 - 16*a*b*c^3*d + 8*a^2*c^2*d^2 + (8*b^2*c^2*d^2 - 27*a*b*c*d^3 + 15*a^2*d^4)*x^4 + (16*b^2*c^3*d - 45*a*b*c^2*d^2 + 25*a^2*c*d^3)*x^2)/((a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^5 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^3 + (a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2)*x)","A",0
259,1,364,0,1.280867," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{4} \log\left(b x^{2} + a\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)}} - \frac{{\left(6 \, b^{2} c^{2} d^{2} - 8 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} \log\left(d x^{2} + c\right)}{2 \, {\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)}} - \frac{2 \, b^{2} c^{4} - 4 \, a b c^{3} d + 2 \, a^{2} c^{2} d^{2} + 2 \, {\left(b^{2} c^{2} d^{2} - 5 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{4} + {\left(4 \, b^{2} c^{3} d - 15 \, a b c^{2} d^{2} + 9 \, a^{2} c d^{3}\right)} x^{2}}{4 \, {\left({\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{6} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{4} + {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2}\right)} x^{2}\right)}} - \frac{{\left(b c + 3 \, a d\right)} \log\left(x^{2}\right)}{2 \, a^{2} c^{4}}"," ",0,"1/2*b^4*log(b*x^2 + a)/(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) - 1/2*(6*b^2*c^2*d^2 - 8*a*b*c*d^3 + 3*a^2*d^4)*log(d*x^2 + c)/(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) - 1/4*(2*b^2*c^4 - 4*a*b*c^3*d + 2*a^2*c^2*d^2 + 2*(b^2*c^2*d^2 - 5*a*b*c*d^3 + 3*a^2*d^4)*x^4 + (4*b^2*c^3*d - 15*a*b*c^2*d^2 + 9*a^2*c*d^3)*x^2)/((a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^6 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^4 + (a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2)*x^2) - 1/2*(b*c + 3*a*d)*log(x^2)/(a^2*c^4)","B",0
260,1,440,0,2.578201," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{8 \, a b^{2} c^{5} - 16 \, a^{2} b c^{4} d + 8 \, a^{3} c^{3} d^{2} - 3 \, {\left(8 \, b^{3} c^{3} d^{2} + 8 \, a b^{2} c^{2} d^{3} - 55 \, a^{2} b c d^{4} + 35 \, a^{3} d^{5}\right)} x^{6} - {\left(48 \, b^{3} c^{4} d + 40 \, a b^{2} c^{3} d^{2} - 275 \, a^{2} b c^{2} d^{3} + 175 \, a^{3} c d^{4}\right)} x^{4} - 8 \, {\left(3 \, b^{3} c^{5} + a b^{2} c^{4} d - 11 \, a^{2} b c^{3} d^{2} + 7 \, a^{3} c^{2} d^{3}\right)} x^{2}}{24 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{7} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{5} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{3}\right)}}"," ",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)) - 1/24*(8*a*b^2*c^5 - 16*a^2*b*c^4*d + 8*a^3*c^3*d^2 - 3*(8*b^3*c^3*d^2 + 8*a*b^2*c^2*d^3 - 55*a^2*b*c*d^4 + 35*a^3*d^5)*x^6 - (48*b^3*c^4*d + 40*a*b^2*c^3*d^2 - 275*a^2*b*c^2*d^3 + 175*a^3*c*d^4)*x^4 - 8*(3*b^3*c^5 + a*b^2*c^4*d - 11*a^2*b*c^3*d^2 + 7*a^3*c^2*d^3)*x^2)/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^7 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^5 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^3)","A",0
261,1,17,0,0.953486," ","integrate(x/(x^2+1)/(x^2+4),x, algorithm=""maxima"")","-\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
262,1,84,0,2.243685," ","integrate(x^4*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b c - a^{2} d\right)} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} - \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{b d x^{3} + 3 \, {\left(b c - 2 \, a d\right)} x}{3 \, b^{3}}"," ",0,"1/2*(a*b*c - a^2*d)*x/(b^4*x^2 + a*b^3) - 1/2*(3*a*b*c - 5*a^2*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/3*(b*d*x^3 + 3*(b*c - 2*a*d)*x)/b^3","A",0
263,1,59,0,0.992714," ","integrate(x^3*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{d x^{2}}{2 \, b^{2}} + \frac{a b c - a^{2} d}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \frac{{\left(b c - 2 \, a d\right)} \log\left(b x^{2} + a\right)}{2 \, b^{3}}"," ",0,"1/2*d*x^2/b^2 + 1/2*(a*b*c - a^2*d)/(b^4*x^2 + a*b^3) + 1/2*(b*c - 2*a*d)*log(b*x^2 + a)/b^3","A",0
264,1,60,0,2.324620," ","integrate(x^2*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b c - a d\right)} x}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \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}}"," ",0,"-1/2*(b*c - a*d)*x/(b^3*x^2 + a*b^2) + d*x/b^2 + 1/2*(b*c - 3*a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2)","A",0
265,1,40,0,1.067818," ","integrate(x*(d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{b c - a d}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{d \log\left(b x^{2} + a\right)}{2 \, b^{2}}"," ",0,"-1/2*(b*c - a*d)/(b^3*x^2 + a*b^2) + 1/2*d*log(b*x^2 + a)/b^2","A",0
266,1,57,0,2.394145," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} x}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} + \frac{{\left(b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b}"," ",0,"1/2*(b*c - a*d)*x/(a*b^2*x^2 + a^2*b) + 1/2*(b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b)","A",0
267,1,51,0,1.073562," ","integrate((d*x^2+c)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{b c - a d}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} - \frac{c \log\left(b x^{2} + a\right)}{2 \, a^{2}} + \frac{c \log\left(x^{2}\right)}{2 \, a^{2}}"," ",0,"1/2*(b*c - a*d)/(a*b^2*x^2 + a^2*b) - 1/2*c*log(b*x^2 + a)/a^2 + 1/2*c*log(x^2)/a^2","A",0
268,1,65,0,2.231166," ","integrate((d*x^2+c)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, b c - a d\right)} x^{2} + 2 \, a c}{2 \, {\left(a^{2} b x^{3} + a^{3} x\right)}} - \frac{{\left(3 \, b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a^{2}}"," ",0,"-1/2*((3*b*c - a*d)*x^2 + 2*a*c)/(a^2*b*x^3 + a^3*x) - 1/2*(3*b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2)","A",0
269,1,78,0,1.000918," ","integrate((d*x^2+c)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, b c - a d\right)} x^{2} + a c}{2 \, {\left(a^{2} b x^{4} + a^{3} x^{2}\right)}} + \frac{{\left(2 \, b c - a d\right)} \log\left(b x^{2} + a\right)}{2 \, a^{3}} - \frac{{\left(2 \, b c - a d\right)} \log\left(x^{2}\right)}{2 \, a^{3}}"," ",0,"-1/2*((2*b*c - a*d)*x^2 + a*c)/(a^2*b*x^4 + a^3*x^2) + 1/2*(2*b*c - a*d)*log(b*x^2 + a)/a^3 - 1/2*(2*b*c - a*d)*log(x^2)/a^3","A",0
270,1,93,0,2.363073," ","integrate((d*x^2+c)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, b^{2} c - 3 \, a b d\right)} x^{4} - 2 \, a^{2} c + 2 \, {\left(5 \, a b c - 3 \, a^{2} d\right)} x^{2}}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}} + \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}}"," ",0,"1/6*(3*(5*b^2*c - 3*a*b*d)*x^4 - 2*a^2*c + 2*(5*a*b*c - 3*a^2*d)*x^2)/(a^3*b*x^5 + a^4*x^3) + 1/2*(5*b^2*c - 3*a*b*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^3)","A",0
271,1,149,0,2.416725," ","integrate(x^4*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} - \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{3 \, b^{2} d^{2} x^{5} + 10 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + 15 \, {\left(b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x}{15 \, b^{4}}"," ",0,"1/2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x/(b^5*x^2 + a*b^4) - 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) + 1/15*(3*b^2*d^2*x^5 + 10*(b^2*c*d - a*b*d^2)*x^3 + 15*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x)/b^4","A",0
272,1,107,0,1.001830," ","integrate(x^3*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{b d^{2} x^{4} + 4 \, {\left(b c d - a d^{2}\right)} x^{2}}{4 \, b^{3}} + \frac{{\left(b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"1/2*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)/(b^5*x^2 + a*b^4) + 1/4*(b*d^2*x^4 + 4*(b*c*d - a*d^2)*x^2)/b^3 + 1/2*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*log(b*x^2 + a)/b^4","A",0
273,1,109,0,2.412013," ","integrate(x^2*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \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 d^{2} x^{3} + 6 \, {\left(b c d - a d^{2}\right)} x}{3 \, b^{3}}"," ",0,"-1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(b^4*x^2 + a*b^3) + 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) + 1/3*(b*d^2*x^3 + 6*(b*c*d - a*d^2)*x)/b^3","A",0
274,1,73,0,1.041699," ","integrate(x*(d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{d^{2} x^{2}}{2 \, b^{2}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \frac{{\left(b c d - a d^{2}\right)} \log\left(b x^{2} + a\right)}{b^{3}}"," ",0,"1/2*d^2*x^2/b^2 - 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(b^4*x^2 + a*b^3) + (b*c*d - a*d^2)*log(b*x^2 + a)/b^3","A",0
275,1,95,0,2.468602," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}} + \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}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x/(a*b^3*x^2 + a^2*b^2) + 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)","A",0
276,1,86,0,1.069507," ","integrate((d*x^2+c)^2/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{c^{2} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{2 \, {\left(a b^{3} x^{2} + a^{2} b^{2}\right)}} - \frac{{\left(b^{2} c^{2} - a^{2} d^{2}\right)} \log\left(b x^{2} + a\right)}{2 \, a^{2} b^{2}}"," ",0,"1/2*c^2*log(x^2)/a^2 + 1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(a*b^3*x^2 + a^2*b^2) - 1/2*(b^2*c^2 - a^2*d^2)*log(b*x^2 + a)/(a^2*b^2)","A",0
277,1,101,0,2.286483," ","integrate((d*x^2+c)^2/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, a b c^{2} + {\left(3 \, b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2}}{2 \, {\left(a^{2} b^{2} x^{3} + a^{3} b x\right)}} - \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}"," ",0,"-1/2*(2*a*b*c^2 + (3*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2)/(a^2*b^2*x^3 + a^3*b*x) - 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)","A",0
278,1,100,0,0.999341," ","integrate((d*x^2+c)^2/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{a b c^{2} + {\left(2 \, b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2}}{2 \, {\left(a^{2} b^{2} x^{4} + a^{3} b x^{2}\right)}} + \frac{{\left(b c^{2} - a c d\right)} \log\left(b x^{2} + a\right)}{a^{3}} - \frac{{\left(b c^{2} - a c d\right)} \log\left(x^{2}\right)}{a^{3}}"," ",0,"-1/2*(a*b*c^2 + (2*b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2)/(a^2*b^2*x^4 + a^3*b*x^2) + (b*c^2 - a*c*d)*log(b*x^2 + a)/a^3 - (b*c^2 - a*c*d)*log(x^2)/a^3","A",0
279,1,118,0,2.439382," ","integrate((d*x^2+c)^2/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, b^{2} c^{2} - 6 \, a b c d + a^{2} d^{2}\right)} x^{4} - 2 \, a^{2} c^{2} + 2 \, {\left(5 \, a b c^{2} - 6 \, a^{2} c d\right)} x^{2}}{6 \, {\left(a^{3} b x^{5} + a^{4} x^{3}\right)}} + \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}}"," ",0,"1/6*(3*(5*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*x^4 - 2*a^2*c^2 + 2*(5*a*b*c^2 - 6*a^2*c*d)*x^2)/(a^3*b*x^5 + a^4*x^3) + 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)","A",0
280,1,228,0,2.625730," ","integrate(x^4*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\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)} x}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} - \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{5 \, b^{3} d^{3} x^{7} + 7 \, {\left(3 \, b^{3} c d^{2} - 2 \, a b^{2} d^{3}\right)} x^{5} + 35 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} + 35 \, {\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)} x}{35 \, b^{5}}"," ",0,"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)*x/(b^6*x^2 + a*b^5) - 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) + 1/35*(5*b^3*d^3*x^7 + 7*(3*b^3*c*d^2 - 2*a*b^2*d^3)*x^5 + 35*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^3 + 35*(b^3*c^3 - 6*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 4*a^3*d^3)*x)/b^5","A",0
281,1,174,0,1.028144," ","integrate(x^3*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} + \frac{2 \, b^{2} d^{3} x^{6} + 3 \, {\left(3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{4} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{2}}{12 \, b^{4}} + \frac{{\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(b x^{2} + a\right)}{2 \, b^{5}}"," ",0,"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)/(b^6*x^2 + a*b^5) + 1/12*(2*b^2*d^3*x^6 + 3*(3*b^2*c*d^2 - 2*a*b*d^3)*x^4 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^2)/b^4 + 1/2*(b^3*c^3 - 6*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 4*a^3*d^3)*log(b*x^2 + a)/b^5","A",0
282,1,176,0,2.290034," ","integrate(x^2*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\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)} x}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \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{3 \, b^{2} d^{3} x^{5} + 5 \, {\left(3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{3} + 45 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x}{15 \, b^{4}}"," ",0,"-1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(b^5*x^2 + a*b^4) + 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) + 1/15*(3*b^2*d^3*x^5 + 5*(3*b^2*c*d^2 - 2*a*b*d^3)*x^3 + 45*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)/b^4","A",0
283,1,124,0,1.000900," ","integrate(x*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{b d^{3} x^{4} + 2 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x^{2}}{4 \, b^{3}} + \frac{3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x^{2} + a\right)}{2 \, b^{4}}"," ",0,"-1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(b^5*x^2 + a*b^4) + 1/4*(b*d^3*x^4 + 2*(3*b*c*d^2 - 2*a*d^3)*x^2)/b^3 + 3/2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(b*x^2 + a)/b^4","A",0
284,1,147,0,2.345045," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\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)} x}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{b d^{3} x^{3} + 3 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x}{3 \, b^{3}} + \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}}"," ",0,"1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x/(a*b^4*x^2 + a^2*b^3) + 1/3*(b*d^3*x^3 + 3*(3*b*c*d^2 - 2*a*d^3)*x)/b^3 + 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)","A",0
285,1,122,0,0.992115," ","integrate((d*x^2+c)^3/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{d^{3} x^{2}}{2 \, b^{2}} + \frac{c^{3} \log\left(x^{2}\right)}{2 \, a^{2}} + \frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} - \frac{{\left(b^{3} c^{3} - 3 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3}\right)} \log\left(b x^{2} + a\right)}{2 \, 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*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(a*b^4*x^2 + a^2*b^3) - 1/2*(b^3*c^3 - 3*a^2*b*c*d^2 + 2*a^3*d^3)*log(b*x^2 + a)/(a^2*b^3)","A",0
286,1,140,0,2.324163," ","integrate((d*x^2+c)^3/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{d^{3} x}{b^{2}} - \frac{2 \, a b^{2} c^{3} + {\left(3 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}}{2 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2} x\right)}} - \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}}"," ",0,"d^3*x/b^2 - 1/2*(2*a*b^2*c^3 + (3*b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2)/(a^2*b^3*x^3 + a^3*b^2*x) - 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)","A",0
287,1,141,0,1.099166," ","integrate((d*x^2+c)^3/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{a b^{2} c^{3} + {\left(2 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}}{2 \, {\left(a^{2} b^{3} x^{4} + a^{3} b^{2} x^{2}\right)}} - \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(b x^{2} + a\right)}{2 \, a^{3} b^{2}}"," ",0,"-1/2*(a*b^2*c^3 + (2*b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2)/(a^2*b^3*x^4 + a^3*b^2*x^2) - 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(b*x^2 + a)/(a^3*b^2)","A",0
288,1,159,0,2.396431," ","integrate((d*x^2+c)^3/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} b c^{3} - 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)} x^{4} - 2 \, {\left(5 \, a b^{2} c^{3} - 9 \, a^{2} b c^{2} d\right)} x^{2}}{6 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{3}\right)}} + \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}"," ",0,"-1/6*(2*a^2*b*c^3 - 3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^4 - 2*(5*a*b^2*c^3 - 9*a^2*b*c^2*d)*x^2)/(a^3*b^2*x^5 + a^4*b*x^3) + 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)","A",0
289,1,133,0,2.429877," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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{a x}{2 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)}} - \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}}"," ",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*a*x/(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2) - 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))","A",0
290,1,105,0,1.075146," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{c \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{c \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{a}{2 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{2}\right)}}"," ",0,"1/2*c*log(b*x^2 + a)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2*c*log(d*x^2 + c)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2*a/(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^2)","A",0
291,1,119,0,2.403996," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\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(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\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/(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)","A",0
292,1,99,0,1.090373," ","integrate(x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\frac{d \log\left(b x^{2} + a\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{d \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{1}{2 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x^{2}\right)}}"," ",0,"-1/2*d*log(b*x^2 + a)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2*d*log(d*x^2 + c)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2/(a*b*c - a^2*d + (b^2*c - a*b*d)*x^2)","A",0
293,1,132,0,2.423470," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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{b x}{2 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)}} + \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}}"," ",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*x/(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2) + 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))","A",0
294,1,137,0,1.116049," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\frac{d^{2} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}} - \frac{{\left(b^{2} c - 2 \, a b d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}} + \frac{b}{2 \, {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c}"," ",0,"-1/2*d^2*log(d*x^2 + c)/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2) - 1/2*(b^2*c - 2*a*b*d)*log(b*x^2 + a)/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2) + 1/2*b/(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^2) + 1/2*log(x^2)/(a^2*c)","A",0
295,1,178,0,2.255480," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\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{2 \, a b c - 2 \, a^{2} d + {\left(3 \, b^{2} c - 2 \, a b d\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3} + {\left(a^{3} b c^{2} - a^{4} c d\right)} 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*(2*a*b*c - 2*a^2*d + (3*b^2*c - 2*a*b*d)*x^2)/((a^2*b^2*c^2 - a^3*b*c*d)*x^3 + (a^3*b*c^2 - a^4*c*d)*x)","A",0
296,1,189,0,1.125731," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{d^{3} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}} + \frac{{\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)}} - \frac{a b c - a^{2} d + {\left(2 \, b^{2} c - a b d\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{4} + {\left(a^{3} b c^{2} - a^{4} c d\right)} 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^3*log(d*x^2 + c)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2) + 1/2*(2*b^3*c - 3*a*b^2*d)*log(b*x^2 + a)/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2) - 1/2*(a*b*c - a^2*d + (2*b^2*c - a*b*d)*x^2)/((a^2*b^2*c^2 - a^3*b*c*d)*x^4 + (a^3*b*c^2 - a^4*c*d)*x^2) - 1/2*(2*b*c + a*d)*log(x^2)/(a^3*c^2)","A",0
297,1,236,0,2.462349," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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{{\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{2 \, a^{2} b c^{2} - 2 \, a^{3} c d - 3 \, {\left(5 \, b^{3} c^{2} - 2 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{4} - 2 \, {\left(5 \, a b^{2} c^{2} - 2 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} x^{2}}{6 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{5} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{3}\right)}}"," ",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*(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)) - 1/6*(2*a^2*b*c^2 - 2*a^3*c*d - 3*(5*b^3*c^2 - 2*a*b^2*c*d - 2*a^2*b*d^2)*x^4 - 2*(5*a*b^2*c^2 - 2*a^2*b*c*d - 3*a^3*d^2)*x^2)/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^5 + (a^4*b*c^3 - a^5*c^2*d)*x^3)","A",0
298,1,258,0,1.122943," ","integrate(1/x^5/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\frac{d^{4} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)}} - \frac{{\left(3 \, b^{4} c - 4 \, a b^{3} d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2}\right)}} - \frac{a^{2} b c^{2} - a^{3} c d - 2 \, {\left(3 \, b^{3} c^{2} - a b^{2} c d - a^{2} b d^{2}\right)} x^{4} - {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{2}}{4 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{6} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{4}\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}}"," ",0,"-1/2*d^4*log(d*x^2 + c)/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2) - 1/2*(3*b^4*c - 4*a*b^3*d)*log(b*x^2 + a)/(a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2) - 1/4*(a^2*b*c^2 - a^3*c*d - 2*(3*b^3*c^2 - a*b^2*c*d - a^2*b*d^2)*x^4 - (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^2)/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^6 + (a^4*b*c^3 - a^5*c^2*d)*x^4) + 1/2*(3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*log(x^2)/(a^4*c^3)","A",0
299,1,303,0,2.408445," ","integrate(1/x^6/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\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{{\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{6 \, a^{3} b c^{3} - 6 \, a^{4} c^{2} d + 15 \, {\left(7 \, b^{4} c^{3} - 2 \, a b^{3} c^{2} d - 2 \, a^{2} b^{2} c d^{2} - 2 \, a^{3} b d^{3}\right)} x^{6} + 10 \, {\left(7 \, a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d - 2 \, a^{3} b c d^{2} - 3 \, a^{4} d^{3}\right)} x^{4} - 2 \, {\left(7 \, a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d - 5 \, a^{4} c d^{2}\right)} x^{2}}{30 \, {\left({\left(a^{4} b^{2} c^{4} - a^{5} b c^{3} d\right)} x^{7} + {\left(a^{5} b c^{4} - a^{6} c^{3} d\right)} x^{5}\right)}}"," ",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*(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)) - 1/30*(6*a^3*b*c^3 - 6*a^4*c^2*d + 15*(7*b^4*c^3 - 2*a*b^3*c^2*d - 2*a^2*b^2*c*d^2 - 2*a^3*b*d^3)*x^6 + 10*(7*a*b^3*c^3 - 2*a^2*b^2*c^2*d - 2*a^3*b*c*d^2 - 3*a^4*d^3)*x^4 - 2*(7*a^2*b^2*c^3 - 2*a^3*b*c^2*d - 5*a^4*c*d^2)*x^2)/((a^4*b^2*c^4 - a^5*b*c^3*d)*x^7 + (a^5*b*c^4 - a^6*c^3*d)*x^5)","A",0
300,1,339,0,1.172750," ","integrate(1/x^7/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{d^{5} \log\left(d x^{2} + c\right)}{2 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)}} + \frac{{\left(4 \, b^{5} c - 5 \, a b^{4} d\right)} \log\left(b x^{2} + a\right)}{2 \, {\left(a^{5} b^{2} c^{2} - 2 \, a^{6} b c d + a^{7} d^{2}\right)}} - \frac{2 \, a^{3} b c^{3} - 2 \, a^{4} c^{2} d + 6 \, {\left(4 \, b^{4} c^{3} - a b^{3} c^{2} d - a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{6} + 3 \, {\left(4 \, a b^{3} c^{3} - a^{2} b^{2} c^{2} d - a^{3} b c d^{2} - 2 \, a^{4} d^{3}\right)} x^{4} - {\left(4 \, a^{2} b^{2} c^{3} - a^{3} b c^{2} d - 3 \, a^{4} c d^{2}\right)} x^{2}}{12 \, {\left({\left(a^{4} b^{2} c^{4} - a^{5} b c^{3} d\right)} x^{8} + {\left(a^{5} b c^{4} - a^{6} c^{3} d\right)} x^{6}\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}}"," ",0,"1/2*d^5*log(d*x^2 + c)/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2) + 1/2*(4*b^5*c - 5*a*b^4*d)*log(b*x^2 + a)/(a^5*b^2*c^2 - 2*a^6*b*c*d + a^7*d^2) - 1/12*(2*a^3*b*c^3 - 2*a^4*c^2*d + 6*(4*b^4*c^3 - a*b^3*c^2*d - a^2*b^2*c*d^2 - a^3*b*d^3)*x^6 + 3*(4*a*b^3*c^3 - a^2*b^2*c^2*d - a^3*b*c*d^2 - 2*a^4*d^3)*x^4 - (4*a^2*b^2*c^3 - a^3*b*c^2*d - 3*a^4*c*d^2)*x^2)/((a^4*b^2*c^4 - a^5*b*c^3*d)*x^8 + (a^5*b*c^4 - a^6*c^3*d)*x^6) - 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)","A",0
301,1,249,0,2.539876," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\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{{\left(b c + a d\right)} x^{3} + 2 \, a c x}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",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 + a*d)*x^3 + 2*a*c*x)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","A",0
302,1,228,0,1.269571," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b c + a d\right)} \log\left(b x^{2} + a\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)}} - \frac{{\left(b c + a d\right)} \log\left(d x^{2} + c\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)}} + \frac{{\left(b c + a d\right)} x^{2} + 2 \, a c}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/2*(b*c + a*d)*log(b*x^2 + a)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*(b*c + a*d)*log(d*x^2 + c)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/2*((b*c + a*d)*x^2 + 2*a*c)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","B",0
303,1,249,0,2.422590," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\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} + {\left(b c + a d\right)} x}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",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 + a*d)*x)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","A",0
304,1,215,0,1.063424," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{b d \log\left(b x^{2} + a\right)}{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}} + \frac{b d \log\left(d x^{2} + c\right)}{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}} - \frac{2 \, b d x^{2} + b c + a d}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"-b*d*log(b*x^2 + a)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + b*d*log(d*x^2 + c)/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*(2*b*d*x^2 + b*c + a*d)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","B",0
305,1,294,0,2.552196," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\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{{\left(b^{2} c d + a b d^{2}\right)} x^{3} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{4} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}\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 + a*b*d^2)*x^3 + (b^2*c^2 + a^2*d^2)*x)/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^4 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2)","B",0
306,1,295,0,1.203775," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c - 3 \, a b^{2} d\right)} \log\left(b x^{2} + a\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)}} - \frac{{\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x^{2} + c\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)}} + \frac{b^{2} c^{2} + a^{2} d^{2} + {\left(b^{2} c d + a b d^{2}\right)} x^{2}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{4} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c^{2}}"," ",0,"-1/2*(b^3*c - 3*a*b^2*d)*log(b*x^2 + a)/(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) - 1/2*(3*b*c*d^2 - a*d^3)*log(d*x^2 + c)/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3) + 1/2*(b^2*c^2 + a^2*d^2 + (b^2*c*d + a*b*d^2)*x^2)/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^4 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2) + 1/2*log(x^2)/(a^2*c^2)","B",0
307,1,378,0,2.495698," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\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{2 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d + 2 \, a^{3} c d^{2} + {\left(3 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x^{4} + {\left(3 \, b^{3} c^{3} - 2 \, a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{5} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{3} + {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} 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*(2*a*b^2*c^3 - 4*a^2*b*c^2*d + 2*a^3*c*d^2 + (3*b^3*c^2*d - 4*a*b^2*c*d^2 + 3*a^2*b*d^3)*x^4 + (3*b^3*c^3 - 2*a*b^2*c^2*d - 2*a^2*b*c*d^2 + 3*a^3*d^3)*x^2)/((a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^5 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^3 + (a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*x)","A",0
308,1,381,0,1.210953," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{4} c - 2 \, a b^{3} d\right)} \log\left(b x^{2} + a\right)}{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}} + \frac{{\left(2 \, b c d^{3} - a d^{4}\right)} \log\left(d x^{2} + c\right)}{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}} - \frac{a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + 2 \, {\left(b^{3} c^{2} d - a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(2 \, b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + 2 \, a^{3} d^{3}\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{6} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{4} + {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{2}\right)}} - \frac{{\left(b c + a d\right)} \log\left(x^{2}\right)}{a^{3} c^{3}}"," ",0,"(b^4*c - 2*a*b^3*d)*log(b*x^2 + a)/(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) + (2*b*c*d^3 - a*d^4)*log(d*x^2 + c)/(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) - 1/2*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + 2*(b^3*c^2*d - a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (2*b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + 2*a^3*d^3)*x^2)/((a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^6 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^4 + (a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*x^2) - (b*c + a*d)*log(x^2)/(a^3*c^3)","B",0
309,1,460,0,2.681262," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\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{2 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + 2 \, a^{4} c^{2} d^{2} - 3 \, {\left(5 \, b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} - 4 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} x^{6} - {\left(15 \, b^{4} c^{4} - 2 \, a b^{3} c^{3} d - 20 \, a^{2} b^{2} c^{2} d^{2} - 2 \, a^{3} b c d^{3} + 15 \, a^{4} d^{4}\right)} x^{4} - 10 \, {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}}{6 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{7} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{5} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{3}\right)}}"," ",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)) - 1/6*(2*a^2*b^2*c^4 - 4*a^3*b*c^3*d + 2*a^4*c^2*d^2 - 3*(5*b^4*c^3*d - 4*a*b^3*c^2*d^2 - 4*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*x^6 - (15*b^4*c^4 - 2*a*b^3*c^3*d - 20*a^2*b^2*c^2*d^2 - 2*a^3*b*c*d^3 + 15*a^4*d^4)*x^4 - 10*(a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2)/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^7 + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^5 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^3)","A",0
310,1,443,0,2.537664," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\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 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{5} + {\left(5 \, b^{2} c^{2} + 14 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{3} + 3 \, {\left(3 \, a b c^{2} + a^{2} c d\right)} x}{8 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}"," ",0,"-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^2*c*d + 3*a*b*d^2)*x^5 + (5*b^2*c^2 + 14*a*b*c*d + 5*a^2*d^2)*x^3 + 3*(3*a*b*c^2 + a^2*c*d)*x)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)","B",0
311,1,415,0,1.231298," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b^{2} c + 2 \, a b d\right)} \log\left(b x^{2} + a\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)}} - \frac{{\left(b^{2} c + 2 \, a b d\right)} \log\left(d x^{2} + c\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)}} + \frac{2 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} x^{4} + 5 \, a b c^{2} + a^{2} c d + {\left(3 \, b^{2} c^{2} + 7 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{2}}{4 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}"," ",0,"1/2*(b^2*c + 2*a*b*d)*log(b*x^2 + a)/(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) - 1/2*(b^2*c + 2*a*b*d)*log(d*x^2 + c)/(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) + 1/4*(2*(b^2*c*d + 2*a*b*d^2)*x^4 + 5*a*b*c^2 + a^2*c*d + (3*b^2*c^2 + 7*a*b*c*d + 2*a^2*d^2)*x^2)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)","B",0
312,1,473,0,2.632106," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{{\left(11 \, b^{2} c d^{2} + a b d^{3}\right)} x^{5} + {\left(17 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + {\left(4 \, b^{2} c^{3} + 9 \, a b c^{2} d - a^{2} c d^{2}\right)} x}{8 \, {\left(a b^{3} c^{6} - 3 \, a^{2} b^{2} c^{5} d + 3 \, a^{3} b c^{4} d^{2} - a^{4} c^{3} d^{3} + {\left(b^{4} c^{4} d^{2} - 3 \, a b^{3} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d^{4} - a^{3} b c d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{5} d - 5 \, a b^{3} c^{4} d^{2} + 3 \, a^{2} b^{2} c^{3} d^{3} + a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right)} x^{4} + {\left(b^{4} c^{6} - a b^{3} c^{5} d - 3 \, a^{2} b^{2} c^{4} d^{2} + 5 \, a^{3} b c^{3} d^{3} - 2 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)}}"," ",0,"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*((11*b^2*c*d^2 + a*b*d^3)*x^5 + (17*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^3 + (4*b^2*c^3 + 9*a*b*c^2*d - a^2*c*d^2)*x)/(a*b^3*c^6 - 3*a^2*b^2*c^5*d + 3*a^3*b*c^4*d^2 - a^4*c^3*d^3 + (b^4*c^4*d^2 - 3*a*b^3*c^3*d^3 + 3*a^2*b^2*c^2*d^4 - a^3*b*c*d^5)*x^6 + (2*b^4*c^5*d - 5*a*b^3*c^4*d^2 + 3*a^2*b^2*c^3*d^3 + a^3*b*c^2*d^4 - a^4*c*d^5)*x^4 + (b^4*c^6 - a*b^3*c^5*d - 3*a^2*b^2*c^4*d^2 + 5*a^3*b*c^3*d^3 - 2*a^4*c^2*d^4)*x^2)","B",0
313,1,394,0,1.262757," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{3 \, b^{2} d \log\left(b x^{2} + a\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)}} + \frac{3 \, b^{2} d \log\left(d x^{2} + c\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)}} - \frac{6 \, b^{2} d^{2} x^{4} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x^{2}}{4 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}}"," ",0,"-3/2*b^2*d*log(b*x^2 + a)/(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) + 3/2*b^2*d*log(d*x^2 + c)/(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) - 1/4*(6*b^2*d^2*x^4 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x^2)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2)","B",0
314,1,529,0,2.681825," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{{\left(4 \, b^{3} c^{2} d^{2} + 11 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} x^{5} + {\left(8 \, b^{3} c^{3} d + 13 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} - 3 \, a^{3} d^{4}\right)} x^{3} + {\left(4 \, b^{3} c^{4} + 13 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x}{8 \, {\left(a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left(a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right)} x^{6} + {\left(2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} x^{4} + {\left(a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right)} x^{2}\right)}}"," ",0,"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*((4*b^3*c^2*d^2 + 11*a*b^2*c*d^3 - 3*a^2*b*d^4)*x^5 + (8*b^3*c^3*d + 13*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 - 3*a^3*d^4)*x^3 + (4*b^3*c^4 + 13*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x)/(a^2*b^3*c^7 - 3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 + (a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2)","B",0
315,1,527,0,1.341845," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(b^{4} c - 4 \, a b^{3} d\right)} \log\left(b x^{2} + a\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)}} - \frac{{\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x^{2} + c\right)}{2 \, {\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)}} + \frac{2 \, b^{3} c^{4} + 7 \, a^{2} b c^{2} d^{2} - 3 \, a^{3} c d^{3} + 2 \, {\left(b^{3} c^{2} d^{2} + 3 \, a b^{2} c d^{3} - a^{2} b d^{4}\right)} x^{4} + {\left(4 \, b^{3} c^{3} d + 7 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 2 \, a^{3} d^{4}\right)} x^{2}}{4 \, {\left(a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left(a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right)} x^{6} + {\left(2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} x^{4} + {\left(a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right)} x^{2}\right)}} + \frac{\log\left(x^{2}\right)}{2 \, a^{2} c^{3}}"," ",0,"-1/2*(b^4*c - 4*a*b^3*d)*log(b*x^2 + a)/(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) - 1/2*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x^2 + c)/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4) + 1/4*(2*b^3*c^4 + 7*a^2*b*c^2*d^2 - 3*a^3*c*d^3 + 2*(b^3*c^2*d^2 + 3*a*b^2*c*d^3 - a^2*b*d^4)*x^4 + (4*b^3*c^3*d + 7*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 2*a^3*d^4)*x^2)/(a^2*b^3*c^7 - 3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 + (a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2) + 1/2*log(x^2)/(a^2*c^3)","B",0
316,1,639,0,2.748006," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\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{8 \, a b^{3} c^{5} - 24 \, a^{2} b^{2} c^{4} d + 24 \, a^{3} b c^{3} d^{2} - 8 \, a^{4} c^{2} d^{3} + 3 \, {\left(4 \, b^{4} c^{3} d^{2} - 8 \, a b^{3} c^{2} d^{3} + 13 \, a^{2} b^{2} c d^{4} - 5 \, a^{3} b d^{5}\right)} x^{6} + {\left(24 \, b^{4} c^{4} d - 40 \, a b^{3} c^{3} d^{2} + 41 \, a^{2} b^{2} c^{2} d^{3} + 14 \, a^{3} b c d^{4} - 15 \, a^{4} d^{5}\right)} x^{4} + {\left(12 \, b^{4} c^{5} - 8 \, a b^{3} c^{4} d - 24 \, a^{2} b^{2} c^{3} d^{2} + 57 \, a^{3} b c^{2} d^{3} - 25 \, a^{4} c d^{4}\right)} x^{2}}{8 \, {\left({\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{7} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{5} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{3} + {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3}\right)} x\right)}}"," ",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)) - 1/8*(8*a*b^3*c^5 - 24*a^2*b^2*c^4*d + 24*a^3*b*c^3*d^2 - 8*a^4*c^2*d^3 + 3*(4*b^4*c^3*d^2 - 8*a*b^3*c^2*d^3 + 13*a^2*b^2*c*d^4 - 5*a^3*b*d^5)*x^6 + (24*b^4*c^4*d - 40*a*b^3*c^3*d^2 + 41*a^2*b^2*c^2*d^3 + 14*a^3*b*c*d^4 - 15*a^4*d^5)*x^4 + (12*b^4*c^5 - 8*a*b^3*c^4*d - 24*a^2*b^2*c^3*d^2 + 57*a^3*b*c^2*d^3 - 25*a^4*c*d^4)*x^2)/((a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^7 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^5 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^3 + (a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3)*x)","B",0
317,1,651,0,1.481227," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, b^{5} c - 5 \, a b^{4} d\right)} \log\left(b x^{2} + a\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)}} + \frac{{\left(10 \, b^{2} c^{2} d^{3} - 10 \, a b c d^{4} + 3 \, a^{2} d^{5}\right)} \log\left(d x^{2} + c\right)}{2 \, {\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)}} - \frac{2 \, a b^{3} c^{5} - 6 \, a^{2} b^{2} c^{4} d + 6 \, a^{3} b c^{3} d^{2} - 2 \, a^{4} c^{2} d^{3} + 2 \, {\left(2 \, b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 7 \, a^{2} b^{2} c d^{4} - 3 \, a^{3} b d^{5}\right)} x^{6} + {\left(8 \, b^{4} c^{4} d - 10 \, a b^{3} c^{3} d^{2} + 15 \, a^{2} b^{2} c^{2} d^{3} + 5 \, a^{3} b c d^{4} - 6 \, a^{4} d^{5}\right)} x^{4} + {\left(4 \, b^{4} c^{5} - 2 \, a b^{3} c^{4} d - 6 \, a^{2} b^{2} c^{3} d^{2} + 19 \, a^{3} b c^{2} d^{3} - 9 \, a^{4} c d^{4}\right)} x^{2}}{4 \, {\left({\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{8} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{6} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{4} + {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3}\right)} x^{2}\right)}} - \frac{{\left(2 \, b c + 3 \, a d\right)} \log\left(x^{2}\right)}{2 \, a^{3} c^{4}}"," ",0,"1/2*(2*b^5*c - 5*a*b^4*d)*log(b*x^2 + a)/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4) + 1/2*(10*b^2*c^2*d^3 - 10*a*b*c*d^4 + 3*a^2*d^5)*log(d*x^2 + c)/(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) - 1/4*(2*a*b^3*c^5 - 6*a^2*b^2*c^4*d + 6*a^3*b*c^3*d^2 - 2*a^4*c^2*d^3 + 2*(2*b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 7*a^2*b^2*c*d^4 - 3*a^3*b*d^5)*x^6 + (8*b^4*c^4*d - 10*a*b^3*c^3*d^2 + 15*a^2*b^2*c^2*d^3 + 5*a^3*b*c*d^4 - 6*a^4*d^5)*x^4 + (4*b^4*c^5 - 2*a*b^3*c^4*d - 6*a^2*b^2*c^3*d^2 + 19*a^3*b*c^2*d^3 - 9*a^4*c*d^4)*x^2)/((a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^8 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^6 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^4 + (a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3)*x^2) - 1/2*(2*b*c + 3*a*d)*log(x^2)/(a^3*c^4)","B",0
318,1,738,0,2.781460," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\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{8 \, a^{2} b^{3} c^{6} - 24 \, a^{3} b^{2} c^{5} d + 24 \, a^{4} b c^{4} d^{2} - 8 \, a^{5} c^{3} d^{3} - 3 \, {\left(20 \, b^{5} c^{4} d^{2} - 24 \, a b^{4} c^{3} d^{3} - 24 \, a^{2} b^{3} c^{2} d^{4} + 75 \, a^{3} b^{2} c d^{5} - 35 \, a^{4} b d^{6}\right)} x^{8} - {\left(120 \, b^{5} c^{5} d - 104 \, a b^{4} c^{4} d^{2} - 192 \, a^{2} b^{3} c^{3} d^{3} + 303 \, a^{3} b^{2} c^{2} d^{4} + 50 \, a^{4} b c d^{5} - 105 \, a^{5} d^{6}\right)} x^{6} - {\left(60 \, b^{5} c^{6} + 8 \, a b^{4} c^{5} d - 176 \, a^{2} b^{3} c^{4} d^{2} + 319 \, a^{4} b c^{2} d^{4} - 175 \, a^{5} c d^{5}\right)} x^{4} - 8 \, {\left(5 \, a b^{4} c^{6} - 8 \, a^{2} b^{3} c^{5} d - 6 \, a^{3} b^{2} c^{4} d^{2} + 16 \, a^{4} b c^{3} d^{3} - 7 \, a^{5} c^{2} d^{4}\right)} x^{2}}{24 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{9} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{7} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{5} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{3}\right)}}"," ",0,"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)) - 1/24*(8*a^2*b^3*c^6 - 24*a^3*b^2*c^5*d + 24*a^4*b*c^4*d^2 - 8*a^5*c^3*d^3 - 3*(20*b^5*c^4*d^2 - 24*a*b^4*c^3*d^3 - 24*a^2*b^3*c^2*d^4 + 75*a^3*b^2*c*d^5 - 35*a^4*b*d^6)*x^8 - (120*b^5*c^5*d - 104*a*b^4*c^4*d^2 - 192*a^2*b^3*c^3*d^3 + 303*a^3*b^2*c^2*d^4 + 50*a^4*b*c*d^5 - 105*a^5*d^6)*x^6 - (60*b^5*c^6 + 8*a*b^4*c^5*d - 176*a^2*b^3*c^4*d^2 + 319*a^4*b*c^2*d^4 - 175*a^5*c*d^5)*x^4 - 8*(5*a*b^4*c^6 - 8*a^2*b^3*c^5*d - 6*a^3*b^2*c^4*d^2 + 16*a^4*b*c^3*d^3 - 7*a^5*c^2*d^4)*x^2)/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^9 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^7 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^5 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^3)","B",0
319,1,129,0,1.072483," ","integrate(x^m*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""maxima"")","\frac{B b^{3} x^{m + 9}}{m + 9} + \frac{3 \, B a b^{2} x^{m + 7}}{m + 7} + \frac{A b^{3} x^{m + 7}}{m + 7} + \frac{3 \, B a^{2} b x^{m + 5}}{m + 5} + \frac{3 \, A a b^{2} x^{m + 5}}{m + 5} + \frac{B a^{3} x^{m + 3}}{m + 3} + \frac{3 \, A a^{2} b x^{m + 3}}{m + 3} + \frac{A a^{3} x^{m + 1}}{m + 1}"," ",0,"B*b^3*x^(m + 9)/(m + 9) + 3*B*a*b^2*x^(m + 7)/(m + 7) + A*b^3*x^(m + 7)/(m + 7) + 3*B*a^2*b*x^(m + 5)/(m + 5) + 3*A*a*b^2*x^(m + 5)/(m + 5) + B*a^3*x^(m + 3)/(m + 3) + 3*A*a^2*b*x^(m + 3)/(m + 3) + A*a^3*x^(m + 1)/(m + 1)","A",0
320,1,91,0,1.013979," ","integrate(x^m*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{B b^{2} x^{m + 7}}{m + 7} + \frac{2 \, B a b x^{m + 5}}{m + 5} + \frac{A b^{2} x^{m + 5}}{m + 5} + \frac{B a^{2} x^{m + 3}}{m + 3} + \frac{2 \, A a b x^{m + 3}}{m + 3} + \frac{A a^{2} x^{m + 1}}{m + 1}"," ",0,"B*b^2*x^(m + 7)/(m + 7) + 2*B*a*b*x^(m + 5)/(m + 5) + A*b^2*x^(m + 5)/(m + 5) + B*a^2*x^(m + 3)/(m + 3) + 2*A*a*b*x^(m + 3)/(m + 3) + A*a^2*x^(m + 1)/(m + 1)","A",0
321,1,53,0,1.062423," ","integrate(x^m*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{B b x^{m + 5}}{m + 5} + \frac{B a x^{m + 3}}{m + 3} + \frac{A b x^{m + 3}}{m + 3} + \frac{A a x^{m + 1}}{m + 1}"," ",0,"B*b*x^(m + 5)/(m + 5) + B*a*x^(m + 3)/(m + 3) + A*b*x^(m + 3)/(m + 3) + A*a*x^(m + 1)/(m + 1)","A",0
322,0,0,0,0.000000," ","integrate(x^m*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
325,1,215,0,1.105336," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{2} d^{3} x^{m + 11}}{m + 11} + \frac{3 \, b^{2} c d^{2} x^{m + 9}}{m + 9} + \frac{2 \, a b d^{3} x^{m + 9}}{m + 9} + \frac{3 \, b^{2} c^{2} d x^{m + 7}}{m + 7} + \frac{6 \, a b c d^{2} x^{m + 7}}{m + 7} + \frac{a^{2} d^{3} x^{m + 7}}{m + 7} + \frac{b^{2} c^{3} x^{m + 5}}{m + 5} + \frac{6 \, a b c^{2} d x^{m + 5}}{m + 5} + \frac{3 \, a^{2} c d^{2} x^{m + 5}}{m + 5} + \frac{2 \, a b c^{3} x^{m + 3}}{m + 3} + \frac{3 \, a^{2} c^{2} d x^{m + 3}}{m + 3} + \frac{a^{2} c^{3} x^{m + 1}}{m + 1}"," ",0,"b^2*d^3*x^(m + 11)/(m + 11) + 3*b^2*c*d^2*x^(m + 9)/(m + 9) + 2*a*b*d^3*x^(m + 9)/(m + 9) + 3*b^2*c^2*d*x^(m + 7)/(m + 7) + 6*a*b*c*d^2*x^(m + 7)/(m + 7) + a^2*d^3*x^(m + 7)/(m + 7) + b^2*c^3*x^(m + 5)/(m + 5) + 6*a*b*c^2*d*x^(m + 5)/(m + 5) + 3*a^2*c*d^2*x^(m + 5)/(m + 5) + 2*a*b*c^3*x^(m + 3)/(m + 3) + 3*a^2*c^2*d*x^(m + 3)/(m + 3) + a^2*c^3*x^(m + 1)/(m + 1)","A",0
326,1,153,0,1.020442," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{2} d^{2} x^{m + 9}}{m + 9} + \frac{2 \, b^{2} c d x^{m + 7}}{m + 7} + \frac{2 \, a b d^{2} x^{m + 7}}{m + 7} + \frac{b^{2} c^{2} x^{m + 5}}{m + 5} + \frac{4 \, a b c d x^{m + 5}}{m + 5} + \frac{a^{2} d^{2} x^{m + 5}}{m + 5} + \frac{2 \, a b c^{2} x^{m + 3}}{m + 3} + \frac{2 \, a^{2} c d x^{m + 3}}{m + 3} + \frac{a^{2} c^{2} x^{m + 1}}{m + 1}"," ",0,"b^2*d^2*x^(m + 9)/(m + 9) + 2*b^2*c*d*x^(m + 7)/(m + 7) + 2*a*b*d^2*x^(m + 7)/(m + 7) + b^2*c^2*x^(m + 5)/(m + 5) + 4*a*b*c*d*x^(m + 5)/(m + 5) + a^2*d^2*x^(m + 5)/(m + 5) + 2*a*b*c^2*x^(m + 3)/(m + 3) + 2*a^2*c*d*x^(m + 3)/(m + 3) + a^2*c^2*x^(m + 1)/(m + 1)","A",0
327,1,91,0,0.945362," ","integrate(x^m*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{b^{2} d x^{m + 7}}{m + 7} + \frac{b^{2} c x^{m + 5}}{m + 5} + \frac{2 \, a b d x^{m + 5}}{m + 5} + \frac{2 \, a b c x^{m + 3}}{m + 3} + \frac{a^{2} d x^{m + 3}}{m + 3} + \frac{a^{2} c x^{m + 1}}{m + 1}"," ",0,"b^2*d*x^(m + 7)/(m + 7) + b^2*c*x^(m + 5)/(m + 5) + 2*a*b*d*x^(m + 5)/(m + 5) + 2*a*b*c*x^(m + 3)/(m + 3) + a^2*d*x^(m + 3)/(m + 3) + a^2*c*x^(m + 1)/(m + 1)","A",0
328,0,0,0,0.000000," ","integrate(x^m*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
343,1,27,0,1.051021," ","integrate(x^(7/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{17} \, B b x^{\frac{17}{2}} + \frac{2}{13} \, {\left(B a + A b\right)} 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 + A*b)*x^(13/2) + 2/9*A*a*x^(9/2)","A",0
344,1,27,0,1.061010," ","integrate(x^(5/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{15} \, B b x^{\frac{15}{2}} + \frac{2}{11} \, {\left(B a + A b\right)} 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 + A*b)*x^(11/2) + 2/7*A*a*x^(7/2)","A",0
345,1,27,0,1.087975," ","integrate(x^(3/2)*(b*x^2+a)*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{9} \, {\left(B a + A b\right)} 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 + A*b)*x^(9/2) + 2/5*A*a*x^(5/2)","A",0
346,1,27,0,0.951236," ","integrate((b*x^2+a)*(B*x^2+A)*x^(1/2),x, algorithm=""maxima"")","\frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \, {\left(B a + A b\right)} 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 + A*b)*x^(7/2) + 2/3*A*a*x^(3/2)","A",0
347,1,27,0,1.059952," ","integrate((b*x^2+a)*(B*x^2+A)/x^(1/2),x, algorithm=""maxima"")","\frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{5} \, {\left(B a + A b\right)} x^{\frac{5}{2}} + 2 \, A a \sqrt{x}"," ",0,"2/9*B*b*x^(9/2) + 2/5*(B*a + A*b)*x^(5/2) + 2*A*a*sqrt(x)","A",0
348,1,27,0,1.103634," ","integrate((b*x^2+a)*(B*x^2+A)/x^(3/2),x, algorithm=""maxima"")","\frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{3} \, {\left(B a + A b\right)} x^{\frac{3}{2}} - \frac{2 \, A a}{\sqrt{x}}"," ",0,"2/7*B*b*x^(7/2) + 2/3*(B*a + A*b)*x^(3/2) - 2*A*a/sqrt(x)","A",0
349,1,27,0,1.032169," ","integrate((b*x^2+a)*(B*x^2+A)/x^(5/2),x, algorithm=""maxima"")","\frac{2}{5} \, B b x^{\frac{5}{2}} + 2 \, {\left(B a + A b\right)} \sqrt{x} - \frac{2 \, A a}{3 \, x^{\frac{3}{2}}}"," ",0,"2/5*B*b*x^(5/2) + 2*(B*a + A*b)*sqrt(x) - 2/3*A*a/x^(3/2)","A",0
350,1,29,0,1.036859," ","integrate((b*x^2+a)*(B*x^2+A)/x^(7/2),x, algorithm=""maxima"")","\frac{2}{3} \, B b x^{\frac{3}{2}} - \frac{2 \, {\left(5 \, {\left(B a + A b\right)} x^{2} + A a\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/3*B*b*x^(3/2) - 2/5*(5*(B*a + A*b)*x^2 + A*a)/x^(5/2)","A",0
351,1,51,0,1.156657," ","integrate(x^(7/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{21} \, B b^{2} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{17}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} + \frac{2}{13} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{13}{2}}"," ",0,"2/21*B*b^2*x^(21/2) + 2/17*(2*B*a*b + A*b^2)*x^(17/2) + 2/9*A*a^2*x^(9/2) + 2/13*(B*a^2 + 2*A*a*b)*x^(13/2)","A",0
352,1,51,0,1.103373," ","integrate(x^(5/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{19} \, B b^{2} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{15}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}} + \frac{2}{11} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{11}{2}}"," ",0,"2/19*B*b^2*x^(19/2) + 2/15*(2*B*a*b + A*b^2)*x^(15/2) + 2/7*A*a^2*x^(7/2) + 2/11*(B*a^2 + 2*A*a*b)*x^(11/2)","A",0
353,1,51,0,1.079668," ","integrate(x^(3/2)*(b*x^2+a)^2*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{13}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}} + \frac{2}{9} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{9}{2}}"," ",0,"2/17*B*b^2*x^(17/2) + 2/13*(2*B*a*b + A*b^2)*x^(13/2) + 2/5*A*a^2*x^(5/2) + 2/9*(B*a^2 + 2*A*a*b)*x^(9/2)","A",0
354,1,51,0,1.054775," ","integrate((b*x^2+a)^2*(B*x^2+A)*x^(1/2),x, algorithm=""maxima"")","\frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{11}{2}} + \frac{2}{3} \, A a^{2} x^{\frac{3}{2}} + \frac{2}{7} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{7}{2}}"," ",0,"2/15*B*b^2*x^(15/2) + 2/11*(2*B*a*b + A*b^2)*x^(11/2) + 2/3*A*a^2*x^(3/2) + 2/7*(B*a^2 + 2*A*a*b)*x^(7/2)","A",0
355,1,51,0,0.955355," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(1/2),x, algorithm=""maxima"")","\frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{9}{2}} + 2 \, A a^{2} \sqrt{x} + \frac{2}{5} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{5}{2}}"," ",0,"2/13*B*b^2*x^(13/2) + 2/9*(2*B*a*b + A*b^2)*x^(9/2) + 2*A*a^2*sqrt(x) + 2/5*(B*a^2 + 2*A*a*b)*x^(5/2)","A",0
356,1,51,0,1.031795," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(3/2),x, algorithm=""maxima"")","\frac{2}{11} \, B b^{2} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{7}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}} + \frac{2}{3} \, {\left(B a^{2} + 2 \, A a b\right)} x^{\frac{3}{2}}"," ",0,"2/11*B*b^2*x^(11/2) + 2/7*(2*B*a*b + A*b^2)*x^(7/2) - 2*A*a^2/sqrt(x) + 2/3*(B*a^2 + 2*A*a*b)*x^(3/2)","A",0
357,1,51,0,0.986680," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(5/2),x, algorithm=""maxima"")","\frac{2}{9} \, B b^{2} x^{\frac{9}{2}} + \frac{2}{5} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{5}{2}} - \frac{2 \, A a^{2}}{3 \, x^{\frac{3}{2}}} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} \sqrt{x}"," ",0,"2/9*B*b^2*x^(9/2) + 2/5*(2*B*a*b + A*b^2)*x^(5/2) - 2/3*A*a^2/x^(3/2) + 2*(B*a^2 + 2*A*a*b)*sqrt(x)","A",0
358,1,53,0,0.985957," ","integrate((b*x^2+a)^2*(B*x^2+A)/x^(7/2),x, algorithm=""maxima"")","\frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{2}{3} \, {\left(2 \, B a b + A b^{2}\right)} x^{\frac{3}{2}} - \frac{2 \, {\left(A a^{2} + 5 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/7*B*b^2*x^(7/2) + 2/3*(2*B*a*b + A*b^2)*x^(3/2) - 2/5*(A*a^2 + 5*(B*a^2 + 2*A*a*b)*x^2)/x^(5/2)","A",0
359,1,73,0,1.135276," ","integrate(x^(7/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{25} \, B b^{3} x^{\frac{25}{2}} + \frac{2}{21} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{21}{2}} + \frac{6}{17} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{17}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}} + \frac{2}{13} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{13}{2}}"," ",0,"2/25*B*b^3*x^(25/2) + 2/21*(3*B*a*b^2 + A*b^3)*x^(21/2) + 6/17*(B*a^2*b + A*a*b^2)*x^(17/2) + 2/9*A*a^3*x^(9/2) + 2/13*(B*a^3 + 3*A*a^2*b)*x^(13/2)","A",0
360,1,73,0,1.041912," ","integrate(x^(5/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{23} \, B b^{3} x^{\frac{23}{2}} + \frac{2}{19} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{19}{2}} + \frac{2}{5} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{15}{2}} + \frac{2}{7} \, A a^{3} x^{\frac{7}{2}} + \frac{2}{11} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{11}{2}}"," ",0,"2/23*B*b^3*x^(23/2) + 2/19*(3*B*a*b^2 + A*b^3)*x^(19/2) + 2/5*(B*a^2*b + A*a*b^2)*x^(15/2) + 2/7*A*a^3*x^(7/2) + 2/11*(B*a^3 + 3*A*a^2*b)*x^(11/2)","A",0
361,1,73,0,1.086816," ","integrate(x^(3/2)*(b*x^2+a)^3*(B*x^2+A),x, algorithm=""maxima"")","\frac{2}{21} \, B b^{3} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{17}{2}} + \frac{6}{13} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{13}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} + \frac{2}{9} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{9}{2}}"," ",0,"2/21*B*b^3*x^(21/2) + 2/17*(3*B*a*b^2 + A*b^3)*x^(17/2) + 6/13*(B*a^2*b + A*a*b^2)*x^(13/2) + 2/5*A*a^3*x^(5/2) + 2/9*(B*a^3 + 3*A*a^2*b)*x^(9/2)","A",0
362,1,73,0,1.165380," ","integrate((b*x^2+a)^3*(B*x^2+A)*x^(1/2),x, algorithm=""maxima"")","\frac{2}{19} \, B b^{3} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{15}{2}} + \frac{6}{11} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{11}{2}} + \frac{2}{3} \, A a^{3} x^{\frac{3}{2}} + \frac{2}{7} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{7}{2}}"," ",0,"2/19*B*b^3*x^(19/2) + 2/15*(3*B*a*b^2 + A*b^3)*x^(15/2) + 6/11*(B*a^2*b + A*a*b^2)*x^(11/2) + 2/3*A*a^3*x^(3/2) + 2/7*(B*a^3 + 3*A*a^2*b)*x^(7/2)","A",0
363,1,73,0,1.063575," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(1/2),x, algorithm=""maxima"")","\frac{2}{17} \, B b^{3} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{13}{2}} + \frac{2}{3} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{9}{2}} + 2 \, A a^{3} \sqrt{x} + \frac{2}{5} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{5}{2}}"," ",0,"2/17*B*b^3*x^(17/2) + 2/13*(3*B*a*b^2 + A*b^3)*x^(13/2) + 2/3*(B*a^2*b + A*a*b^2)*x^(9/2) + 2*A*a^3*sqrt(x) + 2/5*(B*a^3 + 3*A*a^2*b)*x^(5/2)","A",0
364,1,73,0,0.958712," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(3/2),x, algorithm=""maxima"")","\frac{2}{15} \, B b^{3} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{11}{2}} + \frac{6}{7} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{7}{2}} - \frac{2 \, A a^{3}}{\sqrt{x}} + \frac{2}{3} \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{\frac{3}{2}}"," ",0,"2/15*B*b^3*x^(15/2) + 2/11*(3*B*a*b^2 + A*b^3)*x^(11/2) + 6/7*(B*a^2*b + A*a*b^2)*x^(7/2) - 2*A*a^3/sqrt(x) + 2/3*(B*a^3 + 3*A*a^2*b)*x^(3/2)","A",0
365,1,73,0,1.146831," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(5/2),x, algorithm=""maxima"")","\frac{2}{13} \, B b^{3} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{9}{2}} + \frac{6}{5} \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{5}{2}} - \frac{2 \, A a^{3}}{3 \, x^{\frac{3}{2}}} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \sqrt{x}"," ",0,"2/13*B*b^3*x^(13/2) + 2/9*(3*B*a*b^2 + A*b^3)*x^(9/2) + 6/5*(B*a^2*b + A*a*b^2)*x^(5/2) - 2/3*A*a^3/x^(3/2) + 2*(B*a^3 + 3*A*a^2*b)*sqrt(x)","A",0
366,1,75,0,1.013110," ","integrate((b*x^2+a)^3*(B*x^2+A)/x^(7/2),x, algorithm=""maxima"")","\frac{2}{11} \, B b^{3} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{\frac{7}{2}} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} x^{\frac{3}{2}} - \frac{2 \, {\left(A a^{3} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*B*b^3*x^(11/2) + 2/7*(3*B*a*b^2 + A*b^3)*x^(7/2) + 2*(B*a^2*b + A*a*b^2)*x^(3/2) - 2/5*(A*a^3 + 5*(B*a^3 + 3*A*a^2*b)*x^2)/x^(5/2)","A",0
367,1,259,0,2.488460," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a^{2}}{4 \, b^{3}} + \frac{2 \, {\left(5 \, B b^{2} x^{\frac{9}{2}} - 9 \, {\left(B a b - A b^{2}\right)} x^{\frac{5}{2}} + 45 \, {\left(B a^{2} - A a b\right)} \sqrt{x}\right)}}{45 \, b^{3}}"," ",0,"-1/4*(2*sqrt(2)*(B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a^2/b^3 + 2/45*(5*B*b^2*x^(9/2) - 9*(B*a*b - A*b^2)*x^(5/2) + 45*(B*a^2 - A*a*b)*sqrt(x))/b^3","A",0
368,1,214,0,2.413913," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B a^{2} - A a b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, b^{2}} + \frac{2 \, {\left(3 \, B b x^{\frac{7}{2}} - 7 \, {\left(B a - A b\right)} x^{\frac{3}{2}}\right)}}{21 \, b^{2}}"," ",0,"1/4*(B*a^2 - A*a*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^2 + 2/21*(3*B*b*x^(7/2) - 7*(B*a - A*b)*x^(3/2))/b^2","A",0
369,1,235,0,2.240900," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a}{4 \, b^{2}} + \frac{2 \, {\left(B b x^{\frac{5}{2}} - 5 \, {\left(B a - A b\right)} \sqrt{x}\right)}}{5 \, b^{2}}"," ",0,"1/4*(2*sqrt(2)*(B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a/b^2 + 2/5*(B*b*x^(5/2) - 5*(B*a - A*b)*sqrt(x))/b^2","A",0
370,1,194,0,2.329239," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, B x^{\frac{3}{2}}}{3 \, b} - \frac{{\left(B a - A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, b}"," ",0,"2/3*B*x^(3/2)/b - 1/4*(B*a - A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b","A",0
371,1,218,0,2.359332," ","integrate((B*x^2+A)/(b*x^2+a)/x^(1/2),x, algorithm=""maxima"")","\frac{2 \, B \sqrt{x}}{b} - \frac{\frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, b}"," ",0,"2*B*sqrt(x)/b - 1/4*(2*sqrt(2)*(B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b","A",0
372,1,194,0,2.420129," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(B a - A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a} - \frac{2 \, A}{a \sqrt{x}}"," ",0,"1/4*(B*a - A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a - 2*A/(a*sqrt(x))","A",0
373,1,218,0,2.373236," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, a} - \frac{2 \, A}{3 \, a x^{\frac{3}{2}}}"," ",0,"1/4*(2*sqrt(2)*(B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/a - 2/3*A/(a*x^(3/2))","A",0
374,1,213,0,2.377661," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(B a b - A b^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a^{2}} - \frac{2 \, {\left(5 \, {\left(B a - A b\right)} x^{2} + A a\right)}}{5 \, a^{2} x^{\frac{5}{2}}}"," ",0,"-1/4*(B*a*b - A*b^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^2 - 2/5*(5*(B*a - A*b)*x^2 + A*a)/(a^2*x^(5/2))","A",0
375,1,271,0,2.458673," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(B a^{2} - A a b\right)} \sqrt{x}}{2 \, {\left(b^{4} x^{2} + a b^{3}\right)}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(9 \, B a - 5 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(9 \, B a - 5 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(9 \, B a - 5 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(9 \, B a - 5 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a}{16 \, b^{3}} + \frac{2 \, {\left(B b x^{\frac{5}{2}} - 5 \, {\left(2 \, B a - A b\right)} \sqrt{x}\right)}}{5 \, b^{3}}"," ",0,"-1/2*(B*a^2 - A*a*b)*sqrt(x)/(b^4*x^2 + a*b^3) + 1/16*(2*sqrt(2)*(9*B*a - 5*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(9*B*a - 5*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(9*B*a - 5*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(9*B*a - 5*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a/b^3 + 2/5*(B*b*x^(5/2) - 5*(2*B*a - A*b)*sqrt(x))/b^3","A",0
376,1,223,0,2.392905," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - A b\right)} x^{\frac{3}{2}}}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{2 \, B x^{\frac{3}{2}}}{3 \, b^{2}} - \frac{{\left(7 \, B a - 3 \, A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, b^{2}}"," ",0,"1/2*(B*a - A*b)*x^(3/2)/(b^3*x^2 + a*b^2) + 2/3*B*x^(3/2)/b^2 - 1/16*(7*B*a - 3*A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^2","A",0
377,1,250,0,2.488895," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - A b\right)} \sqrt{x}}{2 \, {\left(b^{3} x^{2} + a b^{2}\right)}} + \frac{2 \, B \sqrt{x}}{b^{2}} - \frac{\frac{2 \, \sqrt{2} {\left(5 \, B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(5 \, B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(5 \, B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, b^{2}}"," ",0,"1/2*(B*a - A*b)*sqrt(x)/(b^3*x^2 + a*b^2) + 2*B*sqrt(x)/b^2 - 1/16*(2*sqrt(2)*(5*B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(5*B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(5*B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(5*B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^2","A",0
378,1,217,0,2.280302," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(B a - A b\right)} x^{\frac{3}{2}}}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} + \frac{{\left(3 \, B a + A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a b}"," ",0,"-1/2*(B*a - A*b)*x^(3/2)/(a*b^2*x^2 + a^2*b) + 1/16*(3*B*a + A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b)","A",0
379,1,241,0,2.464695," ","integrate((B*x^2+A)/(b*x^2+a)^2/x^(1/2),x, algorithm=""maxima"")","-\frac{{\left(B a - A b\right)} \sqrt{x}}{2 \, {\left(a b^{2} x^{2} + a^{2} b\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(B a + 3 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a + 3 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a + 3 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a + 3 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, a b}"," ",0,"-1/2*(B*a - A*b)*sqrt(x)/(a*b^2*x^2 + a^2*b) + 1/16*(2*sqrt(2)*(B*a + 3*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a + 3*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a + 3*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a + 3*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b)","A",0
380,1,222,0,2.428081," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(B a - 5 \, A b\right)} x^{2} - 4 \, A a}{2 \, {\left(a^{2} b x^{\frac{5}{2}} + a^{3} \sqrt{x}\right)}} + \frac{{\left(B a - 5 \, A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a^{2}}"," ",0,"1/2*((B*a - 5*A*b)*x^2 - 4*A*a)/(a^2*b*x^(5/2) + a^3*sqrt(x)) + 1/16*(B*a - 5*A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^2","A",0
381,1,251,0,2.706163," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, B a - 7 \, A b\right)} x^{2} - 4 \, A a}{6 \, {\left(a^{2} b x^{\frac{7}{2}} + a^{3} x^{\frac{3}{2}}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, B a - 7 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, B a - 7 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, B a - 7 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, B a - 7 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, a^{2}}"," ",0,"1/6*((3*B*a - 7*A*b)*x^2 - 4*A*a)/(a^2*b*x^(7/2) + a^3*x^(3/2)) + 1/16*(2*sqrt(2)*(3*B*a - 7*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*B*a - 7*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*B*a - 7*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*B*a - 7*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/a^2","A",0
382,1,250,0,2.310418," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{5 \, {\left(5 \, B a b - 9 \, A b^{2}\right)} x^{4} + 4 \, A a^{2} + 4 \, {\left(5 \, B a^{2} - 9 \, A a b\right)} x^{2}}{10 \, {\left(a^{3} b x^{\frac{9}{2}} + a^{4} x^{\frac{5}{2}}\right)}} - \frac{{\left(5 \, B a b - 9 \, A b^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a^{3}}"," ",0,"-1/10*(5*(5*B*a*b - 9*A*b^2)*x^4 + 4*A*a^2 + 4*(5*B*a^2 - 9*A*a*b)*x^2)/(a^3*b*x^(9/2) + a^4*x^(5/2)) - 1/16*(5*B*a*b - 9*A*b^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^3","A",0
383,1,283,0,2.465798," ","integrate(x^(7/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(17 \, B a b - 9 \, A b^{2}\right)} x^{\frac{5}{2}} + {\left(13 \, B a^{2} - 5 \, A a b\right)} \sqrt{x}}{16 \, {\left(b^{5} x^{4} + 2 \, a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{2 \, B \sqrt{x}}{b^{3}} - \frac{5 \, {\left(\frac{2 \, \sqrt{2} {\left(9 \, B a - A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(9 \, B a - A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(9 \, B a - A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(9 \, B a - A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, b^{3}}"," ",0,"1/16*((17*B*a*b - 9*A*b^2)*x^(5/2) + (13*B*a^2 - 5*A*a*b)*sqrt(x))/(b^5*x^4 + 2*a*b^4*x^2 + a^2*b^3) + 2*B*sqrt(x)/b^3 - 5/128*(2*sqrt(2)*(9*B*a - A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(9*B*a - A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(9*B*a - A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(9*B*a - A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^3","A",0
384,1,251,0,2.369081," ","integrate(x^(5/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(11 \, B a b - 3 \, A b^{2}\right)} x^{\frac{7}{2}} + {\left(7 \, B a^{2} + A a b\right)} x^{\frac{3}{2}}}{16 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}} + \frac{3 \, {\left(7 \, B a + A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a b^{2}}"," ",0,"-1/16*((11*B*a*b - 3*A*b^2)*x^(7/2) + (7*B*a^2 + A*a*b)*x^(3/2))/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2) + 3/128*(7*B*a + A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^2)","A",0
385,1,280,0,2.377333," ","integrate(x^(3/2)*(B*x^2+A)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{{\left(9 \, B a b - A b^{2}\right)} x^{\frac{5}{2}} + {\left(5 \, B a^{2} + 3 \, A a b\right)} \sqrt{x}}{16 \, {\left(a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(5 \, B a + 3 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(5 \, B a + 3 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(5 \, B a + 3 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, B a + 3 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{128 \, a b^{2}}"," ",0,"-1/16*((9*B*a*b - A*b^2)*x^(5/2) + (5*B*a^2 + 3*A*a*b)*sqrt(x))/(a*b^4*x^4 + 2*a^2*b^3*x^2 + a^3*b^2) + 1/128*(2*sqrt(2)*(5*B*a + 3*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(5*B*a + 3*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(5*B*a + 3*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(5*B*a + 3*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^2)","A",0
386,1,253,0,2.425479," ","integrate((B*x^2+A)*x^(1/2)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{{\left(3 \, B a b + 5 \, A b^{2}\right)} x^{\frac{7}{2}} - {\left(B a^{2} - 9 \, A a b\right)} x^{\frac{3}{2}}}{16 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} + \frac{{\left(3 \, B a + 5 \, A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{2} b}"," ",0,"1/16*((3*B*a*b + 5*A*b^2)*x^(7/2) - (B*a^2 - 9*A*a*b)*x^(3/2))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) + 1/128*(3*B*a + 5*A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b)","A",0
387,1,276,0,2.329336," ","integrate((B*x^2+A)/(b*x^2+a)^3/x^(1/2),x, algorithm=""maxima"")","\frac{{\left(B a b + 7 \, A b^{2}\right)} x^{\frac{5}{2}} - {\left(3 \, B a^{2} - 11 \, A a b\right)} \sqrt{x}}{16 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(B a + 7 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(B a + 7 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(B a + 7 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(B a + 7 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, a^{2} b}"," ",0,"1/16*((B*a*b + 7*A*b^2)*x^(5/2) - (3*B*a^2 - 11*A*a*b)*sqrt(x))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b) + 3/128*(2*sqrt(2)*(B*a + 7*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(B*a + 7*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(B*a + 7*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(B*a + 7*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^2*b)","A",0
388,1,255,0,2.592733," ","integrate((B*x^2+A)/x^(3/2)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{5 \, {\left(B a b - 9 \, A b^{2}\right)} x^{4} - 32 \, A a^{2} + 9 \, {\left(B a^{2} - 9 \, A a b\right)} x^{2}}{16 \, {\left(a^{3} b^{2} x^{\frac{9}{2}} + 2 \, a^{4} b x^{\frac{5}{2}} + a^{5} \sqrt{x}\right)}} + \frac{5 \, {\left(B a - 9 \, A b\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{3}}"," ",0,"1/16*(5*(B*a*b - 9*A*b^2)*x^4 - 32*A*a^2 + 9*(B*a^2 - 9*A*a*b)*x^2)/(a^3*b^2*x^(9/2) + 2*a^4*b*x^(5/2) + a^5*sqrt(x)) + 5/128*(B*a - 9*A*b)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^3","A",0
389,1,285,0,2.432551," ","integrate((B*x^2+A)/x^(5/2)/(b*x^2+a)^3,x, algorithm=""maxima"")","\frac{7 \, {\left(3 \, B a b - 11 \, A b^{2}\right)} x^{4} - 32 \, A a^{2} + 11 \, {\left(3 \, B a^{2} - 11 \, A a b\right)} x^{2}}{48 \, {\left(a^{3} b^{2} x^{\frac{11}{2}} + 2 \, a^{4} b x^{\frac{7}{2}} + a^{5} x^{\frac{3}{2}}\right)}} + \frac{7 \, {\left(\frac{2 \, \sqrt{2} {\left(3 \, B a - 11 \, A b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, B a - 11 \, A b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, B a - 11 \, A b\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, B a - 11 \, A b\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{128 \, a^{3}}"," ",0,"1/48*(7*(3*B*a*b - 11*A*b^2)*x^4 - 32*A*a^2 + 11*(3*B*a^2 - 11*A*a*b)*x^2)/(a^3*b^2*x^(11/2) + 2*a^4*b*x^(7/2) + a^5*x^(3/2)) + 7/128*(2*sqrt(2)*(3*B*a - 11*A*b)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*B*a - 11*A*b)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*B*a - 11*A*b)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*B*a - 11*A*b)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/a^3","A",0
390,1,285,0,2.455285," ","integrate((B*x^2+A)/x^(7/2)/(b*x^2+a)^3,x, algorithm=""maxima"")","-\frac{45 \, {\left(5 \, B a b^{2} - 13 \, A b^{3}\right)} x^{6} + 81 \, {\left(5 \, B a^{2} b - 13 \, A a b^{2}\right)} x^{4} + 32 \, A a^{3} + 32 \, {\left(5 \, B a^{3} - 13 \, A a^{2} b\right)} x^{2}}{80 \, {\left(a^{4} b^{2} x^{\frac{13}{2}} + 2 \, a^{5} b x^{\frac{9}{2}} + a^{6} x^{\frac{5}{2}}\right)}} - \frac{9 \, {\left(5 \, B a b - 13 \, A b^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{128 \, a^{4}}"," ",0,"-1/80*(45*(5*B*a*b^2 - 13*A*b^3)*x^6 + 81*(5*B*a^2*b - 13*A*a*b^2)*x^4 + 32*A*a^3 + 32*(5*B*a^3 - 13*A*a^2*b)*x^2)/(a^4*b^2*x^(13/2) + 2*a^5*b*x^(9/2) + a^6*x^(5/2)) - 9/128*(5*B*a*b - 13*A*b^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^4","A",0
391,1,51,0,0.999002," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{2}{21} \, b^{2} d x^{\frac{21}{2}} + \frac{2}{17} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{17}{2}} + \frac{2}{9} \, a^{2} c x^{\frac{9}{2}} + \frac{2}{13} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{13}{2}}"," ",0,"2/21*b^2*d*x^(21/2) + 2/17*(b^2*c + 2*a*b*d)*x^(17/2) + 2/9*a^2*c*x^(9/2) + 2/13*(2*a*b*c + a^2*d)*x^(13/2)","A",0
392,1,51,0,1.025975," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{2}{19} \, b^{2} d x^{\frac{19}{2}} + \frac{2}{15} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{15}{2}} + \frac{2}{7} \, a^{2} c x^{\frac{7}{2}} + \frac{2}{11} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{11}{2}}"," ",0,"2/19*b^2*d*x^(19/2) + 2/15*(b^2*c + 2*a*b*d)*x^(15/2) + 2/7*a^2*c*x^(7/2) + 2/11*(2*a*b*c + a^2*d)*x^(11/2)","A",0
393,1,51,0,0.961458," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c),x, algorithm=""maxima"")","\frac{2}{17} \, b^{2} d x^{\frac{17}{2}} + \frac{2}{13} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{13}{2}} + \frac{2}{5} \, a^{2} c x^{\frac{5}{2}} + \frac{2}{9} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{9}{2}}"," ",0,"2/17*b^2*d*x^(17/2) + 2/13*(b^2*c + 2*a*b*d)*x^(13/2) + 2/5*a^2*c*x^(5/2) + 2/9*(2*a*b*c + a^2*d)*x^(9/2)","A",0
394,1,51,0,1.004684," ","integrate((b*x^2+a)^2*(d*x^2+c)*x^(1/2),x, algorithm=""maxima"")","\frac{2}{15} \, b^{2} d x^{\frac{15}{2}} + \frac{2}{11} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{11}{2}} + \frac{2}{3} \, a^{2} c x^{\frac{3}{2}} + \frac{2}{7} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{7}{2}}"," ",0,"2/15*b^2*d*x^(15/2) + 2/11*(b^2*c + 2*a*b*d)*x^(11/2) + 2/3*a^2*c*x^(3/2) + 2/7*(2*a*b*c + a^2*d)*x^(7/2)","A",0
395,1,51,0,0.995065," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(1/2),x, algorithm=""maxima"")","\frac{2}{13} \, b^{2} d x^{\frac{13}{2}} + \frac{2}{9} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{9}{2}} + 2 \, a^{2} c \sqrt{x} + \frac{2}{5} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{5}{2}}"," ",0,"2/13*b^2*d*x^(13/2) + 2/9*(b^2*c + 2*a*b*d)*x^(9/2) + 2*a^2*c*sqrt(x) + 2/5*(2*a*b*c + a^2*d)*x^(5/2)","A",0
396,1,51,0,1.039292," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(3/2),x, algorithm=""maxima"")","\frac{2}{11} \, b^{2} d x^{\frac{11}{2}} + \frac{2}{7} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{7}{2}} - \frac{2 \, a^{2} c}{\sqrt{x}} + \frac{2}{3} \, {\left(2 \, a b c + a^{2} d\right)} x^{\frac{3}{2}}"," ",0,"2/11*b^2*d*x^(11/2) + 2/7*(b^2*c + 2*a*b*d)*x^(7/2) - 2*a^2*c/sqrt(x) + 2/3*(2*a*b*c + a^2*d)*x^(3/2)","A",0
397,1,51,0,1.100283," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(5/2),x, algorithm=""maxima"")","\frac{2}{9} \, b^{2} d x^{\frac{9}{2}} + \frac{2}{5} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{5}{2}} - \frac{2 \, a^{2} c}{3 \, x^{\frac{3}{2}}} + 2 \, {\left(2 \, a b c + a^{2} d\right)} \sqrt{x}"," ",0,"2/9*b^2*d*x^(9/2) + 2/5*(b^2*c + 2*a*b*d)*x^(5/2) - 2/3*a^2*c/x^(3/2) + 2*(2*a*b*c + a^2*d)*sqrt(x)","A",0
398,1,53,0,1.083065," ","integrate((b*x^2+a)^2*(d*x^2+c)/x^(7/2),x, algorithm=""maxima"")","\frac{2}{7} \, b^{2} d x^{\frac{7}{2}} + \frac{2}{3} \, {\left(b^{2} c + 2 \, a b d\right)} x^{\frac{3}{2}} - \frac{2 \, {\left(a^{2} c + 5 \, {\left(2 \, a b c + a^{2} d\right)} x^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/7*b^2*d*x^(7/2) + 2/3*(b^2*c + 2*a*b*d)*x^(3/2) - 2/5*(a^2*c + 5*(2*a*b*c + a^2*d)*x^2)/x^(5/2)","A",0
399,1,85,0,1.022100," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{2}{25} \, b^{2} d^{2} x^{\frac{25}{2}} + \frac{4}{21} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{17}{2}} + \frac{2}{9} \, a^{2} c^{2} x^{\frac{9}{2}} + \frac{4}{13} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{13}{2}}"," ",0,"2/25*b^2*d^2*x^(25/2) + 4/21*(b^2*c*d + a*b*d^2)*x^(21/2) + 2/17*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(17/2) + 2/9*a^2*c^2*x^(9/2) + 4/13*(a*b*c^2 + a^2*c*d)*x^(13/2)","A",0
400,1,85,0,1.169527," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{2}{23} \, b^{2} d^{2} x^{\frac{23}{2}} + \frac{4}{19} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{15}{2}} + \frac{2}{7} \, a^{2} c^{2} x^{\frac{7}{2}} + \frac{4}{11} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{11}{2}}"," ",0,"2/23*b^2*d^2*x^(23/2) + 4/19*(b^2*c*d + a*b*d^2)*x^(19/2) + 2/15*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(15/2) + 2/7*a^2*c^2*x^(7/2) + 4/11*(a*b*c^2 + a^2*c*d)*x^(11/2)","A",0
401,1,85,0,1.092427," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{2}{21} \, b^{2} d^{2} x^{\frac{21}{2}} + \frac{4}{17} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{13}{2}} + \frac{2}{5} \, a^{2} c^{2} x^{\frac{5}{2}} + \frac{4}{9} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{9}{2}}"," ",0,"2/21*b^2*d^2*x^(21/2) + 4/17*(b^2*c*d + a*b*d^2)*x^(17/2) + 2/13*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(13/2) + 2/5*a^2*c^2*x^(5/2) + 4/9*(a*b*c^2 + a^2*c*d)*x^(9/2)","A",0
402,1,85,0,1.060546," ","integrate((b*x^2+a)^2*(d*x^2+c)^2*x^(1/2),x, algorithm=""maxima"")","\frac{2}{19} \, b^{2} d^{2} x^{\frac{19}{2}} + \frac{4}{15} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{11}{2}} + \frac{2}{3} \, a^{2} c^{2} x^{\frac{3}{2}} + \frac{4}{7} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{7}{2}}"," ",0,"2/19*b^2*d^2*x^(19/2) + 4/15*(b^2*c*d + a*b*d^2)*x^(15/2) + 2/11*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(11/2) + 2/3*a^2*c^2*x^(3/2) + 4/7*(a*b*c^2 + a^2*c*d)*x^(7/2)","A",0
403,1,85,0,0.949872," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(1/2),x, algorithm=""maxima"")","\frac{2}{17} \, b^{2} d^{2} x^{\frac{17}{2}} + \frac{4}{13} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{9}{2}} + 2 \, a^{2} c^{2} \sqrt{x} + \frac{4}{5} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{5}{2}}"," ",0,"2/17*b^2*d^2*x^(17/2) + 4/13*(b^2*c*d + a*b*d^2)*x^(13/2) + 2/9*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(9/2) + 2*a^2*c^2*sqrt(x) + 4/5*(a*b*c^2 + a^2*c*d)*x^(5/2)","A",0
404,1,85,0,1.034816," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(3/2),x, algorithm=""maxima"")","\frac{2}{15} \, b^{2} d^{2} x^{\frac{15}{2}} + \frac{4}{11} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{7}{2}} - \frac{2 \, a^{2} c^{2}}{\sqrt{x}} + \frac{4}{3} \, {\left(a b c^{2} + a^{2} c d\right)} x^{\frac{3}{2}}"," ",0,"2/15*b^2*d^2*x^(15/2) + 4/11*(b^2*c*d + a*b*d^2)*x^(11/2) + 2/7*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(7/2) - 2*a^2*c^2/sqrt(x) + 4/3*(a*b*c^2 + a^2*c*d)*x^(3/2)","A",0
405,1,85,0,1.008000," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(5/2),x, algorithm=""maxima"")","\frac{2}{13} \, b^{2} d^{2} x^{\frac{13}{2}} + \frac{4}{9} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{9}{2}} + \frac{2}{5} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{5}{2}} - \frac{2 \, a^{2} c^{2}}{3 \, x^{\frac{3}{2}}} + 4 \, {\left(a b c^{2} + a^{2} c d\right)} \sqrt{x}"," ",0,"2/13*b^2*d^2*x^(13/2) + 4/9*(b^2*c*d + a*b*d^2)*x^(9/2) + 2/5*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(5/2) - 2/3*a^2*c^2/x^(3/2) + 4*(a*b*c^2 + a^2*c*d)*sqrt(x)","A",0
406,1,87,0,1.192755," ","integrate((b*x^2+a)^2*(d*x^2+c)^2/x^(7/2),x, algorithm=""maxima"")","\frac{2}{11} \, b^{2} d^{2} x^{\frac{11}{2}} + \frac{4}{7} \, {\left(b^{2} c d + a b d^{2}\right)} x^{\frac{7}{2}} + \frac{2}{3} \, {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{\frac{3}{2}} - \frac{2 \, {\left(a^{2} c^{2} + 10 \, {\left(a b c^{2} + a^{2} c d\right)} x^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/11*b^2*d^2*x^(11/2) + 4/7*(b^2*c*d + a*b*d^2)*x^(7/2) + 2/3*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(3/2) - 2/5*(a^2*c^2 + 10*(a*b*c^2 + a^2*c*d)*x^2)/x^(5/2)","A",0
407,1,127,0,1.063627," ","integrate(x^(7/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{2}{29} \, b^{2} d^{3} x^{\frac{29}{2}} + \frac{2}{25} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{25}{2}} + \frac{2}{21} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{21}{2}} + \frac{2}{9} \, a^{2} c^{3} x^{\frac{9}{2}} + \frac{2}{17} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{13}{2}}"," ",0,"2/29*b^2*d^3*x^(29/2) + 2/25*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(25/2) + 2/21*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(21/2) + 2/9*a^2*c^3*x^(9/2) + 2/17*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(17/2) + 2/13*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(13/2)","A",0
408,1,127,0,1.059511," ","integrate(x^(5/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{2}{27} \, b^{2} d^{3} x^{\frac{27}{2}} + \frac{2}{23} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{23}{2}} + \frac{2}{19} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{19}{2}} + \frac{2}{7} \, a^{2} c^{3} x^{\frac{7}{2}} + \frac{2}{15} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{11}{2}}"," ",0,"2/27*b^2*d^3*x^(27/2) + 2/23*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(23/2) + 2/19*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(19/2) + 2/7*a^2*c^3*x^(7/2) + 2/15*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(15/2) + 2/11*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(11/2)","A",0
409,1,127,0,1.087366," ","integrate(x^(3/2)*(b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{2}{25} \, b^{2} d^{3} x^{\frac{25}{2}} + \frac{2}{21} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{17}{2}} + \frac{2}{5} \, a^{2} c^{3} x^{\frac{5}{2}} + \frac{2}{13} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{9}{2}}"," ",0,"2/25*b^2*d^3*x^(25/2) + 2/21*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(21/2) + 2/17*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(17/2) + 2/5*a^2*c^3*x^(5/2) + 2/13*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(13/2) + 2/9*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(9/2)","A",0
410,1,127,0,1.033609," ","integrate((b*x^2+a)^2*(d*x^2+c)^3*x^(1/2),x, algorithm=""maxima"")","\frac{2}{23} \, b^{2} d^{3} x^{\frac{23}{2}} + \frac{2}{19} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{15}{2}} + \frac{2}{3} \, a^{2} c^{3} x^{\frac{3}{2}} + \frac{2}{11} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{7}{2}}"," ",0,"2/23*b^2*d^3*x^(23/2) + 2/19*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(19/2) + 2/15*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(15/2) + 2/3*a^2*c^3*x^(3/2) + 2/11*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(11/2) + 2/7*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(7/2)","A",0
411,1,127,0,1.077521," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(1/2),x, algorithm=""maxima"")","\frac{2}{21} \, b^{2} d^{3} x^{\frac{21}{2}} + \frac{2}{17} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{13}{2}} + 2 \, a^{2} c^{3} \sqrt{x} + \frac{2}{9} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{9}{2}} + \frac{2}{5} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{5}{2}}"," ",0,"2/21*b^2*d^3*x^(21/2) + 2/17*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(17/2) + 2/13*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(13/2) + 2*a^2*c^3*sqrt(x) + 2/9*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(9/2) + 2/5*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(5/2)","A",0
412,1,127,0,1.112937," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(3/2),x, algorithm=""maxima"")","\frac{2}{19} \, b^{2} d^{3} x^{\frac{19}{2}} + \frac{2}{15} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{11}{2}} - \frac{2 \, a^{2} c^{3}}{\sqrt{x}} + \frac{2}{7} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{7}{2}} + \frac{2}{3} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{\frac{3}{2}}"," ",0,"2/19*b^2*d^3*x^(19/2) + 2/15*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(15/2) + 2/11*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(11/2) - 2*a^2*c^3/sqrt(x) + 2/7*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(7/2) + 2/3*(2*a*b*c^3 + 3*a^2*c^2*d)*x^(3/2)","A",0
413,1,127,0,1.122399," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(5/2),x, algorithm=""maxima"")","\frac{2}{17} \, b^{2} d^{3} x^{\frac{17}{2}} + \frac{2}{13} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{13}{2}} + \frac{2}{9} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{9}{2}} - \frac{2 \, a^{2} c^{3}}{3 \, x^{\frac{3}{2}}} + \frac{2}{5} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{5}{2}} + 2 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} \sqrt{x}"," ",0,"2/17*b^2*d^3*x^(17/2) + 2/13*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(13/2) + 2/9*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(9/2) - 2/3*a^2*c^3/x^(3/2) + 2/5*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(5/2) + 2*(2*a*b*c^3 + 3*a^2*c^2*d)*sqrt(x)","A",0
414,1,129,0,1.076530," ","integrate((b*x^2+a)^2*(d*x^2+c)^3/x^(7/2),x, algorithm=""maxima"")","\frac{2}{15} \, b^{2} d^{3} x^{\frac{15}{2}} + \frac{2}{11} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{\frac{11}{2}} + \frac{2}{7} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{7}{2}} + \frac{2}{3} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{\frac{3}{2}} - \frac{2 \, {\left(a^{2} c^{3} + 5 \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/15*b^2*d^3*x^(15/2) + 2/11*(3*b^2*c*d^2 + 2*a*b*d^3)*x^(11/2) + 2/7*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^(7/2) + 2/3*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^(3/2) - 2/5*(a^2*c^3 + 5*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2)/x^(5/2)","A",0
415,1,360,0,2.438756," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c^{2}}{4 \, d^{4}} + \frac{2 \, {\left(45 \, b^{2} d^{3} x^{\frac{13}{2}} - 65 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{\frac{9}{2}} + 117 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{5}{2}} - 585 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{x}\right)}}{585 \, d^{4}}"," ",0,"1/4*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c^2/d^4 + 2/585*(45*b^2*d^3*x^(13/2) - 65*(b^2*c*d^2 - 2*a*b*d^3)*x^(9/2) + 117*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^(5/2) - 585*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(x))/d^4","A",0
416,1,263,0,2.446886," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, d^{3}} + \frac{2 \, {\left(21 \, b^{2} d^{2} x^{\frac{11}{2}} - 33 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{\frac{7}{2}} + 77 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{\frac{3}{2}}\right)}}{231 \, d^{3}}"," ",0,"-1/4*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/d^3 + 2/231*(21*b^2*d^2*x^(11/2) - 33*(b^2*c*d - 2*a*b*d^2)*x^(7/2) + 77*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^(3/2))/d^3","A",0
417,1,324,0,2.432834," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c),x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c}{4 \, d^{3}} + \frac{2 \, {\left(5 \, b^{2} d^{2} x^{\frac{9}{2}} - 9 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x^{\frac{5}{2}} + 45 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right)}}{45 \, d^{3}}"," ",0,"-1/4*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c/d^3 + 2/45*(5*b^2*d^2*x^(9/2) - 9*(b^2*c*d - 2*a*b*d^2)*x^(5/2) + 45*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x))/d^3","A",0
418,1,229,0,2.505377," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, d^{2}} + \frac{2 \, {\left(3 \, b^{2} d x^{\frac{7}{2}} - 7 \, {\left(b^{2} c - 2 \, a b d\right)} x^{\frac{3}{2}}\right)}}{21 \, d^{2}}"," ",0,"1/4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/d^2 + 2/21*(3*b^2*d*x^(7/2) - 7*(b^2*c - 2*a*b*d)*x^(3/2))/d^2","A",0
419,1,291,0,2.407988," ","integrate((b*x^2+a)^2/(d*x^2+c)/x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b^{2} d x^{\frac{5}{2}} - 5 \, {\left(b^{2} c - 2 \, a b d\right)} \sqrt{x}\right)}}{5 \, d^{2}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{4 \, d^{2}}"," ",0,"2/5*(b^2*d*x^(5/2) - 5*(b^2*c - 2*a*b*d)*sqrt(x))/d^2 + 1/4*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/d^2","A",0
420,1,223,0,2.383093," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c),x, algorithm=""maxima"")","\frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d} - \frac{2 \, a^{2}}{c \sqrt{x}} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, c d}"," ",0,"2/3*b^2*x^(3/2)/d - 2*a^2/(c*sqrt(x)) - 1/4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c*d)","A",0
421,1,286,0,2.409492," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c),x, algorithm=""maxima"")","\frac{2 \, b^{2} \sqrt{x}}{d} - \frac{2 \, a^{2}}{3 \, c x^{\frac{3}{2}}} - \frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{4 \, c d}"," ",0,"2*b^2*sqrt(x)/d - 2/3*a^2/(c*x^(3/2)) - 1/4*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c*d)","A",0
422,1,229,0,2.469413," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, c^{2}} - \frac{2 \, {\left(a^{2} c + 5 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)}}{5 \, c^{2} x^{\frac{5}{2}}}"," ",0,"1/4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/c^2 - 2/5*(a^2*c + 5*(2*a*b*c - a^2*d)*x^2)/(c^2*x^(5/2))","A",0
423,1,293,0,2.357432," ","integrate((b*x^2+a)^2/x^(9/2)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{4 \, c^{2}} - \frac{2 \, {\left(3 \, a^{2} c + 7 \, {\left(2 \, a b c - a^{2} d\right)} x^{2}\right)}}{21 \, c^{2} x^{\frac{7}{2}}}"," ",0,"1/4*(2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/c^2 - 2/21*(3*a^2*c + 7*(2*a*b*c - a^2*d)*x^2)/(c^2*x^(7/2))","A",0
424,1,263,0,2.596033," ","integrate((d*x^2+c)^2/x^(11/2)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a^{3}} - \frac{2 \, {\left(45 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{4} + 5 \, a^{2} c^{2} - 9 \, {\left(a b c^{2} - 2 \, a^{2} c d\right)} x^{2}\right)}}{45 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-1/4*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^3 - 2/45*(45*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^4 + 5*a^2*c^2 - 9*(a*b*c^2 - 2*a^2*c*d)*x^2)/(a^3*x^(9/2))","A",0
425,1,377,0,2.467135," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{x}}{2 \, {\left(d^{5} x^{2} + c d^{4}\right)}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(13 \, b^{2} c^{2} - 18 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c}{16 \, d^{4}} + \frac{2 \, {\left(5 \, b^{2} d^{2} x^{\frac{9}{2}} - 18 \, {\left(b^{2} c d - a b d^{2}\right)} x^{\frac{5}{2}} + 45 \, {\left(3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}\right)}}{45 \, d^{4}}"," ",0,"1/2*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(x)/(d^5*x^2 + c*d^4) - 1/16*(2*sqrt(2)*(13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(13*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c/d^4 + 2/45*(5*b^2*d^2*x^(9/2) - 18*(b^2*c*d - a*b*d^2)*x^(5/2) + 45*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*sqrt(x))/d^4","A",0
426,1,272,0,2.416480," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{\frac{3}{2}}}{2 \, {\left(d^{4} x^{2} + c d^{3}\right)}} + \frac{{\left(11 \, b^{2} c^{2} - 14 \, a b c d + 3 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, d^{3}} + \frac{2 \, {\left(3 \, b^{2} d x^{\frac{7}{2}} - 14 \, {\left(b^{2} c - a b d\right)} x^{\frac{3}{2}}\right)}}{21 \, d^{3}}"," ",0,"-1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^(3/2)/(d^4*x^2 + c*d^3) + 1/16*(11*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/d^3 + 2/21*(3*b^2*d*x^(7/2) - 14*(b^2*c - a*b*d)*x^(3/2))/d^3","A",0
427,1,336,0,2.449094," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}}{2 \, {\left(d^{4} x^{2} + c d^{3}\right)}} + \frac{2 \, {\left(b^{2} d x^{\frac{5}{2}} - 10 \, {\left(b^{2} c - a b d\right)} \sqrt{x}\right)}}{5 \, d^{3}} + \frac{\frac{2 \, \sqrt{2} {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(9 \, b^{2} c^{2} - 10 \, a b c d + a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, d^{3}}"," ",0,"-1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)/(d^4*x^2 + c*d^3) + 2/5*(b^2*d*x^(5/2) - 10*(b^2*c - a*b*d)*sqrt(x))/d^3 + 1/16*(2*sqrt(2)*(9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(9*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/d^3","A",0
428,1,258,0,2.513515," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{\frac{3}{2}}}{2 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}} + \frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d^{2}} - \frac{{\left(7 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, c d^{2}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^(3/2)/(c*d^3*x^2 + c^2*d^2) + 2/3*b^2*x^(3/2)/d^2 - 1/16*(7*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c*d^2)","A",0
429,1,327,0,2.582321," ","integrate((b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""maxima"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{x}}{2 \, {\left(c d^{3} x^{2} + c^{2} d^{2}\right)}} + \frac{2 \, b^{2} \sqrt{x}}{d^{2}} - \frac{\frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, c d^{2}}"," ",0,"1/2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(x)/(c*d^3*x^2 + c^2*d^2) + 2*b^2*sqrt(x)/d^2 - 1/16*(2*sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c*d^2)","A",0
430,1,260,0,2.376441," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{4 \, a^{2} c d + {\left(b^{2} c^{2} - 2 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2}}{2 \, {\left(c^{2} d^{2} x^{\frac{5}{2}} + c^{3} d \sqrt{x}\right)}} + \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, c^{2} d}"," ",0,"-1/2*(4*a^2*c*d + (b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x^2)/(c^2*d^2*x^(5/2) + c^3*d*sqrt(x)) + 1/16*(3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c^2*d)","A",0
431,1,326,0,2.434100," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{4 \, a^{2} c d + {\left(3 \, b^{2} c^{2} - 6 \, a b c d + 7 \, a^{2} d^{2}\right)} x^{2}}{6 \, {\left(c^{2} d^{2} x^{\frac{7}{2}} + c^{3} d x^{\frac{3}{2}}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{2} c^{2} + 6 \, a b c d - 7 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, c^{2} d}"," ",0,"-1/6*(4*a^2*c*d + (3*b^2*c^2 - 6*a*b*c*d + 7*a^2*d^2)*x^2)/(c^2*d^2*x^(7/2) + c^3*d*x^(3/2)) + 1/16*(2*sqrt(2)*(b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b^2*c^2 + 6*a*b*c*d - 7*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c^2*d)","A",0
432,1,275,0,2.380825," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{5 \, {\left(b^{2} c^{2} - 10 \, a b c d + 9 \, a^{2} d^{2}\right)} x^{4} - 4 \, a^{2} c^{2} - 4 \, {\left(10 \, a b c^{2} - 9 \, a^{2} c d\right)} x^{2}}{10 \, {\left(c^{3} d x^{\frac{9}{2}} + c^{4} x^{\frac{5}{2}}\right)}} + \frac{{\left(b^{2} c^{2} - 10 \, a b c d + 9 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, c^{3}}"," ",0,"1/10*(5*(b^2*c^2 - 10*a*b*c*d + 9*a^2*d^2)*x^4 - 4*a^2*c^2 - 4*(10*a*b*c^2 - 9*a^2*c*d)*x^2)/(c^3*d*x^(9/2) + c^4*x^(5/2)) + 1/16*(b^2*c^2 - 10*a*b*c*d + 9*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/c^3","A",0
433,1,389,0,2.438357," ","integrate(x^(7/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(25 \, b^{2} c^{2} d - 34 \, a b c d^{2} + 9 \, a^{2} d^{3}\right)} x^{\frac{5}{2}} + {\left(21 \, b^{2} c^{3} - 26 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} \sqrt{x}}{16 \, {\left(d^{6} x^{4} + 2 \, c d^{5} x^{2} + c^{2} d^{4}\right)}} + \frac{2 \, {\left(b^{2} d x^{\frac{5}{2}} - 5 \, {\left(3 \, b^{2} c - 2 \, a b d\right)} \sqrt{x}\right)}}{5 \, d^{4}} + \frac{\frac{2 \, \sqrt{2} {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(117 \, b^{2} c^{2} - 90 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, d^{4}}"," ",0,"-1/16*((25*b^2*c^2*d - 34*a*b*c*d^2 + 9*a^2*d^3)*x^(5/2) + (21*b^2*c^3 - 26*a*b*c^2*d + 5*a^2*c*d^2)*sqrt(x))/(d^6*x^4 + 2*c*d^5*x^2 + c^2*d^4) + 2/5*(b^2*d*x^(5/2) - 5*(3*b^2*c - 2*a*b*d)*sqrt(x))/d^4 + 1/128*(2*sqrt(2)*(117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/d^4","A",0
434,1,306,0,2.540612," ","integrate(x^(5/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{2 \, b^{2} x^{\frac{3}{2}}}{3 \, d^{3}} + \frac{{\left(19 \, b^{2} c^{2} d - 22 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} x^{\frac{7}{2}} + {\left(15 \, b^{2} c^{3} - 14 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{\frac{3}{2}}}{16 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}} - \frac{{\left(77 \, b^{2} c^{2} - 42 \, a b c d - 3 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, c d^{3}}"," ",0,"2/3*b^2*x^(3/2)/d^3 + 1/16*((19*b^2*c^2*d - 22*a*b*c*d^2 + 3*a^2*d^3)*x^(7/2) + (15*b^2*c^3 - 14*a*b*c^2*d - a^2*c*d^2)*x^(3/2))/(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3) - 1/128*(77*b^2*c^2 - 42*a*b*c*d - 3*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c*d^3)","A",0
435,1,374,0,2.439559," ","integrate(x^(3/2)*(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(17 \, b^{2} c^{2} d - 18 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{5}{2}} + {\left(13 \, b^{2} c^{3} - 10 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} \sqrt{x}}{16 \, {\left(c d^{5} x^{4} + 2 \, c^{2} d^{4} x^{2} + c^{3} d^{3}\right)}} + \frac{2 \, b^{2} \sqrt{x}}{d^{3}} - \frac{\frac{2 \, \sqrt{2} {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(45 \, b^{2} c^{2} - 10 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, c d^{3}}"," ",0,"1/16*((17*b^2*c^2*d - 18*a*b*c*d^2 + a^2*d^3)*x^(5/2) + (13*b^2*c^3 - 10*a*b*c^2*d - 3*a^2*c*d^2)*sqrt(x))/(c*d^5*x^4 + 2*c^2*d^4*x^2 + c^3*d^3) + 2*b^2*sqrt(x)/d^3 - 1/128*(2*sqrt(2)*(45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c*d^3)","A",0
436,1,297,0,2.544577," ","integrate((b*x^2+a)^2*x^(1/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(11 \, b^{2} c^{2} d - 6 \, a b c d^{2} - 5 \, a^{2} d^{3}\right)} x^{\frac{7}{2}} + {\left(7 \, b^{2} c^{3} + 2 \, a b c^{2} d - 9 \, a^{2} c d^{2}\right)} x^{\frac{3}{2}}}{16 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}} + \frac{{\left(21 \, b^{2} c^{2} + 6 \, a b c d + 5 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, c^{2} d^{2}}"," ",0,"-1/16*((11*b^2*c^2*d - 6*a*b*c*d^2 - 5*a^2*d^3)*x^(7/2) + (7*b^2*c^3 + 2*a*b*c^2*d - 9*a^2*c*d^2)*x^(3/2))/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2) + 1/128*(21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c^2*d^2)","A",0
437,1,366,0,2.431066," ","integrate((b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""maxima"")","-\frac{{\left(9 \, b^{2} c^{2} d - 2 \, a b c d^{2} - 7 \, a^{2} d^{3}\right)} x^{\frac{5}{2}} + {\left(5 \, b^{2} c^{3} + 6 \, a b c^{2} d - 11 \, a^{2} c d^{2}\right)} \sqrt{x}}{16 \, {\left(c^{2} d^{4} x^{4} + 2 \, c^{3} d^{3} x^{2} + c^{4} d^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, c^{2} d^{2}}"," ",0,"-1/16*((9*b^2*c^2*d - 2*a*b*c*d^2 - 7*a^2*d^3)*x^(5/2) + (5*b^2*c^3 + 6*a*b*c^2*d - 11*a^2*c*d^2)*sqrt(x))/(c^2*d^4*x^4 + 2*c^3*d^3*x^2 + c^4*d^2) + 1/128*(2*sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c^2*d^2)","A",0
438,1,307,0,2.520527," ","integrate((b*x^2+a)^2/x^(3/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{32 \, a^{2} c^{2} d - {\left(3 \, b^{2} c^{2} d + 10 \, a b c d^{2} - 45 \, a^{2} d^{3}\right)} x^{4} + {\left(b^{2} c^{3} - 18 \, a b c^{2} d + 81 \, a^{2} c d^{2}\right)} x^{2}}{16 \, {\left(c^{3} d^{3} x^{\frac{9}{2}} + 2 \, c^{4} d^{2} x^{\frac{5}{2}} + c^{5} d \sqrt{x}\right)}} + \frac{{\left(3 \, b^{2} c^{2} + 10 \, a b c d - 45 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, c^{3} d}"," ",0,"-1/16*(32*a^2*c^2*d - (3*b^2*c^2*d + 10*a*b*c*d^2 - 45*a^2*d^3)*x^4 + (b^2*c^3 - 18*a*b*c^2*d + 81*a^2*c*d^2)*x^2)/(c^3*d^3*x^(9/2) + 2*c^4*d^2*x^(5/2) + c^5*d*sqrt(x)) + 1/128*(3*b^2*c^2 + 10*a*b*c*d - 45*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(c^3*d)","A",0
439,1,377,0,2.438668," ","integrate((b*x^2+a)^2/x^(5/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{32 \, a^{2} c^{2} d - {\left(3 \, b^{2} c^{2} d + 42 \, a b c d^{2} - 77 \, a^{2} d^{3}\right)} x^{4} + {\left(9 \, b^{2} c^{3} - 66 \, a b c^{2} d + 121 \, a^{2} c d^{2}\right)} x^{2}}{48 \, {\left(c^{3} d^{3} x^{\frac{11}{2}} + 2 \, c^{4} d^{2} x^{\frac{7}{2}} + c^{5} d x^{\frac{3}{2}}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} + 42 \, a b c d - 77 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, c^{3} d}"," ",0,"-1/48*(32*a^2*c^2*d - (3*b^2*c^2*d + 42*a*b*c*d^2 - 77*a^2*d^3)*x^4 + (9*b^2*c^3 - 66*a*b*c^2*d + 121*a^2*c*d^2)*x^2)/(c^3*d^3*x^(11/2) + 2*c^4*d^2*x^(7/2) + c^5*d*x^(3/2)) + 1/128*(2*sqrt(2)*(3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(3*b^2*c^2 + 42*a*b*c*d - 77*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(c^3*d)","A",0
440,1,324,0,2.411287," ","integrate((b*x^2+a)^2/x^(7/2)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{5 \, {\left(5 \, b^{2} c^{2} d - 90 \, a b c d^{2} + 117 \, a^{2} d^{3}\right)} x^{6} - 32 \, a^{2} c^{3} + 9 \, {\left(5 \, b^{2} c^{3} - 90 \, a b c^{2} d + 117 \, a^{2} c d^{2}\right)} x^{4} - 32 \, {\left(10 \, a b c^{3} - 13 \, a^{2} c^{2} d\right)} x^{2}}{80 \, {\left(c^{4} d^{2} x^{\frac{13}{2}} + 2 \, c^{5} d x^{\frac{9}{2}} + c^{6} x^{\frac{5}{2}}\right)}} + \frac{{\left(5 \, b^{2} c^{2} - 90 \, a b c d + 117 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, c^{4}}"," ",0,"1/80*(5*(5*b^2*c^2*d - 90*a*b*c*d^2 + 117*a^2*d^3)*x^6 - 32*a^2*c^3 + 9*(5*b^2*c^3 - 90*a*b*c^2*d + 117*a^2*c*d^2)*x^4 - 32*(10*a*b*c^3 - 13*a^2*c^2*d)*x^2)/(c^4*d^2*x^(13/2) + 2*c^5*d*x^(9/2) + c^6*x^(5/2)) + 1/128*(5*b^2*c^2 - 90*a*b*c*d + 117*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/c^4","A",0
441,1,331,0,2.466421," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","-\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)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, b^{4}} + \frac{2 \, {\left(77 \, b^{3} d^{3} x^{\frac{15}{2}} + 105 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{\frac{11}{2}} + 165 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{\frac{7}{2}} + 385 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{\frac{3}{2}}\right)}}{1155 \, b^{4}}"," ",0,"-1/4*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^4 + 2/1155*(77*b^3*d^3*x^(15/2) + 105*(3*b^3*c*d^2 - a*b^2*d^3)*x^(11/2) + 165*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^(7/2) + 385*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^(3/2))/b^4","A",0
442,1,437,0,2.417808," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{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)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{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)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a}{4 \, b^{4}} + \frac{2 \, {\left(45 \, b^{3} d^{3} x^{\frac{13}{2}} + 65 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{\frac{9}{2}} + 117 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{\frac{5}{2}} + 585 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}\right)}}{585 \, b^{4}}"," ",0,"-1/4*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a/b^4 + 2/585*(45*b^3*d^3*x^(13/2) + 65*(3*b^3*c*d^2 - a*b^2*d^3)*x^(9/2) + 117*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x^(5/2) + 585*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x))/b^4","A",0
443,1,282,0,2.418504," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\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)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, b^{3}} + \frac{2 \, {\left(21 \, b^{2} d^{3} x^{\frac{11}{2}} + 33 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{\frac{7}{2}} + 77 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{3}{2}}\right)}}{231 \, b^{3}}"," ",0,"1/4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^3 + 2/231*(21*b^2*d^3*x^(11/2) + 33*(3*b^2*c*d^2 - a*b*d^3)*x^(7/2) + 77*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*x^(3/2))/b^3","A",0
444,1,390,0,2.438970," ","integrate((d*x^2+c)^3/(b*x^2+a)/x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, b^{2} d^{3} x^{\frac{9}{2}} + 9 \, {\left(3 \, b^{2} c d^{2} - a b d^{3}\right)} x^{\frac{5}{2}} + 45 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{x}\right)}}{45 \, b^{3}} + \frac{\frac{2 \, \sqrt{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)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{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)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, b^{3}}"," ",0,"2/45*(5*b^2*d^3*x^(9/2) + 9*(3*b^2*c*d^2 - a*b*d^3)*x^(5/2) + 45*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*sqrt(x))/b^3 + 1/4*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^3","A",0
445,1,261,0,2.397381," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{2 \, c^{3}}{a \sqrt{x}} + \frac{2 \, {\left(3 \, b d^{3} x^{\frac{7}{2}} + 7 \, {\left(3 \, b c d^{2} - a d^{3}\right)} x^{\frac{3}{2}}\right)}}{21 \, 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)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a b^{2}}"," ",0,"-2*c^3/(a*sqrt(x)) + 2/21*(3*b*d^3*x^(7/2) + 7*(3*b*c*d^2 - a*d^3)*x^(3/2))/b^2 - 1/4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^2)","A",0
446,1,368,0,2.507839," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{2 \, c^{3}}{3 \, a x^{\frac{3}{2}}} + \frac{2 \, {\left(b d^{3} x^{\frac{5}{2}} + 5 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \sqrt{x}\right)}}{5 \, b^{2}} - \frac{\frac{2 \, \sqrt{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)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{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)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, a b^{2}}"," ",0,"-2/3*c^3/(a*x^(3/2)) + 2/5*(b*d^3*x^(5/2) + 5*(3*b*c*d^2 - a*d^3)*sqrt(x))/b^2 - 1/4*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^2)","A",0
447,1,259,0,2.420409," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, d^{3} x^{\frac{3}{2}}}{3 \, 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)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a^{2} b} - \frac{2 \, {\left(a c^{3} - 5 \, {\left(b c^{3} - 3 \, a c^{2} d\right)} x^{2}\right)}}{5 \, a^{2} x^{\frac{5}{2}}}"," ",0,"2/3*d^3*x^(3/2)/b + 1/4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b) - 2/5*(a*c^3 - 5*(b*c^3 - 3*a*c^2*d)*x^2)/(a^2*x^(5/2))","A",0
448,1,368,0,2.587411," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{2 \, d^{3} \sqrt{x}}{b} + \frac{\frac{2 \, \sqrt{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)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{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)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, a^{2} b} - \frac{2 \, {\left(3 \, a c^{3} - 7 \, {\left(b c^{3} - 3 \, a c^{2} d\right)} x^{2}\right)}}{21 \, a^{2} x^{\frac{7}{2}}}"," ",0,"2*d^3*sqrt(x)/b + 1/4*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^2*b) - 2/21*(3*a*c^3 - 7*(b*c^3 - 3*a*c^2*d)*x^2)/(a^2*x^(7/2))","A",0
449,1,281,0,2.525825," ","integrate((d*x^2+c)^3/x^(11/2)/(b*x^2+a),x, algorithm=""maxima"")","-\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)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a^{3}} - \frac{2 \, {\left(5 \, a^{2} c^{3} + 45 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 9 \, {\left(a b c^{3} - 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{45 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-1/4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^3 - 2/45*(5*a^2*c^3 + 45*(b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 9*(a*b*c^3 - 3*a^2*c^2*d)*x^2)/(a^3*x^(9/2))","A",0
450,1,389,0,2.372952," ","integrate((d*x^2+c)^3/x^(13/2)/(b*x^2+a),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{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)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{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)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{4 \, a^{3}} - \frac{2 \, {\left(21 \, a^{2} c^{3} + 77 \, {\left(b^{2} c^{3} - 3 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{4} - 33 \, {\left(a b c^{3} - 3 \, a^{2} c^{2} d\right)} x^{2}\right)}}{231 \, a^{3} x^{\frac{11}{2}}}"," ",0,"-1/4*(2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/a^3 - 2/231*(21*a^2*c^3 + 77*(b^2*c^3 - 3*a*b*c^2*d + 3*a^2*c*d^2)*x^4 - 33*(a*b*c^3 - 3*a^2*c^2*d)*x^2)/(a^3*x^(11/2))","A",0
451,1,330,0,2.420358," ","integrate((d*x^2+c)^3/x^(15/2)/(b*x^2+a),x, algorithm=""maxima"")","\frac{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, a^{4}} + \frac{2 \, {\left(585 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{6} - 45 \, a^{3} c^{3} - 117 \, {\left(a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{4} + 65 \, {\left(a^{2} b c^{3} - 3 \, a^{3} c^{2} d\right)} x^{2}\right)}}{585 \, a^{4} x^{\frac{13}{2}}}"," ",0,"1/4*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/a^4 + 2/585*(585*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^6 - 45*a^3*c^3 - 117*(a*b^2*c^3 - 3*a^2*b*c^2*d + 3*a^3*c*d^2)*x^4 + 65*(a^2*b*c^3 - 3*a^3*c^2*d)*x^2)/(a^4*x^(13/2))","A",0
452,1,499,0,2.462919," ","integrate(x^(7/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\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)} \sqrt{x}}{2 \, {\left(b^{6} x^{2} + a b^{5}\right)}} - \frac{{\left(\frac{2 \, \sqrt{2} {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 39 \, a^{2} b c d^{2} - 17 \, a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a}{16 \, b^{5}} + \frac{2 \, {\left(45 \, b^{3} d^{3} x^{\frac{13}{2}} + 65 \, {\left(3 \, b^{3} c d^{2} - 2 \, a b^{2} d^{3}\right)} x^{\frac{9}{2}} + 351 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{\frac{5}{2}} + 585 \, {\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)} \sqrt{x}\right)}}{585 \, b^{5}}"," ",0,"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)*sqrt(x)/(b^6*x^2 + a*b^5) - 1/16*(2*sqrt(2)*(5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(5*b^3*c^3 - 27*a*b^2*c^2*d + 39*a^2*b*c*d^2 - 17*a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a/b^5 + 2/585*(45*b^3*d^3*x^(13/2) + 65*(3*b^3*c*d^2 - 2*a*b^2*d^3)*x^(9/2) + 351*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^(5/2) + 585*(b^3*c^3 - 6*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 4*a^3*d^3)*sqrt(x))/b^5","A",0
453,1,337,0,2.361240," ","integrate(x^(5/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\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)} x^{\frac{3}{2}}}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{3 \, {\left(b^{3} c^{3} - 7 \, a b^{2} c^{2} d + 11 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, b^{4}} + \frac{2 \, {\left(7 \, b^{2} d^{3} x^{\frac{11}{2}} + 11 \, {\left(3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{\frac{7}{2}} + 77 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{3}{2}}\right)}}{77 \, b^{4}}"," ",0,"-1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^(3/2)/(b^5*x^2 + a*b^4) + 3/16*(b^3*c^3 - 7*a*b^2*c^2*d + 11*a^2*b*c*d^2 - 5*a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/b^4 + 2/77*(7*b^2*d^3*x^(11/2) + 11*(3*b^2*c*d^2 - 2*a*b*d^3)*x^(7/2) + 77*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^(3/2))/b^4","A",0
454,1,445,0,2.345813," ","integrate(x^(3/2)*(d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}}{2 \, {\left(b^{5} x^{2} + a b^{4}\right)}} + \frac{2 \, {\left(5 \, b^{2} d^{3} x^{\frac{9}{2}} + 9 \, {\left(3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{\frac{5}{2}} + 135 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{x}\right)}}{45 \, b^{4}} + \frac{\frac{2 \, \sqrt{2} {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 13 \, a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, b^{4}}"," ",0,"-1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)/(b^5*x^2 + a*b^4) + 2/45*(5*b^2*d^3*x^(9/2) + 9*(3*b^2*c*d^2 - 2*a*b*d^3)*x^(5/2) + 135*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(x))/b^4 + 1/16*(2*sqrt(2)*(b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 - 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 13*a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/b^4","A",0
455,1,309,0,2.514198," ","integrate((d*x^2+c)^3*x^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\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)} x^{\frac{3}{2}}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{2 \, {\left(3 \, b d^{3} x^{\frac{7}{2}} + 7 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} x^{\frac{3}{2}}\right)}}{21 \, b^{3}} + \frac{{\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d - 21 \, a^{2} b c d^{2} + 11 \, a^{3} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a b^{3}}"," ",0,"1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^(3/2)/(a*b^4*x^2 + a^2*b^3) + 2/21*(3*b*d^3*x^(7/2) + 7*(3*b*c*d^2 - 2*a*d^3)*x^(3/2))/b^3 + 1/16*(b^3*c^3 + 9*a*b^2*c^2*d - 21*a^2*b*c*d^2 + 11*a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^3)","A",0
456,1,412,0,2.580141," ","integrate((d*x^2+c)^3/(b*x^2+a)^2/x^(1/2),x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{x}}{2 \, {\left(a b^{4} x^{2} + a^{2} b^{3}\right)}} + \frac{2 \, {\left(b d^{3} x^{\frac{5}{2}} + 5 \, {\left(3 \, b c d^{2} - 2 \, a d^{3}\right)} \sqrt{x}\right)}}{5 \, b^{3}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b^{3} c^{3} + a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)}}{16 \, a b^{3}}"," ",0,"1/2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(x)/(a*b^4*x^2 + a^2*b^3) + 2/5*(b*d^3*x^(5/2) + 5*(3*b*c*d^2 - 2*a*d^3)*sqrt(x))/b^3 + 3/16*(2*sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b^3*c^3 + a*b^2*c^2*d - 5*a^2*b*c*d^2 + 3*a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a*b^3)","A",0
457,1,304,0,2.479534," ","integrate((d*x^2+c)^3/x^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{2 \, d^{3} x^{\frac{3}{2}}}{3 \, b^{2}} - \frac{4 \, a b^{2} c^{3} + {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2}}{2 \, {\left(a^{2} b^{3} x^{\frac{5}{2}} + a^{3} b^{2} \sqrt{x}\right)}} - \frac{{\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a^{2} b^{2}}"," ",0,"2/3*d^3*x^(3/2)/b^2 - 1/2*(4*a*b^2*c^3 + (5*b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2)/(a^2*b^3*x^(5/2) + a^3*b^2*sqrt(x)) - 1/16*(5*b^3*c^3 - 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 7*a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b^2)","A",0
458,1,415,0,2.466947," ","integrate((d*x^2+c)^3/x^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\frac{2 \, d^{3} \sqrt{x}}{b^{2}} - \frac{4 \, a b^{2} c^{3} + {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3}\right)} x^{2}}{6 \, {\left(a^{2} b^{3} x^{\frac{7}{2}} + a^{3} b^{2} x^{\frac{3}{2}}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, a^{2} b^{2}}"," ",0,"2*d^3*sqrt(x)/b^2 - 1/6*(4*a*b^2*c^3 + (7*b^3*c^3 - 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 3*a^3*d^3)*x^2)/(a^2*b^3*x^(7/2) + a^3*b^2*x^(3/2)) - 1/16*(2*sqrt(2)*(7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(7*b^3*c^3 - 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 5*a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^2*b^2)","A",0
459,1,315,0,2.539861," ","integrate((d*x^2+c)^3/x^(7/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{4 \, a^{2} b c^{3} - 5 \, {\left(9 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{4} - 12 \, {\left(3 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{2}}{10 \, {\left(a^{3} b^{2} x^{\frac{9}{2}} + a^{4} b x^{\frac{5}{2}}\right)}} + \frac{3 \, {\left(3 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d + a^{2} b c d^{2} + a^{3} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, a^{3} b}"," ",0,"-1/10*(4*a^2*b*c^3 - 5*(9*b^3*c^3 - 15*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^4 - 12*(3*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^2)/(a^3*b^2*x^(9/2) + a^4*b*x^(5/2)) + 3/16*(3*b^3*c^3 - 5*a*b^2*c^2*d + a^2*b*c*d^2 + a^3*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^3*b)","A",0
460,1,424,0,2.549784," ","integrate((d*x^2+c)^3/x^(9/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","-\frac{12 \, a^{2} b c^{3} - 7 \, {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3}\right)} x^{4} - 4 \, {\left(11 \, a b^{2} c^{3} - 21 \, a^{2} b c^{2} d\right)} x^{2}}{42 \, {\left(a^{3} b^{2} x^{\frac{11}{2}} + a^{4} b x^{\frac{7}{2}}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(11 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}}{16 \, a^{3} b}"," ",0,"-1/42*(12*a^2*b*c^3 - 7*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 3*a^3*d^3)*x^4 - 4*(11*a*b^2*c^3 - 21*a^2*b*c^2*d)*x^2)/(a^3*b^2*x^(11/2) + a^4*b*x^(7/2)) + 1/16*(2*sqrt(2)*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(11*b^3*c^3 - 21*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))/(a^3*b)","A",0
461,1,390,0,2.613194," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{2} c - a b d\right)}} - \frac{c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, {\left(b c d - a d^{2}\right)}} + \frac{2 \, x^{\frac{3}{2}}}{3 \, b d}"," ",0,"1/4*a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^2*c - a*b*d) - 1/4*c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b*c*d - a*d^2) + 2/3*x^(3/2)/(b*d)","A",0
462,1,384,0,2.590508," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}}{4 \, {\left(b^{2} c - a b d\right)}} - \frac{\frac{2 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} c^{\frac{5}{4}} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{d^{\frac{1}{4}}} - \frac{\sqrt{2} c^{\frac{5}{4}} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{d^{\frac{1}{4}}}}{4 \, {\left(b c d - a d^{2}\right)}} + \frac{2 \, \sqrt{x}}{b d}"," ",0,"1/4*(2*sqrt(2)*a^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*a^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(5/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(5/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))/(b^2*c - a*b*d) - 1/4*(2*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/sqrt(sqrt(c)*sqrt(d)) + 2*sqrt(2)*c^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/sqrt(sqrt(c)*sqrt(d)) + sqrt(2)*c^(5/4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/d^(1/4) - sqrt(2)*c^(5/4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/d^(1/4))/(b*c*d - a*d^2) + 2*sqrt(x)/(b*d)","A",0
463,1,369,0,2.603050," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b c - a d\right)}} + \frac{c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, {\left(b c - a d\right)}}"," ",0,"-1/4*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b*c - a*d) + 1/4*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b*c - a*d)","A",0
464,1,367,0,2.104974," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} \sqrt{a} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{1}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}}{4 \, {\left(b c - a d\right)}} + \frac{\frac{2 \, \sqrt{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} \sqrt{c} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} c^{\frac{1}{4}} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{d^{\frac{1}{4}}} - \frac{\sqrt{2} c^{\frac{1}{4}} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{d^{\frac{1}{4}}}}{4 \, {\left(b c - a d\right)}}"," ",0,"-1/4*(2*sqrt(2)*sqrt(a)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*sqrt(a)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(1/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(1/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))/(b*c - a*d) + 1/4*(2*sqrt(2)*sqrt(c)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/sqrt(sqrt(c)*sqrt(d)) + 2*sqrt(2)*sqrt(c)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/sqrt(sqrt(c)*sqrt(d)) + sqrt(2)*c^(1/4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/d^(1/4) - sqrt(2)*c^(1/4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/d^(1/4))/(b*c - a*d)","A",0
465,1,369,0,2.573283," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b c - a d\right)}} - \frac{d {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, {\left(b c - a d\right)}}"," ",0,"1/4*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b*c - a*d) - 1/4*d*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b*c - a*d)","A",0
466,1,371,0,2.502454," ","integrate(1/(b*x^2+a)/(d*x^2+c)/x^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\left(b c - a d\right)}} - \frac{\frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} d^{\frac{3}{4}} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}}} - \frac{\sqrt{2} d^{\frac{3}{4}} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}}}}{4 \, {\left(b c - a d\right)}}"," ",0,"1/4*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(b*c - a*d) - 1/4*(2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*d^(3/4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/c^(3/4) - sqrt(2)*d^(3/4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/c^(3/4))/(b*c - a*d)","A",0
467,1,390,0,2.544857," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(a b c - a^{2} d\right)}} + \frac{d^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, {\left(b c^{2} - a c d\right)}} - \frac{2}{a c \sqrt{x}}"," ",0,"-1/4*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b*c - a^2*d) + 1/4*d^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b*c^2 - a*c*d) - 2/(a*c*sqrt(x))","A",0
468,1,396,0,2.384295," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\left(a b c - a^{2} d\right)}} + \frac{\frac{2 \, \sqrt{2} d^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} d^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} d^{\frac{7}{4}} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}}} - \frac{\sqrt{2} d^{\frac{7}{4}} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}}}}{4 \, {\left(b c^{2} - a c d\right)}} - \frac{2}{3 \, a c x^{\frac{3}{2}}}"," ",0,"-1/4*(2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(7/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(7/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(a*b*c - a^2*d) + 1/4*(2*sqrt(2)*d^2*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*d^2*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*d^(7/4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/c^(3/4) - sqrt(2)*d^(7/4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/c^(3/4))/(b*c^2 - a*c*d) - 2/3/(a*c*x^(3/2))","A",0
469,1,411,0,2.546892," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(a^{2} b c - a^{3} d\right)}} - \frac{d^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{4 \, {\left(b c^{3} - a c^{2} d\right)}} + \frac{2 \, {\left(5 \, {\left(b c + a d\right)} x^{2} - a c\right)}}{5 \, a^{2} c^{2} x^{\frac{5}{2}}}"," ",0,"1/4*b^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b*c - a^3*d) - 1/4*d^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b*c^3 - a*c^2*d) + 2/5*(5*(b*c + a*d)*x^2 - a*c)/(a^2*c^2*x^(5/2))","A",0
470,1,494,0,2.024737," ","integrate(x^(11/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(5 \, b c - 9 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(5 \, b c - 9 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(5 \, b c - 9 \, a d\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b c - 9 \, a d\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c^{2}}{16 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)}} + \frac{c^{2} \sqrt{x}}{2 \, {\left(b c^{2} d^{2} - a c d^{3} + {\left(b c d^{3} - a d^{4}\right)} x^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} a^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} a^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{9}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{9}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}}{4 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)}} + \frac{2 \, \sqrt{x}}{b d^{2}}"," ",0,"-1/16*(2*sqrt(2)*(5*b*c - 9*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(5*b*c - 9*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(5*b*c - 9*a*d)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(5*b*c - 9*a*d)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c^2/(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4) + 1/2*c^2*sqrt(x)/(b*c^2*d^2 - a*c*d^3 + (b*c*d^3 - a*d^4)*x^2) - 1/4*(2*sqrt(2)*a^(5/2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*a^(5/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(9/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(9/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + 2*sqrt(x)/(b*d^2)","A",0
471,1,450,0,2.531859," ","integrate(x^(9/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{c x^{\frac{3}{2}}}{2 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}} + \frac{{\left(3 \, b c^{2} - 7 \, a c d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}}"," ",0,"1/4*a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2*c*x^(3/2)/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2) + 1/16*(3*b*c^2 - 7*a*c*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)","A",0
472,1,468,0,2.465159," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(b c - 5 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(b c - 5 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(b c - 5 \, a d\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c - 5 \, a d\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c}{16 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}} - \frac{c \sqrt{x}}{2 \, {\left(b c^{2} d - a c d^{2} + {\left(b c d^{2} - a d^{3}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} a^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}} - \frac{\sqrt{2} a^{\frac{5}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{b^{\frac{1}{4}}}}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}}"," ",0,"1/16*(2*sqrt(2)*(b*c - 5*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(b*c - 5*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(b*c - 5*a*d)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(b*c - 5*a*d)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) - 1/2*c*sqrt(x)/(b*c^2*d - a*c*d^2 + (b*c*d^2 - a*d^3)*x^2) + 1/4*(2*sqrt(2)*a^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + 2*sqrt(2)*a^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/sqrt(sqrt(a)*sqrt(b)) + sqrt(2)*a^(5/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4) - sqrt(2)*a^(5/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/b^(1/4))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)","A",0
473,1,436,0,2.449524," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{a b {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{{\left(b c + 3 \, a d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{x^{\frac{3}{2}}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}"," ",0,"-1/4*a*b*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/16*(b*c + 3*a*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2*x^(3/2)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","A",0
474,1,461,0,2.662208," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}\right)} a}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b c + a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c + a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(3 \, b c + a d\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c + a d\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} + \frac{\sqrt{x}}{2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x^{2}\right)}}"," ",0,"-1/4*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))*a/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/16*(2*sqrt(2)*(3*b*c + a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(3*b*c + a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(3*b*c + a*d)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(3*b*c + a*d)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) + 1/2*sqrt(x)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x^2)","A",0
475,1,450,0,2.528202," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{d x^{\frac{3}{2}}}{2 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}} - \frac{{\left(5 \, b c d - a d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}}"," ",0,"1/4*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/2*d*x^(3/2)/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2) - 1/16*(5*b*c*d - a*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)","A",0
476,1,489,0,2.418378," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2/x^(1/2),x, algorithm=""maxima"")","-\frac{d \sqrt{x}}{2 \, {\left(b c^{3} - a c^{2} d + {\left(b c^{2} d - a c d^{2}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b c d - 3 \, a d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}}"," ",0,"-1/2*d*sqrt(x)/(b*c^3 - a*c^2*d + (b*c^2*d - a*c*d^2)*x^2) + 1/4*(2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(7/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(7/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(b^2*c^2 - 2*a*b*c*d + a^2*d^2) - 1/16*(2*sqrt(2)*(7*b*c*d - 3*a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(7*b*c*d - 3*a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(7*b*c*d - 3*a*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(7*b*c*d - 3*a*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)","A",0
477,1,494,0,2.577585," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{b^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} + \frac{{\left(9 \, b c d^{2} - 5 \, a d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}} - \frac{4 \, b c^{2} - 4 \, a c d + {\left(4 \, b c d - 5 \, a d^{2}\right)} x^{2}}{2 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{\frac{5}{2}} + {\left(a b c^{4} - a^{2} c^{3} d\right)} \sqrt{x}\right)}}"," ",0,"-1/4*b^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) + 1/16*(9*b*c*d^2 - 5*a*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2) - 1/2*(4*b*c^2 - 4*a*c*d + (4*b*c*d - 5*a*d^2)*x^2)/((a*b*c^3*d - a^2*c^2*d^2)*x^(5/2) + (a*b*c^4 - a^2*c^3*d)*sqrt(x))","A",0
478,1,539,0,2.487691," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{11}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{11}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)}} - \frac{4 \, b c^{2} - 4 \, a c d + {\left(4 \, b c d - 7 \, a d^{2}\right)} x^{2}}{6 \, {\left({\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{\frac{7}{2}} + {\left(a b c^{4} - a^{2} c^{3} d\right)} x^{\frac{3}{2}}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 7 \, a d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 7 \, a d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(11 \, b c d^{2} - 7 \, a d^{3}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(11 \, b c d^{2} - 7 \, a d^{3}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{16 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)}}"," ",0,"-1/4*(2*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(11/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(11/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2) - 1/6*(4*b*c^2 - 4*a*c*d + (4*b*c*d - 7*a*d^2)*x^2)/((a*b*c^3*d - a^2*c^2*d^2)*x^(7/2) + (a*b*c^4 - a^2*c^3*d)*x^(3/2)) + 1/16*(2*sqrt(2)*(11*b*c*d^2 - 7*a*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(11*b*c*d^2 - 7*a*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(11*b*c*d^2 - 7*a*d^3)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(11*b*c*d^2 - 7*a*d^3)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)","A",0
479,1,551,0,2.496322," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{b^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}} - \frac{{\left(13 \, b c d^{3} - 9 \, a d^{4}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)}} - \frac{4 \, a b c^{3} - 4 \, a^{2} c^{2} d - 5 \, {\left(4 \, b^{2} c^{2} d + 4 \, a b c d^{2} - 9 \, a^{2} d^{3}\right)} x^{4} - 4 \, {\left(5 \, b^{2} c^{3} + 4 \, a b c^{2} d - 9 \, a^{2} c d^{2}\right)} x^{2}}{10 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{\frac{9}{2}} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{\frac{5}{2}}\right)}}"," ",0,"1/4*b^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2) - 1/16*(13*b*c*d^3 - 9*a*d^4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2) - 1/10*(4*a*b*c^3 - 4*a^2*c^2*d - 5*(4*b^2*c^2*d + 4*a*b*c*d^2 - 9*a^2*d^3)*x^4 - 4*(5*b^2*c^3 + 4*a*b*c^2*d - 9*a^2*c*d^2)*x^2)/((a^2*b*c^4*d - a^3*c^3*d^2)*x^(9/2) + (a^2*b*c^5 - a^3*c^4*d)*x^(5/2))","A",0
480,1,653,0,2.635320," ","integrate(x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{3}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}\right)} a^{2}}{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}} + \frac{{\left(b c d - 9 \, a d^{2}\right)} x^{\frac{5}{2}} - {\left(3 \, b c^{2} + 5 \, a c d\right)} \sqrt{x}}{16 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + {\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} x^{4} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} - 30 \, a b c d - 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(3 \, b^{2} c^{2} - 30 \, a b c d - 5 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} - 30 \, a b c d - 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b^{2} c^{2} - 30 \, a b c d - 5 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"1/4*(2*sqrt(2)*b*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(3/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(3/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))*a^2/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/16*((b*c*d - 9*a*d^2)*x^(5/2) - (3*b*c^2 + 5*a*c*d)*sqrt(x))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + (b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*x^4 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^2) + 1/128*(2*sqrt(2)*(3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)","A",0
481,1,583,0,2.609851," ","integrate(x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{a b^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}} + \frac{{\left(5 \, b^{2} c^{2} + 30 \, a b c d - 3 \, a^{2} d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} + \frac{{\left(5 \, b c d + 3 \, a d^{2}\right)} x^{\frac{7}{2}} + {\left(9 \, b c^{2} - a c d\right)} x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/4*a*b^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/128*(5*b^2*c^2 + 30*a*b*c*d - 3*a^2*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3) + 1/16*((5*b*c*d + 3*a*d^2)*x^(7/2) + (9*b*c^2 - a*c*d)*x^(3/2))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2)","A",0
482,1,654,0,2.609978," ","integrate(x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} b^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{7}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}\right)} a}{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}} + \frac{{\left(7 \, b c d + a d^{2}\right)} x^{\frac{5}{2}} + {\left(11 \, b c^{2} - 3 \, a c d\right)} \sqrt{x}}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2} + {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(21 \, b^{2} c^{2} + 14 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(21 \, b^{2} c^{2} + 14 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(21 \, b^{2} c^{2} + 14 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{2} c^{2} + 14 \, a b c d - 3 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"-1/4*(2*sqrt(2)*b^2*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^2*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(7/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(7/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))*a/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/16*((7*b*c*d + a*d^2)*x^(5/2) + (11*b*c^2 - 3*a*c*d)*sqrt(x))/(b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2 + (b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*x^4 + 2*(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*x^2) + 1/128*(2*sqrt(2)*(21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)","A",0
483,1,594,0,2.517884," ","integrate(x^(1/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}} - \frac{{\left(45 \, b^{2} c^{2} d - 18 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{{\left(13 \, b c d^{2} - 5 \, a d^{3}\right)} x^{\frac{7}{2}} + {\left(17 \, b c^{2} d - 9 \, a c d^{2}\right)} x^{\frac{3}{2}}}{16 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/4*b^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/128*(45*b^2*c^2*d - 18*a*b*c*d^2 + 5*a^2*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3) - 1/16*((13*b*c*d^2 - 5*a*d^3)*x^(7/2) + (17*b*c^2*d - 9*a*c*d^2)*x^(3/2))/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*x^4 + 2*(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*x^2)","A",0
484,1,675,0,2.612590," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3/x^(1/2),x, algorithm=""maxima"")","-\frac{{\left(15 \, b c d^{2} - 7 \, a d^{3}\right)} x^{\frac{5}{2}} + {\left(19 \, b c^{2} d - 11 \, a c d^{2}\right)} \sqrt{x}}{16 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} b^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{11}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{11}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(77 \, b^{2} c^{2} d - 66 \, a b c d^{2} + 21 \, a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(77 \, b^{2} c^{2} d - 66 \, a b c d^{2} + 21 \, a^{2} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(77 \, b^{2} c^{2} d - 66 \, a b c d^{2} + 21 \, a^{2} d^{3}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{2} c^{2} d - 66 \, a b c d^{2} + 21 \, a^{2} d^{3}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"-1/16*((15*b*c*d^2 - 7*a*d^3)*x^(5/2) + (19*b*c^2*d - 11*a*c*d^2)*sqrt(x))/(b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*x^4 + 2*(b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*x^2) + 1/4*(2*sqrt(2)*b^3*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^3*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(11/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(11/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/128*(2*sqrt(2)*(77*b^2*c^2*d - 66*a*b*c*d^2 + 21*a^2*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(77*b^2*c^2*d - 66*a*b*c*d^2 + 21*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(77*b^2*c^2*d - 66*a*b*c*d^2 + 21*a^2*d^3)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(77*b^2*c^2*d - 66*a*b*c*d^2 + 21*a^2*d^3)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)","A",0
485,1,668,0,2.842261," ","integrate(1/x^(3/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{b^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\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)}} + \frac{{\left(117 \, b^{2} c^{2} d^{2} - 130 \, a b c d^{3} + 45 \, a^{2} d^{4}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{32 \, b^{2} c^{4} - 64 \, a b c^{3} d + 32 \, a^{2} c^{2} d^{2} + {\left(32 \, b^{2} c^{2} d^{2} - 85 \, a b c d^{3} + 45 \, a^{2} d^{4}\right)} x^{4} + {\left(64 \, b^{2} c^{3} d - 153 \, a b c^{2} d^{2} + 81 \, a^{2} c d^{3}\right)} x^{2}}{16 \, {\left({\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{\frac{9}{2}} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{\frac{5}{2}} + {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2}\right)} \sqrt{x}\right)}}"," ",0,"-1/4*b^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3) + 1/128*(117*b^2*c^2*d^2 - 130*a*b*c*d^3 + 45*a^2*d^4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) - 1/16*(32*b^2*c^4 - 64*a*b*c^3*d + 32*a^2*c^2*d^2 + (32*b^2*c^2*d^2 - 85*a*b*c*d^3 + 45*a^2*d^4)*x^4 + (64*b^2*c^3*d - 153*a*b*c^2*d^2 + 81*a^2*c*d^3)*x^2)/((a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^(9/2) + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^(5/2) + (a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2)*sqrt(x))","A",0
486,1,755,0,2.618591," ","integrate(1/x^(5/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{32 \, b^{2} c^{4} - 64 \, a b c^{3} d + 32 \, a^{2} c^{2} d^{2} + {\left(32 \, b^{2} c^{2} d^{2} - 133 \, a b c d^{3} + 77 \, a^{2} d^{4}\right)} x^{4} + {\left(64 \, b^{2} c^{3} d - 209 \, a b c^{2} d^{2} + 121 \, a^{2} c d^{3}\right)} x^{2}}{48 \, {\left({\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{\frac{11}{2}} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x^{\frac{7}{2}} + {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2}\right)} x^{\frac{3}{2}}\right)}} - \frac{\frac{2 \, \sqrt{2} b^{4} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} b^{4} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} b^{\frac{15}{4}} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}} - \frac{\sqrt{2} b^{\frac{15}{4}} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}}}}{4 \, {\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)}} + \frac{\frac{2 \, \sqrt{2} {\left(165 \, b^{2} c^{2} d^{2} - 210 \, a b c d^{3} + 77 \, a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(165 \, b^{2} c^{2} d^{2} - 210 \, a b c d^{3} + 77 \, a^{2} d^{4}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(165 \, b^{2} c^{2} d^{2} - 210 \, a b c d^{3} + 77 \, a^{2} d^{4}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(165 \, b^{2} c^{2} d^{2} - 210 \, a b c d^{3} + 77 \, a^{2} d^{4}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"-1/48*(32*b^2*c^4 - 64*a*b*c^3*d + 32*a^2*c^2*d^2 + (32*b^2*c^2*d^2 - 133*a*b*c*d^3 + 77*a^2*d^4)*x^4 + (64*b^2*c^3*d - 209*a*b*c^2*d^2 + 121*a^2*c*d^3)*x^2)/((a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^(11/2) + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x^(7/2) + (a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2)*x^(3/2)) - 1/4*(2*sqrt(2)*b^4*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*b^4*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*b^(15/4)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4) - sqrt(2)*b^(15/4)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/a^(3/4))/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3) + 1/128*(2*sqrt(2)*(165*b^2*c^2*d^2 - 210*a*b*c*d^3 + 77*a^2*d^4)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(165*b^2*c^2*d^2 - 210*a*b*c*d^3 + 77*a^2*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(165*b^2*c^2*d^2 - 210*a*b*c*d^3 + 77*a^2*d^4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(165*b^2*c^2*d^2 - 210*a*b*c*d^3 + 77*a^2*d^4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)","A",0
487,1,756,0,2.756982," ","integrate(1/x^(7/2)/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{b^{5} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{4 \, {\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)}} - \frac{{\left(221 \, b^{2} c^{2} d^{3} - 306 \, a b c d^{4} + 117 \, a^{2} d^{5}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{32 \, a b^{2} c^{5} - 64 \, a^{2} b c^{4} d + 32 \, a^{3} c^{3} d^{2} - 5 \, {\left(32 \, b^{3} c^{3} d^{2} + 32 \, a b^{2} c^{2} d^{3} - 189 \, a^{2} b c d^{4} + 117 \, a^{3} d^{5}\right)} x^{6} - {\left(320 \, b^{3} c^{4} d + 288 \, a b^{2} c^{3} d^{2} - 1701 \, a^{2} b c^{2} d^{3} + 1053 \, a^{3} c d^{4}\right)} x^{4} - 32 \, {\left(5 \, b^{3} c^{5} + 3 \, a b^{2} c^{4} d - 21 \, a^{2} b c^{3} d^{2} + 13 \, a^{3} c^{2} d^{3}\right)} x^{2}}{80 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{\frac{13}{2}} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{\frac{9}{2}} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x^{\frac{5}{2}}\right)}}"," ",0,"1/4*b^5*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(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) - 1/128*(221*b^2*c^2*d^3 - 306*a*b*c*d^4 + 117*a^2*d^5)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) - 1/80*(32*a*b^2*c^5 - 64*a^2*b*c^4*d + 32*a^3*c^3*d^2 - 5*(32*b^3*c^3*d^2 + 32*a*b^2*c^2*d^3 - 189*a^2*b*c*d^4 + 117*a^3*d^5)*x^6 - (320*b^3*c^4*d + 288*a*b^2*c^3*d^2 - 1701*a^2*b*c^2*d^3 + 1053*a^3*c*d^4)*x^4 - 32*(5*b^3*c^5 + 3*a*b^2*c^4*d - 21*a^2*b*c^3*d^2 + 13*a^3*c^2*d^3)*x^2)/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^(13/2) + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^(9/2) + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x^(5/2))","A",0
488,1,617,0,2.520358," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(5 \, b c + 3 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(5 \, b c + 3 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(5 \, b c + 3 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b c + 3 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a}{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)}} + \frac{{\left(\frac{2 \, \sqrt{2} {\left(3 \, b c + 5 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c + 5 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(3 \, b c + 5 \, a d\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c + 5 \, a d\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)} c}{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)}} + \frac{{\left(b c + a d\right)} x^{\frac{5}{2}} + 2 \, a c \sqrt{x}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/16*(2*sqrt(2)*(5*b*c + 3*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(5*b*c + 3*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(5*b*c + 3*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(5*b*c + 3*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*a/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/16*(2*sqrt(2)*(3*b*c + 5*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(3*b*c + 5*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(3*b*c + 5*a*d)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(3*b*c + 5*a*d)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))*c/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) + 1/2*((b*c + a*d)*x^(5/2) + 2*a*c*sqrt(x))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","A",0
489,1,567,0,2.530862," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(3 \, b^{2} c + 5 \, a b d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{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)}} - \frac{{\left(5 \, b c d + 3 \, a d^{2}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{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)}} - \frac{2 \, b d x^{\frac{7}{2}} + {\left(b c + a d\right)} x^{\frac{3}{2}}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}}"," ",0,"1/16*(3*b^2*c + 5*a*b*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/16*(5*b*c*d + 3*a*d^2)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*(2*b*d*x^(7/2) + (b*c + a*d)*x^(3/2))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2)","A",0
490,1,620,0,2.576259," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(b c + 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b c + 7 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b c + 7 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c + 7 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b}{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)}} - \frac{2 \, b d x^{\frac{5}{2}} + {\left(b c + a d\right)} \sqrt{x}}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{4} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(7 \, b c d + a d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(7 \, b c d + a d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(7 \, b c d + a d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b c d + a d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{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)}}"," ",0,"1/16*(2*sqrt(2)*(b*c + 7*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b*c + 7*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b*c + 7*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b*c + 7*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3) - 1/2*(2*b*d*x^(5/2) + (b*c + a*d)*sqrt(x))/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^4 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^2) - 1/16*(2*sqrt(2)*(7*b*c*d + a*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(7*b*c*d + a*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(7*b*c*d + a*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(7*b*c*d + a*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)","A",0
491,1,610,0,2.483197," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(b^{3} c - 9 \, a b^{2} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} + \frac{{\left(9 \, b c d^{2} - a d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{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)}} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x^{\frac{7}{2}} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} x^{\frac{3}{2}}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{4} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}\right)}}"," ",0,"1/16*(b^3*c - 9*a*b^2*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3) + 1/16*(9*b*c*d^2 - a*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3) + 1/2*((b^2*c*d + a*b*d^2)*x^(7/2) + (b^2*c^2 + a^2*d^2)*x^(3/2))/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^4 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2)","A",0
492,1,678,0,2.589310," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2/x^(1/2),x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(3 \, b c - 11 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{2}}{16 \, {\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)}} + \frac{{\left(b^{2} c d + a b d^{2}\right)} x^{\frac{5}{2}} + {\left(b^{2} c^{2} + a^{2} d^{2}\right)} \sqrt{x}}{2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x^{4} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(11 \, b c d^{2} - 3 \, a d^{3}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{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)}}"," ",0,"1/16*(2*sqrt(2)*(3*b*c - 11*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(3*b*c - 11*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(3*b*c - 11*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(3*b*c - 11*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^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) + 1/2*((b^2*c*d + a*b*d^2)*x^(5/2) + (b^2*c^2 + a^2*d^2)*sqrt(x))/(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x^4 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2) + 1/16*(2*sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(11*b*c*d^2 - 3*a*d^3)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)","A",0
493,1,694,0,2.934892," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{4} c - 13 \, a b^{3} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} - \frac{{\left(13 \, b c d^{3} - 5 \, a d^{4}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{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)}} - \frac{4 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2} + {\left(5 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x^{4} + {\left(5 \, b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} x^{2}}{2 \, {\left({\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{\frac{9}{2}} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{\frac{5}{2}} + {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} \sqrt{x}\right)}}"," ",0,"-1/16*(5*b^4*c - 13*a*b^3*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(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) - 1/16*(13*b*c*d^3 - 5*a*d^4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3) - 1/2*(4*a*b^2*c^3 - 8*a^2*b*c^2*d + 4*a^3*c*d^2 + (5*b^3*c^2*d - 8*a*b^2*c*d^2 + 5*a^2*b*d^3)*x^4 + (5*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2 + 5*a^3*d^3)*x^2)/((a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^(9/2) + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^(5/2) + (a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*sqrt(x))","A",0
494,1,761,0,2.688523," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(7 \, b c - 15 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(7 \, b c - 15 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(7 \, b c - 15 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b c - 15 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{3}}{16 \, {\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)}} - \frac{4 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2} + {\left(7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 7 \, a^{2} b d^{3}\right)} x^{4} + {\left(7 \, b^{3} c^{3} - 4 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} + 7 \, a^{3} d^{3}\right)} x^{2}}{6 \, {\left({\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{\frac{11}{2}} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x^{\frac{7}{2}} + {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{\frac{3}{2}}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(15 \, b c d^{3} - 7 \, a d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(15 \, b c d^{3} - 7 \, a d^{4}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(15 \, b c d^{3} - 7 \, a d^{4}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(15 \, b c d^{3} - 7 \, a d^{4}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{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)}}"," ",0,"-1/16*(2*sqrt(2)*(7*b*c - 15*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(7*b*c - 15*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(7*b*c - 15*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(7*b*c - 15*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^3/(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) - 1/6*(4*a*b^2*c^3 - 8*a^2*b*c^2*d + 4*a^3*c*d^2 + (7*b^3*c^2*d - 8*a*b^2*c*d^2 + 7*a^2*b*d^3)*x^4 + (7*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2 + 7*a^3*d^3)*x^2)/((a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^(11/2) + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x^(7/2) + (a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2)*x^(3/2)) - 1/16*(2*sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(15*b*c*d^3 - 7*a*d^4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)","A",0
495,1,774,0,2.750778," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(9 \, b^{5} c - 17 \, a b^{4} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} + \frac{{\left(17 \, b c d^{4} - 9 \, a d^{5}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{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)}} - \frac{4 \, a^{2} b^{2} c^{4} - 8 \, a^{3} b c^{3} d + 4 \, a^{4} c^{2} d^{2} - 5 \, {\left(9 \, b^{4} c^{3} d - 8 \, a b^{3} c^{2} d^{2} - 8 \, a^{2} b^{2} c d^{3} + 9 \, a^{3} b d^{4}\right)} x^{6} - {\left(45 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 72 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 45 \, a^{4} d^{4}\right)} x^{4} - 36 \, {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x^{2}}{10 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{\frac{13}{2}} + {\left(a^{3} b^{3} c^{6} - a^{4} b^{2} c^{5} d - a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{\frac{9}{2}} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{\frac{5}{2}}\right)}}"," ",0,"1/16*(9*b^5*c - 17*a*b^4*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(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) + 1/16*(17*b*c*d^4 - 9*a*d^5)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) - 1/10*(4*a^2*b^2*c^4 - 8*a^3*b*c^3*d + 4*a^4*c^2*d^2 - 5*(9*b^4*c^3*d - 8*a*b^3*c^2*d^2 - 8*a^2*b^2*c*d^3 + 9*a^3*b*d^4)*x^6 - (45*b^4*c^4 - 4*a*b^3*c^3*d - 72*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 45*a^4*d^4)*x^4 - 36*(a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x^2)/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^(13/2) + (a^3*b^3*c^6 - a^4*b^2*c^5*d - a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^(9/2) + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^(5/2))","A",0
496,1,855,0,2.650090," ","integrate(x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(5 \, b c + 7 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(5 \, b c + 7 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(5 \, b c + 7 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(5 \, b c + 7 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} a b}{16 \, {\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)}} + \frac{{\left(7 \, b^{2} c d + 17 \, a b d^{2}\right)} x^{\frac{9}{2}} + {\left(11 \, b^{2} c^{2} + 28 \, a b c d + 9 \, a^{2} d^{2}\right)} x^{\frac{5}{2}} + {\left(19 \, a b c^{2} + 5 \, a^{2} c d\right)} \sqrt{x}}{16 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{4} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x^{2}\right)}} + \frac{\frac{2 \, \sqrt{2} {\left(21 \, b^{2} c^{2} + 70 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(21 \, b^{2} c^{2} + 70 \, a b c d + 5 \, a^{2} d^{2}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(21 \, b^{2} c^{2} + 70 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(21 \, b^{2} c^{2} + 70 \, a b c d + 5 \, a^{2} d^{2}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"-1/16*(2*sqrt(2)*(5*b*c + 7*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(5*b*c + 7*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(5*b*c + 7*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(5*b*c + 7*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*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) + 1/16*((7*b^2*c*d + 17*a*b*d^2)*x^(9/2) + (11*b^2*c^2 + 28*a*b*c*d + 9*a^2*d^2)*x^(5/2) + (19*a*b*c^2 + 5*a^2*c*d)*sqrt(x))/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^6 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^4 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x^2) + 1/128*(2*sqrt(2)*(21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)","A",0
497,1,791,0,2.778095," ","integrate(x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(b^{3} c + 3 \, a b^{2} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} - \frac{3 \, {\left(15 \, b^{2} c^{2} d + 18 \, a b c d^{2} - a^{2} d^{3}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{3 \, {\left(7 \, b^{2} c d^{2} + a b d^{3}\right)} x^{\frac{11}{2}} + 3 \, {\left(11 \, b^{2} c^{2} d + 4 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{7}{2}} + {\left(8 \, b^{2} c^{3} + 17 \, a b c^{2} d - a^{2} c d^{2}\right)} x^{\frac{3}{2}}}{16 \, {\left(a b^{3} c^{6} - 3 \, a^{2} b^{2} c^{5} d + 3 \, a^{3} b c^{4} d^{2} - a^{4} c^{3} d^{3} + {\left(b^{4} c^{4} d^{2} - 3 \, a b^{3} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d^{4} - a^{3} b c d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{5} d - 5 \, a b^{3} c^{4} d^{2} + 3 \, a^{2} b^{2} c^{3} d^{3} + a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right)} x^{4} + {\left(b^{4} c^{6} - a b^{3} c^{5} d - 3 \, a^{2} b^{2} c^{4} d^{2} + 5 \, a^{3} b c^{3} d^{3} - 2 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)}}"," ",0,"3/16*(b^3*c + 3*a*b^2*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(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) - 3/128*(15*b^2*c^2*d + 18*a*b*c*d^2 - a^2*d^3)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4) - 1/16*(3*(7*b^2*c*d^2 + a*b*d^3)*x^(11/2) + 3*(11*b^2*c^2*d + 4*a*b*c*d^2 + a^2*d^3)*x^(7/2) + (8*b^2*c^3 + 17*a*b*c^2*d - a^2*c*d^2)*x^(3/2))/(a*b^3*c^6 - 3*a^2*b^2*c^5*d + 3*a^3*b*c^4*d^2 - a^4*c^3*d^3 + (b^4*c^4*d^2 - 3*a*b^3*c^3*d^3 + 3*a^2*b^2*c^2*d^4 - a^3*b*c*d^5)*x^6 + (2*b^4*c^5*d - 5*a*b^3*c^4*d^2 + 3*a^2*b^2*c^3*d^3 + a^3*b*c^2*d^4 - a^4*c*d^5)*x^4 + (b^4*c^6 - a*b^3*c^5*d - 3*a^2*b^2*c^4*d^2 + 5*a^3*b*c^3*d^3 - 2*a^4*c^2*d^4)*x^2)","A",0
498,1,889,0,2.816458," ","integrate(x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, \sqrt{2} {\left(b c + 11 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b c + 11 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b c + 11 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c + 11 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{2}}{16 \, {\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)}} - \frac{{\left(23 \, b^{2} c d^{2} + a b d^{3}\right)} x^{\frac{9}{2}} + {\left(35 \, b^{2} c^{2} d + 12 \, a b c d^{2} + a^{2} d^{3}\right)} x^{\frac{5}{2}} + {\left(8 \, b^{2} c^{3} + 19 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} \sqrt{x}}{16 \, {\left(a b^{3} c^{6} - 3 \, a^{2} b^{2} c^{5} d + 3 \, a^{3} b c^{4} d^{2} - a^{4} c^{3} d^{3} + {\left(b^{4} c^{4} d^{2} - 3 \, a b^{3} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d^{4} - a^{3} b c d^{5}\right)} x^{6} + {\left(2 \, b^{4} c^{5} d - 5 \, a b^{3} c^{4} d^{2} + 3 \, a^{2} b^{2} c^{3} d^{3} + a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right)} x^{4} + {\left(b^{4} c^{6} - a b^{3} c^{5} d - 3 \, a^{2} b^{2} c^{4} d^{2} + 5 \, a^{3} b c^{3} d^{3} - 2 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(77 \, b^{2} c^{2} d + 22 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"1/16*(2*sqrt(2)*(b*c + 11*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b*c + 11*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b*c + 11*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b*c + 11*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^2/(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) - 1/16*((23*b^2*c*d^2 + a*b*d^3)*x^(9/2) + (35*b^2*c^2*d + 12*a*b*c*d^2 + a^2*d^3)*x^(5/2) + (8*b^2*c^3 + 19*a*b*c^2*d - 3*a^2*c*d^2)*sqrt(x))/(a*b^3*c^6 - 3*a^2*b^2*c^5*d + 3*a^3*b*c^4*d^2 - a^4*c^3*d^3 + (b^4*c^4*d^2 - 3*a*b^3*c^3*d^3 + 3*a^2*b^2*c^2*d^4 - a^3*b*c*d^5)*x^6 + (2*b^4*c^5*d - 5*a*b^3*c^4*d^2 + 3*a^2*b^2*c^3*d^3 + a^3*b*c^2*d^4 - a^4*c*d^5)*x^4 + (b^4*c^6 - a*b^3*c^5*d - 3*a^2*b^2*c^4*d^2 + 5*a^3*b*c^3*d^3 - 2*a^4*c^2*d^4)*x^2) - 1/128*(2*sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(77*b^2*c^2*d + 22*a*b*c*d^2 - 3*a^2*d^3)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)","A",0
499,1,845,0,2.883075," ","integrate(x^(1/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(b^{4} c - 13 \, a b^{3} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} + \frac{{\left(117 \, b^{2} c^{2} d^{2} - 26 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} + \frac{{\left(8 \, b^{3} c^{2} d^{2} + 21 \, a b^{2} c d^{3} - 5 \, a^{2} b d^{4}\right)} x^{\frac{11}{2}} + {\left(16 \, b^{3} c^{3} d + 25 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{\frac{7}{2}} + {\left(8 \, b^{3} c^{4} + 25 \, a^{2} b c^{2} d^{2} - 9 \, a^{3} c d^{3}\right)} x^{\frac{3}{2}}}{16 \, {\left(a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left(a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right)} x^{6} + {\left(2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} x^{4} + {\left(a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right)} x^{2}\right)}}"," ",0,"1/16*(b^4*c - 13*a*b^3*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4) + 1/128*(117*b^2*c^2*d^2 - 26*a*b*c*d^3 + 5*a^2*d^4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) + 1/16*((8*b^3*c^2*d^2 + 21*a*b^2*c*d^3 - 5*a^2*b*d^4)*x^(11/2) + (16*b^3*c^3*d + 25*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 - 5*a^3*d^4)*x^(7/2) + (8*b^3*c^4 + 25*a^2*b*c^2*d^2 - 9*a^3*c*d^3)*x^(3/2))/(a^2*b^3*c^7 - 3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 + (a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2)","A",0
500,1,951,0,2.752836," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3/x^(1/2),x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(b c - 5 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(b c - 5 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(b c - 5 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(b c - 5 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{3}}{16 \, {\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)}} + \frac{{\left(8 \, b^{3} c^{2} d^{2} + 23 \, a b^{2} c d^{3} - 7 \, a^{2} b d^{4}\right)} x^{\frac{9}{2}} + {\left(16 \, b^{3} c^{3} d + 27 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} - 7 \, a^{3} d^{4}\right)} x^{\frac{5}{2}} + {\left(8 \, b^{3} c^{4} + 27 \, a^{2} b c^{2} d^{2} - 11 \, a^{3} c d^{3}\right)} \sqrt{x}}{16 \, {\left(a^{2} b^{3} c^{7} - 3 \, a^{3} b^{2} c^{6} d + 3 \, a^{4} b c^{5} d^{2} - a^{5} c^{4} d^{3} + {\left(a b^{4} c^{5} d^{2} - 3 \, a^{2} b^{3} c^{4} d^{3} + 3 \, a^{3} b^{2} c^{3} d^{4} - a^{4} b c^{2} d^{5}\right)} x^{6} + {\left(2 \, a b^{4} c^{6} d - 5 \, a^{2} b^{3} c^{5} d^{2} + 3 \, a^{3} b^{2} c^{4} d^{3} + a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} x^{4} + {\left(a b^{4} c^{7} - a^{2} b^{3} c^{6} d - 3 \, a^{3} b^{2} c^{5} d^{2} + 5 \, a^{4} b c^{4} d^{3} - 2 \, a^{5} c^{3} d^{4}\right)} x^{2}\right)}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} {\left(55 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(55 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(55 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(55 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}\right)}}{128 \, {\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)}}"," ",0,"3/16*(2*sqrt(2)*(b*c - 5*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(b*c - 5*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(b*c - 5*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(b*c - 5*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^3/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4) + 1/16*((8*b^3*c^2*d^2 + 23*a*b^2*c*d^3 - 7*a^2*b*d^4)*x^(9/2) + (16*b^3*c^3*d + 27*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 - 7*a^3*d^4)*x^(5/2) + (8*b^3*c^4 + 27*a^2*b*c^2*d^2 - 11*a^3*c*d^3)*sqrt(x))/(a^2*b^3*c^7 - 3*a^3*b^2*c^6*d + 3*a^4*b*c^5*d^2 - a^5*c^4*d^3 + (a*b^4*c^5*d^2 - 3*a^2*b^3*c^4*d^3 + 3*a^3*b^2*c^3*d^4 - a^4*b*c^2*d^5)*x^6 + (2*a*b^4*c^6*d - 5*a^2*b^3*c^5*d^2 + 3*a^3*b^2*c^4*d^3 + a^4*b*c^3*d^4 - a^5*c^2*d^5)*x^4 + (a*b^4*c^7 - a^2*b^3*c^6*d - 3*a^3*b^2*c^5*d^2 + 5*a^4*b*c^4*d^3 - 2*a^5*c^3*d^4)*x^2) + 3/128*(2*sqrt(2)*(55*b^2*c^2*d^2 - 30*a*b*c*d^3 + 7*a^2*d^4)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(55*b^2*c^2*d^2 - 30*a*b*c*d^3 + 7*a^2*d^4)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(55*b^2*c^2*d^2 - 30*a*b*c*d^3 + 7*a^2*d^4)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(55*b^2*c^2*d^2 - 30*a*b*c*d^3 + 7*a^2*d^4)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)","A",0
501,1,955,0,3.064547," ","integrate(1/x^(3/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(5 \, b^{5} c - 17 \, a b^{4} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} - \frac{{\left(221 \, b^{2} c^{2} d^{3} - 170 \, a b c d^{4} + 45 \, a^{2} d^{5}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{32 \, a b^{3} c^{5} - 96 \, a^{2} b^{2} c^{4} d + 96 \, a^{3} b c^{3} d^{2} - 32 \, a^{4} c^{2} d^{3} + {\left(40 \, b^{4} c^{3} d^{2} - 96 \, a b^{3} c^{2} d^{3} + 125 \, a^{2} b^{2} c d^{4} - 45 \, a^{3} b d^{5}\right)} x^{6} + {\left(80 \, b^{4} c^{4} d - 160 \, a b^{3} c^{3} d^{2} + 129 \, a^{2} b^{2} c^{2} d^{3} + 44 \, a^{3} b c d^{4} - 45 \, a^{4} d^{5}\right)} x^{4} + {\left(40 \, b^{4} c^{5} - 32 \, a b^{3} c^{4} d - 96 \, a^{2} b^{2} c^{3} d^{2} + 193 \, a^{3} b c^{2} d^{3} - 81 \, a^{4} c d^{4}\right)} x^{2}}{16 \, {\left({\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{\frac{13}{2}} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{\frac{9}{2}} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{\frac{5}{2}} + {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3}\right)} \sqrt{x}\right)}}"," ",0,"-1/16*(5*b^5*c - 17*a*b^4*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(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) - 1/128*(221*b^2*c^2*d^3 - 170*a*b*c*d^4 + 45*a^2*d^5)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) - 1/16*(32*a*b^3*c^5 - 96*a^2*b^2*c^4*d + 96*a^3*b*c^3*d^2 - 32*a^4*c^2*d^3 + (40*b^4*c^3*d^2 - 96*a*b^3*c^2*d^3 + 125*a^2*b^2*c*d^4 - 45*a^3*b*d^5)*x^6 + (80*b^4*c^4*d - 160*a*b^3*c^3*d^2 + 129*a^2*b^2*c^2*d^3 + 44*a^3*b*c*d^4 - 45*a^4*d^5)*x^4 + (40*b^4*c^5 - 32*a*b^3*c^4*d - 96*a^2*b^2*c^3*d^2 + 193*a^3*b*c^2*d^3 - 81*a^4*c*d^4)*x^2)/((a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^(13/2) + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^(9/2) + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^(5/2) + (a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3)*sqrt(x))","A",0
502,1,1064,0,2.796086," ","integrate(1/x^(5/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{2} {\left(7 \, b c - 19 \, a d\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{2 \, \sqrt{2} {\left(7 \, b c - 19 \, a d\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{b}}} + \frac{\sqrt{2} {\left(7 \, b c - 19 \, a d\right)} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(7 \, b c - 19 \, a d\right)} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{3}{4}} b^{\frac{1}{4}}}\right)} b^{4}}{16 \, {\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)}} - \frac{32 \, a b^{3} c^{5} - 96 \, a^{2} b^{2} c^{4} d + 96 \, a^{3} b c^{3} d^{2} - 32 \, a^{4} c^{2} d^{3} + {\left(56 \, b^{4} c^{3} d^{2} - 96 \, a b^{3} c^{2} d^{3} + 189 \, a^{2} b^{2} c d^{4} - 77 \, a^{3} b d^{5}\right)} x^{6} + {\left(112 \, b^{4} c^{4} d - 160 \, a b^{3} c^{3} d^{2} + 201 \, a^{2} b^{2} c^{2} d^{3} + 68 \, a^{3} b c d^{4} - 77 \, a^{4} d^{5}\right)} x^{4} + {\left(56 \, b^{4} c^{5} - 32 \, a b^{3} c^{4} d - 96 \, a^{2} b^{2} c^{3} d^{2} + 265 \, a^{3} b c^{2} d^{3} - 121 \, a^{4} c d^{4}\right)} x^{2}}{48 \, {\left({\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{\frac{15}{2}} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{\frac{11}{2}} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x^{\frac{7}{2}} + {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3}\right)} x^{\frac{3}{2}}\right)}} - \frac{\frac{2 \, \sqrt{2} {\left(285 \, b^{2} c^{2} d^{3} - 266 \, a b c d^{4} + 77 \, a^{2} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{2 \, \sqrt{2} {\left(285 \, b^{2} c^{2} d^{3} - 266 \, a b c d^{4} + 77 \, a^{2} d^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{c} \sqrt{\sqrt{c} \sqrt{d}}} + \frac{\sqrt{2} {\left(285 \, b^{2} c^{2} d^{3} - 266 \, a b c d^{4} + 77 \, a^{2} d^{5}\right)} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}} - \frac{\sqrt{2} {\left(285 \, b^{2} c^{2} d^{3} - 266 \, a b c d^{4} + 77 \, a^{2} d^{5}\right)} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{3}{4}} d^{\frac{1}{4}}}}{128 \, {\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)}}"," ",0,"-1/16*(2*sqrt(2)*(7*b*c - 19*a*d)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + 2*sqrt(2)*(7*b*c - 19*a*d)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(b))) + sqrt(2)*(7*b*c - 19*a*d)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)) - sqrt(2)*(7*b*c - 19*a*d)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(3/4)*b^(1/4)))*b^4/(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) - 1/48*(32*a*b^3*c^5 - 96*a^2*b^2*c^4*d + 96*a^3*b*c^3*d^2 - 32*a^4*c^2*d^3 + (56*b^4*c^3*d^2 - 96*a*b^3*c^2*d^3 + 189*a^2*b^2*c*d^4 - 77*a^3*b*d^5)*x^6 + (112*b^4*c^4*d - 160*a*b^3*c^3*d^2 + 201*a^2*b^2*c^2*d^3 + 68*a^3*b*c*d^4 - 77*a^4*d^5)*x^4 + (56*b^4*c^5 - 32*a*b^3*c^4*d - 96*a^2*b^2*c^3*d^2 + 265*a^3*b*c^2*d^3 - 121*a^4*c*d^4)*x^2)/((a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^(15/2) + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^(11/2) + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x^(7/2) + (a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3)*x^(3/2)) - 1/128*(2*sqrt(2)*(285*b^2*c^2*d^3 - 266*a*b*c*d^4 + 77*a^2*d^5)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + 2*sqrt(2)*(285*b^2*c^2*d^3 - 266*a*b*c*d^4 + 77*a^2*d^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(c)*sqrt(sqrt(c)*sqrt(d))) + sqrt(2)*(285*b^2*c^2*d^3 - 266*a*b*c*d^4 + 77*a^2*d^5)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)) - sqrt(2)*(285*b^2*c^2*d^3 - 266*a*b*c*d^4 + 77*a^2*d^5)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(3/4)*d^(1/4)))/(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)","A",0
503,1,1066,0,2.882920," ","integrate(1/x^(7/2)/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(3 \, b^{6} c - 7 \, a b^{5} d\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} + 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} - 2 \, \sqrt{b} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{b}}}\right)}{\sqrt{\sqrt{a} \sqrt{b}} \sqrt{b}} - \frac{\sqrt{2} \log\left(\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} a^{\frac{1}{4}} b^{\frac{1}{4}} \sqrt{x} + \sqrt{b} x + \sqrt{a}\right)}{a^{\frac{1}{4}} b^{\frac{3}{4}}}\right)}}{16 \, {\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)}} + \frac{3 \, {\left(119 \, b^{2} c^{2} d^{4} - 126 \, a b c d^{5} + 39 \, a^{2} d^{6}\right)} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} + 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} - 2 \, \sqrt{d} \sqrt{x}\right)}}{2 \, \sqrt{\sqrt{c} \sqrt{d}}}\right)}{\sqrt{\sqrt{c} \sqrt{d}} \sqrt{d}} - \frac{\sqrt{2} \log\left(\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(-\sqrt{2} c^{\frac{1}{4}} d^{\frac{1}{4}} \sqrt{x} + \sqrt{d} x + \sqrt{c}\right)}{c^{\frac{1}{4}} d^{\frac{3}{4}}}\right)}}{128 \, {\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)}} - \frac{32 \, a^{2} b^{3} c^{6} - 96 \, a^{3} b^{2} c^{5} d + 96 \, a^{4} b c^{4} d^{2} - 32 \, a^{5} c^{3} d^{3} - 15 \, {\left(24 \, b^{5} c^{4} d^{2} - 32 \, a b^{4} c^{3} d^{3} - 32 \, a^{2} b^{3} c^{2} d^{4} + 87 \, a^{3} b^{2} c d^{5} - 39 \, a^{4} b d^{6}\right)} x^{8} - 3 \, {\left(240 \, b^{5} c^{5} d - 224 \, a b^{4} c^{4} d^{2} - 448 \, a^{2} b^{3} c^{3} d^{3} + 623 \, a^{3} b^{2} c^{2} d^{4} + 84 \, a^{4} b c d^{5} - 195 \, a^{5} d^{6}\right)} x^{6} - {\left(360 \, b^{5} c^{6} + 96 \, a b^{4} c^{5} d - 1280 \, a^{2} b^{3} c^{4} d^{2} + 64 \, a^{3} b^{2} c^{3} d^{3} + 1933 \, a^{4} b c^{2} d^{4} - 1053 \, a^{5} c d^{5}\right)} x^{4} - 32 \, {\left(9 \, a b^{4} c^{6} - 14 \, a^{2} b^{3} c^{5} d - 12 \, a^{3} b^{2} c^{4} d^{2} + 30 \, a^{4} b c^{3} d^{3} - 13 \, a^{5} c^{2} d^{4}\right)} x^{2}}{80 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{\frac{17}{2}} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{\frac{13}{2}} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{\frac{9}{2}} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x^{\frac{5}{2}}\right)}}"," ",0,"3/16*(3*b^6*c - 7*a*b^5*d)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) + 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*a^(1/4)*b^(1/4) - 2*sqrt(b)*sqrt(x))/sqrt(sqrt(a)*sqrt(b)))/(sqrt(sqrt(a)*sqrt(b))*sqrt(b)) - sqrt(2)*log(sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)) + sqrt(2)*log(-sqrt(2)*a^(1/4)*b^(1/4)*sqrt(x) + sqrt(b)*x + sqrt(a))/(a^(1/4)*b^(3/4)))/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4) + 3/128*(119*b^2*c^2*d^4 - 126*a*b*c*d^5 + 39*a^2*d^6)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) + 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*d^(1/4) - 2*sqrt(d)*sqrt(x))/sqrt(sqrt(c)*sqrt(d)))/(sqrt(sqrt(c)*sqrt(d))*sqrt(d)) - sqrt(2)*log(sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)) + sqrt(2)*log(-sqrt(2)*c^(1/4)*d^(1/4)*sqrt(x) + sqrt(d)*x + sqrt(c))/(c^(1/4)*d^(3/4)))/(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) - 1/80*(32*a^2*b^3*c^6 - 96*a^3*b^2*c^5*d + 96*a^4*b*c^4*d^2 - 32*a^5*c^3*d^3 - 15*(24*b^5*c^4*d^2 - 32*a*b^4*c^3*d^3 - 32*a^2*b^3*c^2*d^4 + 87*a^3*b^2*c*d^5 - 39*a^4*b*d^6)*x^8 - 3*(240*b^5*c^5*d - 224*a*b^4*c^4*d^2 - 448*a^2*b^3*c^3*d^3 + 623*a^3*b^2*c^2*d^4 + 84*a^4*b*c*d^5 - 195*a^5*d^6)*x^6 - (360*b^5*c^6 + 96*a*b^4*c^5*d - 1280*a^2*b^3*c^4*d^2 + 64*a^3*b^2*c^3*d^3 + 1933*a^4*b*c^2*d^4 - 1053*a^5*c*d^5)*x^4 - 32*(9*a*b^4*c^6 - 14*a^2*b^3*c^5*d - 12*a^3*b^2*c^4*d^2 + 30*a^4*b*c^3*d^3 - 13*a^5*c^2*d^4)*x^2)/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^(17/2) + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^(13/2) + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^(9/2) + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x^(5/2))","A",0
504,1,132,0,0.974184," ","integrate(x^5*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{6}}{9 \, b} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x^{4}}{21 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x^{4}}{7 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x^{2}}{105 \, b^{3}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x^{2}}{35 \, b^{2}} - \frac{16 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3}}{315 \, b^{4}} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2}}{105 \, b^{3}}"," ",0,"1/9*(b*x^2 + a)^(3/2)*B*x^6/b - 2/21*(b*x^2 + a)^(3/2)*B*a*x^4/b^2 + 1/7*(b*x^2 + a)^(3/2)*A*x^4/b + 8/105*(b*x^2 + a)^(3/2)*B*a^2*x^2/b^3 - 4/35*(b*x^2 + a)^(3/2)*A*a*x^2/b^2 - 16/315*(b*x^2 + a)^(3/2)*B*a^3/b^4 + 8/105*(b*x^2 + a)^(3/2)*A*a^2/b^3","A",0
505,1,166,0,1.003006," ","integrate(x^4*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{5}}{8 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x^{3}}{48 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x^{3}}{6 \, b} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x}{64 \, b^{3}} - \frac{5 \, \sqrt{b x^{2} + a} B a^{3} x}{128 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x}{8 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A a^{2} x}{16 \, b^{2}} - \frac{5 \, B a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{7}{2}}} + \frac{A a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{5}{2}}}"," ",0,"1/8*(b*x^2 + a)^(3/2)*B*x^5/b - 5/48*(b*x^2 + a)^(3/2)*B*a*x^3/b^2 + 1/6*(b*x^2 + a)^(3/2)*A*x^3/b + 5/64*(b*x^2 + a)^(3/2)*B*a^2*x/b^3 - 5/128*sqrt(b*x^2 + a)*B*a^3*x/b^3 - 1/8*(b*x^2 + a)^(3/2)*A*a*x/b^2 + 1/16*sqrt(b*x^2 + a)*A*a^2*x/b^2 - 5/128*B*a^4*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 1/16*A*a^3*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
506,1,90,0,1.093083," ","integrate(x^3*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{4}}{7 \, b} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x^{2}}{35 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x^{2}}{5 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2}}{105 \, b^{3}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a}{15 \, b^{2}}"," ",0,"1/7*(b*x^2 + a)^(3/2)*B*x^4/b - 4/35*(b*x^2 + a)^(3/2)*B*a*x^2/b^2 + 1/5*(b*x^2 + a)^(3/2)*A*x^2/b + 8/105*(b*x^2 + a)^(3/2)*B*a^2/b^3 - 2/15*(b*x^2 + a)^(3/2)*A*a/b^2","A",0
507,1,124,0,1.012318," ","integrate(x^2*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{3}}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x}{8 \, b^{2}} + \frac{\sqrt{b x^{2} + a} B a^{2} x}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A x}{4 \, b} - \frac{\sqrt{b x^{2} + a} A a x}{8 \, b} + \frac{B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{5}{2}}} - \frac{A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}}"," ",0,"1/6*(b*x^2 + a)^(3/2)*B*x^3/b - 1/8*(b*x^2 + a)^(3/2)*B*a*x/b^2 + 1/16*sqrt(b*x^2 + a)*B*a^2*x/b^2 + 1/4*(b*x^2 + a)^(3/2)*A*x/b - 1/8*sqrt(b*x^2 + a)*A*a*x/b + 1/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 1/8*A*a^2*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
508,1,50,0,0.981819," ","integrate(x*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x^{2}}{5 \, b} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a}{15 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{3 \, b}"," ",0,"1/5*(b*x^2 + a)^(3/2)*B*x^2/b - 2/15*(b*x^2 + a)^(3/2)*B*a/b^2 + 1/3*(b*x^2 + a)^(3/2)*A/b","A",0
509,1,81,0,1.116029," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} A x + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B x}{4 \, b} - \frac{\sqrt{b x^{2} + a} B a x}{8 \, b} - \frac{B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{3}{2}}} + \frac{A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}}"," ",0,"1/2*sqrt(b*x^2 + a)*A*x + 1/4*(b*x^2 + a)^(3/2)*B*x/b - 1/8*sqrt(b*x^2 + a)*B*a*x/b - 1/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 1/2*A*a*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
510,1,45,0,0.951140," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x,x, algorithm=""maxima"")","-A \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \sqrt{b x^{2} + a} A + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{3 \, b}"," ",0,"-A*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(x))) + sqrt(b*x^2 + a)*A + 1/3*(b*x^2 + a)^(3/2)*B/b","A",0
511,1,59,0,1.037072," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{b x^{2} + a} B x + \frac{B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{b}} + A \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{\sqrt{b x^{2} + a} A}{x}"," ",0,"1/2*sqrt(b*x^2 + a)*B*x + 1/2*B*a*arcsinh(b*x/sqrt(a*b))/sqrt(b) + A*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - sqrt(b*x^2 + a)*A/x","A",0
512,1,83,0,1.098572," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^3,x, algorithm=""maxima"")","-B \sqrt{a} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, \sqrt{a}} + \sqrt{b x^{2} + a} B + \frac{\sqrt{b x^{2} + a} A b}{2 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{2 \, a x^{2}}"," ",0,"-B*sqrt(a)*arcsinh(a/(sqrt(a*b)*abs(x))) - 1/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + sqrt(b*x^2 + a)*B + 1/2*sqrt(b*x^2 + a)*A*b/a - 1/2*(b*x^2 + a)^(3/2)*A/(a*x^2)","A",0
513,1,48,0,1.082366," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^4,x, algorithm=""maxima"")","B \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{\sqrt{b x^{2} + a} B}{x} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{3 \, a x^{3}}"," ",0,"B*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - sqrt(b*x^2 + a)*B/x - 1/3*(b*x^2 + a)^(3/2)*A/(a*x^3)","A",0
514,1,130,0,1.045390," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^5,x, algorithm=""maxima"")","-\frac{B b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, \sqrt{a}} + \frac{A b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{3}{2}}} + \frac{\sqrt{b x^{2} + a} B b}{2 \, a} - \frac{\sqrt{b x^{2} + a} A b^{2}}{8 \, a^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{2 \, a x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{8 \, a^{2} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{4 \, a x^{4}}"," ",0,"-1/2*B*b*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 1/8*A*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 1/2*sqrt(b*x^2 + a)*B*b/a - 1/8*sqrt(b*x^2 + a)*A*b^2/a^2 - 1/2*(b*x^2 + a)^(3/2)*B/(a*x^2) + 1/8*(b*x^2 + a)^(3/2)*A*b/(a^2*x^2) - 1/4*(b*x^2 + a)^(3/2)*A/(a*x^4)","A",0
515,1,56,0,1.075642," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^6,x, algorithm=""maxima"")","-\frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{3 \, a x^{3}} + \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{15 \, a^{2} x^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{5 \, a x^{5}}"," ",0,"-1/3*(b*x^2 + a)^(3/2)*B/(a*x^3) + 2/15*(b*x^2 + a)^(3/2)*A*b/(a^2*x^3) - 1/5*(b*x^2 + a)^(3/2)*A/(a*x^5)","A",0
516,1,174,0,1.129625," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^7,x, algorithm=""maxima"")","\frac{B b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{3}{2}}} - \frac{A b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{5}{2}}} - \frac{\sqrt{b x^{2} + a} B b^{2}}{8 \, a^{2}} + \frac{\sqrt{b x^{2} + a} A b^{3}}{16 \, a^{3}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{8 \, a^{2} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{16 \, a^{3} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{4 \, a x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{8 \, a^{2} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{6 \, a x^{6}}"," ",0,"1/8*B*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 1/16*A*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 1/8*sqrt(b*x^2 + a)*B*b^2/a^2 + 1/16*sqrt(b*x^2 + a)*A*b^3/a^3 + 1/8*(b*x^2 + a)^(3/2)*B*b/(a^2*x^2) - 1/16*(b*x^2 + a)^(3/2)*A*b^2/(a^3*x^2) - 1/4*(b*x^2 + a)^(3/2)*B/(a*x^4) + 1/8*(b*x^2 + a)^(3/2)*A*b/(a^2*x^4) - 1/6*(b*x^2 + a)^(3/2)*A/(a*x^6)","A",0
517,1,96,0,1.097821," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^8,x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{15 \, a^{2} x^{3}} - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{105 \, a^{3} x^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{5 \, a x^{5}} + \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{35 \, a^{2} x^{5}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{7 \, a x^{7}}"," ",0,"2/15*(b*x^2 + a)^(3/2)*B*b/(a^2*x^3) - 8/105*(b*x^2 + a)^(3/2)*A*b^2/(a^3*x^3) - 1/5*(b*x^2 + a)^(3/2)*B/(a*x^5) + 4/35*(b*x^2 + a)^(3/2)*A*b/(a^2*x^5) - 1/7*(b*x^2 + a)^(3/2)*A/(a*x^7)","A",0
518,1,216,0,1.166598," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^9,x, algorithm=""maxima"")","-\frac{B b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{5}{2}}} + \frac{5 \, A b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{7}{2}}} + \frac{\sqrt{b x^{2} + a} B b^{3}}{16 \, a^{3}} - \frac{5 \, \sqrt{b x^{2} + a} A b^{4}}{128 \, a^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2}}{16 \, a^{3} x^{2}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3}}{128 \, a^{4} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{8 \, a^{2} x^{4}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{64 \, a^{3} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{6 \, a x^{6}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{48 \, a^{2} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{8 \, a x^{8}}"," ",0,"-1/16*B*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 5/128*A*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) + 1/16*sqrt(b*x^2 + a)*B*b^3/a^3 - 5/128*sqrt(b*x^2 + a)*A*b^4/a^4 - 1/16*(b*x^2 + a)^(3/2)*B*b^2/(a^3*x^2) + 5/128*(b*x^2 + a)^(3/2)*A*b^3/(a^4*x^2) + 1/8*(b*x^2 + a)^(3/2)*B*b/(a^2*x^4) - 5/64*(b*x^2 + a)^(3/2)*A*b^2/(a^3*x^4) - 1/6*(b*x^2 + a)^(3/2)*B/(a*x^6) + 5/48*(b*x^2 + a)^(3/2)*A*b/(a^2*x^6) - 1/8*(b*x^2 + a)^(3/2)*A/(a*x^8)","A",0
519,1,138,0,0.987376," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^10,x, algorithm=""maxima"")","-\frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2}}{105 \, a^{3} x^{3}} + \frac{16 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3}}{315 \, a^{4} x^{3}} + \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{35 \, a^{2} x^{5}} - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{105 \, a^{3} x^{5}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{7 \, a x^{7}} + \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{21 \, a^{2} x^{7}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{9 \, a x^{9}}"," ",0,"-8/105*(b*x^2 + a)^(3/2)*B*b^2/(a^3*x^3) + 16/315*(b*x^2 + a)^(3/2)*A*b^3/(a^4*x^3) + 4/35*(b*x^2 + a)^(3/2)*B*b/(a^2*x^5) - 8/105*(b*x^2 + a)^(3/2)*A*b^2/(a^3*x^5) - 1/7*(b*x^2 + a)^(3/2)*B/(a*x^7) + 2/21*(b*x^2 + a)^(3/2)*A*b/(a^2*x^7) - 1/9*(b*x^2 + a)^(3/2)*A/(a*x^9)","A",0
520,1,258,0,1.167187," ","integrate((B*x^2+A)*(b*x^2+a)^(1/2)/x^11,x, algorithm=""maxima"")","\frac{5 \, B b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{7}{2}}} - \frac{7 \, A b^{5} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{256 \, a^{\frac{9}{2}}} - \frac{5 \, \sqrt{b x^{2} + a} B b^{4}}{128 \, a^{4}} + \frac{7 \, \sqrt{b x^{2} + a} A b^{5}}{256 \, a^{5}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{3}}{128 \, a^{4} x^{2}} - \frac{7 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{4}}{256 \, a^{5} x^{2}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2}}{64 \, a^{3} x^{4}} + \frac{7 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3}}{128 \, a^{4} x^{4}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{48 \, a^{2} x^{6}} - \frac{7 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{96 \, a^{3} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{8 \, a x^{8}} + \frac{7 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{80 \, a^{2} x^{8}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{10 \, a x^{10}}"," ",0,"5/128*B*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 7/256*A*b^5*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) - 5/128*sqrt(b*x^2 + a)*B*b^4/a^4 + 7/256*sqrt(b*x^2 + a)*A*b^5/a^5 + 5/128*(b*x^2 + a)^(3/2)*B*b^3/(a^4*x^2) - 7/256*(b*x^2 + a)^(3/2)*A*b^4/(a^5*x^2) - 5/64*(b*x^2 + a)^(3/2)*B*b^2/(a^3*x^4) + 7/128*(b*x^2 + a)^(3/2)*A*b^3/(a^4*x^4) + 5/48*(b*x^2 + a)^(3/2)*B*b/(a^2*x^6) - 7/96*(b*x^2 + a)^(3/2)*A*b^2/(a^3*x^6) - 1/8*(b*x^2 + a)^(3/2)*B/(a*x^8) + 7/80*(b*x^2 + a)^(3/2)*A*b/(a^2*x^8) - 1/10*(b*x^2 + a)^(3/2)*A/(a*x^10)","A",0
521,1,132,0,1.052943," ","integrate(x^5*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{6}}{11 \, b} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x^{4}}{33 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x^{4}}{9 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} x^{2}}{231 \, b^{3}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a x^{2}}{63 \, b^{2}} - \frac{16 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{3}}{1155 \, b^{4}} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2}}{315 \, b^{3}}"," ",0,"1/11*(b*x^2 + a)^(5/2)*B*x^6/b - 2/33*(b*x^2 + a)^(5/2)*B*a*x^4/b^2 + 1/9*(b*x^2 + a)^(5/2)*A*x^4/b + 8/231*(b*x^2 + a)^(5/2)*B*a^2*x^2/b^3 - 4/63*(b*x^2 + a)^(5/2)*A*a*x^2/b^2 - 16/1155*(b*x^2 + a)^(5/2)*B*a^3/b^4 + 8/315*(b*x^2 + a)^(5/2)*A*a^2/b^3","A",0
522,1,204,0,1.011065," ","integrate(x^4*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{5}}{10 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x^{3}}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x^{3}}{8 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} x}{32 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} x}{128 \, b^{3}} - \frac{3 \, \sqrt{b x^{2} + a} B a^{4} x}{256 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A a x}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} x}{64 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} A a^{3} x}{128 \, b^{2}} - \frac{3 \, B a^{5} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{7}{2}}} + \frac{3 \, A a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{5}{2}}}"," ",0,"1/10*(b*x^2 + a)^(5/2)*B*x^5/b - 1/16*(b*x^2 + a)^(5/2)*B*a*x^3/b^2 + 1/8*(b*x^2 + a)^(5/2)*A*x^3/b + 1/32*(b*x^2 + a)^(5/2)*B*a^2*x/b^3 - 1/128*(b*x^2 + a)^(3/2)*B*a^3*x/b^3 - 3/256*sqrt(b*x^2 + a)*B*a^4*x/b^3 - 1/16*(b*x^2 + a)^(5/2)*A*a*x/b^2 + 1/64*(b*x^2 + a)^(3/2)*A*a^2*x/b^2 + 3/128*sqrt(b*x^2 + a)*A*a^3*x/b^2 - 3/256*B*a^5*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 3/128*A*a^4*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
523,1,90,0,0.995659," ","integrate(x^3*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{4}}{9 \, b} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x^{2}}{63 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x^{2}}{7 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2}}{315 \, b^{3}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A a}{35 \, b^{2}}"," ",0,"1/9*(b*x^2 + a)^(5/2)*B*x^4/b - 4/63*(b*x^2 + a)^(5/2)*B*a*x^2/b^2 + 1/7*(b*x^2 + a)^(5/2)*A*x^2/b + 8/315*(b*x^2 + a)^(5/2)*B*a^2/b^3 - 2/35*(b*x^2 + a)^(5/2)*A*a/b^2","A",0
524,1,162,0,1.048724," ","integrate(x^2*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{3}}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x}{16 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x}{64 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} B a^{3} x}{128 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A x}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x}{24 \, b} - \frac{\sqrt{b x^{2} + a} A a^{2} x}{16 \, b} + \frac{3 \, B a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{5}{2}}} - \frac{A a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}}"," ",0,"1/8*(b*x^2 + a)^(5/2)*B*x^3/b - 1/16*(b*x^2 + a)^(5/2)*B*a*x/b^2 + 1/64*(b*x^2 + a)^(3/2)*B*a^2*x/b^2 + 3/128*sqrt(b*x^2 + a)*B*a^3*x/b^2 + 1/6*(b*x^2 + a)^(5/2)*A*x/b - 1/24*(b*x^2 + a)^(3/2)*A*a*x/b - 1/16*sqrt(b*x^2 + a)*A*a^2*x/b + 3/128*B*a^4*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 1/16*A*a^3*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
525,1,50,0,1.011451," ","integrate(x*(b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x^{2}}{7 \, b} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B a}{35 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{5 \, b}"," ",0,"1/7*(b*x^2 + a)^(5/2)*B*x^2/b - 2/35*(b*x^2 + a)^(5/2)*B*a/b^2 + 1/5*(b*x^2 + a)^(5/2)*A/b","A",0
526,1,116,0,0.963119," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A x + \frac{3}{8} \, \sqrt{b x^{2} + a} A a x + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B x}{6 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x}{24 \, b} - \frac{\sqrt{b x^{2} + a} B a^{2} x}{16 \, b} - \frac{B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{3}{2}}} + \frac{3 \, A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}}"," ",0,"1/4*(b*x^2 + a)^(3/2)*A*x + 3/8*sqrt(b*x^2 + a)*A*a*x + 1/6*(b*x^2 + a)^(5/2)*B*x/b - 1/24*(b*x^2 + a)^(3/2)*B*a*x/b - 1/16*sqrt(b*x^2 + a)*B*a^2*x/b - 1/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 3/8*A*a^2*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
527,1,58,0,1.035155," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x,x, algorithm=""maxima"")","-A a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A + \sqrt{b x^{2} + a} A a + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{5 \, b}"," ",0,"-A*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/3*(b*x^2 + a)^(3/2)*A + sqrt(b*x^2 + a)*A*a + 1/5*(b*x^2 + a)^(5/2)*B/b","A",0
528,1,91,0,1.139993," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B x + \frac{3}{8} \, \sqrt{b x^{2} + a} B a x + \frac{3}{2} \, \sqrt{b x^{2} + a} A b x + \frac{3 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{b}} + \frac{3}{2} \, A a \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A}{x}"," ",0,"1/4*(b*x^2 + a)^(3/2)*B*x + 3/8*sqrt(b*x^2 + a)*B*a*x + 3/2*sqrt(b*x^2 + a)*A*b*x + 3/8*B*a^2*arcsinh(b*x/sqrt(a*b))/sqrt(b) + 3/2*A*a*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - (b*x^2 + a)^(3/2)*A/x","A",0
529,1,109,0,1.029691," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^3,x, algorithm=""maxima"")","-B a^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{3}{2} \, A \sqrt{a} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B + \sqrt{b x^{2} + a} B a + \frac{3}{2} \, \sqrt{b x^{2} + a} A b + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{2 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{2 \, a x^{2}}"," ",0,"-B*a^(3/2)*arcsinh(a/(sqrt(a*b)*abs(x))) - 3/2*A*sqrt(a)*b*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/3*(b*x^2 + a)^(3/2)*B + sqrt(b*x^2 + a)*B*a + 3/2*sqrt(b*x^2 + a)*A*b + 1/2*(b*x^2 + a)^(3/2)*A*b/a - 1/2*(b*x^2 + a)^(5/2)*A/(a*x^2)","A",0
530,1,115,0,1.009421," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^4,x, algorithm=""maxima"")","\frac{3}{2} \, \sqrt{b x^{2} + a} B b x + \frac{\sqrt{b x^{2} + a} A b^{2} x}{a} + \frac{3}{2} \, B a \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) + A b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B}{x} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b}{3 \, a x} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{3 \, a x^{3}}"," ",0,"3/2*sqrt(b*x^2 + a)*B*b*x + sqrt(b*x^2 + a)*A*b^2*x/a + 3/2*B*a*sqrt(b)*arcsinh(b*x/sqrt(a*b)) + A*b^(3/2)*arcsinh(b*x/sqrt(a*b)) - (b*x^2 + a)^(3/2)*B/x - 2/3*(b*x^2 + a)^(3/2)*A*b/(a*x) - 1/3*(b*x^2 + a)^(5/2)*A/(a*x^3)","A",0
531,1,161,0,1.050308," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^5,x, algorithm=""maxima"")","-\frac{3}{2} \, B \sqrt{a} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{3 \, A b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, \sqrt{a}} + \frac{3}{2} \, \sqrt{b x^{2} + a} B b + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{2 \, a} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{8 \, a^{2}} + \frac{3 \, \sqrt{b x^{2} + a} A b^{2}}{8 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{2 \, a x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{8 \, a^{2} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{4 \, a x^{4}}"," ",0,"-3/2*B*sqrt(a)*b*arcsinh(a/(sqrt(a*b)*abs(x))) - 3/8*A*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 3/2*sqrt(b*x^2 + a)*B*b + 1/2*(b*x^2 + a)^(3/2)*B*b/a + 1/8*(b*x^2 + a)^(3/2)*A*b^2/a^2 + 3/8*sqrt(b*x^2 + a)*A*b^2/a - 1/2*(b*x^2 + a)^(5/2)*B/(a*x^2) - 1/8*(b*x^2 + a)^(5/2)*A*b/(a^2*x^2) - 1/4*(b*x^2 + a)^(5/2)*A/(a*x^4)","A",0
532,1,88,0,1.108796," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^6,x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B b^{2} x}{a} + B b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b}{3 \, a x} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{3 \, a x^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{5 \, a x^{5}}"," ",0,"sqrt(b*x^2 + a)*B*b^2*x/a + B*b^(3/2)*arcsinh(b*x/sqrt(a*b)) - 2/3*(b*x^2 + a)^(3/2)*B*b/(a*x) - 1/3*(b*x^2 + a)^(5/2)*B/(a*x^3) - 1/5*(b*x^2 + a)^(5/2)*A/(a*x^5)","A",0
533,1,210,0,1.088816," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^7,x, algorithm=""maxima"")","-\frac{3 \, B b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, \sqrt{a}} + \frac{A b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{3}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2}}{8 \, a^{2}} + \frac{3 \, \sqrt{b x^{2} + a} B b^{2}}{8 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3}}{48 \, a^{3}} - \frac{\sqrt{b x^{2} + a} A b^{3}}{16 \, a^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{8 \, a^{2} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{48 \, a^{3} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{4 \, a x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{24 \, a^{2} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{6 \, a x^{6}}"," ",0,"-3/8*B*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 1/16*A*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 1/8*(b*x^2 + a)^(3/2)*B*b^2/a^2 + 3/8*sqrt(b*x^2 + a)*B*b^2/a - 1/48*(b*x^2 + a)^(3/2)*A*b^3/a^3 - 1/16*sqrt(b*x^2 + a)*A*b^3/a^2 - 1/8*(b*x^2 + a)^(5/2)*B*b/(a^2*x^2) + 1/48*(b*x^2 + a)^(5/2)*A*b^2/(a^3*x^2) - 1/4*(b*x^2 + a)^(5/2)*B/(a*x^4) + 1/24*(b*x^2 + a)^(5/2)*A*b/(a^2*x^4) - 1/6*(b*x^2 + a)^(5/2)*A/(a*x^6)","B",0
534,1,56,0,1.050192," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^8,x, algorithm=""maxima"")","-\frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{5 \, a x^{5}} + \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{35 \, a^{2} x^{5}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{7 \, a x^{7}}"," ",0,"-1/5*(b*x^2 + a)^(5/2)*B/(a*x^5) + 2/35*(b*x^2 + a)^(5/2)*A*b/(a^2*x^5) - 1/7*(b*x^2 + a)^(5/2)*A/(a*x^7)","A",0
535,1,252,0,1.118535," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^9,x, algorithm=""maxima"")","\frac{B b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{3}{2}}} - \frac{3 \, A b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{5}{2}}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{3}}{48 \, a^{3}} - \frac{\sqrt{b x^{2} + a} B b^{3}}{16 \, a^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{4}}{128 \, a^{4}} + \frac{3 \, \sqrt{b x^{2} + a} A b^{4}}{128 \, a^{3}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{2}}{48 \, a^{3} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{3}}{128 \, a^{4} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{24 \, a^{2} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{64 \, a^{3} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{6 \, a x^{6}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{16 \, a^{2} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{8 \, a x^{8}}"," ",0,"1/16*B*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 3/128*A*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 1/48*(b*x^2 + a)^(3/2)*B*b^3/a^3 - 1/16*sqrt(b*x^2 + a)*B*b^3/a^2 + 1/128*(b*x^2 + a)^(3/2)*A*b^4/a^4 + 3/128*sqrt(b*x^2 + a)*A*b^4/a^3 + 1/48*(b*x^2 + a)^(5/2)*B*b^2/(a^3*x^2) - 1/128*(b*x^2 + a)^(5/2)*A*b^3/(a^4*x^2) + 1/24*(b*x^2 + a)^(5/2)*B*b/(a^2*x^4) - 1/64*(b*x^2 + a)^(5/2)*A*b^2/(a^3*x^4) - 1/6*(b*x^2 + a)^(5/2)*B/(a*x^6) + 1/16*(b*x^2 + a)^(5/2)*A*b/(a^2*x^6) - 1/8*(b*x^2 + a)^(5/2)*A/(a*x^8)","A",0
536,1,96,0,1.220774," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^10,x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{35 \, a^{2} x^{5}} - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{315 \, a^{3} x^{5}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{7 \, a x^{7}} + \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{63 \, a^{2} x^{7}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{9 \, a x^{9}}"," ",0,"2/35*(b*x^2 + a)^(5/2)*B*b/(a^2*x^5) - 8/315*(b*x^2 + a)^(5/2)*A*b^2/(a^3*x^5) - 1/7*(b*x^2 + a)^(5/2)*B/(a*x^7) + 4/63*(b*x^2 + a)^(5/2)*A*b/(a^2*x^7) - 1/9*(b*x^2 + a)^(5/2)*A/(a*x^9)","A",0
537,1,294,0,1.201771," ","integrate((b*x^2+a)^(3/2)*(B*x^2+A)/x^11,x, algorithm=""maxima"")","-\frac{3 \, B b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{5}{2}}} + \frac{3 \, A b^{5} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{256 \, a^{\frac{7}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{4}}{128 \, a^{4}} + \frac{3 \, \sqrt{b x^{2} + a} B b^{4}}{128 \, a^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{5}}{256 \, a^{5}} - \frac{3 \, \sqrt{b x^{2} + a} A b^{5}}{256 \, a^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{3}}{128 \, a^{4} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4}}{256 \, a^{5} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{2}}{64 \, a^{3} x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{3}}{128 \, a^{4} x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{16 \, a^{2} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{32 \, a^{3} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{8 \, a x^{8}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{16 \, a^{2} x^{8}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{10 \, a x^{10}}"," ",0,"-3/128*B*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 3/256*A*b^5*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) + 1/128*(b*x^2 + a)^(3/2)*B*b^4/a^4 + 3/128*sqrt(b*x^2 + a)*B*b^4/a^3 - 1/256*(b*x^2 + a)^(3/2)*A*b^5/a^5 - 3/256*sqrt(b*x^2 + a)*A*b^5/a^4 - 1/128*(b*x^2 + a)^(5/2)*B*b^3/(a^4*x^2) + 1/256*(b*x^2 + a)^(5/2)*A*b^4/(a^5*x^2) - 1/64*(b*x^2 + a)^(5/2)*B*b^2/(a^3*x^4) + 1/128*(b*x^2 + a)^(5/2)*A*b^3/(a^4*x^4) + 1/16*(b*x^2 + a)^(5/2)*B*b/(a^2*x^6) - 1/32*(b*x^2 + a)^(5/2)*A*b^2/(a^3*x^6) - 1/8*(b*x^2 + a)^(5/2)*B/(a*x^8) + 1/16*(b*x^2 + a)^(5/2)*A*b/(a^2*x^8) - 1/10*(b*x^2 + a)^(5/2)*A/(a*x^10)","A",0
538,1,132,0,1.117566," ","integrate(x^5*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{6}}{13 \, b} - \frac{6 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a x^{4}}{143 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x^{4}}{11 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} x^{2}}{429 \, b^{3}} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a x^{2}}{99 \, b^{2}} - \frac{16 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{3}}{3003 \, b^{4}} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a^{2}}{693 \, b^{3}}"," ",0,"1/13*(b*x^2 + a)^(7/2)*B*x^6/b - 6/143*(b*x^2 + a)^(7/2)*B*a*x^4/b^2 + 1/11*(b*x^2 + a)^(7/2)*A*x^4/b + 8/429*(b*x^2 + a)^(7/2)*B*a^2*x^2/b^3 - 4/99*(b*x^2 + a)^(7/2)*A*a*x^2/b^2 - 16/3003*(b*x^2 + a)^(7/2)*B*a^3/b^4 + 8/693*(b*x^2 + a)^(7/2)*A*a^2/b^3","A",0
539,1,242,0,1.117857," ","integrate(x^4*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{5}}{12 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B a x^{3}}{24 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x^{3}}{10 \, b} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2} x}{64 \, b^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{3} x}{384 \, b^{3}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{4} x}{1536 \, b^{3}} - \frac{5 \, \sqrt{b x^{2} + a} B a^{5} x}{1024 \, b^{3}} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a x}{80 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A a^{2} x}{160 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{3} x}{128 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} A a^{4} x}{256 \, b^{2}} - \frac{5 \, B a^{6} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{1024 \, b^{\frac{7}{2}}} + \frac{3 \, A a^{5} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{5}{2}}}"," ",0,"1/12*(b*x^2 + a)^(7/2)*B*x^5/b - 1/24*(b*x^2 + a)^(7/2)*B*a*x^3/b^2 + 1/10*(b*x^2 + a)^(7/2)*A*x^3/b + 1/64*(b*x^2 + a)^(7/2)*B*a^2*x/b^3 - 1/384*(b*x^2 + a)^(5/2)*B*a^3*x/b^3 - 5/1536*(b*x^2 + a)^(3/2)*B*a^4*x/b^3 - 5/1024*sqrt(b*x^2 + a)*B*a^5*x/b^3 - 3/80*(b*x^2 + a)^(7/2)*A*a*x/b^2 + 1/160*(b*x^2 + a)^(5/2)*A*a^2*x/b^2 + 1/128*(b*x^2 + a)^(3/2)*A*a^3*x/b^2 + 3/256*sqrt(b*x^2 + a)*A*a^4*x/b^2 - 5/1024*B*a^6*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 3/256*A*a^5*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
540,1,90,0,1.060636," ","integrate(x^3*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{4}}{11 \, b} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a x^{2}}{99 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x^{2}}{9 \, b} + \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a^{2}}{693 \, b^{3}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A a}{63 \, b^{2}}"," ",0,"1/11*(b*x^2 + a)^(7/2)*B*x^4/b - 4/99*(b*x^2 + a)^(7/2)*B*a*x^2/b^2 + 1/9*(b*x^2 + a)^(7/2)*A*x^2/b + 8/693*(b*x^2 + a)^(7/2)*B*a^2/b^3 - 2/63*(b*x^2 + a)^(7/2)*A*a/b^2","A",0
541,1,200,0,1.055611," ","integrate(x^2*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{3}}{10 \, b} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a x}{80 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a^{2} x}{160 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{3} x}{128 \, b^{2}} + \frac{3 \, \sqrt{b x^{2} + a} B a^{4} x}{256 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A a x}{48 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a^{2} x}{192 \, b} - \frac{5 \, \sqrt{b x^{2} + a} A a^{3} x}{128 \, b} + \frac{3 \, B a^{5} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{256 \, b^{\frac{5}{2}}} - \frac{5 \, A a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}}"," ",0,"1/10*(b*x^2 + a)^(7/2)*B*x^3/b - 3/80*(b*x^2 + a)^(7/2)*B*a*x/b^2 + 1/160*(b*x^2 + a)^(5/2)*B*a^2*x/b^2 + 1/128*(b*x^2 + a)^(3/2)*B*a^3*x/b^2 + 3/256*sqrt(b*x^2 + a)*B*a^4*x/b^2 + 1/8*(b*x^2 + a)^(7/2)*A*x/b - 1/48*(b*x^2 + a)^(5/2)*A*a*x/b - 5/192*(b*x^2 + a)^(3/2)*A*a^2*x/b - 5/128*sqrt(b*x^2 + a)*A*a^3*x/b + 3/256*B*a^5*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 5/128*A*a^4*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
542,1,50,0,1.026505," ","integrate(x*(b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x^{2}}{9 \, b} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B a}{63 \, b^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{7 \, b}"," ",0,"1/9*(b*x^2 + a)^(7/2)*B*x^2/b - 2/63*(b*x^2 + a)^(7/2)*B*a/b^2 + 1/7*(b*x^2 + a)^(7/2)*A/b","A",0
543,1,151,0,1.130383," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a x + \frac{5}{16} \, \sqrt{b x^{2} + a} A a^{2} x + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B x}{8 \, b} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B a x}{48 \, b} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a^{2} x}{192 \, b} - \frac{5 \, \sqrt{b x^{2} + a} B a^{3} x}{128 \, b} - \frac{5 \, B a^{4} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{128 \, b^{\frac{3}{2}}} + \frac{5 \, A a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}}"," ",0,"1/6*(b*x^2 + a)^(5/2)*A*x + 5/24*(b*x^2 + a)^(3/2)*A*a*x + 5/16*sqrt(b*x^2 + a)*A*a^2*x + 1/8*(b*x^2 + a)^(7/2)*B*x/b - 1/48*(b*x^2 + a)^(5/2)*B*a*x/b - 5/192*(b*x^2 + a)^(3/2)*B*a^2*x/b - 5/128*sqrt(b*x^2 + a)*B*a^3*x/b - 5/128*B*a^4*arcsinh(b*x/sqrt(a*b))/b^(3/2) + 5/16*A*a^3*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
544,1,73,0,1.057836," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x,x, algorithm=""maxima"")","-A a^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A a + \sqrt{b x^{2} + a} A a^{2} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{7 \, b}"," ",0,"-A*a^(5/2)*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/5*(b*x^2 + a)^(5/2)*A + 1/3*(b*x^2 + a)^(3/2)*A*a + sqrt(b*x^2 + a)*A*a^2 + 1/7*(b*x^2 + a)^(7/2)*B/b","A",0
545,1,124,0,0.986058," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B x + \frac{5}{24} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a x + \frac{5}{16} \, \sqrt{b x^{2} + a} B a^{2} x + \frac{5}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b x + \frac{15}{8} \, \sqrt{b x^{2} + a} A a b x + \frac{5 \, B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, \sqrt{b}} + \frac{15}{8} \, A a^{2} \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A}{x}"," ",0,"1/6*(b*x^2 + a)^(5/2)*B*x + 5/24*(b*x^2 + a)^(3/2)*B*a*x + 5/16*sqrt(b*x^2 + a)*B*a^2*x + 5/4*(b*x^2 + a)^(3/2)*A*b*x + 15/8*sqrt(b*x^2 + a)*A*a*b*x + 5/16*B*a^3*arcsinh(b*x/sqrt(a*b))/sqrt(b) + 15/8*A*a^2*sqrt(b)*arcsinh(b*x/sqrt(a*b)) - (b*x^2 + a)^(5/2)*A/x","A",0
546,1,138,0,1.059987," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^3,x, algorithm=""maxima"")","-B a^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{5}{2} \, A a^{\frac{3}{2}} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B + \frac{1}{3} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B a + \sqrt{b x^{2} + a} B a^{2} + \frac{5}{6} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{2 \, a} + \frac{5}{2} \, \sqrt{b x^{2} + a} A a b - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{2 \, a x^{2}}"," ",0,"-B*a^(5/2)*arcsinh(a/(sqrt(a*b)*abs(x))) - 5/2*A*a^(3/2)*b*arcsinh(a/(sqrt(a*b)*abs(x))) + 1/5*(b*x^2 + a)^(5/2)*B + 1/3*(b*x^2 + a)^(3/2)*B*a + sqrt(b*x^2 + a)*B*a^2 + 5/6*(b*x^2 + a)^(3/2)*A*b + 1/2*(b*x^2 + a)^(5/2)*A*b/a + 5/2*sqrt(b*x^2 + a)*A*a*b - 1/2*(b*x^2 + a)^(7/2)*A/(a*x^2)","A",0
547,1,151,0,1.054007," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^4,x, algorithm=""maxima"")","\frac{5}{4} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b x + \frac{15}{8} \, \sqrt{b x^{2} + a} B a b x + \frac{5}{2} \, \sqrt{b x^{2} + a} A b^{2} x + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2} x}{3 \, a} + \frac{15}{8} \, B a^{2} \sqrt{b} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) + \frac{5}{2} \, A a b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B}{x} - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b}{3 \, a x} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{3 \, a x^{3}}"," ",0,"5/4*(b*x^2 + a)^(3/2)*B*b*x + 15/8*sqrt(b*x^2 + a)*B*a*b*x + 5/2*sqrt(b*x^2 + a)*A*b^2*x + 5/3*(b*x^2 + a)^(3/2)*A*b^2*x/a + 15/8*B*a^2*sqrt(b)*arcsinh(b*x/sqrt(a*b)) + 5/2*A*a*b^(3/2)*arcsinh(b*x/sqrt(a*b)) - (b*x^2 + a)^(5/2)*B/x - 4/3*(b*x^2 + a)^(5/2)*A*b/(a*x) - 1/3*(b*x^2 + a)^(7/2)*A/(a*x^3)","A",0
548,1,190,0,1.057739," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^5,x, algorithm=""maxima"")","-\frac{5}{2} \, B a^{\frac{3}{2}} b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{15}{8} \, A \sqrt{a} b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) + \frac{5}{6} \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{2 \, a} + \frac{5}{2} \, \sqrt{b x^{2} + a} B a b + \frac{15}{8} \, \sqrt{b x^{2} + a} A b^{2} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{8 \, a^{2}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{2}}{8 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{2 \, a x^{2}} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{8 \, a^{2} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{4 \, a x^{4}}"," ",0,"-5/2*B*a^(3/2)*b*arcsinh(a/(sqrt(a*b)*abs(x))) - 15/8*A*sqrt(a)*b^2*arcsinh(a/(sqrt(a*b)*abs(x))) + 5/6*(b*x^2 + a)^(3/2)*B*b + 1/2*(b*x^2 + a)^(5/2)*B*b/a + 5/2*sqrt(b*x^2 + a)*B*a*b + 15/8*sqrt(b*x^2 + a)*A*b^2 + 3/8*(b*x^2 + a)^(5/2)*A*b^2/a^2 + 5/8*(b*x^2 + a)^(3/2)*A*b^2/a - 1/2*(b*x^2 + a)^(7/2)*B/(a*x^2) - 3/8*(b*x^2 + a)^(7/2)*A*b/(a^2*x^2) - 1/4*(b*x^2 + a)^(7/2)*A/(a*x^4)","A",0
549,1,198,0,1.115197," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^6,x, algorithm=""maxima"")","\frac{5}{2} \, \sqrt{b x^{2} + a} B b^{2} x + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2} x}{3 \, a} + \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3} x}{3 \, a^{2}} + \frac{\sqrt{b x^{2} + a} A b^{3} x}{a} + \frac{5}{2} \, B a b^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) + A b^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{4 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b}{3 \, a x} - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{2}}{15 \, a^{2} x} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{3 \, a x^{3}} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{15 \, a^{2} x^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{5 \, a x^{5}}"," ",0,"5/2*sqrt(b*x^2 + a)*B*b^2*x + 5/3*(b*x^2 + a)^(3/2)*B*b^2*x/a + 2/3*(b*x^2 + a)^(3/2)*A*b^3*x/a^2 + sqrt(b*x^2 + a)*A*b^3*x/a + 5/2*B*a*b^(3/2)*arcsinh(b*x/sqrt(a*b)) + A*b^(5/2)*arcsinh(b*x/sqrt(a*b)) - 4/3*(b*x^2 + a)^(5/2)*B*b/(a*x) - 8/15*(b*x^2 + a)^(5/2)*A*b^2/(a^2*x) - 1/3*(b*x^2 + a)^(7/2)*B/(a*x^3) - 2/15*(b*x^2 + a)^(7/2)*A*b/(a^2*x^3) - 1/5*(b*x^2 + a)^(7/2)*A/(a*x^5)","A",0
550,1,243,0,1.195526," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^7,x, algorithm=""maxima"")","-\frac{15}{8} \, B \sqrt{a} b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right) - \frac{5 \, A b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, \sqrt{a}} + \frac{15}{8} \, \sqrt{b x^{2} + a} B b^{2} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{2}}{8 \, a^{2}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{2}}{8 \, a} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{3}}{16 \, a^{3}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{3}}{48 \, a^{2}} + \frac{5 \, \sqrt{b x^{2} + a} A b^{3}}{16 \, a} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B b}{8 \, a^{2} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{2}}{16 \, a^{3} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{4 \, a x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{24 \, a^{2} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{6 \, a x^{6}}"," ",0,"-15/8*B*sqrt(a)*b^2*arcsinh(a/(sqrt(a*b)*abs(x))) - 5/16*A*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 15/8*sqrt(b*x^2 + a)*B*b^2 + 3/8*(b*x^2 + a)^(5/2)*B*b^2/a^2 + 5/8*(b*x^2 + a)^(3/2)*B*b^2/a + 1/16*(b*x^2 + a)^(5/2)*A*b^3/a^3 + 5/48*(b*x^2 + a)^(3/2)*A*b^3/a^2 + 5/16*sqrt(b*x^2 + a)*A*b^3/a - 3/8*(b*x^2 + a)^(7/2)*B*b/(a^2*x^2) - 1/16*(b*x^2 + a)^(7/2)*A*b^2/(a^3*x^2) - 1/4*(b*x^2 + a)^(7/2)*B/(a*x^4) - 1/24*(b*x^2 + a)^(7/2)*A*b/(a^2*x^4) - 1/6*(b*x^2 + a)^(7/2)*A/(a*x^6)","A",0
551,1,128,0,1.089049," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^8,x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{3} x}{3 \, a^{2}} + \frac{\sqrt{b x^{2} + a} B b^{3} x}{a} + B b^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right) - \frac{8 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{2}}{15 \, a^{2} x} - \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} B b}{15 \, a^{2} x^{3}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{5 \, a x^{5}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{7 \, a x^{7}}"," ",0,"2/3*(b*x^2 + a)^(3/2)*B*b^3*x/a^2 + sqrt(b*x^2 + a)*B*b^3*x/a + B*b^(5/2)*arcsinh(b*x/sqrt(a*b)) - 8/15*(b*x^2 + a)^(5/2)*B*b^2/(a^2*x) - 2/15*(b*x^2 + a)^(7/2)*B*b/(a^2*x^3) - 1/5*(b*x^2 + a)^(7/2)*B/(a*x^5) - 1/7*(b*x^2 + a)^(7/2)*A/(a*x^7)","A",0
552,1,288,0,1.167167," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm=""maxima"")","-\frac{5 \, B b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, \sqrt{a}} + \frac{5 \, A b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{3}{2}}} + \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{3}}{16 \, a^{3}} + \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{3}}{48 \, a^{2}} + \frac{5 \, \sqrt{b x^{2} + a} B b^{3}}{16 \, a} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{4}}{128 \, a^{4}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{4}}{384 \, a^{3}} - \frac{5 \, \sqrt{b x^{2} + a} A b^{4}}{128 \, a^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B b^{2}}{16 \, a^{3} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{3}}{128 \, a^{4} x^{2}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B b}{24 \, a^{2} x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{2}}{192 \, a^{3} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{6 \, a x^{6}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{48 \, a^{2} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{8 \, a x^{8}}"," ",0,"-5/16*B*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 5/128*A*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 1/16*(b*x^2 + a)^(5/2)*B*b^3/a^3 + 5/48*(b*x^2 + a)^(3/2)*B*b^3/a^2 + 5/16*sqrt(b*x^2 + a)*B*b^3/a - 1/128*(b*x^2 + a)^(5/2)*A*b^4/a^4 - 5/384*(b*x^2 + a)^(3/2)*A*b^4/a^3 - 5/128*sqrt(b*x^2 + a)*A*b^4/a^2 - 1/16*(b*x^2 + a)^(7/2)*B*b^2/(a^3*x^2) + 1/128*(b*x^2 + a)^(7/2)*A*b^3/(a^4*x^2) - 1/24*(b*x^2 + a)^(7/2)*B*b/(a^2*x^4) + 1/192*(b*x^2 + a)^(7/2)*A*b^2/(a^3*x^4) - 1/6*(b*x^2 + a)^(7/2)*B/(a*x^6) + 1/48*(b*x^2 + a)^(7/2)*A*b/(a^2*x^6) - 1/8*(b*x^2 + a)^(7/2)*A/(a*x^8)","B",0
553,1,56,0,1.052039," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^10,x, algorithm=""maxima"")","-\frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{7 \, a x^{7}} + \frac{2 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{63 \, a^{2} x^{7}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{9 \, a x^{9}}"," ",0,"-1/7*(b*x^2 + a)^(7/2)*B/(a*x^7) + 2/63*(b*x^2 + a)^(7/2)*A*b/(a^2*x^7) - 1/9*(b*x^2 + a)^(7/2)*A/(a*x^9)","A",0
554,1,330,0,1.269749," ","integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^11,x, algorithm=""maxima"")","\frac{5 \, B b^{4} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{128 \, a^{\frac{3}{2}}} - \frac{3 \, A b^{5} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{256 \, a^{\frac{5}{2}}} - \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}} B b^{4}}{128 \, a^{4}} - \frac{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} B b^{4}}{384 \, a^{3}} - \frac{5 \, \sqrt{b x^{2} + a} B b^{4}}{128 \, a^{2}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{5}{2}} A b^{5}}{1280 \, a^{5}} + \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}} A b^{5}}{256 \, a^{4}} + \frac{3 \, \sqrt{b x^{2} + a} A b^{5}}{256 \, a^{3}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B b^{3}}{128 \, a^{4} x^{2}} - \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{4}}{1280 \, a^{5} x^{2}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B b^{2}}{192 \, a^{3} x^{4}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{3}}{640 \, a^{4} x^{4}} + \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B b}{48 \, a^{2} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A b^{2}}{160 \, a^{3} x^{6}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} B}{8 \, a x^{8}} + \frac{3 \, {\left(b x^{2} + a\right)}^{\frac{7}{2}} A b}{80 \, a^{2} x^{8}} - \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}} A}{10 \, a x^{10}}"," ",0,"5/128*B*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 3/256*A*b^5*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 1/128*(b*x^2 + a)^(5/2)*B*b^4/a^4 - 5/384*(b*x^2 + a)^(3/2)*B*b^4/a^3 - 5/128*sqrt(b*x^2 + a)*B*b^4/a^2 + 3/1280*(b*x^2 + a)^(5/2)*A*b^5/a^5 + 1/256*(b*x^2 + a)^(3/2)*A*b^5/a^4 + 3/256*sqrt(b*x^2 + a)*A*b^5/a^3 + 1/128*(b*x^2 + a)^(7/2)*B*b^3/(a^4*x^2) - 3/1280*(b*x^2 + a)^(7/2)*A*b^4/(a^5*x^2) + 1/192*(b*x^2 + a)^(7/2)*B*b^2/(a^3*x^4) - 1/640*(b*x^2 + a)^(7/2)*A*b^3/(a^4*x^4) + 1/48*(b*x^2 + a)^(7/2)*B*b/(a^2*x^6) - 1/160*(b*x^2 + a)^(7/2)*A*b^2/(a^3*x^6) - 1/8*(b*x^2 + a)^(7/2)*B/(a*x^8) + 3/80*(b*x^2 + a)^(7/2)*A*b/(a^2*x^8) - 1/10*(b*x^2 + a)^(7/2)*A/(a*x^10)","B",0
555,1,132,0,0.959227," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{6}}{7 \, b} - \frac{6 \, \sqrt{b x^{2} + a} B a x^{4}}{35 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A x^{4}}{5 \, b} + \frac{8 \, \sqrt{b x^{2} + a} B a^{2} x^{2}}{35 \, b^{3}} - \frac{4 \, \sqrt{b x^{2} + a} A a x^{2}}{15 \, b^{2}} - \frac{16 \, \sqrt{b x^{2} + a} B a^{3}}{35 \, b^{4}} + \frac{8 \, \sqrt{b x^{2} + a} A a^{2}}{15 \, b^{3}}"," ",0,"1/7*sqrt(b*x^2 + a)*B*x^6/b - 6/35*sqrt(b*x^2 + a)*B*a*x^4/b^2 + 1/5*sqrt(b*x^2 + a)*A*x^4/b + 8/35*sqrt(b*x^2 + a)*B*a^2*x^2/b^3 - 4/15*sqrt(b*x^2 + a)*A*a*x^2/b^2 - 16/35*sqrt(b*x^2 + a)*B*a^3/b^4 + 8/15*sqrt(b*x^2 + a)*A*a^2/b^3","A",0
556,1,128,0,1.061799," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{5}}{6 \, b} - \frac{5 \, \sqrt{b x^{2} + a} B a x^{3}}{24 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A x^{3}}{4 \, b} + \frac{5 \, \sqrt{b x^{2} + a} B a^{2} x}{16 \, b^{3}} - \frac{3 \, \sqrt{b x^{2} + a} A a x}{8 \, b^{2}} - \frac{5 \, B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{7}{2}}} + \frac{3 \, A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/6*sqrt(b*x^2 + a)*B*x^5/b - 5/24*sqrt(b*x^2 + a)*B*a*x^3/b^2 + 1/4*sqrt(b*x^2 + a)*A*x^3/b + 5/16*sqrt(b*x^2 + a)*B*a^2*x/b^3 - 3/8*sqrt(b*x^2 + a)*A*a*x/b^2 - 5/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(7/2) + 3/8*A*a^2*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
557,1,90,0,1.024259," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{4}}{5 \, b} - \frac{4 \, \sqrt{b x^{2} + a} B a x^{2}}{15 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A x^{2}}{3 \, b} + \frac{8 \, \sqrt{b x^{2} + a} B a^{2}}{15 \, b^{3}} - \frac{2 \, \sqrt{b x^{2} + a} A a}{3 \, b^{2}}"," ",0,"1/5*sqrt(b*x^2 + a)*B*x^4/b - 4/15*sqrt(b*x^2 + a)*B*a*x^2/b^2 + 1/3*sqrt(b*x^2 + a)*A*x^2/b + 8/15*sqrt(b*x^2 + a)*B*a^2/b^3 - 2/3*sqrt(b*x^2 + a)*A*a/b^2","A",0
558,1,86,0,1.082739," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{3}}{4 \, b} - \frac{3 \, \sqrt{b x^{2} + a} B a x}{8 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A x}{2 \, b} + \frac{3 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{5}{2}}} - \frac{A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/4*sqrt(b*x^2 + a)*B*x^3/b - 3/8*sqrt(b*x^2 + a)*B*a*x/b^2 + 1/2*sqrt(b*x^2 + a)*A*x/b + 3/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(5/2) - 1/2*A*a*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
559,1,49,0,0.995303," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x^{2}}{3 \, b} - \frac{2 \, \sqrt{b x^{2} + a} B a}{3 \, b^{2}} + \frac{\sqrt{b x^{2} + a} A}{b}"," ",0,"1/3*sqrt(b*x^2 + a)*B*x^2/b - 2/3*sqrt(b*x^2 + a)*B*a/b^2 + sqrt(b*x^2 + a)*A/b","A",0
560,1,47,0,1.158335," ","integrate((B*x^2+A)/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{b x^{2} + a} B x}{2 \, b} - \frac{B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{3}{2}}} + \frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}}"," ",0,"1/2*sqrt(b*x^2 + a)*B*x/b - 1/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(3/2) + A*arcsinh(b*x/sqrt(a*b))/sqrt(b)","A",0
561,1,33,0,1.054794," ","integrate((B*x^2+A)/x/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} + \frac{\sqrt{b x^{2} + a} B}{b}"," ",0,"-A*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + sqrt(b*x^2 + a)*B/b","A",0
562,1,33,0,1.094550," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{b}} - \frac{\sqrt{b x^{2} + a} A}{a x}"," ",0,"B*arcsinh(b*x/sqrt(a*b))/sqrt(b) - sqrt(b*x^2 + a)*A/(a*x)","A",0
563,1,56,0,1.106077," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{\sqrt{a}} + \frac{A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{\sqrt{b x^{2} + a} A}{2 \, a x^{2}}"," ",0,"-B*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 1/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 1/2*sqrt(b*x^2 + a)*A/(a*x^2)","A",0
564,1,56,0,1.121358," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{b x^{2} + a} B}{a x} + \frac{2 \, \sqrt{b x^{2} + a} A b}{3 \, a^{2} x} - \frac{\sqrt{b x^{2} + a} A}{3 \, a x^{3}}"," ",0,"-sqrt(b*x^2 + a)*B/(a*x) + 2/3*sqrt(b*x^2 + a)*A*b/(a^2*x) - 1/3*sqrt(b*x^2 + a)*A/(a*x^3)","A",0
565,1,96,0,1.064268," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{B b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{3}{2}}} - \frac{3 \, A b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{5}{2}}} - \frac{\sqrt{b x^{2} + a} B}{2 \, a x^{2}} + \frac{3 \, \sqrt{b x^{2} + a} A b}{8 \, a^{2} x^{2}} - \frac{\sqrt{b x^{2} + a} A}{4 \, a x^{4}}"," ",0,"1/2*B*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) - 3/8*A*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 1/2*sqrt(b*x^2 + a)*B/(a*x^2) + 3/8*sqrt(b*x^2 + a)*A*b/(a^2*x^2) - 1/4*sqrt(b*x^2 + a)*A/(a*x^4)","A",0
566,1,96,0,1.020605," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{b x^{2} + a} B b}{3 \, a^{2} x} - \frac{8 \, \sqrt{b x^{2} + a} A b^{2}}{15 \, a^{3} x} - \frac{\sqrt{b x^{2} + a} B}{3 \, a x^{3}} + \frac{4 \, \sqrt{b x^{2} + a} A b}{15 \, a^{2} x^{3}} - \frac{\sqrt{b x^{2} + a} A}{5 \, a x^{5}}"," ",0,"2/3*sqrt(b*x^2 + a)*B*b/(a^2*x) - 8/15*sqrt(b*x^2 + a)*A*b^2/(a^3*x) - 1/3*sqrt(b*x^2 + a)*B/(a*x^3) + 4/15*sqrt(b*x^2 + a)*A*b/(a^2*x^3) - 1/5*sqrt(b*x^2 + a)*A/(a*x^5)","A",0
567,1,138,0,0.995593," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, B b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{5}{2}}} + \frac{5 \, A b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{7}{2}}} + \frac{3 \, \sqrt{b x^{2} + a} B b}{8 \, a^{2} x^{2}} - \frac{5 \, \sqrt{b x^{2} + a} A b^{2}}{16 \, a^{3} x^{2}} - \frac{\sqrt{b x^{2} + a} B}{4 \, a x^{4}} + \frac{5 \, \sqrt{b x^{2} + a} A b}{24 \, a^{2} x^{4}} - \frac{\sqrt{b x^{2} + a} A}{6 \, a x^{6}}"," ",0,"-3/8*B*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 5/16*A*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) + 3/8*sqrt(b*x^2 + a)*B*b/(a^2*x^2) - 5/16*sqrt(b*x^2 + a)*A*b^2/(a^3*x^2) - 1/4*sqrt(b*x^2 + a)*B/(a*x^4) + 5/24*sqrt(b*x^2 + a)*A*b/(a^2*x^4) - 1/6*sqrt(b*x^2 + a)*A/(a*x^6)","A",0
568,1,138,0,1.097528," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(1/2),x, algorithm=""maxima"")","-\frac{8 \, \sqrt{b x^{2} + a} B b^{2}}{15 \, a^{3} x} + \frac{16 \, \sqrt{b x^{2} + a} A b^{3}}{35 \, a^{4} x} + \frac{4 \, \sqrt{b x^{2} + a} B b}{15 \, a^{2} x^{3}} - \frac{8 \, \sqrt{b x^{2} + a} A b^{2}}{35 \, a^{3} x^{3}} - \frac{\sqrt{b x^{2} + a} B}{5 \, a x^{5}} + \frac{6 \, \sqrt{b x^{2} + a} A b}{35 \, a^{2} x^{5}} - \frac{\sqrt{b x^{2} + a} A}{7 \, a x^{7}}"," ",0,"-8/15*sqrt(b*x^2 + a)*B*b^2/(a^3*x) + 16/35*sqrt(b*x^2 + a)*A*b^3/(a^4*x) + 4/15*sqrt(b*x^2 + a)*B*b/(a^2*x^3) - 8/35*sqrt(b*x^2 + a)*A*b^2/(a^3*x^3) - 1/5*sqrt(b*x^2 + a)*B/(a*x^5) + 6/35*sqrt(b*x^2 + a)*A*b/(a^2*x^5) - 1/7*sqrt(b*x^2 + a)*A/(a*x^7)","A",0
569,1,170,0,1.060391," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{7}}{6 \, \sqrt{b x^{2} + a} b} - \frac{7 \, B a x^{5}}{24 \, \sqrt{b x^{2} + a} b^{2}} + \frac{A x^{5}}{4 \, \sqrt{b x^{2} + a} b} + \frac{35 \, B a^{2} x^{3}}{48 \, \sqrt{b x^{2} + a} b^{3}} - \frac{5 \, A a x^{3}}{8 \, \sqrt{b x^{2} + a} b^{2}} + \frac{35 \, B a^{3} x}{16 \, \sqrt{b x^{2} + a} b^{4}} - \frac{15 \, A a^{2} x}{8 \, \sqrt{b x^{2} + a} b^{3}} - \frac{35 \, B a^{3} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{16 \, b^{\frac{9}{2}}} + \frac{15 \, A a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{7}{2}}}"," ",0,"1/6*B*x^7/(sqrt(b*x^2 + a)*b) - 7/24*B*a*x^5/(sqrt(b*x^2 + a)*b^2) + 1/4*A*x^5/(sqrt(b*x^2 + a)*b) + 35/48*B*a^2*x^3/(sqrt(b*x^2 + a)*b^3) - 5/8*A*a*x^3/(sqrt(b*x^2 + a)*b^2) + 35/16*B*a^3*x/(sqrt(b*x^2 + a)*b^4) - 15/8*A*a^2*x/(sqrt(b*x^2 + a)*b^3) - 35/16*B*a^3*arcsinh(b*x/sqrt(a*b))/b^(9/2) + 15/8*A*a^2*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
570,1,132,0,1.089420," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{6}}{5 \, \sqrt{b x^{2} + a} b} - \frac{2 \, B a x^{4}}{5 \, \sqrt{b x^{2} + a} b^{2}} + \frac{A x^{4}}{3 \, \sqrt{b x^{2} + a} b} + \frac{8 \, B a^{2} x^{2}}{5 \, \sqrt{b x^{2} + a} b^{3}} - \frac{4 \, A a x^{2}}{3 \, \sqrt{b x^{2} + a} b^{2}} + \frac{16 \, B a^{3}}{5 \, \sqrt{b x^{2} + a} b^{4}} - \frac{8 \, A a^{2}}{3 \, \sqrt{b x^{2} + a} b^{3}}"," ",0,"1/5*B*x^6/(sqrt(b*x^2 + a)*b) - 2/5*B*a*x^4/(sqrt(b*x^2 + a)*b^2) + 1/3*A*x^4/(sqrt(b*x^2 + a)*b) + 8/5*B*a^2*x^2/(sqrt(b*x^2 + a)*b^3) - 4/3*A*a*x^2/(sqrt(b*x^2 + a)*b^2) + 16/5*B*a^3/(sqrt(b*x^2 + a)*b^4) - 8/3*A*a^2/(sqrt(b*x^2 + a)*b^3)","A",0
571,1,126,0,1.146133," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{5}}{4 \, \sqrt{b x^{2} + a} b} - \frac{5 \, B a x^{3}}{8 \, \sqrt{b x^{2} + a} b^{2}} + \frac{A x^{3}}{2 \, \sqrt{b x^{2} + a} b} - \frac{15 \, B a^{2} x}{8 \, \sqrt{b x^{2} + a} b^{3}} + \frac{3 \, A a x}{2 \, \sqrt{b x^{2} + a} b^{2}} + \frac{15 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{7}{2}}} - \frac{3 \, A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{5}{2}}}"," ",0,"1/4*B*x^5/(sqrt(b*x^2 + a)*b) - 5/8*B*a*x^3/(sqrt(b*x^2 + a)*b^2) + 1/2*A*x^3/(sqrt(b*x^2 + a)*b) - 15/8*B*a^2*x/(sqrt(b*x^2 + a)*b^3) + 3/2*A*a*x/(sqrt(b*x^2 + a)*b^2) + 15/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(7/2) - 3/2*A*a*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
572,1,89,0,1.042820," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{4}}{3 \, \sqrt{b x^{2} + a} b} - \frac{4 \, B a x^{2}}{3 \, \sqrt{b x^{2} + a} b^{2}} + \frac{A x^{2}}{\sqrt{b x^{2} + a} b} - \frac{8 \, B a^{2}}{3 \, \sqrt{b x^{2} + a} b^{3}} + \frac{2 \, A a}{\sqrt{b x^{2} + a} b^{2}}"," ",0,"1/3*B*x^4/(sqrt(b*x^2 + a)*b) - 4/3*B*a*x^2/(sqrt(b*x^2 + a)*b^2) + A*x^2/(sqrt(b*x^2 + a)*b) - 8/3*B*a^2/(sqrt(b*x^2 + a)*b^3) + 2*A*a/(sqrt(b*x^2 + a)*b^2)","A",0
573,1,82,0,1.007352," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{3}}{2 \, \sqrt{b x^{2} + a} b} + \frac{3 \, B a x}{2 \, \sqrt{b x^{2} + a} b^{2}} - \frac{A x}{\sqrt{b x^{2} + a} b} - \frac{3 \, B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{5}{2}}} + \frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}}"," ",0,"1/2*B*x^3/(sqrt(b*x^2 + a)*b) + 3/2*B*a*x/(sqrt(b*x^2 + a)*b^2) - A*x/(sqrt(b*x^2 + a)*b) - 3/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(5/2) + A*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
574,1,49,0,1.040109," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x^{2}}{\sqrt{b x^{2} + a} b} + \frac{2 \, B a}{\sqrt{b x^{2} + a} b^{2}} - \frac{A}{\sqrt{b x^{2} + a} b}"," ",0,"B*x^2/(sqrt(b*x^2 + a)*b) + 2*B*a/(sqrt(b*x^2 + a)*b^2) - A/(sqrt(b*x^2 + a)*b)","A",0
575,1,46,0,1.006409," ","integrate((B*x^2+A)/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{A x}{\sqrt{b x^{2} + a} a} - \frac{B x}{\sqrt{b x^{2} + a} b} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{3}{2}}}"," ",0,"A*x/(sqrt(b*x^2 + a)*a) - B*x/(sqrt(b*x^2 + a)*b) + B*arcsinh(b*x/sqrt(a*b))/b^(3/2)","A",0
576,1,48,0,1.057093," ","integrate((B*x^2+A)/x/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{3}{2}}} + \frac{A}{\sqrt{b x^{2} + a} a} - \frac{B}{\sqrt{b x^{2} + a} b}"," ",0,"-A*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + A/(sqrt(b*x^2 + a)*a) - B/(sqrt(b*x^2 + a)*b)","A",0
577,1,51,0,1.044591," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{B x}{\sqrt{b x^{2} + a} a} - \frac{2 \, A b x}{\sqrt{b x^{2} + a} a^{2}} - \frac{A}{\sqrt{b x^{2} + a} a x}"," ",0,"B*x/(sqrt(b*x^2 + a)*a) - 2*A*b*x/(sqrt(b*x^2 + a)*a^2) - A/(sqrt(b*x^2 + a)*a*x)","A",0
578,1,86,0,1.079137," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{3}{2}}} + \frac{3 \, A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{5}{2}}} + \frac{B}{\sqrt{b x^{2} + a} a} - \frac{3 \, A b}{2 \, \sqrt{b x^{2} + a} a^{2}} - \frac{A}{2 \, \sqrt{b x^{2} + a} a x^{2}}"," ",0,"-B*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 3/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + B/(sqrt(b*x^2 + a)*a) - 3/2*A*b/(sqrt(b*x^2 + a)*a^2) - 1/2*A/(sqrt(b*x^2 + a)*a*x^2)","A",0
579,1,92,0,1.008186," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, B b x}{\sqrt{b x^{2} + a} a^{2}} + \frac{8 \, A b^{2} x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{B}{\sqrt{b x^{2} + a} a x} + \frac{4 \, A b}{3 \, \sqrt{b x^{2} + a} a^{2} x} - \frac{A}{3 \, \sqrt{b x^{2} + a} a x^{3}}"," ",0,"-2*B*b*x/(sqrt(b*x^2 + a)*a^2) + 8/3*A*b^2*x/(sqrt(b*x^2 + a)*a^3) - B/(sqrt(b*x^2 + a)*a*x) + 4/3*A*b/(sqrt(b*x^2 + a)*a^2*x) - 1/3*A/(sqrt(b*x^2 + a)*a*x^3)","A",0
580,1,130,0,1.043578," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{3 \, B b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{5}{2}}} - \frac{15 \, A b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{7}{2}}} - \frac{3 \, B b}{2 \, \sqrt{b x^{2} + a} a^{2}} + \frac{15 \, A b^{2}}{8 \, \sqrt{b x^{2} + a} a^{3}} - \frac{B}{2 \, \sqrt{b x^{2} + a} a x^{2}} + \frac{5 \, A b}{8 \, \sqrt{b x^{2} + a} a^{2} x^{2}} - \frac{A}{4 \, \sqrt{b x^{2} + a} a x^{4}}"," ",0,"3/2*B*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) - 15/8*A*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 3/2*B*b/(sqrt(b*x^2 + a)*a^2) + 15/8*A*b^2/(sqrt(b*x^2 + a)*a^3) - 1/2*B/(sqrt(b*x^2 + a)*a*x^2) + 5/8*A*b/(sqrt(b*x^2 + a)*a^2*x^2) - 1/4*A/(sqrt(b*x^2 + a)*a*x^4)","A",0
581,1,134,0,1.052196," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{8 \, B b^{2} x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{16 \, A b^{3} x}{5 \, \sqrt{b x^{2} + a} a^{4}} + \frac{4 \, B b}{3 \, \sqrt{b x^{2} + a} a^{2} x} - \frac{8 \, A b^{2}}{5 \, \sqrt{b x^{2} + a} a^{3} x} - \frac{B}{3 \, \sqrt{b x^{2} + a} a x^{3}} + \frac{2 \, A b}{5 \, \sqrt{b x^{2} + a} a^{2} x^{3}} - \frac{A}{5 \, \sqrt{b x^{2} + a} a x^{5}}"," ",0,"8/3*B*b^2*x/(sqrt(b*x^2 + a)*a^3) - 16/5*A*b^3*x/(sqrt(b*x^2 + a)*a^4) + 4/3*B*b/(sqrt(b*x^2 + a)*a^2*x) - 8/5*A*b^2/(sqrt(b*x^2 + a)*a^3*x) - 1/3*B/(sqrt(b*x^2 + a)*a*x^3) + 2/5*A*b/(sqrt(b*x^2 + a)*a^2*x^3) - 1/5*A/(sqrt(b*x^2 + a)*a*x^5)","A",0
582,1,174,0,1.048923," ","integrate((B*x^2+A)/x^7/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{15 \, B b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{7}{2}}} + \frac{35 \, A b^{3} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{16 \, a^{\frac{9}{2}}} + \frac{15 \, B b^{2}}{8 \, \sqrt{b x^{2} + a} a^{3}} - \frac{35 \, A b^{3}}{16 \, \sqrt{b x^{2} + a} a^{4}} + \frac{5 \, B b}{8 \, \sqrt{b x^{2} + a} a^{2} x^{2}} - \frac{35 \, A b^{2}}{48 \, \sqrt{b x^{2} + a} a^{3} x^{2}} - \frac{B}{4 \, \sqrt{b x^{2} + a} a x^{4}} + \frac{7 \, A b}{24 \, \sqrt{b x^{2} + a} a^{2} x^{4}} - \frac{A}{6 \, \sqrt{b x^{2} + a} a x^{6}}"," ",0,"-15/8*B*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) + 35/16*A*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) + 15/8*B*b^2/(sqrt(b*x^2 + a)*a^3) - 35/16*A*b^3/(sqrt(b*x^2 + a)*a^4) + 5/8*B*b/(sqrt(b*x^2 + a)*a^2*x^2) - 35/48*A*b^2/(sqrt(b*x^2 + a)*a^3*x^2) - 1/4*B/(sqrt(b*x^2 + a)*a*x^4) + 7/24*A*b/(sqrt(b*x^2 + a)*a^2*x^4) - 1/6*A/(sqrt(b*x^2 + a)*a*x^6)","A",0
583,1,176,0,1.063367," ","integrate((B*x^2+A)/x^8/(b*x^2+a)^(3/2),x, algorithm=""maxima"")","-\frac{16 \, B b^{3} x}{5 \, \sqrt{b x^{2} + a} a^{4}} + \frac{128 \, A b^{4} x}{35 \, \sqrt{b x^{2} + a} a^{5}} - \frac{8 \, B b^{2}}{5 \, \sqrt{b x^{2} + a} a^{3} x} + \frac{64 \, A b^{3}}{35 \, \sqrt{b x^{2} + a} a^{4} x} + \frac{2 \, B b}{5 \, \sqrt{b x^{2} + a} a^{2} x^{3}} - \frac{16 \, A b^{2}}{35 \, \sqrt{b x^{2} + a} a^{3} x^{3}} - \frac{B}{5 \, \sqrt{b x^{2} + a} a x^{5}} + \frac{8 \, A b}{35 \, \sqrt{b x^{2} + a} a^{2} x^{5}} - \frac{A}{7 \, \sqrt{b x^{2} + a} a x^{7}}"," ",0,"-16/5*B*b^3*x/(sqrt(b*x^2 + a)*a^4) + 128/35*A*b^4*x/(sqrt(b*x^2 + a)*a^5) - 8/5*B*b^2/(sqrt(b*x^2 + a)*a^3*x) + 64/35*A*b^3/(sqrt(b*x^2 + a)*a^4*x) + 2/5*B*b/(sqrt(b*x^2 + a)*a^2*x^3) - 16/35*A*b^2/(sqrt(b*x^2 + a)*a^3*x^3) - 1/5*B/(sqrt(b*x^2 + a)*a*x^5) + 8/35*A*b/(sqrt(b*x^2 + a)*a^2*x^5) - 1/7*A/(sqrt(b*x^2 + a)*a*x^7)","A",0
584,1,174,0,1.211898," ","integrate(x^7*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{B x^{8}}{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{8 \, B a x^{6}}{15 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} + \frac{A x^{6}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{16 \, B a^{2} x^{4}}{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} - \frac{2 \, A a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} + \frac{64 \, B a^{3} x^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} - \frac{8 \, A a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{128 \, B a^{4}}{15 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{5}} - \frac{16 \, A a^{3}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}}"," ",0,"1/5*B*x^8/((b*x^2 + a)^(3/2)*b) - 8/15*B*a*x^6/((b*x^2 + a)^(3/2)*b^2) + 1/3*A*x^6/((b*x^2 + a)^(3/2)*b) + 16/5*B*a^2*x^4/((b*x^2 + a)^(3/2)*b^3) - 2*A*a*x^4/((b*x^2 + a)^(3/2)*b^2) + 64/5*B*a^3*x^2/((b*x^2 + a)^(3/2)*b^4) - 8*A*a^2*x^2/((b*x^2 + a)^(3/2)*b^3) + 128/15*B*a^4/((b*x^2 + a)^(3/2)*b^5) - 16/3*A*a^3/((b*x^2 + a)^(3/2)*b^4)","A",0
585,1,210,0,1.093705," ","integrate(x^6*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{B x^{7}}{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{7 \, B a x^{5}}{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} + \frac{A x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{35 \, B a^{2} x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{24 \, b^{2}} + \frac{5 \, A a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{6 \, b} - \frac{35 \, B a^{2} x}{24 \, \sqrt{b x^{2} + a} b^{4}} + \frac{5 \, A a x}{6 \, \sqrt{b x^{2} + a} b^{3}} + \frac{35 \, B a^{2} \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, b^{\frac{9}{2}}} - \frac{5 \, A a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{7}{2}}}"," ",0,"1/4*B*x^7/((b*x^2 + a)^(3/2)*b) - 7/8*B*a*x^5/((b*x^2 + a)^(3/2)*b^2) + 1/2*A*x^5/((b*x^2 + a)^(3/2)*b) - 35/24*B*a^2*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b^2 + 5/6*A*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b - 35/24*B*a^2*x/(sqrt(b*x^2 + a)*b^4) + 5/6*A*a*x/(sqrt(b*x^2 + a)*b^3) + 35/8*B*a^2*arcsinh(b*x/sqrt(a*b))/b^(9/2) - 5/2*A*a*arcsinh(b*x/sqrt(a*b))/b^(7/2)","A",0
586,1,131,0,1.160588," ","integrate(x^5*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{B x^{6}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{2 \, B a x^{4}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} + \frac{A x^{4}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{8 \, B a^{2} x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} + \frac{4 \, A a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} - \frac{16 \, B a^{3}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{4}} + \frac{8 \, A a^{2}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}}"," ",0,"1/3*B*x^6/((b*x^2 + a)^(3/2)*b) - 2*B*a*x^4/((b*x^2 + a)^(3/2)*b^2) + A*x^4/((b*x^2 + a)^(3/2)*b) - 8*B*a^2*x^2/((b*x^2 + a)^(3/2)*b^3) + 4*A*a*x^2/((b*x^2 + a)^(3/2)*b^2) - 16/3*B*a^3/((b*x^2 + a)^(3/2)*b^4) + 8/3*A*a^2/((b*x^2 + a)^(3/2)*b^3)","A",0
587,1,160,0,1.125540," ","integrate(x^4*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{B x^{5}}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{1}{3} \, A x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} + \frac{5 \, B a x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)}}{6 \, b} + \frac{5 \, B a x}{6 \, \sqrt{b x^{2} + a} b^{3}} - \frac{A x}{3 \, \sqrt{b x^{2} + a} b^{2}} - \frac{5 \, B a \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, b^{\frac{7}{2}}} + \frac{A \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}}"," ",0,"1/2*B*x^5/((b*x^2 + a)^(3/2)*b) - 1/3*A*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) + 5/6*B*a*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2))/b + 5/6*B*a*x/(sqrt(b*x^2 + a)*b^3) - 1/3*A*x/(sqrt(b*x^2 + a)*b^2) - 5/2*B*a*arcsinh(b*x/sqrt(a*b))/b^(7/2) + A*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
588,1,89,0,1.073524," ","integrate(x^3*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{B x^{4}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{4 \, B a x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} - \frac{A x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{8 \, B a^{2}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{3}} - \frac{2 \, A a}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}"," ",0,"B*x^4/((b*x^2 + a)^(3/2)*b) + 4*B*a*x^2/((b*x^2 + a)^(3/2)*b^2) - A*x^2/((b*x^2 + a)^(3/2)*b) + 8/3*B*a^2/((b*x^2 + a)^(3/2)*b^3) - 2/3*A*a/((b*x^2 + a)^(3/2)*b^2)","A",0
589,1,103,0,1.017140," ","integrate(x^2*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, B x {\left(\frac{3 \, x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{2 \, a}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}}\right)} - \frac{B x}{3 \, \sqrt{b x^{2} + a} b^{2}} - \frac{A x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{A x}{3 \, \sqrt{b x^{2} + a} a b} + \frac{B \operatorname{arsinh}\left(\frac{b x}{\sqrt{a b}}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*B*x*(3*x^2/((b*x^2 + a)^(3/2)*b) + 2*a/((b*x^2 + a)^(3/2)*b^2)) - 1/3*B*x/(sqrt(b*x^2 + a)*b^2) - 1/3*A*x/((b*x^2 + a)^(3/2)*b) + 1/3*A*x/(sqrt(b*x^2 + a)*a*b) + B*arcsinh(b*x/sqrt(a*b))/b^(5/2)","A",0
590,1,50,0,1.016926," ","integrate(x*(B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{B x^{2}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} b} - \frac{2 \, B a}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b^{2}} - \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"-B*x^2/((b*x^2 + a)^(3/2)*b) - 2/3*B*a/((b*x^2 + a)^(3/2)*b^2) - 1/3*A/((b*x^2 + a)^(3/2)*b)","A",0
591,1,68,0,1.008115," ","integrate((B*x^2+A)/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, A x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{A x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{B x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b} + \frac{B x}{3 \, \sqrt{b x^{2} + a} a b}"," ",0,"2/3*A*x/(sqrt(b*x^2 + a)*a^2) + 1/3*A*x/((b*x^2 + a)^(3/2)*a) - 1/3*B*x/((b*x^2 + a)^(3/2)*b) + 1/3*B*x/(sqrt(b*x^2 + a)*a*b)","A",0
592,1,63,0,1.038229," ","integrate((B*x^2+A)/x/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{A \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{5}{2}}} + \frac{A}{\sqrt{b x^{2} + a} a^{2}} + \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} b}"," ",0,"-A*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + A/(sqrt(b*x^2 + a)*a^2) + 1/3*A/((b*x^2 + a)^(3/2)*a) - 1/3*B/((b*x^2 + a)^(3/2)*b)","A",0
593,1,85,0,1.126163," ","integrate((B*x^2+A)/x^2/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{2 \, B x}{3 \, \sqrt{b x^{2} + a} a^{2}} + \frac{B x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{8 \, A b x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{4 \, A b x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{A}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a x}"," ",0,"2/3*B*x/(sqrt(b*x^2 + a)*a^2) + 1/3*B*x/((b*x^2 + a)^(3/2)*a) - 8/3*A*b*x/(sqrt(b*x^2 + a)*a^3) - 4/3*A*b*x/((b*x^2 + a)^(3/2)*a^2) - A/((b*x^2 + a)^(3/2)*a*x)","A",0
594,1,117,0,0.953076," ","integrate((B*x^2+A)/x^3/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{B \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{a^{\frac{5}{2}}} + \frac{5 \, A b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{7}{2}}} + \frac{B}{\sqrt{b x^{2} + a} a^{2}} + \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a} - \frac{5 \, A b}{2 \, \sqrt{b x^{2} + a} a^{3}} - \frac{5 \, A b}{6 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{A}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{2}}"," ",0,"-B*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(5/2) + 5/2*A*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) + B/(sqrt(b*x^2 + a)*a^2) + 1/3*B/((b*x^2 + a)^(3/2)*a) - 5/2*A*b/(sqrt(b*x^2 + a)*a^3) - 5/6*A*b/((b*x^2 + a)^(3/2)*a^2) - 1/2*A/((b*x^2 + a)^(3/2)*a*x^2)","A",0
595,1,128,0,1.125550," ","integrate((B*x^2+A)/x^4/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","-\frac{8 \, B b x}{3 \, \sqrt{b x^{2} + a} a^{3}} - \frac{4 \, B b x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{16 \, A b^{2} x}{3 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, A b^{2} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} - \frac{B}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a x} + \frac{2 \, A b}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} x} - \frac{A}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{3}}"," ",0,"-8/3*B*b*x/(sqrt(b*x^2 + a)*a^3) - 4/3*B*b*x/((b*x^2 + a)^(3/2)*a^2) + 16/3*A*b^2*x/(sqrt(b*x^2 + a)*a^4) + 8/3*A*b^2*x/((b*x^2 + a)^(3/2)*a^3) - B/((b*x^2 + a)^(3/2)*a*x) + 2*A*b/((b*x^2 + a)^(3/2)*a^2*x) - 1/3*A/((b*x^2 + a)^(3/2)*a*x^3)","A",0
596,1,164,0,1.099758," ","integrate((B*x^2+A)/x^5/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{5 \, B b \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{2 \, a^{\frac{7}{2}}} - \frac{35 \, A b^{2} \operatorname{arsinh}\left(\frac{a}{\sqrt{a b} {\left| x \right|}}\right)}{8 \, a^{\frac{9}{2}}} - \frac{5 \, B b}{2 \, \sqrt{b x^{2} + a} a^{3}} - \frac{5 \, B b}{6 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{35 \, A b^{2}}{8 \, \sqrt{b x^{2} + a} a^{4}} + \frac{35 \, A b^{2}}{24 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} - \frac{B}{2 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{2}} + \frac{7 \, A b}{8 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} x^{2}} - \frac{A}{4 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{4}}"," ",0,"5/2*B*b*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(7/2) - 35/8*A*b^2*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(9/2) - 5/2*B*b/(sqrt(b*x^2 + a)*a^3) - 5/6*B*b/((b*x^2 + a)^(3/2)*a^2) + 35/8*A*b^2/(sqrt(b*x^2 + a)*a^4) + 35/24*A*b^2/((b*x^2 + a)^(3/2)*a^3) - 1/2*B/((b*x^2 + a)^(3/2)*a*x^2) + 7/8*A*b/((b*x^2 + a)^(3/2)*a^2*x^2) - 1/4*A/((b*x^2 + a)^(3/2)*a*x^4)","A",0
597,1,172,0,1.180884," ","integrate((B*x^2+A)/x^6/(b*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{16 \, B b^{2} x}{3 \, \sqrt{b x^{2} + a} a^{4}} + \frac{8 \, B b^{2} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3}} - \frac{128 \, A b^{3} x}{15 \, \sqrt{b x^{2} + a} a^{5}} - \frac{64 \, A b^{3} x}{15 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{4}} + \frac{2 \, B b}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} x} - \frac{16 \, A b^{2}}{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{3} x} - \frac{B}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{3}} + \frac{8 \, A b}{15 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a^{2} x^{3}} - \frac{A}{5 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}} a x^{5}}"," ",0,"16/3*B*b^2*x/(sqrt(b*x^2 + a)*a^4) + 8/3*B*b^2*x/((b*x^2 + a)^(3/2)*a^3) - 128/15*A*b^3*x/(sqrt(b*x^2 + a)*a^5) - 64/15*A*b^3*x/((b*x^2 + a)^(3/2)*a^4) + 2*B*b/((b*x^2 + a)^(3/2)*a^2*x) - 16/5*A*b^2/((b*x^2 + a)^(3/2)*a^3*x) - 1/3*B/((b*x^2 + a)^(3/2)*a*x^3) + 8/15*A*b/((b*x^2 + a)^(3/2)*a^2*x^3) - 1/5*A/((b*x^2 + a)^(3/2)*a*x^5)","A",0
598,1,249,0,1.078548," ","integrate(x^5*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{8}}{11 \, d} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x^{6}}{99 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x^{6}}{9 \, d} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} x^{4}}{231 \, d^{3}} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c x^{4}}{21 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} x^{4}}{7 \, d} - \frac{64 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} x^{2}}{1155 \, d^{4}} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} x^{2}}{105 \, d^{3}} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c x^{2}}{35 \, d^{2}} + \frac{128 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{4}}{3465 \, d^{5}} - \frac{32 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{3}}{315 \, d^{4}} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c^{2}}{105 \, d^{3}}"," ",0,"1/11*(d*x^2 + c)^(3/2)*b^2*x^8/d - 8/99*(d*x^2 + c)^(3/2)*b^2*c*x^6/d^2 + 2/9*(d*x^2 + c)^(3/2)*a*b*x^6/d + 16/231*(d*x^2 + c)^(3/2)*b^2*c^2*x^4/d^3 - 4/21*(d*x^2 + c)^(3/2)*a*b*c*x^4/d^2 + 1/7*(d*x^2 + c)^(3/2)*a^2*x^4/d - 64/1155*(d*x^2 + c)^(3/2)*b^2*c^3*x^2/d^4 + 16/105*(d*x^2 + c)^(3/2)*a*b*c^2*x^2/d^3 - 4/35*(d*x^2 + c)^(3/2)*a^2*c*x^2/d^2 + 128/3465*(d*x^2 + c)^(3/2)*b^2*c^4/d^5 - 32/315*(d*x^2 + c)^(3/2)*a*b*c^3/d^4 + 8/105*(d*x^2 + c)^(3/2)*a^2*c^2/d^3","A",0
599,1,181,0,1.033656," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{6}}{9 \, d} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x^{4}}{21 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x^{4}}{7 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} x^{2}}{105 \, d^{3}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c x^{2}}{35 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} x^{2}}{5 \, d} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3}}{315 \, d^{4}} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2}}{105 \, d^{3}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c}{15 \, d^{2}}"," ",0,"1/9*(d*x^2 + c)^(3/2)*b^2*x^6/d - 2/21*(d*x^2 + c)^(3/2)*b^2*c*x^4/d^2 + 2/7*(d*x^2 + c)^(3/2)*a*b*x^4/d + 8/105*(d*x^2 + c)^(3/2)*b^2*c^2*x^2/d^3 - 8/35*(d*x^2 + c)^(3/2)*a*b*c*x^2/d^2 + 1/5*(d*x^2 + c)^(3/2)*a^2*x^2/d - 16/315*(d*x^2 + c)^(3/2)*b^2*c^3/d^4 + 16/105*(d*x^2 + c)^(3/2)*a*b*c^2/d^3 - 2/15*(d*x^2 + c)^(3/2)*a^2*c/d^2","A",0
600,1,115,0,0.918786," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{4}}{7 \, d} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x^{2}}{35 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x^{2}}{5 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2}}{105 \, d^{3}} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c}{15 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{3 \, d}"," ",0,"1/7*(d*x^2 + c)^(3/2)*b^2*x^4/d - 4/35*(d*x^2 + c)^(3/2)*b^2*c*x^2/d^2 + 2/5*(d*x^2 + c)^(3/2)*a*b*x^2/d + 8/105*(d*x^2 + c)^(3/2)*b^2*c^2/d^3 - 4/15*(d*x^2 + c)^(3/2)*a*b*c/d^2 + 1/3*(d*x^2 + c)^(3/2)*a^2/d","A",0
601,1,88,0,1.025138," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{2}}{5 \, d} - a^{2} \sqrt{c} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \sqrt{d x^{2} + c} a^{2} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c}{15 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{3 \, d}"," ",0,"1/5*(d*x^2 + c)^(3/2)*b^2*x^2/d - a^2*sqrt(c)*arcsinh(c/(sqrt(c*d)*abs(x))) + sqrt(d*x^2 + c)*a^2 - 2/15*(d*x^2 + c)^(3/2)*b^2*c/d^2 + 2/3*(d*x^2 + c)^(3/2)*a*b/d","A",0
602,1,109,0,1.063717," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","-2 \, a b \sqrt{c} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{a^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, \sqrt{c}} + 2 \, \sqrt{d x^{2} + c} a b + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{3 \, d} + \frac{\sqrt{d x^{2} + c} a^{2} d}{2 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{2 \, c x^{2}}"," ",0,"-2*a*b*sqrt(c)*arcsinh(c/(sqrt(c*d)*abs(x))) - 1/2*a^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 2*sqrt(d*x^2 + c)*a*b + 1/3*(d*x^2 + c)^(3/2)*b^2/d + 1/2*sqrt(d*x^2 + c)*a^2*d/c - 1/2*(d*x^2 + c)^(3/2)*a^2/(c*x^2)","A",0
603,1,173,0,1.071943," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^5,x, algorithm=""maxima"")","-b^{2} \sqrt{c} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{a b d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{\sqrt{c}} + \frac{a^{2} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{8 \, c^{\frac{3}{2}}} + \sqrt{d x^{2} + c} b^{2} + \frac{\sqrt{d x^{2} + c} a b d}{c} - \frac{\sqrt{d x^{2} + c} a^{2} d^{2}}{8 \, c^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{c x^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{8 \, c^{2} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{4 \, c x^{4}}"," ",0,"-b^2*sqrt(c)*arcsinh(c/(sqrt(c*d)*abs(x))) - a*b*d*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 1/8*a^2*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + sqrt(d*x^2 + c)*b^2 + sqrt(d*x^2 + c)*a*b*d/c - 1/8*sqrt(d*x^2 + c)*a^2*d^2/c^2 - (d*x^2 + c)^(3/2)*a*b/(c*x^2) + 1/8*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^2) - 1/4*(d*x^2 + c)^(3/2)*a^2/(c*x^4)","A",0
604,1,247,0,1.022650," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^7,x, algorithm=""maxima"")","-\frac{b^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, \sqrt{c}} + \frac{a b d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{4 \, c^{\frac{3}{2}}} - \frac{a^{2} d^{3} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{16 \, c^{\frac{5}{2}}} + \frac{\sqrt{d x^{2} + c} b^{2} d}{2 \, c} - \frac{\sqrt{d x^{2} + c} a b d^{2}}{4 \, c^{2}} + \frac{\sqrt{d x^{2} + c} a^{2} d^{3}}{16 \, c^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{2 \, c x^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{4 \, c^{2} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{16 \, c^{3} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{2 \, c x^{4}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{8 \, c^{2} x^{4}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{6 \, c x^{6}}"," ",0,"-1/2*b^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 1/4*a*b*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) - 1/16*a^2*d^3*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + 1/2*sqrt(d*x^2 + c)*b^2*d/c - 1/4*sqrt(d*x^2 + c)*a*b*d^2/c^2 + 1/16*sqrt(d*x^2 + c)*a^2*d^3/c^3 - 1/2*(d*x^2 + c)^(3/2)*b^2/(c*x^2) + 1/4*(d*x^2 + c)^(3/2)*a*b*d/(c^2*x^2) - 1/16*(d*x^2 + c)^(3/2)*a^2*d^2/(c^3*x^2) - 1/2*(d*x^2 + c)^(3/2)*a*b/(c*x^4) + 1/8*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^4) - 1/6*(d*x^2 + c)^(3/2)*a^2/(c*x^6)","A",0
605,1,237,0,1.109774," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{5}}{8 \, d} - \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x^{3}}{48 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x^{3}}{3 \, d} + \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} x}{64 \, d^{3}} - \frac{5 \, \sqrt{d x^{2} + c} b^{2} c^{3} x}{128 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c x}{4 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a b c^{2} x}{8 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} x}{4 \, d} - \frac{\sqrt{d x^{2} + c} a^{2} c x}{8 \, d} - \frac{5 \, b^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{7}{2}}} + \frac{a b c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{5}{2}}} - \frac{a^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{3}{2}}}"," ",0,"1/8*(d*x^2 + c)^(3/2)*b^2*x^5/d - 5/48*(d*x^2 + c)^(3/2)*b^2*c*x^3/d^2 + 1/3*(d*x^2 + c)^(3/2)*a*b*x^3/d + 5/64*(d*x^2 + c)^(3/2)*b^2*c^2*x/d^3 - 5/128*sqrt(d*x^2 + c)*b^2*c^3*x/d^3 - 1/4*(d*x^2 + c)^(3/2)*a*b*c*x/d^2 + 1/8*sqrt(d*x^2 + c)*a*b*c^2*x/d^2 + 1/4*(d*x^2 + c)^(3/2)*a^2*x/d - 1/8*sqrt(d*x^2 + c)*a^2*c*x/d - 5/128*b^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 1/8*a*b*c^3*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 1/8*a^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
606,1,168,0,1.003763," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x^{3}}{6 \, d} + \frac{1}{2} \, \sqrt{d x^{2} + c} a^{2} x - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x}{8 \, d^{2}} + \frac{\sqrt{d x^{2} + c} b^{2} c^{2} x}{16 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x}{2 \, d} - \frac{\sqrt{d x^{2} + c} a b c x}{4 \, d} + \frac{b^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, d^{\frac{5}{2}}} - \frac{a b c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{4 \, d^{\frac{3}{2}}} + \frac{a^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{d}}"," ",0,"1/6*(d*x^2 + c)^(3/2)*b^2*x^3/d + 1/2*sqrt(d*x^2 + c)*a^2*x - 1/8*(d*x^2 + c)^(3/2)*b^2*c*x/d^2 + 1/16*sqrt(d*x^2 + c)*b^2*c^2*x/d^2 + 1/2*(d*x^2 + c)^(3/2)*a*b*x/d - 1/4*sqrt(d*x^2 + c)*a*b*c*x/d + 1/16*b^2*c^3*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 1/4*a*b*c^2*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 1/2*a^2*c*arcsinh(d*x/sqrt(c*d))/sqrt(d)","A",0
607,1,120,0,1.078083," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\sqrt{d x^{2} + c} a b x + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x}{4 \, d} - \frac{\sqrt{d x^{2} + c} b^{2} c x}{8 \, d} - \frac{b^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{3}{2}}} + \frac{a b c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{d}} + a^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{\sqrt{d x^{2} + c} a^{2}}{x}"," ",0,"sqrt(d*x^2 + c)*a*b*x + 1/4*(d*x^2 + c)^(3/2)*b^2*x/d - 1/8*sqrt(d*x^2 + c)*b^2*c*x/d - 1/8*b^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(3/2) + a*b*c*arcsinh(d*x/sqrt(c*d))/sqrt(d) + a^2*sqrt(d)*arcsinh(d*x/sqrt(c*d)) - sqrt(d*x^2 + c)*a^2/x","A",0
608,1,86,0,1.076163," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{d x^{2} + c} b^{2} x + \frac{b^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{d}} + 2 \, a b \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{2 \, \sqrt{d x^{2} + c} a b}{x} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{3 \, c x^{3}}"," ",0,"1/2*sqrt(d*x^2 + c)*b^2*x + 1/2*b^2*c*arcsinh(d*x/sqrt(c*d))/sqrt(d) + 2*a*b*sqrt(d)*arcsinh(d*x/sqrt(c*d)) - 2*sqrt(d*x^2 + c)*a*b/x - 1/3*(d*x^2 + c)^(3/2)*a^2/(c*x^3)","A",0
609,1,94,0,1.013604," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^6,x, algorithm=""maxima"")","b^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{\sqrt{d x^{2} + c} b^{2}}{x} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{3 \, c x^{3}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{15 \, c^{2} x^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{5 \, c x^{5}}"," ",0,"b^2*sqrt(d)*arcsinh(d*x/sqrt(c*d)) - sqrt(d*x^2 + c)*b^2/x - 2/3*(d*x^2 + c)^(3/2)*a*b/(c*x^3) + 2/15*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^3) - 1/5*(d*x^2 + c)^(3/2)*a^2/(c*x^5)","A",0
610,1,124,0,1.099245," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^8,x, algorithm=""maxima"")","-\frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{3 \, c x^{3}} + \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{15 \, c^{2} x^{3}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{105 \, c^{3} x^{3}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{5 \, c x^{5}} + \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{35 \, c^{2} x^{5}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{7 \, c x^{7}}"," ",0,"-1/3*(d*x^2 + c)^(3/2)*b^2/(c*x^3) + 4/15*(d*x^2 + c)^(3/2)*a*b*d/(c^2*x^3) - 8/105*(d*x^2 + c)^(3/2)*a^2*d^2/(c^3*x^3) - 2/5*(d*x^2 + c)^(3/2)*a*b/(c*x^5) + 4/35*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^5) - 1/7*(d*x^2 + c)^(3/2)*a^2/(c*x^7)","A",0
611,1,190,0,1.162148," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^10,x, algorithm=""maxima"")","\frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d}{15 \, c^{2} x^{3}} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2}}{105 \, c^{3} x^{3}} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3}}{315 \, c^{4} x^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{5 \, c x^{5}} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{35 \, c^{2} x^{5}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{105 \, c^{3} x^{5}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{7 \, c x^{7}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{21 \, c^{2} x^{7}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{9 \, c x^{9}}"," ",0,"2/15*(d*x^2 + c)^(3/2)*b^2*d/(c^2*x^3) - 16/105*(d*x^2 + c)^(3/2)*a*b*d^2/(c^3*x^3) + 16/315*(d*x^2 + c)^(3/2)*a^2*d^3/(c^4*x^3) - 1/5*(d*x^2 + c)^(3/2)*b^2/(c*x^5) + 8/35*(d*x^2 + c)^(3/2)*a*b*d/(c^2*x^5) - 8/105*(d*x^2 + c)^(3/2)*a^2*d^2/(c^3*x^5) - 2/7*(d*x^2 + c)^(3/2)*a*b/(c*x^7) + 2/21*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^7) - 1/9*(d*x^2 + c)^(3/2)*a^2/(c*x^9)","A",0
612,1,258,0,1.121228," ","integrate((b*x^2+a)^2*(d*x^2+c)^(1/2)/x^12,x, algorithm=""maxima"")","-\frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d^{2}}{105 \, c^{3} x^{3}} + \frac{32 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{3}}{315 \, c^{4} x^{3}} - \frac{128 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{4}}{3465 \, c^{5} x^{3}} + \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d}{35 \, c^{2} x^{5}} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2}}{105 \, c^{3} x^{5}} + \frac{64 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3}}{1155 \, c^{4} x^{5}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{7 \, c x^{7}} + \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{21 \, c^{2} x^{7}} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{231 \, c^{3} x^{7}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{9 \, c x^{9}} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{99 \, c^{2} x^{9}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{11 \, c x^{11}}"," ",0,"-8/105*(d*x^2 + c)^(3/2)*b^2*d^2/(c^3*x^3) + 32/315*(d*x^2 + c)^(3/2)*a*b*d^3/(c^4*x^3) - 128/3465*(d*x^2 + c)^(3/2)*a^2*d^4/(c^5*x^3) + 4/35*(d*x^2 + c)^(3/2)*b^2*d/(c^2*x^5) - 16/105*(d*x^2 + c)^(3/2)*a*b*d^2/(c^3*x^5) + 64/1155*(d*x^2 + c)^(3/2)*a^2*d^3/(c^4*x^5) - 1/7*(d*x^2 + c)^(3/2)*b^2/(c*x^7) + 4/21*(d*x^2 + c)^(3/2)*a*b*d/(c^2*x^7) - 16/231*(d*x^2 + c)^(3/2)*a^2*d^2/(c^3*x^7) - 2/9*(d*x^2 + c)^(3/2)*a*b/(c*x^9) + 8/99*(d*x^2 + c)^(3/2)*a^2*d/(c^2*x^9) - 1/11*(d*x^2 + c)^(3/2)*a^2/(c*x^11)","A",0
613,1,367,0,1.136347," ","integrate(x^4*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{7}}{12 \, d} - \frac{7 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x^{5}}{120 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x^{5}}{5 \, d} + \frac{7 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} x^{3}}{192 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c x^{3}}{8 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} x^{3}}{8 \, d} - \frac{7 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{3} x}{384 \, d^{4}} + \frac{7 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{4} x}{1536 \, d^{4}} + \frac{7 \, \sqrt{d x^{2} + c} b^{2} c^{5} x}{1024 \, d^{4}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c^{2} x}{16 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{3} x}{64 \, d^{3}} - \frac{3 \, \sqrt{d x^{2} + c} a b c^{4} x}{128 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} c x}{16 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c^{2} x}{64 \, d^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a^{2} c^{3} x}{128 \, d^{2}} + \frac{7 \, b^{2} c^{6} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{1024 \, d^{\frac{9}{2}}} - \frac{3 \, a b c^{5} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{7}{2}}} + \frac{3 \, a^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{5}{2}}}"," ",0,"1/12*(d*x^2 + c)^(5/2)*b^2*x^7/d - 7/120*(d*x^2 + c)^(5/2)*b^2*c*x^5/d^2 + 1/5*(d*x^2 + c)^(5/2)*a*b*x^5/d + 7/192*(d*x^2 + c)^(5/2)*b^2*c^2*x^3/d^3 - 1/8*(d*x^2 + c)^(5/2)*a*b*c*x^3/d^2 + 1/8*(d*x^2 + c)^(5/2)*a^2*x^3/d - 7/384*(d*x^2 + c)^(5/2)*b^2*c^3*x/d^4 + 7/1536*(d*x^2 + c)^(3/2)*b^2*c^4*x/d^4 + 7/1024*sqrt(d*x^2 + c)*b^2*c^5*x/d^4 + 1/16*(d*x^2 + c)^(5/2)*a*b*c^2*x/d^3 - 1/64*(d*x^2 + c)^(3/2)*a*b*c^3*x/d^3 - 3/128*sqrt(d*x^2 + c)*a*b*c^4*x/d^3 - 1/16*(d*x^2 + c)^(5/2)*a^2*c*x/d^2 + 1/64*(d*x^2 + c)^(3/2)*a^2*c^2*x/d^2 + 3/128*sqrt(d*x^2 + c)*a^2*c^3*x/d^2 + 7/1024*b^2*c^6*arcsinh(d*x/sqrt(c*d))/d^(9/2) - 3/128*a*b*c^5*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 3/128*a^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(5/2)","A",0
614,1,181,0,1.113228," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{6}}{11 \, d} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x^{4}}{33 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x^{4}}{9 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} x^{2}}{231 \, d^{3}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c x^{2}}{63 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} x^{2}}{7 \, d} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{3}}{1155 \, d^{4}} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c^{2}}{315 \, d^{3}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} c}{35 \, d^{2}}"," ",0,"1/11*(d*x^2 + c)^(5/2)*b^2*x^6/d - 2/33*(d*x^2 + c)^(5/2)*b^2*c*x^4/d^2 + 2/9*(d*x^2 + c)^(5/2)*a*b*x^4/d + 8/231*(d*x^2 + c)^(5/2)*b^2*c^2*x^2/d^3 - 8/63*(d*x^2 + c)^(5/2)*a*b*c*x^2/d^2 + 1/7*(d*x^2 + c)^(5/2)*a^2*x^2/d - 16/1155*(d*x^2 + c)^(5/2)*b^2*c^3/d^4 + 16/315*(d*x^2 + c)^(5/2)*a*b*c^2/d^3 - 2/35*(d*x^2 + c)^(5/2)*a^2*c/d^2","A",0
615,1,299,0,1.039706," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{5}}{10 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x^{3}}{16 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x^{3}}{4 \, d} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} x}{32 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} x}{128 \, d^{3}} - \frac{3 \, \sqrt{d x^{2} + c} b^{2} c^{4} x}{256 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c x}{8 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} x}{32 \, d^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a b c^{3} x}{64 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} x}{6 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c x}{24 \, d} - \frac{\sqrt{d x^{2} + c} a^{2} c^{2} x}{16 \, d} - \frac{3 \, b^{2} c^{5} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{256 \, d^{\frac{7}{2}}} + \frac{3 \, a b c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{64 \, d^{\frac{5}{2}}} - \frac{a^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, d^{\frac{3}{2}}}"," ",0,"1/10*(d*x^2 + c)^(5/2)*b^2*x^5/d - 1/16*(d*x^2 + c)^(5/2)*b^2*c*x^3/d^2 + 1/4*(d*x^2 + c)^(5/2)*a*b*x^3/d + 1/32*(d*x^2 + c)^(5/2)*b^2*c^2*x/d^3 - 1/128*(d*x^2 + c)^(3/2)*b^2*c^3*x/d^3 - 3/256*sqrt(d*x^2 + c)*b^2*c^4*x/d^3 - 1/8*(d*x^2 + c)^(5/2)*a*b*c*x/d^2 + 1/32*(d*x^2 + c)^(3/2)*a*b*c^2*x/d^2 + 3/64*sqrt(d*x^2 + c)*a*b*c^3*x/d^2 + 1/6*(d*x^2 + c)^(5/2)*a^2*x/d - 1/24*(d*x^2 + c)^(3/2)*a^2*c*x/d - 1/16*sqrt(d*x^2 + c)*a^2*c^2*x/d - 3/256*b^2*c^5*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 3/64*a*b*c^4*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 1/16*a^2*c^3*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
616,1,115,0,1.001024," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{4}}{9 \, d} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x^{2}}{63 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x^{2}}{7 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2}}{315 \, d^{3}} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c}{35 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{5 \, d}"," ",0,"1/9*(d*x^2 + c)^(5/2)*b^2*x^4/d - 4/63*(d*x^2 + c)^(5/2)*b^2*c*x^2/d^2 + 2/7*(d*x^2 + c)^(5/2)*a*b*x^2/d + 8/315*(d*x^2 + c)^(5/2)*b^2*c^2/d^3 - 4/35*(d*x^2 + c)^(5/2)*a*b*c/d^2 + 1/5*(d*x^2 + c)^(5/2)*a^2/d","A",0
617,1,227,0,1.144781," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{3}}{8 \, d} + \frac{1}{4} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} x + \frac{3}{8} \, \sqrt{d x^{2} + c} a^{2} c x - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x}{16 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} x}{64 \, d^{2}} + \frac{3 \, \sqrt{d x^{2} + c} b^{2} c^{3} x}{128 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x}{3 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c x}{12 \, d} - \frac{\sqrt{d x^{2} + c} a b c^{2} x}{8 \, d} + \frac{3 \, b^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{5}{2}}} - \frac{a b c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{3}{2}}} + \frac{3 \, a^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{d}}"," ",0,"1/8*(d*x^2 + c)^(5/2)*b^2*x^3/d + 1/4*(d*x^2 + c)^(3/2)*a^2*x + 3/8*sqrt(d*x^2 + c)*a^2*c*x - 1/16*(d*x^2 + c)^(5/2)*b^2*c*x/d^2 + 1/64*(d*x^2 + c)^(3/2)*b^2*c^2*x/d^2 + 3/128*sqrt(d*x^2 + c)*b^2*c^3*x/d^2 + 1/3*(d*x^2 + c)^(5/2)*a*b*x/d - 1/12*(d*x^2 + c)^(3/2)*a*b*c*x/d - 1/8*sqrt(d*x^2 + c)*a*b*c^2*x/d + 3/128*b^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 1/8*a*b*c^3*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 3/8*a^2*c^2*arcsinh(d*x/sqrt(c*d))/sqrt(d)","A",0
618,1,103,0,1.112402," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x,x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x^{2}}{7 \, d} - a^{2} c^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \frac{1}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} + \sqrt{d x^{2} + c} a^{2} c - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c}{35 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b}{5 \, d}"," ",0,"1/7*(d*x^2 + c)^(5/2)*b^2*x^2/d - a^2*c^(3/2)*arcsinh(c/(sqrt(c*d)*abs(x))) + 1/3*(d*x^2 + c)^(3/2)*a^2 + sqrt(d*x^2 + c)*a^2*c - 2/35*(d*x^2 + c)^(5/2)*b^2*c/d^2 + 2/5*(d*x^2 + c)^(5/2)*a*b/d","A",0
619,1,178,0,1.143936," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b x + \frac{3}{4} \, \sqrt{d x^{2} + c} a b c x + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x}{6 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x}{24 \, d} - \frac{\sqrt{d x^{2} + c} b^{2} c^{2} x}{16 \, d} + \frac{3}{2} \, \sqrt{d x^{2} + c} a^{2} d x - \frac{b^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, d^{\frac{3}{2}}} + \frac{3 \, a b c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{4 \, \sqrt{d}} + \frac{3}{2} \, a^{2} c \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2}}{x}"," ",0,"1/2*(d*x^2 + c)^(3/2)*a*b*x + 3/4*sqrt(d*x^2 + c)*a*b*c*x + 1/6*(d*x^2 + c)^(5/2)*b^2*x/d - 1/24*(d*x^2 + c)^(3/2)*b^2*c*x/d - 1/16*sqrt(d*x^2 + c)*b^2*c^2*x/d + 3/2*sqrt(d*x^2 + c)*a^2*d*x - 1/16*b^2*c^3*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 3/4*a*b*c^2*arcsinh(d*x/sqrt(c*d))/sqrt(d) + 3/2*a^2*c*sqrt(d)*arcsinh(d*x/sqrt(c*d)) - (d*x^2 + c)^(3/2)*a^2/x","A",0
620,1,138,0,1.145289," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^3,x, algorithm=""maxima"")","-2 \, a b c^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{3}{2} \, a^{2} \sqrt{c} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \frac{2}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b + 2 \, \sqrt{d x^{2} + c} a b c + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2}}{5 \, d} + \frac{3}{2} \, \sqrt{d x^{2} + c} a^{2} d + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{2 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{2 \, c x^{2}}"," ",0,"-2*a*b*c^(3/2)*arcsinh(c/(sqrt(c*d)*abs(x))) - 3/2*a^2*sqrt(c)*d*arcsinh(c/(sqrt(c*d)*abs(x))) + 2/3*(d*x^2 + c)^(3/2)*a*b + 2*sqrt(d*x^2 + c)*a*b*c + 1/5*(d*x^2 + c)^(5/2)*b^2/d + 3/2*sqrt(d*x^2 + c)*a^2*d + 1/2*(d*x^2 + c)^(3/2)*a^2*d/c - 1/2*(d*x^2 + c)^(5/2)*a^2/(c*x^2)","A",0
621,1,177,0,1.128726," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^4,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} x + \frac{3}{8} \, \sqrt{d x^{2} + c} b^{2} c x + 3 \, \sqrt{d x^{2} + c} a b d x + \frac{\sqrt{d x^{2} + c} a^{2} d^{2} x}{c} + \frac{3 \, b^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{d}} + 3 \, a b c \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) + a^{2} d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b}{x} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d}{3 \, c x} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{3 \, c x^{3}}"," ",0,"1/4*(d*x^2 + c)^(3/2)*b^2*x + 3/8*sqrt(d*x^2 + c)*b^2*c*x + 3*sqrt(d*x^2 + c)*a*b*d*x + sqrt(d*x^2 + c)*a^2*d^2*x/c + 3/8*b^2*c^2*arcsinh(d*x/sqrt(c*d))/sqrt(d) + 3*a*b*c*sqrt(d)*arcsinh(d*x/sqrt(c*d)) + a^2*d^(3/2)*arcsinh(d*x/sqrt(c*d)) - 2*(d*x^2 + c)^(3/2)*a*b/x - 2/3*(d*x^2 + c)^(3/2)*a^2*d/(c*x) - 1/3*(d*x^2 + c)^(5/2)*a^2/(c*x^3)","A",0
622,1,222,0,1.128597," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^5,x, algorithm=""maxima"")","-b^{2} c^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - 3 \, a b \sqrt{c} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{3 \, a^{2} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{8 \, \sqrt{c}} + \frac{1}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} + \sqrt{d x^{2} + c} b^{2} c + 3 \, \sqrt{d x^{2} + c} a b d + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{c} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{8 \, c^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a^{2} d^{2}}{8 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b}{c x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d}{8 \, c^{2} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{4 \, c x^{4}}"," ",0,"-b^2*c^(3/2)*arcsinh(c/(sqrt(c*d)*abs(x))) - 3*a*b*sqrt(c)*d*arcsinh(c/(sqrt(c*d)*abs(x))) - 3/8*a^2*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 1/3*(d*x^2 + c)^(3/2)*b^2 + sqrt(d*x^2 + c)*b^2*c + 3*sqrt(d*x^2 + c)*a*b*d + (d*x^2 + c)^(3/2)*a*b*d/c + 1/8*(d*x^2 + c)^(3/2)*a^2*d^2/c^2 + 3/8*sqrt(d*x^2 + c)*a^2*d^2/c - (d*x^2 + c)^(5/2)*a*b/(c*x^2) - 1/8*(d*x^2 + c)^(5/2)*a^2*d/(c^2*x^2) - 1/4*(d*x^2 + c)^(5/2)*a^2/(c*x^4)","A",0
623,1,147,0,1.065882," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^6,x, algorithm=""maxima"")","\frac{3}{2} \, \sqrt{d x^{2} + c} b^{2} d x + \frac{2 \, \sqrt{d x^{2} + c} a b d^{2} x}{c} + \frac{3}{2} \, b^{2} c \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) + 2 \, a b d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2}}{x} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d}{3 \, c x} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b}{3 \, c x^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{5 \, c x^{5}}"," ",0,"3/2*sqrt(d*x^2 + c)*b^2*d*x + 2*sqrt(d*x^2 + c)*a*b*d^2*x/c + 3/2*b^2*c*sqrt(d)*arcsinh(d*x/sqrt(c*d)) + 2*a*b*d^(3/2)*arcsinh(d*x/sqrt(c*d)) - (d*x^2 + c)^(3/2)*b^2/x - 4/3*(d*x^2 + c)^(3/2)*a*b*d/(c*x) - 2/3*(d*x^2 + c)^(5/2)*a*b/(c*x^3) - 1/5*(d*x^2 + c)^(5/2)*a^2/(c*x^5)","A",0
624,1,301,0,0.953411," ","integrate((b*x^2+a)^2*(d*x^2+c)^(3/2)/x^7,x, algorithm=""maxima"")","-\frac{3}{2} \, b^{2} \sqrt{c} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{3 \, a b d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{4 \, \sqrt{c}} + \frac{a^{2} d^{3} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{16 \, c^{\frac{3}{2}}} + \frac{3}{2} \, \sqrt{d x^{2} + c} b^{2} d + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d}{2 \, c} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2}}{4 \, c^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a b d^{2}}{4 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3}}{48 \, c^{3}} - \frac{\sqrt{d x^{2} + c} a^{2} d^{3}}{16 \, c^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2}}{2 \, c x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d}{4 \, c^{2} x^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{2}}{48 \, c^{3} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b}{2 \, c x^{4}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d}{24 \, c^{2} x^{4}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{6 \, c x^{6}}"," ",0,"-3/2*b^2*sqrt(c)*d*arcsinh(c/(sqrt(c*d)*abs(x))) - 3/4*a*b*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 1/16*a^2*d^3*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + 3/2*sqrt(d*x^2 + c)*b^2*d + 1/2*(d*x^2 + c)^(3/2)*b^2*d/c + 1/4*(d*x^2 + c)^(3/2)*a*b*d^2/c^2 + 3/4*sqrt(d*x^2 + c)*a*b*d^2/c - 1/48*(d*x^2 + c)^(3/2)*a^2*d^3/c^3 - 1/16*sqrt(d*x^2 + c)*a^2*d^3/c^2 - 1/2*(d*x^2 + c)^(5/2)*b^2/(c*x^2) - 1/4*(d*x^2 + c)^(5/2)*a*b*d/(c^2*x^2) + 1/48*(d*x^2 + c)^(5/2)*a^2*d^2/(c^3*x^2) - 1/2*(d*x^2 + c)^(5/2)*a*b/(c*x^4) + 1/24*(d*x^2 + c)^(5/2)*a^2*d/(c^2*x^4) - 1/6*(d*x^2 + c)^(5/2)*a^2/(c*x^6)","A",0
625,1,181,0,0.964535," ","integrate(x^3*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x^{6}}{13 \, d} - \frac{6 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c x^{4}}{143 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b x^{4}}{11 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2} x^{2}}{429 \, d^{3}} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c x^{2}}{99 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} x^{2}}{9 \, d} - \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{3}}{3003 \, d^{4}} + \frac{16 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c^{2}}{693 \, d^{3}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} c}{63 \, d^{2}}"," ",0,"1/13*(d*x^2 + c)^(7/2)*b^2*x^6/d - 6/143*(d*x^2 + c)^(7/2)*b^2*c*x^4/d^2 + 2/11*(d*x^2 + c)^(7/2)*a*b*x^4/d + 8/429*(d*x^2 + c)^(7/2)*b^2*c^2*x^2/d^3 - 8/99*(d*x^2 + c)^(7/2)*a*b*c*x^2/d^2 + 1/9*(d*x^2 + c)^(7/2)*a^2*x^2/d - 16/3003*(d*x^2 + c)^(7/2)*b^2*c^3/d^4 + 16/693*(d*x^2 + c)^(7/2)*a*b*c^2/d^3 - 2/63*(d*x^2 + c)^(7/2)*a^2*c/d^2","A",0
626,1,361,0,0.965635," ","integrate(x^2*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x^{5}}{12 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c x^{3}}{24 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a b x^{3}}{5 \, d} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2} x}{64 \, d^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{3} x}{384 \, d^{3}} - \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{4} x}{1536 \, d^{3}} - \frac{5 \, \sqrt{d x^{2} + c} b^{2} c^{5} x}{1024 \, d^{3}} - \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c x}{40 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c^{2} x}{80 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{3} x}{64 \, d^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a b c^{4} x}{128 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} x}{8 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} c x}{48 \, d} - \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c^{2} x}{192 \, d} - \frac{5 \, \sqrt{d x^{2} + c} a^{2} c^{3} x}{128 \, d} - \frac{5 \, b^{2} c^{6} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{1024 \, d^{\frac{7}{2}}} + \frac{3 \, a b c^{5} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{5}{2}}} - \frac{5 \, a^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{3}{2}}}"," ",0,"1/12*(d*x^2 + c)^(7/2)*b^2*x^5/d - 1/24*(d*x^2 + c)^(7/2)*b^2*c*x^3/d^2 + 1/5*(d*x^2 + c)^(7/2)*a*b*x^3/d + 1/64*(d*x^2 + c)^(7/2)*b^2*c^2*x/d^3 - 1/384*(d*x^2 + c)^(5/2)*b^2*c^3*x/d^3 - 5/1536*(d*x^2 + c)^(3/2)*b^2*c^4*x/d^3 - 5/1024*sqrt(d*x^2 + c)*b^2*c^5*x/d^3 - 3/40*(d*x^2 + c)^(7/2)*a*b*c*x/d^2 + 1/80*(d*x^2 + c)^(5/2)*a*b*c^2*x/d^2 + 1/64*(d*x^2 + c)^(3/2)*a*b*c^3*x/d^2 + 3/128*sqrt(d*x^2 + c)*a*b*c^4*x/d^2 + 1/8*(d*x^2 + c)^(7/2)*a^2*x/d - 1/48*(d*x^2 + c)^(5/2)*a^2*c*x/d - 5/192*(d*x^2 + c)^(3/2)*a^2*c^2*x/d - 5/128*sqrt(d*x^2 + c)*a^2*c^3*x/d - 5/1024*b^2*c^6*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 3/128*a*b*c^5*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 5/128*a^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
627,1,115,0,0.893747," ","integrate(x*(b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x^{4}}{11 \, d} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c x^{2}}{99 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b x^{2}}{9 \, d} + \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c^{2}}{693 \, d^{3}} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b c}{63 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{7 \, d}"," ",0,"1/11*(d*x^2 + c)^(7/2)*b^2*x^4/d - 4/99*(d*x^2 + c)^(7/2)*b^2*c*x^2/d^2 + 2/9*(d*x^2 + c)^(7/2)*a*b*x^2/d + 8/693*(d*x^2 + c)^(7/2)*b^2*c^2/d^3 - 4/63*(d*x^2 + c)^(7/2)*a*b*c/d^2 + 1/7*(d*x^2 + c)^(7/2)*a^2/d","A",0
628,1,286,0,0.975729," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x^{3}}{10 \, d} + \frac{1}{6} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} x + \frac{5}{24} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c x + \frac{5}{16} \, \sqrt{d x^{2} + c} a^{2} c^{2} x - \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c x}{80 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c^{2} x}{160 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{3} x}{128 \, d^{2}} + \frac{3 \, \sqrt{d x^{2} + c} b^{2} c^{4} x}{256 \, d^{2}} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a b x}{4 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b c x}{24 \, d} - \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c^{2} x}{96 \, d} - \frac{5 \, \sqrt{d x^{2} + c} a b c^{3} x}{64 \, d} + \frac{3 \, b^{2} c^{5} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{256 \, d^{\frac{5}{2}}} - \frac{5 \, a b c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{64 \, d^{\frac{3}{2}}} + \frac{5 \, a^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, \sqrt{d}}"," ",0,"1/10*(d*x^2 + c)^(7/2)*b^2*x^3/d + 1/6*(d*x^2 + c)^(5/2)*a^2*x + 5/24*(d*x^2 + c)^(3/2)*a^2*c*x + 5/16*sqrt(d*x^2 + c)*a^2*c^2*x - 3/80*(d*x^2 + c)^(7/2)*b^2*c*x/d^2 + 1/160*(d*x^2 + c)^(5/2)*b^2*c^2*x/d^2 + 1/128*(d*x^2 + c)^(3/2)*b^2*c^3*x/d^2 + 3/256*sqrt(d*x^2 + c)*b^2*c^4*x/d^2 + 1/4*(d*x^2 + c)^(7/2)*a*b*x/d - 1/24*(d*x^2 + c)^(5/2)*a*b*c*x/d - 5/96*(d*x^2 + c)^(3/2)*a*b*c^2*x/d - 5/64*sqrt(d*x^2 + c)*a*b*c^3*x/d + 3/256*b^2*c^5*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 5/64*a*b*c^4*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 5/16*a^2*c^3*arcsinh(d*x/sqrt(c*d))/sqrt(d)","A",0
629,1,120,0,0.891864," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x,x, algorithm=""maxima"")","\frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x^{2}}{9 \, d} - a^{2} c^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} + \frac{1}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} c + \sqrt{d x^{2} + c} a^{2} c^{2} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} c}{63 \, d^{2}} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b}{7 \, d}"," ",0,"1/9*(d*x^2 + c)^(7/2)*b^2*x^2/d - a^2*c^(5/2)*arcsinh(c/(sqrt(c*d)*abs(x))) + 1/5*(d*x^2 + c)^(5/2)*a^2 + 1/3*(d*x^2 + c)^(3/2)*a^2*c + sqrt(d*x^2 + c)*a^2*c^2 - 2/63*(d*x^2 + c)^(7/2)*b^2*c/d^2 + 2/7*(d*x^2 + c)^(7/2)*a*b/d","A",0
630,1,235,0,0.965814," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b x + \frac{5}{12} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c x + \frac{5}{8} \, \sqrt{d x^{2} + c} a b c^{2} x + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2} x}{8 \, d} - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} c x}{48 \, d} - \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c^{2} x}{192 \, d} - \frac{5 \, \sqrt{d x^{2} + c} b^{2} c^{3} x}{128 \, d} + \frac{5}{4} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d x + \frac{15}{8} \, \sqrt{d x^{2} + c} a^{2} c d x - \frac{5 \, b^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{3}{2}}} + \frac{5 \, a b c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{d}} + \frac{15}{8} \, a^{2} c^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2}}{x}"," ",0,"1/3*(d*x^2 + c)^(5/2)*a*b*x + 5/12*(d*x^2 + c)^(3/2)*a*b*c*x + 5/8*sqrt(d*x^2 + c)*a*b*c^2*x + 1/8*(d*x^2 + c)^(7/2)*b^2*x/d - 1/48*(d*x^2 + c)^(5/2)*b^2*c*x/d - 5/192*(d*x^2 + c)^(3/2)*b^2*c^2*x/d - 5/128*sqrt(d*x^2 + c)*b^2*c^3*x/d + 5/4*(d*x^2 + c)^(3/2)*a^2*d*x + 15/8*sqrt(d*x^2 + c)*a^2*c*d*x - 5/128*b^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 5/8*a*b*c^3*arcsinh(d*x/sqrt(c*d))/sqrt(d) + 15/8*a^2*c^2*sqrt(d)*arcsinh(d*x/sqrt(c*d)) - (d*x^2 + c)^(5/2)*a^2/x","A",0
631,1,170,0,0.947968," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^3,x, algorithm=""maxima"")","-2 \, a b c^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{5}{2} \, a^{2} c^{\frac{3}{2}} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \frac{2}{5} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b + \frac{2}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b c + 2 \, \sqrt{d x^{2} + c} a b c^{2} + \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2}}{7 \, d} + \frac{5}{6} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d}{2 \, c} + \frac{5}{2} \, \sqrt{d x^{2} + c} a^{2} c d - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{2 \, c x^{2}}"," ",0,"-2*a*b*c^(5/2)*arcsinh(c/(sqrt(c*d)*abs(x))) - 5/2*a^2*c^(3/2)*d*arcsinh(c/(sqrt(c*d)*abs(x))) + 2/5*(d*x^2 + c)^(5/2)*a*b + 2/3*(d*x^2 + c)^(3/2)*a*b*c + 2*sqrt(d*x^2 + c)*a*b*c^2 + 1/7*(d*x^2 + c)^(7/2)*b^2/d + 5/6*(d*x^2 + c)^(3/2)*a^2*d + 1/2*(d*x^2 + c)^(5/2)*a^2*d/c + 5/2*sqrt(d*x^2 + c)*a^2*c*d - 1/2*(d*x^2 + c)^(7/2)*a^2/(c*x^2)","A",0
632,1,234,0,0.991114," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} x + \frac{5}{24} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c x + \frac{5}{16} \, \sqrt{d x^{2} + c} b^{2} c^{2} x + \frac{5}{2} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d x + \frac{15}{4} \, \sqrt{d x^{2} + c} a b c d x + \frac{5}{2} \, \sqrt{d x^{2} + c} a^{2} d^{2} x + \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2} x}{3 \, c} + \frac{5 \, b^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, \sqrt{d}} + \frac{15}{4} \, a b c^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) + \frac{5}{2} \, a^{2} c d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b}{x} - \frac{4 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d}{3 \, c x} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{3 \, c x^{3}}"," ",0,"1/6*(d*x^2 + c)^(5/2)*b^2*x + 5/24*(d*x^2 + c)^(3/2)*b^2*c*x + 5/16*sqrt(d*x^2 + c)*b^2*c^2*x + 5/2*(d*x^2 + c)^(3/2)*a*b*d*x + 15/4*sqrt(d*x^2 + c)*a*b*c*d*x + 5/2*sqrt(d*x^2 + c)*a^2*d^2*x + 5/3*(d*x^2 + c)^(3/2)*a^2*d^2*x/c + 5/16*b^2*c^3*arcsinh(d*x/sqrt(c*d))/sqrt(d) + 15/4*a*b*c^2*sqrt(d)*arcsinh(d*x/sqrt(c*d)) + 5/2*a^2*c*d^(3/2)*arcsinh(d*x/sqrt(c*d)) - 2*(d*x^2 + c)^(5/2)*a*b/x - 4/3*(d*x^2 + c)^(5/2)*a^2*d/(c*x) - 1/3*(d*x^2 + c)^(7/2)*a^2/(c*x^3)","A",0
633,1,271,0,0.942480," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^5,x, algorithm=""maxima"")","-b^{2} c^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - 5 \, a b c^{\frac{3}{2}} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{15}{8} \, a^{2} \sqrt{c} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) + \frac{1}{5} \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} + \frac{1}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} c + \sqrt{d x^{2} + c} b^{2} c^{2} + \frac{5}{3} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d}{c} + 5 \, \sqrt{d x^{2} + c} a b c d + \frac{15}{8} \, \sqrt{d x^{2} + c} a^{2} d^{2} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{2}}{8 \, c^{2}} + \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{2}}{8 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a b}{c x^{2}} - \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d}{8 \, c^{2} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{4 \, c x^{4}}"," ",0,"-b^2*c^(5/2)*arcsinh(c/(sqrt(c*d)*abs(x))) - 5*a*b*c^(3/2)*d*arcsinh(c/(sqrt(c*d)*abs(x))) - 15/8*a^2*sqrt(c)*d^2*arcsinh(c/(sqrt(c*d)*abs(x))) + 1/5*(d*x^2 + c)^(5/2)*b^2 + 1/3*(d*x^2 + c)^(3/2)*b^2*c + sqrt(d*x^2 + c)*b^2*c^2 + 5/3*(d*x^2 + c)^(3/2)*a*b*d + (d*x^2 + c)^(5/2)*a*b*d/c + 5*sqrt(d*x^2 + c)*a*b*c*d + 15/8*sqrt(d*x^2 + c)*a^2*d^2 + 3/8*(d*x^2 + c)^(5/2)*a^2*d^2/c^2 + 5/8*(d*x^2 + c)^(3/2)*a^2*d^2/c - (d*x^2 + c)^(7/2)*a*b/(c*x^2) - 3/8*(d*x^2 + c)^(7/2)*a^2*d/(c^2*x^2) - 1/4*(d*x^2 + c)^(7/2)*a^2/(c*x^4)","A",0
634,1,285,0,0.956126," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^6,x, algorithm=""maxima"")","\frac{5}{4} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d x + \frac{15}{8} \, \sqrt{d x^{2} + c} b^{2} c d x + 5 \, \sqrt{d x^{2} + c} a b d^{2} x + \frac{10 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2} x}{3 \, c} + \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3} x}{3 \, c^{2}} + \frac{\sqrt{d x^{2} + c} a^{2} d^{3} x}{c} + \frac{15}{8} \, b^{2} c^{2} \sqrt{d} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) + 5 \, a b c d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) + a^{2} d^{\frac{5}{2}} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right) - \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2}}{x} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d}{3 \, c x} - \frac{8 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{2}}{15 \, c^{2} x} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b}{3 \, c x^{3}} - \frac{2 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d}{15 \, c^{2} x^{3}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{5 \, c x^{5}}"," ",0,"5/4*(d*x^2 + c)^(3/2)*b^2*d*x + 15/8*sqrt(d*x^2 + c)*b^2*c*d*x + 5*sqrt(d*x^2 + c)*a*b*d^2*x + 10/3*(d*x^2 + c)^(3/2)*a*b*d^2*x/c + 2/3*(d*x^2 + c)^(3/2)*a^2*d^3*x/c^2 + sqrt(d*x^2 + c)*a^2*d^3*x/c + 15/8*b^2*c^2*sqrt(d)*arcsinh(d*x/sqrt(c*d)) + 5*a*b*c*d^(3/2)*arcsinh(d*x/sqrt(c*d)) + a^2*d^(5/2)*arcsinh(d*x/sqrt(c*d)) - (d*x^2 + c)^(5/2)*b^2/x - 8/3*(d*x^2 + c)^(5/2)*a*b*d/(c*x) - 8/15*(d*x^2 + c)^(5/2)*a^2*d^2/(c^2*x) - 2/3*(d*x^2 + c)^(7/2)*a*b/(c*x^3) - 2/15*(d*x^2 + c)^(7/2)*a^2*d/(c^2*x^3) - 1/5*(d*x^2 + c)^(7/2)*a^2/(c*x^5)","A",0
635,1,353,0,0.959702," ","integrate((b*x^2+a)^2*(d*x^2+c)^(5/2)/x^7,x, algorithm=""maxima"")","-\frac{5}{2} \, b^{2} c^{\frac{3}{2}} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{15}{4} \, a b \sqrt{c} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right) - \frac{5 \, a^{2} d^{3} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{16 \, \sqrt{c}} + \frac{5}{6} \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} b^{2} d + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} b^{2} d}{2 \, c} + \frac{5}{2} \, \sqrt{d x^{2} + c} b^{2} c d + \frac{15}{4} \, \sqrt{d x^{2} + c} a b d^{2} + \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}} a b d^{2}}{4 \, c^{2}} + \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a b d^{2}}{4 \, c} + \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} a^{2} d^{3}}{16 \, c^{3}} + \frac{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} a^{2} d^{3}}{48 \, c^{2}} + \frac{5 \, \sqrt{d x^{2} + c} a^{2} d^{3}}{16 \, c} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} b^{2}}{2 \, c x^{2}} - \frac{3 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}} a b d}{4 \, c^{2} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d^{2}}{16 \, c^{3} x^{2}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a b}{2 \, c x^{4}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2} d}{24 \, c^{2} x^{4}} - \frac{{\left(d x^{2} + c\right)}^{\frac{7}{2}} a^{2}}{6 \, c x^{6}}"," ",0,"-5/2*b^2*c^(3/2)*d*arcsinh(c/(sqrt(c*d)*abs(x))) - 15/4*a*b*sqrt(c)*d^2*arcsinh(c/(sqrt(c*d)*abs(x))) - 5/16*a^2*d^3*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 5/6*(d*x^2 + c)^(3/2)*b^2*d + 1/2*(d*x^2 + c)^(5/2)*b^2*d/c + 5/2*sqrt(d*x^2 + c)*b^2*c*d + 15/4*sqrt(d*x^2 + c)*a*b*d^2 + 3/4*(d*x^2 + c)^(5/2)*a*b*d^2/c^2 + 5/4*(d*x^2 + c)^(3/2)*a*b*d^2/c + 1/16*(d*x^2 + c)^(5/2)*a^2*d^3/c^3 + 5/48*(d*x^2 + c)^(3/2)*a^2*d^3/c^2 + 5/16*sqrt(d*x^2 + c)*a^2*d^3/c - 1/2*(d*x^2 + c)^(7/2)*b^2/(c*x^2) - 3/4*(d*x^2 + c)^(7/2)*a*b*d/(c^2*x^2) - 1/16*(d*x^2 + c)^(7/2)*a^2*d^2/(c^3*x^2) - 1/2*(d*x^2 + c)^(7/2)*a*b/(c*x^4) - 1/24*(d*x^2 + c)^(7/2)*a^2*d/(c^2*x^4) - 1/6*(d*x^2 + c)^(7/2)*a^2/(c*x^6)","A",0
636,1,243,0,0.940179," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{7}}{8 \, d} - \frac{7 \, \sqrt{d x^{2} + c} b^{2} c x^{5}}{48 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a b x^{5}}{3 \, d} + \frac{35 \, \sqrt{d x^{2} + c} b^{2} c^{2} x^{3}}{192 \, d^{3}} - \frac{5 \, \sqrt{d x^{2} + c} a b c x^{3}}{12 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a^{2} x^{3}}{4 \, d} - \frac{35 \, \sqrt{d x^{2} + c} b^{2} c^{3} x}{128 \, d^{4}} + \frac{5 \, \sqrt{d x^{2} + c} a b c^{2} x}{8 \, d^{3}} - \frac{3 \, \sqrt{d x^{2} + c} a^{2} c x}{8 \, d^{2}} + \frac{35 \, b^{2} c^{4} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{128 \, d^{\frac{9}{2}}} - \frac{5 \, a b c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{7}{2}}} + \frac{3 \, a^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{5}{2}}}"," ",0,"1/8*sqrt(d*x^2 + c)*b^2*x^7/d - 7/48*sqrt(d*x^2 + c)*b^2*c*x^5/d^2 + 1/3*sqrt(d*x^2 + c)*a*b*x^5/d + 35/192*sqrt(d*x^2 + c)*b^2*c^2*x^3/d^3 - 5/12*sqrt(d*x^2 + c)*a*b*c*x^3/d^2 + 1/4*sqrt(d*x^2 + c)*a^2*x^3/d - 35/128*sqrt(d*x^2 + c)*b^2*c^3*x/d^4 + 5/8*sqrt(d*x^2 + c)*a*b*c^2*x/d^3 - 3/8*sqrt(d*x^2 + c)*a^2*c*x/d^2 + 35/128*b^2*c^4*arcsinh(d*x/sqrt(c*d))/d^(9/2) - 5/8*a*b*c^3*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 3/8*a^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(5/2)","A",0
637,1,181,0,0.905569," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{6}}{7 \, d} - \frac{6 \, \sqrt{d x^{2} + c} b^{2} c x^{4}}{35 \, d^{2}} + \frac{2 \, \sqrt{d x^{2} + c} a b x^{4}}{5 \, d} + \frac{8 \, \sqrt{d x^{2} + c} b^{2} c^{2} x^{2}}{35 \, d^{3}} - \frac{8 \, \sqrt{d x^{2} + c} a b c x^{2}}{15 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a^{2} x^{2}}{3 \, d} - \frac{16 \, \sqrt{d x^{2} + c} b^{2} c^{3}}{35 \, d^{4}} + \frac{16 \, \sqrt{d x^{2} + c} a b c^{2}}{15 \, d^{3}} - \frac{2 \, \sqrt{d x^{2} + c} a^{2} c}{3 \, d^{2}}"," ",0,"1/7*sqrt(d*x^2 + c)*b^2*x^6/d - 6/35*sqrt(d*x^2 + c)*b^2*c*x^4/d^2 + 2/5*sqrt(d*x^2 + c)*a*b*x^4/d + 8/35*sqrt(d*x^2 + c)*b^2*c^2*x^2/d^3 - 8/15*sqrt(d*x^2 + c)*a*b*c*x^2/d^2 + 1/3*sqrt(d*x^2 + c)*a^2*x^2/d - 16/35*sqrt(d*x^2 + c)*b^2*c^3/d^4 + 16/15*sqrt(d*x^2 + c)*a*b*c^2/d^3 - 2/3*sqrt(d*x^2 + c)*a^2*c/d^2","A",0
638,1,175,0,0.915828," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{5}}{6 \, d} - \frac{5 \, \sqrt{d x^{2} + c} b^{2} c x^{3}}{24 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a b x^{3}}{2 \, d} + \frac{5 \, \sqrt{d x^{2} + c} b^{2} c^{2} x}{16 \, d^{3}} - \frac{3 \, \sqrt{d x^{2} + c} a b c x}{4 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a^{2} x}{2 \, d} - \frac{5 \, b^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, d^{\frac{7}{2}}} + \frac{3 \, a b c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{4 \, d^{\frac{5}{2}}} - \frac{a^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, d^{\frac{3}{2}}}"," ",0,"1/6*sqrt(d*x^2 + c)*b^2*x^5/d - 5/24*sqrt(d*x^2 + c)*b^2*c*x^3/d^2 + 1/2*sqrt(d*x^2 + c)*a*b*x^3/d + 5/16*sqrt(d*x^2 + c)*b^2*c^2*x/d^3 - 3/4*sqrt(d*x^2 + c)*a*b*c*x/d^2 + 1/2*sqrt(d*x^2 + c)*a^2*x/d - 5/16*b^2*c^3*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 3/4*a*b*c^2*arcsinh(d*x/sqrt(c*d))/d^(5/2) - 1/2*a^2*c*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
639,1,114,0,0.891899," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{4}}{5 \, d} - \frac{4 \, \sqrt{d x^{2} + c} b^{2} c x^{2}}{15 \, d^{2}} + \frac{2 \, \sqrt{d x^{2} + c} a b x^{2}}{3 \, d} + \frac{8 \, \sqrt{d x^{2} + c} b^{2} c^{2}}{15 \, d^{3}} - \frac{4 \, \sqrt{d x^{2} + c} a b c}{3 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a^{2}}{d}"," ",0,"1/5*sqrt(d*x^2 + c)*b^2*x^4/d - 4/15*sqrt(d*x^2 + c)*b^2*c*x^2/d^2 + 2/3*sqrt(d*x^2 + c)*a*b*x^2/d + 8/15*sqrt(d*x^2 + c)*b^2*c^2/d^3 - 4/3*sqrt(d*x^2 + c)*a*b*c/d^2 + sqrt(d*x^2 + c)*a^2/d","A",0
640,1,109,0,0.886141," ","integrate((b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{3}}{4 \, d} - \frac{3 \, \sqrt{d x^{2} + c} b^{2} c x}{8 \, d^{2}} + \frac{\sqrt{d x^{2} + c} a b x}{d} + \frac{3 \, b^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{5}{2}}} - \frac{a b c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{3}{2}}} + \frac{a^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{d}}"," ",0,"1/4*sqrt(d*x^2 + c)*b^2*x^3/d - 3/8*sqrt(d*x^2 + c)*b^2*c*x/d^2 + sqrt(d*x^2 + c)*a*b*x/d + 3/8*b^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(5/2) - a*b*c*arcsinh(d*x/sqrt(c*d))/d^(3/2) + a^2*arcsinh(d*x/sqrt(c*d))/sqrt(d)","A",0
641,1,75,0,0.868000," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x^{2}}{3 \, d} - \frac{a^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{\sqrt{c}} - \frac{2 \, \sqrt{d x^{2} + c} b^{2} c}{3 \, d^{2}} + \frac{2 \, \sqrt{d x^{2} + c} a b}{d}"," ",0,"1/3*sqrt(d*x^2 + c)*b^2*x^2/d - a^2*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) - 2/3*sqrt(d*x^2 + c)*b^2*c/d^2 + 2*sqrt(d*x^2 + c)*a*b/d","A",0
642,1,73,0,0.882720," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{d x^{2} + c} b^{2} x}{2 \, d} - \frac{b^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, d^{\frac{3}{2}}} + \frac{2 \, a b \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{d}} - \frac{\sqrt{d x^{2} + c} a^{2}}{c x}"," ",0,"1/2*sqrt(d*x^2 + c)*b^2*x/d - 1/2*b^2*c*arcsinh(d*x/sqrt(c*d))/d^(3/2) + 2*a*b*arcsinh(d*x/sqrt(c*d))/sqrt(d) - sqrt(d*x^2 + c)*a^2/(c*x)","A",0
643,1,77,0,0.913911," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, a b \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{\sqrt{c}} + \frac{a^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, c^{\frac{3}{2}}} + \frac{\sqrt{d x^{2} + c} b^{2}}{d} - \frac{\sqrt{d x^{2} + c} a^{2}}{2 \, c x^{2}}"," ",0,"-2*a*b*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + 1/2*a^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + sqrt(d*x^2 + c)*b^2/d - 1/2*sqrt(d*x^2 + c)*a^2/(c*x^2)","A",0
644,1,77,0,0.883489," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{d}} - \frac{2 \, \sqrt{d x^{2} + c} a b}{c x} + \frac{2 \, \sqrt{d x^{2} + c} a^{2} d}{3 \, c^{2} x} - \frac{\sqrt{d x^{2} + c} a^{2}}{3 \, c x^{3}}"," ",0,"b^2*arcsinh(d*x/sqrt(c*d))/sqrt(d) - 2*sqrt(d*x^2 + c)*a*b/(c*x) + 2/3*sqrt(d*x^2 + c)*a^2*d/(c^2*x) - 1/3*sqrt(d*x^2 + c)*a^2/(c*x^3)","A",0
645,1,123,0,0.891862," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{b^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{\sqrt{c}} + \frac{a b d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{3}{2}}} - \frac{3 \, a^{2} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{8 \, c^{\frac{5}{2}}} - \frac{\sqrt{d x^{2} + c} a b}{c x^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a^{2} d}{8 \, c^{2} x^{2}} - \frac{\sqrt{d x^{2} + c} a^{2}}{4 \, c x^{4}}"," ",0,"-b^2*arcsinh(c/(sqrt(c*d)*abs(x)))/sqrt(c) + a*b*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) - 3/8*a^2*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) - sqrt(d*x^2 + c)*a*b/(c*x^2) + 3/8*sqrt(d*x^2 + c)*a^2*d/(c^2*x^2) - 1/4*sqrt(d*x^2 + c)*a^2/(c*x^4)","A",0
646,1,124,0,0.907358," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{d x^{2} + c} b^{2}}{c x} + \frac{4 \, \sqrt{d x^{2} + c} a b d}{3 \, c^{2} x} - \frac{8 \, \sqrt{d x^{2} + c} a^{2} d^{2}}{15 \, c^{3} x} - \frac{2 \, \sqrt{d x^{2} + c} a b}{3 \, c x^{3}} + \frac{4 \, \sqrt{d x^{2} + c} a^{2} d}{15 \, c^{2} x^{3}} - \frac{\sqrt{d x^{2} + c} a^{2}}{5 \, c x^{5}}"," ",0,"-sqrt(d*x^2 + c)*b^2/(c*x) + 4/3*sqrt(d*x^2 + c)*a*b*d/(c^2*x) - 8/15*sqrt(d*x^2 + c)*a^2*d^2/(c^3*x) - 2/3*sqrt(d*x^2 + c)*a*b/(c*x^3) + 4/15*sqrt(d*x^2 + c)*a^2*d/(c^2*x^3) - 1/5*sqrt(d*x^2 + c)*a^2/(c*x^5)","A",0
647,1,190,0,0.918394," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, c^{\frac{3}{2}}} - \frac{3 \, a b d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{4 \, c^{\frac{5}{2}}} + \frac{5 \, a^{2} d^{3} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{16 \, c^{\frac{7}{2}}} - \frac{\sqrt{d x^{2} + c} b^{2}}{2 \, c x^{2}} + \frac{3 \, \sqrt{d x^{2} + c} a b d}{4 \, c^{2} x^{2}} - \frac{5 \, \sqrt{d x^{2} + c} a^{2} d^{2}}{16 \, c^{3} x^{2}} - \frac{\sqrt{d x^{2} + c} a b}{2 \, c x^{4}} + \frac{5 \, \sqrt{d x^{2} + c} a^{2} d}{24 \, c^{2} x^{4}} - \frac{\sqrt{d x^{2} + c} a^{2}}{6 \, c x^{6}}"," ",0,"1/2*b^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) - 3/4*a*b*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + 5/16*a^2*d^3*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(7/2) - 1/2*sqrt(d*x^2 + c)*b^2/(c*x^2) + 3/4*sqrt(d*x^2 + c)*a*b*d/(c^2*x^2) - 5/16*sqrt(d*x^2 + c)*a^2*d^2/(c^3*x^2) - 1/2*sqrt(d*x^2 + c)*a*b/(c*x^4) + 5/24*sqrt(d*x^2 + c)*a^2*d/(c^2*x^4) - 1/6*sqrt(d*x^2 + c)*a^2/(c*x^6)","A",0
648,1,241,0,0.958656," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{7}}{6 \, \sqrt{d x^{2} + c} d} - \frac{7 \, b^{2} c x^{5}}{24 \, \sqrt{d x^{2} + c} d^{2}} + \frac{a b x^{5}}{2 \, \sqrt{d x^{2} + c} d} + \frac{35 \, b^{2} c^{2} x^{3}}{48 \, \sqrt{d x^{2} + c} d^{3}} - \frac{5 \, a b c x^{3}}{4 \, \sqrt{d x^{2} + c} d^{2}} + \frac{a^{2} x^{3}}{2 \, \sqrt{d x^{2} + c} d} + \frac{35 \, b^{2} c^{3} x}{16 \, \sqrt{d x^{2} + c} d^{4}} - \frac{15 \, a b c^{2} x}{4 \, \sqrt{d x^{2} + c} d^{3}} + \frac{3 \, a^{2} c x}{2 \, \sqrt{d x^{2} + c} d^{2}} - \frac{35 \, b^{2} c^{3} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{16 \, d^{\frac{9}{2}}} + \frac{15 \, a b c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{4 \, d^{\frac{7}{2}}} - \frac{3 \, a^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, d^{\frac{5}{2}}}"," ",0,"1/6*b^2*x^7/(sqrt(d*x^2 + c)*d) - 7/24*b^2*c*x^5/(sqrt(d*x^2 + c)*d^2) + 1/2*a*b*x^5/(sqrt(d*x^2 + c)*d) + 35/48*b^2*c^2*x^3/(sqrt(d*x^2 + c)*d^3) - 5/4*a*b*c*x^3/(sqrt(d*x^2 + c)*d^2) + 1/2*a^2*x^3/(sqrt(d*x^2 + c)*d) + 35/16*b^2*c^3*x/(sqrt(d*x^2 + c)*d^4) - 15/4*a*b*c^2*x/(sqrt(d*x^2 + c)*d^3) + 3/2*a^2*c*x/(sqrt(d*x^2 + c)*d^2) - 35/16*b^2*c^3*arcsinh(d*x/sqrt(c*d))/d^(9/2) + 15/4*a*b*c^2*arcsinh(d*x/sqrt(c*d))/d^(7/2) - 3/2*a^2*c*arcsinh(d*x/sqrt(c*d))/d^(5/2)","A",0
649,1,180,0,0.923803," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{6}}{5 \, \sqrt{d x^{2} + c} d} - \frac{2 \, b^{2} c x^{4}}{5 \, \sqrt{d x^{2} + c} d^{2}} + \frac{2 \, a b x^{4}}{3 \, \sqrt{d x^{2} + c} d} + \frac{8 \, b^{2} c^{2} x^{2}}{5 \, \sqrt{d x^{2} + c} d^{3}} - \frac{8 \, a b c x^{2}}{3 \, \sqrt{d x^{2} + c} d^{2}} + \frac{a^{2} x^{2}}{\sqrt{d x^{2} + c} d} + \frac{16 \, b^{2} c^{3}}{5 \, \sqrt{d x^{2} + c} d^{4}} - \frac{16 \, a b c^{2}}{3 \, \sqrt{d x^{2} + c} d^{3}} + \frac{2 \, a^{2} c}{\sqrt{d x^{2} + c} d^{2}}"," ",0,"1/5*b^2*x^6/(sqrt(d*x^2 + c)*d) - 2/5*b^2*c*x^4/(sqrt(d*x^2 + c)*d^2) + 2/3*a*b*x^4/(sqrt(d*x^2 + c)*d) + 8/5*b^2*c^2*x^2/(sqrt(d*x^2 + c)*d^3) - 8/3*a*b*c*x^2/(sqrt(d*x^2 + c)*d^2) + a^2*x^2/(sqrt(d*x^2 + c)*d) + 16/5*b^2*c^3/(sqrt(d*x^2 + c)*d^4) - 16/3*a*b*c^2/(sqrt(d*x^2 + c)*d^3) + 2*a^2*c/(sqrt(d*x^2 + c)*d^2)","A",0
650,1,170,0,0.866389," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{5}}{4 \, \sqrt{d x^{2} + c} d} - \frac{5 \, b^{2} c x^{3}}{8 \, \sqrt{d x^{2} + c} d^{2}} + \frac{a b x^{3}}{\sqrt{d x^{2} + c} d} - \frac{15 \, b^{2} c^{2} x}{8 \, \sqrt{d x^{2} + c} d^{3}} + \frac{3 \, a b c x}{\sqrt{d x^{2} + c} d^{2}} - \frac{a^{2} x}{\sqrt{d x^{2} + c} d} + \frac{15 \, b^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{7}{2}}} - \frac{3 \, a b c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{5}{2}}} + \frac{a^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{3}{2}}}"," ",0,"1/4*b^2*x^5/(sqrt(d*x^2 + c)*d) - 5/8*b^2*c*x^3/(sqrt(d*x^2 + c)*d^2) + a*b*x^3/(sqrt(d*x^2 + c)*d) - 15/8*b^2*c^2*x/(sqrt(d*x^2 + c)*d^3) + 3*a*b*c*x/(sqrt(d*x^2 + c)*d^2) - a^2*x/(sqrt(d*x^2 + c)*d) + 15/8*b^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(7/2) - 3*a*b*c*arcsinh(d*x/sqrt(c*d))/d^(5/2) + a^2*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
651,1,115,0,0.844785," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{4}}{3 \, \sqrt{d x^{2} + c} d} - \frac{4 \, b^{2} c x^{2}}{3 \, \sqrt{d x^{2} + c} d^{2}} + \frac{2 \, a b x^{2}}{\sqrt{d x^{2} + c} d} - \frac{8 \, b^{2} c^{2}}{3 \, \sqrt{d x^{2} + c} d^{3}} + \frac{4 \, a b c}{\sqrt{d x^{2} + c} d^{2}} - \frac{a^{2}}{\sqrt{d x^{2} + c} d}"," ",0,"1/3*b^2*x^4/(sqrt(d*x^2 + c)*d) - 4/3*b^2*c*x^2/(sqrt(d*x^2 + c)*d^2) + 2*a*b*x^2/(sqrt(d*x^2 + c)*d) - 8/3*b^2*c^2/(sqrt(d*x^2 + c)*d^3) + 4*a*b*c/(sqrt(d*x^2 + c)*d^2) - a^2/(sqrt(d*x^2 + c)*d)","A",0
652,1,108,0,0.915322," ","integrate((b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{3}}{2 \, \sqrt{d x^{2} + c} d} + \frac{a^{2} x}{\sqrt{d x^{2} + c} c} + \frac{3 \, b^{2} c x}{2 \, \sqrt{d x^{2} + c} d^{2}} - \frac{2 \, a b x}{\sqrt{d x^{2} + c} d} - \frac{3 \, b^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, d^{\frac{5}{2}}} + \frac{2 \, a b \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{3}{2}}}"," ",0,"1/2*b^2*x^3/(sqrt(d*x^2 + c)*d) + a^2*x/(sqrt(d*x^2 + c)*c) + 3/2*b^2*c*x/(sqrt(d*x^2 + c)*d^2) - 2*a*b*x/(sqrt(d*x^2 + c)*d) - 3/2*b^2*c*arcsinh(d*x/sqrt(c*d))/d^(5/2) + 2*a*b*arcsinh(d*x/sqrt(c*d))/d^(3/2)","A",0
653,1,90,0,0.910000," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x^{2}}{\sqrt{d x^{2} + c} d} - \frac{a^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{3}{2}}} + \frac{a^{2}}{\sqrt{d x^{2} + c} c} + \frac{2 \, b^{2} c}{\sqrt{d x^{2} + c} d^{2}} - \frac{2 \, a b}{\sqrt{d x^{2} + c} d}"," ",0,"b^2*x^2/(sqrt(d*x^2 + c)*d) - a^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + a^2/(sqrt(d*x^2 + c)*c) + 2*b^2*c/(sqrt(d*x^2 + c)*d^2) - 2*a*b/(sqrt(d*x^2 + c)*d)","A",0
654,1,91,0,0.901940," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{2 \, a b x}{\sqrt{d x^{2} + c} c} - \frac{b^{2} x}{\sqrt{d x^{2} + c} d} - \frac{2 \, a^{2} d x}{\sqrt{d x^{2} + c} c^{2}} + \frac{b^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{3}{2}}} - \frac{a^{2}}{\sqrt{d x^{2} + c} c x}"," ",0,"2*a*b*x/(sqrt(d*x^2 + c)*c) - b^2*x/(sqrt(d*x^2 + c)*d) - 2*a^2*d*x/(sqrt(d*x^2 + c)*c^2) + b^2*arcsinh(d*x/sqrt(c*d))/d^(3/2) - a^2/(sqrt(d*x^2 + c)*c*x)","A",0
655,1,112,0,0.855511," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, a b \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{3}{2}}} + \frac{3 \, a^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, c^{\frac{5}{2}}} + \frac{2 \, a b}{\sqrt{d x^{2} + c} c} - \frac{b^{2}}{\sqrt{d x^{2} + c} d} - \frac{3 \, a^{2} d}{2 \, \sqrt{d x^{2} + c} c^{2}} - \frac{a^{2}}{2 \, \sqrt{d x^{2} + c} c x^{2}}"," ",0,"-2*a*b*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + 3/2*a^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + 2*a*b/(sqrt(d*x^2 + c)*c) - b^2/(sqrt(d*x^2 + c)*d) - 3/2*a^2*d/(sqrt(d*x^2 + c)*c^2) - 1/2*a^2/(sqrt(d*x^2 + c)*c*x^2)","A",0
656,1,117,0,0.884311," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{b^{2} x}{\sqrt{d x^{2} + c} c} - \frac{4 \, a b d x}{\sqrt{d x^{2} + c} c^{2}} + \frac{8 \, a^{2} d^{2} x}{3 \, \sqrt{d x^{2} + c} c^{3}} - \frac{2 \, a b}{\sqrt{d x^{2} + c} c x} + \frac{4 \, a^{2} d}{3 \, \sqrt{d x^{2} + c} c^{2} x} - \frac{a^{2}}{3 \, \sqrt{d x^{2} + c} c x^{3}}"," ",0,"b^2*x/(sqrt(d*x^2 + c)*c) - 4*a*b*d*x/(sqrt(d*x^2 + c)*c^2) + 8/3*a^2*d^2*x/(sqrt(d*x^2 + c)*c^3) - 2*a*b/(sqrt(d*x^2 + c)*c*x) + 4/3*a^2*d/(sqrt(d*x^2 + c)*c^2*x) - 1/3*a^2/(sqrt(d*x^2 + c)*c*x^3)","A",0
657,1,177,0,0.850866," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{b^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{3}{2}}} + \frac{3 \, a b d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{5}{2}}} - \frac{15 \, a^{2} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{8 \, c^{\frac{7}{2}}} + \frac{b^{2}}{\sqrt{d x^{2} + c} c} - \frac{3 \, a b d}{\sqrt{d x^{2} + c} c^{2}} + \frac{15 \, a^{2} d^{2}}{8 \, \sqrt{d x^{2} + c} c^{3}} - \frac{a b}{\sqrt{d x^{2} + c} c x^{2}} + \frac{5 \, a^{2} d}{8 \, \sqrt{d x^{2} + c} c^{2} x^{2}} - \frac{a^{2}}{4 \, \sqrt{d x^{2} + c} c x^{4}}"," ",0,"-b^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(3/2) + 3*a*b*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) - 15/8*a^2*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(7/2) + b^2/(sqrt(d*x^2 + c)*c) - 3*a*b*d/(sqrt(d*x^2 + c)*c^2) + 15/8*a^2*d^2/(sqrt(d*x^2 + c)*c^3) - a*b/(sqrt(d*x^2 + c)*c*x^2) + 5/8*a^2*d/(sqrt(d*x^2 + c)*c^2*x^2) - 1/4*a^2/(sqrt(d*x^2 + c)*c*x^4)","A",0
658,1,184,0,0.833329," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, b^{2} d x}{\sqrt{d x^{2} + c} c^{2}} + \frac{16 \, a b d^{2} x}{3 \, \sqrt{d x^{2} + c} c^{3}} - \frac{16 \, a^{2} d^{3} x}{5 \, \sqrt{d x^{2} + c} c^{4}} - \frac{b^{2}}{\sqrt{d x^{2} + c} c x} + \frac{8 \, a b d}{3 \, \sqrt{d x^{2} + c} c^{2} x} - \frac{8 \, a^{2} d^{2}}{5 \, \sqrt{d x^{2} + c} c^{3} x} - \frac{2 \, a b}{3 \, \sqrt{d x^{2} + c} c x^{3}} + \frac{2 \, a^{2} d}{5 \, \sqrt{d x^{2} + c} c^{2} x^{3}} - \frac{a^{2}}{5 \, \sqrt{d x^{2} + c} c x^{5}}"," ",0,"-2*b^2*d*x/(sqrt(d*x^2 + c)*c^2) + 16/3*a*b*d^2*x/(sqrt(d*x^2 + c)*c^3) - 16/5*a^2*d^3*x/(sqrt(d*x^2 + c)*c^4) - b^2/(sqrt(d*x^2 + c)*c*x) + 8/3*a*b*d/(sqrt(d*x^2 + c)*c^2*x) - 8/5*a^2*d^2/(sqrt(d*x^2 + c)*c^3*x) - 2/3*a*b/(sqrt(d*x^2 + c)*c*x^3) + 2/5*a^2*d/(sqrt(d*x^2 + c)*c^2*x^3) - 1/5*a^2/(sqrt(d*x^2 + c)*c*x^5)","A",0
659,1,247,0,0.946462," ","integrate((b*x^2+a)^2/x^7/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{3 \, b^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, c^{\frac{5}{2}}} - \frac{15 \, a b d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{4 \, c^{\frac{7}{2}}} + \frac{35 \, a^{2} d^{3} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{16 \, c^{\frac{9}{2}}} - \frac{3 \, b^{2} d}{2 \, \sqrt{d x^{2} + c} c^{2}} + \frac{15 \, a b d^{2}}{4 \, \sqrt{d x^{2} + c} c^{3}} - \frac{35 \, a^{2} d^{3}}{16 \, \sqrt{d x^{2} + c} c^{4}} - \frac{b^{2}}{2 \, \sqrt{d x^{2} + c} c x^{2}} + \frac{5 \, a b d}{4 \, \sqrt{d x^{2} + c} c^{2} x^{2}} - \frac{35 \, a^{2} d^{2}}{48 \, \sqrt{d x^{2} + c} c^{3} x^{2}} - \frac{a b}{2 \, \sqrt{d x^{2} + c} c x^{4}} + \frac{7 \, a^{2} d}{24 \, \sqrt{d x^{2} + c} c^{2} x^{4}} - \frac{a^{2}}{6 \, \sqrt{d x^{2} + c} c x^{6}}"," ",0,"3/2*b^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) - 15/4*a*b*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(7/2) + 35/16*a^2*d^3*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(9/2) - 3/2*b^2*d/(sqrt(d*x^2 + c)*c^2) + 15/4*a*b*d^2/(sqrt(d*x^2 + c)*c^3) - 35/16*a^2*d^3/(sqrt(d*x^2 + c)*c^4) - 1/2*b^2/(sqrt(d*x^2 + c)*c*x^2) + 5/4*a*b*d/(sqrt(d*x^2 + c)*c^2*x^2) - 35/48*a^2*d^2/(sqrt(d*x^2 + c)*c^3*x^2) - 1/2*a*b/(sqrt(d*x^2 + c)*c*x^4) + 7/24*a^2*d/(sqrt(d*x^2 + c)*c^2*x^4) - 1/6*a^2/(sqrt(d*x^2 + c)*c*x^6)","A",0
660,1,296,0,0.885634," ","integrate(x^4*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{b^{2} x^{7}}{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{7 \, b^{2} c x^{5}}{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} + \frac{a b x^{5}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{1}{3} \, a^{2} x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)} - \frac{35 \, b^{2} c^{2} x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)}}{24 \, d^{2}} + \frac{5 \, a b c x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)}}{3 \, d} - \frac{35 \, b^{2} c^{2} x}{24 \, \sqrt{d x^{2} + c} d^{4}} + \frac{5 \, a b c x}{3 \, \sqrt{d x^{2} + c} d^{3}} - \frac{a^{2} x}{3 \, \sqrt{d x^{2} + c} d^{2}} + \frac{35 \, b^{2} c^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, d^{\frac{9}{2}}} - \frac{5 \, a b c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{7}{2}}} + \frac{a^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{5}{2}}}"," ",0,"1/4*b^2*x^7/((d*x^2 + c)^(3/2)*d) - 7/8*b^2*c*x^5/((d*x^2 + c)^(3/2)*d^2) + a*b*x^5/((d*x^2 + c)^(3/2)*d) - 1/3*a^2*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2)) - 35/24*b^2*c^2*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2))/d^2 + 5/3*a*b*c*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2))/d - 35/24*b^2*c^2*x/(sqrt(d*x^2 + c)*d^4) + 5/3*a*b*c*x/(sqrt(d*x^2 + c)*d^3) - 1/3*a^2*x/(sqrt(d*x^2 + c)*d^2) + 35/8*b^2*c^2*arcsinh(d*x/sqrt(c*d))/d^(9/2) - 5*a*b*c*arcsinh(d*x/sqrt(c*d))/d^(7/2) + a^2*arcsinh(d*x/sqrt(c*d))/d^(5/2)","A",0
661,1,181,0,0.909787," ","integrate(x^3*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{b^{2} x^{6}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{2 \, b^{2} c x^{4}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} + \frac{2 \, a b x^{4}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{8 \, b^{2} c^{2} x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{3}} + \frac{8 \, a b c x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} - \frac{a^{2} x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{16 \, b^{2} c^{3}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{4}} + \frac{16 \, a b c^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{3}} - \frac{2 \, a^{2} c}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}"," ",0,"1/3*b^2*x^6/((d*x^2 + c)^(3/2)*d) - 2*b^2*c*x^4/((d*x^2 + c)^(3/2)*d^2) + 2*a*b*x^4/((d*x^2 + c)^(3/2)*d) - 8*b^2*c^2*x^2/((d*x^2 + c)^(3/2)*d^3) + 8*a*b*c*x^2/((d*x^2 + c)^(3/2)*d^2) - a^2*x^2/((d*x^2 + c)^(3/2)*d) - 16/3*b^2*c^3/((d*x^2 + c)^(3/2)*d^4) + 16/3*a*b*c^2/((d*x^2 + c)^(3/2)*d^3) - 2/3*a^2*c/((d*x^2 + c)^(3/2)*d^2)","A",0
662,1,211,0,0.865123," ","integrate(x^2*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{b^{2} x^{5}}{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{2}{3} \, a b x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)} + \frac{5 \, b^{2} c x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)}}{6 \, d} + \frac{5 \, b^{2} c x}{6 \, \sqrt{d x^{2} + c} d^{3}} - \frac{2 \, a b x}{3 \, \sqrt{d x^{2} + c} d^{2}} - \frac{a^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{a^{2} x}{3 \, \sqrt{d x^{2} + c} c d} - \frac{5 \, b^{2} c \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, d^{\frac{7}{2}}} + \frac{2 \, a b \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{5}{2}}}"," ",0,"1/2*b^2*x^5/((d*x^2 + c)^(3/2)*d) - 2/3*a*b*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2)) + 5/6*b^2*c*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2))/d + 5/6*b^2*c*x/(sqrt(d*x^2 + c)*d^3) - 2/3*a*b*x/(sqrt(d*x^2 + c)*d^2) - 1/3*a^2*x/((d*x^2 + c)^(3/2)*d) + 1/3*a^2*x/(sqrt(d*x^2 + c)*c*d) - 5/2*b^2*c*arcsinh(d*x/sqrt(c*d))/d^(7/2) + 2*a*b*arcsinh(d*x/sqrt(c*d))/d^(5/2)","B",0
663,1,114,0,0.923012," ","integrate(x*(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{b^{2} x^{4}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{4 \, b^{2} c x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} - \frac{2 \, a b x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{8 \, b^{2} c^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{3}} - \frac{4 \, a b c}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} - \frac{a^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d}"," ",0,"b^2*x^4/((d*x^2 + c)^(3/2)*d) + 4*b^2*c*x^2/((d*x^2 + c)^(3/2)*d^2) - 2*a*b*x^2/((d*x^2 + c)^(3/2)*d) + 8/3*b^2*c^2/((d*x^2 + c)^(3/2)*d^3) - 4/3*a*b*c/((d*x^2 + c)^(3/2)*d^2) - 1/3*a^2/((d*x^2 + c)^(3/2)*d)","A",0
664,1,147,0,0.950244," ","integrate((b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b^{2} x {\left(\frac{3 \, x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, c}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}}\right)} + \frac{2 \, a^{2} x}{3 \, \sqrt{d x^{2} + c} c^{2}} + \frac{a^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{b^{2} x}{3 \, \sqrt{d x^{2} + c} d^{2}} - \frac{2 \, a b x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{2 \, a b x}{3 \, \sqrt{d x^{2} + c} c d} + \frac{b^{2} \operatorname{arsinh}\left(\frac{d x}{\sqrt{c d}}\right)}{d^{\frac{5}{2}}}"," ",0,"-1/3*b^2*x*(3*x^2/((d*x^2 + c)^(3/2)*d) + 2*c/((d*x^2 + c)^(3/2)*d^2)) + 2/3*a^2*x/(sqrt(d*x^2 + c)*c^2) + 1/3*a^2*x/((d*x^2 + c)^(3/2)*c) - 1/3*b^2*x/(sqrt(d*x^2 + c)*d^2) - 2/3*a*b*x/((d*x^2 + c)^(3/2)*d) + 2/3*a*b*x/(sqrt(d*x^2 + c)*c*d) + b^2*arcsinh(d*x/sqrt(c*d))/d^(5/2)","A",0
665,1,108,0,0.930129," ","integrate((b*x^2+a)^2/x/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{b^{2} x^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{a^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{5}{2}}} + \frac{a^{2}}{\sqrt{d x^{2} + c} c^{2}} + \frac{a^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{2 \, b^{2} c}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d^{2}} - \frac{2 \, a b}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d}"," ",0,"-b^2*x^2/((d*x^2 + c)^(3/2)*d) - a^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + a^2/(sqrt(d*x^2 + c)*c^2) + 1/3*a^2/((d*x^2 + c)^(3/2)*c) - 2/3*b^2*c/((d*x^2 + c)^(3/2)*d^2) - 2/3*a*b/((d*x^2 + c)^(3/2)*d)","A",0
666,1,132,0,0.927916," ","integrate((b*x^2+a)^2/x^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{4 \, a b x}{3 \, \sqrt{d x^{2} + c} c^{2}} + \frac{2 \, a b x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{b^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} + \frac{b^{2} x}{3 \, \sqrt{d x^{2} + c} c d} - \frac{8 \, a^{2} d x}{3 \, \sqrt{d x^{2} + c} c^{3}} - \frac{4 \, a^{2} d x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} - \frac{a^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c x}"," ",0,"4/3*a*b*x/(sqrt(d*x^2 + c)*c^2) + 2/3*a*b*x/((d*x^2 + c)^(3/2)*c) - 1/3*b^2*x/((d*x^2 + c)^(3/2)*d) + 1/3*b^2*x/(sqrt(d*x^2 + c)*c*d) - 8/3*a^2*d*x/(sqrt(d*x^2 + c)*c^3) - 4/3*a^2*d*x/((d*x^2 + c)^(3/2)*c^2) - a^2/((d*x^2 + c)^(3/2)*c*x)","A",0
667,1,146,0,0.963828," ","integrate((b*x^2+a)^2/x^3/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{2 \, a b \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{5}{2}}} + \frac{5 \, a^{2} d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{2 \, c^{\frac{7}{2}}} + \frac{2 \, a b}{\sqrt{d x^{2} + c} c^{2}} + \frac{2 \, a b}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{b^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} d} - \frac{5 \, a^{2} d}{2 \, \sqrt{d x^{2} + c} c^{3}} - \frac{5 \, a^{2} d}{6 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} - \frac{a^{2}}{2 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{2}}"," ",0,"-2*a*b*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + 5/2*a^2*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(7/2) + 2*a*b/(sqrt(d*x^2 + c)*c^2) + 2/3*a*b/((d*x^2 + c)^(3/2)*c) - 1/3*b^2/((d*x^2 + c)^(3/2)*d) - 5/2*a^2*d/(sqrt(d*x^2 + c)*c^3) - 5/6*a^2*d/((d*x^2 + c)^(3/2)*c^2) - 1/2*a^2/((d*x^2 + c)^(3/2)*c*x^2)","A",0
668,1,175,0,0.930521," ","integrate((b*x^2+a)^2/x^4/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{2 \, b^{2} x}{3 \, \sqrt{d x^{2} + c} c^{2}} + \frac{b^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{16 \, a b d x}{3 \, \sqrt{d x^{2} + c} c^{3}} - \frac{8 \, a b d x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{16 \, a^{2} d^{2} x}{3 \, \sqrt{d x^{2} + c} c^{4}} + \frac{8 \, a^{2} d^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} - \frac{2 \, a b}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c x} + \frac{2 \, a^{2} d}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} x} - \frac{a^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{3}}"," ",0,"2/3*b^2*x/(sqrt(d*x^2 + c)*c^2) + 1/3*b^2*x/((d*x^2 + c)^(3/2)*c) - 16/3*a*b*d*x/(sqrt(d*x^2 + c)*c^3) - 8/3*a*b*d*x/((d*x^2 + c)^(3/2)*c^2) + 16/3*a^2*d^2*x/(sqrt(d*x^2 + c)*c^4) + 8/3*a^2*d^2*x/((d*x^2 + c)^(3/2)*c^3) - 2*a*b/((d*x^2 + c)^(3/2)*c*x) + 2*a^2*d/((d*x^2 + c)^(3/2)*c^2*x) - 1/3*a^2/((d*x^2 + c)^(3/2)*c*x^3)","A",0
669,1,231,0,0.938301," ","integrate((b*x^2+a)^2/x^5/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{b^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{5}{2}}} + \frac{5 \, a b d \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{c^{\frac{7}{2}}} - \frac{35 \, a^{2} d^{2} \operatorname{arsinh}\left(\frac{c}{\sqrt{c d} {\left| x \right|}}\right)}{8 \, c^{\frac{9}{2}}} + \frac{b^{2}}{\sqrt{d x^{2} + c} c^{2}} + \frac{b^{2}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c} - \frac{5 \, a b d}{\sqrt{d x^{2} + c} c^{3}} - \frac{5 \, a b d}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{35 \, a^{2} d^{2}}{8 \, \sqrt{d x^{2} + c} c^{4}} + \frac{35 \, a^{2} d^{2}}{24 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} - \frac{a b}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{2}} + \frac{7 \, a^{2} d}{8 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} x^{2}} - \frac{a^{2}}{4 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{4}}"," ",0,"-b^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(5/2) + 5*a*b*d*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(7/2) - 35/8*a^2*d^2*arcsinh(c/(sqrt(c*d)*abs(x)))/c^(9/2) + b^2/(sqrt(d*x^2 + c)*c^2) + 1/3*b^2/((d*x^2 + c)^(3/2)*c) - 5*a*b*d/(sqrt(d*x^2 + c)*c^3) - 5/3*a*b*d/((d*x^2 + c)^(3/2)*c^2) + 35/8*a^2*d^2/(sqrt(d*x^2 + c)*c^4) + 35/24*a^2*d^2/((d*x^2 + c)^(3/2)*c^3) - a*b/((d*x^2 + c)^(3/2)*c*x^2) + 7/8*a^2*d/((d*x^2 + c)^(3/2)*c^2*x^2) - 1/4*a^2/((d*x^2 + c)^(3/2)*c*x^4)","A",0
670,1,244,0,0.963590," ","integrate((b*x^2+a)^2/x^6/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","-\frac{8 \, b^{2} d x}{3 \, \sqrt{d x^{2} + c} c^{3}} - \frac{4 \, b^{2} d x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{32 \, a b d^{2} x}{3 \, \sqrt{d x^{2} + c} c^{4}} + \frac{16 \, a b d^{2} x}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} - \frac{128 \, a^{2} d^{3} x}{15 \, \sqrt{d x^{2} + c} c^{5}} - \frac{64 \, a^{2} d^{3} x}{15 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{4}} - \frac{b^{2}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c x} + \frac{4 \, a b d}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} x} - \frac{16 \, a^{2} d^{2}}{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3} x} - \frac{2 \, a b}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{3}} + \frac{8 \, a^{2} d}{15 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2} x^{3}} - \frac{a^{2}}{5 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}} c x^{5}}"," ",0,"-8/3*b^2*d*x/(sqrt(d*x^2 + c)*c^3) - 4/3*b^2*d*x/((d*x^2 + c)^(3/2)*c^2) + 32/3*a*b*d^2*x/(sqrt(d*x^2 + c)*c^4) + 16/3*a*b*d^2*x/((d*x^2 + c)^(3/2)*c^3) - 128/15*a^2*d^3*x/(sqrt(d*x^2 + c)*c^5) - 64/15*a^2*d^3*x/((d*x^2 + c)^(3/2)*c^4) - b^2/((d*x^2 + c)^(3/2)*c*x) + 4*a*b*d/((d*x^2 + c)^(3/2)*c^2*x) - 16/5*a^2*d^2/((d*x^2 + c)^(3/2)*c^3*x) - 2/3*a*b/((d*x^2 + c)^(3/2)*c*x^3) + 8/15*a^2*d/((d*x^2 + c)^(3/2)*c^2*x^3) - 1/5*a^2/((d*x^2 + c)^(3/2)*c*x^5)","A",0
671,1,67,0,1.826046," ","integrate(x^5/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} d^{3} \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} b^{2}} + \frac{\left(d x^{2}\right)^{\frac{3}{2}} b d - 3 \, \sqrt{d x^{2}} a d^{2}}{b^{2}}}{3 \, d^{3}}"," ",0,"1/3*(3*a^2*d^3*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*b^2) + ((d*x^2)^(3/2)*b*d - 3*sqrt(d*x^2)*a*d^2)/b^2)/d^3","A",0
672,1,49,0,1.792942," ","integrate(x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{a d^{2} \arctan\left(\frac{\sqrt{d x^{2}} b}{\sqrt{a b d}}\right)}{\sqrt{a b d} b} - \frac{\sqrt{d x^{2}} d}{b}}{d^{2}}"," ",0,"-(a*d^2*arctan(sqrt(d*x^2)*b/sqrt(a*b*d))/(sqrt(a*b*d)*b) - sqrt(d*x^2)*d/b)/d^2","A",0
673,1,23,0,1.970148," ","integrate(x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""maxima"")","\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
674,1,35,0,1.989459," ","integrate(1/x/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""maxima"")","-\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a \sqrt{d}} - \frac{1}{a \sqrt{d} x}"," ",0,"-b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*sqrt(d)) - 1/(a*sqrt(d)*x)","A",0
675,1,52,0,2.010426," ","integrate(1/x^3/(b*x^2+a)/(d*x^2)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2} \sqrt{d}} + \frac{3 \, b \sqrt{d} x^{2} - a \sqrt{d}}{3 \, a^{2} d x^{3}}"," ",0,"b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*sqrt(d)) + 1/3*(3*b*sqrt(d)*x^2 - a*sqrt(d))/(a^2*d*x^3)","A",0
676,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c} x^{4}}{b x^{2} + a}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*x^4/(b*x^2 + a), x)","F",0
677,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
678,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c} x^{2}}{b x^{2} + a}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*x^2/(b*x^2 + a), x)","F",0
679,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
680,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{b x^{2} + a}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a), x)","F",0
681,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)} x}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)*x), x)","F",0
682,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)*x^2), x)","F",0
683,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)*x^3), x)","F",0
684,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)*x^4), x)","F",0
685,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{4}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)*x^4/(b*x^2 + a), x)","F",0
686,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
687,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{2}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)*x^2/(b*x^2 + a), x)","F",0
688,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
689,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a), x)","F",0
690,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)} x}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)*x), x)","F",0
691,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)*x^2), x)","F",0
692,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)} x^{3}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)*x^3), x)","F",0
693,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)} x^{4}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)*x^4), x)","F",0
694,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{4}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)*x^4/(b*x^2 + a), x)","F",0
695,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
696,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{2}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)*x^2/(b*x^2 + a), x)","F",0
697,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
698,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{b x^{2} + a}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/(b*x^2 + a), x)","F",0
699,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)} x}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)*x), x)","F",0
700,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)} x^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)*x^2), x)","F",0
701,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)} x^{3}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)*x^3), x)","F",0
702,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)} x^{4}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)*x^4), x)","F",0
703,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
704,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
705,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
706,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)*x), x)","F",0
707,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)*x^3), x)","F",0
708,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
709,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
710,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
711,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)*x^2), x)","F",0
712,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} \sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*sqrt(d*x^2 + c)*x^4), x)","F",0
713,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)*(d*x^2 + c)^(3/2)), x)","F",0
714,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
715,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)*(d*x^2 + c)^(3/2)), x)","F",0
716,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
717,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)), x)","F",0
718,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)*x), x)","F",0
719,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)*x^2), x)","F",0
720,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)*x^3), x)","F",0
721,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(3/2)*x^4), x)","F",0
722,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)*(d*x^2 + c)^(5/2)), x)","F",0
723,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
724,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)*(d*x^2 + c)^(5/2)), x)","F",0
725,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
726,0,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(5/2)), x)","F",0
727,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(5/2)*x), x)","F",0
728,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(5/2)*x^2), x)","F",0
729,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(5/2)*x^3), x)","F",0
730,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)*(d*x^2 + c)^(5/2)*x^4), x)","F",0
731,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c} x^{4}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*x^4/(b*x^2 + a)^2, x)","F",0
732,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
733,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c} x^{2}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*x^2/(b*x^2 + a)^2, x)","F",0
734,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
735,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^2, x)","F",0
736,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{2} x}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)^2*x), x)","F",0
737,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)^2*x^2), x)","F",0
738,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)^2*x^3), x)","F",0
739,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{2} x^{4}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/((b*x^2 + a)^2*x^4), x)","F",0
740,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{4}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)*x^4/(b*x^2 + a)^2, x)","F",0
741,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
742,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{2}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)*x^2/(b*x^2 + a)^2, x)","F",0
743,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
744,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^2, x)","F",0
745,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{2} x}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)^2*x), x)","F",0
746,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)^2*x^2), x)","F",0
747,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)^2*x^3), x)","F",0
748,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{4}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/((b*x^2 + a)^2*x^4), x)","F",0
749,0,0,0,0.000000," ","integrate(x^4*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{4}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)*x^4/(b*x^2 + a)^2, x)","F",0
750,-2,0,0,0.000000," ","integrate(x^3*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
751,0,0,0,0.000000," ","integrate(x^2*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{2}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)*x^2/(b*x^2 + a)^2, x)","F",0
752,-2,0,0,0.000000," ","integrate(x*(d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
753,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/(b*x^2 + a)^2, x)","F",0
754,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{2} x}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)^2*x), x)","F",0
755,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^2/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)^2*x^2), x)","F",0
756,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^3/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)^2*x^3), x)","F",0
757,0,0,0,0.000000," ","integrate((d*x^2+c)^(5/2)/x^4/(b*x^2+a)^2,x, algorithm=""maxima"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{5}{2}}}{{\left(b x^{2} + a\right)}^{2} x^{4}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(5/2)/((b*x^2 + a)^2*x^4), x)","F",0
758,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)^2*sqrt(d*x^2 + c)), x)","F",0
759,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
760,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)^2*sqrt(d*x^2 + c)), x)","F",0
761,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
762,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)), x)","F",0
763,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)*x), x)","F",0
764,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)*x^2), x)","F",0
765,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)*x^3), x)","F",0
766,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} \sqrt{d x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*sqrt(d*x^2 + c)*x^4), x)","F",0
767,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)), x)","F",0
768,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
769,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)), x)","F",0
770,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
771,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)), x)","F",0
772,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*x), x)","F",0
773,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*x^2), x)","F",0
774,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*x^3), x)","F",0
775,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(3/2)*x^4), x)","F",0
776,0,0,0,0.000000," ","integrate(x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)), x)","F",0
777,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
778,0,0,0,0.000000," ","integrate(x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)), x)","F",0
779,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
780,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)), x)","F",0
781,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)*x), x)","F",0
782,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)*x^2), x)","F",0
783,0,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)*x^3), x)","F",0
784,0,0,0,0.000000," ","integrate(1/x^4/(b*x^2+a)^2/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{2} {\left(d x^{2} + c\right)}^{\frac{5}{2}} x^{4}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^2*(d*x^2 + c)^(5/2)*x^4), x)","F",0
785,0,0,0,0.000000," ","integrate((e*x)^(3/2)*(B*x^2+A)*(b*x^2+a)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
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928,0,0,0,0.000000," ","integrate((e*x)^(5/2)/(-b*x^2+a)^2/(-d*x^2+c)^(5/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^5*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
935,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
936,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
937,-2,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
938,-2,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
939,-2,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
940,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^5*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
945,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
946,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
947,-2,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
948,-2,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
949,-2,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
950,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^5*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
955,-2,0,0,0.000000," ","integrate(x^3*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
956,-2,0,0,0.000000," ","integrate(x*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
957,-2,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
958,-2,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x^3/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
959,-2,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/x^5/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
960,0,0,0,0.000000," ","integrate(x^4*(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
965,1,46,0,2.012810," ","integrate(x^3*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{12} \, \sqrt{-9 \, x^{4} + 9 \, x^{2} - 2} x^{2} - \frac{5}{72} \, \sqrt{-9 \, x^{4} + 9 \, x^{2} - 2} + \frac{7}{144} \, \arcsin\left(6 \, x^{2} - 3\right)"," ",0,"-1/12*sqrt(-9*x^4 + 9*x^2 - 2)*x^2 - 5/72*sqrt(-9*x^4 + 9*x^2 - 2) + 7/144*arcsin(6*x^2 - 3)","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=""maxima"")","\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
967,1,27,0,2.001070," ","integrate(x*(3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, \sqrt{-9 \, x^{4} + 9 \, x^{2} - 2} + \frac{1}{12} \, \arcsin\left(6 \, x^{2} - 3\right)"," ",0,"-1/6*sqrt(-9*x^4 + 9*x^2 - 2) + 1/12*arcsin(6*x^2 - 3)","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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
970,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
971,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
972,-2,0,0,0.000000," ","integrate(1/x/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
973,-2,0,0,0.000000," ","integrate(1/x^3/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
974,-2,0,0,0.000000," ","integrate(1/x^5/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
975,0,0,0,0.000000," ","integrate(x^6/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
981,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
982,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
983,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
984,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
985,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
986,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
987,-2,0,0,0.000000," ","integrate(x^3/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
988,-2,0,0,0.000000," ","integrate(x/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
989,-2,0,0,0.000000," ","integrate(x^5/(b*x^2+a)^(9/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
990,-2,0,0,0.000000," ","integrate(x/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
991,-2,0,0,0.000000," ","integrate(x/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c zero or nonzero?","F(-2)",0
992,0,0,0,0.000000," ","integrate(x^2/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
1008,1,108,0,1.937819," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\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
1009,1,97,0,1.998696," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","-\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
1010,1,86,0,2.021600," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\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
1011,0,0,0,0.000000," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)*x), x)","F",0
1012,0,0,0,0.000000," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{3}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)*x^3), x)","F",0
1013,0,0,0,0.000000," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)*x^5), x)","F",0
1014,0,0,0,0.000000," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
1019,1,126,0,1.981000," ","integrate(x^7/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\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
1020,1,115,0,1.957866," ","integrate(x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","-\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
1021,1,104,0,1.947360," ","integrate(x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\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
1022,1,104,0,2.030000," ","integrate(x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\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
1023,0,0,0,0.000000," ","integrate(1/x/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)*x), x)","F",0
1024,0,0,0,0.000000," ","integrate(1/x^3/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{3}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)*x^3), x)","F",0
1025,0,0,0,0.000000," ","integrate(1/x^5/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(x^{2} + 3\right)}^{2} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} x^{5}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)^2*(-x^2 + 1)^(1/3)*x^5), x)","F",0
1026,0,0,0,0.000000," ","integrate(x^4/(-x^2+1)^(1/3)/(x^2+3)^2,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
1031,1,151,0,1.964955," ","integrate(x^7/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","\frac{2}{891} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{11}{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)^(11/4) - 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
1032,1,140,0,2.067015," ","integrate(x^5/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\frac{2}{189} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{7}{4}} - \frac{8}{27} \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{8}{27} \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{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) - 8/27*2^(1/4)*arctan(1/2*2^(1/4)*(2^(3/4) + 2*(-3*x^2 + 2)^(1/4))) - 8/27*2^(1/4)*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
1033,1,129,0,2.043208," ","integrate(x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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
1034,1,118,0,1.901823," ","integrate(x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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
1035,0,0,0,0.000000," ","integrate(1/x/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)*x), x)","F",0
1036,0,0,0,0.000000," ","integrate(1/x^3/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}} x^{3}}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 4)*(-3*x^2 + 2)^(1/4)*x^3), x)","F",0
1037,0,0,0,0.000000," ","integrate(x^4/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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
1042,1,74,0,1.861783," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\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(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\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((3*x^2 - 1)^(1/4) - 1)","A",0
1043,1,63,0,1.929396," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\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(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\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((3*x^2 - 1)^(1/4) - 1)","A",0
1044,1,52,0,1.985898," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\frac{2}{27} \, {\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} + \frac{2}{9} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/27*(3*x^2 - 1)^(3/4) + 2/9*arctan((3*x^2 - 1)^(1/4)) - 1/9*log((3*x^2 - 1)^(1/4) + 1) + 1/9*log((3*x^2 - 1)^(1/4) - 1)","A",0
1045,1,41,0,2.018874," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\frac{1}{3} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log((3*x^2 - 1)^(1/4) - 1)","A",0
1046,0,0,0,0.000000," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)} x}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)*x), x)","F",0
1047,0,0,0,0.000000," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)*x^3), x)","F",0
1048,0,0,0,0.000000," ","integrate(x^4/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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
1061,1,151,0,2.008323," ","integrate(x^7/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","\frac{2}{729} \, {\left(-3 \, x^{2} + 2\right)}^{\frac{9}{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)^(9/4) - 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
1062,1,140,0,2.078729," ","integrate(x^5/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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
1063,1,129,0,2.009387," ","integrate(x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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
1064,1,118,0,2.019401," ","integrate(x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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
1065,0,0,0,0.000000," ","integrate(1/x/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)*x), x)","F",0
1066,0,0,0,0.000000," ","integrate(1/x^3/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\int \frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{3}{4}} x^{3}}\,{d x}"," ",0,"-integrate(1/((3*x^2 - 4)*(-3*x^2 + 2)^(3/4)*x^3), x)","F",0
1067,0,0,0,0.000000," ","integrate(x^6/(-3*x^2+2)^(3/4)/(-3*x^2+4),x, algorithm=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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=""maxima"")","\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=""maxima"")","-\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
1081,1,74,0,2.023469," ","integrate(x^7/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\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(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\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((3*x^2 - 1)^(1/4) - 1)","A",0
1082,1,63,0,1.950625," ","integrate(x^5/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\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(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\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((3*x^2 - 1)^(1/4) - 1)","A",0
1083,1,52,0,1.808765," ","integrate(x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\frac{2}{9} \, {\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - \frac{2}{9} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{9} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"2/9*(3*x^2 - 1)^(1/4) - 2/9*arctan((3*x^2 - 1)^(1/4)) - 1/9*log((3*x^2 - 1)^(1/4) + 1) + 1/9*log((3*x^2 - 1)^(1/4) - 1)","A",0
1084,1,41,0,1.845900," ","integrate(x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","-\frac{1}{3} \, \arctan\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}}\right) - \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} + 1\right) + \frac{1}{6} \, \log\left({\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} - 1\right)"," ",0,"-1/3*arctan((3*x^2 - 1)^(1/4)) - 1/6*log((3*x^2 - 1)^(1/4) + 1) + 1/6*log((3*x^2 - 1)^(1/4) - 1)","A",0
1085,0,0,0,0.000000," ","integrate(1/x/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)} x}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)*x), x)","F",0
1086,0,0,0,0.000000," ","integrate(1/x^3/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{3}{4}} {\left(3 \, x^{2} - 2\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)*x^3), x)","F",0
1087,0,0,0,0.000000," ","integrate(x^6/(3*x^2-2)/(3*x^2-1)^(3/4),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
