1,1,29,0,0.652031," ","integrate(x^2*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} b B + \frac{1}{6} x^{6} a B + \frac{1}{6} x^{6} b A + \frac{1}{3} x^{3} a A"," ",0,"1/9*x^9*b*B + 1/6*x^6*a*B + 1/6*x^6*b*A + 1/3*x^3*a*A","A",0
2,1,29,0,0.698585," ","integrate(x*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{2} x^{2} a A"," ",0,"1/8*x^8*b*B + 1/5*x^5*a*B + 1/5*x^5*b*A + 1/2*x^2*a*A","A",0
3,1,26,0,1.077621," ","integrate((b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b B + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + x a A"," ",0,"1/7*x^7*b*B + 1/4*x^4*a*B + 1/4*x^4*b*A + x*a*A","A",0
4,1,25,0,0.763149," ","integrate((b*x^3+a)*(B*x^3+A)/x,x, algorithm=""fricas"")","\frac{1}{6} \, B b x^{6} + \frac{1}{3} \, {\left(B a + A b\right)} x^{3} + A a \log\left(x\right)"," ",0,"1/6*B*b*x^6 + 1/3*(B*a + A*b)*x^3 + A*a*log(x)","A",0
5,1,29,0,0.727268," ","integrate((b*x^3+a)*(B*x^3+A)/x^2,x, algorithm=""fricas"")","\frac{2 \, B b x^{6} + 5 \, {\left(B a + A b\right)} x^{3} - 10 \, A a}{10 \, x}"," ",0,"1/10*(2*B*b*x^6 + 5*(B*a + A*b)*x^3 - 10*A*a)/x","A",0
6,1,28,0,0.793690," ","integrate((b*x^3+a)*(B*x^3+A)/x^3,x, algorithm=""fricas"")","\frac{B b x^{6} + 4 \, {\left(B a + A b\right)} x^{3} - 2 \, A a}{4 \, x^{2}}"," ",0,"1/4*(B*b*x^6 + 4*(B*a + A*b)*x^3 - 2*A*a)/x^2","A",0
7,1,30,0,0.809567," ","integrate((b*x^3+a)*(B*x^3+A)/x^4,x, algorithm=""fricas"")","\frac{B b x^{6} + 3 \, {\left(B a + A b\right)} x^{3} \log\left(x\right) - A a}{3 \, x^{3}}"," ",0,"1/3*(B*b*x^6 + 3*(B*a + A*b)*x^3*log(x) - A*a)/x^3","A",0
8,1,29,0,1.291134," ","integrate((b*x^3+a)*(B*x^3+A)/x^5,x, algorithm=""fricas"")","\frac{2 \, B b x^{6} - 4 \, {\left(B a + A b\right)} x^{3} - A a}{4 \, x^{4}}"," ",0,"1/4*(2*B*b*x^6 - 4*(B*a + A*b)*x^3 - A*a)/x^4","A",0
9,1,29,0,0.742315," ","integrate((b*x^3+a)*(B*x^3+A)/x^6,x, algorithm=""fricas"")","\frac{10 \, B b x^{6} - 5 \, {\left(B a + A b\right)} x^{3} - 2 \, A a}{10 \, x^{5}}"," ",0,"1/10*(10*B*b*x^6 - 5*(B*a + A*b)*x^3 - 2*A*a)/x^5","A",0
10,1,31,0,0.926680," ","integrate((b*x^3+a)*(B*x^3+A)/x^7,x, algorithm=""fricas"")","\frac{6 \, B b x^{6} \log\left(x\right) - 2 \, {\left(B a + A b\right)} x^{3} - A a}{6 \, x^{6}}"," ",0,"1/6*(6*B*b*x^6*log(x) - 2*(B*a + A*b)*x^3 - A*a)/x^6","A",0
11,1,53,0,1.028204," ","integrate(x^2*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{2} B + \frac{2}{9} x^{9} b a B + \frac{1}{9} x^{9} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/12*x^12*b^2*B + 2/9*x^9*b*a*B + 1/9*x^9*b^2*A + 1/6*x^6*a^2*B + 1/3*x^6*b*a*A + 1/3*x^3*a^2*A","A",0
12,1,53,0,1.061432," ","integrate(x*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{2} B + \frac{1}{4} x^{8} b a B + \frac{1}{8} x^{8} b^{2} A + \frac{1}{5} x^{5} a^{2} B + \frac{2}{5} x^{5} b a A + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/11*x^11*b^2*B + 1/4*x^8*b*a*B + 1/8*x^8*b^2*A + 1/5*x^5*a^2*B + 2/5*x^5*b*a*A + 1/2*x^2*a^2*A","A",0
13,1,50,0,0.642152," ","integrate((b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + x a^{2} A"," ",0,"1/10*x^10*b^2*B + 2/7*x^7*b*a*B + 1/7*x^7*b^2*A + 1/4*x^4*a^2*B + 1/2*x^4*b*a*A + x*a^2*A","A",0
14,1,49,0,0.771912," ","integrate((b*x^3+a)^2*(B*x^3+A)/x,x, algorithm=""fricas"")","\frac{1}{9} \, B b^{2} x^{9} + \frac{1}{6} \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + \frac{1}{3} \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} + A a^{2} \log\left(x\right)"," ",0,"1/9*B*b^2*x^9 + 1/6*(2*B*a*b + A*b^2)*x^6 + 1/3*(B*a^2 + 2*A*a*b)*x^3 + A*a^2*log(x)","A",0
15,1,53,0,0.736001," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^2,x, algorithm=""fricas"")","\frac{5 \, B b^{2} x^{9} + 8 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 20 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 40 \, A a^{2}}{40 \, x}"," ",0,"1/40*(5*B*b^2*x^9 + 8*(2*B*a*b + A*b^2)*x^6 + 20*(B*a^2 + 2*A*a*b)*x^3 - 40*A*a^2)/x","A",0
16,1,53,0,0.825720," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^3,x, algorithm=""fricas"")","\frac{4 \, B b^{2} x^{9} + 7 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 28 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 14 \, A a^{2}}{28 \, x^{2}}"," ",0,"1/28*(4*B*b^2*x^9 + 7*(2*B*a*b + A*b^2)*x^6 + 28*(B*a^2 + 2*A*a*b)*x^3 - 14*A*a^2)/x^2","A",0
17,1,54,0,0.638623," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^4,x, algorithm=""fricas"")","\frac{B b^{2} x^{9} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 6 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} \log\left(x\right) - 2 \, A a^{2}}{6 \, x^{3}}"," ",0,"1/6*(B*b^2*x^9 + 2*(2*B*a*b + A*b^2)*x^6 + 6*(B*a^2 + 2*A*a*b)*x^3*log(x) - 2*A*a^2)/x^3","A",0
18,1,53,0,0.717067," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^5,x, algorithm=""fricas"")","\frac{4 \, B b^{2} x^{9} + 10 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} - 20 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 5 \, A a^{2}}{20 \, x^{4}}"," ",0,"1/20*(4*B*b^2*x^9 + 10*(2*B*a*b + A*b^2)*x^6 - 20*(B*a^2 + 2*A*a*b)*x^3 - 5*A*a^2)/x^4","A",0
19,1,53,0,1.370633," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^6,x, algorithm=""fricas"")","\frac{5 \, B b^{2} x^{9} + 20 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} - 10 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 4 \, A a^{2}}{20 \, x^{5}}"," ",0,"1/20*(5*B*b^2*x^9 + 20*(2*B*a*b + A*b^2)*x^6 - 10*(B*a^2 + 2*A*a*b)*x^3 - 4*A*a^2)/x^5","A",0
20,1,55,0,0.747470," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^7,x, algorithm=""fricas"")","\frac{2 \, B b^{2} x^{9} + 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} \log\left(x\right) - 2 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - A a^{2}}{6 \, x^{6}}"," ",0,"1/6*(2*B*b^2*x^9 + 6*(2*B*a*b + A*b^2)*x^6*log(x) - 2*(B*a^2 + 2*A*a*b)*x^3 - A*a^2)/x^6","A",0
21,1,53,0,0.801613," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^8,x, algorithm=""fricas"")","\frac{14 \, B b^{2} x^{9} - 28 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} - 7 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 4 \, A a^{2}}{28 \, x^{7}}"," ",0,"1/28*(14*B*b^2*x^9 - 28*(2*B*a*b + A*b^2)*x^6 - 7*(B*a^2 + 2*A*a*b)*x^3 - 4*A*a^2)/x^7","A",0
22,1,53,0,0.826446," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^9,x, algorithm=""fricas"")","\frac{40 \, B b^{2} x^{9} - 20 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} - 8 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 5 \, A a^{2}}{40 \, x^{8}}"," ",0,"1/40*(40*B*b^2*x^9 - 20*(2*B*a*b + A*b^2)*x^6 - 8*(B*a^2 + 2*A*a*b)*x^3 - 5*A*a^2)/x^8","A",0
23,1,125,0,0.713531," ","integrate(x^9*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{28} x^{28} b^{5} B + \frac{1}{5} x^{25} b^{4} a B + \frac{1}{25} x^{25} b^{5} A + \frac{5}{11} x^{22} b^{3} a^{2} B + \frac{5}{22} x^{22} b^{4} a A + \frac{10}{19} x^{19} b^{2} a^{3} B + \frac{10}{19} x^{19} b^{3} a^{2} A + \frac{5}{16} x^{16} b a^{4} B + \frac{5}{8} x^{16} b^{2} a^{3} A + \frac{1}{13} x^{13} a^{5} B + \frac{5}{13} x^{13} b a^{4} A + \frac{1}{10} x^{10} a^{5} A"," ",0,"1/28*x^28*b^5*B + 1/5*x^25*b^4*a*B + 1/25*x^25*b^5*A + 5/11*x^22*b^3*a^2*B + 5/22*x^22*b^4*a*A + 10/19*x^19*b^2*a^3*B + 10/19*x^19*b^3*a^2*A + 5/16*x^16*b*a^4*B + 5/8*x^16*b^2*a^3*A + 1/13*x^13*a^5*B + 5/13*x^13*b*a^4*A + 1/10*x^10*a^5*A","A",0
24,1,125,0,0.734218," ","integrate(x^8*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{27} x^{27} b^{5} B + \frac{5}{24} x^{24} b^{4} a B + \frac{1}{24} x^{24} b^{5} A + \frac{10}{21} x^{21} b^{3} a^{2} B + \frac{5}{21} x^{21} b^{4} a A + \frac{5}{9} x^{18} b^{2} a^{3} B + \frac{5}{9} x^{18} b^{3} a^{2} A + \frac{1}{3} x^{15} b a^{4} B + \frac{2}{3} x^{15} b^{2} a^{3} A + \frac{1}{12} x^{12} a^{5} B + \frac{5}{12} x^{12} b a^{4} A + \frac{1}{9} x^{9} a^{5} A"," ",0,"1/27*x^27*b^5*B + 5/24*x^24*b^4*a*B + 1/24*x^24*b^5*A + 10/21*x^21*b^3*a^2*B + 5/21*x^21*b^4*a*A + 5/9*x^18*b^2*a^3*B + 5/9*x^18*b^3*a^2*A + 1/3*x^15*b*a^4*B + 2/3*x^15*b^2*a^3*A + 1/12*x^12*a^5*B + 5/12*x^12*b*a^4*A + 1/9*x^9*a^5*A","A",0
25,1,125,0,0.689151," ","integrate(x^7*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{26} x^{26} b^{5} B + \frac{5}{23} x^{23} b^{4} a B + \frac{1}{23} x^{23} b^{5} A + \frac{1}{2} x^{20} b^{3} a^{2} B + \frac{1}{4} x^{20} b^{4} a A + \frac{10}{17} x^{17} b^{2} a^{3} B + \frac{10}{17} x^{17} b^{3} a^{2} A + \frac{5}{14} x^{14} b a^{4} B + \frac{5}{7} x^{14} b^{2} a^{3} A + \frac{1}{11} x^{11} a^{5} B + \frac{5}{11} x^{11} b a^{4} A + \frac{1}{8} x^{8} a^{5} A"," ",0,"1/26*x^26*b^5*B + 5/23*x^23*b^4*a*B + 1/23*x^23*b^5*A + 1/2*x^20*b^3*a^2*B + 1/4*x^20*b^4*a*A + 10/17*x^17*b^2*a^3*B + 10/17*x^17*b^3*a^2*A + 5/14*x^14*b*a^4*B + 5/7*x^14*b^2*a^3*A + 1/11*x^11*a^5*B + 5/11*x^11*b*a^4*A + 1/8*x^8*a^5*A","A",0
26,1,125,0,0.516632," ","integrate(x^6*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{25} x^{25} b^{5} B + \frac{5}{22} x^{22} b^{4} a B + \frac{1}{22} x^{22} b^{5} A + \frac{10}{19} x^{19} b^{3} a^{2} B + \frac{5}{19} x^{19} b^{4} a A + \frac{5}{8} x^{16} b^{2} a^{3} B + \frac{5}{8} x^{16} b^{3} a^{2} A + \frac{5}{13} x^{13} b a^{4} B + \frac{10}{13} x^{13} b^{2} a^{3} A + \frac{1}{10} x^{10} a^{5} B + \frac{1}{2} x^{10} b a^{4} A + \frac{1}{7} x^{7} a^{5} A"," ",0,"1/25*x^25*b^5*B + 5/22*x^22*b^4*a*B + 1/22*x^22*b^5*A + 10/19*x^19*b^3*a^2*B + 5/19*x^19*b^4*a*A + 5/8*x^16*b^2*a^3*B + 5/8*x^16*b^3*a^2*A + 5/13*x^13*b*a^4*B + 10/13*x^13*b^2*a^3*A + 1/10*x^10*a^5*B + 1/2*x^10*b*a^4*A + 1/7*x^7*a^5*A","A",0
27,1,125,0,1.284947," ","integrate(x^5*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{24} x^{24} b^{5} B + \frac{5}{21} x^{21} b^{4} a B + \frac{1}{21} x^{21} b^{5} A + \frac{5}{9} x^{18} b^{3} a^{2} B + \frac{5}{18} x^{18} b^{4} a A + \frac{2}{3} x^{15} b^{2} a^{3} B + \frac{2}{3} x^{15} b^{3} a^{2} A + \frac{5}{12} x^{12} b a^{4} B + \frac{5}{6} x^{12} b^{2} a^{3} A + \frac{1}{9} x^{9} a^{5} B + \frac{5}{9} x^{9} b a^{4} A + \frac{1}{6} x^{6} a^{5} A"," ",0,"1/24*x^24*b^5*B + 5/21*x^21*b^4*a*B + 1/21*x^21*b^5*A + 5/9*x^18*b^3*a^2*B + 5/18*x^18*b^4*a*A + 2/3*x^15*b^2*a^3*B + 2/3*x^15*b^3*a^2*A + 5/12*x^12*b*a^4*B + 5/6*x^12*b^2*a^3*A + 1/9*x^9*a^5*B + 5/9*x^9*b*a^4*A + 1/6*x^6*a^5*A","B",0
28,1,125,0,0.819914," ","integrate(x^4*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{23} x^{23} b^{5} B + \frac{1}{4} x^{20} b^{4} a B + \frac{1}{20} x^{20} b^{5} A + \frac{10}{17} x^{17} b^{3} a^{2} B + \frac{5}{17} x^{17} b^{4} a A + \frac{5}{7} x^{14} b^{2} a^{3} B + \frac{5}{7} x^{14} b^{3} a^{2} A + \frac{5}{11} x^{11} b a^{4} B + \frac{10}{11} x^{11} b^{2} a^{3} A + \frac{1}{8} x^{8} a^{5} B + \frac{5}{8} x^{8} b a^{4} A + \frac{1}{5} x^{5} a^{5} A"," ",0,"1/23*x^23*b^5*B + 1/4*x^20*b^4*a*B + 1/20*x^20*b^5*A + 10/17*x^17*b^3*a^2*B + 5/17*x^17*b^4*a*A + 5/7*x^14*b^2*a^3*B + 5/7*x^14*b^3*a^2*A + 5/11*x^11*b*a^4*B + 10/11*x^11*b^2*a^3*A + 1/8*x^8*a^5*B + 5/8*x^8*b*a^4*A + 1/5*x^5*a^5*A","A",0
29,1,124,0,0.754019," ","integrate(x^3*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{22} x^{22} b^{5} B + \frac{5}{19} x^{19} b^{4} a B + \frac{1}{19} x^{19} b^{5} A + \frac{5}{8} x^{16} b^{3} a^{2} B + \frac{5}{16} x^{16} b^{4} a A + \frac{10}{13} x^{13} b^{2} a^{3} B + \frac{10}{13} x^{13} b^{3} a^{2} A + \frac{1}{2} x^{10} b a^{4} B + x^{10} b^{2} a^{3} A + \frac{1}{7} x^{7} a^{5} B + \frac{5}{7} x^{7} b a^{4} A + \frac{1}{4} x^{4} a^{5} A"," ",0,"1/22*x^22*b^5*B + 5/19*x^19*b^4*a*B + 1/19*x^19*b^5*A + 5/8*x^16*b^3*a^2*B + 5/16*x^16*b^4*a*A + 10/13*x^13*b^2*a^3*B + 10/13*x^13*b^3*a^2*A + 1/2*x^10*b*a^4*B + x^10*b^2*a^3*A + 1/7*x^7*a^5*B + 5/7*x^7*b*a^4*A + 1/4*x^4*a^5*A","A",0
30,1,125,0,0.716164," ","integrate(x^2*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{5} B + \frac{5}{18} x^{18} b^{4} a B + \frac{1}{18} x^{18} b^{5} A + \frac{2}{3} x^{15} b^{3} a^{2} B + \frac{1}{3} x^{15} b^{4} a A + \frac{5}{6} x^{12} b^{2} a^{3} B + \frac{5}{6} x^{12} b^{3} a^{2} A + \frac{5}{9} x^{9} b a^{4} B + \frac{10}{9} x^{9} b^{2} a^{3} A + \frac{1}{6} x^{6} a^{5} B + \frac{5}{6} x^{6} b a^{4} A + \frac{1}{3} x^{3} a^{5} A"," ",0,"1/21*x^21*b^5*B + 5/18*x^18*b^4*a*B + 1/18*x^18*b^5*A + 2/3*x^15*b^3*a^2*B + 1/3*x^15*b^4*a*A + 5/6*x^12*b^2*a^3*B + 5/6*x^12*b^3*a^2*A + 5/9*x^9*b*a^4*B + 10/9*x^9*b^2*a^3*A + 1/6*x^6*a^5*B + 5/6*x^6*b*a^4*A + 1/3*x^3*a^5*A","B",0
31,1,124,0,0.702581," ","integrate(x*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{20} x^{20} b^{5} B + \frac{5}{17} x^{17} b^{4} a B + \frac{1}{17} x^{17} b^{5} A + \frac{5}{7} x^{14} b^{3} a^{2} B + \frac{5}{14} x^{14} b^{4} a A + \frac{10}{11} x^{11} b^{2} a^{3} B + \frac{10}{11} x^{11} b^{3} a^{2} A + \frac{5}{8} x^{8} b a^{4} B + \frac{5}{4} x^{8} b^{2} a^{3} A + \frac{1}{5} x^{5} a^{5} B + x^{5} b a^{4} A + \frac{1}{2} x^{2} a^{5} A"," ",0,"1/20*x^20*b^5*B + 5/17*x^17*b^4*a*B + 1/17*x^17*b^5*A + 5/7*x^14*b^3*a^2*B + 5/14*x^14*b^4*a*A + 10/11*x^11*b^2*a^3*B + 10/11*x^11*b^3*a^2*A + 5/8*x^8*b*a^4*B + 5/4*x^8*b^2*a^3*A + 1/5*x^5*a^5*B + x^5*b*a^4*A + 1/2*x^2*a^5*A","A",0
32,1,120,0,0.703557," ","integrate((b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{1}{19} x^{19} b^{5} B + \frac{5}{16} x^{16} b^{4} a B + \frac{1}{16} x^{16} b^{5} A + \frac{10}{13} x^{13} b^{3} a^{2} B + \frac{5}{13} x^{13} b^{4} a A + x^{10} b^{2} a^{3} B + x^{10} b^{3} a^{2} A + \frac{5}{7} x^{7} b a^{4} B + \frac{10}{7} x^{7} b^{2} a^{3} A + \frac{1}{4} x^{4} a^{5} B + \frac{5}{4} x^{4} b a^{4} A + x a^{5} A"," ",0,"1/19*x^19*b^5*B + 5/16*x^16*b^4*a*B + 1/16*x^16*b^5*A + 10/13*x^13*b^3*a^2*B + 5/13*x^13*b^4*a*A + x^10*b^2*a^3*B + x^10*b^3*a^2*A + 5/7*x^7*b*a^4*B + 10/7*x^7*b^2*a^3*A + 1/4*x^4*a^5*B + 5/4*x^4*b*a^4*A + x*a^5*A","A",0
33,1,117,0,0.816345," ","integrate((b*x^3+a)^5*(B*x^3+A)/x,x, algorithm=""fricas"")","\frac{1}{18} \, B b^{5} x^{18} + \frac{1}{15} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + \frac{5}{12} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + \frac{10}{9} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + \frac{5}{6} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + A a^{5} \log\left(x\right) + \frac{1}{3} \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}"," ",0,"1/18*B*b^5*x^18 + 1/15*(5*B*a*b^4 + A*b^5)*x^15 + 5/12*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 10/9*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 5/6*(B*a^4*b + 2*A*a^3*b^2)*x^6 + A*a^5*log(x) + 1/3*(B*a^5 + 5*A*a^4*b)*x^3","A",0
34,1,121,0,0.762137," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^2,x, algorithm=""fricas"")","\frac{308 \, B b^{5} x^{18} + 374 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 2380 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 6545 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 5236 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 5236 \, A a^{5} + 2618 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{5236 \, x}"," ",0,"1/5236*(308*B*b^5*x^18 + 374*(5*B*a*b^4 + A*b^5)*x^15 + 2380*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 6545*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 5236*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 5236*A*a^5 + 2618*(B*a^5 + 5*A*a^4*b)*x^3)/x","A",0
35,1,121,0,1.031269," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^3,x, algorithm=""fricas"")","\frac{91 \, B b^{5} x^{18} + 112 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 728 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 2080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 1820 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 728 \, A a^{5} + 1456 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{1456 \, x^{2}}"," ",0,"1/1456*(91*B*b^5*x^18 + 112*(5*B*a*b^4 + A*b^5)*x^15 + 728*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 2080*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 1820*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 728*A*a^5 + 1456*(B*a^5 + 5*A*a^4*b)*x^3)/x^2","A",0
36,1,123,0,0.749556," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^4,x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{18} + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 300 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 60 \, A a^{5} + 180 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3} \log\left(x\right)}{180 \, x^{3}}"," ",0,"1/180*(12*B*b^5*x^18 + 15*(5*B*a*b^4 + A*b^5)*x^15 + 100*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 300*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 300*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 60*A*a^5 + 180*(B*a^5 + 5*A*a^4*b)*x^3*log(x))/x^3","A",0
37,1,121,0,0.731713," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^5,x, algorithm=""fricas"")","\frac{44 \, B b^{5} x^{18} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 385 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 1232 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 1540 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 154 \, A a^{5} - 616 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{616 \, x^{4}}"," ",0,"1/616*(44*B*b^5*x^18 + 56*(5*B*a*b^4 + A*b^5)*x^15 + 385*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 1232*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 1540*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 154*A*a^5 - 616*(B*a^5 + 5*A*a^4*b)*x^3)/x^4","A",0
38,1,121,0,0.526564," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^6,x, algorithm=""fricas"")","\frac{70 \, B b^{5} x^{18} + 91 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 650 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 2275 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 4550 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 182 \, A a^{5} - 455 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{910 \, x^{5}}"," ",0,"1/910*(70*B*b^5*x^18 + 91*(5*B*a*b^4 + A*b^5)*x^15 + 650*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 2275*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 4550*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 182*A*a^5 - 455*(B*a^5 + 5*A*a^4*b)*x^3)/x^5","A",0
39,1,123,0,0.774132," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^7,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{18} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 180 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} \log\left(x\right) - 6 \, A a^{5} - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{36 \, x^{6}}"," ",0,"1/36*(3*B*b^5*x^18 + 4*(5*B*a*b^4 + A*b^5)*x^15 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 120*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 180*(B*a^4*b + 2*A*a^3*b^2)*x^6*log(x) - 6*A*a^5 - 12*(B*a^5 + 5*A*a^4*b)*x^3)/x^6","A",0
40,1,121,0,1.109387," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^8,x, algorithm=""fricas"")","\frac{56 \, B b^{5} x^{18} + 77 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 616 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 3080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 3080 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 88 \, A a^{5} - 154 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{616 \, x^{7}}"," ",0,"1/616*(56*B*b^5*x^18 + 77*(5*B*a*b^4 + A*b^5)*x^15 + 616*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 3080*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 3080*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 88*A*a^5 - 154*(B*a^5 + 5*A*a^4*b)*x^3)/x^7","A",0
41,1,121,0,0.717385," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^9,x, algorithm=""fricas"")","\frac{28 \, B b^{5} x^{18} + 40 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 350 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 2800 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 35 \, A a^{5} - 56 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{280 \, x^{8}}"," ",0,"1/280*(28*B*b^5*x^18 + 40*(5*B*a*b^4 + A*b^5)*x^15 + 350*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 2800*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 700*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 35*A*a^5 - 56*(B*a^5 + 5*A*a^4*b)*x^3)/x^8","A",0
42,1,123,0,0.644996," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^10,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{18} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 180 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} \log\left(x\right) - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 2 \, A a^{5} - 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{18 \, x^{9}}"," ",0,"1/18*(2*B*b^5*x^18 + 3*(5*B*a*b^4 + A*b^5)*x^15 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 180*(B*a^3*b^2 + A*a^2*b^3)*x^9*log(x) - 30*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 2*A*a^5 - 3*(B*a^5 + 5*A*a^4*b)*x^3)/x^9","A",0
43,1,121,0,1.052301," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^11,x, algorithm=""fricas"")","\frac{35 \, B b^{5} x^{18} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 700 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 2800 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 350 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 28 \, A a^{5} - 40 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{280 \, x^{10}}"," ",0,"1/280*(35*B*b^5*x^18 + 56*(5*B*a*b^4 + A*b^5)*x^15 + 700*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 2800*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 350*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 28*A*a^5 - 40*(B*a^5 + 5*A*a^4*b)*x^3)/x^10","A",0
44,1,121,0,0.793028," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^12,x, algorithm=""fricas"")","\frac{88 \, B b^{5} x^{18} + 154 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 3080 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 3080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 616 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 56 \, A a^{5} - 77 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{616 \, x^{11}}"," ",0,"1/616*(88*B*b^5*x^18 + 154*(5*B*a*b^4 + A*b^5)*x^15 + 3080*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 3080*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 616*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 56*A*a^5 - 77*(B*a^5 + 5*A*a^4*b)*x^3)/x^11","A",0
45,1,123,0,0.622491," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^13,x, algorithm=""fricas"")","\frac{6 \, B b^{5} x^{18} + 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 180 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} \log\left(x\right) - 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 3 \, A a^{5} - 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{36 \, x^{12}}"," ",0,"1/36*(6*B*b^5*x^18 + 12*(5*B*a*b^4 + A*b^5)*x^15 + 180*(2*B*a^2*b^3 + A*a*b^4)*x^12*log(x) - 120*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 30*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 3*A*a^5 - 4*(B*a^5 + 5*A*a^4*b)*x^3)/x^12","A",0
46,1,121,0,0.635374," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^14,x, algorithm=""fricas"")","\frac{182 \, B b^{5} x^{18} + 455 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} - 4550 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 2275 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 650 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 70 \, A a^{5} - 91 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{910 \, x^{13}}"," ",0,"1/910*(182*B*b^5*x^18 + 455*(5*B*a*b^4 + A*b^5)*x^15 - 4550*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 2275*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 650*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 70*A*a^5 - 91*(B*a^5 + 5*A*a^4*b)*x^3)/x^13","A",0
47,1,121,0,0.559849," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^15,x, algorithm=""fricas"")","\frac{154 \, B b^{5} x^{18} + 616 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} - 1540 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 1232 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 385 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 44 \, A a^{5} - 56 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{616 \, x^{14}}"," ",0,"1/616*(154*B*b^5*x^18 + 616*(5*B*a*b^4 + A*b^5)*x^15 - 1540*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 1232*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 385*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 44*A*a^5 - 56*(B*a^5 + 5*A*a^4*b)*x^3)/x^14","A",0
48,1,123,0,0.668799," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^16,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{18} + 180 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} \log\left(x\right) - 300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 12 \, A a^{5} - 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{180 \, x^{15}}"," ",0,"1/180*(60*B*b^5*x^18 + 180*(5*B*a*b^4 + A*b^5)*x^15*log(x) - 300*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 300*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 100*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 12*A*a^5 - 15*(B*a^5 + 5*A*a^4*b)*x^3)/x^15","A",0
49,1,121,0,0.559138," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^17,x, algorithm=""fricas"")","\frac{728 \, B b^{5} x^{18} - 1456 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} - 1820 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 2080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 728 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 91 \, A a^{5} - 112 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{1456 \, x^{16}}"," ",0,"1/1456*(728*B*b^5*x^18 - 1456*(5*B*a*b^4 + A*b^5)*x^15 - 1820*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 2080*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 728*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 91*A*a^5 - 112*(B*a^5 + 5*A*a^4*b)*x^3)/x^16","A",0
50,1,121,0,0.674810," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^18,x, algorithm=""fricas"")","\frac{5236 \, B b^{5} x^{18} - 2618 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} - 5236 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 6545 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 2380 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 308 \, A a^{5} - 374 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{5236 \, x^{17}}"," ",0,"1/5236*(5236*B*b^5*x^18 - 2618*(5*B*a*b^4 + A*b^5)*x^15 - 5236*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 6545*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 2380*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 308*A*a^5 - 374*(B*a^5 + 5*A*a^4*b)*x^3)/x^17","A",0
51,1,123,0,0.538715," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^19,x, algorithm=""fricas"")","\frac{180 \, B b^{5} x^{18} \log\left(x\right) - 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} - 150 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} - 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} - 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} - 10 \, A a^{5} - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{180 \, x^{18}}"," ",0,"1/180*(180*B*b^5*x^18*log(x) - 60*(5*B*a*b^4 + A*b^5)*x^15 - 150*(2*B*a^2*b^3 + A*a*b^4)*x^12 - 200*(B*a^3*b^2 + A*a^2*b^3)*x^9 - 75*(B*a^4*b + 2*A*a^3*b^2)*x^6 - 10*A*a^5 - 12*(B*a^5 + 5*A*a^4*b)*x^3)/x^18","A",0
52,1,121,0,0.494970," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^20,x, algorithm=""fricas"")","-\frac{27664 \, B b^{5} x^{18} + 6916 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 19760 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 27664 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 10640 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + 1456 \, A a^{5} + 1729 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{27664 \, x^{19}}"," ",0,"-1/27664*(27664*B*b^5*x^18 + 6916*(5*B*a*b^4 + A*b^5)*x^15 + 19760*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 27664*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 10640*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 1456*A*a^5 + 1729*(B*a^5 + 5*A*a^4*b)*x^3)/x^19","A",0
53,1,121,0,0.529194," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^21,x, algorithm=""fricas"")","-\frac{26180 \, B b^{5} x^{18} + 10472 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 32725 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 47600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 18700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + 2618 \, A a^{5} + 3080 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{52360 \, x^{20}}"," ",0,"-1/52360*(26180*B*b^5*x^18 + 10472*(5*B*a*b^4 + A*b^5)*x^15 + 32725*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 47600*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 18700*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 2618*A*a^5 + 3080*(B*a^5 + 5*A*a^4*b)*x^3)/x^20","A",0
54,1,121,0,0.613730," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^22,x, algorithm=""fricas"")","-\frac{42 \, B b^{5} x^{18} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 70 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + 6 \, A a^{5} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{126 \, x^{21}}"," ",0,"-1/126*(42*B*b^5*x^18 + 21*(5*B*a*b^4 + A*b^5)*x^15 + 70*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 105*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 42*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 6*A*a^5 + 7*(B*a^5 + 5*A*a^4*b)*x^3)/x^21","B",0
55,1,121,0,0.510742," ","integrate((b*x^3+a)^5*(B*x^3+A)/x^23,x, algorithm=""fricas"")","-\frac{76076 \, B b^{5} x^{18} + 43472 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{15} + 152152 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{12} + 234080 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{9} + 95095 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{6} + 13832 \, A a^{5} + 16016 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x^{3}}{304304 \, x^{22}}"," ",0,"-1/304304*(76076*B*b^5*x^18 + 43472*(5*B*a*b^4 + A*b^5)*x^15 + 152152*(2*B*a^2*b^3 + A*a*b^4)*x^12 + 234080*(B*a^3*b^2 + A*a^2*b^3)*x^9 + 95095*(B*a^4*b + 2*A*a^3*b^2)*x^6 + 13832*A*a^5 + 16016*(B*a^5 + 5*A*a^4*b)*x^3)/x^22","A",0
56,1,167,0,0.680973," ","integrate(x^6*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{12 \, B b^{2} x^{7} - 21 \, {\left(B a b - A b^{2}\right)} x^{4} - 28 \, \sqrt{3} {\left(B a^{2} - A a b\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 14 \, {\left(B a^{2} - A a b\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) - 28 \, {\left(B a^{2} - A a b\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) + 84 \, {\left(B a^{2} - A a b\right)} x}{84 \, b^{3}}"," ",0,"1/84*(12*B*b^2*x^7 - 21*(B*a*b - A*b^2)*x^4 - 28*sqrt(3)*(B*a^2 - A*a*b)*(a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a/b)^(2/3) - sqrt(3)*a)/a) + 14*(B*a^2 - A*a*b)*(a/b)^(1/3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3)) - 28*(B*a^2 - A*a*b)*(a/b)^(1/3)*log(x + (a/b)^(1/3)) + 84*(B*a^2 - A*a*b)*x)/b^3","A",0
57,1,51,0,0.559878," ","integrate(x^5*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{B b^{2} x^{6} - 2 \, {\left(B a b - A b^{2}\right)} x^{3} + 2 \, {\left(B a^{2} - A a b\right)} \log\left(b x^{3} + a\right)}{6 \, b^{3}}"," ",0,"1/6*(B*b^2*x^6 - 2*(B*a*b - A*b^2)*x^3 + 2*(B*a^2 - A*a*b)*log(b*x^3 + a))/b^3","A",0
58,1,162,0,0.527824," ","integrate(x^4*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{6 \, B b x^{5} - 15 \, {\left(B a - A b\right)} x^{2} + 10 \, \sqrt{3} {\left(B a - A b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 5 \, {\left(B a - A b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - 10 \, {\left(B a - A b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{30 \, b^{2}}"," ",0,"1/30*(6*B*b*x^5 - 15*(B*a - A*b)*x^2 + 10*sqrt(3)*(B*a - A*b)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) + 5*(B*a - A*b)*(a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) - 10*(B*a - A*b)*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/b^2","A",0
59,1,145,0,0.490414," ","integrate(x^3*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{3 \, B b x^{4} - 4 \, \sqrt{3} {\left(B a - A b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 2 \, {\left(B a - A b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) - 4 \, {\left(B a - A b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) - 12 \, {\left(B a - A b\right)} x}{12 \, b^{2}}"," ",0,"1/12*(3*B*b*x^4 - 4*sqrt(3)*(B*a - A*b)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) + 2*(B*a - A*b)*(-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) - 4*(B*a - A*b)*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) - 12*(B*a - A*b)*x)/b^2","A",0
60,1,30,0,0.580421," ","integrate(x^2*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{B b x^{3} - {\left(B a - A b\right)} \log\left(b x^{3} + a\right)}{3 \, b^{2}}"," ",0,"1/3*(B*b*x^3 - (B*a - A*b)*log(b*x^3 + a))/b^2","A",0
61,1,382,0,0.752056," ","integrate(x*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, B a b^{2} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - \left(-a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{3}}, \frac{3 \, B a b^{2} x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - \left(-a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a b^{3}}\right]"," ",0,"[1/6*(3*B*a*b^2*x^2 - 3*sqrt(1/3)*(B*a^2*b - A*a*b^2)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - (-a*b^2)^(2/3)*(B*a - A*b)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*(-a*b^2)^(2/3)*(B*a - A*b)*log(b*x - (-a*b^2)^(1/3)))/(a*b^3), 1/6*(3*B*a*b^2*x^2 - 6*sqrt(1/3)*(B*a^2*b - A*a*b^2)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - (-a*b^2)^(2/3)*(B*a - A*b)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*(-a*b^2)^(2/3)*(B*a - A*b)*log(b*x - (-a*b^2)^(1/3)))/(a*b^3)]","A",0
62,1,369,0,0.694468," ","integrate((B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{6 \, B a^{2} b x - 3 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + \left(a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b^{2}}, \frac{6 \, B a^{2} b x - 6 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + \left(a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, \left(a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right)}{6 \, a^{2} b^{2}}\right]"," ",0,"[1/6*(6*B*a^2*b*x - 3*sqrt(1/3)*(B*a^2*b - A*a*b^2)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + (a^2*b)^(2/3)*(B*a - A*b)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*(a^2*b)^(2/3)*(B*a - A*b)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^2), 1/6*(6*B*a^2*b*x - 6*sqrt(1/3)*(B*a^2*b - A*a*b^2)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + (a^2*b)^(2/3)*(B*a - A*b)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*(a^2*b)^(2/3)*(B*a - A*b)*log(a*b*x + (a^2*b)^(2/3)))/(a^2*b^2)]","A",0
63,1,32,0,0.481068," ","integrate((B*x^3+A)/x/(b*x^3+a),x, algorithm=""fricas"")","\frac{3 \, A b \log\left(x\right) + {\left(B a - A b\right)} \log\left(b x^{3} + a\right)}{3 \, a b}"," ",0,"1/3*(3*A*b*log(x) + (B*a - A*b)*log(b*x^3 + a))/(a*b)","A",0
64,1,372,0,0.679857," ","integrate((B*x^3+A)/x^2/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{6 \, A a b^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} x \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b - 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - \left(a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} x \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} x \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a^{2} b^{2} x}, -\frac{6 \, A a b^{2} + 6 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} x \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x - \left(a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - \left(a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} x \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} {\left(B a - A b\right)} x \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{6 \, a^{2} b^{2} x}\right]"," ",0,"[-1/6*(6*A*a*b^2 + 3*sqrt(1/3)*(B*a^2*b - A*a*b^2)*x*sqrt(-(a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b - 3*sqrt(1/3)*(a*b*x + 2*(a*b^2)^(2/3)*x^2 - (a*b^2)^(1/3)*a)*sqrt(-(a*b^2)^(1/3)/a) - 3*(a*b^2)^(2/3)*x)/(b*x^3 + a)) - (a*b^2)^(2/3)*(B*a - A*b)*x*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) + 2*(a*b^2)^(2/3)*(B*a - A*b)*x*log(b*x + (a*b^2)^(1/3)))/(a^2*b^2*x), -1/6*(6*A*a*b^2 + 6*sqrt(1/3)*(B*a^2*b - A*a*b^2)*x*sqrt((a*b^2)^(1/3)/a)*arctan(-sqrt(1/3)*(2*b*x - (a*b^2)^(1/3))*sqrt((a*b^2)^(1/3)/a)/b) - (a*b^2)^(2/3)*(B*a - A*b)*x*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) + 2*(a*b^2)^(2/3)*(B*a - A*b)*x*log(b*x + (a*b^2)^(1/3)))/(a^2*b^2*x)]","A",0
65,1,411,0,0.499389," ","integrate((B*x^3+A)/x^3/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} x^{2} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + \left(-a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} x^{2} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} x^{2} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) + 3 \, A a^{2} b}{6 \, a^{3} b x^{2}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(B a^{2} b - A a b^{2}\right)} x^{2} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - \left(-a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} x^{2} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, \left(-a^{2} b\right)^{\frac{2}{3}} {\left(B a - A b\right)} x^{2} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right) - 3 \, A a^{2} b}{6 \, a^{3} b x^{2}}\right]"," ",0,"[-1/6*(3*sqrt(1/3)*(B*a^2*b - A*a*b^2)*x^2*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) + (-a^2*b)^(2/3)*(B*a - A*b)*x^2*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) - 2*(-a^2*b)^(2/3)*(B*a - A*b)*x^2*log(a*b*x + (-a^2*b)^(2/3)) + 3*A*a^2*b)/(a^3*b*x^2), 1/6*(6*sqrt(1/3)*(B*a^2*b - A*a*b^2)*x^2*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - (-a^2*b)^(2/3)*(B*a - A*b)*x^2*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 2*(-a^2*b)^(2/3)*(B*a - A*b)*x^2*log(a*b*x + (-a^2*b)^(2/3)) - 3*A*a^2*b)/(a^3*b*x^2)]","A",0
66,1,47,0,0.504538," ","integrate((B*x^3+A)/x^4/(b*x^3+a),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} x^{3} \log\left(b x^{3} + a\right) - 3 \, {\left(B a - A b\right)} x^{3} \log\left(x\right) + A a}{3 \, a^{2} x^{3}}"," ",0,"-1/3*((B*a - A*b)*x^3*log(b*x^3 + a) - 3*(B*a - A*b)*x^3*log(x) + A*a)/(a^2*x^3)","A",0
67,1,158,0,0.630952," ","integrate((B*x^3+A)/x^5/(b*x^3+a),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} {\left(B a - A b\right)} x^{4} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 2 \, {\left(B a - A b\right)} x^{4} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 4 \, {\left(B a - A b\right)} x^{4} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 12 \, {\left(B a - A b\right)} x^{3} + 3 \, A a}{12 \, a^{2} x^{4}}"," ",0,"-1/12*(4*sqrt(3)*(B*a - A*b)*x^4*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - 2*(B*a - A*b)*x^4*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) + 4*(B*a - A*b)*x^4*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)) + 12*(B*a - A*b)*x^3 + 3*A*a)/(a^2*x^4)","A",0
68,1,176,0,0.601243," ","integrate((B*x^3+A)/x^6/(b*x^3+a),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{3} {\left(B a - A b\right)} x^{5} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 5 \, {\left(B a - A b\right)} x^{5} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 10 \, {\left(B a - A b\right)} x^{5} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 15 \, {\left(B a - A b\right)} x^{3} + 6 \, A a}{30 \, a^{2} x^{5}}"," ",0,"-1/30*(10*sqrt(3)*(B*a - A*b)*x^5*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) - 5*(B*a - A*b)*x^5*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) + 10*(B*a - A*b)*x^5*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)) + 15*(B*a - A*b)*x^3 + 6*A*a)/(a^2*x^5)","A",0
69,1,73,0,0.525910," ","integrate((B*x^3+A)/x^7/(b*x^3+a),x, algorithm=""fricas"")","\frac{2 \, {\left(B a b - A b^{2}\right)} x^{6} \log\left(b x^{3} + a\right) - 6 \, {\left(B a b - A b^{2}\right)} x^{6} \log\left(x\right) - 2 \, {\left(B a^{2} - A a b\right)} x^{3} - A a^{2}}{6 \, a^{3} x^{6}}"," ",0,"1/6*(2*(B*a*b - A*b^2)*x^6*log(b*x^3 + a) - 6*(B*a*b - A*b^2)*x^6*log(x) - 2*(B*a^2 - A*a*b)*x^3 - A*a^2)/(a^3*x^6)","A",0
70,1,180,0,0.851093," ","integrate((B*x^3+A)/x^8/(b*x^3+a),x, algorithm=""fricas"")","\frac{28 \, \sqrt{3} {\left(B a b - A b^{2}\right)} x^{7} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 14 \, {\left(B a b - A b^{2}\right)} x^{7} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 28 \, {\left(B a b - A b^{2}\right)} x^{7} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 84 \, {\left(B a b - A b^{2}\right)} x^{6} - 21 \, {\left(B a^{2} - A a b\right)} x^{3} - 12 \, A a^{2}}{84 \, a^{3} x^{7}}"," ",0,"1/84*(28*sqrt(3)*(B*a*b - A*b^2)*x^7*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + 14*(B*a*b - A*b^2)*x^7*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 28*(B*a*b - A*b^2)*x^7*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 84*(B*a*b - A*b^2)*x^6 - 21*(B*a^2 - A*a*b)*x^3 - 12*A*a^2)/(a^3*x^7)","A",0
71,1,271,0,0.716764," ","integrate(x^9*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{36 \, B b^{3} x^{10} - 9 \, {\left(10 \, B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 63 \, {\left(10 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{4} - 28 \, \sqrt{3} {\left(10 \, B a^{3} - 7 \, A a^{2} b + {\left(10 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 14 \, {\left(10 \, B a^{3} - 7 \, A a^{2} b + {\left(10 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) - 28 \, {\left(10 \, B a^{3} - 7 \, A a^{2} b + {\left(10 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) + 84 \, {\left(10 \, B a^{3} - 7 \, A a^{2} b\right)} x}{252 \, {\left(b^{5} x^{3} + a b^{4}\right)}}"," ",0,"1/252*(36*B*b^3*x^10 - 9*(10*B*a*b^2 - 7*A*b^3)*x^7 + 63*(10*B*a^2*b - 7*A*a*b^2)*x^4 - 28*sqrt(3)*(10*B*a^3 - 7*A*a^2*b + (10*B*a^2*b - 7*A*a*b^2)*x^3)*(a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a/b)^(2/3) - sqrt(3)*a)/a) + 14*(10*B*a^3 - 7*A*a^2*b + (10*B*a^2*b - 7*A*a*b^2)*x^3)*(a/b)^(1/3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3)) - 28*(10*B*a^3 - 7*A*a^2*b + (10*B*a^2*b - 7*A*a*b^2)*x^3)*(a/b)^(1/3)*log(x + (a/b)^(1/3)) + 84*(10*B*a^3 - 7*A*a^2*b)*x)/(b^5*x^3 + a*b^4)","A",0
72,1,121,0,0.571214," ","integrate(x^8*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{B b^{3} x^{9} - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 2 \, B a^{3} - 2 \, A a^{2} b - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{3} + 2 \, {\left(3 \, B a^{3} - 2 \, A a^{2} b + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{3}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{5} x^{3} + a b^{4}\right)}}"," ",0,"1/6*(B*b^3*x^9 - (3*B*a*b^2 - 2*A*b^3)*x^6 + 2*B*a^3 - 2*A*a^2*b - 2*(2*B*a^2*b - A*a*b^2)*x^3 + 2*(3*B*a^3 - 2*A*a^2*b + (3*B*a^2*b - 2*A*a*b^2)*x^3)*log(b*x^3 + a))/(b^5*x^3 + a*b^4)","A",0
73,1,257,0,0.669315," ","integrate(x^7*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{18 \, B b^{2} x^{8} - 9 \, {\left(8 \, B a b - 5 \, A b^{2}\right)} x^{5} - 15 \, {\left(8 \, B a^{2} - 5 \, A a b\right)} x^{2} + 10 \, \sqrt{3} {\left({\left(8 \, B a b - 5 \, A b^{2}\right)} x^{3} + 8 \, B a^{2} - 5 \, A a b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 5 \, {\left({\left(8 \, B a b - 5 \, A b^{2}\right)} x^{3} + 8 \, B a^{2} - 5 \, A a b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - 10 \, {\left({\left(8 \, B a b - 5 \, A b^{2}\right)} x^{3} + 8 \, B a^{2} - 5 \, A a b\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{90 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"1/90*(18*B*b^2*x^8 - 9*(8*B*a*b - 5*A*b^2)*x^5 - 15*(8*B*a^2 - 5*A*a*b)*x^2 + 10*sqrt(3)*((8*B*a*b - 5*A*b^2)*x^3 + 8*B*a^2 - 5*A*a*b)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) + 5*((8*B*a*b - 5*A*b^2)*x^3 + 8*B*a^2 - 5*A*a*b)*(a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) - 10*((8*B*a*b - 5*A*b^2)*x^3 + 8*B*a^2 - 5*A*a*b)*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/(b^4*x^3 + a*b^3)","A",0
74,1,240,0,0.847422," ","integrate(x^6*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{9 \, B b^{2} x^{7} - 9 \, {\left(7 \, B a b - 4 \, A b^{2}\right)} x^{4} - 4 \, \sqrt{3} {\left({\left(7 \, B a b - 4 \, A b^{2}\right)} x^{3} + 7 \, B a^{2} - 4 \, A a b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 2 \, {\left({\left(7 \, B a b - 4 \, A b^{2}\right)} x^{3} + 7 \, B a^{2} - 4 \, A a b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) - 4 \, {\left({\left(7 \, B a b - 4 \, A b^{2}\right)} x^{3} + 7 \, B a^{2} - 4 \, A a b\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) - 12 \, {\left(7 \, B a^{2} - 4 \, A a b\right)} x}{36 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"1/36*(9*B*b^2*x^7 - 9*(7*B*a*b - 4*A*b^2)*x^4 - 4*sqrt(3)*((7*B*a*b - 4*A*b^2)*x^3 + 7*B*a^2 - 4*A*a*b)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) + 2*((7*B*a*b - 4*A*b^2)*x^3 + 7*B*a^2 - 4*A*a*b)*(-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) - 4*((7*B*a*b - 4*A*b^2)*x^3 + 7*B*a^2 - 4*A*a*b)*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) - 12*(7*B*a^2 - 4*A*a*b)*x)/(b^4*x^3 + a*b^3)","A",0
75,1,81,0,0.687027," ","integrate(x^5*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{B b^{2} x^{6} + B a b x^{3} - B a^{2} + A a b - {\left({\left(2 \, B a b - A b^{2}\right)} x^{3} + 2 \, B a^{2} - A a b\right)} \log\left(b x^{3} + a\right)}{3 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"1/3*(B*b^2*x^6 + B*a*b*x^3 - B*a^2 + A*a*b - ((2*B*a*b - A*b^2)*x^3 + 2*B*a^2 - A*a*b)*log(b*x^3 + a))/(b^4*x^3 + a*b^3)","A",0
76,1,578,0,0.788877," ","integrate(x^4*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{9 \, B a b^{3} x^{5} + 3 \, {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(5 \, B a^{3} b - 2 \, A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - {\left({\left(5 \, B a b - 2 \, A b^{2}\right)} x^{3} + 5 \, B a^{2} - 2 \, A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(5 \, B a b - 2 \, A b^{2}\right)} x^{3} + 5 \, B a^{2} - 2 \, A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a b^{5} x^{3} + a^{2} b^{4}\right)}}, \frac{9 \, B a b^{3} x^{5} + 3 \, {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(5 \, B a^{3} b - 2 \, A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left({\left(5 \, B a b - 2 \, A b^{2}\right)} x^{3} + 5 \, B a^{2} - 2 \, A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(5 \, B a b - 2 \, A b^{2}\right)} x^{3} + 5 \, B a^{2} - 2 \, A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a b^{5} x^{3} + a^{2} b^{4}\right)}}\right]"," ",0,"[1/18*(9*B*a*b^3*x^5 + 3*(5*B*a^2*b^2 - 2*A*a*b^3)*x^2 - 3*sqrt(1/3)*(5*B*a^3*b - 2*A*a^2*b^2 + (5*B*a^2*b^2 - 2*A*a*b^3)*x^3)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - ((5*B*a*b - 2*A*b^2)*x^3 + 5*B*a^2 - 2*A*a*b)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((5*B*a*b - 2*A*b^2)*x^3 + 5*B*a^2 - 2*A*a*b)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^5*x^3 + a^2*b^4), 1/18*(9*B*a*b^3*x^5 + 3*(5*B*a^2*b^2 - 2*A*a*b^3)*x^2 - 6*sqrt(1/3)*(5*B*a^3*b - 2*A*a^2*b^2 + (5*B*a^2*b^2 - 2*A*a*b^3)*x^3)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - ((5*B*a*b - 2*A*b^2)*x^3 + 5*B*a^2 - 2*A*a*b)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((5*B*a*b - 2*A*b^2)*x^3 + 5*B*a^2 - 2*A*a*b)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^5*x^3 + a^2*b^4)]","A",0
77,1,573,0,0.554013," ","integrate(x^3*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{18 \, B a^{2} b^{2} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(4 \, B a^{3} b - A a^{2} b^{2} + {\left(4 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + {\left({\left(4 \, B a b - A b^{2}\right)} x^{3} + 4 \, B a^{2} - A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(4 \, B a b - A b^{2}\right)} x^{3} + 4 \, B a^{2} - A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} x}{18 \, {\left(a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}}, \frac{18 \, B a^{2} b^{2} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(4 \, B a^{3} b - A a^{2} b^{2} + {\left(4 \, B a^{2} b^{2} - A a b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left({\left(4 \, B a b - A b^{2}\right)} x^{3} + 4 \, B a^{2} - A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(4 \, B a b - A b^{2}\right)} x^{3} + 4 \, B a^{2} - A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(4 \, B a^{3} b - A a^{2} b^{2}\right)} x}{18 \, {\left(a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}}\right]"," ",0,"[1/18*(18*B*a^2*b^2*x^4 - 3*sqrt(1/3)*(4*B*a^3*b - A*a^2*b^2 + (4*B*a^2*b^2 - A*a*b^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + ((4*B*a*b - A*b^2)*x^3 + 4*B*a^2 - A*a*b)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*((4*B*a*b - A*b^2)*x^3 + 4*B*a^2 - A*a*b)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(4*B*a^3*b - A*a^2*b^2)*x)/(a^2*b^4*x^3 + a^3*b^3), 1/18*(18*B*a^2*b^2*x^4 - 6*sqrt(1/3)*(4*B*a^3*b - A*a^2*b^2 + (4*B*a^2*b^2 - A*a*b^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + ((4*B*a*b - A*b^2)*x^3 + 4*B*a^2 - A*a*b)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*((4*B*a*b - A*b^2)*x^3 + 4*B*a^2 - A*a*b)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(4*B*a^3*b - A*a^2*b^2)*x)/(a^2*b^4*x^3 + a^3*b^3)]","A",0
78,1,44,0,0.563669," ","integrate(x^2*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x^{3} + B a\right)} \log\left(b x^{3} + a\right)}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}}"," ",0,"1/3*(B*a - A*b + (B*b*x^3 + B*a)*log(b*x^3 + a))/(b^3*x^3 + a*b^2)","A",0
79,1,548,0,0.547916," ","integrate(x*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, B a^{3} b + A a^{2} b^{2} + {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - {\left({\left(2 \, B a b + A b^{2}\right)} x^{3} + 2 \, B a^{2} + A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(2 \, B a b + A b^{2}\right)} x^{3} + 2 \, B a^{2} + A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}}, -\frac{6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left(2 \, B a^{3} b + A a^{2} b^{2} + {\left(2 \, B a^{2} b^{2} + A a b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left({\left(2 \, B a b + A b^{2}\right)} x^{3} + 2 \, B a^{2} + A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(2 \, B a b + A b^{2}\right)} x^{3} + 2 \, B a^{2} + A a b\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{2} b^{4} x^{3} + a^{3} b^{3}\right)}}\right]"," ",0,"[-1/18*(6*(B*a^2*b^2 - A*a*b^3)*x^2 - 3*sqrt(1/3)*(2*B*a^3*b + A*a^2*b^2 + (2*B*a^2*b^2 + A*a*b^3)*x^3)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - ((2*B*a*b + A*b^2)*x^3 + 2*B*a^2 + A*a*b)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((2*B*a*b + A*b^2)*x^3 + 2*B*a^2 + A*a*b)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^4*x^3 + a^3*b^3), -1/18*(6*(B*a^2*b^2 - A*a*b^3)*x^2 - 6*sqrt(1/3)*(2*B*a^3*b + A*a^2*b^2 + (2*B*a^2*b^2 + A*a*b^3)*x^3)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - ((2*B*a*b + A*b^2)*x^3 + 2*B*a^2 + A*a*b)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((2*B*a*b + A*b^2)*x^3 + 2*B*a^2 + A*a*b)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^4*x^3 + a^3*b^3)]","A",0
80,1,537,0,0.704764," ","integrate((B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(B a^{3} b + 2 \, A a^{2} b^{2} + {\left(B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left({\left(B a b + 2 \, A b^{2}\right)} x^{3} + B a^{2} + 2 \, A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(B a b + 2 \, A b^{2}\right)} x^{3} + B a^{2} + 2 \, A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) - 6 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x}{18 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(B a^{3} b + 2 \, A a^{2} b^{2} + {\left(B a^{2} b^{2} + 2 \, A a b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left({\left(B a b + 2 \, A b^{2}\right)} x^{3} + B a^{2} + 2 \, A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(B a b + 2 \, A b^{2}\right)} x^{3} + B a^{2} + 2 \, A a b\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) - 6 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x}{18 \, {\left(a^{3} b^{3} x^{3} + a^{4} b^{2}\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(B*a^3*b + 2*A*a^2*b^2 + (B*a^2*b^2 + 2*A*a*b^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - ((B*a*b + 2*A*b^2)*x^3 + B*a^2 + 2*A*a*b)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((B*a*b + 2*A*b^2)*x^3 + B*a^2 + 2*A*a*b)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) - 6*(B*a^3*b - A*a^2*b^2)*x)/(a^3*b^3*x^3 + a^4*b^2), 1/18*(6*sqrt(1/3)*(B*a^3*b + 2*A*a^2*b^2 + (B*a^2*b^2 + 2*A*a*b^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - ((B*a*b + 2*A*b^2)*x^3 + B*a^2 + 2*A*a*b)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((B*a*b + 2*A*b^2)*x^3 + B*a^2 + 2*A*a*b)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) - 6*(B*a^3*b - A*a^2*b^2)*x)/(a^3*b^3*x^3 + a^4*b^2)]","A",0
81,1,70,0,0.698724," ","integrate((B*x^3+A)/x/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{B a^{2} - A a b + {\left(A b^{2} x^{3} + A a b\right)} \log\left(b x^{3} + a\right) - 3 \, {\left(A b^{2} x^{3} + A a b\right)} \log\left(x\right)}{3 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}"," ",0,"-1/3*(B*a^2 - A*a*b + (A*b^2*x^3 + A*a*b)*log(b*x^3 + a) - 3*(A*b^2*x^3 + A*a*b)*log(x))/(a^2*b^2*x^3 + a^3*b)","A",0
82,1,570,0,0.697116," ","integrate((B*x^3+A)/x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{18 \, A a^{2} b^{2} - 6 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{4} + {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b - 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - {\left({\left(B a b - 4 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 4 \, A a b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(B a b - 4 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 4 \, A a b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{3} b^{3} x^{4} + a^{4} b^{2} x\right)}}, -\frac{18 \, A a^{2} b^{2} - 6 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} + 6 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{4} + {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x - \left(a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left({\left(B a b - 4 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 4 \, A a b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(B a b - 4 \, A b^{2}\right)} x^{4} + {\left(B a^{2} - 4 \, A a b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{18 \, {\left(a^{3} b^{3} x^{4} + a^{4} b^{2} x\right)}}\right]"," ",0,"[-1/18*(18*A*a^2*b^2 - 6*(B*a^2*b^2 - 4*A*a*b^3)*x^3 + 3*sqrt(1/3)*((B*a^2*b^2 - 4*A*a*b^3)*x^4 + (B*a^3*b - 4*A*a^2*b^2)*x)*sqrt(-(a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b - 3*sqrt(1/3)*(a*b*x + 2*(a*b^2)^(2/3)*x^2 - (a*b^2)^(1/3)*a)*sqrt(-(a*b^2)^(1/3)/a) - 3*(a*b^2)^(2/3)*x)/(b*x^3 + a)) - ((B*a*b - 4*A*b^2)*x^4 + (B*a^2 - 4*A*a*b)*x)*(a*b^2)^(2/3)*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) + 2*((B*a*b - 4*A*b^2)*x^4 + (B*a^2 - 4*A*a*b)*x)*(a*b^2)^(2/3)*log(b*x + (a*b^2)^(1/3)))/(a^3*b^3*x^4 + a^4*b^2*x), -1/18*(18*A*a^2*b^2 - 6*(B*a^2*b^2 - 4*A*a*b^3)*x^3 + 6*sqrt(1/3)*((B*a^2*b^2 - 4*A*a*b^3)*x^4 + (B*a^3*b - 4*A*a^2*b^2)*x)*sqrt((a*b^2)^(1/3)/a)*arctan(-sqrt(1/3)*(2*b*x - (a*b^2)^(1/3))*sqrt((a*b^2)^(1/3)/a)/b) - ((B*a*b - 4*A*b^2)*x^4 + (B*a^2 - 4*A*a*b)*x)*(a*b^2)^(2/3)*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) + 2*((B*a*b - 4*A*b^2)*x^4 + (B*a^2 - 4*A*a*b)*x)*(a*b^2)^(2/3)*log(b*x + (a*b^2)^(1/3)))/(a^3*b^3*x^4 + a^4*b^2*x)]","A",0
83,1,618,0,0.823349," ","integrate((B*x^3+A)/x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{9 \, A a^{3} b - 3 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{5} + {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + {\left({\left(2 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(2 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(2 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(2 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{4} b^{2} x^{5} + a^{5} b x^{2}\right)}}, -\frac{9 \, A a^{3} b - 3 \, {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3} - 6 \, \sqrt{\frac{1}{3}} {\left({\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{5} + {\left(2 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left({\left(2 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(2 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(2 \, B a b - 5 \, A b^{2}\right)} x^{5} + {\left(2 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{18 \, {\left(a^{4} b^{2} x^{5} + a^{5} b x^{2}\right)}}\right]"," ",0,"[-1/18*(9*A*a^3*b - 3*(2*B*a^3*b - 5*A*a^2*b^2)*x^3 + 3*sqrt(1/3)*((2*B*a^2*b^2 - 5*A*a*b^3)*x^5 + (2*B*a^3*b - 5*A*a^2*b^2)*x^2)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) + ((2*B*a*b - 5*A*b^2)*x^5 + (2*B*a^2 - 5*A*a*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) - 2*((2*B*a*b - 5*A*b^2)*x^5 + (2*B*a^2 - 5*A*a*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)))/(a^4*b^2*x^5 + a^5*b*x^2), -1/18*(9*A*a^3*b - 3*(2*B*a^3*b - 5*A*a^2*b^2)*x^3 - 6*sqrt(1/3)*((2*B*a^2*b^2 - 5*A*a*b^3)*x^5 + (2*B*a^3*b - 5*A*a^2*b^2)*x^2)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) + ((2*B*a*b - 5*A*b^2)*x^5 + (2*B*a^2 - 5*A*a*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) - 2*((2*B*a*b - 5*A*b^2)*x^5 + (2*B*a^2 - 5*A*a*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)))/(a^4*b^2*x^5 + a^5*b*x^2)]","A",0
84,1,118,0,0.489887," ","integrate((B*x^3+A)/x^4/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left(B a^{2} - 2 \, A a b\right)} x^{3} - A a^{2} - {\left({\left(B a b - 2 \, A b^{2}\right)} x^{6} + {\left(B a^{2} - 2 \, A a b\right)} x^{3}\right)} \log\left(b x^{3} + a\right) + 3 \, {\left({\left(B a b - 2 \, A b^{2}\right)} x^{6} + {\left(B a^{2} - 2 \, A a b\right)} x^{3}\right)} \log\left(x\right)}{3 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}"," ",0,"1/3*((B*a^2 - 2*A*a*b)*x^3 - A*a^2 - ((B*a*b - 2*A*b^2)*x^6 + (B*a^2 - 2*A*a*b)*x^3)*log(b*x^3 + a) + 3*((B*a*b - 2*A*b^2)*x^6 + (B*a^2 - 2*A*a*b)*x^3)*log(x))/(a^3*b*x^6 + a^4*x^3)","A",0
85,1,259,0,0.601280," ","integrate((B*x^3+A)/x^5/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(4 \, B a b - 7 \, A b^{2}\right)} x^{6} + 9 \, {\left(4 \, B a^{2} - 7 \, A a b\right)} x^{3} + 9 \, A a^{2} + 4 \, \sqrt{3} {\left({\left(4 \, B a b - 7 \, A b^{2}\right)} x^{7} + {\left(4 \, B a^{2} - 7 \, A a b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 2 \, {\left({\left(4 \, B a b - 7 \, A b^{2}\right)} x^{7} + {\left(4 \, B a^{2} - 7 \, A a b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 4 \, {\left({\left(4 \, B a b - 7 \, A b^{2}\right)} x^{7} + {\left(4 \, B a^{2} - 7 \, A a b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{36 \, {\left(a^{3} b x^{7} + a^{4} x^{4}\right)}}"," ",0,"-1/36*(12*(4*B*a*b - 7*A*b^2)*x^6 + 9*(4*B*a^2 - 7*A*a*b)*x^3 + 9*A*a^2 + 4*sqrt(3)*((4*B*a*b - 7*A*b^2)*x^7 + (4*B*a^2 - 7*A*a*b)*x^4)*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - 2*((4*B*a*b - 7*A*b^2)*x^7 + (4*B*a^2 - 7*A*a*b)*x^4)*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) + 4*((4*B*a*b - 7*A*b^2)*x^7 + (4*B*a^2 - 7*A*a*b)*x^4)*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)))/(a^3*b*x^7 + a^4*x^4)","A",0
86,1,277,0,0.532166," ","integrate((B*x^3+A)/x^6/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{15 \, {\left(5 \, B a b - 8 \, A b^{2}\right)} x^{6} + 9 \, {\left(5 \, B a^{2} - 8 \, A a b\right)} x^{3} + 18 \, A a^{2} + 10 \, \sqrt{3} {\left({\left(5 \, B a b - 8 \, A b^{2}\right)} x^{8} + {\left(5 \, B a^{2} - 8 \, A a b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 5 \, {\left({\left(5 \, B a b - 8 \, A b^{2}\right)} x^{8} + {\left(5 \, B a^{2} - 8 \, A a b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 10 \, {\left({\left(5 \, B a b - 8 \, A b^{2}\right)} x^{8} + {\left(5 \, B a^{2} - 8 \, A a b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right)}{90 \, {\left(a^{3} b x^{8} + a^{4} x^{5}\right)}}"," ",0,"-1/90*(15*(5*B*a*b - 8*A*b^2)*x^6 + 9*(5*B*a^2 - 8*A*a*b)*x^3 + 18*A*a^2 + 10*sqrt(3)*((5*B*a*b - 8*A*b^2)*x^8 + (5*B*a^2 - 8*A*a*b)*x^5)*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) - 5*((5*B*a*b - 8*A*b^2)*x^8 + (5*B*a^2 - 8*A*a*b)*x^5)*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) + 10*((5*B*a*b - 8*A*b^2)*x^8 + (5*B*a^2 - 8*A*a*b)*x^5)*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)))/(a^3*b*x^8 + a^4*x^5)","A",0
87,1,154,0,0.463315," ","integrate((B*x^3+A)/x^7/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{6} + A a^{3} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} x^{3} - 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{9} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{6}\right)} \log\left(b x^{3} + a\right) + 6 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{9} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{6}\right)} \log\left(x\right)}{6 \, {\left(a^{4} b x^{9} + a^{5} x^{6}\right)}}"," ",0,"-1/6*(2*(2*B*a^2*b - 3*A*a*b^2)*x^6 + A*a^3 + (2*B*a^3 - 3*A*a^2*b)*x^3 - 2*((2*B*a*b^2 - 3*A*b^3)*x^9 + (2*B*a^2*b - 3*A*a*b^2)*x^6)*log(b*x^3 + a) + 6*((2*B*a*b^2 - 3*A*b^3)*x^9 + (2*B*a^2*b - 3*A*a*b^2)*x^6)*log(x))/(a^4*b*x^9 + a^5*x^6)","A",0
88,1,179,0,0.639325," ","integrate(x^11*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{B b^{4} x^{12} - 2 \, {\left(2 \, B a b^{3} - A b^{4}\right)} x^{9} - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{6} + 7 \, B a^{4} - 5 \, A a^{3} b + 2 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{3} + 6 \, {\left({\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} x^{6} + 2 \, B a^{4} - A a^{3} b + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} x^{3}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{7} x^{6} + 2 \, a b^{6} x^{3} + a^{2} b^{5}\right)}}"," ",0,"1/6*(B*b^4*x^12 - 2*(2*B*a*b^3 - A*b^4)*x^9 - (11*B*a^2*b^2 - 4*A*a*b^3)*x^6 + 7*B*a^4 - 5*A*a^3*b + 2*(B*a^3*b - 2*A*a^2*b^2)*x^3 + 6*((2*B*a^2*b^2 - A*a*b^3)*x^6 + 2*B*a^4 - A*a^3*b + 2*(2*B*a^3*b - A*a^2*b^2)*x^3)*log(b*x^3 + a))/(b^7*x^6 + 2*a*b^6*x^3 + a^2*b^5)","A",0
89,1,142,0,0.633779," ","integrate(x^8*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{9} + 4 \, B a b^{2} x^{6} - 5 \, B a^{3} + 3 \, A a^{2} b - 4 \, {\left(B a^{2} b - A a b^{2}\right)} x^{3} - 2 \, {\left({\left(3 \, B a b^{2} - A b^{3}\right)} x^{6} + 3 \, B a^{3} - A a^{2} b + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}}"," ",0,"1/6*(2*B*b^3*x^9 + 4*B*a*b^2*x^6 - 5*B*a^3 + 3*A*a^2*b - 4*(B*a^2*b - A*a*b^2)*x^3 - 2*((3*B*a*b^2 - A*b^3)*x^6 + 3*B*a^3 - A*a^2*b + 2*(3*B*a^2*b - A*a*b^2)*x^3)*log(b*x^3 + a))/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4)","A",0
90,1,89,0,0.748626," ","integrate(x^5*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, B a b - A b^{2}\right)} x^{3} + 3 \, B a^{2} - A a b + 2 \, {\left(B b^{2} x^{6} + 2 \, B a b x^{3} + B a^{2}\right)} \log\left(b x^{3} + a\right)}{6 \, {\left(b^{5} x^{6} + 2 \, a b^{4} x^{3} + a^{2} b^{3}\right)}}"," ",0,"1/6*(2*(2*B*a*b - A*b^2)*x^3 + 3*B*a^2 - A*a*b + 2*(B*b^2*x^6 + 2*B*a*b*x^3 + B*a^2)*log(b*x^3 + a))/(b^5*x^6 + 2*a*b^4*x^3 + a^2*b^3)","A",0
91,1,42,0,0.687276," ","integrate(x^2*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{2 \, B b x^{3} + B a + A b}{6 \, {\left(b^{4} x^{6} + 2 \, a b^{3} x^{3} + a^{2} b^{2}\right)}}"," ",0,"-1/6*(2*B*b*x^3 + B*a + A*b)/(b^4*x^6 + 2*a*b^3*x^3 + a^2*b^2)","A",0
92,1,119,0,0.746153," ","integrate((B*x^3+A)/x/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, A a b^{2} x^{3} - B a^{3} + 3 \, A a^{2} b - 2 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{3} + A a^{2} b\right)} \log\left(b x^{3} + a\right) + 6 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{3} + A a^{2} b\right)} \log\left(x\right)}{6 \, {\left(a^{3} b^{3} x^{6} + 2 \, a^{4} b^{2} x^{3} + a^{5} b\right)}}"," ",0,"1/6*(2*A*a*b^2*x^3 - B*a^3 + 3*A*a^2*b - 2*(A*b^3*x^6 + 2*A*a*b^2*x^3 + A*a^2*b)*log(b*x^3 + a) + 6*(A*b^3*x^6 + 2*A*a*b^2*x^3 + A*a^2*b)*log(x))/(a^3*b^3*x^6 + 2*a^4*b^2*x^3 + a^5*b)","A",0
93,1,197,0,0.615860," ","integrate((B*x^3+A)/x^4/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{6} - 2 \, A a^{3} + 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{3} - 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{9} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{6} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{3}\right)} \log\left(b x^{3} + a\right) + 6 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{9} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{6} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{4} b^{2} x^{9} + 2 \, a^{5} b x^{6} + a^{6} x^{3}\right)}}"," ",0,"1/6*(2*(B*a^2*b - 3*A*a*b^2)*x^6 - 2*A*a^3 + 3*(B*a^3 - 3*A*a^2*b)*x^3 - 2*((B*a*b^2 - 3*A*b^3)*x^9 + 2*(B*a^2*b - 3*A*a*b^2)*x^6 + (B*a^3 - 3*A*a^2*b)*x^3)*log(b*x^3 + a) + 6*((B*a*b^2 - 3*A*b^3)*x^9 + 2*(B*a^2*b - 3*A*a*b^2)*x^6 + (B*a^3 - 3*A*a^2*b)*x^3)*log(x))/(a^4*b^2*x^9 + 2*a^5*b*x^6 + a^6*x^3)","B",0
94,1,229,0,0.644305," ","integrate((B*x^3+A)/x^7/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{9} + 9 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{6} + A a^{4} + 2 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} x^{3} - 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{12} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{9} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{6}\right)} \log\left(b x^{3} + a\right) + 18 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{12} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{9} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{6}\right)} \log\left(x\right)}{6 \, {\left(a^{5} b^{2} x^{12} + 2 \, a^{6} b x^{9} + a^{7} x^{6}\right)}}"," ",0,"-1/6*(6*(B*a^2*b^2 - 2*A*a*b^3)*x^9 + 9*(B*a^3*b - 2*A*a^2*b^2)*x^6 + A*a^4 + 2*(B*a^4 - 2*A*a^3*b)*x^3 - 6*((B*a*b^3 - 2*A*b^4)*x^12 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^9 + (B*a^3*b - 2*A*a^2*b^2)*x^6)*log(b*x^3 + a) + 18*((B*a*b^3 - 2*A*b^4)*x^12 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^9 + (B*a^3*b - 2*A*a^2*b^2)*x^6)*log(x))/(a^5*b^2*x^12 + 2*a^6*b*x^9 + a^7*x^6)","B",0
95,1,364,0,0.648638," ","integrate(x^10*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{54 \, B b^{3} x^{11} - 27 \, {\left(11 \, B a b^{2} - 5 \, A b^{3}\right)} x^{8} - 96 \, {\left(11 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{5} - 60 \, {\left(11 \, B a^{3} - 5 \, A a^{2} b\right)} x^{2} + 40 \, \sqrt{3} {\left({\left(11 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 11 \, B a^{3} - 5 \, A a^{2} b + 2 \, {\left(11 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 20 \, {\left({\left(11 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 11 \, B a^{3} - 5 \, A a^{2} b + 2 \, {\left(11 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - 40 \, {\left({\left(11 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 11 \, B a^{3} - 5 \, A a^{2} b + 2 \, {\left(11 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3}\right)} \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{270 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}}"," ",0,"1/270*(54*B*b^3*x^11 - 27*(11*B*a*b^2 - 5*A*b^3)*x^8 - 96*(11*B*a^2*b - 5*A*a*b^2)*x^5 - 60*(11*B*a^3 - 5*A*a^2*b)*x^2 + 40*sqrt(3)*((11*B*a*b^2 - 5*A*b^3)*x^6 + 11*B*a^3 - 5*A*a^2*b + 2*(11*B*a^2*b - 5*A*a*b^2)*x^3)*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) + 20*((11*B*a*b^2 - 5*A*b^3)*x^6 + 11*B*a^3 - 5*A*a^2*b + 2*(11*B*a^2*b - 5*A*a*b^2)*x^3)*(a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) - 40*((11*B*a*b^2 - 5*A*b^3)*x^6 + 11*B*a^3 - 5*A*a^2*b + 2*(11*B*a^2*b - 5*A*a*b^2)*x^3)*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4)","A",0
96,1,347,0,0.604370," ","integrate(x^9*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{27 \, B b^{3} x^{10} - 54 \, {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{7} - 147 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{4} - 28 \, \sqrt{3} {\left({\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 5 \, B a^{3} - 2 \, A a^{2} b + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{3}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 14 \, {\left({\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 5 \, B a^{3} - 2 \, A a^{2} b + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{3}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) - 28 \, {\left({\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{6} + 5 \, B a^{3} - 2 \, A a^{2} b + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x^{3}\right)} \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) - 84 \, {\left(5 \, B a^{3} - 2 \, A a^{2} b\right)} x}{108 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}}"," ",0,"1/108*(27*B*b^3*x^10 - 54*(5*B*a*b^2 - 2*A*b^3)*x^7 - 147*(5*B*a^2*b - 2*A*a*b^2)*x^4 - 28*sqrt(3)*((5*B*a*b^2 - 2*A*b^3)*x^6 + 5*B*a^3 - 2*A*a^2*b + 2*(5*B*a^2*b - 2*A*a*b^2)*x^3)*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) + 14*((5*B*a*b^2 - 2*A*b^3)*x^6 + 5*B*a^3 - 2*A*a^2*b + 2*(5*B*a^2*b - 2*A*a*b^2)*x^3)*(-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) - 28*((5*B*a*b^2 - 2*A*b^3)*x^6 + 5*B*a^3 - 2*A*a^2*b + 2*(5*B*a^2*b - 2*A*a*b^2)*x^3)*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) - 84*(5*B*a^3 - 2*A*a^2*b)*x)/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4)","A",0
97,1,792,0,0.916574," ","integrate(x^7*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{27 \, B a b^{4} x^{8} + 24 \, {\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{5} + 15 \, {\left(4 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} - 15 \, \sqrt{\frac{1}{3}} {\left({\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{6} + 4 \, B a^{4} b - A a^{3} b^{2} + 2 \, {\left(4 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - 5 \, {\left({\left(4 \, B a b^{2} - A b^{3}\right)} x^{6} + 4 \, B a^{3} - A a^{2} b + 2 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 10 \, {\left({\left(4 \, B a b^{2} - A b^{3}\right)} x^{6} + 4 \, B a^{3} - A a^{2} b + 2 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a b^{7} x^{6} + 2 \, a^{2} b^{6} x^{3} + a^{3} b^{5}\right)}}, \frac{27 \, B a b^{4} x^{8} + 24 \, {\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{5} + 15 \, {\left(4 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} - 30 \, \sqrt{\frac{1}{3}} {\left({\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{6} + 4 \, B a^{4} b - A a^{3} b^{2} + 2 \, {\left(4 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - 5 \, {\left({\left(4 \, B a b^{2} - A b^{3}\right)} x^{6} + 4 \, B a^{3} - A a^{2} b + 2 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 10 \, {\left({\left(4 \, B a b^{2} - A b^{3}\right)} x^{6} + 4 \, B a^{3} - A a^{2} b + 2 \, {\left(4 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a b^{7} x^{6} + 2 \, a^{2} b^{6} x^{3} + a^{3} b^{5}\right)}}\right]"," ",0,"[1/54*(27*B*a*b^4*x^8 + 24*(4*B*a^2*b^3 - A*a*b^4)*x^5 + 15*(4*B*a^3*b^2 - A*a^2*b^3)*x^2 - 15*sqrt(1/3)*((4*B*a^2*b^3 - A*a*b^4)*x^6 + 4*B*a^4*b - A*a^3*b^2 + 2*(4*B*a^3*b^2 - A*a^2*b^3)*x^3)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - 5*((4*B*a*b^2 - A*b^3)*x^6 + 4*B*a^3 - A*a^2*b + 2*(4*B*a^2*b - A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 10*((4*B*a*b^2 - A*b^3)*x^6 + 4*B*a^3 - A*a^2*b + 2*(4*B*a^2*b - A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^7*x^6 + 2*a^2*b^6*x^3 + a^3*b^5), 1/54*(27*B*a*b^4*x^8 + 24*(4*B*a^2*b^3 - A*a*b^4)*x^5 + 15*(4*B*a^3*b^2 - A*a^2*b^3)*x^2 - 30*sqrt(1/3)*((4*B*a^2*b^3 - A*a*b^4)*x^6 + 4*B*a^4*b - A*a^3*b^2 + 2*(4*B*a^3*b^2 - A*a^2*b^3)*x^3)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - 5*((4*B*a*b^2 - A*b^3)*x^6 + 4*B*a^3 - A*a^2*b + 2*(4*B*a^2*b - A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 10*((4*B*a*b^2 - A*b^3)*x^6 + 4*B*a^3 - A*a^2*b + 2*(4*B*a^2*b - A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a*b^7*x^6 + 2*a^2*b^6*x^3 + a^3*b^5)]","B",0
98,1,789,0,0.650996," ","integrate(x^6*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{54 \, B a^{2} b^{3} x^{7} + 21 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left({\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} x^{6} + 7 \, B a^{4} b - A a^{3} b^{2} + 2 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + 2 \, {\left({\left(7 \, B a b^{2} - A b^{3}\right)} x^{6} + 7 \, B a^{3} - A a^{2} b + 2 \, {\left(7 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 4 \, {\left({\left(7 \, B a b^{2} - A b^{3}\right)} x^{6} + 7 \, B a^{3} - A a^{2} b + 2 \, {\left(7 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(7 \, B a^{4} b - A a^{3} b^{2}\right)} x}{54 \, {\left(a^{2} b^{6} x^{6} + 2 \, a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}, \frac{54 \, B a^{2} b^{3} x^{7} + 21 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{4} - 12 \, \sqrt{\frac{1}{3}} {\left({\left(7 \, B a^{2} b^{3} - A a b^{4}\right)} x^{6} + 7 \, B a^{4} b - A a^{3} b^{2} + 2 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + 2 \, {\left({\left(7 \, B a b^{2} - A b^{3}\right)} x^{6} + 7 \, B a^{3} - A a^{2} b + 2 \, {\left(7 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 4 \, {\left({\left(7 \, B a b^{2} - A b^{3}\right)} x^{6} + 7 \, B a^{3} - A a^{2} b + 2 \, {\left(7 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 12 \, {\left(7 \, B a^{4} b - A a^{3} b^{2}\right)} x}{54 \, {\left(a^{2} b^{6} x^{6} + 2 \, a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}\right]"," ",0,"[1/54*(54*B*a^2*b^3*x^7 + 21*(7*B*a^3*b^2 - A*a^2*b^3)*x^4 - 6*sqrt(1/3)*((7*B*a^2*b^3 - A*a*b^4)*x^6 + 7*B*a^4*b - A*a^3*b^2 + 2*(7*B*a^3*b^2 - A*a^2*b^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + 2*((7*B*a*b^2 - A*b^3)*x^6 + 7*B*a^3 - A*a^2*b + 2*(7*B*a^2*b - A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 4*((7*B*a*b^2 - A*b^3)*x^6 + 7*B*a^3 - A*a^2*b + 2*(7*B*a^2*b - A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(7*B*a^4*b - A*a^3*b^2)*x)/(a^2*b^6*x^6 + 2*a^3*b^5*x^3 + a^4*b^4), 1/54*(54*B*a^2*b^3*x^7 + 21*(7*B*a^3*b^2 - A*a^2*b^3)*x^4 - 12*sqrt(1/3)*((7*B*a^2*b^3 - A*a*b^4)*x^6 + 7*B*a^4*b - A*a^3*b^2 + 2*(7*B*a^3*b^2 - A*a^2*b^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + 2*((7*B*a*b^2 - A*b^3)*x^6 + 7*B*a^3 - A*a^2*b + 2*(7*B*a^2*b - A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 4*((7*B*a*b^2 - A*b^3)*x^6 + 7*B*a^3 - A*a^2*b + 2*(7*B*a^2*b - A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 12*(7*B*a^4*b - A*a^3*b^2)*x)/(a^2*b^6*x^6 + 2*a^3*b^5*x^3 + a^4*b^4)]","B",0
99,1,756,0,0.540568," ","integrate(x^4*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{5} + 3 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left({\left(5 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 5 \, B a^{4} b + A a^{3} b^{2} + 2 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) - {\left({\left(5 \, B a b^{2} + A b^{3}\right)} x^{6} + 5 \, B a^{3} + A a^{2} b + 2 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(5 \, B a b^{2} + A b^{3}\right)} x^{6} + 5 \, B a^{3} + A a^{2} b + 2 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{6} x^{6} + 2 \, a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}, -\frac{6 \, {\left(4 \, B a^{2} b^{3} - A a b^{4}\right)} x^{5} + 3 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{2} - 6 \, \sqrt{\frac{1}{3}} {\left({\left(5 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 5 \, B a^{4} b + A a^{3} b^{2} + 2 \, {\left(5 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) - {\left({\left(5 \, B a b^{2} + A b^{3}\right)} x^{6} + 5 \, B a^{3} + A a^{2} b + 2 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(5 \, B a b^{2} + A b^{3}\right)} x^{6} + 5 \, B a^{3} + A a^{2} b + 2 \, {\left(5 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{2} b^{6} x^{6} + 2 \, a^{3} b^{5} x^{3} + a^{4} b^{4}\right)}}\right]"," ",0,"[-1/54*(6*(4*B*a^2*b^3 - A*a*b^4)*x^5 + 3*(5*B*a^3*b^2 + A*a^2*b^3)*x^2 - 3*sqrt(1/3)*((5*B*a^2*b^3 + A*a*b^4)*x^6 + 5*B*a^4*b + A*a^3*b^2 + 2*(5*B*a^3*b^2 + A*a^2*b^3)*x^3)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) - ((5*B*a*b^2 + A*b^3)*x^6 + 5*B*a^3 + A*a^2*b + 2*(5*B*a^2*b + A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((5*B*a*b^2 + A*b^3)*x^6 + 5*B*a^3 + A*a^2*b + 2*(5*B*a^2*b + A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^6*x^6 + 2*a^3*b^5*x^3 + a^4*b^4), -1/54*(6*(4*B*a^2*b^3 - A*a*b^4)*x^5 + 3*(5*B*a^3*b^2 + A*a^2*b^3)*x^2 - 6*sqrt(1/3)*((5*B*a^2*b^3 + A*a*b^4)*x^6 + 5*B*a^4*b + A*a^3*b^2 + 2*(5*B*a^3*b^2 + A*a^2*b^3)*x^3)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) - ((5*B*a*b^2 + A*b^3)*x^6 + 5*B*a^3 + A*a^2*b + 2*(5*B*a^2*b + A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) + 2*((5*B*a*b^2 + A*b^3)*x^6 + 5*B*a^3 + A*a^2*b + 2*(5*B*a^2*b + A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^2*b^6*x^6 + 2*a^3*b^5*x^3 + a^4*b^4)]","B",0
100,1,743,0,0.718978," ","integrate(x^3*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 2 \, B a^{4} b + A a^{3} b^{2} + 2 \, {\left(2 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) + {\left({\left(2 \, B a b^{2} + A b^{3}\right)} x^{6} + 2 \, B a^{3} + A a^{2} b + 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(2 \, B a b^{2} + A b^{3}\right)} x^{6} + 2 \, B a^{3} + A a^{2} b + 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(2 \, B a^{4} b + A a^{3} b^{2}\right)} x}{54 \, {\left(a^{3} b^{5} x^{6} + 2 \, a^{4} b^{4} x^{3} + a^{5} b^{3}\right)}}, -\frac{3 \, {\left(7 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{6} + 2 \, B a^{4} b + A a^{3} b^{2} + 2 \, {\left(2 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) + {\left({\left(2 \, B a b^{2} + A b^{3}\right)} x^{6} + 2 \, B a^{3} + A a^{2} b + 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) - 2 \, {\left({\left(2 \, B a b^{2} + A b^{3}\right)} x^{6} + 2 \, B a^{3} + A a^{2} b + 2 \, {\left(2 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) + 6 \, {\left(2 \, B a^{4} b + A a^{3} b^{2}\right)} x}{54 \, {\left(a^{3} b^{5} x^{6} + 2 \, a^{4} b^{4} x^{3} + a^{5} b^{3}\right)}}\right]"," ",0,"[-1/54*(3*(7*B*a^3*b^2 - A*a^2*b^3)*x^4 - 3*sqrt(1/3)*((2*B*a^2*b^3 + A*a*b^4)*x^6 + 2*B*a^4*b + A*a^3*b^2 + 2*(2*B*a^3*b^2 + A*a^2*b^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) + ((2*B*a*b^2 + A*b^3)*x^6 + 2*B*a^3 + A*a^2*b + 2*(2*B*a^2*b + A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*((2*B*a*b^2 + A*b^3)*x^6 + 2*B*a^3 + A*a^2*b + 2*(2*B*a^2*b + A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(2*B*a^4*b + A*a^3*b^2)*x)/(a^3*b^5*x^6 + 2*a^4*b^4*x^3 + a^5*b^3), -1/54*(3*(7*B*a^3*b^2 - A*a^2*b^3)*x^4 - 6*sqrt(1/3)*((2*B*a^2*b^3 + A*a*b^4)*x^6 + 2*B*a^4*b + A*a^3*b^2 + 2*(2*B*a^3*b^2 + A*a^2*b^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) + ((2*B*a*b^2 + A*b^3)*x^6 + 2*B*a^3 + A*a^2*b + 2*(2*B*a^2*b + A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) - 2*((2*B*a*b^2 + A*b^3)*x^6 + 2*B*a^3 + A*a^2*b + 2*(2*B*a^2*b + A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) + 6*(2*B*a^4*b + A*a^3*b^2)*x)/(a^3*b^5*x^6 + 2*a^4*b^4*x^3 + a^5*b^3)]","B",0
101,1,752,0,0.785820," ","integrate(x*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(B a^{2} b^{3} + 2 \, A a b^{4}\right)} x^{5} - 3 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{2} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} + 2 \, A a b^{4}\right)} x^{6} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, {\left(B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b + 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(-a b^{2}\right)^{\frac{2}{3}} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(-a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + {\left({\left(B a b^{2} + 2 \, A b^{3}\right)} x^{6} + B a^{3} + 2 \, A a^{2} b + 2 \, {\left(B a^{2} b + 2 \, A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left({\left(B a b^{2} + 2 \, A b^{3}\right)} x^{6} + B a^{3} + 2 \, A a^{2} b + 2 \, {\left(B a^{2} b + 2 \, A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{5} x^{6} + 2 \, a^{4} b^{4} x^{3} + a^{5} b^{3}\right)}}, \frac{6 \, {\left(B a^{2} b^{3} + 2 \, A a b^{4}\right)} x^{5} - 3 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{2} + 6 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} + 2 \, A a b^{4}\right)} x^{6} + B a^{4} b + 2 \, A a^{3} b^{2} + 2 \, {\left(B a^{3} b^{2} + 2 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x + \left(-a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + {\left({\left(B a b^{2} + 2 \, A b^{3}\right)} x^{6} + B a^{3} + 2 \, A a^{2} b + 2 \, {\left(B a^{2} b + 2 \, A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} + \left(-a b^{2}\right)^{\frac{1}{3}} b x + \left(-a b^{2}\right)^{\frac{2}{3}}\right) - 2 \, {\left({\left(B a b^{2} + 2 \, A b^{3}\right)} x^{6} + B a^{3} + 2 \, A a^{2} b + 2 \, {\left(B a^{2} b + 2 \, A a b^{2}\right)} x^{3}\right)} \left(-a b^{2}\right)^{\frac{2}{3}} \log\left(b x - \left(-a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{3} b^{5} x^{6} + 2 \, a^{4} b^{4} x^{3} + a^{5} b^{3}\right)}}\right]"," ",0,"[1/54*(6*(B*a^2*b^3 + 2*A*a*b^4)*x^5 - 3*(B*a^3*b^2 - 7*A*a^2*b^3)*x^2 + 3*sqrt(1/3)*((B*a^2*b^3 + 2*A*a*b^4)*x^6 + B*a^4*b + 2*A*a^3*b^2 + 2*(B*a^3*b^2 + 2*A*a^2*b^3)*x^3)*sqrt((-a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b + 3*sqrt(1/3)*(a*b*x + 2*(-a*b^2)^(2/3)*x^2 + (-a*b^2)^(1/3)*a)*sqrt((-a*b^2)^(1/3)/a) - 3*(-a*b^2)^(2/3)*x)/(b*x^3 + a)) + ((B*a*b^2 + 2*A*b^3)*x^6 + B*a^3 + 2*A*a^2*b + 2*(B*a^2*b + 2*A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*((B*a*b^2 + 2*A*b^3)*x^6 + B*a^3 + 2*A*a^2*b + 2*(B*a^2*b + 2*A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^5*x^6 + 2*a^4*b^4*x^3 + a^5*b^3), 1/54*(6*(B*a^2*b^3 + 2*A*a*b^4)*x^5 - 3*(B*a^3*b^2 - 7*A*a^2*b^3)*x^2 + 6*sqrt(1/3)*((B*a^2*b^3 + 2*A*a*b^4)*x^6 + B*a^4*b + 2*A*a^3*b^2 + 2*(B*a^3*b^2 + 2*A*a^2*b^3)*x^3)*sqrt(-(-a*b^2)^(1/3)/a)*arctan(sqrt(1/3)*(2*b*x + (-a*b^2)^(1/3))*sqrt(-(-a*b^2)^(1/3)/a)/b) + ((B*a*b^2 + 2*A*b^3)*x^6 + B*a^3 + 2*A*a^2*b + 2*(B*a^2*b + 2*A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b^2*x^2 + (-a*b^2)^(1/3)*b*x + (-a*b^2)^(2/3)) - 2*((B*a*b^2 + 2*A*b^3)*x^6 + B*a^3 + 2*A*a^2*b + 2*(B*a^2*b + 2*A*a*b^2)*x^3)*(-a*b^2)^(2/3)*log(b*x - (-a*b^2)^(1/3)))/(a^3*b^5*x^6 + 2*a^4*b^4*x^3 + a^5*b^3)]","B",0
102,1,743,0,0.636685," ","integrate((B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{4} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{6} + B a^{4} b + 5 \, A a^{3} b^{2} + 2 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} - 3 \, \left(a^{2} b\right)^{\frac{1}{3}} a x - a^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - {\left({\left(B a b^{2} + 5 \, A b^{3}\right)} x^{6} + B a^{3} + 5 \, A a^{2} b + 2 \, {\left(B a^{2} b + 5 \, A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(B a b^{2} + 5 \, A b^{3}\right)} x^{6} + B a^{3} + 5 \, A a^{2} b + 2 \, {\left(B a^{2} b + 5 \, A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) - 6 \, {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x}{54 \, {\left(a^{4} b^{4} x^{6} + 2 \, a^{5} b^{3} x^{3} + a^{6} b^{2}\right)}}, \frac{3 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} + 5 \, A a b^{4}\right)} x^{6} + B a^{4} b + 5 \, A a^{3} b^{2} + 2 \, {\left(B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(a^{2} b\right)^{\frac{2}{3}} x - \left(a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - {\left({\left(B a b^{2} + 5 \, A b^{3}\right)} x^{6} + B a^{3} + 5 \, A a^{2} b + 2 \, {\left(B a^{2} b + 5 \, A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(a^{2} b\right)^{\frac{2}{3}} x + \left(a^{2} b\right)^{\frac{1}{3}} a\right) + 2 \, {\left({\left(B a b^{2} + 5 \, A b^{3}\right)} x^{6} + B a^{3} + 5 \, A a^{2} b + 2 \, {\left(B a^{2} b + 5 \, A a b^{2}\right)} x^{3}\right)} \left(a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(a^{2} b\right)^{\frac{2}{3}}\right) - 6 \, {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x}{54 \, {\left(a^{4} b^{4} x^{6} + 2 \, a^{5} b^{3} x^{3} + a^{6} b^{2}\right)}}\right]"," ",0,"[1/54*(3*(B*a^3*b^2 + 5*A*a^2*b^3)*x^4 + 3*sqrt(1/3)*((B*a^2*b^3 + 5*A*a*b^4)*x^6 + B*a^4*b + 5*A*a^3*b^2 + 2*(B*a^3*b^2 + 5*A*a^2*b^3)*x^3)*sqrt(-(a^2*b)^(1/3)/b)*log((2*a*b*x^3 - 3*(a^2*b)^(1/3)*a*x - a^2 + 3*sqrt(1/3)*(2*a*b*x^2 + (a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt(-(a^2*b)^(1/3)/b))/(b*x^3 + a)) - ((B*a*b^2 + 5*A*b^3)*x^6 + B*a^3 + 5*A*a^2*b + 2*(B*a^2*b + 5*A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((B*a*b^2 + 5*A*b^3)*x^6 + B*a^3 + 5*A*a^2*b + 2*(B*a^2*b + 5*A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) - 6*(B*a^4*b - 4*A*a^3*b^2)*x)/(a^4*b^4*x^6 + 2*a^5*b^3*x^3 + a^6*b^2), 1/54*(3*(B*a^3*b^2 + 5*A*a^2*b^3)*x^4 + 6*sqrt(1/3)*((B*a^2*b^3 + 5*A*a*b^4)*x^6 + B*a^4*b + 5*A*a^3*b^2 + 2*(B*a^3*b^2 + 5*A*a^2*b^3)*x^3)*sqrt((a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(a^2*b)^(2/3)*x - (a^2*b)^(1/3)*a)*sqrt((a^2*b)^(1/3)/b)/a^2) - ((B*a*b^2 + 5*A*b^3)*x^6 + B*a^3 + 5*A*a^2*b + 2*(B*a^2*b + 5*A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x^2 - (a^2*b)^(2/3)*x + (a^2*b)^(1/3)*a) + 2*((B*a*b^2 + 5*A*b^3)*x^6 + B*a^3 + 5*A*a^2*b + 2*(B*a^2*b + 5*A*a*b^2)*x^3)*(a^2*b)^(2/3)*log(a*b*x + (a^2*b)^(2/3)) - 6*(B*a^4*b - 4*A*a^3*b^2)*x)/(a^4*b^4*x^6 + 2*a^5*b^3*x^3 + a^6*b^2)]","B",0
103,1,776,0,0.694327," ","integrate((B*x^3+A)/x^2/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{6} - 54 \, A a^{3} b^{2} + 21 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{3} - 6 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{7} + 2 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{4} + {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b^{2} x^{3} - a b - 3 \, \sqrt{\frac{1}{3}} {\left(a b x + 2 \, \left(a b^{2}\right)^{\frac{2}{3}} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} - 3 \, \left(a b^{2}\right)^{\frac{2}{3}} x}{b x^{3} + a}\right) + 2 \, {\left({\left(B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 7 \, A a^{2} b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left({\left(B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 7 \, A a^{2} b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{4} b^{4} x^{7} + 2 \, a^{5} b^{3} x^{4} + a^{6} b^{2} x\right)}}, \frac{12 \, {\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{6} - 54 \, A a^{3} b^{2} + 21 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{3} - 12 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{7} + 2 \, {\left(B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{4} + {\left(B a^{4} b - 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(2 \, b x - \left(a b^{2}\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(a b^{2}\right)^{\frac{1}{3}}}{a}}}{b}\right) + 2 \, {\left({\left(B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 7 \, A a^{2} b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b^{2} x^{2} - \left(a b^{2}\right)^{\frac{1}{3}} b x + \left(a b^{2}\right)^{\frac{2}{3}}\right) - 4 \, {\left({\left(B a b^{2} - 7 \, A b^{3}\right)} x^{7} + 2 \, {\left(B a^{2} b - 7 \, A a b^{2}\right)} x^{4} + {\left(B a^{3} - 7 \, A a^{2} b\right)} x\right)} \left(a b^{2}\right)^{\frac{2}{3}} \log\left(b x + \left(a b^{2}\right)^{\frac{1}{3}}\right)}{54 \, {\left(a^{4} b^{4} x^{7} + 2 \, a^{5} b^{3} x^{4} + a^{6} b^{2} x\right)}}\right]"," ",0,"[1/54*(12*(B*a^2*b^3 - 7*A*a*b^4)*x^6 - 54*A*a^3*b^2 + 21*(B*a^3*b^2 - 7*A*a^2*b^3)*x^3 - 6*sqrt(1/3)*((B*a^2*b^3 - 7*A*a*b^4)*x^7 + 2*(B*a^3*b^2 - 7*A*a^2*b^3)*x^4 + (B*a^4*b - 7*A*a^3*b^2)*x)*sqrt(-(a*b^2)^(1/3)/a)*log((2*b^2*x^3 - a*b - 3*sqrt(1/3)*(a*b*x + 2*(a*b^2)^(2/3)*x^2 - (a*b^2)^(1/3)*a)*sqrt(-(a*b^2)^(1/3)/a) - 3*(a*b^2)^(2/3)*x)/(b*x^3 + a)) + 2*((B*a*b^2 - 7*A*b^3)*x^7 + 2*(B*a^2*b - 7*A*a*b^2)*x^4 + (B*a^3 - 7*A*a^2*b)*x)*(a*b^2)^(2/3)*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) - 4*((B*a*b^2 - 7*A*b^3)*x^7 + 2*(B*a^2*b - 7*A*a*b^2)*x^4 + (B*a^3 - 7*A*a^2*b)*x)*(a*b^2)^(2/3)*log(b*x + (a*b^2)^(1/3)))/(a^4*b^4*x^7 + 2*a^5*b^3*x^4 + a^6*b^2*x), 1/54*(12*(B*a^2*b^3 - 7*A*a*b^4)*x^6 - 54*A*a^3*b^2 + 21*(B*a^3*b^2 - 7*A*a^2*b^3)*x^3 - 12*sqrt(1/3)*((B*a^2*b^3 - 7*A*a*b^4)*x^7 + 2*(B*a^3*b^2 - 7*A*a^2*b^3)*x^4 + (B*a^4*b - 7*A*a^3*b^2)*x)*sqrt((a*b^2)^(1/3)/a)*arctan(-sqrt(1/3)*(2*b*x - (a*b^2)^(1/3))*sqrt((a*b^2)^(1/3)/a)/b) + 2*((B*a*b^2 - 7*A*b^3)*x^7 + 2*(B*a^2*b - 7*A*a*b^2)*x^4 + (B*a^3 - 7*A*a^2*b)*x)*(a*b^2)^(2/3)*log(b^2*x^2 - (a*b^2)^(1/3)*b*x + (a*b^2)^(2/3)) - 4*((B*a*b^2 - 7*A*b^3)*x^7 + 2*(B*a^2*b - 7*A*a*b^2)*x^4 + (B*a^3 - 7*A*a^2*b)*x)*(a*b^2)^(2/3)*log(b*x + (a*b^2)^(1/3)))/(a^4*b^4*x^7 + 2*a^5*b^3*x^4 + a^6*b^2*x)]","B",0
104,1,812,0,0.519504," ","integrate((B*x^3+A)/x^3/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{6} - 27 \, A a^{4} b + 24 \, {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{3} - 15 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{8} + 2 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{5} + {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \log\left(\frac{2 \, a b x^{3} + 3 \, \left(-a^{2} b\right)^{\frac{1}{3}} a x - a^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b x^{2} + \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{b x^{3} + a}\right) - 5 \, {\left({\left(B a b^{2} - 4 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 4 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 4 \, A a^{2} b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left({\left(B a b^{2} - 4 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 4 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 4 \, A a^{2} b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{5} b^{3} x^{8} + 2 \, a^{6} b^{2} x^{5} + a^{7} b x^{2}\right)}}, \frac{15 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{6} - 27 \, A a^{4} b + 24 \, {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{3} + 30 \, \sqrt{\frac{1}{3}} {\left({\left(B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{8} + 2 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{5} + {\left(B a^{4} b - 4 \, A a^{3} b^{2}\right)} x^{2}\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-a^{2} b\right)^{\frac{2}{3}} x + \left(-a^{2} b\right)^{\frac{1}{3}} a\right)} \sqrt{-\frac{\left(-a^{2} b\right)^{\frac{1}{3}}}{b}}}{a^{2}}\right) - 5 \, {\left({\left(B a b^{2} - 4 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 4 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 4 \, A a^{2} b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x^{2} - \left(-a^{2} b\right)^{\frac{2}{3}} x - \left(-a^{2} b\right)^{\frac{1}{3}} a\right) + 10 \, {\left({\left(B a b^{2} - 4 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 4 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 4 \, A a^{2} b\right)} x^{2}\right)} \left(-a^{2} b\right)^{\frac{2}{3}} \log\left(a b x + \left(-a^{2} b\right)^{\frac{2}{3}}\right)}{54 \, {\left(a^{5} b^{3} x^{8} + 2 \, a^{6} b^{2} x^{5} + a^{7} b x^{2}\right)}}\right]"," ",0,"[1/54*(15*(B*a^3*b^2 - 4*A*a^2*b^3)*x^6 - 27*A*a^4*b + 24*(B*a^4*b - 4*A*a^3*b^2)*x^3 - 15*sqrt(1/3)*((B*a^2*b^3 - 4*A*a*b^4)*x^8 + 2*(B*a^3*b^2 - 4*A*a^2*b^3)*x^5 + (B*a^4*b - 4*A*a^3*b^2)*x^2)*sqrt((-a^2*b)^(1/3)/b)*log((2*a*b*x^3 + 3*(-a^2*b)^(1/3)*a*x - a^2 - 3*sqrt(1/3)*(2*a*b*x^2 + (-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt((-a^2*b)^(1/3)/b))/(b*x^3 + a)) - 5*((B*a*b^2 - 4*A*b^3)*x^8 + 2*(B*a^2*b - 4*A*a*b^2)*x^5 + (B*a^3 - 4*A*a^2*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 10*((B*a*b^2 - 4*A*b^3)*x^8 + 2*(B*a^2*b - 4*A*a*b^2)*x^5 + (B*a^3 - 4*A*a^2*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)))/(a^5*b^3*x^8 + 2*a^6*b^2*x^5 + a^7*b*x^2), 1/54*(15*(B*a^3*b^2 - 4*A*a^2*b^3)*x^6 - 27*A*a^4*b + 24*(B*a^4*b - 4*A*a^3*b^2)*x^3 + 30*sqrt(1/3)*((B*a^2*b^3 - 4*A*a*b^4)*x^8 + 2*(B*a^3*b^2 - 4*A*a^2*b^3)*x^5 + (B*a^4*b - 4*A*a^3*b^2)*x^2)*sqrt(-(-a^2*b)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-a^2*b)^(2/3)*x + (-a^2*b)^(1/3)*a)*sqrt(-(-a^2*b)^(1/3)/b)/a^2) - 5*((B*a*b^2 - 4*A*b^3)*x^8 + 2*(B*a^2*b - 4*A*a*b^2)*x^5 + (B*a^3 - 4*A*a^2*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x^2 - (-a^2*b)^(2/3)*x - (-a^2*b)^(1/3)*a) + 10*((B*a*b^2 - 4*A*b^3)*x^8 + 2*(B*a^2*b - 4*A*a*b^2)*x^5 + (B*a^3 - 4*A*a^2*b)*x^2)*(-a^2*b)^(2/3)*log(a*b*x + (-a^2*b)^(2/3)))/(a^5*b^3*x^8 + 2*a^6*b^2*x^5 + a^7*b*x^2)]","B",0
105,1,366,0,0.920266," ","integrate((B*x^3+A)/x^5/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{84 \, {\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{9} + 147 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} + 27 \, A a^{3} + 54 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3} + 28 \, \sqrt{3} {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{10} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{7} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 14 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{10} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{7} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 28 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{10} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{7} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{4}\right)} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right)}{108 \, {\left(a^{4} b^{2} x^{10} + 2 \, a^{5} b x^{7} + a^{6} x^{4}\right)}}"," ",0,"-1/108*(84*(2*B*a*b^2 - 5*A*b^3)*x^9 + 147*(2*B*a^2*b - 5*A*a*b^2)*x^6 + 27*A*a^3 + 54*(2*B*a^3 - 5*A*a^2*b)*x^3 + 28*sqrt(3)*((2*B*a*b^2 - 5*A*b^3)*x^10 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^7 + (2*B*a^3 - 5*A*a^2*b)*x^4)*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - 14*((2*B*a*b^2 - 5*A*b^3)*x^10 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^7 + (2*B*a^3 - 5*A*a^2*b)*x^4)*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) + 28*((2*B*a*b^2 - 5*A*b^3)*x^10 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^7 + (2*B*a^3 - 5*A*a^2*b)*x^4)*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)))/(a^4*b^2*x^10 + 2*a^5*b*x^7 + a^6*x^4)","A",0
106,1,384,0,0.663591," ","integrate((B*x^3+A)/x^6/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{60 \, {\left(5 \, B a b^{2} - 11 \, A b^{3}\right)} x^{9} + 96 \, {\left(5 \, B a^{2} b - 11 \, A a b^{2}\right)} x^{6} + 54 \, A a^{3} + 27 \, {\left(5 \, B a^{3} - 11 \, A a^{2} b\right)} x^{3} + 40 \, \sqrt{3} {\left({\left(5 \, B a b^{2} - 11 \, A b^{3}\right)} x^{11} + 2 \, {\left(5 \, B a^{2} b - 11 \, A a b^{2}\right)} x^{8} + {\left(5 \, B a^{3} - 11 \, A a^{2} b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - 20 \, {\left({\left(5 \, B a b^{2} - 11 \, A b^{3}\right)} x^{11} + 2 \, {\left(5 \, B a^{2} b - 11 \, A a b^{2}\right)} x^{8} + {\left(5 \, B a^{3} - 11 \, A a^{2} b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 40 \, {\left({\left(5 \, B a b^{2} - 11 \, A b^{3}\right)} x^{11} + 2 \, {\left(5 \, B a^{2} b - 11 \, A a b^{2}\right)} x^{8} + {\left(5 \, B a^{3} - 11 \, A a^{2} b\right)} x^{5}\right)} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right)}{270 \, {\left(a^{4} b^{2} x^{11} + 2 \, a^{5} b x^{8} + a^{6} x^{5}\right)}}"," ",0,"-1/270*(60*(5*B*a*b^2 - 11*A*b^3)*x^9 + 96*(5*B*a^2*b - 11*A*a*b^2)*x^6 + 54*A*a^3 + 27*(5*B*a^3 - 11*A*a^2*b)*x^3 + 40*sqrt(3)*((5*B*a*b^2 - 11*A*b^3)*x^11 + 2*(5*B*a^2*b - 11*A*a*b^2)*x^8 + (5*B*a^3 - 11*A*a^2*b)*x^5)*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) - 20*((5*B*a*b^2 - 11*A*b^3)*x^11 + 2*(5*B*a^2*b - 11*A*a*b^2)*x^8 + (5*B*a^3 - 11*A*a^2*b)*x^5)*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) + 40*((5*B*a*b^2 - 11*A*b^3)*x^11 + 2*(5*B*a^2*b - 11*A*a*b^2)*x^8 + (5*B*a^3 - 11*A*a^2*b)*x^5)*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)))/(a^4*b^2*x^11 + 2*a^5*b*x^8 + a^6*x^5)","A",0
107,1,72,0,1.163626," ","integrate(x^8/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{a^{2} d^{2} \log\left(b x^{3} + a\right) - b^{2} c^{2} \log\left(d x^{3} + c\right) + {\left(b^{2} c d - a b d^{2}\right)} x^{3}}{3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}"," ",0,"1/3*(a^2*d^2*log(b*x^3 + a) - b^2*c^2*log(d*x^3 + c) + (b^2*c*d - a*b*d^2)*x^3)/(b^3*c*d^2 - a*b^2*d^3)","A",0
108,1,273,0,1.359047," ","integrate(x^7/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} a d \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - 2 \, \sqrt{3} b c \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} d x \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} + \sqrt{3} c}{3 \, c}\right) + a d \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + b c \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(c x^{2} - d x \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{2}{3}} - c \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) - 2 \, a d \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right) - 2 \, b c \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(c x + d \left(-\frac{c^{2}}{d^{2}}\right)^{\frac{2}{3}}\right) + 3 \, {\left(b c - a d\right)} x^{2}}{6 \, {\left(b^{2} c d - a b d^{2}\right)}}"," ",0,"1/6*(2*sqrt(3)*a*d*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - 2*sqrt(3)*b*c*(-c^2/d^2)^(1/3)*arctan(1/3*(2*sqrt(3)*d*x*(-c^2/d^2)^(1/3) + sqrt(3)*c)/c) + a*d*(a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + b*c*(-c^2/d^2)^(1/3)*log(c*x^2 - d*x*(-c^2/d^2)^(2/3) - c*(-c^2/d^2)^(1/3)) - 2*a*d*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)) - 2*b*c*(-c^2/d^2)^(1/3)*log(c*x + d*(-c^2/d^2)^(2/3)) + 3*(b*c - a*d)*x^2)/(b^2*c*d - a*b*d^2)","A",0
109,1,228,0,0.937169," ","integrate(x^6/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} a d \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 2 \, \sqrt{3} b c \left(\frac{c}{d}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} d x \left(\frac{c}{d}\right)^{\frac{2}{3}} - \sqrt{3} c}{3 \, c}\right) - a d \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) - b c \left(\frac{c}{d}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{c}{d}\right)^{\frac{1}{3}} + \left(\frac{c}{d}\right)^{\frac{2}{3}}\right) + 2 \, a d \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) + 2 \, b c \left(\frac{c}{d}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{c}{d}\right)^{\frac{1}{3}}\right) - 6 \, {\left(b c - a d\right)} x}{6 \, {\left(b^{2} c d - a b d^{2}\right)}}"," ",0,"-1/6*(2*sqrt(3)*a*d*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) + 2*sqrt(3)*b*c*(c/d)^(1/3)*arctan(1/3*(2*sqrt(3)*d*x*(c/d)^(2/3) - sqrt(3)*c)/c) - a*d*(-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) - b*c*(c/d)^(1/3)*log(x^2 - x*(c/d)^(1/3) + (c/d)^(2/3)) + 2*a*d*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) + 2*b*c*(c/d)^(1/3)*log(x + (c/d)^(1/3)) - 6*(b*c - a*d)*x)/(b^2*c*d - a*b*d^2)","A",0
110,1,42,0,0.985751," ","integrate(x^5/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{a d \log\left(b x^{3} + a\right) - b c \log\left(d x^{3} + c\right)}{3 \, {\left(b^{2} c d - a b d^{2}\right)}}"," ",0,"-1/3*(a*d*log(b*x^3 + a) - b*c*log(d*x^3 + c))/(b^2*c*d - a*b*d^2)","A",0
111,1,244,0,1.051945," ","integrate(x^4/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} + \sqrt{3} a}{3 \, a}\right) - 2 \, \sqrt{3} \left(\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} d x \left(\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} - \sqrt{3} c}{3 \, c}\right) - \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} - a \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) - \left(\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(c x^{2} - d x \left(\frac{c^{2}}{d^{2}}\right)^{\frac{2}{3}} + c \left(\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right) + 2 \, \left(\frac{c^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(c x + d \left(\frac{c^{2}}{d^{2}}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b c - a d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(-a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a^2/b^2)^(1/3) + sqrt(3)*a)/a) - 2*sqrt(3)*(c^2/d^2)^(1/3)*arctan(1/3*(2*sqrt(3)*d*x*(c^2/d^2)^(1/3) - sqrt(3)*c)/c) - (-a^2/b^2)^(1/3)*log(a*x^2 - b*x*(-a^2/b^2)^(2/3) - a*(-a^2/b^2)^(1/3)) - (c^2/d^2)^(1/3)*log(c*x^2 - d*x*(c^2/d^2)^(2/3) + c*(c^2/d^2)^(1/3)) + 2*(-a^2/b^2)^(1/3)*log(a*x + b*(-a^2/b^2)^(2/3)) + 2*(c^2/d^2)^(1/3)*log(c*x + d*(c^2/d^2)^(2/3)))/(b*c - a*d)","A",0
112,1,199,0,0.796826," ","integrate(x^3/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) + 2 \, \sqrt{3} \left(-\frac{c}{d}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} d x \left(-\frac{c}{d}\right)^{\frac{2}{3}} - \sqrt{3} c}{3 \, c}\right) - \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) - \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{c}{d}\right)^{\frac{1}{3}} + \left(-\frac{c}{d}\right)^{\frac{2}{3}}\right) + 2 \, \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(-\frac{c}{d}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{c}{d}\right)^{\frac{1}{3}}\right)}{6 \, {\left(b c - a d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a/b)^(2/3) - sqrt(3)*a)/a) + 2*sqrt(3)*(-c/d)^(1/3)*arctan(1/3*(2*sqrt(3)*d*x*(-c/d)^(2/3) - sqrt(3)*c)/c) - (a/b)^(1/3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3)) - (-c/d)^(1/3)*log(x^2 + x*(-c/d)^(1/3) + (-c/d)^(2/3)) + 2*(a/b)^(1/3)*log(x + (a/b)^(1/3)) + 2*(-c/d)^(1/3)*log(x - (-c/d)^(1/3)))/(b*c - a*d)","A",0
113,1,31,0,0.844604," ","integrate(x^2/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{\log\left(b x^{3} + a\right) - \log\left(d x^{3} + c\right)}{3 \, {\left(b c - a d\right)}}"," ",0,"1/3*(log(b*x^3 + a) - log(d*x^3 + c))/(b*c - a*d)","A",0
114,1,201,0,0.841250," ","integrate(x/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 2 \, \sqrt{3} \left(-\frac{d}{c}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{d}{c}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) + \left(-\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x^{2} - c x \left(-\frac{d}{c}\right)^{\frac{2}{3}} - c \left(-\frac{d}{c}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) - 2 \, \left(-\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x + c \left(-\frac{d}{c}\right)^{\frac{2}{3}}\right)}{6 \, {\left(b c - a d\right)}}"," ",0,"1/6*(2*sqrt(3)*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) - 2*sqrt(3)*(-d/c)^(1/3)*arctan(2/3*sqrt(3)*x*(-d/c)^(1/3) + 1/3*sqrt(3)) + (b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) + (-d/c)^(1/3)*log(d*x^2 - c*x*(-d/c)^(2/3) - c*(-d/c)^(1/3)) - 2*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) - 2*(-d/c)^(1/3)*log(d*x + c*(-d/c)^(2/3)))/(b*c - a*d)","A",0
115,1,254,0,0.981911," ","integrate(1/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 2 \, \sqrt{3} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} - c d x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 2 \, \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right)}{6 \, {\left(b c - a d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 2*sqrt(3)*(d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(d^2/c^2)^(2/3) - sqrt(3)*d)/d) - (-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - (d^2/c^2)^(1/3)*log(d^2*x^2 - c*d*x*(d^2/c^2)^(1/3) + c^2*(d^2/c^2)^(2/3)) + 2*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) + 2*(d^2/c^2)^(1/3)*log(d*x + c*(d^2/c^2)^(1/3)))/(b*c - a*d)","A",0
116,1,54,0,1.558141," ","integrate(1/x/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{b c \log\left(b x^{3} + a\right) - a d \log\left(d x^{3} + c\right) - 3 \, {\left(b c - a d\right)} \log\left(x\right)}{3 \, {\left(a b c^{2} - a^{2} c d\right)}}"," ",0,"-1/3*(b*c*log(b*x^3 + a) - a*d*log(d*x^3 + c) - 3*(b*c - a*d)*log(x))/(a*b*c^2 - a^2*c*d)","A",0
117,1,238,0,0.893228," ","integrate(1/x^2/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b c x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 2 \, \sqrt{3} a d x \left(\frac{d}{c}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{d}{c}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - b c x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) - a d x \left(\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x^{2} - c x \left(\frac{d}{c}\right)^{\frac{2}{3}} + c \left(\frac{d}{c}\right)^{\frac{1}{3}}\right) + 2 \, b c x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 2 \, a d x \left(\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d}{c}\right)^{\frac{2}{3}}\right) + 6 \, b c - 6 \, a d}{6 \, {\left(a b c^{2} - a^{2} c d\right)} x}"," ",0,"-1/6*(2*sqrt(3)*b*c*x*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - 2*sqrt(3)*a*d*x*(d/c)^(1/3)*arctan(2/3*sqrt(3)*x*(d/c)^(1/3) - 1/3*sqrt(3)) - b*c*x*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) - a*d*x*(d/c)^(1/3)*log(d*x^2 - c*x*(d/c)^(2/3) + c*(d/c)^(1/3)) + 2*b*c*x*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)) + 2*a*d*x*(d/c)^(1/3)*log(d*x + c*(d/c)^(2/3)) + 6*b*c - 6*a*d)/((a*b*c^2 - a^2*c*d)*x)","A",0
118,1,301,0,2.623046," ","integrate(1/x^3/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b c x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 2 \, \sqrt{3} a d x^{2} \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - b c x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - a d x^{2} \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} + c d x \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 2 \, b c x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 2 \, a d x^{2} \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x - c \left(-\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right) + 3 \, b c - 3 \, a d}{6 \, {\left(a b c^{2} - a^{2} c d\right)} x^{2}}"," ",0,"-1/6*(2*sqrt(3)*b*c*x^2*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 2*sqrt(3)*a*d*x^2*(-d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(-d^2/c^2)^(2/3) - sqrt(3)*d)/d) - b*c*x^2*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) - a*d*x^2*(-d^2/c^2)^(1/3)*log(d^2*x^2 + c*d*x*(-d^2/c^2)^(1/3) + c^2*(-d^2/c^2)^(2/3)) + 2*b*c*x^2*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)) + 2*a*d*x^2*(-d^2/c^2)^(1/3)*log(d*x - c*(-d^2/c^2)^(1/3)) + 3*b*c - 3*a*d)/((a*b*c^2 - a^2*c*d)*x^2)","A",0
119,1,99,0,4.787434," ","integrate(1/x^4/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{b^{2} c^{2} x^{3} \log\left(b x^{3} + a\right) - a^{2} d^{2} x^{3} \log\left(d x^{3} + c\right) - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3} \log\left(x\right) - a b c^{2} + a^{2} c d}{3 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{3}}"," ",0,"1/3*(b^2*c^2*x^3*log(b*x^3 + a) - a^2*d^2*x^3*log(d*x^3 + c) - 3*(b^2*c^2 - a^2*d^2)*x^3*log(x) - a*b*c^2 + a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^3)","A",0
120,1,305,0,3.409482," ","integrate(1/x^5/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} b^{2} c^{2} x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 4 \, \sqrt{3} a^{2} d^{2} x^{4} \left(-\frac{d}{c}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{d}{c}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 2 \, b^{2} c^{2} x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) + 2 \, a^{2} d^{2} x^{4} \left(-\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x^{2} - c x \left(-\frac{d}{c}\right)^{\frac{2}{3}} - c \left(-\frac{d}{c}\right)^{\frac{1}{3}}\right) - 4 \, b^{2} c^{2} x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) - 4 \, a^{2} d^{2} x^{4} \left(-\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x + c \left(-\frac{d}{c}\right)^{\frac{2}{3}}\right) - 3 \, a b c^{2} + 3 \, a^{2} c d + 12 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3}}{12 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{4}}"," ",0,"1/12*(4*sqrt(3)*b^2*c^2*x^4*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) - 4*sqrt(3)*a^2*d^2*x^4*(-d/c)^(1/3)*arctan(2/3*sqrt(3)*x*(-d/c)^(1/3) + 1/3*sqrt(3)) + 2*b^2*c^2*x^4*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) + 2*a^2*d^2*x^4*(-d/c)^(1/3)*log(d*x^2 - c*x*(-d/c)^(2/3) - c*(-d/c)^(1/3)) - 4*b^2*c^2*x^4*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) - 4*a^2*d^2*x^4*(-d/c)^(1/3)*log(d*x + c*(-d/c)^(2/3)) - 3*a*b*c^2 + 3*a^2*c*d + 12*(b^2*c^2 - a^2*d^2)*x^3)/((a^2*b*c^3 - a^3*c^2*d)*x^4)","A",0
121,1,356,0,1.041601," ","integrate(1/x^6/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{3} b^{2} c^{2} x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) + 10 \, \sqrt{3} a^{2} d^{2} x^{5} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} c x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) - 5 \, b^{2} c^{2} x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) - 5 \, a^{2} d^{2} x^{5} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d^{2} x^{2} - c d x \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} + c^{2} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{2}{3}}\right) + 10 \, b^{2} c^{2} x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) + 10 \, a^{2} d^{2} x^{5} \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d^{2}}{c^{2}}\right)^{\frac{1}{3}}\right) + 6 \, a b c^{2} - 6 \, a^{2} c d - 15 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{3}}{30 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{5}}"," ",0,"-1/30*(10*sqrt(3)*b^2*c^2*x^5*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) + 10*sqrt(3)*a^2*d^2*x^5*(d^2/c^2)^(1/3)*arctan(1/3*(2*sqrt(3)*c*x*(d^2/c^2)^(2/3) - sqrt(3)*d)/d) - 5*b^2*c^2*x^5*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) - 5*a^2*d^2*x^5*(d^2/c^2)^(1/3)*log(d^2*x^2 - c*d*x*(d^2/c^2)^(1/3) + c^2*(d^2/c^2)^(2/3)) + 10*b^2*c^2*x^5*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) + 10*a^2*d^2*x^5*(d^2/c^2)^(1/3)*log(d*x + c*(d^2/c^2)^(1/3)) + 6*a*b*c^2 - 6*a^2*c*d - 15*(b^2*c^2 - a^2*d^2)*x^3)/((a^2*b*c^3 - a^3*c^2*d)*x^5)","A",0
122,1,127,0,11.767165," ","integrate(1/x^7/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} x^{6} \log\left(b x^{3} + a\right) - 2 \, a^{3} d^{3} x^{6} \log\left(d x^{3} + c\right) - 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{6} \log\left(x\right) + a^{2} b c^{3} - a^{3} c^{2} d - 2 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{3}}{6 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{6}}"," ",0,"-1/6*(2*b^3*c^3*x^6*log(b*x^3 + a) - 2*a^3*d^3*x^6*log(d*x^3 + c) - 6*(b^3*c^3 - a^3*d^3)*x^6*log(x) + a^2*b*c^3 - a^3*c^2*d - 2*(a*b^2*c^3 - a^3*c*d^2)*x^3)/((a^3*b*c^4 - a^4*c^3*d)*x^6)","A",0
123,1,332,0,1.203523," ","integrate(1/x^8/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{3} b^{3} c^{3} x^{7} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 28 \, \sqrt{3} a^{3} d^{3} x^{7} \left(\frac{d}{c}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{d}{c}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 14 \, b^{3} c^{3} x^{7} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) - 14 \, a^{3} d^{3} x^{7} \left(\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x^{2} - c x \left(\frac{d}{c}\right)^{\frac{2}{3}} + c \left(\frac{d}{c}\right)^{\frac{1}{3}}\right) + 28 \, b^{3} c^{3} x^{7} \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) + 28 \, a^{3} d^{3} x^{7} \left(\frac{d}{c}\right)^{\frac{1}{3}} \log\left(d x + c \left(\frac{d}{c}\right)^{\frac{2}{3}}\right) + 84 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{6} + 12 \, a^{2} b c^{3} - 12 \, a^{3} c^{2} d - 21 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x^{3}}{84 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{7}}"," ",0,"-1/84*(28*sqrt(3)*b^3*c^3*x^7*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - 28*sqrt(3)*a^3*d^3*x^7*(d/c)^(1/3)*arctan(2/3*sqrt(3)*x*(d/c)^(1/3) - 1/3*sqrt(3)) - 14*b^3*c^3*x^7*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) - 14*a^3*d^3*x^7*(d/c)^(1/3)*log(d*x^2 - c*x*(d/c)^(2/3) + c*(d/c)^(1/3)) + 28*b^3*c^3*x^7*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)) + 28*a^3*d^3*x^7*(d/c)^(1/3)*log(d*x + c*(d/c)^(2/3)) + 84*(b^3*c^3 - a^3*d^3)*x^6 + 12*a^2*b*c^3 - 12*a^3*c^2*d - 21*(a*b^2*c^3 - a^3*c*d^2)*x^3)/((a^3*b*c^4 - a^4*c^3*d)*x^7)","A",0
124,1,851,0,0.914866," ","integrate(x^m*(b*x^3+a)^5*(B*x^3+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{5} m^{6} + 51 \, B b^{5} m^{5} + 1005 \, B b^{5} m^{4} + 9605 \, B b^{5} m^{3} + 45474 \, B b^{5} m^{2} + 95064 \, B b^{5} m + 58240 \, B b^{5}\right)} x^{19} + {\left({\left(5 \, B a b^{4} + A b^{5}\right)} m^{6} + 345800 \, B a b^{4} + 69160 \, A b^{5} + 54 \, {\left(5 \, B a b^{4} + A b^{5}\right)} m^{5} + 1110 \, {\left(5 \, B a b^{4} + A b^{5}\right)} m^{4} + 10940 \, {\left(5 \, B a b^{4} + A b^{5}\right)} m^{3} + 52929 \, {\left(5 \, B a b^{4} + A b^{5}\right)} m^{2} + 112206 \, {\left(5 \, B a b^{4} + A b^{5}\right)} m\right)} x^{16} + 5 \, {\left({\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m^{6} + 170240 \, B a^{2} b^{3} + 85120 \, A a b^{4} + 57 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m^{5} + 1233 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m^{4} + 12671 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m^{3} + 63246 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m^{2} + 136872 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} m\right)} x^{13} + 10 \, {\left({\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m^{6} + 110656 \, B a^{3} b^{2} + 110656 \, A a^{2} b^{3} + 60 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m^{5} + 1374 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m^{4} + 14960 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m^{3} + 78369 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m^{2} + 175380 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} m\right)} x^{10} + 5 \, {\left({\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m^{6} + 158080 \, B a^{4} b + 316160 \, A a^{3} b^{2} + 63 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m^{5} + 1533 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m^{4} + 17969 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m^{3} + 102186 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m^{2} + 243768 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} m\right)} x^{7} + {\left({\left(B a^{5} + 5 \, A a^{4} b\right)} m^{6} + 276640 \, B a^{5} + 1383200 \, A a^{4} b + 66 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} m^{5} + 1710 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} m^{4} + 21860 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} m^{3} + 140529 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} m^{2} + 396954 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} m\right)} x^{4} + {\left(A a^{5} m^{6} + 69 \, A a^{5} m^{5} + 1905 \, A a^{5} m^{4} + 26795 \, A a^{5} m^{3} + 201174 \, A a^{5} m^{2} + 757896 \, A a^{5} m + 1106560 \, A a^{5}\right)} x\right)} x^{m}}{m^{7} + 70 \, m^{6} + 1974 \, m^{5} + 28700 \, m^{4} + 227969 \, m^{3} + 959070 \, m^{2} + 1864456 \, m + 1106560}"," ",0,"((B*b^5*m^6 + 51*B*b^5*m^5 + 1005*B*b^5*m^4 + 9605*B*b^5*m^3 + 45474*B*b^5*m^2 + 95064*B*b^5*m + 58240*B*b^5)*x^19 + ((5*B*a*b^4 + A*b^5)*m^6 + 345800*B*a*b^4 + 69160*A*b^5 + 54*(5*B*a*b^4 + A*b^5)*m^5 + 1110*(5*B*a*b^4 + A*b^5)*m^4 + 10940*(5*B*a*b^4 + A*b^5)*m^3 + 52929*(5*B*a*b^4 + A*b^5)*m^2 + 112206*(5*B*a*b^4 + A*b^5)*m)*x^16 + 5*((2*B*a^2*b^3 + A*a*b^4)*m^6 + 170240*B*a^2*b^3 + 85120*A*a*b^4 + 57*(2*B*a^2*b^3 + A*a*b^4)*m^5 + 1233*(2*B*a^2*b^3 + A*a*b^4)*m^4 + 12671*(2*B*a^2*b^3 + A*a*b^4)*m^3 + 63246*(2*B*a^2*b^3 + A*a*b^4)*m^2 + 136872*(2*B*a^2*b^3 + A*a*b^4)*m)*x^13 + 10*((B*a^3*b^2 + A*a^2*b^3)*m^6 + 110656*B*a^3*b^2 + 110656*A*a^2*b^3 + 60*(B*a^3*b^2 + A*a^2*b^3)*m^5 + 1374*(B*a^3*b^2 + A*a^2*b^3)*m^4 + 14960*(B*a^3*b^2 + A*a^2*b^3)*m^3 + 78369*(B*a^3*b^2 + A*a^2*b^3)*m^2 + 175380*(B*a^3*b^2 + A*a^2*b^3)*m)*x^10 + 5*((B*a^4*b + 2*A*a^3*b^2)*m^6 + 158080*B*a^4*b + 316160*A*a^3*b^2 + 63*(B*a^4*b + 2*A*a^3*b^2)*m^5 + 1533*(B*a^4*b + 2*A*a^3*b^2)*m^4 + 17969*(B*a^4*b + 2*A*a^3*b^2)*m^3 + 102186*(B*a^4*b + 2*A*a^3*b^2)*m^2 + 243768*(B*a^4*b + 2*A*a^3*b^2)*m)*x^7 + ((B*a^5 + 5*A*a^4*b)*m^6 + 276640*B*a^5 + 1383200*A*a^4*b + 66*(B*a^5 + 5*A*a^4*b)*m^5 + 1710*(B*a^5 + 5*A*a^4*b)*m^4 + 21860*(B*a^5 + 5*A*a^4*b)*m^3 + 140529*(B*a^5 + 5*A*a^4*b)*m^2 + 396954*(B*a^5 + 5*A*a^4*b)*m)*x^4 + (A*a^5*m^6 + 69*A*a^5*m^5 + 1905*A*a^5*m^4 + 26795*A*a^5*m^3 + 201174*A*a^5*m^2 + 757896*A*a^5*m + 1106560*A*a^5)*x)*x^m/(m^7 + 70*m^6 + 1974*m^5 + 28700*m^4 + 227969*m^3 + 959070*m^2 + 1864456*m + 1106560)","B",0
125,1,215,0,0.892333," ","integrate(x^m*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} m^{3} + 12 \, B b^{2} m^{2} + 39 \, B b^{2} m + 28 \, B b^{2}\right)} x^{10} + {\left({\left(2 \, B a b + A b^{2}\right)} m^{3} + 80 \, B a b + 40 \, A b^{2} + 15 \, {\left(2 \, B a b + A b^{2}\right)} m^{2} + 54 \, {\left(2 \, B a b + A b^{2}\right)} m\right)} x^{7} + {\left({\left(B a^{2} + 2 \, A a b\right)} m^{3} + 70 \, B a^{2} + 140 \, A a b + 18 \, {\left(B a^{2} + 2 \, A a b\right)} m^{2} + 87 \, {\left(B a^{2} + 2 \, A a b\right)} m\right)} x^{4} + {\left(A a^{2} m^{3} + 21 \, A a^{2} m^{2} + 138 \, A a^{2} m + 280 \, A a^{2}\right)} x\right)} x^{m}}{m^{4} + 22 \, m^{3} + 159 \, m^{2} + 418 \, m + 280}"," ",0,"((B*b^2*m^3 + 12*B*b^2*m^2 + 39*B*b^2*m + 28*B*b^2)*x^10 + ((2*B*a*b + A*b^2)*m^3 + 80*B*a*b + 40*A*b^2 + 15*(2*B*a*b + A*b^2)*m^2 + 54*(2*B*a*b + A*b^2)*m)*x^7 + ((B*a^2 + 2*A*a*b)*m^3 + 70*B*a^2 + 140*A*a*b + 18*(B*a^2 + 2*A*a*b)*m^2 + 87*(B*a^2 + 2*A*a*b)*m)*x^4 + (A*a^2*m^3 + 21*A*a^2*m^2 + 138*A*a^2*m + 280*A*a^2)*x)*x^m/(m^4 + 22*m^3 + 159*m^2 + 418*m + 280)","B",0
126,1,92,0,0.848072," ","integrate(x^m*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b m^{2} + 5 \, B b m + 4 \, B b\right)} x^{7} + {\left({\left(B a + A b\right)} m^{2} + 7 \, B a + 7 \, A b + 8 \, {\left(B a + A b\right)} m\right)} x^{4} + {\left(A a m^{2} + 11 \, A a m + 28 \, A a\right)} x\right)} x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28}"," ",0,"((B*b*m^2 + 5*B*b*m + 4*B*b)*x^7 + ((B*a + A*b)*m^2 + 7*B*a + 7*A*b + 8*(B*a + A*b)*m)*x^4 + (A*a*m^2 + 11*A*a*m + 28*A*a)*x)*x^m/(m^3 + 12*m^2 + 39*m + 28)","B",0
127,0,0,0,0.811175," ","integrate(x^m*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} x^{m}}{b x^{3} + a}, x\right)"," ",0,"integral((B*x^3 + A)*x^m/(b*x^3 + a), x)","F",0
128,0,0,0,0.666765," ","integrate(x^m*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} x^{m}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*x^m/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
129,0,0,0,0.817158," ","integrate(x^m*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} x^{m}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*x^m/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
130,0,0,0,0.603132," ","integrate((e*x)^m/(b*x^3+a)/(d*x^3+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral((e*x)^m/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
131,1,32,0,0.878896," ","integrate(x^(7/2)*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(15 \, B b x^{10} + 21 \, {\left(B a + A b\right)} x^{7} + 35 \, A a x^{4}\right)} \sqrt{x}"," ",0,"2/315*(15*B*b*x^10 + 21*(B*a + A*b)*x^7 + 35*A*a*x^4)*sqrt(x)","A",0
132,1,32,0,1.318249," ","integrate(x^(5/2)*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{1729} \, {\left(91 \, B b x^{9} + 133 \, {\left(B a + A b\right)} x^{6} + 247 \, A a x^{3}\right)} \sqrt{x}"," ",0,"2/1729*(91*B*b*x^9 + 133*(B*a + A*b)*x^6 + 247*A*a*x^3)*sqrt(x)","A",0
133,1,32,0,0.930107," ","integrate(x^(3/2)*(b*x^3+a)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{935} \, {\left(55 \, B b x^{8} + 85 \, {\left(B a + A b\right)} x^{5} + 187 \, A a x^{2}\right)} \sqrt{x}"," ",0,"2/935*(55*B*b*x^8 + 85*(B*a + A*b)*x^5 + 187*A*a*x^2)*sqrt(x)","A",0
134,1,30,0,0.889036," ","integrate((b*x^3+a)*(B*x^3+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{45} \, {\left(3 \, B b x^{7} + 5 \, {\left(B a + A b\right)} x^{4} + 15 \, A a x\right)} \sqrt{x}"," ",0,"2/45*(3*B*b*x^7 + 5*(B*a + A*b)*x^4 + 15*A*a*x)*sqrt(x)","A",0
135,1,29,0,0.745318," ","integrate((b*x^3+a)*(B*x^3+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{91} \, {\left(7 \, B b x^{6} + 13 \, {\left(B a + A b\right)} x^{3} + 91 \, A a\right)} \sqrt{x}"," ",0,"2/91*(7*B*b*x^6 + 13*(B*a + A*b)*x^3 + 91*A*a)*sqrt(x)","A",0
136,1,29,0,0.783372," ","integrate((b*x^3+a)*(B*x^3+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b x^{6} + 11 \, {\left(B a + A b\right)} x^{3} - 55 \, A a\right)}}{55 \, \sqrt{x}}"," ",0,"2/55*(5*B*b*x^6 + 11*(B*a + A*b)*x^3 - 55*A*a)/sqrt(x)","A",0
137,1,28,0,0.893914," ","integrate((b*x^3+a)*(B*x^3+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x^{6} + 3 \, {\left(B a + A b\right)} x^{3} - 3 \, A a\right)}}{9 \, x^{\frac{3}{2}}}"," ",0,"2/9*(B*b*x^6 + 3*(B*a + A*b)*x^3 - 3*A*a)/x^(3/2)","A",0
138,1,29,0,0.748736," ","integrate((b*x^3+a)*(B*x^3+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b x^{6} + 35 \, {\left(B a + A b\right)} x^{3} - 7 \, A a\right)}}{35 \, x^{\frac{5}{2}}}"," ",0,"2/35*(5*B*b*x^6 + 35*(B*a + A*b)*x^3 - 7*A*a)/x^(5/2)","A",0
139,1,56,0,0.759914," ","integrate(x^(7/2)*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{945} \, {\left(35 \, B b^{2} x^{13} + 45 \, {\left(2 \, B a b + A b^{2}\right)} x^{10} + 63 \, {\left(B a^{2} + 2 \, A a b\right)} x^{7} + 105 \, A a^{2} x^{4}\right)} \sqrt{x}"," ",0,"2/945*(35*B*b^2*x^13 + 45*(2*B*a*b + A*b^2)*x^10 + 63*(B*a^2 + 2*A*a*b)*x^7 + 105*A*a^2*x^4)*sqrt(x)","A",0
140,1,56,0,0.760662," ","integrate(x^(5/2)*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{43225} \, {\left(1729 \, B b^{2} x^{12} + 2275 \, {\left(2 \, B a b + A b^{2}\right)} x^{9} + 3325 \, {\left(B a^{2} + 2 \, A a b\right)} x^{6} + 6175 \, A a^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/43225*(1729*B*b^2*x^12 + 2275*(2*B*a*b + A*b^2)*x^9 + 3325*(B*a^2 + 2*A*a*b)*x^6 + 6175*A*a^2*x^3)*sqrt(x)","A",0
141,1,56,0,0.777385," ","integrate(x^(3/2)*(b*x^3+a)^2*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{21505} \, {\left(935 \, B b^{2} x^{11} + 1265 \, {\left(2 \, B a b + A b^{2}\right)} x^{8} + 1955 \, {\left(B a^{2} + 2 \, A a b\right)} x^{5} + 4301 \, A a^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/21505*(935*B*b^2*x^11 + 1265*(2*B*a*b + A*b^2)*x^8 + 1955*(B*a^2 + 2*A*a*b)*x^5 + 4301*A*a^2*x^2)*sqrt(x)","A",0
142,1,54,0,0.625113," ","integrate((b*x^3+a)^2*(B*x^3+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(15 \, B b^{2} x^{10} + 21 \, {\left(2 \, B a b + A b^{2}\right)} x^{7} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} x^{4} + 105 \, A a^{2} x\right)} \sqrt{x}"," ",0,"2/315*(15*B*b^2*x^10 + 21*(2*B*a*b + A*b^2)*x^7 + 35*(B*a^2 + 2*A*a*b)*x^4 + 105*A*a^2*x)*sqrt(x)","A",0
143,1,53,0,0.823412," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{1729} \, {\left(91 \, B b^{2} x^{9} + 133 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 247 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} + 1729 \, A a^{2}\right)} \sqrt{x}"," ",0,"2/1729*(91*B*b^2*x^9 + 133*(2*B*a*b + A*b^2)*x^6 + 247*(B*a^2 + 2*A*a*b)*x^3 + 1729*A*a^2)*sqrt(x)","A",0
144,1,53,0,0.714076," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(55 \, B b^{2} x^{9} + 85 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 187 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 935 \, A a^{2}\right)}}{935 \, \sqrt{x}}"," ",0,"2/935*(55*B*b^2*x^9 + 85*(2*B*a*b + A*b^2)*x^6 + 187*(B*a^2 + 2*A*a*b)*x^3 - 935*A*a^2)/sqrt(x)","A",0
145,1,53,0,0.768984," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{9} + 5 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 15 \, A a^{2}\right)}}{45 \, x^{\frac{3}{2}}}"," ",0,"2/45*(3*B*b^2*x^9 + 5*(2*B*a*b + A*b^2)*x^6 + 15*(B*a^2 + 2*A*a*b)*x^3 - 15*A*a^2)/x^(3/2)","A",0
146,1,53,0,0.883976," ","integrate((b*x^3+a)^2*(B*x^3+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{2} x^{9} + 65 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 455 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3} - 91 \, A a^{2}\right)}}{455 \, x^{\frac{5}{2}}}"," ",0,"2/455*(35*B*b^2*x^9 + 65*(2*B*a*b + A*b^2)*x^6 + 455*(B*a^2 + 2*A*a*b)*x^3 - 91*A*a^2)/x^(5/2)","A",0
147,1,78,0,0.724533," ","integrate(x^(7/2)*(b*x^3+a)^3*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{10395} \, {\left(315 \, B b^{3} x^{16} + 385 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{13} + 1485 \, {\left(B a^{2} b + A a b^{2}\right)} x^{10} + 1155 \, A a^{3} x^{4} + 693 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{7}\right)} \sqrt{x}"," ",0,"2/10395*(315*B*b^3*x^16 + 385*(3*B*a*b^2 + A*b^3)*x^13 + 1485*(B*a^2*b + A*a*b^2)*x^10 + 1155*A*a^3*x^4 + 693*(B*a^3 + 3*A*a^2*b)*x^7)*sqrt(x)","A",0
148,1,78,0,0.815012," ","integrate(x^(5/2)*(b*x^3+a)^3*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{1339975} \, {\left(43225 \, B b^{3} x^{15} + 53599 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{12} + 211575 \, {\left(B a^{2} b + A a b^{2}\right)} x^{9} + 191425 \, A a^{3} x^{3} + 103075 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{6}\right)} \sqrt{x}"," ",0,"2/1339975*(43225*B*b^3*x^15 + 53599*(3*B*a*b^2 + A*b^3)*x^12 + 211575*(B*a^2*b + A*a*b^2)*x^9 + 191425*A*a^3*x^3 + 103075*(B*a^3 + 3*A*a^2*b)*x^6)*sqrt(x)","A",0
149,1,78,0,0.828847," ","integrate(x^(3/2)*(b*x^3+a)^3*(B*x^3+A),x, algorithm=""fricas"")","\frac{2}{623645} \, {\left(21505 \, B b^{3} x^{14} + 27115 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{11} + 110055 \, {\left(B a^{2} b + A a b^{2}\right)} x^{8} + 124729 \, A a^{3} x^{2} + 56695 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/623645*(21505*B*b^3*x^14 + 27115*(3*B*a*b^2 + A*b^3)*x^11 + 110055*(B*a^2*b + A*a*b^2)*x^8 + 124729*A*a^3*x^2 + 56695*(B*a^3 + 3*A*a^2*b)*x^5)*sqrt(x)","A",0
150,1,76,0,0.797624," ","integrate((b*x^3+a)^3*(B*x^3+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{945} \, {\left(35 \, B b^{3} x^{13} + 45 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{10} + 189 \, {\left(B a^{2} b + A a b^{2}\right)} x^{7} + 315 \, A a^{3} x + 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/945*(35*B*b^3*x^13 + 45*(3*B*a*b^2 + A*b^3)*x^10 + 189*(B*a^2*b + A*a*b^2)*x^7 + 315*A*a^3*x + 105*(B*a^3 + 3*A*a^2*b)*x^4)*sqrt(x)","A",0
151,1,75,0,0.800889," ","integrate((b*x^3+a)^3*(B*x^3+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{43225} \, {\left(1729 \, B b^{3} x^{12} + 2275 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + 9975 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} + 43225 \, A a^{3} + 6175 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/43225*(1729*B*b^3*x^12 + 2275*(3*B*a*b^2 + A*b^3)*x^9 + 9975*(B*a^2*b + A*a*b^2)*x^6 + 43225*A*a^3 + 6175*(B*a^3 + 3*A*a^2*b)*x^3)*sqrt(x)","A",0
152,1,75,0,1.000162," ","integrate((b*x^3+a)^3*(B*x^3+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(935 \, B b^{3} x^{12} + 1265 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + 5865 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} - 21505 \, A a^{3} + 4301 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)}}{21505 \, \sqrt{x}}"," ",0,"2/21505*(935*B*b^3*x^12 + 1265*(3*B*a*b^2 + A*b^3)*x^9 + 5865*(B*a^2*b + A*a*b^2)*x^6 - 21505*A*a^3 + 4301*(B*a^3 + 3*A*a^2*b)*x^3)/sqrt(x)","A",0
153,1,75,0,0.794188," ","integrate((b*x^3+a)^3*(B*x^3+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{12} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + 35 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} - 35 \, A a^{3} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)}}{105 \, x^{\frac{3}{2}}}"," ",0,"2/105*(5*B*b^3*x^12 + 7*(3*B*a*b^2 + A*b^3)*x^9 + 35*(B*a^2*b + A*a*b^2)*x^6 - 35*A*a^3 + 35*(B*a^3 + 3*A*a^2*b)*x^3)/x^(3/2)","A",0
154,1,75,0,0.675528," ","integrate((b*x^3+a)^3*(B*x^3+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(455 \, B b^{3} x^{12} + 665 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{9} + 3705 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} - 1729 \, A a^{3} + 8645 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)}}{8645 \, x^{\frac{5}{2}}}"," ",0,"2/8645*(455*B*b^3*x^12 + 665*(3*B*a*b^2 + A*b^3)*x^9 + 3705*(B*a^2*b + A*a*b^2)*x^6 - 1729*A*a^3 + 8645*(B*a^3 + 3*A*a^2*b)*x^3)/x^(5/2)","A",0
155,1,143,0,0.682106," ","integrate(x^(7/2)*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{3} - 2 \, b x^{\frac{3}{2}} \sqrt{-\frac{a}{b}} - a}{b x^{3} + a}\right) - 2 \, {\left(B b x^{4} - 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}}{9 \, b^{2}}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{\frac{3}{2}} \sqrt{\frac{a}{b}}}{a}\right) + {\left(B b x^{4} - 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}\right)}}{9 \, b^{2}}\right]"," ",0,"[-1/9*(3*(B*a - A*b)*sqrt(-a/b)*log((b*x^3 - 2*b*x^(3/2)*sqrt(-a/b) - a)/(b*x^3 + a)) - 2*(B*b*x^4 - 3*(B*a - A*b)*x)*sqrt(x))/b^2, 2/9*(3*(B*a - A*b)*sqrt(a/b)*arctan(b*x^(3/2)*sqrt(a/b)/a) + (B*b*x^4 - 3*(B*a - A*b)*x)*sqrt(x))/b^2]","A",0
156,1,2433,0,1.074888," ","integrate(x^(5/2)*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{3} b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{b^{4} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + {\left(B a b^{2} - A b^{3}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}}} b^{11} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a b^{11} - A b^{12}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}\right)}}{3 \, {\left(B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}\right)}}\right) + 28 \, \sqrt{3} b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{b^{4} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - {\left(B a b^{2} - A b^{3}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}}} b^{11} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a b^{11} - A b^{12}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}\right)}}{3 \, {\left(B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}\right)}}\right) - 7 \, b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \log\left(4 \, b^{4} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + 4 \, {\left(B a b^{2} - A b^{3}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}}\right) + 7 \, b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \log\left(4 \, b^{4} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - 4 \, {\left(B a b^{2} - A b^{3}\right)} \sqrt{x} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}}\right) + 14 \, b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \log\left(b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) - 14 \, b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} \log\left(-b^{2} \left(-\frac{B^{6} a^{7} - 6 \, A B^{5} a^{6} b + 15 \, A^{2} B^{4} a^{5} b^{2} - 20 \, A^{3} B^{3} a^{4} b^{3} + 15 \, A^{4} B^{2} a^{3} b^{4} - 6 \, A^{5} B a^{2} b^{5} + A^{6} a b^{6}}{b^{13}}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) - 12 \, {\left(B b x^{3} - 7 \, B a + 7 \, A b\right)} \sqrt{x}}{42 \, b^{2}}"," ",0,"-1/42*(28*sqrt(3)*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(b^4*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + (B*a*b^2 - A*b^3)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6))*b^11*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(5/6) + 2*sqrt(3)*(B*a*b^11 - A*b^12)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(5/6) - sqrt(3)*(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6))/(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)) + 28*sqrt(3)*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(b^4*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - (B*a*b^2 - A*b^3)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6))*b^11*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(5/6) + 2*sqrt(3)*(B*a*b^11 - A*b^12)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(5/6) + sqrt(3)*(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6))/(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)) - 7*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*log(4*b^4*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + 4*(B*a*b^2 - A*b^3)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)) + 7*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*log(4*b^4*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - 4*(B*a*b^2 - A*b^3)*sqrt(x)*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)) + 14*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*log(b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6) - (B*a - A*b)*sqrt(x)) - 14*b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6)*log(-b^2*(-(B^6*a^7 - 6*A*B^5*a^6*b + 15*A^2*B^4*a^5*b^2 - 20*A^3*B^3*a^4*b^3 + 15*A^4*B^2*a^3*b^4 - 6*A^5*B*a^2*b^5 + A^6*a*b^6)/b^13)^(1/6) - (B*a - A*b)*sqrt(x)) - 12*(B*b*x^3 - 7*B*a + 7*A*b)*sqrt(x))/b^2","B",0
157,1,3635,0,1.080661," ","integrate(x^(3/2)*(B*x^3+A)/(b*x^3+a),x, algorithm=""fricas"")","\frac{12 \, B x^{\frac{5}{2}} - 20 \, \sqrt{3} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(B^{5} a^{6} b^{9} - 5 \, A B^{4} a^{5} b^{10} + 10 \, A^{2} B^{3} a^{4} b^{11} - 10 \, A^{3} B^{2} a^{3} b^{12} + 5 \, A^{4} B a^{2} b^{13} - A^{5} a b^{14}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(B^{6} a^{7} b^{7} - 6 \, A B^{5} a^{6} b^{8} + 15 \, A^{2} B^{4} a^{5} b^{9} - 20 \, A^{3} B^{3} a^{4} b^{10} + 15 \, A^{4} B^{2} a^{3} b^{11} - 6 \, A^{5} B a^{2} b^{12} + A^{6} a b^{13}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{2}{3}}} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{5} b^{2} - 5 \, A B^{4} a^{4} b^{3} + 10 \, A^{2} B^{3} a^{3} b^{4} - 10 \, A^{3} B^{2} a^{2} b^{5} + 5 \, A^{4} B a b^{6} - A^{5} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - 20 \, \sqrt{3} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} \sqrt{-4 \, {\left(B^{5} a^{6} b^{9} - 5 \, A B^{4} a^{5} b^{10} + 10 \, A^{2} B^{3} a^{4} b^{11} - 10 \, A^{3} B^{2} a^{3} b^{12} + 5 \, A^{4} B a^{2} b^{13} - A^{5} a b^{14}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{7} b^{7} - 6 \, A B^{5} a^{6} b^{8} + 15 \, A^{2} B^{4} a^{5} b^{9} - 20 \, A^{3} B^{3} a^{4} b^{10} + 15 \, A^{4} B^{2} a^{3} b^{11} - 6 \, A^{5} B a^{2} b^{12} + A^{6} a b^{13}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{2}{3}}} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{5} b^{2} - 5 \, A B^{4} a^{4} b^{3} + 10 \, A^{2} B^{3} a^{3} b^{4} - 10 \, A^{3} B^{2} a^{2} b^{5} + 5 \, A^{4} B a b^{6} - A^{5} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} + \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 10 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \log\left(a b^{9} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 5 \, A B^{4} a^{4} b + 10 \, A^{2} B^{3} a^{3} b^{2} - 10 \, A^{3} B^{2} a^{2} b^{3} + 5 \, A^{4} B a b^{4} - A^{5} b^{5}\right)} \sqrt{x}\right) - 10 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \log\left(-a b^{9} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 5 \, A B^{4} a^{4} b + 10 \, A^{2} B^{3} a^{3} b^{2} - 10 \, A^{3} B^{2} a^{2} b^{3} + 5 \, A^{4} B a b^{4} - A^{5} b^{5}\right)} \sqrt{x}\right) - 5 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \log\left(4 \, {\left(B^{5} a^{6} b^{9} - 5 \, A B^{4} a^{5} b^{10} + 10 \, A^{2} B^{3} a^{4} b^{11} - 10 \, A^{3} B^{2} a^{3} b^{12} + 5 \, A^{4} B a^{2} b^{13} - A^{5} a b^{14}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{7} b^{7} - 6 \, A B^{5} a^{6} b^{8} + 15 \, A^{2} B^{4} a^{5} b^{9} - 20 \, A^{3} B^{3} a^{4} b^{10} + 15 \, A^{4} B^{2} a^{3} b^{11} - 6 \, A^{5} B a^{2} b^{12} + A^{6} a b^{13}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{2}{3}}\right) + 5 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{1}{6}} \log\left(-4 \, {\left(B^{5} a^{6} b^{9} - 5 \, A B^{4} a^{5} b^{10} + 10 \, A^{2} B^{3} a^{4} b^{11} - 10 \, A^{3} B^{2} a^{3} b^{12} + 5 \, A^{4} B a^{2} b^{13} - A^{5} a b^{14}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{7} b^{7} - 6 \, A B^{5} a^{6} b^{8} + 15 \, A^{2} B^{4} a^{5} b^{9} - 20 \, A^{3} B^{3} a^{4} b^{10} + 15 \, A^{4} B^{2} a^{3} b^{11} - 6 \, A^{5} B a^{2} b^{12} + A^{6} a b^{13}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a b^{11}}\right)^{\frac{2}{3}}\right)}{30 \, b}"," ",0,"1/30*(12*B*x^(5/2) - 20*sqrt(3)*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((B^5*a^6*b^9 - 5*A*B^4*a^5*b^10 + 10*A^2*B^3*a^4*b^11 - 10*A^3*B^2*a^3*b^12 + 5*A^4*B*a^2*b^13 - A^5*a*b^14)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) + (B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - (B^6*a^7*b^7 - 6*A*B^5*a^6*b^8 + 15*A^2*B^4*a^5*b^9 - 20*A^3*B^3*a^4*b^10 + 15*A^4*B^2*a^3*b^11 - 6*A^5*B*a^2*b^12 + A^6*a*b^13)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(2/3))*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6) + 2*sqrt(3)*(B^5*a^5*b^2 - 5*A*B^4*a^4*b^3 + 10*A^2*B^3*a^3*b^4 - 10*A^3*B^2*a^2*b^5 + 5*A^4*B*a*b^6 - A^5*b^7)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6) - sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) - 20*sqrt(3)*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*arctan(1/3*(sqrt(3)*sqrt(-4*(B^5*a^6*b^9 - 5*A*B^4*a^5*b^10 + 10*A^2*B^3*a^4*b^11 - 10*A^3*B^2*a^3*b^12 + 5*A^4*B*a^2*b^13 - A^5*a*b^14)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^7*b^7 - 6*A*B^5*a^6*b^8 + 15*A^2*B^4*a^5*b^9 - 20*A^3*B^3*a^4*b^10 + 15*A^4*B^2*a^3*b^11 - 6*A^5*B*a^2*b^12 + A^6*a*b^13)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(2/3))*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6) + 2*sqrt(3)*(B^5*a^5*b^2 - 5*A*B^4*a^4*b^3 + 10*A^2*B^3*a^3*b^4 - 10*A^3*B^2*a^2*b^5 + 5*A^4*B*a*b^6 - A^5*b^7)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6) + sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) + 10*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*log(a*b^9*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) - (B^5*a^5 - 5*A*B^4*a^4*b + 10*A^2*B^3*a^3*b^2 - 10*A^3*B^2*a^2*b^3 + 5*A^4*B*a*b^4 - A^5*b^5)*sqrt(x)) - 10*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*log(-a*b^9*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) - (B^5*a^5 - 5*A*B^4*a^4*b + 10*A^2*B^3*a^3*b^2 - 10*A^3*B^2*a^2*b^3 + 5*A^4*B*a*b^4 - A^5*b^5)*sqrt(x)) - 5*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*log(4*(B^5*a^6*b^9 - 5*A*B^4*a^5*b^10 + 10*A^2*B^3*a^4*b^11 - 10*A^3*B^2*a^3*b^12 + 5*A^4*B*a^2*b^13 - A^5*a*b^14)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^7*b^7 - 6*A*B^5*a^6*b^8 + 15*A^2*B^4*a^5*b^9 - 20*A^3*B^3*a^4*b^10 + 15*A^4*B^2*a^3*b^11 - 6*A^5*B*a^2*b^12 + A^6*a*b^13)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(2/3)) + 5*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(1/6)*log(-4*(B^5*a^6*b^9 - 5*A*B^4*a^5*b^10 + 10*A^2*B^3*a^4*b^11 - 10*A^3*B^2*a^3*b^12 + 5*A^4*B*a^2*b^13 - A^5*a*b^14)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^7*b^7 - 6*A*B^5*a^6*b^8 + 15*A^2*B^4*a^5*b^9 - 20*A^3*B^3*a^4*b^10 + 15*A^4*B^2*a^3*b^11 - 6*A^5*B*a^2*b^12 + A^6*a*b^13)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a*b^11))^(2/3)))/b","B",0
158,1,108,0,0.807118," ","integrate((B*x^3+A)*x^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{2 \, B a b x^{\frac{3}{2}} + {\left(B a - A b\right)} \sqrt{-a b} \log\left(\frac{b x^{3} - 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right)}{3 \, a b^{2}}, \frac{2 \, {\left(B a b x^{\frac{3}{2}} - {\left(B a - A b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right)\right)}}{3 \, a b^{2}}\right]"," ",0,"[1/3*(2*B*a*b*x^(3/2) + (B*a - A*b)*sqrt(-a*b)*log((b*x^3 - 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)))/(a*b^2), 2/3*(B*a*b*x^(3/2) - (B*a - A*b)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a))/(a*b^2)]","A",0
159,1,2424,0,0.995483," ","integrate((B*x^3+A)/(b*x^3+a)/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{2} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}}} a^{4} b^{6} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a^{5} b^{6} - A a^{4} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{2} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}}} a^{4} b^{6} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a^{5} b^{6} - A a^{4} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(4 \, a^{2} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + 4 \, {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}}\right) + b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(4 \, a^{2} b^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - 4 \, {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}}\right) + 2 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(a b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) - 2 \, b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} \log\left(-a b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{7}}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) + 12 \, B \sqrt{x}}{6 \, b}"," ",0,"1/6*(4*sqrt(3)*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^2*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + (B*a^2*b - A*a*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6))*a^4*b^6*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(5/6) + 2*sqrt(3)*(B*a^5*b^6 - A*a^4*b^7)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(5/6) - sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) + 4*sqrt(3)*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^2*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - (B*a^2*b - A*a*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6))*a^4*b^6*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(5/6) + 2*sqrt(3)*(B*a^5*b^6 - A*a^4*b^7)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(5/6) + sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) - b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*log(4*a^2*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + 4*(B*a^2*b - A*a*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)) + b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*log(4*a^2*b^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - 4*(B*a^2*b - A*a*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)) + 2*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*log(a*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6) - (B*a - A*b)*sqrt(x)) - 2*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6)*log(-a*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^7))^(1/6) - (B*a - A*b)*sqrt(x)) + 12*B*sqrt(x))/b","B",0
160,1,3663,0,1.148996," ","integrate((B*x^3+A)/x^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(B^{5} a^{11} b^{4} - 5 \, A B^{4} a^{10} b^{5} + 10 \, A^{2} B^{3} a^{9} b^{6} - 10 \, A^{3} B^{2} a^{8} b^{7} + 5 \, A^{4} B a^{7} b^{8} - A^{5} a^{6} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(B^{6} a^{11} b^{3} - 6 \, A B^{5} a^{10} b^{4} + 15 \, A^{2} B^{4} a^{9} b^{5} - 20 \, A^{3} B^{3} a^{8} b^{6} + 15 \, A^{4} B^{2} a^{7} b^{7} - 6 \, A^{5} B a^{6} b^{8} + A^{6} a^{5} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{2}{3}}} a b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{6} b - 5 \, A B^{4} a^{5} b^{2} + 10 \, A^{2} B^{3} a^{4} b^{3} - 10 \, A^{3} B^{2} a^{3} b^{4} + 5 \, A^{4} B a^{2} b^{5} - A^{5} a b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{\sqrt{3} \sqrt{-4 \, {\left(B^{5} a^{11} b^{4} - 5 \, A B^{4} a^{10} b^{5} + 10 \, A^{2} B^{3} a^{9} b^{6} - 10 \, A^{3} B^{2} a^{8} b^{7} + 5 \, A^{4} B a^{7} b^{8} - A^{5} a^{6} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{11} b^{3} - 6 \, A B^{5} a^{10} b^{4} + 15 \, A^{2} B^{4} a^{9} b^{5} - 20 \, A^{3} B^{3} a^{8} b^{6} + 15 \, A^{4} B^{2} a^{7} b^{7} - 6 \, A^{5} B a^{6} b^{8} + A^{6} a^{5} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{2}{3}}} a b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{6} b - 5 \, A B^{4} a^{5} b^{2} + 10 \, A^{2} B^{3} a^{4} b^{3} - 10 \, A^{3} B^{2} a^{3} b^{4} + 5 \, A^{4} B a^{2} b^{5} - A^{5} a b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} + \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - 2 \, a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(a^{6} b^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 5 \, A B^{4} a^{4} b + 10 \, A^{2} B^{3} a^{3} b^{2} - 10 \, A^{3} B^{2} a^{2} b^{3} + 5 \, A^{4} B a b^{4} - A^{5} b^{5}\right)} \sqrt{x}\right) + 2 \, a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(-a^{6} b^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 5 \, A B^{4} a^{4} b + 10 \, A^{2} B^{3} a^{3} b^{2} - 10 \, A^{3} B^{2} a^{2} b^{3} + 5 \, A^{4} B a b^{4} - A^{5} b^{5}\right)} \sqrt{x}\right) + a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(4 \, {\left(B^{5} a^{11} b^{4} - 5 \, A B^{4} a^{10} b^{5} + 10 \, A^{2} B^{3} a^{9} b^{6} - 10 \, A^{3} B^{2} a^{8} b^{7} + 5 \, A^{4} B a^{7} b^{8} - A^{5} a^{6} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{11} b^{3} - 6 \, A B^{5} a^{10} b^{4} + 15 \, A^{2} B^{4} a^{9} b^{5} - 20 \, A^{3} B^{3} a^{8} b^{6} + 15 \, A^{4} B^{2} a^{7} b^{7} - 6 \, A^{5} B a^{6} b^{8} + A^{6} a^{5} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{2}{3}}\right) - a x \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{1}{6}} \log\left(-4 \, {\left(B^{5} a^{11} b^{4} - 5 \, A B^{4} a^{10} b^{5} + 10 \, A^{2} B^{3} a^{9} b^{6} - 10 \, A^{3} B^{2} a^{8} b^{7} + 5 \, A^{4} B a^{7} b^{8} - A^{5} a^{6} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{5}{6}} + 4 \, {\left(B^{10} a^{10} - 10 \, A B^{9} a^{9} b + 45 \, A^{2} B^{8} a^{8} b^{2} - 120 \, A^{3} B^{7} a^{7} b^{3} + 210 \, A^{4} B^{6} a^{6} b^{4} - 252 \, A^{5} B^{5} a^{5} b^{5} + 210 \, A^{6} B^{4} a^{4} b^{6} - 120 \, A^{7} B^{3} a^{3} b^{7} + 45 \, A^{8} B^{2} a^{2} b^{8} - 10 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - 4 \, {\left(B^{6} a^{11} b^{3} - 6 \, A B^{5} a^{10} b^{4} + 15 \, A^{2} B^{4} a^{9} b^{5} - 20 \, A^{3} B^{3} a^{8} b^{6} + 15 \, A^{4} B^{2} a^{7} b^{7} - 6 \, A^{5} B a^{6} b^{8} + A^{6} a^{5} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{5}}\right)^{\frac{2}{3}}\right) - 12 \, A \sqrt{x}}{6 \, a x}"," ",0,"1/6*(4*sqrt(3)*a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((B^5*a^11*b^4 - 5*A*B^4*a^10*b^5 + 10*A^2*B^3*a^9*b^6 - 10*A^3*B^2*a^8*b^7 + 5*A^4*B*a^7*b^8 - A^5*a^6*b^9)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) + (B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - (B^6*a^11*b^3 - 6*A*B^5*a^10*b^4 + 15*A^2*B^4*a^9*b^5 - 20*A^3*B^3*a^8*b^6 + 15*A^4*B^2*a^7*b^7 - 6*A^5*B*a^6*b^8 + A^6*a^5*b^9)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(2/3))*a*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6) + 2*sqrt(3)*(B^5*a^6*b - 5*A*B^4*a^5*b^2 + 10*A^2*B^3*a^4*b^3 - 10*A^3*B^2*a^3*b^4 + 5*A^4*B*a^2*b^5 - A^5*a*b^6)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6) - sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) + 4*sqrt(3)*a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*arctan(1/3*(sqrt(3)*sqrt(-4*(B^5*a^11*b^4 - 5*A*B^4*a^10*b^5 + 10*A^2*B^3*a^9*b^6 - 10*A^3*B^2*a^8*b^7 + 5*A^4*B*a^7*b^8 - A^5*a^6*b^9)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^11*b^3 - 6*A*B^5*a^10*b^4 + 15*A^2*B^4*a^9*b^5 - 20*A^3*B^3*a^8*b^6 + 15*A^4*B^2*a^7*b^7 - 6*A^5*B*a^6*b^8 + A^6*a^5*b^9)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(2/3))*a*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6) + 2*sqrt(3)*(B^5*a^6*b - 5*A*B^4*a^5*b^2 + 10*A^2*B^3*a^4*b^3 - 10*A^3*B^2*a^3*b^4 + 5*A^4*B*a^2*b^5 - A^5*a*b^6)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6) + sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) - 2*a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*log(a^6*b^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) - (B^5*a^5 - 5*A*B^4*a^4*b + 10*A^2*B^3*a^3*b^2 - 10*A^3*B^2*a^2*b^3 + 5*A^4*B*a*b^4 - A^5*b^5)*sqrt(x)) + 2*a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*log(-a^6*b^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) - (B^5*a^5 - 5*A*B^4*a^4*b + 10*A^2*B^3*a^3*b^2 - 10*A^3*B^2*a^2*b^3 + 5*A^4*B*a*b^4 - A^5*b^5)*sqrt(x)) + a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*log(4*(B^5*a^11*b^4 - 5*A*B^4*a^10*b^5 + 10*A^2*B^3*a^9*b^6 - 10*A^3*B^2*a^8*b^7 + 5*A^4*B*a^7*b^8 - A^5*a^6*b^9)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^11*b^3 - 6*A*B^5*a^10*b^4 + 15*A^2*B^4*a^9*b^5 - 20*A^3*B^3*a^8*b^6 + 15*A^4*B^2*a^7*b^7 - 6*A^5*B*a^6*b^8 + A^6*a^5*b^9)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(2/3)) - a*x*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(1/6)*log(-4*(B^5*a^11*b^4 - 5*A*B^4*a^10*b^5 + 10*A^2*B^3*a^9*b^6 - 10*A^3*B^2*a^8*b^7 + 5*A^4*B*a^7*b^8 - A^5*a^6*b^9)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(5/6) + 4*(B^10*a^10 - 10*A*B^9*a^9*b + 45*A^2*B^8*a^8*b^2 - 120*A^3*B^7*a^7*b^3 + 210*A^4*B^6*a^6*b^4 - 252*A^5*B^5*a^5*b^5 + 210*A^6*B^4*a^4*b^6 - 120*A^7*B^3*a^3*b^7 + 45*A^8*B^2*a^2*b^8 - 10*A^9*B*a*b^9 + A^10*b^10)*x - 4*(B^6*a^11*b^3 - 6*A*B^5*a^10*b^4 + 15*A^2*B^4*a^9*b^5 - 20*A^3*B^3*a^8*b^6 + 15*A^4*B^2*a^7*b^7 - 6*A^5*B*a^6*b^8 + A^6*a^5*b^9)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^5))^(2/3)) - 12*A*sqrt(x))/(a*x)","B",0
161,1,120,0,0.776449," ","integrate((B*x^3+A)/x^(5/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{{\left(B a - A b\right)} \sqrt{-a b} x^{2} \log\left(\frac{b x^{3} + 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) - 2 \, A a b \sqrt{x}}{3 \, a^{2} b x^{2}}, \frac{2 \, {\left({\left(B a - A b\right)} \sqrt{a b} x^{2} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) - A a b \sqrt{x}\right)}}{3 \, a^{2} b x^{2}}\right]"," ",0,"[1/3*((B*a - A*b)*sqrt(-a*b)*x^2*log((b*x^3 + 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) - 2*A*a*b*sqrt(x))/(a^2*b*x^2), 2/3*((B*a - A*b)*sqrt(a*b)*x^2*arctan(sqrt(a*b)*x^(3/2)/a) - A*a*b*sqrt(x))/(a^2*b*x^2)]","A",0
162,1,2424,0,0.952893," ","integrate((B*x^3+A)/x^(7/2)/(b*x^3+a),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{3} a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + {\left(B a^{3} - A a^{2} b\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}}} a^{9} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a^{10} b - A a^{9} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{5}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 20 \, \sqrt{3} a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - {\left(B a^{3} - A a^{2} b\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}}} a^{9} b \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(B a^{10} b - A a^{9} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{5}{6}} + \sqrt{3} {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - 5 \, a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \log\left(4 \, a^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x + 4 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}}\right) + 5 \, a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \log\left(4 \, a^{4} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{3}} + 4 \, {\left(B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2}\right)} x - 4 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}}\right) + 10 \, a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \log\left(a^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) - 10 \, a x^{3} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} \log\left(-a^{2} \left(-\frac{B^{6} a^{6} - 6 \, A B^{5} a^{5} b + 15 \, A^{2} B^{4} a^{4} b^{2} - 20 \, A^{3} B^{3} a^{3} b^{3} + 15 \, A^{4} B^{2} a^{2} b^{4} - 6 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{11} b}\right)^{\frac{1}{6}} - {\left(B a - A b\right)} \sqrt{x}\right) + 12 \, A \sqrt{x}}{30 \, a x^{3}}"," ",0,"-1/30*(20*sqrt(3)*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + (B*a^3 - A*a^2*b)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6))*a^9*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(5/6) + 2*sqrt(3)*(B*a^10*b - A*a^9*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(5/6) - sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) + 20*sqrt(3)*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/3) + (B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - (B*a^3 - A*a^2*b)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6))*a^9*b*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(5/6) + 2*sqrt(3)*(B*a^10*b - A*a^9*b^2)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(5/6) + sqrt(3)*(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6))/(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)) - 5*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*log(4*a^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x + 4*(B*a^3 - A*a^2*b)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)) + 5*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*log(4*a^4*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/3) + 4*(B^2*a^2 - 2*A*B*a*b + A^2*b^2)*x - 4*(B*a^3 - A*a^2*b)*sqrt(x)*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)) + 10*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*log(a^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6) - (B*a - A*b)*sqrt(x)) - 10*a*x^3*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6)*log(-a^2*(-(B^6*a^6 - 6*A*B^5*a^5*b + 15*A^2*B^4*a^4*b^2 - 20*A^3*B^3*a^3*b^3 + 15*A^4*B^2*a^2*b^4 - 6*A^5*B*a*b^5 + A^6*b^6)/(a^11*b))^(1/6) - (B*a - A*b)*sqrt(x)) + 12*A*sqrt(x))/(a*x^3)","B",0
163,1,222,0,0.720762," ","integrate(x^(7/2)*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, B a b - A b^{2}\right)} x^{3} + 3 \, B a^{2} - A a b\right)} \sqrt{-a b} \log\left(\frac{b x^{3} - 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) + 2 \, {\left(2 \, B a b^{2} x^{4} + {\left(3 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}}{6 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}, -\frac{{\left({\left(3 \, B a b - A b^{2}\right)} x^{3} + 3 \, B a^{2} - A a b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) - {\left(2 \, B a b^{2} x^{4} + {\left(3 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}}{3 \, {\left(a b^{4} x^{3} + a^{2} b^{3}\right)}}\right]"," ",0,"[1/6*(((3*B*a*b - A*b^2)*x^3 + 3*B*a^2 - A*a*b)*sqrt(-a*b)*log((b*x^3 - 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) + 2*(2*B*a*b^2*x^4 + (3*B*a^2*b - A*a*b^2)*x)*sqrt(x))/(a*b^4*x^3 + a^2*b^3), -1/3*(((3*B*a*b - A*b^2)*x^3 + 3*B*a^2 - A*a*b)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a) - (2*B*a*b^2*x^4 + (3*B*a^2*b - A*a*b^2)*x)*sqrt(x))/(a*b^4*x^3 + a^2*b^3)]","A",0
164,1,2566,0,0.839742," ","integrate(x^(5/2)*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{2} b^{4} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} - 14 \, A B a b + A^{2} b^{2}\right)} x + {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}}} a^{4} b^{11} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(7 \, B a^{5} b^{11} - A a^{4} b^{12}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{2} b^{4} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} - 14 \, A B a b + A^{2} b^{2}\right)} x - {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}}} a^{4} b^{11} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(7 \, B a^{5} b^{11} - A a^{4} b^{12}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \log\left(a^{2} b^{4} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} - 14 \, A B a b + A^{2} b^{2}\right)} x + {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}}\right) + {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \log\left(a^{2} b^{4} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} - 14 \, A B a b + A^{2} b^{2}\right)} x - {\left(7 \, B a^{2} b^{2} - A a b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}}\right) + 2 \, {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \log\left(a b^{2} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} - {\left(7 \, B a - A b\right)} \sqrt{x}\right) - 2 \, {\left(b^{3} x^{3} + a b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} \log\left(-a b^{2} \left(-\frac{117649 \, B^{6} a^{6} - 100842 \, A B^{5} a^{5} b + 36015 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 735 \, A^{4} B^{2} a^{2} b^{4} - 42 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{5} b^{13}}\right)^{\frac{1}{6}} - {\left(7 \, B a - A b\right)} \sqrt{x}\right) + 12 \, {\left(6 \, B b x^{3} + 7 \, B a - A b\right)} \sqrt{x}}{36 \, {\left(b^{3} x^{3} + a b^{2}\right)}}"," ",0,"1/36*(4*sqrt(3)*(b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^2*b^4*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/3) + (49*B^2*a^2 - 14*A*B*a*b + A^2*b^2)*x + (7*B*a^2*b^2 - A*a*b^3)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6))*a^4*b^11*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(5/6) + 2*sqrt(3)*(7*B*a^5*b^11 - A*a^4*b^12)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(5/6) - sqrt(3)*(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6))/(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)) + 4*sqrt(3)*(b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^2*b^4*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/3) + (49*B^2*a^2 - 14*A*B*a*b + A^2*b^2)*x - (7*B*a^2*b^2 - A*a*b^3)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6))*a^4*b^11*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(5/6) + 2*sqrt(3)*(7*B*a^5*b^11 - A*a^4*b^12)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(5/6) + sqrt(3)*(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6))/(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)) - (b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*log(a^2*b^4*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/3) + (49*B^2*a^2 - 14*A*B*a*b + A^2*b^2)*x + (7*B*a^2*b^2 - A*a*b^3)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)) + (b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*log(a^2*b^4*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/3) + (49*B^2*a^2 - 14*A*B*a*b + A^2*b^2)*x - (7*B*a^2*b^2 - A*a*b^3)*sqrt(x)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)) + 2*(b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*log(a*b^2*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6) - (7*B*a - A*b)*sqrt(x)) - 2*(b^3*x^3 + a*b^2)*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6)*log(-a*b^2*(-(117649*B^6*a^6 - 100842*A*B^5*a^5*b + 36015*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 735*A^4*B^2*a^2*b^4 - 42*A^5*B*a*b^5 + A^6*b^6)/(a^5*b^13))^(1/6) - (7*B*a - A*b)*sqrt(x)) + 12*(6*B*b*x^3 + 7*B*a - A*b)*sqrt(x))/(b^3*x^3 + a*b^2)","B",0
165,1,3787,0,1.132567," ","integrate(x^(3/2)*(B*x^3+A)/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(B a - A b\right)} x^{\frac{5}{2}} + 4 \, \sqrt{3} {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(3125 \, B^{5} a^{11} b^{9} + 3125 \, A B^{4} a^{10} b^{10} + 1250 \, A^{2} B^{3} a^{9} b^{11} + 250 \, A^{3} B^{2} a^{8} b^{12} + 25 \, A^{4} B a^{7} b^{13} + A^{5} a^{6} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 19531250 \, A B^{9} a^{9} b + 17578125 \, A^{2} B^{8} a^{8} b^{2} + 9375000 \, A^{3} B^{7} a^{7} b^{3} + 3281250 \, A^{4} B^{6} a^{6} b^{4} + 787500 \, A^{5} B^{5} a^{5} b^{5} + 131250 \, A^{6} B^{4} a^{4} b^{6} + 15000 \, A^{7} B^{3} a^{3} b^{7} + 1125 \, A^{8} B^{2} a^{2} b^{8} + 50 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{11} b^{7} + 18750 \, A B^{5} a^{10} b^{8} + 9375 \, A^{2} B^{4} a^{9} b^{9} + 2500 \, A^{3} B^{3} a^{8} b^{10} + 375 \, A^{4} B^{2} a^{7} b^{11} + 30 \, A^{5} B a^{6} b^{12} + A^{6} a^{5} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{2}{3}}} a b^{2} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} - 2 \, \sqrt{3} {\left(3125 \, B^{5} a^{6} b^{2} + 3125 \, A B^{4} a^{5} b^{3} + 1250 \, A^{2} B^{3} a^{4} b^{4} + 250 \, A^{3} B^{2} a^{3} b^{5} + 25 \, A^{4} B a^{2} b^{6} + A^{5} a b^{7}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} + \sqrt{3} {\left(15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{-{\left(3125 \, B^{5} a^{11} b^{9} + 3125 \, A B^{4} a^{10} b^{10} + 1250 \, A^{2} B^{3} a^{9} b^{11} + 250 \, A^{3} B^{2} a^{8} b^{12} + 25 \, A^{4} B a^{7} b^{13} + A^{5} a^{6} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 19531250 \, A B^{9} a^{9} b + 17578125 \, A^{2} B^{8} a^{8} b^{2} + 9375000 \, A^{3} B^{7} a^{7} b^{3} + 3281250 \, A^{4} B^{6} a^{6} b^{4} + 787500 \, A^{5} B^{5} a^{5} b^{5} + 131250 \, A^{6} B^{4} a^{4} b^{6} + 15000 \, A^{7} B^{3} a^{3} b^{7} + 1125 \, A^{8} B^{2} a^{2} b^{8} + 50 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{11} b^{7} + 18750 \, A B^{5} a^{10} b^{8} + 9375 \, A^{2} B^{4} a^{9} b^{9} + 2500 \, A^{3} B^{3} a^{8} b^{10} + 375 \, A^{4} B^{2} a^{7} b^{11} + 30 \, A^{5} B a^{6} b^{12} + A^{6} a^{5} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{2}{3}}} a b^{2} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} - 2 \, \sqrt{3} {\left(3125 \, B^{5} a^{6} b^{2} + 3125 \, A B^{4} a^{5} b^{3} + 1250 \, A^{2} B^{3} a^{4} b^{4} + 250 \, A^{3} B^{2} a^{3} b^{5} + 25 \, A^{4} B a^{2} b^{6} + A^{5} a b^{7}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}\right)}}\right) - 2 \, {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \log\left(a^{6} b^{9} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(3125 \, B^{5} a^{5} + 3125 \, A B^{4} a^{4} b + 1250 \, A^{2} B^{3} a^{3} b^{2} + 250 \, A^{3} B^{2} a^{2} b^{3} + 25 \, A^{4} B a b^{4} + A^{5} b^{5}\right)} \sqrt{x}\right) + 2 \, {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \log\left(-a^{6} b^{9} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(3125 \, B^{5} a^{5} + 3125 \, A B^{4} a^{4} b + 1250 \, A^{2} B^{3} a^{3} b^{2} + 250 \, A^{3} B^{2} a^{2} b^{3} + 25 \, A^{4} B a b^{4} + A^{5} b^{5}\right)} \sqrt{x}\right) - {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \log\left({\left(3125 \, B^{5} a^{11} b^{9} + 3125 \, A B^{4} a^{10} b^{10} + 1250 \, A^{2} B^{3} a^{9} b^{11} + 250 \, A^{3} B^{2} a^{8} b^{12} + 25 \, A^{4} B a^{7} b^{13} + A^{5} a^{6} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 19531250 \, A B^{9} a^{9} b + 17578125 \, A^{2} B^{8} a^{8} b^{2} + 9375000 \, A^{3} B^{7} a^{7} b^{3} + 3281250 \, A^{4} B^{6} a^{6} b^{4} + 787500 \, A^{5} B^{5} a^{5} b^{5} + 131250 \, A^{6} B^{4} a^{4} b^{6} + 15000 \, A^{7} B^{3} a^{3} b^{7} + 1125 \, A^{8} B^{2} a^{2} b^{8} + 50 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{11} b^{7} + 18750 \, A B^{5} a^{10} b^{8} + 9375 \, A^{2} B^{4} a^{9} b^{9} + 2500 \, A^{3} B^{3} a^{8} b^{10} + 375 \, A^{4} B^{2} a^{7} b^{11} + 30 \, A^{5} B a^{6} b^{12} + A^{6} a^{5} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{2}{3}}\right) + {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{1}{6}} \log\left(-{\left(3125 \, B^{5} a^{11} b^{9} + 3125 \, A B^{4} a^{10} b^{10} + 1250 \, A^{2} B^{3} a^{9} b^{11} + 250 \, A^{3} B^{2} a^{8} b^{12} + 25 \, A^{4} B a^{7} b^{13} + A^{5} a^{6} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 19531250 \, A B^{9} a^{9} b + 17578125 \, A^{2} B^{8} a^{8} b^{2} + 9375000 \, A^{3} B^{7} a^{7} b^{3} + 3281250 \, A^{4} B^{6} a^{6} b^{4} + 787500 \, A^{5} B^{5} a^{5} b^{5} + 131250 \, A^{6} B^{4} a^{4} b^{6} + 15000 \, A^{7} B^{3} a^{3} b^{7} + 1125 \, A^{8} B^{2} a^{2} b^{8} + 50 \, A^{9} B a b^{9} + A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{11} b^{7} + 18750 \, A B^{5} a^{10} b^{8} + 9375 \, A^{2} B^{4} a^{9} b^{9} + 2500 \, A^{3} B^{3} a^{8} b^{10} + 375 \, A^{4} B^{2} a^{7} b^{11} + 30 \, A^{5} B a^{6} b^{12} + A^{6} a^{5} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 18750 \, A B^{5} a^{5} b + 9375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 375 \, A^{4} B^{2} a^{2} b^{4} + 30 \, A^{5} B a b^{5} + A^{6} b^{6}}{a^{7} b^{11}}\right)^{\frac{2}{3}}\right)}{36 \, {\left(a b^{2} x^{3} + a^{2} b\right)}}"," ",0,"-1/36*(12*(B*a - A*b)*x^(5/2) + 4*sqrt(3)*(a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((3125*B^5*a^11*b^9 + 3125*A*B^4*a^10*b^10 + 1250*A^2*B^3*a^9*b^11 + 250*A^3*B^2*a^8*b^12 + 25*A^4*B*a^7*b^13 + A^5*a^6*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (9765625*B^10*a^10 + 19531250*A*B^9*a^9*b + 17578125*A^2*B^8*a^8*b^2 + 9375000*A^3*B^7*a^7*b^3 + 3281250*A^4*B^6*a^6*b^4 + 787500*A^5*B^5*a^5*b^5 + 131250*A^6*B^4*a^4*b^6 + 15000*A^7*B^3*a^3*b^7 + 1125*A^8*B^2*a^2*b^8 + 50*A^9*B*a*b^9 + A^10*b^10)*x - (15625*B^6*a^11*b^7 + 18750*A*B^5*a^10*b^8 + 9375*A^2*B^4*a^9*b^9 + 2500*A^3*B^3*a^8*b^10 + 375*A^4*B^2*a^7*b^11 + 30*A^5*B*a^6*b^12 + A^6*a^5*b^13)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(2/3))*a*b^2*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6) - 2*sqrt(3)*(3125*B^5*a^6*b^2 + 3125*A*B^4*a^5*b^3 + 1250*A^2*B^3*a^4*b^4 + 250*A^3*B^2*a^3*b^5 + 25*A^4*B*a^2*b^6 + A^5*a*b^7)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6) + sqrt(3)*(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6))/(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)) + 4*sqrt(3)*(a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(-(3125*B^5*a^11*b^9 + 3125*A*B^4*a^10*b^10 + 1250*A^2*B^3*a^9*b^11 + 250*A^3*B^2*a^8*b^12 + 25*A^4*B*a^7*b^13 + A^5*a^6*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (9765625*B^10*a^10 + 19531250*A*B^9*a^9*b + 17578125*A^2*B^8*a^8*b^2 + 9375000*A^3*B^7*a^7*b^3 + 3281250*A^4*B^6*a^6*b^4 + 787500*A^5*B^5*a^5*b^5 + 131250*A^6*B^4*a^4*b^6 + 15000*A^7*B^3*a^3*b^7 + 1125*A^8*B^2*a^2*b^8 + 50*A^9*B*a*b^9 + A^10*b^10)*x - (15625*B^6*a^11*b^7 + 18750*A*B^5*a^10*b^8 + 9375*A^2*B^4*a^9*b^9 + 2500*A^3*B^3*a^8*b^10 + 375*A^4*B^2*a^7*b^11 + 30*A^5*B*a^6*b^12 + A^6*a^5*b^13)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(2/3))*a*b^2*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6) - 2*sqrt(3)*(3125*B^5*a^6*b^2 + 3125*A*B^4*a^5*b^3 + 1250*A^2*B^3*a^4*b^4 + 250*A^3*B^2*a^3*b^5 + 25*A^4*B*a^2*b^6 + A^5*a*b^7)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6) - sqrt(3)*(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6))/(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)) - 2*(a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*log(a^6*b^9*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (3125*B^5*a^5 + 3125*A*B^4*a^4*b + 1250*A^2*B^3*a^3*b^2 + 250*A^3*B^2*a^2*b^3 + 25*A^4*B*a*b^4 + A^5*b^5)*sqrt(x)) + 2*(a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*log(-a^6*b^9*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (3125*B^5*a^5 + 3125*A*B^4*a^4*b + 1250*A^2*B^3*a^3*b^2 + 250*A^3*B^2*a^2*b^3 + 25*A^4*B*a*b^4 + A^5*b^5)*sqrt(x)) - (a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*log((3125*B^5*a^11*b^9 + 3125*A*B^4*a^10*b^10 + 1250*A^2*B^3*a^9*b^11 + 250*A^3*B^2*a^8*b^12 + 25*A^4*B*a^7*b^13 + A^5*a^6*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (9765625*B^10*a^10 + 19531250*A*B^9*a^9*b + 17578125*A^2*B^8*a^8*b^2 + 9375000*A^3*B^7*a^7*b^3 + 3281250*A^4*B^6*a^6*b^4 + 787500*A^5*B^5*a^5*b^5 + 131250*A^6*B^4*a^4*b^6 + 15000*A^7*B^3*a^3*b^7 + 1125*A^8*B^2*a^2*b^8 + 50*A^9*B*a*b^9 + A^10*b^10)*x - (15625*B^6*a^11*b^7 + 18750*A*B^5*a^10*b^8 + 9375*A^2*B^4*a^9*b^9 + 2500*A^3*B^3*a^8*b^10 + 375*A^4*B^2*a^7*b^11 + 30*A^5*B*a^6*b^12 + A^6*a^5*b^13)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(2/3)) + (a*b^2*x^3 + a^2*b)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(1/6)*log(-(3125*B^5*a^11*b^9 + 3125*A*B^4*a^10*b^10 + 1250*A^2*B^3*a^9*b^11 + 250*A^3*B^2*a^8*b^12 + 25*A^4*B*a^7*b^13 + A^5*a^6*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(5/6) + (9765625*B^10*a^10 + 19531250*A*B^9*a^9*b + 17578125*A^2*B^8*a^8*b^2 + 9375000*A^3*B^7*a^7*b^3 + 3281250*A^4*B^6*a^6*b^4 + 787500*A^5*B^5*a^5*b^5 + 131250*A^6*B^4*a^4*b^6 + 15000*A^7*B^3*a^3*b^7 + 1125*A^8*B^2*a^2*b^8 + 50*A^9*B*a*b^9 + A^10*b^10)*x - (15625*B^6*a^11*b^7 + 18750*A*B^5*a^10*b^8 + 9375*A^2*B^4*a^9*b^9 + 2500*A^3*B^3*a^8*b^10 + 375*A^4*B^2*a^7*b^11 + 30*A^5*B*a^6*b^12 + A^6*a^5*b^13)*(-(15625*B^6*a^6 + 18750*A*B^5*a^5*b + 9375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 375*A^4*B^2*a^2*b^4 + 30*A^5*B*a*b^5 + A^6*b^6)/(a^7*b^11))^(2/3)))/(a*b^2*x^3 + a^2*b)","B",0
166,1,190,0,0.802641," ","integrate((B*x^3+A)*x^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(B a^{2} b - A a b^{2}\right)} x^{\frac{3}{2}} + {\left({\left(B a b + A b^{2}\right)} x^{3} + B a^{2} + A a b\right)} \sqrt{-a b} \log\left(\frac{b x^{3} - 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right)}{6 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}, -\frac{{\left(B a^{2} b - A a b^{2}\right)} x^{\frac{3}{2}} - {\left({\left(B a b + A b^{2}\right)} x^{3} + B a^{2} + A a b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right)}{3 \, {\left(a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}\right]"," ",0,"[-1/6*(2*(B*a^2*b - A*a*b^2)*x^(3/2) + ((B*a*b + A*b^2)*x^3 + B*a^2 + A*a*b)*sqrt(-a*b)*log((b*x^3 - 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)))/(a^2*b^3*x^3 + a^3*b^2), -1/3*((B*a^2*b - A*a*b^2)*x^(3/2) - ((B*a*b + A*b^2)*x^3 + B*a^2 + A*a*b)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a))/(a^2*b^3*x^3 + a^3*b^2)]","A",0
167,1,2555,0,1.065160," ","integrate((B*x^3+A)/(b*x^3+a)^2/x^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} b^{2} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 10 \, A B a b + 25 \, A^{2} b^{2}\right)} x + {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}}} a^{9} b^{6} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(B a^{10} b^{6} + 5 \, A a^{9} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} b^{2} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 10 \, A B a b + 25 \, A^{2} b^{2}\right)} x - {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}}} a^{9} b^{6} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(B a^{10} b^{6} + 5 \, A a^{9} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}\right) + {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \log\left(a^{4} b^{2} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 10 \, A B a b + 25 \, A^{2} b^{2}\right)} x + {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}}\right) - {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \log\left(a^{4} b^{2} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 10 \, A B a b + 25 \, A^{2} b^{2}\right)} x - {\left(B a^{3} b + 5 \, A a^{2} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}}\right) + 2 \, {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \log\left(a^{2} b \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} + {\left(B a + 5 \, A b\right)} \sqrt{x}\right) - 2 \, {\left(a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} \log\left(-a^{2} b \left(-\frac{B^{6} a^{6} + 30 \, A B^{5} a^{5} b + 375 \, A^{2} B^{4} a^{4} b^{2} + 2500 \, A^{3} B^{3} a^{3} b^{3} + 9375 \, A^{4} B^{2} a^{2} b^{4} + 18750 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{7}}\right)^{\frac{1}{6}} + {\left(B a + 5 \, A b\right)} \sqrt{x}\right) - 12 \, {\left(B a - A b\right)} \sqrt{x}}{36 \, {\left(a b^{2} x^{3} + a^{2} b\right)}}"," ",0,"1/36*(4*sqrt(3)*(a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*b^2*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/3) + (B^2*a^2 + 10*A*B*a*b + 25*A^2*b^2)*x + (B*a^3*b + 5*A*a^2*b^2)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6))*a^9*b^6*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(5/6) - 2*sqrt(3)*(B*a^10*b^6 + 5*A*a^9*b^7)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(5/6) + sqrt(3)*(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6))/(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)) + 4*sqrt(3)*(a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*b^2*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/3) + (B^2*a^2 + 10*A*B*a*b + 25*A^2*b^2)*x - (B*a^3*b + 5*A*a^2*b^2)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6))*a^9*b^6*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(5/6) - 2*sqrt(3)*(B*a^10*b^6 + 5*A*a^9*b^7)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(5/6) - sqrt(3)*(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6))/(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)) + (a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*log(a^4*b^2*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/3) + (B^2*a^2 + 10*A*B*a*b + 25*A^2*b^2)*x + (B*a^3*b + 5*A*a^2*b^2)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)) - (a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*log(a^4*b^2*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/3) + (B^2*a^2 + 10*A*B*a*b + 25*A^2*b^2)*x - (B*a^3*b + 5*A*a^2*b^2)*sqrt(x)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)) + 2*(a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*log(a^2*b*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6) + (B*a + 5*A*b)*sqrt(x)) - 2*(a*b^2*x^3 + a^2*b)*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6)*log(-a^2*b*(-(B^6*a^6 + 30*A*B^5*a^5*b + 375*A^2*B^4*a^4*b^2 + 2500*A^3*B^3*a^3*b^3 + 9375*A^4*B^2*a^2*b^4 + 18750*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^7))^(1/6) + (B*a + 5*A*b)*sqrt(x)) - 12*(B*a - A*b)*sqrt(x))/(a*b^2*x^3 + a^2*b)","B",0
168,1,3798,0,0.965985," ","integrate((B*x^3+A)/x^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(B^{5} a^{16} b^{4} - 35 \, A B^{4} a^{15} b^{5} + 490 \, A^{2} B^{3} a^{14} b^{6} - 3430 \, A^{3} B^{2} a^{13} b^{7} + 12005 \, A^{4} B a^{12} b^{8} - 16807 \, A^{5} a^{11} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 70 \, A B^{9} a^{9} b + 2205 \, A^{2} B^{8} a^{8} b^{2} - 41160 \, A^{3} B^{7} a^{7} b^{3} + 504210 \, A^{4} B^{6} a^{6} b^{4} - 4235364 \, A^{5} B^{5} a^{5} b^{5} + 24706290 \, A^{6} B^{4} a^{4} b^{6} - 98825160 \, A^{7} B^{3} a^{3} b^{7} + 259416045 \, A^{8} B^{2} a^{2} b^{8} - 403536070 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(B^{6} a^{15} b^{3} - 42 \, A B^{5} a^{14} b^{4} + 735 \, A^{2} B^{4} a^{13} b^{5} - 6860 \, A^{3} B^{3} a^{12} b^{6} + 36015 \, A^{4} B^{2} a^{11} b^{7} - 100842 \, A^{5} B a^{10} b^{8} + 117649 \, A^{6} a^{9} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{2}{3}}} a^{2} b \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{7} b - 35 \, A B^{4} a^{6} b^{2} + 490 \, A^{2} B^{3} a^{5} b^{3} - 3430 \, A^{3} B^{2} a^{4} b^{4} + 12005 \, A^{4} B a^{3} b^{5} - 16807 \, A^{5} a^{2} b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{-{\left(B^{5} a^{16} b^{4} - 35 \, A B^{4} a^{15} b^{5} + 490 \, A^{2} B^{3} a^{14} b^{6} - 3430 \, A^{3} B^{2} a^{13} b^{7} + 12005 \, A^{4} B a^{12} b^{8} - 16807 \, A^{5} a^{11} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 70 \, A B^{9} a^{9} b + 2205 \, A^{2} B^{8} a^{8} b^{2} - 41160 \, A^{3} B^{7} a^{7} b^{3} + 504210 \, A^{4} B^{6} a^{6} b^{4} - 4235364 \, A^{5} B^{5} a^{5} b^{5} + 24706290 \, A^{6} B^{4} a^{4} b^{6} - 98825160 \, A^{7} B^{3} a^{3} b^{7} + 259416045 \, A^{8} B^{2} a^{2} b^{8} - 403536070 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(B^{6} a^{15} b^{3} - 42 \, A B^{5} a^{14} b^{4} + 735 \, A^{2} B^{4} a^{13} b^{5} - 6860 \, A^{3} B^{3} a^{12} b^{6} + 36015 \, A^{4} B^{2} a^{11} b^{7} - 100842 \, A^{5} B a^{10} b^{8} + 117649 \, A^{6} a^{9} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{2}{3}}} a^{2} b \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{7} b - 35 \, A B^{4} a^{6} b^{2} + 490 \, A^{2} B^{3} a^{5} b^{3} - 3430 \, A^{3} B^{2} a^{4} b^{4} + 12005 \, A^{4} B a^{3} b^{5} - 16807 \, A^{5} a^{2} b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} + \sqrt{3} {\left(B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}\right) - 2 \, {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \log\left(a^{11} b^{4} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 35 \, A B^{4} a^{4} b + 490 \, A^{2} B^{3} a^{3} b^{2} - 3430 \, A^{3} B^{2} a^{2} b^{3} + 12005 \, A^{4} B a b^{4} - 16807 \, A^{5} b^{5}\right)} \sqrt{x}\right) + 2 \, {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \log\left(-a^{11} b^{4} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} - {\left(B^{5} a^{5} - 35 \, A B^{4} a^{4} b + 490 \, A^{2} B^{3} a^{3} b^{2} - 3430 \, A^{3} B^{2} a^{2} b^{3} + 12005 \, A^{4} B a b^{4} - 16807 \, A^{5} b^{5}\right)} \sqrt{x}\right) + {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \log\left({\left(B^{5} a^{16} b^{4} - 35 \, A B^{4} a^{15} b^{5} + 490 \, A^{2} B^{3} a^{14} b^{6} - 3430 \, A^{3} B^{2} a^{13} b^{7} + 12005 \, A^{4} B a^{12} b^{8} - 16807 \, A^{5} a^{11} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 70 \, A B^{9} a^{9} b + 2205 \, A^{2} B^{8} a^{8} b^{2} - 41160 \, A^{3} B^{7} a^{7} b^{3} + 504210 \, A^{4} B^{6} a^{6} b^{4} - 4235364 \, A^{5} B^{5} a^{5} b^{5} + 24706290 \, A^{6} B^{4} a^{4} b^{6} - 98825160 \, A^{7} B^{3} a^{3} b^{7} + 259416045 \, A^{8} B^{2} a^{2} b^{8} - 403536070 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(B^{6} a^{15} b^{3} - 42 \, A B^{5} a^{14} b^{4} + 735 \, A^{2} B^{4} a^{13} b^{5} - 6860 \, A^{3} B^{3} a^{12} b^{6} + 36015 \, A^{4} B^{2} a^{11} b^{7} - 100842 \, A^{5} B a^{10} b^{8} + 117649 \, A^{6} a^{9} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{2}{3}}\right) - {\left(a^{2} b x^{4} + a^{3} x\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{1}{6}} \log\left(-{\left(B^{5} a^{16} b^{4} - 35 \, A B^{4} a^{15} b^{5} + 490 \, A^{2} B^{3} a^{14} b^{6} - 3430 \, A^{3} B^{2} a^{13} b^{7} + 12005 \, A^{4} B a^{12} b^{8} - 16807 \, A^{5} a^{11} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 70 \, A B^{9} a^{9} b + 2205 \, A^{2} B^{8} a^{8} b^{2} - 41160 \, A^{3} B^{7} a^{7} b^{3} + 504210 \, A^{4} B^{6} a^{6} b^{4} - 4235364 \, A^{5} B^{5} a^{5} b^{5} + 24706290 \, A^{6} B^{4} a^{4} b^{6} - 98825160 \, A^{7} B^{3} a^{3} b^{7} + 259416045 \, A^{8} B^{2} a^{2} b^{8} - 403536070 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(B^{6} a^{15} b^{3} - 42 \, A B^{5} a^{14} b^{4} + 735 \, A^{2} B^{4} a^{13} b^{5} - 6860 \, A^{3} B^{3} a^{12} b^{6} + 36015 \, A^{4} B^{2} a^{11} b^{7} - 100842 \, A^{5} B a^{10} b^{8} + 117649 \, A^{6} a^{9} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 42 \, A B^{5} a^{5} b + 735 \, A^{2} B^{4} a^{4} b^{2} - 6860 \, A^{3} B^{3} a^{3} b^{3} + 36015 \, A^{4} B^{2} a^{2} b^{4} - 100842 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{5}}\right)^{\frac{2}{3}}\right) + 12 \, {\left({\left(B a - 7 \, A b\right)} x^{3} - 6 \, A a\right)} \sqrt{x}}{36 \, {\left(a^{2} b x^{4} + a^{3} x\right)}}"," ",0,"1/36*(4*sqrt(3)*(a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((B^5*a^16*b^4 - 35*A*B^4*a^15*b^5 + 490*A^2*B^3*a^14*b^6 - 3430*A^3*B^2*a^13*b^7 + 12005*A^4*B*a^12*b^8 - 16807*A^5*a^11*b^9)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) + (B^10*a^10 - 70*A*B^9*a^9*b + 2205*A^2*B^8*a^8*b^2 - 41160*A^3*B^7*a^7*b^3 + 504210*A^4*B^6*a^6*b^4 - 4235364*A^5*B^5*a^5*b^5 + 24706290*A^6*B^4*a^4*b^6 - 98825160*A^7*B^3*a^3*b^7 + 259416045*A^8*B^2*a^2*b^8 - 403536070*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (B^6*a^15*b^3 - 42*A*B^5*a^14*b^4 + 735*A^2*B^4*a^13*b^5 - 6860*A^3*B^3*a^12*b^6 + 36015*A^4*B^2*a^11*b^7 - 100842*A^5*B*a^10*b^8 + 117649*A^6*a^9*b^9)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(2/3))*a^2*b*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6) + 2*sqrt(3)*(B^5*a^7*b - 35*A*B^4*a^6*b^2 + 490*A^2*B^3*a^5*b^3 - 3430*A^3*B^2*a^4*b^4 + 12005*A^4*B*a^3*b^5 - 16807*A^5*a^2*b^6)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6) - sqrt(3)*(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6))/(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)) + 4*sqrt(3)*(a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(-(B^5*a^16*b^4 - 35*A*B^4*a^15*b^5 + 490*A^2*B^3*a^14*b^6 - 3430*A^3*B^2*a^13*b^7 + 12005*A^4*B*a^12*b^8 - 16807*A^5*a^11*b^9)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) + (B^10*a^10 - 70*A*B^9*a^9*b + 2205*A^2*B^8*a^8*b^2 - 41160*A^3*B^7*a^7*b^3 + 504210*A^4*B^6*a^6*b^4 - 4235364*A^5*B^5*a^5*b^5 + 24706290*A^6*B^4*a^4*b^6 - 98825160*A^7*B^3*a^3*b^7 + 259416045*A^8*B^2*a^2*b^8 - 403536070*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (B^6*a^15*b^3 - 42*A*B^5*a^14*b^4 + 735*A^2*B^4*a^13*b^5 - 6860*A^3*B^3*a^12*b^6 + 36015*A^4*B^2*a^11*b^7 - 100842*A^5*B*a^10*b^8 + 117649*A^6*a^9*b^9)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(2/3))*a^2*b*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6) + 2*sqrt(3)*(B^5*a^7*b - 35*A*B^4*a^6*b^2 + 490*A^2*B^3*a^5*b^3 - 3430*A^3*B^2*a^4*b^4 + 12005*A^4*B*a^3*b^5 - 16807*A^5*a^2*b^6)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6) + sqrt(3)*(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6))/(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)) - 2*(a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*log(a^11*b^4*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) - (B^5*a^5 - 35*A*B^4*a^4*b + 490*A^2*B^3*a^3*b^2 - 3430*A^3*B^2*a^2*b^3 + 12005*A^4*B*a*b^4 - 16807*A^5*b^5)*sqrt(x)) + 2*(a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*log(-a^11*b^4*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) - (B^5*a^5 - 35*A*B^4*a^4*b + 490*A^2*B^3*a^3*b^2 - 3430*A^3*B^2*a^2*b^3 + 12005*A^4*B*a*b^4 - 16807*A^5*b^5)*sqrt(x)) + (a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*log((B^5*a^16*b^4 - 35*A*B^4*a^15*b^5 + 490*A^2*B^3*a^14*b^6 - 3430*A^3*B^2*a^13*b^7 + 12005*A^4*B*a^12*b^8 - 16807*A^5*a^11*b^9)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) + (B^10*a^10 - 70*A*B^9*a^9*b + 2205*A^2*B^8*a^8*b^2 - 41160*A^3*B^7*a^7*b^3 + 504210*A^4*B^6*a^6*b^4 - 4235364*A^5*B^5*a^5*b^5 + 24706290*A^6*B^4*a^4*b^6 - 98825160*A^7*B^3*a^3*b^7 + 259416045*A^8*B^2*a^2*b^8 - 403536070*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (B^6*a^15*b^3 - 42*A*B^5*a^14*b^4 + 735*A^2*B^4*a^13*b^5 - 6860*A^3*B^3*a^12*b^6 + 36015*A^4*B^2*a^11*b^7 - 100842*A^5*B*a^10*b^8 + 117649*A^6*a^9*b^9)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(2/3)) - (a^2*b*x^4 + a^3*x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(1/6)*log(-(B^5*a^16*b^4 - 35*A*B^4*a^15*b^5 + 490*A^2*B^3*a^14*b^6 - 3430*A^3*B^2*a^13*b^7 + 12005*A^4*B*a^12*b^8 - 16807*A^5*a^11*b^9)*sqrt(x)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(5/6) + (B^10*a^10 - 70*A*B^9*a^9*b + 2205*A^2*B^8*a^8*b^2 - 41160*A^3*B^7*a^7*b^3 + 504210*A^4*B^6*a^6*b^4 - 4235364*A^5*B^5*a^5*b^5 + 24706290*A^6*B^4*a^4*b^6 - 98825160*A^7*B^3*a^3*b^7 + 259416045*A^8*B^2*a^2*b^8 - 403536070*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (B^6*a^15*b^3 - 42*A*B^5*a^14*b^4 + 735*A^2*B^4*a^13*b^5 - 6860*A^3*B^3*a^12*b^6 + 36015*A^4*B^2*a^11*b^7 - 100842*A^5*B*a^10*b^8 + 117649*A^6*a^9*b^9)*(-(B^6*a^6 - 42*A*B^5*a^5*b + 735*A^2*B^4*a^4*b^2 - 6860*A^3*B^3*a^3*b^3 + 36015*A^4*B^2*a^2*b^4 - 100842*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^5))^(2/3)) + 12*((B*a - 7*A*b)*x^3 - 6*A*a)*sqrt(x))/(a^2*b*x^4 + a^3*x)","B",0
169,1,232,0,0.815448," ","integrate((B*x^3+A)/x^(5/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{5} + {\left(B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{3} + 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) - 2 \, {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{3}\right)} \sqrt{x}}{6 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{2}\right)}}, \frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{5} + {\left(B a^{2} - 3 \, A a b\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) - {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{3}\right)} \sqrt{x}}{3 \, {\left(a^{3} b^{2} x^{5} + a^{4} b x^{2}\right)}}\right]"," ",0,"[1/6*(((B*a*b - 3*A*b^2)*x^5 + (B*a^2 - 3*A*a*b)*x^2)*sqrt(-a*b)*log((b*x^3 + 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) - 2*(2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x^3)*sqrt(x))/(a^3*b^2*x^5 + a^4*b*x^2), 1/3*(((B*a*b - 3*A*b^2)*x^5 + (B*a^2 - 3*A*a*b)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a) - (2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x^3)*sqrt(x))/(a^3*b^2*x^5 + a^4*b*x^2)]","A",0
170,1,2584,0,1.085249," ","integrate((B*x^3+A)/x^(7/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{20 \, \sqrt{3} {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{6} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 110 \, A B a b + 121 \, A^{2} b^{2}\right)} x + {\left(5 \, B a^{4} - 11 \, A a^{3} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}}} a^{14} b \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(5 \, B a^{15} b - 11 \, A a^{14} b^{2}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{5}{6}} - \sqrt{3} {\left(15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}\right) + 20 \, \sqrt{3} {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{6} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 110 \, A B a b + 121 \, A^{2} b^{2}\right)} x - {\left(5 \, B a^{4} - 11 \, A a^{3} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}}} a^{14} b \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(5 \, B a^{15} b - 11 \, A a^{14} b^{2}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{5}{6}} + \sqrt{3} {\left(15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}\right) - 5 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \log\left(a^{6} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 110 \, A B a b + 121 \, A^{2} b^{2}\right)} x + {\left(5 \, B a^{4} - 11 \, A a^{3} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}}\right) + 5 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \log\left(a^{6} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 110 \, A B a b + 121 \, A^{2} b^{2}\right)} x - {\left(5 \, B a^{4} - 11 \, A a^{3} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}}\right) + 10 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \log\left(a^{3} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} - {\left(5 \, B a - 11 \, A b\right)} \sqrt{x}\right) - 10 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} \log\left(-a^{3} \left(-\frac{15625 \, B^{6} a^{6} - 206250 \, A B^{5} a^{5} b + 1134375 \, A^{2} B^{4} a^{4} b^{2} - 3327500 \, A^{3} B^{3} a^{3} b^{3} + 5490375 \, A^{4} B^{2} a^{2} b^{4} - 4831530 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b}\right)^{\frac{1}{6}} - {\left(5 \, B a - 11 \, A b\right)} \sqrt{x}\right) - 12 \, {\left({\left(5 \, B a - 11 \, A b\right)} x^{3} - 6 \, A a\right)} \sqrt{x}}{180 \, {\left(a^{2} b x^{6} + a^{3} x^{3}\right)}}"," ",0,"-1/180*(20*sqrt(3)*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^6*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/3) + (25*B^2*a^2 - 110*A*B*a*b + 121*A^2*b^2)*x + (5*B*a^4 - 11*A*a^3*b)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6))*a^14*b*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(5/6) + 2*sqrt(3)*(5*B*a^15*b - 11*A*a^14*b^2)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(5/6) - sqrt(3)*(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6))/(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)) + 20*sqrt(3)*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^6*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/3) + (25*B^2*a^2 - 110*A*B*a*b + 121*A^2*b^2)*x - (5*B*a^4 - 11*A*a^3*b)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6))*a^14*b*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(5/6) + 2*sqrt(3)*(5*B*a^15*b - 11*A*a^14*b^2)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(5/6) + sqrt(3)*(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6))/(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)) - 5*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*log(a^6*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/3) + (25*B^2*a^2 - 110*A*B*a*b + 121*A^2*b^2)*x + (5*B*a^4 - 11*A*a^3*b)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)) + 5*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*log(a^6*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/3) + (25*B^2*a^2 - 110*A*B*a*b + 121*A^2*b^2)*x - (5*B*a^4 - 11*A*a^3*b)*sqrt(x)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)) + 10*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*log(a^3*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6) - (5*B*a - 11*A*b)*sqrt(x)) - 10*(a^2*b*x^6 + a^3*x^3)*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6)*log(-a^3*(-(15625*B^6*a^6 - 206250*A*B^5*a^5*b + 1134375*A^2*B^4*a^4*b^2 - 3327500*A^3*B^3*a^3*b^3 + 5490375*A^4*B^2*a^2*b^4 - 4831530*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b))^(1/6) - (5*B*a - 11*A*b)*sqrt(x)) - 12*((5*B*a - 11*A*b)*x^3 - 6*A*a)*sqrt(x))/(a^2*b*x^6 + a^3*x^3)","B",0
171,1,314,0,0.770028," ","integrate(x^(7/2)*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 3 \, B a^{3} + A a^{2} b + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{3} - 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) + 2 \, {\left({\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{4} + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}, \frac{{\left({\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 3 \, B a^{3} + A a^{2} b + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) - {\left({\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x^{4} + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{12 \, {\left(a^{2} b^{5} x^{6} + 2 \, a^{3} b^{4} x^{3} + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/24*(((3*B*a*b^2 + A*b^3)*x^6 + 3*B*a^3 + A*a^2*b + 2*(3*B*a^2*b + A*a*b^2)*x^3)*sqrt(-a*b)*log((b*x^3 - 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) + 2*((5*B*a^2*b^2 - A*a*b^3)*x^4 + (3*B*a^3*b + A*a^2*b^2)*x)*sqrt(x))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3), 1/12*(((3*B*a*b^2 + A*b^3)*x^6 + 3*B*a^3 + A*a^2*b + 2*(3*B*a^2*b + A*a*b^2)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a) - ((5*B*a^2*b^2 - A*a*b^3)*x^4 + (3*B*a^3*b + A*a^2*b^2)*x)*sqrt(x))/(a^2*b^5*x^6 + 2*a^3*b^4*x^3 + a^4*b^3)]","A",0
172,1,2714,0,0.786031," ","integrate(x^(5/2)*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} b^{4} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} + 70 \, A B a b + 25 \, A^{2} b^{2}\right)} x + {\left(7 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}}} a^{9} b^{11} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(7 \, B a^{10} b^{11} + 5 \, A a^{9} b^{12}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}{3 \, {\left(117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{4} b^{4} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} + 70 \, A B a b + 25 \, A^{2} b^{2}\right)} x - {\left(7 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}}} a^{9} b^{11} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(7 \, B a^{10} b^{11} + 5 \, A a^{9} b^{12}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}{3 \, {\left(117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}\right)}}\right) + {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \log\left(a^{4} b^{4} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} + 70 \, A B a b + 25 \, A^{2} b^{2}\right)} x + {\left(7 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}}\right) - {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \log\left(a^{4} b^{4} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{3}} + {\left(49 \, B^{2} a^{2} + 70 \, A B a b + 25 \, A^{2} b^{2}\right)} x - {\left(7 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} \sqrt{x} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}}\right) + 2 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \log\left(a^{2} b^{2} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} + {\left(7 \, B a + 5 \, A b\right)} \sqrt{x}\right) - 2 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} \log\left(-a^{2} b^{2} \left(-\frac{117649 \, B^{6} a^{6} + 504210 \, A B^{5} a^{5} b + 900375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 459375 \, A^{4} B^{2} a^{2} b^{4} + 131250 \, A^{5} B a b^{5} + 15625 \, A^{6} b^{6}}{a^{11} b^{13}}\right)^{\frac{1}{6}} + {\left(7 \, B a + 5 \, A b\right)} \sqrt{x}\right) - 12 \, {\left({\left(13 \, B a b - A b^{2}\right)} x^{3} + 7 \, B a^{2} + 5 \, A a b\right)} \sqrt{x}}{432 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}"," ",0,"1/432*(4*sqrt(3)*(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*b^4*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/3) + (49*B^2*a^2 + 70*A*B*a*b + 25*A^2*b^2)*x + (7*B*a^3*b^2 + 5*A*a^2*b^3)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6))*a^9*b^11*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(5/6) - 2*sqrt(3)*(7*B*a^10*b^11 + 5*A*a^9*b^12)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(5/6) + sqrt(3)*(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6))/(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)) + 4*sqrt(3)*(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^4*b^4*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/3) + (49*B^2*a^2 + 70*A*B*a*b + 25*A^2*b^2)*x - (7*B*a^3*b^2 + 5*A*a^2*b^3)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6))*a^9*b^11*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(5/6) - 2*sqrt(3)*(7*B*a^10*b^11 + 5*A*a^9*b^12)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(5/6) - sqrt(3)*(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6))/(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)) + (a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*log(a^4*b^4*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/3) + (49*B^2*a^2 + 70*A*B*a*b + 25*A^2*b^2)*x + (7*B*a^3*b^2 + 5*A*a^2*b^3)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)) - (a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*log(a^4*b^4*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/3) + (49*B^2*a^2 + 70*A*B*a*b + 25*A^2*b^2)*x - (7*B*a^3*b^2 + 5*A*a^2*b^3)*sqrt(x)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)) + 2*(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*log(a^2*b^2*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6) + (7*B*a + 5*A*b)*sqrt(x)) - 2*(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6)*log(-a^2*b^2*(-(117649*B^6*a^6 + 504210*A*B^5*a^5*b + 900375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 459375*A^4*B^2*a^2*b^4 + 131250*A^5*B*a*b^5 + 15625*A^6*b^6)/(a^11*b^13))^(1/6) + (7*B*a + 5*A*b)*sqrt(x)) - 12*((13*B*a*b - A*b^2)*x^3 + 7*B*a^2 + 5*A*a*b)*sqrt(x))/(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)","B",0
173,1,3951,0,0.814871," ","integrate(x^(3/2)*(B*x^3+A)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(3125 \, B^{5} a^{16} b^{9} + 21875 \, A B^{4} a^{15} b^{10} + 61250 \, A^{2} B^{3} a^{14} b^{11} + 85750 \, A^{3} B^{2} a^{13} b^{12} + 60025 \, A^{4} B a^{12} b^{13} + 16807 \, A^{5} a^{11} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 136718750 \, A B^{9} a^{9} b + 861328125 \, A^{2} B^{8} a^{8} b^{2} + 3215625000 \, A^{3} B^{7} a^{7} b^{3} + 7878281250 \, A^{4} B^{6} a^{6} b^{4} + 13235512500 \, A^{5} B^{5} a^{5} b^{5} + 15441431250 \, A^{6} B^{4} a^{4} b^{6} + 12353145000 \, A^{7} B^{3} a^{3} b^{7} + 6485401125 \, A^{8} B^{2} a^{2} b^{8} + 2017680350 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{15} b^{7} + 131250 \, A B^{5} a^{14} b^{8} + 459375 \, A^{2} B^{4} a^{13} b^{9} + 857500 \, A^{3} B^{3} a^{12} b^{10} + 900375 \, A^{4} B^{2} a^{11} b^{11} + 504210 \, A^{5} B a^{10} b^{12} + 117649 \, A^{6} a^{9} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{2}{3}}} a^{2} b^{2} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} - 2 \, \sqrt{3} {\left(3125 \, B^{5} a^{7} b^{2} + 21875 \, A B^{4} a^{6} b^{3} + 61250 \, A^{2} B^{3} a^{5} b^{4} + 85750 \, A^{3} B^{2} a^{4} b^{5} + 60025 \, A^{4} B a^{3} b^{6} + 16807 \, A^{5} a^{2} b^{7}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} + \sqrt{3} {\left(15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}\right) + 4 \, \sqrt{3} {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{-{\left(3125 \, B^{5} a^{16} b^{9} + 21875 \, A B^{4} a^{15} b^{10} + 61250 \, A^{2} B^{3} a^{14} b^{11} + 85750 \, A^{3} B^{2} a^{13} b^{12} + 60025 \, A^{4} B a^{12} b^{13} + 16807 \, A^{5} a^{11} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 136718750 \, A B^{9} a^{9} b + 861328125 \, A^{2} B^{8} a^{8} b^{2} + 3215625000 \, A^{3} B^{7} a^{7} b^{3} + 7878281250 \, A^{4} B^{6} a^{6} b^{4} + 13235512500 \, A^{5} B^{5} a^{5} b^{5} + 15441431250 \, A^{6} B^{4} a^{4} b^{6} + 12353145000 \, A^{7} B^{3} a^{3} b^{7} + 6485401125 \, A^{8} B^{2} a^{2} b^{8} + 2017680350 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{15} b^{7} + 131250 \, A B^{5} a^{14} b^{8} + 459375 \, A^{2} B^{4} a^{13} b^{9} + 857500 \, A^{3} B^{3} a^{12} b^{10} + 900375 \, A^{4} B^{2} a^{11} b^{11} + 504210 \, A^{5} B a^{10} b^{12} + 117649 \, A^{6} a^{9} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{2}{3}}} a^{2} b^{2} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} - 2 \, \sqrt{3} {\left(3125 \, B^{5} a^{7} b^{2} + 21875 \, A B^{4} a^{6} b^{3} + 61250 \, A^{2} B^{3} a^{5} b^{4} + 85750 \, A^{3} B^{2} a^{4} b^{5} + 60025 \, A^{4} B a^{3} b^{6} + 16807 \, A^{5} a^{2} b^{7}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}\right)}}\right) - 2 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \log\left(a^{11} b^{9} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(3125 \, B^{5} a^{5} + 21875 \, A B^{4} a^{4} b + 61250 \, A^{2} B^{3} a^{3} b^{2} + 85750 \, A^{3} B^{2} a^{2} b^{3} + 60025 \, A^{4} B a b^{4} + 16807 \, A^{5} b^{5}\right)} \sqrt{x}\right) + 2 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \log\left(-a^{11} b^{9} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(3125 \, B^{5} a^{5} + 21875 \, A B^{4} a^{4} b + 61250 \, A^{2} B^{3} a^{3} b^{2} + 85750 \, A^{3} B^{2} a^{2} b^{3} + 60025 \, A^{4} B a b^{4} + 16807 \, A^{5} b^{5}\right)} \sqrt{x}\right) - {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \log\left({\left(3125 \, B^{5} a^{16} b^{9} + 21875 \, A B^{4} a^{15} b^{10} + 61250 \, A^{2} B^{3} a^{14} b^{11} + 85750 \, A^{3} B^{2} a^{13} b^{12} + 60025 \, A^{4} B a^{12} b^{13} + 16807 \, A^{5} a^{11} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 136718750 \, A B^{9} a^{9} b + 861328125 \, A^{2} B^{8} a^{8} b^{2} + 3215625000 \, A^{3} B^{7} a^{7} b^{3} + 7878281250 \, A^{4} B^{6} a^{6} b^{4} + 13235512500 \, A^{5} B^{5} a^{5} b^{5} + 15441431250 \, A^{6} B^{4} a^{4} b^{6} + 12353145000 \, A^{7} B^{3} a^{3} b^{7} + 6485401125 \, A^{8} B^{2} a^{2} b^{8} + 2017680350 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{15} b^{7} + 131250 \, A B^{5} a^{14} b^{8} + 459375 \, A^{2} B^{4} a^{13} b^{9} + 857500 \, A^{3} B^{3} a^{12} b^{10} + 900375 \, A^{4} B^{2} a^{11} b^{11} + 504210 \, A^{5} B a^{10} b^{12} + 117649 \, A^{6} a^{9} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{2}{3}}\right) + {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{1}{6}} \log\left(-{\left(3125 \, B^{5} a^{16} b^{9} + 21875 \, A B^{4} a^{15} b^{10} + 61250 \, A^{2} B^{3} a^{14} b^{11} + 85750 \, A^{3} B^{2} a^{13} b^{12} + 60025 \, A^{4} B a^{12} b^{13} + 16807 \, A^{5} a^{11} b^{14}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{5}{6}} + {\left(9765625 \, B^{10} a^{10} + 136718750 \, A B^{9} a^{9} b + 861328125 \, A^{2} B^{8} a^{8} b^{2} + 3215625000 \, A^{3} B^{7} a^{7} b^{3} + 7878281250 \, A^{4} B^{6} a^{6} b^{4} + 13235512500 \, A^{5} B^{5} a^{5} b^{5} + 15441431250 \, A^{6} B^{4} a^{4} b^{6} + 12353145000 \, A^{7} B^{3} a^{3} b^{7} + 6485401125 \, A^{8} B^{2} a^{2} b^{8} + 2017680350 \, A^{9} B a b^{9} + 282475249 \, A^{10} b^{10}\right)} x - {\left(15625 \, B^{6} a^{15} b^{7} + 131250 \, A B^{5} a^{14} b^{8} + 459375 \, A^{2} B^{4} a^{13} b^{9} + 857500 \, A^{3} B^{3} a^{12} b^{10} + 900375 \, A^{4} B^{2} a^{11} b^{11} + 504210 \, A^{5} B a^{10} b^{12} + 117649 \, A^{6} a^{9} b^{13}\right)} \left(-\frac{15625 \, B^{6} a^{6} + 131250 \, A B^{5} a^{5} b + 459375 \, A^{2} B^{4} a^{4} b^{2} + 857500 \, A^{3} B^{3} a^{3} b^{3} + 900375 \, A^{4} B^{2} a^{2} b^{4} + 504210 \, A^{5} B a b^{5} + 117649 \, A^{6} b^{6}}{a^{13} b^{11}}\right)^{\frac{2}{3}}\right) - 12 \, {\left({\left(5 \, B a b + 7 \, A b^{2}\right)} x^{5} - {\left(B a^{2} - 13 \, A a b\right)} x^{2}\right)} \sqrt{x}}{432 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}}"," ",0,"-1/432*(4*sqrt(3)*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((3125*B^5*a^16*b^9 + 21875*A*B^4*a^15*b^10 + 61250*A^2*B^3*a^14*b^11 + 85750*A^3*B^2*a^13*b^12 + 60025*A^4*B*a^12*b^13 + 16807*A^5*a^11*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (9765625*B^10*a^10 + 136718750*A*B^9*a^9*b + 861328125*A^2*B^8*a^8*b^2 + 3215625000*A^3*B^7*a^7*b^3 + 7878281250*A^4*B^6*a^6*b^4 + 13235512500*A^5*B^5*a^5*b^5 + 15441431250*A^6*B^4*a^4*b^6 + 12353145000*A^7*B^3*a^3*b^7 + 6485401125*A^8*B^2*a^2*b^8 + 2017680350*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (15625*B^6*a^15*b^7 + 131250*A*B^5*a^14*b^8 + 459375*A^2*B^4*a^13*b^9 + 857500*A^3*B^3*a^12*b^10 + 900375*A^4*B^2*a^11*b^11 + 504210*A^5*B*a^10*b^12 + 117649*A^6*a^9*b^13)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(2/3))*a^2*b^2*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6) - 2*sqrt(3)*(3125*B^5*a^7*b^2 + 21875*A*B^4*a^6*b^3 + 61250*A^2*B^3*a^5*b^4 + 85750*A^3*B^2*a^4*b^5 + 60025*A^4*B*a^3*b^6 + 16807*A^5*a^2*b^7)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6) + sqrt(3)*(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6))/(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)) + 4*sqrt(3)*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(-(3125*B^5*a^16*b^9 + 21875*A*B^4*a^15*b^10 + 61250*A^2*B^3*a^14*b^11 + 85750*A^3*B^2*a^13*b^12 + 60025*A^4*B*a^12*b^13 + 16807*A^5*a^11*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (9765625*B^10*a^10 + 136718750*A*B^9*a^9*b + 861328125*A^2*B^8*a^8*b^2 + 3215625000*A^3*B^7*a^7*b^3 + 7878281250*A^4*B^6*a^6*b^4 + 13235512500*A^5*B^5*a^5*b^5 + 15441431250*A^6*B^4*a^4*b^6 + 12353145000*A^7*B^3*a^3*b^7 + 6485401125*A^8*B^2*a^2*b^8 + 2017680350*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (15625*B^6*a^15*b^7 + 131250*A*B^5*a^14*b^8 + 459375*A^2*B^4*a^13*b^9 + 857500*A^3*B^3*a^12*b^10 + 900375*A^4*B^2*a^11*b^11 + 504210*A^5*B*a^10*b^12 + 117649*A^6*a^9*b^13)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(2/3))*a^2*b^2*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6) - 2*sqrt(3)*(3125*B^5*a^7*b^2 + 21875*A*B^4*a^6*b^3 + 61250*A^2*B^3*a^5*b^4 + 85750*A^3*B^2*a^4*b^5 + 60025*A^4*B*a^3*b^6 + 16807*A^5*a^2*b^7)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6) - sqrt(3)*(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6))/(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)) - 2*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*log(a^11*b^9*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (3125*B^5*a^5 + 21875*A*B^4*a^4*b + 61250*A^2*B^3*a^3*b^2 + 85750*A^3*B^2*a^2*b^3 + 60025*A^4*B*a*b^4 + 16807*A^5*b^5)*sqrt(x)) + 2*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*log(-a^11*b^9*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (3125*B^5*a^5 + 21875*A*B^4*a^4*b + 61250*A^2*B^3*a^3*b^2 + 85750*A^3*B^2*a^2*b^3 + 60025*A^4*B*a*b^4 + 16807*A^5*b^5)*sqrt(x)) - (a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*log((3125*B^5*a^16*b^9 + 21875*A*B^4*a^15*b^10 + 61250*A^2*B^3*a^14*b^11 + 85750*A^3*B^2*a^13*b^12 + 60025*A^4*B*a^12*b^13 + 16807*A^5*a^11*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (9765625*B^10*a^10 + 136718750*A*B^9*a^9*b + 861328125*A^2*B^8*a^8*b^2 + 3215625000*A^3*B^7*a^7*b^3 + 7878281250*A^4*B^6*a^6*b^4 + 13235512500*A^5*B^5*a^5*b^5 + 15441431250*A^6*B^4*a^4*b^6 + 12353145000*A^7*B^3*a^3*b^7 + 6485401125*A^8*B^2*a^2*b^8 + 2017680350*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (15625*B^6*a^15*b^7 + 131250*A*B^5*a^14*b^8 + 459375*A^2*B^4*a^13*b^9 + 857500*A^3*B^3*a^12*b^10 + 900375*A^4*B^2*a^11*b^11 + 504210*A^5*B*a^10*b^12 + 117649*A^6*a^9*b^13)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(2/3)) + (a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(1/6)*log(-(3125*B^5*a^16*b^9 + 21875*A*B^4*a^15*b^10 + 61250*A^2*B^3*a^14*b^11 + 85750*A^3*B^2*a^13*b^12 + 60025*A^4*B*a^12*b^13 + 16807*A^5*a^11*b^14)*sqrt(x)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(5/6) + (9765625*B^10*a^10 + 136718750*A*B^9*a^9*b + 861328125*A^2*B^8*a^8*b^2 + 3215625000*A^3*B^7*a^7*b^3 + 7878281250*A^4*B^6*a^6*b^4 + 13235512500*A^5*B^5*a^5*b^5 + 15441431250*A^6*B^4*a^4*b^6 + 12353145000*A^7*B^3*a^3*b^7 + 6485401125*A^8*B^2*a^2*b^8 + 2017680350*A^9*B*a*b^9 + 282475249*A^10*b^10)*x - (15625*B^6*a^15*b^7 + 131250*A*B^5*a^14*b^8 + 459375*A^2*B^4*a^13*b^9 + 857500*A^3*B^3*a^12*b^10 + 900375*A^4*B^2*a^11*b^11 + 504210*A^5*B*a^10*b^12 + 117649*A^6*a^9*b^13)*(-(15625*B^6*a^6 + 131250*A*B^5*a^5*b + 459375*A^2*B^4*a^4*b^2 + 857500*A^3*B^3*a^3*b^3 + 900375*A^4*B^2*a^2*b^4 + 504210*A^5*B*a*b^5 + 117649*A^6*b^6)/(a^13*b^11))^(2/3)) - 12*((5*B*a*b + 7*A*b^2)*x^5 - (B*a^2 - 13*A*a*b)*x^2)*sqrt(x))/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)","B",0
174,1,313,0,0.567657," ","integrate((B*x^3+A)*x^(1/2)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(B a b^{2} + 3 \, A b^{3}\right)} x^{6} + B a^{3} + 3 \, A a^{2} b + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x^{3}\right)} \sqrt{-a b} \log\left(\frac{b x^{3} - 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) - 2 \, {\left({\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{4} - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}, \frac{{\left({\left(B a b^{2} + 3 \, A b^{3}\right)} x^{6} + B a^{3} + 3 \, A a^{2} b + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) + {\left({\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x^{4} - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{12 \, {\left(a^{3} b^{4} x^{6} + 2 \, a^{4} b^{3} x^{3} + a^{5} b^{2}\right)}}\right]"," ",0,"[-1/24*(((B*a*b^2 + 3*A*b^3)*x^6 + B*a^3 + 3*A*a^2*b + 2*(B*a^2*b + 3*A*a*b^2)*x^3)*sqrt(-a*b)*log((b*x^3 - 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) - 2*((B*a^2*b^2 + 3*A*a*b^3)*x^4 - (B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2), 1/12*(((B*a*b^2 + 3*A*b^3)*x^6 + B*a^3 + 3*A*a^2*b + 2*(B*a^2*b + 3*A*a*b^2)*x^3)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a) + ((B*a^2*b^2 + 3*A*a*b^3)*x^4 - (B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^3*b^4*x^6 + 2*a^4*b^3*x^3 + a^5*b^2)]","A",0
175,1,2674,0,1.002423," ","integrate((B*x^3+A)/(b*x^3+a)^3/x^(1/2),x, algorithm=""fricas"")","\frac{20 \, \sqrt{3} {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{6} b^{2} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 22 \, A B a b + 121 \, A^{2} b^{2}\right)} x + {\left(B a^{4} b + 11 \, A a^{3} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}}} a^{14} b^{6} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(B a^{15} b^{6} + 11 \, A a^{14} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{5}{6}} + \sqrt{3} {\left(B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}\right) + 20 \, \sqrt{3} {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{6} b^{2} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{3}} + {\left(B^{2} a^{2} + 22 \, A B a b + 121 \, A^{2} b^{2}\right)} x - {\left(B a^{4} b + 11 \, A a^{3} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}}} a^{14} b^{6} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{5}{6}} - 2 \, \sqrt{3} {\left(B a^{15} b^{6} + 11 \, A a^{14} b^{7}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{5}{6}} - \sqrt{3} {\left(B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}\right)}}\right) + 5 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \log\left(25 \, a^{6} b^{2} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{3}} + 25 \, {\left(B^{2} a^{2} + 22 \, A B a b + 121 \, A^{2} b^{2}\right)} x + 25 \, {\left(B a^{4} b + 11 \, A a^{3} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}}\right) - 5 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \log\left(25 \, a^{6} b^{2} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{3}} + 25 \, {\left(B^{2} a^{2} + 22 \, A B a b + 121 \, A^{2} b^{2}\right)} x - 25 \, {\left(B a^{4} b + 11 \, A a^{3} b^{2}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}}\right) + 10 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \log\left(5 \, a^{3} b \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} + 5 \, {\left(B a + 11 \, A b\right)} \sqrt{x}\right) - 10 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} \log\left(-5 \, a^{3} b \left(-\frac{B^{6} a^{6} + 66 \, A B^{5} a^{5} b + 1815 \, A^{2} B^{4} a^{4} b^{2} + 26620 \, A^{3} B^{3} a^{3} b^{3} + 219615 \, A^{4} B^{2} a^{2} b^{4} + 966306 \, A^{5} B a b^{5} + 1771561 \, A^{6} b^{6}}{a^{17} b^{7}}\right)^{\frac{1}{6}} + 5 \, {\left(B a + 11 \, A b\right)} \sqrt{x}\right) + 12 \, {\left({\left(B a b + 11 \, A b^{2}\right)} x^{3} - 5 \, B a^{2} + 17 \, A a b\right)} \sqrt{x}}{432 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}}"," ",0,"1/432*(20*sqrt(3)*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^6*b^2*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/3) + (B^2*a^2 + 22*A*B*a*b + 121*A^2*b^2)*x + (B*a^4*b + 11*A*a^3*b^2)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6))*a^14*b^6*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(5/6) - 2*sqrt(3)*(B*a^15*b^6 + 11*A*a^14*b^7)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(5/6) + sqrt(3)*(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6))/(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)) + 20*sqrt(3)*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^6*b^2*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/3) + (B^2*a^2 + 22*A*B*a*b + 121*A^2*b^2)*x - (B*a^4*b + 11*A*a^3*b^2)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6))*a^14*b^6*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(5/6) - 2*sqrt(3)*(B*a^15*b^6 + 11*A*a^14*b^7)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(5/6) - sqrt(3)*(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6))/(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)) + 5*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*log(25*a^6*b^2*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/3) + 25*(B^2*a^2 + 22*A*B*a*b + 121*A^2*b^2)*x + 25*(B*a^4*b + 11*A*a^3*b^2)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)) - 5*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*log(25*a^6*b^2*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/3) + 25*(B^2*a^2 + 22*A*B*a*b + 121*A^2*b^2)*x - 25*(B*a^4*b + 11*A*a^3*b^2)*sqrt(x)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)) + 10*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*log(5*a^3*b*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6) + 5*(B*a + 11*A*b)*sqrt(x)) - 10*(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6)*log(-5*a^3*b*(-(B^6*a^6 + 66*A*B^5*a^5*b + 1815*A^2*B^4*a^4*b^2 + 26620*A^3*B^3*a^3*b^3 + 219615*A^4*B^2*a^2*b^4 + 966306*A^5*B*a*b^5 + 1771561*A^6*b^6)/(a^17*b^7))^(1/6) + 5*(B*a + 11*A*b)*sqrt(x)) + 12*((B*a*b + 11*A*b^2)*x^3 - 5*B*a^2 + 17*A*a*b)*sqrt(x))/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)","B",0
176,1,3904,0,0.971254," ","integrate((B*x^3+A)/x^(3/2)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{28 \, \sqrt{3} {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{{\left(B^{5} a^{21} b^{4} - 65 \, A B^{4} a^{20} b^{5} + 1690 \, A^{2} B^{3} a^{19} b^{6} - 21970 \, A^{3} B^{2} a^{18} b^{7} + 142805 \, A^{4} B a^{17} b^{8} - 371293 \, A^{5} a^{16} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} + {\left(B^{10} a^{10} - 130 \, A B^{9} a^{9} b + 7605 \, A^{2} B^{8} a^{8} b^{2} - 263640 \, A^{3} B^{7} a^{7} b^{3} + 5997810 \, A^{4} B^{6} a^{6} b^{4} - 93565836 \, A^{5} B^{5} a^{5} b^{5} + 1013629890 \, A^{6} B^{4} a^{4} b^{6} - 7529822040 \, A^{7} B^{3} a^{3} b^{7} + 36707882445 \, A^{8} B^{2} a^{2} b^{8} - 106044993730 \, A^{9} B a b^{9} + 137858491849 \, A^{10} b^{10}\right)} x - {\left(B^{6} a^{19} b^{3} - 78 \, A B^{5} a^{18} b^{4} + 2535 \, A^{2} B^{4} a^{17} b^{5} - 43940 \, A^{3} B^{3} a^{16} b^{6} + 428415 \, A^{4} B^{2} a^{15} b^{7} - 2227758 \, A^{5} B a^{14} b^{8} + 4826809 \, A^{6} a^{13} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{2}{3}}} a^{3} b \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} + 2 \, \sqrt{3} {\left(B^{5} a^{8} b - 65 \, A B^{4} a^{7} b^{2} + 1690 \, A^{2} B^{3} a^{6} b^{3} - 21970 \, A^{3} B^{2} a^{5} b^{4} + 142805 \, A^{4} B a^{4} b^{5} - 371293 \, A^{5} a^{3} b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}\right)}}{3 \, {\left(B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}\right)}}\right) + 28 \, \sqrt{3} {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{-282475249 \, {\left(B^{5} a^{21} b^{4} - 65 \, A B^{4} a^{20} b^{5} + 1690 \, A^{2} B^{3} a^{19} b^{6} - 21970 \, A^{3} B^{2} a^{18} b^{7} + 142805 \, A^{4} B a^{17} b^{8} - 371293 \, A^{5} a^{16} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} + 282475249 \, {\left(B^{10} a^{10} - 130 \, A B^{9} a^{9} b + 7605 \, A^{2} B^{8} a^{8} b^{2} - 263640 \, A^{3} B^{7} a^{7} b^{3} + 5997810 \, A^{4} B^{6} a^{6} b^{4} - 93565836 \, A^{5} B^{5} a^{5} b^{5} + 1013629890 \, A^{6} B^{4} a^{4} b^{6} - 7529822040 \, A^{7} B^{3} a^{3} b^{7} + 36707882445 \, A^{8} B^{2} a^{2} b^{8} - 106044993730 \, A^{9} B a b^{9} + 137858491849 \, A^{10} b^{10}\right)} x - 282475249 \, {\left(B^{6} a^{19} b^{3} - 78 \, A B^{5} a^{18} b^{4} + 2535 \, A^{2} B^{4} a^{17} b^{5} - 43940 \, A^{3} B^{3} a^{16} b^{6} + 428415 \, A^{4} B^{2} a^{15} b^{7} - 2227758 \, A^{5} B a^{14} b^{8} + 4826809 \, A^{6} a^{13} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{2}{3}}} a^{3} b \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} + 33614 \, \sqrt{3} {\left(B^{5} a^{8} b - 65 \, A B^{4} a^{7} b^{2} + 1690 \, A^{2} B^{3} a^{6} b^{3} - 21970 \, A^{3} B^{2} a^{5} b^{4} + 142805 \, A^{4} B a^{4} b^{5} - 371293 \, A^{5} a^{3} b^{6}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} + 16807 \, \sqrt{3} {\left(B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}\right)}}{50421 \, {\left(B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}\right)}}\right) - 14 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \log\left(16807 \, a^{16} b^{4} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} - 16807 \, {\left(B^{5} a^{5} - 65 \, A B^{4} a^{4} b + 1690 \, A^{2} B^{3} a^{3} b^{2} - 21970 \, A^{3} B^{2} a^{2} b^{3} + 142805 \, A^{4} B a b^{4} - 371293 \, A^{5} b^{5}\right)} \sqrt{x}\right) + 14 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \log\left(-16807 \, a^{16} b^{4} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} - 16807 \, {\left(B^{5} a^{5} - 65 \, A B^{4} a^{4} b + 1690 \, A^{2} B^{3} a^{3} b^{2} - 21970 \, A^{3} B^{2} a^{2} b^{3} + 142805 \, A^{4} B a b^{4} - 371293 \, A^{5} b^{5}\right)} \sqrt{x}\right) + 7 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \log\left(282475249 \, {\left(B^{5} a^{21} b^{4} - 65 \, A B^{4} a^{20} b^{5} + 1690 \, A^{2} B^{3} a^{19} b^{6} - 21970 \, A^{3} B^{2} a^{18} b^{7} + 142805 \, A^{4} B a^{17} b^{8} - 371293 \, A^{5} a^{16} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} + 282475249 \, {\left(B^{10} a^{10} - 130 \, A B^{9} a^{9} b + 7605 \, A^{2} B^{8} a^{8} b^{2} - 263640 \, A^{3} B^{7} a^{7} b^{3} + 5997810 \, A^{4} B^{6} a^{6} b^{4} - 93565836 \, A^{5} B^{5} a^{5} b^{5} + 1013629890 \, A^{6} B^{4} a^{4} b^{6} - 7529822040 \, A^{7} B^{3} a^{3} b^{7} + 36707882445 \, A^{8} B^{2} a^{2} b^{8} - 106044993730 \, A^{9} B a b^{9} + 137858491849 \, A^{10} b^{10}\right)} x - 282475249 \, {\left(B^{6} a^{19} b^{3} - 78 \, A B^{5} a^{18} b^{4} + 2535 \, A^{2} B^{4} a^{17} b^{5} - 43940 \, A^{3} B^{3} a^{16} b^{6} + 428415 \, A^{4} B^{2} a^{15} b^{7} - 2227758 \, A^{5} B a^{14} b^{8} + 4826809 \, A^{6} a^{13} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{2}{3}}\right) - 7 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{1}{6}} \log\left(-282475249 \, {\left(B^{5} a^{21} b^{4} - 65 \, A B^{4} a^{20} b^{5} + 1690 \, A^{2} B^{3} a^{19} b^{6} - 21970 \, A^{3} B^{2} a^{18} b^{7} + 142805 \, A^{4} B a^{17} b^{8} - 371293 \, A^{5} a^{16} b^{9}\right)} \sqrt{x} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{5}{6}} + 282475249 \, {\left(B^{10} a^{10} - 130 \, A B^{9} a^{9} b + 7605 \, A^{2} B^{8} a^{8} b^{2} - 263640 \, A^{3} B^{7} a^{7} b^{3} + 5997810 \, A^{4} B^{6} a^{6} b^{4} - 93565836 \, A^{5} B^{5} a^{5} b^{5} + 1013629890 \, A^{6} B^{4} a^{4} b^{6} - 7529822040 \, A^{7} B^{3} a^{3} b^{7} + 36707882445 \, A^{8} B^{2} a^{2} b^{8} - 106044993730 \, A^{9} B a b^{9} + 137858491849 \, A^{10} b^{10}\right)} x - 282475249 \, {\left(B^{6} a^{19} b^{3} - 78 \, A B^{5} a^{18} b^{4} + 2535 \, A^{2} B^{4} a^{17} b^{5} - 43940 \, A^{3} B^{3} a^{16} b^{6} + 428415 \, A^{4} B^{2} a^{15} b^{7} - 2227758 \, A^{5} B a^{14} b^{8} + 4826809 \, A^{6} a^{13} b^{9}\right)} \left(-\frac{B^{6} a^{6} - 78 \, A B^{5} a^{5} b + 2535 \, A^{2} B^{4} a^{4} b^{2} - 43940 \, A^{3} B^{3} a^{3} b^{3} + 428415 \, A^{4} B^{2} a^{2} b^{4} - 2227758 \, A^{5} B a b^{5} + 4826809 \, A^{6} b^{6}}{a^{19} b^{5}}\right)^{\frac{2}{3}}\right) + 12 \, {\left(7 \, {\left(B a b - 13 \, A b^{2}\right)} x^{6} + 13 \, {\left(B a^{2} - 13 \, A a b\right)} x^{3} - 72 \, A a^{2}\right)} \sqrt{x}}{432 \, {\left(a^{3} b^{2} x^{7} + 2 \, a^{4} b x^{4} + a^{5} x\right)}}"," ",0,"1/432*(28*sqrt(3)*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt((B^5*a^21*b^4 - 65*A*B^4*a^20*b^5 + 1690*A^2*B^3*a^19*b^6 - 21970*A^3*B^2*a^18*b^7 + 142805*A^4*B*a^17*b^8 - 371293*A^5*a^16*b^9)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) + (B^10*a^10 - 130*A*B^9*a^9*b + 7605*A^2*B^8*a^8*b^2 - 263640*A^3*B^7*a^7*b^3 + 5997810*A^4*B^6*a^6*b^4 - 93565836*A^5*B^5*a^5*b^5 + 1013629890*A^6*B^4*a^4*b^6 - 7529822040*A^7*B^3*a^3*b^7 + 36707882445*A^8*B^2*a^2*b^8 - 106044993730*A^9*B*a*b^9 + 137858491849*A^10*b^10)*x - (B^6*a^19*b^3 - 78*A*B^5*a^18*b^4 + 2535*A^2*B^4*a^17*b^5 - 43940*A^3*B^3*a^16*b^6 + 428415*A^4*B^2*a^15*b^7 - 2227758*A^5*B*a^14*b^8 + 4826809*A^6*a^13*b^9)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(2/3))*a^3*b*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6) + 2*sqrt(3)*(B^5*a^8*b - 65*A*B^4*a^7*b^2 + 1690*A^2*B^3*a^6*b^3 - 21970*A^3*B^2*a^5*b^4 + 142805*A^4*B*a^4*b^5 - 371293*A^5*a^3*b^6)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6) - sqrt(3)*(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6))/(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)) + 28*sqrt(3)*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*arctan(1/50421*(2*sqrt(3)*sqrt(-282475249*(B^5*a^21*b^4 - 65*A*B^4*a^20*b^5 + 1690*A^2*B^3*a^19*b^6 - 21970*A^3*B^2*a^18*b^7 + 142805*A^4*B*a^17*b^8 - 371293*A^5*a^16*b^9)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) + 282475249*(B^10*a^10 - 130*A*B^9*a^9*b + 7605*A^2*B^8*a^8*b^2 - 263640*A^3*B^7*a^7*b^3 + 5997810*A^4*B^6*a^6*b^4 - 93565836*A^5*B^5*a^5*b^5 + 1013629890*A^6*B^4*a^4*b^6 - 7529822040*A^7*B^3*a^3*b^7 + 36707882445*A^8*B^2*a^2*b^8 - 106044993730*A^9*B*a*b^9 + 137858491849*A^10*b^10)*x - 282475249*(B^6*a^19*b^3 - 78*A*B^5*a^18*b^4 + 2535*A^2*B^4*a^17*b^5 - 43940*A^3*B^3*a^16*b^6 + 428415*A^4*B^2*a^15*b^7 - 2227758*A^5*B*a^14*b^8 + 4826809*A^6*a^13*b^9)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(2/3))*a^3*b*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6) + 33614*sqrt(3)*(B^5*a^8*b - 65*A*B^4*a^7*b^2 + 1690*A^2*B^3*a^6*b^3 - 21970*A^3*B^2*a^5*b^4 + 142805*A^4*B*a^4*b^5 - 371293*A^5*a^3*b^6)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6) + 16807*sqrt(3)*(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6))/(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)) - 14*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*log(16807*a^16*b^4*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) - 16807*(B^5*a^5 - 65*A*B^4*a^4*b + 1690*A^2*B^3*a^3*b^2 - 21970*A^3*B^2*a^2*b^3 + 142805*A^4*B*a*b^4 - 371293*A^5*b^5)*sqrt(x)) + 14*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*log(-16807*a^16*b^4*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) - 16807*(B^5*a^5 - 65*A*B^4*a^4*b + 1690*A^2*B^3*a^3*b^2 - 21970*A^3*B^2*a^2*b^3 + 142805*A^4*B*a*b^4 - 371293*A^5*b^5)*sqrt(x)) + 7*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*log(282475249*(B^5*a^21*b^4 - 65*A*B^4*a^20*b^5 + 1690*A^2*B^3*a^19*b^6 - 21970*A^3*B^2*a^18*b^7 + 142805*A^4*B*a^17*b^8 - 371293*A^5*a^16*b^9)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) + 282475249*(B^10*a^10 - 130*A*B^9*a^9*b + 7605*A^2*B^8*a^8*b^2 - 263640*A^3*B^7*a^7*b^3 + 5997810*A^4*B^6*a^6*b^4 - 93565836*A^5*B^5*a^5*b^5 + 1013629890*A^6*B^4*a^4*b^6 - 7529822040*A^7*B^3*a^3*b^7 + 36707882445*A^8*B^2*a^2*b^8 - 106044993730*A^9*B*a*b^9 + 137858491849*A^10*b^10)*x - 282475249*(B^6*a^19*b^3 - 78*A*B^5*a^18*b^4 + 2535*A^2*B^4*a^17*b^5 - 43940*A^3*B^3*a^16*b^6 + 428415*A^4*B^2*a^15*b^7 - 2227758*A^5*B*a^14*b^8 + 4826809*A^6*a^13*b^9)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(2/3)) - 7*(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(1/6)*log(-282475249*(B^5*a^21*b^4 - 65*A*B^4*a^20*b^5 + 1690*A^2*B^3*a^19*b^6 - 21970*A^3*B^2*a^18*b^7 + 142805*A^4*B*a^17*b^8 - 371293*A^5*a^16*b^9)*sqrt(x)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(5/6) + 282475249*(B^10*a^10 - 130*A*B^9*a^9*b + 7605*A^2*B^8*a^8*b^2 - 263640*A^3*B^7*a^7*b^3 + 5997810*A^4*B^6*a^6*b^4 - 93565836*A^5*B^5*a^5*b^5 + 1013629890*A^6*B^4*a^4*b^6 - 7529822040*A^7*B^3*a^3*b^7 + 36707882445*A^8*B^2*a^2*b^8 - 106044993730*A^9*B*a*b^9 + 137858491849*A^10*b^10)*x - 282475249*(B^6*a^19*b^3 - 78*A*B^5*a^18*b^4 + 2535*A^2*B^4*a^17*b^5 - 43940*A^3*B^3*a^16*b^6 + 428415*A^4*B^2*a^15*b^7 - 2227758*A^5*B*a^14*b^8 + 4826809*A^6*a^13*b^9)*(-(B^6*a^6 - 78*A*B^5*a^5*b + 2535*A^2*B^4*a^4*b^2 - 43940*A^3*B^3*a^3*b^3 + 428415*A^4*B^2*a^2*b^4 - 2227758*A^5*B*a*b^5 + 4826809*A^6*b^6)/(a^19*b^5))^(2/3)) + 12*(7*(B*a*b - 13*A*b^2)*x^6 + 13*(B*a^2 - 13*A*a*b)*x^3 - 72*A*a^2)*sqrt(x))/(a^3*b^2*x^7 + 2*a^4*b*x^4 + a^5*x)","B",0
177,1,347,0,0.831510," ","integrate((B*x^3+A)/x^(5/2)/(b*x^3+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{-a b} \log\left(\frac{b x^{3} + 2 \, \sqrt{-a b} x^{\frac{3}{2}} - a}{b x^{3} + a}\right) + 2 \, {\left(3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{6} - 8 \, A a^{3} b + 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{x}}{24 \, {\left(a^{4} b^{3} x^{8} + 2 \, a^{5} b^{2} x^{5} + a^{6} b x^{2}\right)}}, \frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{8} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{5} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x^{\frac{3}{2}}}{a}\right) + {\left(3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{6} - 8 \, A a^{3} b + 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{x}}{12 \, {\left(a^{4} b^{3} x^{8} + 2 \, a^{5} b^{2} x^{5} + a^{6} b x^{2}\right)}}\right]"," ",0,"[1/24*(3*((B*a*b^2 - 5*A*b^3)*x^8 + 2*(B*a^2*b - 5*A*a*b^2)*x^5 + (B*a^3 - 5*A*a^2*b)*x^2)*sqrt(-a*b)*log((b*x^3 + 2*sqrt(-a*b)*x^(3/2) - a)/(b*x^3 + a)) + 2*(3*(B*a^2*b^2 - 5*A*a*b^3)*x^6 - 8*A*a^3*b + 5*(B*a^3*b - 5*A*a^2*b^2)*x^3)*sqrt(x))/(a^4*b^3*x^8 + 2*a^5*b^2*x^5 + a^6*b*x^2), 1/12*(3*((B*a*b^2 - 5*A*b^3)*x^8 + 2*(B*a^2*b - 5*A*a*b^2)*x^5 + (B*a^3 - 5*A*a^2*b)*x^2)*sqrt(a*b)*arctan(sqrt(a*b)*x^(3/2)/a) + (3*(B*a^2*b^2 - 5*A*a*b^3)*x^6 - 8*A*a^3*b + 5*(B*a^3*b - 5*A*a^2*b^2)*x^3)*sqrt(x))/(a^4*b^3*x^8 + 2*a^5*b^2*x^5 + a^6*b*x^2)]","A",0
178,1,2690,0,1.332453," ","integrate((B*x^3+A)/x^(7/2)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{220 \, \sqrt{3} {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{8} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 170 \, A B a b + 289 \, A^{2} b^{2}\right)} x + {\left(5 \, B a^{5} - 17 \, A a^{4} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}}} a^{19} b \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(5 \, B a^{20} b - 17 \, A a^{19} b^{2}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{5}{6}} - \sqrt{3} {\left(15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}\right)}}\right) + 220 \, \sqrt{3} {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \arctan\left(\frac{2 \, \sqrt{3} \sqrt{a^{8} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{3}} + {\left(25 \, B^{2} a^{2} - 170 \, A B a b + 289 \, A^{2} b^{2}\right)} x - {\left(5 \, B a^{5} - 17 \, A a^{4} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}}} a^{19} b \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{5}{6}} + 2 \, \sqrt{3} {\left(5 \, B a^{20} b - 17 \, A a^{19} b^{2}\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{5}{6}} + \sqrt{3} {\left(15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}\right)}}{3 \, {\left(15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}\right)}}\right) - 55 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \log\left(121 \, a^{8} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{3}} + 121 \, {\left(25 \, B^{2} a^{2} - 170 \, A B a b + 289 \, A^{2} b^{2}\right)} x + 121 \, {\left(5 \, B a^{5} - 17 \, A a^{4} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}}\right) + 55 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \log\left(121 \, a^{8} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{3}} + 121 \, {\left(25 \, B^{2} a^{2} - 170 \, A B a b + 289 \, A^{2} b^{2}\right)} x - 121 \, {\left(5 \, B a^{5} - 17 \, A a^{4} b\right)} \sqrt{x} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}}\right) + 110 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \log\left(11 \, a^{4} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} - 11 \, {\left(5 \, B a - 17 \, A b\right)} \sqrt{x}\right) - 110 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} \log\left(-11 \, a^{4} \left(-\frac{15625 \, B^{6} a^{6} - 318750 \, A B^{5} a^{5} b + 2709375 \, A^{2} B^{4} a^{4} b^{2} - 12282500 \, A^{3} B^{3} a^{3} b^{3} + 31320375 \, A^{4} B^{2} a^{2} b^{4} - 42595710 \, A^{5} B a b^{5} + 24137569 \, A^{6} b^{6}}{a^{23} b}\right)^{\frac{1}{6}} - 11 \, {\left(5 \, B a - 17 \, A b\right)} \sqrt{x}\right) - 12 \, {\left(11 \, {\left(5 \, B a b - 17 \, A b^{2}\right)} x^{6} + 17 \, {\left(5 \, B a^{2} - 17 \, A a b\right)} x^{3} - 72 \, A a^{2}\right)} \sqrt{x}}{2160 \, {\left(a^{3} b^{2} x^{9} + 2 \, a^{4} b x^{6} + a^{5} x^{3}\right)}}"," ",0,"-1/2160*(220*sqrt(3)*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^8*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/3) + (25*B^2*a^2 - 170*A*B*a*b + 289*A^2*b^2)*x + (5*B*a^5 - 17*A*a^4*b)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6))*a^19*b*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(5/6) + 2*sqrt(3)*(5*B*a^20*b - 17*A*a^19*b^2)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(5/6) - sqrt(3)*(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6))/(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)) + 220*sqrt(3)*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*arctan(1/3*(2*sqrt(3)*sqrt(a^8*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/3) + (25*B^2*a^2 - 170*A*B*a*b + 289*A^2*b^2)*x - (5*B*a^5 - 17*A*a^4*b)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6))*a^19*b*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(5/6) + 2*sqrt(3)*(5*B*a^20*b - 17*A*a^19*b^2)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(5/6) + sqrt(3)*(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6))/(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)) - 55*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*log(121*a^8*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/3) + 121*(25*B^2*a^2 - 170*A*B*a*b + 289*A^2*b^2)*x + 121*(5*B*a^5 - 17*A*a^4*b)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)) + 55*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*log(121*a^8*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/3) + 121*(25*B^2*a^2 - 170*A*B*a*b + 289*A^2*b^2)*x - 121*(5*B*a^5 - 17*A*a^4*b)*sqrt(x)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)) + 110*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*log(11*a^4*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6) - 11*(5*B*a - 17*A*b)*sqrt(x)) - 110*(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6)*log(-11*a^4*(-(15625*B^6*a^6 - 318750*A*B^5*a^5*b + 2709375*A^2*B^4*a^4*b^2 - 12282500*A^3*B^3*a^3*b^3 + 31320375*A^4*B^2*a^2*b^4 - 42595710*A^5*B*a*b^5 + 24137569*A^6*b^6)/(a^23*b))^(1/6) - 11*(5*B*a - 17*A*b)*sqrt(x)) - 12*(11*(5*B*a*b - 17*A*b^2)*x^6 + 17*(5*B*a^2 - 17*A*a*b)*x^3 - 72*A*a^2)*sqrt(x))/(a^3*b^2*x^9 + 2*a^4*b*x^6 + a^5*x^3)","B",0
179,1,99,0,0.790956," ","integrate(x^8*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{12} + 5 \, {\left(B a b^{3} + 9 \, A b^{4}\right)} x^{9} - 3 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{6} - 16 \, B a^{4} + 24 \, A a^{3} b + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{945 \, b^{4}}"," ",0,"2/945*(35*B*b^4*x^12 + 5*(B*a*b^3 + 9*A*b^4)*x^9 - 3*(2*B*a^2*b^2 - 3*A*a*b^3)*x^6 - 16*B*a^4 + 24*A*a^3*b + 4*(2*B*a^3*b - 3*A*a^2*b^2)*x^3)*sqrt(b*x^3 + a)/b^4","A",0
180,1,75,0,0.834780," ","integrate(x^5*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{3} x^{9} + 3 \, {\left(B a b^{2} + 7 \, A b^{3}\right)} x^{6} + 8 \, B a^{3} - 14 \, A a^{2} b - {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{315 \, b^{3}}"," ",0,"2/315*(15*B*b^3*x^9 + 3*(B*a*b^2 + 7*A*b^3)*x^6 + 8*B*a^3 - 14*A*a^2*b - (4*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(b*x^3 + a)/b^3","A",0
181,1,50,0,0.710494," ","integrate(x^2*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{6} + {\left(B a b + 5 \, A b^{2}\right)} x^{3} - 2 \, B a^{2} + 5 \, A a b\right)} \sqrt{b x^{3} + a}}{45 \, b^{2}}"," ",0,"2/45*(3*B*b^2*x^6 + (B*a*b + 5*A*b^2)*x^3 - 2*B*a^2 + 5*A*a*b)*sqrt(b*x^3 + a)/b^2","A",0
182,1,125,0,0.767012," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{a} b \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(B b x^{3} + B a + 3 \, A b\right)} \sqrt{b x^{3} + a}}{9 \, b}, \frac{2 \, {\left(3 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(B b x^{3} + B a + 3 \, A b\right)} \sqrt{b x^{3} + a}\right)}}{9 \, b}\right]"," ",0,"[1/9*(3*A*sqrt(a)*b*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(B*b*x^3 + B*a + 3*A*b)*sqrt(b*x^3 + a))/b, 2/9*(3*A*sqrt(-a)*b*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (B*b*x^3 + B*a + 3*A*b)*sqrt(b*x^3 + a))/b]","A",0
183,1,143,0,0.902274," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a + A b\right)} \sqrt{a} x^{3} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(2 \, B a x^{3} - A a\right)} \sqrt{b x^{3} + a}}{6 \, a x^{3}}, \frac{{\left(2 \, B a + A b\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(2 \, B a x^{3} - A a\right)} \sqrt{b x^{3} + a}}{3 \, a x^{3}}\right]"," ",0,"[1/6*((2*B*a + A*b)*sqrt(a)*x^3*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(2*B*a*x^3 - A*a)*sqrt(b*x^3 + a))/(a*x^3), 1/3*((2*B*a + A*b)*sqrt(-a)*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (2*B*a*x^3 - A*a)*sqrt(b*x^3 + a))/(a*x^3)]","A",0
184,1,172,0,0.757599," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{a} x^{6} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left({\left(4 \, B a^{2} + A a b\right)} x^{3} + 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a^{2} x^{6}}, \frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) - {\left({\left(4 \, B a^{2} + A a b\right)} x^{3} + 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a^{2} x^{6}}\right]"," ",0,"[-1/24*((4*B*a*b - A*b^2)*sqrt(a)*x^6*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*((4*B*a^2 + A*a*b)*x^3 + 2*A*a^2)*sqrt(b*x^3 + a))/(a^2*x^6), 1/12*((4*B*a*b - A*b^2)*sqrt(-a)*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) - ((4*B*a^2 + A*a*b)*x^3 + 2*A*a^2)*sqrt(b*x^3 + a))/(a^2*x^6)]","A",0
185,0,0,0,0.763962," ","integrate(x^3*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{6} + A x^{3}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*x^6 + A*x^3)*sqrt(b*x^3 + a), x)","F",0
186,0,0,0,0.857892," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a), x)","F",0
187,0,0,0,0.774828," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^3, x)","F",0
188,0,0,0,0.691526," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{6}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^6, x)","F",0
189,0,0,0,0.761634," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^9,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{9}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^9, x)","F",0
190,0,0,0,0.827918," ","integrate(x^4*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{7} + A x^{4}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*x^7 + A*x^4)*sqrt(b*x^3 + a), x)","F",0
191,0,0,0,0.635009," ","integrate(x*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{4} + A x\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*x^4 + A*x)*sqrt(b*x^3 + a), x)","F",0
192,0,0,0,0.792633," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^2, x)","F",0
193,0,0,0,0.738239," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{5}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^5, x)","F",0
194,0,0,0,1.156103," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{8}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^8, x)","F",0
195,0,0,0,0.579343," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{11}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^11, x)","F",0
196,1,124,0,1.114989," ","integrate(x^8*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{5} x^{15} + 35 \, {\left(12 \, B a b^{4} + 11 \, A b^{5}\right)} x^{12} + 5 \, {\left(3 \, B a^{2} b^{3} + 110 \, A a b^{4}\right)} x^{9} - 3 \, {\left(6 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{6} - 48 \, B a^{5} + 88 \, A a^{4} b + 4 \, {\left(6 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{10395 \, b^{4}}"," ",0,"2/10395*(315*B*b^5*x^15 + 35*(12*B*a*b^4 + 11*A*b^5)*x^12 + 5*(3*B*a^2*b^3 + 110*A*a*b^4)*x^9 - 3*(6*B*a^3*b^2 - 11*A*a^2*b^3)*x^6 - 48*B*a^5 + 88*A*a^4*b + 4*(6*B*a^4*b - 11*A*a^3*b^2)*x^3)*sqrt(b*x^3 + a)/b^4","A",0
197,1,99,0,0.818483," ","integrate(x^5*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{12} + 5 \, {\left(10 \, B a b^{3} + 9 \, A b^{4}\right)} x^{9} + 3 \, {\left(B a^{2} b^{2} + 24 \, A a b^{3}\right)} x^{6} + 8 \, B a^{4} - 18 \, A a^{3} b - {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{945 \, b^{3}}"," ",0,"2/945*(35*B*b^4*x^12 + 5*(10*B*a*b^3 + 9*A*b^4)*x^9 + 3*(B*a^2*b^2 + 24*A*a*b^3)*x^6 + 8*B*a^4 - 18*A*a^3*b - (4*B*a^3*b - 9*A*a^2*b^2)*x^3)*sqrt(b*x^3 + a)/b^3","A",0
198,1,73,0,1.019562," ","integrate(x^2*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{9} + {\left(8 \, B a b^{2} + 7 \, A b^{3}\right)} x^{6} - 2 \, B a^{3} + 7 \, A a^{2} b + {\left(B a^{2} b + 14 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{105 \, b^{2}}"," ",0,"2/105*(5*B*b^3*x^9 + (8*B*a*b^2 + 7*A*b^3)*x^6 - 2*B*a^3 + 7*A*a^2*b + (B*a^2*b + 14*A*a*b^2)*x^3)*sqrt(b*x^3 + a)/b^2","A",0
199,1,172,0,0.822585," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x,x, algorithm=""fricas"")","\left[\frac{15 \, A a^{\frac{3}{2}} b \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(3 \, B b^{2} x^{6} + {\left(6 \, B a b + 5 \, A b^{2}\right)} x^{3} + 3 \, B a^{2} + 20 \, A a b\right)} \sqrt{b x^{3} + a}}{45 \, b}, \frac{2 \, {\left(15 \, A \sqrt{-a} a b \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, B b^{2} x^{6} + {\left(6 \, B a b + 5 \, A b^{2}\right)} x^{3} + 3 \, B a^{2} + 20 \, A a b\right)} \sqrt{b x^{3} + a}\right)}}{45 \, b}\right]"," ",0,"[1/45*(15*A*a^(3/2)*b*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(3*B*b^2*x^6 + (6*B*a*b + 5*A*b^2)*x^3 + 3*B*a^2 + 20*A*a*b)*sqrt(b*x^3 + a))/b, 2/45*(15*A*sqrt(-a)*a*b*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*B*b^2*x^6 + (6*B*a*b + 5*A*b^2)*x^3 + 3*B*a^2 + 20*A*a*b)*sqrt(b*x^3 + a))/b]","A",0
200,1,169,0,0.565883," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{a} x^{3} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(2 \, B b x^{6} + 2 \, {\left(4 \, B a + 3 \, A b\right)} x^{3} - 3 \, A a\right)} \sqrt{b x^{3} + a}}{18 \, x^{3}}, \frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(2 \, B b x^{6} + 2 \, {\left(4 \, B a + 3 \, A b\right)} x^{3} - 3 \, A a\right)} \sqrt{b x^{3} + a}}{9 \, x^{3}}\right]"," ",0,"[1/18*(3*(2*B*a + 3*A*b)*sqrt(a)*x^3*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(2*B*b*x^6 + 2*(4*B*a + 3*A*b)*x^3 - 3*A*a)*sqrt(b*x^3 + a))/x^3, 1/9*(3*(2*B*a + 3*A*b)*sqrt(-a)*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (2*B*b*x^6 + 2*(4*B*a + 3*A*b)*x^3 - 3*A*a)*sqrt(b*x^3 + a))/x^3]","A",0
201,1,191,0,0.894096," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{a} x^{6} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(8 \, B a b x^{6} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x^{3} - 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a x^{6}}, \frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(8 \, B a b x^{6} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x^{3} - 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a x^{6}}\right]"," ",0,"[1/24*(3*(4*B*a*b + A*b^2)*sqrt(a)*x^6*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(8*B*a*b*x^6 - (4*B*a^2 + 5*A*a*b)*x^3 - 2*A*a^2)*sqrt(b*x^3 + a))/(a*x^6), 1/12*(3*(4*B*a*b + A*b^2)*sqrt(-a)*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (8*B*a*b*x^6 - (4*B*a^2 + 5*A*a*b)*x^3 - 2*A*a^2)*sqrt(b*x^3 + a))/(a*x^6)]","A",0
202,0,0,0,0.889327," ","integrate(x^3*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{9} + {\left(B a + A b\right)} x^{6} + A a x^{3}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*b*x^9 + (B*a + A*b)*x^6 + A*a*x^3)*sqrt(b*x^3 + a), x)","F",0
203,0,0,0,0.999166," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a), x)","F",0
204,0,0,0,1.248304," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{3}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^3, x)","F",0
205,0,0,0,1.019443," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{6}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^6, x)","F",0
206,0,0,0,1.103351," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^9,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{9}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^9, x)","F",0
207,0,0,0,1.070742," ","integrate(x^4*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{10} + {\left(B a + A b\right)} x^{7} + A a x^{4}\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*b*x^10 + (B*a + A*b)*x^7 + A*a*x^4)*sqrt(b*x^3 + a), x)","F",0
208,0,0,0,1.058819," ","integrate(x*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{7} + {\left(B a + A b\right)} x^{4} + A a x\right)} \sqrt{b x^{3} + a}, x\right)"," ",0,"integral((B*b*x^7 + (B*a + A*b)*x^4 + A*a*x)*sqrt(b*x^3 + a), x)","F",0
209,0,0,0,0.971349," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{2}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^2, x)","F",0
210,0,0,0,1.341824," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{5}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^5, x)","F",0
211,0,0,0,1.114282," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{8}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^8, x)","F",0
212,0,0,0,1.460721," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/x^11,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a}}{x^{11}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)/x^11, x)","F",0
213,1,76,0,0.923995," ","integrate(x^8*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{3} x^{9} - 3 \, {\left(6 \, B a b^{2} - 7 \, A b^{3}\right)} x^{6} - 48 \, B a^{3} + 56 \, A a^{2} b + 4 \, {\left(6 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{315 \, b^{4}}"," ",0,"2/315*(15*B*b^3*x^9 - 3*(6*B*a*b^2 - 7*A*b^3)*x^6 - 48*B*a^3 + 56*A*a^2*b + 4*(6*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(b*x^3 + a)/b^4","A",0
214,1,52,0,0.809820," ","integrate(x^5*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{6} - {\left(4 \, B a b - 5 \, A b^{2}\right)} x^{3} + 8 \, B a^{2} - 10 \, A a b\right)} \sqrt{b x^{3} + a}}{45 \, b^{3}}"," ",0,"2/45*(3*B*b^2*x^6 - (4*B*a*b - 5*A*b^2)*x^3 + 8*B*a^2 - 10*A*a*b)*sqrt(b*x^3 + a)/b^3","A",0
215,1,29,0,1.113879," ","integrate(x^2*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x^{3} - 2 \, B a + 3 \, A b\right)} \sqrt{b x^{3} + a}}{9 \, b^{2}}"," ",0,"2/9*(B*b*x^3 - 2*B*a + 3*A*b)*sqrt(b*x^3 + a)/b^2","A",0
216,1,105,0,1.009332," ","integrate((B*x^3+A)/x/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{a} b \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, \sqrt{b x^{3} + a} B a}{3 \, a b}, \frac{2 \, {\left(A \sqrt{-a} b \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + \sqrt{b x^{3} + a} B a\right)}}{3 \, a b}\right]"," ",0,"[1/3*(A*sqrt(a)*b*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*sqrt(b*x^3 + a)*B*a)/(a*b), 2/3*(A*sqrt(-a)*b*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + sqrt(b*x^3 + a)*B*a)/(a*b)]","A",0
217,1,126,0,1.505764," ","integrate((B*x^3+A)/x^4/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{a} x^{3} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, \sqrt{b x^{3} + a} A a}{6 \, a^{2} x^{3}}, \frac{{\left(2 \, B a - A b\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) - \sqrt{b x^{3} + a} A a}{3 \, a^{2} x^{3}}\right]"," ",0,"[-1/6*((2*B*a - A*b)*sqrt(a)*x^3*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*sqrt(b*x^3 + a)*A*a)/(a^2*x^3), 1/3*((2*B*a - A*b)*sqrt(-a)*x^3*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) - sqrt(b*x^3 + a)*A*a)/(a^2*x^3)]","A",0
218,1,173,0,1.083101," ","integrate((B*x^3+A)/x^7/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{a} x^{6} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left({\left(4 \, B a^{2} - 3 \, A a b\right)} x^{3} + 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{24 \, a^{3} x^{6}}, -\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left({\left(4 \, B a^{2} - 3 \, A a b\right)} x^{3} + 2 \, A a^{2}\right)} \sqrt{b x^{3} + a}}{12 \, a^{3} x^{6}}\right]"," ",0,"[-1/24*((4*B*a*b - 3*A*b^2)*sqrt(a)*x^6*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*((4*B*a^2 - 3*A*a*b)*x^3 + 2*A*a^2)*sqrt(b*x^3 + a))/(a^3*x^6), -1/12*((4*B*a*b - 3*A*b^2)*sqrt(-a)*x^6*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + ((4*B*a^2 - 3*A*a*b)*x^3 + 2*A*a^2)*sqrt(b*x^3 + a))/(a^3*x^6)]","A",0
219,0,0,0,1.039308," ","integrate(x^3*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{6} + A x^{3}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*x^6 + A*x^3)/sqrt(b*x^3 + a), x)","F",0
220,0,0,0,0.991556," ","integrate((B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{3} + A}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*x^3 + A)/sqrt(b*x^3 + a), x)","F",0
221,0,0,0,0.994377," ","integrate((B*x^3+A)/x^3/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b x^{6} + a x^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b*x^6 + a*x^3), x)","F",0
222,0,0,0,0.710385," ","integrate((B*x^3+A)/x^6/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b x^{9} + a x^{6}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b*x^9 + a*x^6), x)","F",0
223,0,0,0,1.016396," ","integrate(x^4*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{7} + A x^{4}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*x^7 + A*x^4)/sqrt(b*x^3 + a), x)","F",0
224,0,0,0,1.233322," ","integrate(x*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{4} + A x}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*x^4 + A*x)/sqrt(b*x^3 + a), x)","F",0
225,0,0,0,1.312094," ","integrate((B*x^3+A)/x^2/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b x^{5} + a x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b*x^5 + a*x^2), x)","F",0
226,0,0,0,1.281757," ","integrate((B*x^3+A)/x^5/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b x^{8} + a x^{5}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b*x^8 + a*x^5), x)","F",0
227,0,0,0,0.920077," ","integrate((B*x^3+A)/x^8/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b x^{11} + a x^{8}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b*x^11 + a*x^8), x)","F",0
228,1,88,0,1.036357," ","integrate(x^8*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} x^{9} - {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} x^{6} + 48 \, B a^{3} - 40 \, A a^{2} b + 4 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{45 \, {\left(b^{5} x^{3} + a b^{4}\right)}}"," ",0,"2/45*(3*B*b^3*x^9 - (6*B*a*b^2 - 5*A*b^3)*x^6 + 48*B*a^3 - 40*A*a^2*b + 4*(6*B*a^2*b - 5*A*a*b^2)*x^3)*sqrt(b*x^3 + a)/(b^5*x^3 + a*b^4)","A",0
229,1,63,0,0.979457," ","integrate(x^5*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} x^{6} - {\left(4 \, B a b - 3 \, A b^{2}\right)} x^{3} - 8 \, B a^{2} + 6 \, A a b\right)} \sqrt{b x^{3} + a}}{9 \, {\left(b^{4} x^{3} + a b^{3}\right)}}"," ",0,"2/9*(B*b^2*x^6 - (4*B*a*b - 3*A*b^2)*x^3 - 8*B*a^2 + 6*A*a*b)*sqrt(b*x^3 + a)/(b^4*x^3 + a*b^3)","A",0
230,1,41,0,0.551707," ","integrate(x^2*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x^{3} + 2 \, B a - A b\right)} \sqrt{b x^{3} + a}}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}}"," ",0,"2/3*(B*b*x^3 + 2*B*a - A*b)*sqrt(b*x^3 + a)/(b^3*x^3 + a*b^2)","A",0
231,1,170,0,1.065069," ","integrate((B*x^3+A)/x/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A b^{2} x^{3} + A a b\right)} \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, \sqrt{b x^{3} + a} {\left(B a^{2} - A a b\right)}}{3 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}, \frac{2 \, {\left({\left(A b^{2} x^{3} + A a b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) - \sqrt{b x^{3} + a} {\left(B a^{2} - A a b\right)}\right)}}{3 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}\right]"," ",0,"[1/3*((A*b^2*x^3 + A*a*b)*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*sqrt(b*x^3 + a)*(B*a^2 - A*a*b))/(a^2*b^2*x^3 + a^3*b), 2/3*((A*b^2*x^3 + A*a*b)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) - sqrt(b*x^3 + a)*(B*a^2 - A*a*b))/(a^2*b^2*x^3 + a^3*b)]","A",0
232,1,233,0,0.960508," ","integrate((B*x^3+A)/x^4/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{6} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{3}\right)} \sqrt{a} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, {\left({\left(2 \, B a^{2} - 3 \, A a b\right)} x^{3} - A a^{2}\right)} \sqrt{b x^{3} + a}}{6 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}, \frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{6} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left({\left(2 \, B a^{2} - 3 \, A a b\right)} x^{3} - A a^{2}\right)} \sqrt{b x^{3} + a}}{3 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}\right]"," ",0,"[-1/6*(((2*B*a*b - 3*A*b^2)*x^6 + (2*B*a^2 - 3*A*a*b)*x^3)*sqrt(a)*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*((2*B*a^2 - 3*A*a*b)*x^3 - A*a^2)*sqrt(b*x^3 + a))/(a^3*b*x^6 + a^4*x^3), 1/3*(((2*B*a*b - 3*A*b^2)*x^6 + (2*B*a^2 - 3*A*a*b)*x^3)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + ((2*B*a^2 - 3*A*a*b)*x^3 - A*a^2)*sqrt(b*x^3 + a))/(a^3*b*x^6 + a^4*x^3)]","A",0
233,1,289,0,0.927647," ","integrate((B*x^3+A)/x^7/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{9} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6}\right)} \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} + 2 \, A a^{3} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{24 \, {\left(a^{4} b x^{9} + a^{5} x^{6}\right)}}, -\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{9} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} + 2 \, A a^{3} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{12 \, {\left(a^{4} b x^{9} + a^{5} x^{6}\right)}}\right]"," ",0,"[-1/24*(3*((4*B*a*b^2 - 5*A*b^3)*x^9 + (4*B*a^2*b - 5*A*a*b^2)*x^6)*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(3*(4*B*a^2*b - 5*A*a*b^2)*x^6 + 2*A*a^3 + (4*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(b*x^3 + a))/(a^4*b*x^9 + a^5*x^6), -1/12*(3*((4*B*a*b^2 - 5*A*b^3)*x^9 + (4*B*a^2*b - 5*A*a*b^2)*x^6)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*(4*B*a^2*b - 5*A*a*b^2)*x^6 + 2*A*a^3 + (4*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(b*x^3 + a))/(a^4*b*x^9 + a^5*x^6)]","A",0
234,0,0,0,1.117862," ","integrate(x^6*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{9} + A x^{6}\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^9 + A*x^6)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
235,0,0,0,0.997512," ","integrate(x^3*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{6} + A x^{3}\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^6 + A*x^3)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
236,0,0,0,1.139680," ","integrate((B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
237,0,0,0,1.134317," ","integrate((B*x^3+A)/x^3/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{9} + 2 \, a b x^{6} + a^{2} x^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^9 + 2*a*b*x^6 + a^2*x^3), x)","F",0
238,0,0,0,1.203787," ","integrate((B*x^3+A)/x^6/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{12} + 2 \, a b x^{9} + a^{2} x^{6}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^12 + 2*a*b*x^9 + a^2*x^6), x)","F",0
239,0,0,0,1.333132," ","integrate(x^4*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{7} + A x^{4}\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^7 + A*x^4)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
240,0,0,0,0.991235," ","integrate(x*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{4} + A x\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^4 + A*x)*sqrt(b*x^3 + a)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
241,0,0,0,1.330169," ","integrate((B*x^3+A)/x^2/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{8} + 2 \, a b x^{5} + a^{2} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^8 + 2*a*b*x^5 + a^2*x^2), x)","F",0
242,0,0,0,0.900584," ","integrate((B*x^3+A)/x^5/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{11} + 2 \, a b x^{8} + a^{2} x^{5}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^11 + 2*a*b*x^8 + a^2*x^5), x)","F",0
243,0,0,0,1.131970," ","integrate((B*x^3+A)/x^8/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{2} x^{14} + 2 \, a b x^{11} + a^{2} x^{8}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^2*x^14 + 2*a*b*x^11 + a^2*x^8), x)","F",0
244,1,98,0,0.841506," ","integrate(x^8*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{3} x^{9} - 3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} x^{6} - 16 \, B a^{3} + 8 \, A a^{2} b - 12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{9 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{3} + a^{2} b^{4}\right)}}"," ",0,"2/9*(B*b^3*x^9 - 3*(2*B*a*b^2 - A*b^3)*x^6 - 16*B*a^3 + 8*A*a^2*b - 12*(2*B*a^2*b - A*a*b^2)*x^3)*sqrt(b*x^3 + a)/(b^6*x^6 + 2*a*b^5*x^3 + a^2*b^4)","A",0
245,1,75,0,0.713939," ","integrate(x^5*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{6} + 3 \, {\left(4 \, B a b - A b^{2}\right)} x^{3} + 8 \, B a^{2} - 2 \, A a b\right)} \sqrt{b x^{3} + a}}{9 \, {\left(b^{5} x^{6} + 2 \, a b^{4} x^{3} + a^{2} b^{3}\right)}}"," ",0,"2/9*(3*B*b^2*x^6 + 3*(4*B*a*b - A*b^2)*x^3 + 8*B*a^2 - 2*A*a*b)*sqrt(b*x^3 + a)/(b^5*x^6 + 2*a*b^4*x^3 + a^2*b^3)","A",0
246,1,52,0,0.731960," ","integrate(x^2*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B b x^{3} + 2 \, B a + A b\right)} \sqrt{b x^{3} + a}}{9 \, {\left(b^{4} x^{6} + 2 \, a b^{3} x^{3} + a^{2} b^{2}\right)}}"," ",0,"-2/9*(3*B*b*x^3 + 2*B*a + A*b)*sqrt(b*x^3 + a)/(b^4*x^6 + 2*a*b^3*x^3 + a^2*b^2)","A",0
247,1,243,0,0.558896," ","integrate((B*x^3+A)/x/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{3} + A a^{2} b\right)} \sqrt{a} \log\left(\frac{b x^{3} - 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) + 2 \, {\left(3 \, A a b^{2} x^{3} - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x^{3} + a}}{9 \, {\left(a^{3} b^{3} x^{6} + 2 \, a^{4} b^{2} x^{3} + a^{5} b\right)}}, \frac{2 \, {\left(3 \, {\left(A b^{3} x^{6} + 2 \, A a b^{2} x^{3} + A a^{2} b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, A a b^{2} x^{3} - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x^{3} + a}\right)}}{9 \, {\left(a^{3} b^{3} x^{6} + 2 \, a^{4} b^{2} x^{3} + a^{5} b\right)}}\right]"," ",0,"[1/9*(3*(A*b^3*x^6 + 2*A*a*b^2*x^3 + A*a^2*b)*sqrt(a)*log((b*x^3 - 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) + 2*(3*A*a*b^2*x^3 - B*a^3 + 4*A*a^2*b)*sqrt(b*x^3 + a))/(a^3*b^3*x^6 + 2*a^4*b^2*x^3 + a^5*b), 2/9*(3*(A*b^3*x^6 + 2*A*a*b^2*x^3 + A*a^2*b)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*A*a*b^2*x^3 - B*a^3 + 4*A*a^2*b)*sqrt(b*x^3 + a))/(a^3*b^3*x^6 + 2*a^4*b^2*x^3 + a^5*b)]","A",0
248,1,351,0,0.746557," ","integrate((B*x^3+A)/x^4/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{9} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{a} \log\left(\frac{b x^{3} + 2 \, \sqrt{b x^{3} + a} \sqrt{a} + 2 \, a}{x^{3}}\right) - 2 \, {\left(3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} - 3 \, A a^{3} + 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{18 \, {\left(a^{4} b^{2} x^{9} + 2 \, a^{5} b x^{6} + a^{6} x^{3}\right)}}, \frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{9} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x^{3} + a} \sqrt{-a}}{a}\right) + {\left(3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{6} - 3 \, A a^{3} + 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x^{3}\right)} \sqrt{b x^{3} + a}}{9 \, {\left(a^{4} b^{2} x^{9} + 2 \, a^{5} b x^{6} + a^{6} x^{3}\right)}}\right]"," ",0,"[-1/18*(3*((2*B*a*b^2 - 5*A*b^3)*x^9 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^6 + (2*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(a)*log((b*x^3 + 2*sqrt(b*x^3 + a)*sqrt(a) + 2*a)/x^3) - 2*(3*(2*B*a^2*b - 5*A*a*b^2)*x^6 - 3*A*a^3 + 4*(2*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(b*x^3 + a))/(a^4*b^2*x^9 + 2*a^5*b*x^6 + a^6*x^3), 1/9*(3*((2*B*a*b^2 - 5*A*b^3)*x^9 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^6 + (2*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(-a)*arctan(sqrt(b*x^3 + a)*sqrt(-a)/a) + (3*(2*B*a^2*b - 5*A*a*b^2)*x^6 - 3*A*a^3 + 4*(2*B*a^3 - 5*A*a^2*b)*x^3)*sqrt(b*x^3 + a))/(a^4*b^2*x^9 + 2*a^5*b*x^6 + a^6*x^3)]","A",0
249,0,0,0,0.636964," ","integrate(x^6*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{9} + A x^{6}\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^9 + A*x^6)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
250,0,0,0,0.834552," ","integrate(x^3*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{6} + A x^{3}\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^6 + A*x^3)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
251,0,0,0,0.862779," ","integrate((B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
252,0,0,0,0.849987," ","integrate((B*x^3+A)/x^3/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{3} x^{12} + 3 \, a b^{2} x^{9} + 3 \, a^{2} b x^{6} + a^{3} x^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^3*x^12 + 3*a*b^2*x^9 + 3*a^2*b*x^6 + a^3*x^3), x)","F",0
253,0,0,0,0.877530," ","integrate((B*x^3+A)/x^6/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{3} x^{15} + 3 \, a b^{2} x^{12} + 3 \, a^{2} b x^{9} + a^{3} x^{6}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^3*x^15 + 3*a*b^2*x^12 + 3*a^2*b*x^9 + a^3*x^6), x)","F",0
254,0,0,0,0.780264," ","integrate(x^7*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{10} + A x^{7}\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^10 + A*x^7)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
255,0,0,0,1.168135," ","integrate(x^4*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{7} + A x^{4}\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^7 + A*x^4)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
256,0,0,0,0.622668," ","integrate(x*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{4} + A x\right)} \sqrt{b x^{3} + a}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^4 + A*x)*sqrt(b*x^3 + a)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
257,0,0,0,0.749531," ","integrate((B*x^3+A)/x^2/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{3} x^{11} + 3 \, a b^{2} x^{8} + 3 \, a^{2} b x^{5} + a^{3} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^3*x^11 + 3*a*b^2*x^8 + 3*a^2*b*x^5 + a^3*x^2), x)","F",0
258,0,0,0,0.863402," ","integrate((B*x^3+A)/x^5/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{b^{3} x^{14} + 3 \, a b^{2} x^{11} + 3 \, a^{2} b x^{8} + a^{3} x^{5}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/(b^3*x^14 + 3*a*b^2*x^11 + 3*a^2*b*x^8 + a^3*x^5), x)","F",0
259,1,156,0,1.154804," ","integrate(x^8*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(120 \, \sqrt{3} \sqrt{-c} c^{2} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + {\left(3 \, d^{2} x^{6} - 19 \, c d x^{3} + 218 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{3}}, -\frac{2 \, {\left(240 \, \sqrt{3} c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) - {\left(3 \, d^{2} x^{6} - 19 \, c d x^{3} + 218 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{3}}\right]"," ",0,"[2/45*(120*sqrt(3)*sqrt(-c)*c^2*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + (3*d^2*x^6 - 19*c*d*x^3 + 218*c^2)*sqrt(d*x^3 + c))/d^3, -2/45*(240*sqrt(3)*c^(5/2)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) - (3*d^2*x^6 - 19*c*d*x^3 + 218*c^2)*sqrt(d*x^3 + c))/d^3]","A",0
260,1,129,0,0.929893," ","integrate(x^5*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, \sqrt{3} \sqrt{-c} c \log\left(\frac{d x^{3} + 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + \sqrt{d x^{3} + c} {\left(d x^{3} - 11 \, c\right)}\right)}}{9 \, d^{2}}, \frac{2 \, {\left(12 \, \sqrt{3} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) + \sqrt{d x^{3} + c} {\left(d x^{3} - 11 \, c\right)}\right)}}{9 \, d^{2}}\right]"," ",0,"[2/9*(6*sqrt(3)*sqrt(-c)*c*log((d*x^3 + 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + sqrt(d*x^3 + c)*(d*x^3 - 11*c))/d^2, 2/9*(12*sqrt(3)*c^(3/2)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) + sqrt(d*x^3 + c)*(d*x^3 - 11*c))/d^2]","A",0
261,1,110,0,0.776865," ","integrate(x^2*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} \sqrt{-c} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + 2 \, \sqrt{d x^{3} + c}}{3 \, d}, -\frac{2 \, {\left(\sqrt{3} \sqrt{c} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) - \sqrt{d x^{3} + c}\right)}}{3 \, d}\right]"," ",0,"[1/3*(sqrt(3)*sqrt(-c)*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + 2*sqrt(d*x^3 + c))/d, -2/3*(sqrt(3)*sqrt(c)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) - sqrt(d*x^3 + c))/d]","A",0
262,1,147,0,0.815409," ","integrate((d*x^3+c)^(1/2)/x/(d*x^3+4*c),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{3} \sqrt{c} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{12 \, c}, -\frac{\sqrt{3} \sqrt{-c} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)}{12 \, c}\right]"," ",0,"[1/12*(2*sqrt(3)*sqrt(c)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/c, -1/12*(sqrt(3)*sqrt(-c)*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) - 2*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/c]","A",0
263,1,194,0,0.950182," ","integrate((d*x^3+c)^(1/2)/x^4/(d*x^3+4*c),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{3} \sqrt{c} d x^{3} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) - \sqrt{c} d x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 4 \, \sqrt{d x^{3} + c} c}{48 \, c^{2} x^{3}}, -\frac{\sqrt{3} \sqrt{-c} d x^{3} \log\left(\frac{d x^{3} + 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) - 2 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 4 \, \sqrt{d x^{3} + c} c}{48 \, c^{2} x^{3}}\right]"," ",0,"[-1/48*(2*sqrt(3)*sqrt(c)*d*x^3*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) - sqrt(c)*d*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 4*sqrt(d*x^3 + c)*c)/(c^2*x^3), -1/48*(sqrt(3)*sqrt(-c)*d*x^3*log((d*x^3 + 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) - 2*sqrt(-c)*d*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 4*sqrt(d*x^3 + c)*c)/(c^2*x^3)]","A",0
264,0,0,0,8.884495," ","integrate(x^4*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{4}}{d x^{3} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^4/(d*x^3 + 4*c), x)","F",0
265,0,0,0,3.005515," ","integrate(x*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x}{d x^{3} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x/(d*x^3 + 4*c), x)","F",0
266,0,0,0,1.735729," ","integrate((d*x^3+c)^(1/2)/x^2/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d x^{5} + 4 \, c x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d*x^5 + 4*c*x^2), x)","F",0
267,0,0,0,5.608091," ","integrate(x^3*(d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{3}}{d x^{3} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^3/(d*x^3 + 4*c), x)","F",0
268,0,0,0,1.293041," ","integrate((d*x^3+c)^(1/2)/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d x^{3} + 4 \, c}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d*x^3 + 4*c), x)","F",0
269,0,0,0,2.714744," ","integrate((d*x^3+c)^(1/2)/x^3/(d*x^3+4*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d x^{6} + 4 \, c x^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d*x^6 + 4*c*x^3), x)","F",0
270,1,129,0,0.814063," ","integrate(x^8/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(8 \, \sqrt{3} \sqrt{-c} c \log\left(\frac{d x^{3} + 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + \sqrt{d x^{3} + c} {\left(d x^{3} - 14 \, c\right)}\right)}}{9 \, d^{3}}, \frac{2 \, {\left(16 \, \sqrt{3} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) + \sqrt{d x^{3} + c} {\left(d x^{3} - 14 \, c\right)}\right)}}{9 \, d^{3}}\right]"," ",0,"[2/9*(8*sqrt(3)*sqrt(-c)*c*log((d*x^3 + 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + sqrt(d*x^3 + c)*(d*x^3 - 14*c))/d^3, 2/9*(16*sqrt(3)*c^(3/2)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) + sqrt(d*x^3 + c)*(d*x^3 - 14*c))/d^3]","A",0
271,1,112,0,0.845597," ","integrate(x^5/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2 \, \sqrt{3} \sqrt{-c} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + 3 \, \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}, -\frac{2 \, {\left(4 \, \sqrt{3} \sqrt{c} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) - 3 \, \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}\right]"," ",0,"[2/9*(2*sqrt(3)*sqrt(-c)*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + 3*sqrt(d*x^3 + c))/d^2, -2/9*(4*sqrt(3)*sqrt(c)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) - 3*sqrt(d*x^3 + c))/d^2]","A",0
272,1,87,0,0.721996," ","integrate(x^2/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{3} \sqrt{-c} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right)}{9 \, c d}, \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right)}{9 \, \sqrt{c} d}\right]"," ",0,"[-1/9*sqrt(3)*sqrt(-c)*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c))/(c*d), 2/9*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c))/(sqrt(c)*d)]","A",0
273,1,148,0,0.837530," ","integrate(1/x/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{3} \sqrt{c} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) - 3 \, \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{36 \, c^{2}}, -\frac{\sqrt{3} \sqrt{-c} \log\left(\frac{d x^{3} + 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) - 6 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)}{36 \, c^{2}}\right]"," ",0,"[-1/36*(2*sqrt(3)*sqrt(c)*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) - 3*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/c^2, -1/36*(sqrt(3)*sqrt(-c)*log((d*x^3 + 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) - 6*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/c^2]","A",0
274,1,194,0,0.647672," ","integrate(1/x^4/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{3} \sqrt{c} d x^{3} \arctan\left(\frac{\sqrt{3} \sqrt{d x^{3} + c}}{3 \, \sqrt{c}}\right) + 9 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 12 \, \sqrt{d x^{3} + c} c}{144 \, c^{3} x^{3}}, -\frac{\sqrt{3} \sqrt{-c} d x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{3} \sqrt{d x^{3} + c} \sqrt{-c} - 2 \, c}{d x^{3} + 4 \, c}\right) + 18 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 12 \, \sqrt{d x^{3} + c} c}{144 \, c^{3} x^{3}}\right]"," ",0,"[1/144*(2*sqrt(3)*sqrt(c)*d*x^3*arctan(1/3*sqrt(3)*sqrt(d*x^3 + c)/sqrt(c)) + 9*sqrt(c)*d*x^3*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 12*sqrt(d*x^3 + c)*c)/(c^3*x^3), -1/144*(sqrt(3)*sqrt(-c)*d*x^3*log((d*x^3 - 2*sqrt(3)*sqrt(d*x^3 + c)*sqrt(-c) - 2*c)/(d*x^3 + 4*c)) + 18*sqrt(-c)*d*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*sqrt(d*x^3 + c)*c)/(c^3*x^3)]","A",0
275,0,0,0,5.858576," ","integrate(x^4/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{4}}{d^{2} x^{6} + 5 \, c d x^{3} + 4 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^4/(d^2*x^6 + 5*c*d*x^3 + 4*c^2), x)","F",0
276,1,2274,0,2.365574," ","integrate(x/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{3 \, {\left(\sqrt{3} \sqrt{\frac{1}{3}} c^{3} d^{2} x \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} c d x^{2} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} + 24 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{5}{6}} {\left(c^{4} d^{4} x^{3} + 4 \, c^{5} d^{3}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}}\right)} \sqrt{d x^{3} + c} + {\left(2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{2} x^{3} + c^{3} d\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(d x^{4} + c x\right)} + 3 \, {\left(\sqrt{3} \sqrt{\frac{1}{3}} c^{3} d^{2} x \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} c d x^{2} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} - 24 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{5}{6}} {\left(c^{4} d^{4} x^{3} - 2 \, c^{5} d^{3}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}}\right)} \sqrt{d x^{3} + c}\right)} \sqrt{\frac{d^{3} x^{9} + 60 \, c d^{2} x^{6} - 32 \, c^{3} - 24 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} + 5 \, c^{5} d^{4} x^{4} + 4 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + 12 \, {\left(648 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{3}} {\left(c^{3} d^{4} x^{6} - 16 \, c^{4} d^{3} x^{3} - 8 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} - \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} + 2 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}}}{3 \, {\left(d x^{4} + c x\right)}}\right) + \frac{1}{9} \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{3 \, {\left(\sqrt{3} \sqrt{\frac{1}{3}} c^{3} d^{2} x \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} c d x^{2} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} + 24 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{5}{6}} {\left(c^{4} d^{4} x^{3} + 4 \, c^{5} d^{3}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}}\right)} \sqrt{d x^{3} + c} - {\left(2 \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{2} x^{3} + c^{3} d\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(d x^{4} + c x\right)} - 3 \, {\left(\sqrt{3} \sqrt{\frac{1}{3}} c^{3} d^{2} x \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{1}{6}} c d x^{2} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} - 24 \, \sqrt{3} \left(\frac{1}{432}\right)^{\frac{5}{6}} {\left(c^{4} d^{4} x^{3} - 2 \, c^{5} d^{3}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}}\right)} \sqrt{d x^{3} + c}\right)} \sqrt{\frac{d^{3} x^{9} + 60 \, c d^{2} x^{6} - 32 \, c^{3} - 24 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} + 5 \, c^{5} d^{4} x^{4} + 4 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} - 12 \, {\left(648 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{3}} {\left(c^{3} d^{4} x^{6} - 16 \, c^{4} d^{3} x^{3} - 8 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} - \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} + 2 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}}}{3 \, {\left(d x^{4} + c x\right)}}\right) - \frac{1}{36} \, \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} + 60 \, c d^{2} x^{6} - 32 \, c^{3} - 24 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} + 5 \, c^{5} d^{4} x^{4} + 4 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + 12 \, {\left(648 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{3}} {\left(c^{3} d^{4} x^{6} - 16 \, c^{4} d^{3} x^{3} - 8 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} - \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} + 2 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}\right) + \frac{1}{36} \, \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} + 60 \, c d^{2} x^{6} - 32 \, c^{3} - 24 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} + 5 \, c^{5} d^{4} x^{4} + 4 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} - 12 \, {\left(648 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{3}} {\left(c^{3} d^{4} x^{6} - 16 \, c^{4} d^{3} x^{3} - 8 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} - \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} + 2 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}\right) + \frac{1}{18} \, \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} - 66 \, c d^{2} x^{6} - 72 \, c^{2} d x^{3} - 32 \, c^{3} + 48 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} - c^{5} d^{4} x^{4} - 2 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + 6 \, {\left(1296 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{3}} {\left(5 \, c^{3} d^{4} x^{6} - 20 \, c^{4} d^{3} x^{3} - 16 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} - 16 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}\right) - \frac{1}{18} \, \left(\frac{1}{432}\right)^{\frac{1}{6}} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} - 66 \, c d^{2} x^{6} - 72 \, c^{2} d x^{3} - 32 \, c^{3} + 48 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(c^{4} d^{5} x^{7} - c^{5} d^{4} x^{4} - 2 \, c^{6} d^{3} x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(c^{2} d^{4} x^{8} - 7 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} - 6 \, {\left(1296 \, \left(\frac{1}{432}\right)^{\frac{5}{6}} c^{5} d^{5} x^{5} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{3}} {\left(5 \, c^{3} d^{4} x^{6} - 20 \, c^{4} d^{3} x^{3} - 16 \, c^{5} d^{2}\right)} \sqrt{-\frac{1}{c^{5} d^{4}}} + 2 \, \left(\frac{1}{432}\right)^{\frac{1}{6}} {\left(c d^{3} x^{7} - 16 \, c^{2} d^{2} x^{4} - 8 \, c^{3} d x\right)} \left(-\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} \sqrt{d x^{3} + c}}{d^{3} x^{9} + 12 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}\right)"," ",0,"1/9*sqrt(3)*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*arctan(-1/3*(3*(sqrt(3)*sqrt(1/3)*c^3*d^2*x*sqrt(-1/(c^5*d^4)) + 2*sqrt(3)*(1/432)^(1/6)*c*d*x^2*(-1/(c^5*d^4))^(1/6) + 24*sqrt(3)*(1/432)^(5/6)*(c^4*d^4*x^3 + 4*c^5*d^3)*(-1/(c^5*d^4))^(5/6))*sqrt(d*x^3 + c) + (2*sqrt(3)*(1/2)^(1/3)*(c^2*d^2*x^3 + c^3*d)*(-1/(c^5*d^4))^(1/3) + sqrt(3)*(d*x^4 + c*x) + 3*(sqrt(3)*sqrt(1/3)*c^3*d^2*x*sqrt(-1/(c^5*d^4)) + 2*sqrt(3)*(1/432)^(1/6)*c*d*x^2*(-1/(c^5*d^4))^(1/6) - 24*sqrt(3)*(1/432)^(5/6)*(c^4*d^4*x^3 - 2*c^5*d^3)*(-1/(c^5*d^4))^(5/6))*sqrt(d*x^3 + c))*sqrt((d^3*x^9 + 60*c*d^2*x^6 - 32*c^3 - 24*(1/2)^(2/3)*(c^4*d^5*x^7 + 5*c^5*d^4*x^4 + 4*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) + 12*(648*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) - sqrt(1/3)*(c^3*d^4*x^6 - 16*c^4*d^3*x^3 - 8*c^5*d^2)*sqrt(-1/(c^5*d^4)) - (1/432)^(1/6)*(c*d^3*x^7 + 2*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3)))/(d*x^4 + c*x)) + 1/9*sqrt(3)*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*arctan(-1/3*(3*(sqrt(3)*sqrt(1/3)*c^3*d^2*x*sqrt(-1/(c^5*d^4)) + 2*sqrt(3)*(1/432)^(1/6)*c*d*x^2*(-1/(c^5*d^4))^(1/6) + 24*sqrt(3)*(1/432)^(5/6)*(c^4*d^4*x^3 + 4*c^5*d^3)*(-1/(c^5*d^4))^(5/6))*sqrt(d*x^3 + c) - (2*sqrt(3)*(1/2)^(1/3)*(c^2*d^2*x^3 + c^3*d)*(-1/(c^5*d^4))^(1/3) + sqrt(3)*(d*x^4 + c*x) - 3*(sqrt(3)*sqrt(1/3)*c^3*d^2*x*sqrt(-1/(c^5*d^4)) + 2*sqrt(3)*(1/432)^(1/6)*c*d*x^2*(-1/(c^5*d^4))^(1/6) - 24*sqrt(3)*(1/432)^(5/6)*(c^4*d^4*x^3 - 2*c^5*d^3)*(-1/(c^5*d^4))^(5/6))*sqrt(d*x^3 + c))*sqrt((d^3*x^9 + 60*c*d^2*x^6 - 32*c^3 - 24*(1/2)^(2/3)*(c^4*d^5*x^7 + 5*c^5*d^4*x^4 + 4*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) - 12*(648*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) - sqrt(1/3)*(c^3*d^4*x^6 - 16*c^4*d^3*x^3 - 8*c^5*d^2)*sqrt(-1/(c^5*d^4)) - (1/432)^(1/6)*(c*d^3*x^7 + 2*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3)))/(d*x^4 + c*x)) - 1/36*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*log((d^3*x^9 + 60*c*d^2*x^6 - 32*c^3 - 24*(1/2)^(2/3)*(c^4*d^5*x^7 + 5*c^5*d^4*x^4 + 4*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) + 12*(648*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) - sqrt(1/3)*(c^3*d^4*x^6 - 16*c^4*d^3*x^3 - 8*c^5*d^2)*sqrt(-1/(c^5*d^4)) - (1/432)^(1/6)*(c*d^3*x^7 + 2*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3)) + 1/36*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*log((d^3*x^9 + 60*c*d^2*x^6 - 32*c^3 - 24*(1/2)^(2/3)*(c^4*d^5*x^7 + 5*c^5*d^4*x^4 + 4*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) - 12*(648*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) - sqrt(1/3)*(c^3*d^4*x^6 - 16*c^4*d^3*x^3 - 8*c^5*d^2)*sqrt(-1/(c^5*d^4)) - (1/432)^(1/6)*(c*d^3*x^7 + 2*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3)) + 1/18*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*log((d^3*x^9 - 66*c*d^2*x^6 - 72*c^2*d*x^3 - 32*c^3 + 48*(1/2)^(2/3)*(c^4*d^5*x^7 - c^5*d^4*x^4 - 2*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) + 6*(1296*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) + sqrt(1/3)*(5*c^3*d^4*x^6 - 20*c^4*d^3*x^3 - 16*c^5*d^2)*sqrt(-1/(c^5*d^4)) + 2*(1/432)^(1/6)*(c*d^3*x^7 - 16*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3)) - 1/18*(1/432)^(1/6)*(-1/(c^5*d^4))^(1/6)*log((d^3*x^9 - 66*c*d^2*x^6 - 72*c^2*d*x^3 - 32*c^3 + 48*(1/2)^(2/3)*(c^4*d^5*x^7 - c^5*d^4*x^4 - 2*c^6*d^3*x)*(-1/(c^5*d^4))^(2/3) + 12*(1/2)^(1/3)*(c^2*d^4*x^8 - 7*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(-1/(c^5*d^4))^(1/3) - 6*(1296*(1/432)^(5/6)*c^5*d^5*x^5*(-1/(c^5*d^4))^(5/6) + sqrt(1/3)*(5*c^3*d^4*x^6 - 20*c^4*d^3*x^3 - 16*c^5*d^2)*sqrt(-1/(c^5*d^4)) + 2*(1/432)^(1/6)*(c*d^3*x^7 - 16*c^2*d^2*x^4 - 8*c^3*d*x)*(-1/(c^5*d^4))^(1/6))*sqrt(d*x^3 + c))/(d^3*x^9 + 12*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3))","B",0
277,0,0,0,2.648499," ","integrate(1/x^2/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{8} + 5 \, c d x^{5} + 4 \, c^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^8 + 5*c*d*x^5 + 4*c^2*x^2), x)","F",0
278,0,0,0,1.728600," ","integrate(x^3/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{3}}{d^{2} x^{6} + 5 \, c d x^{3} + 4 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^3/(d^2*x^6 + 5*c*d*x^3 + 4*c^2), x)","F",0
279,0,0,0,1.979167," ","integrate(1/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{6} + 5 \, c d x^{3} + 4 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^6 + 5*c*d*x^3 + 4*c^2), x)","F",0
280,0,0,0,4.700508," ","integrate(1/x^3/(d*x^3+4*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{9} + 5 \, c d x^{6} + 4 \, c^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^9 + 5*c*d*x^6 + 4*c^2*x^3), x)","F",0
281,1,1191,0,1.259684," ","integrate(x/(-x^3+4)/(-x^3+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{31104} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{144 \, {\left(36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} + {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304\right)}}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}\right) - \frac{1}{31104} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{36 \, {\left(36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} + {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304\right)}}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}\right) + \frac{1}{31104} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{144 \, {\left(36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} - {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304\right)}}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}\right) + \frac{1}{31104} \cdot 432^{\frac{5}{6}} \sqrt{3} \log\left(\frac{36 \, {\left(36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} - {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304\right)}}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}\right) - \frac{1}{1944} \cdot 432^{\frac{5}{6}} \arctan\left(\frac{\sqrt{-x^{3} + 1} {\left(72 \cdot 432^{\frac{1}{6}} x^{2} + 432^{\frac{5}{6}} x + 72 \, \sqrt{3}\right)}}{216 \, {\left(2 \, x^{3} - 1\right)}}\right) + \frac{1}{3888} \cdot 432^{\frac{5}{6}} \arctan\left(-\frac{6 \, \sqrt{-x^{3} + 1} {\left(432^{\frac{5}{6}} {\left(x^{4} + 2 \, x\right)} - 36 \, \sqrt{3} {\left(x^{3} - 4\right)} + 18 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 8 \, x^{2}\right)}\right)} + {\left(108 \, \sqrt{3} 2^{\frac{2}{3}} {\left(x^{5} - x^{2}\right)} - 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(x^{4} - x\right)} - 108 \, \sqrt{3} {\left(x^{6} - x^{3}\right)} - \sqrt{-x^{3} + 1} {\left(432^{\frac{5}{6}} {\left(2 \, x^{4} + x\right)} - 36 \, \sqrt{3} {\left(5 \, x^{3} - 8\right)} - 18 \cdot 432^{\frac{1}{6}} {\left(x^{5} - 10 \, x^{2}\right)}\right)}\right)} \sqrt{\frac{36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} + {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}}}{648 \, {\left(x^{6} + 3 \, x^{3} - 4\right)}}\right) + \frac{1}{3888} \cdot 432^{\frac{5}{6}} \arctan\left(-\frac{6 \, \sqrt{-x^{3} + 1} {\left(432^{\frac{5}{6}} {\left(x^{4} + 2 \, x\right)} - 36 \, \sqrt{3} {\left(x^{3} - 4\right)} + 18 \cdot 432^{\frac{1}{6}} {\left(x^{5} + 8 \, x^{2}\right)}\right)} - {\left(108 \, \sqrt{3} 2^{\frac{2}{3}} {\left(x^{5} - x^{2}\right)} - 216 \, \sqrt{3} 2^{\frac{1}{3}} {\left(x^{4} - x\right)} - 108 \, \sqrt{3} {\left(x^{6} - x^{3}\right)} + \sqrt{-x^{3} + 1} {\left(432^{\frac{5}{6}} {\left(2 \, x^{4} + x\right)} - 36 \, \sqrt{3} {\left(5 \, x^{3} - 8\right)} - 18 \cdot 432^{\frac{1}{6}} {\left(x^{5} - 10 \, x^{2}\right)}\right)}\right)} \sqrt{\frac{36 \, x^{9} - 8208 \, x^{6} + 9504 \, x^{3} - 648 \cdot 2^{\frac{2}{3}} {\left(x^{8} - 5 \, x^{5} + 4 \, x^{2}\right)} - {\left(2592 \, x^{6} - 2592 \, x^{3} - 432^{\frac{5}{6}} \sqrt{3} {\left(x^{7} - 26 \, x^{4} + 16 \, x\right)} - 216 \cdot 432^{\frac{1}{6}} \sqrt{3} {\left(7 \, x^{5} - 4 \, x^{2}\right)}\right)} \sqrt{-x^{3} + 1} + 3888 \cdot 2^{\frac{1}{3}} {\left(x^{7} - x^{4}\right)} - 2304}{x^{9} - 12 \, x^{6} + 48 \, x^{3} - 64}}}{648 \, {\left(x^{6} + 3 \, x^{3} - 4\right)}}\right)"," ",0,"-1/31104*432^(5/6)*sqrt(3)*log(144*(36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) + (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)) - 1/31104*432^(5/6)*sqrt(3)*log(36*(36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) + (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)) + 1/31104*432^(5/6)*sqrt(3)*log(144*(36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) - (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)) + 1/31104*432^(5/6)*sqrt(3)*log(36*(36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) - (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)) - 1/1944*432^(5/6)*arctan(1/216*sqrt(-x^3 + 1)*(72*432^(1/6)*x^2 + 432^(5/6)*x + 72*sqrt(3))/(2*x^3 - 1)) + 1/3888*432^(5/6)*arctan(-1/648*(6*sqrt(-x^3 + 1)*(432^(5/6)*(x^4 + 2*x) - 36*sqrt(3)*(x^3 - 4) + 18*432^(1/6)*(x^5 + 8*x^2)) + (108*sqrt(3)*2^(2/3)*(x^5 - x^2) - 216*sqrt(3)*2^(1/3)*(x^4 - x) - 108*sqrt(3)*(x^6 - x^3) - sqrt(-x^3 + 1)*(432^(5/6)*(2*x^4 + x) - 36*sqrt(3)*(5*x^3 - 8) - 18*432^(1/6)*(x^5 - 10*x^2)))*sqrt((36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) + (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)))/(x^6 + 3*x^3 - 4)) + 1/3888*432^(5/6)*arctan(-1/648*(6*sqrt(-x^3 + 1)*(432^(5/6)*(x^4 + 2*x) - 36*sqrt(3)*(x^3 - 4) + 18*432^(1/6)*(x^5 + 8*x^2)) - (108*sqrt(3)*2^(2/3)*(x^5 - x^2) - 216*sqrt(3)*2^(1/3)*(x^4 - x) - 108*sqrt(3)*(x^6 - x^3) + sqrt(-x^3 + 1)*(432^(5/6)*(2*x^4 + x) - 36*sqrt(3)*(5*x^3 - 8) - 18*432^(1/6)*(x^5 - 10*x^2)))*sqrt((36*x^9 - 8208*x^6 + 9504*x^3 - 648*2^(2/3)*(x^8 - 5*x^5 + 4*x^2) - (2592*x^6 - 2592*x^3 - 432^(5/6)*sqrt(3)*(x^7 - 26*x^4 + 16*x) - 216*432^(1/6)*sqrt(3)*(7*x^5 - 4*x^2))*sqrt(-x^3 + 1) + 3888*2^(1/3)*(x^7 - x^4) - 2304)/(x^9 - 12*x^6 + 48*x^3 - 64)))/(x^6 + 3*x^3 - 4))","B",0
282,1,169,0,0.903579," ","integrate(x^11*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(26880 \, c^{\frac{7}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(5 \, d^{3} x^{9} + 57 \, c d^{2} x^{6} + 764 \, c^{2} d x^{3} + 18632 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{105 \, d^{4}}, -\frac{2 \, {\left(53760 \, \sqrt{-c} c^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(5 \, d^{3} x^{9} + 57 \, c d^{2} x^{6} + 764 \, c^{2} d x^{3} + 18632 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{105 \, d^{4}}\right]"," ",0,"[2/105*(26880*c^(7/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (5*d^3*x^9 + 57*c*d^2*x^6 + 764*c^2*d*x^3 + 18632*c^3)*sqrt(d*x^3 + c))/d^4, -2/105*(53760*sqrt(-c)*c^3*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (5*d^3*x^9 + 57*c*d^2*x^6 + 764*c^2*d*x^3 + 18632*c^3)*sqrt(d*x^3 + c))/d^4]","A",0
283,1,147,0,0.751956," ","integrate(x^8*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(1440 \, c^{\frac{5}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(3 \, d^{2} x^{6} + 41 \, c d x^{3} + 998 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{3}}, -\frac{2 \, {\left(2880 \, \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(3 \, d^{2} x^{6} + 41 \, c d x^{3} + 998 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{3}}\right]"," ",0,"[2/45*(1440*c^(5/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (3*d^2*x^6 + 41*c*d*x^3 + 998*c^2)*sqrt(d*x^3 + c))/d^3, -2/45*(2880*sqrt(-c)*c^2*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (3*d^2*x^6 + 41*c*d*x^3 + 998*c^2)*sqrt(d*x^3 + c))/d^3]","A",0
284,1,121,0,0.994899," ","integrate(x^5*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(36 \, c^{\frac{3}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(d x^{3} + 25 \, c\right)} \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}, -\frac{2 \, {\left(72 \, \sqrt{-c} c \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d x^{3} + 25 \, c\right)} \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}\right]"," ",0,"[2/9*(36*c^(3/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (d*x^3 + 25*c)*sqrt(d*x^3 + c))/d^2, -2/9*(72*sqrt(-c)*c*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d*x^3 + 25*c)*sqrt(d*x^3 + c))/d^2]","A",0
285,1,101,0,0.815604," ","integrate(x^2*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 2 \, \sqrt{d x^{3} + c}}{3 \, d}, -\frac{2 \, {\left(3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + \sqrt{d x^{3} + c}\right)}}{3 \, d}\right]"," ",0,"[1/3*(3*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 2*sqrt(d*x^3 + c))/d, -2/3*(3*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(d*x^3 + c))/d]","A",0
286,1,138,0,0.908910," ","integrate((d*x^3+c)^(1/2)/x/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{24 \, c}, \frac{\sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right)}{12 \, c}\right]"," ",0,"[1/24*(3*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/c, 1/12*(sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 3*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c))/c]","A",0
287,1,186,0,0.759788," ","integrate((d*x^3+c)^(1/2)/x^4/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 5 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 8 \, \sqrt{d x^{3} + c} c}{192 \, c^{2} x^{3}}, \frac{5 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 3 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 4 \, \sqrt{d x^{3} + c} c}{96 \, c^{2} x^{3}}\right]"," ",0,"[1/192*(3*sqrt(c)*d*x^3*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 5*sqrt(c)*d*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 8*sqrt(d*x^3 + c)*c)/(c^2*x^3), 1/96*(5*sqrt(-c)*d*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 3*sqrt(-c)*d*x^3*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 4*sqrt(d*x^3 + c)*c)/(c^2*x^3)]","A",0
288,1,188,0,0.795389," ","integrate((d*x^3+c)^(1/2)/x^7/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{c} d^{2} x^{6} \log\left(\frac{d^{2} x^{6} + 24 \, c d x^{3} + 8 \, {\left(d x^{3} + 4 \, c\right)} \sqrt{d x^{3} + c} \sqrt{c} + 32 \, c^{2}}{d x^{6} - 8 \, c x^{3}}\right) - 8 \, {\left(3 \, c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{1536 \, c^{3} x^{6}}, -\frac{3 \, \sqrt{-c} d^{2} x^{6} \arctan\left(\frac{{\left(d x^{3} + 4 \, c\right)} \sqrt{d x^{3} + c} \sqrt{-c}}{4 \, {\left(c d x^{3} + c^{2}\right)}}\right) + 4 \, {\left(3 \, c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{768 \, c^{3} x^{6}}\right]"," ",0,"[1/1536*(3*sqrt(c)*d^2*x^6*log((d^2*x^6 + 24*c*d*x^3 + 8*(d*x^3 + 4*c)*sqrt(d*x^3 + c)*sqrt(c) + 32*c^2)/(d*x^6 - 8*c*x^3)) - 8*(3*c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^3*x^6), -1/768*(3*sqrt(-c)*d^2*x^6*arctan(1/4*(d*x^3 + 4*c)*sqrt(d*x^3 + c)*sqrt(-c)/(c*d*x^3 + c^2)) + 4*(3*c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^3*x^6)]","A",0
289,0,0,0,52.126941," ","integrate(x^7*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{7}}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^7/(d*x^3 - 8*c), x)","F",0
290,0,0,0,13.260201," ","integrate(x^4*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{4}}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^4/(d*x^3 - 8*c), x)","F",0
291,0,0,0,2.768464," ","integrate(x*(d*x^3+c)^(1/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x/(d*x^3 - 8*c), x)","F",0
292,0,0,0,1.676609," ","integrate((d*x^3+c)^(1/2)/x^2/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d x^{5} - 8 \, c x^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d*x^5 - 8*c*x^2), x)","F",0
293,0,0,0,3.043324," ","integrate((d*x^3+c)^(1/2)/x^5/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d x^{8} - 8 \, c x^{5}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d*x^8 - 8*c*x^5), x)","F",0
294,0,0,0,6.519759," ","integrate((d*x^3+c)^(1/2)/x^8/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d x^{11} - 8 \, c x^{8}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d*x^11 - 8*c*x^8), x)","F",0
295,1,191,0,0.552805," ","integrate(x^11*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(2177280 \, c^{\frac{9}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(35 \, d^{4} x^{12} + 410 \, c d^{3} x^{9} + 4611 \, c^{2} d^{2} x^{6} + 61892 \, c^{3} d x^{3} + 1509176 \, c^{4}\right)} \sqrt{d x^{3} + c}\right)}}{945 \, d^{4}}, -\frac{2 \, {\left(4354560 \, \sqrt{-c} c^{4} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(35 \, d^{4} x^{12} + 410 \, c d^{3} x^{9} + 4611 \, c^{2} d^{2} x^{6} + 61892 \, c^{3} d x^{3} + 1509176 \, c^{4}\right)} \sqrt{d x^{3} + c}\right)}}{945 \, d^{4}}\right]"," ",0,"[2/945*(2177280*c^(9/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (35*d^4*x^12 + 410*c*d^3*x^9 + 4611*c^2*d^2*x^6 + 61892*c^3*d*x^3 + 1509176*c^4)*sqrt(d*x^3 + c))/d^4, -2/945*(4354560*sqrt(-c)*c^4*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (35*d^4*x^12 + 410*c*d^3*x^9 + 4611*c^2*d^2*x^6 + 61892*c^3*d*x^3 + 1509176*c^4)*sqrt(d*x^3 + c))/d^4]","A",0
296,1,169,0,0.962303," ","integrate(x^8*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(90720 \, c^{\frac{7}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(15 \, d^{3} x^{9} + 192 \, c d^{2} x^{6} + 2579 \, c^{2} d x^{3} + 62882 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{315 \, d^{3}}, -\frac{2 \, {\left(181440 \, \sqrt{-c} c^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(15 \, d^{3} x^{9} + 192 \, c d^{2} x^{6} + 2579 \, c^{2} d x^{3} + 62882 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{315 \, d^{3}}\right]"," ",0,"[2/315*(90720*c^(7/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (15*d^3*x^9 + 192*c*d^2*x^6 + 2579*c^2*d*x^3 + 62882*c^3)*sqrt(d*x^3 + c))/d^3, -2/315*(181440*sqrt(-c)*c^3*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (15*d^3*x^9 + 192*c*d^2*x^6 + 2579*c^2*d*x^3 + 62882*c^3)*sqrt(d*x^3 + c))/d^3]","A",0
297,1,147,0,0.627132," ","integrate(x^5*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(1620 \, c^{\frac{5}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(3 \, d^{2} x^{6} + 46 \, c d x^{3} + 1123 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{2}}, -\frac{2 \, {\left(3240 \, \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(3 \, d^{2} x^{6} + 46 \, c d x^{3} + 1123 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{2}}\right]"," ",0,"[2/45*(1620*c^(5/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (3*d^2*x^6 + 46*c*d*x^3 + 1123*c^2)*sqrt(d*x^3 + c))/d^2, -2/45*(3240*sqrt(-c)*c^2*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (3*d^2*x^6 + 46*c*d*x^3 + 1123*c^2)*sqrt(d*x^3 + c))/d^2]","A",0
298,1,121,0,0.576783," ","integrate(x^2*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{81 \, c^{\frac{3}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 2 \, {\left(d x^{3} + 28 \, c\right)} \sqrt{d x^{3} + c}}{9 \, d}, -\frac{2 \, {\left(81 \, \sqrt{-c} c \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d x^{3} + 28 \, c\right)} \sqrt{d x^{3} + c}\right)}}{9 \, d}\right]"," ",0,"[1/9*(81*c^(3/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 2*(d*x^3 + 28*c)*sqrt(d*x^3 + c))/d, -2/9*(81*sqrt(-c)*c*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d*x^3 + 28*c)*sqrt(d*x^3 + c))/d]","A",0
299,1,152,0,0.848995," ","integrate((d*x^3+c)^(3/2)/x/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{9}{8} \, \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + \frac{1}{24} \, \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - \frac{2}{3} \, \sqrt{d x^{3} + c}, \frac{1}{12} \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \frac{9}{4} \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - \frac{2}{3} \, \sqrt{d x^{3} + c}\right]"," ",0,"[9/8*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 1/24*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2/3*sqrt(d*x^3 + c), 1/12*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 9/4*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 2/3*sqrt(d*x^3 + c)]","A",0
300,1,186,0,0.863555," ","integrate((d*x^3+c)^(3/2)/x^4/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{27 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 13 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 8 \, \sqrt{d x^{3} + c} c}{192 \, c x^{3}}, \frac{13 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 27 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 4 \, \sqrt{d x^{3} + c} c}{96 \, c x^{3}}\right]"," ",0,"[1/192*(27*sqrt(c)*d*x^3*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 13*sqrt(c)*d*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 8*sqrt(d*x^3 + c)*c)/(c*x^3), 1/96*(13*sqrt(-c)*d*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 27*sqrt(-c)*d*x^3*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 4*sqrt(d*x^3 + c)*c)/(c*x^3)]","A",0
301,1,218,0,0.873515," ","integrate((d*x^3+c)^(3/2)/x^7/(-d*x^3+8*c),x, algorithm=""fricas"")","\left[\frac{27 \, \sqrt{c} d^{2} x^{6} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 37 \, \sqrt{c} d^{2} x^{6} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 8 \, {\left(11 \, c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{1536 \, c^{2} x^{6}}, \frac{37 \, \sqrt{-c} d^{2} x^{6} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 27 \, \sqrt{-c} d^{2} x^{6} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 4 \, {\left(11 \, c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{768 \, c^{2} x^{6}}\right]"," ",0,"[1/1536*(27*sqrt(c)*d^2*x^6*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 37*sqrt(c)*d^2*x^6*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 8*(11*c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^2*x^6), 1/768*(37*sqrt(-c)*d^2*x^6*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 27*sqrt(-c)*d^2*x^6*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 4*(11*c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^2*x^6)]","A",0
302,0,0,0,121.673783," ","integrate(x^7*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{10} + c x^{7}\right)} \sqrt{d x^{3} + c}}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-(d*x^10 + c*x^7)*sqrt(d*x^3 + c)/(d*x^3 - 8*c), x)","F",0
303,0,0,0,36.331746," ","integrate(x^4*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{7} + c x^{4}\right)} \sqrt{d x^{3} + c}}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-(d*x^7 + c*x^4)*sqrt(d*x^3 + c)/(d*x^3 - 8*c), x)","F",0
304,0,0,0,6.699184," ","integrate(x*(d*x^3+c)^(3/2)/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{4} + c x\right)} \sqrt{d x^{3} + c}}{d x^{3} - 8 \, c}, x\right)"," ",0,"integral(-(d*x^4 + c*x)*sqrt(d*x^3 + c)/(d*x^3 - 8*c), x)","F",0
305,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/x^2/(-d*x^3+8*c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,0,0,0,2.299750," ","integrate((d*x^3+c)^(3/2)/x^5/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{3} + c\right)}^{\frac{3}{2}}}{d x^{8} - 8 \, c x^{5}}, x\right)"," ",0,"integral(-(d*x^3 + c)^(3/2)/(d*x^8 - 8*c*x^5), x)","F",0
307,0,0,0,6.376929," ","integrate((d*x^3+c)^(3/2)/x^8/(-d*x^3+8*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x^{3} + c\right)}^{\frac{3}{2}}}{d x^{11} - 8 \, c x^{8}}, x\right)"," ",0,"integral(-(d*x^3 + c)^(3/2)/(d*x^11 - 8*c*x^8), x)","F",0
308,1,146,0,0.917722," ","integrate(x^11/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(1280 \, c^{\frac{5}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 3 \, {\left(d^{2} x^{6} + 12 \, c d x^{3} + 296 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{4}}, -\frac{2 \, {\left(2560 \, \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(d^{2} x^{6} + 12 \, c d x^{3} + 296 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, d^{4}}\right]"," ",0,"[2/45*(1280*c^(5/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 3*(d^2*x^6 + 12*c*d*x^3 + 296*c^2)*sqrt(d*x^3 + c))/d^4, -2/45*(2560*sqrt(-c)*c^2*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(d^2*x^6 + 12*c*d*x^3 + 296*c^2)*sqrt(d*x^3 + c))/d^4]","A",0
309,1,121,0,1.098249," ","integrate(x^8/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(32 \, c^{\frac{3}{2}} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - {\left(d x^{3} + 22 \, c\right)} \sqrt{d x^{3} + c}\right)}}{9 \, d^{3}}, -\frac{2 \, {\left(64 \, \sqrt{-c} c \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d x^{3} + 22 \, c\right)} \sqrt{d x^{3} + c}\right)}}{9 \, d^{3}}\right]"," ",0,"[2/9*(32*c^(3/2)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - (d*x^3 + 22*c)*sqrt(d*x^3 + c))/d^3, -2/9*(64*sqrt(-c)*c*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d*x^3 + 22*c)*sqrt(d*x^3 + c))/d^3]","A",0
310,1,103,0,0.646487," ","integrate(x^5/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 3 \, \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}, -\frac{2 \, {\left(8 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, \sqrt{d x^{3} + c}\right)}}{9 \, d^{2}}\right]"," ",0,"[2/9*(4*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 3*sqrt(d*x^3 + c))/d^2, -2/9*(8*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*sqrt(d*x^3 + c))/d^2]","A",0
311,1,78,0,0.835892," ","integrate(x^2/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right)}{9 \, \sqrt{c} d}, -\frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right)}{9 \, c d}\right]"," ",0,"[1/9*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c))/(sqrt(c)*d), -2/9*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c)/(c*d)]","A",0
312,1,139,0,0.887129," ","integrate(1/x/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{72 \, c^{2}}, \frac{3 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right)}{36 \, c^{2}}\right]"," ",0,"[1/72*(sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/c^2, 1/36*(3*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c))/c^2]","A",0
313,1,184,0,0.801245," ","integrate(1/x^4/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d x^{3} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 9 \, \sqrt{c} d x^{3} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, \sqrt{d x^{3} + c} c}{576 \, c^{3} x^{3}}, -\frac{9 \, \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{-c} d x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, \sqrt{d x^{3} + c} c}{288 \, c^{3} x^{3}}\right]"," ",0,"[1/576*(sqrt(c)*d*x^3*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 9*sqrt(c)*d*x^3*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*sqrt(d*x^3 + c)*c)/(c^3*x^3), -1/288*(9*sqrt(-c)*d*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(-c)*d*x^3*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*sqrt(d*x^3 + c)*c)/(c^3*x^3)]","A",0
314,1,217,0,0.808112," ","integrate(1/x^7/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d^{2} x^{6} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 63 \, \sqrt{c} d^{2} x^{6} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 24 \, {\left(5 \, c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{4608 \, c^{4} x^{6}}, \frac{63 \, \sqrt{-c} d^{2} x^{6} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \sqrt{-c} d^{2} x^{6} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(5 \, c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{2304 \, c^{4} x^{6}}\right]"," ",0,"[1/4608*(sqrt(c)*d^2*x^6*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 63*sqrt(c)*d^2*x^6*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 24*(5*c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^4*x^6), 1/2304*(63*sqrt(-c)*d^2*x^6*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - sqrt(-c)*d^2*x^6*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(5*c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^4*x^6)]","A",0
315,0,0,0,24.036325," ","integrate(x^7/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{7}}{d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^7/(d^2*x^6 - 7*c*d*x^3 - 8*c^2), x)","F",0
316,0,0,0,4.825625," ","integrate(x^4/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{4}}{d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^4/(d^2*x^6 - 7*c*d*x^3 - 8*c^2), x)","F",0
317,1,2459,0,2.470628," ","integrate(x/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","-\frac{1}{54} \, \sqrt{3} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \arctan\left(\frac{{\left(9 \, \sqrt{3} c d^{2} x^{5} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(c^{4} d^{5} x^{6} - 40 \, c^{5} d^{4} x^{3} - 32 \, c^{6} d^{3}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + 3 \, \sqrt{3} {\left(5 \, c^{3} d^{3} x^{4} + 8 \, c^{4} d^{2} x\right)} \sqrt{\frac{1}{c^{5} d^{4}}}\right)} \sqrt{d x^{3} + c} + {\left(18 \, \sqrt{3} {\left(c^{4} d^{4} x^{5} + c^{5} d^{3} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \sqrt{3} {\left(c^{2} d^{3} x^{6} - c^{3} d^{2} x^{3} - 2 \, c^{4} d\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + 3 \, \sqrt{3} {\left(d^{2} x^{7} + 5 \, c d x^{4} + 4 \, c^{2} x\right)} + \sqrt{d x^{3} + c} {\left(\sqrt{3} {\left(c^{4} d^{5} x^{6} + 32 \, c^{5} d^{4} x^{3} + 40 \, c^{6} d^{3}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + 3 \, \sqrt{3} {\left(7 \, c^{3} d^{3} x^{4} + 4 \, c^{4} d^{2} x\right)} \sqrt{\frac{1}{c^{5} d^{4}}} + 9 \, \sqrt{3} {\left(c d^{2} x^{5} + 2 \, c^{2} d x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{d^{3} x^{9} - 276 \, c d^{2} x^{6} - 1608 \, c^{2} d x^{3} - 1088 \, c^{3} - 18 \, {\left(c^{4} d^{5} x^{7} - 52 \, c^{5} d^{4} x^{4} - 80 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 6 \, \sqrt{d x^{3} + c} {\left(24 \, {\left(c^{5} d^{5} x^{5} + c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - 4 \, {\left(c^{3} d^{4} x^{6} + 41 \, c^{4} d^{3} x^{3} + 40 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} - {\left(c d^{3} x^{7} - 28 \, c^{2} d^{2} x^{4} - 272 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 20 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}}}{9 \, {\left(d^{2} x^{7} - 7 \, c d x^{4} - 8 \, c^{2} x\right)}}\right) - \frac{1}{54} \, \sqrt{3} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \arctan\left(\frac{{\left(9 \, \sqrt{3} c d^{2} x^{5} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} - \sqrt{3} {\left(c^{4} d^{5} x^{6} - 40 \, c^{5} d^{4} x^{3} - 32 \, c^{6} d^{3}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + 3 \, \sqrt{3} {\left(5 \, c^{3} d^{3} x^{4} + 8 \, c^{4} d^{2} x\right)} \sqrt{\frac{1}{c^{5} d^{4}}}\right)} \sqrt{d x^{3} + c} - {\left(18 \, \sqrt{3} {\left(c^{4} d^{4} x^{5} + c^{5} d^{3} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 12 \, \sqrt{3} {\left(c^{2} d^{3} x^{6} - c^{3} d^{2} x^{3} - 2 \, c^{4} d\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}} + 3 \, \sqrt{3} {\left(d^{2} x^{7} + 5 \, c d x^{4} + 4 \, c^{2} x\right)} - \sqrt{d x^{3} + c} {\left(\sqrt{3} {\left(c^{4} d^{5} x^{6} + 32 \, c^{5} d^{4} x^{3} + 40 \, c^{6} d^{3}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + 3 \, \sqrt{3} {\left(7 \, c^{3} d^{3} x^{4} + 4 \, c^{4} d^{2} x\right)} \sqrt{\frac{1}{c^{5} d^{4}}} + 9 \, \sqrt{3} {\left(c d^{2} x^{5} + 2 \, c^{2} d x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{d^{3} x^{9} - 276 \, c d^{2} x^{6} - 1608 \, c^{2} d x^{3} - 1088 \, c^{3} - 18 \, {\left(c^{4} d^{5} x^{7} - 52 \, c^{5} d^{4} x^{4} - 80 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} - 6 \, \sqrt{d x^{3} + c} {\left(24 \, {\left(c^{5} d^{5} x^{5} + c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - 4 \, {\left(c^{3} d^{4} x^{6} + 41 \, c^{4} d^{3} x^{3} + 40 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} - {\left(c d^{3} x^{7} - 28 \, c^{2} d^{2} x^{4} - 272 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 20 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}}}{9 \, {\left(d^{2} x^{7} - 7 \, c d x^{4} - 8 \, c^{2} x\right)}}\right) + \frac{1}{108} \, \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} + 318 \, c d^{2} x^{6} + 1200 \, c^{2} d x^{3} + 640 \, c^{3} + 18 \, {\left(5 \, c^{4} d^{5} x^{7} + 64 \, c^{5} d^{4} x^{4} + 32 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 6 \, \sqrt{d x^{3} + c} {\left(6 \, {\left(5 \, c^{5} d^{5} x^{5} + 32 \, c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + {\left(7 \, c^{3} d^{4} x^{6} + 152 \, c^{4} d^{3} x^{3} + 64 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} + {\left(c d^{3} x^{7} + 80 \, c^{2} d^{2} x^{4} + 160 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 38 \, c^{3} d^{3} x^{5} + 64 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}\right) - \frac{1}{108} \, \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} + 318 \, c d^{2} x^{6} + 1200 \, c^{2} d x^{3} + 640 \, c^{3} + 18 \, {\left(5 \, c^{4} d^{5} x^{7} + 64 \, c^{5} d^{4} x^{4} + 32 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} - 6 \, \sqrt{d x^{3} + c} {\left(6 \, {\left(5 \, c^{5} d^{5} x^{5} + 32 \, c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} + {\left(7 \, c^{3} d^{4} x^{6} + 152 \, c^{4} d^{3} x^{3} + 64 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} + {\left(c d^{3} x^{7} + 80 \, c^{2} d^{2} x^{4} + 160 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 38 \, c^{3} d^{3} x^{5} + 64 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}\right) - \frac{1}{216} \, \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} - 276 \, c d^{2} x^{6} - 1608 \, c^{2} d x^{3} - 1088 \, c^{3} - 18 \, {\left(c^{4} d^{5} x^{7} - 52 \, c^{5} d^{4} x^{4} - 80 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} + 6 \, \sqrt{d x^{3} + c} {\left(24 \, {\left(c^{5} d^{5} x^{5} + c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - 4 \, {\left(c^{3} d^{4} x^{6} + 41 \, c^{4} d^{3} x^{3} + 40 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} - {\left(c d^{3} x^{7} - 28 \, c^{2} d^{2} x^{4} - 272 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 20 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}\right) + \frac{1}{216} \, \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}} \log\left(\frac{d^{3} x^{9} - 276 \, c d^{2} x^{6} - 1608 \, c^{2} d x^{3} - 1088 \, c^{3} - 18 \, {\left(c^{4} d^{5} x^{7} - 52 \, c^{5} d^{4} x^{4} - 80 \, c^{6} d^{3} x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{2}{3}} - 6 \, \sqrt{d x^{3} + c} {\left(24 \, {\left(c^{5} d^{5} x^{5} + c^{6} d^{4} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{5}{6}} - 4 \, {\left(c^{3} d^{4} x^{6} + 41 \, c^{4} d^{3} x^{3} + 40 \, c^{5} d^{2}\right)} \sqrt{\frac{1}{c^{5} d^{4}}} - {\left(c d^{3} x^{7} - 28 \, c^{2} d^{2} x^{4} - 272 \, c^{3} d x\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{6}}\right)} + 18 \, {\left(c^{2} d^{4} x^{8} + 20 \, c^{3} d^{3} x^{5} - 8 \, c^{4} d^{2} x^{2}\right)} \left(\frac{1}{c^{5} d^{4}}\right)^{\frac{1}{3}}}{d^{3} x^{9} - 24 \, c d^{2} x^{6} + 192 \, c^{2} d x^{3} - 512 \, c^{3}}\right)"," ",0,"-1/54*sqrt(3)*(1/(c^5*d^4))^(1/6)*arctan(1/9*((9*sqrt(3)*c*d^2*x^5*(1/(c^5*d^4))^(1/6) - sqrt(3)*(c^4*d^5*x^6 - 40*c^5*d^4*x^3 - 32*c^6*d^3)*(1/(c^5*d^4))^(5/6) + 3*sqrt(3)*(5*c^3*d^3*x^4 + 8*c^4*d^2*x)*sqrt(1/(c^5*d^4)))*sqrt(d*x^3 + c) + (18*sqrt(3)*(c^4*d^4*x^5 + c^5*d^3*x^2)*(1/(c^5*d^4))^(2/3) + 12*sqrt(3)*(c^2*d^3*x^6 - c^3*d^2*x^3 - 2*c^4*d)*(1/(c^5*d^4))^(1/3) + 3*sqrt(3)*(d^2*x^7 + 5*c*d*x^4 + 4*c^2*x) + sqrt(d*x^3 + c)*(sqrt(3)*(c^4*d^5*x^6 + 32*c^5*d^4*x^3 + 40*c^6*d^3)*(1/(c^5*d^4))^(5/6) + 3*sqrt(3)*(7*c^3*d^3*x^4 + 4*c^4*d^2*x)*sqrt(1/(c^5*d^4)) + 9*sqrt(3)*(c*d^2*x^5 + 2*c^2*d*x^2)*(1/(c^5*d^4))^(1/6)))*sqrt((d^3*x^9 - 276*c*d^2*x^6 - 1608*c^2*d*x^3 - 1088*c^3 - 18*(c^4*d^5*x^7 - 52*c^5*d^4*x^4 - 80*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) + 6*sqrt(d*x^3 + c)*(24*(c^5*d^5*x^5 + c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) - 4*(c^3*d^4*x^6 + 41*c^4*d^3*x^3 + 40*c^5*d^2)*sqrt(1/(c^5*d^4)) - (c*d^3*x^7 - 28*c^2*d^2*x^4 - 272*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 20*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3)))/(d^2*x^7 - 7*c*d*x^4 - 8*c^2*x)) - 1/54*sqrt(3)*(1/(c^5*d^4))^(1/6)*arctan(1/9*((9*sqrt(3)*c*d^2*x^5*(1/(c^5*d^4))^(1/6) - sqrt(3)*(c^4*d^5*x^6 - 40*c^5*d^4*x^3 - 32*c^6*d^3)*(1/(c^5*d^4))^(5/6) + 3*sqrt(3)*(5*c^3*d^3*x^4 + 8*c^4*d^2*x)*sqrt(1/(c^5*d^4)))*sqrt(d*x^3 + c) - (18*sqrt(3)*(c^4*d^4*x^5 + c^5*d^3*x^2)*(1/(c^5*d^4))^(2/3) + 12*sqrt(3)*(c^2*d^3*x^6 - c^3*d^2*x^3 - 2*c^4*d)*(1/(c^5*d^4))^(1/3) + 3*sqrt(3)*(d^2*x^7 + 5*c*d*x^4 + 4*c^2*x) - sqrt(d*x^3 + c)*(sqrt(3)*(c^4*d^5*x^6 + 32*c^5*d^4*x^3 + 40*c^6*d^3)*(1/(c^5*d^4))^(5/6) + 3*sqrt(3)*(7*c^3*d^3*x^4 + 4*c^4*d^2*x)*sqrt(1/(c^5*d^4)) + 9*sqrt(3)*(c*d^2*x^5 + 2*c^2*d*x^2)*(1/(c^5*d^4))^(1/6)))*sqrt((d^3*x^9 - 276*c*d^2*x^6 - 1608*c^2*d*x^3 - 1088*c^3 - 18*(c^4*d^5*x^7 - 52*c^5*d^4*x^4 - 80*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) - 6*sqrt(d*x^3 + c)*(24*(c^5*d^5*x^5 + c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) - 4*(c^3*d^4*x^6 + 41*c^4*d^3*x^3 + 40*c^5*d^2)*sqrt(1/(c^5*d^4)) - (c*d^3*x^7 - 28*c^2*d^2*x^4 - 272*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 20*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3)))/(d^2*x^7 - 7*c*d*x^4 - 8*c^2*x)) + 1/108*(1/(c^5*d^4))^(1/6)*log((d^3*x^9 + 318*c*d^2*x^6 + 1200*c^2*d*x^3 + 640*c^3 + 18*(5*c^4*d^5*x^7 + 64*c^5*d^4*x^4 + 32*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) + 6*sqrt(d*x^3 + c)*(6*(5*c^5*d^5*x^5 + 32*c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) + (7*c^3*d^4*x^6 + 152*c^4*d^3*x^3 + 64*c^5*d^2)*sqrt(1/(c^5*d^4)) + (c*d^3*x^7 + 80*c^2*d^2*x^4 + 160*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 38*c^3*d^3*x^5 + 64*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3)) - 1/108*(1/(c^5*d^4))^(1/6)*log((d^3*x^9 + 318*c*d^2*x^6 + 1200*c^2*d*x^3 + 640*c^3 + 18*(5*c^4*d^5*x^7 + 64*c^5*d^4*x^4 + 32*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) - 6*sqrt(d*x^3 + c)*(6*(5*c^5*d^5*x^5 + 32*c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) + (7*c^3*d^4*x^6 + 152*c^4*d^3*x^3 + 64*c^5*d^2)*sqrt(1/(c^5*d^4)) + (c*d^3*x^7 + 80*c^2*d^2*x^4 + 160*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 38*c^3*d^3*x^5 + 64*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3)) - 1/216*(1/(c^5*d^4))^(1/6)*log((d^3*x^9 - 276*c*d^2*x^6 - 1608*c^2*d*x^3 - 1088*c^3 - 18*(c^4*d^5*x^7 - 52*c^5*d^4*x^4 - 80*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) + 6*sqrt(d*x^3 + c)*(24*(c^5*d^5*x^5 + c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) - 4*(c^3*d^4*x^6 + 41*c^4*d^3*x^3 + 40*c^5*d^2)*sqrt(1/(c^5*d^4)) - (c*d^3*x^7 - 28*c^2*d^2*x^4 - 272*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 20*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3)) + 1/216*(1/(c^5*d^4))^(1/6)*log((d^3*x^9 - 276*c*d^2*x^6 - 1608*c^2*d*x^3 - 1088*c^3 - 18*(c^4*d^5*x^7 - 52*c^5*d^4*x^4 - 80*c^6*d^3*x)*(1/(c^5*d^4))^(2/3) - 6*sqrt(d*x^3 + c)*(24*(c^5*d^5*x^5 + c^6*d^4*x^2)*(1/(c^5*d^4))^(5/6) - 4*(c^3*d^4*x^6 + 41*c^4*d^3*x^3 + 40*c^5*d^2)*sqrt(1/(c^5*d^4)) - (c*d^3*x^7 - 28*c^2*d^2*x^4 - 272*c^3*d*x)*(1/(c^5*d^4))^(1/6)) + 18*(c^2*d^4*x^8 + 20*c^3*d^3*x^5 - 8*c^4*d^2*x^2)*(1/(c^5*d^4))^(1/3))/(d^3*x^9 - 24*c*d^2*x^6 + 192*c^2*d*x^3 - 512*c^3))","B",0
318,0,0,0,1.618512," ","integrate(1/x^2/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{8} - 7 \, c d x^{5} - 8 \, c^{2} x^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^8 - 7*c*d*x^5 - 8*c^2*x^2), x)","F",0
319,0,0,0,3.599081," ","integrate(1/x^5/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{11} - 7 \, c d x^{8} - 8 \, c^{2} x^{5}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^11 - 7*c*d*x^8 - 8*c^2*x^5), x)","F",0
320,0,0,0,7.677192," ","integrate(1/x^8/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{14} - 7 \, c d x^{11} - 8 \, c^{2} x^{8}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^14 - 7*c*d*x^11 - 8*c^2*x^8), x)","F",0
321,0,0,0,1.458408," ","integrate(x^3/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{3}}{d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^3/(d^2*x^6 - 7*c*d*x^3 - 8*c^2), x)","F",0
322,0,0,0,1.128091," ","integrate(1/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^6 - 7*c*d*x^3 - 8*c^2), x)","F",0
323,0,0,0,2.333808," ","integrate(1/x^3/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{9} - 7 \, c d x^{6} - 8 \, c^{2} x^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^9 - 7*c*d*x^6 - 8*c^2*x^3), x)","F",0
324,0,0,0,6.180526," ","integrate(1/x^6/(-d*x^3+8*c)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{2} x^{12} - 7 \, c d x^{9} - 8 \, c^{2} x^{6}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^2*x^12 - 7*c*d*x^9 - 8*c^2*x^6), x)","F",0
325,1,189,0,0.725492," ","integrate(x^11/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(256 \, {\left(c d x^{3} + c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 3 \, {\left(3 \, d^{2} x^{6} + 60 \, c d x^{3} + 56 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{5} x^{3} + c d^{4}\right)}}, -\frac{2 \, {\left(512 \, {\left(c d x^{3} + c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(3 \, d^{2} x^{6} + 60 \, c d x^{3} + 56 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{5} x^{3} + c d^{4}\right)}}\right]"," ",0,"[2/81*(256*(c*d*x^3 + c^2)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 3*(3*d^2*x^6 + 60*c*d*x^3 + 56*c^2)*sqrt(d*x^3 + c))/(d^5*x^3 + c*d^4), -2/81*(512*(c*d*x^3 + c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(3*d^2*x^6 + 60*c*d*x^3 + 56*c^2)*sqrt(d*x^3 + c))/(d^5*x^3 + c*d^4)]","A",0
326,1,161,0,0.624251," ","integrate(x^8/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(32 \, {\left(d x^{3} + c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 3 \, {\left(9 \, d x^{3} + 10 \, c\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{4} x^{3} + c d^{3}\right)}}, -\frac{2 \, {\left(64 \, {\left(d x^{3} + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(9 \, d x^{3} + 10 \, c\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{4} x^{3} + c d^{3}\right)}}\right]"," ",0,"[2/81*(32*(d*x^3 + c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 3*(9*d*x^3 + 10*c)*sqrt(d*x^3 + c))/(d^4*x^3 + c*d^3), -2/81*(64*(d*x^3 + c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(9*d*x^3 + 10*c)*sqrt(d*x^3 + c))/(d^4*x^3 + c*d^3)]","A",0
327,1,149,0,0.507914," ","integrate(x^5/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4 \, {\left(d x^{3} + c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, \sqrt{d x^{3} + c} c\right)}}{81 \, {\left(c d^{3} x^{3} + c^{2} d^{2}\right)}}, -\frac{2 \, {\left(8 \, {\left(d x^{3} + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 3 \, \sqrt{d x^{3} + c} c\right)}}{81 \, {\left(c d^{3} x^{3} + c^{2} d^{2}\right)}}\right]"," ",0,"[2/81*(4*(d*x^3 + c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*sqrt(d*x^3 + c)*c)/(c*d^3*x^3 + c^2*d^2), -2/81*(8*(d*x^3 + c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 3*sqrt(d*x^3 + c)*c)/(c*d^3*x^3 + c^2*d^2)]","A",0
328,1,147,0,0.724589," ","integrate(x^2/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d x^{3} + c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 6 \, \sqrt{d x^{3} + c} c}{81 \, {\left(c^{2} d^{2} x^{3} + c^{3} d\right)}}, -\frac{2 \, {\left({\left(d x^{3} + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, \sqrt{d x^{3} + c} c\right)}}{81 \, {\left(c^{2} d^{2} x^{3} + c^{3} d\right)}}\right]"," ",0,"[1/81*((d*x^3 + c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 6*sqrt(d*x^3 + c)*c)/(c^2*d^2*x^3 + c^3*d), -2/81*((d*x^3 + c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*sqrt(d*x^3 + c)*c)/(c^2*d^2*x^3 + c^3*d)]","A",0
329,1,213,0,0.656959," ","integrate(1/x/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d x^{3} + c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 27 \, {\left(d x^{3} + c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 48 \, \sqrt{d x^{3} + c} c}{648 \, {\left(c^{3} d x^{3} + c^{4}\right)}}, \frac{27 \, {\left(d x^{3} + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left(d x^{3} + c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 24 \, \sqrt{d x^{3} + c} c}{324 \, {\left(c^{3} d x^{3} + c^{4}\right)}}\right]"," ",0,"[1/648*((d*x^3 + c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 27*(d*x^3 + c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 48*sqrt(d*x^3 + c)*c)/(c^3*d*x^3 + c^4), 1/324*(27*(d*x^3 + c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - (d*x^3 + c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 24*sqrt(d*x^3 + c)*c)/(c^3*d*x^3 + c^4)]","A",0
330,1,272,0,0.657946," ","integrate(1/x^4/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d^{2} x^{6} + c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 297 \, {\left(d^{2} x^{6} + c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, {\left(25 \, c d x^{3} + 9 \, c^{2}\right)} \sqrt{d x^{3} + c}}{5184 \, {\left(c^{4} d x^{6} + c^{5} x^{3}\right)}}, -\frac{297 \, {\left(d^{2} x^{6} + c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(d^{2} x^{6} + c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(25 \, c d x^{3} + 9 \, c^{2}\right)} \sqrt{d x^{3} + c}}{2592 \, {\left(c^{4} d x^{6} + c^{5} x^{3}\right)}}\right]"," ",0,"[1/5184*((d^2*x^6 + c*d*x^3)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 297*(d^2*x^6 + c*d*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*(25*c*d*x^3 + 9*c^2)*sqrt(d*x^3 + c))/(c^4*d*x^6 + c^5*x^3), -1/2592*(297*(d^2*x^6 + c*d*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (d^2*x^6 + c*d*x^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(25*c*d*x^3 + 9*c^2)*sqrt(d*x^3 + c))/(c^4*d*x^6 + c^5*x^3)]","A",0
331,1,303,0,0.790846," ","integrate(1/x^7/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d^{3} x^{9} + c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 2943 \, {\left(d^{3} x^{9} + c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 24 \, {\left(245 \, c d^{2} x^{6} + 81 \, c^{2} d x^{3} - 36 \, c^{3}\right)} \sqrt{d x^{3} + c}}{41472 \, {\left(c^{5} d x^{9} + c^{6} x^{6}\right)}}, \frac{2943 \, {\left(d^{3} x^{9} + c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left(d^{3} x^{9} + c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(245 \, c d^{2} x^{6} + 81 \, c^{2} d x^{3} - 36 \, c^{3}\right)} \sqrt{d x^{3} + c}}{20736 \, {\left(c^{5} d x^{9} + c^{6} x^{6}\right)}}\right]"," ",0,"[1/41472*((d^3*x^9 + c*d^2*x^6)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 2943*(d^3*x^9 + c*d^2*x^6)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 24*(245*c*d^2*x^6 + 81*c^2*d*x^3 - 36*c^3)*sqrt(d*x^3 + c))/(c^5*d*x^9 + c^6*x^6), 1/20736*(2943*(d^3*x^9 + c*d^2*x^6)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - (d^3*x^9 + c*d^2*x^6)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(245*c*d^2*x^6 + 81*c^2*d*x^3 - 36*c^3)*sqrt(d*x^3 + c))/(c^5*d*x^9 + c^6*x^6)]","A",0
332,0,0,0,9.965329," ","integrate(x^7/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{7}}{d^{3} x^{9} - 6 \, c d^{2} x^{6} - 15 \, c^{2} d x^{3} - 8 \, c^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^7/(d^3*x^9 - 6*c*d^2*x^6 - 15*c^2*d*x^3 - 8*c^3), x)","F",0
333,0,0,0,1.395155," ","integrate(x^4/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{4}}{d^{3} x^{9} - 6 \, c d^{2} x^{6} - 15 \, c^{2} d x^{3} - 8 \, c^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^4/(d^3*x^9 - 6*c*d^2*x^6 - 15*c^2*d*x^3 - 8*c^3), x)","F",0
334,0,0,0,1.447573," ","integrate(x/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x}{d^{3} x^{9} - 6 \, c d^{2} x^{6} - 15 \, c^{2} d x^{3} - 8 \, c^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x/(d^3*x^9 - 6*c*d^2*x^6 - 15*c^2*d*x^3 - 8*c^3), x)","F",0
335,0,0,0,1.733977," ","integrate(1/x^2/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{11} - 6 \, c d^{2} x^{8} - 15 \, c^{2} d x^{5} - 8 \, c^{3} x^{2}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^11 - 6*c*d^2*x^8 - 15*c^2*d*x^5 - 8*c^3*x^2), x)","F",0
336,0,0,0,5.422683," ","integrate(1/x^5/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{14} - 6 \, c d^{2} x^{11} - 15 \, c^{2} d x^{8} - 8 \, c^{3} x^{5}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^14 - 6*c*d^2*x^11 - 15*c^2*d*x^8 - 8*c^3*x^5), x)","F",0
337,0,0,0,12.501374," ","integrate(1/x^8/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{17} - 6 \, c d^{2} x^{14} - 15 \, c^{2} d x^{11} - 8 \, c^{3} x^{8}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^17 - 6*c*d^2*x^14 - 15*c^2*d*x^11 - 8*c^3*x^8), x)","F",0
338,0,0,0,1.850770," ","integrate(x^3/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c} x^{3}}{d^{3} x^{9} - 6 \, c d^{2} x^{6} - 15 \, c^{2} d x^{3} - 8 \, c^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)*x^3/(d^3*x^9 - 6*c*d^2*x^6 - 15*c^2*d*x^3 - 8*c^3), x)","F",0
339,0,0,0,1.832638," ","integrate(1/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{9} - 6 \, c d^{2} x^{6} - 15 \, c^{2} d x^{3} - 8 \, c^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^9 - 6*c*d^2*x^6 - 15*c^2*d*x^3 - 8*c^3), x)","F",0
340,0,0,0,4.168809," ","integrate(1/x^3/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{12} - 6 \, c d^{2} x^{9} - 15 \, c^{2} d x^{6} - 8 \, c^{3} x^{3}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^12 - 6*c*d^2*x^9 - 15*c^2*d*x^6 - 8*c^3*x^3), x)","F",0
341,0,0,0,10.113993," ","integrate(1/x^6/(-d*x^3+8*c)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{d x^{3} + c}}{d^{3} x^{15} - 6 \, c d^{2} x^{12} - 15 \, c^{2} d x^{9} - 8 \, c^{3} x^{6}}, x\right)"," ",0,"integral(-sqrt(d*x^3 + c)/(d^3*x^15 - 6*c*d^2*x^12 - 15*c^2*d*x^9 - 8*c^3*x^6), x)","F",0
342,0,0,0,39.016905," ","integrate(x*(b*x^3+a)^(1/2)/(b*x^3+2*a*(5+3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} - 6 \, \sqrt{3} a x + 10 \, a x\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral((b*x^4 - 6*sqrt(3)*a*x + 10*a*x)*sqrt(b*x^3 + a)/(b^2*x^6 + 20*a*b*x^3 - 8*a^2), x)","F",0
343,0,0,0,42.947214," ","integrate(x*(-b*x^3+a)^(1/2)/(-b*x^3+2*a*(5+3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} + 6 \, \sqrt{3} a x - 10 \, a x\right)} \sqrt{-b x^{3} + a}}{b^{2} x^{6} - 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral(-(b*x^4 + 6*sqrt(3)*a*x - 10*a*x)*sqrt(-b*x^3 + a)/(b^2*x^6 - 20*a*b*x^3 - 8*a^2), x)","F",0
344,0,0,0,41.458166," ","integrate(x*(b*x^3-a)^(1/2)/(b*x^3-2*a*(5+3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + 6 \, \sqrt{3} a x - 10 \, a x\right)} \sqrt{b x^{3} - a}}{b^{2} x^{6} - 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral((b*x^4 + 6*sqrt(3)*a*x - 10*a*x)*sqrt(b*x^3 - a)/(b^2*x^6 - 20*a*b*x^3 - 8*a^2), x)","F",0
345,0,0,0,40.153123," ","integrate(x*(-b*x^3-a)^(1/2)/(-b*x^3-2*a*(5+3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} - 6 \, \sqrt{3} a x + 10 \, a x\right)} \sqrt{-b x^{3} - a}}{b^{2} x^{6} + 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral(-(b*x^4 - 6*sqrt(3)*a*x + 10*a*x)*sqrt(-b*x^3 - a)/(b^2*x^6 + 20*a*b*x^3 - 8*a^2), x)","F",0
346,0,0,0,37.650196," ","integrate(x*(b*x^3+a)^(1/2)/(b*x^3+2*a*(5-3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + 6 \, \sqrt{3} a x + 10 \, a x\right)} \sqrt{b x^{3} + a}}{b^{2} x^{6} + 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral((b*x^4 + 6*sqrt(3)*a*x + 10*a*x)*sqrt(b*x^3 + a)/(b^2*x^6 + 20*a*b*x^3 - 8*a^2), x)","F",0
347,0,0,0,39.836977," ","integrate(x*(-b*x^3+a)^(1/2)/(-b*x^3+2*a*(5-3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} - 6 \, \sqrt{3} a x - 10 \, a x\right)} \sqrt{-b x^{3} + a}}{b^{2} x^{6} - 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral(-(b*x^4 - 6*sqrt(3)*a*x - 10*a*x)*sqrt(-b*x^3 + a)/(b^2*x^6 - 20*a*b*x^3 - 8*a^2), x)","F",0
348,0,0,0,41.573332," ","integrate(x*(b*x^3-a)^(1/2)/(-b*x^3+2*a*(5-3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} - 6 \, \sqrt{3} a x - 10 \, a x\right)} \sqrt{b x^{3} - a}}{b^{2} x^{6} - 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral(-(b*x^4 - 6*sqrt(3)*a*x - 10*a*x)*sqrt(b*x^3 - a)/(b^2*x^6 - 20*a*b*x^3 - 8*a^2), x)","F",0
349,0,0,0,39.109301," ","integrate(x*(-b*x^3-a)^(1/2)/(b*x^3+2*a*(5-3*3^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + 6 \, \sqrt{3} a x + 10 \, a x\right)} \sqrt{-b x^{3} - a}}{b^{2} x^{6} + 20 \, a b x^{3} - 8 \, a^{2}}, x\right)"," ",0,"integral((b*x^4 + 6*sqrt(3)*a*x + 10*a*x)*sqrt(-b*x^3 - a)/(b^2*x^6 + 20*a*b*x^3 - 8*a^2), x)","F",0
350,-2,0,0,0.000000," ","integrate(x/(b*x^3+2*a*(5+3*3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
351,-2,0,0,0.000000," ","integrate(x/(-b*x^3+2*a*(5+3*3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
352,-1,0,0,0.000000," ","integrate(x/(b*x^3-2*a*(5+3*3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-1,0,0,0.000000," ","integrate(x/(-b*x^3-2*a*(5+3*3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-2,0,0,0.000000," ","integrate(x/(b*x^3+2*a*(5-3*3^(1/2)))/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
355,-2,0,0,0.000000," ","integrate(x/(-b*x^3+2*a*(5-3*3^(1/2)))/(-b*x^3+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
356,1,5060,0,22.764454," ","integrate(x/(-b*x^3+2*a*(5-3*3^(1/2)))/(b*x^3-a)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \arctan\left(\frac{3 \, \sqrt{b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} - 1978 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} - 1142 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)} - {\left(6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(7 \, a^{2} b^{2} x^{3} - 7 \, a^{3} b - 4 \, \sqrt{3} {\left(a^{2} b^{2} x^{3} - a^{3} b\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b x^{4} - a x\right)} + 3 \, \sqrt{b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} + 1448 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} + 836 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{b^{4} x^{12} - 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} - 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} - 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} - 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} - 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} - 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 32 \, \sqrt{3} {\left(a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} + 8 \, a^{4}\right)} + 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} + 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} + 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} + 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} + 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} + 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} - 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}}}{3 \, {\left(b x^{4} - a x\right)}}\right) - \frac{1}{6} \, \sqrt{3} \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \arctan\left(\frac{3 \, \sqrt{b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} - 1978 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} - 1142 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)} + {\left(6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(7 \, a^{2} b^{2} x^{3} - 7 \, a^{3} b - 4 \, \sqrt{3} {\left(a^{2} b^{2} x^{3} - a^{3} b\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b x^{4} - a x\right)} - 3 \, \sqrt{b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} + 1448 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} + 836 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{b^{4} x^{12} - 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} - 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} - 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} - 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} - 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} - 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 32 \, \sqrt{3} {\left(a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} + 8 \, a^{4}\right)} - 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} + 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} + 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} + 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} + 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} + 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} - 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}}}{3 \, {\left(b x^{4} - a x\right)}}\right) + \frac{1}{12} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} + 68 \, a b^{3} x^{9} + 168 \, a^{2} b^{2} x^{6} - 544 \, a^{3} b x^{3} + 64 \, a^{4} + 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(2799 \, a^{4} b^{6} x^{10} + 11556 \, a^{5} b^{5} x^{7} + 7776 \, a^{6} b^{4} x^{4} + 1440 \, a^{7} b^{3} x - 8 \, \sqrt{3} {\left(202 \, a^{4} b^{6} x^{10} + 834 \, a^{5} b^{5} x^{7} + 561 \, a^{6} b^{4} x^{4} + 104 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 64 \, \sqrt{3} {\left(a b^{3} x^{9} - 3 \, a^{2} b^{2} x^{6} + 3 \, a^{3} b x^{3} - a^{4}\right)} + 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 4 \, \sqrt{\frac{1}{6}} {\left(168 \, a^{3} b^{5} x^{9} + 1845 \, a^{4} b^{4} x^{6} + 1368 \, a^{5} b^{3} x^{3} + 264 \, a^{6} b^{2} - \sqrt{3} {\left(97 \, a^{3} b^{5} x^{9} + 1065 \, a^{4} b^{4} x^{6} + 792 \, a^{5} b^{3} x^{3} + 152 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 216 \, a^{2} b^{3} x^{7} + 120 \, a^{3} b^{2} x^{4} + 64 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 40 \, a^{2} b^{3} x^{7} + 40 \, a^{3} b^{2} x^{4}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) - \frac{1}{12} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} + 68 \, a b^{3} x^{9} + 168 \, a^{2} b^{2} x^{6} - 544 \, a^{3} b x^{3} + 64 \, a^{4} + 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(2799 \, a^{4} b^{6} x^{10} + 11556 \, a^{5} b^{5} x^{7} + 7776 \, a^{6} b^{4} x^{4} + 1440 \, a^{7} b^{3} x - 8 \, \sqrt{3} {\left(202 \, a^{4} b^{6} x^{10} + 834 \, a^{5} b^{5} x^{7} + 561 \, a^{6} b^{4} x^{4} + 104 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 64 \, \sqrt{3} {\left(a b^{3} x^{9} - 3 \, a^{2} b^{2} x^{6} + 3 \, a^{3} b x^{3} - a^{4}\right)} - 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 4 \, \sqrt{\frac{1}{6}} {\left(168 \, a^{3} b^{5} x^{9} + 1845 \, a^{4} b^{4} x^{6} + 1368 \, a^{5} b^{3} x^{3} + 264 \, a^{6} b^{2} - \sqrt{3} {\left(97 \, a^{3} b^{5} x^{9} + 1065 \, a^{4} b^{4} x^{6} + 792 \, a^{5} b^{3} x^{3} + 152 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 216 \, a^{2} b^{3} x^{7} + 120 \, a^{3} b^{2} x^{4} + 64 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 40 \, a^{2} b^{3} x^{7} + 40 \, a^{3} b^{2} x^{4}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) - \frac{1}{24} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} - 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} - 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} - 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} - 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} - 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} - 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 32 \, \sqrt{3} {\left(a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} + 8 \, a^{4}\right)} + 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} + 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} + 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} + 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} + 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} + 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} - 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) + \frac{1}{24} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} - 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} - 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} - 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} - 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} - 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} - 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} + 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} + 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} + 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} + 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} + 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 32 \, \sqrt{3} {\left(a b^{3} x^{9} + 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} + 8 \, a^{4}\right)} - 2 \, \sqrt{b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} + 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} + 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} + 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} + 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} + 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} + 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} + 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} - 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} - 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} + 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right)"," ",0,"-1/6*sqrt(3)*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*arctan(1/3*(3*sqrt(b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 - 1978*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 - 1142*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)) - (6*(1/9)^(1/3)*(7*a^2*b^2*x^3 - 7*a^3*b - 4*sqrt(3)*(a^2*b^2*x^3 - a^3*b))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - sqrt(3)*(b*x^4 - a*x) + 3*sqrt(b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 + 1448*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 + 836*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))*sqrt((b^4*x^12 - 100*a*b^3*x^9 + 240*a^2*b^2*x^6 - 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 - 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 - 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 - 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 - 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 32*sqrt(3)*(a*b^3*x^9 + 6*a^2*b^2*x^6 - 15*a^3*b*x^3 + 8*a^4) + 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 2*sqrt(1/6)*(123*a^3*b^5*x^9 + 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 + 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 + 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 + 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 + 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 - 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4)))/(b*x^4 - a*x)) - 1/6*sqrt(3)*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*arctan(1/3*(3*sqrt(b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 - 1978*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 - 1142*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)) + (6*(1/9)^(1/3)*(7*a^2*b^2*x^3 - 7*a^3*b - 4*sqrt(3)*(a^2*b^2*x^3 - a^3*b))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - sqrt(3)*(b*x^4 - a*x) - 3*sqrt(b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 + 1448*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 + 836*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))*sqrt((b^4*x^12 - 100*a*b^3*x^9 + 240*a^2*b^2*x^6 - 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 - 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 - 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 - 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 - 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 32*sqrt(3)*(a*b^3*x^9 + 6*a^2*b^2*x^6 - 15*a^3*b*x^3 + 8*a^4) - 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 2*sqrt(1/6)*(123*a^3*b^5*x^9 + 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 + 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 + 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 + 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 + 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 - 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4)))/(b*x^4 - a*x)) + 1/12*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 + 68*a*b^3*x^9 + 168*a^2*b^2*x^6 - 544*a^3*b*x^3 + 64*a^4 + 6*(1/9)^(2/3)*(2799*a^4*b^6*x^10 + 11556*a^5*b^5*x^7 + 7776*a^6*b^4*x^4 + 1440*a^7*b^3*x - 8*sqrt(3)*(202*a^4*b^6*x^10 + 834*a^5*b^5*x^7 + 561*a^6*b^4*x^4 + 104*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 64*sqrt(3)*(a*b^3*x^9 - 3*a^2*b^2*x^6 + 3*a^3*b*x^3 - a^4) + 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 4*sqrt(1/6)*(168*a^3*b^5*x^9 + 1845*a^4*b^4*x^6 + 1368*a^5*b^3*x^3 + 264*a^6*b^2 - sqrt(3)*(97*a^3*b^5*x^9 + 1065*a^4*b^4*x^6 + 792*a^5*b^3*x^3 + 152*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 216*a^2*b^3*x^7 + 120*a^3*b^2*x^4 + 64*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 40*a^2*b^3*x^7 + 40*a^3*b^2*x^4))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4)) - 1/12*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 + 68*a*b^3*x^9 + 168*a^2*b^2*x^6 - 544*a^3*b*x^3 + 64*a^4 + 6*(1/9)^(2/3)*(2799*a^4*b^6*x^10 + 11556*a^5*b^5*x^7 + 7776*a^6*b^4*x^4 + 1440*a^7*b^3*x - 8*sqrt(3)*(202*a^4*b^6*x^10 + 834*a^5*b^5*x^7 + 561*a^6*b^4*x^4 + 104*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 64*sqrt(3)*(a*b^3*x^9 - 3*a^2*b^2*x^6 + 3*a^3*b*x^3 - a^4) - 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 4*sqrt(1/6)*(168*a^3*b^5*x^9 + 1845*a^4*b^4*x^6 + 1368*a^5*b^3*x^3 + 264*a^6*b^2 - sqrt(3)*(97*a^3*b^5*x^9 + 1065*a^4*b^4*x^6 + 792*a^5*b^3*x^3 + 152*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 216*a^2*b^3*x^7 + 120*a^3*b^2*x^4 + 64*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 40*a^2*b^3*x^7 + 40*a^3*b^2*x^4))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4)) - 1/24*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 - 100*a*b^3*x^9 + 240*a^2*b^2*x^6 - 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 - 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 - 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 - 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 - 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 32*sqrt(3)*(a*b^3*x^9 + 6*a^2*b^2*x^6 - 15*a^3*b*x^3 + 8*a^4) + 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 2*sqrt(1/6)*(123*a^3*b^5*x^9 + 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 + 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 + 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 + 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 + 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 - 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4)) + 1/24*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 - 100*a*b^3*x^9 + 240*a^2*b^2*x^6 - 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 - 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 - 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 - 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 - 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) + 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 + 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 + 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 + 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 + 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 32*sqrt(3)*(a*b^3*x^9 + 6*a^2*b^2*x^6 - 15*a^3*b*x^3 + 8*a^4) - 2*sqrt(b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 + 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 + 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 2*sqrt(1/6)*(123*a^3*b^5*x^9 + 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 + 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 + 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 + 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 + 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 - 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 - 40*a*b^3*x^9 + 384*a^2*b^2*x^6 + 320*a^3*b*x^3 + 64*a^4))","B",0
357,1,5060,0,21.049352," ","integrate(x/(b*x^3+2*a*(5-3*3^(1/2)))/(-b*x^3-a)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{3 \, \sqrt{-b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} + 1978 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} + 1142 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)} + {\left(6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(7 \, a^{2} b^{2} x^{3} + 7 \, a^{3} b - 4 \, \sqrt{3} {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b x^{4} + a x\right)} + 3 \, \sqrt{-b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} - 1448 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} - 836 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{b^{4} x^{12} + 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} + 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} + 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} + 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} + 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} + 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 32 \, \sqrt{3} {\left(a b^{3} x^{9} - 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} - 8 \, a^{4}\right)} + 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} - 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} - 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} - 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} - 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} - 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} + 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}}}{3 \, {\left(b x^{4} + a x\right)}}\right) - \frac{1}{6} \, \sqrt{3} \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{3 \, \sqrt{-b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} + 1978 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} + 1142 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)} - {\left(6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(7 \, a^{2} b^{2} x^{3} + 7 \, a^{3} b - 4 \, \sqrt{3} {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b x^{4} + a x\right)} - 3 \, \sqrt{-b x^{3} - a} {\left(108 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(265 \, a^{4} b^{4} x^{3} - 1448 \, a^{5} b^{3} - \sqrt{3} {\left(153 \, a^{4} b^{4} x^{3} - 836 \, a^{5} b^{3}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - \sqrt{\frac{1}{6}} {\left(41 \, \sqrt{3} a^{3} b^{2} x - 71 \, a^{3} b^{2} x\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, \sqrt{3} a b x^{2} - 9 \, a b x^{2}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}\right)} \sqrt{\frac{b^{4} x^{12} + 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} + 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} + 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} + 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} + 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} + 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 32 \, \sqrt{3} {\left(a b^{3} x^{9} - 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} - 8 \, a^{4}\right)} - 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} - 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} - 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} - 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} - 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} - 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} + 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}}}{3 \, {\left(b x^{4} + a x\right)}}\right) - \frac{1}{24} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} + 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} + 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} + 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} + 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} + 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} + 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 32 \, \sqrt{3} {\left(a b^{3} x^{9} - 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} - 8 \, a^{4}\right)} + 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} - 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} - 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} - 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} - 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} - 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} + 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) + \frac{1}{24} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(\frac{b^{4} x^{12} + 100 \, a b^{3} x^{9} + 240 \, a^{2} b^{2} x^{6} + 832 \, a^{3} b x^{3} + 448 \, a^{4} - 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(1545 \, a^{4} b^{6} x^{10} + 12492 \, a^{5} b^{5} x^{7} - 10512 \, a^{6} b^{4} x^{4} + 2112 \, a^{7} b^{3} x - 4 \, \sqrt{3} {\left(223 \, a^{4} b^{6} x^{10} + 1803 \, a^{5} b^{5} x^{7} - 1518 \, a^{6} b^{4} x^{4} + 304 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} - 32 \, \sqrt{3} {\left(a b^{3} x^{9} - 6 \, a^{2} b^{2} x^{6} - 15 \, a^{3} b x^{3} - 8 \, a^{4}\right)} - 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} + 2 \, \sqrt{\frac{1}{6}} {\left(123 \, a^{3} b^{5} x^{9} - 5112 \, a^{4} b^{4} x^{6} + 3960 \, a^{5} b^{3} x^{3} - 768 \, a^{6} b^{2} - \sqrt{3} {\left(71 \, a^{3} b^{5} x^{9} - 2952 \, a^{4} b^{4} x^{6} + 2280 \, a^{5} b^{3} x^{3} - 448 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} - 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} + 12 \, a^{2} b^{3} x^{7} - 72 \, a^{3} b^{2} x^{4} - 160 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} + 4 \, a^{2} b^{3} x^{7} + 8 \, a^{3} b^{2} x^{4} + 32 \, a^{4} b x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) + \frac{1}{12} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(-\frac{b^{4} x^{12} - 68 \, a b^{3} x^{9} + 168 \, a^{2} b^{2} x^{6} + 544 \, a^{3} b x^{3} + 64 \, a^{4} + 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(2799 \, a^{4} b^{6} x^{10} - 11556 \, a^{5} b^{5} x^{7} + 7776 \, a^{6} b^{4} x^{4} - 1440 \, a^{7} b^{3} x - 8 \, \sqrt{3} {\left(202 \, a^{4} b^{6} x^{10} - 834 \, a^{5} b^{5} x^{7} + 561 \, a^{6} b^{4} x^{4} - 104 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 64 \, \sqrt{3} {\left(a b^{3} x^{9} + 3 \, a^{2} b^{2} x^{6} + 3 \, a^{3} b x^{3} + a^{4}\right)} + 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 4 \, \sqrt{\frac{1}{6}} {\left(168 \, a^{3} b^{5} x^{9} - 1845 \, a^{4} b^{4} x^{6} + 1368 \, a^{5} b^{3} x^{3} - 264 \, a^{6} b^{2} - \sqrt{3} {\left(97 \, a^{3} b^{5} x^{9} - 1065 \, a^{4} b^{4} x^{6} + 792 \, a^{5} b^{3} x^{3} - 152 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 216 \, a^{2} b^{3} x^{7} + 120 \, a^{3} b^{2} x^{4} - 64 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 40 \, a^{2} b^{3} x^{7} + 40 \, a^{3} b^{2} x^{4}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right) - \frac{1}{12} \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}} \log\left(-\frac{b^{4} x^{12} - 68 \, a b^{3} x^{9} + 168 \, a^{2} b^{2} x^{6} + 544 \, a^{3} b x^{3} + 64 \, a^{4} + 6 \, \left(\frac{1}{9}\right)^{\frac{2}{3}} {\left(2799 \, a^{4} b^{6} x^{10} - 11556 \, a^{5} b^{5} x^{7} + 7776 \, a^{6} b^{4} x^{4} - 1440 \, a^{7} b^{3} x - 8 \, \sqrt{3} {\left(202 \, a^{4} b^{6} x^{10} - 834 \, a^{5} b^{5} x^{7} + 561 \, a^{6} b^{4} x^{4} - 104 \, a^{7} b^{3} x\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{2}{3}} - 6 \, \left(\frac{1}{9}\right)^{\frac{1}{3}} {\left(26 \, a^{2} b^{5} x^{11} - 498 \, a^{3} b^{4} x^{8} + 384 \, a^{4} b^{3} x^{5} - 64 \, a^{5} b^{2} x^{2} - 3 \, \sqrt{3} {\left(5 \, a^{2} b^{5} x^{11} - 96 \, a^{3} b^{4} x^{8} + 72 \, a^{4} b^{3} x^{5} - 16 \, a^{5} b^{2} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{3}} + 64 \, \sqrt{3} {\left(a b^{3} x^{9} + 3 \, a^{2} b^{2} x^{6} + 3 \, a^{3} b x^{3} + a^{4}\right)} - 2 \, \sqrt{-b x^{3} - a} {\left(1944 \, \left(\frac{1}{1944}\right)^{\frac{5}{6}} {\left(3691 \, a^{5} b^{6} x^{8} - 2896 \, a^{6} b^{5} x^{5} + 568 \, a^{7} b^{4} x^{2} - \sqrt{3} {\left(2131 \, a^{5} b^{6} x^{8} - 1672 \, a^{6} b^{5} x^{5} + 328 \, a^{7} b^{4} x^{2}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{5}{6}} - 4 \, \sqrt{\frac{1}{6}} {\left(168 \, a^{3} b^{5} x^{9} - 1845 \, a^{4} b^{4} x^{6} + 1368 \, a^{5} b^{3} x^{3} - 264 \, a^{6} b^{2} - \sqrt{3} {\left(97 \, a^{3} b^{5} x^{9} - 1065 \, a^{4} b^{4} x^{6} + 792 \, a^{5} b^{3} x^{3} - 152 \, a^{6} b^{2}\right)}\right)} \sqrt{-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}} + 3 \, \left(\frac{1}{1944}\right)^{\frac{1}{6}} {\left(5 \, a b^{4} x^{10} - 216 \, a^{2} b^{3} x^{7} + 120 \, a^{3} b^{2} x^{4} - 64 \, a^{4} b x - 3 \, \sqrt{3} {\left(a b^{4} x^{10} - 40 \, a^{2} b^{3} x^{7} + 40 \, a^{3} b^{2} x^{4}\right)}\right)} \left(-\frac{1351 \, \sqrt{3} + 2340}{a^{5} b^{4}}\right)^{\frac{1}{6}}\right)}}{b^{4} x^{12} + 40 \, a b^{3} x^{9} + 384 \, a^{2} b^{2} x^{6} - 320 \, a^{3} b x^{3} + 64 \, a^{4}}\right)"," ",0,"-1/6*sqrt(3)*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*arctan(-1/3*(3*sqrt(-b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 + 1978*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 + 1142*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)) + (6*(1/9)^(1/3)*(7*a^2*b^2*x^3 + 7*a^3*b - 4*sqrt(3)*(a^2*b^2*x^3 + a^3*b))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + sqrt(3)*(b*x^4 + a*x) + 3*sqrt(-b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 - 1448*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 - 836*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))*sqrt((b^4*x^12 + 100*a*b^3*x^9 + 240*a^2*b^2*x^6 + 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 + 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 + 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 + 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 + 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 32*sqrt(3)*(a*b^3*x^9 - 6*a^2*b^2*x^6 - 15*a^3*b*x^3 - 8*a^4) + 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 2*sqrt(1/6)*(123*a^3*b^5*x^9 - 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 - 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 - 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 - 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 - 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 + 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4)))/(b*x^4 + a*x)) - 1/6*sqrt(3)*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*arctan(-1/3*(3*sqrt(-b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 + 1978*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 + 1142*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)) - (6*(1/9)^(1/3)*(7*a^2*b^2*x^3 + 7*a^3*b - 4*sqrt(3)*(a^2*b^2*x^3 + a^3*b))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + sqrt(3)*(b*x^4 + a*x) - 3*sqrt(-b*x^3 - a)*(108*(1/1944)^(5/6)*(265*a^4*b^4*x^3 - 1448*a^5*b^3 - sqrt(3)*(153*a^4*b^4*x^3 - 836*a^5*b^3))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - sqrt(1/6)*(41*sqrt(3)*a^3*b^2*x - 71*a^3*b^2*x)*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + (1/1944)^(1/6)*(5*sqrt(3)*a*b*x^2 - 9*a*b*x^2)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))*sqrt((b^4*x^12 + 100*a*b^3*x^9 + 240*a^2*b^2*x^6 + 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 + 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 + 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 + 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 + 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 32*sqrt(3)*(a*b^3*x^9 - 6*a^2*b^2*x^6 - 15*a^3*b*x^3 - 8*a^4) - 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 2*sqrt(1/6)*(123*a^3*b^5*x^9 - 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 - 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 - 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 - 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 - 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 + 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4)))/(b*x^4 + a*x)) - 1/24*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 + 100*a*b^3*x^9 + 240*a^2*b^2*x^6 + 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 + 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 + 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 + 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 + 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 32*sqrt(3)*(a*b^3*x^9 - 6*a^2*b^2*x^6 - 15*a^3*b*x^3 - 8*a^4) + 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 2*sqrt(1/6)*(123*a^3*b^5*x^9 - 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 - 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 - 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 - 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 - 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 + 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4)) + 1/24*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log((b^4*x^12 + 100*a*b^3*x^9 + 240*a^2*b^2*x^6 + 832*a^3*b*x^3 + 448*a^4 - 6*(1/9)^(2/3)*(1545*a^4*b^6*x^10 + 12492*a^5*b^5*x^7 - 10512*a^6*b^4*x^4 + 2112*a^7*b^3*x - 4*sqrt(3)*(223*a^4*b^6*x^10 + 1803*a^5*b^5*x^7 - 1518*a^6*b^4*x^4 + 304*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) - 32*sqrt(3)*(a*b^3*x^9 - 6*a^2*b^2*x^6 - 15*a^3*b*x^3 - 8*a^4) - 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) + 2*sqrt(1/6)*(123*a^3*b^5*x^9 - 5112*a^4*b^4*x^6 + 3960*a^5*b^3*x^3 - 768*a^6*b^2 - sqrt(3)*(71*a^3*b^5*x^9 - 2952*a^4*b^4*x^6 + 2280*a^5*b^3*x^3 - 448*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) - 3*(1/1944)^(1/6)*(5*a*b^4*x^10 + 12*a^2*b^3*x^7 - 72*a^3*b^2*x^4 - 160*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 + 4*a^2*b^3*x^7 + 8*a^3*b^2*x^4 + 32*a^4*b*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4)) + 1/12*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log(-(b^4*x^12 - 68*a*b^3*x^9 + 168*a^2*b^2*x^6 + 544*a^3*b*x^3 + 64*a^4 + 6*(1/9)^(2/3)*(2799*a^4*b^6*x^10 - 11556*a^5*b^5*x^7 + 7776*a^6*b^4*x^4 - 1440*a^7*b^3*x - 8*sqrt(3)*(202*a^4*b^6*x^10 - 834*a^5*b^5*x^7 + 561*a^6*b^4*x^4 - 104*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 64*sqrt(3)*(a*b^3*x^9 + 3*a^2*b^2*x^6 + 3*a^3*b*x^3 + a^4) + 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 4*sqrt(1/6)*(168*a^3*b^5*x^9 - 1845*a^4*b^4*x^6 + 1368*a^5*b^3*x^3 - 264*a^6*b^2 - sqrt(3)*(97*a^3*b^5*x^9 - 1065*a^4*b^4*x^6 + 792*a^5*b^3*x^3 - 152*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 216*a^2*b^3*x^7 + 120*a^3*b^2*x^4 - 64*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 40*a^2*b^3*x^7 + 40*a^3*b^2*x^4))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4)) - 1/12*(1/1944)^(1/6)*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)*log(-(b^4*x^12 - 68*a*b^3*x^9 + 168*a^2*b^2*x^6 + 544*a^3*b*x^3 + 64*a^4 + 6*(1/9)^(2/3)*(2799*a^4*b^6*x^10 - 11556*a^5*b^5*x^7 + 7776*a^6*b^4*x^4 - 1440*a^7*b^3*x - 8*sqrt(3)*(202*a^4*b^6*x^10 - 834*a^5*b^5*x^7 + 561*a^6*b^4*x^4 - 104*a^7*b^3*x))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(2/3) - 6*(1/9)^(1/3)*(26*a^2*b^5*x^11 - 498*a^3*b^4*x^8 + 384*a^4*b^3*x^5 - 64*a^5*b^2*x^2 - 3*sqrt(3)*(5*a^2*b^5*x^11 - 96*a^3*b^4*x^8 + 72*a^4*b^3*x^5 - 16*a^5*b^2*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/3) + 64*sqrt(3)*(a*b^3*x^9 + 3*a^2*b^2*x^6 + 3*a^3*b*x^3 + a^4) - 2*sqrt(-b*x^3 - a)*(1944*(1/1944)^(5/6)*(3691*a^5*b^6*x^8 - 2896*a^6*b^5*x^5 + 568*a^7*b^4*x^2 - sqrt(3)*(2131*a^5*b^6*x^8 - 1672*a^6*b^5*x^5 + 328*a^7*b^4*x^2))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(5/6) - 4*sqrt(1/6)*(168*a^3*b^5*x^9 - 1845*a^4*b^4*x^6 + 1368*a^5*b^3*x^3 - 264*a^6*b^2 - sqrt(3)*(97*a^3*b^5*x^9 - 1065*a^4*b^4*x^6 + 792*a^5*b^3*x^3 - 152*a^6*b^2))*sqrt(-(1351*sqrt(3) + 2340)/(a^5*b^4)) + 3*(1/1944)^(1/6)*(5*a*b^4*x^10 - 216*a^2*b^3*x^7 + 120*a^3*b^2*x^4 - 64*a^4*b*x - 3*sqrt(3)*(a*b^4*x^10 - 40*a^2*b^3*x^7 + 40*a^3*b^2*x^4))*(-(1351*sqrt(3) + 2340)/(a^5*b^4))^(1/6)))/(b^4*x^12 + 40*a*b^3*x^9 + 384*a^2*b^2*x^6 - 320*a^3*b*x^3 + 64*a^4))","B",0
358,1,280,0,0.700253," ","integrate(x^8*(d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} d^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{6} - 2 \, b^{2} c^{2} - 5 \, a b c d + 15 \, a^{2} d^{2} + {\left(b^{2} c d - 5 \, a b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{45 \, b^{3} d^{2}}, -\frac{2 \, {\left(15 \, a^{2} d^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(3 \, b^{2} d^{2} x^{6} - 2 \, b^{2} c^{2} - 5 \, a b c d + 15 \, a^{2} d^{2} + {\left(b^{2} c d - 5 \, a b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, b^{3} d^{2}}\right]"," ",0,"[1/45*(15*a^2*d^2*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*(3*b^2*d^2*x^6 - 2*b^2*c^2 - 5*a*b*c*d + 15*a^2*d^2 + (b^2*c*d - 5*a*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^3*d^2), -2/45*(15*a^2*d^2*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (3*b^2*d^2*x^6 - 2*b^2*c^2 - 5*a*b*c*d + 15*a^2*d^2 + (b^2*c*d - 5*a*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^3*d^2)]","A",0
359,1,195,0,0.552361," ","integrate(x^5*(d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{3 \, a d \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, {\left(b d x^{3} + b c - 3 \, a d\right)} \sqrt{d x^{3} + c}}{9 \, b^{2} d}, \frac{2 \, {\left(3 \, a d \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(b d x^{3} + b c - 3 \, a d\right)} \sqrt{d x^{3} + c}\right)}}{9 \, b^{2} d}\right]"," ",0,"[1/9*(3*a*d*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*(b*d*x^3 + b*c - 3*a*d)*sqrt(d*x^3 + c))/(b^2*d), 2/9*(3*a*d*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (b*d*x^3 + b*c - 3*a*d)*sqrt(d*x^3 + c))/(b^2*d)]","A",0
360,1,156,0,0.639699," ","integrate(x^2*(d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, \sqrt{d x^{3} + c}}{3 \, b}, -\frac{2 \, {\left(\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - \sqrt{d x^{3} + c}\right)}}{3 \, b}\right]"," ",0,"[1/3*(sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*sqrt(d*x^3 + c))/b, -2/3*(sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - sqrt(d*x^3 + c))/b]","A",0
361,1,383,0,0.539066," ","integrate((d*x^3+c)^(1/2)/x/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, a}, \frac{2 \, \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, a}, \frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right)}{3 \, a}, \frac{2 \, {\left(\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)\right)}}{3 \, a}\right]"," ",0,"[1/3*(sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/a, 1/3*(2*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/a, 1/3*(2*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)))/a, 2/3*(sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/a]","A",0
362,1,513,0,0.517931," ","integrate((d*x^3+c)^(1/2)/x^4/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b^{2} c - a b d} c x^{3} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - {\left(2 \, b c - a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} c x^{3}}, \frac{4 \, \sqrt{-b^{2} c + a b d} c x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(2 \, b c - a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} c x^{3}}, -\frac{{\left(2 \, b c - a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \sqrt{b^{2} c - a b d} c x^{3} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + \sqrt{d x^{3} + c} a c}{3 \, a^{2} c x^{3}}, \frac{2 \, \sqrt{-b^{2} c + a b d} c x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(2 \, b c - a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{3} + c} a c}{3 \, a^{2} c x^{3}}\right]"," ",0,"[1/6*(2*sqrt(b^2*c - a*b*d)*c*x^3*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - (2*b*c - a*d)*sqrt(c)*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*sqrt(d*x^3 + c)*a*c)/(a^2*c*x^3), 1/6*(4*sqrt(-b^2*c + a*b*d)*c*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (2*b*c - a*d)*sqrt(c)*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*sqrt(d*x^3 + c)*a*c)/(a^2*c*x^3), -1/3*((2*b*c - a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - sqrt(b^2*c - a*b*d)*c*x^3*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + sqrt(d*x^3 + c)*a*c)/(a^2*c*x^3), 1/3*(2*sqrt(-b^2*c + a*b*d)*c*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (2*b*c - a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - sqrt(d*x^3 + c)*a*c)/(a^2*c*x^3)]","A",0
363,-1,0,0,0.000000," ","integrate(x^3*(d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(x*(d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-2,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Not integrable (provided residues have no relations)","F(-2)",0
366,-1,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/x^2/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-2,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/x^3/(b*x^3+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Not integrable (provided residues have no relations)","F(-2)",0
368,1,410,0,0.917762," ","integrate(x^8*(d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) - 2 \, {\left(15 \, b^{3} d^{3} x^{9} + 3 \, {\left(8 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{6} - 6 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 140 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 42 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{315 \, b^{4} d^{2}}, -\frac{2 \, {\left(105 \, {\left(a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(15 \, b^{3} d^{3} x^{9} + 3 \, {\left(8 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{6} - 6 \, b^{3} c^{3} - 21 \, a b^{2} c^{2} d + 140 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + {\left(3 \, b^{3} c^{2} d - 42 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}\right)}}{315 \, b^{4} d^{2}}\right]"," ",0,"[-1/315*(105*(a^2*b*c*d^2 - a^3*d^3)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) - 2*(15*b^3*d^3*x^9 + 3*(8*b^3*c*d^2 - 7*a*b^2*d^3)*x^6 - 6*b^3*c^3 - 21*a*b^2*c^2*d + 140*a^2*b*c*d^2 - 105*a^3*d^3 + (3*b^3*c^2*d - 42*a*b^2*c*d^2 + 35*a^2*b*d^3)*x^3)*sqrt(d*x^3 + c))/(b^4*d^2), -2/315*(105*(a^2*b*c*d^2 - a^3*d^3)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (15*b^3*d^3*x^9 + 3*(8*b^3*c*d^2 - 7*a*b^2*d^3)*x^6 - 6*b^3*c^3 - 21*a*b^2*c^2*d + 140*a^2*b*c*d^2 - 105*a^3*d^3 + (3*b^3*c^2*d - 42*a*b^2*c*d^2 + 35*a^2*b*d^3)*x^3)*sqrt(d*x^3 + c))/(b^4*d^2)]","A",0
369,1,297,0,0.777054," ","integrate(x^5*(d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{6} + 3 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2} + {\left(6 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{45 \, b^{3} d}, \frac{2 \, {\left(15 \, {\left(a b c d - a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(3 \, b^{2} d^{2} x^{6} + 3 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2} + {\left(6 \, b^{2} c d - 5 \, a b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, b^{3} d}\right]"," ",0,"[-1/45*(15*(a*b*c*d - a^2*d^2)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) - 2*(3*b^2*d^2*x^6 + 3*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 + (6*b^2*c*d - 5*a*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^3*d), 2/45*(15*(a*b*c*d - a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (3*b^2*d^2*x^6 + 3*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2 + (6*b^2*c*d - 5*a*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^3*d)]","A",0
370,1,204,0,0.689781," ","integrate(x^2*(d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) - 2 \, {\left(b d x^{3} + 4 \, b c - 3 \, a d\right)} \sqrt{d x^{3} + c}}{9 \, b^{2}}, -\frac{2 \, {\left(3 \, {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(b d x^{3} + 4 \, b c - 3 \, a d\right)} \sqrt{d x^{3} + c}\right)}}{9 \, b^{2}}\right]"," ",0,"[-1/9*(3*(b*c - a*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) - 2*(b*d*x^3 + 4*b*c - 3*a*d)*sqrt(d*x^3 + c))/b^2, -2/9*(3*(b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (b*d*x^3 + 4*b*c - 3*a*d)*sqrt(d*x^3 + c))/b^2]","A",0
371,1,486,0,0.999403," ","integrate((d*x^3+c)^(3/2)/x/(b*x^3+a),x, algorithm=""fricas"")","\left[\frac{b c^{\frac{3}{2}} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} a d - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right)}{3 \, a b}, \frac{b c^{\frac{3}{2}} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} a d + 2 \, {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right)}{3 \, a b}, \frac{2 \, b \sqrt{-c} c \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 2 \, \sqrt{d x^{3} + c} a d - {\left(b c - a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right)}{3 \, a b}, \frac{2 \, {\left(b \sqrt{-c} c \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{3} + c} a d + {\left(b c - a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right)\right)}}{3 \, a b}\right]"," ",0,"[1/3*(b*c^(3/2)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*a*d - (b*c - a*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)))/(a*b), 1/3*(b*c^(3/2)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*a*d + 2*(b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)))/(a*b), 1/3*(2*b*sqrt(-c)*c*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 2*sqrt(d*x^3 + c)*a*d - (b*c - a*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)))/(a*b), 2/3*(b*sqrt(-c)*c*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(d*x^3 + c)*a*d + (b*c - a*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)))/(a*b)]","A",0
372,1,538,0,0.875284," ","integrate((d*x^3+c)^(3/2)/x^4/(b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b c - a d\right)} x^{3} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} x^{3}}, -\frac{4 \, {\left(b c - a d\right)} x^{3} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} x^{3}}, -\frac{{\left(2 \, b c - 3 \, a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(b c - a d\right)} x^{3} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + \sqrt{d x^{3} + c} a c}{3 \, a^{2} x^{3}}, -\frac{2 \, {\left(b c - a d\right)} x^{3} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(2 \, b c - 3 \, a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{3} + c} a c}{3 \, a^{2} x^{3}}\right]"," ",0,"[-1/6*(2*(b*c - a*d)*x^3*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + (2*b*c - 3*a*d)*sqrt(c)*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*a*c)/(a^2*x^3), -1/6*(4*(b*c - a*d)*x^3*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (2*b*c - 3*a*d)*sqrt(c)*x^3*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*a*c)/(a^2*x^3), -1/3*((2*b*c - 3*a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (b*c - a*d)*x^3*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + sqrt(d*x^3 + c)*a*c)/(a^2*x^3), -1/3*(2*(b*c - a*d)*x^3*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (2*b*c - 3*a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(d*x^3 + c)*a*c)/(a^2*x^3)]","A",0
373,-1,0,0,0.000000," ","integrate(x^3*(d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(x*(d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/x^2/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/x^3/(b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,1,289,0,0.867609," ","integrate(x^8/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} c - a b d} a^{2} d^{2} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{9 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}, \frac{2 \, {\left(3 \, \sqrt{-b^{2} c + a b d} a^{2} d^{2} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}\right)}}{9 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}\right]"," ",0,"[1/9*(3*sqrt(b^2*c - a*b*d)*a^2*d^2*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*(2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(b^4*c*d^2 - a*b^3*d^3), 2/9*(3*sqrt(-b^2*c + a*b*d)*a^2*d^2*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(b^4*c*d^2 - a*b^3*d^3)]","A",0
379,1,205,0,0.876495," ","integrate(x^5/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} a d \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}}{3 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}, -\frac{2 \, {\left(\sqrt{-b^{2} c + a b d} a d \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}\right)}}{3 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}\right]"," ",0,"[1/3*(sqrt(b^2*c - a*b*d)*a*d*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2), -2/3*(sqrt(-b^2*c + a*b*d)*a*d*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2)]","A",0
380,1,130,0,0.851298," ","integrate(x^2/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right)}{3 \, \sqrt{b^{2} c - a b d}}, \frac{2 \, \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right)}{3 \, {\left(b^{2} c - a b d\right)}}\right]"," ",0,"[1/3*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a))/sqrt(b^2*c - a*b*d), 2/3*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c))/(b^2*c - a*b*d)]","A",0
381,1,431,0,0.456968," ","integrate(1/x/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, a c}, \frac{2 \, c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, a c}, \frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)}{3 \, a c}, \frac{2 \, {\left(c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)\right)}}{3 \, a c}\right]"," ",0,"[1/3*(c*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a*c), 1/3*(2*c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a*c), 1/3*(c*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/(a*c), 2/3*(c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/(a*c)]","A",0
382,1,565,0,0.485374," ","integrate(1/x^4/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{3} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} c^{2} x^{3}}, -\frac{4 \, b c^{2} x^{3} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left(2 \, b c + a d\right)} \sqrt{c} x^{3} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} a c}{6 \, a^{2} c^{2} x^{3}}, \frac{b c^{2} x^{3} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - {\left(2 \, b c + a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{3} + c} a c}{3 \, a^{2} c^{2} x^{3}}, -\frac{2 \, b c^{2} x^{3} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left(2 \, b c + a d\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{3} + c} a c}{3 \, a^{2} c^{2} x^{3}}\right]"," ",0,"[1/6*(2*b*c^2*x^3*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + (2*b*c + a*d)*sqrt(c)*x^3*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3), -1/6*(4*b*c^2*x^3*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - (2*b*c + a*d)*sqrt(c)*x^3*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3), 1/3*(b*c^2*x^3*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - (2*b*c + a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3), -1/3*(2*b*c^2*x^3*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + (2*b*c + a*d)*sqrt(-c)*x^3*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3)]","A",0
383,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,1,440,0,0.801840," ","integrate(x^8/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} d^{3} x^{3} + a^{2} c d^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, {\left(2 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + a^{2} b c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(b^{4} c^{3} d^{2} - 2 \, a b^{3} c^{2} d^{3} + a^{2} b^{2} c d^{4} + {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{3}\right)}}, \frac{2 \, {\left({\left(a^{2} d^{3} x^{3} + a^{2} c d^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(2 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d + a^{2} b c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}\right)}}{3 \, {\left(b^{4} c^{3} d^{2} - 2 \, a b^{3} c^{2} d^{3} + a^{2} b^{2} c d^{4} + {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{3}\right)}}\right]"," ",0,"[-1/3*((a^2*d^3*x^3 + a^2*c*d^2)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*(2*b^3*c^3 - 3*a*b^2*c^2*d + a^2*b*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^3)*sqrt(d*x^3 + c))/(b^4*c^3*d^2 - 2*a*b^3*c^2*d^3 + a^2*b^2*c*d^4 + (b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^3), 2/3*((a^2*d^3*x^3 + a^2*c*d^2)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (2*b^3*c^3 - 3*a*b^2*c^2*d + a^2*b*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^3)*sqrt(d*x^3 + c))/(b^4*c^3*d^2 - 2*a*b^3*c^2*d^3 + a^2*b^2*c*d^4 + (b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^3)]","B",0
389,1,326,0,0.811816," ","integrate(x^5/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a d^{2} x^{3} + a c d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(b^{2} c^{2} - a b c d\right)} \sqrt{d x^{3} + c}}{3 \, {\left(b^{3} c^{3} d - 2 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(a d^{2} x^{3} + a c d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(b^{2} c^{2} - a b c d\right)} \sqrt{d x^{3} + c}\right)}}{3 \, {\left(b^{3} c^{3} d - 2 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)}}\right]"," ",0,"[-1/3*((a*d^2*x^3 + a*c*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(b^2*c^2 - a*b*c*d)*sqrt(d*x^3 + c))/(b^3*c^3*d - 2*a*b^2*c^2*d^2 + a^2*b*c*d^3 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3), -2/3*((a*d^2*x^3 + a*c*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (b^2*c^2 - a*b*c*d)*sqrt(d*x^3 + c))/(b^3*c^3*d - 2*a*b^2*c^2*d^2 + a^2*b*c*d^3 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3)]","B",0
390,1,236,0,0.699157," ","integrate(x^2/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(d x^{3} + c\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - 2 \, \sqrt{d x^{3} + c}}{3 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)}}, -\frac{2 \, {\left({\left(d x^{3} + c\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - \sqrt{d x^{3} + c}\right)}}{3 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)}}\right]"," ",0,"[-1/3*((d*x^3 + c)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - 2*sqrt(d*x^3 + c))/((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d), -2/3*((d*x^3 + c)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - sqrt(d*x^3 + c))/((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d)]","A",0
391,1,790,0,0.575306," ","integrate(1/x/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{d x^{3} + c} a c d + {\left(b c^{2} d x^{3} + b c^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, \sqrt{d x^{3} + c} a c d - 2 \, {\left(b c^{2} d x^{3} + b c^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, \sqrt{d x^{3} + c} a c d - 2 \, {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(b c^{2} d x^{3} + b c^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right)}{3 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, {\left(\sqrt{d x^{3} + c} a c d - {\left(b c^{2} d x^{3} + b c^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left({\left(b c d - a d^{2}\right)} x^{3} + b c^{2} - a c d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)\right)}}{3 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/3*(2*sqrt(d*x^3 + c)*a*c*d + (b*c^2*d*x^3 + b*c^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - ((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^3), -1/3*(2*sqrt(d*x^3 + c)*a*c*d - 2*(b*c^2*d*x^3 + b*c^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - ((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^3), -1/3*(2*sqrt(d*x^3 + c)*a*c*d - 2*((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (b*c^2*d*x^3 + b*c^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^3), -2/3*(sqrt(d*x^3 + c)*a*c*d - (b*c^2*d*x^3 + b*c^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - ((b*c*d - a*d^2)*x^3 + b*c^2 - a*c*d)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x^3)]","B",0
392,1,1120,0,0.865132," ","integrate(1/x^4/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c^{3} d x^{6} + b^{2} c^{4} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{6} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{3}\right)}}, -\frac{4 \, {\left(b^{2} c^{3} d x^{6} + b^{2} c^{4} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{6} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{3}\right)}}, -\frac{{\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(b^{2} c^{3} d x^{6} + b^{2} c^{4} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{6} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{3}\right)}}, -\frac{2 \, {\left(b^{2} c^{3} d x^{6} + b^{2} c^{4} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(2 \, b^{2} c^{2} d + a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{6} + {\left(2 \, b^{2} c^{3} + a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{6} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(2*(b^2*c^3*d*x^6 + b^2*c^4*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^6 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(d*x^3 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^6 + (a^2*b*c^5 - a^3*c^4*d)*x^3), -1/6*(4*(b^2*c^3*d*x^6 + b^2*c^4*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^6 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(d*x^3 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^6 + (a^2*b*c^5 - a^3*c^4*d)*x^3), -1/3*(((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^6 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (b^2*c^3*d*x^6 + b^2*c^4*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + (a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(d*x^3 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^6 + (a^2*b*c^5 - a^3*c^4*d)*x^3), -1/3*(2*(b^2*c^3*d*x^6 + b^2*c^4*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((2*b^2*c^2*d + a*b*c*d^2 - 3*a^2*d^3)*x^6 + (2*b^2*c^3 + a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x^3)*sqrt(d*x^3 + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^6 + (a^2*b*c^5 - a^3*c^4*d)*x^3)]","B",0
393,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,1,219,0,0.640250," ","integrate(x^11*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(4960 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, {\left(d^{3} x^{9} + 19 \, c d^{2} x^{6} + 770 \, c^{2} d x^{3} - 9168 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}, \frac{2 \, {\left(9920 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(d^{3} x^{9} + 19 \, c d^{2} x^{6} + 770 \, c^{2} d x^{3} - 9168 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}\right]"," ",0,"[2/45*(4960*(c^2*d*x^3 - 8*c^3)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*(d^3*x^9 + 19*c*d^2*x^6 + 770*c^2*d*x^3 - 9168*c^3)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4), 2/45*(9920*(c^2*d*x^3 - 8*c^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(d^3*x^9 + 19*c*d^2*x^6 + 770*c^2*d*x^3 - 9168*c^3)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4)]","A",0
399,1,191,0,0.679954," ","integrate(x^8*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(88 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + {\left(d^{2} x^{6} + 41 \, c d x^{3} - 488 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{9 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}, \frac{2 \, {\left(176 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d^{2} x^{6} + 41 \, c d x^{3} - 488 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{9 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}\right]"," ",0,"[2/9*(88*(c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + (d^2*x^6 + 41*c*d*x^3 - 488*c^2)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3), 2/9*(176*(c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d^2*x^6 + 41*c*d*x^3 - 488*c^2)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3)]","A",0
400,1,165,0,0.465102," ","integrate(x^5*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{13 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 6 \, \sqrt{d x^{3} + c} {\left(d x^{3} - 12 \, c\right)}}{9 \, {\left(d^{3} x^{3} - 8 \, c d^{2}\right)}}, \frac{2 \, {\left(13 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, \sqrt{d x^{3} + c} {\left(d x^{3} - 12 \, c\right)}\right)}}{9 \, {\left(d^{3} x^{3} - 8 \, c d^{2}\right)}}\right]"," ",0,"[1/9*(13*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 6*sqrt(d*x^3 + c)*(d*x^3 - 12*c))/(d^3*x^3 - 8*c*d^2), 2/9*(13*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*sqrt(d*x^3 + c)*(d*x^3 - 12*c))/(d^3*x^3 - 8*c*d^2)]","A",0
401,1,149,0,0.487390," ","integrate(x^2*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{{\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 6 \, \sqrt{d x^{3} + c} c}{18 \, {\left(c d^{2} x^{3} - 8 \, c^{2} d\right)}}, \frac{{\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 3 \, \sqrt{d x^{3} + c} c}{9 \, {\left(c d^{2} x^{3} - 8 \, c^{2} d\right)}}\right]"," ",0,"[1/18*((d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 6*sqrt(d*x^3 + c)*c)/(c*d^2*x^3 - 8*c^2*d), 1/9*((d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 3*sqrt(d*x^3 + c)*c)/(c*d^2*x^3 - 8*c^2*d)]","A",0
402,1,226,0,0.533774," ","integrate((d*x^3+c)^(1/2)/x/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{5 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, \sqrt{d x^{3} + c} c}{576 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)}}, \frac{3 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 5 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 12 \, \sqrt{d x^{3} + c} c}{288 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)}}\right]"," ",0,"[1/576*(5*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*sqrt(d*x^3 + c)*c)/(c^2*d*x^3 - 8*c^3), 1/288*(3*(d*x^3 - 8*c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 5*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 12*sqrt(d*x^3 + c)*c)/(c^2*d*x^3 - 8*c^3)]","A",0
403,1,278,0,0.522336," ","integrate((d*x^3+c)^(1/2)/x^4/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{7 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 9 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, {\left(c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{2304 \, {\left(c^{3} d x^{6} - 8 \, c^{4} x^{3}\right)}}, \frac{9 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 7 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 12 \, {\left(c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{1152 \, {\left(c^{3} d x^{6} - 8 \, c^{4} x^{3}\right)}}\right]"," ",0,"[1/2304*(7*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 9*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*(c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^3*d*x^6 - 8*c^4*x^3), 1/1152*(9*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 7*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 12*(c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^3*d*x^6 - 8*c^4*x^3)]","A",0
404,1,310,0,0.472631," ","integrate((d*x^3+c)^(1/2)/x^7/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{23 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 9 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, {\left(5 \, c d^{2} x^{6} - 28 \, c^{2} d x^{3} - 32 \, c^{3}\right)} \sqrt{d x^{3} + c}}{36864 \, {\left(c^{4} d x^{9} - 8 \, c^{5} x^{6}\right)}}, \frac{9 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 23 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 12 \, {\left(5 \, c d^{2} x^{6} - 28 \, c^{2} d x^{3} - 32 \, c^{3}\right)} \sqrt{d x^{3} + c}}{18432 \, {\left(c^{4} d x^{9} - 8 \, c^{5} x^{6}\right)}}\right]"," ",0,"[1/36864*(23*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 9*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*(5*c*d^2*x^6 - 28*c^2*d*x^3 - 32*c^3)*sqrt(d*x^3 + c))/(c^4*d*x^9 - 8*c^5*x^6), 1/18432*(9*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 23*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 12*(5*c*d^2*x^6 - 28*c^2*d*x^3 - 32*c^3)*sqrt(d*x^3 + c))/(c^4*d*x^9 - 8*c^5*x^6)]","A",0
405,0,0,0,17.274464," ","integrate(x^7*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{7}}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^7/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
406,0,0,0,3.418646," ","integrate(x^4*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{4}}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^4/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
407,0,0,0,0.888616," ","integrate(x*(d*x^3+c)^(1/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
408,0,0,0,1.096237," ","integrate((d*x^3+c)^(1/2)/x^2/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{8} - 16 \, c d x^{5} + 64 \, c^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^8 - 16*c*d*x^5 + 64*c^2*x^2), x)","F",0
409,0,0,0,2.897880," ","integrate((d*x^3+c)^(1/2)/x^5/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{11} - 16 \, c d x^{8} + 64 \, c^{2} x^{5}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^11 - 16*c*d*x^8 + 64*c^2*x^5), x)","F",0
410,0,0,0,5.771639," ","integrate((d*x^3+c)^(1/2)/x^8/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{2} x^{14} - 16 \, c d x^{11} + 64 \, c^{2} x^{8}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^2*x^14 - 16*c*d*x^11 + 64*c^2*x^8), x)","F",0
411,1,239,0,0.441846," ","integrate(x^11*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(26208 \, {\left(c^{3} d x^{3} - 8 \, c^{4}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + {\left(d^{4} x^{12} + 16 \, c d^{3} x^{9} + 301 \, c^{2} d^{2} x^{6} + 12206 \, c^{3} d x^{3} - 145328 \, c^{4}\right)} \sqrt{d x^{3} + c}\right)}}{21 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}, \frac{2 \, {\left(52416 \, {\left(c^{3} d x^{3} - 8 \, c^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d^{4} x^{12} + 16 \, c d^{3} x^{9} + 301 \, c^{2} d^{2} x^{6} + 12206 \, c^{3} d x^{3} - 145328 \, c^{4}\right)} \sqrt{d x^{3} + c}\right)}}{21 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}\right]"," ",0,"[2/21*(26208*(c^3*d*x^3 - 8*c^4)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + (d^4*x^12 + 16*c*d^3*x^9 + 301*c^2*d^2*x^6 + 12206*c^3*d*x^3 - 145328*c^4)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4), 2/21*(52416*(c^3*d*x^3 - 8*c^4)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d^4*x^12 + 16*c*d^3*x^9 + 301*c^2*d^2*x^6 + 12206*c^3*d*x^3 - 145328*c^4)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4)]","A",0
412,1,219,0,0.444365," ","integrate(x^8*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(5400 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + {\left(3 \, d^{3} x^{9} + 62 \, c d^{2} x^{6} + 2515 \, c^{2} d x^{3} - 29944 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}, \frac{2 \, {\left(10800 \, {\left(c^{2} d x^{3} - 8 \, c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(3 \, d^{3} x^{9} + 62 \, c d^{2} x^{6} + 2515 \, c^{2} d x^{3} - 29944 \, c^{3}\right)} \sqrt{d x^{3} + c}\right)}}{45 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}\right]"," ",0,"[2/45*(5400*(c^2*d*x^3 - 8*c^3)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + (3*d^3*x^9 + 62*c*d^2*x^6 + 2515*c^2*d*x^3 - 29944*c^3)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3), 2/45*(10800*(c^2*d*x^3 - 8*c^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (3*d^3*x^9 + 62*c*d^2*x^6 + 2515*c^2*d*x^3 - 29944*c^3)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3)]","A",0
413,1,192,0,0.445379," ","integrate(x^5*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{189 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 2 \, {\left(d^{2} x^{6} + 44 \, c d x^{3} - 524 \, c^{2}\right)} \sqrt{d x^{3} + c}}{9 \, {\left(d^{3} x^{3} - 8 \, c d^{2}\right)}}, \frac{2 \, {\left(189 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(d^{2} x^{6} + 44 \, c d x^{3} - 524 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{9 \, {\left(d^{3} x^{3} - 8 \, c d^{2}\right)}}\right]"," ",0,"[1/9*(189*(c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 2*(d^2*x^6 + 44*c*d*x^3 - 524*c^2)*sqrt(d*x^3 + c))/(d^3*x^3 - 8*c*d^2), 2/9*(189*(c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (d^2*x^6 + 44*c*d*x^3 - 524*c^2)*sqrt(d*x^3 + c))/(d^3*x^3 - 8*c*d^2)]","A",0
414,1,162,0,0.439463," ","integrate(x^2*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{9 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 2 \, {\left(2 \, d x^{3} - 25 \, c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(d^{2} x^{3} - 8 \, c d\right)}}, \frac{9 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + {\left(2 \, d x^{3} - 25 \, c\right)} \sqrt{d x^{3} + c}}{3 \, {\left(d^{2} x^{3} - 8 \, c d\right)}}\right]"," ",0,"[1/6*(9*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 2*(2*d*x^3 - 25*c)*sqrt(d*x^3 + c))/(d^2*x^3 - 8*c*d), 1/3*(9*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + (2*d*x^3 - 25*c)*sqrt(d*x^3 + c))/(d^2*x^3 - 8*c*d)]","A",0
415,1,220,0,0.458092," ","integrate((d*x^3+c)^(3/2)/x/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{9 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 72 \, \sqrt{d x^{3} + c} c}{192 \, {\left(c d x^{3} - 8 \, c^{2}\right)}}, \frac{{\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 9 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 36 \, \sqrt{d x^{3} + c} c}{96 \, {\left(c d x^{3} - 8 \, c^{2}\right)}}\right]"," ",0,"[1/192*(9*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + (d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 72*sqrt(d*x^3 + c)*c)/(c*d*x^3 - 8*c^2), 1/96*((d*x^3 - 8*c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 9*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 36*sqrt(d*x^3 + c)*c)/(c*d*x^3 - 8*c^2)]","A",0
416,1,280,0,0.454088," ","integrate((d*x^3+c)^(3/2)/x^4/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{9 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 7 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 8 \, {\left(5 \, c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{768 \, {\left(c^{2} d x^{6} - 8 \, c^{3} x^{3}\right)}}, \frac{7 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 9 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 4 \, {\left(5 \, c d x^{3} - 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{384 \, {\left(c^{2} d x^{6} - 8 \, c^{3} x^{3}\right)}}\right]"," ",0,"[1/768*(9*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 7*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 8*(5*c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^2*d*x^6 - 8*c^3*x^3), 1/384*(7*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 9*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 4*(5*c*d*x^3 - 4*c^2)*sqrt(d*x^3 + c))/(c^2*d*x^6 - 8*c^3*x^3)]","A",0
417,1,310,0,0.473900," ","integrate((d*x^3+c)^(3/2)/x^7/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","\left[\frac{45 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 51 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 8 \, {\left(21 \, c d^{2} x^{6} - 92 \, c^{2} d x^{3} - 32 \, c^{3}\right)} \sqrt{d x^{3} + c}}{12288 \, {\left(c^{3} d x^{9} - 8 \, c^{4} x^{6}\right)}}, \frac{51 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 45 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 4 \, {\left(21 \, c d^{2} x^{6} - 92 \, c^{2} d x^{3} - 32 \, c^{3}\right)} \sqrt{d x^{3} + c}}{6144 \, {\left(c^{3} d x^{9} - 8 \, c^{4} x^{6}\right)}}\right]"," ",0,"[1/12288*(45*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 51*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 8*(21*c*d^2*x^6 - 92*c^2*d*x^3 - 32*c^3)*sqrt(d*x^3 + c))/(c^3*d*x^9 - 8*c^4*x^6), 1/6144*(51*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 45*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 4*(21*c*d^2*x^6 - 92*c^2*d*x^3 - 32*c^3)*sqrt(d*x^3 + c))/(c^3*d*x^9 - 8*c^4*x^6)]","A",0
418,0,0,0,32.503546," ","integrate(x^7*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{10} + c x^{7}\right)} \sqrt{d x^{3} + c}}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral((d*x^10 + c*x^7)*sqrt(d*x^3 + c)/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
419,0,0,0,6.992033," ","integrate(x^4*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{7} + c x^{4}\right)} \sqrt{d x^{3} + c}}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral((d*x^7 + c*x^4)*sqrt(d*x^3 + c)/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
420,0,0,0,1.841200," ","integrate(x*(d*x^3+c)^(3/2)/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{4} + c x\right)} \sqrt{d x^{3} + c}}{d^{2} x^{6} - 16 \, c d x^{3} + 64 \, c^{2}}, x\right)"," ",0,"integral((d*x^4 + c*x)*sqrt(d*x^3 + c)/(d^2*x^6 - 16*c*d*x^3 + 64*c^2), x)","F",0
421,0,0,0,0.493557," ","integrate((d*x^3+c)^(3/2)/x^2/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)}^{\frac{3}{2}}}{d^{2} x^{8} - 16 \, c d x^{5} + 64 \, c^{2} x^{2}}, x\right)"," ",0,"integral((d*x^3 + c)^(3/2)/(d^2*x^8 - 16*c*d*x^5 + 64*c^2*x^2), x)","F",0
422,0,0,0,1.766361," ","integrate((d*x^3+c)^(3/2)/x^5/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)}^{\frac{3}{2}}}{d^{2} x^{11} - 16 \, c d x^{8} + 64 \, c^{2} x^{5}}, x\right)"," ",0,"integral((d*x^3 + c)^(3/2)/(d^2*x^11 - 16*c*d*x^8 + 64*c^2*x^5), x)","F",0
423,0,0,0,3.886733," ","integrate((d*x^3+c)^(3/2)/x^8/(-d*x^3+8*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x^{3} + c\right)}^{\frac{3}{2}}}{d^{2} x^{14} - 16 \, c d x^{11} + 64 \, c^{2} x^{8}}, x\right)"," ",0,"integral((d*x^3 + c)^(3/2)/(d^2*x^14 - 16*c*d*x^11 + 64*c^2*x^8), x)","F",0
424,1,195,0,0.439760," ","integrate(x^11/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(736 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, {\left(3 \, d^{2} x^{6} + 114 \, c d x^{3} - 1360 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}, \frac{2 \, {\left(1472 \, {\left(c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(3 \, d^{2} x^{6} + 114 \, c d x^{3} - 1360 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{5} x^{3} - 8 \, c d^{4}\right)}}\right]"," ",0,"[2/81*(736*(c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*(3*d^2*x^6 + 114*c*d*x^3 - 1360*c^2)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4), 2/81*(1472*(c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(3*d^2*x^6 + 114*c*d*x^3 - 1360*c^2)*sqrt(d*x^3 + c))/(d^5*x^3 - 8*c*d^4)]","A",0
425,1,167,0,0.430762," ","integrate(x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(56 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, {\left(9 \, d x^{3} - 104 \, c\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}, \frac{2 \, {\left(112 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(9 \, d x^{3} - 104 \, c\right)} \sqrt{d x^{3} + c}\right)}}{81 \, {\left(d^{4} x^{3} - 8 \, c d^{3}\right)}}\right]"," ",0,"[2/81*(56*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*(9*d*x^3 - 104*c)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3), 2/81*(112*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(9*d*x^3 - 104*c)*sqrt(d*x^3 + c))/(d^4*x^3 - 8*c*d^3)]","A",0
426,1,155,0,0.469967," ","integrate(x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 24 \, \sqrt{d x^{3} + c} c}{81 \, {\left(c d^{3} x^{3} - 8 \, c^{2} d^{2}\right)}}, \frac{2 \, {\left(5 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 12 \, \sqrt{d x^{3} + c} c\right)}}{81 \, {\left(c d^{3} x^{3} - 8 \, c^{2} d^{2}\right)}}\right]"," ",0,"[1/81*(5*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 24*sqrt(d*x^3 + c)*c)/(c*d^3*x^3 - 8*c^2*d^2), 2/81*(5*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 12*sqrt(d*x^3 + c)*c)/(c*d^3*x^3 - 8*c^2*d^2)]","A",0
427,1,153,0,0.437967," ","integrate(x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 6 \, \sqrt{d x^{3} + c} c}{162 \, {\left(c^{2} d^{2} x^{3} - 8 \, c^{3} d\right)}}, -\frac{{\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, \sqrt{d x^{3} + c} c}{81 \, {\left(c^{2} d^{2} x^{3} - 8 \, c^{3} d\right)}}\right]"," ",0,"[1/162*((d*x^3 - 8*c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 6*sqrt(d*x^3 + c)*c)/(c^2*d^2*x^3 - 8*c^3*d), -1/81*((d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*sqrt(d*x^3 + c)*c)/(c^2*d^2*x^3 - 8*c^3*d)]","A",0
428,1,226,0,0.467915," ","integrate(1/x/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{13 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 27 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, \sqrt{d x^{3} + c} c}{5184 \, {\left(c^{3} d x^{3} - 8 \, c^{4}\right)}}, \frac{27 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 13 \, {\left(d x^{3} - 8 \, c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 12 \, \sqrt{d x^{3} + c} c}{2592 \, {\left(c^{3} d x^{3} - 8 \, c^{4}\right)}}\right]"," ",0,"[1/5184*(13*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 27*(d*x^3 - 8*c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*sqrt(d*x^3 + c)*c)/(c^3*d*x^3 - 8*c^4), 1/2592*(27*(d*x^3 - 8*c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 13*(d*x^3 - 8*c)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 12*sqrt(d*x^3 + c)*c)/(c^3*d*x^3 - 8*c^4)]","A",0
429,1,280,0,0.450067," ","integrate(1/x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{11 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 27 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, {\left(5 \, c d x^{3} - 36 \, c^{2}\right)} \sqrt{d x^{3} + c}}{20736 \, {\left(c^{4} d x^{6} - 8 \, c^{5} x^{3}\right)}}, -\frac{27 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 11 \, {\left(d^{2} x^{6} - 8 \, c d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(5 \, c d x^{3} - 36 \, c^{2}\right)} \sqrt{d x^{3} + c}}{10368 \, {\left(c^{4} d x^{6} - 8 \, c^{5} x^{3}\right)}}\right]"," ",0,"[1/20736*(11*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 27*(d^2*x^6 - 8*c*d*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*(5*c*d*x^3 - 36*c^2)*sqrt(d*x^3 + c))/(c^4*d*x^6 - 8*c^5*x^3), -1/10368*(27*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 11*(d^2*x^6 - 8*c*d*x^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(5*c*d*x^3 - 36*c^2)*sqrt(d*x^3 + c))/(c^4*d*x^6 - 8*c^5*x^3)]","A",0
430,1,310,0,0.649596," ","integrate(1/x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{31 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 513 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 24 \, {\left(35 \, c d^{2} x^{6} - 324 \, c^{2} d x^{3} + 288 \, c^{3}\right)} \sqrt{d x^{3} + c}}{331776 \, {\left(c^{5} d x^{9} - 8 \, c^{6} x^{6}\right)}}, \frac{513 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 31 \, {\left(d^{3} x^{9} - 8 \, c d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(35 \, c d^{2} x^{6} - 324 \, c^{2} d x^{3} + 288 \, c^{3}\right)} \sqrt{d x^{3} + c}}{165888 \, {\left(c^{5} d x^{9} - 8 \, c^{6} x^{6}\right)}}\right]"," ",0,"[1/331776*(31*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 513*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 24*(35*c*d^2*x^6 - 324*c^2*d*x^3 + 288*c^3)*sqrt(d*x^3 + c))/(c^5*d*x^9 - 8*c^6*x^6), 1/165888*(513*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 31*(d^3*x^9 - 8*c*d^2*x^6)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(35*c*d^2*x^6 - 324*c^2*d*x^3 + 288*c^3)*sqrt(d*x^3 + c))/(c^5*d*x^9 - 8*c^6*x^6)]","A",0
431,0,0,0,10.388537," ","integrate(x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{7}}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^7/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
432,0,0,0,1.425689," ","integrate(x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{4}}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^4/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
433,0,0,0,1.424938," ","integrate(x/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
434,0,0,0,2.317054," ","integrate(1/x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{11} - 15 \, c d^{2} x^{8} + 48 \, c^{2} d x^{5} + 64 \, c^{3} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^11 - 15*c*d^2*x^8 + 48*c^2*d*x^5 + 64*c^3*x^2), x)","F",0
435,0,0,0,6.287103," ","integrate(1/x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{14} - 15 \, c d^{2} x^{11} + 48 \, c^{2} d x^{8} + 64 \, c^{3} x^{5}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^14 - 15*c*d^2*x^11 + 48*c^2*d*x^8 + 64*c^3*x^5), x)","F",0
436,0,0,0,14.697634," ","integrate(1/x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{17} - 15 \, c d^{2} x^{14} + 48 \, c^{2} d x^{11} + 64 \, c^{3} x^{8}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^17 - 15*c*d^2*x^14 + 48*c^2*d*x^11 + 64*c^3*x^8), x)","F",0
437,0,0,0,1.604962," ","integrate(x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{6}}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^6/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
438,0,0,0,1.711414," ","integrate(x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{3}}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^3/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
439,0,0,0,1.820098," ","integrate(1/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{9} - 15 \, c d^{2} x^{6} + 48 \, c^{2} d x^{3} + 64 \, c^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^9 - 15*c*d^2*x^6 + 48*c^2*d*x^3 + 64*c^3), x)","F",0
440,0,0,0,4.185727," ","integrate(1/x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{12} - 15 \, c d^{2} x^{9} + 48 \, c^{2} d x^{6} + 64 \, c^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^12 - 15*c*d^2*x^9 + 48*c^2*d*x^6 + 64*c^3*x^3), x)","F",0
441,0,0,0,10.624193," ","integrate(1/x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{3} x^{15} - 15 \, c d^{2} x^{12} + 48 \, c^{2} d x^{9} + 64 \, c^{3} x^{6}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^3*x^15 - 15*c*d^2*x^12 + 48*c^2*d*x^9 + 64*c^3*x^6), x)","F",0
442,1,233,0,0.758367," ","integrate(x^11/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(160 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 3 \, {\left(27 \, d^{2} x^{6} - 274 \, c d x^{3} - 304 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{243 \, {\left(d^{6} x^{6} - 7 \, c d^{5} x^{3} - 8 \, c^{2} d^{4}\right)}}, \frac{2 \, {\left(320 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(27 \, d^{2} x^{6} - 274 \, c d x^{3} - 304 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{243 \, {\left(d^{6} x^{6} - 7 \, c d^{5} x^{3} - 8 \, c^{2} d^{4}\right)}}\right]"," ",0,"[2/243*(160*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 3*(27*d^2*x^6 - 274*c*d*x^3 - 304*c^2)*sqrt(d*x^3 + c))/(d^6*x^6 - 7*c*d^5*x^3 - 8*c^2*d^4), 2/243*(320*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(27*d^2*x^6 - 274*c*d*x^3 - 304*c^2)*sqrt(d*x^3 + c))/(d^6*x^6 - 7*c*d^5*x^3 - 8*c^2*d^4)]","A",0
443,1,223,0,0.712449," ","integrate(x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(8 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 3 \, {\left(11 \, c d x^{3} + 8 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{243 \, {\left(c d^{5} x^{6} - 7 \, c^{2} d^{4} x^{3} - 8 \, c^{3} d^{3}\right)}}, \frac{2 \, {\left(16 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) - 3 \, {\left(11 \, c d x^{3} + 8 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{243 \, {\left(c d^{5} x^{6} - 7 \, c^{2} d^{4} x^{3} - 8 \, c^{3} d^{3}\right)}}\right]"," ",0,"[2/243*(8*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 3*(11*c*d*x^3 + 8*c^2)*sqrt(d*x^3 + c))/(c*d^5*x^6 - 7*c^2*d^4*x^3 - 8*c^3*d^3), 2/243*(16*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) - 3*(11*c*d*x^3 + 8*c^2)*sqrt(d*x^3 + c))/(c*d^5*x^6 - 7*c^2*d^4*x^3 - 8*c^3*d^3)]","A",0
444,1,223,0,0.711802," ","integrate(x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 6 \, {\left(c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}}{243 \, {\left(c^{2} d^{4} x^{6} - 7 \, c^{3} d^{3} x^{3} - 8 \, c^{4} d^{2}\right)}}, -\frac{2 \, {\left({\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(c d x^{3} + 4 \, c^{2}\right)} \sqrt{d x^{3} + c}\right)}}{243 \, {\left(c^{2} d^{4} x^{6} - 7 \, c^{3} d^{3} x^{3} - 8 \, c^{4} d^{2}\right)}}\right]"," ",0,"[1/243*((d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 6*(c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^2*d^4*x^6 - 7*c^3*d^3*x^3 - 8*c^4*d^2), -2/243*((d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(c*d*x^3 + 4*c^2)*sqrt(d*x^3 + c))/(c^2*d^4*x^6 - 7*c^3*d^3*x^3 - 8*c^4*d^2)]","A",0
445,1,219,0,0.594523," ","integrate(x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) - 6 \, {\left(c d x^{3} - 5 \, c^{2}\right)} \sqrt{d x^{3} + c}}{486 \, {\left(c^{3} d^{3} x^{6} - 7 \, c^{4} d^{2} x^{3} - 8 \, c^{5} d\right)}}, -\frac{{\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 3 \, {\left(c d x^{3} - 5 \, c^{2}\right)} \sqrt{d x^{3} + c}}{243 \, {\left(c^{3} d^{3} x^{6} - 7 \, c^{4} d^{2} x^{3} - 8 \, c^{5} d\right)}}\right]"," ",0,"[1/486*((d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) - 6*(c*d*x^3 - 5*c^2)*sqrt(d*x^3 + c))/(c^3*d^3*x^6 - 7*c^4*d^2*x^3 - 8*c^5*d), -1/243*((d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 3*(c*d*x^3 - 5*c^2)*sqrt(d*x^3 + c))/(c^3*d^3*x^6 - 7*c^4*d^2*x^3 - 8*c^5*d)]","A",0
446,1,316,0,0.663868," ","integrate(1/x/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{7 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 81 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 24 \, {\left(5 \, c d x^{3} - 43 \, c^{2}\right)} \sqrt{d x^{3} + c}}{15552 \, {\left(c^{4} d^{2} x^{6} - 7 \, c^{5} d x^{3} - 8 \, c^{6}\right)}}, \frac{81 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 7 \, {\left(d^{2} x^{6} - 7 \, c d x^{3} - 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(5 \, c d x^{3} - 43 \, c^{2}\right)} \sqrt{d x^{3} + c}}{7776 \, {\left(c^{4} d^{2} x^{6} - 7 \, c^{5} d x^{3} - 8 \, c^{6}\right)}}\right]"," ",0,"[1/15552*(7*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 81*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 24*(5*c*d*x^3 - 43*c^2)*sqrt(d*x^3 + c))/(c^4*d^2*x^6 - 7*c^5*d*x^3 - 8*c^6), 1/7776*(81*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 7*(d^2*x^6 - 7*c*d*x^3 - 8*c^2)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(5*c*d*x^3 - 43*c^2)*sqrt(d*x^3 + c))/(c^4*d^2*x^6 - 7*c^5*d*x^3 - 8*c^6)]","A",0
447,1,368,0,0.779251," ","integrate(1/x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(d^{3} x^{9} - 7 \, c d^{2} x^{6} - 8 \, c^{2} d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 405 \, {\left(d^{3} x^{9} - 7 \, c d^{2} x^{6} - 8 \, c^{2} d x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 24 \, {\left(35 \, c d^{2} x^{6} - 265 \, c^{2} d x^{3} - 108 \, c^{3}\right)} \sqrt{d x^{3} + c}}{62208 \, {\left(c^{5} d^{2} x^{9} - 7 \, c^{6} d x^{6} - 8 \, c^{7} x^{3}\right)}}, -\frac{405 \, {\left(d^{3} x^{9} - 7 \, c d^{2} x^{6} - 8 \, c^{2} d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + 5 \, {\left(d^{3} x^{9} - 7 \, c d^{2} x^{6} - 8 \, c^{2} d x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(35 \, c d^{2} x^{6} - 265 \, c^{2} d x^{3} - 108 \, c^{3}\right)} \sqrt{d x^{3} + c}}{31104 \, {\left(c^{5} d^{2} x^{9} - 7 \, c^{6} d x^{6} - 8 \, c^{7} x^{3}\right)}}\right]"," ",0,"[1/62208*(5*(d^3*x^9 - 7*c*d^2*x^6 - 8*c^2*d*x^3)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 405*(d^3*x^9 - 7*c*d^2*x^6 - 8*c^2*d*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 24*(35*c*d^2*x^6 - 265*c^2*d*x^3 - 108*c^3)*sqrt(d*x^3 + c))/(c^5*d^2*x^9 - 7*c^6*d*x^6 - 8*c^7*x^3), -1/31104*(405*(d^3*x^9 - 7*c*d^2*x^6 - 8*c^2*d*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + 5*(d^3*x^9 - 7*c*d^2*x^6 - 8*c^2*d*x^3)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(35*c*d^2*x^6 - 265*c^2*d*x^3 - 108*c^3)*sqrt(d*x^3 + c))/(c^5*d^2*x^9 - 7*c^6*d*x^6 - 8*c^7*x^3)]","A",0
448,1,398,0,0.895779," ","integrate(1/x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{13 \, {\left(d^{4} x^{12} - 7 \, c d^{3} x^{9} - 8 \, c^{2} d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 6 \, \sqrt{d x^{3} + c} \sqrt{c} + 10 \, c}{d x^{3} - 8 \, c}\right) + 8019 \, {\left(d^{4} x^{12} - 7 \, c d^{3} x^{9} - 8 \, c^{2} d^{2} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 24 \, {\left(665 \, c d^{3} x^{9} - 5107 \, c^{2} d^{2} x^{6} - 1836 \, c^{3} d x^{3} + 864 \, c^{4}\right)} \sqrt{d x^{3} + c}}{995328 \, {\left(c^{6} d^{2} x^{12} - 7 \, c^{7} d x^{9} - 8 \, c^{8} x^{6}\right)}}, \frac{8019 \, {\left(d^{4} x^{12} - 7 \, c d^{3} x^{9} - 8 \, c^{2} d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - 13 \, {\left(d^{4} x^{12} - 7 \, c d^{3} x^{9} - 8 \, c^{2} d^{2} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{3 \, c}\right) + 12 \, {\left(665 \, c d^{3} x^{9} - 5107 \, c^{2} d^{2} x^{6} - 1836 \, c^{3} d x^{3} + 864 \, c^{4}\right)} \sqrt{d x^{3} + c}}{497664 \, {\left(c^{6} d^{2} x^{12} - 7 \, c^{7} d x^{9} - 8 \, c^{8} x^{6}\right)}}\right]"," ",0,"[1/995328*(13*(d^4*x^12 - 7*c*d^3*x^9 - 8*c^2*d^2*x^6)*sqrt(c)*log((d*x^3 + 6*sqrt(d*x^3 + c)*sqrt(c) + 10*c)/(d*x^3 - 8*c)) + 8019*(d^4*x^12 - 7*c*d^3*x^9 - 8*c^2*d^2*x^6)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 24*(665*c*d^3*x^9 - 5107*c^2*d^2*x^6 - 1836*c^3*d*x^3 + 864*c^4)*sqrt(d*x^3 + c))/(c^6*d^2*x^12 - 7*c^7*d*x^9 - 8*c^8*x^6), 1/497664*(8019*(d^4*x^12 - 7*c*d^3*x^9 - 8*c^2*d^2*x^6)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - 13*(d^4*x^12 - 7*c*d^3*x^9 - 8*c^2*d^2*x^6)*sqrt(-c)*arctan(1/3*sqrt(d*x^3 + c)*sqrt(-c)/c) + 12*(665*c*d^3*x^9 - 5107*c^2*d^2*x^6 - 1836*c^3*d*x^3 + 864*c^4)*sqrt(d*x^3 + c))/(c^6*d^2*x^12 - 7*c^7*d*x^9 - 8*c^8*x^6)]","A",0
449,0,0,0,1.992567," ","integrate(x^7/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{7}}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^7/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
450,0,0,0,1.541972," ","integrate(x^4/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{4}}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^4/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
451,0,0,0,2.332283," ","integrate(x/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
452,0,0,0,2.775350," ","integrate(1/x^2/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{14} - 14 \, c d^{3} x^{11} + 33 \, c^{2} d^{2} x^{8} + 112 \, c^{3} d x^{5} + 64 \, c^{4} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^14 - 14*c*d^3*x^11 + 33*c^2*d^2*x^8 + 112*c^3*d*x^5 + 64*c^4*x^2), x)","F",0
453,0,0,0,7.412805," ","integrate(1/x^5/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{17} - 14 \, c d^{3} x^{14} + 33 \, c^{2} d^{2} x^{11} + 112 \, c^{3} d x^{8} + 64 \, c^{4} x^{5}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^17 - 14*c*d^3*x^14 + 33*c^2*d^2*x^11 + 112*c^3*d*x^8 + 64*c^4*x^5), x)","F",0
454,0,0,0,16.751184," ","integrate(1/x^8/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{20} - 14 \, c d^{3} x^{17} + 33 \, c^{2} d^{2} x^{14} + 112 \, c^{3} d x^{11} + 64 \, c^{4} x^{8}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^20 - 14*c*d^3*x^17 + 33*c^2*d^2*x^14 + 112*c^3*d*x^11 + 64*c^4*x^8), x)","F",0
455,0,0,0,0.706555," ","integrate(x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{6}}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^6/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
456,0,0,0,2.463067," ","integrate(x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c} x^{3}}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)*x^3/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
457,0,0,0,2.751033," ","integrate(1/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{12} - 14 \, c d^{3} x^{9} + 33 \, c^{2} d^{2} x^{6} + 112 \, c^{3} d x^{3} + 64 \, c^{4}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^12 - 14*c*d^3*x^9 + 33*c^2*d^2*x^6 + 112*c^3*d*x^3 + 64*c^4), x)","F",0
458,0,0,0,6.104530," ","integrate(1/x^3/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{15} - 14 \, c d^{3} x^{12} + 33 \, c^{2} d^{2} x^{9} + 112 \, c^{3} d x^{6} + 64 \, c^{4} x^{3}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^15 - 14*c*d^3*x^12 + 33*c^2*d^2*x^9 + 112*c^3*d*x^6 + 64*c^4*x^3), x)","F",0
459,0,0,0,15.288430," ","integrate(1/x^6/(-d*x^3+8*c)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{3} + c}}{d^{4} x^{18} - 14 \, c d^{3} x^{15} + 33 \, c^{2} d^{2} x^{12} + 112 \, c^{3} d x^{9} + 64 \, c^{4} x^{6}}, x\right)"," ",0,"integral(sqrt(d*x^3 + c)/(d^4*x^18 - 14*c*d^3*x^15 + 33*c^2*d^2*x^12 + 112*c^3*d*x^9 + 64*c^4*x^6), x)","F",0
460,1,469,0,0.917073," ","integrate(x^8*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a^{2} b c d - 5 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 5 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, {\left(2 \, {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + 2 \, a b^{3} c^{2} - 17 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{3} c d + 5 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{18 \, {\left(a b^{5} c d - a^{2} b^{4} d^{2} + {\left(b^{6} c d - a b^{5} d^{2}\right)} x^{3}\right)}}, -\frac{3 \, {\left(4 \, a^{2} b c d - 5 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 5 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(2 \, {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + 2 \, a b^{3} c^{2} - 17 \, a^{2} b^{2} c d + 15 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{3} c d + 5 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{9 \, {\left(a b^{5} c d - a^{2} b^{4} d^{2} + {\left(b^{6} c d - a b^{5} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/18*(3*(4*a^2*b*c*d - 5*a^3*d^2 + (4*a*b^2*c*d - 5*a^2*b*d^2)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*(2*(b^4*c*d - a*b^3*d^2)*x^6 + 2*a*b^3*c^2 - 17*a^2*b^2*c*d + 15*a^3*b*d^2 + 2*(b^4*c^2 - 6*a*b^3*c*d + 5*a^2*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c*d - a^2*b^4*d^2 + (b^6*c*d - a*b^5*d^2)*x^3), -1/9*(3*(4*a^2*b*c*d - 5*a^3*d^2 + (4*a*b^2*c*d - 5*a^2*b*d^2)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (2*(b^4*c*d - a*b^3*d^2)*x^6 + 2*a*b^3*c^2 - 17*a^2*b^2*c*d + 15*a^3*b*d^2 + 2*(b^4*c^2 - 6*a*b^3*c*d + 5*a^2*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c*d - a^2*b^4*d^2 + (b^6*c*d - a*b^5*d^2)*x^3)]","A",0
461,1,334,0,0.625688," ","integrate(x^5*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, b^{2} c - 3 \, a b d\right)} x^{3} + 2 \, a b c - 3 \, a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, {\left(3 \, a b^{2} c - 3 \, a^{2} b d + 2 \, {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a b^{4} c - a^{2} b^{3} d + {\left(b^{5} c - a b^{4} d\right)} x^{3}\right)}}, \frac{{\left({\left(2 \, b^{2} c - 3 \, a b d\right)} x^{3} + 2 \, a b c - 3 \, a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(3 \, a b^{2} c - 3 \, a^{2} b d + 2 \, {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a b^{4} c - a^{2} b^{3} d + {\left(b^{5} c - a b^{4} d\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(((2*b^2*c - 3*a*b*d)*x^3 + 2*a*b*c - 3*a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*(3*a*b^2*c - 3*a^2*b*d + 2*(b^3*c - a*b^2*d)*x^3)*sqrt(d*x^3 + c))/(a*b^4*c - a^2*b^3*d + (b^5*c - a*b^4*d)*x^3), 1/3*(((2*b^2*c - 3*a*b*d)*x^3 + 2*a*b*c - 3*a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (3*a*b^2*c - 3*a^2*b*d + 2*(b^3*c - a*b^2*d)*x^3)*sqrt(d*x^3 + c))/(a*b^4*c - a^2*b^3*d + (b^5*c - a*b^4*d)*x^3)]","A",0
462,1,255,0,0.808508," ","integrate(x^2*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b d x^{3} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}}{6 \, {\left(a b^{3} c - a^{2} b^{2} d + {\left(b^{4} c - a b^{3} d\right)} x^{3}\right)}}, \frac{{\left(b d x^{3} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}}{3 \, {\left(a b^{3} c - a^{2} b^{2} d + {\left(b^{4} c - a b^{3} d\right)} x^{3}\right)}}\right]"," ",0,"[1/6*((b*d*x^3 + a*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(a*b^3*c - a^2*b^2*d + (b^4*c - a*b^3*d)*x^3), 1/3*((b*d*x^3 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(a*b^3*c - a^2*b^2*d + (b^4*c - a*b^3*d)*x^3)]","A",0
463,1,856,0,0.731040," ","integrate((d*x^3+c)^(1/2)/x/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) - 2 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{3}\right)}}, -\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{3}\right)}}, \frac{4 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{3}\right)}}, -\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - 2 \, {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b^{2} c - a^{4} b d + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) - 2*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^3), -1/3*(((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - (a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^3), 1/6*(4*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - ((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^3), -1/3*(((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - 2*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - (a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a^3*b^2*c - a^4*b*d + (a^2*b^3*c - a^3*b^2*d)*x^3)]","B",0
464,1,870,0,1.105613," ","integrate((d*x^3+c)^(1/2)/x^4/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(2 \, a b c x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b c x^{6} + a^{4} c x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(2 \, a b c x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b c x^{6} + a^{4} c x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, {\left(2 \, a b c x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b c x^{6} + a^{4} c x^{3}\right)}}, -\frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(2 \, a b c x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b c x^{6} + a^{4} c x^{3}\right)}}\right]"," ",0,"[-1/6*(((4*b^2*c^2 - 3*a*b*c*d)*x^6 + (4*a*b*c^2 - 3*a^2*c*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + ((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(2*a*b*c*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*c*x^6 + a^4*c*x^3), -1/6*(2*((4*b^2*c^2 - 3*a*b*c*d)*x^6 + (4*a*b*c^2 - 3*a^2*c*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(2*a*b*c*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*c*x^6 + a^4*c*x^3), -1/6*(2*((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + ((4*b^2*c^2 - 3*a*b*c*d)*x^6 + (4*a*b*c^2 - 3*a^2*c*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*(2*a*b*c*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*c*x^6 + a^4*c*x^3), -1/3*(((4*b^2*c^2 - 3*a*b*c*d)*x^6 + (4*a*b*c^2 - 3*a^2*c*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (2*a*b*c*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*c*x^6 + a^4*c*x^3)]","A",0
465,-1,0,0,0.000000," ","integrate(x^3*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate(x*(d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate((d*x^3+c)^(1/2)/x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,1,443,0,0.687686," ","integrate(x^8*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, a^{2} b c d - 7 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 7 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) - 2 \, {\left(6 \, b^{3} d^{2} x^{9} + 2 \, {\left(6 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{6} + 6 \, a b^{2} c^{2} - 95 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(3 \, b^{3} c^{2} - 34 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{90 \, {\left(b^{5} d x^{3} + a b^{4} d\right)}}, \frac{15 \, {\left(4 \, a^{2} b c d - 7 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 7 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(6 \, b^{3} d^{2} x^{9} + 2 \, {\left(6 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{6} + 6 \, a b^{2} c^{2} - 95 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(3 \, b^{3} c^{2} - 34 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{45 \, {\left(b^{5} d x^{3} + a b^{4} d\right)}}\right]"," ",0,"[-1/90*(15*(4*a^2*b*c*d - 7*a^3*d^2 + (4*a*b^2*c*d - 7*a^2*b*d^2)*x^3)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) - 2*(6*b^3*d^2*x^9 + 2*(6*b^3*c*d - 7*a*b^2*d^2)*x^6 + 6*a*b^2*c^2 - 95*a^2*b*c*d + 105*a^3*d^2 + 2*(3*b^3*c^2 - 34*a*b^2*c*d + 35*a^2*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^5*d*x^3 + a*b^4*d), 1/45*(15*(4*a^2*b*c*d - 7*a^3*d^2 + (4*a*b^2*c*d - 7*a^2*b*d^2)*x^3)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (6*b^3*d^2*x^9 + 2*(6*b^3*c*d - 7*a*b^2*d^2)*x^6 + 6*a*b^2*c^2 - 95*a^2*b*c*d + 105*a^3*d^2 + 2*(3*b^3*c^2 - 34*a*b^2*c*d + 35*a^2*b*d^2)*x^3)*sqrt(d*x^3 + c))/(b^5*d*x^3 + a*b^4*d)]","A",0
471,1,314,0,1.104136," ","integrate(x^5*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, b^{2} c - 5 \, a b d\right)} x^{3} + 2 \, a b c - 5 \, a^{2} d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) - 2 \, {\left(2 \, b^{2} d x^{6} + 2 \, {\left(4 \, b^{2} c - 5 \, a b d\right)} x^{3} + 11 \, a b c - 15 \, a^{2} d\right)} \sqrt{d x^{3} + c}}{18 \, {\left(b^{4} x^{3} + a b^{3}\right)}}, -\frac{3 \, {\left({\left(2 \, b^{2} c - 5 \, a b d\right)} x^{3} + 2 \, a b c - 5 \, a^{2} d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(2 \, b^{2} d x^{6} + 2 \, {\left(4 \, b^{2} c - 5 \, a b d\right)} x^{3} + 11 \, a b c - 15 \, a^{2} d\right)} \sqrt{d x^{3} + c}}{9 \, {\left(b^{4} x^{3} + a b^{3}\right)}}\right]"," ",0,"[-1/18*(3*((2*b^2*c - 5*a*b*d)*x^3 + 2*a*b*c - 5*a^2*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) - 2*(2*b^2*d*x^6 + 2*(4*b^2*c - 5*a*b*d)*x^3 + 11*a*b*c - 15*a^2*d)*sqrt(d*x^3 + c))/(b^4*x^3 + a*b^3), -1/9*(3*((2*b^2*c - 5*a*b*d)*x^3 + 2*a*b*c - 5*a^2*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (2*b^2*d*x^6 + 2*(4*b^2*c - 5*a*b*d)*x^3 + 11*a*b*c - 15*a^2*d)*sqrt(d*x^3 + c))/(b^4*x^3 + a*b^3)]","A",0
472,1,234,0,0.903539," ","integrate(x^2*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d x^{3} + a d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, {\left(2 \, b d x^{3} - b c + 3 \, a d\right)} \sqrt{d x^{3} + c}}{6 \, {\left(b^{3} x^{3} + a b^{2}\right)}}, -\frac{3 \, {\left(b d x^{3} + a d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(2 \, b d x^{3} - b c + 3 \, a d\right)} \sqrt{d x^{3} + c}}{3 \, {\left(b^{3} x^{3} + a b^{2}\right)}}\right]"," ",0,"[1/6*(3*(b*d*x^3 + a*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*(2*b*d*x^3 - b*c + 3*a*d)*sqrt(d*x^3 + c))/(b^3*x^3 + a*b^2), -1/3*(3*(b*d*x^3 + a*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (2*b*d*x^3 - b*c + 3*a*d)*sqrt(d*x^3 + c))/(b^3*x^3 + a*b^2)]","A",0
473,1,686,0,1.070028," ","integrate((d*x^3+c)^(3/2)/x/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, {\left(b^{2} c x^{3} + a b c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, \sqrt{d x^{3} + c} {\left(a b c - a^{2} d\right)}}{6 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}, \frac{{\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(b^{2} c x^{3} + a b c\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + \sqrt{d x^{3} + c} {\left(a b c - a^{2} d\right)}}{3 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}, \frac{4 \, {\left(b^{2} c x^{3} + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, \sqrt{d x^{3} + c} {\left(a b c - a^{2} d\right)}}{6 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}, \frac{{\left({\left(2 \, b^{2} c + a b d\right)} x^{3} + 2 \, a b c + a^{2} d\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + 2 \, {\left(b^{2} c x^{3} + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{3} + c} {\left(a b c - a^{2} d\right)}}{3 \, {\left(a^{2} b^{2} x^{3} + a^{3} b\right)}}\right]"," ",0,"[1/6*(((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*(b^2*c*x^3 + a*b*c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*sqrt(d*x^3 + c)*(a*b*c - a^2*d))/(a^2*b^2*x^3 + a^3*b), 1/3*(((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (b^2*c*x^3 + a*b*c)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + sqrt(d*x^3 + c)*(a*b*c - a^2*d))/(a^2*b^2*x^3 + a^3*b), 1/6*(4*(b^2*c*x^3 + a*b*c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + ((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*sqrt(d*x^3 + c)*(a*b*c - a^2*d))/(a^2*b^2*x^3 + a^3*b), 1/3*(((2*b^2*c + a*b*d)*x^3 + 2*a*b*c + a^2*d)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + 2*(b^2*c*x^3 + a*b*c)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + sqrt(d*x^3 + c)*(a*b*c - a^2*d))/(a^2*b^2*x^3 + a^3*b)]","A",0
474,1,838,0,1.182088," ","integrate((d*x^3+c)^(3/2)/x^4/(b*x^3+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{6} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left({\left(2 \, a b c - a^{2} d\right)} x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{6} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left({\left(2 \, a b c - a^{2} d\right)} x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{6} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{3} + a}\right) + 2 \, {\left({\left(2 \, a b c - a^{2} d\right)} x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}, -\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{6} + {\left(4 \, a b c - a^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{3} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{6} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, a b c - a^{2} d\right)} x^{3} + a^{2} c\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b x^{6} + a^{4} x^{3}\right)}}\right]"," ",0,"[-1/6*(((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + ((4*b^2*c - 3*a*b*d)*x^6 + (4*a*b*c - 3*a^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*((2*a*b*c - a^2*d)*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*x^6 + a^4*x^3), -1/6*(2*((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^2*c - 3*a*b*d)*x^6 + (4*a*b*c - 3*a^2*d)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*((2*a*b*c - a^2*d)*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*x^6 + a^4*x^3), -1/6*(2*((4*b^2*c - 3*a*b*d)*x^6 + (4*a*b*c - 3*a^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + ((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt((b*c - a*d)/b)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*b*sqrt((b*c - a*d)/b))/(b*x^3 + a)) + 2*((2*a*b*c - a^2*d)*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*x^6 + a^4*x^3), -1/3*(((4*b^2*c - a*b*d)*x^6 + (4*a*b*c - a^2*d)*x^3)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^3 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^2*c - 3*a*b*d)*x^6 + (4*a*b*c - 3*a^2*d)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + ((2*a*b*c - a^2*d)*x^3 + a^2*c)*sqrt(d*x^3 + c))/(a^3*b*x^6 + a^4*x^3)]","A",0
475,-1,0,0,0.000000," ","integrate(x^3*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(x*(d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate((d*x^3+c)^(3/2)/x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,1,475,0,1.143342," ","integrate(x^8/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{3}\right)}}, -\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) - {\left(2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2 + 2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^3), -1/3*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) - (2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2 + 2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^3)]","B",0
481,1,348,0,1.108883," ","integrate(x^5/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{3}\right)}}, \frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{3} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(a b^{2} c - a^{2} b d\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^3), 1/3*(((2*b^2*c - a*b*d)*x^3 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (a*b^2*c - a^2*b*d)*sqrt(d*x^3 + c))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^3)]","A",0
482,1,302,0,0.894226," ","integrate(x^2/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b d x^{3} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}}{6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{3}\right)}}, -\frac{{\left(b d x^{3} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + \sqrt{d x^{3} + c} {\left(b^{2} c - a b d\right)}}{3 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*((b*d*x^3 + a*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^3), -1/3*((b*d*x^3 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + sqrt(d*x^3 + c)*(b^2*c - a*b*d))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^3)]","B",0
483,1,862,0,0.927369," ","integrate(1/x/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{3} + c} a b c + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{6 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}, \frac{\sqrt{d x^{3} + c} a b c + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right)}{3 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}, \frac{2 \, \sqrt{d x^{3} + c} a b c + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right)}{6 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}, \frac{\sqrt{d x^{3} + c} a b c + {\left(2 \, a b c^{2} - 3 \, a^{2} c d + {\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right)}{3 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(2*sqrt(d*x^3 + c)*a*b*c + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3), 1/3*(sqrt(d*x^3 + c)*a*b*c + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3), 1/6*(2*sqrt(d*x^3 + c)*a*b*c + 4*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3), 1/3*(sqrt(d*x^3 + c)*a*b*c + (2*a*b*c^2 - 3*a^2*c*d + (2*b^2*c^2 - 3*a*b*c*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3)]","A",0
484,1,1236,0,0.905109," ","integrate(1/x^4/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{6} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\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^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{6} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\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^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{6} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\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^{3}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{6} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\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^{3}\right)}}\right]"," ",0,"[1/6*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^6 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^3)*sqrt(d*x^3 + c))/((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^3), -1/6*(2*((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^6 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^3)*sqrt(d*x^3 + c))/((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^3), -1/6*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^6 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^3)*sqrt(d*x^3 + c))/((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^3), -1/3*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^6 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^3)*sqrt(d*x^3 + c))/((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^3)]","A",0
485,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^2/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,1,746,0,0.922412," ","integrate(x^8/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{6} + 4 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(4 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(2 \, a b^{3} c^{3} - a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + {\left(2 \, b^{4} c^{3} - 2 \, a b^{3} c^{2} d + a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a b^{5} c^{4} d - 3 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - a^{4} b^{2} c d^{4} + {\left(b^{6} c^{3} d^{2} - 3 \, a b^{5} c^{2} d^{3} + 3 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{6} + {\left(b^{6} c^{4} d - 2 \, a b^{5} c^{3} d^{2} + 2 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{3}\right)}}, -\frac{{\left({\left(4 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x^{6} + 4 \, a^{2} b c^{2} d - a^{3} c d^{2} + {\left(4 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(2 \, a b^{3} c^{3} - a^{2} b^{2} c^{2} d - a^{3} b c d^{2} + {\left(2 \, b^{4} c^{3} - 2 \, a b^{3} c^{2} d + a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a b^{5} c^{4} d - 3 \, a^{2} b^{4} c^{3} d^{2} + 3 \, a^{3} b^{3} c^{2} d^{3} - a^{4} b^{2} c d^{4} + {\left(b^{6} c^{3} d^{2} - 3 \, a b^{5} c^{2} d^{3} + 3 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{6} + {\left(b^{6} c^{4} d - 2 \, a b^{5} c^{3} d^{2} + 2 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(((4*a*b^2*c*d^2 - a^2*b*d^3)*x^6 + 4*a^2*b*c^2*d - a^3*c*d^2 + (4*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(2*a*b^3*c^3 - a^2*b^2*c^2*d - a^3*b*c*d^2 + (2*b^4*c^3 - 2*a*b^3*c^2*d + a^2*b^2*c*d^2 - a^3*b*d^3)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c^4*d - 3*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - a^4*b^2*c*d^4 + (b^6*c^3*d^2 - 3*a*b^5*c^2*d^3 + 3*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^6 + (b^6*c^4*d - 2*a*b^5*c^3*d^2 + 2*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^3), -1/3*(((4*a*b^2*c*d^2 - a^2*b*d^3)*x^6 + 4*a^2*b*c^2*d - a^3*c*d^2 + (4*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (2*a*b^3*c^3 - a^2*b^2*c^2*d - a^3*b*c*d^2 + (2*b^4*c^3 - 2*a*b^3*c^2*d + a^2*b^2*c*d^2 - a^3*b*d^3)*x^3)*sqrt(d*x^3 + c))/(a*b^5*c^4*d - 3*a^2*b^4*c^3*d^2 + 3*a^3*b^3*c^2*d^3 - a^4*b^2*c*d^4 + (b^6*c^3*d^2 - 3*a*b^5*c^2*d^3 + 3*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^6 + (b^6*c^4*d - 2*a*b^5*c^3*d^2 + 2*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^3)]","B",0
491,1,630,0,1.419922," ","integrate(x^5/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c d + a b d^{2}\right)} x^{6} + 2 \, a b c^{2} + a^{2} c d + {\left(2 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} \sqrt{b^{2} c - a b d}}{b x^{3} + a}\right) + 2 \, {\left(3 \, a b^{2} c^{2} - 3 \, a^{2} b c d + {\left(2 \, b^{3} c^{2} - a b^{2} c d - a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a b^{4} c^{4} - 3 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} - a^{4} b c d^{3} + {\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(b^{5} c^{4} - 2 \, a b^{4} c^{3} d + 2 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{3}\right)}}, \frac{{\left({\left(2 \, b^{2} c d + a b d^{2}\right)} x^{6} + 2 \, a b c^{2} + a^{2} c d + {\left(2 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-b^{2} c + a b d}}{b d x^{3} + b c}\right) + {\left(3 \, a b^{2} c^{2} - 3 \, a^{2} b c d + {\left(2 \, b^{3} c^{2} - a b^{2} c d - a^{2} b d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a b^{4} c^{4} - 3 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} - a^{4} b c d^{3} + {\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{6} + {\left(b^{5} c^{4} - 2 \, a b^{4} c^{3} d + 2 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(((2*b^2*c*d + a*b*d^2)*x^6 + 2*a*b*c^2 + a^2*c*d + (2*b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*sqrt(b^2*c - a*b*d))/(b*x^3 + a)) + 2*(3*a*b^2*c^2 - 3*a^2*b*c*d + (2*b^3*c^2 - a*b^2*c*d - a^2*b*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^4*c^4 - 3*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 - a^4*b*c*d^3 + (b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (b^5*c^4 - 2*a*b^4*c^3*d + 2*a^3*b^2*c*d^3 - a^4*b*d^4)*x^3), 1/3*(((2*b^2*c*d + a*b*d^2)*x^6 + 2*a*b*c^2 + a^2*c*d + (2*b^2*c^2 + 3*a*b*c*d + a^2*d^2)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^3 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^3 + b*c)) + (3*a*b^2*c^2 - 3*a^2*b*c*d + (2*b^3*c^2 - a*b^2*c*d - a^2*b*d^2)*x^3)*sqrt(d*x^3 + c))/(a*b^4*c^4 - 3*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 - a^4*b*c*d^3 + (b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^6 + (b^5*c^4 - 2*a*b^4*c^3*d + 2*a^3*b^2*c*d^3 - a^4*b*d^4)*x^3)]","B",0
492,1,450,0,1.465216," ","integrate(x^2/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d^{2} x^{6} + {\left(b c d + a d^{2}\right)} x^{3} + a c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - 2 \, {\left(3 \, b d x^{3} + b c + 2 \, a d\right)} \sqrt{d x^{3} + c}}{6 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)}}, \frac{3 \, {\left(b d^{2} x^{6} + {\left(b c d + a d^{2}\right)} x^{3} + a c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left(3 \, b d x^{3} + b c + 2 \, a d\right)} \sqrt{d x^{3} + c}}{3 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(3*(b*d^2*x^6 + (b*c*d + a*d^2)*x^3 + a*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - 2*(3*b*d*x^3 + b*c + 2*a*d)*sqrt(d*x^3 + c))/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3), 1/3*(3*(b*d^2*x^6 + (b*c*d + a*d^2)*x^3 + a*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - (3*b*d*x^3 + b*c + 2*a*d)*sqrt(d*x^3 + c))/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3)]","B",0
493,1,1819,0,1.661987," ","integrate(1/x/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{6} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - 2 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) - 2 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{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^{3}\right)}}, \frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{6} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} - 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{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^{3}\right)}}, \frac{4 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) - {\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{6} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d - 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{6 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{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^{3}\right)}}, \frac{{\left(2 \, a b^{2} c^{4} - 5 \, a^{2} b c^{3} d + {\left(2 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2}\right)} x^{6} + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - 5 \, a^{2} b c^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + 2 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{6} + a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(a b^{2} c^{3} + 2 \, a^{3} c d^{2} + {\left(a b^{2} c^{2} d + 2 \, a^{2} b c d^{2}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\left(a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2} + {\left(a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{4} b c^{2} d^{3}\right)} x^{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^{3}\right)}}\right]"," ",0,"[-1/6*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^6 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - 2*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) - 2*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^3)*sqrt(d*x^3 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^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^3), 1/3*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^6 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3)*sqrt(c)*log((d*x^3 - 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + (a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^3)*sqrt(d*x^3 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^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^3), 1/6*(4*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) - (2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^6 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d - 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*(a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^3)*sqrt(d*x^3 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^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^3), 1/3*((2*a*b^2*c^4 - 5*a^2*b*c^3*d + (2*b^3*c^3*d - 5*a*b^2*c^2*d^2)*x^6 + (2*b^3*c^4 - 3*a*b^2*c^3*d - 5*a^2*b*c^2*d^2)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + 2*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^6 + a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (a*b^2*c^3 + 2*a^3*c*d^2 + (a*b^2*c^2*d + 2*a^2*b*c*d^2)*x^3)*sqrt(d*x^3 + c))/(a^3*b^2*c^5 - 2*a^4*b*c^4*d + a^5*c^3*d^2 + (a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 + a^4*b*c^2*d^3)*x^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^3)]","B",0
494,1,2384,0,2.004203," ","integrate(1/x^4/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{9} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{6} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) - {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{9} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{6} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{6} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{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^{9} + {\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^{6} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{9} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{6} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) - {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{9} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{6} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x^{3} + 2 \, \sqrt{d x^{3} + c} \sqrt{c} + 2 \, c}{x^{3}}\right) + 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{6} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{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^{9} + {\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^{6} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{9} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{6} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{9} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{6} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{3}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{3} + 2 \, b c - a d + 2 \, \sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{3} + a}\right) + 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{6} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{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^{9} + {\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^{6} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{3}\right)}}, -\frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{9} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{6} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x^{3}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{3} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{3} + b c}\right) + {\left({\left(4 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x^{9} + {\left(4 \, b^{4} c^{4} - a b^{3} c^{3} d - 7 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} x^{6} + {\left(4 \, a b^{3} c^{4} - 5 \, a^{2} b^{2} c^{3} d - 2 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{3} + c} \sqrt{-c}}{c}\right) + {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(2 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{6} + {\left(2 \, a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3}\right)} \sqrt{d x^{3} + c}}{3 \, {\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^{9} + {\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^{6} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^9 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^6 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) - ((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^9 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^6 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^6 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(d*x^3 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^9 + (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^6 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^3), -1/6*(2*((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^9 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^6 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) - ((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^9 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^6 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(c)*log((d*x^3 + 2*sqrt(d*x^3 + c)*sqrt(c) + 2*c)/x^3) + 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^6 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(d*x^3 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^9 + (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^6 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^3), -1/6*(2*((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^9 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^6 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + ((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^9 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^6 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^3)*sqrt(b/(b*c - a*d))*log((b*d*x^3 + 2*b*c - a*d + 2*sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^3 + a)) + 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^6 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(d*x^3 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^9 + (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^6 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^3), -1/3*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^9 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^6 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x^3)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^3 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^3 + b*c)) + ((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^9 + (4*b^4*c^4 - a*b^3*c^3*d - 7*a^2*b^2*c^2*d^2 + a^3*b*c*d^3 + 3*a^4*d^4)*x^6 + (4*a*b^3*c^4 - 5*a^2*b^2*c^3*d - 2*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x^3 + c)*sqrt(-c)/c) + (a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (2*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^6 + (2*a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3)*sqrt(d*x^3 + c))/((a^3*b^3*c^5*d - 2*a^4*b^2*c^4*d^2 + a^5*b*c^3*d^3)*x^9 + (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^6 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x^3)]","B",0
495,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^2/(d*x^3+c)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,0,0,0,0.967636," ","integrate((e*x)^m*(b*x^3+a)^(5/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} x^{9} + {\left(2 \, B a b + A b^{2}\right)} x^{6} + {\left(B a^{2} + 2 \, A a b\right)} x^{3} + A a^{2}\right)} \sqrt{b x^{3} + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*b^2*x^9 + (2*B*a*b + A*b^2)*x^6 + (B*a^2 + 2*A*a*b)*x^3 + A*a^2)*sqrt(b*x^3 + a)*(e*x)^m, x)","F",0
501,0,0,0,1.017470," ","integrate((e*x)^m*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*(e*x)^m, x)","F",0
502,0,0,0,0.708941," ","integrate((e*x)^m*(b*x^3+a)^(1/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \left(e x\right)^{m}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*(e*x)^m, x)","F",0
503,0,0,0,0.600308," ","integrate((e*x)^m*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \left(e x\right)^{m}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*x^3 + A)*(e*x)^m/sqrt(b*x^3 + a), x)","F",0
504,0,0,0,0.670538," ","integrate((e*x)^m*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \left(e x\right)^{m}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*(e*x)^m/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
505,0,0,0,0.647614," ","integrate((e*x)^m*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \left(e x\right)^{m}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*(e*x)^m/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
506,1,256,0,0.577080," ","integrate(x^5/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{6} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{3} - 4 \, {\left(2 \, b d x^{3} + b c + a d\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{b d}\right)}{12 \, b^{2} d^{2}}, \frac{2 \, \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} b d + {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{3} + b c + a d\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{6} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{3}\right)}}\right)}{6 \, b^{2} d^{2}}\right]"," ",0,"[1/12*(4*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^6 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^3 - 4*(2*b*d*x^3 + b*c + a*d)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(b*d)))/(b^2*d^2), 1/6*(2*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*b*d + (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x^3 + b*c + a*d)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(-b*d)/(b^2*d^2*x^6 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^3)))/(b^2*d^2)]","A",0
507,1,194,0,0.639388," ","integrate(x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{6} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{3} + 4 \, {\left(2 \, b d x^{3} + b c + a d\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{b d}\right)}{6 \, b d}, -\frac{\sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x^{3} + b c + a d\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{-b d}}{2 \, {\left(b^{2} d^{2} x^{6} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{3}\right)}}\right)}{3 \, b d}\right]"," ",0,"[1/6*sqrt(b*d)*log(8*b^2*d^2*x^6 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 8*(b^2*c*d + a*b*d^2)*x^3 + 4*(2*b*d*x^3 + b*c + a*d)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(b*d))/(b*d), -1/3*sqrt(-b*d)*arctan(1/2*(2*b*d*x^3 + b*c + a*d)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(-b*d)/(b^2*d^2*x^6 + a*b*c*d + (b^2*c*d + a*b*d^2)*x^3))/(b*d)]","B",0
508,1,204,0,0.649202," ","integrate(1/x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{6} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{3} - 4 \, {\left({\left(b c + a d\right)} x^{3} + 2 \, a c\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{a c}}{x^{6}}\right)}{6 \, a c}, \frac{\sqrt{-a c} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{3} + 2 \, a c\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{6} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{3}\right)}}\right)}{3 \, a c}\right]"," ",0,"[1/6*sqrt(a*c)*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^6 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^3 - 4*((b*c + a*d)*x^3 + 2*a*c)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(a*c))/x^6)/(a*c), 1/3*sqrt(-a*c)*arctan(1/2*((b*c + a*d)*x^3 + 2*a*c)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(-a*c)/(a*b*c*d*x^6 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^3))/(a*c)]","B",0
509,1,278,0,0.787466," ","integrate(1/x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} {\left(b c + a d\right)} x^{3} \log\left(\frac{{\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{6} + 8 \, a^{2} c^{2} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x^{3} + 4 \, {\left({\left(b c + a d\right)} x^{3} + 2 \, a c\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{a c}}{x^{6}}\right) - 4 \, \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} a c}{12 \, a^{2} c^{2} x^{3}}, -\frac{\sqrt{-a c} {\left(b c + a d\right)} x^{3} \arctan\left(\frac{{\left({\left(b c + a d\right)} x^{3} + 2 \, a c\right)} \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} \sqrt{-a c}}{2 \, {\left(a b c d x^{6} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x^{3}\right)}}\right) + 2 \, \sqrt{b x^{3} + a} \sqrt{d x^{3} + c} a c}{6 \, a^{2} c^{2} x^{3}}\right]"," ",0,"[1/12*(sqrt(a*c)*(b*c + a*d)*x^3*log(((b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^6 + 8*a^2*c^2 + 8*(a*b*c^2 + a^2*c*d)*x^3 + 4*((b*c + a*d)*x^3 + 2*a*c)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(a*c))/x^6) - 4*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3), -1/6*(sqrt(-a*c)*(b*c + a*d)*x^3*arctan(1/2*((b*c + a*d)*x^3 + 2*a*c)*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*sqrt(-a*c)/(a*b*c*d*x^6 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x^3)) + 2*sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*a*c)/(a^2*c^2*x^3)]","A",0
510,0,0,0,0.583760," ","integrate(x^4/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c} x^{4}}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*x^4/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
511,0,0,0,0.564390," ","integrate(x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c} x^{3}}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*x^3/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
512,0,0,0,0.613576," ","integrate(x/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c} x}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)*x/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
513,0,0,0,0.701978," ","integrate(1/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c}}{b d x^{6} + {\left(b c + a d\right)} x^{3} + a c}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)/(b*d*x^6 + (b*c + a*d)*x^3 + a*c), x)","F",0
514,0,0,0,0.486642," ","integrate(1/x^2/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c}}{b d x^{8} + {\left(b c + a d\right)} x^{5} + a c x^{2}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)/(b*d*x^8 + (b*c + a*d)*x^5 + a*c*x^2), x)","F",0
515,0,0,0,0.783258," ","integrate(1/x^3/(b*x^3+a)^(1/2)/(d*x^3+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x^{3} + a} \sqrt{d x^{3} + c}}{b d x^{9} + {\left(b c + a d\right)} x^{6} + a c x^{3}}, x\right)"," ",0,"integral(sqrt(b*x^3 + a)*sqrt(d*x^3 + c)/(b*d*x^9 + (b*c + a*d)*x^6 + a*c*x^3), x)","F",0
516,1,295,0,1.260492," ","integrate((e*x)^(7/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} e^{3} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e + 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(8 \, B b^{2} e^{3} x^{7} + 2 \, {\left(B a b + 6 \, A b^{2}\right)} e^{3} x^{4} - 3 \, {\left(B a^{2} - 2 \, A a b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{288 \, b^{2}}, -\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} e^{3} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(8 \, B b^{2} e^{3} x^{7} + 2 \, {\left(B a b + 6 \, A b^{2}\right)} e^{3} x^{4} - 3 \, {\left(B a^{2} - 2 \, A a b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{144 \, b^{2}}\right]"," ",0,"[-1/288*(3*(B*a^3 - 2*A*a^2*b)*e^3*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e + 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(8*B*b^2*e^3*x^7 + 2*(B*a*b + 6*A*b^2)*e^3*x^4 - 3*(B*a^2 - 2*A*a*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2, -1/144*(3*(B*a^3 - 2*A*a^2*b)*e^3*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) - 2*(8*B*b^2*e^3*x^7 + 2*(B*a*b + 6*A*b^2)*e^3*x^4 - 3*(B*a^2 - 2*A*a*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2]","A",0
517,0,0,0,0.890431," ","integrate((e*x)^(5/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e^{2} x^{5} + A e^{2} x^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e^2*x^5 + A*e^2*x^2)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
518,0,0,0,0.646611," ","integrate((e*x)^(3/2)*(B*x^3+A)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B e x^{4} + A e x\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*e*x^4 + A*e*x)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
519,1,221,0,1.157683," ","integrate((B*x^3+A)*(e*x)^(1/2)*(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(2 \, B b x^{4} + {\left(B a + 4 \, A b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{48 \, b}, \frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) + 2 \, {\left(2 \, B b x^{4} + {\left(B a + 4 \, A b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{24 \, b}\right]"," ",0,"[-1/48*((B*a^2 - 4*A*a*b)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(2*B*b*x^4 + (B*a + 4*A*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b, 1/24*((B*a^2 - 4*A*a*b)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) + 2*(2*B*b*x^4 + (B*a + 4*A*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b]","A",0
520,0,0,0,0.545887," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(e*x), x)","F",0
521,0,0,0,0.708056," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
522,1,207,0,1.547024," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(B a + 2 \, A b\right)} \sqrt{b e} x^{2} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b x^{4} + a x\right)} \sqrt{b x^{3} + a} \sqrt{b e} \sqrt{e x}\right) + 4 \, {\left(B b x^{3} - 2 \, A b\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{12 \, b e^{3} x^{2}}, -\frac{{\left(B a + 2 \, A b\right)} \sqrt{-b e} x^{2} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{-b e} \sqrt{e x} x}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(B b x^{3} - 2 \, A b\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{6 \, b e^{3} x^{2}}\right]"," ",0,"[1/12*((B*a + 2*A*b)*sqrt(b*e)*x^2*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b*x^4 + a*x)*sqrt(b*x^3 + a)*sqrt(b*e)*sqrt(e*x)) + 4*(B*b*x^3 - 2*A*b)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2), -1/6*((B*a + 2*A*b)*sqrt(-b*e)*x^2*arctan(2*sqrt(b*x^3 + a)*sqrt(-b*e)*sqrt(e*x)*x/(2*b*e*x^3 + a*e)) - 2*(B*b*x^3 - 2*A*b)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2)]","A",0
523,0,0,0,0.606381," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
524,0,0,0,0.459743," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^(9/2), x)","F",0
525,1,180,0,0.948131," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, B a \sqrt{b} x^{5} \log\left(-8 \, b^{2} x^{6} - 8 \, a b x^{3} - 4 \, {\left(2 \, b x^{4} + a x\right)} \sqrt{b x^{3} + a} \sqrt{b} \sqrt{x} - a^{2}\right) - 4 \, {\left({\left(3 \, B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \sqrt{x}}{18 \, a x^{5}}, -\frac{3 \, B a \sqrt{-b} x^{5} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{-b} x^{\frac{3}{2}}}{2 \, b x^{3} + a}\right) + 2 \, {\left({\left(3 \, B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \sqrt{x}}{9 \, a x^{5}}\right]"," ",0,"[1/18*(3*B*a*sqrt(b)*x^5*log(-8*b^2*x^6 - 8*a*b*x^3 - 4*(2*b*x^4 + a*x)*sqrt(b*x^3 + a)*sqrt(b)*sqrt(x) - a^2) - 4*((3*B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*sqrt(x))/(a*x^5), -1/9*(3*B*a*sqrt(-b)*x^5*arctan(2*sqrt(b*x^3 + a)*sqrt(-b)*x^(3/2)/(2*b*x^3 + a)) + 2*((3*B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*sqrt(x))/(a*x^5)]","A",0
526,0,0,0,0.504989," ","integrate((B*x^3+A)*(b*x^3+a)^(1/2)/x^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a}}{x^{\frac{13}{2}}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)/x^(13/2), x)","F",0
527,1,355,0,1.203212," ","integrate((e*x)^(7/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} e^{3} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e + 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(48 \, B b^{3} e^{3} x^{10} + 8 \, {\left(9 \, B a b^{2} + 8 \, A b^{3}\right)} e^{3} x^{7} + 2 \, {\left(3 \, B a^{2} b + 56 \, A a b^{2}\right)} e^{3} x^{4} - 3 \, {\left(3 \, B a^{3} - 8 \, A a^{2} b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{2304 \, b^{2}}, -\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} e^{3} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(48 \, B b^{3} e^{3} x^{10} + 8 \, {\left(9 \, B a b^{2} + 8 \, A b^{3}\right)} e^{3} x^{7} + 2 \, {\left(3 \, B a^{2} b + 56 \, A a b^{2}\right)} e^{3} x^{4} - 3 \, {\left(3 \, B a^{3} - 8 \, A a^{2} b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{1152 \, b^{2}}\right]"," ",0,"[-1/2304*(3*(3*B*a^4 - 8*A*a^3*b)*e^3*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e + 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(48*B*b^3*e^3*x^10 + 8*(9*B*a*b^2 + 8*A*b^3)*e^3*x^7 + 2*(3*B*a^2*b + 56*A*a*b^2)*e^3*x^4 - 3*(3*B*a^3 - 8*A*a^2*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2, -1/1152*(3*(3*B*a^4 - 8*A*a^3*b)*e^3*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) - 2*(48*B*b^3*e^3*x^10 + 8*(9*B*a*b^2 + 8*A*b^3)*e^3*x^7 + 2*(3*B*a^2*b + 56*A*a*b^2)*e^3*x^4 - 3*(3*B*a^3 - 8*A*a^2*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2]","A",0
528,0,0,0,0.740474," ","integrate((e*x)^(5/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b e^{2} x^{8} + {\left(B a + A b\right)} e^{2} x^{5} + A a e^{2} x^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b*e^2*x^8 + (B*a + A*b)*e^2*x^5 + A*a*e^2*x^2)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
529,0,0,0,0.504343," ","integrate((e*x)^(3/2)*(b*x^3+a)^(3/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b e x^{7} + {\left(B a + A b\right)} e x^{4} + A a e x\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b*e*x^7 + (B*a + A*b)*e*x^4 + A*a*e*x)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
530,1,273,0,1.558695," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)*(e*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(8 \, B b^{2} x^{7} + 2 \, {\left(7 \, B a b + 6 \, A b^{2}\right)} x^{4} + 3 \, {\left(B a^{2} + 10 \, A a b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{288 \, b}, \frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) + 2 \, {\left(8 \, B b^{2} x^{7} + 2 \, {\left(7 \, B a b + 6 \, A b^{2}\right)} x^{4} + 3 \, {\left(B a^{2} + 10 \, A a b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{144 \, b}\right]"," ",0,"[-1/288*(3*(B*a^3 - 6*A*a^2*b)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(8*B*b^2*x^7 + 2*(7*B*a*b + 6*A*b^2)*x^4 + 3*(B*a^2 + 10*A*a*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b, 1/144*(3*(B*a^3 - 6*A*a^2*b)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) + 2*(8*B*b^2*x^7 + 2*(7*B*a*b + 6*A*b^2)*x^4 + 3*(B*a^2 + 10*A*a*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b]","A",0
531,0,0,0,0.758368," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*sqrt(e*x)/(e*x), x)","F",0
532,0,0,0,0.637797," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
533,1,255,0,1.449562," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{b e} x^{2} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b x^{4} + a x\right)} \sqrt{b x^{3} + a} \sqrt{b e} \sqrt{e x}\right) + 4 \, {\left(2 \, B b^{2} x^{6} + {\left(5 \, B a b + 4 \, A b^{2}\right)} x^{3} - 8 \, A a b\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{48 \, b e^{3} x^{2}}, -\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{-b e} x^{2} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{-b e} \sqrt{e x} x}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(2 \, B b^{2} x^{6} + {\left(5 \, B a b + 4 \, A b^{2}\right)} x^{3} - 8 \, A a b\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{24 \, b e^{3} x^{2}}\right]"," ",0,"[1/48*(3*(B*a^2 + 4*A*a*b)*sqrt(b*e)*x^2*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b*x^4 + a*x)*sqrt(b*x^3 + a)*sqrt(b*e)*sqrt(e*x)) + 4*(2*B*b^2*x^6 + (5*B*a*b + 4*A*b^2)*x^3 - 8*A*a*b)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2), -1/24*(3*(B*a^2 + 4*A*a*b)*sqrt(-b*e)*x^2*arctan(2*sqrt(b*x^3 + a)*sqrt(-b*e)*sqrt(e*x)*x/(2*b*e*x^3 + a*e)) - 2*(2*B*b^2*x^6 + (5*B*a*b + 4*A*b^2)*x^3 - 8*A*a*b)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2)]","A",0
534,0,0,0,0.698188," ","integrate((b*x^3+a)^(3/2)*(B*x^3+A)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b x^{6} + {\left(B a + A b\right)} x^{3} + A a\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*b*x^6 + (B*a + A*b)*x^3 + A*a)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
535,1,409,0,1.331656," ","integrate((e*x)^(7/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} e^{3} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e + 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(384 \, B b^{4} e^{3} x^{13} + 48 \, {\left(21 \, B a b^{3} + 10 \, A b^{4}\right)} e^{3} x^{10} + 8 \, {\left(93 \, B a^{2} b^{2} + 170 \, A a b^{3}\right)} e^{3} x^{7} + 10 \, {\left(3 \, B a^{3} b + 118 \, A a^{2} b^{2}\right)} e^{3} x^{4} - 15 \, {\left(3 \, B a^{4} - 10 \, A a^{3} b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{23040 \, b^{2}}, -\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} e^{3} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(384 \, B b^{4} e^{3} x^{13} + 48 \, {\left(21 \, B a b^{3} + 10 \, A b^{4}\right)} e^{3} x^{10} + 8 \, {\left(93 \, B a^{2} b^{2} + 170 \, A a b^{3}\right)} e^{3} x^{7} + 10 \, {\left(3 \, B a^{3} b + 118 \, A a^{2} b^{2}\right)} e^{3} x^{4} - 15 \, {\left(3 \, B a^{4} - 10 \, A a^{3} b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{11520 \, b^{2}}\right]"," ",0,"[-1/23040*(15*(3*B*a^5 - 10*A*a^4*b)*e^3*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e + 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(384*B*b^4*e^3*x^13 + 48*(21*B*a*b^3 + 10*A*b^4)*e^3*x^10 + 8*(93*B*a^2*b^2 + 170*A*a*b^3)*e^3*x^7 + 10*(3*B*a^3*b + 118*A*a^2*b^2)*e^3*x^4 - 15*(3*B*a^4 - 10*A*a^3*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2, -1/11520*(15*(3*B*a^5 - 10*A*a^4*b)*e^3*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) - 2*(384*B*b^4*e^3*x^13 + 48*(21*B*a*b^3 + 10*A*b^4)*e^3*x^10 + 8*(93*B*a^2*b^2 + 170*A*a*b^3)*e^3*x^7 + 10*(3*B*a^3*b + 118*A*a^2*b^2)*e^3*x^4 - 15*(3*B*a^4 - 10*A*a^3*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2]","A",0
536,0,0,0,0.838710," ","integrate((e*x)^(5/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} e^{2} x^{11} + {\left(2 \, B a b + A b^{2}\right)} e^{2} x^{8} + {\left(B a^{2} + 2 \, A a b\right)} e^{2} x^{5} + A a^{2} e^{2} x^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b^2*e^2*x^11 + (2*B*a*b + A*b^2)*e^2*x^8 + (B*a^2 + 2*A*a*b)*e^2*x^5 + A*a^2*e^2*x^2)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
537,0,0,0,0.789766," ","integrate((e*x)^(3/2)*(b*x^3+a)^(5/2)*(B*x^3+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(B b^{2} e x^{10} + {\left(2 \, B a b + A b^{2}\right)} e x^{7} + {\left(B a^{2} + 2 \, A a b\right)} e x^{4} + A a^{2} e x\right)} \sqrt{b x^{3} + a} \sqrt{e x}, x\right)"," ",0,"integral((B*b^2*e*x^10 + (2*B*a*b + A*b^2)*e*x^7 + (B*a^2 + 2*A*a*b)*e*x^4 + A*a^2*e*x)*sqrt(b*x^3 + a)*sqrt(e*x), x)","F",0
538,1,323,0,1.385514," ","integrate((b*x^3+a)^(5/2)*(B*x^3+A)*(e*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(48 \, B b^{3} x^{10} + 8 \, {\left(17 \, B a b^{2} + 8 \, A b^{3}\right)} x^{7} + 2 \, {\left(59 \, B a^{2} b + 104 \, A a b^{2}\right)} x^{4} + 3 \, {\left(5 \, B a^{3} + 88 \, A a^{2} b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{2304 \, b}, \frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) + 2 \, {\left(48 \, B b^{3} x^{10} + 8 \, {\left(17 \, B a b^{2} + 8 \, A b^{3}\right)} x^{7} + 2 \, {\left(59 \, B a^{2} b + 104 \, A a b^{2}\right)} x^{4} + 3 \, {\left(5 \, B a^{3} + 88 \, A a^{2} b\right)} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{1152 \, b}\right]"," ",0,"[-1/2304*(15*(B*a^4 - 8*A*a^3*b)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(48*B*b^3*x^10 + 8*(17*B*a*b^2 + 8*A*b^3)*x^7 + 2*(59*B*a^2*b + 104*A*a*b^2)*x^4 + 3*(5*B*a^3 + 88*A*a^2*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b, 1/1152*(15*(B*a^4 - 8*A*a^3*b)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) + 2*(48*B*b^3*x^10 + 8*(17*B*a*b^2 + 8*A*b^3)*x^7 + 2*(59*B*a^2*b + 104*A*a*b^2)*x^4 + 3*(5*B*a^3 + 88*A*a^2*b)*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b]","A",0
539,0,0,0,0.834599," ","integrate((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{9} + {\left(2 \, B a b + A b^{2}\right)} x^{6} + {\left(B a^{2} + 2 \, A a b\right)} x^{3} + A a^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e x}, x\right)"," ",0,"integral((B*b^2*x^9 + (2*B*a*b + A*b^2)*x^6 + (B*a^2 + 2*A*a*b)*x^3 + A*a^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(e*x), x)","F",0
540,0,0,0,0.802606," ","integrate((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{9} + {\left(2 \, B a b + A b^{2}\right)} x^{6} + {\left(B a^{2} + 2 \, A a b\right)} x^{3} + A a^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{2} x^{2}}, x\right)"," ",0,"integral((B*b^2*x^9 + (2*B*a*b + A*b^2)*x^6 + (B*a^2 + 2*A*a*b)*x^3 + A*a^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^2*x^2), x)","F",0
541,1,309,0,1.280678," ","integrate((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{b e} x^{2} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b x^{4} + a x\right)} \sqrt{b x^{3} + a} \sqrt{b e} \sqrt{e x}\right) + 4 \, {\left(8 \, B b^{3} x^{9} + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{6} - 48 \, A a^{2} b + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{288 \, b e^{3} x^{2}}, -\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{-b e} x^{2} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{-b e} \sqrt{e x} x}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(8 \, B b^{3} x^{9} + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{6} - 48 \, A a^{2} b + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x^{3}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{144 \, b e^{3} x^{2}}\right]"," ",0,"[1/288*(15*(B*a^3 + 6*A*a^2*b)*sqrt(b*e)*x^2*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b*x^4 + a*x)*sqrt(b*x^3 + a)*sqrt(b*e)*sqrt(e*x)) + 4*(8*B*b^3*x^9 + 2*(13*B*a*b^2 + 6*A*b^3)*x^6 - 48*A*a^2*b + 3*(11*B*a^2*b + 18*A*a*b^2)*x^3)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2), -1/144*(15*(B*a^3 + 6*A*a^2*b)*sqrt(-b*e)*x^2*arctan(2*sqrt(b*x^3 + a)*sqrt(-b*e)*sqrt(e*x)*x/(2*b*e*x^3 + a*e)) - 2*(8*B*b^3*x^9 + 2*(13*B*a*b^2 + 6*A*b^3)*x^6 - 48*A*a^2*b + 3*(11*B*a^2*b + 18*A*a*b^2)*x^3)*sqrt(b*x^3 + a)*sqrt(e*x))/(b*e^3*x^2)]","A",0
542,0,0,0,0.909575," ","integrate((b*x^3+a)^(5/2)*(B*x^3+A)/(e*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B b^{2} x^{9} + {\left(2 \, B a b + A b^{2}\right)} x^{6} + {\left(B a^{2} + 2 \, A a b\right)} x^{3} + A a^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{e^{4} x^{4}}, x\right)"," ",0,"integral((B*b^2*x^9 + (2*B*a*b + A*b^2)*x^6 + (B*a^2 + 2*A*a*b)*x^3 + A*a^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(e^4*x^4), x)","F",0
543,1,245,0,1.441490," ","integrate((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} e^{3} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e + 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(2 \, B b e^{3} x^{4} - {\left(3 \, B a - 4 \, A b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{48 \, b^{2}}, -\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} e^{3} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) - 2 \, {\left(2 \, B b e^{3} x^{4} - {\left(3 \, B a - 4 \, A b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{24 \, b^{2}}\right]"," ",0,"[-1/48*((3*B*a^2 - 4*A*a*b)*e^3*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e + 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(2*B*b*e^3*x^4 - (3*B*a - 4*A*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2, -1/24*((3*B*a^2 - 4*A*a*b)*e^3*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) - 2*(2*B*b*e^3*x^4 - (3*B*a - 4*A*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/b^2]","A",0
544,0,0,0,0.669651," ","integrate((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{5} + A e^{2} x^{2}\right)} \sqrt{e x}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*e^2*x^5 + A*e^2*x^2)*sqrt(e*x)/sqrt(b*x^3 + a), x)","F",0
545,0,0,0,0.749385," ","integrate((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{4} + A e x\right)} \sqrt{e x}}{\sqrt{b x^{3} + a}}, x\right)"," ",0,"integral((B*e*x^4 + A*e*x)*sqrt(e*x)/sqrt(b*x^3 + a), x)","F",0
546,1,184,0,1.279823," ","integrate((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{3} + a} \sqrt{e x} B x - {\left(B a - 2 \, A b\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right)}{12 \, b}, \frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} B x + {\left(B a - 2 \, A b\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right)}{6 \, b}\right]"," ",0,"[1/12*(4*sqrt(b*x^3 + a)*sqrt(e*x)*B*x - (B*a - 2*A*b)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)))/b, 1/6*(2*sqrt(b*x^3 + a)*sqrt(e*x)*B*x + (B*a - 2*A*b)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)))/b]","A",0
547,0,0,0,0.667705," ","integrate((B*x^3+A)/(e*x)^(1/2)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b e x^{4} + a e x}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b*e*x^4 + a*e*x), x)","F",0
548,0,0,0,0.739299," ","integrate((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b e^{2} x^{5} + a e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b*e^2*x^5 + a*e^2*x^2), x)","F",0
549,1,183,0,1.192453," ","integrate((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b e} B a x^{2} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b x^{4} + a x\right)} \sqrt{b x^{3} + a} \sqrt{b e} \sqrt{e x}\right) - 4 \, \sqrt{b x^{3} + a} \sqrt{e x} A b}{6 \, a b e^{3} x^{2}}, -\frac{\sqrt{-b e} B a x^{2} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{-b e} \sqrt{e x} x}{2 \, b e x^{3} + a e}\right) + 2 \, \sqrt{b x^{3} + a} \sqrt{e x} A b}{3 \, a b e^{3} x^{2}}\right]"," ",0,"[1/6*(sqrt(b*e)*B*a*x^2*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b*x^4 + a*x)*sqrt(b*x^3 + a)*sqrt(b*e)*sqrt(e*x)) - 4*sqrt(b*x^3 + a)*sqrt(e*x)*A*b)/(a*b*e^3*x^2), -1/3*(sqrt(-b*e)*B*a*x^2*arctan(2*sqrt(b*x^3 + a)*sqrt(-b*e)*sqrt(e*x)*x/(2*b*e*x^3 + a*e)) + 2*sqrt(b*x^3 + a)*sqrt(e*x)*A*b)/(a*b*e^3*x^2)]","A",0
550,0,0,0,0.533249," ","integrate((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b e^{4} x^{7} + a e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b*e^4*x^7 + a*e^4*x^4), x)","F",0
551,1,307,0,1.924595," ","integrate((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, B a b - 2 \, A b^{2}\right)} e^{3} x^{3} + {\left(3 \, B a^{2} - 2 \, A a b\right)} e^{3}\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left(B b e^{3} x^{4} + {\left(3 \, B a - 2 \, A b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{12 \, {\left(b^{3} x^{3} + a b^{2}\right)}}, \frac{{\left({\left(3 \, B a b - 2 \, A b^{2}\right)} e^{3} x^{3} + {\left(3 \, B a^{2} - 2 \, A a b\right)} e^{3}\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) + 2 \, {\left(B b e^{3} x^{4} + {\left(3 \, B a - 2 \, A b\right)} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{6 \, {\left(b^{3} x^{3} + a b^{2}\right)}}\right]"," ",0,"[-1/12*(((3*B*a*b - 2*A*b^2)*e^3*x^3 + (3*B*a^2 - 2*A*a*b)*e^3)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*(B*b*e^3*x^4 + (3*B*a - 2*A*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/(b^3*x^3 + a*b^2), 1/6*(((3*B*a*b - 2*A*b^2)*e^3*x^3 + (3*B*a^2 - 2*A*a*b)*e^3)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) + 2*(B*b*e^3*x^4 + (3*B*a - 2*A*b)*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/(b^3*x^3 + a*b^2)]","A",0
552,0,0,0,0.749349," ","integrate((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{5} + A e^{2} x^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^5 + A*e^2*x^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
553,0,0,0,0.603509," ","integrate((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{4} + A e x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{2} x^{6} + 2 \, a b x^{3} + a^{2}}, x\right)"," ",0,"integral((B*e*x^4 + A*e*x)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^2*x^6 + 2*a*b*x^3 + a^2), x)","F",0
554,1,234,0,0.861347," ","integrate((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{b x^{3} + a} {\left(B a - A b\right)} \sqrt{e x} x - {\left(B a b x^{3} + B a^{2}\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right)}{6 \, {\left(a b^{2} x^{3} + a^{2} b\right)}}, -\frac{2 \, \sqrt{b x^{3} + a} {\left(B a - A b\right)} \sqrt{e x} x + {\left(B a b x^{3} + B a^{2}\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right)}{3 \, {\left(a b^{2} x^{3} + a^{2} b\right)}}\right]"," ",0,"[-1/6*(4*sqrt(b*x^3 + a)*(B*a - A*b)*sqrt(e*x)*x - (B*a*b*x^3 + B*a^2)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)))/(a*b^2*x^3 + a^2*b), -1/3*(2*sqrt(b*x^3 + a)*(B*a - A*b)*sqrt(e*x)*x + (B*a*b*x^3 + B*a^2)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)))/(a*b^2*x^3 + a^2*b)]","A",0
555,0,0,0,0.815408," ","integrate((B*x^3+A)/(b*x^3+a)^(3/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{2} e x^{7} + 2 \, a b e x^{4} + a^{2} e x}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^2*e*x^7 + 2*a*b*e*x^4 + a^2*e*x), x)","F",0
556,0,0,0,0.576247," ","integrate((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{2} e^{2} x^{8} + 2 \, a b e^{2} x^{5} + a^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^2*e^2*x^8 + 2*a*b*e^2*x^5 + a^2*e^2*x^2), x)","F",0
557,1,57,0,0.653358," ","integrate((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(B a - 2 \, A b\right)} x^{3} - A a\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{3 \, {\left(a^{2} b e^{3} x^{5} + a^{3} e^{3} x^{2}\right)}}"," ",0,"2/3*((B*a - 2*A*b)*x^3 - A*a)*sqrt(b*x^3 + a)*sqrt(e*x)/(a^2*b*e^3*x^5 + a^3*e^3*x^2)","A",0
558,0,0,0,0.571069," ","integrate((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{2} e^{4} x^{10} + 2 \, a b e^{4} x^{7} + a^{2} e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^2*e^4*x^10 + 2*a*b*e^4*x^7 + a^2*e^4*x^4), x)","F",0
559,1,345,0,0.835315," ","integrate((e*x)^(7/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b^{2} e^{3} x^{6} + 2 \, B a^{2} b e^{3} x^{3} + B a^{3} e^{3}\right)} \sqrt{\frac{e}{b}} \log\left(-8 \, b^{2} e x^{6} - 8 \, a b e x^{3} - a^{2} e - 4 \, {\left(2 \, b^{2} x^{4} + a b x\right)} \sqrt{b x^{3} + a} \sqrt{e x} \sqrt{\frac{e}{b}}\right) - 4 \, {\left({\left(4 \, B a b - A b^{2}\right)} e^{3} x^{4} + 3 \, B a^{2} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{18 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}, -\frac{3 \, {\left(B a b^{2} e^{3} x^{6} + 2 \, B a^{2} b e^{3} x^{3} + B a^{3} e^{3}\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{2 \, \sqrt{b x^{3} + a} \sqrt{e x} b x \sqrt{-\frac{e}{b}}}{2 \, b e x^{3} + a e}\right) + 2 \, {\left({\left(4 \, B a b - A b^{2}\right)} e^{3} x^{4} + 3 \, B a^{2} e^{3} x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{9 \, {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)}}\right]"," ",0,"[1/18*(3*(B*a*b^2*e^3*x^6 + 2*B*a^2*b*e^3*x^3 + B*a^3*e^3)*sqrt(e/b)*log(-8*b^2*e*x^6 - 8*a*b*e*x^3 - a^2*e - 4*(2*b^2*x^4 + a*b*x)*sqrt(b*x^3 + a)*sqrt(e*x)*sqrt(e/b)) - 4*((4*B*a*b - A*b^2)*e^3*x^4 + 3*B*a^2*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2), -1/9*(3*(B*a*b^2*e^3*x^6 + 2*B*a^2*b*e^3*x^3 + B*a^3*e^3)*sqrt(-e/b)*arctan(2*sqrt(b*x^3 + a)*sqrt(e*x)*b*x*sqrt(-e/b)/(2*b*e*x^3 + a*e)) + 2*((4*B*a*b - A*b^2)*e^3*x^4 + 3*B*a^2*e^3*x)*sqrt(b*x^3 + a)*sqrt(e*x))/(a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)]","A",0
560,0,0,0,0.608638," ","integrate((e*x)^(5/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{5} + A e^{2} x^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*e^2*x^5 + A*e^2*x^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
561,0,0,0,0.602074," ","integrate((e*x)^(3/2)*(B*x^3+A)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{4} + A e x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{3} x^{9} + 3 \, a b^{2} x^{6} + 3 \, a^{2} b x^{3} + a^{3}}, x\right)"," ",0,"integral((B*e*x^4 + A*e*x)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^3*x^9 + 3*a*b^2*x^6 + 3*a^2*b*x^3 + a^3), x)","F",0
562,1,59,0,0.614700," ","integrate((B*x^3+A)*(e*x)^(1/2)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(B a + 2 \, A b\right)} x^{4} + 3 \, A a x\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{9 \, {\left(a^{2} b^{2} x^{6} + 2 \, a^{3} b x^{3} + a^{4}\right)}}"," ",0,"2/9*((B*a + 2*A*b)*x^4 + 3*A*a*x)*sqrt(b*x^3 + a)*sqrt(e*x)/(a^2*b^2*x^6 + 2*a^3*b*x^3 + a^4)","A",0
563,0,0,0,0.567374," ","integrate((B*x^3+A)/(b*x^3+a)^(5/2)/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{3} e x^{10} + 3 \, a b^{2} e x^{7} + 3 \, a^{2} b e x^{4} + a^{3} e x}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^3*e*x^10 + 3*a*b^2*e*x^7 + 3*a^2*b*e*x^4 + a^3*e*x), x)","F",0
564,0,0,0,1.006784," ","integrate((B*x^3+A)/(e*x)^(3/2)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{3} e^{2} x^{11} + 3 \, a b^{2} e^{2} x^{8} + 3 \, a^{2} b e^{2} x^{5} + a^{3} e^{2} x^{2}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^3*e^2*x^11 + 3*a*b^2*e^2*x^8 + 3*a^2*b*e^2*x^5 + a^3*e^2*x^2), x)","F",0
565,1,93,0,0.628960," ","integrate((B*x^3+A)/(e*x)^(5/2)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(B a b - 4 \, A b^{2}\right)} x^{6} + 3 \, {\left(B a^{2} - 4 \, A a b\right)} x^{3} - 3 \, A a^{2}\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{9 \, {\left(a^{3} b^{2} e^{3} x^{8} + 2 \, a^{4} b e^{3} x^{5} + a^{5} e^{3} x^{2}\right)}}"," ",0,"2/9*(2*(B*a*b - 4*A*b^2)*x^6 + 3*(B*a^2 - 4*A*a*b)*x^3 - 3*A*a^2)*sqrt(b*x^3 + a)*sqrt(e*x)/(a^3*b^2*e^3*x^8 + 2*a^4*b*e^3*x^5 + a^5*e^3*x^2)","A",0
566,0,0,0,0.503474," ","integrate((B*x^3+A)/(e*x)^(7/2)/(b*x^3+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{3} + A\right)} \sqrt{b x^{3} + a} \sqrt{e x}}{b^{3} e^{4} x^{13} + 3 \, a b^{2} e^{4} x^{10} + 3 \, a^{2} b e^{4} x^{7} + a^{3} e^{4} x^{4}}, x\right)"," ",0,"integral((B*x^3 + A)*sqrt(b*x^3 + a)*sqrt(e*x)/(b^3*e^4*x^13 + 3*a*b^2*e^4*x^10 + 3*a^2*b*e^4*x^7 + a^3*e^4*x^4), x)","F",0
567,1,186,0,0.743434," ","integrate(x^11*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{140 \, \sqrt{3} 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{3} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + 70 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{3} \log\left(2^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 140 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{3} \log\left(2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 3 \, {\left(14 \, b^{3} x^{9} + 22 \, a b^{2} x^{6} + 37 \, a^{2} b x^{3} + 169 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{420 \, b^{4} d}"," ",0,"-1/420*(140*sqrt(3)*2^(1/3)*(-a)^(1/3)*a^3*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*(-a)^(2/3) + sqrt(3)*a)/a) + 70*2^(1/3)*(-a)^(1/3)*a^3*log(2^(2/3)*(-a)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(2/3)) - 140*2^(1/3)*(-a)^(1/3)*a^3*log(2^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(1/3)) + 3*(14*b^3*x^9 + 22*a*b^2*x^6 + 37*a^2*b*x^3 + 169*a^3)*(b*x^3 + a)^(1/3))/(b^4*d)","A",0
568,1,174,0,0.491021," ","integrate(x^8*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{14 \, \sqrt{3} 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{2} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + 7 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{2} \log\left(2^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 14 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a^{2} \log\left(2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 6 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + 8 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{42 \, b^{3} d}"," ",0,"-1/42*(14*sqrt(3)*2^(1/3)*(-a)^(1/3)*a^2*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*(-a)^(2/3) + sqrt(3)*a)/a) + 7*2^(1/3)*(-a)^(1/3)*a^2*log(2^(2/3)*(-a)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(2/3)) - 14*2^(1/3)*(-a)^(1/3)*a^2*log(2^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(1/3)) + 6*(b^2*x^6 + 2*a*b*x^3 + 8*a^2)*(b*x^3 + a)^(1/3))/(b^3*d)","A",0
569,1,157,0,0.781168," ","integrate(x^5*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + 2 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a \log\left(2^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 4 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} a \log\left(2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 3 \, {\left(b x^{3} + 5 \, a\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{12 \, b^{2} d}"," ",0,"-1/12*(4*sqrt(3)*2^(1/3)*(-a)^(1/3)*a*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*(-a)^(2/3) + sqrt(3)*a)/a) + 2*2^(1/3)*(-a)^(1/3)*a*log(2^(2/3)*(-a)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(2/3)) - 4*2^(1/3)*(-a)^(1/3)*a*log(2^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(1/3)) + 3*(b*x^3 + 5*a)*(b*x^3 + a)^(1/3))/(b^2*d)","A",0
570,1,144,0,0.695593," ","integrate(x^2*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{6 \, b d}"," ",0,"-1/6*(2*sqrt(3)*2^(1/3)*(-a)^(1/3)*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*(-a)^(2/3) + sqrt(3)*a)/a) + 2^(1/3)*(-a)^(1/3)*log(2^(2/3)*(-a)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(2/3)) - 2*2^(1/3)*(-a)^(1/3)*log(2^(1/3)*(-a)^(1/3) + (b*x^3 + a)^(1/3)) + 6*(b*x^3 + a)^(1/3))/(b*d)","A",0
571,1,1046,0,0.719733," ","integrate((b*x^3+a)^(1/3)/x/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{12} \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} a^{3} d^{5} \sqrt{\frac{1}{a^{4} d^{6}}} - 3 \, \sqrt{3} a d^{2}\right)} \sqrt{-4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{3} d^{4} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + 4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{2} d^{2} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} + 4 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} a^{3} d^{5} \sqrt{\frac{1}{a^{4} d^{6}}} - 3 \, \sqrt{3} a d^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3}\right) + \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} a^{3} d^{5} \sqrt{\frac{1}{a^{4} d^{6}}} + 3 \, \sqrt{3} a d^{2}\right)} \sqrt{\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{3} d^{4} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{2} d^{2} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} a^{3} d^{5} \sqrt{\frac{1}{a^{4} d^{6}}} + 3 \, \sqrt{3} a d^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} - \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(-4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{3} d^{4} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + 4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{2} d^{2} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} + 4 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(4 \, \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{3} d^{4} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + 4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a^{2} d^{2} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{2}{3}} + 4 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} a^{3} d^{4} \left(-\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} + 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \log\left(-\left(\frac{1}{2}\right)^{\frac{1}{3}} a^{3} d^{4} \left(\frac{3 \, a^{2} d^{3} \sqrt{\frac{1}{a^{4} d^{6}}} - 1}{a^{2} d^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{1}{a^{4} d^{6}}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)"," ",0,"-2/3*sqrt(3)*(1/2)^(1/3)*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*arctan(1/12*(1/2)^(2/3)*(sqrt(3)*a^3*d^5*sqrt(1/(a^4*d^6)) - 3*sqrt(3)*a*d^2)*sqrt(-4*(1/2)^(1/3)*(b*x^3 + a)^(1/3)*a^3*d^4*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + 4*(1/2)^(2/3)*a^2*d^2*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(2/3) + 4*(b*x^3 + a)^(2/3))*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(2/3) - 1/6*(1/2)^(2/3)*(sqrt(3)*a^3*d^5*sqrt(1/(a^4*d^6)) - 3*sqrt(3)*a*d^2)*(b*x^3 + a)^(1/3)*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(2/3) + 1/3*sqrt(3)) + 2/3*sqrt(3)*(1/2)^(1/3)*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*arctan(1/6*(1/2)^(2/3)*(sqrt(3)*a^3*d^5*sqrt(1/(a^4*d^6)) + 3*sqrt(3)*a*d^2)*sqrt((1/2)^(1/3)*(b*x^3 + a)^(1/3)*a^3*d^4*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + (1/2)^(2/3)*a^2*d^2*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(2/3) + (b*x^3 + a)^(2/3))*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(2/3) - 1/6*(1/2)^(2/3)*(sqrt(3)*a^3*d^5*sqrt(1/(a^4*d^6)) + 3*sqrt(3)*a*d^2)*(b*x^3 + a)^(1/3)*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(2/3) - 1/3*sqrt(3)) - 1/6*(1/2)^(1/3)*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*log(-4*(1/2)^(1/3)*(b*x^3 + a)^(1/3)*a^3*d^4*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + 4*(1/2)^(2/3)*a^2*d^2*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(2/3) + 4*(b*x^3 + a)^(2/3)) - 1/6*(1/2)^(1/3)*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*log(4*(1/2)^(1/3)*(b*x^3 + a)^(1/3)*a^3*d^4*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + 4*(1/2)^(2/3)*a^2*d^2*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(2/3) + 4*(b*x^3 + a)^(2/3)) + 1/3*(1/2)^(1/3)*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*log((1/2)^(1/3)*a^3*d^4*(-(3*a^2*d^3*sqrt(1/(a^4*d^6)) + 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + (b*x^3 + a)^(1/3)) + 1/3*(1/2)^(1/3)*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*log(-(1/2)^(1/3)*a^3*d^4*((3*a^2*d^3*sqrt(1/(a^4*d^6)) - 1)/(a^2*d^3))^(1/3)*sqrt(1/(a^4*d^6)) + (b*x^3 + a)^(1/3))","B",0
572,1,321,0,0.737692," ","integrate((b*x^3+a)^(1/3)/x^4/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{3} 2^{\frac{1}{3}} a^{2} b x^{3} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 3 \cdot 2^{\frac{1}{3}} a^{2} b x^{3} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{2} \left(-\frac{1}{a^{2}}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 6 \cdot 2^{\frac{1}{3}} a^{2} b x^{3} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 8 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{6}} a b x^{3} \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) + 4 \, {\left(a^{2}\right)}^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 8 \, {\left(a^{2}\right)}^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2}}{18 \, a^{3} d x^{3}}"," ",0,"-1/18*(6*sqrt(3)*2^(1/3)*a^2*b*x^3*(-1/a^2)^(1/3)*arctan(1/3*sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a^2)^(2/3) + 1/3*sqrt(3)) + 3*2^(1/3)*a^2*b*x^3*(-1/a^2)^(1/3)*log(2^(2/3)*a^2*(-1/a^2)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*a*(-1/a^2)^(1/3) + (b*x^3 + a)^(2/3)) - 6*2^(1/3)*a^2*b*x^3*(-1/a^2)^(1/3)*log(2^(1/3)*a*(-1/a^2)^(1/3) + (b*x^3 + a)^(1/3)) + 8*sqrt(3)*(a^2)^(1/6)*a*b*x^3*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) + 4*(a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 8*(a^2)^(2/3)*b*x^3*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 6*(b*x^3 + a)^(1/3)*a^2)/(a^3*d*x^3)","A",0
573,1,345,0,0.637001," ","integrate((b*x^3+a)^(1/3)/x^7/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{18 \, \sqrt{3} 2^{\frac{1}{3}} a^{2} b^{2} x^{6} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{2}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 9 \cdot 2^{\frac{1}{3}} a^{2} b^{2} x^{6} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{2} \left(-\frac{1}{a^{2}}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 18 \cdot 2^{\frac{1}{3}} a^{2} b^{2} x^{6} \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} a \left(-\frac{1}{a^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 22 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{6}} a b^{2} x^{6} \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) + 11 \, {\left(a^{2}\right)}^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 22 \, {\left(a^{2}\right)}^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 3 \, {\left(7 \, a^{2} b x^{3} + 3 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, a^{4} d x^{6}}"," ",0,"-1/54*(18*sqrt(3)*2^(1/3)*a^2*b^2*x^6*(-1/a^2)^(1/3)*arctan(1/3*sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a^2)^(2/3) + 1/3*sqrt(3)) + 9*2^(1/3)*a^2*b^2*x^6*(-1/a^2)^(1/3)*log(2^(2/3)*a^2*(-1/a^2)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*a*(-1/a^2)^(1/3) + (b*x^3 + a)^(2/3)) - 18*2^(1/3)*a^2*b^2*x^6*(-1/a^2)^(1/3)*log(2^(1/3)*a*(-1/a^2)^(1/3) + (b*x^3 + a)^(1/3)) + 22*sqrt(3)*(a^2)^(1/6)*a*b^2*x^6*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) + 11*(a^2)^(2/3)*b^2*x^6*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 22*(a^2)^(2/3)*b^2*x^6*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 3*(7*a^2*b*x^3 + 3*a^3)*(b*x^3 + a)^(1/3))/(a^4*d*x^6)","A",0
574,1,362,0,0.637375," ","integrate(x^7*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{18 \, \sqrt{3} 2^{\frac{1}{3}} a^{2} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} + \sqrt{3} x}{3 \, x}\right) - 18 \cdot 2^{\frac{1}{3}} a^{2} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 9 \cdot 2^{\frac{1}{3}} a^{2} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{2}{3}} b^{2} x^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 22 \, \sqrt{3} a^{2} {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) - 22 \, a^{2} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 11 \, a^{2} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + 3 \, {\left(3 \, b^{3} x^{5} + 7 \, a b^{2} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, b^{4} d}"," ",0,"-1/54*(18*sqrt(3)*2^(1/3)*a^2*b^2*(-1/b^2)^(1/3)*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*b*(-1/b^2)^(2/3) + sqrt(3)*x)/x) - 18*2^(1/3)*a^2*b^2*(-1/b^2)^(1/3)*log((2^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(1/3))/x) + 9*2^(1/3)*a^2*b^2*(-1/b^2)^(1/3)*log((2^(2/3)*b^2*x^2*(-1/b^2)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(2/3))/x^2) + 22*sqrt(3)*a^2*(b^2)^(1/6)*b*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) - 22*a^2*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 11*a^2*(b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2) + 3*(3*b^3*x^5 + 7*a*b^2*x^2)*(b*x^3 + a)^(1/3))/(b^4*d)","A",0
575,1,338,0,0.634583," ","integrate(x^4*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{3} 2^{\frac{1}{3}} a b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} + \sqrt{3} x}{3 \, x}\right) - 6 \cdot 2^{\frac{1}{3}} a b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 3 \cdot 2^{\frac{1}{3}} a b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{2}{3}} b^{2} x^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{2} x^{2} + 8 \, \sqrt{3} a {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) - 8 \, a {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + 4 \, a {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{18 \, b^{3} d}"," ",0,"-1/18*(6*sqrt(3)*2^(1/3)*a*b^2*(-1/b^2)^(1/3)*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*b*(-1/b^2)^(2/3) + sqrt(3)*x)/x) - 6*2^(1/3)*a*b^2*(-1/b^2)^(1/3)*log((2^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(1/3))/x) + 3*2^(1/3)*a*b^2*(-1/b^2)^(1/3)*log((2^(2/3)*b^2*x^2*(-1/b^2)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(2/3))/x^2) + 6*(b*x^3 + a)^(1/3)*b^2*x^2 + 8*sqrt(3)*a*(b^2)^(1/6)*b*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) - 8*a*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + 4*a*(b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2))/(b^3*d)","A",0
576,1,313,0,0.615232," ","integrate(x*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} 2^{\frac{1}{3}} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} + \sqrt{3} x}{3 \, x}\right) - 2 \cdot 2^{\frac{1}{3}} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 2^{\frac{1}{3}} b^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} \log\left(\frac{2^{\frac{2}{3}} b^{2} x^{2} \left(-\frac{1}{b^{2}}\right)^{\frac{2}{3}} - 2^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 2 \, \sqrt{3} {\left(b^{2}\right)}^{\frac{1}{6}} b \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) - 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{6 \, b^{2} d}"," ",0,"-1/6*(2*sqrt(3)*2^(1/3)*b^2*(-1/b^2)^(1/3)*arctan(1/3*(sqrt(3)*2^(2/3)*(b*x^3 + a)^(1/3)*b*(-1/b^2)^(2/3) + sqrt(3)*x)/x) - 2*2^(1/3)*b^2*(-1/b^2)^(1/3)*log((2^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(1/3))/x) + 2^(1/3)*b^2*(-1/b^2)^(1/3)*log((2^(2/3)*b^2*x^2*(-1/b^2)^(2/3) - 2^(1/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b^2)^(1/3) + (b*x^3 + a)^(2/3))/x^2) + 2*sqrt(3)*(b^2)^(1/6)*b*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) - 2*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2))/(b^2*d)","B",0
577,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^2/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^5/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^8/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^11/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate(x^6*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^3/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^6/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,1,209,0,0.647773," ","integrate(x^11*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{440 \cdot 4^{\frac{1}{3}} \sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a^{3} \arctan\left(\frac{4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 220 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a^{3} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a - 2 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a\right) - 440 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a^{3} \log\left(-4^{\frac{2}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a\right) + 3 \, {\left(40 \, b^{3} x^{9} + 65 \, a b^{2} x^{6} + 98 \, a^{2} b x^{3} + 293 \, a^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1320 \, b^{4} d}"," ",0,"-1/1320*(440*4^(1/3)*sqrt(3)*(-a^2)^(1/3)*a^3*arctan(1/3*(4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(1/3) - sqrt(3)*a)/a) + 220*4^(1/3)*(-a^2)^(1/3)*a^3*log(4^(2/3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(2/3)*a - 2*4^(1/3)*(-a^2)^(1/3)*a) - 440*4^(1/3)*(-a^2)^(1/3)*a^3*log(-4^(2/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(1/3)*a) + 3*(40*b^3*x^9 + 65*a*b^2*x^6 + 98*a^2*b*x^3 + 293*a^3)*(b*x^3 + a)^(2/3))/(b^4*d)","A",0
587,1,197,0,0.724894," ","integrate(x^8*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{8 \cdot 4^{\frac{1}{3}} \sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a^{2} \arctan\left(\frac{4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 4 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a^{2} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a - 2 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a\right) - 8 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a^{2} \log\left(-4^{\frac{2}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a\right) + 3 \, {\left(b^{2} x^{6} + 2 \, a b x^{3} + 5 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{24 \, b^{3} d}"," ",0,"-1/24*(8*4^(1/3)*sqrt(3)*(-a^2)^(1/3)*a^2*arctan(1/3*(4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(1/3) - sqrt(3)*a)/a) + 4*4^(1/3)*(-a^2)^(1/3)*a^2*log(4^(2/3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(2/3)*a - 2*4^(1/3)*(-a^2)^(1/3)*a) - 8*4^(1/3)*(-a^2)^(1/3)*a^2*log(-4^(2/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(1/3)*a) + 3*(b^2*x^6 + 2*a*b*x^3 + 5*a^2)*(b*x^3 + a)^(2/3))/(b^3*d)","A",0
588,1,181,0,0.939700," ","integrate(x^5*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{10 \cdot 4^{\frac{1}{3}} \sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a \arctan\left(\frac{4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 5 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a - 2 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a\right) - 10 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a \log\left(-4^{\frac{2}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a\right) + 3 \, {\left(2 \, b x^{3} + 7 \, a\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, b^{2} d}"," ",0,"-1/30*(10*4^(1/3)*sqrt(3)*(-a^2)^(1/3)*a*arctan(1/3*(4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(1/3) - sqrt(3)*a)/a) + 5*4^(1/3)*(-a^2)^(1/3)*a*log(4^(2/3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(2/3)*a - 2*4^(1/3)*(-a^2)^(1/3)*a) - 10*4^(1/3)*(-a^2)^(1/3)*a*log(-4^(2/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(1/3)*a) + 3*(2*b*x^3 + 7*a)*(b*x^3 + a)^(2/3))/(b^2*d)","A",0
589,1,167,0,1.169107," ","integrate(x^2*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) + 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a - 2 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} a\right) - 2 \cdot 4^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} \left(-a^{2}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a\right) + 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, b d}"," ",0,"-1/6*(2*4^(1/3)*sqrt(3)*(-a^2)^(1/3)*arctan(1/3*(4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(1/3) - sqrt(3)*a)/a) + 4^(1/3)*(-a^2)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(2/3)*a - 2*4^(1/3)*(-a^2)^(1/3)*a) - 2*4^(1/3)*(-a^2)^(1/3)*log(-4^(2/3)*(-a^2)^(2/3) + 2*(b*x^3 + a)^(1/3)*a) + 3*(b*x^3 + a)^(2/3))/(b*d)","A",0
590,1,530,0,0.738645," ","integrate((b*x^3+a)^(2/3)/x/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 3 \, \sqrt{\frac{1}{3}} a \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a d}, -\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 6 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) + a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a d}\right]"," ",0,"[-1/6*(2*4^(1/3)*sqrt(3)*a*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) - 3*sqrt(1/3)*a*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) + 4^(1/3)*a*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 2*4^(1/3)*a*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) + a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/(a*d), -1/6*(2*4^(1/3)*sqrt(3)*a*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) + 4^(1/3)*a*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 2*4^(1/3)*a*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) - 6*sqrt(1/3)*a^(2/3)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) + a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/(a*d)]","A",0
591,1,612,0,0.512632," ","integrate((b*x^3+a)^(2/3)/x^4/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{6 \cdot 4^{\frac{1}{3}} \sqrt{3} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 15 \, \sqrt{\frac{1}{3}} a b x^{3} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + 3 \cdot 4^{\frac{1}{3}} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 6 \cdot 4^{\frac{1}{3}} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 5 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 10 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{18 \, a^{2} d x^{3}}, -\frac{6 \cdot 4^{\frac{1}{3}} \sqrt{3} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 3 \cdot 4^{\frac{1}{3}} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 6 \cdot 4^{\frac{1}{3}} a b x^{3} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 30 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} b x^{3} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) + 5 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 10 \, a^{\frac{2}{3}} b x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a}{18 \, a^{2} d x^{3}}\right]"," ",0,"[-1/18*(6*4^(1/3)*sqrt(3)*a*b*x^3*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) - 15*sqrt(1/3)*a*b*x^3*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) + 3*4^(1/3)*a*b*x^3*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 6*4^(1/3)*a*b*x^3*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) + 5*a^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 10*a^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) - a^(1/3)) + 6*(b*x^3 + a)^(2/3)*a)/(a^2*d*x^3), -1/18*(6*4^(1/3)*sqrt(3)*a*b*x^3*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) + 3*4^(1/3)*a*b*x^3*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 6*4^(1/3)*a*b*x^3*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) - 30*sqrt(1/3)*a^(2/3)*b*x^3*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) + 5*a^(2/3)*b*x^3*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 10*a^(2/3)*b*x^3*log((b*x^3 + a)^(1/3) - a^(1/3)) + 6*(b*x^3 + a)^(2/3)*a)/(a^2*d*x^3)]","A",0
592,1,660,0,0.498952," ","integrate((b*x^3+a)^(2/3)/x^7/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{18 \cdot 4^{\frac{1}{3}} \sqrt{3} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - 42 \, \sqrt{\frac{1}{3}} a b^{2} x^{6} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + 9 \cdot 4^{\frac{1}{3}} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 18 \cdot 4^{\frac{1}{3}} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 14 \, a^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 28 \, a^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + 3 \, {\left(8 \, a b x^{3} + 3 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, a^{3} d x^{6}}, -\frac{18 \cdot 4^{\frac{1}{3}} \sqrt{3} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{1}{3} \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + 9 \cdot 4^{\frac{1}{3}} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} - 2 \cdot 4^{\frac{1}{3}} a \left(-\frac{1}{a}\right)^{\frac{1}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}\right) - 18 \cdot 4^{\frac{1}{3}} a b^{2} x^{6} \left(-\frac{1}{a}\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} a \left(-\frac{1}{a}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 84 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} b^{2} x^{6} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) + 14 \, a^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 28 \, a^{\frac{2}{3}} b^{2} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + 3 \, {\left(8 \, a b x^{3} + 3 \, a^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, a^{3} d x^{6}}\right]"," ",0,"[-1/54*(18*4^(1/3)*sqrt(3)*a*b^2*x^6*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) - 42*sqrt(1/3)*a*b^2*x^6*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) + 9*4^(1/3)*a*b^2*x^6*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 18*4^(1/3)*a*b^2*x^6*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) + 14*a^(2/3)*b^2*x^6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 28*a^(2/3)*b^2*x^6*log((b*x^3 + a)^(1/3) - a^(1/3)) + 3*(8*a*b*x^3 + 3*a^2)*(b*x^3 + a)^(2/3))/(a^3*d*x^6), -1/54*(18*4^(1/3)*sqrt(3)*a*b^2*x^6*(-1/a)^(1/3)*arctan(1/3*4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/a)^(1/3) - 1/3*sqrt(3)) + 9*4^(1/3)*a*b^2*x^6*(-1/a)^(1/3)*log(4^(2/3)*(b*x^3 + a)^(1/3)*a*(-1/a)^(2/3) - 2*4^(1/3)*a*(-1/a)^(1/3) + 2*(b*x^3 + a)^(2/3)) - 18*4^(1/3)*a*b^2*x^6*(-1/a)^(1/3)*log(-4^(2/3)*a*(-1/a)^(2/3) + 2*(b*x^3 + a)^(1/3)) - 84*sqrt(1/3)*a^(2/3)*b^2*x^6*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) + 14*a^(2/3)*b^2*x^6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 28*a^(2/3)*b^2*x^6*log((b*x^3 + a)^(1/3) - a^(1/3)) + 3*(8*a*b*x^3 + 3*a^2)*(b*x^3 + a)^(2/3))/(a^3*d*x^6)]","A",0
593,1,701,0,0.518043," ","integrate(x^6*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{18 \cdot 4^{\frac{1}{3}} \sqrt{3} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 42 \, \sqrt{\frac{1}{3}} a^{2} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 18 \cdot 4^{\frac{1}{3}} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 9 \cdot 4^{\frac{1}{3}} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 28 \, a^{2} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 14 \, a^{2} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} + 8 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{3} d}, -\frac{18 \cdot 4^{\frac{1}{3}} \sqrt{3} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 18 \cdot 4^{\frac{1}{3}} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 9 \cdot 4^{\frac{1}{3}} a^{2} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 84 \, \sqrt{\frac{1}{3}} a^{2} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) - 28 \, a^{2} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 14 \, a^{2} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(3 \, b^{2} x^{4} + 8 \, a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{3} d}\right]"," ",0,"[-1/54*(18*4^(1/3)*sqrt(3)*a^2*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 42*sqrt(1/3)*a^2*b*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 18*4^(1/3)*a^2*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 9*4^(1/3)*a^2*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) - 28*a^2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + 14*a^2*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 + 8*a*b*x)*(b*x^3 + a)^(2/3))/(b^3*d), -1/54*(18*4^(1/3)*sqrt(3)*a^2*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 18*4^(1/3)*a^2*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 9*4^(1/3)*a^2*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) - 84*sqrt(1/3)*a^2*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x)) - 28*a^2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + 14*a^2*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(3*b^2*x^4 + 8*a*b*x)*(b*x^3 + a)^(2/3))/(b^3*d)]","A",0
594,1,653,0,0.508831," ","integrate(x^3*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{6 \cdot 4^{\frac{1}{3}} \sqrt{3} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 15 \, \sqrt{\frac{1}{3}} a b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 6 \cdot 4^{\frac{1}{3}} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 3 \cdot 4^{\frac{1}{3}} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x - 10 \, a b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 5 \, a b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2} d}, -\frac{6 \cdot 4^{\frac{1}{3}} \sqrt{3} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 6 \cdot 4^{\frac{1}{3}} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 3 \cdot 4^{\frac{1}{3}} a b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 30 \, \sqrt{\frac{1}{3}} a b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x - 10 \, a b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 5 \, a b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2} d}\right]"," ",0,"[-1/18*(6*4^(1/3)*sqrt(3)*a*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 15*sqrt(1/3)*a*b*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 6*4^(1/3)*a*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 3*4^(1/3)*a*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) + 6*(b*x^3 + a)^(2/3)*b*x - 10*a*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + 5*a*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^2*d), -1/18*(6*4^(1/3)*sqrt(3)*a*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 6*4^(1/3)*a*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 3*4^(1/3)*a*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) - 30*sqrt(1/3)*a*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x)) + 6*(b*x^3 + a)^(2/3)*b*x - 10*a*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + 5*a*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^2*d)]","A",0
595,1,611,0,0.540619," ","integrate((b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\left[-\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 3 \, \sqrt{\frac{1}{3}} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 2 \cdot 4^{\frac{1}{3}} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 4^{\frac{1}{3}} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 2 \, b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b d}, -\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 4^{\frac{1}{3}} \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{1}{b}\right)^{\frac{1}{3}}}{3 \, x}\right) - 2 \cdot 4^{\frac{1}{3}} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 4^{\frac{1}{3}} b \left(-\frac{1}{b}\right)^{\frac{1}{3}} \log\left(-\frac{2 \cdot 4^{\frac{1}{3}} b x^{2} \left(-\frac{1}{b}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x \left(-\frac{1}{b}\right)^{\frac{2}{3}} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 6 \, \sqrt{\frac{1}{3}} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right) - 2 \, b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b d}\right]"," ",0,"[-1/6*(2*4^(1/3)*sqrt(3)*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 3*sqrt(1/3)*b*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 2*4^(1/3)*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 4^(1/3)*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) - 2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b*d), -1/6*(2*4^(1/3)*sqrt(3)*b*(-1/b)^(1/3)*arctan(-1/3*(sqrt(3)*x - 4^(1/3)*sqrt(3)*(b*x^3 + a)^(1/3)*(-1/b)^(1/3))/x) - 2*4^(1/3)*b*(-1/b)^(1/3)*log(-(4^(2/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(1/3))/x) + 4^(1/3)*b*(-1/b)^(1/3)*log(-(2*4^(1/3)*b*x^2*(-1/b)^(1/3) - 4^(2/3)*(b*x^3 + a)^(1/3)*b*x*(-1/b)^(2/3) - 2*(b*x^3 + a)^(2/3))/x^2) - 6*sqrt(1/3)*b^(2/3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x)) - 2*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b*d)]","A",0
596,1,434,0,144.749456," ","integrate((b*x^3+a)^(2/3)/x^3/(-b*d*x^3+a*d),x, algorithm=""fricas"")","-\frac{2 \cdot 4^{\frac{1}{3}} \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} x^{2} \arctan\left(\frac{3 \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(5 \, b^{2} x^{7} - 4 \, a b x^{4} - a^{2} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b^{2}\right)^{\frac{2}{3}} + 6 \cdot 4^{\frac{1}{3}} \sqrt{3} {\left(19 \, b^{3} x^{8} + 16 \, a b^{2} x^{5} + a^{2} b x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}} - \sqrt{3} {\left(71 \, b^{4} x^{9} + 111 \, a b^{3} x^{6} + 33 \, a^{2} b^{2} x^{3} + a^{3} b\right)}}{3 \, {\left(109 \, b^{4} x^{9} + 105 \, a b^{3} x^{6} + 3 \, a^{2} b^{2} x^{3} - a^{3} b\right)}}\right) - 2 \cdot 4^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}} x^{2} \log\left(\frac{3 \cdot 4^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x^{2} - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b x + 4^{\frac{1}{3}} {\left(b x^{3} - a\right)} \left(-b^{2}\right)^{\frac{1}{3}}}{b x^{3} - a}\right) + 4^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}} x^{2} \log\left(-\frac{6 \cdot 4^{\frac{1}{3}} {\left(5 \, b^{2} x^{4} + a b x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b^{2}\right)^{\frac{1}{3}} - 4^{\frac{2}{3}} {\left(19 \, b^{2} x^{6} + 16 \, a b x^{3} + a^{2}\right)} \left(-b^{2}\right)^{\frac{2}{3}} - 24 \, {\left(2 \, b^{3} x^{5} + a b^{2} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{b^{2} x^{6} - 2 \, a b x^{3} + a^{2}}\right) + 9 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{18 \, a d x^{2}}"," ",0,"-1/18*(2*4^(1/3)*sqrt(3)*(-b^2)^(1/3)*x^2*arctan(1/3*(3*4^(2/3)*sqrt(3)*(5*b^2*x^7 - 4*a*b*x^4 - a^2*x)*(b*x^3 + a)^(2/3)*(-b^2)^(2/3) + 6*4^(1/3)*sqrt(3)*(19*b^3*x^8 + 16*a*b^2*x^5 + a^2*b*x^2)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3) - sqrt(3)*(71*b^4*x^9 + 111*a*b^3*x^6 + 33*a^2*b^2*x^3 + a^3*b))/(109*b^4*x^9 + 105*a*b^3*x^6 + 3*a^2*b^2*x^3 - a^3*b)) - 2*4^(1/3)*(-b^2)^(1/3)*x^2*log((3*4^(2/3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x^2 - 6*(b*x^3 + a)^(2/3)*b*x + 4^(1/3)*(b*x^3 - a)*(-b^2)^(1/3))/(b*x^3 - a)) + 4^(1/3)*(-b^2)^(1/3)*x^2*log(-(6*4^(1/3)*(5*b^2*x^4 + a*b*x)*(b*x^3 + a)^(2/3)*(-b^2)^(1/3) - 4^(2/3)*(19*b^2*x^6 + 16*a*b*x^3 + a^2)*(-b^2)^(2/3) - 24*(2*b^3*x^5 + a*b^2*x^2)*(b*x^3 + a)^(1/3))/(b^2*x^6 - 2*a*b*x^3 + a^2)) + 9*(b*x^3 + a)^(2/3))/(a*d*x^2)","B",0
597,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^6/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^9/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^12/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(x^7*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(x*(b*x^3+a)^(2/3)/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^2/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^5/(-b*d*x^3+a*d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,1,118,0,0.934288," ","integrate(x^14/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{220} \, {\left(20 \, x^{9} - 5 \, x^{6} + 38 \, x^{3} - 53\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + \frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"-1/220*(20*x^9 - 5*x^6 + 38*x^3 - 53)*(-x^3 + 1)^(2/3) + 1/6*sqrt(6)*2^(1/6)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 1/6*2^(2/3)*log(-2^(1/3) + (-x^3 + 1)^(1/3))","A",0
606,1,137,0,0.870036," ","integrate(x^11/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{40} \, {\left(5 \, x^{6} - 2 \, x^{3} + 17\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}"," ",0,"-1/6*sqrt(6)*2^(1/6)*(-1)^(1/3)*arctan(1/6*2^(1/6)*(2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3))) - 1/12*2^(2/3)*(-1)^(1/3)*log(2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3) + (-x^3 + 1)^(2/3)) + 1/6*2^(2/3)*(-1)^(1/3)*log(-2^(1/3)*(-1)^(2/3) + (-x^3 + 1)^(1/3)) - 1/40*(5*x^6 - 2*x^3 + 17)*(-x^3 + 1)^(2/3)","A",0
607,1,106,0,1.164673," ","integrate(x^8/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{5} \, {\left(x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + \frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"-1/5*(x^3 - 1)*(-x^3 + 1)^(2/3) + 1/6*sqrt(6)*2^(1/6)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 1/6*2^(2/3)*log(-2^(1/3) + (-x^3 + 1)^(1/3))","A",0
608,1,125,0,1.008493," ","integrate(x^5/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{2} \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}"," ",0,"-1/6*sqrt(6)*2^(1/6)*(-1)^(1/3)*arctan(1/6*2^(1/6)*(2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3))) - 1/12*2^(2/3)*(-1)^(1/3)*log(2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3) + (-x^3 + 1)^(2/3)) + 1/6*2^(2/3)*(-1)^(1/3)*log(-2^(1/3)*(-1)^(2/3) + (-x^3 + 1)^(1/3)) - 1/2*(-x^3 + 1)^(2/3)","A",0
609,1,90,0,0.575129," ","integrate(x^2/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"1/6*sqrt(6)*2^(1/6)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 1/12*2^(2/3)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 1/6*2^(2/3)*log(-2^(1/3) + (-x^3 + 1)^(1/3))","A",0
610,1,410,0,1.482240," ","integrate(1/x/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","\frac{1}{12} \cdot 2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} \log\left(\frac{1}{8} \, {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{3} - \frac{3}{4} \cdot 2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} + 3 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) - \frac{1}{24} \, {\left(2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} - 2 \, \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}}\right)} \log\left(\frac{3}{8} \cdot 2^{\frac{2}{3}} \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} + \frac{3}{8} \cdot 2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} + 3 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{24} \, {\left(2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} + 2 \, \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}}\right)} \log\left(-\frac{3}{8} \cdot 2^{\frac{2}{3}} \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} + \frac{3}{8} \cdot 2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} + 3 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + \frac{1}{3} \, \log\left(-\frac{1}{24} \, {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{3} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \frac{4}{3}\right) - \frac{1}{6} \, \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right)"," ",0,"1/12*2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))*log(1/8*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^3 - 3/4*2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 + 3*(-x^3 + 1)^(1/3) + 1) - 1/24*(2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) - 2*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2))*log(3/8*2^(2/3)*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) + 3/8*2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 + 3*(-x^3 + 1)^(1/3)) - 1/24*(2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) + 2*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2))*log(-3/8*2^(2/3)*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) + 3/8*2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 + 3*(-x^3 + 1)^(1/3)) + 1/3*sqrt(3)*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) + 1/3*log(-1/24*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^3 + (-x^3 + 1)^(1/3) - 4/3) - 1/6*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1)","C",0
611,1,187,0,0.476362," ","integrate(1/x^4/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","\frac{6 \, \sqrt{6} 2^{\frac{1}{6}} x^{3} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - 3 \cdot 2^{\frac{2}{3}} x^{3} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + 6 \cdot 2^{\frac{2}{3}} x^{3} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - 8 \, \sqrt{3} x^{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 4 \, x^{3} \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) - 8 \, x^{3} \log\left({\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 1\right) - 12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{36 \, x^{3}}"," ",0,"1/36*(6*sqrt(6)*2^(1/6)*x^3*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 3*2^(2/3)*x^3*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 6*2^(2/3)*x^3*log(-2^(1/3) + (-x^3 + 1)^(1/3)) - 8*sqrt(3)*x^3*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) + 4*x^3*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1) - 8*x^3*log((-x^3 + 1)^(1/3) - 1) - 12*(-x^3 + 1)^(2/3))/x^3","A",0
612,1,201,0,0.472371," ","integrate(x^6/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x - \frac{1}{6} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(-\frac{2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} x - 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, x}\right) + \frac{1}{6} \cdot 2^{\frac{2}{3}} \log\left(\frac{2^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(\frac{2^{\frac{2}{3}} x^{2} - 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{2}{9} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) - \frac{2}{9} \, \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) + \frac{1}{9} \, \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"-1/3*(-x^3 + 1)^(2/3)*x - 1/6*sqrt(6)*2^(1/6)*arctan(-1/6*2^(1/6)*(sqrt(6)*2^(1/3)*x - 2*sqrt(6)*(-x^3 + 1)^(1/3))/x) + 1/6*2^(2/3)*log((2^(1/3)*x + (-x^3 + 1)^(1/3))/x) - 1/12*2^(2/3)*log((2^(2/3)*x^2 - 2^(1/3)*(-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2) + 2/9*sqrt(3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) - 2/9*log((x + (-x^3 + 1)^(1/3))/x) + 1/9*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2)","A",0
613,1,452,0,1.430277," ","integrate(x^3/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","\frac{1}{12} \cdot 2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} \log\left(-\frac{x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{3} - 6 \cdot 2^{\frac{1}{3}} x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} + 8 \, x - 24 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{8 \, x}\right) - \frac{1}{24} \, {\left(2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} - 2 \, \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}}\right)} \log\left(-\frac{3 \, {\left(2^{\frac{2}{3}} \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}} x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} + 2^{\frac{1}{3}} x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} - 8 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{8 \, x}\right) - \frac{1}{24} \, {\left(2^{\frac{2}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} + 2 \, \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}}\right)} \log\left(\frac{3 \, {\left(2^{\frac{2}{3}} \sqrt{\frac{3}{2}} \sqrt{-2^{\frac{1}{3}} {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2}} x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)} - 2^{\frac{1}{3}} x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{2} + 8 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{8 \, x}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) + \frac{1}{3} \, \log\left(\frac{x {\left(i \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} - \left(-1\right)^{\frac{1}{3}}\right)}^{3} + 32 \, x + 24 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{24 \, x}\right) - \frac{1}{6} \, \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"1/12*2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))*log(-1/8*(x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^3 - 6*2^(1/3)*x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 + 8*x - 24*(-x^3 + 1)^(1/3))/x) - 1/24*(2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) - 2*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2))*log(-3/8*(2^(2/3)*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2)*x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) + 2^(1/3)*x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 - 8*(-x^3 + 1)^(1/3))/x) - 1/24*(2^(2/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) + 2*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2))*log(3/8*(2^(2/3)*sqrt(3/2)*sqrt(-2^(1/3)*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2)*x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3)) - 2^(1/3)*x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^2 + 8*(-x^3 + 1)^(1/3))/x) - 1/3*sqrt(3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) + 1/3*log(1/24*(x*(I*sqrt(3)*(-1)^(1/3) - (-1)^(1/3))^3 + 32*x + 24*(-x^3 + 1)^(1/3))/x) - 1/6*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2)","C",0
614,1,253,0,2.601739," ","integrate(1/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{18} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)} + 12 \, \sqrt{6} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) + \frac{1}{18} \cdot 2^{\frac{2}{3}} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + 2^{\frac{2}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) - \frac{1}{36} \cdot 2^{\frac{2}{3}} \log\left(\frac{3 \cdot 2^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right)"," ",0,"-1/18*sqrt(6)*2^(1/6)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1) + 12*sqrt(6)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) + 1/18*2^(2/3)*log((6*2^(1/3)*(-x^3 + 1)^(1/3)*x^2 + 2^(2/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) - 1/36*2^(2/3)*log((3*2^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) + 2^(1/3)*(19*x^6 - 16*x^3 + 1) - 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1))","B",0
615,1,307,0,2.578274," ","integrate(1/x^3/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} x^{2} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 2 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{2} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{2} \log\left(-\frac{3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} + 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 18 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{36 \, x^{2}}"," ",0,"-1/36*(2*sqrt(6)*2^(1/6)*(-1)^(1/3)*x^2*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(-1)^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 12*sqrt(6)*(-1)^(1/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 2*2^(2/3)*(-1)^(1/3)*x^2*log((6*2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x^2 - 2^(2/3)*(-1)^(1/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 2^(2/3)*(-1)^(1/3)*x^2*log(-(3*2^(2/3)*(-1)^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(19*x^6 - 16*x^3 + 1) + 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 18*(-x^3 + 1)^(2/3))/x^2","B",0
616,1,283,0,2.550685," ","integrate(1/x^6/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{6} 2^{\frac{1}{6}} x^{5} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)} + 12 \, \sqrt{6} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 10 \cdot 2^{\frac{2}{3}} x^{5} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + 2^{\frac{2}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 5 \cdot 2^{\frac{2}{3}} x^{5} \log\left(\frac{3 \cdot 2^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) - 36 \, {\left(x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{180 \, x^{5}}"," ",0,"-1/180*(10*sqrt(6)*2^(1/6)*x^5*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1) + 12*sqrt(6)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 10*2^(2/3)*x^5*log((6*2^(1/3)*(-x^3 + 1)^(1/3)*x^2 + 2^(2/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 5*2^(2/3)*x^5*log((3*2^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) + 2^(1/3)*(19*x^6 - 16*x^3 + 1) - 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) - 36*(x^3 - 1)*(-x^3 + 1)^(2/3))/x^5","B",0
617,1,320,0,2.607122," ","integrate(1/x^9/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{20 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} x^{8} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 20 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{8} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 10 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{8} \log\left(-\frac{3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} + 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 9 \, {\left(17 \, x^{6} - 2 \, x^{3} + 5\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{360 \, x^{8}}"," ",0,"-1/360*(20*sqrt(6)*2^(1/6)*(-1)^(1/3)*x^8*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(-1)^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 12*sqrt(6)*(-1)^(1/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 20*2^(2/3)*(-1)^(1/3)*x^8*log((6*2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x^2 - 2^(2/3)*(-1)^(1/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 10*2^(2/3)*(-1)^(1/3)*x^8*log(-(3*2^(2/3)*(-1)^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(19*x^6 - 16*x^3 + 1) + 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 9*(17*x^6 - 2*x^3 + 5)*(-x^3 + 1)^(2/3))/x^8","B",0
618,0,0,0,2.268556," ","integrate(x^7/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{7}}{x^{6} - 1}, x\right)"," ",0,"integral(-(-x^3 + 1)^(2/3)*x^7/(x^6 - 1), x)","F",0
619,0,0,0,2.293866," ","integrate(x^4/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{4}}{x^{6} - 1}, x\right)"," ",0,"integral(-(-x^3 + 1)^(2/3)*x^4/(x^6 - 1), x)","F",0
620,1,373,0,2.317773," ","integrate(x/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{36} \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{2^{\frac{1}{6}} {\left(24 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{14} - 2 \, x^{11} - 6 \, x^{8} - 2 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(x^{16} - 33 \, x^{13} + 110 \, x^{10} - 110 \, x^{7} + 33 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \sqrt{6} 2^{\frac{1}{3}} {\left(x^{18} + 42 \, x^{15} - 417 \, x^{12} + 812 \, x^{9} - 417 \, x^{6} + 42 \, x^{3} + 1\right)}\right)}}{6 \, {\left(x^{18} - 102 \, x^{15} + 447 \, x^{12} - 628 \, x^{9} + 447 \, x^{6} - 102 \, x^{3} + 1\right)}}\right) - \frac{1}{72} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{12 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{8} - 4 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{12} - 32 \, x^{9} + 78 \, x^{6} - 32 \, x^{3} + 1\right)} - 6 \, {\left(x^{10} - 11 \, x^{7} + 11 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{12} + 4 \, x^{9} + 6 \, x^{6} + 4 \, x^{3} + 1}\right) + \frac{1}{36} \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{2} - 6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{6} + 2 \, x^{3} + 1\right)}}{x^{6} + 2 \, x^{3} + 1}\right)"," ",0,"-1/36*sqrt(6)*2^(1/6)*(-1)^(1/3)*arctan(1/6*2^(1/6)*(24*sqrt(6)*2^(2/3)*(-1)^(2/3)*(x^14 - 2*x^11 - 6*x^8 - 2*x^5 + x^2)*(-x^3 + 1)^(2/3) + 12*sqrt(6)*(-1)^(1/3)*(x^16 - 33*x^13 + 110*x^10 - 110*x^7 + 33*x^4 - x)*(-x^3 + 1)^(1/3) + sqrt(6)*2^(1/3)*(x^18 + 42*x^15 - 417*x^12 + 812*x^9 - 417*x^6 + 42*x^3 + 1))/(x^18 - 102*x^15 + 447*x^12 - 628*x^9 + 447*x^6 - 102*x^3 + 1)) - 1/72*2^(2/3)*(-1)^(1/3)*log(-(12*2^(2/3)*(-1)^(1/3)*(x^8 - 4*x^5 + x^2)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(x^12 - 32*x^9 + 78*x^6 - 32*x^3 + 1) - 6*(x^10 - 11*x^7 + 11*x^4 - x)*(-x^3 + 1)^(1/3))/(x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 1)) + 1/36*2^(2/3)*(-1)^(1/3)*log(-(12*(-x^3 + 1)^(2/3)*x^2 - 6*2^(1/3)*(-1)^(2/3)*(x^4 - x)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3)*(x^6 + 2*x^3 + 1))/(x^6 + 2*x^3 + 1))","B",0
621,0,0,0,2.364441," ","integrate(1/x^2/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{8} - x^{2}}, x\right)"," ",0,"integral(-(-x^3 + 1)^(2/3)/(x^8 - x^2), x)","F",0
622,0,0,0,2.361688," ","integrate(1/x^5/(-x^3+1)^(1/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{11} - x^{5}}, x\right)"," ",0,"integral(-(-x^3 + 1)^(2/3)/(x^11 - x^5), x)","F",0
623,1,142,0,0.450572," ","integrate(x^11/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{28} \, {\left(4 \, x^{6} - x^{3} + 25\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}"," ",0,"-1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) - 1/24*4^(2/3)*(-1)^(1/3)*log(-4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3) + 2*4^(1/3)*(-1)^(2/3) + 2*(-x^3 + 1)^(2/3)) + 1/12*4^(2/3)*(-1)^(1/3)*log(4^(2/3)*(-1)^(1/3) + 2*(-x^3 + 1)^(1/3)) - 1/28*(4*x^6 - x^3 + 25)*(-x^3 + 1)^(1/3)","A",0
624,1,114,0,0.479104," ","integrate(x^8/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2 \cdot 4^{\frac{1}{3}}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(-4^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{4} \, {\left(x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}"," ",0,"-1/6*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) - 1/24*4^(2/3)*log(4^(2/3)*(-x^3 + 1)^(1/3) + 2*(-x^3 + 1)^(2/3) + 2*4^(1/3)) + 1/12*4^(2/3)*log(-4^(2/3) + 2*(-x^3 + 1)^(1/3)) - 1/4*(x^3 - 1)*(-x^3 + 1)^(1/3)","A",0
625,1,130,0,0.464883," ","integrate(x^5/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - {\left(-x^{3} + 1\right)}^{\frac{1}{3}}"," ",0,"-1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) - 1/24*4^(2/3)*(-1)^(1/3)*log(-4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3) + 2*4^(1/3)*(-1)^(2/3) + 2*(-x^3 + 1)^(2/3)) + 1/12*4^(2/3)*(-1)^(1/3)*log(4^(2/3)*(-1)^(1/3) + 2*(-x^3 + 1)^(1/3)) - (-x^3 + 1)^(1/3)","A",0
626,1,98,0,0.492225," ","integrate(x^2/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2 \cdot 4^{\frac{1}{3}}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(-4^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) - 1/24*4^(2/3)*log(4^(2/3)*(-x^3 + 1)^(1/3) + 2*(-x^3 + 1)^(2/3) + 2*4^(1/3)) + 1/12*4^(2/3)*log(-4^(2/3) + 2*(-x^3 + 1)^(1/3))","A",0
627,1,182,0,0.484717," ","integrate(1/x/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - \frac{1}{6} \, \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + \frac{1}{3} \, \log\left({\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 1\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) - 1/24*4^(2/3)*(-1)^(1/3)*log(-4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3) + 2*4^(1/3)*(-1)^(2/3) + 2*(-x^3 + 1)^(2/3)) + 1/12*4^(2/3)*(-1)^(1/3)*log(4^(2/3)*(-1)^(1/3) + 2*(-x^3 + 1)^(1/3)) - 1/3*sqrt(3)*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) - 1/6*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1) + 1/3*log((-x^3 + 1)^(1/3) - 1)","A",0
628,1,195,0,0.486216," ","integrate(1/x^4/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{12 \cdot 4^{\frac{1}{6}} \sqrt{3} x^{3} \arctan\left(\frac{1}{6} \cdot 4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \sqrt{3}\right)}\right) + 3 \cdot 4^{\frac{2}{3}} x^{3} \log\left(4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2 \cdot 4^{\frac{1}{3}}\right) - 6 \cdot 4^{\frac{2}{3}} x^{3} \log\left(-4^{\frac{2}{3}} + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - 8 \, \sqrt{3} x^{3} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 4 \, x^{3} \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + 8 \, x^{3} \log\left({\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 1\right) + 24 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{72 \, x^{3}}"," ",0,"-1/72*(12*4^(1/6)*sqrt(3)*x^3*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-x^3 + 1)^(1/3) + 4^(1/3)*sqrt(3))) + 3*4^(2/3)*x^3*log(4^(2/3)*(-x^3 + 1)^(1/3) + 2*(-x^3 + 1)^(2/3) + 2*4^(1/3)) - 6*4^(2/3)*x^3*log(-4^(2/3) + 2*(-x^3 + 1)^(1/3)) - 8*sqrt(3)*x^3*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) - 4*x^3*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1) + 8*x^3*log((-x^3 + 1)^(1/3) - 1) + 24*(-x^3 + 1)^(1/3))/x^3","A",0
629,1,232,0,0.461675," ","integrate(x^7/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + \frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{4^{\frac{1}{6}} {\left(4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 4^{\frac{1}{3}} \sqrt{3} x\right)}}{6 \, x}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x - 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(\frac{2 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} x^{2} + 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{1}{9} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) + \frac{1}{9} \, \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - \frac{1}{18} \, \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"-1/3*(-x^3 + 1)^(1/3)*x^2 + 1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*(4^(2/3)*sqrt(3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 4^(1/3)*sqrt(3)*x)/x) + 1/12*4^(2/3)*(-1)^(1/3)*log(-(4^(2/3)*(-1)^(1/3)*x - 2*(-x^3 + 1)^(1/3))/x) - 1/24*4^(2/3)*(-1)^(1/3)*log((2*4^(1/3)*(-1)^(2/3)*x^2 + 4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3)*x + 2*(-x^3 + 1)^(2/3))/x^2) + 1/9*sqrt(3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) + 1/9*log((x + (-x^3 + 1)^(1/3))/x) - 1/18*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2)","A",0
630,1,197,0,0.459233," ","integrate(x^4/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(-\frac{4^{\frac{1}{6}} {\left(4^{\frac{1}{3}} \sqrt{3} x - 4^{\frac{2}{3}} \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, x}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(\frac{4^{\frac{2}{3}} x + 2 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(\frac{2 \cdot 4^{\frac{1}{3}} x^{2} - 4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + 2 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) - \frac{1}{3} \, \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) + \frac{1}{6} \, \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right)"," ",0,"1/6*4^(1/6)*sqrt(3)*arctan(-1/6*4^(1/6)*(4^(1/3)*sqrt(3)*x - 4^(2/3)*sqrt(3)*(-x^3 + 1)^(1/3))/x) + 1/12*4^(2/3)*log((4^(2/3)*x + 2*(-x^3 + 1)^(1/3))/x) - 1/24*4^(2/3)*log((2*4^(1/3)*x^2 - 4^(2/3)*(-x^3 + 1)^(1/3)*x + 2*(-x^3 + 1)^(2/3))/x^2) - 1/3*sqrt(3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) - 1/3*log((x + (-x^3 + 1)^(1/3))/x) + 1/6*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2)","A",0
631,1,283,0,1.923537," ","integrate(x/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{1}{18} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(-\frac{4^{\frac{1}{6}} {\left(6 \cdot 4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 12 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \sqrt{3} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) + \frac{1}{36} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{3 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{3} + 1\right)} - 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) - \frac{1}{72} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(\frac{6 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 24 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right)"," ",0,"-1/18*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(-1/6*4^(1/6)*(6*4^(2/3)*sqrt(3)*(-1)^(2/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - 12*sqrt(3)*(-1)^(1/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 4^(1/3)*sqrt(3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) + 1/36*4^(2/3)*(-1)^(1/3)*log(-(3*4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3)*x^2 - 4^(1/3)*(-1)^(2/3)*(x^3 + 1) - 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) - 1/72*4^(2/3)*(-1)^(1/3)*log((6*4^(1/3)*(-1)^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 4^(2/3)*(-1)^(1/3)*(19*x^6 - 16*x^3 + 1) - 24*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1))","B",0
632,1,272,0,1.939485," ","integrate(1/x^2/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} x \arctan\left(\frac{4^{\frac{1}{6}} {\left(6 \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 12 \, \sqrt{3} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \sqrt{3} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) + 2 \cdot 4^{\frac{2}{3}} x \log\left(\frac{3 \cdot 4^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x + 4^{\frac{1}{3}} {\left(x^{3} + 1\right)}}{x^{3} + 1}\right) - 4^{\frac{2}{3}} x \log\left(\frac{6 \cdot 4^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 4^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 24 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) - 72 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{72 \, x}"," ",0,"1/72*(4*4^(1/6)*sqrt(3)*x*arctan(1/6*4^(1/6)*(6*4^(2/3)*sqrt(3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) + 12*sqrt(3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 4^(1/3)*sqrt(3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) + 2*4^(2/3)*x*log((3*4^(2/3)*(-x^3 + 1)^(1/3)*x^2 + 6*(-x^3 + 1)^(2/3)*x + 4^(1/3)*(x^3 + 1))/(x^3 + 1)) - 4^(2/3)*x*log((6*4^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) + 4^(2/3)*(19*x^6 - 16*x^3 + 1) - 24*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) - 72*(-x^3 + 1)^(1/3))/x","B",0
633,1,312,0,1.856127," ","integrate(1/x^5/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} x^{4} \arctan\left(-\frac{4^{\frac{1}{6}} {\left(6 \cdot 4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 12 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \sqrt{3} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 2 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{4} \log\left(-\frac{3 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{3} + 1\right)} - 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{4} \log\left(\frac{6 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 24 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) - 18 \, {\left(x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{72 \, x^{4}}"," ",0,"-1/72*(4*4^(1/6)*sqrt(3)*(-1)^(1/3)*x^4*arctan(-1/6*4^(1/6)*(6*4^(2/3)*sqrt(3)*(-1)^(2/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - 12*sqrt(3)*(-1)^(1/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 4^(1/3)*sqrt(3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 2*4^(2/3)*(-1)^(1/3)*x^4*log(-(3*4^(2/3)*(-1)^(1/3)*(-x^3 + 1)^(1/3)*x^2 - 4^(1/3)*(-1)^(2/3)*(x^3 + 1) - 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 4^(2/3)*(-1)^(1/3)*x^4*log((6*4^(1/3)*(-1)^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 4^(2/3)*(-1)^(1/3)*(19*x^6 - 16*x^3 + 1) - 24*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) - 18*(x^3 - 1)*(-x^3 + 1)^(1/3))/x^4","B",0
634,1,356,0,2.518262," ","integrate(x^6/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","\frac{1}{36} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(-\frac{4^{\frac{1}{6}} {\left(6 \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(x^{16} - 33 \, x^{13} + 110 \, x^{10} - 110 \, x^{7} + 33 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 48 \, \sqrt{3} {\left(x^{14} - 2 \, x^{11} - 6 \, x^{8} - 2 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \sqrt{3} {\left(x^{18} + 42 \, x^{15} - 417 \, x^{12} + 812 \, x^{9} - 417 \, x^{6} + 42 \, x^{3} + 1\right)}\right)}}{6 \, {\left(x^{18} - 102 \, x^{15} + 447 \, x^{12} - 628 \, x^{9} + 447 \, x^{6} - 102 \, x^{3} + 1\right)}}\right) + \frac{1}{72} \cdot 4^{\frac{2}{3}} \log\left(-\frac{12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{2} - 3 \cdot 4^{\frac{2}{3}} {\left(x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} {\left(x^{6} + 2 \, x^{3} + 1\right)}}{x^{6} + 2 \, x^{3} + 1}\right) - \frac{1}{144} \cdot 4^{\frac{2}{3}} \log\left(\frac{24 \cdot 4^{\frac{1}{3}} {\left(x^{8} - 4 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 4^{\frac{2}{3}} {\left(x^{12} - 32 \, x^{9} + 78 \, x^{6} - 32 \, x^{3} + 1\right)} + 12 \, {\left(x^{10} - 11 \, x^{7} + 11 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{12} + 4 \, x^{9} + 6 \, x^{6} + 4 \, x^{3} + 1}\right) - \frac{1}{2} \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x"," ",0,"1/36*4^(1/6)*sqrt(3)*arctan(-1/6*4^(1/6)*(6*4^(2/3)*sqrt(3)*(x^16 - 33*x^13 + 110*x^10 - 110*x^7 + 33*x^4 - x)*(-x^3 + 1)^(1/3) - 48*sqrt(3)*(x^14 - 2*x^11 - 6*x^8 - 2*x^5 + x^2)*(-x^3 + 1)^(2/3) - 4^(1/3)*sqrt(3)*(x^18 + 42*x^15 - 417*x^12 + 812*x^9 - 417*x^6 + 42*x^3 + 1))/(x^18 - 102*x^15 + 447*x^12 - 628*x^9 + 447*x^6 - 102*x^3 + 1)) + 1/72*4^(2/3)*log(-(12*(-x^3 + 1)^(2/3)*x^2 - 3*4^(2/3)*(x^4 - x)*(-x^3 + 1)^(1/3) + 4^(1/3)*(x^6 + 2*x^3 + 1))/(x^6 + 2*x^3 + 1)) - 1/144*4^(2/3)*log((24*4^(1/3)*(x^8 - 4*x^5 + x^2)*(-x^3 + 1)^(2/3) + 4^(2/3)*(x^12 - 32*x^9 + 78*x^6 - 32*x^3 + 1) + 12*(x^10 - 11*x^7 + 11*x^4 - x)*(-x^3 + 1)^(1/3))/(x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 1)) - 1/2*(-x^3 + 1)^(1/3)*x","A",0
635,0,0,0,2.591685," ","integrate(x^3/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{3}}{x^{6} - 1}, x\right)"," ",0,"integral(-(-x^3 + 1)^(1/3)*x^3/(x^6 - 1), x)","F",0
636,0,0,0,2.614286," ","integrate(1/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} - 1}, x\right)"," ",0,"integral(-(-x^3 + 1)^(1/3)/(x^6 - 1), x)","F",0
637,1,396,0,2.415620," ","integrate(1/x^3/(-x^3+1)^(2/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{4 \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} x^{2} \arctan\left(\frac{4^{\frac{1}{6}} {\left(6 \cdot 4^{\frac{2}{3}} \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(x^{16} - 33 \, x^{13} + 110 \, x^{10} - 110 \, x^{7} + 33 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 48 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(x^{14} - 2 \, x^{11} - 6 \, x^{8} - 2 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} \sqrt{3} {\left(x^{18} + 42 \, x^{15} - 417 \, x^{12} + 812 \, x^{9} - 417 \, x^{6} + 42 \, x^{3} + 1\right)}\right)}}{6 \, {\left(x^{18} - 102 \, x^{15} + 447 \, x^{12} - 628 \, x^{9} + 447 \, x^{6} - 102 \, x^{3} + 1\right)}}\right) + 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{2} \log\left(\frac{24 \cdot 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{8} - 4 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{12} - 32 \, x^{9} + 78 \, x^{6} - 32 \, x^{3} + 1\right)} + 12 \, {\left(x^{10} - 11 \, x^{7} + 11 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{12} + 4 \, x^{9} + 6 \, x^{6} + 4 \, x^{3} + 1}\right) - 2 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{2} \log\left(-\frac{12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{2} + 3 \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 4^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(x^{6} + 2 \, x^{3} + 1\right)}}{x^{6} + 2 \, x^{3} + 1}\right) + 72 \, {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{144 \, x^{2}}"," ",0,"-1/144*(4*4^(1/6)*sqrt(3)*(-1)^(1/3)*x^2*arctan(1/6*4^(1/6)*(6*4^(2/3)*sqrt(3)*(-1)^(2/3)*(x^16 - 33*x^13 + 110*x^10 - 110*x^7 + 33*x^4 - x)*(-x^3 + 1)^(1/3) + 48*sqrt(3)*(-1)^(1/3)*(x^14 - 2*x^11 - 6*x^8 - 2*x^5 + x^2)*(-x^3 + 1)^(2/3) - 4^(1/3)*sqrt(3)*(x^18 + 42*x^15 - 417*x^12 + 812*x^9 - 417*x^6 + 42*x^3 + 1))/(x^18 - 102*x^15 + 447*x^12 - 628*x^9 + 447*x^6 - 102*x^3 + 1)) + 4^(2/3)*(-1)^(1/3)*x^2*log((24*4^(1/3)*(-1)^(2/3)*(x^8 - 4*x^5 + x^2)*(-x^3 + 1)^(2/3) - 4^(2/3)*(-1)^(1/3)*(x^12 - 32*x^9 + 78*x^6 - 32*x^3 + 1) + 12*(x^10 - 11*x^7 + 11*x^4 - x)*(-x^3 + 1)^(1/3))/(x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 1)) - 2*4^(2/3)*(-1)^(1/3)*x^2*log(-(12*(-x^3 + 1)^(2/3)*x^2 + 3*4^(2/3)*(-1)^(1/3)*(x^4 - x)*(-x^3 + 1)^(1/3) + 4^(1/3)*(-1)^(2/3)*(x^6 + 2*x^3 + 1))/(x^6 + 2*x^3 + 1)) + 72*(-x^3 + 1)^(1/3))/x^2","A",0
638,1,140,0,0.468280," ","integrate(x^14/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","\frac{10 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - 5 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + 10 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) + 3 \, {\left(5 \, x^{9} + x^{6} + 23 \, x^{3} - 49\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{120 \, {\left(x^{3} - 1\right)}}"," ",0,"1/120*(10*sqrt(6)*2^(1/6)*(x^3 - 1)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 5*2^(2/3)*(x^3 - 1)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 10*2^(2/3)*(x^3 - 1)*log(-2^(1/3) + (-x^3 + 1)^(1/3)) + 3*(5*x^9 + x^6 + 23*x^3 - 49)*(-x^3 + 1)^(2/3))/(x^3 - 1)","A",0
639,1,159,0,0.454356," ","integrate(x^11/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}}\right)}\right) + 5 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) - 10 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - 12 \, {\left(2 \, x^{6} + x^{3} - 8\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{120 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/120*(10*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^3 - 1)*arctan(1/6*2^(1/6)*(2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3))) + 5*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3) + (-x^3 + 1)^(2/3)) - 10*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(-2^(1/3)*(-1)^(2/3) + (-x^3 + 1)^(1/3)) - 12*(2*x^6 + x^3 - 8)*(-x^3 + 1)^(2/3))/(x^3 - 1)","A",0
640,1,130,0,0.471828," ","integrate(x^8/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) + 12 \, {\left(x^{3} - 2\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{24 \, {\left(x^{3} - 1\right)}}"," ",0,"1/24*(2*sqrt(6)*2^(1/6)*(x^3 - 1)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 2^(2/3)*(x^3 - 1)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 2*2^(2/3)*(x^3 - 1)*log(-2^(1/3) + (-x^3 + 1)^(1/3)) + 12*(x^3 - 2)*(-x^3 + 1)^(2/3))/(x^3 - 1)","A",0
641,1,148,0,0.464611," ","integrate(x^5/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}}\right)}\right) + 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) + 12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{24 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/24*(2*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^3 - 1)*arctan(1/6*2^(1/6)*(2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3))) + 2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3) + (-x^3 + 1)^(2/3)) - 2*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(-2^(1/3)*(-1)^(2/3) + (-x^3 + 1)^(1/3)) + 12*(-x^3 + 1)^(2/3))/(x^3 - 1)","B",0
642,1,125,0,0.466899," ","integrate(x^2/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - 12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{24 \, {\left(x^{3} - 1\right)}}"," ",0,"1/24*(2*sqrt(6)*2^(1/6)*(x^3 - 1)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 2^(2/3)*(x^3 - 1)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 2*2^(2/3)*(x^3 - 1)*log(-2^(1/3) + (-x^3 + 1)^(1/3)) - 12*(-x^3 + 1)^(2/3))/(x^3 - 1)","A",0
643,1,226,0,0.489824," ","integrate(1/x/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}}\right)}\right) + 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(-2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) - 8 \, \sqrt{3} {\left(x^{3} - 1\right)} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + 4 \, {\left(x^{3} - 1\right)} \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) - 8 \, {\left(x^{3} - 1\right)} \log\left({\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 1\right) + 12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{24 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/24*(2*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^3 - 1)*arctan(1/6*2^(1/6)*(2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3))) + 2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3) - 2^(2/3)*(-1)^(1/3) + (-x^3 + 1)^(2/3)) - 2*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(-2^(1/3)*(-1)^(2/3) + (-x^3 + 1)^(1/3)) - 8*sqrt(3)*(x^3 - 1)*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) + 4*(x^3 - 1)*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1) - 8*(x^3 - 1)*log((-x^3 + 1)^(1/3) - 1) + 12*(-x^3 + 1)^(2/3))/(x^3 - 1)","A",0
644,1,238,0,0.464507," ","integrate(1/x^4/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","\frac{6 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{6} - x^{3}\right)} \arctan\left(\frac{1}{6} \cdot 2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} + 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}\right) - 3 \cdot 2^{\frac{2}{3}} {\left(x^{6} - x^{3}\right)} \log\left(2^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}\right) + 6 \cdot 2^{\frac{2}{3}} {\left(x^{6} - x^{3}\right)} \log\left(-2^{\frac{1}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right) + 8 \, \sqrt{3} {\left(x^{6} - x^{3}\right)} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 4 \, {\left(x^{6} - x^{3}\right)} \log\left({\left(-x^{3} + 1\right)}^{\frac{2}{3}} + {\left(-x^{3} + 1\right)}^{\frac{1}{3}} + 1\right) + 8 \, {\left(x^{6} - x^{3}\right)} \log\left({\left(-x^{3} + 1\right)}^{\frac{1}{3}} - 1\right) - 12 \, {\left(5 \, x^{3} - 2\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{72 \, {\left(x^{6} - x^{3}\right)}}"," ",0,"1/72*(6*sqrt(6)*2^(1/6)*(x^6 - x^3)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3) + 2*sqrt(6)*(-x^3 + 1)^(1/3))) - 3*2^(2/3)*(x^6 - x^3)*log(2^(2/3) + 2^(1/3)*(-x^3 + 1)^(1/3) + (-x^3 + 1)^(2/3)) + 6*2^(2/3)*(x^6 - x^3)*log(-2^(1/3) + (-x^3 + 1)^(1/3)) + 8*sqrt(3)*(x^6 - x^3)*arctan(2/3*sqrt(3)*(-x^3 + 1)^(1/3) + 1/3*sqrt(3)) - 4*(x^6 - x^3)*log((-x^3 + 1)^(2/3) + (-x^3 + 1)^(1/3) + 1) + 8*(x^6 - x^3)*log((-x^3 + 1)^(1/3) - 1) - 12*(5*x^3 - 2)*(-x^3 + 1)^(2/3))/(x^6 - x^3)","A",0
645,1,271,0,0.493564," ","integrate(x^9/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","\frac{6 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} x + 2 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, x}\right) + 6 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - 3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(-\frac{2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} x^{2} + 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x - {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) + 8 \, \sqrt{3} {\left(x^{3} - 1\right)} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) - 8 \, {\left(x^{3} - 1\right)} \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) + 4 \, {\left(x^{3} - 1\right)} \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) + 12 \, {\left(2 \, x^{4} - 5 \, x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{72 \, {\left(x^{3} - 1\right)}}"," ",0,"1/72*(6*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^3 - 1)*arctan(1/6*2^(1/6)*(sqrt(6)*2^(1/3)*x + 2*sqrt(6)*(-1)^(1/3)*(-x^3 + 1)^(1/3))/x) + 6*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log((2^(1/3)*(-1)^(2/3)*x + (-x^3 + 1)^(1/3))/x) - 3*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(-(2^(2/3)*(-1)^(1/3)*x^2 + 2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x - (-x^3 + 1)^(2/3))/x^2) + 8*sqrt(3)*(x^3 - 1)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) - 8*(x^3 - 1)*log((x + (-x^3 + 1)^(1/3))/x) + 4*(x^3 - 1)*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2) + 12*(2*x^4 - 5*x)*(-x^3 + 1)^(2/3))/(x^3 - 1)","B",0
646,1,239,0,0.456053," ","integrate(x^6/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{3} - 1\right)} \arctan\left(-\frac{2^{\frac{1}{6}} {\left(\sqrt{6} 2^{\frac{1}{3}} x - 2 \, \sqrt{6} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, x}\right) - 2 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{2^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) + 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{2^{\frac{2}{3}} x^{2} - 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) - 8 \, \sqrt{3} {\left(x^{3} - 1\right)} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{3 \, x}\right) + 8 \, {\left(x^{3} - 1\right)} \log\left(\frac{x + {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x}\right) - 4 \, {\left(x^{3} - 1\right)} \log\left(\frac{x^{2} - {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x + {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{2}}\right) + 12 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{24 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/24*(2*sqrt(6)*2^(1/6)*(x^3 - 1)*arctan(-1/6*2^(1/6)*(sqrt(6)*2^(1/3)*x - 2*sqrt(6)*(-x^3 + 1)^(1/3))/x) - 2*2^(2/3)*(x^3 - 1)*log((2^(1/3)*x + (-x^3 + 1)^(1/3))/x) + 2^(2/3)*(x^3 - 1)*log((2^(2/3)*x^2 - 2^(1/3)*(-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2) - 8*sqrt(3)*(x^3 - 1)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(-x^3 + 1)^(1/3))/x) + 8*(x^3 - 1)*log((x + (-x^3 + 1)^(1/3))/x) - 4*(x^3 - 1)*log((x^2 - (-x^3 + 1)^(1/3)*x + (-x^3 + 1)^(2/3))/x^2) + 12*(-x^3 + 1)^(2/3)*x)/(x^3 - 1)","B",0
647,1,318,0,2.584342," ","integrate(x^3/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 2 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} - 1\right)} \log\left(-\frac{3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} + 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 36 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{72 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/72*(2*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^3 - 1)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(-1)^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 12*sqrt(6)*(-1)^(1/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 2*2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log((6*2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x^2 - 2^(2/3)*(-1)^(1/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 2^(2/3)*(-1)^(1/3)*(x^3 - 1)*log(-(3*2^(2/3)*(-1)^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(19*x^6 - 16*x^3 + 1) + 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 36*(-x^3 + 1)^(2/3)*x)/(x^3 - 1)","B",0
648,1,288,0,2.599070," ","integrate(1/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{3} - 1\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)} + 12 \, \sqrt{6} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 2 \cdot 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + 2^{\frac{2}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 2^{\frac{2}{3}} {\left(x^{3} - 1\right)} \log\left(\frac{3 \cdot 2^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 36 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{72 \, {\left(x^{3} - 1\right)}}"," ",0,"-1/72*(2*sqrt(6)*2^(1/6)*(x^3 - 1)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1) + 12*sqrt(6)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 2*2^(2/3)*(x^3 - 1)*log((6*2^(1/3)*(-x^3 + 1)^(1/3)*x^2 + 2^(2/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 2^(2/3)*(x^3 - 1)*log((3*2^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) + 2^(1/3)*(19*x^6 - 16*x^3 + 1) - 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 36*(-x^3 + 1)^(2/3)*x)/(x^3 - 1)","B",0
649,1,340,0,2.599304," ","integrate(1/x^3/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{5} - x^{2}\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 2 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{5} - x^{2}\right)} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{5} - x^{2}\right)} \log\left(-\frac{3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} + 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 36 \, {\left(2 \, x^{3} - 1\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{72 \, {\left(x^{5} - x^{2}\right)}}"," ",0,"-1/72*(2*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^5 - x^2)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(-1)^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 12*sqrt(6)*(-1)^(1/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 2*2^(2/3)*(-1)^(1/3)*(x^5 - x^2)*log((6*2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x^2 - 2^(2/3)*(-1)^(1/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 2^(2/3)*(-1)^(1/3)*(x^5 - x^2)*log(-(3*2^(2/3)*(-1)^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(19*x^6 - 16*x^3 + 1) + 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 36*(2*x^3 - 1)*(-x^3 + 1)^(2/3))/(x^5 - x^2)","B",0
650,1,316,0,2.707855," ","integrate(1/x^6/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{6} 2^{\frac{1}{6}} {\left(x^{8} - x^{5}\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)} + 12 \, \sqrt{6} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 10 \cdot 2^{\frac{2}{3}} {\left(x^{8} - x^{5}\right)} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} + 2^{\frac{2}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 5 \cdot 2^{\frac{2}{3}} {\left(x^{8} - x^{5}\right)} \log\left(\frac{3 \cdot 2^{\frac{2}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} - 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 36 \, {\left(8 \, x^{6} - x^{3} - 2\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{360 \, {\left(x^{8} - x^{5}\right)}}"," ",0,"-1/360*(10*sqrt(6)*2^(1/6)*(x^8 - x^5)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1) + 12*sqrt(6)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 10*2^(2/3)*(x^8 - x^5)*log((6*2^(1/3)*(-x^3 + 1)^(1/3)*x^2 + 2^(2/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 5*2^(2/3)*(x^8 - x^5)*log((3*2^(2/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) + 2^(1/3)*(19*x^6 - 16*x^3 + 1) - 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 36*(8*x^6 - x^3 - 2)*(-x^3 + 1)^(2/3))/(x^8 - x^5)","B",0
651,1,351,0,2.587251," ","integrate(1/x^9/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{6} 2^{\frac{1}{6}} \left(-1\right)^{\frac{1}{3}} {\left(x^{11} - x^{8}\right)} \arctan\left(\frac{2^{\frac{1}{6}} {\left(6 \, \sqrt{6} 2^{\frac{2}{3}} \left(-1\right)^{\frac{2}{3}} {\left(5 \, x^{7} + 4 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{6} \left(-1\right)^{\frac{1}{3}} {\left(19 \, x^{8} - 16 \, x^{5} + x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} - \sqrt{6} 2^{\frac{1}{3}} {\left(71 \, x^{9} - 111 \, x^{6} + 33 \, x^{3} - 1\right)}\right)}}{6 \, {\left(109 \, x^{9} - 105 \, x^{6} + 3 \, x^{3} + 1\right)}}\right) - 10 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{11} - x^{8}\right)} \log\left(\frac{6 \cdot 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(-x^{3} + 1\right)}^{\frac{1}{3}} x^{2} - 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{3} + 1\right)} + 6 \, {\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{3} + 1}\right) + 5 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(x^{11} - x^{8}\right)} \log\left(-\frac{3 \cdot 2^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} {\left(5 \, x^{4} - x\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}} - 2^{\frac{1}{3}} \left(-1\right)^{\frac{2}{3}} {\left(19 \, x^{6} - 16 \, x^{3} + 1\right)} + 12 \, {\left(2 \, x^{5} - x^{2}\right)} {\left(-x^{3} + 1\right)}^{\frac{1}{3}}}{x^{6} + 2 \, x^{3} + 1}\right) + 9 \, {\left(49 \, x^{9} - 23 \, x^{6} - x^{3} - 5\right)} {\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{360 \, {\left(x^{11} - x^{8}\right)}}"," ",0,"-1/360*(10*sqrt(6)*2^(1/6)*(-1)^(1/3)*(x^11 - x^8)*arctan(1/6*2^(1/6)*(6*sqrt(6)*2^(2/3)*(-1)^(2/3)*(5*x^7 + 4*x^4 - x)*(-x^3 + 1)^(2/3) - 12*sqrt(6)*(-1)^(1/3)*(19*x^8 - 16*x^5 + x^2)*(-x^3 + 1)^(1/3) - sqrt(6)*2^(1/3)*(71*x^9 - 111*x^6 + 33*x^3 - 1))/(109*x^9 - 105*x^6 + 3*x^3 + 1)) - 10*2^(2/3)*(-1)^(1/3)*(x^11 - x^8)*log((6*2^(1/3)*(-1)^(2/3)*(-x^3 + 1)^(1/3)*x^2 - 2^(2/3)*(-1)^(1/3)*(x^3 + 1) + 6*(-x^3 + 1)^(2/3)*x)/(x^3 + 1)) + 5*2^(2/3)*(-1)^(1/3)*(x^11 - x^8)*log(-(3*2^(2/3)*(-1)^(1/3)*(5*x^4 - x)*(-x^3 + 1)^(2/3) - 2^(1/3)*(-1)^(2/3)*(19*x^6 - 16*x^3 + 1) + 12*(2*x^5 - x^2)*(-x^3 + 1)^(1/3))/(x^6 + 2*x^3 + 1)) + 9*(49*x^9 - 23*x^6 - x^3 - 5)*(-x^3 + 1)^(2/3))/(x^11 - x^8)","B",0
652,0,0,0,2.230695," ","integrate(x^10/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{10}}{x^{9} - x^{6} - x^{3} + 1}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)*x^10/(x^9 - x^6 - x^3 + 1), x)","F",0
653,0,0,0,2.245330," ","integrate(x^7/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{7}}{x^{9} - x^{6} - x^{3} + 1}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)*x^7/(x^9 - x^6 - x^3 + 1), x)","F",0
654,0,0,0,2.275086," ","integrate(x^4/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x^{4}}{x^{9} - x^{6} - x^{3} + 1}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)*x^4/(x^9 - x^6 - x^3 + 1), x)","F",0
655,0,0,0,2.292682," ","integrate(x/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}} x}{x^{9} - x^{6} - x^{3} + 1}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)*x/(x^9 - x^6 - x^3 + 1), x)","F",0
656,0,0,0,2.233568," ","integrate(1/x^2/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{11} - x^{8} - x^{5} + x^{2}}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)/(x^11 - x^8 - x^5 + x^2), x)","F",0
657,0,0,0,2.215570," ","integrate(1/x^5/(-x^3+1)^(4/3)/(x^3+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{3} + 1\right)}^{\frac{2}{3}}}{x^{14} - x^{11} - x^{8} + x^{5}}, x\right)"," ",0,"integral((-x^3 + 1)^(2/3)/(x^14 - x^11 - x^8 + x^5), x)","F",0
658,1,325,0,0.448028," ","integrate(x^11*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{140 \, \sqrt{3} b^{3} c^{3} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 70 \, b^{3} c^{3} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 140 \, b^{3} c^{3} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) - 3 \, {\left(14 \, b^{3} d^{3} x^{9} - 2 \, {\left(10 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{6} - 140 \, b^{3} c^{3} + 35 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 9 \, a^{3} d^{3} + {\left(35 \, b^{3} c^{2} d - 5 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{420 \, b^{3} d^{4}}"," ",0,"-1/420*(140*sqrt(3)*b^3*c^3*((b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 70*b^3*c^3*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*((b*c - a*d)/d)^(1/3) + ((b*c - a*d)/d)^(2/3)) - 140*b^3*c^3*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) + ((b*c - a*d)/d)^(1/3)) - 3*(14*b^3*d^3*x^9 - 2*(10*b^3*c*d^2 - a*b^2*d^3)*x^6 - 140*b^3*c^3 + 35*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 9*a^3*d^3 + (35*b^3*c^2*d - 5*a*b^2*c*d^2 - 3*a^2*b*d^3)*x^3)*(b*x^3 + a)^(1/3))/(b^3*d^4)","A",0
659,1,282,0,0.455770," ","integrate(x^8*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{28 \, \sqrt{3} b^{2} c^{2} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 14 \, b^{2} c^{2} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 28 \, b^{2} c^{2} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) - 3 \, {\left(4 \, b^{2} d^{2} x^{6} + 28 \, b^{2} c^{2} - 7 \, a b c d - 3 \, a^{2} d^{2} - {\left(7 \, b^{2} c d - a b d^{2}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{84 \, b^{2} d^{3}}"," ",0,"-1/84*(28*sqrt(3)*b^2*c^2*(-(b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 14*b^2*c^2*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(-(b*c - a*d)/d)^(1/3) + (-(b*c - a*d)/d)^(2/3)) - 28*b^2*c^2*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) - (-(b*c - a*d)/d)^(1/3)) - 3*(4*b^2*d^2*x^6 + 28*b^2*c^2 - 7*a*b*c*d - 3*a^2*d^2 - (7*b^2*c*d - a*b*d^2)*x^3)*(b*x^3 + a)^(1/3))/(b^2*d^3)","A",0
660,1,222,0,0.447133," ","integrate(x^5*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} b c \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 2 \, b c \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 4 \, b c \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) - 3 \, {\left(b d x^{3} - 4 \, b c + a d\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{12 \, b d^{2}}"," ",0,"-1/12*(4*sqrt(3)*b*c*((b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 2*b*c*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*((b*c - a*d)/d)^(1/3) + ((b*c - a*d)/d)^(2/3)) - 4*b*c*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) + ((b*c - a*d)/d)^(1/3)) - 3*(b*d*x^3 - 4*b*c + a*d)*(b*x^3 + a)^(1/3))/(b*d^2)","A",0
661,1,206,0,0.438140," ","integrate(x^2*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 2 \, \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{6 \, d}"," ",0,"-1/6*(2*sqrt(3)*(-(b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + (-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(-(b*c - a*d)/d)^(1/3) + (-(b*c - a*d)/d)^(2/3)) - 2*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) - (-(b*c - a*d)/d)^(1/3)) - 6*(b*x^3 + a)^(1/3))/d","A",0
662,1,276,0,0.445972," ","integrate((b*x^3+a)^(1/3)/x/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 2 \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + a^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 2 \, a^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) - 2 \, \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right)}{6 \, c}"," ",0,"-1/6*(2*sqrt(3)*((b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 2*sqrt(3)*a^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*a^(2/3) + sqrt(3)*a)/a) + a^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + ((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*((b*c - a*d)/d)^(1/3) + ((b*c - a*d)/d)^(2/3)) - 2*a^(1/3)*log((b*x^3 + a)^(1/3) - a^(1/3)) - 2*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) + ((b*c - a*d)/d)^(1/3)))/c","A",0
663,1,429,0,0.557708," ","integrate((b*x^3+a)^(1/3)/x^4/(d*x^3+c),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{3} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} a^{2} x^{3} \arctan\left(-\frac{2 \, \sqrt{3} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \sqrt{3} {\left(b c d - a d^{2}\right)}}{3 \, {\left(b c d - a d^{2}\right)}}\right) + 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} a^{2} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 6 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} a^{2} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) + 2 \, \sqrt{3} {\left(a b c - 3 \, a^{2} d\right)} x^{3} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}}}{3 \, a^{2}}\right) + \left(-a^{2}\right)^{\frac{2}{3}} {\left(b c - 3 \, a d\right)} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a - \left(-a^{2}\right)^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right) - 2 \, \left(-a^{2}\right)^{\frac{2}{3}} {\left(b c - 3 \, a d\right)} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - \left(-a^{2}\right)^{\frac{2}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2} c}{18 \, a^{2} c^{2} x^{3}}"," ",0,"-1/18*(6*sqrt(3)*(-b*c*d^2 + a*d^3)^(1/3)*a^2*x^3*arctan(-1/3*(2*sqrt(3)*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3) - sqrt(3)*(b*c*d - a*d^2))/(b*c*d - a*d^2)) + 3*(-b*c*d^2 + a*d^3)^(1/3)*a^2*x^3*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 6*(-b*c*d^2 + a*d^3)^(1/3)*a^2*x^3*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) + 2*sqrt(3)*(a*b*c - 3*a^2*d)*x^3*sqrt(-(-a^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-a^2)^(1/3)*a - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3))*sqrt(-(-a^2)^(1/3))/a^2) + (-a^2)^(2/3)*(b*c - 3*a*d)*x^3*log((b*x^3 + a)^(2/3)*a - (-a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(-a^2)^(2/3)) - 2*(-a^2)^(2/3)*(b*c - 3*a*d)*x^3*log((b*x^3 + a)^(1/3)*a - (-a^2)^(2/3)) + 6*(b*x^3 + a)^(1/3)*a^2*c)/(a^2*c^2*x^3)","A",0
664,1,472,0,2.002605," ","integrate((b*x^3+a)^(1/3)/x^7/(d*x^3+c),x, algorithm=""fricas"")","-\frac{18 \, \sqrt{3} {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} a^{3} d x^{6} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \sqrt{3} {\left(b c d - a d^{2}\right)}}{3 \, {\left(b c d - a d^{2}\right)}}\right) + 9 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} a^{3} d x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 18 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} a^{3} d x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 2 \, \sqrt{3} {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 9 \, a^{3} d^{2}\right)} {\left(a^{2}\right)}^{\frac{1}{6}} x^{6} \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) - {\left(b^{2} c^{2} + 3 \, a b c d - 9 \, a^{2} d^{2}\right)} {\left(a^{2}\right)}^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 2 \, {\left(b^{2} c^{2} + 3 \, a b c d - 9 \, a^{2} d^{2}\right)} {\left(a^{2}\right)}^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 3 \, {\left(3 \, a^{3} c^{2} + {\left(a^{2} b c^{2} - 6 \, a^{3} c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, a^{3} c^{3} x^{6}}"," ",0,"-1/54*(18*sqrt(3)*(b*c*d^2 - a*d^3)^(1/3)*a^3*d*x^6*arctan(-1/3*(2*sqrt(3)*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3) - sqrt(3)*(b*c*d - a*d^2))/(b*c*d - a*d^2)) + 9*(b*c*d^2 - a*d^3)^(1/3)*a^3*d*x^6*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 18*(b*c*d^2 - a*d^3)^(1/3)*a^3*d*x^6*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 2*sqrt(3)*(a*b^2*c^2 + 3*a^2*b*c*d - 9*a^3*d^2)*(a^2)^(1/6)*x^6*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) - (b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*(a^2)^(2/3)*x^6*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) + 2*(b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*(a^2)^(2/3)*x^6*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 3*(3*a^3*c^2 + (a^2*b*c^2 - 6*a^3*c*d)*x^3)*(b*x^3 + a)^(1/3))/(a^3*c^3*x^6)","A",0
665,1,494,0,1.949231," ","integrate(x^7*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{18 \, \sqrt{3} {\left(b c^{3} - a c^{2} d\right)}^{\frac{1}{3}} b^{3} c \arctan\left(-\frac{\sqrt{3} {\left(b c^{2} - a c d\right)} x + 2 \, \sqrt{3} {\left(b c^{3} - a c^{2} d\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c^{2} - a c d\right)} x}\right) + 18 \, {\left(b c^{3} - a c^{2} d\right)}^{\frac{1}{3}} b^{3} c \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} c - {\left(b c^{3} - a c^{2} d\right)}^{\frac{1}{3}} x}{x}\right) - 9 \, {\left(b c^{3} - a c^{2} d\right)}^{\frac{1}{3}} b^{3} c \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} c^{2} + {\left(b c^{3} - a c^{2} d\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x + {\left(b c^{3} - a c^{2} d\right)}^{\frac{2}{3}} x^{2}}{x^{2}}\right) + 2 \, \sqrt{3} {\left(9 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} {\left(b^{2}\right)}^{\frac{1}{6}} \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) - 2 \, {\left(9 \, b^{2} c^{2} - 3 \, a b c d - a^{2} d^{2}\right)} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + {\left(9 \, b^{2} c^{2} - 3 \, a b c d - a^{2} d^{2}\right)} {\left(b^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + 3 \, {\left(3 \, b^{3} d^{2} x^{5} - {\left(6 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, b^{3} d^{3}}"," ",0,"1/54*(18*sqrt(3)*(b*c^3 - a*c^2*d)^(1/3)*b^3*c*arctan(-1/3*(sqrt(3)*(b*c^2 - a*c*d)*x + 2*sqrt(3)*(b*c^3 - a*c^2*d)^(2/3)*(b*x^3 + a)^(1/3))/((b*c^2 - a*c*d)*x)) + 18*(b*c^3 - a*c^2*d)^(1/3)*b^3*c*log(((b*x^3 + a)^(1/3)*c - (b*c^3 - a*c^2*d)^(1/3)*x)/x) - 9*(b*c^3 - a*c^2*d)^(1/3)*b^3*c*log(((b*x^3 + a)^(2/3)*c^2 + (b*c^3 - a*c^2*d)^(1/3)*(b*x^3 + a)^(1/3)*c*x + (b*c^3 - a*c^2*d)^(2/3)*x^2)/x^2) + 2*sqrt(3)*(9*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*(b^2)^(1/6)*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) - 2*(9*b^2*c^2 - 3*a*b*c*d - a^2*d^2)*(b^2)^(2/3)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (9*b^2*c^2 - 3*a*b*c*d - a^2*d^2)*(b^2)^(2/3)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2) + 3*(3*b^3*d^2*x^5 - (6*b^3*c*d - a*b^2*d^2)*x^2)*(b*x^3 + a)^(1/3))/(b^3*d^3)","A",0
666,1,452,0,0.548311," ","integrate(x^4*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{2} d x^{2} + 6 \, \sqrt{3} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} b^{2} \arctan\left(-\frac{\sqrt{3} {\left(b c^{2} - a c d\right)} x + 2 \, \sqrt{3} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c^{2} - a c d\right)} x}\right) + 6 \, {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} b^{2} \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} c + {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} x}{x}\right) - 3 \, {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} b^{2} \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} c^{2} - {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x + {\left(-b c^{3} + a c^{2} d\right)}^{\frac{2}{3}} x^{2}}{x^{2}}\right) - 2 \, \sqrt{3} {\left(3 \, b^{2} c - a b d\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) + 2 \, \left(-b^{2}\right)^{\frac{2}{3}} {\left(3 \, b c - a d\right)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) - \left(-b^{2}\right)^{\frac{2}{3}} {\left(3 \, b c - a d\right)} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{18 \, b^{2} d^{2}}"," ",0,"1/18*(6*(b*x^3 + a)^(1/3)*b^2*d*x^2 + 6*sqrt(3)*(-b*c^3 + a*c^2*d)^(1/3)*b^2*arctan(-1/3*(sqrt(3)*(b*c^2 - a*c*d)*x + 2*sqrt(3)*(-b*c^3 + a*c^2*d)^(2/3)*(b*x^3 + a)^(1/3))/((b*c^2 - a*c*d)*x)) + 6*(-b*c^3 + a*c^2*d)^(1/3)*b^2*log(((b*x^3 + a)^(1/3)*c + (-b*c^3 + a*c^2*d)^(1/3)*x)/x) - 3*(-b*c^3 + a*c^2*d)^(1/3)*b^2*log(((b*x^3 + a)^(2/3)*c^2 - (-b*c^3 + a*c^2*d)^(1/3)*(b*x^3 + a)^(1/3)*c*x + (-b*c^3 + a*c^2*d)^(2/3)*x^2)/x^2) - 2*sqrt(3)*(3*b^2*c - a*b*d)*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) + 2*(-b^2)^(2/3)*(3*b*c - a*d)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) - (-b^2)^(2/3)*(3*b*c - a*d)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2))/(b^2*d^2)","B",0
667,1,330,0,0.483970," ","integrate(x*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b c - a d}{c}\right)^{\frac{2}{3}}}{3 \, {\left(b c - a d\right)} x}\right) - 2 \, \sqrt{3} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}}}{3 \, b x}\right) + 2 \, \left(-b\right)^{\frac{1}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + 2 \, \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \log\left(-\frac{x \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - \left(-b\right)^{\frac{1}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \log\left(\frac{x^{2} \left(\frac{b c - a d}{c}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} x \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, d}"," ",0,"1/6*(2*sqrt(3)*((b*c - a*d)/c)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b*c - a*d)/c)^(2/3))/((b*c - a*d)*x)) - 2*sqrt(3)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b)^(2/3))/(b*x)) + 2*(-b)^(1/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + 2*((b*c - a*d)/c)^(1/3)*log(-(x*((b*c - a*d)/c)^(1/3) - (b*x^3 + a)^(1/3))/x) - (-b)^(1/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - ((b*c - a*d)/c)^(1/3)*log((x^2*((b*c - a*d)/c)^(2/3) + (b*x^3 + a)^(1/3)*x*((b*c - a*d)/c)^(1/3) + (b*x^3 + a)^(2/3))/x^2))/d","A",0
668,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^2/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^5/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
670,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^8/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
671,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^11/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
672,-1,0,0,0.000000," ","integrate(x^6*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
673,-1,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^3/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate((b*x^3+a)^(1/3)/x^6/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,1,455,0,0.686877," ","integrate(x^11*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{440 \, \sqrt{3} b^{3} c^{3} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 220 \, b^{3} c^{3} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)} + {\left(b c - a d\right)} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) - 440 \, b^{3} c^{3} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(-d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right) - 3 \, {\left(40 \, b^{3} d^{3} x^{9} - 5 \, {\left(11 \, b^{3} c d^{2} - 2 \, a b^{2} d^{3}\right)} x^{6} - 220 \, b^{3} c^{3} + 88 \, a b^{2} c^{2} d + 33 \, a^{2} b c d^{2} + 18 \, a^{3} d^{3} + 2 \, {\left(44 \, b^{3} c^{2} d - 11 \, a b^{2} c d^{2} - 6 \, a^{2} b d^{3}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1320 \, b^{3} d^{4}}"," ",0,"-1/1320*(440*sqrt(3)*b^3*c^3*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3) + sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 220*b^3*c^3*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log((b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(2/3)*(b*c - a*d) + (b*c - a*d)*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)) - 440*b^3*c^3*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log(-d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)) - 3*(40*b^3*d^3*x^9 - 5*(11*b^3*c*d^2 - 2*a*b^2*d^3)*x^6 - 220*b^3*c^3 + 88*a*b^2*c^2*d + 33*a^2*b*c*d^2 + 18*a^3*d^3 + 2*(44*b^3*c^2*d - 11*a*b^2*c*d^2 - 6*a^2*b*d^3)*x^3)*(b*x^3 + a)^(2/3))/(b^3*d^4)","B",0
678,1,398,0,0.606661," ","integrate(x^8*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{40 \, \sqrt{3} b^{2} c^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) - 20 \, b^{2} c^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)} - {\left(b c - a d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) + 40 \, b^{2} c^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(-d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right) + 3 \, {\left(5 \, b^{2} d^{2} x^{6} + 20 \, b^{2} c^{2} - 8 \, a b c d - 3 \, a^{2} d^{2} - 2 \, {\left(4 \, b^{2} c d - a b d^{2}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{120 \, b^{2} d^{3}}"," ",0,"1/120*(40*sqrt(3)*b^2*c^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) - 20*b^2*c^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log((b*x^3 + a)^(1/3)*d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(2/3)*(b*c - a*d) - (b*c - a*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)) + 40*b^2*c^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log(-d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)) + 3*(5*b^2*d^2*x^6 + 20*b^2*c^2 - 8*a*b*c*d - 3*a^2*d^2 - 2*(4*b^2*c*d - a*b*d^2)*x^3)*(b*x^3 + a)^(2/3))/(b^2*d^3)","B",0
679,1,353,0,0.413827," ","integrate(x^5*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{10 \, \sqrt{3} b c \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 5 \, b c \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)} + {\left(b c - a d\right)} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) - 10 \, b c \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(-d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right) - 3 \, {\left(2 \, b d x^{3} - 5 \, b c + 2 \, a d\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, b d^{2}}"," ",0,"-1/30*(10*sqrt(3)*b*c*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3) + sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 5*b*c*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log((b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(2/3)*(b*c - a*d) + (b*c - a*d)*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)) - 10*b*c*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log(-d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)) - 3*(2*b*d*x^3 - 5*b*c + 2*a*d)*(b*x^3 + a)^(2/3))/(b*d^2)","B",0
680,1,323,0,0.435974," ","integrate(x^2*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) - \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)} - {\left(b c - a d\right)} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(-d \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right) + 3 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, d}"," ",0,"1/6*(2*sqrt(3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) - ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log((b*x^3 + a)^(1/3)*d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(2/3)*(b*c - a*d) - (b*c - a*d)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)) + 2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log(-d*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)) + 3*(b*x^3 + a)^(2/3))/d","B",0
681,1,425,0,0.460646," ","integrate((b*x^3+a)^(2/3)/x/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) - 2 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{1}{3}}}{3 \, a}\right) + \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)} + {\left(b c - a d\right)} \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}}\right) + {\left(a^{2}\right)}^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 2 \, \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{1}{3}} \log\left(-d \left(-\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{d^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right) - 2 \, {\left(a^{2}\right)}^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right)}{6 \, c}"," ",0,"-1/6*(2*sqrt(3)*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3) + sqrt(3)*(b*c - a*d))/(b*c - a*d)) - 2*sqrt(3)*(a^2)^(1/3)*arctan(1/3*(sqrt(3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(1/3))/a) + (-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log((b*x^3 + a)^(1/3)*d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(2/3)*(b*c - a*d) + (b*c - a*d)*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)) + (a^2)^(1/3)*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 2*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(1/3)*log(-d*(-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)/d^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)) - 2*(a^2)^(1/3)*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)))/c","B",0
682,1,1030,0,0.547323," ","integrate((b*x^3+a)^(2/3)/x^4/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(2 \, a b c - 3 \, a^{2} d\right)} x^{3} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a + \left(-a\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - 6 \, \sqrt{3} {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \arctan\left(\frac{\sqrt{3} {\left(b c - a d\right)} - 2 \, \sqrt{3} {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)}}\right) + {\left(2 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) - 2 \, {\left(2 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a c}{18 \, a c^{2} x^{3}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(2 \, a b c - 3 \, a^{2} d\right)} x^{3} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \arctan\left(\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-a\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}}\right) + 6 \, \sqrt{3} {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \arctan\left(\frac{\sqrt{3} {\left(b c - a d\right)} - 2 \, \sqrt{3} {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)}}\right) - {\left(2 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) + 2 \, {\left(2 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} a x^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a c}{18 \, a c^{2} x^{3}}\right]"," ",0,"[-1/18*(3*sqrt(1/3)*(2*a*b*c - 3*a^2*d)*x^3*sqrt((-a)^(1/3)/a)*log((2*b*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(-a)^(2/3) - (b*x^3 + a)^(1/3)*a + (-a)^(1/3)*a)*sqrt((-a)^(1/3)/a) - 3*(b*x^3 + a)^(1/3)*(-a)^(2/3) + 3*a)/x^3) - 6*sqrt(3)*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*arctan(1/3*(sqrt(3)*(b*c - a*d) - 2*sqrt(3)*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3))/(b*c - a*d)) + (2*b*c - 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) - 2*(2*b*c - 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)) + 6*(b*x^3 + a)^(2/3)*a*c)/(a*c^2*x^3), 1/18*(6*sqrt(1/3)*(2*a*b*c - 3*a^2*d)*x^3*sqrt(-(-a)^(1/3)/a)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) - (-a)^(1/3))*sqrt(-(-a)^(1/3)/a)) + 6*sqrt(3)*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*arctan(1/3*(sqrt(3)*(b*c - a*d) - 2*sqrt(3)*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3))/(b*c - a*d)) - (2*b*c - 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) + 2*(2*b*c - 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*a*x^3*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)) - 6*(b*x^3 + a)^(2/3)*a*c)/(a*c^2*x^3)]","A",0
683,1,1151,0,1.615983," ","integrate((b*x^3+a)^(2/3)/x^7/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{18 \, \sqrt{3} {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} + 2 \, \sqrt{3} {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)}}\right) + 9 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 18 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{2} + 6 \, a^{2} b c d - 9 \, a^{3} d^{2}\right)} x^{6} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - {\left(b^{2} c^{2} + 6 \, a b c d - 9 \, a^{2} d^{2}\right)} a^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, {\left(b^{2} c^{2} + 6 \, a b c d - 9 \, a^{2} d^{2}\right)} a^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + 3 \, {\left(3 \, a^{2} c^{2} + 2 \, {\left(a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, a^{2} c^{3} x^{6}}, -\frac{18 \, \sqrt{3} {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} + 2 \, \sqrt{3} {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)}}\right) + 9 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 18 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} a^{2} d x^{6} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - {\left(b^{2} c^{2} + 6 \, a b c d - 9 \, a^{2} d^{2}\right)} a^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, {\left(b^{2} c^{2} + 6 \, a b c d - 9 \, a^{2} d^{2}\right)} a^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{2} + 6 \, a^{2} b c d - 9 \, a^{3} d^{2}\right)} x^{6} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}} + 3 \, {\left(3 \, a^{2} c^{2} + 2 \, {\left(a b c^{2} - 3 \, a^{2} c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, a^{2} c^{3} x^{6}}\right]"," ",0,"[-1/54*(18*sqrt(3)*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*arctan(-1/3*(sqrt(3)*(b*c - a*d) + 2*sqrt(3)*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3))/(b*c - a*d)) + 9*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 18*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) + 3*sqrt(1/3)*(a*b^2*c^2 + 6*a^2*b*c*d - 9*a^3*d^2)*x^6*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) - (b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*a^(2/3)*x^6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*(b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*a^(2/3)*x^6*log((b*x^3 + a)^(1/3) - a^(1/3)) + 3*(3*a^2*c^2 + 2*(a*b*c^2 - 3*a^2*c*d)*x^3)*(b*x^3 + a)^(2/3))/(a^2*c^3*x^6), -1/54*(18*sqrt(3)*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*arctan(-1/3*(sqrt(3)*(b*c - a*d) + 2*sqrt(3)*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3))/(b*c - a*d)) + 9*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 18*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*a^2*d*x^6*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) - (b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*a^(2/3)*x^6*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*(b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*a^(2/3)*x^6*log((b*x^3 + a)^(1/3) - a^(1/3)) + 6*sqrt(1/3)*(a*b^2*c^2 + 6*a^2*b*c*d - 9*a^3*d^2)*x^6*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3) + 3*(3*a^2*c^2 + 2*(a*b*c^2 - 3*a^2*c*d)*x^3)*(b*x^3 + a)^(2/3))/(a^2*c^3*x^6)]","A",0
684,1,1164,0,1.599735," ","integrate(x^6*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{18 \, \sqrt{3} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) - 18 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \log\left(\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)}}{x}\right) + 9 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \log\left(-\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c^{2} - a c d\right)}}{x^{2}}\right) + 3 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} c^{2} - 6 \, a b^{2} c d - a^{2} b d^{2}\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) + 2 \, {\left(9 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(9 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 3 \, {\left(3 \, b^{2} d^{2} x^{4} - 2 \, {\left(3 \, b^{2} c d - a b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2} d^{3}}, -\frac{18 \, \sqrt{3} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) - 18 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \log\left(\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)}}{x}\right) + 9 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} b^{2} c \log\left(-\frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x^{2} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c^{2} - a c d\right)}}{x^{2}}\right) + 2 \, {\left(9 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(9 \, b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} c^{2} - 6 \, a b^{2} c d - a^{2} b d^{2}\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} - 3 \, {\left(3 \, b^{2} d^{2} x^{4} - 2 \, {\left(3 \, b^{2} c d - a b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{54 \, b^{2} d^{3}}\right]"," ",0,"[-1/54*(18*sqrt(3)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*(b*x^3 + a)^(1/3))/((b*c - a*d)*x)) - 18*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*log(((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(2/3)*x - (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d))/x) + 9*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*log(-((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*(b*c - a*d)*x^2 + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(2/3)*(b*x^3 + a)^(1/3)*x + (b*x^3 + a)^(2/3)*(b*c^2 - a*c*d))/x^2) + 3*sqrt(1/3)*(9*b^3*c^2 - 6*a*b^2*c*d - a^2*b*d^2)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) + 2*(9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 3*(3*b^2*d^2*x^4 - 2*(3*b^2*c*d - a*b*d^2)*x)*(b*x^3 + a)^(2/3))/(b^2*d^3), -1/54*(18*sqrt(3)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*(b*x^3 + a)^(1/3))/((b*c - a*d)*x)) - 18*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*log(((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(2/3)*x - (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d))/x) + 9*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*b^2*c*log(-((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(1/3)*(b*c - a*d)*x^2 + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)^(2/3)*(b*x^3 + a)^(1/3)*x + (b*x^3 + a)^(2/3)*(b*c^2 - a*c*d))/x^2) + 2*(9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*sqrt(1/3)*(9*b^3*c^2 - 6*a*b^2*c*d - a^2*b*d^2)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) - 3*(3*b^2*d^2*x^4 - 2*(3*b^2*c*d - a*b*d^2)*x)*(b*x^3 + a)^(2/3))/(b^2*d^3)]","B",0
685,1,1091,0,0.567645," ","integrate(x^3*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x - 3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c - 2 \, a b d\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 6 \, \sqrt{3} {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left(b c - a d\right)} x - 2 \, \sqrt{3} {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, {\left(3 \, b c - 2 \, a d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(3 \, b c - 2 \, a d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 6 \, {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \log\left(\frac{{\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)}}{x}\right) - 3 \, {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \log\left(\frac{{\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x^{2} - {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c^{2} - a c d\right)}}{x^{2}}\right)}{18 \, b d^{2}}, \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x + 6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c - 2 \, a b d\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 6 \, \sqrt{3} {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \arctan\left(\frac{\sqrt{3} {\left(b c - a d\right)} x - 2 \, \sqrt{3} {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, {\left(3 \, b c - 2 \, a d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(3 \, b c - 2 \, a d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 6 \, {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \log\left(\frac{{\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)}}{x}\right) - 3 \, {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} b \log\left(\frac{{\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x^{2} - {\left(-b^{2} c^{3} + 2 \, a b c^{2} d - a^{2} c d^{2}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c^{2} - a c d\right)}}{x^{2}}\right)}{18 \, b d^{2}}\right]"," ",0,"[1/18*(6*(b*x^3 + a)^(2/3)*b*d*x - 3*sqrt(1/3)*(3*b^2*c - 2*a*b*d)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 6*sqrt(3)*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*arctan(1/3*(sqrt(3)*(b*c - a*d)*x - 2*sqrt(3)*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*(b*x^3 + a)^(1/3))/((b*c - a*d)*x)) + 2*(3*b*c - 2*a*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (3*b*c - 2*a*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*log(((-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(2/3)*x - (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d))/x) - 3*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*log(((-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*(b*c - a*d)*x^2 - (-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(2/3)*(b*x^3 + a)^(1/3)*x - (b*x^3 + a)^(2/3)*(b*c^2 - a*c*d))/x^2))/(b*d^2), 1/18*(6*(b*x^3 + a)^(2/3)*b*d*x + 6*sqrt(1/3)*(3*b^2*c - 2*a*b*d)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 6*sqrt(3)*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*arctan(1/3*(sqrt(3)*(b*c - a*d)*x - 2*sqrt(3)*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*(b*x^3 + a)^(1/3))/((b*c - a*d)*x)) + 2*(3*b*c - 2*a*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (3*b*c - 2*a*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*log(((-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(2/3)*x - (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d))/x) - 3*(-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*b*log(((-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(1/3)*(b*c - a*d)*x^2 - (-b^2*c^3 + 2*a*b*c^2*d - a^2*c*d^2)^(2/3)*(b*x^3 + a)^(1/3)*x - (b*x^3 + a)^(2/3)*(b*c^2 - a*c*d))/x^2))/(b*d^2)]","B",0
686,1,469,0,0.449723," ","integrate((b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{1}{3}}}{3 \, b x}\right) - 2 \, \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(\frac{c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{x}\right) - 2 \, \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{1}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) + \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x \left(\frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{2}}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c - a d\right)}}{x^{2}}\right)}{6 \, d}"," ",0,"-1/6*(2*sqrt(3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(-b^2)^(1/3)*arctan(-1/3*(sqrt(3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(1/3))/(b*x)) - 2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log((c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) - (b*x^3 + a)^(1/3)*(b*c - a*d))/x) - 2*(-b^2)^(1/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(1/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) + ((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3)*log(-((b*c - a*d)*x^2*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(1/3) + (b*x^3 + a)^(1/3)*c*x*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)/c^2)^(2/3) + (b*x^3 + a)^(2/3)*(b*c - a*d))/x^2))/d","B",0
687,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^3/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
688,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^6/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^9/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^12/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate(x^7*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate(x^4*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate(x*(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^2/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate((b*x^3+a)^(2/3)/x^5/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,1,369,0,0.562731," ","integrate(x^8*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{140 \, \sqrt{3} {\left(b^{3} c^{3} - a b^{2} c^{2} d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 70 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 140 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) + 3 \, {\left(14 \, b^{3} d^{3} x^{9} - 2 \, {\left(10 \, b^{3} c d^{2} - 11 \, a b^{2} d^{3}\right)} x^{6} - 140 \, b^{3} c^{3} + 175 \, a b^{2} c^{2} d - 20 \, a^{2} b c d^{2} - 6 \, a^{3} d^{3} + {\left(35 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{420 \, b^{2} d^{4}}"," ",0,"1/420*(140*sqrt(3)*(b^3*c^3 - a*b^2*c^2*d)*(-(b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 70*(b^3*c^3 - a*b^2*c^2*d)*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(-(b*c - a*d)/d)^(1/3) + (-(b*c - a*d)/d)^(2/3)) - 140*(b^3*c^3 - a*b^2*c^2*d)*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) - (-(b*c - a*d)/d)^(1/3)) + 3*(14*b^3*d^3*x^9 - 2*(10*b^3*c*d^2 - 11*a*b^2*d^3)*x^6 - 140*b^3*c^3 + 175*a*b^2*c^2*d - 20*a^2*b*c*d^2 - 6*a^3*d^3 + (35*b^3*c^2*d - 40*a*b^2*c*d^2 + 2*a^2*b*d^3)*x^3)*(b*x^3 + a)^(1/3))/(b^2*d^4)","A",0
697,1,298,0,0.429565," ","integrate(x^5*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{28 \, \sqrt{3} {\left(b^{2} c^{2} - a b c d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 14 \, {\left(b^{2} c^{2} - a b c d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 28 \, {\left(b^{2} c^{2} - a b c d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) + 3 \, {\left(4 \, b^{2} d^{2} x^{6} + 28 \, b^{2} c^{2} - 35 \, a b c d + 4 \, a^{2} d^{2} - {\left(7 \, b^{2} c d - 8 \, a b d^{2}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{84 \, b d^{3}}"," ",0,"1/84*(28*sqrt(3)*(b^2*c^2 - a*b*c*d)*((b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 14*(b^2*c^2 - a*b*c*d)*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*((b*c - a*d)/d)^(1/3) + ((b*c - a*d)/d)^(2/3)) - 28*(b^2*c^2 - a*b*c*d)*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) + ((b*c - a*d)/d)^(1/3)) + 3*(4*b^2*d^2*x^6 + 28*b^2*c^2 - 35*a*b*c*d + 4*a^2*d^2 - (7*b^2*c*d - 8*a*b*d^2)*x^3)*(b*x^3 + a)^(1/3))/(b*d^3)","A",0
698,1,246,0,0.439791," ","integrate(x^2*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(b c - a d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 2 \, {\left(b c - a d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 4 \, {\left(b c - a d\right)} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) + 3 \, {\left(b d x^{3} - 4 \, b c + 5 \, a d\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{12 \, d^{2}}"," ",0,"1/12*(4*sqrt(3)*(b*c - a*d)*(-(b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 2*(b*c - a*d)*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(-(b*c - a*d)/d)^(1/3) + (-(b*c - a*d)/d)^(2/3)) - 4*(b*c - a*d)*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) - (-(b*c - a*d)/d)^(1/3)) + 3*(b*d*x^3 - 4*b*c + 5*a*d)*(b*x^3 + a)^(1/3))/d^2","A",0
699,1,320,0,0.450011," ","integrate((b*x^3+a)^(4/3)/x/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} a^{\frac{4}{3}} d \arctan\left(\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + a^{\frac{4}{3}} d \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 2 \, a^{\frac{4}{3}} d \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) - 2 \, \sqrt{3} {\left(b c - a d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b c - {\left(b c - a d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) + 2 \, {\left(b c - a d\right)} \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right)}{6 \, c d}"," ",0,"-1/6*(2*sqrt(3)*a^(4/3)*d*arctan(1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*a^(2/3) + sqrt(3)*a)/a) + a^(4/3)*d*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 2*a^(4/3)*d*log((b*x^3 + a)^(1/3) - a^(1/3)) - 2*sqrt(3)*(b*c - a*d)*((b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*((b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) - 6*(b*x^3 + a)^(1/3)*b*c - (b*c - a*d)*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*((b*c - a*d)/d)^(1/3) + ((b*c - a*d)/d)^(2/3)) + 2*(b*c - a*d)*((b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) + ((b*c - a*d)/d)^(1/3)))/(c*d)","A",0
700,1,383,0,0.701333," ","integrate((b*x^3+a)^(4/3)/x^4/(d*x^3+c),x, algorithm=""fricas"")","\frac{6 \, \sqrt{3} {\left(b c - a d\right)} x^{3} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}} - \sqrt{3} {\left(b c - a d\right)}}{3 \, {\left(b c - a d\right)}}\right) + 2 \, \sqrt{3} {\left(4 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{1}{3}} x^{3} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + \sqrt{3} a}{3 \, a}\right) + {\left(4 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{1}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) + 3 \, {\left(b c - a d\right)} x^{3} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} + \left(-\frac{b c - a d}{d}\right)^{\frac{2}{3}}\right) - 2 \, {\left(4 \, b c - 3 \, a d\right)} \left(-a\right)^{\frac{1}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 6 \, {\left(b c - a d\right)} x^{3} \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-\frac{b c - a d}{d}\right)^{\frac{1}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a c}{18 \, c^{2} x^{3}}"," ",0,"1/18*(6*sqrt(3)*(b*c - a*d)*x^3*(-(b*c - a*d)/d)^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*d*(-(b*c - a*d)/d)^(2/3) - sqrt(3)*(b*c - a*d))/(b*c - a*d)) + 2*sqrt(3)*(4*b*c - 3*a*d)*(-a)^(1/3)*x^3*arctan(1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*(-a)^(2/3) + sqrt(3)*a)/a) + (4*b*c - 3*a*d)*(-a)^(1/3)*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) + 3*(b*c - a*d)*x^3*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(-(b*c - a*d)/d)^(1/3) + (-(b*c - a*d)/d)^(2/3)) - 2*(4*b*c - 3*a*d)*(-a)^(1/3)*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 6*(b*c - a*d)*x^3*(-(b*c - a*d)/d)^(1/3)*log((b*x^3 + a)^(1/3) - (-(b*c - a*d)/d)^(1/3)) - 6*(b*x^3 + a)^(1/3)*a*c)/(c^2*x^3)","A",0
701,1,503,0,2.020354," ","integrate((b*x^3+a)^(4/3)/x^7/(d*x^3+c),x, algorithm=""fricas"")","\frac{18 \, \sqrt{3} {\left(a^{2} b c - a^{3} d\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} x^{6} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \sqrt{3} {\left(b c d - a d^{2}\right)}}{3 \, {\left(b c d - a d^{2}\right)}}\right) - 2 \, \sqrt{3} {\left(2 \, a b^{2} c^{2} - 12 \, a^{2} b c d + 9 \, a^{3} d^{2}\right)} {\left(a^{2}\right)}^{\frac{1}{6}} x^{6} \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) - {\left(2 \, b^{2} c^{2} - 12 \, a b c d + 9 \, a^{2} d^{2}\right)} {\left(a^{2}\right)}^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 2 \, {\left(2 \, b^{2} c^{2} - 12 \, a b c d + 9 \, a^{2} d^{2}\right)} {\left(a^{2}\right)}^{\frac{2}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right) + 9 \, {\left(a^{2} b c - a^{3} d\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 18 \, {\left(a^{2} b c - a^{3} d\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} x^{6} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(3 \, a^{3} c^{2} + {\left(7 \, a^{2} b c^{2} - 6 \, a^{3} c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, a^{2} c^{3} x^{6}}"," ",0,"1/54*(18*sqrt(3)*(a^2*b*c - a^3*d)*(b*c*d^2 - a*d^3)^(1/3)*x^6*arctan(-1/3*(2*sqrt(3)*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3) - sqrt(3)*(b*c*d - a*d^2))/(b*c*d - a*d^2)) - 2*sqrt(3)*(2*a*b^2*c^2 - 12*a^2*b*c*d + 9*a^3*d^2)*(a^2)^(1/6)*x^6*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) - (2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*(a^2)^(2/3)*x^6*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) + 2*(2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*(a^2)^(2/3)*x^6*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)) + 9*(a^2*b*c - a^3*d)*(b*c*d^2 - a*d^3)^(1/3)*x^6*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 18*(a^2*b*c - a^3*d)*(b*c*d^2 - a*d^3)^(1/3)*x^6*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 3*(3*a^3*c^2 + (7*a^2*b*c^2 - 6*a^3*c*d)*x^3)*(b*x^3 + a)^(1/3))/(a^2*c^3*x^6)","A",0
702,1,550,0,2.051517," ","integrate(x^4*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} {\left(9 \, b^{3} c^{2} - 12 \, a b^{2} c d + 2 \, a^{2} b d^{2}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) - 18 \, \sqrt{3} {\left(b^{3} c - a b^{2} d\right)} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c^{2} - a c d\right)} x + 2 \, \sqrt{3} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{3 \, {\left(b c^{2} - a c d\right)} x}\right) - 2 \, {\left(9 \, b^{2} c^{2} - 12 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + {\left(9 \, b^{2} c^{2} - 12 \, a b c d + 2 \, a^{2} d^{2}\right)} \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right) - 18 \, {\left(b^{3} c - a b^{2} d\right)} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{1}{3}} c + {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} x}{x}\right) + 9 \, {\left(b^{3} c - a b^{2} d\right)} {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} \log\left(\frac{{\left(b x^{3} + a\right)}^{\frac{2}{3}} c^{2} - {\left(-b c^{3} + a c^{2} d\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c x + {\left(-b c^{3} + a c^{2} d\right)}^{\frac{2}{3}} x^{2}}{x^{2}}\right) + 3 \, {\left(3 \, b^{3} d^{2} x^{5} - {\left(6 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{2}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{54 \, b^{2} d^{3}}"," ",0,"1/54*(2*sqrt(3)*(9*b^3*c^2 - 12*a*b^2*c*d + 2*a^2*b*d^2)*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) - 18*sqrt(3)*(b^3*c - a*b^2*d)*(-b*c^3 + a*c^2*d)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c^2 - a*c*d)*x + 2*sqrt(3)*(-b*c^3 + a*c^2*d)^(2/3)*(b*x^3 + a)^(1/3))/((b*c^2 - a*c*d)*x)) - 2*(9*b^2*c^2 - 12*a*b*c*d + 2*a^2*d^2)*(-b^2)^(2/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (9*b^2*c^2 - 12*a*b*c*d + 2*a^2*d^2)*(-b^2)^(2/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2) - 18*(b^3*c - a*b^2*d)*(-b*c^3 + a*c^2*d)^(1/3)*log(((b*x^3 + a)^(1/3)*c + (-b*c^3 + a*c^2*d)^(1/3)*x)/x) + 9*(b^3*c - a*b^2*d)*(-b*c^3 + a*c^2*d)^(1/3)*log(((b*x^3 + a)^(2/3)*c^2 - (-b*c^3 + a*c^2*d)^(1/3)*(b*x^3 + a)^(1/3)*c*x + (-b*c^3 + a*c^2*d)^(2/3)*x^2)/x^2) + 3*(3*b^3*d^2*x^5 - (6*b^3*c*d - 7*a*b^2*d^2)*x^2)*(b*x^3 + a)^(1/3))/(b^2*d^3)","A",0
703,1,396,0,0.708446," ","integrate(x*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b d x^{2} - 6 \, \sqrt{3} {\left(b c - a d\right)} \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} {\left(b c - a d\right)} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} c \left(\frac{b c - a d}{c}\right)^{\frac{2}{3}}}{3 \, {\left(b c - a d\right)} x}\right) + 2 \, \sqrt{3} {\left(3 \, b c - 4 \, a d\right)} \left(-b\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}}}{3 \, b x}\right) - 2 \, {\left(3 \, b c - 4 \, a d\right)} \left(-b\right)^{\frac{1}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - 6 \, {\left(b c - a d\right)} \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \log\left(-\frac{x \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, b c - 4 \, a d\right)} \left(-b\right)^{\frac{1}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 3 \, {\left(b c - a d\right)} \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} \log\left(\frac{x^{2} \left(\frac{b c - a d}{c}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} x \left(\frac{b c - a d}{c}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, d^{2}}"," ",0,"1/18*(6*(b*x^3 + a)^(1/3)*b*d*x^2 - 6*sqrt(3)*(b*c - a*d)*((b*c - a*d)/c)^(1/3)*arctan(-1/3*(sqrt(3)*(b*c - a*d)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*c*((b*c - a*d)/c)^(2/3))/((b*c - a*d)*x)) + 2*sqrt(3)*(3*b*c - 4*a*d)*(-b)^(1/3)*arctan(1/3*(sqrt(3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b)^(2/3))/(b*x)) - 2*(3*b*c - 4*a*d)*(-b)^(1/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - 6*(b*c - a*d)*((b*c - a*d)/c)^(1/3)*log(-(x*((b*c - a*d)/c)^(1/3) - (b*x^3 + a)^(1/3))/x) + (3*b*c - 4*a*d)*(-b)^(1/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 3*(b*c - a*d)*((b*c - a*d)/c)^(1/3)*log((x^2*((b*c - a*d)/c)^(2/3) + (b*x^3 + a)^(1/3)*x*((b*c - a*d)/c)^(1/3) + (b*x^3 + a)^(2/3))/x^2))/d^2","A",0
704,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^2/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^5/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^8/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^11/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^14/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
709,-1,0,0,0.000000," ","integrate(x^6*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,-1,0,0,0.000000," ","integrate(x^3*(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^3/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate((b*x^3+a)^(4/3)/x^6/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,1,1004,0,0.759991," ","integrate(x^14/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{220 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{4} c^{4} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 440 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{4} c^{4} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) + 660 \, \sqrt{\frac{1}{3}} {\left(b^{5} c^{5} d - a b^{4} c^{4} d^{2}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - 3 \, {\left(220 \, b^{4} c^{4} d^{2} - 88 \, a b^{3} c^{3} d^{3} - 33 \, a^{2} b^{2} c^{2} d^{4} - 18 \, a^{3} b c d^{5} - 81 \, a^{4} d^{6} - 40 \, {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)} x^{9} + 5 \, {\left(11 \, b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} - 9 \, a^{2} b^{2} d^{6}\right)} x^{6} - 2 \, {\left(44 \, b^{4} c^{3} d^{3} - 11 \, a b^{3} c^{2} d^{4} - 6 \, a^{2} b^{2} c d^{5} - 27 \, a^{3} b d^{6}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1320 \, {\left(b^{5} c d^{6} - a b^{4} d^{7}\right)}}, \frac{220 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{4} c^{4} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 440 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{4} c^{4} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) + 1320 \, \sqrt{\frac{1}{3}} {\left(b^{5} c^{5} d - a b^{4} c^{4} d^{2}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) - 3 \, {\left(220 \, b^{4} c^{4} d^{2} - 88 \, a b^{3} c^{3} d^{3} - 33 \, a^{2} b^{2} c^{2} d^{4} - 18 \, a^{3} b c d^{5} - 81 \, a^{4} d^{6} - 40 \, {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)} x^{9} + 5 \, {\left(11 \, b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} - 9 \, a^{2} b^{2} d^{6}\right)} x^{6} - 2 \, {\left(44 \, b^{4} c^{3} d^{3} - 11 \, a b^{3} c^{2} d^{4} - 6 \, a^{2} b^{2} c d^{5} - 27 \, a^{3} b d^{6}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{1320 \, {\left(b^{5} c d^{6} - a b^{4} d^{7}\right)}}\right]"," ",0,"[1/1320*(220*(-b*c*d^2 + a*d^3)^(2/3)*b^4*c^4*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 440*(-b*c*d^2 + a*d^3)^(2/3)*b^4*c^4*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) + 660*sqrt(1/3)*(b^5*c^5*d - a*b^4*c^4*d^2)*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 + 3*sqrt(1/3)*(2*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) + (-b*c*d^2 + a*d^3)^(1/3)*(b*c - a*d))*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d)) - 3*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - 3*(220*b^4*c^4*d^2 - 88*a*b^3*c^3*d^3 - 33*a^2*b^2*c^2*d^4 - 18*a^3*b*c*d^5 - 81*a^4*d^6 - 40*(b^4*c*d^5 - a*b^3*d^6)*x^9 + 5*(11*b^4*c^2*d^4 - 2*a*b^3*c*d^5 - 9*a^2*b^2*d^6)*x^6 - 2*(44*b^4*c^3*d^3 - 11*a*b^3*c^2*d^4 - 6*a^2*b^2*c*d^5 - 27*a^3*b*d^6)*x^3)*(b*x^3 + a)^(2/3))/(b^5*c*d^6 - a*b^4*d^7), 1/1320*(220*(-b*c*d^2 + a*d^3)^(2/3)*b^4*c^4*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 440*(-b*c*d^2 + a*d^3)^(2/3)*b^4*c^4*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) + 1320*sqrt(1/3)*(b^5*c^5*d - a*b^4*c^4*d^2)*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(1/3))*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))/d) - 3*(220*b^4*c^4*d^2 - 88*a*b^3*c^3*d^3 - 33*a^2*b^2*c^2*d^4 - 18*a^3*b*c*d^5 - 81*a^4*d^6 - 40*(b^4*c*d^5 - a*b^3*d^6)*x^9 + 5*(11*b^4*c^2*d^4 - 2*a*b^3*c*d^5 - 9*a^2*b^2*d^6)*x^6 - 2*(44*b^4*c^3*d^3 - 11*a*b^3*c^2*d^4 - 6*a^2*b^2*c*d^5 - 27*a^3*b*d^6)*x^3)*(b*x^3 + a)^(2/3))/(b^5*c*d^6 - a*b^4*d^7)]","A",0
715,1,873,0,0.735890," ","integrate(x^11/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{20 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 40 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 60 \, \sqrt{\frac{1}{3}} {\left(b^{4} c^{4} d - a b^{3} c^{3} d^{2}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - 3 \, {\left(20 \, b^{3} c^{3} d^{2} - 8 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4} - 9 \, a^{3} d^{5} + 5 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x^{6} - 2 \, {\left(4 \, b^{3} c^{2} d^{3} - a b^{2} c d^{4} - 3 \, a^{2} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{120 \, {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)}}, -\frac{20 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 40 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) + 120 \, \sqrt{\frac{1}{3}} {\left(b^{4} c^{4} d - a b^{3} c^{3} d^{2}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) - 3 \, {\left(20 \, b^{3} c^{3} d^{2} - 8 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4} - 9 \, a^{3} d^{5} + 5 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x^{6} - 2 \, {\left(4 \, b^{3} c^{2} d^{3} - a b^{2} c d^{4} - 3 \, a^{2} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{120 \, {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)}}\right]"," ",0,"[-1/120*(20*(b*c*d^2 - a*d^3)^(2/3)*b^3*c^3*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 40*(b*c*d^2 - a*d^3)^(2/3)*b^3*c^3*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 60*sqrt(1/3)*(b^4*c^4*d - a*b^3*c^3*d^2)*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 - 3*sqrt(1/3)*(2*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b*c*d^2 - a*d^3)^(1/3)*(b*c - a*d))*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d)) - 3*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - 3*(20*b^3*c^3*d^2 - 8*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4 - 9*a^3*d^5 + 5*(b^3*c*d^4 - a*b^2*d^5)*x^6 - 2*(4*b^3*c^2*d^3 - a*b^2*c*d^4 - 3*a^2*b*d^5)*x^3)*(b*x^3 + a)^(2/3))/(b^4*c*d^5 - a*b^3*d^6), -1/120*(20*(b*c*d^2 - a*d^3)^(2/3)*b^3*c^3*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 40*(b*c*d^2 - a*d^3)^(2/3)*b^3*c^3*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) + 120*sqrt(1/3)*(b^4*c^4*d - a*b^3*c^3*d^2)*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d - (b*c*d^2 - a*d^3)^(1/3))*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))/d) - 3*(20*b^3*c^3*d^2 - 8*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4 - 9*a^3*d^5 + 5*(b^3*c*d^4 - a*b^2*d^5)*x^6 - 2*(4*b^3*c^2*d^3 - a*b^2*c*d^4 - 3*a^2*b*d^5)*x^3)*(b*x^3 + a)^(2/3))/(b^4*c*d^5 - a*b^3*d^6)]","A",0
716,1,768,0,0.786197," ","integrate(x^8/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 10 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) + 15 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{3} d - a b^{2} c^{2} d^{2}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - 3 \, {\left(5 \, b^{2} c^{2} d^{2} - 2 \, a b c d^{3} - 3 \, a^{2} d^{4} - 2 \, {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)}}, \frac{5 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 10 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) + 30 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{3} d - a b^{2} c^{2} d^{2}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) - 3 \, {\left(5 \, b^{2} c^{2} d^{2} - 2 \, a b c d^{3} - 3 \, a^{2} d^{4} - 2 \, {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)}}\right]"," ",0,"[1/30*(5*(-b*c*d^2 + a*d^3)^(2/3)*b^2*c^2*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 10*(-b*c*d^2 + a*d^3)^(2/3)*b^2*c^2*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) + 15*sqrt(1/3)*(b^3*c^3*d - a*b^2*c^2*d^2)*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 + 3*sqrt(1/3)*(2*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) + (-b*c*d^2 + a*d^3)^(1/3)*(b*c - a*d))*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d)) - 3*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - 3*(5*b^2*c^2*d^2 - 2*a*b*c*d^3 - 3*a^2*d^4 - 2*(b^2*c*d^3 - a*b*d^4)*x^3)*(b*x^3 + a)^(2/3))/(b^3*c*d^4 - a*b^2*d^5), 1/30*(5*(-b*c*d^2 + a*d^3)^(2/3)*b^2*c^2*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 10*(-b*c*d^2 + a*d^3)^(2/3)*b^2*c^2*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) + 30*sqrt(1/3)*(b^3*c^3*d - a*b^2*c^2*d^2)*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(1/3))*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))/d) - 3*(5*b^2*c^2*d^2 - 2*a*b*c*d^3 - 3*a^2*d^4 - 2*(b^2*c*d^3 - a*b*d^4)*x^3)*(b*x^3 + a)^(2/3))/(b^3*c*d^4 - a*b^2*d^5)]","B",0
717,1,667,0,0.731769," ","integrate(x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b c \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b c \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{2} d - a b c d^{2}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} c d^{3} - a b d^{4}\right)}}, -\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b c \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} b c \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) + 6 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{2} d - a b c d^{2}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} c d^{3} - a b d^{4}\right)}}\right]"," ",0,"[-1/6*((b*c*d^2 - a*d^3)^(2/3)*b*c*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 2*(b*c*d^2 - a*d^3)^(2/3)*b*c*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 3*sqrt(1/3)*(b^2*c^2*d - a*b*c*d^2)*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 - 3*sqrt(1/3)*(2*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b*c*d^2 - a*d^3)^(1/3)*(b*c - a*d))*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d)) - 3*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - 3*(b*c*d^2 - a*d^3)*(b*x^3 + a)^(2/3))/(b^2*c*d^3 - a*b*d^4), -1/6*((b*c*d^2 - a*d^3)^(2/3)*b*c*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 2*(b*c*d^2 - a*d^3)^(2/3)*b*c*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) + 6*sqrt(1/3)*(b^2*c^2*d - a*b*c*d^2)*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d - (b*c*d^2 - a*d^3)^(1/3))*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))/d) - 3*(b*c*d^2 - a*d^3)*(b*x^3 + a)^(2/3))/(b^2*c*d^3 - a*b*d^4)]","B",0
718,1,592,0,0.816933," ","integrate(x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)}{6 \, {\left(b c d^{2} - a d^{3}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)}{6 \, {\left(b c d^{2} - a d^{3}\right)}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(b*c*d - a*d^2)*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 + 3*sqrt(1/3)*(2*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) + (-b*c*d^2 + a*d^3)^(1/3)*(b*c - a*d))*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d)) - 3*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) + (-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 2*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)))/(b*c*d^2 - a*d^3), 1/6*(6*sqrt(1/3)*(b*c*d - a*d^2)*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(1/3))*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))/d) + (-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 2*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)))/(b*c*d^2 - a*d^3)]","B",0
719,1,628,0,0.446685," ","integrate(1/x/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} a \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - 2 \, \sqrt{3} a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d + {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) + 2 \, a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) - a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a c}, -\frac{2 \, \sqrt{3} a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d + {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) - 2 \, a \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) - 6 \, \sqrt{\frac{1}{3}} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right) + a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) - 2 \, a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{6 \, a c}\right]"," ",0,"[1/6*(3*sqrt(1/3)*a*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) - 2*sqrt(3)*a*(d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(d/(b*c - a*d))^(1/3) - 1/3*sqrt(3)) - a*(d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d + (b*c - a*d)*(d/(b*c - a*d))^(1/3)) + 2*a*(d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) - a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/(a*c), -1/6*(2*sqrt(3)*a*(d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(d/(b*c - a*d))^(1/3) - 1/3*sqrt(3)) + a*(d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d + (b*c - a*d)*(d/(b*c - a*d))^(1/3)) - 2*a*(d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) - 6*sqrt(1/3)*a^(2/3)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3)) + a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) - 2*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)))/(a*c)]","A",0
720,1,837,0,0.624185," ","integrate(1/x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{3} a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 3 \, a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d - {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) + 6 \, a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) + 3 \, \sqrt{\frac{1}{3}} {\left(a b c + 3 \, a^{2} d\right)} x^{3} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a + \left(-a\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + {\left(b c + 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) - 2 \, {\left(b c + 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a c}{18 \, a^{2} c^{2} x^{3}}, \frac{6 \, \sqrt{3} a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - 3 \, a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d - {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) + 6 \, a^{2} d x^{3} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) - 6 \, \sqrt{\frac{1}{3}} {\left(a b c + 3 \, a^{2} d\right)} x^{3} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \arctan\left(\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-a\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}}\right) + {\left(b c + 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) - 2 \, {\left(b c + 3 \, a d\right)} \left(-a\right)^{\frac{2}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a c}{18 \, a^{2} c^{2} x^{3}}\right]"," ",0,"[1/18*(6*sqrt(3)*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(-d/(b*c - a*d))^(1/3) + 1/3*sqrt(3)) - 3*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d - (b*c - a*d)*(-d/(b*c - a*d))^(1/3)) + 6*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) + 3*sqrt(1/3)*(a*b*c + 3*a^2*d)*x^3*sqrt((-a)^(1/3)/a)*log((2*b*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(-a)^(2/3) - (b*x^3 + a)^(1/3)*a + (-a)^(1/3)*a)*sqrt((-a)^(1/3)/a) - 3*(b*x^3 + a)^(1/3)*(-a)^(2/3) + 3*a)/x^3) + (b*c + 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) - 2*(b*c + 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 6*(b*x^3 + a)^(2/3)*a*c)/(a^2*c^2*x^3), 1/18*(6*sqrt(3)*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(-d/(b*c - a*d))^(1/3) + 1/3*sqrt(3)) - 3*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d - (b*c - a*d)*(-d/(b*c - a*d))^(1/3)) + 6*a^2*d*x^3*(-d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) - 6*sqrt(1/3)*(a*b*c + 3*a^2*d)*x^3*sqrt(-(-a)^(1/3)/a)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) - (-a)^(1/3))*sqrt(-(-a)^(1/3)/a)) + (b*c + 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) - 2*(b*c + 3*a*d)*(-a)^(2/3)*x^3*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 6*(b*x^3 + a)^(2/3)*a*c)/(a^2*c^2*x^3)]","A",0
721,1,826,0,0.632722," ","integrate(x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{3} b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 6 \, b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + 3 \, b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x - 3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c + a b d\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 2 \, {\left(3 \, b c + a d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, b c + a d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{18 \, b^{2} d^{2}}, -\frac{6 \, \sqrt{3} b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 6 \, b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + 3 \, b^{2} c \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) - 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b d x - 2 \, {\left(3 \, b c + a d\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, b c + a d\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - \frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} c + a b d\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}}}{18 \, b^{2} d^{2}}\right]"," ",0,"[-1/18*(6*sqrt(3)*b^2*c*(-c/(b*c - a*d))^(1/3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-c/(b*c - a*d))^(1/3))/x) - 6*b^2*c*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + 3*b^2*c*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x^2*(-c/(b*c - a*d))^(1/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(2/3)*c)/x^2) - 6*(b*x^3 + a)^(2/3)*b*d*x - 3*sqrt(1/3)*(3*b^2*c + a*b*d)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 2*(3*b*c + a*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + (3*b*c + a*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b^2*d^2), -1/18*(6*sqrt(3)*b^2*c*(-c/(b*c - a*d))^(1/3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-c/(b*c - a*d))^(1/3))/x) - 6*b^2*c*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + 3*b^2*c*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x^2*(-c/(b*c - a*d))^(1/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(2/3)*c)/x^2) - 6*(b*x^3 + a)^(2/3)*b*d*x - 2*(3*b*c + a*d)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + (3*b*c + a*d)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 6*sqrt(1/3)*(3*b^2*c + a*b*d)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3))/(b^2*d^2)]","A",0
722,1,761,0,0.474281," ","integrate(x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} b \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 2 \, \sqrt{3} b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) + 2 \, b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) - b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b c - a d\right)} x^{2} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) - 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b d}, -\frac{6 \, \sqrt{\frac{1}{3}} b \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) - 2 \, \sqrt{3} b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 2 \, b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + b \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b c - a d\right)} x^{2} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) + 2 \, \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right)}{6 \, b d}\right]"," ",0,"[1/6*(3*sqrt(1/3)*b*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 2*sqrt(3)*b*(c/(b*c - a*d))^(1/3)*arctan(1/3*(sqrt(3)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(c/(b*c - a*d))^(1/3))/x) + 2*b*(c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) - b*(c/(b*c - a*d))^(1/3)*log(((b*c - a*d)*x^2*(c/(b*c - a*d))^(1/3) + (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(c/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*c)/x^2) - 2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + (-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b*d), -1/6*(6*sqrt(1/3)*b*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) - 2*sqrt(3)*b*(c/(b*c - a*d))^(1/3)*arctan(1/3*(sqrt(3)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(c/(b*c - a*d))^(1/3))/x) - 2*b*(c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + b*(c/(b*c - a*d))^(1/3)*log(((b*c - a*d)*x^2*(c/(b*c - a*d))^(1/3) + (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(c/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*c)/x^2) + 2*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) - (-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2))/(b*d)]","A",0
723,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,-1,0,0,0.000000," ","integrate(1/x^9/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
727,-1,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(1/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,1,1322,0,0.833448," ","integrate(x^11/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{14 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 28 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 42 \, \sqrt{\frac{1}{3}} {\left(b^{4} c^{4} d - a b^{3} c^{3} d^{2}\right)} \sqrt{\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \log\left(\frac{b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} - 3 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{d x^{3} + c}\right) + 3 \, {\left(28 \, b^{4} c^{4} d - 35 \, a b^{3} c^{3} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{3} - 15 \, a^{3} b c d^{4} + 18 \, a^{4} d^{5} + 4 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{6} - {\left(7 \, b^{4} c^{3} d^{2} - 8 \, a b^{3} c^{2} d^{3} - 5 \, a^{2} b^{2} c d^{4} + 6 \, a^{3} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{84 \, {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)}}, \frac{14 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 28 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b^{3} c^{3} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 84 \, \sqrt{\frac{1}{3}} {\left(b^{4} c^{4} d - a b^{3} c^{3} d^{2}\right)} \sqrt{-\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left({\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + 2 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right) + 3 \, {\left(28 \, b^{4} c^{4} d - 35 \, a b^{3} c^{3} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{3} - 15 \, a^{3} b c d^{4} + 18 \, a^{4} d^{5} + 4 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{6} - {\left(7 \, b^{4} c^{3} d^{2} - 8 \, a b^{3} c^{2} d^{3} - 5 \, a^{2} b^{2} c d^{4} + 6 \, a^{3} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{84 \, {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)}}\right]"," ",0,"[1/84*(14*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b^3*c^3*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 28*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b^3*c^3*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) - 42*sqrt(1/3)*(b^4*c^4*d - a*b^3*c^3*d^2)*sqrt((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)*log((b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2 - 2*(b^2*c*d - a*b*d^2)*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d) - 3*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3)*(b*c - a*d))/(d*x^3 + c)) + 3*(28*b^4*c^4*d - 35*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3 - 15*a^3*b*c*d^4 + 18*a^4*d^5 + 4*(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^6 - (7*b^4*c^3*d^2 - 8*a*b^3*c^2*d^3 - 5*a^2*b^2*c*d^4 + 6*a^3*b*d^5)*x^3)*(b*x^3 + a)^(1/3))/(b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6), 1/84*(14*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b^3*c^3*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 28*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b^3*c^3*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) - 84*sqrt(1/3)*(b^4*c^4*d - a*b^3*c^3*d^2)*sqrt(-(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)*arctan(sqrt(1/3)*((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + 2*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt(-(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) + 3*(28*b^4*c^4*d - 35*a*b^3*c^3*d^2 + 4*a^2*b^2*c^2*d^3 - 15*a^3*b*c*d^4 + 18*a^4*d^5 + 4*(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^6 - (7*b^4*c^3*d^2 - 8*a*b^3*c^2*d^3 - 5*a^2*b^2*c*d^4 + 6*a^3*b*d^5)*x^3)*(b*x^3 + a)^(1/3))/(b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)]","B",0
733,1,1156,0,0.472008," ","integrate(x^8/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right) + 6 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{3} d - a b^{2} c^{2} d^{2}\right)} \sqrt{-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \log\left(\frac{b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{d x^{3} + c}\right) + 3 \, {\left(4 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + 3 \, a^{3} d^{4} - {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{12 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)}}, -\frac{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} b^{2} c^{2} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 12 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{3} d - a b^{2} c^{2} d^{2}\right)} \sqrt{\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right) + 3 \, {\left(4 \, b^{3} c^{3} d - 5 \, a b^{2} c^{2} d^{2} - 2 \, a^{2} b c d^{3} + 3 \, a^{3} d^{4} - {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{12 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)}}\right]"," ",0,"[-1/12*(2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*b^2*c^2*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*b^2*c^2*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)) + 6*sqrt(1/3)*(b^3*c^3*d - a*b^2*c^2*d^2)*sqrt(-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)*log((b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2 - 2*(b^2*c*d - a*b*d^2)*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt(-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3)*(b*c - a*d))/(d*x^3 + c)) + 3*(4*b^3*c^3*d - 5*a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + 3*a^3*d^4 - (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3)*(b*x^3 + a)^(1/3))/(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5), -1/12*(2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*b^2*c^2*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*b^2*c^2*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)) - 12*sqrt(1/3)*(b^3*c^3*d - a*b^2*c^2*d^2)*sqrt((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)*arctan(-sqrt(1/3)*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) - 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) + 3*(4*b^3*c^3*d - 5*a*b^2*c^2*d^2 - 2*a^2*b*c*d^3 + 3*a^3*d^4 - (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3)*(b*x^3 + a)^(1/3))/(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)]","B",0
734,1,1060,0,0.606892," ","integrate(x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b c \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 2 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b c \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 3 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{2} d - a b c d^{2}\right)} \sqrt{\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \log\left(\frac{b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} - 3 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{d x^{3} + c}\right) + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{6 \, {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)}}, \frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b c \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 2 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} b c \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}}\right) - 6 \, \sqrt{\frac{1}{3}} {\left(b^{2} c^{2} d - a b c d^{2}\right)} \sqrt{-\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left({\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + 2 \, {\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right) + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{6 \, {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)}}\right]"," ",0,"[1/6*((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b*c*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 2*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b*c*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) - 3*sqrt(1/3)*(b^2*c^2*d - a*b*c*d^2)*sqrt((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)*log((b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2 - 2*(b^2*c*d - a*b*d^2)*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d) - 3*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3)*(b*c - a*d))/(d*x^3 + c)) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x^3 + a)^(1/3))/(b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4), 1/6*((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b*c*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 2*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*b*c*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)) - 6*sqrt(1/3)*(b^2*c^2*d - a*b*c*d^2)*sqrt(-(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)*arctan(sqrt(1/3)*((-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)*(b*c - a*d) + 2*(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt(-(-b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)^(1/3)/d)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x^3 + a)^(1/3))/(b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)]","B",0
735,1,927,0,0.556397," ","integrate(x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \sqrt{-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \log\left(\frac{b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)}}{d x^{3} + c}\right) + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right)}{6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \sqrt{\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}}}{d}}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right) - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{2}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right) + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}^{\frac{2}{3}}\right)}{6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)}}\right]"," ",0,"[-1/6*(3*sqrt(1/3)*(b*c*d - a*d^2)*sqrt(-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)*log((b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2 - 2*(b^2*c*d - a*b*d^2)*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt(-(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*x^3 + a)^(1/3)*(b*c - a*d))/(d*x^3 + c)) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) - 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3), 1/6*(6*sqrt(1/3)*(b*c*d - a*d^2)*sqrt((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)*arctan(-sqrt(1/3)*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) - 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3))*sqrt((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)/d)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2)) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*log(-(b*x^3 + a)^(2/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(1/3)*(b*c - a*d) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*(b*x^3 + a)^(1/3)) + 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)*log(-(b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)^(2/3)))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)]","B",0
736,1,472,0,0.501041," ","integrate(1/x/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} a^{2} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) + a^{2} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}}\right) - 2 \, a^{2} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(b c - a d\right)} \left(-\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}}\right) + 2 \, \sqrt{3} {\left(a^{2}\right)}^{\frac{1}{6}} a \arctan\left(\frac{{\left(a^{2}\right)}^{\frac{1}{6}} {\left(\sqrt{3} {\left(a^{2}\right)}^{\frac{1}{3}} a + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right)}}{3 \, a^{2}}\right) + {\left(a^{2}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a + {\left(a^{2}\right)}^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(a^{2}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(a^{2}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - {\left(a^{2}\right)}^{\frac{2}{3}}\right)}{6 \, a^{2} c}"," ",0,"-1/6*(2*sqrt(3)*a^2*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3) - sqrt(3)*d)/d) + a^2*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log((b*x^3 + a)^(2/3)*d^2 + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2)*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3)) - 2*a^2*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log((b*x^3 + a)^(1/3)*d - (b*c - a*d)*(-d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)) + 2*sqrt(3)*(a^2)^(1/6)*a*arctan(1/3*(a^2)^(1/6)*(sqrt(3)*(a^2)^(1/3)*a + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(a^2)^(2/3))/a^2) + (a^2)^(2/3)*log((b*x^3 + a)^(2/3)*a + (a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(a^2)^(2/3)) - 2*(a^2)^(2/3)*log((b*x^3 + a)^(1/3)*a - (a^2)^(2/3)))/(a^2*c)","B",0
737,1,562,0,1.246705," ","integrate(1/x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{3} a^{3} d \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x^{3} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} - \sqrt{3} d}{3 \, d}\right) + 3 \, a^{3} d \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}}\right) - 6 \, a^{3} d \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c - a d\right)} \left(\frac{d^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}}\right) - 2 \, \sqrt{3} {\left(2 \, a b c + 3 \, a^{2} d\right)} x^{3} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-a^{2}\right)^{\frac{1}{3}} a - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-a^{2}\right)^{\frac{1}{3}}}}{3 \, a^{2}}\right) - \left(-a^{2}\right)^{\frac{2}{3}} {\left(2 \, b c + 3 \, a d\right)} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} a - \left(-a^{2}\right)^{\frac{1}{3}} a + {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a^{2}\right)^{\frac{2}{3}}\right) + 2 \, \left(-a^{2}\right)^{\frac{2}{3}} {\left(2 \, b c + 3 \, a d\right)} x^{3} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} a - \left(-a^{2}\right)^{\frac{2}{3}}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{2} c}{18 \, a^{3} c^{2} x^{3}}"," ",0,"-1/18*(6*sqrt(3)*a^3*d*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x^3*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*(b*c - a*d)*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3) - sqrt(3)*d)/d) + 3*a^3*d*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x^3*log((b*x^3 + a)^(2/3)*d^2 - (b*x^3 + a)^(1/3)*(b*c*d - a*d^2)*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3)) - 6*a^3*d*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x^3*log((b*x^3 + a)^(1/3)*d + (b*c - a*d)*(d^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)) - 2*sqrt(3)*(2*a*b*c + 3*a^2*d)*x^3*sqrt(-(-a^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-a^2)^(1/3)*a - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-a^2)^(2/3))*sqrt(-(-a^2)^(1/3))/a^2) - (-a^2)^(2/3)*(2*b*c + 3*a*d)*x^3*log((b*x^3 + a)^(2/3)*a - (-a^2)^(1/3)*a + (b*x^3 + a)^(1/3)*(-a^2)^(2/3)) + 2*(-a^2)^(2/3)*(2*b*c + 3*a*d)*x^3*log((b*x^3 + a)^(1/3)*a - (-a^2)^(2/3)) + 6*(b*x^3 + a)^(1/3)*a^2*c)/(a^3*c^2*x^3)","B",0
738,1,558,0,1.284187," ","integrate(x^7/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{6 \, \sqrt{3} b^{3} c \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} + \sqrt{3} c x}{3 \, c x}\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{2} d x^{2} + 6 \, b^{3} c \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b c - a d\right)} \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) - 3 \, b^{3} c \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)} \left(-\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x}{x^{2}}\right) - 2 \, \sqrt{3} {\left(3 \, b^{2} c + 2 \, a b d\right)} {\left(b^{2}\right)}^{\frac{1}{6}} \arctan\left(\frac{{\left(\sqrt{3} {\left(b^{2}\right)}^{\frac{1}{3}} b x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}}\right)} {\left(b^{2}\right)}^{\frac{1}{6}}}{3 \, b^{2} x}\right) + 2 \, {\left(b^{2}\right)}^{\frac{2}{3}} {\left(3 \, b c + 2 \, a d\right)} \log\left(-\frac{{\left(b^{2}\right)}^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) - {\left(b^{2}\right)}^{\frac{2}{3}} {\left(3 \, b c + 2 \, a d\right)} \log\left(\frac{{\left(b^{2}\right)}^{\frac{1}{3}} b x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b^{2}\right)}^{\frac{2}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{18 \, b^{3} d^{2}}"," ",0,"1/18*(6*sqrt(3)*b^3*c*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*(b*c - a*d)*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3) + sqrt(3)*c*x)/(c*x)) + 6*(b*x^3 + a)^(1/3)*b^2*d*x^2 + 6*b^3*c*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log(((b*c - a*d)*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x + (b*x^3 + a)^(1/3)*c)/x) - 3*b^3*c*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3)*x^2 + (b*x^3 + a)^(2/3)*c^2 - (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d)*(-c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x)/x^2) - 2*sqrt(3)*(3*b^2*c + 2*a*b*d)*(b^2)^(1/6)*arctan(1/3*(sqrt(3)*(b^2)^(1/3)*b*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(b^2)^(2/3))*(b^2)^(1/6)/(b^2*x)) + 2*(b^2)^(2/3)*(3*b*c + 2*a*d)*log(-((b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) - (b^2)^(2/3)*(3*b*c + 2*a*d)*log(((b^2)^(1/3)*b*x^2 + (b*x^3 + a)^(1/3)*(b^2)^(2/3)*x + (b*x^3 + a)^(2/3)*b)/x^2))/(b^3*d^2)","B",0
739,1,530,0,0.552345," ","integrate(x^4/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} b^{2} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} + \sqrt{3} c x}{3 \, c x}\right) + 2 \, b^{2} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) - b^{2} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c^{2} - a c d\right)} \left(\frac{c^{2}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}\right)^{\frac{1}{3}} x}{x^{2}}\right) + 2 \, \sqrt{3} b \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}} \arctan\left(-\frac{{\left(\sqrt{3} \left(-b^{2}\right)^{\frac{1}{3}} b x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}}\right)} \sqrt{-\left(-b^{2}\right)^{\frac{1}{3}}}}{3 \, b^{2} x}\right) - 2 \, \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b}{x}\right) + \left(-b^{2}\right)^{\frac{2}{3}} \log\left(-\frac{\left(-b^{2}\right)^{\frac{1}{3}} b x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b^{2}\right)^{\frac{2}{3}} x - {\left(b x^{3} + a\right)}^{\frac{2}{3}} b}{x^{2}}\right)}{6 \, b^{2} d}"," ",0,"1/6*(2*sqrt(3)*b^2*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*arctan(-1/3*(2*sqrt(3)*(b*x^3 + a)^(1/3)*(b*c - a*d)*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3) + sqrt(3)*c*x)/(c*x)) + 2*b^2*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log(-((b*c - a*d)*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x - (b*x^3 + a)^(1/3)*c)/x) - b^2*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*log(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(2/3)*x^2 + (b*x^3 + a)^(2/3)*c^2 + (b*x^3 + a)^(1/3)*(b*c^2 - a*c*d)*(c^2/(b^2*c^2 - 2*a*b*c*d + a^2*d^2))^(1/3)*x)/x^2) + 2*sqrt(3)*b*sqrt(-(-b^2)^(1/3))*arctan(-1/3*(sqrt(3)*(-b^2)^(1/3)*b*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-b^2)^(2/3))*sqrt(-(-b^2)^(1/3))/(b^2*x)) - 2*(-b^2)^(2/3)*log(-((-b^2)^(2/3)*x - (b*x^3 + a)^(1/3)*b)/x) + (-b^2)^(2/3)*log(-((-b^2)^(1/3)*b*x^2 - (b*x^3 + a)^(1/3)*(-b^2)^(2/3)*x - (b*x^3 + a)^(2/3)*b)/x^2))/(b^2*d)","B",0
740,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate(x^6/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(2/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,1,1300,0,0.838646," ","integrate(x^14/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{60 \, \sqrt{\frac{1}{3}} {\left(a b^{5} c^{5} d - a^{2} b^{4} c^{4} d^{2} + {\left(b^{6} c^{5} d - a b^{5} c^{4} d^{2}\right)} x^{3}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) + 20 \, {\left(b^{5} c^{4} x^{3} + a b^{4} c^{4}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 40 \, {\left(b^{5} c^{4} x^{3} + a b^{4} c^{4}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(20 \, a b^{4} c^{4} d^{2} - 8 \, a^{2} b^{3} c^{3} d^{3} - 3 \, a^{3} b^{2} c^{2} d^{4} - 90 \, a^{4} b c d^{5} + 81 \, a^{5} d^{6} + 5 \, {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)} x^{9} - {\left(8 \, b^{5} c^{3} d^{3} - 7 \, a b^{4} c^{2} d^{4} - 10 \, a^{2} b^{3} c d^{5} + 9 \, a^{3} b^{2} d^{6}\right)} x^{6} + {\left(20 \, b^{5} c^{4} d^{2} - 16 \, a b^{4} c^{3} d^{3} - a^{2} b^{3} c^{2} d^{4} - 30 \, a^{3} b^{2} c d^{5} + 27 \, a^{4} b d^{6}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{120 \, {\left(a b^{6} c^{2} d^{5} - 2 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7} + {\left(b^{7} c^{2} d^{5} - 2 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right)} x^{3}\right)}}, -\frac{120 \, \sqrt{\frac{1}{3}} {\left(a b^{5} c^{5} d - a^{2} b^{4} c^{4} d^{2} + {\left(b^{6} c^{5} d - a b^{5} c^{4} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) + 20 \, {\left(b^{5} c^{4} x^{3} + a b^{4} c^{4}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 40 \, {\left(b^{5} c^{4} x^{3} + a b^{4} c^{4}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(20 \, a b^{4} c^{4} d^{2} - 8 \, a^{2} b^{3} c^{3} d^{3} - 3 \, a^{3} b^{2} c^{2} d^{4} - 90 \, a^{4} b c d^{5} + 81 \, a^{5} d^{6} + 5 \, {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)} x^{9} - {\left(8 \, b^{5} c^{3} d^{3} - 7 \, a b^{4} c^{2} d^{4} - 10 \, a^{2} b^{3} c d^{5} + 9 \, a^{3} b^{2} d^{6}\right)} x^{6} + {\left(20 \, b^{5} c^{4} d^{2} - 16 \, a b^{4} c^{3} d^{3} - a^{2} b^{3} c^{2} d^{4} - 30 \, a^{3} b^{2} c d^{5} + 27 \, a^{4} b d^{6}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{120 \, {\left(a b^{6} c^{2} d^{5} - 2 \, a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7} + {\left(b^{7} c^{2} d^{5} - 2 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right)} x^{3}\right)}}\right]"," ",0,"[-1/120*(60*sqrt(1/3)*(a*b^5*c^5*d - a^2*b^4*c^4*d^2 + (b^6*c^5*d - a*b^5*c^4*d^2)*x^3)*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 + 3*sqrt(1/3)*(2*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) + (-b*c*d^2 + a*d^3)^(1/3)*(b*c - a*d))*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d)) - 3*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) + 20*(b^5*c^4*x^3 + a*b^4*c^4)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 40*(b^5*c^4*x^3 + a*b^4*c^4)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) - 3*(20*a*b^4*c^4*d^2 - 8*a^2*b^3*c^3*d^3 - 3*a^3*b^2*c^2*d^4 - 90*a^4*b*c*d^5 + 81*a^5*d^6 + 5*(b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)*x^9 - (8*b^5*c^3*d^3 - 7*a*b^4*c^2*d^4 - 10*a^2*b^3*c*d^5 + 9*a^3*b^2*d^6)*x^6 + (20*b^5*c^4*d^2 - 16*a*b^4*c^3*d^3 - a^2*b^3*c^2*d^4 - 30*a^3*b^2*c*d^5 + 27*a^4*b*d^6)*x^3)*(b*x^3 + a)^(2/3))/(a*b^6*c^2*d^5 - 2*a^2*b^5*c*d^6 + a^3*b^4*d^7 + (b^7*c^2*d^5 - 2*a*b^6*c*d^6 + a^2*b^5*d^7)*x^3), -1/120*(120*sqrt(1/3)*(a*b^5*c^5*d - a^2*b^4*c^4*d^2 + (b^6*c^5*d - a*b^5*c^4*d^2)*x^3)*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(1/3))*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))/d) + 20*(b^5*c^4*x^3 + a*b^4*c^4)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 40*(b^5*c^4*x^3 + a*b^4*c^4)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) - 3*(20*a*b^4*c^4*d^2 - 8*a^2*b^3*c^3*d^3 - 3*a^3*b^2*c^2*d^4 - 90*a^4*b*c*d^5 + 81*a^5*d^6 + 5*(b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)*x^9 - (8*b^5*c^3*d^3 - 7*a*b^4*c^2*d^4 - 10*a^2*b^3*c*d^5 + 9*a^3*b^2*d^6)*x^6 + (20*b^5*c^4*d^2 - 16*a*b^4*c^3*d^3 - a^2*b^3*c^2*d^4 - 30*a^3*b^2*c*d^5 + 27*a^4*b*d^6)*x^3)*(b*x^3 + a)^(2/3))/(a*b^6*c^2*d^5 - 2*a^2*b^5*c*d^6 + a^3*b^4*d^7 + (b^7*c^2*d^5 - 2*a*b^6*c*d^6 + a^2*b^5*d^7)*x^3)]","B",0
748,1,1141,0,0.725733," ","integrate(x^11/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{15 \, \sqrt{\frac{1}{3}} {\left(a b^{4} c^{4} d - a^{2} b^{3} c^{3} d^{2} + {\left(b^{5} c^{4} d - a b^{4} c^{3} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - 5 \, {\left(b^{4} c^{3} x^{3} + a b^{3} c^{3}\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) + 10 \, {\left(b^{4} c^{3} x^{3} + a b^{3} c^{3}\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) + 3 \, {\left(5 \, a b^{3} c^{3} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{3} - 21 \, a^{3} b c d^{4} + 18 \, a^{4} d^{5} - 2 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{6} + {\left(5 \, b^{4} c^{3} d^{2} - 4 \, a b^{3} c^{2} d^{3} - 7 \, a^{2} b^{2} c d^{4} + 6 \, a^{3} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, {\left(a b^{5} c^{2} d^{4} - 2 \, a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6} + {\left(b^{6} c^{2} d^{4} - 2 \, a b^{5} c d^{5} + a^{2} b^{4} d^{6}\right)} x^{3}\right)}}, \frac{30 \, \sqrt{\frac{1}{3}} {\left(a b^{4} c^{4} d - a^{2} b^{3} c^{3} d^{2} + {\left(b^{5} c^{4} d - a b^{4} c^{3} d^{2}\right)} x^{3}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) + 5 \, {\left(b^{4} c^{3} x^{3} + a b^{3} c^{3}\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 10 \, {\left(b^{4} c^{3} x^{3} + a b^{3} c^{3}\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(5 \, a b^{3} c^{3} d^{2} - 2 \, a^{2} b^{2} c^{2} d^{3} - 21 \, a^{3} b c d^{4} + 18 \, a^{4} d^{5} - 2 \, {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{6} + {\left(5 \, b^{4} c^{3} d^{2} - 4 \, a b^{3} c^{2} d^{3} - 7 \, a^{2} b^{2} c d^{4} + 6 \, a^{3} b d^{5}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{30 \, {\left(a b^{5} c^{2} d^{4} - 2 \, a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6} + {\left(b^{6} c^{2} d^{4} - 2 \, a b^{5} c d^{5} + a^{2} b^{4} d^{6}\right)} x^{3}\right)}}\right]"," ",0,"[-1/30*(15*sqrt(1/3)*(a*b^4*c^4*d - a^2*b^3*c^3*d^2 + (b^5*c^4*d - a*b^4*c^3*d^2)*x^3)*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 - 3*sqrt(1/3)*(2*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b*c*d^2 - a*d^3)^(1/3)*(b*c - a*d))*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d)) - 3*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - 5*(b^4*c^3*x^3 + a*b^3*c^3)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) + 10*(b^4*c^3*x^3 + a*b^3*c^3)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) + 3*(5*a*b^3*c^3*d^2 - 2*a^2*b^2*c^2*d^3 - 21*a^3*b*c*d^4 + 18*a^4*d^5 - 2*(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^6 + (5*b^4*c^3*d^2 - 4*a*b^3*c^2*d^3 - 7*a^2*b^2*c*d^4 + 6*a^3*b*d^5)*x^3)*(b*x^3 + a)^(2/3))/(a*b^5*c^2*d^4 - 2*a^2*b^4*c*d^5 + a^3*b^3*d^6 + (b^6*c^2*d^4 - 2*a*b^5*c*d^5 + a^2*b^4*d^6)*x^3), 1/30*(30*sqrt(1/3)*(a*b^4*c^4*d - a^2*b^3*c^3*d^2 + (b^5*c^4*d - a*b^4*c^3*d^2)*x^3)*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d - (b*c*d^2 - a*d^3)^(1/3))*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))/d) + 5*(b^4*c^3*x^3 + a*b^3*c^3)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 10*(b^4*c^3*x^3 + a*b^3*c^3)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 3*(5*a*b^3*c^3*d^2 - 2*a^2*b^2*c^2*d^3 - 21*a^3*b*c*d^4 + 18*a^4*d^5 - 2*(b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^6 + (5*b^4*c^3*d^2 - 4*a*b^3*c^2*d^3 - 7*a^2*b^2*c*d^4 + 6*a^3*b*d^5)*x^3)*(b*x^3 + a)^(2/3))/(a*b^5*c^2*d^4 - 2*a^2*b^4*c*d^5 + a^3*b^3*d^6 + (b^6*c^2*d^4 - 2*a*b^5*c*d^5 + a^2*b^4*d^6)*x^3)]","B",0
749,1,1004,0,0.705189," ","integrate(x^8/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{3} d - a^{2} b^{2} c^{2} d^{2} + {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2}\right)} x^{3}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) + {\left(b^{3} c^{2} x^{3} + a b^{2} c^{2}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(b^{3} c^{2} x^{3} + a b^{2} c^{2}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(a b^{2} c^{2} d^{2} - 4 \, a^{2} b c d^{3} + 3 \, a^{3} d^{4} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(a b^{4} c^{2} d^{3} - 2 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5} + {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{3}\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(a b^{3} c^{3} d - a^{2} b^{2} c^{2} d^{2} + {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{{\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) + {\left(b^{3} c^{2} x^{3} + a b^{2} c^{2}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(b^{3} c^{2} x^{3} + a b^{2} c^{2}\right)} {\left(-b c d^{2} + a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(-b c d^{2} + a d^{3}\right)}^{\frac{1}{3}}\right) - 3 \, {\left(a b^{2} c^{2} d^{2} - 4 \, a^{2} b c d^{3} + 3 \, a^{3} d^{4} + {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(a b^{4} c^{2} d^{3} - 2 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5} + {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(3*sqrt(1/3)*(a*b^3*c^3*d - a^2*b^2*c^2*d^2 + (b^4*c^3*d - a*b^3*c^2*d^2)*x^3)*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 + 3*sqrt(1/3)*(2*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) + (-b*c*d^2 + a*d^3)^(1/3)*(b*c - a*d))*sqrt((-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d)) - 3*(-b*c*d^2 + a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) + (b^3*c^2*x^3 + a*b^2*c^2)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 2*(b^3*c^2*x^3 + a*b^2*c^2)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) - 3*(a*b^2*c^2*d^2 - 4*a^2*b*c*d^3 + 3*a^3*d^4 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3)*(b*x^3 + a)^(2/3))/(a*b^4*c^2*d^3 - 2*a^2*b^3*c*d^4 + a^3*b^2*d^5 + (b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^3), -1/6*(6*sqrt(1/3)*(a*b^3*c^3*d - a^2*b^2*c^2*d^2 + (b^4*c^3*d - a*b^3*c^2*d^2)*x^3)*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(1/3))*sqrt(-(-b*c*d^2 + a*d^3)^(1/3)/(b*c - a*d))/d) + (b^3*c^2*x^3 + a*b^2*c^2)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 + (-b*c*d^2 + a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (-b*c*d^2 + a*d^3)^(2/3)) - 2*(b^3*c^2*x^3 + a*b^2*c^2)*(-b*c*d^2 + a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d - (-b*c*d^2 + a*d^3)^(1/3)) - 3*(a*b^2*c^2*d^2 - 4*a^2*b*c*d^3 + 3*a^3*d^4 + (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^3)*(b*x^3 + a)^(2/3))/(a*b^4*c^2*d^3 - 2*a^2*b^3*c*d^4 + a^3*b^2*d^5 + (b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^3)]","B",0
750,1,872,0,0.821062," ","integrate(x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{2} d - a^{2} b c d^{2} + {\left(b^{3} c^{2} d - a b^{2} c d^{2}\right)} x^{3}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \log\left(\frac{2 \, b d^{2} x^{3} - b c d + 3 \, a d^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c d - a d^{2}\right)} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b c - a d\right)}\right)} \sqrt{-\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} - 3 \, {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{d x^{3} + c}\right) - {\left(b^{2} c x^{3} + a b c\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) + 2 \, {\left(b^{2} c x^{3} + a b c\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) - 6 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{3}\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c^{2} d - a^{2} b c d^{2} + {\left(b^{3} c^{2} d - a b^{2} c d^{2}\right)} x^{3}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} d - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right)} \sqrt{\frac{{\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}}{b c - a d}}}{d}\right) + {\left(b^{2} c x^{3} + a b c\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} d^{2} - {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}} {\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}}\right) - 2 \, {\left(b^{2} c x^{3} + a b c\right)} {\left(b c d^{2} - a d^{3}\right)}^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} d + {\left(b c d^{2} - a d^{3}\right)}^{\frac{1}{3}}\right) + 6 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left(a b^{3} c^{2} d^{2} - 2 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{3}\right)}}\right]"," ",0,"[-1/6*(3*sqrt(1/3)*(a*b^2*c^2*d - a^2*b*c*d^2 + (b^3*c^2*d - a*b^2*c*d^2)*x^3)*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*log((2*b*d^2*x^3 - b*c*d + 3*a*d^2 - 3*sqrt(1/3)*(2*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*(b*c*d - a*d^2) - (b*c*d^2 - a*d^3)^(1/3)*(b*c - a*d))*sqrt(-(b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d)) - 3*(b*c*d^2 - a*d^3)^(2/3)*(b*x^3 + a)^(1/3))/(d*x^3 + c)) - (b^2*c*x^3 + a*b*c)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) + 2*(b^2*c*x^3 + a*b*c)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) - 6*(a*b*c*d^2 - a^2*d^3)*(b*x^3 + a)^(2/3))/(a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + a^3*b*d^4 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^3), 1/6*(6*sqrt(1/3)*(a*b^2*c^2*d - a^2*b*c*d^2 + (b^3*c^2*d - a*b^2*c*d^2)*x^3)*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3)*d - (b*c*d^2 - a*d^3)^(1/3))*sqrt((b*c*d^2 - a*d^3)^(1/3)/(b*c - a*d))/d) + (b^2*c*x^3 + a*b*c)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(2/3)*d^2 - (b*c*d^2 - a*d^3)^(1/3)*(b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(2/3)) - 2*(b^2*c*x^3 + a*b*c)*(b*c*d^2 - a*d^3)^(2/3)*log((b*x^3 + a)^(1/3)*d + (b*c*d^2 - a*d^3)^(1/3)) + 6*(a*b*c*d^2 - a^2*d^3)*(b*x^3 + a)^(2/3))/(a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + a^3*b*d^4 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^3)]","B",0
751,1,262,0,0.669552," ","integrate(x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} {\left(b x^{3} + a\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - {\left(b x^{3} + a\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d - {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) + 2 \, {\left(b x^{3} + a\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) + 6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{6 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)}}"," ",0,"-1/6*(2*sqrt(3)*(b*x^3 + a)*(-d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(-d/(b*c - a*d))^(1/3) + 1/3*sqrt(3)) - (b*x^3 + a)*(-d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d - (b*c - a*d)*(-d/(b*c - a*d))^(1/3)) + 2*(b*x^3 + a)*(-d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) + 6*(b*x^3 + a)^(2/3))/((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)","A",0
752,1,975,0,0.797931," ","integrate(1/x/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a b c + 3 \, \sqrt{\frac{1}{3}} {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{3}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} \log\left(\frac{2 \, b x^{3} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a - a^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{a^{\frac{2}{3}}}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) + 2 \, \sqrt{3} {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d + {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) - 2 \, {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right)}{6 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}, \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a b c + 2 \, \sqrt{3} {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) - {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} a^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d + {\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) - 2 \, {\left(a^{2} b d x^{3} + a^{3} d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) + \frac{6 \, \sqrt{\frac{1}{3}} {\left(a^{2} b c - a^{3} d + {\left(a b^{2} c - a^{2} b d\right)} x^{3}\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}}}{6 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(6*(b*x^3 + a)^(2/3)*a*b*c + 3*sqrt(1/3)*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^3)*sqrt(-1/a^(2/3))*log((2*b*x^3 + 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*a^(2/3) - (b*x^3 + a)^(1/3)*a - a^(4/3))*sqrt(-1/a^(2/3)) - 3*(b*x^3 + a)^(1/3)*a^(2/3) + 3*a)/x^3) + 2*sqrt(3)*(a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(d/(b*c - a*d))^(1/3) - 1/3*sqrt(3)) - ((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)) + (a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d + (b*c - a*d)*(d/(b*c - a*d))^(1/3)) - 2*(a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3), 1/6*(6*(b*x^3 + a)^(2/3)*a*b*c + 2*sqrt(3)*(a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(d/(b*c - a*d))^(1/3) - 1/3*sqrt(3)) - ((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*a^(2/3)*log((b*x^3 + a)^(2/3) + (b*x^3 + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*a^(2/3)*log((b*x^3 + a)^(1/3) - a^(1/3)) + (a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d + (b*c - a*d)*(d/(b*c - a*d))^(1/3)) - 2*(a^2*b*d*x^3 + a^3*d)*(d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) + 6*sqrt(1/3)*(a^2*b*c - a^3*d + (a*b^2*c - a^2*b*d)*x^3)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^3)]","B",0
753,1,1386,0,1.385947," ","integrate(1/x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left({\left(4 \, a b^{3} c^{2} - a^{2} b^{2} c d - 3 \, a^{3} b d^{2}\right)} x^{6} + {\left(4 \, a^{2} b^{2} c^{2} - a^{3} b c d - 3 \, a^{4} d^{2}\right)} x^{3}\right)} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \log\left(\frac{2 \, b x^{3} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-a\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} a + \left(-a\right)^{\frac{1}{3}} a\right)} \sqrt{\frac{\left(-a\right)^{\frac{1}{3}}}{a}} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{2}{3}} + 3 \, a}{x^{3}}\right) - 6 \, \sqrt{3} {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) + {\left({\left(4 \, b^{3} c^{2} - a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2}\right)} x^{3}\right)} \left(-a\right)^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) - 2 \, {\left({\left(4 \, b^{3} c^{2} - a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2}\right)} x^{3}\right)} \left(-a\right)^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) + 3 \, {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d - {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) - 6 \, {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) - 6 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(4 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{18 \, {\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^{3}\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left({\left(4 \, a b^{3} c^{2} - a^{2} b^{2} c d - 3 \, a^{3} b d^{2}\right)} x^{6} + {\left(4 \, a^{2} b^{2} c^{2} - a^{3} b c d - 3 \, a^{4} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}} \arctan\left(\sqrt{\frac{1}{3}} {\left(2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} - \left(-a\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-a\right)^{\frac{1}{3}}}{a}}\right) + 6 \, \sqrt{3} {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - {\left({\left(4 \, b^{3} c^{2} - a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2}\right)} x^{3}\right)} \left(-a\right)^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-a\right)^{\frac{1}{3}} + \left(-a\right)^{\frac{2}{3}}\right) + 2 \, {\left({\left(4 \, b^{3} c^{2} - a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2}\right)} x^{3}\right)} \left(-a\right)^{\frac{2}{3}} \log\left({\left(b x^{3} + a\right)}^{\frac{1}{3}} + \left(-a\right)^{\frac{1}{3}}\right) - 3 \, {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left(-{\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} d - {\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}}\right) + 6 \, {\left(a^{3} b d^{2} x^{6} + a^{4} d^{2} x^{3}\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{1}{3}} \log\left({\left(b c - a d\right)} \left(-\frac{d}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} d\right) + 6 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(4 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{3}\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{18 \, {\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^{3}\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*((4*a*b^3*c^2 - a^2*b^2*c*d - 3*a^3*b*d^2)*x^6 + (4*a^2*b^2*c^2 - a^3*b*c*d - 3*a^4*d^2)*x^3)*sqrt((-a)^(1/3)/a)*log((2*b*x^3 - 3*sqrt(1/3)*(2*(b*x^3 + a)^(2/3)*(-a)^(2/3) - (b*x^3 + a)^(1/3)*a + (-a)^(1/3)*a)*sqrt((-a)^(1/3)/a) - 3*(b*x^3 + a)^(1/3)*(-a)^(2/3) + 3*a)/x^3) - 6*sqrt(3)*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(-d/(b*c - a*d))^(1/3) + 1/3*sqrt(3)) + ((4*b^3*c^2 - a*b^2*c*d - 3*a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2)*x^3)*(-a)^(2/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) - 2*((4*b^3*c^2 - a*b^2*c*d - 3*a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2)*x^3)*(-a)^(2/3)*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) + 3*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d - (b*c - a*d)*(-d/(b*c - a*d))^(1/3)) - 6*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) - 6*(a^2*b*c^2 - a^3*c*d + (4*a*b^2*c^2 - a^2*b*c*d)*x^3)*(b*x^3 + a)^(2/3))/((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^3), -1/18*(6*sqrt(1/3)*((4*a*b^3*c^2 - a^2*b^2*c*d - 3*a^3*b*d^2)*x^6 + (4*a^2*b^2*c^2 - a^3*b*c*d - 3*a^4*d^2)*x^3)*sqrt(-(-a)^(1/3)/a)*arctan(sqrt(1/3)*(2*(b*x^3 + a)^(1/3) - (-a)^(1/3))*sqrt(-(-a)^(1/3)/a)) + 6*sqrt(3)*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*arctan(2/3*sqrt(3)*(b*x^3 + a)^(1/3)*(-d/(b*c - a*d))^(1/3) + 1/3*sqrt(3)) - ((4*b^3*c^2 - a*b^2*c*d - 3*a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2)*x^3)*(-a)^(2/3)*log((b*x^3 + a)^(2/3) - (b*x^3 + a)^(1/3)*(-a)^(1/3) + (-a)^(2/3)) + 2*((4*b^3*c^2 - a*b^2*c*d - 3*a^2*b*d^2)*x^6 + (4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2)*x^3)*(-a)^(2/3)*log((b*x^3 + a)^(1/3) + (-a)^(1/3)) - 3*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*log(-(b*x^3 + a)^(1/3)*(b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*d - (b*c - a*d)*(-d/(b*c - a*d))^(1/3)) + 6*(a^3*b*d^2*x^6 + a^4*d^2*x^3)*(-d/(b*c - a*d))^(1/3)*log((b*c - a*d)*(-d/(b*c - a*d))^(2/3) + (b*x^3 + a)^(1/3)*d) + 6*(a^2*b*c^2 - a^3*c*d + (4*a*b^2*c^2 - a^2*b*c*d)*x^3)*(b*x^3 + a)^(2/3))/((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^3)]","B",0
754,1,1329,0,1.364879," ","integrate(x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, a b^{3} c^{2} + a^{2} b^{2} c d - 4 \, a^{3} b d^{2} + {\left(3 \, b^{4} c^{2} + a b^{3} c d - 4 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(b^{\frac{4}{3}} x^{3} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} - 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} b^{\frac{2}{3}} x\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} + 2 \, a\right) - 6 \, \sqrt{3} {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) + 2 \, {\left(3 \, a b^{2} c^{2} + a^{2} b c d - 4 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) - {\left(3 \, a b^{2} c^{2} + a^{2} b c d - 4 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 6 \, {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + 3 \, {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b c - a d\right)} x^{2} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) + 6 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{4} + {\left(a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{18 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{3}\right)}}, -\frac{6 \, \sqrt{3} {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} x + 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 2 \, {\left(3 \, a b^{2} c^{2} + a^{2} b c d - 4 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(-\frac{b^{\frac{1}{3}} x - {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left(3 \, a b^{2} c^{2} + a^{2} b c d - 4 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{3}\right)} b^{\frac{2}{3}} \log\left(\frac{b^{\frac{2}{3}} x^{2} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} b^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) + 6 \, {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) - 3 \, {\left(b^{4} c^{2} x^{3} + a b^{3} c^{2}\right)} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b c - a d\right)} x^{2} \left(\frac{c}{b c - a d}\right)^{\frac{1}{3}} + {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(\frac{c}{b c - a d}\right)^{\frac{2}{3}} + {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right) - \frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, a b^{3} c^{2} + a^{2} b^{2} c d - 4 \, a^{3} b d^{2} + {\left(3 \, b^{4} c^{2} + a b^{3} c d - 4 \, a^{2} b^{2} d^{2}\right)} x^{3}\right)} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(b^{\frac{1}{3}} x + 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)}}{b^{\frac{1}{3}} x}\right)}{b^{\frac{1}{3}}} - 6 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{4} + {\left(a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{18 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{3}\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(3*a*b^3*c^2 + a^2*b^2*c*d - 4*a^3*b*d^2 + (3*b^4*c^2 + a*b^3*c*d - 4*a^2*b^2*d^2)*x^3)*sqrt(-1/b^(2/3))*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*b^(2/3)*x^2 - 3*sqrt(1/3)*(b^(4/3)*x^3 + (b*x^3 + a)^(1/3)*b*x^2 - 2*(b*x^3 + a)^(2/3)*b^(2/3)*x)*sqrt(-1/b^(2/3)) + 2*a) - 6*sqrt(3)*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*arctan(1/3*(sqrt(3)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(c/(b*c - a*d))^(1/3))/x) + 2*(3*a*b^2*c^2 + a^2*b*c*d - 4*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x^3)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) - (3*a*b^2*c^2 + a^2*b*c*d - 4*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x^3)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 6*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + 3*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*log(((b*c - a*d)*x^2*(c/(b*c - a*d))^(1/3) + (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(c/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*c)/x^2) + 6*((b^3*c*d - a*b^2*d^2)*x^4 + (a*b^2*c*d - 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^3), -1/18*(6*sqrt(3)*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*arctan(1/3*(sqrt(3)*x + 2*sqrt(3)*(b*x^3 + a)^(1/3)*(c/(b*c - a*d))^(1/3))/x) - 2*(3*a*b^2*c^2 + a^2*b*c*d - 4*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x^3)*b^(2/3)*log(-(b^(1/3)*x - (b*x^3 + a)^(1/3))/x) + (3*a*b^2*c^2 + a^2*b*c*d - 4*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x^3)*b^(2/3)*log((b^(2/3)*x^2 + (b*x^3 + a)^(1/3)*b^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) + 6*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) - 3*(b^4*c^2*x^3 + a*b^3*c^2)*(c/(b*c - a*d))^(1/3)*log(((b*c - a*d)*x^2*(c/(b*c - a*d))^(1/3) + (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(c/(b*c - a*d))^(2/3) + (b*x^3 + a)^(2/3)*c)/x^2) - 6*sqrt(1/3)*(3*a*b^3*c^2 + a^2*b^2*c*d - 4*a^3*b*d^2 + (3*b^4*c^2 + a*b^3*c*d - 4*a^2*b^2*d^2)*x^3)*arctan(sqrt(1/3)*(b^(1/3)*x + 2*(b*x^3 + a)^(1/3))/(b^(1/3)*x))/b^(1/3) - 6*((b^3*c*d - a*b^2*d^2)*x^4 + (a*b^2*c*d - 4*a^2*b*d^2)*x)*(b*x^3 + a)^(2/3))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^3)]","B",0
755,1,1127,0,0.483929," ","integrate(x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a b d x + 3 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \log\left(3 \, b x^{3} - 3 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{2}{3}} x^{2} - 3 \, \sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} b x^{3} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} b x^{2} + 2 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} \left(-b\right)^{\frac{2}{3}} x\right)} \sqrt{\frac{\left(-b\right)^{\frac{1}{3}}}{b}} + 2 \, a\right) + 2 \, \sqrt{3} {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 2 \, {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right)}{6 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{3}\right)}}, \frac{6 \, {\left(b x^{3} + a\right)}^{\frac{2}{3}} a b d x - 6 \, \sqrt{\frac{1}{3}} {\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x^{3}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left(\left(-b\right)^{\frac{1}{3}} x - 2 \, {\left(b x^{3} + a\right)}^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-b\right)^{\frac{1}{3}}}{b}}}{x}\right) + 2 \, \sqrt{3} {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} x - 2 \, \sqrt{3} {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}}}{3 \, x}\right) - 2 \, {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{1}{3}}}{x}\right) + {\left({\left(b^{2} c - a b d\right)} x^{3} + a b c - a^{2} d\right)} \left(-b\right)^{\frac{2}{3}} \log\left(\frac{\left(-b\right)^{\frac{2}{3}} x^{2} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} \left(-b\right)^{\frac{1}{3}} x + {\left(b x^{3} + a\right)}^{\frac{2}{3}}}{x^{2}}\right) - 2 \, {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} c}{x}\right) + {\left(b^{3} c x^{3} + a b^{2} c\right)} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(b c - a d\right)} x^{2} \left(-\frac{c}{b c - a d}\right)^{\frac{1}{3}} - {\left(b x^{3} + a\right)}^{\frac{1}{3}} {\left(b c - a d\right)} x \left(-\frac{c}{b c - a d}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)}^{\frac{2}{3}} c}{x^{2}}\right)}{6 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[1/6*(6*(b*x^3 + a)^(2/3)*a*b*d*x + 3*sqrt(1/3)*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt((-b)^(1/3)/b)*log(3*b*x^3 - 3*(b*x^3 + a)^(1/3)*(-b)^(2/3)*x^2 - 3*sqrt(1/3)*((-b)^(1/3)*b*x^3 - (b*x^3 + a)^(1/3)*b*x^2 + 2*(b*x^3 + a)^(2/3)*(-b)^(2/3)*x)*sqrt((-b)^(1/3)/b) + 2*a) + 2*sqrt(3)*(b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-c/(b*c - a*d))^(1/3))/x) - 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + ((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 2*(b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + (b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x^2*(-c/(b*c - a*d))^(1/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(2/3)*c)/x^2))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^3), 1/6*(6*(b*x^3 + a)^(2/3)*a*b*d*x - 6*sqrt(1/3)*(a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x^3)*sqrt(-(-b)^(1/3)/b)*arctan(-sqrt(1/3)*((-b)^(1/3)*x - 2*(b*x^3 + a)^(1/3))*sqrt(-(-b)^(1/3)/b)/x) + 2*sqrt(3)*(b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*arctan(-1/3*(sqrt(3)*x - 2*sqrt(3)*(b*x^3 + a)^(1/3)*(-c/(b*c - a*d))^(1/3))/x) - 2*((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*(-b)^(2/3)*log(((-b)^(1/3)*x + (b*x^3 + a)^(1/3))/x) + ((b^2*c - a*b*d)*x^3 + a*b*c - a^2*d)*(-b)^(2/3)*log(((-b)^(2/3)*x^2 - (b*x^3 + a)^(1/3)*(-b)^(1/3)*x + (b*x^3 + a)^(2/3))/x^2) - 2*(b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(1/3)*c)/x) + (b^3*c*x^3 + a*b^2*c)*(-c/(b*c - a*d))^(1/3)*log(-((b*c - a*d)*x^2*(-c/(b*c - a*d))^(1/3) - (b*x^3 + a)^(1/3)*(b*c - a*d)*x*(-c/(b*c - a*d))^(2/3) - (b*x^3 + a)^(2/3)*c)/x^2))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^3)]","B",0
756,-1,0,0,0.000000," ","integrate(x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(1/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate(1/x^6/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,-1,0,0,0.000000," ","integrate(1/x^9/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
761,-1,0,0,0.000000," ","integrate(x^10/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
762,-1,0,0,0.000000," ","integrate(x^7/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(x^4/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(x/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(1/x^5/(b*x^3+a)^(4/3)/(d*x^3+c),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,1,100,0,6.244373," ","integrate(x^15/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{{\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{8} - 2 \, a^{3} d^{3} \log\left(b x^{4} + a\right) + 2 \, b^{3} c^{3} \log\left(d x^{4} + c\right) - 2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{4}}{8 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)}}"," ",0,"1/8*((b^3*c*d^2 - a*b^2*d^3)*x^8 - 2*a^3*d^3*log(b*x^4 + a) + 2*b^3*c^3*log(d*x^4 + c) - 2*(b^3*c^2*d - a^2*b*d^3)*x^4)/(b^4*c*d^3 - a*b^3*d^4)","A",0
768,1,72,0,1.683254," ","integrate(x^11/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{{\left(b^{2} c d - a b d^{2}\right)} x^{4} + a^{2} d^{2} \log\left(b x^{4} + a\right) - b^{2} c^{2} \log\left(d x^{4} + c\right)}{4 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}"," ",0,"1/4*((b^2*c*d - a*b*d^2)*x^4 + a^2*d^2*log(b*x^4 + a) - b^2*c^2*log(d*x^4 + c))/(b^3*c*d^2 - a*b^2*d^3)","A",0
769,1,42,0,0.746379," ","integrate(x^7/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\frac{a d \log\left(b x^{4} + a\right) - b c \log\left(d x^{4} + c\right)}{4 \, {\left(b^{2} c d - a b d^{2}\right)}}"," ",0,"-1/4*(a*d*log(b*x^4 + a) - b*c*log(d*x^4 + c))/(b^2*c*d - a*b*d^2)","A",0
770,1,31,0,0.422294," ","integrate(x^3/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{\log\left(b x^{4} + a\right) - \log\left(d x^{4} + c\right)}{4 \, {\left(b c - a d\right)}}"," ",0,"1/4*(log(b*x^4 + a) - log(d*x^4 + c))/(b*c - a*d)","A",0
771,1,54,0,1.997071," ","integrate(1/x/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\frac{b c \log\left(b x^{4} + a\right) - a d \log\left(d x^{4} + c\right) - 4 \, {\left(b c - a d\right)} \log\left(x\right)}{4 \, {\left(a b c^{2} - a^{2} c d\right)}}"," ",0,"-1/4*(b*c*log(b*x^4 + a) - a*d*log(d*x^4 + c) - 4*(b*c - a*d)*log(x))/(a*b*c^2 - a^2*c*d)","A",0
772,1,99,0,8.265261," ","integrate(1/x^5/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{b^{2} c^{2} x^{4} \log\left(b x^{4} + a\right) - a^{2} d^{2} x^{4} \log\left(d x^{4} + c\right) - 4 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{4} \log\left(x\right) - a b c^{2} + a^{2} c d}{4 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{4}}"," ",0,"1/4*(b^2*c^2*x^4*log(b*x^4 + a) - a^2*d^2*x^4*log(d*x^4 + c) - 4*(b^2*c^2 - a^2*d^2)*x^4*log(x) - a*b*c^2 + a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^4)","A",0
773,1,576,0,2.635432," ","integrate(x^13/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{6} - 3 \, a^{2} d^{2} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} + 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right) - 3 \, b^{2} c^{2} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} - 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right) - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{12 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}, \frac{2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{6} - 6 \, a^{2} d^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) - 3 \, b^{2} c^{2} \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} - 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right) - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{12 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}, \frac{2 \, {\left(b^{2} c d - a b d^{2}\right)} x^{6} + 6 \, b^{2} c^{2} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right) - 3 \, a^{2} d^{2} \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} + 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right) - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{12 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}, \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{6} - 3 \, a^{2} d^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) + 3 \, b^{2} c^{2} \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right) - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{2}}{6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)}}\right]"," ",0,"[1/12*(2*(b^2*c*d - a*b*d^2)*x^6 - 3*a^2*d^2*sqrt(-a/b)*log((b*x^4 + 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)) - 3*b^2*c^2*sqrt(-c/d)*log((d*x^4 - 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)) - 6*(b^2*c^2 - a^2*d^2)*x^2)/(b^3*c*d^2 - a*b^2*d^3), 1/12*(2*(b^2*c*d - a*b*d^2)*x^6 - 6*a^2*d^2*sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) - 3*b^2*c^2*sqrt(-c/d)*log((d*x^4 - 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)) - 6*(b^2*c^2 - a^2*d^2)*x^2)/(b^3*c*d^2 - a*b^2*d^3), 1/12*(2*(b^2*c*d - a*b*d^2)*x^6 + 6*b^2*c^2*sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c) - 3*a^2*d^2*sqrt(-a/b)*log((b*x^4 + 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)) - 6*(b^2*c^2 - a^2*d^2)*x^2)/(b^3*c*d^2 - a*b^2*d^3), 1/6*((b^2*c*d - a*b*d^2)*x^6 - 3*a^2*d^2*sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) + 3*b^2*c^2*sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c) - 3*(b^2*c^2 - a^2*d^2)*x^2)/(b^3*c*d^2 - a*b^2*d^3)]","A",0
774,1,416,0,0.793072," ","integrate(x^9/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[-\frac{a d \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} - 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right) + b c \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} + 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right) - 2 \, {\left(b c - a d\right)} x^{2}}{4 \, {\left(b^{2} c d - a b d^{2}\right)}}, \frac{2 \, a d \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) - b c \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} + 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right) + 2 \, {\left(b c - a d\right)} x^{2}}{4 \, {\left(b^{2} c d - a b d^{2}\right)}}, -\frac{2 \, b c \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right) + a d \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} - 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right) - 2 \, {\left(b c - a d\right)} x^{2}}{4 \, {\left(b^{2} c d - a b d^{2}\right)}}, \frac{a d \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) - b c \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right) + {\left(b c - a d\right)} x^{2}}{2 \, {\left(b^{2} c d - a b d^{2}\right)}}\right]"," ",0,"[-1/4*(a*d*sqrt(-a/b)*log((b*x^4 - 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)) + b*c*sqrt(-c/d)*log((d*x^4 + 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)) - 2*(b*c - a*d)*x^2)/(b^2*c*d - a*b*d^2), 1/4*(2*a*d*sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) - b*c*sqrt(-c/d)*log((d*x^4 + 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)) + 2*(b*c - a*d)*x^2)/(b^2*c*d - a*b*d^2), -1/4*(2*b*c*sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c) + a*d*sqrt(-a/b)*log((b*x^4 - 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)) - 2*(b*c - a*d)*x^2)/(b^2*c*d - a*b*d^2), 1/2*(a*d*sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) - b*c*sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c) + (b*c - a*d)*x^2)/(b^2*c*d - a*b*d^2)]","A",0
775,1,325,0,0.494025," ","integrate(x^5/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} + 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right) + \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} - 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right)}{4 \, {\left(b c - a d\right)}}, -\frac{2 \, \sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) + \sqrt{-\frac{c}{d}} \log\left(\frac{d x^{4} - 2 \, d x^{2} \sqrt{-\frac{c}{d}} - c}{d x^{4} + c}\right)}{4 \, {\left(b c - a d\right)}}, \frac{2 \, \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right) - \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{4} + 2 \, b x^{2} \sqrt{-\frac{a}{b}} - a}{b x^{4} + a}\right)}{4 \, {\left(b c - a d\right)}}, -\frac{\sqrt{\frac{a}{b}} \arctan\left(\frac{b x^{2} \sqrt{\frac{a}{b}}}{a}\right) - \sqrt{\frac{c}{d}} \arctan\left(\frac{d x^{2} \sqrt{\frac{c}{d}}}{c}\right)}{2 \, {\left(b c - a d\right)}}\right]"," ",0,"[-1/4*(sqrt(-a/b)*log((b*x^4 + 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)) + sqrt(-c/d)*log((d*x^4 - 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)))/(b*c - a*d), -1/4*(2*sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) + sqrt(-c/d)*log((d*x^4 - 2*d*x^2*sqrt(-c/d) - c)/(d*x^4 + c)))/(b*c - a*d), 1/4*(2*sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c) - sqrt(-a/b)*log((b*x^4 + 2*b*x^2*sqrt(-a/b) - a)/(b*x^4 + a)))/(b*c - a*d), -1/2*(sqrt(a/b)*arctan(b*x^2*sqrt(a/b)/a) - sqrt(c/d)*arctan(d*x^2*sqrt(c/d)/c))/(b*c - a*d)]","A",0
776,1,325,0,0.499801," ","integrate(x/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} - 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right) + \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} + 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right)}{4 \, {\left(b c - a d\right)}}, \frac{2 \, \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right) - \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} - 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right)}{4 \, {\left(b c - a d\right)}}, -\frac{2 \, \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) + \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} + 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right)}{4 \, {\left(b c - a d\right)}}, -\frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) - \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right)}{2 \, {\left(b c - a d\right)}}\right]"," ",0,"[-1/4*(sqrt(-b/a)*log((b*x^4 - 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)) + sqrt(-d/c)*log((d*x^4 + 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)))/(b*c - a*d), 1/4*(2*sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)) - sqrt(-b/a)*log((b*x^4 - 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)))/(b*c - a*d), -1/4*(2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) + sqrt(-d/c)*log((d*x^4 + 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)))/(b*c - a*d), -1/2*(sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) - sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)))/(b*c - a*d)]","A",0
777,1,432,0,0.881858," ","integrate(1/x^3/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[-\frac{b c x^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} + 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right) + a d x^{2} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} - 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right) + 2 \, b c - 2 \, a d}{4 \, {\left(a b c^{2} - a^{2} c d\right)} x^{2}}, -\frac{2 \, a d x^{2} \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right) + b c x^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} + 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right) + 2 \, b c - 2 \, a d}{4 \, {\left(a b c^{2} - a^{2} c d\right)} x^{2}}, \frac{2 \, b c x^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) - a d x^{2} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} - 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right) - 2 \, b c + 2 \, a d}{4 \, {\left(a b c^{2} - a^{2} c d\right)} x^{2}}, \frac{b c x^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) - a d x^{2} \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right) - b c + a d}{2 \, {\left(a b c^{2} - a^{2} c d\right)} x^{2}}\right]"," ",0,"[-1/4*(b*c*x^2*sqrt(-b/a)*log((b*x^4 + 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)) + a*d*x^2*sqrt(-d/c)*log((d*x^4 - 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)) + 2*b*c - 2*a*d)/((a*b*c^2 - a^2*c*d)*x^2), -1/4*(2*a*d*x^2*sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)) + b*c*x^2*sqrt(-b/a)*log((b*x^4 + 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)) + 2*b*c - 2*a*d)/((a*b*c^2 - a^2*c*d)*x^2), 1/4*(2*b*c*x^2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) - a*d*x^2*sqrt(-d/c)*log((d*x^4 - 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)) - 2*b*c + 2*a*d)/((a*b*c^2 - a^2*c*d)*x^2), 1/2*(b*c*x^2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) - a*d*x^2*sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)) - b*c + a*d)/((a*b*c^2 - a^2*c*d)*x^2)]","A",0
778,1,592,0,3.446706," ","integrate(1/x^7/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left[-\frac{3 \, b^{2} c^{2} x^{6} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} - 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right) + 3 \, a^{2} d^{2} x^{6} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} + 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right) - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{4} + 2 \, a b c^{2} - 2 \, a^{2} c d}{12 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{6}}, \frac{6 \, a^{2} d^{2} x^{6} \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right) - 3 \, b^{2} c^{2} x^{6} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{4} - 2 \, a x^{2} \sqrt{-\frac{b}{a}} - a}{b x^{4} + a}\right) + 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{4} - 2 \, a b c^{2} + 2 \, a^{2} c d}{12 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{6}}, -\frac{6 \, b^{2} c^{2} x^{6} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) + 3 \, a^{2} d^{2} x^{6} \sqrt{-\frac{d}{c}} \log\left(\frac{d x^{4} + 2 \, c x^{2} \sqrt{-\frac{d}{c}} - c}{d x^{4} + c}\right) - 6 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{4} + 2 \, a b c^{2} - 2 \, a^{2} c d}{12 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{6}}, -\frac{3 \, b^{2} c^{2} x^{6} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b x^{2}}\right) - 3 \, a^{2} d^{2} x^{6} \sqrt{\frac{d}{c}} \arctan\left(\frac{c \sqrt{\frac{d}{c}}}{d x^{2}}\right) - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x^{4} + a b c^{2} - a^{2} c d}{6 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x^{6}}\right]"," ",0,"[-1/12*(3*b^2*c^2*x^6*sqrt(-b/a)*log((b*x^4 - 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)) + 3*a^2*d^2*x^6*sqrt(-d/c)*log((d*x^4 + 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)) - 6*(b^2*c^2 - a^2*d^2)*x^4 + 2*a*b*c^2 - 2*a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^6), 1/12*(6*a^2*d^2*x^6*sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)) - 3*b^2*c^2*x^6*sqrt(-b/a)*log((b*x^4 - 2*a*x^2*sqrt(-b/a) - a)/(b*x^4 + a)) + 6*(b^2*c^2 - a^2*d^2)*x^4 - 2*a*b*c^2 + 2*a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^6), -1/12*(6*b^2*c^2*x^6*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) + 3*a^2*d^2*x^6*sqrt(-d/c)*log((d*x^4 + 2*c*x^2*sqrt(-d/c) - c)/(d*x^4 + c)) - 6*(b^2*c^2 - a^2*d^2)*x^4 + 2*a*b*c^2 - 2*a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^6), -1/6*(3*b^2*c^2*x^6*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*x^2)) - 3*a^2*d^2*x^6*sqrt(d/c)*arctan(c*sqrt(d/c)/(d*x^2)) - 3*(b^2*c^2 - a^2*d^2)*x^4 + a*b*c^2 - a^2*c*d)/((a^2*b*c^3 - a^3*c^2*d)*x^6)]","A",0
779,1,1378,0,0.721617," ","integrate(x^8/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\frac{4 \, \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \arctan\left(\frac{{\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{3}{4}} x - {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{a^{2} x^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \sqrt{-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}}}{a^{2}}}}{a^{4}}\right) - 4 \, \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \arctan\left(\frac{{\left(b^{3} c^{3} d^{4} - 3 \, a b^{2} c^{2} d^{5} + 3 \, a^{2} b c d^{6} - a^{3} d^{7}\right)} \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{3}{4}} x - {\left(b^{3} c^{3} d^{4} - 3 \, a b^{2} c^{2} d^{5} + 3 \, a^{2} b c d^{6} - a^{3} d^{7}\right)} \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{3}{4}} \sqrt{\frac{c^{2} x^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \sqrt{-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}}}{c^{2}}}}{c^{4}}\right) - \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a x + \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b^{2} c - a b d\right)}\right) + \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} b d \log\left(a x - \left(-\frac{a^{5}}{b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b^{2} c - a b d\right)}\right) + \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \log\left(c x + \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} {\left(b c d - a d^{2}\right)}\right) - \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} b d \log\left(c x - \left(-\frac{c^{5}}{b^{4} c^{4} d^{5} - 4 \, a b^{3} c^{3} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}}\right)^{\frac{1}{4}} {\left(b c d - a d^{2}\right)}\right) - 4 \, x}{4 \, b d}"," ",0,"-1/4*(4*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*arctan(((b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(3/4)*x - (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(3/4)*sqrt((a^2*x^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*sqrt(-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4)))/a^2))/a^4) - 4*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*arctan(((b^3*c^3*d^4 - 3*a*b^2*c^2*d^5 + 3*a^2*b*c*d^6 - a^3*d^7)*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(3/4)*x - (b^3*c^3*d^4 - 3*a*b^2*c^2*d^5 + 3*a^2*b*c*d^6 - a^3*d^7)*(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(3/4)*sqrt((c^2*x^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*sqrt(-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9)))/c^2))/c^4) - (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*log(a*x + (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*(b^2*c - a*b*d)) + (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*b*d*log(a*x - (-a^5/(b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4))^(1/4)*(b^2*c - a*b*d)) + (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*log(c*x + (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*(b*c*d - a*d^2)) - (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*b*d*log(c*x - (-c^5/(b^4*c^4*d^5 - 4*a*b^3*c^3*d^6 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9))^(1/4)*(b*c*d - a*d^2)) - 4*x)/(b*d)","B",0
780,1,1358,0,0.538131," ","integrate(x^6/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{2} c - a b d\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} x - {\left(b^{2} c - a b d\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \sqrt{\frac{a x^{2} - {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} \sqrt{-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}}}{a}}}{a}\right) + \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b c d - a d^{2}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} x - {\left(b c d - a d^{2}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \sqrt{\frac{c x^{2} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sqrt{-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}}}{c}}}{c}\right) - \frac{1}{4} \, \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(a^{2} x + {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(a^{2} x - {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \left(-\frac{a^{3}}{b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{2} x + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{3}{4}}\right) - \frac{1}{4} \, \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{1}{4}} \log\left(c^{2} x - {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \left(-\frac{c^{3}}{b^{4} c^{4} d^{3} - 4 \, a b^{3} c^{3} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{5} - 4 \, a^{3} b c d^{6} + a^{4} d^{7}}\right)^{\frac{3}{4}}\right)"," ",0,"-(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*arctan(((b^2*c - a*b*d)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*x - (b^2*c - a*b*d)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*sqrt((a*x^2 - (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*sqrt(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)))/a))/a) + (-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*arctan(((b*c*d - a*d^2)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*x - (b*c*d - a*d^2)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*sqrt((c*x^2 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sqrt(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7)))/c))/c) - 1/4*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*log(a^2*x + (b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(3/4)) + 1/4*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(1/4)*log(a^2*x - (b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*(-a^3/(b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4))^(3/4)) + 1/4*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*log(c^2*x + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(3/4)) - 1/4*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(1/4)*log(c^2*x - (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*(-c^3/(b^4*c^4*d^3 - 4*a*b^3*c^3*d^4 + 6*a^2*b^2*c^2*d^5 - 4*a^3*b*c*d^6 + a^4*d^7))^(3/4))","B",0
781,1,1238,0,0.469521," ","integrate(x^4/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{3}{4}} - {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} \sqrt{x^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}}} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{3}{4}}}{a}\right) - \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{3}{4}} - {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \sqrt{x^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}}} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{3}{4}}}{c}\right) - \frac{1}{4} \, \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \log\left({\left(b c - a d\right)} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} + x\right) + \frac{1}{4} \, \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - a d\right)} \left(-\frac{a}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}}\right)^{\frac{1}{4}} + x\right) + \frac{1}{4} \, \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \log\left({\left(b c - a d\right)} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} \log\left(-{\left(b c - a d\right)} \left(-\frac{c}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}}\right)^{\frac{1}{4}} + x\right)"," ",0,"(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*arctan(((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(3/4) - (b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*sqrt(x^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)))*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(3/4))/a) - (-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*arctan(((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*x*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(3/4) - (b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*sqrt(x^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)))*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(3/4))/c) - 1/4*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*log((b*c - a*d)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4) + x) + 1/4*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4)*log(-(b*c - a*d)*(-a/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4))^(1/4) + x) + 1/4*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*log((b*c - a*d)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4) + x) - 1/4*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4)*log(-(b*c - a*d)*(-c/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5))^(1/4) + x)","B",0
782,1,1258,0,0.501626," ","integrate(x^2/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \arctan\left({\left(b c - a d\right)} x \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} \sqrt{\frac{b x^{2} - {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}}}{b}} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}}\right) - \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \arctan\left({\left(b c - a d\right)} x \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} - {\left(b c - a d\right)} \sqrt{\frac{d x^{2} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}}}{d}} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \log\left(b x + {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{3}{4}}\right) - \frac{1}{4} \, \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{1}{4}} \log\left(b x - {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \left(-\frac{b}{a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}}\right)^{\frac{3}{4}}\right) - \frac{1}{4} \, \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \log\left(d x + {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{1}{4}} \log\left(d x - {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \left(-\frac{d}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}}\right)^{\frac{3}{4}}\right)"," ",0,"(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*arctan((b*c - a*d)*x*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4) - (b*c - a*d)*sqrt((b*x^2 - (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4)))/b)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)) - (-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*arctan((b*c - a*d)*x*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4) - (b*c - a*d)*sqrt((d*x^2 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4)))/d)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)) + 1/4*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*log(b*x + (a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(3/4)) - 1/4*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(1/4)*log(b*x - (a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(-b/(a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4))^(3/4)) - 1/4*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*log(d*x + (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(3/4)) + 1/4*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(1/4)*log(d*x - (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(-d/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4))^(3/4))","B",0
783,1,1356,0,0.627217," ","integrate(1/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} x - {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{b^{2} x^{2} + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}}}{b^{2}}}}{b^{2}}\right) + \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} x - {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{d^{2} x^{2} + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \sqrt{-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}}}{d^{2}}}}{d^{2}}\right) + \frac{1}{4} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b x + {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{4} \, \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}} \log\left(b x - {\left(a b c - a^{2} d\right)} \left(-\frac{b^{3}}{a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}}\right)^{\frac{1}{4}}\right) - \frac{1}{4} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d x + {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right) + \frac{1}{4} \, \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}} \log\left(d x - {\left(b c^{2} - a c d\right)} \left(-\frac{d^{3}}{b^{4} c^{7} - 4 \, a b^{3} c^{6} d + 6 \, a^{2} b^{2} c^{5} d^{2} - 4 \, a^{3} b c^{4} d^{3} + a^{4} c^{3} d^{4}}\right)^{\frac{1}{4}}\right)"," ",0,"-(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*arctan(((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4)*x - (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(3/4)*sqrt((b^2*x^2 + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)))/b^2))/b^2) + (-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*arctan(((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4)*x - (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(3/4)*sqrt((d^2*x^2 + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*sqrt(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4)))/d^2))/d^2) + 1/4*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*x + (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/4*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)*log(b*x - (a*b*c - a^2*d)*(-b^3/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4))^(1/4)) - 1/4*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*x + (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)) + 1/4*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4)*log(d*x - (b*c^2 - a*c*d)*(-d^3/(b^4*c^7 - 4*a*b^3*c^6*d + 6*a^2*b^2*c^5*d^2 - 4*a^3*b*c^4*d^3 + a^4*c^3*d^4))^(1/4))","B",0
784,1,1395,0,0.893969," ","integrate(1/x^2/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","-\frac{4 \, \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \arctan\left(\frac{\left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} {\left(a b c - a^{2} d\right)} x - \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} {\left(a b c - a^{2} d\right)} \sqrt{\frac{b^{3} x^{2} - {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} \sqrt{-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}}}{b^{3}}}}{b}\right) - 4 \, \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \arctan\left(\frac{\left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d\right)} x - \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{2} - a c d\right)} \sqrt{\frac{d^{3} x^{2} - {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} \sqrt{-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}}}{d^{3}}}}{d}\right) + \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(b^{4} x + {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3}\right)} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{3}{4}}\right) - \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(b^{4} x - {\left(a^{4} b^{3} c^{3} - 3 \, a^{5} b^{2} c^{2} d + 3 \, a^{6} b c d^{2} - a^{7} d^{3}\right)} \left(-\frac{b^{5}}{a^{5} b^{4} c^{4} - 4 \, a^{6} b^{3} c^{3} d + 6 \, a^{7} b^{2} c^{2} d^{2} - 4 \, a^{8} b c d^{3} + a^{9} d^{4}}\right)^{\frac{3}{4}}\right) - \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(d^{4} x + {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3}\right)} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{3}{4}}\right) + \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{1}{4}} a c x \log\left(d^{4} x - {\left(b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c^{5} d^{2} - a^{3} c^{4} d^{3}\right)} \left(-\frac{d^{5}}{b^{4} c^{9} - 4 \, a b^{3} c^{8} d + 6 \, a^{2} b^{2} c^{7} d^{2} - 4 \, a^{3} b c^{6} d^{3} + a^{4} c^{5} d^{4}}\right)^{\frac{3}{4}}\right) + 4}{4 \, a c x}"," ",0,"-1/4*(4*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*arctan(((-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*(a*b*c - a^2*d)*x - (-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*(a*b*c - a^2*d)*sqrt((b^3*x^2 - (a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*sqrt(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4)))/b^3))/b) - 4*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*arctan(((-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*(b*c^2 - a*c*d)*x - (-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*(b*c^2 - a*c*d)*sqrt((d^3*x^2 - (b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*sqrt(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4)))/d^3))/d) + (-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*log(b^4*x + (a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3)*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(3/4)) - (-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(1/4)*a*c*x*log(b^4*x - (a^4*b^3*c^3 - 3*a^5*b^2*c^2*d + 3*a^6*b*c*d^2 - a^7*d^3)*(-b^5/(a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3 + a^9*d^4))^(3/4)) - (-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*log(d^4*x + (b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3)*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(3/4)) + (-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(1/4)*a*c*x*log(d^4*x - (b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c^5*d^2 - a^3*c^4*d^3)*(-d^5/(b^4*c^9 - 4*a*b^3*c^8*d + 6*a^2*b^2*c^7*d^2 - 4*a^3*b*c^6*d^3 + a^4*c^5*d^4))^(3/4)) + 4)/(a*c*x)","B",0
785,1,1415,0,5.399481," ","integrate(1/x^4/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{12 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \arctan\left(\frac{{\left(a^{5} b^{3} c^{3} - 3 \, a^{6} b^{2} c^{2} d + 3 \, a^{7} b c d^{2} - a^{8} d^{3}\right)} \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{3}{4}} x - {\left(a^{5} b^{3} c^{3} - 3 \, a^{6} b^{2} c^{2} d + 3 \, a^{7} b c d^{2} - a^{8} d^{3}\right)} \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{b^{4} x^{2} + {\left(a^{4} b^{2} c^{2} - 2 \, a^{5} b c d + a^{6} d^{2}\right)} \sqrt{-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}}}{b^{4}}}}{b^{5}}\right) - 12 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \arctan\left(\frac{{\left(b^{3} c^{8} - 3 \, a b^{2} c^{7} d + 3 \, a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3}\right)} \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{3}{4}} x - {\left(b^{3} c^{8} - 3 \, a b^{2} c^{7} d + 3 \, a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3}\right)} \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{3}{4}} \sqrt{\frac{d^{4} x^{2} + {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)} \sqrt{-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}}}{d^{4}}}}{d^{5}}\right) - 3 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \log\left(b^{2} x + \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)}\right) + 3 \, \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \log\left(b^{2} x - \left(-\frac{b^{7}}{a^{7} b^{4} c^{4} - 4 \, a^{8} b^{3} c^{3} d + 6 \, a^{9} b^{2} c^{2} d^{2} - 4 \, a^{10} b c d^{3} + a^{11} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)}\right) + 3 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \log\left(d^{2} x + \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)}\right) - 3 \, \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} a c x^{3} \log\left(d^{2} x - \left(-\frac{d^{7}}{b^{4} c^{11} - 4 \, a b^{3} c^{10} d + 6 \, a^{2} b^{2} c^{9} d^{2} - 4 \, a^{3} b c^{8} d^{3} + a^{4} c^{7} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)}\right) - 4}{12 \, a c x^{3}}"," ",0,"1/12*(12*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^3*arctan(((a^5*b^3*c^3 - 3*a^6*b^2*c^2*d + 3*a^7*b*c*d^2 - a^8*d^3)*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(3/4)*x - (a^5*b^3*c^3 - 3*a^6*b^2*c^2*d + 3*a^7*b*c*d^2 - a^8*d^3)*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(3/4)*sqrt((b^4*x^2 + (a^4*b^2*c^2 - 2*a^5*b*c*d + a^6*d^2)*sqrt(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4)))/b^4))/b^5) - 12*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^3*arctan(((b^3*c^8 - 3*a*b^2*c^7*d + 3*a^2*b*c^6*d^2 - a^3*c^5*d^3)*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(3/4)*x - (b^3*c^8 - 3*a*b^2*c^7*d + 3*a^2*b*c^6*d^2 - a^3*c^5*d^3)*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(3/4)*sqrt((d^4*x^2 + (b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2)*sqrt(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4)))/d^4))/d^5) - 3*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^3*log(b^2*x + (-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*(a^2*b*c - a^3*d)) + 3*(-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*a*c*x^3*log(b^2*x - (-b^7/(a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3 + a^11*d^4))^(1/4)*(a^2*b*c - a^3*d)) + 3*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^3*log(d^2*x + (-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*(b*c^3 - a*c^2*d)) - 3*(-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*a*c*x^3*log(d^2*x - (-d^7/(b^4*c^11 - 4*a*b^3*c^10*d + 6*a^2*b^2*c^9*d^2 - 4*a^3*b*c^8*d^3 + a^4*c^7*d^4))^(1/4)*(b*c^3 - a*c^2*d)) - 4)/(a*c*x^3)","B",0
786,1,1456,0,9.196753," ","integrate(1/x^6/(b*x^4+a)/(d*x^4+c),x, algorithm=""fricas"")","\frac{20 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \arctan\left(\frac{\left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)} x - \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} {\left(a^{2} b c - a^{3} d\right)} \sqrt{\frac{b^{5} x^{2} - {\left(a^{5} b^{2} c^{2} - 2 \, a^{6} b c d + a^{7} d^{2}\right)} \sqrt{-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}}}{b^{5}}}}{b^{2}}\right) - 20 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \arctan\left(\frac{\left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)} x - \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} {\left(b c^{3} - a c^{2} d\right)} \sqrt{\frac{d^{5} x^{2} - {\left(b^{2} c^{7} - 2 \, a b c^{6} d + a^{2} c^{5} d^{2}\right)} \sqrt{-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}}}{d^{5}}}}{d^{2}}\right) + 5 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \log\left(b^{7} x + {\left(a^{7} b^{3} c^{3} - 3 \, a^{8} b^{2} c^{2} d + 3 \, a^{9} b c d^{2} - a^{10} d^{3}\right)} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{3}{4}}\right) - 5 \, \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \log\left(b^{7} x - {\left(a^{7} b^{3} c^{3} - 3 \, a^{8} b^{2} c^{2} d + 3 \, a^{9} b c d^{2} - a^{10} d^{3}\right)} \left(-\frac{b^{9}}{a^{9} b^{4} c^{4} - 4 \, a^{10} b^{3} c^{3} d + 6 \, a^{11} b^{2} c^{2} d^{2} - 4 \, a^{12} b c d^{3} + a^{13} d^{4}}\right)^{\frac{3}{4}}\right) - 5 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \log\left(d^{7} x + {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3}\right)} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{3}{4}}\right) + 5 \, \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{1}{4}} a^{2} c^{2} x^{5} \log\left(d^{7} x - {\left(b^{3} c^{10} - 3 \, a b^{2} c^{9} d + 3 \, a^{2} b c^{8} d^{2} - a^{3} c^{7} d^{3}\right)} \left(-\frac{d^{9}}{b^{4} c^{13} - 4 \, a b^{3} c^{12} d + 6 \, a^{2} b^{2} c^{11} d^{2} - 4 \, a^{3} b c^{10} d^{3} + a^{4} c^{9} d^{4}}\right)^{\frac{3}{4}}\right) + 20 \, {\left(b c + a d\right)} x^{4} - 4 \, a c}{20 \, a^{2} c^{2} x^{5}}"," ",0,"1/20*(20*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^5*arctan(((-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*(a^2*b*c - a^3*d)*x - (-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*(a^2*b*c - a^3*d)*sqrt((b^5*x^2 - (a^5*b^2*c^2 - 2*a^6*b*c*d + a^7*d^2)*sqrt(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4)))/b^5))/b^2) - 20*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^5*arctan(((-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*(b*c^3 - a*c^2*d)*x - (-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*(b*c^3 - a*c^2*d)*sqrt((d^5*x^2 - (b^2*c^7 - 2*a*b*c^6*d + a^2*c^5*d^2)*sqrt(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4)))/d^5))/d^2) + 5*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^5*log(b^7*x + (a^7*b^3*c^3 - 3*a^8*b^2*c^2*d + 3*a^9*b*c*d^2 - a^10*d^3)*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(3/4)) - 5*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(1/4)*a^2*c^2*x^5*log(b^7*x - (a^7*b^3*c^3 - 3*a^8*b^2*c^2*d + 3*a^9*b*c*d^2 - a^10*d^3)*(-b^9/(a^9*b^4*c^4 - 4*a^10*b^3*c^3*d + 6*a^11*b^2*c^2*d^2 - 4*a^12*b*c*d^3 + a^13*d^4))^(3/4)) - 5*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^5*log(d^7*x + (b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3)*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(3/4)) + 5*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(1/4)*a^2*c^2*x^5*log(d^7*x - (b^3*c^10 - 3*a*b^2*c^9*d + 3*a^2*b*c^8*d^2 - a^3*c^7*d^3)*(-d^9/(b^4*c^13 - 4*a*b^3*c^12*d + 6*a^2*b^2*c^11*d^2 - 4*a^3*b*c^10*d^3 + a^4*c^9*d^4))^(3/4)) + 20*(b*c + a*d)*x^4 - 4*a*c)/(a^2*c^2*x^5)","B",0
787,1,195,0,0.432754," ","integrate(x^7*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{3 \, a d \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{4} + a}\right) + 2 \, {\left(b d x^{4} + b c - 3 \, a d\right)} \sqrt{d x^{4} + c}}{12 \, b^{2} d}, \frac{3 \, a d \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{4} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(b d x^{4} + b c - 3 \, a d\right)} \sqrt{d x^{4} + c}}{6 \, b^{2} d}\right]"," ",0,"[1/12*(3*a*d*sqrt((b*c - a*d)/b)*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*b*sqrt((b*c - a*d)/b))/(b*x^4 + a)) + 2*(b*d*x^4 + b*c - 3*a*d)*sqrt(d*x^4 + c))/(b^2*d), 1/6*(3*a*d*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^4 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (b*d*x^4 + b*c - 3*a*d)*sqrt(d*x^4 + c))/(b^2*d)]","A",0
788,1,714,0,0.557311," ","integrate(x^5*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{4} + c} b d x^{2} - {\left(b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right) + \sqrt{-a b c + a^{2} d} d \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{8 \, b^{2} d}, \frac{2 \, \sqrt{d x^{4} + c} b d x^{2} - 2 \, {\left(b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) + \sqrt{-a b c + a^{2} d} d \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{8 \, b^{2} d}, \frac{2 \, \sqrt{d x^{4} + c} b d x^{2} - 2 \, \sqrt{a b c - a^{2} d} d \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right) - {\left(b c - 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{8 \, b^{2} d}, \frac{\sqrt{d x^{4} + c} b d x^{2} - {\left(b c - 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) - \sqrt{a b c - a^{2} d} d \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right)}{4 \, b^{2} d}\right]"," ",0,"[1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 - (b*c - 2*a*d)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c) + sqrt(-a*b*c + a^2*d)*d*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(b^2*d), 1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 - 2*(b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) + sqrt(-a*b*c + a^2*d)*d*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(b^2*d), 1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 - 2*sqrt(a*b*c - a^2*d)*d*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)) - (b*c - 2*a*d)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(b^2*d), 1/4*(sqrt(d*x^4 + c)*b*d*x^2 - (b*c - 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) - sqrt(a*b*c - a^2*d)*d*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)))/(b^2*d)]","A",0
789,1,156,0,0.446313," ","integrate(x^3*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{4} + a}\right) + 2 \, \sqrt{d x^{4} + c}}{4 \, b}, -\frac{\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{4} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - \sqrt{d x^{4} + c}}{2 \, b}\right]"," ",0,"[1/4*(sqrt((b*c - a*d)/b)*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*b*sqrt((b*c - a*d)/b))/(b*x^4 + a)) + 2*sqrt(d*x^4 + c))/b, -1/2*(sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^4 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - sqrt(d*x^4 + c))/b]","A",0
790,1,612,0,0.493982," ","integrate(x*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right) + \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(a b c - 2 \, a^{2} d\right)} x^{6} - a^{2} c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{8 \, b}, -\frac{4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) - \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(a b c - 2 \, a^{2} d\right)} x^{6} - a^{2} c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{8 \, b}, \frac{\sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{6} + {\left(b c^{2} - a c d\right)} x^{2}\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{4 \, b}, -\frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) - \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{6} + {\left(b c^{2} - a c d\right)} x^{2}\right)}}\right)}{4 \, b}\right]"," ",0,"[1/8*(2*sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c) + sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((a*b*c - 2*a^2*d)*x^6 - a^2*c*x^2)*sqrt(d*x^4 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/b, -1/8*(4*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) - sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((a*b*c - 2*a^2*d)*x^6 - a^2*c*x^2)*sqrt(d*x^4 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/b, 1/4*(sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^6 + (b*c^2 - a*c*d)*x^2)) + sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/b, -1/4*(2*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) - sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^6 + (b*c^2 - a*c*d)*x^2)))/b]","A",0
791,1,383,0,0.464044," ","integrate((d*x^4+c)^(1/2)/x/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{4} + a}\right) + \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{4 \, a}, \frac{2 \, \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{4} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{4 \, a}, \frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) + \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} b \sqrt{\frac{b c - a d}{b}}}{b x^{4} + a}\right)}{4 \, a}, \frac{\sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x^{4} + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right)}{2 \, a}\right]"," ",0,"[1/4*(sqrt((b*c - a*d)/b)*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*b*sqrt((b*c - a*d)/b))/(b*x^4 + a)) + sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/a, 1/4*(2*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^4 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/a, 1/4*(2*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) + sqrt((b*c - a*d)/b)*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*b*sqrt((b*c - a*d)/b))/(b*x^4 + a)))/a, 1/2*(sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x^4 + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c))/a]","A",0
792,1,281,0,0.455344," ","integrate((d*x^4+c)^(1/2)/x^3/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{x^{2} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(a b c - 2 \, a^{2} d\right)} x^{6} - a^{2} c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) - 4 \, \sqrt{d x^{4} + c}}{8 \, a x^{2}}, -\frac{x^{2} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{6} + {\left(b c^{2} - a c d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{d x^{4} + c}}{4 \, a x^{2}}\right]"," ",0,"[1/8*(x^2*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((a*b*c - 2*a^2*d)*x^6 - a^2*c*x^2)*sqrt(d*x^4 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^8 + 2*a*b*x^4 + a^2)) - 4*sqrt(d*x^4 + c))/(a*x^2), -1/4*(x^2*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^6 + (b*c^2 - a*c*d)*x^2)) + 2*sqrt(d*x^4 + c))/(a*x^2)]","A",0
793,1,513,0,0.470623," ","integrate((d*x^4+c)^(1/2)/x^5/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b^{2} c - a b d} c x^{4} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) - {\left(2 \, b c - a d\right)} \sqrt{c} x^{4} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) - 2 \, \sqrt{d x^{4} + c} a c}{8 \, a^{2} c x^{4}}, \frac{4 \, \sqrt{-b^{2} c + a b d} c x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) - {\left(2 \, b c - a d\right)} \sqrt{c} x^{4} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) - 2 \, \sqrt{d x^{4} + c} a c}{8 \, a^{2} c x^{4}}, -\frac{{\left(2 \, b c - a d\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) - \sqrt{b^{2} c - a b d} c x^{4} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + \sqrt{d x^{4} + c} a c}{4 \, a^{2} c x^{4}}, \frac{2 \, \sqrt{-b^{2} c + a b d} c x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) - {\left(2 \, b c - a d\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{4} + c} a c}{4 \, a^{2} c x^{4}}\right]"," ",0,"[1/8*(2*sqrt(b^2*c - a*b*d)*c*x^4*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) - (2*b*c - a*d)*sqrt(c)*x^4*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) - 2*sqrt(d*x^4 + c)*a*c)/(a^2*c*x^4), 1/8*(4*sqrt(-b^2*c + a*b*d)*c*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) - (2*b*c - a*d)*sqrt(c)*x^4*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) - 2*sqrt(d*x^4 + c)*a*c)/(a^2*c*x^4), -1/4*((2*b*c - a*d)*sqrt(-c)*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) - sqrt(b^2*c - a*b*d)*c*x^4*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + sqrt(d*x^4 + c)*a*c)/(a^2*c*x^4), 1/4*(2*sqrt(-b^2*c + a*b*d)*c*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) - (2*b*c - a*d)*sqrt(-c)*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) - sqrt(d*x^4 + c)*a*c)/(a^2*c*x^4)]","A",0
794,1,329,0,0.520785," ","integrate((d*x^4+c)^(1/2)/x^7/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{3 \, b c x^{6} \sqrt{-\frac{b c - a d}{a}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(a b c - 2 \, a^{2} d\right)} x^{6} - a^{2} c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{b c - a d}{a}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, {\left({\left(3 \, b c - a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c}}{24 \, a^{2} c x^{6}}, \frac{3 \, b c x^{6} \sqrt{\frac{b c - a d}{a}} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{b c - a d}{a}}}{2 \, {\left({\left(b c d - a d^{2}\right)} x^{6} + {\left(b c^{2} - a c d\right)} x^{2}\right)}}\right) + 2 \, {\left({\left(3 \, b c - a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c}}{12 \, a^{2} c x^{6}}\right]"," ",0,"[1/24*(3*b*c*x^6*sqrt(-(b*c - a*d)/a)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((a*b*c - 2*a^2*d)*x^6 - a^2*c*x^2)*sqrt(d*x^4 + c)*sqrt(-(b*c - a*d)/a))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*((3*b*c - a*d)*x^4 - a*c)*sqrt(d*x^4 + c))/(a^2*c*x^6), 1/12*(3*b*c*x^6*sqrt((b*c - a*d)/a)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt((b*c - a*d)/a)/((b*c*d - a*d^2)*x^6 + (b*c^2 - a*c*d)*x^2)) + 2*((3*b*c - a*d)*x^4 - a*c)*sqrt(d*x^4 + c))/(a^2*c*x^6)]","A",0
795,-1,0,0,0.000000," ","integrate(x^6*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,-1,0,0,0.000000," ","integrate(x^4*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,-1,0,0,0.000000," ","integrate(x^2*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
798,-1,0,0,0.000000," ","integrate((d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,-1,0,0,0.000000," ","integrate((d*x^4+c)^(1/2)/x^2/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,-1,0,0,0.000000," ","integrate((d*x^4+c)^(1/2)/x^4/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
801,0,0,0,0.712092," ","integrate((e*x)^(3/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \sqrt{e x} e x}{b x^{4} + a}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*sqrt(e*x)*e*x/(b*x^4 + a), x)","F",0
802,-1,0,0,0.000000," ","integrate((e*x)^(1/2)*(d*x^4+c)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((d*x^4+c)^(1/2)/(e*x)^(1/2)/(b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,0,0,0,0.621555," ","integrate((d*x^4+c)^(1/2)/(e*x)^(3/2)/(b*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \sqrt{e x}}{b e^{2} x^{6} + a e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*sqrt(e*x)/(b*e^2*x^6 + a*e^2*x^2), x)","F",0
805,1,289,0,0.716793," ","integrate(x^11/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} c - a b d} a^{2} d^{2} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) - 2 \, {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{12 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}, \frac{3 \, \sqrt{-b^{2} c + a b d} a^{2} d^{2} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) - {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2} - {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{6 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}\right]"," ",0,"[1/12*(3*sqrt(b^2*c - a*b*d)*a^2*d^2*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) - 2*(2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^4)*sqrt(d*x^4 + c))/(b^4*c*d^2 - a*b^3*d^3), 1/6*(3*sqrt(-b^2*c + a*b*d)*a^2*d^2*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) - (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2 - (b^3*c*d - a*b^2*d^2)*x^4)*sqrt(d*x^4 + c))/(b^4*c*d^2 - a*b^3*d^3)]","A",0
806,1,205,0,0.740099," ","integrate(x^7/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} a d \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + 2 \, \sqrt{d x^{4} + c} {\left(b^{2} c - a b d\right)}}{4 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}, -\frac{\sqrt{-b^{2} c + a b d} a d \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) - \sqrt{d x^{4} + c} {\left(b^{2} c - a b d\right)}}{2 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(b^2*c - a*b*d)*a*d*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + 2*sqrt(d*x^4 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2), -1/2*(sqrt(-b^2*c + a*b*d)*a*d*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) - sqrt(d*x^4 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2)]","A",0
807,1,130,0,0.693631," ","integrate(x^3/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right)}{4 \, \sqrt{b^{2} c - a b d}}, \frac{\sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right)}{2 \, {\left(b^{2} c - a b d\right)}}\right]"," ",0,"[1/4*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a))/sqrt(b^2*c - a*b*d), 1/2*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c))/(b^2*c - a*b*d)]","A",0
808,1,431,0,0.726783," ","integrate(1/x/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{4 \, a c}, \frac{2 \, c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{4 \, a c}, \frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right)}{4 \, a c}, \frac{c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right)}{2 \, a c}\right]"," ",0,"[1/4*(c*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/(a*c), 1/4*(2*c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/(a*c), 1/4*(c*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + 2*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c))/(a*c), 1/2*(c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c))/(a*c)]","A",0
809,1,565,0,0.702483," ","integrate(1/x^5/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{4} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{4} \log\left(\frac{d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) - 2 \, \sqrt{d x^{4} + c} a c}{8 \, a^{2} c^{2} x^{4}}, -\frac{4 \, b c^{2} x^{4} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) - {\left(2 \, b c + a d\right)} \sqrt{c} x^{4} \log\left(\frac{d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) + 2 \, \sqrt{d x^{4} + c} a c}{8 \, a^{2} c^{2} x^{4}}, \frac{b c^{2} x^{4} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) - {\left(2 \, b c + a d\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{4} + c} a c}{4 \, a^{2} c^{2} x^{4}}, -\frac{2 \, b c^{2} x^{4} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + {\left(2 \, b c + a d\right)} \sqrt{-c} x^{4} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{4} + c} a c}{4 \, a^{2} c^{2} x^{4}}\right]"," ",0,"[1/8*(2*b*c^2*x^4*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + (2*b*c + a*d)*sqrt(c)*x^4*log((d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) - 2*sqrt(d*x^4 + c)*a*c)/(a^2*c^2*x^4), -1/8*(4*b*c^2*x^4*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) - (2*b*c + a*d)*sqrt(c)*x^4*log((d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) + 2*sqrt(d*x^4 + c)*a*c)/(a^2*c^2*x^4), 1/4*(b*c^2*x^4*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) - (2*b*c + a*d)*sqrt(-c)*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) - sqrt(d*x^4 + c)*a*c)/(a^2*c^2*x^4), -1/4*(2*b*c^2*x^4*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + (2*b*c + a*d)*sqrt(-c)*x^4*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) + sqrt(d*x^4 + c)*a*c)/(a^2*c^2*x^4)]","A",0
810,1,739,0,0.752110," ","integrate(x^9/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{4} + c} b d x^{2} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{8 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{4} + c} b d x^{2} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 2 \, {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right)}{8 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{4} + c} b d x^{2} - 2 \, a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{8 \, b^{2} d^{2}}, \frac{\sqrt{d x^{4} + c} b d x^{2} - a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right)}{4 \, b^{2} d^{2}}\right]"," ",0,"[1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(b^2*d^2), 1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 2*(b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)))/(b^2*d^2), 1/8*(2*sqrt(d*x^4 + c)*b*d*x^2 - 2*a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(b^2*d^2), 1/4*(sqrt(d*x^4 + c)*b*d*x^2 - a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) + (b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)))/(b^2*d^2)]","A",0
811,1,632,0,0.674098," ","integrate(x^5/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 2 \, \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{8 \, b d}, \frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) - 4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right)}{8 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{4 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) - 2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right)}{4 \, b d}\right]"," ",0,"[1/8*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 2*sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(b*d), 1/8*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) - 4*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)))/(b*d), 1/4*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) + sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(b*d), 1/4*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) - 2*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)))/(b*d)]","A",0
812,1,245,0,0.505246," ","integrate(x/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{8 \, {\left(a b c - a^{2} d\right)}}, \frac{\arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right)}{4 \, \sqrt{a b c - a^{2} d}}\right]"," ",0,"[-1/8*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2))/(a*b*c - a^2*d), 1/4*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2))/sqrt(a*b*c - a^2*d)]","B",0
813,1,332,0,0.530433," ","integrate(1/x^3/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} b c x^{2} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, \sqrt{d x^{4} + c} {\left(a b c - a^{2} d\right)}}{8 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2}}, -\frac{\sqrt{a b c - a^{2} d} b c x^{2} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right) + 2 \, \sqrt{d x^{4} + c} {\left(a b c - a^{2} d\right)}}{4 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{2}}\right]"," ",0,"[-1/8*(sqrt(-a*b*c + a^2*d)*b*c*x^2*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*sqrt(d*x^4 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^2), -1/4*(sqrt(a*b*c - a^2*d)*b*c*x^2*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)) + 2*sqrt(d*x^4 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^2)]","B",0
814,1,418,0,0.543836," ","integrate(1/x^7/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a b c + a^{2} d} b^{2} c^{2} x^{6} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, {\left(a^{2} b c^{2} - a^{3} c d - {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{24 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{6}}, \frac{3 \, \sqrt{a b c - a^{2} d} b^{2} c^{2} x^{6} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d - {\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{12 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{6}}\right]"," ",0,"[-1/24*(3*sqrt(-a*b*c + a^2*d)*b^2*c^2*x^6*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*(a^2*b*c^2 - a^3*c*d - (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^4)*sqrt(d*x^4 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^6), 1/12*(3*sqrt(a*b*c - a^2*d)*b^2*c^2*x^6*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)) - 2*(a^2*b*c^2 - a^3*c*d - (3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^4)*sqrt(d*x^4 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^6)]","A",0
815,-1,0,0,0.000000," ","integrate(x^8/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate(x^4/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate(x^6/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(x^2/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,1,622,0,0.550954," ","integrate(x^15/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(6 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(6 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + 2 \, {\left(2 \, {\left(b^{5} c^{2} d - 2 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{8} - 4 \, a b^{4} c^{3} - 4 \, a^{2} b^{3} c^{2} d + 23 \, a^{3} b^{2} c d^{2} - 15 \, a^{4} b d^{3} - 2 \, {\left(2 \, b^{5} c^{3} + a b^{4} c^{2} d - 8 \, a^{2} b^{3} c d^{2} + 5 \, a^{3} b^{2} d^{3}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{24 \, {\left(a b^{6} c^{2} d^{2} - 2 \, a^{2} b^{5} c d^{3} + a^{3} b^{4} d^{4} + {\left(b^{7} c^{2} d^{2} - 2 \, a b^{6} c d^{3} + a^{2} b^{5} d^{4}\right)} x^{4}\right)}}, \frac{3 \, {\left(6 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(6 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) + {\left(2 \, {\left(b^{5} c^{2} d - 2 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{8} - 4 \, a b^{4} c^{3} - 4 \, a^{2} b^{3} c^{2} d + 23 \, a^{3} b^{2} c d^{2} - 15 \, a^{4} b d^{3} - 2 \, {\left(2 \, b^{5} c^{3} + a b^{4} c^{2} d - 8 \, a^{2} b^{3} c d^{2} + 5 \, a^{3} b^{2} d^{3}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{12 \, {\left(a b^{6} c^{2} d^{2} - 2 \, a^{2} b^{5} c d^{3} + a^{3} b^{4} d^{4} + {\left(b^{7} c^{2} d^{2} - 2 \, a b^{6} c d^{3} + a^{2} b^{5} d^{4}\right)} x^{4}\right)}}\right]"," ",0,"[1/24*(3*(6*a^3*b*c*d^2 - 5*a^4*d^3 + (6*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4)*sqrt(b^2*c - a*b*d)*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + 2*(2*(b^5*c^2*d - 2*a*b^4*c*d^2 + a^2*b^3*d^3)*x^8 - 4*a*b^4*c^3 - 4*a^2*b^3*c^2*d + 23*a^3*b^2*c*d^2 - 15*a^4*b*d^3 - 2*(2*b^5*c^3 + a*b^4*c^2*d - 8*a^2*b^3*c*d^2 + 5*a^3*b^2*d^3)*x^4)*sqrt(d*x^4 + c))/(a*b^6*c^2*d^2 - 2*a^2*b^5*c*d^3 + a^3*b^4*d^4 + (b^7*c^2*d^2 - 2*a*b^6*c*d^3 + a^2*b^5*d^4)*x^4), 1/12*(3*(6*a^3*b*c*d^2 - 5*a^4*d^3 + (6*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) + (2*(b^5*c^2*d - 2*a*b^4*c*d^2 + a^2*b^3*d^3)*x^8 - 4*a*b^4*c^3 - 4*a^2*b^3*c^2*d + 23*a^3*b^2*c*d^2 - 15*a^4*b*d^3 - 2*(2*b^5*c^3 + a*b^4*c^2*d - 8*a^2*b^3*c*d^2 + 5*a^3*b^2*d^3)*x^4)*sqrt(d*x^4 + c))/(a*b^6*c^2*d^2 - 2*a^2*b^5*c*d^3 + a^3*b^4*d^4 + (b^7*c^2*d^2 - 2*a*b^6*c*d^3 + a^2*b^5*d^4)*x^4)]","A",0
823,1,475,0,0.616309," ","integrate(x^11/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + 2 \, {\left(2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{8 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{4}\right)}}, -\frac{{\left(4 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) - {\left(2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2} + 2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{4 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{4}\right)}}\right]"," ",0,"[1/8*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^4)*sqrt(b^2*c - a*b*d)*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + 2*(2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2 + 2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4)*sqrt(d*x^4 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^4), -1/4*((4*a^2*b*c*d - 3*a^3*d^2 + (4*a*b^2*c*d - 3*a^2*b*d^2)*x^4)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) - (2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2 + 2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4)*sqrt(d*x^4 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^4)]","B",0
824,1,348,0,0.708384," ","integrate(x^7/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{4} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + 2 \, \sqrt{d x^{4} + c} {\left(a b^{2} c - a^{2} b d\right)}}{8 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{4}\right)}}, \frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{4} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) + \sqrt{d x^{4} + c} {\left(a b^{2} c - a^{2} b d\right)}}{4 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(((2*b^2*c - a*b*d)*x^4 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + 2*sqrt(d*x^4 + c)*(a*b^2*c - a^2*b*d))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^4), 1/4*(((2*b^2*c - a*b*d)*x^4 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) + sqrt(d*x^4 + c)*(a*b^2*c - a^2*b*d))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^4)]","A",0
825,1,302,0,0.720625," ","integrate(x^3/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b d x^{4} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} \sqrt{b^{2} c - a b d}}{b x^{4} + a}\right) + 2 \, \sqrt{d x^{4} + c} {\left(b^{2} c - a b d\right)}}{8 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4}\right)}}, -\frac{{\left(b d x^{4} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-b^{2} c + a b d}}{b d x^{4} + b c}\right) + \sqrt{d x^{4} + c} {\left(b^{2} c - a b d\right)}}{4 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[-1/8*((b*d*x^4 + a*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*sqrt(b^2*c - a*b*d))/(b*x^4 + a)) + 2*sqrt(d*x^4 + c)*(b^2*c - a*b*d))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4), -1/4*((b*d*x^4 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^4 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^4 + b*c)) + sqrt(d*x^4 + c)*(b^2*c - a*b*d))/(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4)]","B",0
826,1,862,0,0.681988," ","integrate(1/x/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{4} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{8 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{4}\right)}}, \frac{\sqrt{d x^{4} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right)}{4 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{4}\right)}}, \frac{2 \, \sqrt{d x^{4} + c} a b c + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d + 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right)}{8 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{4}\right)}}, \frac{\sqrt{d x^{4} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{4} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right)}{4 \, {\left(a^{3} b c^{2} - a^{4} c d + {\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(2*sqrt(d*x^4 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^4 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + 2*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^4), 1/4*(sqrt(d*x^4 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^4 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + ((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(c)*log((d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^4), 1/8*(2*sqrt(d*x^4 + c)*a*b*c + 4*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) + ((2*b^2*c^2 - 3*a*b*c*d)*x^4 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d + 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^4), 1/4*(sqrt(d*x^4 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^4 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + 2*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c))/(a^3*b*c^2 - a^4*c*d + (a^2*b^2*c^2 - a^3*b*c*d)*x^4)]","A",0
827,1,1236,0,0.914706," ","integrate(1/x^5/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{8} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{4}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{8} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{4}\right)} \sqrt{c} \log\left(\frac{d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) - 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{8} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{4}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{8} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{4}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) - {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{8} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{4}\right)} \sqrt{c} \log\left(\frac{d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{c} + 2 \, c}{x^{4}}\right) + 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{8} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{4}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{8} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{8} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{4}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{4} + 2 \, b c - a d - 2 \, \sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{4} + a}\right) + 2 \, {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{8} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{4}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{8} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{4}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{4} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{4} + b c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{8} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{4} + c} \sqrt{-c}}{c}\right) + {\left(a^{2} b c^{2} - a^{3} c d + {\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{4 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{8} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{4}\right)}}\right]"," ",0,"[1/8*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^8 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^4)*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^8 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^4)*sqrt(c)*log((d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) - 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^4)*sqrt(d*x^4 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^8 + (a^4*b*c^3 - a^5*c^2*d)*x^4), -1/8*(2*((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^8 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^4)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) - ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^8 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^4)*sqrt(c)*log((d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(c) + 2*c)/x^4) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^4)*sqrt(d*x^4 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^8 + (a^4*b*c^3 - a^5*c^2*d)*x^4), -1/8*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^8 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^4)*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^8 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^4)*sqrt(b/(b*c - a*d))*log((b*d*x^4 + 2*b*c - a*d - 2*sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^4 + a)) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^4)*sqrt(d*x^4 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^8 + (a^4*b*c^3 - a^5*c^2*d)*x^4), -1/4*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^8 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^4)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^4 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^4 + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^8 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^4)*sqrt(-c)*arctan(sqrt(d*x^4 + c)*sqrt(-c)/c) + (a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x^4)*sqrt(d*x^4 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^8 + (a^4*b*c^3 - a^5*c^2*d)*x^4)]","A",0
828,1,1386,0,1.937619," ","integrate(x^13/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right) + {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a b^{2} c d^{2} - 4 \, a^{2} b d^{3}\right)} x^{4}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} + {\left(a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{4} + c}}{16 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{4}\right)}}, \frac{4 \, {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) + {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a b^{2} c d^{2} - 4 \, a^{2} b d^{3}\right)} x^{4}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} + {\left(a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{4} + c}}{16 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{4}\right)}}, -\frac{{\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a b^{2} c d^{2} - 4 \, a^{2} b d^{3}\right)} x^{4}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) - {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{d} \log\left(-2 \, d x^{4} + 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right) - 2 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} + {\left(a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{4} + c}}{8 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{4}\right)}}, \frac{2 \, {\left(a b^{2} c^{2} + 3 \, a^{2} b c d - 4 \, a^{3} d^{2} + {\left(b^{3} c^{2} + 3 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x^{4}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) - {\left(5 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} + {\left(5 \, a b^{2} c d^{2} - 4 \, a^{2} b d^{3}\right)} x^{4}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) + 2 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} + {\left(a b^{2} c d - 2 \, a^{2} b d^{2}\right)} x^{2}\right)} \sqrt{d x^{4} + c}}{8 \, {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3} + {\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{4}\right)}}\right]"," ",0,"[1/16*(2*(a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^4)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c) + (5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a*b^2*c*d^2 - 4*a^2*b*d^3)*x^4)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*((b^3*c*d - a*b^2*d^2)*x^6 + (a*b^2*c*d - 2*a^2*b*d^2)*x^2)*sqrt(d*x^4 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^4), 1/16*(4*(a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^4)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) + (5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a*b^2*c*d^2 - 4*a^2*b*d^3)*x^4)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*((b^3*c*d - a*b^2*d^2)*x^6 + (a*b^2*c*d - 2*a^2*b*d^2)*x^2)*sqrt(d*x^4 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^4), -1/8*((5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a*b^2*c*d^2 - 4*a^2*b*d^3)*x^4)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) - (a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^4)*sqrt(d)*log(-2*d*x^4 + 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c) - 2*((b^3*c*d - a*b^2*d^2)*x^6 + (a*b^2*c*d - 2*a^2*b*d^2)*x^2)*sqrt(d*x^4 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^4), 1/8*(2*(a*b^2*c^2 + 3*a^2*b*c*d - 4*a^3*d^2 + (b^3*c^2 + 3*a*b^2*c*d - 4*a^2*b*d^2)*x^4)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) - (5*a^2*b*c*d^2 - 4*a^3*d^3 + (5*a*b^2*c*d^2 - 4*a^2*b*d^3)*x^4)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) + 2*((b^3*c*d - a*b^2*d^2)*x^6 + (a*b^2*c*d - 2*a^2*b*d^2)*x^2)*sqrt(d*x^4 + c))/(a*b^4*c*d^2 - a^2*b^3*d^3 + (b^5*c*d^2 - a*b^4*d^3)*x^4)]","A",0
829,1,1077,0,0.837861," ","integrate(x^9/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{4} + c} a b d x^{2} + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{4} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{16 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{4}\right)}}, \frac{4 \, \sqrt{d x^{4} + c} a b d x^{2} - 8 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{4} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{6} - {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{16 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{4}\right)}}, \frac{2 \, \sqrt{d x^{4} + c} a b d x^{2} + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{4} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{4} - 2 \, \sqrt{d x^{4} + c} \sqrt{d} x^{2} - c\right)}{8 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{4}\right)}}, \frac{2 \, \sqrt{d x^{4} + c} a b d x^{2} - 4 \, {\left({\left(b^{2} c - a b d\right)} x^{4} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{2}}{\sqrt{d x^{4} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{4} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{6} + a c x^{2}\right)}}\right)}{8 \, {\left(a b^{3} c d - a^{2} b^{2} d^{2} + {\left(b^{4} c d - a b^{3} d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[1/16*(4*sqrt(d*x^4 + c)*a*b*d*x^2 + 4*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c) + ((3*b^2*c*d - 2*a*b*d^2)*x^4 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^4), 1/16*(4*sqrt(d*x^4 + c)*a*b*d*x^2 - 8*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^4 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^6 - (a*b*c^2 - a^2*c*d)*x^2)*sqrt(d*x^4 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^4), 1/8*(2*sqrt(d*x^4 + c)*a*b*d*x^2 + ((3*b^2*c*d - 2*a*b*d^2)*x^4 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)) + 2*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^4 - 2*sqrt(d*x^4 + c)*sqrt(d)*x^2 - c))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^4), 1/8*(2*sqrt(d*x^4 + c)*a*b*d*x^2 - 4*((b^2*c - a*b*d)*x^4 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^2/sqrt(d*x^4 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^4 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a/(b*c - a*d))/(a*d*x^6 + a*c*x^2)))/(a*b^3*c*d - a^2*b^2*d^2 + (b^4*c*d - a*b^3*d^2)*x^4)]","A",0
830,1,426,0,0.536627," ","integrate(x^5/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{d x^{4} + c} {\left(a b c - a^{2} d\right)} x^{2} - {\left(b c x^{4} + a c\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{16 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{4}\right)}}, -\frac{2 \, \sqrt{d x^{4} + c} {\left(a b c - a^{2} d\right)} x^{2} - {\left(b c x^{4} + a c\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right)}{8 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[-1/16*(4*sqrt(d*x^4 + c)*(a*b*c - a^2*d)*x^2 - (b*c*x^4 + a*c)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^4), -1/8*(2*sqrt(d*x^4 + c)*(a*b*c - a^2*d)*x^2 - (b*c*x^4 + a*c)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)))/(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^4)]","B",0
831,1,467,0,0.599375," ","integrate(x/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{4} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{2} - {\left({\left(b^{2} c - 2 \, a b d\right)} x^{4} + a b c - 2 \, a^{2} d\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right)}{16 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{4}\right)}}, \frac{2 \, \sqrt{d x^{4} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{2} + {\left({\left(b^{2} c - 2 \, a b d\right)} x^{4} + a b c - 2 \, a^{2} d\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right)}{8 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[1/16*(4*sqrt(d*x^4 + c)*(a*b^2*c - a^2*b*d)*x^2 - ((b^2*c - 2*a*b*d)*x^4 + a*b*c - 2*a^2*d)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^4), 1/8*(2*sqrt(d*x^4 + c)*(a*b^2*c - a^2*b*d)*x^2 + ((b^2*c - 2*a*b*d)*x^4 + a*b*c - 2*a^2*d)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^4)]","B",0
832,1,612,0,0.616845," ","integrate(1/x^3/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{6} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) + 4 \, {\left(2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2} + {\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{16 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{6} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{2}\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{6} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{2}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2} + {\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{8 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{6} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^6 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^2)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 + 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 4*(2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2 + (3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^4)*sqrt(d*x^4 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^6 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^2), -1/8*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^6 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^2)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)) + 2*(2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2 + (3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^4)*sqrt(d*x^4 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^6 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^2)]","B",0
833,1,760,0,0.775560," ","integrate(1/x^7/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{10} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{6}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{8} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{4} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{6} - a c x^{2}\right)} \sqrt{d x^{4} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}\right) - 4 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{8} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{48 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{10} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{6}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{10} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{6}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{4} - a c\right)} \sqrt{d x^{4} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{6} + {\left(a b c^{2} - a^{2} c d\right)} x^{2}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{8} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{4}\right)} \sqrt{d x^{4} + c}}{24 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{10} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{6}\right)}}\right]"," ",0,"[-1/48*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^10 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^6)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^8 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^4 + a^2*c^2 - 4*((b*c - 2*a*d)*x^6 - a*c*x^2)*sqrt(d*x^4 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^8 + 2*a*b*x^4 + a^2)) - 4*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^8 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^4)*sqrt(d*x^4 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^10 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^6), 1/24*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^10 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^6)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^4 - a*c)*sqrt(d*x^4 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^6 + (a*b*c^2 - a^2*c*d)*x^2)) + 2*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^8 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^4)*sqrt(d*x^4 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^10 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^6)]","A",0
834,-1,0,0,0.000000," ","integrate(x^8/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
835,-1,0,0,0.000000," ","integrate(x^4/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
836,-1,0,0,0.000000," ","integrate(1/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(1/x^4/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,-1,0,0,0.000000," ","integrate(x^6/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate(x^2/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate(1/x^2/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,0,0,0,0.632557," ","integrate((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} \left(e x\right)^{m}}{\sqrt{d x^{4} + c}}, x\right)"," ",0,"integral((b^2*x^8 + 2*a*b*x^4 + a^2)*(e*x)^m/sqrt(d*x^4 + c), x)","F",0
842,0,0,0,0.549896," ","integrate((e*x)^m*(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)} \left(e x\right)^{m}}{\sqrt{d x^{4} + c}}, x\right)"," ",0,"integral((b*x^4 + a)*(e*x)^m/sqrt(d*x^4 + c), x)","F",0
843,0,0,0,0.683671," ","integrate((e*x)^m/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{\sqrt{d x^{4} + c}}, x\right)"," ",0,"integral((e*x)^m/sqrt(d*x^4 + c), x)","F",0
844,0,0,0,0.580389," ","integrate((e*x)^m/(b*x^4+a)/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b d x^{8} + {\left(b c + a d\right)} x^{4} + a c}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b*d*x^8 + (b*c + a*d)*x^4 + a*c), x)","F",0
845,0,0,0,0.816834," ","integrate((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b^{2} d x^{12} + {\left(b^{2} c + 2 \, a b d\right)} x^{8} + {\left(2 \, a b c + a^{2} d\right)} x^{4} + a^{2} c}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b^2*d*x^12 + (b^2*c + 2*a*b*d)*x^8 + (2*a*b*c + a^2*d)*x^4 + a^2*c), x)","F",0
846,0,0,0,0.704887," ","integrate((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b^{3} d x^{16} + {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{12} + 3 \, {\left(a b^{2} c + a^{2} b d\right)} x^{8} + {\left(3 \, a^{2} b c + a^{3} d\right)} x^{4} + a^{3} c}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b^3*d*x^16 + (b^3*c + 3*a*b^2*d)*x^12 + 3*(a*b^2*c + a^2*b*d)*x^8 + (3*a^2*b*c + a^3*d)*x^4 + a^3*c), x)","F",0
847,0,0,0,0.649619," ","integrate((e*x)^m*(b*x^4+a)^2/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} \sqrt{d x^{4} + c} \left(e x\right)^{m}}{d^{2} x^{8} + 2 \, c d x^{4} + c^{2}}, x\right)"," ",0,"integral((b^2*x^8 + 2*a*b*x^4 + a^2)*sqrt(d*x^4 + c)*(e*x)^m/(d^2*x^8 + 2*c*d*x^4 + c^2), x)","F",0
848,0,0,0,0.666133," ","integrate((e*x)^m*(b*x^4+a)/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)} \sqrt{d x^{4} + c} \left(e x\right)^{m}}{d^{2} x^{8} + 2 \, c d x^{4} + c^{2}}, x\right)"," ",0,"integral((b*x^4 + a)*sqrt(d*x^4 + c)*(e*x)^m/(d^2*x^8 + 2*c*d*x^4 + c^2), x)","F",0
849,0,0,0,0.744153," ","integrate((e*x)^m/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{d^{2} x^{8} + 2 \, c d x^{4} + c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(d^2*x^8 + 2*c*d*x^4 + c^2), x)","F",0
850,0,0,0,0.444922," ","integrate((e*x)^m/(b*x^4+a)/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b d^{2} x^{12} + {\left(2 \, b c d + a d^{2}\right)} x^{8} + {\left(b c^{2} + 2 \, a c d\right)} x^{4} + a c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b*d^2*x^12 + (2*b*c*d + a*d^2)*x^8 + (b*c^2 + 2*a*c*d)*x^4 + a*c^2), x)","F",0
851,0,0,0,0.448709," ","integrate((e*x)^m/(b*x^4+a)^2/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b^{2} d^{2} x^{16} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x^{12} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} x^{8} + 2 \, {\left(a b c^{2} + a^{2} c d\right)} x^{4} + a^{2} c^{2}}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b^2*d^2*x^16 + 2*(b^2*c*d + a*b*d^2)*x^12 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^8 + 2*(a*b*c^2 + a^2*c*d)*x^4 + a^2*c^2), x)","F",0
852,0,0,0,0.452678," ","integrate((e*x)^m/(b*x^4+a)^3/(d*x^4+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{4} + c} \left(e x\right)^{m}}{b^{3} d^{2} x^{20} + {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} x^{16} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x^{12} + {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{8} + a^{3} c^{2} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(d*x^4 + c)*(e*x)^m/(b^3*d^2*x^20 + (2*b^3*c*d + 3*a*b^2*d^2)*x^16 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*x^12 + (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*x^8 + a^3*c^2 + (3*a^2*b*c^2 + 2*a^3*c*d)*x^4), x)","F",0
853,1,288,0,0.433302," ","integrate(x^17/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} c - a b d} a^{2} d^{2} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right) + 2 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} - 2 \, b^{3} c^{2} - a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \sqrt{d x^{6} + c}}{18 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}, \frac{3 \, \sqrt{-b^{2} c + a b d} a^{2} d^{2} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right) + {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{6} - 2 \, b^{3} c^{2} - a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \sqrt{d x^{6} + c}}{9 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}\right]"," ",0,"[1/18*(3*sqrt(b^2*c - a*b*d)*a^2*d^2*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a)) + 2*((b^3*c*d - a*b^2*d^2)*x^6 - 2*b^3*c^2 - a*b^2*c*d + 3*a^2*b*d^2)*sqrt(d*x^6 + c))/(b^4*c*d^2 - a*b^3*d^3), 1/9*(3*sqrt(-b^2*c + a*b*d)*a^2*d^2*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c)) + ((b^3*c*d - a*b^2*d^2)*x^6 - 2*b^3*c^2 - a*b^2*c*d + 3*a^2*b*d^2)*sqrt(d*x^6 + c))/(b^4*c*d^2 - a*b^3*d^3)]","A",0
854,1,205,0,0.417694," ","integrate(x^11/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} a d \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right) + 2 \, \sqrt{d x^{6} + c} {\left(b^{2} c - a b d\right)}}{6 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}, -\frac{\sqrt{-b^{2} c + a b d} a d \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right) - \sqrt{d x^{6} + c} {\left(b^{2} c - a b d\right)}}{3 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}\right]"," ",0,"[1/6*(sqrt(b^2*c - a*b*d)*a*d*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a)) + 2*sqrt(d*x^6 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2), -1/3*(sqrt(-b^2*c + a*b*d)*a*d*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c)) - sqrt(d*x^6 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2)]","A",0
855,1,130,0,0.412100," ","integrate(x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right)}{6 \, \sqrt{b^{2} c - a b d}}, \frac{\sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right)}{3 \, {\left(b^{2} c - a b d\right)}}\right]"," ",0,"[1/6*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a))/sqrt(b^2*c - a*b*d), 1/3*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c))/(b^2*c - a*b*d)]","A",0
856,1,431,0,0.450166," ","integrate(1/x/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + \sqrt{c} \log\left(\frac{d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right)}{6 \, a c}, \frac{2 \, c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + \sqrt{c} \log\left(\frac{d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right)}{6 \, a c}, \frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right)}{6 \, a c}, \frac{c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right)}{3 \, a c}\right]"," ",0,"[1/6*(c*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + sqrt(c)*log((d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6))/(a*c), 1/6*(2*c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + sqrt(c)*log((d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6))/(a*c), 1/6*(c*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + 2*sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c))/(a*c), 1/3*(c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c))/(a*c)]","A",0
857,1,565,0,0.467335," ","integrate(1/x^7/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{6} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{6} \log\left(\frac{d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right) - 2 \, \sqrt{d x^{6} + c} a c}{12 \, a^{2} c^{2} x^{6}}, -\frac{4 \, b c^{2} x^{6} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) - {\left(2 \, b c + a d\right)} \sqrt{c} x^{6} \log\left(\frac{d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right) + 2 \, \sqrt{d x^{6} + c} a c}{12 \, a^{2} c^{2} x^{6}}, \frac{b c^{2} x^{6} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) - {\left(2 \, b c + a d\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{6} + c} a c}{6 \, a^{2} c^{2} x^{6}}, -\frac{2 \, b c^{2} x^{6} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + {\left(2 \, b c + a d\right)} \sqrt{-c} x^{6} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{6} + c} a c}{6 \, a^{2} c^{2} x^{6}}\right]"," ",0,"[1/12*(2*b*c^2*x^6*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + (2*b*c + a*d)*sqrt(c)*x^6*log((d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6) - 2*sqrt(d*x^6 + c)*a*c)/(a^2*c^2*x^6), -1/12*(4*b*c^2*x^6*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) - (2*b*c + a*d)*sqrt(c)*x^6*log((d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6) + 2*sqrt(d*x^6 + c)*a*c)/(a^2*c^2*x^6), 1/6*(b*c^2*x^6*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) - (2*b*c + a*d)*sqrt(-c)*x^6*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c) - sqrt(d*x^6 + c)*a*c)/(a^2*c^2*x^6), -1/6*(2*b*c^2*x^6*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + (2*b*c + a*d)*sqrt(-c)*x^6*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c) + sqrt(d*x^6 + c)*a*c)/(a^2*c^2*x^6)]","A",0
858,1,739,0,0.546289," ","integrate(x^14/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{6} + c} b d x^{3} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right)}{12 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{6} + c} b d x^{3} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) + 2 \, {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right)}{12 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{6} + c} b d x^{3} - 2 \, a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right)}{12 \, b^{2} d^{2}}, \frac{\sqrt{d x^{6} + c} b d x^{3} - a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right)}{6 \, b^{2} d^{2}}\right]"," ",0,"[1/12*(2*sqrt(d*x^6 + c)*b*d*x^3 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c))/(b^2*d^2), 1/12*(2*sqrt(d*x^6 + c)*b*d*x^3 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)) + 2*(b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)))/(b^2*d^2), 1/12*(2*sqrt(d*x^6 + c)*b*d*x^3 - 2*a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c))/(b^2*d^2), 1/6*(sqrt(d*x^6 + c)*b*d*x^3 - a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)) + (b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)))/(b^2*d^2)]","A",0
859,1,632,0,0.524935," ","integrate(x^8/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) + 2 \, \sqrt{d} \log\left(-2 \, d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right)}{12 \, b d}, \frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) - 4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right)}{12 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right)}{6 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right) - 2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right)}{6 \, b d}\right]"," ",0,"[1/12*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)) + 2*sqrt(d)*log(-2*d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c))/(b*d), 1/12*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)) - 4*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)))/(b*d), 1/6*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)) + sqrt(d)*log(-2*d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c))/(b*d), 1/6*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)) - 2*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)))/(b*d)]","A",0
860,1,245,0,0.495031," ","integrate(x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right)}{12 \, {\left(a b c - a^{2} d\right)}}, \frac{\arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right)}{6 \, \sqrt{a b c - a^{2} d}}\right]"," ",0,"[-1/12*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2))/(a*b*c - a^2*d), 1/6*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3))/sqrt(a*b*c - a^2*d)]","B",0
861,1,332,0,0.511258," ","integrate(1/x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} b c x^{3} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) + 4 \, \sqrt{d x^{6} + c} {\left(a b c - a^{2} d\right)}}{12 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{3}}, -\frac{\sqrt{a b c - a^{2} d} b c x^{3} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right) + 2 \, \sqrt{d x^{6} + c} {\left(a b c - a^{2} d\right)}}{6 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{3}}\right]"," ",0,"[-1/12*(sqrt(-a*b*c + a^2*d)*b*c*x^3*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 + 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)) + 4*sqrt(d*x^6 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^3), -1/6*(sqrt(a*b*c - a^2*d)*b*c*x^3*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)) + 2*sqrt(d*x^6 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^3)]","B",0
862,1,416,0,0.529979," ","integrate(1/x^10/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a b c + a^{2} d} b^{2} c^{2} x^{9} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) - 4 \, {\left({\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{6} - a^{2} b c^{2} + a^{3} c d\right)} \sqrt{d x^{6} + c}}{36 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{9}}, \frac{3 \, \sqrt{a b c - a^{2} d} b^{2} c^{2} x^{9} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{6} - a^{2} b c^{2} + a^{3} c d\right)} \sqrt{d x^{6} + c}}{18 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{9}}\right]"," ",0,"[-1/36*(3*sqrt(-a*b*c + a^2*d)*b^2*c^2*x^9*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)) - 4*((3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^6 - a^2*b*c^2 + a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^9), 1/18*(3*sqrt(a*b*c - a^2*d)*b^2*c^2*x^9*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)) + 2*((3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^6 - a^2*b*c^2 + a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^9)]","A",0
863,-2,0,0,0.000000," ","integrate(x^4/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Not integrable (provided residues have no relations)","F(-2)",0
864,-1,0,0,0.000000," ","integrate(x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate(x/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-2,0,0,0.000000," ","integrate(1/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Not integrable (provided residues have no relations)","F(-2)",0
867,0,0,0,0.411526," ","integrate(1/x^2/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{6} + c}}{b d x^{14} + {\left(b c + a d\right)} x^{8} + a c x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^6 + c)/(b*d*x^14 + (b*c + a*d)*x^8 + a*c*x^2), x)","F",0
868,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate(1/x^5/(b*x^6+a)/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,1,475,0,0.645849," ","integrate(x^17/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + 4 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right) + 2 \, {\left(2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{6} + 2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} \sqrt{d x^{6} + c}}{12 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{6}\right)}}, -\frac{{\left({\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{6} + 4 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right) - {\left(2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{6} + 2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} \sqrt{d x^{6} + c}}{6 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{6}\right)}}\right]"," ",0,"[1/12*(((4*a*b^2*c*d - 3*a^2*b*d^2)*x^6 + 4*a^2*b*c*d - 3*a^3*d^2)*sqrt(b^2*c - a*b*d)*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a)) + 2*(2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^6 + 2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2)*sqrt(d*x^6 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^6), -1/6*(((4*a*b^2*c*d - 3*a^2*b*d^2)*x^6 + 4*a^2*b*c*d - 3*a^3*d^2)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c)) - (2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^6 + 2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2)*sqrt(d*x^6 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^6)]","B",0
871,1,348,0,0.688175," ","integrate(x^11/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{6} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right) + 2 \, \sqrt{d x^{6} + c} {\left(a b^{2} c - a^{2} b d\right)}}{12 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{6}\right)}}, \frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{6} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right) + \sqrt{d x^{6} + c} {\left(a b^{2} c - a^{2} b d\right)}}{6 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{6}\right)}}\right]"," ",0,"[1/12*(((2*b^2*c - a*b*d)*x^6 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a)) + 2*sqrt(d*x^6 + c)*(a*b^2*c - a^2*b*d))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^6), 1/6*(((2*b^2*c - a*b*d)*x^6 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c)) + sqrt(d*x^6 + c)*(a*b^2*c - a^2*b*d))/(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^6)]","A",0
872,1,302,0,0.754118," ","integrate(x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b d x^{6} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} \sqrt{b^{2} c - a b d}}{b x^{6} + a}\right) + 2 \, \sqrt{d x^{6} + c} {\left(b^{2} c - a b d\right)}}{12 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{6} + a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)}}, -\frac{{\left(b d x^{6} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-b^{2} c + a b d}}{b d x^{6} + b c}\right) + \sqrt{d x^{6} + c} {\left(b^{2} c - a b d\right)}}{6 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{6} + a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)}}\right]"," ",0,"[-1/12*((b*d*x^6 + a*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*sqrt(b^2*c - a*b*d))/(b*x^6 + a)) + 2*sqrt(d*x^6 + c)*(b^2*c - a*b*d))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^6 + a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2), -1/6*((b*d*x^6 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^6 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^6 + b*c)) + sqrt(d*x^6 + c)*(b^2*c - a*b*d))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^6 + a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)]","B",0
873,1,862,0,0.925440," ","integrate(1/x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{6} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right)}{12 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{6} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{\sqrt{d x^{6} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right)}{6 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{6} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{2 \, \sqrt{d x^{6} + c} a b c + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d + 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right)}{12 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{6} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{\sqrt{d x^{6} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{6} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right)}{6 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{6} + a^{3} b c^{2} - a^{4} c d\right)}}\right]"," ",0,"[1/12*(2*sqrt(d*x^6 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^6 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + 2*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(c)*log((d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6))/((a^2*b^2*c^2 - a^3*b*c*d)*x^6 + a^3*b*c^2 - a^4*c*d), 1/6*(sqrt(d*x^6 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^6 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + ((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(c)*log((d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6))/((a^2*b^2*c^2 - a^3*b*c*d)*x^6 + a^3*b*c^2 - a^4*c*d), 1/12*(2*sqrt(d*x^6 + c)*a*b*c + 4*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c) + ((2*b^2*c^2 - 3*a*b*c*d)*x^6 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d + 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)))/((a^2*b^2*c^2 - a^3*b*c*d)*x^6 + a^3*b*c^2 - a^4*c*d), 1/6*(sqrt(d*x^6 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^6 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + 2*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c))/((a^2*b^2*c^2 - a^3*b*c*d)*x^6 + a^3*b*c^2 - a^4*c*d)]","A",0
874,1,1236,0,0.918736," ","integrate(1/x^7/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{12} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{6}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{12} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right) - 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{6} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{6} + c}}{12 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{12} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{6}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{12} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{6}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) - {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{12} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{6}\right)} \sqrt{c} \log\left(\frac{d x^{6} + 2 \, \sqrt{d x^{6} + c} \sqrt{c} + 2 \, c}{x^{6}}\right) + 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{6} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{6} + c}}{12 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{12} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{6}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{12} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{12} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{6}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{6} + 2 \, b c - a d - 2 \, \sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{6} + a}\right) + 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{6} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{6} + c}}{12 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{12} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{6}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{12} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{6}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{6} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{6} + b c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{12} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{6} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{6} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{6} + c}}{6 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{12} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{6}\right)}}\right]"," ",0,"[1/12*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^12 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^6)*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^12 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^6)*sqrt(c)*log((d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6) - 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^6 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^12 + (a^4*b*c^3 - a^5*c^2*d)*x^6), -1/12*(2*((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^12 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^6)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) - ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^12 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^6)*sqrt(c)*log((d*x^6 + 2*sqrt(d*x^6 + c)*sqrt(c) + 2*c)/x^6) + 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^6 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^12 + (a^4*b*c^3 - a^5*c^2*d)*x^6), -1/12*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^12 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^6)*sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^12 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^6)*sqrt(b/(b*c - a*d))*log((b*d*x^6 + 2*b*c - a*d - 2*sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^6 + a)) + 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^6 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^12 + (a^4*b*c^3 - a^5*c^2*d)*x^6), -1/6*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^12 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^6)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^6 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^6 + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^12 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^6)*sqrt(-c)*arctan(sqrt(d*x^6 + c)*sqrt(-c)/c) + ((2*a*b^2*c^2 - a^2*b*c*d)*x^6 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^6 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^12 + (a^4*b*c^3 - a^5*c^2*d)*x^6)]","A",0
875,1,1077,0,1.408064," ","integrate(x^14/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{6} + c} a b d x^{3} + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{6} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right)}{24 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{4 \, \sqrt{d x^{6} + c} a b d x^{3} - 8 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{6} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{9} - {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right)}{24 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{2 \, \sqrt{d x^{6} + c} a b d x^{3} + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{6} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{6} - 2 \, \sqrt{d x^{6} + c} \sqrt{d} x^{3} - c\right)}{12 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{2 \, \sqrt{d x^{6} + c} a b d x^{3} - 4 \, {\left({\left(b^{2} c - a b d\right)} x^{6} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{3}}{\sqrt{d x^{6} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{6} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{9} + a c x^{3}\right)}}\right)}{12 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{6} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}\right]"," ",0,"[1/24*(4*sqrt(d*x^6 + c)*a*b*d*x^3 + 4*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c) + ((3*b^2*c*d - 2*a*b*d^2)*x^6 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)))/((b^4*c*d - a*b^3*d^2)*x^6 + a*b^3*c*d - a^2*b^2*d^2), 1/24*(4*sqrt(d*x^6 + c)*a*b*d*x^3 - 8*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^6 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^9 - (a*b*c^2 - a^2*c*d)*x^3)*sqrt(d*x^6 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^12 + 2*a*b*x^6 + a^2)))/((b^4*c*d - a*b^3*d^2)*x^6 + a*b^3*c*d - a^2*b^2*d^2), 1/12*(2*sqrt(d*x^6 + c)*a*b*d*x^3 + ((3*b^2*c*d - 2*a*b*d^2)*x^6 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)) + 2*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^6 - 2*sqrt(d*x^6 + c)*sqrt(d)*x^3 - c))/((b^4*c*d - a*b^3*d^2)*x^6 + a*b^3*c*d - a^2*b^2*d^2), 1/12*(2*sqrt(d*x^6 + c)*a*b*d*x^3 - 4*((b^2*c - a*b*d)*x^6 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^3/sqrt(d*x^6 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^6 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a/(b*c - a*d))/(a*d*x^9 + a*c*x^3)))/((b^4*c*d - a*b^3*d^2)*x^6 + a*b^3*c*d - a^2*b^2*d^2)]","A",0
876,1,426,0,0.789667," ","integrate(x^8/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{d x^{6} + c} {\left(a b c - a^{2} d\right)} x^{3} - {\left(b c x^{6} + a c\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right)}{24 \, {\left({\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{6} + a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}}, -\frac{2 \, \sqrt{d x^{6} + c} {\left(a b c - a^{2} d\right)} x^{3} - {\left(b c x^{6} + a c\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right)}{12 \, {\left({\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{6} + a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}}\right]"," ",0,"[-1/24*(4*sqrt(d*x^6 + c)*(a*b*c - a^2*d)*x^3 - (b*c*x^6 + a*c)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 + 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)))/((a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^6 + a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2), -1/12*(2*sqrt(d*x^6 + c)*(a*b*c - a^2*d)*x^3 - (b*c*x^6 + a*c)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)))/((a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^6 + a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)]","B",0
877,1,467,0,0.591922," ","integrate(x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{6} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{3} - {\left({\left(b^{2} c - 2 \, a b d\right)} x^{6} + a b c - 2 \, a^{2} d\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right)}{24 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{6}\right)}}, \frac{2 \, \sqrt{d x^{6} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{3} + {\left({\left(b^{2} c - 2 \, a b d\right)} x^{6} + a b c - 2 \, a^{2} d\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right)}{12 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2} + {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{6}\right)}}\right]"," ",0,"[1/24*(4*sqrt(d*x^6 + c)*(a*b^2*c - a^2*b*d)*x^3 - ((b^2*c - 2*a*b*d)*x^6 + a*b*c - 2*a^2*d)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^6), 1/12*(2*sqrt(d*x^6 + c)*(a*b^2*c - a^2*b*d)*x^3 + ((b^2*c - 2*a*b*d)*x^6 + a*b*c - 2*a^2*d)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)))/(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2 + (a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^6)]","B",0
878,1,612,0,0.607921," ","integrate(1/x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{9} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{3}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) + 4 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{6} + 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2}\right)} \sqrt{d x^{6} + c}}{24 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{9} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{3}\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{9} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{3}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{6} + 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2}\right)} \sqrt{d x^{6} + c}}{12 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{9} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{3}\right)}}\right]"," ",0,"[-1/24*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^9 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^3)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 + 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)) + 4*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^6 + 2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2)*sqrt(d*x^6 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^9 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^3), -1/12*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^9 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^3)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)) + 2*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^6 + 2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2)*sqrt(d*x^6 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^9 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^3)]","B",0
879,1,760,0,0.774681," ","integrate(1/x^10/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{15} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{9}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{12} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{6} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{9} - a c x^{3}\right)} \sqrt{d x^{6} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{12} + 2 \, a b x^{6} + a^{2}}\right) - 4 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{12} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{6}\right)} \sqrt{d x^{6} + c}}{72 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{15} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{9}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{15} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{9}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{6} - a c\right)} \sqrt{d x^{6} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{9} + {\left(a b c^{2} - a^{2} c d\right)} x^{3}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{12} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{6}\right)} \sqrt{d x^{6} + c}}{36 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{15} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{9}\right)}}\right]"," ",0,"[-1/72*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^15 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^9)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^12 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^6 + a^2*c^2 - 4*((b*c - 2*a*d)*x^9 - a*c*x^3)*sqrt(d*x^6 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^12 + 2*a*b*x^6 + a^2)) - 4*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^12 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^6)*sqrt(d*x^6 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^15 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^9), 1/36*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^15 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^9)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^6 - a*c)*sqrt(d*x^6 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^9 + (a*b*c^2 - a^2*c*d)*x^3)) + 2*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^12 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^6)*sqrt(d*x^6 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^15 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^9)]","A",0
880,0,0,0,0.413672," ","integrate(x^4/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{6} + c} x^{4}}{b^{2} d x^{18} + {\left(b^{2} c + 2 \, a b d\right)} x^{12} + {\left(2 \, a b c + a^{2} d\right)} x^{6} + a^{2} c}, x\right)"," ",0,"integral(sqrt(d*x^6 + c)*x^4/(b^2*d*x^18 + (b^2*c + 2*a*b*d)*x^12 + (2*a*b*c + a^2*d)*x^6 + a^2*c), x)","F",0
881,-1,0,0,0.000000," ","integrate(x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(x/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate(1/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,0,0,0,0.428971," ","integrate(1/x^2/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{6} + c}}{b^{2} d x^{20} + {\left(b^{2} c + 2 \, a b d\right)} x^{14} + {\left(2 \, a b c + a^{2} d\right)} x^{8} + a^{2} c x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^6 + c)/(b^2*d*x^20 + (b^2*c + 2*a*b*d)*x^14 + (2*a*b*c + a^2*d)*x^8 + a^2*c*x^2), x)","F",0
885,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate(1/x^5/(b*x^6+a)^2/(d*x^6+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,1,288,0,0.427758," ","integrate(x^23/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b^{2} c - a b d} a^{2} d^{2} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right) + 2 \, {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{8} - 2 \, b^{3} c^{2} - a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \sqrt{d x^{8} + c}}{24 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}, \frac{3 \, \sqrt{-b^{2} c + a b d} a^{2} d^{2} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right) + {\left({\left(b^{3} c d - a b^{2} d^{2}\right)} x^{8} - 2 \, b^{3} c^{2} - a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \sqrt{d x^{8} + c}}{12 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)}}\right]"," ",0,"[1/24*(3*sqrt(b^2*c - a*b*d)*a^2*d^2*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a)) + 2*((b^3*c*d - a*b^2*d^2)*x^8 - 2*b^3*c^2 - a*b^2*c*d + 3*a^2*b*d^2)*sqrt(d*x^8 + c))/(b^4*c*d^2 - a*b^3*d^3), 1/12*(3*sqrt(-b^2*c + a*b*d)*a^2*d^2*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c)) + ((b^3*c*d - a*b^2*d^2)*x^8 - 2*b^3*c^2 - a*b^2*c*d + 3*a^2*b*d^2)*sqrt(d*x^8 + c))/(b^4*c*d^2 - a*b^3*d^3)]","A",0
888,1,205,0,0.459483," ","integrate(x^15/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} c - a b d} a d \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right) + 2 \, \sqrt{d x^{8} + c} {\left(b^{2} c - a b d\right)}}{8 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}, -\frac{\sqrt{-b^{2} c + a b d} a d \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right) - \sqrt{d x^{8} + c} {\left(b^{2} c - a b d\right)}}{4 \, {\left(b^{3} c d - a b^{2} d^{2}\right)}}\right]"," ",0,"[1/8*(sqrt(b^2*c - a*b*d)*a*d*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a)) + 2*sqrt(d*x^8 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2), -1/4*(sqrt(-b^2*c + a*b*d)*a*d*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c)) - sqrt(d*x^8 + c)*(b^2*c - a*b*d))/(b^3*c*d - a*b^2*d^2)]","A",0
889,1,130,0,0.421315," ","integrate(x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right)}{8 \, \sqrt{b^{2} c - a b d}}, \frac{\sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right)}{4 \, {\left(b^{2} c - a b d\right)}}\right]"," ",0,"[1/8*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a))/sqrt(b^2*c - a*b*d), 1/4*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c))/(b^2*c - a*b*d)]","A",0
890,1,431,0,0.478439," ","integrate(1/x/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + \sqrt{c} \log\left(\frac{d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right)}{8 \, a c}, \frac{2 \, c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + \sqrt{c} \log\left(\frac{d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right)}{8 \, a c}, \frac{c \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + 2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right)}{8 \, a c}, \frac{c \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right)}{4 \, a c}\right]"," ",0,"[1/8*(c*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + sqrt(c)*log((d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8))/(a*c), 1/8*(2*c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + sqrt(c)*log((d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8))/(a*c), 1/8*(c*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + 2*sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c))/(a*c), 1/4*(c*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c))/(a*c)]","A",0
891,1,565,0,0.469153," ","integrate(1/x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{8} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + {\left(2 \, b c + a d\right)} \sqrt{c} x^{8} \log\left(\frac{d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right) - 2 \, \sqrt{d x^{8} + c} a c}{16 \, a^{2} c^{2} x^{8}}, -\frac{4 \, b c^{2} x^{8} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) - {\left(2 \, b c + a d\right)} \sqrt{c} x^{8} \log\left(\frac{d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right) + 2 \, \sqrt{d x^{8} + c} a c}{16 \, a^{2} c^{2} x^{8}}, \frac{b c^{2} x^{8} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) - {\left(2 \, b c + a d\right)} \sqrt{-c} x^{8} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right) - \sqrt{d x^{8} + c} a c}{8 \, a^{2} c^{2} x^{8}}, -\frac{2 \, b c^{2} x^{8} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + {\left(2 \, b c + a d\right)} \sqrt{-c} x^{8} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right) + \sqrt{d x^{8} + c} a c}{8 \, a^{2} c^{2} x^{8}}\right]"," ",0,"[1/16*(2*b*c^2*x^8*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + (2*b*c + a*d)*sqrt(c)*x^8*log((d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8) - 2*sqrt(d*x^8 + c)*a*c)/(a^2*c^2*x^8), -1/16*(4*b*c^2*x^8*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) - (2*b*c + a*d)*sqrt(c)*x^8*log((d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8) + 2*sqrt(d*x^8 + c)*a*c)/(a^2*c^2*x^8), 1/8*(b*c^2*x^8*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) - (2*b*c + a*d)*sqrt(-c)*x^8*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c) - sqrt(d*x^8 + c)*a*c)/(a^2*c^2*x^8), -1/8*(2*b*c^2*x^8*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + (2*b*c + a*d)*sqrt(-c)*x^8*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c) + sqrt(d*x^8 + c)*a*c)/(a^2*c^2*x^8)]","A",0
892,1,739,0,0.557714," ","integrate(x^19/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{8} + c} b d x^{4} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right)}{16 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{8} + c} b d x^{4} + a d^{2} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} + 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) + 2 \, {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right)}{16 \, b^{2} d^{2}}, \frac{2 \, \sqrt{d x^{8} + c} b d x^{4} - 2 \, a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{d} \log\left(-2 \, d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right)}{16 \, b^{2} d^{2}}, \frac{\sqrt{d x^{8} + c} b d x^{4} - a d^{2} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right) + {\left(b c + 2 \, a d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right)}{8 \, b^{2} d^{2}}\right]"," ",0,"[1/16*(2*sqrt(d*x^8 + c)*b*d*x^4 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c))/(b^2*d^2), 1/16*(2*sqrt(d*x^8 + c)*b*d*x^4 + a*d^2*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 + 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)) + 2*(b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)))/(b^2*d^2), 1/16*(2*sqrt(d*x^8 + c)*b*d*x^4 - 2*a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)) + (b*c + 2*a*d)*sqrt(d)*log(-2*d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c))/(b^2*d^2), 1/8*(sqrt(d*x^8 + c)*b*d*x^4 - a*d^2*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)) + (b*c + 2*a*d)*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)))/(b^2*d^2)]","A",0
893,1,632,0,0.522102," ","integrate(x^11/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) + 2 \, \sqrt{d} \log\left(-2 \, d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right)}{16 \, b d}, \frac{d \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) - 4 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right)}{16 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right) + \sqrt{d} \log\left(-2 \, d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right)}{8 \, b d}, \frac{d \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right) - 2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right)}{8 \, b d}\right]"," ",0,"[1/16*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)) + 2*sqrt(d)*log(-2*d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c))/(b*d), 1/16*(d*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)) - 4*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)))/(b*d), 1/8*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)) + sqrt(d)*log(-2*d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c))/(b*d), 1/8*(d*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)) - 2*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)))/(b*d)]","A",0
894,1,245,0,0.485863," ","integrate(x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right)}{16 \, {\left(a b c - a^{2} d\right)}}, \frac{\arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right)}{8 \, \sqrt{a b c - a^{2} d}}\right]"," ",0,"[-1/16*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2))/(a*b*c - a^2*d), 1/8*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4))/sqrt(a*b*c - a^2*d)]","B",0
895,1,332,0,0.502797," ","integrate(1/x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b c + a^{2} d} b c x^{4} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) + 4 \, \sqrt{d x^{8} + c} {\left(a b c - a^{2} d\right)}}{16 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{4}}, -\frac{\sqrt{a b c - a^{2} d} b c x^{4} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right) + 2 \, \sqrt{d x^{8} + c} {\left(a b c - a^{2} d\right)}}{8 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x^{4}}\right]"," ",0,"[-1/16*(sqrt(-a*b*c + a^2*d)*b*c*x^4*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 + 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)) + 4*sqrt(d*x^8 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^4), -1/8*(sqrt(a*b*c - a^2*d)*b*c*x^4*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)) + 2*sqrt(d*x^8 + c)*(a*b*c - a^2*d))/((a^2*b*c^2 - a^3*c*d)*x^4)]","B",0
896,1,416,0,0.523875," ","integrate(1/x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a b c + a^{2} d} b^{2} c^{2} x^{12} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) - 4 \, {\left({\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{8} - a^{2} b c^{2} + a^{3} c d\right)} \sqrt{d x^{8} + c}}{48 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{12}}, \frac{3 \, \sqrt{a b c - a^{2} d} b^{2} c^{2} x^{12} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{2} c^{2} - a^{2} b c d - 2 \, a^{3} d^{2}\right)} x^{8} - a^{2} b c^{2} + a^{3} c d\right)} \sqrt{d x^{8} + c}}{24 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x^{12}}\right]"," ",0,"[-1/48*(3*sqrt(-a*b*c + a^2*d)*b^2*c^2*x^12*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)) - 4*((3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^8 - a^2*b*c^2 + a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^12), 1/24*(3*sqrt(a*b*c - a^2*d)*b^2*c^2*x^12*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)) + 2*((3*a*b^2*c^2 - a^2*b*c*d - 2*a^3*d^2)*x^8 - a^2*b*c^2 + a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b*c^3 - a^4*c^2*d)*x^12)]","A",0
897,-1,0,0,0.000000," ","integrate(x^9/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate(x/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate(1/x^7/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate(x^13/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate(x^5/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate(x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate(x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate(1/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,0,0,0,0.625956," ","integrate(1/x^2/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{8} + c}}{b d x^{18} + {\left(b c + a d\right)} x^{10} + a c x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^8 + c)/(b*d*x^18 + (b*c + a*d)*x^10 + a*c*x^2), x)","F",0
907,-1,0,0,0.000000," ","integrate(1/x^4/(b*x^8+a)/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,1,475,0,0.474487," ","integrate(x^23/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{8} + 4 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right) + 2 \, {\left(2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{8} + 2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} \sqrt{d x^{8} + c}}{16 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{8}\right)}}, -\frac{{\left({\left(4 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x^{8} + 4 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right) - {\left(2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{8} + 2 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} \sqrt{d x^{8} + c}}{8 \, {\left(a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2} + a^{3} b^{3} d^{3} + {\left(b^{6} c^{2} d - 2 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{8}\right)}}\right]"," ",0,"[1/16*(((4*a*b^2*c*d - 3*a^2*b*d^2)*x^8 + 4*a^2*b*c*d - 3*a^3*d^2)*sqrt(b^2*c - a*b*d)*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a)) + 2*(2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^8 + 2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2)*sqrt(d*x^8 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^8), -1/8*(((4*a*b^2*c*d - 3*a^2*b*d^2)*x^8 + 4*a^2*b*c*d - 3*a^3*d^2)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c)) - (2*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^8 + 2*a*b^3*c^2 - 5*a^2*b^2*c*d + 3*a^3*b*d^2)*sqrt(d*x^8 + c))/(a*b^5*c^2*d - 2*a^2*b^4*c*d^2 + a^3*b^3*d^3 + (b^6*c^2*d - 2*a*b^5*c*d^2 + a^2*b^4*d^3)*x^8)]","B",0
909,1,348,0,0.434097," ","integrate(x^15/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{8} + 2 \, a b c - a^{2} d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right) + 2 \, \sqrt{d x^{8} + c} {\left(a b^{2} c - a^{2} b d\right)}}{16 \, {\left({\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{8} + a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)}}, \frac{{\left({\left(2 \, b^{2} c - a b d\right)} x^{8} + 2 \, a b c - a^{2} d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right) + \sqrt{d x^{8} + c} {\left(a b^{2} c - a^{2} b d\right)}}{8 \, {\left({\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{8} + a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)}}\right]"," ",0,"[1/16*(((2*b^2*c - a*b*d)*x^8 + 2*a*b*c - a^2*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a)) + 2*sqrt(d*x^8 + c)*(a*b^2*c - a^2*b*d))/((b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^8 + a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2), 1/8*(((2*b^2*c - a*b*d)*x^8 + 2*a*b*c - a^2*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c)) + sqrt(d*x^8 + c)*(a*b^2*c - a^2*b*d))/((b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^8 + a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)]","A",0
910,1,302,0,0.438234," ","integrate(x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b d x^{8} + a d\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} \sqrt{b^{2} c - a b d}}{b x^{8} + a}\right) + 2 \, \sqrt{d x^{8} + c} {\left(b^{2} c - a b d\right)}}{16 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{8} + a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)}}, -\frac{{\left(b d x^{8} + a d\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-b^{2} c + a b d}}{b d x^{8} + b c}\right) + \sqrt{d x^{8} + c} {\left(b^{2} c - a b d\right)}}{8 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{8} + a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)}}\right]"," ",0,"[-1/16*((b*d*x^8 + a*d)*sqrt(b^2*c - a*b*d)*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*sqrt(b^2*c - a*b*d))/(b*x^8 + a)) + 2*sqrt(d*x^8 + c)*(b^2*c - a*b*d))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^8 + a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2), -1/8*((b*d*x^8 + a*d)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(d*x^8 + c)*sqrt(-b^2*c + a*b*d)/(b*d*x^8 + b*c)) + sqrt(d*x^8 + c)*(b^2*c - a*b*d))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^8 + a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)]","B",0
911,1,862,0,0.490030," ","integrate(1/x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{d x^{8} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{8} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right)}{16 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{8} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{\sqrt{d x^{8} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{8} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{c} \log\left(\frac{d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right)}{8 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{8} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{2 \, \sqrt{d x^{8} + c} a b c + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{8} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d + 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right)}{16 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{8} + a^{3} b c^{2} - a^{4} c d\right)}}, \frac{\sqrt{d x^{8} + c} a b c + {\left({\left(2 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{8} + 2 \, a b c^{2} - 3 \, a^{2} c d\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right)}{8 \, {\left({\left(a^{2} b^{2} c^{2} - a^{3} b c d\right)} x^{8} + a^{3} b c^{2} - a^{4} c d\right)}}\right]"," ",0,"[1/16*(2*sqrt(d*x^8 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^8 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + 2*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(c)*log((d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8))/((a^2*b^2*c^2 - a^3*b*c*d)*x^8 + a^3*b*c^2 - a^4*c*d), 1/8*(sqrt(d*x^8 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^8 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + ((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(c)*log((d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8))/((a^2*b^2*c^2 - a^3*b*c*d)*x^8 + a^3*b*c^2 - a^4*c*d), 1/16*(2*sqrt(d*x^8 + c)*a*b*c + 4*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c) + ((2*b^2*c^2 - 3*a*b*c*d)*x^8 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d + 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)))/((a^2*b^2*c^2 - a^3*b*c*d)*x^8 + a^3*b*c^2 - a^4*c*d), 1/8*(sqrt(d*x^8 + c)*a*b*c + ((2*b^2*c^2 - 3*a*b*c*d)*x^8 + 2*a*b*c^2 - 3*a^2*c*d)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + 2*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c))/((a^2*b^2*c^2 - a^3*b*c*d)*x^8 + a^3*b*c^2 - a^4*c*d)]","A",0
912,1,1236,0,0.555584," ","integrate(1/x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{16} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{8}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{16} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{8}\right)} \sqrt{c} \log\left(\frac{d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right) - 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{8} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{8} + c}}{16 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{16} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{8}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{16} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{8}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) - {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{16} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{8}\right)} \sqrt{c} \log\left(\frac{d x^{8} + 2 \, \sqrt{d x^{8} + c} \sqrt{c} + 2 \, c}{x^{8}}\right) + 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{8} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{8} + c}}{16 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{16} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{8}\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{16} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{8}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{16} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{8}\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x^{8} + 2 \, b c - a d - 2 \, \sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{\frac{b}{b c - a d}}}{b x^{8} + a}\right) + 2 \, {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{8} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{8} + c}}{16 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{16} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{8}\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{16} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x^{8}\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{\sqrt{d x^{8} + c} {\left(b c - a d\right)} \sqrt{-\frac{b}{b c - a d}}}{b d x^{8} + b c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{16} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x^{8}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x^{8} + c} \sqrt{-c}}{c}\right) + {\left({\left(2 \, a b^{2} c^{2} - a^{2} b c d\right)} x^{8} + a^{2} b c^{2} - a^{3} c d\right)} \sqrt{d x^{8} + c}}{8 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{16} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x^{8}\right)}}\right]"," ",0,"[1/16*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^16 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^8)*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^16 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^8)*sqrt(c)*log((d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8) - 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^8 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^16 + (a^4*b*c^3 - a^5*c^2*d)*x^8), -1/16*(2*((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^16 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^8)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) - ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^16 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^8)*sqrt(c)*log((d*x^8 + 2*sqrt(d*x^8 + c)*sqrt(c) + 2*c)/x^8) + 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^8 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^16 + (a^4*b*c^3 - a^5*c^2*d)*x^8), -1/16*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^16 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^8)*sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^16 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^8)*sqrt(b/(b*c - a*d))*log((b*d*x^8 + 2*b*c - a*d - 2*sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(b/(b*c - a*d)))/(b*x^8 + a)) + 2*((2*a*b^2*c^2 - a^2*b*c*d)*x^8 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^16 + (a^4*b*c^3 - a^5*c^2*d)*x^8), -1/8*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^16 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x^8)*sqrt(-b/(b*c - a*d))*arctan(-sqrt(d*x^8 + c)*(b*c - a*d)*sqrt(-b/(b*c - a*d))/(b*d*x^8 + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^16 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x^8)*sqrt(-c)*arctan(sqrt(d*x^8 + c)*sqrt(-c)/c) + ((2*a*b^2*c^2 - a^2*b*c*d)*x^8 + a^2*b*c^2 - a^3*c*d)*sqrt(d*x^8 + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^16 + (a^4*b*c^3 - a^5*c^2*d)*x^8)]","A",0
913,1,1077,0,0.818990," ","integrate(x^19/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{8} + c} a b d x^{4} + 4 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{8} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right)}{32 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{8} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{4 \, \sqrt{d x^{8} + c} a b d x^{4} - 8 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{8} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{-\frac{a}{b c - a d}} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b^{2} c^{2} - 3 \, a b c d + 2 \, a^{2} d^{2}\right)} x^{12} - {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-\frac{a}{b c - a d}}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right)}{32 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{8} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{2 \, \sqrt{d x^{8} + c} a b d x^{4} + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{8} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{d} \log\left(-2 \, d x^{8} - 2 \, \sqrt{d x^{8} + c} \sqrt{d} x^{4} - c\right)}{16 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{8} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}, \frac{2 \, \sqrt{d x^{8} + c} a b d x^{4} - 4 \, {\left({\left(b^{2} c - a b d\right)} x^{8} + a b c - a^{2} d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x^{4}}{\sqrt{d x^{8} + c}}\right) + {\left({\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} x^{8} + 3 \, a b c d - 2 \, a^{2} d^{2}\right)} \sqrt{\frac{a}{b c - a d}} \arctan\left(-\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{\frac{a}{b c - a d}}}{2 \, {\left(a d x^{12} + a c x^{4}\right)}}\right)}{16 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} x^{8} + a b^{3} c d - a^{2} b^{2} d^{2}\right)}}\right]"," ",0,"[1/32*(4*sqrt(d*x^8 + c)*a*b*d*x^4 + 4*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c) + ((3*b^2*c*d - 2*a*b*d^2)*x^8 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)))/((b^4*c*d - a*b^3*d^2)*x^8 + a*b^3*c*d - a^2*b^2*d^2), 1/32*(4*sqrt(d*x^8 + c)*a*b*d*x^4 - 8*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^8 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(-a/(b*c - a*d))*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b^2*c^2 - 3*a*b*c*d + 2*a^2*d^2)*x^12 - (a*b*c^2 - a^2*c*d)*x^4)*sqrt(d*x^8 + c)*sqrt(-a/(b*c - a*d)))/(b^2*x^16 + 2*a*b*x^8 + a^2)))/((b^4*c*d - a*b^3*d^2)*x^8 + a*b^3*c*d - a^2*b^2*d^2), 1/16*(2*sqrt(d*x^8 + c)*a*b*d*x^4 + ((3*b^2*c*d - 2*a*b*d^2)*x^8 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)) + 2*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(d)*log(-2*d*x^8 - 2*sqrt(d*x^8 + c)*sqrt(d)*x^4 - c))/((b^4*c*d - a*b^3*d^2)*x^8 + a*b^3*c*d - a^2*b^2*d^2), 1/16*(2*sqrt(d*x^8 + c)*a*b*d*x^4 - 4*((b^2*c - a*b*d)*x^8 + a*b*c - a^2*d)*sqrt(-d)*arctan(sqrt(-d)*x^4/sqrt(d*x^8 + c)) + ((3*b^2*c*d - 2*a*b*d^2)*x^8 + 3*a*b*c*d - 2*a^2*d^2)*sqrt(a/(b*c - a*d))*arctan(-1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a/(b*c - a*d))/(a*d*x^12 + a*c*x^4)))/((b^4*c*d - a*b^3*d^2)*x^8 + a*b^3*c*d - a^2*b^2*d^2)]","A",0
914,1,426,0,0.539446," ","integrate(x^11/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{d x^{8} + c} {\left(a b c - a^{2} d\right)} x^{4} - {\left(b c x^{8} + a c\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right)}{32 \, {\left({\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{8} + a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}}, -\frac{2 \, \sqrt{d x^{8} + c} {\left(a b c - a^{2} d\right)} x^{4} - {\left(b c x^{8} + a c\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right)}{16 \, {\left({\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{8} + a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)}}\right]"," ",0,"[-1/32*(4*sqrt(d*x^8 + c)*(a*b*c - a^2*d)*x^4 - (b*c*x^8 + a*c)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 + 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)))/((a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^8 + a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2), -1/16*(2*sqrt(d*x^8 + c)*(a*b*c - a^2*d)*x^4 - (b*c*x^8 + a*c)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)))/((a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^8 + a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)]","B",0
915,1,467,0,0.576945," ","integrate(x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{8} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{4} - {\left({\left(b^{2} c - 2 \, a b d\right)} x^{8} + a b c - 2 \, a^{2} d\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right)}{32 \, {\left({\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{8} + a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)}}, \frac{2 \, \sqrt{d x^{8} + c} {\left(a b^{2} c - a^{2} b d\right)} x^{4} + {\left({\left(b^{2} c - 2 \, a b d\right)} x^{8} + a b c - 2 \, a^{2} d\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right)}{16 \, {\left({\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x^{8} + a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)}}\right]"," ",0,"[1/32*(4*sqrt(d*x^8 + c)*(a*b^2*c - a^2*b*d)*x^4 - ((b^2*c - 2*a*b*d)*x^8 + a*b*c - 2*a^2*d)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)))/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^8 + a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2), 1/16*(2*sqrt(d*x^8 + c)*(a*b^2*c - a^2*b*d)*x^4 + ((b^2*c - 2*a*b*d)*x^8 + a*b*c - 2*a^2*d)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)))/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x^8 + a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)]","B",0
916,1,612,0,0.610069," ","integrate(1/x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{12} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{4}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} + 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) + 4 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{8} + 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2}\right)} \sqrt{d x^{8} + c}}{32 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{12} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{4}\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d\right)} x^{12} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d\right)} x^{4}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right) + 2 \, {\left({\left(3 \, a b^{3} c^{2} - 5 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x^{8} + 2 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + 2 \, a^{4} d^{2}\right)} \sqrt{d x^{8} + c}}{16 \, {\left({\left(a^{3} b^{3} c^{3} - 2 \, a^{4} b^{2} c^{2} d + a^{5} b c d^{2}\right)} x^{12} + {\left(a^{4} b^{2} c^{3} - 2 \, a^{5} b c^{2} d + a^{6} c d^{2}\right)} x^{4}\right)}}\right]"," ",0,"[-1/32*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^12 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^4)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 + 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)) + 4*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^8 + 2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2)*sqrt(d*x^8 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^12 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^4), -1/16*(((3*b^3*c^2 - 4*a*b^2*c*d)*x^12 + (3*a*b^2*c^2 - 4*a^2*b*c*d)*x^4)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)) + 2*((3*a*b^3*c^2 - 5*a^2*b^2*c*d + 2*a^3*b*d^2)*x^8 + 2*a^2*b^2*c^2 - 4*a^3*b*c*d + 2*a^4*d^2)*sqrt(d*x^8 + c))/((a^3*b^3*c^3 - 2*a^4*b^2*c^2*d + a^5*b*c*d^2)*x^12 + (a^4*b^2*c^3 - 2*a^5*b*c^2*d + a^6*c*d^2)*x^4)]","B",0
917,1,760,0,0.762983," ","integrate(1/x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{20} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{12}\right)} \sqrt{-a b c + a^{2} d} \log\left(\frac{{\left(b^{2} c^{2} - 8 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{16} - 2 \, {\left(3 \, a b c^{2} - 4 \, a^{2} c d\right)} x^{8} + a^{2} c^{2} - 4 \, {\left({\left(b c - 2 \, a d\right)} x^{12} - a c x^{4}\right)} \sqrt{d x^{8} + c} \sqrt{-a b c + a^{2} d}}{b^{2} x^{16} + 2 \, a b x^{8} + a^{2}}\right) - 4 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{16} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{8} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2}\right)} \sqrt{d x^{8} + c}}{96 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{20} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{12}\right)}}, \frac{3 \, {\left({\left(5 \, b^{4} c^{3} - 6 \, a b^{3} c^{2} d\right)} x^{20} + {\left(5 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d\right)} x^{12}\right)} \sqrt{a b c - a^{2} d} \arctan\left(\frac{{\left({\left(b c - 2 \, a d\right)} x^{8} - a c\right)} \sqrt{d x^{8} + c} \sqrt{a b c - a^{2} d}}{2 \, {\left({\left(a b c d - a^{2} d^{2}\right)} x^{12} + {\left(a b c^{2} - a^{2} c d\right)} x^{4}\right)}}\right) + 2 \, {\left({\left(15 \, a b^{4} c^{3} - 23 \, a^{2} b^{3} c^{2} d + 4 \, a^{3} b^{2} c d^{2} + 4 \, a^{4} b d^{3}\right)} x^{16} + 2 \, {\left(5 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2} + 2 \, a^{5} d^{3}\right)} x^{8} - 2 \, a^{3} b^{2} c^{3} + 4 \, a^{4} b c^{2} d - 2 \, a^{5} c d^{2}\right)} \sqrt{d x^{8} + c}}{48 \, {\left({\left(a^{4} b^{3} c^{4} - 2 \, a^{5} b^{2} c^{3} d + a^{6} b c^{2} d^{2}\right)} x^{20} + {\left(a^{5} b^{2} c^{4} - 2 \, a^{6} b c^{3} d + a^{7} c^{2} d^{2}\right)} x^{12}\right)}}\right]"," ",0,"[-1/96*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^20 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^12)*sqrt(-a*b*c + a^2*d)*log(((b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*x^16 - 2*(3*a*b*c^2 - 4*a^2*c*d)*x^8 + a^2*c^2 - 4*((b*c - 2*a*d)*x^12 - a*c*x^4)*sqrt(d*x^8 + c)*sqrt(-a*b*c + a^2*d))/(b^2*x^16 + 2*a*b*x^8 + a^2)) - 4*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^16 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^8 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2)*sqrt(d*x^8 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^20 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^12), 1/48*(3*((5*b^4*c^3 - 6*a*b^3*c^2*d)*x^20 + (5*a*b^3*c^3 - 6*a^2*b^2*c^2*d)*x^12)*sqrt(a*b*c - a^2*d)*arctan(1/2*((b*c - 2*a*d)*x^8 - a*c)*sqrt(d*x^8 + c)*sqrt(a*b*c - a^2*d)/((a*b*c*d - a^2*d^2)*x^12 + (a*b*c^2 - a^2*c*d)*x^4)) + 2*((15*a*b^4*c^3 - 23*a^2*b^3*c^2*d + 4*a^3*b^2*c*d^2 + 4*a^4*b*d^3)*x^16 + 2*(5*a^2*b^3*c^3 - 8*a^3*b^2*c^2*d + a^4*b*c*d^2 + 2*a^5*d^3)*x^8 - 2*a^3*b^2*c^3 + 4*a^4*b*c^2*d - 2*a^5*c*d^2)*sqrt(d*x^8 + c))/((a^4*b^3*c^4 - 2*a^5*b^2*c^3*d + a^6*b*c^2*d^2)*x^20 + (a^5*b^2*c^4 - 2*a^6*b*c^3*d + a^7*c^2*d^2)*x^12)]","A",0
918,-1,0,0,0.000000," ","integrate(x^9/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate(x/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,-1,0,0,0.000000," ","integrate(1/x^7/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
921,-1,0,0,0.000000," ","integrate(x^13/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
922,-1,0,0,0.000000," ","integrate(x^5/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
923,-1,0,0,0.000000," ","integrate(1/x^3/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
924,-1,0,0,0.000000," ","integrate(x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate(x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate(1/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,0,0,0,0.859134," ","integrate(1/x^2/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x^{8} + c}}{b^{2} d x^{26} + {\left(b^{2} c + 2 \, a b d\right)} x^{18} + {\left(2 \, a b c + a^{2} d\right)} x^{10} + a^{2} c x^{2}}, x\right)"," ",0,"integral(sqrt(d*x^8 + c)/(b^2*d*x^26 + (b^2*c + 2*a*b*d)*x^18 + (2*a*b*c + a^2*d)*x^10 + a^2*c*x^2), x)","F",0
928,-1,0,0,0.000000," ","integrate(1/x^4/(b*x^8+a)^2/(d*x^8+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
929,1,242,0,0.436667," ","integrate((a+b/x^2)*x^5*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, b c d^{2} - a d^{3}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(8 \, a c^{3} x^{6} + 2 \, {\left(6 \, b c^{3} + a c^{2} d\right)} x^{4} + 3 \, {\left(2 \, b c^{2} d - a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{96 \, c^{3}}, \frac{3 \, {\left(2 \, b c d^{2} - a d^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(8 \, a c^{3} x^{6} + 2 \, {\left(6 \, b c^{3} + a c^{2} d\right)} x^{4} + 3 \, {\left(2 \, b c^{2} d - a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{48 \, c^{3}}\right]"," ",0,"[-1/96*(3*(2*b*c*d^2 - a*d^3)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(8*a*c^3*x^6 + 2*(6*b*c^3 + a*c^2*d)*x^4 + 3*(2*b*c^2*d - a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/c^3, 1/48*(3*(2*b*c*d^2 - a*d^3)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (8*a*c^3*x^6 + 2*(6*b*c^3 + a*c^2*d)*x^4 + 3*(2*b*c^2*d - a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/c^3]","A",0
930,1,191,0,0.438185," ","integrate((a+b/x^2)*x^3*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, b c d - a d^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(2 \, a c^{2} x^{4} + {\left(4 \, b c^{2} + a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, c^{2}}, -\frac{{\left(4 \, b c d - a d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(2 \, a c^{2} x^{4} + {\left(4 \, b c^{2} + a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, c^{2}}\right]"," ",0,"[-1/16*((4*b*c*d - a*d^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(2*a*c^2*x^4 + (4*b*c^2 + a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c^2, -1/8*((4*b*c*d - a*d^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (2*a*c^2*x^4 + (4*b*c^2 + a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c^2]","A",0
931,1,155,0,0.432836," ","integrate((a+b/x^2)*x*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, b c + a d\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) + 2 \, {\left(a c x^{2} - 2 \, b c\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{4 \, c}, -\frac{{\left(2 \, b c + a d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(a c x^{2} - 2 \, b c\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, c}\right]"," ",0,"[1/4*((2*b*c + a*d)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) + 2*(a*c*x^2 - 2*b*c)*sqrt((c*x^2 + d)/x^2))/c, -1/2*((2*b*c + a*d)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (a*c*x^2 - 2*b*c)*sqrt((c*x^2 + d)/x^2))/c]","A",0
932,1,166,0,0.441151," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{c} d x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left({\left(b c + 3 \, a d\right)} x^{2} + b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{6 \, d x^{2}}, -\frac{3 \, a \sqrt{-c} d x^{2} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left({\left(b c + 3 \, a d\right)} x^{2} + b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, d x^{2}}\right]"," ",0,"[1/6*(3*a*sqrt(c)*d*x^2*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*((b*c + 3*a*d)*x^2 + b*d)*sqrt((c*x^2 + d)/x^2))/(d*x^2), -1/3*(3*a*sqrt(-c)*d*x^2*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + ((b*c + 3*a*d)*x^2 + b*d)*sqrt((c*x^2 + d)/x^2))/(d*x^2)]","A",0
933,1,60,0,0.432268," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b c^{2} - 5 \, a c d\right)} x^{4} - 3 \, b d^{2} - {\left(b c d + 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, d^{2} x^{4}}"," ",0,"1/15*((2*b*c^2 - 5*a*c*d)*x^4 - 3*b*d^2 - (b*c*d + 5*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^2*x^4)","A",0
934,1,85,0,0.432113," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(4 \, b c^{3} - 7 \, a c^{2} d\right)} x^{6} - {\left(4 \, b c^{2} d - 7 \, a c d^{2}\right)} x^{4} + 15 \, b d^{3} + 3 \, {\left(b c d^{2} + 7 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{105 \, d^{3} x^{6}}"," ",0,"-1/105*(2*(4*b*c^3 - 7*a*c^2*d)*x^6 - (4*b*c^2*d - 7*a*c*d^2)*x^4 + 15*b*d^3 + 3*(b*c*d^2 + 7*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^3*x^6)","A",0
935,1,109,0,0.482471," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^7,x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(2 \, b c^{4} - 3 \, a c^{3} d\right)} x^{8} - 4 \, {\left(2 \, b c^{3} d - 3 \, a c^{2} d^{2}\right)} x^{6} - 35 \, b d^{4} + 3 \, {\left(2 \, b c^{2} d^{2} - 3 \, a c d^{3}\right)} x^{4} - 5 \, {\left(b c d^{3} + 9 \, a d^{4}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{315 \, d^{4} x^{8}}"," ",0,"1/315*(8*(2*b*c^4 - 3*a*c^3*d)*x^8 - 4*(2*b*c^3*d - 3*a*c^2*d^2)*x^6 - 35*b*d^4 + 3*(2*b*c^2*d^2 - 3*a*c*d^3)*x^4 - 5*(b*c*d^3 + 9*a*d^4)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^4*x^8)","A",0
936,1,133,0,0.526032," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^9,x, algorithm=""fricas"")","-\frac{{\left(16 \, {\left(8 \, b c^{5} - 11 \, a c^{4} d\right)} x^{10} - 8 \, {\left(8 \, b c^{4} d - 11 \, a c^{3} d^{2}\right)} x^{8} + 6 \, {\left(8 \, b c^{3} d^{2} - 11 \, a c^{2} d^{3}\right)} x^{6} + 315 \, b d^{5} - 5 \, {\left(8 \, b c^{2} d^{3} - 11 \, a c d^{4}\right)} x^{4} + 35 \, {\left(b c d^{4} + 11 \, a d^{5}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3465 \, d^{5} x^{10}}"," ",0,"-1/3465*(16*(8*b*c^5 - 11*a*c^4*d)*x^10 - 8*(8*b*c^4*d - 11*a*c^3*d^2)*x^8 + 6*(8*b*c^3*d^2 - 11*a*c^2*d^3)*x^6 + 315*b*d^5 - 5*(8*b*c^2*d^3 - 11*a*c*d^4)*x^4 + 35*(b*c*d^4 + 11*a*d^5)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^5*x^10)","A",0
937,1,131,0,0.431607," ","integrate((a+b/x^2)*x^10*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(315 \, a c^{5} x^{11} + 35 \, {\left(11 \, b c^{5} + a c^{4} d\right)} x^{9} + 5 \, {\left(11 \, b c^{4} d - 8 \, a c^{3} d^{2}\right)} x^{7} - 6 \, {\left(11 \, b c^{3} d^{2} - 8 \, a c^{2} d^{3}\right)} x^{5} + 8 \, {\left(11 \, b c^{2} d^{3} - 8 \, a c d^{4}\right)} x^{3} - 16 \, {\left(11 \, b c d^{4} - 8 \, a d^{5}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3465 \, c^{5}}"," ",0,"1/3465*(315*a*c^5*x^11 + 35*(11*b*c^5 + a*c^4*d)*x^9 + 5*(11*b*c^4*d - 8*a*c^3*d^2)*x^7 - 6*(11*b*c^3*d^2 - 8*a*c^2*d^3)*x^5 + 8*(11*b*c^2*d^3 - 8*a*c*d^4)*x^3 - 16*(11*b*c*d^4 - 8*a*d^5)*x)*sqrt((c*x^2 + d)/x^2)/c^5","A",0
938,1,107,0,0.417653," ","integrate((a+b/x^2)*x^8*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(35 \, a c^{4} x^{9} + 5 \, {\left(9 \, b c^{4} + a c^{3} d\right)} x^{7} + 3 \, {\left(3 \, b c^{3} d - 2 \, a c^{2} d^{2}\right)} x^{5} - 4 \, {\left(3 \, b c^{2} d^{2} - 2 \, a c d^{3}\right)} x^{3} + 8 \, {\left(3 \, b c d^{3} - 2 \, a d^{4}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{315 \, c^{4}}"," ",0,"1/315*(35*a*c^4*x^9 + 5*(9*b*c^4 + a*c^3*d)*x^7 + 3*(3*b*c^3*d - 2*a*c^2*d^2)*x^5 - 4*(3*b*c^2*d^2 - 2*a*c*d^3)*x^3 + 8*(3*b*c*d^3 - 2*a*d^4)*x)*sqrt((c*x^2 + d)/x^2)/c^4","A",0
939,1,82,0,0.416684," ","integrate((a+b/x^2)*x^6*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, a c^{3} x^{7} + 3 \, {\left(7 \, b c^{3} + a c^{2} d\right)} x^{5} + {\left(7 \, b c^{2} d - 4 \, a c d^{2}\right)} x^{3} - 2 \, {\left(7 \, b c d^{2} - 4 \, a d^{3}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{105 \, c^{3}}"," ",0,"1/105*(15*a*c^3*x^7 + 3*(7*b*c^3 + a*c^2*d)*x^5 + (7*b*c^2*d - 4*a*c*d^2)*x^3 - 2*(7*b*c*d^2 - 4*a*d^3)*x)*sqrt((c*x^2 + d)/x^2)/c^3","A",0
940,1,57,0,0.417252," ","integrate((a+b/x^2)*x^4*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c^{2} x^{5} + {\left(5 \, b c^{2} + a c d\right)} x^{3} + {\left(5 \, b c d - 2 \, a d^{2}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, c^{2}}"," ",0,"1/15*(3*a*c^2*x^5 + (5*b*c^2 + a*c*d)*x^3 + (5*b*c*d - 2*a*d^2)*x)*sqrt((c*x^2 + d)/x^2)/c^2","A",0
941,1,156,0,0.438851," ","integrate((a+b/x^2)*x^2*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b c \sqrt{d} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(a c x^{3} + {\left(3 \, b c + a d\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{6 \, c}, \frac{3 \, b c \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(a c x^{3} + {\left(3 \, b c + a d\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, c}\right]"," ",0,"[1/6*(3*b*c*sqrt(d)*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(a*c*x^3 + (3*b*c + a*d)*x)*sqrt((c*x^2 + d)/x^2))/c, 1/3*(3*b*c*sqrt(-d)*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (a*c*x^3 + (3*b*c + a*d)*x)*sqrt((c*x^2 + d)/x^2))/c]","A",0
942,1,164,0,0.446147," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c + 2 \, a d\right)} \sqrt{d} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a d x^{2} - b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{4 \, d x}, \frac{{\left(b c + 2 \, a d\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(2 \, a d x^{2} - b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, d x}\right]"," ",0,"[1/4*((b*c + 2*a*d)*sqrt(d)*x*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(2*a*d*x^2 - b*d)*sqrt((c*x^2 + d)/x^2))/(d*x), 1/2*((b*c + 2*a*d)*sqrt(-d)*x*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (2*a*d*x^2 - b*d)*sqrt((c*x^2 + d)/x^2))/(d*x)]","A",0
943,1,194,0,0.436759," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{2} - 4 \, a c d\right)} \sqrt{d} x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, b d^{2} + {\left(b c d + 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, d^{2} x^{3}}, -\frac{{\left(b c^{2} - 4 \, a c d\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(2 \, b d^{2} + {\left(b c d + 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, d^{2} x^{3}}\right]"," ",0,"[-1/16*((b*c^2 - 4*a*c*d)*sqrt(d)*x^3*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(2*b*d^2 + (b*c*d + 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^2*x^3), -1/8*((b*c^2 - 4*a*c*d)*sqrt(-d)*x^3*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (2*b*d^2 + (b*c*d + 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^2*x^3)]","A",0
944,1,244,0,0.455065," ","integrate((a+b/x^2)*(c+d/x^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c^{3} - 2 \, a c^{2} d\right)} \sqrt{d} x^{5} \log\left(-\frac{c x^{2} + 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) - 2 \, {\left(3 \, {\left(b c^{2} d - 2 \, a c d^{2}\right)} x^{4} - 8 \, b d^{3} - 2 \, {\left(b c d^{2} + 6 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{96 \, d^{3} x^{5}}, \frac{3 \, {\left(b c^{3} - 2 \, a c^{2} d\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(3 \, {\left(b c^{2} d - 2 \, a c d^{2}\right)} x^{4} - 8 \, b d^{3} - 2 \, {\left(b c d^{2} + 6 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{48 \, d^{3} x^{5}}\right]"," ",0,"[-1/96*(3*(b*c^3 - 2*a*c^2*d)*sqrt(d)*x^5*log(-(c*x^2 + 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) - 2*(3*(b*c^2*d - 2*a*c*d^2)*x^4 - 8*b*d^3 - 2*(b*c*d^2 + 6*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^5), 1/48*(3*(b*c^3 - 2*a*c^2*d)*sqrt(-d)*x^5*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (3*(b*c^2*d - 2*a*c*d^2)*x^4 - 8*b*d^3 - 2*(b*c*d^2 + 6*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^5)]","A",0
945,1,243,0,0.448285," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, b c d^{2} - a d^{3}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(8 \, a c^{3} x^{6} + 2 \, {\left(6 \, b c^{3} + 7 \, a c^{2} d\right)} x^{4} + 3 \, {\left(10 \, b c^{2} d + a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{96 \, c^{2}}, -\frac{3 \, {\left(6 \, b c d^{2} - a d^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(8 \, a c^{3} x^{6} + 2 \, {\left(6 \, b c^{3} + 7 \, a c^{2} d\right)} x^{4} + 3 \, {\left(10 \, b c^{2} d + a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{48 \, c^{2}}\right]"," ",0,"[-1/96*(3*(6*b*c*d^2 - a*d^3)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(8*a*c^3*x^6 + 2*(6*b*c^3 + 7*a*c^2*d)*x^4 + 3*(10*b*c^2*d + a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/c^2, -1/48*(3*(6*b*c*d^2 - a*d^3)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (8*a*c^3*x^6 + 2*(6*b*c^3 + 7*a*c^2*d)*x^4 + 3*(10*b*c^2*d + a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/c^2]","A",0
946,1,203,0,0.454854," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, b c d + a d^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) + 2 \, {\left(2 \, a c^{2} x^{4} - 8 \, b c d + {\left(4 \, b c^{2} + 5 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, c}, -\frac{3 \, {\left(4 \, b c d + a d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(2 \, a c^{2} x^{4} - 8 \, b c d + {\left(4 \, b c^{2} + 5 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, c}\right]"," ",0,"[1/16*(3*(4*b*c*d + a*d^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) + 2*(2*a*c^2*x^4 - 8*b*c*d + (4*b*c^2 + 5*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c, -1/8*(3*(4*b*c*d + a*d^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (2*a*c^2*x^4 - 8*b*c*d + (4*b*c^2 + 5*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c]","A",0
947,1,195,0,0.441627," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, b c + 3 \, a d\right)} \sqrt{c} x^{2} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) + 2 \, {\left(3 \, a c x^{4} - 2 \, {\left(4 \, b c + 3 \, a d\right)} x^{2} - 2 \, b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{12 \, x^{2}}, -\frac{3 \, {\left(2 \, b c + 3 \, a d\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(3 \, a c x^{4} - 2 \, {\left(4 \, b c + 3 \, a d\right)} x^{2} - 2 \, b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{6 \, x^{2}}\right]"," ",0,"[1/12*(3*(2*b*c + 3*a*d)*sqrt(c)*x^2*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) + 2*(3*a*c*x^4 - 2*(4*b*c + 3*a*d)*x^2 - 2*b*d)*sqrt((c*x^2 + d)/x^2))/x^2, -1/6*(3*(2*b*c + 3*a*d)*sqrt(-c)*x^2*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (3*a*c*x^4 - 2*(4*b*c + 3*a*d)*x^2 - 2*b*d)*sqrt((c*x^2 + d)/x^2))/x^2]","A",0
948,1,213,0,0.434670," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a c^{\frac{3}{2}} d x^{4} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left({\left(3 \, b c^{2} + 20 \, a c d\right)} x^{4} + 3 \, b d^{2} + {\left(6 \, b c d + 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{30 \, d x^{4}}, -\frac{15 \, a \sqrt{-c} c d x^{4} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left({\left(3 \, b c^{2} + 20 \, a c d\right)} x^{4} + 3 \, b d^{2} + {\left(6 \, b c d + 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, d x^{4}}\right]"," ",0,"[1/30*(15*a*c^(3/2)*d*x^4*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*((3*b*c^2 + 20*a*c*d)*x^4 + 3*b*d^2 + (6*b*c*d + 5*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d*x^4), -1/15*(15*a*sqrt(-c)*c*d*x^4*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + ((3*b*c^2 + 20*a*c*d)*x^4 + 3*b*d^2 + (6*b*c*d + 5*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d*x^4)]","A",0
949,1,84,0,0.424410," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b c^{3} - 7 \, a c^{2} d\right)} x^{6} - {\left(b c^{2} d + 14 \, a c d^{2}\right)} x^{4} - 5 \, b d^{3} - {\left(8 \, b c d^{2} + 7 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{35 \, d^{2} x^{6}}"," ",0,"1/35*((2*b*c^3 - 7*a*c^2*d)*x^6 - (b*c^2*d + 14*a*c*d^2)*x^4 - 5*b*d^3 - (8*b*c*d^2 + 7*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^2*x^6)","B",0
950,1,109,0,0.481499," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(4 \, b c^{4} - 9 \, a c^{3} d\right)} x^{8} - {\left(4 \, b c^{3} d - 9 \, a c^{2} d^{2}\right)} x^{6} + 35 \, b d^{4} + 3 \, {\left(b c^{2} d^{2} + 24 \, a c d^{3}\right)} x^{4} + 5 \, {\left(10 \, b c d^{3} + 9 \, a d^{4}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{315 \, d^{3} x^{8}}"," ",0,"-1/315*(2*(4*b*c^4 - 9*a*c^3*d)*x^8 - (4*b*c^3*d - 9*a*c^2*d^2)*x^6 + 35*b*d^4 + 3*(b*c^2*d^2 + 24*a*c*d^3)*x^4 + 5*(10*b*c*d^3 + 9*a*d^4)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^3*x^8)","A",0
951,1,134,0,0.540604," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^7,x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(6 \, b c^{5} - 11 \, a c^{4} d\right)} x^{10} - 4 \, {\left(6 \, b c^{4} d - 11 \, a c^{3} d^{2}\right)} x^{8} + 3 \, {\left(6 \, b c^{3} d^{2} - 11 \, a c^{2} d^{3}\right)} x^{6} - 315 \, b d^{5} - 5 \, {\left(3 \, b c^{2} d^{3} + 110 \, a c d^{4}\right)} x^{4} - 35 \, {\left(12 \, b c d^{4} + 11 \, a d^{5}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3465 \, d^{4} x^{10}}"," ",0,"1/3465*(8*(6*b*c^5 - 11*a*c^4*d)*x^10 - 4*(6*b*c^4*d - 11*a*c^3*d^2)*x^8 + 3*(6*b*c^3*d^2 - 11*a*c^2*d^3)*x^6 - 315*b*d^5 - 5*(3*b*c^2*d^3 + 110*a*c*d^4)*x^4 - 35*(12*b*c*d^4 + 11*a*d^5)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^4*x^10)","A",0
952,1,157,0,0.607578," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{{\left(16 \, {\left(8 \, b c^{6} - 13 \, a c^{5} d\right)} x^{12} - 8 \, {\left(8 \, b c^{5} d - 13 \, a c^{4} d^{2}\right)} x^{10} + 6 \, {\left(8 \, b c^{4} d^{2} - 13 \, a c^{3} d^{3}\right)} x^{8} + 1155 \, b d^{6} - 5 \, {\left(8 \, b c^{3} d^{3} - 13 \, a c^{2} d^{4}\right)} x^{6} + 35 \, {\left(b c^{2} d^{4} + 52 \, a c d^{5}\right)} x^{4} + 105 \, {\left(14 \, b c d^{5} + 13 \, a d^{6}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15015 \, d^{5} x^{12}}"," ",0,"-1/15015*(16*(8*b*c^6 - 13*a*c^5*d)*x^12 - 8*(8*b*c^5*d - 13*a*c^4*d^2)*x^10 + 6*(8*b*c^4*d^2 - 13*a*c^3*d^3)*x^8 + 1155*b*d^6 - 5*(8*b*c^3*d^3 - 13*a*c^2*d^4)*x^6 + 35*(b*c^2*d^4 + 52*a*c*d^5)*x^4 + 105*(14*b*c*d^5 + 13*a*d^6)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^5*x^12)","A",0
953,1,155,0,0.417959," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^12,x, algorithm=""fricas"")","\frac{{\left(1155 \, a c^{6} x^{13} + 105 \, {\left(13 \, b c^{6} + 14 \, a c^{5} d\right)} x^{11} + 35 \, {\left(52 \, b c^{5} d + a c^{4} d^{2}\right)} x^{9} + 5 \, {\left(13 \, b c^{4} d^{2} - 8 \, a c^{3} d^{3}\right)} x^{7} - 6 \, {\left(13 \, b c^{3} d^{3} - 8 \, a c^{2} d^{4}\right)} x^{5} + 8 \, {\left(13 \, b c^{2} d^{4} - 8 \, a c d^{5}\right)} x^{3} - 16 \, {\left(13 \, b c d^{5} - 8 \, a d^{6}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15015 \, c^{5}}"," ",0,"1/15015*(1155*a*c^6*x^13 + 105*(13*b*c^6 + 14*a*c^5*d)*x^11 + 35*(52*b*c^5*d + a*c^4*d^2)*x^9 + 5*(13*b*c^4*d^2 - 8*a*c^3*d^3)*x^7 - 6*(13*b*c^3*d^3 - 8*a*c^2*d^4)*x^5 + 8*(13*b*c^2*d^4 - 8*a*c*d^5)*x^3 - 16*(13*b*c*d^5 - 8*a*d^6)*x)*sqrt((c*x^2 + d)/x^2)/c^5","A",0
954,1,132,0,0.435628," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^10,x, algorithm=""fricas"")","\frac{{\left(315 \, a c^{5} x^{11} + 35 \, {\left(11 \, b c^{5} + 12 \, a c^{4} d\right)} x^{9} + 5 \, {\left(110 \, b c^{4} d + 3 \, a c^{3} d^{2}\right)} x^{7} + 3 \, {\left(11 \, b c^{3} d^{2} - 6 \, a c^{2} d^{3}\right)} x^{5} - 4 \, {\left(11 \, b c^{2} d^{3} - 6 \, a c d^{4}\right)} x^{3} + 8 \, {\left(11 \, b c d^{4} - 6 \, a d^{5}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3465 \, c^{4}}"," ",0,"1/3465*(315*a*c^5*x^11 + 35*(11*b*c^5 + 12*a*c^4*d)*x^9 + 5*(110*b*c^4*d + 3*a*c^3*d^2)*x^7 + 3*(11*b*c^3*d^2 - 6*a*c^2*d^3)*x^5 - 4*(11*b*c^2*d^3 - 6*a*c*d^4)*x^3 + 8*(11*b*c*d^4 - 6*a*d^5)*x)*sqrt((c*x^2 + d)/x^2)/c^4","A",0
955,1,106,0,0.425176," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^8,x, algorithm=""fricas"")","\frac{{\left(35 \, a c^{4} x^{9} + 5 \, {\left(9 \, b c^{4} + 10 \, a c^{3} d\right)} x^{7} + 3 \, {\left(24 \, b c^{3} d + a c^{2} d^{2}\right)} x^{5} + {\left(9 \, b c^{2} d^{2} - 4 \, a c d^{3}\right)} x^{3} - 2 \, {\left(9 \, b c d^{3} - 4 \, a d^{4}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{315 \, c^{3}}"," ",0,"1/315*(35*a*c^4*x^9 + 5*(9*b*c^4 + 10*a*c^3*d)*x^7 + 3*(24*b*c^3*d + a*c^2*d^2)*x^5 + (9*b*c^2*d^2 - 4*a*c*d^3)*x^3 - 2*(9*b*c*d^3 - 4*a*d^4)*x)*sqrt((c*x^2 + d)/x^2)/c^3","A",0
956,1,80,0,0.410086," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^6,x, algorithm=""fricas"")","\frac{{\left(5 \, a c^{3} x^{7} + {\left(7 \, b c^{3} + 8 \, a c^{2} d\right)} x^{5} + {\left(14 \, b c^{2} d + a c d^{2}\right)} x^{3} + {\left(7 \, b c d^{2} - 2 \, a d^{3}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{35 \, c^{2}}"," ",0,"1/35*(5*a*c^3*x^7 + (7*b*c^3 + 8*a*c^2*d)*x^5 + (14*b*c^2*d + a*c*d^2)*x^3 + (7*b*c*d^2 - 2*a*d^3)*x)*sqrt((c*x^2 + d)/x^2)/c^2","A",0
957,1,203,0,0.452297," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^4,x, algorithm=""fricas"")","\left[\frac{15 \, b c d^{\frac{3}{2}} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(3 \, a c^{2} x^{5} + {\left(5 \, b c^{2} + 6 \, a c d\right)} x^{3} + {\left(20 \, b c d + 3 \, a d^{2}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{30 \, c}, \frac{15 \, b c \sqrt{-d} d \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(3 \, a c^{2} x^{5} + {\left(5 \, b c^{2} + 6 \, a c d\right)} x^{3} + {\left(20 \, b c d + 3 \, a d^{2}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, c}\right]"," ",0,"[1/30*(15*b*c*d^(3/2)*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(3*a*c^2*x^5 + (5*b*c^2 + 6*a*c*d)*x^3 + (20*b*c*d + 3*a*d^2)*x)*sqrt((c*x^2 + d)/x^2))/c, 1/15*(15*b*c*sqrt(-d)*d*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (3*a*c^2*x^5 + (5*b*c^2 + 6*a*c*d)*x^3 + (20*b*c*d + 3*a*d^2)*x)*sqrt((c*x^2 + d)/x^2))/c]","A",0
958,1,190,0,0.438946," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)*x^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b c + 2 \, a d\right)} \sqrt{d} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, a c x^{4} + 2 \, {\left(3 \, b c + 4 \, a d\right)} x^{2} - 3 \, b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{12 \, x}, \frac{3 \, {\left(3 \, b c + 2 \, a d\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(2 \, a c x^{4} + 2 \, {\left(3 \, b c + 4 \, a d\right)} x^{2} - 3 \, b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{6 \, x}\right]"," ",0,"[1/12*(3*(3*b*c + 2*a*d)*sqrt(d)*x*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(2*a*c*x^4 + 2*(3*b*c + 4*a*d)*x^2 - 3*b*d)*sqrt((c*x^2 + d)/x^2))/x, 1/6*(3*(3*b*c + 2*a*d)*sqrt(-d)*x*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (2*a*c*x^4 + 2*(3*b*c + 4*a*d)*x^2 - 3*b*d)*sqrt((c*x^2 + d)/x^2))/x]","A",0
959,1,216,0,0.439118," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c^{2} + 4 \, a c d\right)} \sqrt{d} x^{3} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(8 \, a c d x^{4} - 2 \, b d^{2} - {\left(5 \, b c d + 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, d x^{3}}, \frac{3 \, {\left(b c^{2} + 4 \, a c d\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(8 \, a c d x^{4} - 2 \, b d^{2} - {\left(5 \, b c d + 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, d x^{3}}\right]"," ",0,"[1/16*(3*(b*c^2 + 4*a*c*d)*sqrt(d)*x^3*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(8*a*c*d*x^4 - 2*b*d^2 - (5*b*c*d + 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d*x^3), 1/8*(3*(b*c^2 + 4*a*c*d)*sqrt(-d)*x^3*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (8*a*c*d*x^4 - 2*b*d^2 - (5*b*c*d + 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d*x^3)]","A",0
960,1,246,0,0.462998," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c^{3} - 6 \, a c^{2} d\right)} \sqrt{d} x^{5} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(3 \, {\left(b c^{2} d + 10 \, a c d^{2}\right)} x^{4} + 8 \, b d^{3} + 2 \, {\left(7 \, b c d^{2} + 6 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{96 \, d^{2} x^{5}}, -\frac{3 \, {\left(b c^{3} - 6 \, a c^{2} d\right)} \sqrt{-d} x^{5} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(3 \, {\left(b c^{2} d + 10 \, a c d^{2}\right)} x^{4} + 8 \, b d^{3} + 2 \, {\left(7 \, b c d^{2} + 6 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{48 \, d^{2} x^{5}}\right]"," ",0,"[-1/96*(3*(b*c^3 - 6*a*c^2*d)*sqrt(d)*x^5*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(3*(b*c^2*d + 10*a*c*d^2)*x^4 + 8*b*d^3 + 2*(7*b*c*d^2 + 6*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^2*x^5), -1/48*(3*(b*c^3 - 6*a*c^2*d)*sqrt(-d)*x^5*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (3*(b*c^2*d + 10*a*c*d^2)*x^4 + 8*b*d^3 + 2*(7*b*c*d^2 + 6*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^2*x^5)]","A",0
961,1,298,0,0.474015," ","integrate((a+b/x^2)*(c+d/x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, b c^{4} - 8 \, a c^{3} d\right)} \sqrt{d} x^{7} \log\left(-\frac{c x^{2} + 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) - 2 \, {\left(3 \, {\left(3 \, b c^{3} d - 8 \, a c^{2} d^{2}\right)} x^{6} - 48 \, b d^{4} - 2 \, {\left(3 \, b c^{2} d^{2} + 56 \, a c d^{3}\right)} x^{4} - 8 \, {\left(9 \, b c d^{3} + 8 \, a d^{4}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{768 \, d^{3} x^{7}}, \frac{3 \, {\left(3 \, b c^{4} - 8 \, a c^{3} d\right)} \sqrt{-d} x^{7} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(3 \, {\left(3 \, b c^{3} d - 8 \, a c^{2} d^{2}\right)} x^{6} - 48 \, b d^{4} - 2 \, {\left(3 \, b c^{2} d^{2} + 56 \, a c d^{3}\right)} x^{4} - 8 \, {\left(9 \, b c d^{3} + 8 \, a d^{4}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{384 \, d^{3} x^{7}}\right]"," ",0,"[-1/768*(3*(3*b*c^4 - 8*a*c^3*d)*sqrt(d)*x^7*log(-(c*x^2 + 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) - 2*(3*(3*b*c^3*d - 8*a*c^2*d^2)*x^6 - 48*b*d^4 - 2*(3*b*c^2*d^2 + 56*a*c*d^3)*x^4 - 8*(9*b*c*d^3 + 8*a*d^4)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^7), 1/384*(3*(3*b*c^4 - 8*a*c^3*d)*sqrt(-d)*x^7*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (3*(3*b*c^3*d - 8*a*c^2*d^2)*x^6 - 48*b*d^4 - 2*(3*b*c^2*d^2 + 56*a*c*d^3)*x^4 - 8*(9*b*c*d^3 + 8*a*d^4)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^7)]","A",0
962,1,192,0,0.436440," ","integrate((a+b/x^2)*x^3/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, b c d - 3 \, a d^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(2 \, a c^{2} x^{4} + {\left(4 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, c^{3}}, \frac{{\left(4 \, b c d - 3 \, a d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(2 \, a c^{2} x^{4} + {\left(4 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((4*b*c*d - 3*a*d^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(2*a*c^2*x^4 + (4*b*c^2 - 3*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c^3, 1/8*((4*b*c*d - 3*a*d^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (2*a*c^2*x^4 + (4*b*c^2 - 3*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/c^3]","A",0
963,1,146,0,0.440354," ","integrate((a+b/x^2)*x/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a c x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - {\left(2 \, b c - a d\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right)}{4 \, c^{2}}, \frac{a c x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - {\left(2 \, b c - a d\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right)}{2 \, c^{2}}\right]"," ",0,"[1/4*(2*a*c*x^2*sqrt((c*x^2 + d)/x^2) - (2*b*c - a*d)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d))/c^2, 1/2*(a*c*x^2*sqrt((c*x^2 + d)/x^2) - (2*b*c - a*d)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)))/c^2]","A",0
964,1,130,0,0.438902," ","integrate((a+b/x^2)/x/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, b c \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, c d}, -\frac{a \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + b c \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c d}\right]"," ",0,"[1/2*(a*sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*b*c*sqrt((c*x^2 + d)/x^2))/(c*d), -(a*sqrt(-c)*d*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + b*c*sqrt((c*x^2 + d)/x^2))/(c*d)]","A",0
965,1,39,0,0.408993," ","integrate((a+b/x^2)/x^3/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b c - 3 \, a d\right)} x^{2} - b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, d^{2} x^{2}}"," ",0,"1/3*((2*b*c - 3*a*d)*x^2 - b*d)*sqrt((c*x^2 + d)/x^2)/(d^2*x^2)","A",0
966,1,62,0,0.430207," ","integrate((a+b/x^2)/x^5/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(4 \, b c^{2} - 5 \, a c d\right)} x^{4} + 3 \, b d^{2} - {\left(4 \, b c d - 5 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, d^{3} x^{4}}"," ",0,"-1/15*(2*(4*b*c^2 - 5*a*c*d)*x^4 + 3*b*d^2 - (4*b*c*d - 5*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^3*x^4)","A",0
967,1,86,0,0.429679," ","integrate((a+b/x^2)/x^7/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(6 \, b c^{3} - 7 \, a c^{2} d\right)} x^{6} - 4 \, {\left(6 \, b c^{2} d - 7 \, a c d^{2}\right)} x^{4} - 15 \, b d^{3} + 3 \, {\left(6 \, b c d^{2} - 7 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{105 \, d^{4} x^{6}}"," ",0,"1/105*(8*(6*b*c^3 - 7*a*c^2*d)*x^6 - 4*(6*b*c^2*d - 7*a*c*d^2)*x^4 - 15*b*d^3 + 3*(6*b*c*d^2 - 7*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2)/(d^4*x^6)","A",0
968,1,59,0,0.412511," ","integrate((a+b/x^2)*x^4/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c^{2} x^{5} + {\left(5 \, b c^{2} - 4 \, a c d\right)} x^{3} - 2 \, {\left(5 \, b c d - 4 \, a d^{2}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, c^{3}}"," ",0,"1/15*(3*a*c^2*x^5 + (5*b*c^2 - 4*a*c*d)*x^3 - 2*(5*b*c*d - 4*a*d^2)*x)*sqrt((c*x^2 + d)/x^2)/c^3","A",0
969,1,36,0,0.424245," ","integrate((a+b/x^2)*x^2/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a c x^{3} + {\left(3 \, b c - 2 \, a d\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, c^{2}}"," ",0,"1/3*(a*c*x^3 + (3*b*c - 2*a*d)*x)*sqrt((c*x^2 + d)/x^2)/c^2","A",0
970,1,131,0,0.444095," ","integrate((a+b/x^2)/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a d x \sqrt{\frac{c x^{2} + d}{x^{2}}} + b c \sqrt{d} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right)}{2 \, c d}, \frac{a d x \sqrt{\frac{c x^{2} + d}{x^{2}}} + b c \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right)}{c d}\right]"," ",0,"[1/2*(2*a*d*x*sqrt((c*x^2 + d)/x^2) + b*c*sqrt(d)*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2))/(c*d), (a*d*x*sqrt((c*x^2 + d)/x^2) + b*c*sqrt(-d)*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)))/(c*d)]","A",0
971,1,144,0,0.423392," ","integrate((a+b/x^2)/x^2/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c - 2 \, a d\right)} \sqrt{d} x \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, b d \sqrt{\frac{c x^{2} + d}{x^{2}}}}{4 \, d^{2} x}, -\frac{{\left(b c - 2 \, a d\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + b d \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, d^{2} x}\right]"," ",0,"[-1/4*((b*c - 2*a*d)*sqrt(d)*x*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*b*d*sqrt((c*x^2 + d)/x^2))/(d^2*x), -1/2*((b*c - 2*a*d)*sqrt(-d)*x*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + b*d*sqrt((c*x^2 + d)/x^2))/(d^2*x)]","A",0
972,1,201,0,0.453901," ","integrate((a+b/x^2)/x^4/(c+d/x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b c^{2} - 4 \, a c d\right)} \sqrt{d} x^{3} \log\left(-\frac{c x^{2} + 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(2 \, b d^{2} - {\left(3 \, b c d - 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, d^{3} x^{3}}, \frac{{\left(3 \, b c^{2} - 4 \, a c d\right)} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(2 \, b d^{2} - {\left(3 \, b c d - 4 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, d^{3} x^{3}}\right]"," ",0,"[-1/16*((3*b*c^2 - 4*a*c*d)*sqrt(d)*x^3*log(-(c*x^2 + 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(2*b*d^2 - (3*b*c*d - 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^3), 1/8*((3*b*c^2 - 4*a*c*d)*sqrt(-d)*x^3*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (2*b*d^2 - (3*b*c*d - 4*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(d^3*x^3)]","A",0
973,1,304,0,0.462111," ","integrate((a+b/x^2)*x^3/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, b c d^{2} - 5 \, a d^{3} + {\left(4 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(2 \, a c^{3} x^{6} + {\left(4 \, b c^{3} - 5 \, a c^{2} d\right)} x^{4} + 3 \, {\left(4 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, {\left(c^{5} x^{2} + c^{4} d\right)}}, \frac{3 \, {\left(4 \, b c d^{2} - 5 \, a d^{3} + {\left(4 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(2 \, a c^{3} x^{6} + {\left(4 \, b c^{3} - 5 \, a c^{2} d\right)} x^{4} + 3 \, {\left(4 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, {\left(c^{5} x^{2} + c^{4} d\right)}}\right]"," ",0,"[-1/16*(3*(4*b*c*d^2 - 5*a*d^3 + (4*b*c^2*d - 5*a*c*d^2)*x^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(2*a*c^3*x^6 + (4*b*c^3 - 5*a*c^2*d)*x^4 + 3*(4*b*c^2*d - 5*a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(c^5*x^2 + c^4*d), 1/8*(3*(4*b*c*d^2 - 5*a*d^3 + (4*b*c^2*d - 5*a*c*d^2)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (2*a*c^3*x^6 + (4*b*c^3 - 5*a*c^2*d)*x^4 + 3*(4*b*c^2*d - 5*a*c*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(c^5*x^2 + c^4*d)]","A",0
974,1,249,0,0.437573," ","integrate((a+b/x^2)*x/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, b c d - 3 \, a d^{2} + {\left(2 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right) - 2 \, {\left(a c^{2} x^{4} - {\left(2 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{4 \, {\left(c^{4} x^{2} + c^{3} d\right)}}, -\frac{{\left(2 \, b c d - 3 \, a d^{2} + {\left(2 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) - {\left(a c^{2} x^{4} - {\left(2 \, b c^{2} - 3 \, a c d\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, {\left(c^{4} x^{2} + c^{3} d\right)}}\right]"," ",0,"[-1/4*((2*b*c*d - 3*a*d^2 + (2*b*c^2 - 3*a*c*d)*x^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d) - 2*(a*c^2*x^4 - (2*b*c^2 - 3*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/(c^4*x^2 + c^3*d), -1/2*((2*b*c*d - 3*a*d^2 + (2*b*c^2 - 3*a*c*d)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) - (a*c^2*x^4 - (2*b*c^2 - 3*a*c*d)*x^2)*sqrt((c*x^2 + d)/x^2))/(c^4*x^2 + c^3*d)]","A",0
975,1,200,0,0.460786," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c^{2} - a c d\right)} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} + {\left(a c d x^{2} + a d^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - d\right)}{2 \, {\left(c^{3} d x^{2} + c^{2} d^{2}\right)}}, \frac{{\left(b c^{2} - a c d\right)} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}} - {\left(a c d x^{2} + a d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x^{2} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right)}{c^{3} d x^{2} + c^{2} d^{2}}\right]"," ",0,"[1/2*(2*(b*c^2 - a*c*d)*x^2*sqrt((c*x^2 + d)/x^2) + (a*c*d*x^2 + a*d^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c)*x^2*sqrt((c*x^2 + d)/x^2) - d))/(c^3*d*x^2 + c^2*d^2), ((b*c^2 - a*c*d)*x^2*sqrt((c*x^2 + d)/x^2) - (a*c*d*x^2 + a*d^2)*sqrt(-c)*arctan(sqrt(-c)*x^2*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)))/(c^3*d*x^2 + c^2*d^2)]","B",0
976,1,46,0,0.421617," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^3,x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, b c - a d\right)} x^{2} + b d\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c d^{2} x^{2} + d^{3}}"," ",0,"-((2*b*c - a*d)*x^2 + b*d)*sqrt((c*x^2 + d)/x^2)/(c*d^2*x^2 + d^3)","A",0
977,1,73,0,0.421787," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^5,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(4 \, b c^{2} - 3 \, a c d\right)} x^{4} - b d^{2} + {\left(4 \, b c d - 3 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, {\left(c d^{3} x^{4} + d^{4} x^{2}\right)}}"," ",0,"1/3*(2*(4*b*c^2 - 3*a*c*d)*x^4 - b*d^2 + (4*b*c*d - 3*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2)/(c*d^3*x^4 + d^4*x^2)","A",0
978,1,98,0,0.428637," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(6 \, b c^{3} - 5 \, a c^{2} d\right)} x^{6} + 4 \, {\left(6 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{4} + 3 \, b d^{3} - {\left(6 \, b c d^{2} - 5 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, {\left(c d^{4} x^{6} + d^{5} x^{4}\right)}}"," ",0,"-1/15*(8*(6*b*c^3 - 5*a*c^2*d)*x^6 + 4*(6*b*c^2*d - 5*a*c*d^2)*x^4 + 3*b*d^3 - (6*b*c*d^2 - 5*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2)/(c*d^4*x^6 + d^5*x^4)","A",0
979,1,121,0,0.453614," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^9,x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(8 \, b c^{4} - 7 \, a c^{3} d\right)} x^{8} + 8 \, {\left(8 \, b c^{3} d - 7 \, a c^{2} d^{2}\right)} x^{6} - 5 \, b d^{4} - 2 \, {\left(8 \, b c^{2} d^{2} - 7 \, a c d^{3}\right)} x^{4} + {\left(8 \, b c d^{3} - 7 \, a d^{4}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{35 \, {\left(c d^{5} x^{8} + d^{6} x^{6}\right)}}"," ",0,"1/35*(16*(8*b*c^4 - 7*a*c^3*d)*x^8 + 8*(8*b*c^3*d - 7*a*c^2*d^2)*x^6 - 5*b*d^4 - 2*(8*b*c^2*d^2 - 7*a*c*d^3)*x^4 + (8*b*c*d^3 - 7*a*d^4)*x^2)*sqrt((c*x^2 + d)/x^2)/(c*d^5*x^8 + d^6*x^6)","A",0
980,1,95,0,0.425202," ","integrate((a+b/x^2)*x^4/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c^{3} x^{7} + {\left(5 \, b c^{3} - 6 \, a c^{2} d\right)} x^{5} - 4 \, {\left(5 \, b c^{2} d - 6 \, a c d^{2}\right)} x^{3} - 8 \, {\left(5 \, b c d^{2} - 6 \, a d^{3}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{15 \, {\left(c^{5} x^{2} + c^{4} d\right)}}"," ",0,"1/15*(3*a*c^3*x^7 + (5*b*c^3 - 6*a*c^2*d)*x^5 - 4*(5*b*c^2*d - 6*a*c*d^2)*x^3 - 8*(5*b*c*d^2 - 6*a*d^3)*x)*sqrt((c*x^2 + d)/x^2)/(c^5*x^2 + c^4*d)","A",0
981,1,70,0,0.428664," ","integrate((a+b/x^2)*x^2/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a c^{2} x^{5} + {\left(3 \, b c^{2} - 4 \, a c d\right)} x^{3} + 2 \, {\left(3 \, b c d - 4 \, a d^{2}\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{3 \, {\left(c^{4} x^{2} + c^{3} d\right)}}"," ",0,"1/3*(a*c^2*x^5 + (3*b*c^2 - 4*a*c*d)*x^3 + 2*(3*b*c*d - 4*a*d^2)*x)*sqrt((c*x^2 + d)/x^2)/(c^4*x^2 + c^3*d)","A",0
982,1,47,0,0.478533," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a c x^{3} - {\left(b c - 2 \, a d\right)} x\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c^{3} x^{2} + c^{2} d}"," ",0,"(a*c*x^3 - (b*c - 2*a*d)*x)*sqrt((c*x^2 + d)/x^2)/(c^3*x^2 + c^2*d)","A",0
983,1,195,0,0.462777," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c d - a d^{2}\right)} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + {\left(b c^{2} x^{2} + b c d\right)} \sqrt{d} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right)}{2 \, {\left(c^{2} d^{2} x^{2} + c d^{3}\right)}}, \frac{{\left(b c d - a d^{2}\right)} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + {\left(b c^{2} x^{2} + b c d\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right)}{c^{2} d^{2} x^{2} + c d^{3}}\right]"," ",0,"[1/2*(2*(b*c*d - a*d^2)*x*sqrt((c*x^2 + d)/x^2) + (b*c^2*x^2 + b*c*d)*sqrt(d)*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2))/(c^2*d^2*x^2 + c*d^3), ((b*c*d - a*d^2)*x*sqrt((c*x^2 + d)/x^2) + (b*c^2*x^2 + b*c*d)*sqrt(-d)*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)))/(c^2*d^2*x^2 + c*d^3)]","A",0
984,1,248,0,0.438768," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, b c^{2} - 2 \, a c d\right)} x^{3} + {\left(3 \, b c d - 2 \, a d^{2}\right)} x\right)} \sqrt{d} \log\left(-\frac{c x^{2} - 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) + 2 \, {\left(b d^{2} + {\left(3 \, b c d - 2 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{4 \, {\left(c d^{3} x^{3} + d^{4} x\right)}}, -\frac{{\left({\left(3 \, b c^{2} - 2 \, a c d\right)} x^{3} + {\left(3 \, b c d - 2 \, a d^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(b d^{2} + {\left(3 \, b c d - 2 \, a d^{2}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{2 \, {\left(c d^{3} x^{3} + d^{4} x\right)}}\right]"," ",0,"[-1/4*(((3*b*c^2 - 2*a*c*d)*x^3 + (3*b*c*d - 2*a*d^2)*x)*sqrt(d)*log(-(c*x^2 - 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) + 2*(b*d^2 + (3*b*c*d - 2*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(c*d^3*x^3 + d^4*x), -1/2*(((3*b*c^2 - 2*a*c*d)*x^3 + (3*b*c*d - 2*a*d^2)*x)*sqrt(-d)*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (b*d^2 + (3*b*c*d - 2*a*d^2)*x^2)*sqrt((c*x^2 + d)/x^2))/(c*d^3*x^3 + d^4*x)]","A",0
985,1,314,0,0.445829," ","integrate((a+b/x^2)/(c+d/x^2)^(3/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, b c^{3} - 4 \, a c^{2} d\right)} x^{5} + {\left(5 \, b c^{2} d - 4 \, a c d^{2}\right)} x^{3}\right)} \sqrt{d} \log\left(-\frac{c x^{2} + 2 \, \sqrt{d} x \sqrt{\frac{c x^{2} + d}{x^{2}}} + 2 \, d}{x^{2}}\right) - 2 \, {\left(3 \, {\left(5 \, b c^{2} d - 4 \, a c d^{2}\right)} x^{4} - 2 \, b d^{3} + {\left(5 \, b c d^{2} - 4 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{16 \, {\left(c d^{4} x^{5} + d^{5} x^{3}\right)}}, \frac{3 \, {\left({\left(5 \, b c^{3} - 4 \, a c^{2} d\right)} x^{5} + {\left(5 \, b c^{2} d - 4 \, a c d^{2}\right)} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x \sqrt{\frac{c x^{2} + d}{x^{2}}}}{c x^{2} + d}\right) + {\left(3 \, {\left(5 \, b c^{2} d - 4 \, a c d^{2}\right)} x^{4} - 2 \, b d^{3} + {\left(5 \, b c d^{2} - 4 \, a d^{3}\right)} x^{2}\right)} \sqrt{\frac{c x^{2} + d}{x^{2}}}}{8 \, {\left(c d^{4} x^{5} + d^{5} x^{3}\right)}}\right]"," ",0,"[-1/16*(3*((5*b*c^3 - 4*a*c^2*d)*x^5 + (5*b*c^2*d - 4*a*c*d^2)*x^3)*sqrt(d)*log(-(c*x^2 + 2*sqrt(d)*x*sqrt((c*x^2 + d)/x^2) + 2*d)/x^2) - 2*(3*(5*b*c^2*d - 4*a*c*d^2)*x^4 - 2*b*d^3 + (5*b*c*d^2 - 4*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(c*d^4*x^5 + d^5*x^3), 1/8*(3*((5*b*c^3 - 4*a*c^2*d)*x^5 + (5*b*c^2*d - 4*a*c*d^2)*x^3)*sqrt(-d)*arctan(sqrt(-d)*x*sqrt((c*x^2 + d)/x^2)/(c*x^2 + d)) + (3*(5*b*c^2*d - 4*a*c*d^2)*x^4 - 2*b*d^3 + (5*b*c*d^2 - 4*a*d^3)*x^2)*sqrt((c*x^2 + d)/x^2))/(c*d^4*x^5 + d^5*x^3)]","A",0
986,0,0,0,0.625015," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral((e*x)^m*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
987,0,0,0,0.535435," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*x^4,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(x^4*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
988,0,0,0,0.458457," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*x^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(x^3*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
989,0,0,0,0.482919," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*x^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(x^2*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
990,0,0,0,0.484720," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*x,x, algorithm=""fricas"")","{\rm integral}\left(x \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(x*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
991,0,0,0,0.463055," ","integrate((a+b/x^2)^p*(c+d/x^2)^q,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
992,0,0,0,0.467660," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{x}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/x, x)","F",0
993,0,0,0,0.490474," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{x^{2}}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/x^2, x)","F",0
994,0,0,0,0.477575," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{x^{3}}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/x^3, x)","F",0
995,0,0,0,0.537145," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{x^{4}}, x\right)"," ",0,"integral(((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/x^4, x)","F",0
996,0,0,0,0.522727," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} e^{2} x^{2} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(sqrt(e*x)*e^2*x^2*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
997,0,0,0,0.516782," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} e x \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(sqrt(e*x)*e*x*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
998,0,0,0,0.517597," ","integrate((a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}, x\right)"," ",0,"integral(sqrt(e*x)*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q, x)","F",0
999,0,0,0,0.502753," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{e x}, x\right)"," ",0,"integral(sqrt(e*x)*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/(e*x), x)","F",0
1000,0,0,0,0.506929," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{e^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(e*x)*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/(e^2*x^2), x)","F",0
1001,0,0,0,0.502739," ","integrate((a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x} \left(\frac{a x^{2} + b}{x^{2}}\right)^{p} \left(\frac{c x^{2} + d}{x^{2}}\right)^{q}}{e^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x)*((a*x^2 + b)/x^2)^p*((c*x^2 + d)/x^2)^q/(e^3*x^3), x)","F",0
1002,1,62,0,0.393607," ","integrate(x^(5/2)*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{192} \, {\left(48 \, x^{3} - 8 \, x^{2} - 10 \, x - 15\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + \frac{5}{128} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"1/192*(48*x^3 - 8*x^2 - 10*x - 15)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 5/128*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1003,1,57,0,0.409946," ","integrate(x^(3/2)*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(8 \, x^{2} - 2 \, x - 3\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + \frac{1}{16} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"1/24*(8*x^2 - 2*x - 3)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 1/16*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1004,1,52,0,0.404619," ","integrate(x^(1/2)*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(2 \, x - 1\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + \frac{1}{8} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"1/4*(2*x - 1)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 1/8*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1005,1,46,0,0.411649," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(1/2),x, algorithm=""fricas"")","\sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + \frac{1}{2} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 1/2*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1006,1,55,0,0.396284," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(3/2),x, algorithm=""fricas"")","-\frac{x \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right) + 2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + 2 \, x}{x}"," ",0,"-(x*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1) + 2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 2*x)/x","A",0
1007,1,30,0,0.421495," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(x - 1\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + x^{2}\right)}}{3 \, x^{2}}"," ",0,"2/3*((x - 1)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + x^2)/x^2","A",0
1008,1,37,0,0.408291," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, x^{3} + {\left(2 \, x^{2} + x - 3\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1}\right)}}{15 \, x^{3}}"," ",0,"2/15*(2*x^3 + (2*x^2 + x - 3)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1))/x^3","A",0
1009,1,44,0,0.396623," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, x^{4} + {\left(8 \, x^{3} + 4 \, x^{2} + 3 \, x - 15\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1}\right)}}{105 \, x^{4}}"," ",0,"2/105*(8*x^4 + (8*x^3 + 4*x^2 + 3*x - 15)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1))/x^4","A",0
1010,1,49,0,0.404521," ","integrate((-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, x^{5} + {\left(16 \, x^{4} + 8 \, x^{3} + 6 \, x^{2} + 5 \, x - 35\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1}\right)}}{315 \, x^{5}}"," ",0,"2/315*(16*x^5 + (16*x^4 + 8*x^3 + 6*x^2 + 5*x - 35)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1))/x^5","A",0
1011,1,57,0,0.405831," ","integrate(x^(5/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(8 \, x^{2} + 10 \, x + 15\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - \frac{5}{16} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"1/24*(8*x^2 + 10*x + 15)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 5/16*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1012,1,52,0,0.404943," ","integrate(x^(3/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(2 \, x + 3\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - \frac{3}{8} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"1/4*(2*x + 3)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 3/8*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1013,1,46,0,0.413358," ","integrate(x^(1/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - \frac{1}{2} \, \log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 1/2*log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","A",0
1014,1,27,0,0.406682," ","integrate(1/x^(1/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","-\log\left(2 \, \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} - 2 \, x + 1\right)"," ",0,"-log(2*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) - 2*x + 1)","B",0
1015,1,25,0,0.415653," ","integrate(1/x^(3/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + x\right)}}{x}"," ",0,"2*(sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + x)/x","A",0
1016,1,34,0,0.399705," ","integrate(1/x^(5/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, x + 1\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1} + 2 \, x^{2}\right)}}{3 \, x^{2}}"," ",0,"2/3*((2*x + 1)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1) + 2*x^2)/x^2","A",0
1017,1,39,0,0.407057," ","integrate(1/x^(7/2)/(-1+x^(1/2))^(1/2)/(1+x^(1/2))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, x^{3} + {\left(8 \, x^{2} + 4 \, x + 3\right)} \sqrt{x} \sqrt{\sqrt{x} + 1} \sqrt{\sqrt{x} - 1}\right)}}{15 \, x^{3}}"," ",0,"2/15*(8*x^3 + (8*x^2 + 4*x + 3)*sqrt(x)*sqrt(sqrt(x) + 1)*sqrt(sqrt(x) - 1))/x^3","A",0
1018,0,0,0,0.447507," ","integrate(x^2*(-a+b*x^n)^p*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} {\left(b x^{n} - a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*x^n + a)^p*(b*x^n - a)^p*x^2, x)","F",0
1019,0,0,0,0.455264," ","integrate(x*(-a+b*x^n)^p*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} {\left(b x^{n} - a\right)}^{p} x, x\right)"," ",0,"integral((b*x^n + a)^p*(b*x^n - a)^p*x, x)","F",0
1020,0,0,0,0.439828," ","integrate((-a+b*x^n)^p*(a+b*x^n)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{n} + a\right)}^{p} {\left(b x^{n} - a\right)}^{p}, x\right)"," ",0,"integral((b*x^n + a)^p*(b*x^n - a)^p, x)","F",0
1021,0,0,0,0.445953," ","integrate((-a+b*x^n)^p*(a+b*x^n)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p} {\left(b x^{n} - a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*x^n + a)^p*(b*x^n - a)^p/x, x)","F",0
1022,0,0,0,0.437100," ","integrate((-a+b*x^n)^p*(a+b*x^n)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{n} + a\right)}^{p} {\left(b x^{n} - a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*x^n + a)^p*(b*x^n - a)^p/x^2, x)","F",0
1023,1,11,0,0.398973," ","integrate((x^6+1)/x/(-x^6+1),x, algorithm=""fricas"")","-\frac{1}{3} \, \log\left(x^{6} - 1\right) + \log\left(x\right)"," ",0,"-1/3*log(x^6 - 1) + log(x)","A",0
1024,1,40,0,0.410862," ","integrate((e*x)^m*(a+b*x^n)^p*(a*(1+m)+b*(n*p+m+n+1)*x^n),x, algorithm=""fricas"")","{\left(b x x^{n} e^{\left(m \log\left(e\right) + m \log\left(x\right)\right)} + a x e^{\left(m \log\left(e\right) + m \log\left(x\right)\right)}\right)} {\left(b x^{n} + a\right)}^{p}"," ",0,"(b*x*x^n*e^(m*log(e) + m*log(x)) + a*x*e^(m*log(e) + m*log(x)))*(b*x^n + a)^p","A",0
1025,0,0,0,0.417618," ","integrate((e*x)^m/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}}, x\right)"," ",0,"integral((e*x)^m/(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n), x)","F",0
1026,0,0,0,0.413246," ","integrate(x^2/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}}, x\right)"," ",0,"integral(x^2/(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n), x)","F",0
1027,0,0,0,0.422825," ","integrate(x/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}}, x\right)"," ",0,"integral(x/(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n), x)","F",0
1028,0,0,0,0.426151," ","integrate(1/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d x^{2 \, n} + a c + {\left(b c + a d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*d*x^(2*n) + a*c + (b*c + a*d)*x^n), x)","F",0
1029,1,58,0,0.450019," ","integrate(1/x/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","-\frac{b c \log\left(b x^{n} + a\right) - a d \log\left(d x^{n} + c\right) - {\left(b c - a d\right)} n \log\left(x\right)}{{\left(a b c^{2} - a^{2} c d\right)} n}"," ",0,"-(b*c*log(b*x^n + a) - a*d*log(d*x^n + c) - (b*c - a*d)*n*log(x))/((a*b*c^2 - a^2*c*d)*n)","A",0
1030,0,0,0,0.420116," ","integrate(1/x^2/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d x^{2} x^{2 \, n} + {\left(b c + a d\right)} x^{2} x^{n} + a c x^{2}}, x\right)"," ",0,"integral(1/(b*d*x^2*x^(2*n) + (b*c + a*d)*x^2*x^n + a*c*x^2), x)","F",0
1031,0,0,0,0.422061," ","integrate(1/x^3/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b d x^{3} x^{2 \, n} + {\left(b c + a d\right)} x^{3} x^{n} + a c x^{3}}, x\right)"," ",0,"integral(1/(b*d*x^3*x^(2*n) + (b*c + a*d)*x^3*x^n + a*c*x^3), x)","F",0
1032,0,0,0,0.428511," ","integrate((e*x)^m/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b^{2} d x^{3 \, n} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{n}}, x\right)"," ",0,"integral((e*x)^m/(b^2*d*x^(3*n) + a^2*c + (b^2*c + 2*a*b*d)*x^(2*n) + (2*a*b*c + a^2*d)*x^n), x)","F",0
1033,0,0,0,0.433181," ","integrate(x^2/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} d x^{3 \, n} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(x^2/(b^2*d*x^(3*n) + a^2*c + (b^2*c + 2*a*b*d)*x^(2*n) + (2*a*b*c + a^2*d)*x^n), x)","F",0
1034,0,0,0,0.432256," ","integrate(x/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} d x^{3 \, n} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(x/(b^2*d*x^(3*n) + a^2*c + (b^2*c + 2*a*b*d)*x^(2*n) + (2*a*b*c + a^2*d)*x^n), x)","F",0
1035,0,0,0,0.444453," ","integrate(1/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d x^{3 \, n} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d*x^(3*n) + a^2*c + (b^2*c + 2*a*b*d)*x^(2*n) + (2*a*b*c + a^2*d)*x^n), x)","F",0
1036,1,224,0,0.466394," ","integrate(1/x/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","\frac{a b^{2} c^{2} - a^{2} b c d + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} n x^{n} \log\left(x\right) + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} n \log\left(x\right) - {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + {\left(b^{3} c^{2} - 2 \, a b^{2} c d\right)} x^{n}\right)} \log\left(b x^{n} + a\right) - {\left(a^{2} b d^{2} x^{n} + a^{3} d^{2}\right)} \log\left(d x^{n} + c\right)}{{\left(a^{2} b^{3} c^{3} - 2 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} n x^{n} + {\left(a^{3} b^{2} c^{3} - 2 \, a^{4} b c^{2} d + a^{5} c d^{2}\right)} n}"," ",0,"(a*b^2*c^2 - a^2*b*c*d + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*n*x^n*log(x) + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*n*log(x) - (a*b^2*c^2 - 2*a^2*b*c*d + (b^3*c^2 - 2*a*b^2*c*d)*x^n)*log(b*x^n + a) - (a^2*b*d^2*x^n + a^3*d^2)*log(d*x^n + c))/((a^2*b^3*c^3 - 2*a^3*b^2*c^2*d + a^4*b*c*d^2)*n*x^n + (a^3*b^2*c^3 - 2*a^4*b*c^2*d + a^5*c*d^2)*n)","B",0
1037,0,0,0,0.449136," ","integrate(1/x^2/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d x^{2} x^{3 \, n} + a^{2} c x^{2} + {\left(b^{2} c + 2 \, a b d\right)} x^{2} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{2} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d*x^2*x^(3*n) + a^2*c*x^2 + (b^2*c + 2*a*b*d)*x^2*x^(2*n) + (2*a*b*c + a^2*d)*x^2*x^n), x)","F",0
1038,0,0,0,0.432376," ","integrate(1/x^3/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} d x^{3} x^{3 \, n} + a^{2} c x^{3} + {\left(b^{2} c + 2 \, a b d\right)} x^{3} x^{2 \, n} + {\left(2 \, a b c + a^{2} d\right)} x^{3} x^{n}}, x\right)"," ",0,"integral(1/(b^2*d*x^3*x^(3*n) + a^2*c*x^3 + (b^2*c + 2*a*b*d)*x^3*x^(2*n) + (2*a*b*c + a^2*d)*x^3*x^n), x)","F",0
1039,1,177,0,0.453826," ","integrate(x^(-1+2*n)*(a+b*x^n)^3/(c+d*x^n),x, algorithm=""fricas"")","\frac{3 \, b^{3} d^{4} x^{4 \, n} - 4 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} x^{3 \, n} + 6 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} x^{2 \, n} - 12 \, {\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)} x^{n} + 12 \, {\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)} \log\left(d x^{n} + c\right)}{12 \, d^{5} n}"," ",0,"1/12*(3*b^3*d^4*x^(4*n) - 4*(b^3*c*d^3 - 3*a*b^2*d^4)*x^(3*n) + 6*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*x^(2*n) - 12*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*x^n + 12*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*log(d*x^n + c))/(d^5*n)","A",0
1040,1,108,0,0.441150," ","integrate(x^(-1+2*n)*(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{3} x^{3 \, n} - 3 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2 \, n} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{n} - 6 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \log\left(d x^{n} + c\right)}{6 \, d^{4} n}"," ",0,"1/6*(2*b^2*d^3*x^(3*n) - 3*(b^2*c*d^2 - 2*a*b*d^3)*x^(2*n) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^n - 6*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*log(d*x^n + c))/(d^4*n)","A",0
1041,1,56,0,0.431144," ","integrate(x^(-1+2*n)*(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","\frac{b d^{2} x^{2 \, n} - 2 \, {\left(b c d - a d^{2}\right)} x^{n} + 2 \, {\left(b c^{2} - a c d\right)} \log\left(d x^{n} + c\right)}{2 \, d^{3} n}"," ",0,"1/2*(b*d^2*x^(2*n) - 2*(b*c*d - a*d^2)*x^n + 2*(b*c^2 - a*c*d)*log(d*x^n + c))/(d^3*n)","A",0
1042,1,45,0,0.443863," ","integrate(x^(-1+2*n)/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","-\frac{a d \log\left(b x^{n} + a\right) - b c \log\left(d x^{n} + c\right)}{{\left(b^{2} c d - a b d^{2}\right)} n}"," ",0,"-(a*d*log(b*x^n + a) - b*c*log(d*x^n + c))/((b^2*c*d - a*b*d^2)*n)","A",0
1043,1,120,0,0.447085," ","integrate(x^(-1+2*n)/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","\frac{a b c - a^{2} d + {\left(b^{2} c x^{n} + a b c\right)} \log\left(b x^{n} + a\right) - {\left(b^{2} c x^{n} + a b c\right)} \log\left(d x^{n} + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} n x^{n} + {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} n}"," ",0,"(a*b*c - a^2*d + (b^2*c*x^n + a*b*c)*log(b*x^n + a) - (b^2*c*x^n + a*b*c)*log(d*x^n + c))/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*n*x^n + (a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*n)","A",0
1044,1,267,0,0.462015," ","integrate(x^(-1+2*n)/(a+b*x^n)^3/(c+d*x^n),x, algorithm=""fricas"")","-\frac{a b^{2} c^{2} - a^{3} d^{2} + 2 \, {\left(b^{3} c^{2} - a b^{2} c d\right)} x^{n} + 2 \, {\left(b^{3} c d x^{2 \, n} + 2 \, a b^{2} c d x^{n} + a^{2} b c d\right)} \log\left(b x^{n} + a\right) - 2 \, {\left(b^{3} c d x^{2 \, n} + 2 \, a b^{2} c d x^{n} + a^{2} b c d\right)} \log\left(d x^{n} + c\right)}{2 \, {\left({\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} n x^{2 \, n} + 2 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} n x^{n} + {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} n\right)}}"," ",0,"-1/2*(a*b^2*c^2 - a^3*d^2 + 2*(b^3*c^2 - a*b^2*c*d)*x^n + 2*(b^3*c*d*x^(2*n) + 2*a*b^2*c*d*x^n + a^2*b*c*d)*log(b*x^n + a) - 2*(b^3*c*d*x^(2*n) + 2*a*b^2*c*d*x^n + a^2*b*c*d)*log(d*x^n + c))/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*n*x^(2*n) + 2*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*n*x^n + (a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*n)","B",0
1045,1,230,0,0.485885," ","integrate(x^(-1+3*n)*(a+b*x^n)^3/(c+d*x^n),x, algorithm=""fricas"")","\frac{12 \, b^{3} d^{5} x^{5 \, n} - 15 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} x^{4 \, n} + 20 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} x^{3 \, n} - 30 \, {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{2 \, n} + 60 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x^{n} - 60 \, {\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)} \log\left(d x^{n} + c\right)}{60 \, d^{6} n}"," ",0,"1/60*(12*b^3*d^5*x^(5*n) - 15*(b^3*c*d^4 - 3*a*b^2*d^5)*x^(4*n) + 20*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*x^(3*n) - 30*(b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*x^(2*n) + 60*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x^n - 60*(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)*log(d*x^n + c))/(d^6*n)","A",0
1046,1,146,0,0.477350," ","integrate(x^(-1+3*n)*(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{4} x^{4 \, n} - 4 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} x^{3 \, n} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2 \, n} - 12 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x^{n} + 12 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} \log\left(d x^{n} + c\right)}{12 \, d^{5} n}"," ",0,"1/12*(3*b^2*d^4*x^(4*n) - 4*(b^2*c*d^3 - 2*a*b*d^4)*x^(3*n) + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^(2*n) - 12*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x^n + 12*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*log(d*x^n + c))/(d^5*n)","A",0
1047,1,82,0,0.434869," ","integrate(x^(-1+3*n)*(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","\frac{2 \, b d^{3} x^{3 \, n} - 3 \, {\left(b c d^{2} - a d^{3}\right)} x^{2 \, n} + 6 \, {\left(b c^{2} d - a c d^{2}\right)} x^{n} - 6 \, {\left(b c^{3} - a c^{2} d\right)} \log\left(d x^{n} + c\right)}{6 \, d^{4} n}"," ",0,"1/6*(2*b*d^3*x^(3*n) - 3*(b*c*d^2 - a*d^3)*x^(2*n) + 6*(b*c^2*d - a*c*d^2)*x^n - 6*(b*c^3 - a*c^2*d)*log(d*x^n + c))/(d^4*n)","A",0
1048,1,74,0,0.463258," ","integrate(x^(-1+3*n)/(a+b*x^n)/(c+d*x^n),x, algorithm=""fricas"")","\frac{a^{2} d^{2} \log\left(b x^{n} + a\right) - b^{2} c^{2} \log\left(d x^{n} + c\right) + {\left(b^{2} c d - a b d^{2}\right)} x^{n}}{{\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} n}"," ",0,"(a^2*d^2*log(b*x^n + a) - b^2*c^2*log(d*x^n + c) + (b^2*c*d - a*b*d^2)*x^n)/((b^3*c*d^2 - a*b^2*d^3)*n)","A",0
1049,1,166,0,0.451326," ","integrate(x^(-1+3*n)/(a+b*x^n)^2/(c+d*x^n),x, algorithm=""fricas"")","-\frac{a^{2} b c d - a^{3} d^{2} + {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{n}\right)} \log\left(b x^{n} + a\right) - {\left(b^{3} c^{2} x^{n} + a b^{2} c^{2}\right)} \log\left(d x^{n} + c\right)}{{\left(b^{5} c^{2} d - 2 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} n x^{n} + {\left(a b^{4} c^{2} d - 2 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} n}"," ",0,"-(a^2*b*c*d - a^3*d^2 + (2*a^2*b*c*d - a^3*d^2 + (2*a*b^2*c*d - a^2*b*d^2)*x^n)*log(b*x^n + a) - (b^3*c^2*x^n + a*b^2*c^2)*log(d*x^n + c))/((b^5*c^2*d - 2*a*b^4*c*d^2 + a^2*b^3*d^3)*n*x^n + (a*b^4*c^2*d - 2*a^2*b^3*c*d^2 + a^3*b^2*d^3)*n)","A",0
1050,1,301,0,0.453982," ","integrate(x^(-1+3*n)/(a+b*x^n)^3/(c+d*x^n),x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d + a^{4} d^{2} + 2 \, {\left(2 \, a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{n} + 2 \, {\left(b^{4} c^{2} x^{2 \, n} + 2 \, a b^{3} c^{2} x^{n} + a^{2} b^{2} c^{2}\right)} \log\left(b x^{n} + a\right) - 2 \, {\left(b^{4} c^{2} x^{2 \, n} + 2 \, a b^{3} c^{2} x^{n} + a^{2} b^{2} c^{2}\right)} \log\left(d x^{n} + c\right)}{2 \, {\left({\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} n x^{2 \, n} + 2 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} n x^{n} + {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} n\right)}}"," ",0,"1/2*(3*a^2*b^2*c^2 - 4*a^3*b*c*d + a^4*d^2 + 2*(2*a*b^3*c^2 - 3*a^2*b^2*c*d + a^3*b*d^2)*x^n + 2*(b^4*c^2*x^(2*n) + 2*a*b^3*c^2*x^n + a^2*b^2*c^2)*log(b*x^n + a) - 2*(b^4*c^2*x^(2*n) + 2*a*b^3*c^2*x^n + a^2*b^2*c^2)*log(d*x^n + c))/((b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*n*x^(2*n) + 2*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*n*x^n + (a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*n)","B",0
1051,1,154,0,0.354314," ","integrate(x^13*(c*x+b)^13*(2*c*x+b),x, algorithm=""fricas"")","\frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} + 26 x^{25} c^{11} b^{3} + \frac{143}{2} x^{24} c^{10} b^{4} + 143 x^{23} c^{9} b^{5} + \frac{429}{2} x^{22} c^{8} b^{6} + \frac{1716}{7} x^{21} c^{7} b^{7} + \frac{429}{2} x^{20} c^{6} b^{8} + 143 x^{19} c^{5} b^{9} + \frac{143}{2} x^{18} c^{4} b^{10} + 26 x^{17} c^{3} b^{11} + \frac{13}{2} x^{16} c^{2} b^{12} + x^{15} c b^{13} + \frac{1}{14} x^{14} b^{14}"," ",0,"1/14*x^28*c^14 + x^27*c^13*b + 13/2*x^26*c^12*b^2 + 26*x^25*c^11*b^3 + 143/2*x^24*c^10*b^4 + 143*x^23*c^9*b^5 + 429/2*x^22*c^8*b^6 + 1716/7*x^21*c^7*b^7 + 429/2*x^20*c^6*b^8 + 143*x^19*c^5*b^9 + 143/2*x^18*c^4*b^10 + 26*x^17*c^3*b^11 + 13/2*x^16*c^2*b^12 + x^15*c*b^13 + 1/14*x^14*b^14","B",0
1052,1,156,0,0.359065," ","integrate(x^27*(c*x^2+b)^13*(2*c*x^2+b),x, algorithm=""fricas"")","\frac{1}{28} x^{56} c^{14} + \frac{1}{2} x^{54} c^{13} b + \frac{13}{4} x^{52} c^{12} b^{2} + 13 x^{50} c^{11} b^{3} + \frac{143}{4} x^{48} c^{10} b^{4} + \frac{143}{2} x^{46} c^{9} b^{5} + \frac{429}{4} x^{44} c^{8} b^{6} + \frac{858}{7} x^{42} c^{7} b^{7} + \frac{429}{4} x^{40} c^{6} b^{8} + \frac{143}{2} x^{38} c^{5} b^{9} + \frac{143}{4} x^{36} c^{4} b^{10} + 13 x^{34} c^{3} b^{11} + \frac{13}{4} x^{32} c^{2} b^{12} + \frac{1}{2} x^{30} c b^{13} + \frac{1}{28} x^{28} b^{14}"," ",0,"1/28*x^56*c^14 + 1/2*x^54*c^13*b + 13/4*x^52*c^12*b^2 + 13*x^50*c^11*b^3 + 143/4*x^48*c^10*b^4 + 143/2*x^46*c^9*b^5 + 429/4*x^44*c^8*b^6 + 858/7*x^42*c^7*b^7 + 429/4*x^40*c^6*b^8 + 143/2*x^38*c^5*b^9 + 143/4*x^36*c^4*b^10 + 13*x^34*c^3*b^11 + 13/4*x^32*c^2*b^12 + 1/2*x^30*c*b^13 + 1/28*x^28*b^14","B",0
1053,1,156,0,0.360395," ","integrate(x^41*(c*x^3+b)^13*(2*c*x^3+b),x, algorithm=""fricas"")","\frac{1}{42} x^{84} c^{14} + \frac{1}{3} x^{81} c^{13} b + \frac{13}{6} x^{78} c^{12} b^{2} + \frac{26}{3} x^{75} c^{11} b^{3} + \frac{143}{6} x^{72} c^{10} b^{4} + \frac{143}{3} x^{69} c^{9} b^{5} + \frac{143}{2} x^{66} c^{8} b^{6} + \frac{572}{7} x^{63} c^{7} b^{7} + \frac{143}{2} x^{60} c^{6} b^{8} + \frac{143}{3} x^{57} c^{5} b^{9} + \frac{143}{6} x^{54} c^{4} b^{10} + \frac{26}{3} x^{51} c^{3} b^{11} + \frac{13}{6} x^{48} c^{2} b^{12} + \frac{1}{3} x^{45} c b^{13} + \frac{1}{42} x^{42} b^{14}"," ",0,"1/42*x^84*c^14 + 1/3*x^81*c^13*b + 13/6*x^78*c^12*b^2 + 26/3*x^75*c^11*b^3 + 143/6*x^72*c^10*b^4 + 143/3*x^69*c^9*b^5 + 143/2*x^66*c^8*b^6 + 572/7*x^63*c^7*b^7 + 143/2*x^60*c^6*b^8 + 143/3*x^57*c^5*b^9 + 143/6*x^54*c^4*b^10 + 26/3*x^51*c^3*b^11 + 13/6*x^48*c^2*b^12 + 1/3*x^45*c*b^13 + 1/42*x^42*b^14","B",0
1054,1,189,0,0.457091," ","integrate(x^(-1+14*n)*(b+c*x^n)^13*(b+2*c*x^n),x, algorithm=""fricas"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) + 364*b^3*c^11*x^(25*n) + 1001*b^4*c^10*x^(24*n) + 2002*b^5*c^9*x^(23*n) + 3003*b^6*c^8*x^(22*n) + 3432*b^7*c^7*x^(21*n) + 3003*b^8*c^6*x^(20*n) + 2002*b^9*c^5*x^(19*n) + 1001*b^10*c^4*x^(18*n) + 364*b^11*c^3*x^(17*n) + 91*b^12*c^2*x^(16*n) + 14*b^13*c*x^(15*n) + b^14*x^(14*n))/n","B",0
1055,1,32,0,0.433369," ","integrate(x^(-1+m)*(a+b*x^n)^(-1+p)*(a*m+b*(n*p+m)*x^n),x, algorithm=""fricas"")","{\left(b x x^{m - 1} x^{n} + a x x^{m - 1}\right)} {\left(b x^{n} + a\right)}^{p - 1}"," ",0,"(b*x*x^(m - 1)*x^n + a*x*x^(m - 1))*(b*x^n + a)^(p - 1)","B",0
1056,1,10,0,0.400094," ","integrate((2*c*x+b)/x/(c*x+b),x, algorithm=""fricas"")","\log\left(c x^{2} + b x\right)"," ",0,"log(c*x^2 + b*x)","A",0
1057,1,13,0,0.396972," ","integrate((2*c*x^2+b)/x/(c*x^2+b),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(c x^{2} + b\right) + \log\left(x\right)"," ",0,"1/2*log(c*x^2 + b) + log(x)","A",0
1058,1,13,0,0.402624," ","integrate((2*c*x^3+b)/x/(c*x^3+b),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(c x^{3} + b\right) + \log\left(x\right)"," ",0,"1/3*log(c*x^3 + b) + log(x)","A",0
1059,1,17,0,0.435472," ","integrate((b+2*c*x^n)/x/(b+c*x^n),x, algorithm=""fricas"")","\frac{n \log\left(x\right) + \log\left(c x^{n} + b\right)}{n}"," ",0,"(n*log(x) + log(c*x^n + b))/n","A",0
1060,1,81,0,0.423382," ","integrate((2*c*x+b)/x^8/(c*x+b)^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right)}}"," ",0,"-1/7/(c^7*x^14 + 7*b*c^6*x^13 + 21*b^2*c^5*x^12 + 35*b^3*c^4*x^11 + 35*b^4*c^3*x^10 + 21*b^5*c^2*x^9 + 7*b^6*c*x^8 + b^7*x^7)","B",0
1061,1,81,0,0.407955," ","integrate((2*c*x^2+b)/x^15/(c*x^2+b)^8,x, algorithm=""fricas"")","-\frac{1}{14 \, {\left(c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right)}}"," ",0,"-1/14/(c^7*x^28 + 7*b*c^6*x^26 + 21*b^2*c^5*x^24 + 35*b^3*c^4*x^22 + 35*b^4*c^3*x^20 + 21*b^5*c^2*x^18 + 7*b^6*c*x^16 + b^7*x^14)","B",0
1062,1,81,0,0.393811," ","integrate((2*c*x^3+b)/x^22/(c*x^3+b)^8,x, algorithm=""fricas"")","-\frac{1}{21 \, {\left(c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\right)}}"," ",0,"-1/21/(c^7*x^42 + 7*b*c^6*x^39 + 21*b^2*c^5*x^36 + 35*b^3*c^4*x^33 + 35*b^4*c^3*x^30 + 21*b^5*c^2*x^27 + 7*b^6*c*x^24 + b^7*x^21)","B",0
1063,1,105,0,0.475742," ","integrate(x^(-1-7*n)*(b+2*c*x^n)/(b+c*x^n)^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} n x^{14 \, n} + 7 \, b c^{6} n x^{13 \, n} + 21 \, b^{2} c^{5} n x^{12 \, n} + 35 \, b^{3} c^{4} n x^{11 \, n} + 35 \, b^{4} c^{3} n x^{10 \, n} + 21 \, b^{5} c^{2} n x^{9 \, n} + 7 \, b^{6} c n x^{8 \, n} + b^{7} n x^{7 \, n}\right)}}"," ",0,"-1/7/(c^7*n*x^(14*n) + 7*b*c^6*n*x^(13*n) + 21*b^2*c^5*n*x^(12*n) + 35*b^3*c^4*n*x^(11*n) + 35*b^4*c^3*n*x^(10*n) + 21*b^5*c^2*n*x^(9*n) + 7*b^6*c*n*x^(8*n) + b^7*n*x^(7*n))","B",0
1064,1,46,0,0.422591," ","integrate(x^31*(x^16+1)^(1/2)/(-x^16+1),x, algorithm=""fricas"")","-\frac{1}{24} \, {\left(x^{16} + 4\right)} \sqrt{x^{16} + 1} + \frac{1}{16} \, \sqrt{2} \log\left(\frac{x^{16} + 2 \, \sqrt{2} \sqrt{x^{16} + 1} + 3}{x^{16} - 1}\right)"," ",0,"-1/24*(x^16 + 4)*sqrt(x^16 + 1) + 1/16*sqrt(2)*log((x^16 + 2*sqrt(2)*sqrt(x^16 + 1) + 3)/(x^16 - 1))","A",0
1065,1,757,0,0.706415," ","integrate((c+d/x)^(1/2)/x/(a+b/x)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{c}{a}} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} - 4 \, {\left(2 \, a^{2} c x^{2} + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{\frac{c}{a}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right) + \frac{1}{2} \, \sqrt{\frac{d}{b}} \log\left(-\frac{8 \, b^{2} d^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} d x + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{\frac{d}{b}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x}{x^{2}}\right), -\sqrt{-\frac{c}{a}} \arctan\left(\frac{2 \, a x \sqrt{-\frac{c}{a}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right) + \frac{1}{2} \, \sqrt{\frac{d}{b}} \log\left(-\frac{8 \, b^{2} d^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, b^{2} d x + {\left(b^{2} c + a b d\right)} x^{2}\right)} \sqrt{\frac{d}{b}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x}{x^{2}}\right), \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{-\frac{d}{b}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, {\left(a c d x^{2} + b d^{2} + {\left(b c d + a d^{2}\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{c}{a}} \log\left(-8 \, a^{2} c^{2} x^{2} - b^{2} c^{2} - 6 \, a b c d - a^{2} d^{2} - 4 \, {\left(2 \, a^{2} c x^{2} + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{\frac{c}{a}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} x\right), -\sqrt{-\frac{c}{a}} \arctan\left(\frac{2 \, a x \sqrt{-\frac{c}{a}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, a c x + b c + a d}\right) + \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + {\left(b c + a d\right)} x^{2}\right)} \sqrt{-\frac{d}{b}} \sqrt{\frac{a x + b}{x}} \sqrt{\frac{c x + d}{x}}}{2 \, {\left(a c d x^{2} + b d^{2} + {\left(b c d + a d^{2}\right)} x\right)}}\right)\right]"," ",0,"[1/2*sqrt(c/a)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 - 4*(2*a^2*c*x^2 + (a*b*c + a^2*d)*x)*sqrt(c/a)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x) + 1/2*sqrt(d/b)*log(-(8*b^2*d^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*b^2*d*x + (b^2*c + a*b*d)*x^2)*sqrt(d/b)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 8*(b^2*c*d + a*b*d^2)*x)/x^2), -sqrt(-c/a)*arctan(2*a*x*sqrt(-c/a)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)) + 1/2*sqrt(d/b)*log(-(8*b^2*d^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*b^2*d*x + (b^2*c + a*b*d)*x^2)*sqrt(d/b)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) + 8*(b^2*c*d + a*b*d^2)*x)/x^2), sqrt(-d/b)*arctan(1/2*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(-d/b)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(a*c*d*x^2 + b*d^2 + (b*c*d + a*d^2)*x)) + 1/2*sqrt(c/a)*log(-8*a^2*c^2*x^2 - b^2*c^2 - 6*a*b*c*d - a^2*d^2 - 4*(2*a^2*c*x^2 + (a*b*c + a^2*d)*x)*sqrt(c/a)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x) - 8*(a*b*c^2 + a^2*c*d)*x), -sqrt(-c/a)*arctan(2*a*x*sqrt(-c/a)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(2*a*c*x + b*c + a*d)) + sqrt(-d/b)*arctan(1/2*(2*b*d*x + (b*c + a*d)*x^2)*sqrt(-d/b)*sqrt((a*x + b)/x)*sqrt((c*x + d)/x)/(a*c*d*x^2 + b*d^2 + (b*c*d + a*d^2)*x))]","B",0
1066,1,607,0,0.541668," ","integrate(x^(-1+2*n)*(a+b*x^n)^(5/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3 \, n} - 105 \, b^{4} c^{3} d + 265 \, a b^{3} c^{2} d^{2} - 191 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 17 \, a b^{3} d^{4}\right)} x^{2 \, n} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{768 \, b^{2} d^{5} n}, -\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3 \, n} - 105 \, b^{4} c^{3} d + 265 \, a b^{3} c^{2} d^{2} - 191 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 17 \, a b^{3} d^{4}\right)} x^{2 \, n} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{384 \, b^{2} d^{5} n}\right]"," ",0,"[-1/768*(15*(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) - 4*(48*b^4*d^4*x^(3*n) - 105*b^4*c^3*d + 265*a*b^3*c^2*d^2 - 191*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 17*a*b^3*d^4)*x^(2*n) + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^5*n), -1/384*(15*(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) - 2*(48*b^4*d^4*x^(3*n) - 105*b^4*c^3*d + 265*a*b^3*c^2*d^2 - 191*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 17*a*b^3*d^4)*x^(2*n) + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^5*n)]","A",0
1067,1,469,0,0.496144," ","integrate(x^(-1+2*n)*(a+b*x^n)^(3/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2 \, n} + 15 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{96 \, b^{2} d^{4} n}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2 \, n} + 15 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{48 \, b^{2} d^{4} n}\right]"," ",0,"[1/96*(3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) + 4*(8*b^3*d^3*x^(2*n) + 15*b^3*c^2*d - 22*a*b^2*c*d^2 + 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 7*a*b^2*d^3)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^4*n), 1/48*(3*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) + 2*(8*b^3*d^3*x^(2*n) + 15*b^3*c^2*d - 22*a*b^2*c*d^2 + 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 7*a*b^2*d^3)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^4*n)]","A",0
1068,1,359,0,0.460514," ","integrate(x^(-1+2*n)*(a+b*x^n)^(1/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) - 4 \, {\left(2 \, b^{2} d^{2} x^{n} - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{16 \, b^{2} d^{3} n}, -\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{n} - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{8 \, b^{2} d^{3} n}\right]"," ",0,"[-1/16*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) - 4*(2*b^2*d^2*x^n - 3*b^2*c*d + a*b*d^2)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^3*n), -1/8*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) - 2*(2*b^2*d^2*x^n - 3*b^2*c*d + a*b*d^2)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^2*d^3*n)]","A",0
1069,1,281,0,0.523833," ","integrate(x^(-1+2*n)/(a+b*x^n)^(1/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}{4 \, b^{2} d^{2} n}, \frac{2 \, \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} b d + {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right)}{2 \, b^{2} d^{2} n}\right]"," ",0,"[1/4*(4*sqrt(b*x^n + a)*sqrt(d*x^n + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n))/(b^2*d^2*n), 1/2*(2*sqrt(b*x^n + a)*sqrt(d*x^n + c)*b*d + (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)))/(b^2*d^2*n)]","A",0
1070,1,408,0,0.596837," ","integrate(x^(-1+2*n)/(a+b*x^n)^(3/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} a b d + {\left({\left(b^{2} c - a b d\right)} \sqrt{b d} x^{n} + {\left(a b c - a^{2} d\right)} \sqrt{b d}\right)} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}{2 \, {\left({\left(b^{4} c d - a b^{3} d^{2}\right)} n x^{n} + {\left(a b^{3} c d - a^{2} b^{2} d^{2}\right)} n\right)}}, \frac{2 \, \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} a b d - {\left({\left(b^{2} c - a b d\right)} \sqrt{-b d} x^{n} + {\left(a b c - a^{2} d\right)} \sqrt{-b d}\right)} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right)}{{\left(b^{4} c d - a b^{3} d^{2}\right)} n x^{n} + {\left(a b^{3} c d - a^{2} b^{2} d^{2}\right)} n}\right]"," ",0,"[1/2*(4*sqrt(b*x^n + a)*sqrt(d*x^n + c)*a*b*d + ((b^2*c - a*b*d)*sqrt(b*d)*x^n + (a*b*c - a^2*d)*sqrt(b*d))*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n))/((b^4*c*d - a*b^3*d^2)*n*x^n + (a*b^3*c*d - a^2*b^2*d^2)*n), (2*sqrt(b*x^n + a)*sqrt(d*x^n + c)*a*b*d - ((b^2*c - a*b*d)*sqrt(-b*d)*x^n + (a*b*c - a^2*d)*sqrt(-b*d))*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)))/((b^4*c*d - a*b^3*d^2)*n*x^n + (a*b^3*c*d - a^2*b^2*d^2)*n)]","B",0
1071,1,135,0,0.739078," ","integrate(x^(-1+2*n)/(a+b*x^n)^(5/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a c + {\left(3 \, b c - a d\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{3 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} n x^{2 \, n} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} n x^{n} + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} n\right)}}"," ",0,"-2/3*(2*a*c + (3*b*c - a*d)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*n*x^(2*n) + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*n*x^n + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*n)","A",0
1072,1,771,0,0.584402," ","integrate(x^(-1+3*n)*(a+b*x^n)^(5/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{4 \, n} + 945 \, b^{5} c^{4} d - 2310 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 90 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} - 144 \, {\left(3 \, b^{5} c d^{4} - 7 \, a b^{4} d^{5}\right)} x^{3 \, n} + 8 \, {\left(63 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2 \, n} - 2 \, {\left(315 \, b^{5} c^{3} d^{2} - 749 \, a b^{4} c^{2} d^{3} + 481 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{7680 \, b^{3} d^{6} n}, \frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{4 \, n} + 945 \, b^{5} c^{4} d - 2310 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 90 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} - 144 \, {\left(3 \, b^{5} c d^{4} - 7 \, a b^{4} d^{5}\right)} x^{3 \, n} + 8 \, {\left(63 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2 \, n} - 2 \, {\left(315 \, b^{5} c^{3} d^{2} - 749 \, a b^{4} c^{2} d^{3} + 481 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{3840 \, b^{3} d^{6} n}\right]"," ",0,"[-1/7680*(15*(63*b^5*c^5 - 175*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) - 4*(384*b^5*d^5*x^(4*n) + 945*b^5*c^4*d - 2310*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 90*a^3*b^2*c*d^4 - 45*a^4*b*d^5 - 144*(3*b^5*c*d^4 - 7*a*b^4*d^5)*x^(3*n) + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^(2*n) - 2*(315*b^5*c^3*d^2 - 749*a*b^4*c^2*d^3 + 481*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^6*n), 1/3840*(15*(63*b^5*c^5 - 175*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) + 2*(384*b^5*d^5*x^(4*n) + 945*b^5*c^4*d - 2310*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 90*a^3*b^2*c*d^4 - 45*a^4*b*d^5 - 144*(3*b^5*c*d^4 - 7*a*b^4*d^5)*x^(3*n) + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^(2*n) - 2*(315*b^5*c^3*d^2 - 749*a*b^4*c^2*d^3 + 481*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^6*n)]","A",0
1073,1,607,0,0.541792," ","integrate(x^(-1+3*n)*(a+b*x^n)^(3/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3 \, n} - 105 \, b^{4} c^{3} d + 145 \, a b^{3} c^{2} d^{2} - 15 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{2 \, n} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{768 \, b^{3} d^{5} n}, -\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3 \, n} - 105 \, b^{4} c^{3} d + 145 \, a b^{3} c^{2} d^{2} - 15 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{2 \, n} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{384 \, b^{3} d^{5} n}\right]"," ",0,"[1/768*(3*(35*b^4*c^4 - 60*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + 3*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) + 4*(48*b^4*d^4*x^(3*n) - 105*b^4*c^3*d + 145*a*b^3*c^2*d^2 - 15*a^2*b^2*c*d^3 - 9*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 9*a*b^3*d^4)*x^(2*n) + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^5*n), -1/384*(3*(35*b^4*c^4 - 60*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + 3*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) - 2*(48*b^4*d^4*x^(3*n) - 105*b^4*c^3*d + 145*a*b^3*c^2*d^2 - 15*a^2*b^2*c*d^3 - 9*a^3*b*d^4 - 8*(7*b^4*c*d^3 - 9*a*b^3*d^4)*x^(2*n) + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^5*n)]","A",0
1074,1,471,0,0.513094," ","integrate(x^(-1+3*n)*(a+b*x^n)^(1/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2 \, n} + 15 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{96 \, b^{3} d^{4} n}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2 \, n} + 15 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{48 \, b^{3} d^{4} n}\right]"," ",0,"[-1/96*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) - 4*(8*b^3*d^3*x^(2*n) + 15*b^3*c^2*d - 4*a*b^2*c*d^2 - 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - a*b^2*d^3)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^4*n), 1/48*(3*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) + 2*(8*b^3*d^3*x^(2*n) + 15*b^3*c^2*d - 4*a*b^2*c*d^2 - 3*a^2*b*d^3 - 2*(5*b^3*c*d^2 - a*b^2*d^3)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^4*n)]","A",0
1075,1,361,0,0.500231," ","integrate(x^(-1+3*n)/(a+b*x^n)^(1/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{n} - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{16 \, b^{3} d^{3} n}, -\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{n} - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{8 \, b^{3} d^{3} n}\right]"," ",0,"[1/16*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n) + 4*(2*b^2*d^2*x^n - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^3*n), -1/8*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)) - 2*(2*b^2*d^2*x^n - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x^n + a)*sqrt(d*x^n + c))/(b^3*d^3*n)]","A",0
1076,1,540,0,0.573600," ","integrate(x^(-1+3*n)/(a+b*x^n)^(3/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b^{2} c d - 3 \, a^{2} b d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + {\left({\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} \sqrt{b d} x^{n} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{b d}\right)} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}{4 \, {\left({\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} n x^{n} + {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3}\right)} n\right)}}, \frac{2 \, {\left(a b^{2} c d - 3 \, a^{2} b d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + {\left({\left(b^{3} c^{2} + 2 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} \sqrt{-b d} x^{n} + {\left(a b^{2} c^{2} + 2 \, a^{2} b c d - 3 \, a^{3} d^{2}\right)} \sqrt{-b d}\right)} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right)}{2 \, {\left({\left(b^{5} c d^{2} - a b^{4} d^{3}\right)} n x^{n} + {\left(a b^{4} c d^{2} - a^{2} b^{3} d^{3}\right)} n\right)}}\right]"," ",0,"[1/4*(4*(a*b^2*c*d - 3*a^2*b*d^2 + (b^3*c*d - a*b^2*d^2)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c) + ((b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*sqrt(b*d)*x^n + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2)*sqrt(b*d))*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n))/((b^5*c*d^2 - a*b^4*d^3)*n*x^n + (a*b^4*c*d^2 - a^2*b^3*d^3)*n), 1/2*(2*(a*b^2*c*d - 3*a^2*b*d^2 + (b^3*c*d - a*b^2*d^2)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c) + ((b^3*c^2 + 2*a*b^2*c*d - 3*a^2*b*d^2)*sqrt(-b*d)*x^n + (a*b^2*c^2 + 2*a^2*b*c*d - 3*a^3*d^2)*sqrt(-b*d))*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)))/((b^5*c*d^2 - a*b^4*d^3)*n*x^n + (a*b^4*c*d^2 - a^2*b^3*d^3)*n)]","B",0
1077,1,769,0,0.793994," ","integrate(x^(-1+3*n)/(a+b*x^n)^(5/2)/(c+d*x^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 3 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \sqrt{b d} x^{2 \, n} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} \sqrt{b d} x^{n} + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{b d}\right)} \log\left(8 \, b^{2} d^{2} x^{2 \, n} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, \sqrt{b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}{6 \, {\left({\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} n x^{2 \, n} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} n x^{n} + {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3}\right)} n\right)}}, \frac{2 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{n}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c} - 3 \, {\left({\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \sqrt{-b d} x^{2 \, n} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} \sqrt{-b d} x^{n} + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \sqrt{-b d}\right)} \arctan\left(\frac{{\left(2 \, \sqrt{-b d} b d x^{n} + {\left(b c + a d\right)} \sqrt{-b d}\right)} \sqrt{b x^{n} + a} \sqrt{d x^{n} + c}}{2 \, {\left(b^{2} d^{2} x^{2 \, n} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x^{n}\right)}}\right)}{3 \, {\left({\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} n x^{2 \, n} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} n x^{n} + {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3}\right)} n\right)}}\right]"," ",0,"[1/6*(4*(5*a^2*b^2*c*d - 3*a^3*b*d^2 + 2*(3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 3*((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*sqrt(b*d)*x^(2*n) + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*sqrt(b*d)*x^n + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(b*d))*log(8*b^2*d^2*x^(2*n) + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*sqrt(b*d)*b*d*x^n + (b*c + a*d)*sqrt(b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c) + 8*(b^2*c*d + a*b*d^2)*x^n))/((b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*n*x^(2*n) + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*n*x^n + (a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3)*n), 1/3*(2*(5*a^2*b^2*c*d - 3*a^3*b*d^2 + 2*(3*a*b^3*c*d - 2*a^2*b^2*d^2)*x^n)*sqrt(b*x^n + a)*sqrt(d*x^n + c) - 3*((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*sqrt(-b*d)*x^(2*n) + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*sqrt(-b*d)*x^n + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*sqrt(-b*d))*arctan(1/2*(2*sqrt(-b*d)*b*d*x^n + (b*c + a*d)*sqrt(-b*d))*sqrt(b*x^n + a)*sqrt(d*x^n + c)/(b^2*d^2*x^(2*n) + a*b*c*d + (b^2*c*d + a*b*d^2)*x^n)))/((b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*n*x^(2*n) + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*n*x^n + (a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3)*n)]","B",0
1078,1,25,0,0.420119," ","integrate(x^p*(c*x+b)^p*(2*c*x+b),x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b x\right)} {\left(c x + b\right)}^{p} x^{p}}{p + 1}"," ",0,"(c*x^2 + b*x)*(c*x + b)^p*x^p/(p + 1)","A",0
1079,1,32,0,0.432667," ","integrate(x^(1+2*p)*(c*x^2+b)^p*(2*c*x^2+b),x, algorithm=""fricas"")","\frac{{\left(c x^{3} + b x\right)} {\left(c x^{2} + b\right)}^{p} x^{2 \, p + 1}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^3 + b*x)*(c*x^2 + b)^p*x^(2*p + 1)/(p + 1)","A",0
1080,1,32,0,0.433519," ","integrate(x^(2+3*p)*(c*x^3+b)^p*(2*c*x^3+b),x, algorithm=""fricas"")","\frac{{\left(c x^{4} + b x\right)} {\left(c x^{3} + b\right)}^{p} x^{3 \, p + 2}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^4 + b*x)*(c*x^3 + b)^p*x^(3*p + 2)/(p + 1)","A",0
1081,1,35,0,0.451427," ","integrate(x^(-1+n*(1+p))*(b+c*x^n)^p*(b+2*c*x^n),x, algorithm=""fricas"")","\frac{{\left(c x x^{n} + b x\right)} {\left(c x^{n} + b\right)}^{p} x^{n p + n - 1}}{n p + n}"," ",0,"(c*x*x^n + b*x)*(c*x^n + b)^p*x^(n*p + n - 1)/(n*p + n)","A",0
