1,1,34,0,1.547144," ","integrate(x^2/(-1+x)^2/(1+x)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} - 1\right)} \log\left(x + 1\right) - {\left(x^{2} - 1\right)} \log\left(x - 1\right) + 2 \, x}{4 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/4*((x^2 - 1)*log(x + 1) - (x^2 - 1)*log(x - 1) + 2*x)/(x^2 - 1)","B",0
2,1,47,0,1.215463," ","integrate(x^2*(b*x+a)*(-b*c*x+a*c)^3,x, algorithm=""fricas"")","-\frac{1}{7} x^{7} c^{3} b^{4} + \frac{1}{3} x^{6} c^{3} b^{3} a - \frac{1}{2} x^{4} c^{3} b a^{3} + \frac{1}{3} x^{3} c^{3} a^{4}"," ",0,"-1/7*x^7*c^3*b^4 + 1/3*x^6*c^3*b^3*a - 1/2*x^4*c^3*b*a^3 + 1/3*x^3*c^3*a^4","A",0
3,1,47,0,1.191366," ","integrate(x*(b*x+a)*(-b*c*x+a*c)^3,x, algorithm=""fricas"")","-\frac{1}{6} x^{6} c^{3} b^{4} + \frac{2}{5} x^{5} c^{3} b^{3} a - \frac{2}{3} x^{3} c^{3} b a^{3} + \frac{1}{2} x^{2} c^{3} a^{4}"," ",0,"-1/6*x^6*c^3*b^4 + 2/5*x^5*c^3*b^3*a - 2/3*x^3*c^3*b*a^3 + 1/2*x^2*c^3*a^4","A",0
4,1,44,0,1.129510," ","integrate((b*x+a)*(-b*c*x+a*c)^3,x, algorithm=""fricas"")","-\frac{1}{5} x^{5} c^{3} b^{4} + \frac{1}{2} x^{4} c^{3} b^{3} a - x^{2} c^{3} b a^{3} + x c^{3} a^{4}"," ",0,"-1/5*x^5*c^3*b^4 + 1/2*x^4*c^3*b^3*a - x^2*c^3*b*a^3 + x*c^3*a^4","A",0
5,1,43,0,1.393615," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x,x, algorithm=""fricas"")","-\frac{1}{4} \, b^{4} c^{3} x^{4} + \frac{2}{3} \, a b^{3} c^{3} x^{3} - 2 \, a^{3} b c^{3} x + a^{4} c^{3} \log\left(x\right)"," ",0,"-1/4*b^4*c^3*x^4 + 2/3*a*b^3*c^3*x^3 - 2*a^3*b*c^3*x + a^4*c^3*log(x)","A",0
6,1,48,0,1.333056," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^2,x, algorithm=""fricas"")","-\frac{b^{4} c^{3} x^{4} - 3 \, a b^{3} c^{3} x^{3} + 6 \, a^{3} b c^{3} x \log\left(x\right) + 3 \, a^{4} c^{3}}{3 \, x}"," ",0,"-1/3*(b^4*c^3*x^4 - 3*a*b^3*c^3*x^3 + 6*a^3*b*c^3*x*log(x) + 3*a^4*c^3)/x","A",0
7,1,45,0,1.160087," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{3} x^{4} - 4 \, a b^{3} c^{3} x^{3} - 4 \, a^{3} b c^{3} x + a^{4} c^{3}}{2 \, x^{2}}"," ",0,"-1/2*(b^4*c^3*x^4 - 4*a*b^3*c^3*x^3 - 4*a^3*b*c^3*x + a^4*c^3)/x^2","B",0
8,1,48,0,1.546493," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^4,x, algorithm=""fricas"")","-\frac{3 \, b^{4} c^{3} x^{4} - 6 \, a b^{3} c^{3} x^{3} \log\left(x\right) - 3 \, a^{3} b c^{3} x + a^{4} c^{3}}{3 \, x^{3}}"," ",0,"-1/3*(3*b^4*c^3*x^4 - 6*a*b^3*c^3*x^3*log(x) - 3*a^3*b*c^3*x + a^4*c^3)/x^3","A",0
9,1,49,0,0.984858," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^5,x, algorithm=""fricas"")","-\frac{12 \, b^{4} c^{3} x^{4} \log\left(x\right) + 24 \, a b^{3} c^{3} x^{3} - 8 \, a^{3} b c^{3} x + 3 \, a^{4} c^{3}}{12 \, x^{4}}"," ",0,"-1/12*(12*b^4*c^3*x^4*log(x) + 24*a*b^3*c^3*x^3 - 8*a^3*b*c^3*x + 3*a^4*c^3)/x^4","A",0
10,1,47,0,1.309612," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^6,x, algorithm=""fricas"")","\frac{10 \, b^{4} c^{3} x^{4} - 10 \, a b^{3} c^{3} x^{3} + 5 \, a^{3} b c^{3} x - 2 \, a^{4} c^{3}}{10 \, x^{5}}"," ",0,"1/10*(10*b^4*c^3*x^4 - 10*a*b^3*c^3*x^3 + 5*a^3*b*c^3*x - 2*a^4*c^3)/x^5","A",0
11,1,47,0,1.108220," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^7,x, algorithm=""fricas"")","\frac{15 \, b^{4} c^{3} x^{4} - 20 \, a b^{3} c^{3} x^{3} + 12 \, a^{3} b c^{3} x - 5 \, a^{4} c^{3}}{30 \, x^{6}}"," ",0,"1/30*(15*b^4*c^3*x^4 - 20*a*b^3*c^3*x^3 + 12*a^3*b*c^3*x - 5*a^4*c^3)/x^6","A",0
12,1,47,0,1.448987," ","integrate((b*x+a)*(-b*c*x+a*c)^3/x^8,x, algorithm=""fricas"")","\frac{14 \, b^{4} c^{3} x^{4} - 21 \, a b^{3} c^{3} x^{3} + 14 \, a^{3} b c^{3} x - 6 \, a^{4} c^{3}}{42 \, x^{7}}"," ",0,"1/42*(14*b^4*c^3*x^4 - 21*a*b^3*c^3*x^3 + 14*a^3*b*c^3*x - 6*a^4*c^3)/x^7","A",0
13,1,75,0,1.305754," ","integrate(x^4*(b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{1}{10} x^{10} c^{4} b^{5} - \frac{1}{3} x^{9} c^{4} b^{4} a + \frac{1}{4} x^{8} c^{4} b^{3} a^{2} + \frac{2}{7} x^{7} c^{4} b^{2} a^{3} - \frac{1}{2} x^{6} c^{4} b a^{4} + \frac{1}{5} x^{5} c^{4} a^{5}"," ",0,"1/10*x^10*c^4*b^5 - 1/3*x^9*c^4*b^4*a + 1/4*x^8*c^4*b^3*a^2 + 2/7*x^7*c^4*b^2*a^3 - 1/2*x^6*c^4*b*a^4 + 1/5*x^5*c^4*a^5","A",0
14,1,75,0,1.310093," ","integrate(x^3*(b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{4} b^{5} - \frac{3}{8} x^{8} c^{4} b^{4} a + \frac{2}{7} x^{7} c^{4} b^{3} a^{2} + \frac{1}{3} x^{6} c^{4} b^{2} a^{3} - \frac{3}{5} x^{5} c^{4} b a^{4} + \frac{1}{4} x^{4} c^{4} a^{5}"," ",0,"1/9*x^9*c^4*b^5 - 3/8*x^8*c^4*b^4*a + 2/7*x^7*c^4*b^3*a^2 + 1/3*x^6*c^4*b^2*a^3 - 3/5*x^5*c^4*b*a^4 + 1/4*x^4*c^4*a^5","A",0
15,1,75,0,1.165650," ","integrate(x^2*(b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{1}{8} x^{8} c^{4} b^{5} - \frac{3}{7} x^{7} c^{4} b^{4} a + \frac{1}{3} x^{6} c^{4} b^{3} a^{2} + \frac{2}{5} x^{5} c^{4} b^{2} a^{3} - \frac{3}{4} x^{4} c^{4} b a^{4} + \frac{1}{3} x^{3} c^{4} a^{5}"," ",0,"1/8*x^8*c^4*b^5 - 3/7*x^7*c^4*b^4*a + 1/3*x^6*c^4*b^3*a^2 + 2/5*x^5*c^4*b^2*a^3 - 3/4*x^4*c^4*b*a^4 + 1/3*x^3*c^4*a^5","A",0
16,1,75,0,1.127013," ","integrate(x*(b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{4} b^{5} - \frac{1}{2} x^{6} c^{4} b^{4} a + \frac{2}{5} x^{5} c^{4} b^{3} a^{2} + \frac{1}{2} x^{4} c^{4} b^{2} a^{3} - x^{3} c^{4} b a^{4} + \frac{1}{2} x^{2} c^{4} a^{5}"," ",0,"1/7*x^7*c^4*b^5 - 1/2*x^6*c^4*b^4*a + 2/5*x^5*c^4*b^3*a^2 + 1/2*x^4*c^4*b^2*a^3 - x^3*c^4*b*a^4 + 1/2*x^2*c^4*a^5","A",0
17,1,72,0,1.376481," ","integrate((b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{1}{6} x^{6} c^{4} b^{5} - \frac{3}{5} x^{5} c^{4} b^{4} a + \frac{1}{2} x^{4} c^{4} b^{3} a^{2} + \frac{2}{3} x^{3} c^{4} b^{2} a^{3} - \frac{3}{2} x^{2} c^{4} b a^{4} + x c^{4} a^{5}"," ",0,"1/6*x^6*c^4*b^5 - 3/5*x^5*c^4*b^4*a + 1/2*x^4*c^4*b^3*a^2 + 2/3*x^3*c^4*b^2*a^3 - 3/2*x^2*c^4*b*a^4 + x*c^4*a^5","A",0
18,1,70,0,1.048122," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x,x, algorithm=""fricas"")","\frac{1}{5} \, b^{5} c^{4} x^{5} - \frac{3}{4} \, a b^{4} c^{4} x^{4} + \frac{2}{3} \, a^{2} b^{3} c^{4} x^{3} + a^{3} b^{2} c^{4} x^{2} - 3 \, a^{4} b c^{4} x + a^{5} c^{4} \log\left(x\right)"," ",0,"1/5*b^5*c^4*x^5 - 3/4*a*b^4*c^4*x^4 + 2/3*a^2*b^3*c^4*x^3 + a^3*b^2*c^4*x^2 - 3*a^4*b*c^4*x + a^5*c^4*log(x)","A",0
19,1,76,0,1.444491," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^2,x, algorithm=""fricas"")","\frac{b^{5} c^{4} x^{5} - 4 \, a b^{4} c^{4} x^{4} + 4 \, a^{2} b^{3} c^{4} x^{3} + 8 \, a^{3} b^{2} c^{4} x^{2} - 12 \, a^{4} b c^{4} x \log\left(x\right) - 4 \, a^{5} c^{4}}{4 \, x}"," ",0,"1/4*(b^5*c^4*x^5 - 4*a*b^4*c^4*x^4 + 4*a^2*b^3*c^4*x^3 + 8*a^3*b^2*c^4*x^2 - 12*a^4*b*c^4*x*log(x) - 4*a^5*c^4)/x","A",0
20,1,77,0,1.433484," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} c^{4} x^{5} - 9 \, a b^{4} c^{4} x^{4} + 12 \, a^{2} b^{3} c^{4} x^{3} + 12 \, a^{3} b^{2} c^{4} x^{2} \log\left(x\right) + 18 \, a^{4} b c^{4} x - 3 \, a^{5} c^{4}}{6 \, x^{2}}"," ",0,"1/6*(2*b^5*c^4*x^5 - 9*a*b^4*c^4*x^4 + 12*a^2*b^3*c^4*x^3 + 12*a^3*b^2*c^4*x^2*log(x) + 18*a^4*b*c^4*x - 3*a^5*c^4)/x^2","A",0
21,1,77,0,1.317025," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} c^{4} x^{5} - 18 \, a b^{4} c^{4} x^{4} + 12 \, a^{2} b^{3} c^{4} x^{3} \log\left(x\right) - 12 \, a^{3} b^{2} c^{4} x^{2} + 9 \, a^{4} b c^{4} x - 2 \, a^{5} c^{4}}{6 \, x^{3}}"," ",0,"1/6*(3*b^5*c^4*x^5 - 18*a*b^4*c^4*x^4 + 12*a^2*b^3*c^4*x^3*log(x) - 12*a^3*b^2*c^4*x^2 + 9*a^4*b*c^4*x - 2*a^5*c^4)/x^3","A",0
22,1,77,0,1.257133," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^5,x, algorithm=""fricas"")","\frac{4 \, b^{5} c^{4} x^{5} - 12 \, a b^{4} c^{4} x^{4} \log\left(x\right) - 8 \, a^{2} b^{3} c^{4} x^{3} - 4 \, a^{3} b^{2} c^{4} x^{2} + 4 \, a^{4} b c^{4} x - a^{5} c^{4}}{4 \, x^{4}}"," ",0,"1/4*(4*b^5*c^4*x^5 - 12*a*b^4*c^4*x^4*log(x) - 8*a^2*b^3*c^4*x^3 - 4*a^3*b^2*c^4*x^2 + 4*a^4*b*c^4*x - a^5*c^4)/x^4","A",0
23,1,77,0,0.797755," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^6,x, algorithm=""fricas"")","\frac{60 \, b^{5} c^{4} x^{5} \log\left(x\right) + 180 \, a b^{4} c^{4} x^{4} - 60 \, a^{2} b^{3} c^{4} x^{3} - 40 \, a^{3} b^{2} c^{4} x^{2} + 45 \, a^{4} b c^{4} x - 12 \, a^{5} c^{4}}{60 \, x^{5}}"," ",0,"1/60*(60*b^5*c^4*x^5*log(x) + 180*a*b^4*c^4*x^4 - 60*a^2*b^3*c^4*x^3 - 40*a^3*b^2*c^4*x^2 + 45*a^4*b*c^4*x - 12*a^5*c^4)/x^5","A",0
24,1,75,0,1.411465," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^7,x, algorithm=""fricas"")","-\frac{30 \, b^{5} c^{4} x^{5} - 45 \, a b^{4} c^{4} x^{4} + 20 \, a^{2} b^{3} c^{4} x^{3} + 15 \, a^{3} b^{2} c^{4} x^{2} - 18 \, a^{4} b c^{4} x + 5 \, a^{5} c^{4}}{30 \, x^{6}}"," ",0,"-1/30*(30*b^5*c^4*x^5 - 45*a*b^4*c^4*x^4 + 20*a^2*b^3*c^4*x^3 + 15*a^3*b^2*c^4*x^2 - 18*a^4*b*c^4*x + 5*a^5*c^4)/x^6","A",0
25,1,75,0,1.321402," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^8,x, algorithm=""fricas"")","-\frac{35 \, b^{5} c^{4} x^{5} - 70 \, a b^{4} c^{4} x^{4} + 35 \, a^{2} b^{3} c^{4} x^{3} + 28 \, a^{3} b^{2} c^{4} x^{2} - 35 \, a^{4} b c^{4} x + 10 \, a^{5} c^{4}}{70 \, x^{7}}"," ",0,"-1/70*(35*b^5*c^4*x^5 - 70*a*b^4*c^4*x^4 + 35*a^2*b^3*c^4*x^3 + 28*a^3*b^2*c^4*x^2 - 35*a^4*b*c^4*x + 10*a^5*c^4)/x^7","A",0
26,1,75,0,1.327392," ","integrate((b*x+a)*(-b*c*x+a*c)^4/x^9,x, algorithm=""fricas"")","-\frac{280 \, b^{5} c^{4} x^{5} - 630 \, a b^{4} c^{4} x^{4} + 336 \, a^{2} b^{3} c^{4} x^{3} + 280 \, a^{3} b^{2} c^{4} x^{2} - 360 \, a^{4} b c^{4} x + 105 \, a^{5} c^{4}}{840 \, x^{8}}"," ",0,"-1/840*(280*b^5*c^4*x^5 - 630*a*b^4*c^4*x^4 + 336*a^2*b^3*c^4*x^3 + 280*a^3*b^2*c^4*x^2 - 360*a^4*b*c^4*x + 105*a^5*c^4)/x^8","A",0
27,1,75,0,1.357884," ","integrate(x^4*(b*x+a)*(-b*c*x+a*c)^5,x, algorithm=""fricas"")","-\frac{1}{11} x^{11} c^{5} b^{6} + \frac{2}{5} x^{10} c^{5} b^{5} a - \frac{5}{9} x^{9} c^{5} b^{4} a^{2} + \frac{5}{7} x^{7} c^{5} b^{2} a^{4} - \frac{2}{3} x^{6} c^{5} b a^{5} + \frac{1}{5} x^{5} c^{5} a^{6}"," ",0,"-1/11*x^11*c^5*b^6 + 2/5*x^10*c^5*b^5*a - 5/9*x^9*c^5*b^4*a^2 + 5/7*x^7*c^5*b^2*a^4 - 2/3*x^6*c^5*b*a^5 + 1/5*x^5*c^5*a^6","A",0
28,1,75,0,1.211955," ","integrate(x^3*(b*x+a)*(-b*c*x+a*c)^5,x, algorithm=""fricas"")","-\frac{1}{10} x^{10} c^{5} b^{6} + \frac{4}{9} x^{9} c^{5} b^{5} a - \frac{5}{8} x^{8} c^{5} b^{4} a^{2} + \frac{5}{6} x^{6} c^{5} b^{2} a^{4} - \frac{4}{5} x^{5} c^{5} b a^{5} + \frac{1}{4} x^{4} c^{5} a^{6}"," ",0,"-1/10*x^10*c^5*b^6 + 4/9*x^9*c^5*b^5*a - 5/8*x^8*c^5*b^4*a^2 + 5/6*x^6*c^5*b^2*a^4 - 4/5*x^5*c^5*b*a^5 + 1/4*x^4*c^5*a^6","A",0
29,1,74,0,1.027687," ","integrate(x^2*(b*x+a)*(-b*c*x+a*c)^5,x, algorithm=""fricas"")","-\frac{1}{9} x^{9} c^{5} b^{6} + \frac{1}{2} x^{8} c^{5} b^{5} a - \frac{5}{7} x^{7} c^{5} b^{4} a^{2} + x^{5} c^{5} b^{2} a^{4} - x^{4} c^{5} b a^{5} + \frac{1}{3} x^{3} c^{5} a^{6}"," ",0,"-1/9*x^9*c^5*b^6 + 1/2*x^8*c^5*b^5*a - 5/7*x^7*c^5*b^4*a^2 + x^5*c^5*b^2*a^4 - x^4*c^5*b*a^5 + 1/3*x^3*c^5*a^6","A",0
30,1,75,0,1.014285," ","integrate(x*(b*x+a)*(-b*c*x+a*c)^5,x, algorithm=""fricas"")","-\frac{1}{8} x^{8} c^{5} b^{6} + \frac{4}{7} x^{7} c^{5} b^{5} a - \frac{5}{6} x^{6} c^{5} b^{4} a^{2} + \frac{5}{4} x^{4} c^{5} b^{2} a^{4} - \frac{4}{3} x^{3} c^{5} b a^{5} + \frac{1}{2} x^{2} c^{5} a^{6}"," ",0,"-1/8*x^8*c^5*b^6 + 4/7*x^7*c^5*b^5*a - 5/6*x^6*c^5*b^4*a^2 + 5/4*x^4*c^5*b^2*a^4 - 4/3*x^3*c^5*b*a^5 + 1/2*x^2*c^5*a^6","A",0
31,1,72,0,0.576631," ","integrate((b*x+a)*(-b*c*x+a*c)^5,x, algorithm=""fricas"")","-\frac{1}{7} x^{7} c^{5} b^{6} + \frac{2}{3} x^{6} c^{5} b^{5} a - x^{5} c^{5} b^{4} a^{2} + \frac{5}{3} x^{3} c^{5} b^{2} a^{4} - 2 x^{2} c^{5} b a^{5} + x c^{5} a^{6}"," ",0,"-1/7*x^7*c^5*b^6 + 2/3*x^6*c^5*b^5*a - x^5*c^5*b^4*a^2 + 5/3*x^3*c^5*b^2*a^4 - 2*x^2*c^5*b*a^5 + x*c^5*a^6","A",0
32,1,71,0,1.611015," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x,x, algorithm=""fricas"")","-\frac{1}{6} \, b^{6} c^{5} x^{6} + \frac{4}{5} \, a b^{5} c^{5} x^{5} - \frac{5}{4} \, a^{2} b^{4} c^{5} x^{4} + \frac{5}{2} \, a^{4} b^{2} c^{5} x^{2} - 4 \, a^{5} b c^{5} x + a^{6} c^{5} \log\left(x\right)"," ",0,"-1/6*b^6*c^5*x^6 + 4/5*a*b^5*c^5*x^5 - 5/4*a^2*b^4*c^5*x^4 + 5/2*a^4*b^2*c^5*x^2 - 4*a^5*b*c^5*x + a^6*c^5*log(x)","A",0
33,1,77,0,1.229219," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^2,x, algorithm=""fricas"")","-\frac{3 \, b^{6} c^{5} x^{6} - 15 \, a b^{5} c^{5} x^{5} + 25 \, a^{2} b^{4} c^{5} x^{4} - 75 \, a^{4} b^{2} c^{5} x^{2} + 60 \, a^{5} b c^{5} x \log\left(x\right) + 15 \, a^{6} c^{5}}{15 \, x}"," ",0,"-1/15*(3*b^6*c^5*x^6 - 15*a*b^5*c^5*x^5 + 25*a^2*b^4*c^5*x^4 - 75*a^4*b^2*c^5*x^2 + 60*a^5*b*c^5*x*log(x) + 15*a^6*c^5)/x","A",0
34,1,77,0,1.545133," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^3,x, algorithm=""fricas"")","-\frac{3 \, b^{6} c^{5} x^{6} - 16 \, a b^{5} c^{5} x^{5} + 30 \, a^{2} b^{4} c^{5} x^{4} - 60 \, a^{4} b^{2} c^{5} x^{2} \log\left(x\right) - 48 \, a^{5} b c^{5} x + 6 \, a^{6} c^{5}}{12 \, x^{2}}"," ",0,"-1/12*(3*b^6*c^5*x^6 - 16*a*b^5*c^5*x^5 + 30*a^2*b^4*c^5*x^4 - 60*a^4*b^2*c^5*x^2*log(x) - 48*a^5*b*c^5*x + 6*a^6*c^5)/x^2","A",0
35,1,73,0,1.117738," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^4,x, algorithm=""fricas"")","-\frac{b^{6} c^{5} x^{6} - 6 \, a b^{5} c^{5} x^{5} + 15 \, a^{2} b^{4} c^{5} x^{4} + 15 \, a^{4} b^{2} c^{5} x^{2} - 6 \, a^{5} b c^{5} x + a^{6} c^{5}}{3 \, x^{3}}"," ",0,"-1/3*(b^6*c^5*x^6 - 6*a*b^5*c^5*x^5 + 15*a^2*b^4*c^5*x^4 + 15*a^4*b^2*c^5*x^2 - 6*a^5*b*c^5*x + a^6*c^5)/x^3","B",0
36,1,77,0,0.895686," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^5,x, algorithm=""fricas"")","-\frac{6 \, b^{6} c^{5} x^{6} - 48 \, a b^{5} c^{5} x^{5} + 60 \, a^{2} b^{4} c^{5} x^{4} \log\left(x\right) + 30 \, a^{4} b^{2} c^{5} x^{2} - 16 \, a^{5} b c^{5} x + 3 \, a^{6} c^{5}}{12 \, x^{4}}"," ",0,"-1/12*(6*b^6*c^5*x^6 - 48*a*b^5*c^5*x^5 + 60*a^2*b^4*c^5*x^4*log(x) + 30*a^4*b^2*c^5*x^2 - 16*a^5*b*c^5*x + 3*a^6*c^5)/x^4","A",0
37,1,77,0,2.373020," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^6,x, algorithm=""fricas"")","-\frac{15 \, b^{6} c^{5} x^{6} - 60 \, a b^{5} c^{5} x^{5} \log\left(x\right) - 75 \, a^{2} b^{4} c^{5} x^{4} + 25 \, a^{4} b^{2} c^{5} x^{2} - 15 \, a^{5} b c^{5} x + 3 \, a^{6} c^{5}}{15 \, x^{5}}"," ",0,"-1/15*(15*b^6*c^5*x^6 - 60*a*b^5*c^5*x^5*log(x) - 75*a^2*b^4*c^5*x^4 + 25*a^4*b^2*c^5*x^2 - 15*a^5*b*c^5*x + 3*a^6*c^5)/x^5","A",0
38,1,77,0,1.591971," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^7,x, algorithm=""fricas"")","-\frac{60 \, b^{6} c^{5} x^{6} \log\left(x\right) + 240 \, a b^{5} c^{5} x^{5} - 150 \, a^{2} b^{4} c^{5} x^{4} + 75 \, a^{4} b^{2} c^{5} x^{2} - 48 \, a^{5} b c^{5} x + 10 \, a^{6} c^{5}}{60 \, x^{6}}"," ",0,"-1/60*(60*b^6*c^5*x^6*log(x) + 240*a*b^5*c^5*x^5 - 150*a^2*b^4*c^5*x^4 + 75*a^4*b^2*c^5*x^2 - 48*a^5*b*c^5*x + 10*a^6*c^5)/x^6","A",0
39,1,75,0,1.140897," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^8,x, algorithm=""fricas"")","\frac{21 \, b^{6} c^{5} x^{6} - 42 \, a b^{5} c^{5} x^{5} + 35 \, a^{2} b^{4} c^{5} x^{4} - 21 \, a^{4} b^{2} c^{5} x^{2} + 14 \, a^{5} b c^{5} x - 3 \, a^{6} c^{5}}{21 \, x^{7}}"," ",0,"1/21*(21*b^6*c^5*x^6 - 42*a*b^5*c^5*x^5 + 35*a^2*b^4*c^5*x^4 - 21*a^4*b^2*c^5*x^2 + 14*a^5*b*c^5*x - 3*a^6*c^5)/x^7","A",0
40,1,75,0,1.327899," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^9,x, algorithm=""fricas"")","\frac{84 \, b^{6} c^{5} x^{6} - 224 \, a b^{5} c^{5} x^{5} + 210 \, a^{2} b^{4} c^{5} x^{4} - 140 \, a^{4} b^{2} c^{5} x^{2} + 96 \, a^{5} b c^{5} x - 21 \, a^{6} c^{5}}{168 \, x^{8}}"," ",0,"1/168*(84*b^6*c^5*x^6 - 224*a*b^5*c^5*x^5 + 210*a^2*b^4*c^5*x^4 - 140*a^4*b^2*c^5*x^2 + 96*a^5*b*c^5*x - 21*a^6*c^5)/x^8","A",0
41,1,75,0,0.871361," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^10,x, algorithm=""fricas"")","\frac{42 \, b^{6} c^{5} x^{6} - 126 \, a b^{5} c^{5} x^{5} + 126 \, a^{2} b^{4} c^{5} x^{4} - 90 \, a^{4} b^{2} c^{5} x^{2} + 63 \, a^{5} b c^{5} x - 14 \, a^{6} c^{5}}{126 \, x^{9}}"," ",0,"1/126*(42*b^6*c^5*x^6 - 126*a*b^5*c^5*x^5 + 126*a^2*b^4*c^5*x^4 - 90*a^4*b^2*c^5*x^2 + 63*a^5*b*c^5*x - 14*a^6*c^5)/x^9","A",0
42,1,75,0,1.576386," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^11,x, algorithm=""fricas"")","\frac{90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}}"," ",0,"1/360*(90*b^6*c^5*x^6 - 288*a*b^5*c^5*x^5 + 300*a^2*b^4*c^5*x^4 - 225*a^4*b^2*c^5*x^2 + 160*a^5*b*c^5*x - 36*a^6*c^5)/x^10","A",0
43,1,75,0,0.990782," ","integrate((b*x+a)*(-b*c*x+a*c)^5/x^12,x, algorithm=""fricas"")","\frac{693 \, b^{6} c^{5} x^{6} - 2310 \, a b^{5} c^{5} x^{5} + 2475 \, a^{2} b^{4} c^{5} x^{4} - 1925 \, a^{4} b^{2} c^{5} x^{2} + 1386 \, a^{5} b c^{5} x - 315 \, a^{6} c^{5}}{3465 \, x^{11}}"," ",0,"1/3465*(693*b^6*c^5*x^6 - 2310*a*b^5*c^5*x^5 + 2475*a^2*b^4*c^5*x^4 - 1925*a^4*b^2*c^5*x^2 + 1386*a^5*b*c^5*x - 315*a^6*c^5)/x^11","A",0
44,1,105,0,1.439075," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^8,x, algorithm=""fricas"")","\frac{420 \, b^{7} c^{6} x^{7} \log\left(x\right) + 2100 \, a b^{6} c^{6} x^{6} - 1890 \, a^{2} b^{5} c^{6} x^{5} + 700 \, a^{3} b^{4} c^{6} x^{4} + 525 \, a^{4} b^{3} c^{6} x^{3} - 756 \, a^{5} b^{2} c^{6} x^{2} + 350 \, a^{6} b c^{6} x - 60 \, a^{7} c^{6}}{420 \, x^{7}}"," ",0,"1/420*(420*b^7*c^6*x^7*log(x) + 2100*a*b^6*c^6*x^6 - 1890*a^2*b^5*c^6*x^5 + 700*a^3*b^4*c^6*x^4 + 525*a^4*b^3*c^6*x^3 - 756*a^5*b^2*c^6*x^2 + 350*a^6*b*c^6*x - 60*a^7*c^6)/x^7","A",0
45,1,103,0,1.205607," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^9,x, algorithm=""fricas"")","-\frac{56 \, b^{7} c^{6} x^{7} - 140 \, a b^{6} c^{6} x^{6} + 168 \, a^{2} b^{5} c^{6} x^{5} - 70 \, a^{3} b^{4} c^{6} x^{4} - 56 \, a^{4} b^{3} c^{6} x^{3} + 84 \, a^{5} b^{2} c^{6} x^{2} - 40 \, a^{6} b c^{6} x + 7 \, a^{7} c^{6}}{56 \, x^{8}}"," ",0,"-1/56*(56*b^7*c^6*x^7 - 140*a*b^6*c^6*x^6 + 168*a^2*b^5*c^6*x^5 - 70*a^3*b^4*c^6*x^4 - 56*a^4*b^3*c^6*x^3 + 84*a^5*b^2*c^6*x^2 - 40*a^6*b*c^6*x + 7*a^7*c^6)/x^8","B",0
46,1,103,0,1.109899," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^10,x, algorithm=""fricas"")","-\frac{252 \, b^{7} c^{6} x^{7} - 840 \, a b^{6} c^{6} x^{6} + 1134 \, a^{2} b^{5} c^{6} x^{5} - 504 \, a^{3} b^{4} c^{6} x^{4} - 420 \, a^{4} b^{3} c^{6} x^{3} + 648 \, a^{5} b^{2} c^{6} x^{2} - 315 \, a^{6} b c^{6} x + 56 \, a^{7} c^{6}}{504 \, x^{9}}"," ",0,"-1/504*(252*b^7*c^6*x^7 - 840*a*b^6*c^6*x^6 + 1134*a^2*b^5*c^6*x^5 - 504*a^3*b^4*c^6*x^4 - 420*a^4*b^3*c^6*x^3 + 648*a^5*b^2*c^6*x^2 - 315*a^6*b*c^6*x + 56*a^7*c^6)/x^9","A",0
47,1,103,0,0.839375," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^11,x, algorithm=""fricas"")","-\frac{840 \, b^{7} c^{6} x^{7} - 3150 \, a b^{6} c^{6} x^{6} + 4536 \, a^{2} b^{5} c^{6} x^{5} - 2100 \, a^{3} b^{4} c^{6} x^{4} - 1800 \, a^{4} b^{3} c^{6} x^{3} + 2835 \, a^{5} b^{2} c^{6} x^{2} - 1400 \, a^{6} b c^{6} x + 252 \, a^{7} c^{6}}{2520 \, x^{10}}"," ",0,"-1/2520*(840*b^7*c^6*x^7 - 3150*a*b^6*c^6*x^6 + 4536*a^2*b^5*c^6*x^5 - 2100*a^3*b^4*c^6*x^4 - 1800*a^4*b^3*c^6*x^3 + 2835*a^5*b^2*c^6*x^2 - 1400*a^6*b*c^6*x + 252*a^7*c^6)/x^10","A",0
48,1,103,0,1.335238," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^12,x, algorithm=""fricas"")","-\frac{154 \, b^{7} c^{6} x^{7} - 616 \, a b^{6} c^{6} x^{6} + 924 \, a^{2} b^{5} c^{6} x^{5} - 440 \, a^{3} b^{4} c^{6} x^{4} - 385 \, a^{4} b^{3} c^{6} x^{3} + 616 \, a^{5} b^{2} c^{6} x^{2} - 308 \, a^{6} b c^{6} x + 56 \, a^{7} c^{6}}{616 \, x^{11}}"," ",0,"-1/616*(154*b^7*c^6*x^7 - 616*a*b^6*c^6*x^6 + 924*a^2*b^5*c^6*x^5 - 440*a^3*b^4*c^6*x^4 - 385*a^4*b^3*c^6*x^3 + 616*a^5*b^2*c^6*x^2 - 308*a^6*b*c^6*x + 56*a^7*c^6)/x^11","A",0
49,1,103,0,1.227085," ","integrate((b*x+a)*(-b*c*x+a*c)^6/x^13,x, algorithm=""fricas"")","-\frac{5544 \, b^{7} c^{6} x^{7} - 23100 \, a b^{6} c^{6} x^{6} + 35640 \, a^{2} b^{5} c^{6} x^{5} - 17325 \, a^{3} b^{4} c^{6} x^{4} - 15400 \, a^{4} b^{3} c^{6} x^{3} + 24948 \, a^{5} b^{2} c^{6} x^{2} - 12600 \, a^{6} b c^{6} x + 2310 \, a^{7} c^{6}}{27720 \, x^{12}}"," ",0,"-1/27720*(5544*b^7*c^6*x^7 - 23100*a*b^6*c^6*x^6 + 35640*a^2*b^5*c^6*x^5 - 17325*a^3*b^4*c^6*x^4 - 15400*a^4*b^3*c^6*x^3 + 24948*a^5*b^2*c^6*x^2 - 12600*a^6*b*c^6*x + 2310*a^7*c^6)/x^12","A",0
50,1,216,0,1.756480," ","integrate((e*x)^(5/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{e x} b e^{2} x + 6 \, a \sqrt{\frac{a e}{b}} e^{2} \arctan\left(\frac{\sqrt{e x} b \sqrt{\frac{a e}{b}}}{a e}\right) - 3 \, a \sqrt{\frac{a e}{b}} e^{2} \log\left(\frac{b e x + 2 \, \sqrt{e x} b \sqrt{\frac{a e}{b}} + a e}{b x - a}\right)}{6 \, b^{3} c}, -\frac{4 \, \sqrt{e x} b e^{2} x + 6 \, a \sqrt{-\frac{a e}{b}} e^{2} \arctan\left(\frac{\sqrt{e x} b \sqrt{-\frac{a e}{b}}}{a e}\right) - 3 \, a \sqrt{-\frac{a e}{b}} e^{2} \log\left(\frac{b e x - 2 \, \sqrt{e x} b \sqrt{-\frac{a e}{b}} - a e}{b x + a}\right)}{6 \, b^{3} c}\right]"," ",0,"[-1/6*(4*sqrt(e*x)*b*e^2*x + 6*a*sqrt(a*e/b)*e^2*arctan(sqrt(e*x)*b*sqrt(a*e/b)/(a*e)) - 3*a*sqrt(a*e/b)*e^2*log((b*e*x + 2*sqrt(e*x)*b*sqrt(a*e/b) + a*e)/(b*x - a)))/(b^3*c), -1/6*(4*sqrt(e*x)*b*e^2*x + 6*a*sqrt(-a*e/b)*e^2*arctan(sqrt(e*x)*b*sqrt(-a*e/b)/(a*e)) - 3*a*sqrt(-a*e/b)*e^2*log((b*e*x - 2*sqrt(e*x)*b*sqrt(-a*e/b) - a*e)/(b*x + a)))/(b^3*c)]","A",0
51,1,195,0,1.538444," ","integrate((e*x)^(3/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{\frac{a e}{b}} e \arctan\left(\frac{\sqrt{e x} b \sqrt{\frac{a e}{b}}}{a e}\right) + \sqrt{\frac{a e}{b}} e \log\left(\frac{b e x + 2 \, \sqrt{e x} b \sqrt{\frac{a e}{b}} + a e}{b x - a}\right) - 4 \, \sqrt{e x} e}{2 \, b^{2} c}, -\frac{2 \, \sqrt{-\frac{a e}{b}} e \arctan\left(\frac{\sqrt{e x} b \sqrt{-\frac{a e}{b}}}{a e}\right) - \sqrt{-\frac{a e}{b}} e \log\left(\frac{b e x + 2 \, \sqrt{e x} b \sqrt{-\frac{a e}{b}} - a e}{b x + a}\right) + 4 \, \sqrt{e x} e}{2 \, b^{2} c}\right]"," ",0,"[1/2*(2*sqrt(a*e/b)*e*arctan(sqrt(e*x)*b*sqrt(a*e/b)/(a*e)) + sqrt(a*e/b)*e*log((b*e*x + 2*sqrt(e*x)*b*sqrt(a*e/b) + a*e)/(b*x - a)) - 4*sqrt(e*x)*e)/(b^2*c), -1/2*(2*sqrt(-a*e/b)*e*arctan(sqrt(e*x)*b*sqrt(-a*e/b)/(a*e)) - sqrt(-a*e/b)*e*log((b*e*x + 2*sqrt(e*x)*b*sqrt(-a*e/b) - a*e)/(b*x + a)) + 4*sqrt(e*x)*e)/(b^2*c)]","A",0
52,1,193,0,1.709820," ","integrate((e*x)^(1/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{\frac{e}{a b}} \arctan\left(\frac{\sqrt{e x} a \sqrt{\frac{e}{a b}}}{e x}\right) + \sqrt{\frac{e}{a b}} \log\left(\frac{b e x + 2 \, \sqrt{e x} a b \sqrt{\frac{e}{a b}} + a e}{b x - a}\right)}{2 \, b c}, -\frac{2 \, \sqrt{-\frac{e}{a b}} \arctan\left(\frac{\sqrt{e x} a \sqrt{-\frac{e}{a b}}}{e x}\right) - \sqrt{-\frac{e}{a b}} \log\left(\frac{b e x - 2 \, \sqrt{e x} a b \sqrt{-\frac{e}{a b}} - a e}{b x + a}\right)}{2 \, b c}\right]"," ",0,"[1/2*(2*sqrt(e/(a*b))*arctan(sqrt(e*x)*a*sqrt(e/(a*b))/(e*x)) + sqrt(e/(a*b))*log((b*e*x + 2*sqrt(e*x)*a*b*sqrt(e/(a*b)) + a*e)/(b*x - a)))/(b*c), -1/2*(2*sqrt(-e/(a*b))*arctan(sqrt(e*x)*a*sqrt(-e/(a*b))/(e*x)) - sqrt(-e/(a*b))*log((b*e*x - 2*sqrt(e*x)*a*b*sqrt(-e/(a*b)) - a*e)/(b*x + a)))/(b*c)]","A",0
53,1,173,0,1.396244," ","integrate(1/(e*x)^(1/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{a b e} \arctan\left(\frac{\sqrt{a b e} \sqrt{e x}}{b e x}\right) - \sqrt{a b e} \log\left(\frac{b e x + a e + 2 \, \sqrt{a b e} \sqrt{e x}}{b x - a}\right)}{2 \, a^{2} b c e}, -\frac{2 \, \sqrt{-a b e} \arctan\left(\frac{\sqrt{-a b e} \sqrt{e x}}{b e x}\right) + \sqrt{-a b e} \log\left(\frac{b e x - a e - 2 \, \sqrt{-a b e} \sqrt{e x}}{b x + a}\right)}{2 \, a^{2} b c e}\right]"," ",0,"[-1/2*(2*sqrt(a*b*e)*arctan(sqrt(a*b*e)*sqrt(e*x)/(b*e*x)) - sqrt(a*b*e)*log((b*e*x + a*e + 2*sqrt(a*b*e)*sqrt(e*x))/(b*x - a)))/(a^2*b*c*e), -1/2*(2*sqrt(-a*b*e)*arctan(sqrt(-a*b*e)*sqrt(e*x)/(b*e*x)) + sqrt(-a*b*e)*log((b*e*x - a*e - 2*sqrt(-a*b*e)*sqrt(e*x))/(b*x + a)))/(a^2*b*c*e)]","A",0
54,1,220,0,1.368465," ","integrate(1/(e*x)^(3/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[\frac{2 \, e x \sqrt{\frac{b}{a e}} \arctan\left(\frac{\sqrt{e x} a \sqrt{\frac{b}{a e}}}{b x}\right) + e x \sqrt{\frac{b}{a e}} \log\left(\frac{b x + 2 \, \sqrt{e x} a \sqrt{\frac{b}{a e}} + a}{b x - a}\right) - 4 \, \sqrt{e x}}{2 \, a^{2} c e^{2} x}, -\frac{2 \, e x \sqrt{-\frac{b}{a e}} \arctan\left(\frac{\sqrt{e x} a \sqrt{-\frac{b}{a e}}}{b x}\right) - e x \sqrt{-\frac{b}{a e}} \log\left(\frac{b x - 2 \, \sqrt{e x} a \sqrt{-\frac{b}{a e}} - a}{b x + a}\right) + 4 \, \sqrt{e x}}{2 \, a^{2} c e^{2} x}\right]"," ",0,"[1/2*(2*e*x*sqrt(b/(a*e))*arctan(sqrt(e*x)*a*sqrt(b/(a*e))/(b*x)) + e*x*sqrt(b/(a*e))*log((b*x + 2*sqrt(e*x)*a*sqrt(b/(a*e)) + a)/(b*x - a)) - 4*sqrt(e*x))/(a^2*c*e^2*x), -1/2*(2*e*x*sqrt(-b/(a*e))*arctan(sqrt(e*x)*a*sqrt(-b/(a*e))/(b*x)) - e*x*sqrt(-b/(a*e))*log((b*x - 2*sqrt(e*x)*a*sqrt(-b/(a*e)) - a)/(b*x + a)) + 4*sqrt(e*x))/(a^2*c*e^2*x)]","A",0
55,1,235,0,1.617075," ","integrate(1/(e*x)^(5/2)/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","\left[-\frac{6 \, b e x^{2} \sqrt{\frac{b}{a e}} \arctan\left(\frac{\sqrt{e x} a \sqrt{\frac{b}{a e}}}{b x}\right) - 3 \, b e x^{2} \sqrt{\frac{b}{a e}} \log\left(\frac{b x + 2 \, \sqrt{e x} a \sqrt{\frac{b}{a e}} + a}{b x - a}\right) + 4 \, \sqrt{e x} a}{6 \, a^{3} c e^{3} x^{2}}, -\frac{6 \, b e x^{2} \sqrt{-\frac{b}{a e}} \arctan\left(\frac{\sqrt{e x} a \sqrt{-\frac{b}{a e}}}{b x}\right) - 3 \, b e x^{2} \sqrt{-\frac{b}{a e}} \log\left(\frac{b x + 2 \, \sqrt{e x} a \sqrt{-\frac{b}{a e}} - a}{b x + a}\right) + 4 \, \sqrt{e x} a}{6 \, a^{3} c e^{3} x^{2}}\right]"," ",0,"[-1/6*(6*b*e*x^2*sqrt(b/(a*e))*arctan(sqrt(e*x)*a*sqrt(b/(a*e))/(b*x)) - 3*b*e*x^2*sqrt(b/(a*e))*log((b*x + 2*sqrt(e*x)*a*sqrt(b/(a*e)) + a)/(b*x - a)) + 4*sqrt(e*x)*a)/(a^3*c*e^3*x^2), -1/6*(6*b*e*x^2*sqrt(-b/(a*e))*arctan(sqrt(e*x)*a*sqrt(-b/(a*e))/(b*x)) - 3*b*e*x^2*sqrt(-b/(a*e))*log((b*x + 2*sqrt(e*x)*a*sqrt(-b/(a*e)) - a)/(b*x + a)) + 4*sqrt(e*x)*a)/(a^3*c*e^3*x^2)]","A",0
56,1,514,0,1.447982," ","integrate((e*x)^m*(-2*a*x+2)^3*(a*x+1)^4,x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(a^{7} m^{7} + 28 \, a^{7} m^{6} + 322 \, a^{7} m^{5} + 1960 \, a^{7} m^{4} + 6769 \, a^{7} m^{3} + 13132 \, a^{7} m^{2} + 13068 \, a^{7} m + 5040 \, a^{7}\right)} x^{8} + {\left(a^{6} m^{7} + 29 \, a^{6} m^{6} + 343 \, a^{6} m^{5} + 2135 \, a^{6} m^{4} + 7504 \, a^{6} m^{3} + 14756 \, a^{6} m^{2} + 14832 \, a^{6} m + 5760 \, a^{6}\right)} x^{7} - 3 \, {\left(a^{5} m^{7} + 30 \, a^{5} m^{6} + 366 \, a^{5} m^{5} + 2340 \, a^{5} m^{4} + 8409 \, a^{5} m^{3} + 16830 \, a^{5} m^{2} + 17144 \, a^{5} m + 6720 \, a^{5}\right)} x^{6} - 3 \, {\left(a^{4} m^{7} + 31 \, a^{4} m^{6} + 391 \, a^{4} m^{5} + 2581 \, a^{4} m^{4} + 9544 \, a^{4} m^{3} + 19564 \, a^{4} m^{2} + 20304 \, a^{4} m + 8064 \, a^{4}\right)} x^{5} + 3 \, {\left(a^{3} m^{7} + 32 \, a^{3} m^{6} + 418 \, a^{3} m^{5} + 2864 \, a^{3} m^{4} + 10993 \, a^{3} m^{3} + 23312 \, a^{3} m^{2} + 24876 \, a^{3} m + 10080 \, a^{3}\right)} x^{4} + 3 \, {\left(a^{2} m^{7} + 33 \, a^{2} m^{6} + 447 \, a^{2} m^{5} + 3195 \, a^{2} m^{4} + 12864 \, a^{2} m^{3} + 28692 \, a^{2} m^{2} + 32048 \, a^{2} m + 13440 \, a^{2}\right)} x^{3} - {\left(a m^{7} + 34 \, a m^{6} + 478 \, a m^{5} + 3580 \, a m^{4} + 15289 \, a m^{3} + 36706 \, a m^{2} + 44712 \, a m + 20160 \, a\right)} x^{2} - {\left(m^{7} + 35 \, m^{6} + 511 \, m^{5} + 4025 \, m^{4} + 18424 \, m^{3} + 48860 \, m^{2} + 69264 \, m + 40320\right)} x\right)} \left(e x\right)^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"-8*((a^7*m^7 + 28*a^7*m^6 + 322*a^7*m^5 + 1960*a^7*m^4 + 6769*a^7*m^3 + 13132*a^7*m^2 + 13068*a^7*m + 5040*a^7)*x^8 + (a^6*m^7 + 29*a^6*m^6 + 343*a^6*m^5 + 2135*a^6*m^4 + 7504*a^6*m^3 + 14756*a^6*m^2 + 14832*a^6*m + 5760*a^6)*x^7 - 3*(a^5*m^7 + 30*a^5*m^6 + 366*a^5*m^5 + 2340*a^5*m^4 + 8409*a^5*m^3 + 16830*a^5*m^2 + 17144*a^5*m + 6720*a^5)*x^6 - 3*(a^4*m^7 + 31*a^4*m^6 + 391*a^4*m^5 + 2581*a^4*m^4 + 9544*a^4*m^3 + 19564*a^4*m^2 + 20304*a^4*m + 8064*a^4)*x^5 + 3*(a^3*m^7 + 32*a^3*m^6 + 418*a^3*m^5 + 2864*a^3*m^4 + 10993*a^3*m^3 + 23312*a^3*m^2 + 24876*a^3*m + 10080*a^3)*x^4 + 3*(a^2*m^7 + 33*a^2*m^6 + 447*a^2*m^5 + 3195*a^2*m^4 + 12864*a^2*m^3 + 28692*a^2*m^2 + 32048*a^2*m + 13440*a^2)*x^3 - (a*m^7 + 34*a*m^6 + 478*a*m^5 + 3580*a*m^4 + 15289*a*m^3 + 36706*a*m^2 + 44712*a*m + 20160*a)*x^2 - (m^7 + 35*m^6 + 511*m^5 + 4025*m^4 + 18424*m^3 + 48860*m^2 + 69264*m + 40320)*x)*(e*x)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
57,1,288,0,1.999826," ","integrate((e*x)^m*(-2*a*x+2)^2*(a*x+1)^3,x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a^{5} m^{5} + 15 \, a^{5} m^{4} + 85 \, a^{5} m^{3} + 225 \, a^{5} m^{2} + 274 \, a^{5} m + 120 \, a^{5}\right)} x^{6} + {\left(a^{4} m^{5} + 16 \, a^{4} m^{4} + 95 \, a^{4} m^{3} + 260 \, a^{4} m^{2} + 324 \, a^{4} m + 144 \, a^{4}\right)} x^{5} - 2 \, {\left(a^{3} m^{5} + 17 \, a^{3} m^{4} + 107 \, a^{3} m^{3} + 307 \, a^{3} m^{2} + 396 \, a^{3} m + 180 \, a^{3}\right)} x^{4} - 2 \, {\left(a^{2} m^{5} + 18 \, a^{2} m^{4} + 121 \, a^{2} m^{3} + 372 \, a^{2} m^{2} + 508 \, a^{2} m + 240 \, a^{2}\right)} x^{3} + {\left(a m^{5} + 19 \, a m^{4} + 137 \, a m^{3} + 461 \, a m^{2} + 702 \, a m + 360 \, a\right)} x^{2} + {\left(m^{5} + 20 \, m^{4} + 155 \, m^{3} + 580 \, m^{2} + 1044 \, m + 720\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"4*((a^5*m^5 + 15*a^5*m^4 + 85*a^5*m^3 + 225*a^5*m^2 + 274*a^5*m + 120*a^5)*x^6 + (a^4*m^5 + 16*a^4*m^4 + 95*a^4*m^3 + 260*a^4*m^2 + 324*a^4*m + 144*a^4)*x^5 - 2*(a^3*m^5 + 17*a^3*m^4 + 107*a^3*m^3 + 307*a^3*m^2 + 396*a^3*m + 180*a^3)*x^4 - 2*(a^2*m^5 + 18*a^2*m^4 + 121*a^2*m^3 + 372*a^2*m^2 + 508*a^2*m + 240*a^2)*x^3 + (a*m^5 + 19*a*m^4 + 137*a*m^3 + 461*a*m^2 + 702*a*m + 360*a)*x^2 + (m^5 + 20*m^4 + 155*m^3 + 580*m^2 + 1044*m + 720)*x)*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
58,1,130,0,1.114805," ","integrate((e*x)^m*(-2*a*x+2)*(a*x+1)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} m^{3} + 6 \, a^{3} m^{2} + 11 \, a^{3} m + 6 \, a^{3}\right)} x^{4} + {\left(a^{2} m^{3} + 7 \, a^{2} m^{2} + 14 \, a^{2} m + 8 \, a^{2}\right)} x^{3} - {\left(a m^{3} + 8 \, a m^{2} + 19 \, a m + 12 \, a\right)} x^{2} - {\left(m^{3} + 9 \, m^{2} + 26 \, m + 24\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"-2*((a^3*m^3 + 6*a^3*m^2 + 11*a^3*m + 6*a^3)*x^4 + (a^2*m^3 + 7*a^2*m^2 + 14*a^2*m + 8*a^2)*x^3 - (a*m^3 + 8*a*m^2 + 19*a*m + 12*a)*x^2 - (m^3 + 9*m^2 + 26*m + 24)*x)*(e*x)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","A",0
59,0,0,0,1.209344," ","integrate((e*x)^m/(-2*a*x+2)^2/(a*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{4 \, {\left(a^{3} x^{3} - a^{2} x^{2} - a x + 1\right)}}, x\right)"," ",0,"integral(1/4*(e*x)^m/(a^3*x^3 - a^2*x^2 - a*x + 1), x)","F",0
60,0,0,0,1.140258," ","integrate((e*x)^m/(-2*a*x+2)^3/(a*x+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{8 \, {\left(a^{5} x^{5} - a^{4} x^{4} - 2 \, a^{3} x^{3} + 2 \, a^{2} x^{2} + a x - 1\right)}}, x\right)"," ",0,"integral(-1/8*(e*x)^m/(a^5*x^5 - a^4*x^4 - 2*a^3*x^3 + 2*a^2*x^2 + a*x - 1), x)","F",0
61,0,0,0,1.516995," ","integrate((e*x)^m/(-2*a*x+2)^4/(a*x+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{16 \, {\left(a^{7} x^{7} - a^{6} x^{6} - 3 \, a^{5} x^{5} + 3 \, a^{4} x^{4} + 3 \, a^{3} x^{3} - 3 \, a^{2} x^{2} - a x + 1\right)}}, x\right)"," ",0,"integral(1/16*(e*x)^m/(a^7*x^7 - a^6*x^6 - 3*a^5*x^5 + 3*a^4*x^4 + 3*a^3*x^3 - 3*a^2*x^2 - a*x + 1), x)","F",0
62,1,860,0,1.723707," ","integrate((e*x)^m*(b*x+a)^4*(-b*d*x+a*d)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(b^{7} d^{3} m^{7} + 28 \, b^{7} d^{3} m^{6} + 322 \, b^{7} d^{3} m^{5} + 1960 \, b^{7} d^{3} m^{4} + 6769 \, b^{7} d^{3} m^{3} + 13132 \, b^{7} d^{3} m^{2} + 13068 \, b^{7} d^{3} m + 5040 \, b^{7} d^{3}\right)} x^{8} + {\left(a b^{6} d^{3} m^{7} + 29 \, a b^{6} d^{3} m^{6} + 343 \, a b^{6} d^{3} m^{5} + 2135 \, a b^{6} d^{3} m^{4} + 7504 \, a b^{6} d^{3} m^{3} + 14756 \, a b^{6} d^{3} m^{2} + 14832 \, a b^{6} d^{3} m + 5760 \, a b^{6} d^{3}\right)} x^{7} - 3 \, {\left(a^{2} b^{5} d^{3} m^{7} + 30 \, a^{2} b^{5} d^{3} m^{6} + 366 \, a^{2} b^{5} d^{3} m^{5} + 2340 \, a^{2} b^{5} d^{3} m^{4} + 8409 \, a^{2} b^{5} d^{3} m^{3} + 16830 \, a^{2} b^{5} d^{3} m^{2} + 17144 \, a^{2} b^{5} d^{3} m + 6720 \, a^{2} b^{5} d^{3}\right)} x^{6} - 3 \, {\left(a^{3} b^{4} d^{3} m^{7} + 31 \, a^{3} b^{4} d^{3} m^{6} + 391 \, a^{3} b^{4} d^{3} m^{5} + 2581 \, a^{3} b^{4} d^{3} m^{4} + 9544 \, a^{3} b^{4} d^{3} m^{3} + 19564 \, a^{3} b^{4} d^{3} m^{2} + 20304 \, a^{3} b^{4} d^{3} m + 8064 \, a^{3} b^{4} d^{3}\right)} x^{5} + 3 \, {\left(a^{4} b^{3} d^{3} m^{7} + 32 \, a^{4} b^{3} d^{3} m^{6} + 418 \, a^{4} b^{3} d^{3} m^{5} + 2864 \, a^{4} b^{3} d^{3} m^{4} + 10993 \, a^{4} b^{3} d^{3} m^{3} + 23312 \, a^{4} b^{3} d^{3} m^{2} + 24876 \, a^{4} b^{3} d^{3} m + 10080 \, a^{4} b^{3} d^{3}\right)} x^{4} + 3 \, {\left(a^{5} b^{2} d^{3} m^{7} + 33 \, a^{5} b^{2} d^{3} m^{6} + 447 \, a^{5} b^{2} d^{3} m^{5} + 3195 \, a^{5} b^{2} d^{3} m^{4} + 12864 \, a^{5} b^{2} d^{3} m^{3} + 28692 \, a^{5} b^{2} d^{3} m^{2} + 32048 \, a^{5} b^{2} d^{3} m + 13440 \, a^{5} b^{2} d^{3}\right)} x^{3} - {\left(a^{6} b d^{3} m^{7} + 34 \, a^{6} b d^{3} m^{6} + 478 \, a^{6} b d^{3} m^{5} + 3580 \, a^{6} b d^{3} m^{4} + 15289 \, a^{6} b d^{3} m^{3} + 36706 \, a^{6} b d^{3} m^{2} + 44712 \, a^{6} b d^{3} m + 20160 \, a^{6} b d^{3}\right)} x^{2} - {\left(a^{7} d^{3} m^{7} + 35 \, a^{7} d^{3} m^{6} + 511 \, a^{7} d^{3} m^{5} + 4025 \, a^{7} d^{3} m^{4} + 18424 \, a^{7} d^{3} m^{3} + 48860 \, a^{7} d^{3} m^{2} + 69264 \, a^{7} d^{3} m + 40320 \, a^{7} d^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"-((b^7*d^3*m^7 + 28*b^7*d^3*m^6 + 322*b^7*d^3*m^5 + 1960*b^7*d^3*m^4 + 6769*b^7*d^3*m^3 + 13132*b^7*d^3*m^2 + 13068*b^7*d^3*m + 5040*b^7*d^3)*x^8 + (a*b^6*d^3*m^7 + 29*a*b^6*d^3*m^6 + 343*a*b^6*d^3*m^5 + 2135*a*b^6*d^3*m^4 + 7504*a*b^6*d^3*m^3 + 14756*a*b^6*d^3*m^2 + 14832*a*b^6*d^3*m + 5760*a*b^6*d^3)*x^7 - 3*(a^2*b^5*d^3*m^7 + 30*a^2*b^5*d^3*m^6 + 366*a^2*b^5*d^3*m^5 + 2340*a^2*b^5*d^3*m^4 + 8409*a^2*b^5*d^3*m^3 + 16830*a^2*b^5*d^3*m^2 + 17144*a^2*b^5*d^3*m + 6720*a^2*b^5*d^3)*x^6 - 3*(a^3*b^4*d^3*m^7 + 31*a^3*b^4*d^3*m^6 + 391*a^3*b^4*d^3*m^5 + 2581*a^3*b^4*d^3*m^4 + 9544*a^3*b^4*d^3*m^3 + 19564*a^3*b^4*d^3*m^2 + 20304*a^3*b^4*d^3*m + 8064*a^3*b^4*d^3)*x^5 + 3*(a^4*b^3*d^3*m^7 + 32*a^4*b^3*d^3*m^6 + 418*a^4*b^3*d^3*m^5 + 2864*a^4*b^3*d^3*m^4 + 10993*a^4*b^3*d^3*m^3 + 23312*a^4*b^3*d^3*m^2 + 24876*a^4*b^3*d^3*m + 10080*a^4*b^3*d^3)*x^4 + 3*(a^5*b^2*d^3*m^7 + 33*a^5*b^2*d^3*m^6 + 447*a^5*b^2*d^3*m^5 + 3195*a^5*b^2*d^3*m^4 + 12864*a^5*b^2*d^3*m^3 + 28692*a^5*b^2*d^3*m^2 + 32048*a^5*b^2*d^3*m + 13440*a^5*b^2*d^3)*x^3 - (a^6*b*d^3*m^7 + 34*a^6*b*d^3*m^6 + 478*a^6*b*d^3*m^5 + 3580*a^6*b*d^3*m^4 + 15289*a^6*b*d^3*m^3 + 36706*a^6*b*d^3*m^2 + 44712*a^6*b*d^3*m + 20160*a^6*b*d^3)*x^2 - (a^7*d^3*m^7 + 35*a^7*d^3*m^6 + 511*a^7*d^3*m^5 + 4025*a^7*d^3*m^4 + 18424*a^7*d^3*m^3 + 48860*a^7*d^3*m^2 + 69264*a^7*d^3*m + 40320*a^7*d^3)*x)*(e*x)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
63,1,475,0,1.375685," ","integrate((e*x)^m*(b*x+a)^3*(-b*d*x+a*d)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} d^{2} m^{5} + 15 \, b^{5} d^{2} m^{4} + 85 \, b^{5} d^{2} m^{3} + 225 \, b^{5} d^{2} m^{2} + 274 \, b^{5} d^{2} m + 120 \, b^{5} d^{2}\right)} x^{6} + {\left(a b^{4} d^{2} m^{5} + 16 \, a b^{4} d^{2} m^{4} + 95 \, a b^{4} d^{2} m^{3} + 260 \, a b^{4} d^{2} m^{2} + 324 \, a b^{4} d^{2} m + 144 \, a b^{4} d^{2}\right)} x^{5} - 2 \, {\left(a^{2} b^{3} d^{2} m^{5} + 17 \, a^{2} b^{3} d^{2} m^{4} + 107 \, a^{2} b^{3} d^{2} m^{3} + 307 \, a^{2} b^{3} d^{2} m^{2} + 396 \, a^{2} b^{3} d^{2} m + 180 \, a^{2} b^{3} d^{2}\right)} x^{4} - 2 \, {\left(a^{3} b^{2} d^{2} m^{5} + 18 \, a^{3} b^{2} d^{2} m^{4} + 121 \, a^{3} b^{2} d^{2} m^{3} + 372 \, a^{3} b^{2} d^{2} m^{2} + 508 \, a^{3} b^{2} d^{2} m + 240 \, a^{3} b^{2} d^{2}\right)} x^{3} + {\left(a^{4} b d^{2} m^{5} + 19 \, a^{4} b d^{2} m^{4} + 137 \, a^{4} b d^{2} m^{3} + 461 \, a^{4} b d^{2} m^{2} + 702 \, a^{4} b d^{2} m + 360 \, a^{4} b d^{2}\right)} x^{2} + {\left(a^{5} d^{2} m^{5} + 20 \, a^{5} d^{2} m^{4} + 155 \, a^{5} d^{2} m^{3} + 580 \, a^{5} d^{2} m^{2} + 1044 \, a^{5} d^{2} m + 720 \, a^{5} d^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((b^5*d^2*m^5 + 15*b^5*d^2*m^4 + 85*b^5*d^2*m^3 + 225*b^5*d^2*m^2 + 274*b^5*d^2*m + 120*b^5*d^2)*x^6 + (a*b^4*d^2*m^5 + 16*a*b^4*d^2*m^4 + 95*a*b^4*d^2*m^3 + 260*a*b^4*d^2*m^2 + 324*a*b^4*d^2*m + 144*a*b^4*d^2)*x^5 - 2*(a^2*b^3*d^2*m^5 + 17*a^2*b^3*d^2*m^4 + 107*a^2*b^3*d^2*m^3 + 307*a^2*b^3*d^2*m^2 + 396*a^2*b^3*d^2*m + 180*a^2*b^3*d^2)*x^4 - 2*(a^3*b^2*d^2*m^5 + 18*a^3*b^2*d^2*m^4 + 121*a^3*b^2*d^2*m^3 + 372*a^3*b^2*d^2*m^2 + 508*a^3*b^2*d^2*m + 240*a^3*b^2*d^2)*x^3 + (a^4*b*d^2*m^5 + 19*a^4*b*d^2*m^4 + 137*a^4*b*d^2*m^3 + 461*a^4*b*d^2*m^2 + 702*a^4*b*d^2*m + 360*a^4*b*d^2)*x^2 + (a^5*d^2*m^5 + 20*a^5*d^2*m^4 + 155*a^5*d^2*m^3 + 580*a^5*d^2*m^2 + 1044*a^5*d^2*m + 720*a^5*d^2)*x)*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
64,1,176,0,1.230642," ","integrate((e*x)^m*(b*x+a)^2*(-b*d*x+a*d),x, algorithm=""fricas"")","-\frac{{\left({\left(b^{3} d m^{3} + 6 \, b^{3} d m^{2} + 11 \, b^{3} d m + 6 \, b^{3} d\right)} x^{4} + {\left(a b^{2} d m^{3} + 7 \, a b^{2} d m^{2} + 14 \, a b^{2} d m + 8 \, a b^{2} d\right)} x^{3} - {\left(a^{2} b d m^{3} + 8 \, a^{2} b d m^{2} + 19 \, a^{2} b d m + 12 \, a^{2} b d\right)} x^{2} - {\left(a^{3} d m^{3} + 9 \, a^{3} d m^{2} + 26 \, a^{3} d m + 24 \, a^{3} d\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"-((b^3*d*m^3 + 6*b^3*d*m^2 + 11*b^3*d*m + 6*b^3*d)*x^4 + (a*b^2*d*m^3 + 7*a*b^2*d*m^2 + 14*a*b^2*d*m + 8*a*b^2*d)*x^3 - (a^2*b*d*m^3 + 8*a^2*b*d*m^2 + 19*a^2*b*d*m + 12*a^2*b*d)*x^2 - (a^3*d*m^3 + 9*a^3*d*m^2 + 26*a^3*d*m + 24*a^3*d)*x)*(e*x)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
65,0,0,0,1.312058," ","integrate((e*x)^m/(b*x+a)/(-b*d*x+a*d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b^{3} d^{2} x^{3} - a b^{2} d^{2} x^{2} - a^{2} b d^{2} x + a^{3} d^{2}}, x\right)"," ",0,"integral((e*x)^m/(b^3*d^2*x^3 - a*b^2*d^2*x^2 - a^2*b*d^2*x + a^3*d^2), x)","F",0
66,0,0,0,1.395613," ","integrate((e*x)^m/(b*x+a)^2/(-b*d*x+a*d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{b^{5} d^{3} x^{5} - a b^{4} d^{3} x^{4} - 2 \, a^{2} b^{3} d^{3} x^{3} + 2 \, a^{3} b^{2} d^{3} x^{2} + a^{4} b d^{3} x - a^{5} d^{3}}, x\right)"," ",0,"integral(-(e*x)^m/(b^5*d^3*x^5 - a*b^4*d^3*x^4 - 2*a^2*b^3*d^3*x^3 + 2*a^3*b^2*d^3*x^2 + a^4*b*d^3*x - a^5*d^3), x)","F",0
67,0,0,0,1.384215," ","integrate((e*x)^m/(b*x+a)^3/(-b*d*x+a*d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b^{7} d^{4} x^{7} - a b^{6} d^{4} x^{6} - 3 \, a^{2} b^{5} d^{4} x^{5} + 3 \, a^{3} b^{4} d^{4} x^{4} + 3 \, a^{4} b^{3} d^{4} x^{3} - 3 \, a^{5} b^{2} d^{4} x^{2} - a^{6} b d^{4} x + a^{7} d^{4}}, x\right)"," ",0,"integral((e*x)^m/(b^7*d^4*x^7 - a*b^6*d^4*x^6 - 3*a^2*b^5*d^4*x^5 + 3*a^3*b^4*d^4*x^4 + 3*a^4*b^3*d^4*x^3 - 3*a^5*b^2*d^4*x^2 - a^6*b*d^4*x + a^7*d^4), x)","F",0
68,1,477,0,1.394669," ","integrate((e*x)^m*(b*x+a)*(-b*c*x+a*c)^4,x, algorithm=""fricas"")","\frac{{\left({\left(b^{5} c^{4} m^{5} + 15 \, b^{5} c^{4} m^{4} + 85 \, b^{5} c^{4} m^{3} + 225 \, b^{5} c^{4} m^{2} + 274 \, b^{5} c^{4} m + 120 \, b^{5} c^{4}\right)} x^{6} - 3 \, {\left(a b^{4} c^{4} m^{5} + 16 \, a b^{4} c^{4} m^{4} + 95 \, a b^{4} c^{4} m^{3} + 260 \, a b^{4} c^{4} m^{2} + 324 \, a b^{4} c^{4} m + 144 \, a b^{4} c^{4}\right)} x^{5} + 2 \, {\left(a^{2} b^{3} c^{4} m^{5} + 17 \, a^{2} b^{3} c^{4} m^{4} + 107 \, a^{2} b^{3} c^{4} m^{3} + 307 \, a^{2} b^{3} c^{4} m^{2} + 396 \, a^{2} b^{3} c^{4} m + 180 \, a^{2} b^{3} c^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{2} c^{4} m^{5} + 18 \, a^{3} b^{2} c^{4} m^{4} + 121 \, a^{3} b^{2} c^{4} m^{3} + 372 \, a^{3} b^{2} c^{4} m^{2} + 508 \, a^{3} b^{2} c^{4} m + 240 \, a^{3} b^{2} c^{4}\right)} x^{3} - 3 \, {\left(a^{4} b c^{4} m^{5} + 19 \, a^{4} b c^{4} m^{4} + 137 \, a^{4} b c^{4} m^{3} + 461 \, a^{4} b c^{4} m^{2} + 702 \, a^{4} b c^{4} m + 360 \, a^{4} b c^{4}\right)} x^{2} + {\left(a^{5} c^{4} m^{5} + 20 \, a^{5} c^{4} m^{4} + 155 \, a^{5} c^{4} m^{3} + 580 \, a^{5} c^{4} m^{2} + 1044 \, a^{5} c^{4} m + 720 \, a^{5} c^{4}\right)} x\right)} \left(e x\right)^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((b^5*c^4*m^5 + 15*b^5*c^4*m^4 + 85*b^5*c^4*m^3 + 225*b^5*c^4*m^2 + 274*b^5*c^4*m + 120*b^5*c^4)*x^6 - 3*(a*b^4*c^4*m^5 + 16*a*b^4*c^4*m^4 + 95*a*b^4*c^4*m^3 + 260*a*b^4*c^4*m^2 + 324*a*b^4*c^4*m + 144*a*b^4*c^4)*x^5 + 2*(a^2*b^3*c^4*m^5 + 17*a^2*b^3*c^4*m^4 + 107*a^2*b^3*c^4*m^3 + 307*a^2*b^3*c^4*m^2 + 396*a^2*b^3*c^4*m + 180*a^2*b^3*c^4)*x^4 + 2*(a^3*b^2*c^4*m^5 + 18*a^3*b^2*c^4*m^4 + 121*a^3*b^2*c^4*m^3 + 372*a^3*b^2*c^4*m^2 + 508*a^3*b^2*c^4*m + 240*a^3*b^2*c^4)*x^3 - 3*(a^4*b*c^4*m^5 + 19*a^4*b*c^4*m^4 + 137*a^4*b*c^4*m^3 + 461*a^4*b*c^4*m^2 + 702*a^4*b*c^4*m + 360*a^4*b*c^4)*x^2 + (a^5*c^4*m^5 + 20*a^5*c^4*m^4 + 155*a^5*c^4*m^3 + 580*a^5*c^4*m^2 + 1044*a^5*c^4*m + 720*a^5*c^4)*x)*(e*x)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
69,1,209,0,1.094589," ","integrate((e*x)^m*(b*x+a)*(-b*c*x+a*c)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(b^{4} c^{3} m^{3} + 7 \, b^{4} c^{3} m^{2} + 14 \, b^{4} c^{3} m + 8 \, b^{4} c^{3}\right)} x^{5} - 2 \, {\left(a b^{3} c^{3} m^{3} + 8 \, a b^{3} c^{3} m^{2} + 17 \, a b^{3} c^{3} m + 10 \, a b^{3} c^{3}\right)} x^{4} + 2 \, {\left(a^{3} b c^{3} m^{3} + 10 \, a^{3} b c^{3} m^{2} + 29 \, a^{3} b c^{3} m + 20 \, a^{3} b c^{3}\right)} x^{2} - {\left(a^{4} c^{3} m^{3} + 11 \, a^{4} c^{3} m^{2} + 38 \, a^{4} c^{3} m + 40 \, a^{4} c^{3}\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 12 \, m^{3} + 49 \, m^{2} + 78 \, m + 40}"," ",0,"-((b^4*c^3*m^3 + 7*b^4*c^3*m^2 + 14*b^4*c^3*m + 8*b^4*c^3)*x^5 - 2*(a*b^3*c^3*m^3 + 8*a*b^3*c^3*m^2 + 17*a*b^3*c^3*m + 10*a*b^3*c^3)*x^4 + 2*(a^3*b*c^3*m^3 + 10*a^3*b*c^3*m^2 + 29*a^3*b*c^3*m + 20*a^3*b*c^3)*x^2 - (a^4*c^3*m^3 + 11*a^4*c^3*m^2 + 38*a^4*c^3*m + 40*a^4*c^3)*x)*(e*x)^m/(m^4 + 12*m^3 + 49*m^2 + 78*m + 40)","B",0
70,1,207,0,1.220699," ","integrate((e*x)^m*(b*x+a)*(-b*c*x+a*c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} c^{2} m^{3} + 6 \, b^{3} c^{2} m^{2} + 11 \, b^{3} c^{2} m + 6 \, b^{3} c^{2}\right)} x^{4} - {\left(a b^{2} c^{2} m^{3} + 7 \, a b^{2} c^{2} m^{2} + 14 \, a b^{2} c^{2} m + 8 \, a b^{2} c^{2}\right)} x^{3} - {\left(a^{2} b c^{2} m^{3} + 8 \, a^{2} b c^{2} m^{2} + 19 \, a^{2} b c^{2} m + 12 \, a^{2} b c^{2}\right)} x^{2} + {\left(a^{3} c^{2} m^{3} + 9 \, a^{3} c^{2} m^{2} + 26 \, a^{3} c^{2} m + 24 \, a^{3} c^{2}\right)} x\right)} \left(e x\right)^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"((b^3*c^2*m^3 + 6*b^3*c^2*m^2 + 11*b^3*c^2*m + 6*b^3*c^2)*x^4 - (a*b^2*c^2*m^3 + 7*a*b^2*c^2*m^2 + 14*a*b^2*c^2*m + 8*a*b^2*c^2)*x^3 - (a^2*b*c^2*m^3 + 8*a^2*b*c^2*m^2 + 19*a^2*b*c^2*m + 12*a^2*b*c^2)*x^2 + (a^3*c^2*m^3 + 9*a^3*c^2*m^2 + 26*a^3*c^2*m + 24*a^3*c^2)*x)*(e*x)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
71,1,50,0,1.488954," ","integrate((e*x)^m*(b*x+a)*(-b*c*x+a*c),x, algorithm=""fricas"")","-\frac{{\left({\left(b^{2} c m + b^{2} c\right)} x^{3} - {\left(a^{2} c m + 3 \, a^{2} c\right)} x\right)} \left(e x\right)^{m}}{m^{2} + 4 \, m + 3}"," ",0,"-((b^2*c*m + b^2*c)*x^3 - (a^2*c*m + 3*a^2*c)*x)*(e*x)^m/(m^2 + 4*m + 3)","A",0
72,0,0,0,0.805094," ","integrate((e*x)^m*(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x + a\right)} \left(e x\right)^{m}}{b c x - a c}, x\right)"," ",0,"integral(-(b*x + a)*(e*x)^m/(b*c*x - a*c), x)","F",0
73,0,0,0,0.708812," ","integrate((e*x)^m*(b*x+a)/(-b*c*x+a*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} \left(e x\right)^{m}}{b^{2} c^{2} x^{2} - 2 \, a b c^{2} x + a^{2} c^{2}}, x\right)"," ",0,"integral((b*x + a)*(e*x)^m/(b^2*c^2*x^2 - 2*a*b*c^2*x + a^2*c^2), x)","F",0
74,0,0,0,1.169889," ","integrate((e*x)^m*(-b*c*x+a*c)^3/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{3} c^{3} x^{3} - 3 \, a b^{2} c^{3} x^{2} + 3 \, a^{2} b c^{3} x - a^{3} c^{3}\right)} \left(e x\right)^{m}}{b x + a}, x\right)"," ",0,"integral(-(b^3*c^3*x^3 - 3*a*b^2*c^3*x^2 + 3*a^2*b*c^3*x - a^3*c^3)*(e*x)^m/(b*x + a), x)","F",0
75,0,0,0,1.337824," ","integrate((e*x)^m*(-b*c*x+a*c)^2/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} c^{2} x^{2} - 2 \, a b c^{2} x + a^{2} c^{2}\right)} \left(e x\right)^{m}}{b x + a}, x\right)"," ",0,"integral((b^2*c^2*x^2 - 2*a*b*c^2*x + a^2*c^2)*(e*x)^m/(b*x + a), x)","F",0
76,0,0,0,1.406237," ","integrate((e*x)^m*(-b*c*x+a*c)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b c x - a c\right)} \left(e x\right)^{m}}{b x + a}, x\right)"," ",0,"integral(-(b*c*x - a*c)*(e*x)^m/(b*x + a), x)","F",0
77,0,0,0,1.469294," ","integrate((e*x)^m/(b*x+a)/(-b*c*x+a*c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{b^{2} c x^{2} - a^{2} c}, x\right)"," ",0,"integral(-(e*x)^m/(b^2*c*x^2 - a^2*c), x)","F",0
78,0,0,0,1.589596," ","integrate((e*x)^m/(b*x+a)/(-b*c*x+a*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b^{3} c^{2} x^{3} - a b^{2} c^{2} x^{2} - a^{2} b c^{2} x + a^{3} c^{2}}, x\right)"," ",0,"integral((e*x)^m/(b^3*c^2*x^3 - a*b^2*c^2*x^2 - a^2*b*c^2*x + a^3*c^2), x)","F",0
79,0,0,0,1.235668," ","integrate((e*x)^m/(b*x+a)/(-b*c*x+a*c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{b^{4} c^{3} x^{4} - 2 \, a b^{3} c^{3} x^{3} + 2 \, a^{3} b c^{3} x - a^{4} c^{3}}, x\right)"," ",0,"integral(-(e*x)^m/(b^4*c^3*x^4 - 2*a*b^3*c^3*x^3 + 2*a^3*b*c^3*x - a^4*c^3), x)","F",0
80,1,29,0,1.111464," ","integrate(x^4*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b B + \frac{1}{6} x^{6} a B + \frac{1}{6} x^{6} b A + \frac{1}{5} x^{5} a A"," ",0,"1/7*x^7*b*B + 1/6*x^6*a*B + 1/6*x^6*b*A + 1/5*x^5*a*A","A",0
81,1,29,0,1.244938," ","integrate(x^3*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a A"," ",0,"1/6*x^6*b*B + 1/5*x^5*a*B + 1/5*x^5*b*A + 1/4*x^4*a*A","A",0
82,1,29,0,1.183458," ","integrate(x^2*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b B + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + \frac{1}{3} x^{3} a A"," ",0,"1/5*x^5*b*B + 1/4*x^4*a*B + 1/4*x^4*b*A + 1/3*x^3*a*A","A",0
83,1,29,0,1.161073," ","integrate(x*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b B + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + \frac{1}{2} x^{2} a A"," ",0,"1/4*x^4*b*B + 1/3*x^3*a*B + 1/3*x^3*b*A + 1/2*x^2*a*A","A",0
84,1,26,0,1.135513," ","integrate((b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{3} x^{3} b B + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A"," ",0,"1/3*x^3*b*B + 1/2*x^2*a*B + 1/2*x^2*b*A + x*a*A","A",0
85,1,22,0,1.239931," ","integrate((b*x+a)*(B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{2} \, B b x^{2} + A a \log\left(x\right) + {\left(B a + A b\right)} x"," ",0,"1/2*B*b*x^2 + A*a*log(x) + (B*a + A*b)*x","A",0
86,1,26,0,1.260661," ","integrate((b*x+a)*(B*x+A)/x^2,x, algorithm=""fricas"")","\frac{B b x^{2} + {\left(B a + A b\right)} x \log\left(x\right) - A a}{x}"," ",0,"(B*b*x^2 + (B*a + A*b)*x*log(x) - A*a)/x","A",0
87,1,29,0,1.177383," ","integrate((b*x+a)*(B*x+A)/x^3,x, algorithm=""fricas"")","\frac{2 \, B b x^{2} \log\left(x\right) - A a - 2 \, {\left(B a + A b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*b*x^2*log(x) - A*a - 2*(B*a + A*b)*x)/x^2","A",0
88,1,27,0,1.270378," ","integrate((b*x+a)*(B*x+A)/x^4,x, algorithm=""fricas"")","-\frac{6 \, B b x^{2} + 2 \, A a + 3 \, {\left(B a + A b\right)} x}{6 \, x^{3}}"," ",0,"-1/6*(6*B*b*x^2 + 2*A*a + 3*(B*a + A*b)*x)/x^3","A",0
89,1,27,0,1.204623," ","integrate((b*x+a)*(B*x+A)/x^5,x, algorithm=""fricas"")","-\frac{6 \, B b x^{2} + 3 \, A a + 4 \, {\left(B a + A b\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(6*B*b*x^2 + 3*A*a + 4*(B*a + A*b)*x)/x^4","A",0
90,1,27,0,1.544997," ","integrate((b*x+a)*(B*x+A)/x^6,x, algorithm=""fricas"")","-\frac{20 \, B b x^{2} + 12 \, A a + 15 \, {\left(B a + A b\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(20*B*b*x^2 + 12*A*a + 15*(B*a + A*b)*x)/x^5","A",0
91,1,53,0,1.126141," ","integrate(x^4*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{2} B + \frac{2}{7} x^{7} b a B + \frac{1}{7} x^{7} b^{2} A + \frac{1}{6} x^{6} a^{2} B + \frac{1}{3} x^{6} b a A + \frac{1}{5} x^{5} a^{2} A"," ",0,"1/8*x^8*b^2*B + 2/7*x^7*b*a*B + 1/7*x^7*b^2*A + 1/6*x^6*a^2*B + 1/3*x^6*b*a*A + 1/5*x^5*a^2*A","A",0
92,1,53,0,1.115683," ","integrate(x^3*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{2} B + \frac{1}{3} x^{6} b a B + \frac{1}{6} x^{6} b^{2} A + \frac{1}{5} x^{5} a^{2} B + \frac{2}{5} x^{5} b a A + \frac{1}{4} x^{4} a^{2} A"," ",0,"1/7*x^7*b^2*B + 1/3*x^6*b*a*B + 1/6*x^6*b^2*A + 1/5*x^5*a^2*B + 2/5*x^5*b*a*A + 1/4*x^4*a^2*A","A",0
93,1,53,0,1.115183," ","integrate(x^2*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{2} B + \frac{2}{5} x^{5} b a B + \frac{1}{5} x^{5} b^{2} A + \frac{1}{4} x^{4} a^{2} B + \frac{1}{2} x^{4} b a A + \frac{1}{3} x^{3} a^{2} A"," ",0,"1/6*x^6*b^2*B + 2/5*x^5*b*a*B + 1/5*x^5*b^2*A + 1/4*x^4*a^2*B + 1/2*x^4*b*a*A + 1/3*x^3*a^2*A","A",0
94,1,53,0,1.128264," ","integrate(x*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{2} B + \frac{1}{2} x^{4} b a B + \frac{1}{4} x^{4} b^{2} A + \frac{1}{3} x^{3} a^{2} B + \frac{2}{3} x^{3} b a A + \frac{1}{2} x^{2} a^{2} A"," ",0,"1/5*x^5*b^2*B + 1/2*x^4*b*a*B + 1/4*x^4*b^2*A + 1/3*x^3*a^2*B + 2/3*x^3*b*a*A + 1/2*x^2*a^2*A","A",0
95,1,49,0,0.587109," ","integrate((b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b^{2} B + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/4*x^4*b^2*B + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
96,1,46,0,0.710795," ","integrate((b*x+a)^2*(B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{3} \, B b^{2} x^{3} + A a^{2} \log\left(x\right) + \frac{1}{2} \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + {\left(B a^{2} + 2 \, A a b\right)} x"," ",0,"1/3*B*b^2*x^3 + A*a^2*log(x) + 1/2*(2*B*a*b + A*b^2)*x^2 + (B*a^2 + 2*A*a*b)*x","A",0
97,1,52,0,1.337420," ","integrate((b*x+a)^2*(B*x+A)/x^2,x, algorithm=""fricas"")","\frac{B b^{2} x^{3} - 2 \, A a^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} x \log\left(x\right)}{2 \, x}"," ",0,"1/2*(B*b^2*x^3 - 2*A*a^2 + 2*(2*B*a*b + A*b^2)*x^2 + 2*(B*a^2 + 2*A*a*b)*x*log(x))/x","A",0
98,1,53,0,1.423474," ","integrate((b*x+a)^2*(B*x+A)/x^3,x, algorithm=""fricas"")","\frac{2 \, B b^{2} x^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} + 2 \, A a b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(2*B*b^2*x^3 + 2*(2*B*a*b + A*b^2)*x^2*log(x) - A*a^2 - 2*(B*a^2 + 2*A*a*b)*x)/x^2","A",0
99,1,53,0,1.155353," ","integrate((b*x+a)^2*(B*x+A)/x^4,x, algorithm=""fricas"")","\frac{6 \, B b^{2} x^{3} \log\left(x\right) - 2 \, A a^{2} - 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*b^2*x^3*log(x) - 2*A*a^2 - 6*(2*B*a*b + A*b^2)*x^2 - 3*(B*a^2 + 2*A*a*b)*x)/x^3","A",0
100,1,51,0,1.319070," ","integrate((b*x+a)^2*(B*x+A)/x^5,x, algorithm=""fricas"")","-\frac{12 \, B b^{2} x^{3} + 3 \, A a^{2} + 6 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 4 \, {\left(B a^{2} + 2 \, A a b\right)} x}{12 \, x^{4}}"," ",0,"-1/12*(12*B*b^2*x^3 + 3*A*a^2 + 6*(2*B*a*b + A*b^2)*x^2 + 4*(B*a^2 + 2*A*a*b)*x)/x^4","A",0
101,1,51,0,1.265427," ","integrate((b*x+a)^2*(B*x+A)/x^6,x, algorithm=""fricas"")","-\frac{30 \, B b^{2} x^{3} + 12 \, A a^{2} + 20 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{5}}"," ",0,"-1/60*(30*B*b^2*x^3 + 12*A*a^2 + 20*(2*B*a*b + A*b^2)*x^2 + 15*(B*a^2 + 2*A*a*b)*x)/x^5","A",0
102,1,51,0,1.308458," ","integrate((b*x+a)^2*(B*x+A)/x^7,x, algorithm=""fricas"")","-\frac{20 \, B b^{2} x^{3} + 10 \, A a^{2} + 15 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 12 \, {\left(B a^{2} + 2 \, A a b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(20*B*b^2*x^3 + 10*A*a^2 + 15*(2*B*a*b + A*b^2)*x^2 + 12*(B*a^2 + 2*A*a*b)*x)/x^6","A",0
103,1,51,0,1.398184," ","integrate((b*x+a)^2*(B*x+A)/x^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{2} x^{3} + 60 \, A a^{2} + 84 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 70 \, {\left(B a^{2} + 2 \, A a b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(105*B*b^2*x^3 + 60*A*a^2 + 84*(2*B*a*b + A*b^2)*x^2 + 70*(B*a^2 + 2*A*a*b)*x)/x^7","A",0
104,1,77,0,1.123839," ","integrate(x^4*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{3} B + \frac{3}{8} x^{8} b^{2} a B + \frac{1}{8} x^{8} b^{3} A + \frac{3}{7} x^{7} b a^{2} B + \frac{3}{7} x^{7} b^{2} a A + \frac{1}{6} x^{6} a^{3} B + \frac{1}{2} x^{6} b a^{2} A + \frac{1}{5} x^{5} a^{3} A"," ",0,"1/9*x^9*b^3*B + 3/8*x^8*b^2*a*B + 1/8*x^8*b^3*A + 3/7*x^7*b*a^2*B + 3/7*x^7*b^2*a*A + 1/6*x^6*a^3*B + 1/2*x^6*b*a^2*A + 1/5*x^5*a^3*A","A",0
105,1,77,0,1.188857," ","integrate(x^3*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{3} B + \frac{3}{7} x^{7} b^{2} a B + \frac{1}{7} x^{7} b^{3} A + \frac{1}{2} x^{6} b a^{2} B + \frac{1}{2} x^{6} b^{2} a A + \frac{1}{5} x^{5} a^{3} B + \frac{3}{5} x^{5} b a^{2} A + \frac{1}{4} x^{4} a^{3} A"," ",0,"1/8*x^8*b^3*B + 3/7*x^7*b^2*a*B + 1/7*x^7*b^3*A + 1/2*x^6*b*a^2*B + 1/2*x^6*b^2*a*A + 1/5*x^5*a^3*B + 3/5*x^5*b*a^2*A + 1/4*x^4*a^3*A","A",0
106,1,77,0,1.136868," ","integrate(x^2*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{3} B + \frac{1}{2} x^{6} b^{2} a B + \frac{1}{6} x^{6} b^{3} A + \frac{3}{5} x^{5} b a^{2} B + \frac{3}{5} x^{5} b^{2} a A + \frac{1}{4} x^{4} a^{3} B + \frac{3}{4} x^{4} b a^{2} A + \frac{1}{3} x^{3} a^{3} A"," ",0,"1/7*x^7*b^3*B + 1/2*x^6*b^2*a*B + 1/6*x^6*b^3*A + 3/5*x^5*b*a^2*B + 3/5*x^5*b^2*a*A + 1/4*x^4*a^3*B + 3/4*x^4*b*a^2*A + 1/3*x^3*a^3*A","A",0
107,1,76,0,0.763407," ","integrate(x*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{6} x^{6} b^{3} B + \frac{3}{5} x^{5} b^{2} a B + \frac{1}{5} x^{5} b^{3} A + \frac{3}{4} x^{4} b a^{2} B + \frac{3}{4} x^{4} b^{2} a A + \frac{1}{3} x^{3} a^{3} B + x^{3} b a^{2} A + \frac{1}{2} x^{2} a^{3} A"," ",0,"1/6*x^6*b^3*B + 3/5*x^5*b^2*a*B + 1/5*x^5*b^3*A + 3/4*x^4*b*a^2*B + 3/4*x^4*b^2*a*A + 1/3*x^3*a^3*B + x^3*b*a^2*A + 1/2*x^2*a^3*A","A",0
108,1,72,0,1.037142," ","integrate((b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{3} B + \frac{3}{4} x^{4} b^{2} a B + \frac{1}{4} x^{4} b^{3} A + x^{3} b a^{2} B + x^{3} b^{2} a A + \frac{1}{2} x^{2} a^{3} B + \frac{3}{2} x^{2} b a^{2} A + x a^{3} A"," ",0,"1/5*x^5*b^3*B + 3/4*x^4*b^2*a*B + 1/4*x^4*b^3*A + x^3*b*a^2*B + x^3*b^2*a*A + 1/2*x^2*a^3*B + 3/2*x^2*b*a^2*A + x*a^3*A","B",0
109,1,68,0,1.105132," ","integrate((b*x+a)^3*(B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{4} \, B b^{3} x^{4} + A a^{3} \log\left(x\right) + \frac{1}{3} \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + \frac{3}{2} \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} x"," ",0,"1/4*B*b^3*x^4 + A*a^3*log(x) + 1/3*(3*B*a*b^2 + A*b^3)*x^3 + 3/2*(B*a^2*b + A*a*b^2)*x^2 + (B*a^3 + 3*A*a^2*b)*x","A",0
110,1,75,0,1.200398," ","integrate((b*x+a)^3*(B*x+A)/x^2,x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{4} - 6 \, A a^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x \log\left(x\right)}{6 \, x}"," ",0,"1/6*(2*B*b^3*x^4 - 6*A*a^3 + 3*(3*B*a*b^2 + A*b^3)*x^3 + 18*(B*a^2*b + A*a*b^2)*x^2 + 6*(B*a^3 + 3*A*a^2*b)*x*log(x))/x","A",0
111,1,74,0,1.291045," ","integrate((b*x+a)^3*(B*x+A)/x^3,x, algorithm=""fricas"")","\frac{B b^{3} x^{4} - A a^{3} + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2 \, x^{2}}"," ",0,"1/2*(B*b^3*x^4 - A*a^3 + 2*(3*B*a*b^2 + A*b^3)*x^3 + 6*(B*a^2*b + A*a*b^2)*x^2*log(x) - 2*(B*a^3 + 3*A*a^2*b)*x)/x^2","A",0
112,1,75,0,1.257427," ","integrate((b*x+a)^3*(B*x+A)/x^4,x, algorithm=""fricas"")","\frac{6 \, B b^{3} x^{4} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} \log\left(x\right) - 2 \, A a^{3} - 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(6*B*b^3*x^4 + 6*(3*B*a*b^2 + A*b^3)*x^3*log(x) - 2*A*a^3 - 18*(B*a^2*b + A*a*b^2)*x^2 - 3*(B*a^3 + 3*A*a^2*b)*x)/x^3","A",0
113,1,75,0,1.138914," ","integrate((b*x+a)^3*(B*x+A)/x^5,x, algorithm=""fricas"")","\frac{12 \, B b^{3} x^{4} \log\left(x\right) - 3 \, A a^{3} - 12 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} - 18 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(12*B*b^3*x^4*log(x) - 3*A*a^3 - 12*(3*B*a*b^2 + A*b^3)*x^3 - 18*(B*a^2*b + A*a*b^2)*x^2 - 4*(B*a^3 + 3*A*a^2*b)*x)/x^4","A",0
114,1,73,0,1.222046," ","integrate((b*x+a)^3*(B*x+A)/x^6,x, algorithm=""fricas"")","-\frac{20 \, B b^{3} x^{4} + 4 \, A a^{3} + 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 20 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{20 \, x^{5}}"," ",0,"-1/20*(20*B*b^3*x^4 + 4*A*a^3 + 10*(3*B*a*b^2 + A*b^3)*x^3 + 20*(B*a^2*b + A*a*b^2)*x^2 + 5*(B*a^3 + 3*A*a^2*b)*x)/x^5","A",0
115,1,73,0,1.241033," ","integrate((b*x+a)^3*(B*x+A)/x^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{3} x^{4} + 10 \, A a^{3} + 20 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{60 \, x^{6}}"," ",0,"-1/60*(30*B*b^3*x^4 + 10*A*a^3 + 20*(3*B*a*b^2 + A*b^3)*x^3 + 45*(B*a^2*b + A*a*b^2)*x^2 + 12*(B*a^3 + 3*A*a^2*b)*x)/x^6","A",0
116,1,73,0,0.865557," ","integrate((b*x+a)^3*(B*x+A)/x^8,x, algorithm=""fricas"")","-\frac{140 \, B b^{3} x^{4} + 60 \, A a^{3} + 105 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 252 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 70 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{420 \, x^{7}}"," ",0,"-1/420*(140*B*b^3*x^4 + 60*A*a^3 + 105*(3*B*a*b^2 + A*b^3)*x^3 + 252*(B*a^2*b + A*a*b^2)*x^2 + 70*(B*a^3 + 3*A*a^2*b)*x)/x^7","A",0
117,1,73,0,1.232393," ","integrate((b*x+a)^3*(B*x+A)/x^9,x, algorithm=""fricas"")","-\frac{70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 140 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 40 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{280 \, x^{8}}"," ",0,"-1/280*(70*B*b^3*x^4 + 35*A*a^3 + 56*(3*B*a*b^2 + A*b^3)*x^3 + 140*(B*a^2*b + A*a*b^2)*x^2 + 40*(B*a^3 + 3*A*a^2*b)*x)/x^8","A",0
118,1,73,0,1.324718," ","integrate((b*x+a)^3*(B*x+A)/x^10,x, algorithm=""fricas"")","-\frac{504 \, B b^{3} x^{4} + 280 \, A a^{3} + 420 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 1080 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 315 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x}{2520 \, x^{9}}"," ",0,"-1/2520*(504*B*b^3*x^4 + 280*A*a^3 + 420*(3*B*a*b^2 + A*b^3)*x^3 + 1080*(B*a^2*b + A*a*b^2)*x^2 + 315*(B*a^3 + 3*A*a^2*b)*x)/x^9","A",0
119,1,124,0,1.142327," ","integrate(x^5*(b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{5} B + \frac{5}{11} x^{11} b^{4} a B + \frac{1}{11} x^{11} b^{5} A + x^{10} b^{3} a^{2} B + \frac{1}{2} x^{10} b^{4} a A + \frac{10}{9} x^{9} b^{2} a^{3} B + \frac{10}{9} x^{9} b^{3} a^{2} A + \frac{5}{8} x^{8} b a^{4} B + \frac{5}{4} x^{8} b^{2} a^{3} A + \frac{1}{7} x^{7} a^{5} B + \frac{5}{7} x^{7} b a^{4} A + \frac{1}{6} x^{6} a^{5} A"," ",0,"1/12*x^12*b^5*B + 5/11*x^11*b^4*a*B + 1/11*x^11*b^5*A + x^10*b^3*a^2*B + 1/2*x^10*b^4*a*A + 10/9*x^9*b^2*a^3*B + 10/9*x^9*b^3*a^2*A + 5/8*x^8*b*a^4*B + 5/4*x^8*b^2*a^3*A + 1/7*x^7*a^5*B + 5/7*x^7*b*a^4*A + 1/6*x^6*a^5*A","A",0
120,1,125,0,0.755362," ","integrate(x^4*(b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{11} x^{11} b^{5} B + \frac{1}{2} x^{10} b^{4} a B + \frac{1}{10} x^{10} b^{5} A + \frac{10}{9} x^{9} b^{3} a^{2} B + \frac{5}{9} x^{9} b^{4} a A + \frac{5}{4} x^{8} b^{2} a^{3} B + \frac{5}{4} x^{8} b^{3} a^{2} A + \frac{5}{7} x^{7} b a^{4} B + \frac{10}{7} x^{7} b^{2} a^{3} A + \frac{1}{6} x^{6} a^{5} B + \frac{5}{6} x^{6} b a^{4} A + \frac{1}{5} x^{5} a^{5} A"," ",0,"1/11*x^11*b^5*B + 1/2*x^10*b^4*a*B + 1/10*x^10*b^5*A + 10/9*x^9*b^3*a^2*B + 5/9*x^9*b^4*a*A + 5/4*x^8*b^2*a^3*B + 5/4*x^8*b^3*a^2*A + 5/7*x^7*b*a^4*B + 10/7*x^7*b^2*a^3*A + 1/6*x^6*a^5*B + 5/6*x^6*b*a^4*A + 1/5*x^5*a^5*A","A",0
121,1,124,0,0.561577," ","integrate(x^3*(b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{10} x^{10} b^{5} B + \frac{5}{9} x^{9} b^{4} a B + \frac{1}{9} x^{9} b^{5} A + \frac{5}{4} x^{8} b^{3} a^{2} B + \frac{5}{8} x^{8} b^{4} a A + \frac{10}{7} x^{7} b^{2} a^{3} B + \frac{10}{7} x^{7} b^{3} a^{2} A + \frac{5}{6} x^{6} b a^{4} B + \frac{5}{3} x^{6} b^{2} a^{3} A + \frac{1}{5} x^{5} a^{5} B + x^{5} b a^{4} A + \frac{1}{4} x^{4} a^{5} A"," ",0,"1/10*x^10*b^5*B + 5/9*x^9*b^4*a*B + 1/9*x^9*b^5*A + 5/4*x^8*b^3*a^2*B + 5/8*x^8*b^4*a*A + 10/7*x^7*b^2*a^3*B + 10/7*x^7*b^3*a^2*A + 5/6*x^6*b*a^4*B + 5/3*x^6*b^2*a^3*A + 1/5*x^5*a^5*B + x^5*b*a^4*A + 1/4*x^4*a^5*A","A",0
122,1,124,0,0.835263," ","integrate(x^2*(b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{9} x^{9} b^{5} B + \frac{5}{8} x^{8} b^{4} a B + \frac{1}{8} x^{8} b^{5} A + \frac{10}{7} x^{7} b^{3} a^{2} B + \frac{5}{7} x^{7} b^{4} a A + \frac{5}{3} x^{6} b^{2} a^{3} B + \frac{5}{3} x^{6} b^{3} a^{2} A + x^{5} b a^{4} B + 2 x^{5} b^{2} a^{3} A + \frac{1}{4} x^{4} a^{5} B + \frac{5}{4} x^{4} b a^{4} A + \frac{1}{3} x^{3} a^{5} A"," ",0,"1/9*x^9*b^5*B + 5/8*x^8*b^4*a*B + 1/8*x^8*b^5*A + 10/7*x^7*b^3*a^2*B + 5/7*x^7*b^4*a*A + 5/3*x^6*b^2*a^3*B + 5/3*x^6*b^3*a^2*A + x^5*b*a^4*B + 2*x^5*b^2*a^3*A + 1/4*x^4*a^5*B + 5/4*x^4*b*a^4*A + 1/3*x^3*a^5*A","A",0
123,1,125,0,0.853046," ","integrate(x*(b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{5} B + \frac{5}{7} x^{7} b^{4} a B + \frac{1}{7} x^{7} b^{5} A + \frac{5}{3} x^{6} b^{3} a^{2} B + \frac{5}{6} x^{6} b^{4} a A + 2 x^{5} b^{2} a^{3} B + 2 x^{5} b^{3} a^{2} A + \frac{5}{4} x^{4} b a^{4} B + \frac{5}{2} x^{4} b^{2} a^{3} A + \frac{1}{3} x^{3} a^{5} B + \frac{5}{3} x^{3} b a^{4} A + \frac{1}{2} x^{2} a^{5} A"," ",0,"1/8*x^8*b^5*B + 5/7*x^7*b^4*a*B + 1/7*x^7*b^5*A + 5/3*x^6*b^3*a^2*B + 5/6*x^6*b^4*a*A + 2*x^5*b^2*a^3*B + 2*x^5*b^3*a^2*A + 5/4*x^4*b*a^4*B + 5/2*x^4*b^2*a^3*A + 1/3*x^3*a^5*B + 5/3*x^3*b*a^4*A + 1/2*x^2*a^5*A","B",0
124,1,121,0,1.188392," ","integrate((b*x+a)^5*(B*x+A),x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{5} B + \frac{5}{6} x^{6} b^{4} a B + \frac{1}{6} x^{6} b^{5} A + 2 x^{5} b^{3} a^{2} B + x^{5} b^{4} a A + \frac{5}{2} x^{4} b^{2} a^{3} B + \frac{5}{2} x^{4} b^{3} a^{2} A + \frac{5}{3} x^{3} b a^{4} B + \frac{10}{3} x^{3} b^{2} a^{3} A + \frac{1}{2} x^{2} a^{5} B + \frac{5}{2} x^{2} b a^{4} A + x a^{5} A"," ",0,"1/7*x^7*b^5*B + 5/6*x^6*b^4*a*B + 1/6*x^6*b^5*A + 2*x^5*b^3*a^2*B + x^5*b^4*a*A + 5/2*x^4*b^2*a^3*B + 5/2*x^4*b^3*a^2*A + 5/3*x^3*b*a^4*B + 10/3*x^3*b^2*a^3*A + 1/2*x^2*a^5*B + 5/2*x^2*b*a^4*A + x*a^5*A","B",0
125,1,114,0,0.988390," ","integrate((b*x+a)^5*(B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{6} \, B b^{5} x^{6} + A a^{5} \log\left(x\right) + \frac{1}{5} \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + \frac{5}{4} \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + \frac{10}{3} \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + \frac{5}{2} \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + {\left(B a^{5} + 5 \, A a^{4} b\right)} x"," ",0,"1/6*B*b^5*x^6 + A*a^5*log(x) + 1/5*(5*B*a*b^4 + A*b^5)*x^5 + 5/4*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 10/3*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 5/2*(B*a^4*b + 2*A*a^3*b^2)*x^2 + (B*a^5 + 5*A*a^4*b)*x","A",0
126,1,121,0,1.258735," ","integrate((b*x+a)^5*(B*x+A)/x^2,x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{6} - 60 \, A a^{5} + 15 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 300 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 60 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x \log\left(x\right)}{60 \, x}"," ",0,"1/60*(12*B*b^5*x^6 - 60*A*a^5 + 15*(5*B*a*b^4 + A*b^5)*x^5 + 100*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 300*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 300*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 60*(B*a^5 + 5*A*a^4*b)*x*log(x))/x","A",0
127,1,121,0,1.319509," ","integrate((b*x+a)^5*(B*x+A)/x^3,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{6} - 6 \, A a^{5} + 4 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 60 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} \log\left(x\right) - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{12 \, x^{2}}"," ",0,"1/12*(3*B*b^5*x^6 - 6*A*a^5 + 4*(5*B*a*b^4 + A*b^5)*x^5 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 120*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 60*(B*a^4*b + 2*A*a^3*b^2)*x^2*log(x) - 12*(B*a^5 + 5*A*a^4*b)*x)/x^2","A",0
128,1,121,0,1.319166," ","integrate((b*x+a)^5*(B*x+A)/x^4,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{6} - 2 \, A a^{5} + 3 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 30 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 60 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} \log\left(x\right) - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 3 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{6 \, x^{3}}"," ",0,"1/6*(2*B*b^5*x^6 - 2*A*a^5 + 3*(5*B*a*b^4 + A*b^5)*x^5 + 30*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 60*(B*a^3*b^2 + A*a^2*b^3)*x^3*log(x) - 30*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 3*(B*a^5 + 5*A*a^4*b)*x)/x^3","A",0
129,1,121,0,1.184254," ","integrate((b*x+a)^5*(B*x+A)/x^5,x, algorithm=""fricas"")","\frac{6 \, B b^{5} x^{6} - 3 \, A a^{5} + 12 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 60 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} \log\left(x\right) - 120 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 30 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 4 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{12 \, x^{4}}"," ",0,"1/12*(6*B*b^5*x^6 - 3*A*a^5 + 12*(5*B*a*b^4 + A*b^5)*x^5 + 60*(2*B*a^2*b^3 + A*a*b^4)*x^4*log(x) - 120*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 30*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 4*(B*a^5 + 5*A*a^4*b)*x)/x^4","A",0
130,1,121,0,1.192093," ","integrate((b*x+a)^5*(B*x+A)/x^6,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{6} + 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} \log\left(x\right) - 12 \, A a^{5} - 300 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} - 300 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 100 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 15 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{60 \, x^{5}}"," ",0,"1/60*(60*B*b^5*x^6 + 60*(5*B*a*b^4 + A*b^5)*x^5*log(x) - 12*A*a^5 - 300*(2*B*a^2*b^3 + A*a*b^4)*x^4 - 300*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 100*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 15*(B*a^5 + 5*A*a^4*b)*x)/x^5","A",0
131,1,121,0,1.044611," ","integrate((b*x+a)^5*(B*x+A)/x^7,x, algorithm=""fricas"")","\frac{60 \, B b^{5} x^{6} \log\left(x\right) - 10 \, A a^{5} - 60 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} - 150 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} - 200 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} - 75 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} - 12 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{60 \, x^{6}}"," ",0,"1/60*(60*B*b^5*x^6*log(x) - 10*A*a^5 - 60*(5*B*a*b^4 + A*b^5)*x^5 - 150*(2*B*a^2*b^3 + A*a*b^4)*x^4 - 200*(B*a^3*b^2 + A*a^2*b^3)*x^3 - 75*(B*a^4*b + 2*A*a^3*b^2)*x^2 - 12*(B*a^5 + 5*A*a^4*b)*x)/x^6","A",0
132,1,119,0,1.334676," ","integrate((b*x+a)^5*(B*x+A)/x^8,x, algorithm=""fricas"")","-\frac{42 \, B b^{5} x^{6} + 6 \, A a^{5} + 21 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 70 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 105 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 42 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 7 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{42 \, x^{7}}"," ",0,"-1/42*(42*B*b^5*x^6 + 6*A*a^5 + 21*(5*B*a*b^4 + A*b^5)*x^5 + 70*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 105*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 42*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 7*(B*a^5 + 5*A*a^4*b)*x)/x^7","B",0
133,1,119,0,1.134804," ","integrate((b*x+a)^5*(B*x+A)/x^9,x, algorithm=""fricas"")","-\frac{84 \, B b^{5} x^{6} + 21 \, A a^{5} + 56 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 210 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 336 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 140 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 24 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{168 \, x^{8}}"," ",0,"-1/168*(84*B*b^5*x^6 + 21*A*a^5 + 56*(5*B*a*b^4 + A*b^5)*x^5 + 210*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 336*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 140*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 24*(B*a^5 + 5*A*a^4*b)*x)/x^8","A",0
134,1,119,0,1.134662," ","integrate((b*x+a)^5*(B*x+A)/x^10,x, algorithm=""fricas"")","-\frac{168 \, B b^{5} x^{6} + 56 \, A a^{5} + 126 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 504 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 840 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 360 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 63 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{504 \, x^{9}}"," ",0,"-1/504*(168*B*b^5*x^6 + 56*A*a^5 + 126*(5*B*a*b^4 + A*b^5)*x^5 + 504*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 840*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 360*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 63*(B*a^5 + 5*A*a^4*b)*x)/x^9","A",0
135,1,119,0,1.231448," ","integrate((b*x+a)^5*(B*x+A)/x^11,x, algorithm=""fricas"")","-\frac{630 \, B b^{5} x^{6} + 252 \, A a^{5} + 504 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 2100 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 3600 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 1575 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 280 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{2520 \, x^{10}}"," ",0,"-1/2520*(630*B*b^5*x^6 + 252*A*a^5 + 504*(5*B*a*b^4 + A*b^5)*x^5 + 2100*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 3600*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 1575*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 280*(B*a^5 + 5*A*a^4*b)*x)/x^10","A",0
136,1,119,0,1.148211," ","integrate((b*x+a)^5*(B*x+A)/x^12,x, algorithm=""fricas"")","-\frac{2772 \, B b^{5} x^{6} + 1260 \, A a^{5} + 2310 \, {\left(5 \, B a b^{4} + A b^{5}\right)} x^{5} + 9900 \, {\left(2 \, B a^{2} b^{3} + A a b^{4}\right)} x^{4} + 17325 \, {\left(B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + 7700 \, {\left(B a^{4} b + 2 \, A a^{3} b^{2}\right)} x^{2} + 1386 \, {\left(B a^{5} + 5 \, A a^{4} b\right)} x}{13860 \, x^{11}}"," ",0,"-1/13860*(2772*B*b^5*x^6 + 1260*A*a^5 + 2310*(5*B*a*b^4 + A*b^5)*x^5 + 9900*(2*B*a^2*b^3 + A*a*b^4)*x^4 + 17325*(B*a^3*b^2 + A*a^2*b^3)*x^3 + 7700*(B*a^4*b + 2*A*a^3*b^2)*x^2 + 1386*(B*a^5 + 5*A*a^4*b)*x)/x^11","A",0
137,1,245,0,1.123169," ","integrate(x^10*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{22} x^{22} b^{10} B + \frac{10}{21} x^{21} b^{9} a B + \frac{1}{21} x^{21} b^{10} A + \frac{9}{4} x^{20} b^{8} a^{2} B + \frac{1}{2} x^{20} b^{9} a A + \frac{120}{19} x^{19} b^{7} a^{3} B + \frac{45}{19} x^{19} b^{8} a^{2} A + \frac{35}{3} x^{18} b^{6} a^{4} B + \frac{20}{3} x^{18} b^{7} a^{3} A + \frac{252}{17} x^{17} b^{5} a^{5} B + \frac{210}{17} x^{17} b^{6} a^{4} A + \frac{105}{8} x^{16} b^{4} a^{6} B + \frac{63}{4} x^{16} b^{5} a^{5} A + 8 x^{15} b^{3} a^{7} B + 14 x^{15} b^{4} a^{6} A + \frac{45}{14} x^{14} b^{2} a^{8} B + \frac{60}{7} x^{14} b^{3} a^{7} A + \frac{10}{13} x^{13} b a^{9} B + \frac{45}{13} x^{13} b^{2} a^{8} A + \frac{1}{12} x^{12} a^{10} B + \frac{5}{6} x^{12} b a^{9} A + \frac{1}{11} x^{11} a^{10} A"," ",0,"1/22*x^22*b^10*B + 10/21*x^21*b^9*a*B + 1/21*x^21*b^10*A + 9/4*x^20*b^8*a^2*B + 1/2*x^20*b^9*a*A + 120/19*x^19*b^7*a^3*B + 45/19*x^19*b^8*a^2*A + 35/3*x^18*b^6*a^4*B + 20/3*x^18*b^7*a^3*A + 252/17*x^17*b^5*a^5*B + 210/17*x^17*b^6*a^4*A + 105/8*x^16*b^4*a^6*B + 63/4*x^16*b^5*a^5*A + 8*x^15*b^3*a^7*B + 14*x^15*b^4*a^6*A + 45/14*x^14*b^2*a^8*B + 60/7*x^14*b^3*a^7*A + 10/13*x^13*b*a^9*B + 45/13*x^13*b^2*a^8*A + 1/12*x^12*a^10*B + 5/6*x^12*b*a^9*A + 1/11*x^11*a^10*A","A",0
138,1,245,0,0.841994," ","integrate(x^9*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{21} x^{21} b^{10} B + \frac{1}{2} x^{20} b^{9} a B + \frac{1}{20} x^{20} b^{10} A + \frac{45}{19} x^{19} b^{8} a^{2} B + \frac{10}{19} x^{19} b^{9} a A + \frac{20}{3} x^{18} b^{7} a^{3} B + \frac{5}{2} x^{18} b^{8} a^{2} A + \frac{210}{17} x^{17} b^{6} a^{4} B + \frac{120}{17} x^{17} b^{7} a^{3} A + \frac{63}{4} x^{16} b^{5} a^{5} B + \frac{105}{8} x^{16} b^{6} a^{4} A + 14 x^{15} b^{4} a^{6} B + \frac{84}{5} x^{15} b^{5} a^{5} A + \frac{60}{7} x^{14} b^{3} a^{7} B + 15 x^{14} b^{4} a^{6} A + \frac{45}{13} x^{13} b^{2} a^{8} B + \frac{120}{13} x^{13} b^{3} a^{7} A + \frac{5}{6} x^{12} b a^{9} B + \frac{15}{4} x^{12} b^{2} a^{8} A + \frac{1}{11} x^{11} a^{10} B + \frac{10}{11} x^{11} b a^{9} A + \frac{1}{10} x^{10} a^{10} A"," ",0,"1/21*x^21*b^10*B + 1/2*x^20*b^9*a*B + 1/20*x^20*b^10*A + 45/19*x^19*b^8*a^2*B + 10/19*x^19*b^9*a*A + 20/3*x^18*b^7*a^3*B + 5/2*x^18*b^8*a^2*A + 210/17*x^17*b^6*a^4*B + 120/17*x^17*b^7*a^3*A + 63/4*x^16*b^5*a^5*B + 105/8*x^16*b^6*a^4*A + 14*x^15*b^4*a^6*B + 84/5*x^15*b^5*a^5*A + 60/7*x^14*b^3*a^7*B + 15*x^14*b^4*a^6*A + 45/13*x^13*b^2*a^8*B + 120/13*x^13*b^3*a^7*A + 5/6*x^12*b*a^9*B + 15/4*x^12*b^2*a^8*A + 1/11*x^11*a^10*B + 10/11*x^11*b*a^9*A + 1/10*x^10*a^10*A","A",0
139,1,244,0,1.165058," ","integrate(x^8*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{20} x^{20} b^{10} B + \frac{10}{19} x^{19} b^{9} a B + \frac{1}{19} x^{19} b^{10} A + \frac{5}{2} x^{18} b^{8} a^{2} B + \frac{5}{9} x^{18} b^{9} a A + \frac{120}{17} x^{17} b^{7} a^{3} B + \frac{45}{17} x^{17} b^{8} a^{2} A + \frac{105}{8} x^{16} b^{6} a^{4} B + \frac{15}{2} x^{16} b^{7} a^{3} A + \frac{84}{5} x^{15} b^{5} a^{5} B + 14 x^{15} b^{6} a^{4} A + 15 x^{14} b^{4} a^{6} B + 18 x^{14} b^{5} a^{5} A + \frac{120}{13} x^{13} b^{3} a^{7} B + \frac{210}{13} x^{13} b^{4} a^{6} A + \frac{15}{4} x^{12} b^{2} a^{8} B + 10 x^{12} b^{3} a^{7} A + \frac{10}{11} x^{11} b a^{9} B + \frac{45}{11} x^{11} b^{2} a^{8} A + \frac{1}{10} x^{10} a^{10} B + x^{10} b a^{9} A + \frac{1}{9} x^{9} a^{10} A"," ",0,"1/20*x^20*b^10*B + 10/19*x^19*b^9*a*B + 1/19*x^19*b^10*A + 5/2*x^18*b^8*a^2*B + 5/9*x^18*b^9*a*A + 120/17*x^17*b^7*a^3*B + 45/17*x^17*b^8*a^2*A + 105/8*x^16*b^6*a^4*B + 15/2*x^16*b^7*a^3*A + 84/5*x^15*b^5*a^5*B + 14*x^15*b^6*a^4*A + 15*x^14*b^4*a^6*B + 18*x^14*b^5*a^5*A + 120/13*x^13*b^3*a^7*B + 210/13*x^13*b^4*a^6*A + 15/4*x^12*b^2*a^8*B + 10*x^12*b^3*a^7*A + 10/11*x^11*b*a^9*B + 45/11*x^11*b^2*a^8*A + 1/10*x^10*a^10*B + x^10*b*a^9*A + 1/9*x^9*a^10*A","A",0
140,1,244,0,0.491074," ","integrate(x^7*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{19} x^{19} b^{10} B + \frac{5}{9} x^{18} b^{9} a B + \frac{1}{18} x^{18} b^{10} A + \frac{45}{17} x^{17} b^{8} a^{2} B + \frac{10}{17} x^{17} b^{9} a A + \frac{15}{2} x^{16} b^{7} a^{3} B + \frac{45}{16} x^{16} b^{8} a^{2} A + 14 x^{15} b^{6} a^{4} B + 8 x^{15} b^{7} a^{3} A + 18 x^{14} b^{5} a^{5} B + 15 x^{14} b^{6} a^{4} A + \frac{210}{13} x^{13} b^{4} a^{6} B + \frac{252}{13} x^{13} b^{5} a^{5} A + 10 x^{12} b^{3} a^{7} B + \frac{35}{2} x^{12} b^{4} a^{6} A + \frac{45}{11} x^{11} b^{2} a^{8} B + \frac{120}{11} x^{11} b^{3} a^{7} A + x^{10} b a^{9} B + \frac{9}{2} x^{10} b^{2} a^{8} A + \frac{1}{9} x^{9} a^{10} B + \frac{10}{9} x^{9} b a^{9} A + \frac{1}{8} x^{8} a^{10} A"," ",0,"1/19*x^19*b^10*B + 5/9*x^18*b^9*a*B + 1/18*x^18*b^10*A + 45/17*x^17*b^8*a^2*B + 10/17*x^17*b^9*a*A + 15/2*x^16*b^7*a^3*B + 45/16*x^16*b^8*a^2*A + 14*x^15*b^6*a^4*B + 8*x^15*b^7*a^3*A + 18*x^14*b^5*a^5*B + 15*x^14*b^6*a^4*A + 210/13*x^13*b^4*a^6*B + 252/13*x^13*b^5*a^5*A + 10*x^12*b^3*a^7*B + 35/2*x^12*b^4*a^6*A + 45/11*x^11*b^2*a^8*B + 120/11*x^11*b^3*a^7*A + x^10*b*a^9*B + 9/2*x^10*b^2*a^8*A + 1/9*x^9*a^10*B + 10/9*x^9*b*a^9*A + 1/8*x^8*a^10*A","A",0
141,1,245,0,1.053374," ","integrate(x^6*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{18} x^{18} b^{10} B + \frac{10}{17} x^{17} b^{9} a B + \frac{1}{17} x^{17} b^{10} A + \frac{45}{16} x^{16} b^{8} a^{2} B + \frac{5}{8} x^{16} b^{9} a A + 8 x^{15} b^{7} a^{3} B + 3 x^{15} b^{8} a^{2} A + 15 x^{14} b^{6} a^{4} B + \frac{60}{7} x^{14} b^{7} a^{3} A + \frac{252}{13} x^{13} b^{5} a^{5} B + \frac{210}{13} x^{13} b^{6} a^{4} A + \frac{35}{2} x^{12} b^{4} a^{6} B + 21 x^{12} b^{5} a^{5} A + \frac{120}{11} x^{11} b^{3} a^{7} B + \frac{210}{11} x^{11} b^{4} a^{6} A + \frac{9}{2} x^{10} b^{2} a^{8} B + 12 x^{10} b^{3} a^{7} A + \frac{10}{9} x^{9} b a^{9} B + 5 x^{9} b^{2} a^{8} A + \frac{1}{8} x^{8} a^{10} B + \frac{5}{4} x^{8} b a^{9} A + \frac{1}{7} x^{7} a^{10} A"," ",0,"1/18*x^18*b^10*B + 10/17*x^17*b^9*a*B + 1/17*x^17*b^10*A + 45/16*x^16*b^8*a^2*B + 5/8*x^16*b^9*a*A + 8*x^15*b^7*a^3*B + 3*x^15*b^8*a^2*A + 15*x^14*b^6*a^4*B + 60/7*x^14*b^7*a^3*A + 252/13*x^13*b^5*a^5*B + 210/13*x^13*b^6*a^4*A + 35/2*x^12*b^4*a^6*B + 21*x^12*b^5*a^5*A + 120/11*x^11*b^3*a^7*B + 210/11*x^11*b^4*a^6*A + 9/2*x^10*b^2*a^8*B + 12*x^10*b^3*a^7*A + 10/9*x^9*b*a^9*B + 5*x^9*b^2*a^8*A + 1/8*x^8*a^10*B + 5/4*x^8*b*a^9*A + 1/7*x^7*a^10*A","A",0
142,1,245,0,0.752439," ","integrate(x^5*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{17} x^{17} b^{10} B + \frac{5}{8} x^{16} b^{9} a B + \frac{1}{16} x^{16} b^{10} A + 3 x^{15} b^{8} a^{2} B + \frac{2}{3} x^{15} b^{9} a A + \frac{60}{7} x^{14} b^{7} a^{3} B + \frac{45}{14} x^{14} b^{8} a^{2} A + \frac{210}{13} x^{13} b^{6} a^{4} B + \frac{120}{13} x^{13} b^{7} a^{3} A + 21 x^{12} b^{5} a^{5} B + \frac{35}{2} x^{12} b^{6} a^{4} A + \frac{210}{11} x^{11} b^{4} a^{6} B + \frac{252}{11} x^{11} b^{5} a^{5} A + 12 x^{10} b^{3} a^{7} B + 21 x^{10} b^{4} a^{6} A + 5 x^{9} b^{2} a^{8} B + \frac{40}{3} x^{9} b^{3} a^{7} A + \frac{5}{4} x^{8} b a^{9} B + \frac{45}{8} x^{8} b^{2} a^{8} A + \frac{1}{7} x^{7} a^{10} B + \frac{10}{7} x^{7} b a^{9} A + \frac{1}{6} x^{6} a^{10} A"," ",0,"1/17*x^17*b^10*B + 5/8*x^16*b^9*a*B + 1/16*x^16*b^10*A + 3*x^15*b^8*a^2*B + 2/3*x^15*b^9*a*A + 60/7*x^14*b^7*a^3*B + 45/14*x^14*b^8*a^2*A + 210/13*x^13*b^6*a^4*B + 120/13*x^13*b^7*a^3*A + 21*x^12*b^5*a^5*B + 35/2*x^12*b^6*a^4*A + 210/11*x^11*b^4*a^6*B + 252/11*x^11*b^5*a^5*A + 12*x^10*b^3*a^7*B + 21*x^10*b^4*a^6*A + 5*x^9*b^2*a^8*B + 40/3*x^9*b^3*a^7*A + 5/4*x^8*b*a^9*B + 45/8*x^8*b^2*a^8*A + 1/7*x^7*a^10*B + 10/7*x^7*b*a^9*A + 1/6*x^6*a^10*A","A",0
143,1,245,0,1.225016," ","integrate(x^4*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{16} x^{16} b^{10} B + \frac{2}{3} x^{15} b^{9} a B + \frac{1}{15} x^{15} b^{10} A + \frac{45}{14} x^{14} b^{8} a^{2} B + \frac{5}{7} x^{14} b^{9} a A + \frac{120}{13} x^{13} b^{7} a^{3} B + \frac{45}{13} x^{13} b^{8} a^{2} A + \frac{35}{2} x^{12} b^{6} a^{4} B + 10 x^{12} b^{7} a^{3} A + \frac{252}{11} x^{11} b^{5} a^{5} B + \frac{210}{11} x^{11} b^{6} a^{4} A + 21 x^{10} b^{4} a^{6} B + \frac{126}{5} x^{10} b^{5} a^{5} A + \frac{40}{3} x^{9} b^{3} a^{7} B + \frac{70}{3} x^{9} b^{4} a^{6} A + \frac{45}{8} x^{8} b^{2} a^{8} B + 15 x^{8} b^{3} a^{7} A + \frac{10}{7} x^{7} b a^{9} B + \frac{45}{7} x^{7} b^{2} a^{8} A + \frac{1}{6} x^{6} a^{10} B + \frac{5}{3} x^{6} b a^{9} A + \frac{1}{5} x^{5} a^{10} A"," ",0,"1/16*x^16*b^10*B + 2/3*x^15*b^9*a*B + 1/15*x^15*b^10*A + 45/14*x^14*b^8*a^2*B + 5/7*x^14*b^9*a*A + 120/13*x^13*b^7*a^3*B + 45/13*x^13*b^8*a^2*A + 35/2*x^12*b^6*a^4*B + 10*x^12*b^7*a^3*A + 252/11*x^11*b^5*a^5*B + 210/11*x^11*b^6*a^4*A + 21*x^10*b^4*a^6*B + 126/5*x^10*b^5*a^5*A + 40/3*x^9*b^3*a^7*B + 70/3*x^9*b^4*a^6*A + 45/8*x^8*b^2*a^8*B + 15*x^8*b^3*a^7*A + 10/7*x^7*b*a^9*B + 45/7*x^7*b^2*a^8*A + 1/6*x^6*a^10*B + 5/3*x^6*b*a^9*A + 1/5*x^5*a^10*A","A",0
144,1,245,0,1.206278," ","integrate(x^3*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{15} x^{15} b^{10} B + \frac{5}{7} x^{14} b^{9} a B + \frac{1}{14} x^{14} b^{10} A + \frac{45}{13} x^{13} b^{8} a^{2} B + \frac{10}{13} x^{13} b^{9} a A + 10 x^{12} b^{7} a^{3} B + \frac{15}{4} x^{12} b^{8} a^{2} A + \frac{210}{11} x^{11} b^{6} a^{4} B + \frac{120}{11} x^{11} b^{7} a^{3} A + \frac{126}{5} x^{10} b^{5} a^{5} B + 21 x^{10} b^{6} a^{4} A + \frac{70}{3} x^{9} b^{4} a^{6} B + 28 x^{9} b^{5} a^{5} A + 15 x^{8} b^{3} a^{7} B + \frac{105}{4} x^{8} b^{4} a^{6} A + \frac{45}{7} x^{7} b^{2} a^{8} B + \frac{120}{7} x^{7} b^{3} a^{7} A + \frac{5}{3} x^{6} b a^{9} B + \frac{15}{2} x^{6} b^{2} a^{8} A + \frac{1}{5} x^{5} a^{10} B + 2 x^{5} b a^{9} A + \frac{1}{4} x^{4} a^{10} A"," ",0,"1/15*x^15*b^10*B + 5/7*x^14*b^9*a*B + 1/14*x^14*b^10*A + 45/13*x^13*b^8*a^2*B + 10/13*x^13*b^9*a*A + 10*x^12*b^7*a^3*B + 15/4*x^12*b^8*a^2*A + 210/11*x^11*b^6*a^4*B + 120/11*x^11*b^7*a^3*A + 126/5*x^10*b^5*a^5*B + 21*x^10*b^6*a^4*A + 70/3*x^9*b^4*a^6*B + 28*x^9*b^5*a^5*A + 15*x^8*b^3*a^7*B + 105/4*x^8*b^4*a^6*A + 45/7*x^7*b^2*a^8*B + 120/7*x^7*b^3*a^7*A + 5/3*x^6*b*a^9*B + 15/2*x^6*b^2*a^8*A + 1/5*x^5*a^10*B + 2*x^5*b*a^9*A + 1/4*x^4*a^10*A","B",0
145,1,245,0,0.512753," ","integrate(x^2*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{14} x^{14} b^{10} B + \frac{10}{13} x^{13} b^{9} a B + \frac{1}{13} x^{13} b^{10} A + \frac{15}{4} x^{12} b^{8} a^{2} B + \frac{5}{6} x^{12} b^{9} a A + \frac{120}{11} x^{11} b^{7} a^{3} B + \frac{45}{11} x^{11} b^{8} a^{2} A + 21 x^{10} b^{6} a^{4} B + 12 x^{10} b^{7} a^{3} A + 28 x^{9} b^{5} a^{5} B + \frac{70}{3} x^{9} b^{6} a^{4} A + \frac{105}{4} x^{8} b^{4} a^{6} B + \frac{63}{2} x^{8} b^{5} a^{5} A + \frac{120}{7} x^{7} b^{3} a^{7} B + 30 x^{7} b^{4} a^{6} A + \frac{15}{2} x^{6} b^{2} a^{8} B + 20 x^{6} b^{3} a^{7} A + 2 x^{5} b a^{9} B + 9 x^{5} b^{2} a^{8} A + \frac{1}{4} x^{4} a^{10} B + \frac{5}{2} x^{4} b a^{9} A + \frac{1}{3} x^{3} a^{10} A"," ",0,"1/14*x^14*b^10*B + 10/13*x^13*b^9*a*B + 1/13*x^13*b^10*A + 15/4*x^12*b^8*a^2*B + 5/6*x^12*b^9*a*A + 120/11*x^11*b^7*a^3*B + 45/11*x^11*b^8*a^2*A + 21*x^10*b^6*a^4*B + 12*x^10*b^7*a^3*A + 28*x^9*b^5*a^5*B + 70/3*x^9*b^6*a^4*A + 105/4*x^8*b^4*a^6*B + 63/2*x^8*b^5*a^5*A + 120/7*x^7*b^3*a^7*B + 30*x^7*b^4*a^6*A + 15/2*x^6*b^2*a^8*B + 20*x^6*b^3*a^7*A + 2*x^5*b*a^9*B + 9*x^5*b^2*a^8*A + 1/4*x^4*a^10*B + 5/2*x^4*b*a^9*A + 1/3*x^3*a^10*A","B",0
146,1,245,0,1.296129," ","integrate(x*(b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{13} x^{13} b^{10} B + \frac{5}{6} x^{12} b^{9} a B + \frac{1}{12} x^{12} b^{10} A + \frac{45}{11} x^{11} b^{8} a^{2} B + \frac{10}{11} x^{11} b^{9} a A + 12 x^{10} b^{7} a^{3} B + \frac{9}{2} x^{10} b^{8} a^{2} A + \frac{70}{3} x^{9} b^{6} a^{4} B + \frac{40}{3} x^{9} b^{7} a^{3} A + \frac{63}{2} x^{8} b^{5} a^{5} B + \frac{105}{4} x^{8} b^{6} a^{4} A + 30 x^{7} b^{4} a^{6} B + 36 x^{7} b^{5} a^{5} A + 20 x^{6} b^{3} a^{7} B + 35 x^{6} b^{4} a^{6} A + 9 x^{5} b^{2} a^{8} B + 24 x^{5} b^{3} a^{7} A + \frac{5}{2} x^{4} b a^{9} B + \frac{45}{4} x^{4} b^{2} a^{8} A + \frac{1}{3} x^{3} a^{10} B + \frac{10}{3} x^{3} b a^{9} A + \frac{1}{2} x^{2} a^{10} A"," ",0,"1/13*x^13*b^10*B + 5/6*x^12*b^9*a*B + 1/12*x^12*b^10*A + 45/11*x^11*b^8*a^2*B + 10/11*x^11*b^9*a*A + 12*x^10*b^7*a^3*B + 9/2*x^10*b^8*a^2*A + 70/3*x^9*b^6*a^4*B + 40/3*x^9*b^7*a^3*A + 63/2*x^8*b^5*a^5*B + 105/4*x^8*b^6*a^4*A + 30*x^7*b^4*a^6*B + 36*x^7*b^5*a^5*A + 20*x^6*b^3*a^7*B + 35*x^6*b^4*a^6*A + 9*x^5*b^2*a^8*B + 24*x^5*b^3*a^7*A + 5/2*x^4*b*a^9*B + 45/4*x^4*b^2*a^8*A + 1/3*x^3*a^10*B + 10/3*x^3*b*a^9*A + 1/2*x^2*a^10*A","B",0
147,1,241,0,1.009197," ","integrate((b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{10} B + \frac{10}{11} x^{11} b^{9} a B + \frac{1}{11} x^{11} b^{10} A + \frac{9}{2} x^{10} b^{8} a^{2} B + x^{10} b^{9} a A + \frac{40}{3} x^{9} b^{7} a^{3} B + 5 x^{9} b^{8} a^{2} A + \frac{105}{4} x^{8} b^{6} a^{4} B + 15 x^{8} b^{7} a^{3} A + 36 x^{7} b^{5} a^{5} B + 30 x^{7} b^{6} a^{4} A + 35 x^{6} b^{4} a^{6} B + 42 x^{6} b^{5} a^{5} A + 24 x^{5} b^{3} a^{7} B + 42 x^{5} b^{4} a^{6} A + \frac{45}{4} x^{4} b^{2} a^{8} B + 30 x^{4} b^{3} a^{7} A + \frac{10}{3} x^{3} b a^{9} B + 15 x^{3} b^{2} a^{8} A + \frac{1}{2} x^{2} a^{10} B + 5 x^{2} b a^{9} A + x a^{10} A"," ",0,"1/12*x^12*b^10*B + 10/11*x^11*b^9*a*B + 1/11*x^11*b^10*A + 9/2*x^10*b^8*a^2*B + x^10*b^9*a*A + 40/3*x^9*b^7*a^3*B + 5*x^9*b^8*a^2*A + 105/4*x^8*b^6*a^4*B + 15*x^8*b^7*a^3*A + 36*x^7*b^5*a^5*B + 30*x^7*b^6*a^4*A + 35*x^6*b^4*a^6*B + 42*x^6*b^5*a^5*A + 24*x^5*b^3*a^7*B + 42*x^5*b^4*a^6*A + 45/4*x^4*b^2*a^8*B + 30*x^4*b^3*a^7*A + 10/3*x^3*b*a^9*B + 15*x^3*b^2*a^8*A + 1/2*x^2*a^10*B + 5*x^2*b*a^9*A + x*a^10*A","B",0
148,1,238,0,1.212721," ","integrate((b*x+a)^10*(B*x+A)/x,x, algorithm=""fricas"")","\frac{1}{11} \, B b^{10} x^{11} + A a^{10} \log\left(x\right) + \frac{1}{10} \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + \frac{5}{9} \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + \frac{15}{8} \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + \frac{30}{7} \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 7 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + \frac{42}{5} \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + \frac{15}{2} \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 5 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + \frac{5}{2} \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + {\left(B a^{10} + 10 \, A a^{9} b\right)} x"," ",0,"1/11*B*b^10*x^11 + A*a^10*log(x) + 1/10*(10*B*a*b^9 + A*b^10)*x^10 + 5/9*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 15/8*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 30/7*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 7*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 42/5*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 15/2*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 5*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 5/2*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + (B*a^10 + 10*A*a^9*b)*x","A",0
149,1,245,0,1.094704," ","integrate((b*x+a)^10*(B*x+A)/x^2,x, algorithm=""fricas"")","\frac{252 \, B b^{10} x^{11} - 2520 \, A a^{10} + 280 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 1575 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 5400 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 12600 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 21168 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 26460 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 25200 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 18900 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 12600 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 2520 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x \log\left(x\right)}{2520 \, x}"," ",0,"1/2520*(252*B*b^10*x^11 - 2520*A*a^10 + 280*(10*B*a*b^9 + A*b^10)*x^10 + 1575*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 5400*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 12600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 21168*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 26460*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 25200*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 18900*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 12600*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 2520*(B*a^10 + 10*A*a^9*b)*x*log(x))/x","A",0
150,1,245,0,1.184536," ","integrate((b*x+a)^10*(B*x+A)/x^3,x, algorithm=""fricas"")","\frac{56 \, B b^{10} x^{11} - 252 \, A a^{10} + 63 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 360 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 1260 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 3024 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 5292 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 7056 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 7560 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 7560 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 2520 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} \log\left(x\right) - 504 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{504 \, x^{2}}"," ",0,"1/504*(56*B*b^10*x^11 - 252*A*a^10 + 63*(10*B*a*b^9 + A*b^10)*x^10 + 360*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 1260*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 3024*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 5292*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 7056*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 7560*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 7560*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 2520*(2*B*a^9*b + 9*A*a^8*b^2)*x^2*log(x) - 504*(B*a^10 + 10*A*a^9*b)*x)/x^2","A",0
151,1,245,0,1.120761," ","integrate((b*x+a)^10*(B*x+A)/x^4,x, algorithm=""fricas"")","\frac{21 \, B b^{10} x^{11} - 56 \, A a^{10} + 24 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 140 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 504 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 1260 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 2352 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 3528 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 5040 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 2520 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} \log\left(x\right) - 840 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 84 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{168 \, x^{3}}"," ",0,"1/168*(21*B*b^10*x^11 - 56*A*a^10 + 24*(10*B*a*b^9 + A*b^10)*x^10 + 140*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 504*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 1260*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 2352*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 3528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 5040*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 2520*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3*log(x) - 840*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 84*(B*a^10 + 10*A*a^9*b)*x)/x^3","A",0
152,1,245,0,1.369703," ","integrate((b*x+a)^10*(B*x+A)/x^5,x, algorithm=""fricas"")","\frac{12 \, B b^{10} x^{11} - 21 \, A a^{10} + 14 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 84 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 315 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 840 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 1764 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 3528 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 2520 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} \log\left(x\right) - 1260 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 210 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 28 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{84 \, x^{4}}"," ",0,"1/84*(12*B*b^10*x^11 - 21*A*a^10 + 14*(10*B*a*b^9 + A*b^10)*x^10 + 84*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 315*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 840*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 1764*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 3528*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 2520*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4*log(x) - 1260*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 210*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 28*(B*a^10 + 10*A*a^9*b)*x)/x^4","A",0
153,1,245,0,1.399776," ","integrate((b*x+a)^10*(B*x+A)/x^6,x, algorithm=""fricas"")","\frac{10 \, B b^{10} x^{11} - 12 \, A a^{10} + 12 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 75 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 300 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 900 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 2520 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 2520 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} \log\left(x\right) - 1800 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 450 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 100 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 15 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{60 \, x^{5}}"," ",0,"1/60*(10*B*b^10*x^11 - 12*A*a^10 + 12*(10*B*a*b^9 + A*b^10)*x^10 + 75*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 300*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 900*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 2520*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 2520*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5*log(x) - 1800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 450*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 100*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 15*(B*a^10 + 10*A*a^9*b)*x)/x^5","A",0
154,1,245,0,1.247561," ","integrate((b*x+a)^10*(B*x+A)/x^7,x, algorithm=""fricas"")","\frac{12 \, B b^{10} x^{11} - 10 \, A a^{10} + 15 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 100 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 450 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 1800 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 2520 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} \log\left(x\right) - 2520 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 900 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 300 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 75 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 12 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{60 \, x^{6}}"," ",0,"1/60*(12*B*b^10*x^11 - 10*A*a^10 + 15*(10*B*a*b^9 + A*b^10)*x^10 + 100*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 1800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 2520*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6*log(x) - 2520*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 900*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 300*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 75*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 12*(B*a^10 + 10*A*a^9*b)*x)/x^6","A",0
155,1,245,0,1.658904," ","integrate((b*x+a)^10*(B*x+A)/x^8,x, algorithm=""fricas"")","\frac{21 \, B b^{10} x^{11} - 12 \, A a^{10} + 28 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 210 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 1260 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 2520 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} \log\left(x\right) - 3528 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} - 1764 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 840 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 315 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 84 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 14 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{84 \, x^{7}}"," ",0,"1/84*(21*B*b^10*x^11 - 12*A*a^10 + 28*(10*B*a*b^9 + A*b^10)*x^10 + 210*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 1260*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 2520*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7*log(x) - 3528*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 1764*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 840*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 315*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 84*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 14*(B*a^10 + 10*A*a^9*b)*x)/x^7","A",0
156,1,245,0,1.116892," ","integrate((b*x+a)^10*(B*x+A)/x^9,x, algorithm=""fricas"")","\frac{56 \, B b^{10} x^{11} - 21 \, A a^{10} + 84 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 840 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 2520 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} \log\left(x\right) - 5040 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} - 3528 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} - 2352 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 1260 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 504 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 140 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 24 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{168 \, x^{8}}"," ",0,"1/168*(56*B*b^10*x^11 - 21*A*a^10 + 84*(10*B*a*b^9 + A*b^10)*x^10 + 840*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 2520*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8*log(x) - 5040*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 3528*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 2352*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 1260*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 504*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 140*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 24*(B*a^10 + 10*A*a^9*b)*x)/x^8","A",0
157,1,245,0,1.479780," ","integrate((b*x+a)^10*(B*x+A)/x^10,x, algorithm=""fricas"")","\frac{252 \, B b^{10} x^{11} - 56 \, A a^{10} + 504 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 2520 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} \log\left(x\right) - 7560 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} - 7560 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} - 7056 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} - 5292 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 3024 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 1260 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 360 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 63 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{504 \, x^{9}}"," ",0,"1/504*(252*B*b^10*x^11 - 56*A*a^10 + 504*(10*B*a*b^9 + A*b^10)*x^10 + 2520*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9*log(x) - 7560*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 - 7560*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 7056*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 5292*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 3024*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 1260*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 360*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 63*(B*a^10 + 10*A*a^9*b)*x)/x^9","A",0
158,1,245,0,1.084980," ","integrate((b*x+a)^10*(B*x+A)/x^11,x, algorithm=""fricas"")","\frac{2520 \, B b^{10} x^{11} + 2520 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} \log\left(x\right) - 252 \, A a^{10} - 12600 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} - 18900 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} - 25200 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} - 26460 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} - 21168 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 12600 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 5400 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 1575 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 280 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{2520 \, x^{10}}"," ",0,"1/2520*(2520*B*b^10*x^11 + 2520*(10*B*a*b^9 + A*b^10)*x^10*log(x) - 252*A*a^10 - 12600*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 - 18900*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 - 25200*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 26460*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 21168*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 12600*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 5400*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 1575*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 280*(B*a^10 + 10*A*a^9*b)*x)/x^10","A",0
159,1,245,0,1.299409," ","integrate((b*x+a)^10*(B*x+A)/x^12,x, algorithm=""fricas"")","\frac{27720 \, B b^{10} x^{11} \log\left(x\right) - 2520 \, A a^{10} - 27720 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} - 69300 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} - 138600 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} - 207900 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} - 232848 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} - 194040 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} - 118800 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} - 51975 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} - 15400 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} - 2772 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{27720 \, x^{11}}"," ",0,"1/27720*(27720*B*b^10*x^11*log(x) - 2520*A*a^10 - 27720*(10*B*a*b^9 + A*b^10)*x^10 - 69300*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 - 138600*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 - 207900*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 - 232848*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 - 194040*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 - 118800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 - 51975*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 - 15400*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 - 2772*(B*a^10 + 10*A*a^9*b)*x)/x^11","A",0
160,1,243,0,0.975729," ","integrate((b*x+a)^10*(B*x+A)/x^13,x, algorithm=""fricas"")","-\frac{132 \, B b^{10} x^{11} + 11 \, A a^{10} + 66 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 220 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 495 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 792 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 924 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 792 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 495 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 220 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 66 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 12 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{132 \, x^{12}}"," ",0,"-1/132*(132*B*b^10*x^11 + 11*A*a^10 + 66*(10*B*a*b^9 + A*b^10)*x^10 + 220*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 495*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 792*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 924*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 792*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 495*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 220*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 66*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 12*(B*a^10 + 10*A*a^9*b)*x)/x^12","B",0
161,1,243,0,0.948154," ","integrate((b*x+a)^10*(B*x+A)/x^14,x, algorithm=""fricas"")","-\frac{858 \, B b^{10} x^{11} + 132 \, A a^{10} + 572 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 2145 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 5148 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 8580 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 10296 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 9009 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 5720 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 2574 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 780 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 143 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{1716 \, x^{13}}"," ",0,"-1/1716*(858*B*b^10*x^11 + 132*A*a^10 + 572*(10*B*a*b^9 + A*b^10)*x^10 + 2145*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 5148*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 8580*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 10296*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 9009*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 5720*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 2574*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 780*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 143*(B*a^10 + 10*A*a^9*b)*x)/x^13","B",0
162,1,243,0,1.078528," ","integrate((b*x+a)^10*(B*x+A)/x^15,x, algorithm=""fricas"")","-\frac{4004 \, B b^{10} x^{11} + 858 \, A a^{10} + 3003 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 12012 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 30030 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 51480 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 63063 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 56056 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 36036 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 16380 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 5005 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 924 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{12012 \, x^{14}}"," ",0,"-1/12012*(4004*B*b^10*x^11 + 858*A*a^10 + 3003*(10*B*a*b^9 + A*b^10)*x^10 + 12012*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 30030*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 51480*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 63063*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 56056*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 36036*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 16380*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 5005*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 924*(B*a^10 + 10*A*a^9*b)*x)/x^14","B",0
163,1,243,0,1.100232," ","integrate((b*x+a)^10*(B*x+A)/x^16,x, algorithm=""fricas"")","-\frac{15015 \, B b^{10} x^{11} + 4004 \, A a^{10} + 12012 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 50050 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 128700 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 225225 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 280280 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 252252 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 163800 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 75075 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 23100 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 4290 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{60060 \, x^{15}}"," ",0,"-1/60060*(15015*B*b^10*x^11 + 4004*A*a^10 + 12012*(10*B*a*b^9 + A*b^10)*x^10 + 50050*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 128700*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 225225*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 280280*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 252252*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 163800*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 75075*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 23100*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 4290*(B*a^10 + 10*A*a^9*b)*x)/x^15","B",0
164,1,243,0,1.147950," ","integrate((b*x+a)^10*(B*x+A)/x^17,x, algorithm=""fricas"")","-\frac{48048 \, B b^{10} x^{11} + 15015 \, A a^{10} + 40040 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 171600 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 450450 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 800800 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 1009008 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 917280 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 600600 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 277200 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 85800 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 16016 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{240240 \, x^{16}}"," ",0,"-1/240240*(48048*B*b^10*x^11 + 15015*A*a^10 + 40040*(10*B*a*b^9 + A*b^10)*x^10 + 171600*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 450450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 800800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 1009008*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 917280*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 600600*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 277200*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 85800*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 16016*(B*a^10 + 10*A*a^9*b)*x)/x^16","A",0
165,1,243,0,1.077886," ","integrate((b*x+a)^10*(B*x+A)/x^18,x, algorithm=""fricas"")","-\frac{136136 \, B b^{10} x^{11} + 48048 \, A a^{10} + 116688 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 510510 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 1361360 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 2450448 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 3118752 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 2858856 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 1884960 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 875160 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 272272 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 51051 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{816816 \, x^{17}}"," ",0,"-1/816816*(136136*B*b^10*x^11 + 48048*A*a^10 + 116688*(10*B*a*b^9 + A*b^10)*x^10 + 510510*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 1361360*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 2450448*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 3118752*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 2858856*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 1884960*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 875160*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 272272*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 51051*(B*a^10 + 10*A*a^9*b)*x)/x^17","A",0
166,1,243,0,1.167344," ","integrate((b*x+a)^10*(B*x+A)/x^19,x, algorithm=""fricas"")","-\frac{350064 \, B b^{10} x^{11} + 136136 \, A a^{10} + 306306 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 1361360 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 3675672 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 6683040 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 8576568 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 7916832 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 5250960 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 2450448 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 765765 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 144144 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{2450448 \, x^{18}}"," ",0,"-1/2450448*(350064*B*b^10*x^11 + 136136*A*a^10 + 306306*(10*B*a*b^9 + A*b^10)*x^10 + 1361360*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 3675672*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 6683040*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 8576568*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 7916832*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 5250960*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 2450448*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 765765*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 144144*(B*a^10 + 10*A*a^9*b)*x)/x^18","A",0
167,1,243,0,1.035715," ","integrate((b*x+a)^10*(B*x+A)/x^20,x, algorithm=""fricas"")","-\frac{831402 \, B b^{10} x^{11} + 350064 \, A a^{10} + 739024 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 3325608 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 9069840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 16628040 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 21488544 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 19953648 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 13302432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 6235515 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 1956240 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 369512 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{6651216 \, x^{19}}"," ",0,"-1/6651216*(831402*B*b^10*x^11 + 350064*A*a^10 + 739024*(10*B*a*b^9 + A*b^10)*x^10 + 3325608*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 9069840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 16628040*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 21488544*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 19953648*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 13302432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 6235515*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 1956240*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 369512*(B*a^10 + 10*A*a^9*b)*x)/x^19","A",0
168,1,243,0,0.861712," ","integrate((b*x+a)^10*(B*x+A)/x^21,x, algorithm=""fricas"")","-\frac{1847560 \, B b^{10} x^{11} + 831402 \, A a^{10} + 1662804 \, {\left(10 \, B a b^{9} + A b^{10}\right)} x^{10} + 7558200 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} x^{9} + 20785050 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} x^{8} + 38372400 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} x^{7} + 49884120 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} x^{6} + 46558512 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} x^{5} + 31177575 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} x^{4} + 14671800 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} x^{3} + 4618900 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} x^{2} + 875160 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} x}{16628040 \, x^{20}}"," ",0,"-1/16628040*(1847560*B*b^10*x^11 + 831402*A*a^10 + 1662804*(10*B*a*b^9 + A*b^10)*x^10 + 7558200*(9*B*a^2*b^8 + 2*A*a*b^9)*x^9 + 20785050*(8*B*a^3*b^7 + 3*A*a^2*b^8)*x^8 + 38372400*(7*B*a^4*b^6 + 4*A*a^3*b^7)*x^7 + 49884120*(6*B*a^5*b^5 + 5*A*a^4*b^6)*x^6 + 46558512*(5*B*a^6*b^4 + 6*A*a^5*b^5)*x^5 + 31177575*(4*B*a^7*b^3 + 7*A*a^6*b^4)*x^4 + 14671800*(3*B*a^8*b^2 + 8*A*a^7*b^3)*x^3 + 4618900*(2*B*a^9*b + 9*A*a^8*b^2)*x^2 + 875160*(B*a^10 + 10*A*a^9*b)*x)/x^20","A",0
169,1,389,0,0.912653," ","integrate(x^3*(b*x+a)*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{21} x^{21} d^{16} b + \frac{4}{5} x^{20} d^{15} c b + \frac{1}{20} x^{20} d^{16} a + \frac{120}{19} x^{19} d^{14} c^{2} b + \frac{16}{19} x^{19} d^{15} c a + \frac{280}{9} x^{18} d^{13} c^{3} b + \frac{20}{3} x^{18} d^{14} c^{2} a + \frac{1820}{17} x^{17} d^{12} c^{4} b + \frac{560}{17} x^{17} d^{13} c^{3} a + 273 x^{16} d^{11} c^{5} b + \frac{455}{4} x^{16} d^{12} c^{4} a + \frac{8008}{15} x^{15} d^{10} c^{6} b + \frac{1456}{5} x^{15} d^{11} c^{5} a + \frac{5720}{7} x^{14} d^{9} c^{7} b + 572 x^{14} d^{10} c^{6} a + 990 x^{13} d^{8} c^{8} b + 880 x^{13} d^{9} c^{7} a + \frac{2860}{3} x^{12} d^{7} c^{9} b + \frac{2145}{2} x^{12} d^{8} c^{8} a + 728 x^{11} d^{6} c^{10} b + 1040 x^{11} d^{7} c^{9} a + \frac{2184}{5} x^{10} d^{5} c^{11} b + \frac{4004}{5} x^{10} d^{6} c^{10} a + \frac{1820}{9} x^{9} d^{4} c^{12} b + \frac{1456}{3} x^{9} d^{5} c^{11} a + 70 x^{8} d^{3} c^{13} b + \frac{455}{2} x^{8} d^{4} c^{12} a + \frac{120}{7} x^{7} d^{2} c^{14} b + 80 x^{7} d^{3} c^{13} a + \frac{8}{3} x^{6} d c^{15} b + 20 x^{6} d^{2} c^{14} a + \frac{1}{5} x^{5} c^{16} b + \frac{16}{5} x^{5} d c^{15} a + \frac{1}{4} x^{4} c^{16} a"," ",0,"1/21*x^21*d^16*b + 4/5*x^20*d^15*c*b + 1/20*x^20*d^16*a + 120/19*x^19*d^14*c^2*b + 16/19*x^19*d^15*c*a + 280/9*x^18*d^13*c^3*b + 20/3*x^18*d^14*c^2*a + 1820/17*x^17*d^12*c^4*b + 560/17*x^17*d^13*c^3*a + 273*x^16*d^11*c^5*b + 455/4*x^16*d^12*c^4*a + 8008/15*x^15*d^10*c^6*b + 1456/5*x^15*d^11*c^5*a + 5720/7*x^14*d^9*c^7*b + 572*x^14*d^10*c^6*a + 990*x^13*d^8*c^8*b + 880*x^13*d^9*c^7*a + 2860/3*x^12*d^7*c^9*b + 2145/2*x^12*d^8*c^8*a + 728*x^11*d^6*c^10*b + 1040*x^11*d^7*c^9*a + 2184/5*x^10*d^5*c^11*b + 4004/5*x^10*d^6*c^10*a + 1820/9*x^9*d^4*c^12*b + 1456/3*x^9*d^5*c^11*a + 70*x^8*d^3*c^13*b + 455/2*x^8*d^4*c^12*a + 120/7*x^7*d^2*c^14*b + 80*x^7*d^3*c^13*a + 8/3*x^6*d*c^15*b + 20*x^6*d^2*c^14*a + 1/5*x^5*c^16*b + 16/5*x^5*d*c^15*a + 1/4*x^4*c^16*a","B",0
170,1,389,0,0.836564," ","integrate(x^2*(b*x+a)*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{20} x^{20} d^{16} b + \frac{16}{19} x^{19} d^{15} c b + \frac{1}{19} x^{19} d^{16} a + \frac{20}{3} x^{18} d^{14} c^{2} b + \frac{8}{9} x^{18} d^{15} c a + \frac{560}{17} x^{17} d^{13} c^{3} b + \frac{120}{17} x^{17} d^{14} c^{2} a + \frac{455}{4} x^{16} d^{12} c^{4} b + 35 x^{16} d^{13} c^{3} a + \frac{1456}{5} x^{15} d^{11} c^{5} b + \frac{364}{3} x^{15} d^{12} c^{4} a + 572 x^{14} d^{10} c^{6} b + 312 x^{14} d^{11} c^{5} a + 880 x^{13} d^{9} c^{7} b + 616 x^{13} d^{10} c^{6} a + \frac{2145}{2} x^{12} d^{8} c^{8} b + \frac{2860}{3} x^{12} d^{9} c^{7} a + 1040 x^{11} d^{7} c^{9} b + 1170 x^{11} d^{8} c^{8} a + \frac{4004}{5} x^{10} d^{6} c^{10} b + 1144 x^{10} d^{7} c^{9} a + \frac{1456}{3} x^{9} d^{5} c^{11} b + \frac{8008}{9} x^{9} d^{6} c^{10} a + \frac{455}{2} x^{8} d^{4} c^{12} b + 546 x^{8} d^{5} c^{11} a + 80 x^{7} d^{3} c^{13} b + 260 x^{7} d^{4} c^{12} a + 20 x^{6} d^{2} c^{14} b + \frac{280}{3} x^{6} d^{3} c^{13} a + \frac{16}{5} x^{5} d c^{15} b + 24 x^{5} d^{2} c^{14} a + \frac{1}{4} x^{4} c^{16} b + 4 x^{4} d c^{15} a + \frac{1}{3} x^{3} c^{16} a"," ",0,"1/20*x^20*d^16*b + 16/19*x^19*d^15*c*b + 1/19*x^19*d^16*a + 20/3*x^18*d^14*c^2*b + 8/9*x^18*d^15*c*a + 560/17*x^17*d^13*c^3*b + 120/17*x^17*d^14*c^2*a + 455/4*x^16*d^12*c^4*b + 35*x^16*d^13*c^3*a + 1456/5*x^15*d^11*c^5*b + 364/3*x^15*d^12*c^4*a + 572*x^14*d^10*c^6*b + 312*x^14*d^11*c^5*a + 880*x^13*d^9*c^7*b + 616*x^13*d^10*c^6*a + 2145/2*x^12*d^8*c^8*b + 2860/3*x^12*d^9*c^7*a + 1040*x^11*d^7*c^9*b + 1170*x^11*d^8*c^8*a + 4004/5*x^10*d^6*c^10*b + 1144*x^10*d^7*c^9*a + 1456/3*x^9*d^5*c^11*b + 8008/9*x^9*d^6*c^10*a + 455/2*x^8*d^4*c^12*b + 546*x^8*d^5*c^11*a + 80*x^7*d^3*c^13*b + 260*x^7*d^4*c^12*a + 20*x^6*d^2*c^14*b + 280/3*x^6*d^3*c^13*a + 16/5*x^5*d*c^15*b + 24*x^5*d^2*c^14*a + 1/4*x^4*c^16*b + 4*x^4*d*c^15*a + 1/3*x^3*c^16*a","B",0
171,1,389,0,0.855822," ","integrate(x*(b*x+a)*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{19} x^{19} d^{16} b + \frac{8}{9} x^{18} d^{15} c b + \frac{1}{18} x^{18} d^{16} a + \frac{120}{17} x^{17} d^{14} c^{2} b + \frac{16}{17} x^{17} d^{15} c a + 35 x^{16} d^{13} c^{3} b + \frac{15}{2} x^{16} d^{14} c^{2} a + \frac{364}{3} x^{15} d^{12} c^{4} b + \frac{112}{3} x^{15} d^{13} c^{3} a + 312 x^{14} d^{11} c^{5} b + 130 x^{14} d^{12} c^{4} a + 616 x^{13} d^{10} c^{6} b + 336 x^{13} d^{11} c^{5} a + \frac{2860}{3} x^{12} d^{9} c^{7} b + \frac{2002}{3} x^{12} d^{10} c^{6} a + 1170 x^{11} d^{8} c^{8} b + 1040 x^{11} d^{9} c^{7} a + 1144 x^{10} d^{7} c^{9} b + 1287 x^{10} d^{8} c^{8} a + \frac{8008}{9} x^{9} d^{6} c^{10} b + \frac{11440}{9} x^{9} d^{7} c^{9} a + 546 x^{8} d^{5} c^{11} b + 1001 x^{8} d^{6} c^{10} a + 260 x^{7} d^{4} c^{12} b + 624 x^{7} d^{5} c^{11} a + \frac{280}{3} x^{6} d^{3} c^{13} b + \frac{910}{3} x^{6} d^{4} c^{12} a + 24 x^{5} d^{2} c^{14} b + 112 x^{5} d^{3} c^{13} a + 4 x^{4} d c^{15} b + 30 x^{4} d^{2} c^{14} a + \frac{1}{3} x^{3} c^{16} b + \frac{16}{3} x^{3} d c^{15} a + \frac{1}{2} x^{2} c^{16} a"," ",0,"1/19*x^19*d^16*b + 8/9*x^18*d^15*c*b + 1/18*x^18*d^16*a + 120/17*x^17*d^14*c^2*b + 16/17*x^17*d^15*c*a + 35*x^16*d^13*c^3*b + 15/2*x^16*d^14*c^2*a + 364/3*x^15*d^12*c^4*b + 112/3*x^15*d^13*c^3*a + 312*x^14*d^11*c^5*b + 130*x^14*d^12*c^4*a + 616*x^13*d^10*c^6*b + 336*x^13*d^11*c^5*a + 2860/3*x^12*d^9*c^7*b + 2002/3*x^12*d^10*c^6*a + 1170*x^11*d^8*c^8*b + 1040*x^11*d^9*c^7*a + 1144*x^10*d^7*c^9*b + 1287*x^10*d^8*c^8*a + 8008/9*x^9*d^6*c^10*b + 11440/9*x^9*d^7*c^9*a + 546*x^8*d^5*c^11*b + 1001*x^8*d^6*c^10*a + 260*x^7*d^4*c^12*b + 624*x^7*d^5*c^11*a + 280/3*x^6*d^3*c^13*b + 910/3*x^6*d^4*c^12*a + 24*x^5*d^2*c^14*b + 112*x^5*d^3*c^13*a + 4*x^4*d*c^15*b + 30*x^4*d^2*c^14*a + 1/3*x^3*c^16*b + 16/3*x^3*d*c^15*a + 1/2*x^2*c^16*a","B",0
172,1,385,0,1.120014," ","integrate((b*x+a)*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{18} x^{18} d^{16} b + \frac{16}{17} x^{17} d^{15} c b + \frac{1}{17} x^{17} d^{16} a + \frac{15}{2} x^{16} d^{14} c^{2} b + x^{16} d^{15} c a + \frac{112}{3} x^{15} d^{13} c^{3} b + 8 x^{15} d^{14} c^{2} a + 130 x^{14} d^{12} c^{4} b + 40 x^{14} d^{13} c^{3} a + 336 x^{13} d^{11} c^{5} b + 140 x^{13} d^{12} c^{4} a + \frac{2002}{3} x^{12} d^{10} c^{6} b + 364 x^{12} d^{11} c^{5} a + 1040 x^{11} d^{9} c^{7} b + 728 x^{11} d^{10} c^{6} a + 1287 x^{10} d^{8} c^{8} b + 1144 x^{10} d^{9} c^{7} a + \frac{11440}{9} x^{9} d^{7} c^{9} b + 1430 x^{9} d^{8} c^{8} a + 1001 x^{8} d^{6} c^{10} b + 1430 x^{8} d^{7} c^{9} a + 624 x^{7} d^{5} c^{11} b + 1144 x^{7} d^{6} c^{10} a + \frac{910}{3} x^{6} d^{4} c^{12} b + 728 x^{6} d^{5} c^{11} a + 112 x^{5} d^{3} c^{13} b + 364 x^{5} d^{4} c^{12} a + 30 x^{4} d^{2} c^{14} b + 140 x^{4} d^{3} c^{13} a + \frac{16}{3} x^{3} d c^{15} b + 40 x^{3} d^{2} c^{14} a + \frac{1}{2} x^{2} c^{16} b + 8 x^{2} d c^{15} a + x c^{16} a"," ",0,"1/18*x^18*d^16*b + 16/17*x^17*d^15*c*b + 1/17*x^17*d^16*a + 15/2*x^16*d^14*c^2*b + x^16*d^15*c*a + 112/3*x^15*d^13*c^3*b + 8*x^15*d^14*c^2*a + 130*x^14*d^12*c^4*b + 40*x^14*d^13*c^3*a + 336*x^13*d^11*c^5*b + 140*x^13*d^12*c^4*a + 2002/3*x^12*d^10*c^6*b + 364*x^12*d^11*c^5*a + 1040*x^11*d^9*c^7*b + 728*x^11*d^10*c^6*a + 1287*x^10*d^8*c^8*b + 1144*x^10*d^9*c^7*a + 11440/9*x^9*d^7*c^9*b + 1430*x^9*d^8*c^8*a + 1001*x^8*d^6*c^10*b + 1430*x^8*d^7*c^9*a + 624*x^7*d^5*c^11*b + 1144*x^7*d^6*c^10*a + 910/3*x^6*d^4*c^12*b + 728*x^6*d^5*c^11*a + 112*x^5*d^3*c^13*b + 364*x^5*d^4*c^12*a + 30*x^4*d^2*c^14*b + 140*x^4*d^3*c^13*a + 16/3*x^3*d*c^15*b + 40*x^3*d^2*c^14*a + 1/2*x^2*c^16*b + 8*x^2*d*c^15*a + x*c^16*a","B",0
173,1,36,0,1.271821," ","integrate(x^2*(2+x)^5*(2+3*x),x, algorithm=""fricas"")","\frac{1}{3} x^{9} + 4 x^{8} + 20 x^{7} + \frac{160}{3} x^{6} + 80 x^{5} + 64 x^{4} + \frac{64}{3} x^{3}"," ",0,"1/3*x^9 + 4*x^8 + 20*x^7 + 160/3*x^6 + 80*x^5 + 64*x^4 + 64/3*x^3","B",0
174,1,117,0,1.443484," ","integrate(x^4*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{12 \, B b^{5} x^{5} - 15 \, {\left(B a b^{4} - A b^{5}\right)} x^{4} + 20 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} x^{3} - 30 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{2} + 60 \, {\left(B a^{4} b - A a^{3} b^{2}\right)} x - 60 \, {\left(B a^{5} - A a^{4} b\right)} \log\left(b x + a\right)}{60 \, b^{6}}"," ",0,"1/60*(12*B*b^5*x^5 - 15*(B*a*b^4 - A*b^5)*x^4 + 20*(B*a^2*b^3 - A*a*b^4)*x^3 - 30*(B*a^3*b^2 - A*a^2*b^3)*x^2 + 60*(B*a^4*b - A*a^3*b^2)*x - 60*(B*a^5 - A*a^4*b)*log(b*x + a))/b^6","A",0
175,1,94,0,1.339504," ","integrate(x^3*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{3 \, B b^{4} x^{4} - 4 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 12 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x + 12 \, {\left(B a^{4} - A a^{3} b\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*B*b^4*x^4 - 4*(B*a*b^3 - A*b^4)*x^3 + 6*(B*a^2*b^2 - A*a*b^3)*x^2 - 12*(B*a^3*b - A*a^2*b^2)*x + 12*(B*a^4 - A*a^3*b)*log(b*x + a))/b^5","A",0
176,1,71,0,1.097774," ","integrate(x^2*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{3} - 3 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 6 \, {\left(B a^{2} b - A a b^{2}\right)} x - 6 \, {\left(B a^{3} - A a^{2} b\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*B*b^3*x^3 - 3*(B*a*b^2 - A*b^3)*x^2 + 6*(B*a^2*b - A*a*b^2)*x - 6*(B*a^3 - A*a^2*b)*log(b*x + a))/b^4","A",0
177,1,47,0,0.743531," ","integrate(x*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{B b^{2} x^{2} - 2 \, {\left(B a b - A b^{2}\right)} x + 2 \, {\left(B a^{2} - A a b\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(B*b^2*x^2 - 2*(B*a*b - A*b^2)*x + 2*(B*a^2 - A*a*b)*log(b*x + a))/b^3","A",0
178,1,25,0,1.061328," ","integrate((B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{B b x - {\left(B a - A b\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(B*b*x - (B*a - A*b)*log(b*x + a))/b^2","A",0
179,1,28,0,1.103001," ","integrate((B*x+A)/x/(b*x+a),x, algorithm=""fricas"")","\frac{A b \log\left(x\right) + {\left(B a - A b\right)} \log\left(b x + a\right)}{a b}"," ",0,"(A*b*log(x) + (B*a - A*b)*log(b*x + a))/(a*b)","A",0
180,1,41,0,1.416430," ","integrate((B*x+A)/x^2/(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} x \log\left(b x + a\right) - {\left(B a - A b\right)} x \log\left(x\right) + A a}{a^{2} x}"," ",0,"-((B*a - A*b)*x*log(b*x + a) - (B*a - A*b)*x*log(x) + A*a)/(a^2*x)","A",0
181,1,69,0,1.369066," ","integrate((B*x+A)/x^3/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(B a b - A b^{2}\right)} x^{2} \log\left(b x + a\right) - 2 \, {\left(B a b - A b^{2}\right)} x^{2} \log\left(x\right) - A a^{2} - 2 \, {\left(B a^{2} - A a b\right)} x}{2 \, a^{3} x^{2}}"," ",0,"1/2*(2*(B*a*b - A*b^2)*x^2*log(b*x + a) - 2*(B*a*b - A*b^2)*x^2*log(x) - A*a^2 - 2*(B*a^2 - A*a*b)*x)/(a^3*x^2)","A",0
182,1,94,0,1.410904," ","integrate((B*x+A)/x^4/(b*x+a),x, algorithm=""fricas"")","-\frac{6 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} \log\left(b x + a\right) - 6 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} \log\left(x\right) + 2 \, A a^{3} - 6 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 3 \, {\left(B a^{3} - A a^{2} b\right)} x}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(6*(B*a*b^2 - A*b^3)*x^3*log(b*x + a) - 6*(B*a*b^2 - A*b^3)*x^3*log(x) + 2*A*a^3 - 6*(B*a^2*b - A*a*b^2)*x^2 + 3*(B*a^3 - A*a^2*b)*x)/(a^4*x^3)","A",0
183,1,117,0,1.329214," ","integrate((B*x+A)/x^5/(b*x+a),x, algorithm=""fricas"")","\frac{12 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} \log\left(b x + a\right) - 12 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} \log\left(x\right) - 3 \, A a^{4} - 12 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{3} + 6 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x^{2} - 4 \, {\left(B a^{4} - A a^{3} b\right)} x}{12 \, a^{5} x^{4}}"," ",0,"1/12*(12*(B*a*b^3 - A*b^4)*x^4*log(b*x + a) - 12*(B*a*b^3 - A*b^4)*x^4*log(x) - 3*A*a^4 - 12*(B*a^2*b^2 - A*a*b^3)*x^3 + 6*(B*a^3*b - A*a^2*b^2)*x^2 - 4*(B*a^4 - A*a^3*b)*x)/(a^5*x^4)","A",0
184,1,164,0,1.220037," ","integrate(x^4*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{5} x^{5} + 12 \, B a^{5} - 12 \, A a^{4} b - {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} x^{4} + 2 \, {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{3} - 6 \, {\left(5 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} x^{2} - 12 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x + 12 \, {\left(5 \, B a^{5} - 4 \, A a^{4} b + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*B*b^5*x^5 + 12*B*a^5 - 12*A*a^4*b - (5*B*a*b^4 - 4*A*b^5)*x^4 + 2*(5*B*a^2*b^3 - 4*A*a*b^4)*x^3 - 6*(5*B*a^3*b^2 - 4*A*a^2*b^3)*x^2 - 12*(4*B*a^4*b - 3*A*a^3*b^2)*x + 12*(5*B*a^5 - 4*A*a^4*b + (5*B*a^4*b - 4*A*a^3*b^2)*x)*log(b*x + a))/(b^7*x + a*b^6)","A",0
185,1,140,0,0.727206," ","integrate(x^3*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{4} x^{4} - 6 \, B a^{4} + 6 \, A a^{3} b - {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} x^{3} + 3 \, {\left(4 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{2} + 6 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} x - 6 \, {\left(4 \, B a^{4} - 3 \, A a^{3} b + {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/6*(2*B*b^4*x^4 - 6*B*a^4 + 6*A*a^3*b - (4*B*a*b^3 - 3*A*b^4)*x^3 + 3*(4*B*a^2*b^2 - 3*A*a*b^3)*x^2 + 6*(3*B*a^3*b - 2*A*a^2*b^2)*x - 6*(4*B*a^4 - 3*A*a^3*b + (4*B*a^3*b - 3*A*a^2*b^2)*x)*log(b*x + a))/(b^6*x + a*b^5)","A",0
186,1,113,0,1.349027," ","integrate(x^2*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B b^{3} x^{3} + 2 \, B a^{3} - 2 \, A a^{2} b - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} x^{2} - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x + 2 \, {\left(3 \, B a^{3} - 2 \, A a^{2} b + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(B*b^3*x^3 + 2*B*a^3 - 2*A*a^2*b - (3*B*a*b^2 - 2*A*b^3)*x^2 - 2*(2*B*a^2*b - A*a*b^2)*x + 2*(3*B*a^3 - 2*A*a^2*b + (3*B*a^2*b - 2*A*a*b^2)*x)*log(b*x + a))/(b^5*x + a*b^4)","A",0
187,1,72,0,1.415130," ","integrate(x*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B b^{2} x^{2} + B a b x - B a^{2} + A a b - {\left(2 \, B a^{2} - A a b + {\left(2 \, B a b - A b^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(B*b^2*x^2 + B*a*b*x - B*a^2 + A*a*b - (2*B*a^2 - A*a*b + (2*B*a*b - A*b^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
188,1,37,0,1.143808," ","integrate((B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x + B a\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"(B*a - A*b + (B*b*x + B*a)*log(b*x + a))/(b^3*x + a*b^2)","A",0
189,1,62,0,1.413332," ","integrate((B*x+A)/x/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{B a^{2} - A a b + {\left(A b^{2} x + A a b\right)} \log\left(b x + a\right) - {\left(A b^{2} x + A a b\right)} \log\left(x\right)}{a^{2} b^{2} x + a^{3} b}"," ",0,"-(B*a^2 - A*a*b + (A*b^2*x + A*a*b)*log(b*x + a) - (A*b^2*x + A*a*b)*log(x))/(a^2*b^2*x + a^3*b)","A",0
190,1,107,0,1.241664," ","integrate((B*x+A)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{A a^{2} - {\left(B a^{2} - 2 \, A a b\right)} x + {\left({\left(B a b - 2 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 2 \, A a b\right)} x\right)} \log\left(b x + a\right) - {\left({\left(B a b - 2 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 2 \, A a b\right)} x\right)} \log\left(x\right)}{a^{3} b x^{2} + a^{4} x}"," ",0,"-(A*a^2 - (B*a^2 - 2*A*a*b)*x + ((B*a*b - 2*A*b^2)*x^2 + (B*a^2 - 2*A*a*b)*x)*log(b*x + a) - ((B*a*b - 2*A*b^2)*x^2 + (B*a^2 - 2*A*a*b)*x)*log(x))/(a^3*b*x^2 + a^4*x)","A",0
191,1,150,0,1.161928," ","integrate((B*x+A)/x^3/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{A a^{3} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} x - 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} x^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}"," ",0,"-1/2*(A*a^3 + 2*(2*B*a^2*b - 3*A*a*b^2)*x^2 + (2*B*a^3 - 3*A*a^2*b)*x - 2*((2*B*a*b^2 - 3*A*b^3)*x^3 + (2*B*a^2*b - 3*A*a*b^2)*x^2)*log(b*x + a) + 2*((2*B*a*b^2 - 3*A*b^3)*x^3 + (2*B*a^2*b - 3*A*a*b^2)*x^2)*log(x))/(a^4*b*x^3 + a^5*x^2)","A",0
192,1,179,0,0.716209," ","integrate((B*x+A)/x^4/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, A a^{4} - 6 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} - 3 \, {\left(3 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x^{2} + {\left(3 \, B a^{4} - 4 \, A a^{3} b\right)} x + 6 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3}\right)} \log\left(b x + a\right) - 6 \, {\left({\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} x^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}"," ",0,"-1/6*(2*A*a^4 - 6*(3*B*a^2*b^2 - 4*A*a*b^3)*x^3 - 3*(3*B*a^3*b - 4*A*a^2*b^2)*x^2 + (3*B*a^4 - 4*A*a^3*b)*x + 6*((3*B*a*b^3 - 4*A*b^4)*x^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^3)*log(b*x + a) - 6*((3*B*a*b^3 - 4*A*b^4)*x^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*x^3)*log(x))/(a^5*b*x^4 + a^6*x^3)","A",0
193,1,197,0,1.034843," ","integrate(x^4*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{5} x^{5} - 27 \, B a^{5} + 21 \, A a^{4} b - {\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} x^{4} + 4 \, {\left(5 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{3} + 3 \, {\left(21 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{2} + 6 \, {\left(B a^{4} b + A a^{3} b^{2}\right)} x - 12 \, {\left(5 \, B a^{5} - 3 \, A a^{4} b + {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"1/6*(2*B*b^5*x^5 - 27*B*a^5 + 21*A*a^4*b - (5*B*a*b^4 - 3*A*b^5)*x^4 + 4*(5*B*a^2*b^3 - 3*A*a*b^4)*x^3 + 3*(21*B*a^3*b^2 - 11*A*a^2*b^3)*x^2 + 6*(B*a^4*b + A*a^3*b^2)*x - 12*(5*B*a^5 - 3*A*a^4*b + (5*B*a^3*b^2 - 3*A*a^2*b^3)*x^2 + 2*(5*B*a^4*b - 3*A*a^3*b^2)*x)*log(b*x + a))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","A",0
194,1,171,0,1.303068," ","integrate(x^3*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{B b^{4} x^{4} + 7 \, B a^{4} - 5 \, A a^{3} b - 2 \, {\left(2 \, B a b^{3} - A b^{4}\right)} x^{3} - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{2} + 2 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x + 6 \, {\left(2 \, B a^{4} - A a^{3} b + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} x^{2} + 2 \, {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(B*b^4*x^4 + 7*B*a^4 - 5*A*a^3*b - 2*(2*B*a*b^3 - A*b^4)*x^3 - (11*B*a^2*b^2 - 4*A*a*b^3)*x^2 + 2*(B*a^3*b - 2*A*a^2*b^2)*x + 6*(2*B*a^4 - A*a^3*b + (2*B*a^2*b^2 - A*a*b^3)*x^2 + 2*(2*B*a^3*b - A*a^2*b^2)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
195,1,134,0,1.127421," ","integrate(x^2*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{3} x^{3} + 4 \, B a b^{2} x^{2} - 5 \, B a^{3} + 3 \, A a^{2} b - 4 \, {\left(B a^{2} b - A a b^{2}\right)} x - 2 \, {\left(3 \, B a^{3} - A a^{2} b + {\left(3 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*B*b^3*x^3 + 4*B*a*b^2*x^2 - 5*B*a^3 + 3*A*a^2*b - 4*(B*a^2*b - A*a*b^2)*x - 2*(3*B*a^3 - A*a^2*b + (3*B*a*b^2 - A*b^3)*x^2 + 2*(3*B*a^2*b - A*a*b^2)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
196,1,81,0,1.307567," ","integrate(x*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, B a^{2} - A a b + 2 \, {\left(2 \, B a b - A b^{2}\right)} x + 2 \, {\left(B b^{2} x^{2} + 2 \, B a b x + B a^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"1/2*(3*B*a^2 - A*a*b + 2*(2*B*a*b - A*b^2)*x + 2*(B*b^2*x^2 + 2*B*a*b*x + B*a^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
197,1,38,0,1.296850," ","integrate((B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, B b x + B a + A b}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*B*b*x + B*a + A*b)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
198,1,109,0,1.176588," ","integrate((B*x+A)/x/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, A a b^{2} x - B a^{3} + 3 \, A a^{2} b - 2 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \log\left(b x + a\right) + 2 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"1/2*(2*A*a*b^2*x - B*a^3 + 3*A*a^2*b - 2*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*log(b*x + a) + 2*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*log(x))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b)","A",0
199,1,187,0,1.034162," ","integrate((B*x+A)/x^2/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, A a^{3} - 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} - 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} x + 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(B a b^{2} - 3 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}"," ",0,"-1/2*(2*A*a^3 - 2*(B*a^2*b - 3*A*a*b^2)*x^2 - 3*(B*a^3 - 3*A*a^2*b)*x + 2*((B*a*b^2 - 3*A*b^3)*x^3 + 2*(B*a^2*b - 3*A*a*b^2)*x^2 + (B*a^3 - 3*A*a^2*b)*x)*log(b*x + a) - 2*((B*a*b^2 - 3*A*b^3)*x^3 + 2*(B*a^2*b - 3*A*a*b^2)*x^2 + (B*a^3 - 3*A*a^2*b)*x)*log(x))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)","B",0
200,1,225,0,1.256602," ","integrate((B*x+A)/x^3/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{A a^{4} + 6 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + 9 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2} + 2 \, {\left(B a^{4} - 2 \, A a^{3} b\right)} x - 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{4} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + 6 \, {\left({\left(B a b^{3} - 2 \, A b^{4}\right)} x^{4} + 2 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"-1/2*(A*a^4 + 6*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + 9*(B*a^3*b - 2*A*a^2*b^2)*x^2 + 2*(B*a^4 - 2*A*a^3*b)*x - 6*((B*a*b^3 - 2*A*b^4)*x^4 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + (B*a^3*b - 2*A*a^2*b^2)*x^2)*log(b*x + a) + 6*((B*a*b^3 - 2*A*b^4)*x^4 + 2*(B*a^2*b^2 - 2*A*a*b^3)*x^3 + (B*a^3*b - 2*A*a^2*b^2)*x^2)*log(x))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","B",0
201,1,262,0,1.231611," ","integrate((B*x+A)/x^4/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, A a^{5} - 12 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} - 18 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3} - 4 \, {\left(3 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} x^{2} + {\left(3 \, B a^{5} - 5 \, A a^{4} b\right)} x + 12 \, {\left({\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3}\right)} \log\left(b x + a\right) - 12 \, {\left({\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} x^{5} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} x^{4} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}"," ",0,"-1/6*(2*A*a^5 - 12*(3*B*a^2*b^3 - 5*A*a*b^4)*x^4 - 18*(3*B*a^3*b^2 - 5*A*a^2*b^3)*x^3 - 4*(3*B*a^4*b - 5*A*a^3*b^2)*x^2 + (3*B*a^5 - 5*A*a^4*b)*x + 12*((3*B*a*b^4 - 5*A*b^5)*x^5 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*x^4 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*x^3)*log(b*x + a) - 12*((3*B*a*b^4 - 5*A*b^5)*x^5 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*x^4 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*x^3)*log(x))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3)","A",0
202,1,668,0,0.993885," ","integrate(x^3*(b*x+a)^2*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{22} x^{22} d^{16} b^{2} + \frac{16}{21} x^{21} d^{15} c b^{2} + \frac{2}{21} x^{21} d^{16} b a + 6 x^{20} d^{14} c^{2} b^{2} + \frac{8}{5} x^{20} d^{15} c b a + \frac{1}{20} x^{20} d^{16} a^{2} + \frac{560}{19} x^{19} d^{13} c^{3} b^{2} + \frac{240}{19} x^{19} d^{14} c^{2} b a + \frac{16}{19} x^{19} d^{15} c a^{2} + \frac{910}{9} x^{18} d^{12} c^{4} b^{2} + \frac{560}{9} x^{18} d^{13} c^{3} b a + \frac{20}{3} x^{18} d^{14} c^{2} a^{2} + \frac{4368}{17} x^{17} d^{11} c^{5} b^{2} + \frac{3640}{17} x^{17} d^{12} c^{4} b a + \frac{560}{17} x^{17} d^{13} c^{3} a^{2} + \frac{1001}{2} x^{16} d^{10} c^{6} b^{2} + 546 x^{16} d^{11} c^{5} b a + \frac{455}{4} x^{16} d^{12} c^{4} a^{2} + \frac{2288}{3} x^{15} d^{9} c^{7} b^{2} + \frac{16016}{15} x^{15} d^{10} c^{6} b a + \frac{1456}{5} x^{15} d^{11} c^{5} a^{2} + \frac{6435}{7} x^{14} d^{8} c^{8} b^{2} + \frac{11440}{7} x^{14} d^{9} c^{7} b a + 572 x^{14} d^{10} c^{6} a^{2} + 880 x^{13} d^{7} c^{9} b^{2} + 1980 x^{13} d^{8} c^{8} b a + 880 x^{13} d^{9} c^{7} a^{2} + \frac{2002}{3} x^{12} d^{6} c^{10} b^{2} + \frac{5720}{3} x^{12} d^{7} c^{9} b a + \frac{2145}{2} x^{12} d^{8} c^{8} a^{2} + \frac{4368}{11} x^{11} d^{5} c^{11} b^{2} + 1456 x^{11} d^{6} c^{10} b a + 1040 x^{11} d^{7} c^{9} a^{2} + 182 x^{10} d^{4} c^{12} b^{2} + \frac{4368}{5} x^{10} d^{5} c^{11} b a + \frac{4004}{5} x^{10} d^{6} c^{10} a^{2} + \frac{560}{9} x^{9} d^{3} c^{13} b^{2} + \frac{3640}{9} x^{9} d^{4} c^{12} b a + \frac{1456}{3} x^{9} d^{5} c^{11} a^{2} + 15 x^{8} d^{2} c^{14} b^{2} + 140 x^{8} d^{3} c^{13} b a + \frac{455}{2} x^{8} d^{4} c^{12} a^{2} + \frac{16}{7} x^{7} d c^{15} b^{2} + \frac{240}{7} x^{7} d^{2} c^{14} b a + 80 x^{7} d^{3} c^{13} a^{2} + \frac{1}{6} x^{6} c^{16} b^{2} + \frac{16}{3} x^{6} d c^{15} b a + 20 x^{6} d^{2} c^{14} a^{2} + \frac{2}{5} x^{5} c^{16} b a + \frac{16}{5} x^{5} d c^{15} a^{2} + \frac{1}{4} x^{4} c^{16} a^{2}"," ",0,"1/22*x^22*d^16*b^2 + 16/21*x^21*d^15*c*b^2 + 2/21*x^21*d^16*b*a + 6*x^20*d^14*c^2*b^2 + 8/5*x^20*d^15*c*b*a + 1/20*x^20*d^16*a^2 + 560/19*x^19*d^13*c^3*b^2 + 240/19*x^19*d^14*c^2*b*a + 16/19*x^19*d^15*c*a^2 + 910/9*x^18*d^12*c^4*b^2 + 560/9*x^18*d^13*c^3*b*a + 20/3*x^18*d^14*c^2*a^2 + 4368/17*x^17*d^11*c^5*b^2 + 3640/17*x^17*d^12*c^4*b*a + 560/17*x^17*d^13*c^3*a^2 + 1001/2*x^16*d^10*c^6*b^2 + 546*x^16*d^11*c^5*b*a + 455/4*x^16*d^12*c^4*a^2 + 2288/3*x^15*d^9*c^7*b^2 + 16016/15*x^15*d^10*c^6*b*a + 1456/5*x^15*d^11*c^5*a^2 + 6435/7*x^14*d^8*c^8*b^2 + 11440/7*x^14*d^9*c^7*b*a + 572*x^14*d^10*c^6*a^2 + 880*x^13*d^7*c^9*b^2 + 1980*x^13*d^8*c^8*b*a + 880*x^13*d^9*c^7*a^2 + 2002/3*x^12*d^6*c^10*b^2 + 5720/3*x^12*d^7*c^9*b*a + 2145/2*x^12*d^8*c^8*a^2 + 4368/11*x^11*d^5*c^11*b^2 + 1456*x^11*d^6*c^10*b*a + 1040*x^11*d^7*c^9*a^2 + 182*x^10*d^4*c^12*b^2 + 4368/5*x^10*d^5*c^11*b*a + 4004/5*x^10*d^6*c^10*a^2 + 560/9*x^9*d^3*c^13*b^2 + 3640/9*x^9*d^4*c^12*b*a + 1456/3*x^9*d^5*c^11*a^2 + 15*x^8*d^2*c^14*b^2 + 140*x^8*d^3*c^13*b*a + 455/2*x^8*d^4*c^12*a^2 + 16/7*x^7*d*c^15*b^2 + 240/7*x^7*d^2*c^14*b*a + 80*x^7*d^3*c^13*a^2 + 1/6*x^6*c^16*b^2 + 16/3*x^6*d*c^15*b*a + 20*x^6*d^2*c^14*a^2 + 2/5*x^5*c^16*b*a + 16/5*x^5*d*c^15*a^2 + 1/4*x^4*c^16*a^2","B",0
203,1,668,0,0.780315," ","integrate(x^2*(b*x+a)^2*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{21} x^{21} d^{16} b^{2} + \frac{4}{5} x^{20} d^{15} c b^{2} + \frac{1}{10} x^{20} d^{16} b a + \frac{120}{19} x^{19} d^{14} c^{2} b^{2} + \frac{32}{19} x^{19} d^{15} c b a + \frac{1}{19} x^{19} d^{16} a^{2} + \frac{280}{9} x^{18} d^{13} c^{3} b^{2} + \frac{40}{3} x^{18} d^{14} c^{2} b a + \frac{8}{9} x^{18} d^{15} c a^{2} + \frac{1820}{17} x^{17} d^{12} c^{4} b^{2} + \frac{1120}{17} x^{17} d^{13} c^{3} b a + \frac{120}{17} x^{17} d^{14} c^{2} a^{2} + 273 x^{16} d^{11} c^{5} b^{2} + \frac{455}{2} x^{16} d^{12} c^{4} b a + 35 x^{16} d^{13} c^{3} a^{2} + \frac{8008}{15} x^{15} d^{10} c^{6} b^{2} + \frac{2912}{5} x^{15} d^{11} c^{5} b a + \frac{364}{3} x^{15} d^{12} c^{4} a^{2} + \frac{5720}{7} x^{14} d^{9} c^{7} b^{2} + 1144 x^{14} d^{10} c^{6} b a + 312 x^{14} d^{11} c^{5} a^{2} + 990 x^{13} d^{8} c^{8} b^{2} + 1760 x^{13} d^{9} c^{7} b a + 616 x^{13} d^{10} c^{6} a^{2} + \frac{2860}{3} x^{12} d^{7} c^{9} b^{2} + 2145 x^{12} d^{8} c^{8} b a + \frac{2860}{3} x^{12} d^{9} c^{7} a^{2} + 728 x^{11} d^{6} c^{10} b^{2} + 2080 x^{11} d^{7} c^{9} b a + 1170 x^{11} d^{8} c^{8} a^{2} + \frac{2184}{5} x^{10} d^{5} c^{11} b^{2} + \frac{8008}{5} x^{10} d^{6} c^{10} b a + 1144 x^{10} d^{7} c^{9} a^{2} + \frac{1820}{9} x^{9} d^{4} c^{12} b^{2} + \frac{2912}{3} x^{9} d^{5} c^{11} b a + \frac{8008}{9} x^{9} d^{6} c^{10} a^{2} + 70 x^{8} d^{3} c^{13} b^{2} + 455 x^{8} d^{4} c^{12} b a + 546 x^{8} d^{5} c^{11} a^{2} + \frac{120}{7} x^{7} d^{2} c^{14} b^{2} + 160 x^{7} d^{3} c^{13} b a + 260 x^{7} d^{4} c^{12} a^{2} + \frac{8}{3} x^{6} d c^{15} b^{2} + 40 x^{6} d^{2} c^{14} b a + \frac{280}{3} x^{6} d^{3} c^{13} a^{2} + \frac{1}{5} x^{5} c^{16} b^{2} + \frac{32}{5} x^{5} d c^{15} b a + 24 x^{5} d^{2} c^{14} a^{2} + \frac{1}{2} x^{4} c^{16} b a + 4 x^{4} d c^{15} a^{2} + \frac{1}{3} x^{3} c^{16} a^{2}"," ",0,"1/21*x^21*d^16*b^2 + 4/5*x^20*d^15*c*b^2 + 1/10*x^20*d^16*b*a + 120/19*x^19*d^14*c^2*b^2 + 32/19*x^19*d^15*c*b*a + 1/19*x^19*d^16*a^2 + 280/9*x^18*d^13*c^3*b^2 + 40/3*x^18*d^14*c^2*b*a + 8/9*x^18*d^15*c*a^2 + 1820/17*x^17*d^12*c^4*b^2 + 1120/17*x^17*d^13*c^3*b*a + 120/17*x^17*d^14*c^2*a^2 + 273*x^16*d^11*c^5*b^2 + 455/2*x^16*d^12*c^4*b*a + 35*x^16*d^13*c^3*a^2 + 8008/15*x^15*d^10*c^6*b^2 + 2912/5*x^15*d^11*c^5*b*a + 364/3*x^15*d^12*c^4*a^2 + 5720/7*x^14*d^9*c^7*b^2 + 1144*x^14*d^10*c^6*b*a + 312*x^14*d^11*c^5*a^2 + 990*x^13*d^8*c^8*b^2 + 1760*x^13*d^9*c^7*b*a + 616*x^13*d^10*c^6*a^2 + 2860/3*x^12*d^7*c^9*b^2 + 2145*x^12*d^8*c^8*b*a + 2860/3*x^12*d^9*c^7*a^2 + 728*x^11*d^6*c^10*b^2 + 2080*x^11*d^7*c^9*b*a + 1170*x^11*d^8*c^8*a^2 + 2184/5*x^10*d^5*c^11*b^2 + 8008/5*x^10*d^6*c^10*b*a + 1144*x^10*d^7*c^9*a^2 + 1820/9*x^9*d^4*c^12*b^2 + 2912/3*x^9*d^5*c^11*b*a + 8008/9*x^9*d^6*c^10*a^2 + 70*x^8*d^3*c^13*b^2 + 455*x^8*d^4*c^12*b*a + 546*x^8*d^5*c^11*a^2 + 120/7*x^7*d^2*c^14*b^2 + 160*x^7*d^3*c^13*b*a + 260*x^7*d^4*c^12*a^2 + 8/3*x^6*d*c^15*b^2 + 40*x^6*d^2*c^14*b*a + 280/3*x^6*d^3*c^13*a^2 + 1/5*x^5*c^16*b^2 + 32/5*x^5*d*c^15*b*a + 24*x^5*d^2*c^14*a^2 + 1/2*x^4*c^16*b*a + 4*x^4*d*c^15*a^2 + 1/3*x^3*c^16*a^2","B",0
204,1,668,0,1.127340," ","integrate(x*(b*x+a)^2*(d*x+c)^16,x, algorithm=""fricas"")","\frac{1}{20} x^{20} d^{16} b^{2} + \frac{16}{19} x^{19} d^{15} c b^{2} + \frac{2}{19} x^{19} d^{16} b a + \frac{20}{3} x^{18} d^{14} c^{2} b^{2} + \frac{16}{9} x^{18} d^{15} c b a + \frac{1}{18} x^{18} d^{16} a^{2} + \frac{560}{17} x^{17} d^{13} c^{3} b^{2} + \frac{240}{17} x^{17} d^{14} c^{2} b a + \frac{16}{17} x^{17} d^{15} c a^{2} + \frac{455}{4} x^{16} d^{12} c^{4} b^{2} + 70 x^{16} d^{13} c^{3} b a + \frac{15}{2} x^{16} d^{14} c^{2} a^{2} + \frac{1456}{5} x^{15} d^{11} c^{5} b^{2} + \frac{728}{3} x^{15} d^{12} c^{4} b a + \frac{112}{3} x^{15} d^{13} c^{3} a^{2} + 572 x^{14} d^{10} c^{6} b^{2} + 624 x^{14} d^{11} c^{5} b a + 130 x^{14} d^{12} c^{4} a^{2} + 880 x^{13} d^{9} c^{7} b^{2} + 1232 x^{13} d^{10} c^{6} b a + 336 x^{13} d^{11} c^{5} a^{2} + \frac{2145}{2} x^{12} d^{8} c^{8} b^{2} + \frac{5720}{3} x^{12} d^{9} c^{7} b a + \frac{2002}{3} x^{12} d^{10} c^{6} a^{2} + 1040 x^{11} d^{7} c^{9} b^{2} + 2340 x^{11} d^{8} c^{8} b a + 1040 x^{11} d^{9} c^{7} a^{2} + \frac{4004}{5} x^{10} d^{6} c^{10} b^{2} + 2288 x^{10} d^{7} c^{9} b a + 1287 x^{10} d^{8} c^{8} a^{2} + \frac{1456}{3} x^{9} d^{5} c^{11} b^{2} + \frac{16016}{9} x^{9} d^{6} c^{10} b a + \frac{11440}{9} x^{9} d^{7} c^{9} a^{2} + \frac{455}{2} x^{8} d^{4} c^{12} b^{2} + 1092 x^{8} d^{5} c^{11} b a + 1001 x^{8} d^{6} c^{10} a^{2} + 80 x^{7} d^{3} c^{13} b^{2} + 520 x^{7} d^{4} c^{12} b a + 624 x^{7} d^{5} c^{11} a^{2} + 20 x^{6} d^{2} c^{14} b^{2} + \frac{560}{3} x^{6} d^{3} c^{13} b a + \frac{910}{3} x^{6} d^{4} c^{12} a^{2} + \frac{16}{5} x^{5} d c^{15} b^{2} + 48 x^{5} d^{2} c^{14} b a + 112 x^{5} d^{3} c^{13} a^{2} + \frac{1}{4} x^{4} c^{16} b^{2} + 8 x^{4} d c^{15} b a + 30 x^{4} d^{2} c^{14} a^{2} + \frac{2}{3} x^{3} c^{16} b a + \frac{16}{3} x^{3} d c^{15} a^{2} + \frac{1}{2} x^{2} c^{16} a^{2}"," ",0,"1/20*x^20*d^16*b^2 + 16/19*x^19*d^15*c*b^2 + 2/19*x^19*d^16*b*a + 20/3*x^18*d^14*c^2*b^2 + 16/9*x^18*d^15*c*b*a + 1/18*x^18*d^16*a^2 + 560/17*x^17*d^13*c^3*b^2 + 240/17*x^17*d^14*c^2*b*a + 16/17*x^17*d^15*c*a^2 + 455/4*x^16*d^12*c^4*b^2 + 70*x^16*d^13*c^3*b*a + 15/2*x^16*d^14*c^2*a^2 + 1456/5*x^15*d^11*c^5*b^2 + 728/3*x^15*d^12*c^4*b*a + 112/3*x^15*d^13*c^3*a^2 + 572*x^14*d^10*c^6*b^2 + 624*x^14*d^11*c^5*b*a + 130*x^14*d^12*c^4*a^2 + 880*x^13*d^9*c^7*b^2 + 1232*x^13*d^10*c^6*b*a + 336*x^13*d^11*c^5*a^2 + 2145/2*x^12*d^8*c^8*b^2 + 5720/3*x^12*d^9*c^7*b*a + 2002/3*x^12*d^10*c^6*a^2 + 1040*x^11*d^7*c^9*b^2 + 2340*x^11*d^8*c^8*b*a + 1040*x^11*d^9*c^7*a^2 + 4004/5*x^10*d^6*c^10*b^2 + 2288*x^10*d^7*c^9*b*a + 1287*x^10*d^8*c^8*a^2 + 1456/3*x^9*d^5*c^11*b^2 + 16016/9*x^9*d^6*c^10*b*a + 11440/9*x^9*d^7*c^9*a^2 + 455/2*x^8*d^4*c^12*b^2 + 1092*x^8*d^5*c^11*b*a + 1001*x^8*d^6*c^10*a^2 + 80*x^7*d^3*c^13*b^2 + 520*x^7*d^4*c^12*b*a + 624*x^7*d^5*c^11*a^2 + 20*x^6*d^2*c^14*b^2 + 560/3*x^6*d^3*c^13*b*a + 910/3*x^6*d^4*c^12*a^2 + 16/5*x^5*d*c^15*b^2 + 48*x^5*d^2*c^14*b*a + 112*x^5*d^3*c^13*a^2 + 1/4*x^4*c^16*b^2 + 8*x^4*d*c^15*b*a + 30*x^4*d^2*c^14*a^2 + 2/3*x^3*c^16*b*a + 16/3*x^3*d*c^15*a^2 + 1/2*x^2*c^16*a^2","B",0
205,1,94,0,0.880629," ","integrate(x^3*(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} d x^{4} + 4 \, {\left(b^{4} c - a b^{3} d\right)} x^{3} - 6 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x^{2} + 12 \, {\left(a^{2} b^{2} c - a^{3} b d\right)} x - 12 \, {\left(a^{3} b c - a^{4} d\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*d*x^4 + 4*(b^4*c - a*b^3*d)*x^3 - 6*(a*b^3*c - a^2*b^2*d)*x^2 + 12*(a^2*b^2*c - a^3*b*d)*x - 12*(a^3*b*c - a^4*d)*log(b*x + a))/b^5","A",0
206,1,71,0,1.325949," ","integrate(x^2*(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d x^{3} + 3 \, {\left(b^{3} c - a b^{2} d\right)} x^{2} - 6 \, {\left(a b^{2} c - a^{2} b d\right)} x + 6 \, {\left(a^{2} b c - a^{3} d\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*d*x^3 + 3*(b^3*c - a*b^2*d)*x^2 - 6*(a*b^2*c - a^2*b*d)*x + 6*(a^2*b*c - a^3*d)*log(b*x + a))/b^4","A",0
207,1,47,0,1.287488," ","integrate(x*(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d x^{2} + 2 \, {\left(b^{2} c - a b d\right)} x - 2 \, {\left(a b c - a^{2} d\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*d*x^2 + 2*(b^2*c - a*b*d)*x - 2*(a*b*c - a^2*d)*log(b*x + a))/b^3","A",0
208,1,24,0,1.145943," ","integrate((d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{b d x + {\left(b c - a d\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*d*x + (b*c - a*d)*log(b*x + a))/b^2","A",0
209,1,29,0,1.343673," ","integrate((d*x+c)/x/(b*x+a),x, algorithm=""fricas"")","\frac{b c \log\left(x\right) - {\left(b c - a d\right)} \log\left(b x + a\right)}{a b}"," ",0,"(b*c*log(x) - (b*c - a*d)*log(b*x + a))/(a*b)","A",0
210,1,41,0,1.075336," ","integrate((d*x+c)/x^2/(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b c - a d\right)} x \log\left(b x + a\right) - {\left(b c - a d\right)} x \log\left(x\right) - a c}{a^{2} x}"," ",0,"((b*c - a*d)*x*log(b*x + a) - (b*c - a*d)*x*log(x) - a*c)/(a^2*x)","A",0
211,1,68,0,1.202048," ","integrate((d*x+c)/x^3/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} c - a b d\right)} x^{2} \log\left(b x + a\right) - 2 \, {\left(b^{2} c - a b d\right)} x^{2} \log\left(x\right) + a^{2} c - 2 \, {\left(a b c - a^{2} d\right)} x}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(2*(b^2*c - a*b*d)*x^2*log(b*x + a) - 2*(b^2*c - a*b*d)*x^2*log(x) + a^2*c - 2*(a*b*c - a^2*d)*x)/(a^3*x^2)","A",0
212,1,94,0,1.413397," ","integrate((d*x+c)/x^4/(b*x+a),x, algorithm=""fricas"")","\frac{6 \, {\left(b^{3} c - a b^{2} d\right)} x^{3} \log\left(b x + a\right) - 6 \, {\left(b^{3} c - a b^{2} d\right)} x^{3} \log\left(x\right) - 2 \, a^{3} c - 6 \, {\left(a b^{2} c - a^{2} b d\right)} x^{2} + 3 \, {\left(a^{2} b c - a^{3} d\right)} x}{6 \, a^{4} x^{3}}"," ",0,"1/6*(6*(b^3*c - a*b^2*d)*x^3*log(b*x + a) - 6*(b^3*c - a*b^2*d)*x^3*log(x) - 2*a^3*c - 6*(a*b^2*c - a^2*b*d)*x^2 + 3*(a^2*b*c - a^3*d)*x)/(a^4*x^3)","A",0
213,1,170,0,1.564201," ","integrate(x^3*(d*x+c)^2/(b*x+a),x, algorithm=""fricas"")","\frac{12 \, b^{5} d^{2} x^{5} + 15 \, {\left(2 \, b^{5} c d - a b^{4} d^{2}\right)} x^{4} + 20 \, {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{3} - 30 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x^{2} + 60 \, {\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2}\right)} x - 60 \, {\left(a^{3} b^{2} c^{2} - 2 \, a^{4} b c d + a^{5} d^{2}\right)} \log\left(b x + a\right)}{60 \, b^{6}}"," ",0,"1/60*(12*b^5*d^2*x^5 + 15*(2*b^5*c*d - a*b^4*d^2)*x^4 + 20*(b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^3 - 30*(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x^2 + 60*(a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2)*x - 60*(a^3*b^2*c^2 - 2*a^4*b*c*d + a^5*d^2)*log(b*x + a))/b^6","A",0
214,1,134,0,1.477633," ","integrate(x^2*(d*x+c)^2/(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} d^{2} x^{4} + 4 \, {\left(2 \, b^{4} c d - a b^{3} d^{2}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} - 12 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x + 12 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*d^2*x^4 + 4*(2*b^4*c*d - a*b^3*d^2)*x^3 + 6*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2 - 12*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x + 12*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*log(b*x + a))/b^5","A",0
215,1,98,0,1.248121," ","integrate(x*(d*x+c)^2/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{2} x^{3} + 3 \, {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 6 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x - 6 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*d^2*x^3 + 3*(2*b^3*c*d - a*b^2*d^2)*x^2 + 6*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x - 6*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*log(b*x + a))/b^4","A",0
216,1,63,0,1.286572," ","integrate((d*x+c)^2/(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*(2*b^2*c*d - a*b*d^2)*x + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x + a))/b^3","A",0
217,1,53,0,1.357456," ","integrate((d*x+c)^2/x/(b*x+a),x, algorithm=""fricas"")","\frac{a b d^{2} x + b^{2} c^{2} \log\left(x\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x + a\right)}{a b^{2}}"," ",0,"(a*b*d^2*x + b^2*c^2*log(x) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x + a))/(a*b^2)","A",0
218,1,66,0,1.276154," ","integrate((d*x+c)^2/x^2/(b*x+a),x, algorithm=""fricas"")","-\frac{a b c^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \log\left(b x + a\right) + {\left(b^{2} c^{2} - 2 \, a b c d\right)} x \log\left(x\right)}{a^{2} b x}"," ",0,"-(a*b*c^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*log(b*x + a) + (b^2*c^2 - 2*a*b*c*d)*x*log(x))/(a^2*b*x)","A",0
219,1,93,0,1.069967," ","integrate((d*x+c)^2/x^3/(b*x+a),x, algorithm=""fricas"")","-\frac{a^{2} c^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \log\left(b x + a\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(a b c^{2} - 2 \, a^{2} c d\right)} x}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(a^2*c^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*log(b*x + a) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*log(x) - 2*(a*b*c^2 - 2*a^2*c*d)*x)/(a^3*x^2)","A",0
220,1,131,0,1.279538," ","integrate((d*x+c)^2/x^4/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a^{3} c^{2} - 6 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} \log\left(b x + a\right) + 6 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} \log\left(x\right) + 6 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2} - 3 \, {\left(a^{2} b c^{2} - 2 \, a^{3} c d\right)} x}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(2*a^3*c^2 - 6*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3*log(b*x + a) + 6*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3*log(x) + 6*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2 - 3*(a^2*b*c^2 - 2*a^3*c*d)*x)/(a^4*x^3)","A",0
221,1,169,0,1.292325," ","integrate((d*x+c)^2/x^5/(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, a^{4} c^{2} + 12 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} \log\left(b x + a\right) - 12 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} \log\left(x\right) - 12 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} b c^{2} - 2 \, a^{4} c d\right)} x}{12 \, a^{5} x^{4}}"," ",0,"-1/12*(3*a^4*c^2 + 12*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4*log(b*x + a) - 12*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^4*log(x) - 12*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x^3 + 6*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*x^2 - 4*(a^3*b*c^2 - 2*a^4*c*d)*x)/(a^5*x^4)","A",0
222,1,267,0,1.317402," ","integrate(x^3*(d*x+c)^3/(b*x+a),x, algorithm=""fricas"")","\frac{10 \, b^{6} d^{3} x^{6} + 12 \, {\left(3 \, b^{6} c d^{2} - a b^{5} d^{3}\right)} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d - 3 \, a b^{5} c d^{2} + a^{2} b^{4} d^{3}\right)} x^{4} + 20 \, {\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{3} - 30 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{2} + 60 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} x - 60 \, {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} \log\left(b x + a\right)}{60 \, b^{7}}"," ",0,"1/60*(10*b^6*d^3*x^6 + 12*(3*b^6*c*d^2 - a*b^5*d^3)*x^5 + 15*(3*b^6*c^2*d - 3*a*b^5*c*d^2 + a^2*b^4*d^3)*x^4 + 20*(b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^3 - 30*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^2 + 60*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*x - 60*(a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*log(b*x + a))/b^7","A",0
223,1,216,0,1.169888," ","integrate(x^2*(d*x+c)^3/(b*x+a),x, algorithm=""fricas"")","\frac{12 \, b^{5} d^{3} x^{5} + 15 \, {\left(3 \, b^{5} c d^{2} - a b^{4} d^{3}\right)} x^{4} + 20 \, {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 30 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{2} - 60 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x + 60 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \log\left(b x + a\right)}{60 \, b^{6}}"," ",0,"1/60*(12*b^5*d^3*x^5 + 15*(3*b^5*c*d^2 - a*b^4*d^3)*x^4 + 20*(3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 30*(b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^2 - 60*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x + 60*(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*log(b*x + a))/b^6","A",0
224,1,165,0,1.259036," ","integrate(x*(d*x+c)^3/(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} d^{3} x^{4} + 4 \, {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 6 \, {\left(3 \, b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + a^{2} b^{2} d^{3}\right)} x^{2} + 12 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x - 12 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*d^3*x^4 + 4*(3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 6*(3*b^4*c^2*d - 3*a*b^3*c*d^2 + a^2*b^2*d^3)*x^2 + 12*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x - 12*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*log(b*x + a))/b^5","A",0
225,1,116,0,1.317554," ","integrate((d*x+c)^3/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*d^3*x^3 + 3*(3*b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x + a))/b^4","A",0
226,1,97,0,1.248375," ","integrate((d*x+c)^3/x/(b*x+a),x, algorithm=""fricas"")","\frac{a b^{2} d^{3} x^{2} + 2 \, b^{3} c^{3} \log\left(x\right) + 2 \, {\left(3 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(b x + a\right)}{2 \, a b^{3}}"," ",0,"1/2*(a*b^2*d^3*x^2 + 2*b^3*c^3*log(x) + 2*(3*a*b^2*c*d^2 - a^2*b*d^3)*x - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x + a))/(a*b^3)","A",0
227,1,98,0,1.391527," ","integrate((d*x+c)^3/x^2/(b*x+a),x, algorithm=""fricas"")","\frac{a^{2} b d^{3} x^{2} - a b^{2} c^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x \log\left(b x + a\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d\right)} x \log\left(x\right)}{a^{2} b^{2} x}"," ",0,"(a^2*b*d^3*x^2 - a*b^2*c^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x*log(b*x + a) - (b^3*c^3 - 3*a*b^2*c^2*d)*x*log(x))/(a^2*b^2*x)","A",0
228,1,124,0,1.266598," ","integrate((d*x+c)^3/x^3/(b*x+a),x, algorithm=""fricas"")","-\frac{a^{2} b c^{3} + 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{2} \log\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2}\right)} x^{2} \log\left(x\right) - 2 \, {\left(a b^{2} c^{3} - 3 \, a^{2} b c^{2} d\right)} x}{2 \, a^{3} b x^{2}}"," ",0,"-1/2*(a^2*b*c^3 + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^2*log(b*x + a) - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2)*x^2*log(x) - 2*(a*b^2*c^3 - 3*a^2*b*c^2*d)*x)/(a^3*b*x^2)","A",0
229,1,161,0,0.732125," ","integrate((d*x+c)^3/x^4/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a^{3} c^{3} - 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{3} \log\left(b x + a\right) + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} x^{3} \log\left(x\right) + 6 \, {\left(a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 3 \, {\left(a^{2} b c^{3} - 3 \, a^{3} c^{2} d\right)} x}{6 \, a^{4} x^{3}}"," ",0,"-1/6*(2*a^3*c^3 - 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^3*log(b*x + a) + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*x^3*log(x) + 6*(a*b^2*c^3 - 3*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 3*(a^2*b*c^3 - 3*a^3*c^2*d)*x)/(a^4*x^3)","A",0
230,1,213,0,1.052294," ","integrate((d*x+c)^3/x^5/(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, a^{4} c^{3} + 12 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} \log\left(b x + a\right) - 12 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} \log\left(x\right) - 12 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{2} c^{3} - 3 \, a^{3} b c^{2} d + 3 \, a^{4} c d^{2}\right)} x^{2} - 4 \, {\left(a^{3} b c^{3} - 3 \, a^{4} c^{2} d\right)} x}{12 \, a^{5} x^{4}}"," ",0,"-1/12*(3*a^4*c^3 + 12*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4*log(b*x + a) - 12*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4*log(x) - 12*(a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x^3 + 6*(a^2*b^2*c^3 - 3*a^3*b*c^2*d + 3*a^4*c*d^2)*x^2 - 4*(a^3*b*c^3 - 3*a^4*c^2*d)*x)/(a^5*x^4)","A",0
231,1,266,0,1.073927," ","integrate((d*x+c)^3/x^6/(b*x+a),x, algorithm=""fricas"")","-\frac{12 \, a^{5} c^{3} - 60 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} \log\left(b x + a\right) + 60 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} \log\left(x\right) + 60 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} - 30 \, {\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)} x^{3} + 20 \, {\left(a^{3} b^{2} c^{3} - 3 \, a^{4} b c^{2} d + 3 \, a^{5} c d^{2}\right)} x^{2} - 15 \, {\left(a^{4} b c^{3} - 3 \, a^{5} c^{2} d\right)} x}{60 \, a^{6} x^{5}}"," ",0,"-1/60*(12*a^5*c^3 - 60*(b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5*log(b*x + a) + 60*(b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5*log(x) + 60*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 - 30*(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)*x^3 + 20*(a^3*b^2*c^3 - 3*a^4*b*c^2*d + 3*a^5*c*d^2)*x^2 - 15*(a^4*b*c^3 - 3*a^5*c^2*d)*x)/(a^6*x^5)","A",0
232,1,149,0,1.337114," ","integrate(x^5/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{12 \, a^{5} d^{5} \log\left(b x + a\right) - 12 \, b^{5} c^{5} \log\left(d x + c\right) - 3 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{2} + 12 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x}{12 \, {\left(b^{6} c d^{5} - a b^{5} d^{6}\right)}}"," ",0,"-1/12*(12*a^5*d^5*log(b*x + a) - 12*b^5*c^5*log(d*x + c) - 3*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 4*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^3 - 6*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^2 + 12*(b^5*c^4*d - a^4*b*d^5)*x)/(b^6*c*d^5 - a*b^5*d^6)","A",0
233,1,122,0,1.343774," ","integrate(x^4/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{6 \, a^{4} d^{4} \log\left(b x + a\right) - 6 \, b^{4} c^{4} \log\left(d x + c\right) + 2 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{2} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x}{6 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)}}"," ",0,"1/6*(6*a^4*d^4*log(b*x + a) - 6*b^4*c^4*log(d*x + c) + 2*(b^4*c*d^3 - a*b^3*d^4)*x^3 - 3*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^2 + 6*(b^4*c^3*d - a^3*b*d^4)*x)/(b^5*c*d^4 - a*b^4*d^5)","A",0
234,1,95,0,1.348474," ","integrate(x^3/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, a^{3} d^{3} \log\left(b x + a\right) - 2 \, b^{3} c^{3} \log\left(d x + c\right) - {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x}{2 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)}}"," ",0,"-1/2*(2*a^3*d^3*log(b*x + a) - 2*b^3*c^3*log(d*x + c) - (b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(b^3*c^2*d - a^2*b*d^3)*x)/(b^4*c*d^3 - a*b^3*d^4)","A",0
235,1,65,0,1.381539," ","integrate(x^2/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{a^{2} d^{2} \log\left(b x + a\right) - b^{2} c^{2} \log\left(d x + c\right) + {\left(b^{2} c d - a b d^{2}\right)} x}{b^{3} c d^{2} - a b^{2} d^{3}}"," ",0,"(a^2*d^2*log(b*x + a) - b^2*c^2*log(d*x + c) + (b^2*c*d - a*b*d^2)*x)/(b^3*c*d^2 - a*b^2*d^3)","A",0
236,1,38,0,1.202946," ","integrate(x/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{a d \log\left(b x + a\right) - b c \log\left(d x + c\right)}{b^{2} c d - a b d^{2}}"," ",0,"-(a*d*log(b*x + a) - b*c*log(d*x + c))/(b^2*c*d - a*b*d^2)","A",0
237,1,26,0,0.977546," ","integrate(1/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right) - \log\left(d x + c\right)}{b c - a d}"," ",0,"(log(b*x + a) - log(d*x + c))/(b*c - a*d)","A",0
238,1,50,0,1.551800," ","integrate(1/x/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{b c \log\left(b x + a\right) - a d \log\left(d x + c\right) - {\left(b c - a d\right)} \log\left(x\right)}{a b c^{2} - a^{2} c d}"," ",0,"-(b*c*log(b*x + a) - a*d*log(d*x + c) - (b*c - a*d)*log(x))/(a*b*c^2 - a^2*c*d)","A",0
239,1,88,0,1.607857," ","integrate(1/x^2/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{b^{2} c^{2} x \log\left(b x + a\right) - a^{2} d^{2} x \log\left(d x + c\right) - a b c^{2} + a^{2} c d - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x \log\left(x\right)}{{\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} x}"," ",0,"(b^2*c^2*x*log(b*x + a) - a^2*d^2*x*log(d*x + c) - a*b*c^2 + a^2*c*d - (b^2*c^2 - a^2*d^2)*x*log(x))/((a^2*b*c^3 - a^3*c^2*d)*x)","A",0
240,1,121,0,8.195148," ","integrate(1/x^3/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} x^{2} \log\left(b x + a\right) - 2 \, a^{3} d^{3} x^{2} \log\left(d x + c\right) + a^{2} b c^{3} - a^{3} c^{2} d - 2 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x^{2} \log\left(x\right) - 2 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} x}{2 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} x^{2}}"," ",0,"-1/2*(2*b^3*c^3*x^2*log(b*x + a) - 2*a^3*d^3*x^2*log(d*x + c) + a^2*b*c^3 - a^3*c^2*d - 2*(b^3*c^3 - a^3*d^3)*x^2*log(x) - 2*(a*b^2*c^3 - a^3*c*d^2)*x)/((a^3*b*c^4 - a^4*c^3*d)*x^2)","A",0
241,1,149,0,10.821200," ","integrate(1/x^4/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{6 \, b^{4} c^{4} x^{3} \log\left(b x + a\right) - 6 \, a^{4} d^{4} x^{3} \log\left(d x + c\right) - 2 \, a^{3} b c^{4} + 2 \, a^{4} c^{3} d - 6 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x^{3} \log\left(x\right) - 6 \, {\left(a b^{3} c^{4} - a^{4} c d^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} c^{4} - a^{4} c^{2} d^{2}\right)} x}{6 \, {\left(a^{4} b c^{5} - a^{5} c^{4} d\right)} x^{3}}"," ",0,"1/6*(6*b^4*c^4*x^3*log(b*x + a) - 6*a^4*d^4*x^3*log(d*x + c) - 2*a^3*b*c^4 + 2*a^4*c^3*d - 6*(b^4*c^4 - a^4*d^4)*x^3*log(x) - 6*(a*b^3*c^4 - a^4*c*d^3)*x^2 + 3*(a^2*b^2*c^4 - a^4*c^2*d^2)*x)/((a^4*b*c^5 - a^5*c^4*d)*x^3)","A",0
242,1,337,0,1.361144," ","integrate(x^5/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{6 \, b^{5} c^{6} - 6 \, a b^{4} c^{5} d - 2 \, {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)} x^{4} + {\left(4 \, b^{5} c^{3} d^{3} - 5 \, a b^{4} c^{2} d^{4} - 2 \, a^{2} b^{3} c d^{5} + 3 \, a^{3} b^{2} d^{6}\right)} x^{3} - 3 \, {\left(4 \, b^{5} c^{4} d^{2} - 5 \, a b^{4} c^{3} d^{3} - a^{3} b^{2} c d^{5} + 2 \, a^{4} b d^{6}\right)} x^{2} - 6 \, {\left(3 \, b^{5} c^{5} d - 4 \, a b^{4} c^{4} d^{2} + a^{4} b c d^{5}\right)} x + 6 \, {\left(a^{5} d^{6} x + a^{5} c d^{5}\right)} \log\left(b x + a\right) + 6 \, {\left(4 \, b^{5} c^{6} - 5 \, a b^{4} c^{5} d + {\left(4 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2}\right)} x\right)} \log\left(d x + c\right)}{6 \, {\left(b^{6} c^{3} d^{5} - 2 \, a b^{5} c^{2} d^{6} + a^{2} b^{4} c d^{7} + {\left(b^{6} c^{2} d^{6} - 2 \, a b^{5} c d^{7} + a^{2} b^{4} d^{8}\right)} x\right)}}"," ",0,"-1/6*(6*b^5*c^6 - 6*a*b^4*c^5*d - 2*(b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)*x^4 + (4*b^5*c^3*d^3 - 5*a*b^4*c^2*d^4 - 2*a^2*b^3*c*d^5 + 3*a^3*b^2*d^6)*x^3 - 3*(4*b^5*c^4*d^2 - 5*a*b^4*c^3*d^3 - a^3*b^2*c*d^5 + 2*a^4*b*d^6)*x^2 - 6*(3*b^5*c^5*d - 4*a*b^4*c^4*d^2 + a^4*b*c*d^5)*x + 6*(a^5*d^6*x + a^5*c*d^5)*log(b*x + a) + 6*(4*b^5*c^6 - 5*a*b^4*c^5*d + (4*b^5*c^5*d - 5*a*b^4*c^4*d^2)*x)*log(d*x + c))/(b^6*c^3*d^5 - 2*a*b^5*c^2*d^6 + a^2*b^4*c*d^7 + (b^6*c^2*d^6 - 2*a*b^5*c*d^7 + a^2*b^4*d^8)*x)","B",0
243,1,285,0,1.367405," ","integrate(x^4/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} c^{5} - 2 \, a b^{3} c^{4} d + {\left(b^{4} c^{2} d^{3} - 2 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} x^{3} - {\left(3 \, b^{4} c^{3} d^{2} - 4 \, a b^{3} c^{2} d^{3} - a^{2} b^{2} c d^{4} + 2 \, a^{3} b d^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{4} c^{4} d - 3 \, a b^{3} c^{3} d^{2} + a^{3} b c d^{4}\right)} x + 2 \, {\left(a^{4} d^{5} x + a^{4} c d^{4}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{4} c^{5} - 4 \, a b^{3} c^{4} d + {\left(3 \, b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(b^{5} c^{3} d^{4} - 2 \, a b^{4} c^{2} d^{5} + a^{2} b^{3} c d^{6} + {\left(b^{5} c^{2} d^{5} - 2 \, a b^{4} c d^{6} + a^{2} b^{3} d^{7}\right)} x\right)}}"," ",0,"1/2*(2*b^4*c^5 - 2*a*b^3*c^4*d + (b^4*c^2*d^3 - 2*a*b^3*c*d^4 + a^2*b^2*d^5)*x^3 - (3*b^4*c^3*d^2 - 4*a*b^3*c^2*d^3 - a^2*b^2*c*d^4 + 2*a^3*b*d^5)*x^2 - 2*(2*b^4*c^4*d - 3*a*b^3*c^3*d^2 + a^3*b*c*d^4)*x + 2*(a^4*d^5*x + a^4*c*d^4)*log(b*x + a) + 2*(3*b^4*c^5 - 4*a*b^3*c^4*d + (3*b^4*c^4*d - 4*a*b^3*c^3*d^2)*x)*log(d*x + c))/(b^5*c^3*d^4 - 2*a*b^4*c^2*d^5 + a^2*b^3*c*d^6 + (b^5*c^2*d^5 - 2*a*b^4*c*d^6 + a^2*b^3*d^7)*x)","B",0
244,1,230,0,1.352437," ","integrate(x^3/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b^{3} c^{4} - a b^{2} c^{3} d - {\left(b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{2} - {\left(b^{3} c^{3} d - 2 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} x + {\left(a^{3} d^{4} x + a^{3} c d^{3}\right)} \log\left(b x + a\right) + {\left(2 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d + {\left(2 \, b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} x\right)} \log\left(d x + c\right)}{b^{4} c^{3} d^{3} - 2 \, a b^{3} c^{2} d^{4} + a^{2} b^{2} c d^{5} + {\left(b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} + a^{2} b^{2} d^{6}\right)} x}"," ",0,"-(b^3*c^4 - a*b^2*c^3*d - (b^3*c^2*d^2 - 2*a*b^2*c*d^3 + a^2*b*d^4)*x^2 - (b^3*c^3*d - 2*a*b^2*c^2*d^2 + a^2*b*c*d^3)*x + (a^3*d^4*x + a^3*c*d^3)*log(b*x + a) + (2*b^3*c^4 - 3*a*b^2*c^3*d + (2*b^3*c^3*d - 3*a*b^2*c^2*d^2)*x)*log(d*x + c))/(b^4*c^3*d^3 - 2*a*b^3*c^2*d^4 + a^2*b^2*c*d^5 + (b^4*c^2*d^4 - 2*a*b^3*c*d^5 + a^2*b^2*d^6)*x)","B",0
245,1,148,0,1.255857," ","integrate(x^2/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{2} c^{3} - a b c^{2} d + {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \log\left(b x + a\right) + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(d x + c\right)}{b^{3} c^{3} d^{2} - 2 \, a b^{2} c^{2} d^{3} + a^{2} b c d^{4} + {\left(b^{3} c^{2} d^{3} - 2 \, a b^{2} c d^{4} + a^{2} b d^{5}\right)} x}"," ",0,"(b^2*c^3 - a*b*c^2*d + (a^2*d^3*x + a^2*c*d^2)*log(b*x + a) + (b^2*c^3 - 2*a*b*c^2*d + (b^2*c^2*d - 2*a*b*c*d^2)*x)*log(d*x + c))/(b^3*c^3*d^2 - 2*a*b^2*c^2*d^3 + a^2*b*c*d^4 + (b^3*c^2*d^3 - 2*a*b^2*c*d^4 + a^2*b*d^5)*x)","A",0
246,1,107,0,1.717304," ","integrate(x/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b c^{2} - a c d + {\left(a d^{2} x + a c d\right)} \log\left(b x + a\right) - {\left(a d^{2} x + a c d\right)} \log\left(d x + c\right)}{b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x}"," ",0,"-(b*c^2 - a*c*d + (a*d^2*x + a*c*d)*log(b*x + a) - (a*d^2*x + a*c*d)*log(d*x + c))/(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x)","A",0
247,1,92,0,1.252362," ","integrate(1/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{b c - a d + {\left(b d x + b c\right)} \log\left(b x + a\right) - {\left(b d x + b c\right)} \log\left(d x + c\right)}{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x}"," ",0,"(b*c - a*d + (b*d*x + b*c)*log(b*x + a) - (b*d*x + b*c)*log(d*x + c))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)","A",0
248,1,207,0,3.456762," ","integrate(1/x/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a b c^{2} d - a^{2} c d^{2} + {\left(b^{2} c^{2} d x + b^{2} c^{3}\right)} \log\left(b x + a\right) - {\left(2 \, a b c^{2} d - a^{2} c d^{2} + {\left(2 \, a b c d^{2} - a^{2} d^{3}\right)} x\right)} \log\left(d x + c\right) - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \log\left(x\right)}{a b^{2} c^{5} - 2 \, a^{2} b c^{4} d + a^{3} c^{3} d^{2} + {\left(a b^{2} c^{4} d - 2 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3}\right)} x}"," ",0,"-(a*b*c^2*d - a^2*c*d^2 + (b^2*c^2*d*x + b^2*c^3)*log(b*x + a) - (2*a*b*c^2*d - a^2*c*d^2 + (2*a*b*c*d^2 - a^2*d^3)*x)*log(d*x + c) - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*log(x))/(a*b^2*c^5 - 2*a^2*b*c^4*d + a^3*c^3*d^2 + (a*b^2*c^4*d - 2*a^2*b*c^3*d^2 + a^3*c^2*d^3)*x)","B",0
249,1,287,0,12.602710," ","integrate(1/x^2/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a b^{2} c^{4} - 2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x - {\left(b^{3} c^{3} d x^{2} + b^{3} c^{4} x\right)} \log\left(b x + a\right) + {\left({\left(3 \, a^{2} b c d^{3} - 2 \, a^{3} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b c^{2} d^{2} - 2 \, a^{3} c d^{3}\right)} x\right)} \log\left(d x + c\right) + {\left({\left(b^{3} c^{3} d - 3 \, a^{2} b c d^{3} + 2 \, a^{3} d^{4}\right)} x^{2} + {\left(b^{3} c^{4} - 3 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x\right)} \log\left(x\right)}{{\left(a^{2} b^{2} c^{5} d - 2 \, a^{3} b c^{4} d^{2} + a^{4} c^{3} d^{3}\right)} x^{2} + {\left(a^{2} b^{2} c^{6} - 2 \, a^{3} b c^{5} d + a^{4} c^{4} d^{2}\right)} x}"," ",0,"-(a*b^2*c^4 - 2*a^2*b*c^3*d + a^3*c^2*d^2 + (a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x - (b^3*c^3*d*x^2 + b^3*c^4*x)*log(b*x + a) + ((3*a^2*b*c*d^3 - 2*a^3*d^4)*x^2 + (3*a^2*b*c^2*d^2 - 2*a^3*c*d^3)*x)*log(d*x + c) + ((b^3*c^3*d - 3*a^2*b*c*d^3 + 2*a^3*d^4)*x^2 + (b^3*c^4 - 3*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x)*log(x))/((a^2*b^2*c^5*d - 2*a^3*b*c^4*d^2 + a^4*c^3*d^3)*x^2 + (a^2*b^2*c^6 - 2*a^3*b*c^5*d + a^4*c^4*d^2)*x)","B",0
250,1,350,0,18.508682," ","integrate(1/x^3/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{2} c^{5} - 2 \, a^{3} b c^{4} d + a^{4} c^{3} d^{2} - 2 \, {\left(a b^{3} c^{4} d - 4 \, a^{3} b c^{2} d^{3} + 3 \, a^{4} c d^{4}\right)} x^{2} - {\left(2 \, a b^{3} c^{5} - a^{2} b^{2} c^{4} d - 4 \, a^{3} b c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3}\right)} x + 2 \, {\left(b^{4} c^{4} d x^{3} + b^{4} c^{5} x^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(4 \, a^{3} b c d^{4} - 3 \, a^{4} d^{5}\right)} x^{3} + {\left(4 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \log\left(d x + c\right) - 2 \, {\left({\left(b^{4} c^{4} d - 4 \, a^{3} b c d^{4} + 3 \, a^{4} d^{5}\right)} x^{3} + {\left(b^{4} c^{5} - 4 \, a^{3} b c^{2} d^{3} + 3 \, a^{4} c d^{4}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{2} c^{6} d - 2 \, a^{4} b c^{5} d^{2} + a^{5} c^{4} d^{3}\right)} x^{3} + {\left(a^{3} b^{2} c^{7} - 2 \, a^{4} b c^{6} d + a^{5} c^{5} d^{2}\right)} x^{2}\right)}}"," ",0,"-1/2*(a^2*b^2*c^5 - 2*a^3*b*c^4*d + a^4*c^3*d^2 - 2*(a*b^3*c^4*d - 4*a^3*b*c^2*d^3 + 3*a^4*c*d^4)*x^2 - (2*a*b^3*c^5 - a^2*b^2*c^4*d - 4*a^3*b*c^3*d^2 + 3*a^4*c^2*d^3)*x + 2*(b^4*c^4*d*x^3 + b^4*c^5*x^2)*log(b*x + a) - 2*((4*a^3*b*c*d^4 - 3*a^4*d^5)*x^3 + (4*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x^2)*log(d*x + c) - 2*((b^4*c^4*d - 4*a^3*b*c*d^4 + 3*a^4*d^5)*x^3 + (b^4*c^5 - 4*a^3*b*c^2*d^3 + 3*a^4*c*d^4)*x^2)*log(x))/((a^3*b^2*c^6*d - 2*a^4*b*c^5*d^2 + a^5*c^4*d^3)*x^3 + (a^3*b^2*c^7 - 2*a^4*b*c^6*d + a^5*c^5*d^2)*x^2)","B",0
251,1,579,0,1.113079," ","integrate(x^5/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{7 \, b^{5} c^{7} - 16 \, a b^{4} c^{6} d + 9 \, a^{2} b^{3} c^{5} d^{2} + {\left(b^{5} c^{3} d^{4} - 3 \, a b^{4} c^{2} d^{5} + 3 \, a^{2} b^{3} c d^{6} - a^{3} b^{2} d^{7}\right)} x^{4} - 2 \, {\left(2 \, b^{5} c^{4} d^{3} - 5 \, a b^{4} c^{3} d^{4} + 3 \, a^{2} b^{3} c^{2} d^{5} + a^{3} b^{2} c d^{6} - a^{4} b d^{7}\right)} x^{3} - {\left(11 \, b^{5} c^{5} d^{2} - 29 \, a b^{4} c^{4} d^{3} + 21 \, a^{2} b^{3} c^{3} d^{4} + a^{3} b^{2} c^{2} d^{5} - 4 \, a^{4} b c d^{6}\right)} x^{2} + 2 \, {\left(b^{5} c^{6} d - a b^{4} c^{5} d^{2} - a^{2} b^{3} c^{4} d^{3} + a^{4} b c^{2} d^{5}\right)} x - 2 \, {\left(a^{5} d^{7} x^{2} + 2 \, a^{5} c d^{6} x + a^{5} c^{2} d^{5}\right)} \log\left(b x + a\right) + 2 \, {\left(6 \, b^{5} c^{7} - 15 \, a b^{4} c^{6} d + 10 \, a^{2} b^{3} c^{5} d^{2} + {\left(6 \, b^{5} c^{5} d^{2} - 15 \, a b^{4} c^{4} d^{3} + 10 \, a^{2} b^{3} c^{3} d^{4}\right)} x^{2} + 2 \, {\left(6 \, b^{5} c^{6} d - 15 \, a b^{4} c^{5} d^{2} + 10 \, a^{2} b^{3} c^{4} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(b^{6} c^{5} d^{5} - 3 \, a b^{5} c^{4} d^{6} + 3 \, a^{2} b^{4} c^{3} d^{7} - a^{3} b^{3} c^{2} d^{8} + {\left(b^{6} c^{3} d^{7} - 3 \, a b^{5} c^{2} d^{8} + 3 \, a^{2} b^{4} c d^{9} - a^{3} b^{3} d^{10}\right)} x^{2} + 2 \, {\left(b^{6} c^{4} d^{6} - 3 \, a b^{5} c^{3} d^{7} + 3 \, a^{2} b^{4} c^{2} d^{8} - a^{3} b^{3} c d^{9}\right)} x\right)}}"," ",0,"1/2*(7*b^5*c^7 - 16*a*b^4*c^6*d + 9*a^2*b^3*c^5*d^2 + (b^5*c^3*d^4 - 3*a*b^4*c^2*d^5 + 3*a^2*b^3*c*d^6 - a^3*b^2*d^7)*x^4 - 2*(2*b^5*c^4*d^3 - 5*a*b^4*c^3*d^4 + 3*a^2*b^3*c^2*d^5 + a^3*b^2*c*d^6 - a^4*b*d^7)*x^3 - (11*b^5*c^5*d^2 - 29*a*b^4*c^4*d^3 + 21*a^2*b^3*c^3*d^4 + a^3*b^2*c^2*d^5 - 4*a^4*b*c*d^6)*x^2 + 2*(b^5*c^6*d - a*b^4*c^5*d^2 - a^2*b^3*c^4*d^3 + a^4*b*c^2*d^5)*x - 2*(a^5*d^7*x^2 + 2*a^5*c*d^6*x + a^5*c^2*d^5)*log(b*x + a) + 2*(6*b^5*c^7 - 15*a*b^4*c^6*d + 10*a^2*b^3*c^5*d^2 + (6*b^5*c^5*d^2 - 15*a*b^4*c^4*d^3 + 10*a^2*b^3*c^3*d^4)*x^2 + 2*(6*b^5*c^6*d - 15*a*b^4*c^5*d^2 + 10*a^2*b^3*c^4*d^3)*x)*log(d*x + c))/(b^6*c^5*d^5 - 3*a*b^5*c^4*d^6 + 3*a^2*b^4*c^3*d^7 - a^3*b^3*c^2*d^8 + (b^6*c^3*d^7 - 3*a*b^5*c^2*d^8 + 3*a^2*b^4*c*d^9 - a^3*b^3*d^10)*x^2 + 2*(b^6*c^4*d^6 - 3*a*b^5*c^3*d^7 + 3*a^2*b^4*c^2*d^8 - a^3*b^3*c*d^9)*x)","B",0
252,1,501,0,1.205090," ","integrate(x^4/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{5 \, b^{4} c^{6} - 12 \, a b^{3} c^{5} d + 7 \, a^{2} b^{2} c^{4} d^{2} - 2 \, {\left(b^{4} c^{3} d^{3} - 3 \, a b^{3} c^{2} d^{4} + 3 \, a^{2} b^{2} c d^{5} - a^{3} b d^{6}\right)} x^{3} - 4 \, {\left(b^{4} c^{4} d^{2} - 3 \, a b^{3} c^{3} d^{3} + 3 \, a^{2} b^{2} c^{2} d^{4} - a^{3} b c d^{5}\right)} x^{2} + 2 \, {\left(2 \, b^{4} c^{5} d - 4 \, a b^{3} c^{4} d^{2} + a^{2} b^{2} c^{3} d^{3} + a^{3} b c^{2} d^{4}\right)} x - 2 \, {\left(a^{4} d^{6} x^{2} + 2 \, a^{4} c d^{5} x + a^{4} c^{2} d^{4}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{4} c^{6} - 8 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} + {\left(3 \, b^{4} c^{4} d^{2} - 8 \, a b^{3} c^{3} d^{3} + 6 \, a^{2} b^{2} c^{2} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{5} d - 8 \, a b^{3} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{3} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(b^{5} c^{5} d^{4} - 3 \, a b^{4} c^{4} d^{5} + 3 \, a^{2} b^{3} c^{3} d^{6} - a^{3} b^{2} c^{2} d^{7} + {\left(b^{5} c^{3} d^{6} - 3 \, a b^{4} c^{2} d^{7} + 3 \, a^{2} b^{3} c d^{8} - a^{3} b^{2} d^{9}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d^{5} - 3 \, a b^{4} c^{3} d^{6} + 3 \, a^{2} b^{3} c^{2} d^{7} - a^{3} b^{2} c d^{8}\right)} x\right)}}"," ",0,"-1/2*(5*b^4*c^6 - 12*a*b^3*c^5*d + 7*a^2*b^2*c^4*d^2 - 2*(b^4*c^3*d^3 - 3*a*b^3*c^2*d^4 + 3*a^2*b^2*c*d^5 - a^3*b*d^6)*x^3 - 4*(b^4*c^4*d^2 - 3*a*b^3*c^3*d^3 + 3*a^2*b^2*c^2*d^4 - a^3*b*c*d^5)*x^2 + 2*(2*b^4*c^5*d - 4*a*b^3*c^4*d^2 + a^2*b^2*c^3*d^3 + a^3*b*c^2*d^4)*x - 2*(a^4*d^6*x^2 + 2*a^4*c*d^5*x + a^4*c^2*d^4)*log(b*x + a) + 2*(3*b^4*c^6 - 8*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 + (3*b^4*c^4*d^2 - 8*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4)*x^2 + 2*(3*b^4*c^5*d - 8*a*b^3*c^4*d^2 + 6*a^2*b^2*c^3*d^3)*x)*log(d*x + c))/(b^5*c^5*d^4 - 3*a*b^4*c^4*d^5 + 3*a^2*b^3*c^3*d^6 - a^3*b^2*c^2*d^7 + (b^5*c^3*d^6 - 3*a*b^4*c^2*d^7 + 3*a^2*b^3*c*d^8 - a^3*b^2*d^9)*x^2 + 2*(b^5*c^4*d^5 - 3*a*b^4*c^3*d^6 + 3*a^2*b^3*c^2*d^7 - a^3*b^2*c*d^8)*x)","B",0
253,1,369,0,1.127837," ","integrate(x^3/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} c^{5} - 8 \, a b^{2} c^{4} d + 5 \, a^{2} b c^{3} d^{2} + 2 \, {\left(2 \, b^{3} c^{4} d - 5 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3}\right)} x - 2 \, {\left(a^{3} d^{5} x^{2} + 2 \, a^{3} c d^{4} x + a^{3} c^{2} d^{3}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(b^{4} c^{5} d^{3} - 3 \, a b^{3} c^{4} d^{4} + 3 \, a^{2} b^{2} c^{3} d^{5} - a^{3} b c^{2} d^{6} + {\left(b^{4} c^{3} d^{5} - 3 \, a b^{3} c^{2} d^{6} + 3 \, a^{2} b^{2} c d^{7} - a^{3} b d^{8}\right)} x^{2} + 2 \, {\left(b^{4} c^{4} d^{4} - 3 \, a b^{3} c^{3} d^{5} + 3 \, a^{2} b^{2} c^{2} d^{6} - a^{3} b c d^{7}\right)} x\right)}}"," ",0,"1/2*(3*b^3*c^5 - 8*a*b^2*c^4*d + 5*a^2*b*c^3*d^2 + 2*(2*b^3*c^4*d - 5*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3)*x - 2*(a^3*d^5*x^2 + 2*a^3*c*d^4*x + a^3*c^2*d^3)*log(b*x + a) + 2*(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4)*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3)*x)*log(d*x + c))/(b^4*c^5*d^3 - 3*a*b^3*c^4*d^4 + 3*a^2*b^2*c^3*d^5 - a^3*b*c^2*d^6 + (b^4*c^3*d^5 - 3*a*b^3*c^2*d^6 + 3*a^2*b^2*c*d^7 - a^3*b*d^8)*x^2 + 2*(b^4*c^4*d^4 - 3*a*b^3*c^3*d^5 + 3*a^2*b^2*c^2*d^6 - a^3*b*c*d^7)*x)","B",0
254,1,278,0,1.329644," ","integrate(x^2/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{4} - 4 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + 2 \, {\left(b^{2} c^{3} d - 3 \, a b c^{2} d^{2} + 2 \, a^{2} c d^{3}\right)} x - 2 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(b^{3} c^{5} d^{2} - 3 \, a b^{2} c^{4} d^{3} + 3 \, a^{2} b c^{3} d^{4} - a^{3} c^{2} d^{5} + {\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)} x^{2} + 2 \, {\left(b^{3} c^{4} d^{3} - 3 \, a b^{2} c^{3} d^{4} + 3 \, a^{2} b c^{2} d^{5} - a^{3} c d^{6}\right)} x\right)}}"," ",0,"-1/2*(b^2*c^4 - 4*a*b*c^3*d + 3*a^2*c^2*d^2 + 2*(b^2*c^3*d - 3*a*b*c^2*d^2 + 2*a^2*c*d^3)*x - 2*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*log(b*x + a) + 2*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*log(d*x + c))/(b^3*c^5*d^2 - 3*a*b^2*c^4*d^3 + 3*a^2*b*c^3*d^4 - a^3*c^2*d^5 + (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)*x^2 + 2*(b^3*c^4*d^3 - 3*a*b^2*c^3*d^4 + 3*a^2*b*c^2*d^5 - a^3*c*d^6)*x)","B",0
255,1,244,0,1.193289," ","integrate(x/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{3} - a^{2} c d^{2} + 2 \, {\left(a b c d^{2} - a^{2} d^{3}\right)} x + 2 \, {\left(a b d^{3} x^{2} + 2 \, a b c d^{2} x + a b c^{2} d\right)} \log\left(b x + a\right) - 2 \, {\left(a b d^{3} x^{2} + 2 \, a b c d^{2} x + a b c^{2} d\right)} \log\left(d x + c\right)}{2 \, {\left(b^{3} c^{5} d - 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{3} d^{3} - a^{3} c^{2} d^{4} + {\left(b^{3} c^{3} d^{3} - 3 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d^{2} - 3 \, a b^{2} c^{3} d^{3} + 3 \, a^{2} b c^{2} d^{4} - a^{3} c d^{5}\right)} x\right)}}"," ",0,"-1/2*(b^2*c^3 - a^2*c*d^2 + 2*(a*b*c*d^2 - a^2*d^3)*x + 2*(a*b*d^3*x^2 + 2*a*b*c*d^2*x + a*b*c^2*d)*log(b*x + a) - 2*(a*b*d^3*x^2 + 2*a*b*c*d^2*x + a*b*c^2*d)*log(d*x + c))/(b^3*c^5*d - 3*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 - a^3*c^2*d^4 + (b^3*c^3*d^3 - 3*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5 - a^3*d^6)*x^2 + 2*(b^3*c^4*d^2 - 3*a*b^2*c^3*d^3 + 3*a^2*b*c^2*d^4 - a^3*c*d^5)*x)","B",0
256,1,242,0,1.261115," ","integrate(1/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\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} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x\right)}}"," ",0,"1/2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x)","B",0
257,1,506,0,20.167018," ","integrate(1/x/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{5 \, a b^{2} c^{4} d - 8 \, a^{2} b c^{3} d^{2} + 3 \, a^{3} c^{2} d^{3} + 2 \, {\left(2 \, a b^{2} c^{3} d^{2} - 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x + 2 \, {\left(b^{3} c^{3} d^{2} x^{2} + 2 \, b^{3} c^{4} d x + b^{3} c^{5}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, a b^{2} c^{4} d - 3 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(3 \, a b^{2} c^{2} d^{3} - 3 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{3} d^{2} - 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x\right)} \log\left(d x + c\right) - 2 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\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} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x\right)} \log\left(x\right)}{2 \, {\left(a b^{3} c^{8} - 3 \, a^{2} b^{2} c^{7} d + 3 \, a^{3} b c^{6} d^{2} - a^{4} c^{5} d^{3} + {\left(a b^{3} c^{6} d^{2} - 3 \, a^{2} b^{2} c^{5} d^{3} + 3 \, a^{3} b c^{4} d^{4} - a^{4} c^{3} d^{5}\right)} x^{2} + 2 \, {\left(a b^{3} c^{7} d - 3 \, a^{2} b^{2} c^{6} d^{2} + 3 \, a^{3} b c^{5} d^{3} - a^{4} c^{4} d^{4}\right)} x\right)}}"," ",0,"-1/2*(5*a*b^2*c^4*d - 8*a^2*b*c^3*d^2 + 3*a^3*c^2*d^3 + 2*(2*a*b^2*c^3*d^2 - 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x + 2*(b^3*c^3*d^2*x^2 + 2*b^3*c^4*d*x + b^3*c^5)*log(b*x + a) - 2*(3*a*b^2*c^4*d - 3*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (3*a*b^2*c^2*d^3 - 3*a^2*b*c*d^4 + a^3*d^5)*x^2 + 2*(3*a*b^2*c^3*d^2 - 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x)*log(d*x + c) - 2*(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (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 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x)*log(x))/(a*b^3*c^8 - 3*a^2*b^2*c^7*d + 3*a^3*b*c^6*d^2 - a^4*c^5*d^3 + (a*b^3*c^6*d^2 - 3*a^2*b^2*c^5*d^3 + 3*a^3*b*c^4*d^4 - a^4*c^3*d^5)*x^2 + 2*(a*b^3*c^7*d - 3*a^2*b^2*c^6*d^2 + 3*a^3*b*c^5*d^3 - a^4*c^4*d^4)*x)","B",0
258,1,626,0,24.248625," ","integrate(1/x^2/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a b^{3} c^{6} - 6 \, a^{2} b^{2} c^{5} d + 6 \, a^{3} b c^{4} d^{2} - 2 \, a^{4} c^{3} d^{3} + 2 \, {\left(a b^{3} c^{4} d^{2} - 6 \, a^{2} b^{2} c^{3} d^{3} + 8 \, a^{3} b c^{2} d^{4} - 3 \, a^{4} c d^{5}\right)} x^{2} + {\left(4 \, a b^{3} c^{5} d - 19 \, a^{2} b^{2} c^{4} d^{2} + 24 \, a^{3} b c^{3} d^{3} - 9 \, a^{4} c^{2} d^{4}\right)} x - 2 \, {\left(b^{4} c^{4} d^{2} x^{3} + 2 \, b^{4} c^{5} d x^{2} + b^{4} c^{6} x\right)} \log\left(b x + a\right) + 2 \, {\left({\left(6 \, a^{2} b^{2} c^{2} d^{4} - 8 \, a^{3} b c d^{5} + 3 \, a^{4} d^{6}\right)} x^{3} + 2 \, {\left(6 \, a^{2} b^{2} c^{3} d^{3} - 8 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x^{2} + {\left(6 \, a^{2} b^{2} c^{4} d^{2} - 8 \, a^{3} b c^{3} d^{3} + 3 \, a^{4} c^{2} d^{4}\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left({\left(b^{4} c^{4} d^{2} - 6 \, a^{2} b^{2} c^{2} d^{4} + 8 \, a^{3} b c d^{5} - 3 \, a^{4} d^{6}\right)} x^{3} + 2 \, {\left(b^{4} c^{5} d - 6 \, a^{2} b^{2} c^{3} d^{3} + 8 \, a^{3} b c^{2} d^{4} - 3 \, a^{4} c d^{5}\right)} x^{2} + {\left(b^{4} c^{6} - 6 \, a^{2} b^{2} c^{4} d^{2} + 8 \, a^{3} b c^{3} d^{3} - 3 \, a^{4} c^{2} d^{4}\right)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{2} b^{3} c^{7} d^{2} - 3 \, a^{3} b^{2} c^{6} d^{3} + 3 \, a^{4} b c^{5} d^{4} - a^{5} c^{4} d^{5}\right)} x^{3} + 2 \, {\left(a^{2} b^{3} c^{8} d - 3 \, a^{3} b^{2} c^{7} d^{2} + 3 \, a^{4} b c^{6} d^{3} - a^{5} c^{5} d^{4}\right)} x^{2} + {\left(a^{2} b^{3} c^{9} - 3 \, a^{3} b^{2} c^{8} d + 3 \, a^{4} b c^{7} d^{2} - a^{5} c^{6} d^{3}\right)} x\right)}}"," ",0,"-1/2*(2*a*b^3*c^6 - 6*a^2*b^2*c^5*d + 6*a^3*b*c^4*d^2 - 2*a^4*c^3*d^3 + 2*(a*b^3*c^4*d^2 - 6*a^2*b^2*c^3*d^3 + 8*a^3*b*c^2*d^4 - 3*a^4*c*d^5)*x^2 + (4*a*b^3*c^5*d - 19*a^2*b^2*c^4*d^2 + 24*a^3*b*c^3*d^3 - 9*a^4*c^2*d^4)*x - 2*(b^4*c^4*d^2*x^3 + 2*b^4*c^5*d*x^2 + b^4*c^6*x)*log(b*x + a) + 2*((6*a^2*b^2*c^2*d^4 - 8*a^3*b*c*d^5 + 3*a^4*d^6)*x^3 + 2*(6*a^2*b^2*c^3*d^3 - 8*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x^2 + (6*a^2*b^2*c^4*d^2 - 8*a^3*b*c^3*d^3 + 3*a^4*c^2*d^4)*x)*log(d*x + c) + 2*((b^4*c^4*d^2 - 6*a^2*b^2*c^2*d^4 + 8*a^3*b*c*d^5 - 3*a^4*d^6)*x^3 + 2*(b^4*c^5*d - 6*a^2*b^2*c^3*d^3 + 8*a^3*b*c^2*d^4 - 3*a^4*c*d^5)*x^2 + (b^4*c^6 - 6*a^2*b^2*c^4*d^2 + 8*a^3*b*c^3*d^3 - 3*a^4*c^2*d^4)*x)*log(x))/((a^2*b^3*c^7*d^2 - 3*a^3*b^2*c^6*d^3 + 3*a^4*b*c^5*d^4 - a^5*c^4*d^5)*x^3 + 2*(a^2*b^3*c^8*d - 3*a^3*b^2*c^7*d^2 + 3*a^4*b*c^6*d^3 - a^5*c^5*d^4)*x^2 + (a^2*b^3*c^9 - 3*a^3*b^2*c^8*d + 3*a^4*b*c^7*d^2 - a^5*c^6*d^3)*x)","B",0
259,1,286,0,0.613518," ","integrate(x^4*(d*x+c)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, b^{6} d^{2} x^{6} - 30 \, a^{4} b^{2} c^{2} + 60 \, a^{5} b c d - 30 \, a^{6} d^{2} + 3 \, {\left(5 \, b^{6} c d - 3 \, a b^{5} d^{2}\right)} x^{5} + 5 \, {\left(2 \, b^{6} c^{2} - 5 \, a b^{5} c d + 3 \, a^{2} b^{4} d^{2}\right)} x^{4} - 10 \, {\left(2 \, a b^{5} c^{2} - 5 \, a^{2} b^{4} c d + 3 \, a^{3} b^{3} d^{2}\right)} x^{3} + 30 \, {\left(2 \, a^{2} b^{4} c^{2} - 5 \, a^{3} b^{3} c d + 3 \, a^{4} b^{2} d^{2}\right)} x^{2} + 30 \, {\left(3 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b^{2} c d + 5 \, a^{5} b d^{2}\right)} x - 60 \, {\left(2 \, a^{4} b^{2} c^{2} - 5 \, a^{5} b c d + 3 \, a^{6} d^{2} + {\left(2 \, a^{3} b^{3} c^{2} - 5 \, a^{4} b^{2} c d + 3 \, a^{5} b d^{2}\right)} x\right)} \log\left(b x + a\right)}{30 \, {\left(b^{8} x + a b^{7}\right)}}"," ",0,"1/30*(6*b^6*d^2*x^6 - 30*a^4*b^2*c^2 + 60*a^5*b*c*d - 30*a^6*d^2 + 3*(5*b^6*c*d - 3*a*b^5*d^2)*x^5 + 5*(2*b^6*c^2 - 5*a*b^5*c*d + 3*a^2*b^4*d^2)*x^4 - 10*(2*a*b^5*c^2 - 5*a^2*b^4*c*d + 3*a^3*b^3*d^2)*x^3 + 30*(2*a^2*b^4*c^2 - 5*a^3*b^3*c*d + 3*a^4*b^2*d^2)*x^2 + 30*(3*a^3*b^3*c^2 - 8*a^4*b^2*c*d + 5*a^5*b*d^2)*x - 60*(2*a^4*b^2*c^2 - 5*a^5*b*c*d + 3*a^6*d^2 + (2*a^3*b^3*c^2 - 5*a^4*b^2*c*d + 3*a^5*b*d^2)*x)*log(b*x + a))/(b^8*x + a*b^7)","A",0
260,1,246,0,0.922848," ","integrate(x^3*(d*x+c)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} d^{2} x^{5} + 12 \, a^{3} b^{2} c^{2} - 24 \, a^{4} b c d + 12 \, a^{5} d^{2} + {\left(8 \, b^{5} c d - 5 \, a b^{4} d^{2}\right)} x^{4} + 2 \, {\left(3 \, b^{5} c^{2} - 8 \, a b^{4} c d + 5 \, a^{2} b^{3} d^{2}\right)} x^{3} - 6 \, {\left(3 \, a b^{4} c^{2} - 8 \, a^{2} b^{3} c d + 5 \, a^{3} b^{2} d^{2}\right)} x^{2} - 24 \, {\left(a^{2} b^{3} c^{2} - 3 \, a^{3} b^{2} c d + 2 \, a^{4} b d^{2}\right)} x + 12 \, {\left(3 \, a^{3} b^{2} c^{2} - 8 \, a^{4} b c d + 5 \, a^{5} d^{2} + {\left(3 \, a^{2} b^{3} c^{2} - 8 \, a^{3} b^{2} c d + 5 \, a^{4} b d^{2}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*b^5*d^2*x^5 + 12*a^3*b^2*c^2 - 24*a^4*b*c*d + 12*a^5*d^2 + (8*b^5*c*d - 5*a*b^4*d^2)*x^4 + 2*(3*b^5*c^2 - 8*a*b^4*c*d + 5*a^2*b^3*d^2)*x^3 - 6*(3*a*b^4*c^2 - 8*a^2*b^3*c*d + 5*a^3*b^2*d^2)*x^2 - 24*(a^2*b^3*c^2 - 3*a^3*b^2*c*d + 2*a^4*b*d^2)*x + 12*(3*a^3*b^2*c^2 - 8*a^4*b*c*d + 5*a^5*d^2 + (3*a^2*b^3*c^2 - 8*a^3*b^2*c*d + 5*a^4*b*d^2)*x)*log(b*x + a))/(b^7*x + a*b^6)","A",0
261,1,202,0,1.010385," ","integrate(x^2*(d*x+c)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{4} d^{2} x^{4} - 3 \, a^{2} b^{2} c^{2} + 6 \, a^{3} b c d - 3 \, a^{4} d^{2} + {\left(3 \, b^{4} c d - 2 \, a b^{3} d^{2}\right)} x^{3} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{3} c d + 2 \, a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x - 6 \, {\left(a^{2} b^{2} c^{2} - 3 \, a^{3} b c d + 2 \, a^{4} d^{2} + {\left(a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x\right)} \log\left(b x + a\right)}{3 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/3*(b^4*d^2*x^4 - 3*a^2*b^2*c^2 + 6*a^3*b*c*d - 3*a^4*d^2 + (3*b^4*c*d - 2*a*b^3*d^2)*x^3 + 3*(b^4*c^2 - 3*a*b^3*c*d + 2*a^2*b^2*d^2)*x^2 + 3*(a*b^3*c^2 - 4*a^2*b^2*c*d + 3*a^3*b*d^2)*x - 6*(a^2*b^2*c^2 - 3*a^3*b*c*d + 2*a^4*d^2 + (a*b^3*c^2 - 3*a^2*b^2*c*d + 2*a^3*b*d^2)*x)*log(b*x + a))/(b^6*x + a*b^5)","A",0
262,1,152,0,1.214335," ","integrate(x*(d*x+c)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{2} x^{3} + 2 \, a b^{2} c^{2} - 4 \, a^{2} b c d + 2 \, a^{3} d^{2} + {\left(4 \, b^{3} c d - 3 \, a b^{2} d^{2}\right)} x^{2} + 4 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x + 2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} b c d + 3 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 4 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*d^2*x^3 + 2*a*b^2*c^2 - 4*a^2*b*c*d + 2*a^3*d^2 + (4*b^3*c*d - 3*a*b^2*d^2)*x^2 + 4*(a*b^2*c*d - a^2*b*d^2)*x + 2*(a*b^2*c^2 - 4*a^2*b*c*d + 3*a^3*d^2 + (b^3*c^2 - 4*a*b^2*c*d + 3*a^2*b*d^2)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
263,1,92,0,0.591522," ","integrate((d*x+c)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + a b d^{2} x - b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} + 2 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(b^2*d^2*x^2 + a*b*d^2*x - b^2*c^2 + 2*a*b*c*d - a^2*d^2 + 2*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
264,1,107,0,0.952078," ","integrate((d*x+c)^2/x/(b*x+a)^2,x, algorithm=""fricas"")","\frac{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} - {\left(a b^{2} c^{2} - a^{3} d^{2} + {\left(b^{3} c^{2} - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right) + {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \log\left(x\right)}{a^{2} b^{3} x + a^{3} b^{2}}"," ",0,"(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 - (a*b^2*c^2 - a^3*d^2 + (b^3*c^2 - a^2*b*d^2)*x)*log(b*x + a) + (b^3*c^2*x + a*b^2*c^2)*log(x))/(a^2*b^3*x + a^3*b^2)","A",0
265,1,149,0,0.731330," ","integrate((d*x+c)^2/x^2/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x - 2 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{2} + {\left(a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{2} + {\left(a b^{2} c^{2} - a^{2} b c d\right)} x\right)} \log\left(x\right)}{a^{3} b^{2} x^{2} + a^{4} b x}"," ",0,"-(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x - 2*((b^3*c^2 - a*b^2*c*d)*x^2 + (a*b^2*c^2 - a^2*b*c*d)*x)*log(b*x + a) + 2*((b^3*c^2 - a*b^2*c*d)*x^2 + (a*b^2*c^2 - a^2*b*c*d)*x)*log(x))/(a^3*b^2*x^2 + a^4*b*x)","B",0
266,1,208,0,0.934932," ","integrate((d*x+c)^2/x^3/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{a^{3} c^{2} - 2 \, {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2} - {\left(3 \, a^{2} b c^{2} - 4 \, a^{3} c d\right)} x + 2 \, {\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(3 \, b^{3} c^{2} - 4 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(3 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}"," ",0,"-1/2*(a^3*c^2 - 2*(3*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*x^2 - (3*a^2*b*c^2 - 4*a^3*c*d)*x + 2*((3*b^3*c^2 - 4*a*b^2*c*d + a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*x^2)*log(b*x + a) - 2*((3*b^3*c^2 - 4*a*b^2*c*d + a^2*b*d^2)*x^3 + (3*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*x^2)*log(x))/(a^4*b*x^3 + a^5*x^2)","B",0
267,1,253,0,1.051052," ","integrate((d*x+c)^2/x^4/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{a^{4} c^{2} + 6 \, {\left(2 \, a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{2} c^{2} - 3 \, a^{3} b c d + a^{4} d^{2}\right)} x^{2} - {\left(2 \, a^{3} b c^{2} - 3 \, a^{4} c d\right)} x - 6 \, {\left({\left(2 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + {\left(2 \, a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{3}\right)} \log\left(b x + a\right) + 6 \, {\left({\left(2 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{4} + {\left(2 \, a b^{3} c^{2} - 3 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x^{3}\right)} \log\left(x\right)}{3 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}"," ",0,"-1/3*(a^4*c^2 + 6*(2*a*b^3*c^2 - 3*a^2*b^2*c*d + a^3*b*d^2)*x^3 + 3*(2*a^2*b^2*c^2 - 3*a^3*b*c*d + a^4*d^2)*x^2 - (2*a^3*b*c^2 - 3*a^4*c*d)*x - 6*((2*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^4 + (2*a*b^3*c^2 - 3*a^2*b^2*c*d + a^3*b*d^2)*x^3)*log(b*x + a) + 6*((2*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^4 + (2*a*b^3*c^2 - 3*a^2*b^2*c*d + a^3*b*d^2)*x^3)*log(x))/(a^5*b*x^4 + a^6*x^3)","A",0
268,1,302,0,0.954518," ","integrate((d*x+c)^2/x^5/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{3 \, a^{5} c^{2} - 12 \, {\left(5 \, a b^{4} c^{2} - 8 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} x^{4} - 6 \, {\left(5 \, a^{2} b^{3} c^{2} - 8 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{2} c^{2} - 8 \, a^{4} b c d + 3 \, a^{5} d^{2}\right)} x^{2} - {\left(5 \, a^{4} b c^{2} - 8 \, a^{5} c d\right)} x + 12 \, {\left({\left(5 \, b^{5} c^{2} - 8 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{2} - 8 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} x^{4}\right)} \log\left(b x + a\right) - 12 \, {\left({\left(5 \, b^{5} c^{2} - 8 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} x^{5} + {\left(5 \, a b^{4} c^{2} - 8 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} x^{4}\right)} \log\left(x\right)}{12 \, {\left(a^{6} b x^{5} + a^{7} x^{4}\right)}}"," ",0,"-1/12*(3*a^5*c^2 - 12*(5*a*b^4*c^2 - 8*a^2*b^3*c*d + 3*a^3*b^2*d^2)*x^4 - 6*(5*a^2*b^3*c^2 - 8*a^3*b^2*c*d + 3*a^4*b*d^2)*x^3 + 2*(5*a^3*b^2*c^2 - 8*a^4*b*c*d + 3*a^5*d^2)*x^2 - (5*a^4*b*c^2 - 8*a^5*c*d)*x + 12*((5*b^5*c^2 - 8*a*b^4*c*d + 3*a^2*b^3*d^2)*x^5 + (5*a*b^4*c^2 - 8*a^2*b^3*c*d + 3*a^3*b^2*d^2)*x^4)*log(b*x + a) - 12*((5*b^5*c^2 - 8*a*b^4*c*d + 3*a^2*b^3*d^2)*x^5 + (5*a*b^4*c^2 - 8*a^2*b^3*c*d + 3*a^3*b^2*d^2)*x^4)*log(x))/(a^6*b*x^5 + a^7*x^4)","A",0
269,1,421,0,1.099212," ","integrate(x^4*(d*x+c)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{10 \, b^{7} d^{3} x^{7} - 60 \, a^{4} b^{3} c^{3} + 180 \, a^{5} b^{2} c^{2} d - 180 \, a^{6} b c d^{2} + 60 \, a^{7} d^{3} + 2 \, {\left(18 \, b^{7} c d^{2} - 7 \, a b^{6} d^{3}\right)} x^{6} + 3 \, {\left(15 \, b^{7} c^{2} d - 18 \, a b^{6} c d^{2} + 7 \, a^{2} b^{5} d^{3}\right)} x^{5} + 5 \, {\left(4 \, b^{7} c^{3} - 15 \, a b^{6} c^{2} d + 18 \, a^{2} b^{5} c d^{2} - 7 \, a^{3} b^{4} d^{3}\right)} x^{4} - 10 \, {\left(4 \, a b^{6} c^{3} - 15 \, a^{2} b^{5} c^{2} d + 18 \, a^{3} b^{4} c d^{2} - 7 \, a^{4} b^{3} d^{3}\right)} x^{3} + 30 \, {\left(4 \, a^{2} b^{5} c^{3} - 15 \, a^{3} b^{4} c^{2} d + 18 \, a^{4} b^{3} c d^{2} - 7 \, a^{5} b^{2} d^{3}\right)} x^{2} + 180 \, {\left(a^{3} b^{4} c^{3} - 4 \, a^{4} b^{3} c^{2} d + 5 \, a^{5} b^{2} c d^{2} - 2 \, a^{6} b d^{3}\right)} x - 60 \, {\left(4 \, a^{4} b^{3} c^{3} - 15 \, a^{5} b^{2} c^{2} d + 18 \, a^{6} b c d^{2} - 7 \, a^{7} d^{3} + {\left(4 \, a^{3} b^{4} c^{3} - 15 \, a^{4} b^{3} c^{2} d + 18 \, a^{5} b^{2} c d^{2} - 7 \, a^{6} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{60 \, {\left(b^{9} x + a b^{8}\right)}}"," ",0,"1/60*(10*b^7*d^3*x^7 - 60*a^4*b^3*c^3 + 180*a^5*b^2*c^2*d - 180*a^6*b*c*d^2 + 60*a^7*d^3 + 2*(18*b^7*c*d^2 - 7*a*b^6*d^3)*x^6 + 3*(15*b^7*c^2*d - 18*a*b^6*c*d^2 + 7*a^2*b^5*d^3)*x^5 + 5*(4*b^7*c^3 - 15*a*b^6*c^2*d + 18*a^2*b^5*c*d^2 - 7*a^3*b^4*d^3)*x^4 - 10*(4*a*b^6*c^3 - 15*a^2*b^5*c^2*d + 18*a^3*b^4*c*d^2 - 7*a^4*b^3*d^3)*x^3 + 30*(4*a^2*b^5*c^3 - 15*a^3*b^4*c^2*d + 18*a^4*b^3*c*d^2 - 7*a^5*b^2*d^3)*x^2 + 180*(a^3*b^4*c^3 - 4*a^4*b^3*c^2*d + 5*a^5*b^2*c*d^2 - 2*a^6*b*d^3)*x - 60*(4*a^4*b^3*c^3 - 15*a^5*b^2*c^2*d + 18*a^6*b*c*d^2 - 7*a^7*d^3 + (4*a^3*b^4*c^3 - 15*a^4*b^3*c^2*d + 18*a^5*b^2*c*d^2 - 7*a^6*b*d^3)*x)*log(b*x + a))/(b^9*x + a*b^8)","B",0
270,1,366,0,1.219213," ","integrate(x^3*(d*x+c)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b^{6} d^{3} x^{6} + 20 \, a^{3} b^{3} c^{3} - 60 \, a^{4} b^{2} c^{2} d + 60 \, a^{5} b c d^{2} - 20 \, a^{6} d^{3} + 3 \, {\left(5 \, b^{6} c d^{2} - 2 \, a b^{5} d^{3}\right)} x^{5} + 5 \, {\left(4 \, b^{6} c^{2} d - 5 \, a b^{5} c d^{2} + 2 \, a^{2} b^{4} d^{3}\right)} x^{4} + 10 \, {\left(b^{6} c^{3} - 4 \, a b^{5} c^{2} d + 5 \, a^{2} b^{4} c d^{2} - 2 \, a^{3} b^{3} d^{3}\right)} x^{3} - 30 \, {\left(a b^{5} c^{3} - 4 \, a^{2} b^{4} c^{2} d + 5 \, a^{3} b^{3} c d^{2} - 2 \, a^{4} b^{2} d^{3}\right)} x^{2} - 20 \, {\left(2 \, a^{2} b^{4} c^{3} - 9 \, a^{3} b^{3} c^{2} d + 12 \, a^{4} b^{2} c d^{2} - 5 \, a^{5} b d^{3}\right)} x + 60 \, {\left(a^{3} b^{3} c^{3} - 4 \, a^{4} b^{2} c^{2} d + 5 \, a^{5} b c d^{2} - 2 \, a^{6} d^{3} + {\left(a^{2} b^{4} c^{3} - 4 \, a^{3} b^{3} c^{2} d + 5 \, a^{4} b^{2} c d^{2} - 2 \, a^{5} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{20 \, {\left(b^{8} x + a b^{7}\right)}}"," ",0,"1/20*(4*b^6*d^3*x^6 + 20*a^3*b^3*c^3 - 60*a^4*b^2*c^2*d + 60*a^5*b*c*d^2 - 20*a^6*d^3 + 3*(5*b^6*c*d^2 - 2*a*b^5*d^3)*x^5 + 5*(4*b^6*c^2*d - 5*a*b^5*c*d^2 + 2*a^2*b^4*d^3)*x^4 + 10*(b^6*c^3 - 4*a*b^5*c^2*d + 5*a^2*b^4*c*d^2 - 2*a^3*b^3*d^3)*x^3 - 30*(a*b^5*c^3 - 4*a^2*b^4*c^2*d + 5*a^3*b^3*c*d^2 - 2*a^4*b^2*d^3)*x^2 - 20*(2*a^2*b^4*c^3 - 9*a^3*b^3*c^2*d + 12*a^4*b^2*c*d^2 - 5*a^5*b*d^3)*x + 60*(a^3*b^3*c^3 - 4*a^4*b^2*c^2*d + 5*a^5*b*c*d^2 - 2*a^6*d^3 + (a^2*b^4*c^3 - 4*a^3*b^3*c^2*d + 5*a^4*b^2*c*d^2 - 2*a^5*b*d^3)*x)*log(b*x + a))/(b^8*x + a*b^7)","B",0
271,1,314,0,0.979217," ","integrate(x^2*(d*x+c)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} d^{3} x^{5} - 12 \, a^{2} b^{3} c^{3} + 36 \, a^{3} b^{2} c^{2} d - 36 \, a^{4} b c d^{2} + 12 \, a^{5} d^{3} + {\left(12 \, b^{5} c d^{2} - 5 \, a b^{4} d^{3}\right)} x^{4} + 2 \, {\left(9 \, b^{5} c^{2} d - 12 \, a b^{4} c d^{2} + 5 \, a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(2 \, b^{5} c^{3} - 9 \, a b^{4} c^{2} d + 12 \, a^{2} b^{3} c d^{2} - 5 \, a^{3} b^{2} d^{3}\right)} x^{2} + 12 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 4 \, a^{4} b d^{3}\right)} x - 12 \, {\left(2 \, a^{2} b^{3} c^{3} - 9 \, a^{3} b^{2} c^{2} d + 12 \, a^{4} b c d^{2} - 5 \, a^{5} d^{3} + {\left(2 \, a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 12 \, a^{3} b^{2} c d^{2} - 5 \, a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*b^5*d^3*x^5 - 12*a^2*b^3*c^3 + 36*a^3*b^2*c^2*d - 36*a^4*b*c*d^2 + 12*a^5*d^3 + (12*b^5*c*d^2 - 5*a*b^4*d^3)*x^4 + 2*(9*b^5*c^2*d - 12*a*b^4*c*d^2 + 5*a^2*b^3*d^3)*x^3 + 6*(2*b^5*c^3 - 9*a*b^4*c^2*d + 12*a^2*b^3*c*d^2 - 5*a^3*b^2*d^3)*x^2 + 12*(a*b^4*c^3 - 6*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 4*a^4*b*d^3)*x - 12*(2*a^2*b^3*c^3 - 9*a^3*b^2*c^2*d + 12*a^4*b*c*d^2 - 5*a^5*d^3 + (2*a*b^4*c^3 - 9*a^2*b^3*c^2*d + 12*a^3*b^2*c*d^2 - 5*a^4*b*d^3)*x)*log(b*x + a))/(b^7*x + a*b^6)","B",0
272,1,246,0,0.783082," ","integrate(x*(d*x+c)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} d^{3} x^{4} + 6 \, a b^{3} c^{3} - 18 \, a^{2} b^{2} c^{2} d + 18 \, a^{3} b c d^{2} - 6 \, a^{4} d^{3} + {\left(9 \, b^{4} c d^{2} - 4 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(6 \, b^{4} c^{2} d - 9 \, a b^{3} c d^{2} + 4 \, a^{2} b^{2} d^{3}\right)} x^{2} + 18 \, {\left(a b^{3} c^{2} d - 2 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x + 6 \, {\left(a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} - 4 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 6 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} - 4 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/6*(2*b^4*d^3*x^4 + 6*a*b^3*c^3 - 18*a^2*b^2*c^2*d + 18*a^3*b*c*d^2 - 6*a^4*d^3 + (9*b^4*c*d^2 - 4*a*b^3*d^3)*x^3 + 3*(6*b^4*c^2*d - 9*a*b^3*c*d^2 + 4*a^2*b^2*d^3)*x^2 + 18*(a*b^3*c^2*d - 2*a^2*b^2*c*d^2 + a^3*b*d^3)*x + 6*(a*b^3*c^3 - 6*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 - 4*a^4*d^3 + (b^4*c^3 - 6*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 - 4*a^3*b*d^3)*x)*log(b*x + a))/(b^6*x + a*b^5)","B",0
273,1,173,0,0.914402," ","integrate((d*x+c)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} - 2 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3} + 3 \, {\left(2 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} x + 6 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*d^3*x^3 - 2*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + 3*(2*b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(3*a*b^2*c*d^2 - 2*a^2*b*d^3)*x + 6*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
274,1,166,0,1.249858," ","integrate((d*x+c)^3/x/(b*x+a)^2,x, algorithm=""fricas"")","\frac{a^{2} b^{2} d^{3} x^{2} + a^{3} b d^{3} x + a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3} - {\left(a b^{3} c^{3} - 3 \, a^{3} b c d^{2} + 2 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 3 \, a^{2} b^{2} c d^{2} + 2 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right) + {\left(b^{4} c^{3} x + a b^{3} c^{3}\right)} \log\left(x\right)}{a^{2} b^{4} x + a^{3} b^{3}}"," ",0,"(a^2*b^2*d^3*x^2 + a^3*b*d^3*x + a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3 - (a*b^3*c^3 - 3*a^3*b*c*d^2 + 2*a^4*d^3 + (b^4*c^3 - 3*a^2*b^2*c*d^2 + 2*a^3*b*d^3)*x)*log(b*x + a) + (b^4*c^3*x + a*b^3*c^3)*log(x))/(a^2*b^4*x + a^3*b^3)","B",0
275,1,198,0,1.247011," ","integrate((d*x+c)^3/x^2/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{2} c^{3} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x - {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d + a^{3} b d^{3}\right)} x^{2} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + a^{4} d^{3}\right)} x\right)} \log\left(b x + a\right) + {\left({\left(2 \, b^{4} c^{3} - 3 \, a b^{3} c^{2} d\right)} x^{2} + {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d\right)} x\right)} \log\left(x\right)}{a^{3} b^{3} x^{2} + a^{4} b^{2} x}"," ",0,"-(a^2*b^2*c^3 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x - ((2*b^4*c^3 - 3*a*b^3*c^2*d + a^3*b*d^3)*x^2 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + a^4*d^3)*x)*log(b*x + a) + ((2*b^4*c^3 - 3*a*b^3*c^2*d)*x^2 + (2*a*b^3*c^3 - 3*a^2*b^2*c^2*d)*x)*log(x))/(a^3*b^3*x^2 + a^4*b^2*x)","B",0
276,1,249,0,1.226546," ","integrate((d*x+c)^3/x^3/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{a^{3} b c^{3} - 2 \, {\left(3 \, a b^{3} c^{3} - 6 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{2} - 3 \, {\left(a^{2} b^{2} c^{3} - 2 \, a^{3} b c^{2} d\right)} x + 6 \, {\left({\left(b^{4} c^{3} - 2 \, a b^{3} c^{2} d + a^{2} b^{2} c d^{2}\right)} x^{3} + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d + a^{3} b c d^{2}\right)} x^{2}\right)} \log\left(b x + a\right) - 6 \, {\left({\left(b^{4} c^{3} - 2 \, a b^{3} c^{2} d + a^{2} b^{2} c d^{2}\right)} x^{3} + {\left(a b^{3} c^{3} - 2 \, a^{2} b^{2} c^{2} d + a^{3} b c d^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{2} x^{3} + a^{5} b x^{2}\right)}}"," ",0,"-1/2*(a^3*b*c^3 - 2*(3*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*x^2 - 3*(a^2*b^2*c^3 - 2*a^3*b*c^2*d)*x + 6*((b^4*c^3 - 2*a*b^3*c^2*d + a^2*b^2*c*d^2)*x^3 + (a*b^3*c^3 - 2*a^2*b^2*c^2*d + a^3*b*c*d^2)*x^2)*log(b*x + a) - 6*((b^4*c^3 - 2*a*b^3*c^2*d + a^2*b^2*c*d^2)*x^3 + (a*b^3*c^3 - 2*a^2*b^2*c^2*d + a^3*b*c*d^2)*x^2)*log(x))/(a^4*b^2*x^3 + a^5*b*x^2)","B",0
277,1,322,0,0.859243," ","integrate((d*x+c)^3/x^4/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{4} c^{3} + 6 \, {\left(4 \, a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3} + 3 \, {\left(4 \, a^{2} b^{2} c^{3} - 9 \, a^{3} b c^{2} d + 6 \, a^{4} c d^{2}\right)} x^{2} - {\left(4 \, a^{3} b c^{3} - 9 \, a^{4} c^{2} d\right)} x - 6 \, {\left({\left(4 \, b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 6 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} + {\left(4 \, a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3}\right)} \log\left(b x + a\right) + 6 \, {\left({\left(4 \, b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 6 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} + {\left(4 \, a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}"," ",0,"-1/6*(2*a^4*c^3 + 6*(4*a*b^3*c^3 - 9*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - a^4*d^3)*x^3 + 3*(4*a^2*b^2*c^3 - 9*a^3*b*c^2*d + 6*a^4*c*d^2)*x^2 - (4*a^3*b*c^3 - 9*a^4*c^2*d)*x - 6*((4*b^4*c^3 - 9*a*b^3*c^2*d + 6*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4 + (4*a*b^3*c^3 - 9*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - a^4*d^3)*x^3)*log(b*x + a) + 6*((4*b^4*c^3 - 9*a*b^3*c^2*d + 6*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4 + (4*a*b^3*c^3 - 9*a^2*b^2*c^2*d + 6*a^3*b*c*d^2 - a^4*d^3)*x^3)*log(x))/(a^5*b*x^4 + a^6*x^3)","B",0
278,1,382,0,1.036763," ","integrate((d*x+c)^3/x^5/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{3 \, a^{5} c^{3} - 12 \, {\left(5 \, a b^{4} c^{3} - 12 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 2 \, a^{4} b d^{3}\right)} x^{4} - 6 \, {\left(5 \, a^{2} b^{3} c^{3} - 12 \, a^{3} b^{2} c^{2} d + 9 \, a^{4} b c d^{2} - 2 \, a^{5} d^{3}\right)} x^{3} + 2 \, {\left(5 \, a^{3} b^{2} c^{3} - 12 \, a^{4} b c^{2} d + 9 \, a^{5} c d^{2}\right)} x^{2} - {\left(5 \, a^{4} b c^{3} - 12 \, a^{5} c^{2} d\right)} x + 12 \, {\left({\left(5 \, b^{5} c^{3} - 12 \, a b^{4} c^{2} d + 9 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b^{2} d^{3}\right)} x^{5} + {\left(5 \, a b^{4} c^{3} - 12 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 2 \, a^{4} b d^{3}\right)} x^{4}\right)} \log\left(b x + a\right) - 12 \, {\left({\left(5 \, b^{5} c^{3} - 12 \, a b^{4} c^{2} d + 9 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b^{2} d^{3}\right)} x^{5} + {\left(5 \, a b^{4} c^{3} - 12 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - 2 \, a^{4} b d^{3}\right)} x^{4}\right)} \log\left(x\right)}{12 \, {\left(a^{6} b x^{5} + a^{7} x^{4}\right)}}"," ",0,"-1/12*(3*a^5*c^3 - 12*(5*a*b^4*c^3 - 12*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 2*a^4*b*d^3)*x^4 - 6*(5*a^2*b^3*c^3 - 12*a^3*b^2*c^2*d + 9*a^4*b*c*d^2 - 2*a^5*d^3)*x^3 + 2*(5*a^3*b^2*c^3 - 12*a^4*b*c^2*d + 9*a^5*c*d^2)*x^2 - (5*a^4*b*c^3 - 12*a^5*c^2*d)*x + 12*((5*b^5*c^3 - 12*a*b^4*c^2*d + 9*a^2*b^3*c*d^2 - 2*a^3*b^2*d^3)*x^5 + (5*a*b^4*c^3 - 12*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 2*a^4*b*d^3)*x^4)*log(b*x + a) - 12*((5*b^5*c^3 - 12*a*b^4*c^2*d + 9*a^2*b^3*c*d^2 - 2*a^3*b^2*d^3)*x^5 + (5*a*b^4*c^3 - 12*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - 2*a^4*b*d^3)*x^4)*log(x))/(a^6*b*x^5 + a^7*x^4)","B",0
279,1,438,0,1.192275," ","integrate((d*x+c)^3/x^6/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, a^{6} c^{3} + 60 \, {\left(2 \, a b^{5} c^{3} - 5 \, a^{2} b^{4} c^{2} d + 4 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{5} + 30 \, {\left(2 \, a^{2} b^{4} c^{3} - 5 \, a^{3} b^{3} c^{2} d + 4 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} x^{4} - 10 \, {\left(2 \, a^{3} b^{3} c^{3} - 5 \, a^{4} b^{2} c^{2} d + 4 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} x^{3} + 5 \, {\left(2 \, a^{4} b^{2} c^{3} - 5 \, a^{5} b c^{2} d + 4 \, a^{6} c d^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{5} b c^{3} - 5 \, a^{6} c^{2} d\right)} x - 60 \, {\left({\left(2 \, b^{6} c^{3} - 5 \, a b^{5} c^{2} d + 4 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{6} + {\left(2 \, a b^{5} c^{3} - 5 \, a^{2} b^{4} c^{2} d + 4 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{5}\right)} \log\left(b x + a\right) + 60 \, {\left({\left(2 \, b^{6} c^{3} - 5 \, a b^{5} c^{2} d + 4 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{6} + {\left(2 \, a b^{5} c^{3} - 5 \, a^{2} b^{4} c^{2} d + 4 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} x^{5}\right)} \log\left(x\right)}{20 \, {\left(a^{7} b x^{6} + a^{8} x^{5}\right)}}"," ",0,"-1/20*(4*a^6*c^3 + 60*(2*a*b^5*c^3 - 5*a^2*b^4*c^2*d + 4*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^5 + 30*(2*a^2*b^4*c^3 - 5*a^3*b^3*c^2*d + 4*a^4*b^2*c*d^2 - a^5*b*d^3)*x^4 - 10*(2*a^3*b^3*c^3 - 5*a^4*b^2*c^2*d + 4*a^5*b*c*d^2 - a^6*d^3)*x^3 + 5*(2*a^4*b^2*c^3 - 5*a^5*b*c^2*d + 4*a^6*c*d^2)*x^2 - 3*(2*a^5*b*c^3 - 5*a^6*c^2*d)*x - 60*((2*b^6*c^3 - 5*a*b^5*c^2*d + 4*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^6 + (2*a*b^5*c^3 - 5*a^2*b^4*c^2*d + 4*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^5)*log(b*x + a) + 60*((2*b^6*c^3 - 5*a*b^5*c^2*d + 4*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^6 + (2*a*b^5*c^3 - 5*a^2*b^4*c^2*d + 4*a^3*b^3*c*d^2 - a^4*b^2*d^3)*x^5)*log(x))/(a^7*b*x^6 + a^8*x^5)","B",0
280,1,700,0,1.205210," ","integrate(x^6/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{3 \, a b^{6} c^{7} - 3 \, a^{2} b^{5} c^{6} d + 3 \, a^{6} b c^{2} d^{5} - 3 \, a^{7} c d^{6} - {\left(b^{7} c^{3} d^{4} - 3 \, a b^{6} c^{2} d^{5} + 3 \, a^{2} b^{5} c d^{6} - a^{3} b^{4} d^{7}\right)} x^{5} + 2 \, {\left(b^{7} c^{4} d^{3} - 2 \, a b^{6} c^{3} d^{4} + 2 \, a^{3} b^{4} c d^{6} - a^{4} b^{3} d^{7}\right)} x^{4} - {\left(6 \, b^{7} c^{5} d^{2} - 11 \, a b^{6} c^{4} d^{3} + 3 \, a^{2} b^{5} c^{3} d^{4} - 3 \, a^{3} b^{4} c^{2} d^{5} + 11 \, a^{4} b^{3} c d^{6} - 6 \, a^{5} b^{2} d^{7}\right)} x^{3} - 9 \, {\left(b^{7} c^{6} d - a b^{6} c^{5} d^{2} - a^{2} b^{5} c^{4} d^{3} + a^{4} b^{3} c^{2} d^{5} + a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{2} + 3 \, {\left(b^{7} c^{7} - 4 \, a b^{6} c^{6} d + 5 \, a^{2} b^{5} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{2} d^{5} + 4 \, a^{6} b c d^{6} - a^{7} d^{7}\right)} x + 6 \, {\left(3 \, a^{6} b c^{2} d^{5} - 2 \, a^{7} c d^{6} + {\left(3 \, a^{5} b^{2} c d^{6} - 2 \, a^{6} b d^{7}\right)} x^{2} + {\left(3 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - 2 \, a^{7} d^{7}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(2 \, a b^{6} c^{7} - 3 \, a^{2} b^{5} c^{6} d + {\left(2 \, b^{7} c^{6} d - 3 \, a b^{6} c^{5} d^{2}\right)} x^{2} + {\left(2 \, b^{7} c^{7} - a b^{6} c^{6} d - 3 \, a^{2} b^{5} c^{5} d^{2}\right)} x\right)} \log\left(d x + c\right)}{3 \, {\left(a b^{8} c^{4} d^{5} - 3 \, a^{2} b^{7} c^{3} d^{6} + 3 \, a^{3} b^{6} c^{2} d^{7} - a^{4} b^{5} c d^{8} + {\left(b^{9} c^{3} d^{6} - 3 \, a b^{8} c^{2} d^{7} + 3 \, a^{2} b^{7} c d^{8} - a^{3} b^{6} d^{9}\right)} x^{2} + {\left(b^{9} c^{4} d^{5} - 2 \, a b^{8} c^{3} d^{6} + 2 \, a^{3} b^{6} c d^{8} - a^{4} b^{5} d^{9}\right)} x\right)}}"," ",0,"-1/3*(3*a*b^6*c^7 - 3*a^2*b^5*c^6*d + 3*a^6*b*c^2*d^5 - 3*a^7*c*d^6 - (b^7*c^3*d^4 - 3*a*b^6*c^2*d^5 + 3*a^2*b^5*c*d^6 - a^3*b^4*d^7)*x^5 + 2*(b^7*c^4*d^3 - 2*a*b^6*c^3*d^4 + 2*a^3*b^4*c*d^6 - a^4*b^3*d^7)*x^4 - (6*b^7*c^5*d^2 - 11*a*b^6*c^4*d^3 + 3*a^2*b^5*c^3*d^4 - 3*a^3*b^4*c^2*d^5 + 11*a^4*b^3*c*d^6 - 6*a^5*b^2*d^7)*x^3 - 9*(b^7*c^6*d - a*b^6*c^5*d^2 - a^2*b^5*c^4*d^3 + a^4*b^3*c^2*d^5 + a^5*b^2*c*d^6 - a^6*b*d^7)*x^2 + 3*(b^7*c^7 - 4*a*b^6*c^6*d + 5*a^2*b^5*c^5*d^2 - 5*a^5*b^2*c^2*d^5 + 4*a^6*b*c*d^6 - a^7*d^7)*x + 6*(3*a^6*b*c^2*d^5 - 2*a^7*c*d^6 + (3*a^5*b^2*c*d^6 - 2*a^6*b*d^7)*x^2 + (3*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - 2*a^7*d^7)*x)*log(b*x + a) + 6*(2*a*b^6*c^7 - 3*a^2*b^5*c^6*d + (2*b^7*c^6*d - 3*a*b^6*c^5*d^2)*x^2 + (2*b^7*c^7 - a*b^6*c^6*d - 3*a^2*b^5*c^5*d^2)*x)*log(d*x + c))/(a*b^8*c^4*d^5 - 3*a^2*b^7*c^3*d^6 + 3*a^3*b^6*c^2*d^7 - a^4*b^5*c*d^8 + (b^9*c^3*d^6 - 3*a*b^8*c^2*d^7 + 3*a^2*b^7*c*d^8 - a^3*b^6*d^9)*x^2 + (b^9*c^4*d^5 - 2*a*b^8*c^3*d^6 + 2*a^3*b^6*c*d^8 - a^4*b^5*d^9)*x)","B",0
281,1,623,0,1.094438," ","integrate(x^5/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, a b^{5} c^{6} - 2 \, a^{2} b^{4} c^{5} d + 2 \, a^{5} b c^{2} d^{4} - 2 \, a^{6} c d^{5} + {\left(b^{6} c^{3} d^{3} - 3 \, a b^{5} c^{2} d^{4} + 3 \, a^{2} b^{4} c d^{5} - a^{3} b^{3} d^{6}\right)} x^{4} - 3 \, {\left(b^{6} c^{4} d^{2} - 2 \, a b^{5} c^{3} d^{3} + 2 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x^{3} - {\left(4 \, b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} - 5 \, a^{2} b^{4} c^{3} d^{3} + 5 \, a^{3} b^{3} c^{2} d^{4} + 5 \, a^{4} b^{2} c d^{5} - 4 \, a^{5} b d^{6}\right)} x^{2} + 2 \, {\left(b^{6} c^{6} - 3 \, a b^{5} c^{5} d + 4 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{4} b^{2} c^{2} d^{4} + 3 \, a^{5} b c d^{5} - a^{6} d^{6}\right)} x + 2 \, {\left(5 \, a^{5} b c^{2} d^{4} - 3 \, a^{6} c d^{5} + {\left(5 \, a^{4} b^{2} c d^{5} - 3 \, a^{5} b d^{6}\right)} x^{2} + {\left(5 \, a^{4} b^{2} c^{2} d^{4} + 2 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + {\left(3 \, b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2}\right)} x^{2} + {\left(3 \, b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{7} c^{4} d^{4} - 3 \, a^{2} b^{6} c^{3} d^{5} + 3 \, a^{3} b^{5} c^{2} d^{6} - a^{4} b^{4} c d^{7} + {\left(b^{8} c^{3} d^{5} - 3 \, a b^{7} c^{2} d^{6} + 3 \, a^{2} b^{6} c d^{7} - a^{3} b^{5} d^{8}\right)} x^{2} + {\left(b^{8} c^{4} d^{4} - 2 \, a b^{7} c^{3} d^{5} + 2 \, a^{3} b^{5} c d^{7} - a^{4} b^{4} d^{8}\right)} x\right)}}"," ",0,"1/2*(2*a*b^5*c^6 - 2*a^2*b^4*c^5*d + 2*a^5*b*c^2*d^4 - 2*a^6*c*d^5 + (b^6*c^3*d^3 - 3*a*b^5*c^2*d^4 + 3*a^2*b^4*c*d^5 - a^3*b^3*d^6)*x^4 - 3*(b^6*c^4*d^2 - 2*a*b^5*c^3*d^3 + 2*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x^3 - (4*b^6*c^5*d - 5*a*b^5*c^4*d^2 - 5*a^2*b^4*c^3*d^3 + 5*a^3*b^3*c^2*d^4 + 5*a^4*b^2*c*d^5 - 4*a^5*b*d^6)*x^2 + 2*(b^6*c^6 - 3*a*b^5*c^5*d + 4*a^2*b^4*c^4*d^2 - 4*a^4*b^2*c^2*d^4 + 3*a^5*b*c*d^5 - a^6*d^6)*x + 2*(5*a^5*b*c^2*d^4 - 3*a^6*c*d^5 + (5*a^4*b^2*c*d^5 - 3*a^5*b*d^6)*x^2 + (5*a^4*b^2*c^2*d^4 + 2*a^5*b*c*d^5 - 3*a^6*d^6)*x)*log(b*x + a) + 2*(3*a*b^5*c^6 - 5*a^2*b^4*c^5*d + (3*b^6*c^5*d - 5*a*b^5*c^4*d^2)*x^2 + (3*b^6*c^6 - 2*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2)*x)*log(d*x + c))/(a*b^7*c^4*d^4 - 3*a^2*b^6*c^3*d^5 + 3*a^3*b^5*c^2*d^6 - a^4*b^4*c*d^7 + (b^8*c^3*d^5 - 3*a*b^7*c^2*d^6 + 3*a^2*b^6*c*d^7 - a^3*b^5*d^8)*x^2 + (b^8*c^4*d^4 - 2*a*b^7*c^3*d^5 + 2*a^3*b^5*c*d^7 - a^4*b^4*d^8)*x)","B",0
282,1,537,0,0.932052," ","integrate(x^4/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a b^{4} c^{5} - a^{2} b^{3} c^{4} d + a^{4} b c^{2} d^{3} - a^{5} c d^{4} - {\left(b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} + 3 \, a^{2} b^{3} c d^{4} - a^{3} b^{2} d^{5}\right)} x^{3} - {\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} + 2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{2} + {\left(b^{5} c^{5} - 2 \, a b^{4} c^{4} d + 3 \, a^{2} b^{3} c^{3} d^{2} - 3 \, a^{3} b^{2} c^{2} d^{3} + 2 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} x + 2 \, {\left(2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4} + {\left(2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{2} + {\left(2 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} - a^{5} d^{5}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + {\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2}\right)} x^{2} + {\left(b^{5} c^{5} - a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{6} c^{4} d^{3} - 3 \, a^{2} b^{5} c^{3} d^{4} + 3 \, a^{3} b^{4} c^{2} d^{5} - a^{4} b^{3} c d^{6} + {\left(b^{7} c^{3} d^{4} - 3 \, a b^{6} c^{2} d^{5} + 3 \, a^{2} b^{5} c d^{6} - a^{3} b^{4} d^{7}\right)} x^{2} + {\left(b^{7} c^{4} d^{3} - 2 \, a b^{6} c^{3} d^{4} + 2 \, a^{3} b^{4} c d^{6} - a^{4} b^{3} d^{7}\right)} x}"," ",0,"-(a*b^4*c^5 - a^2*b^3*c^4*d + a^4*b*c^2*d^3 - a^5*c*d^4 - (b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 + 3*a^2*b^3*c*d^4 - a^3*b^2*d^5)*x^3 - (b^5*c^4*d - 2*a*b^4*c^3*d^2 + 2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^2 + (b^5*c^5 - 2*a*b^4*c^4*d + 3*a^2*b^3*c^3*d^2 - 3*a^3*b^2*c^2*d^3 + 2*a^4*b*c*d^4 - a^5*d^5)*x + 2*(2*a^4*b*c^2*d^3 - a^5*c*d^4 + (2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^2 + (2*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 - a^5*d^5)*x)*log(b*x + a) + 2*(a*b^4*c^5 - 2*a^2*b^3*c^4*d + (b^5*c^4*d - 2*a*b^4*c^3*d^2)*x^2 + (b^5*c^5 - a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2)*x)*log(d*x + c))/(a*b^6*c^4*d^3 - 3*a^2*b^5*c^3*d^4 + 3*a^3*b^4*c^2*d^5 - a^4*b^3*c*d^6 + (b^7*c^3*d^4 - 3*a*b^6*c^2*d^5 + 3*a^2*b^5*c*d^6 - a^3*b^4*d^7)*x^2 + (b^7*c^4*d^3 - 2*a*b^6*c^3*d^4 + 2*a^3*b^4*c*d^6 - a^4*b^3*d^7)*x)","B",0
283,1,408,0,1.087214," ","integrate(x^3/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{a b^{3} c^{4} - a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{4} - a b^{3} c^{3} d + a^{3} b c d^{3} - a^{4} d^{4}\right)} x + {\left(3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x\right)} \log\left(b x + a\right) + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{5} c^{4} d^{2} - 3 \, a^{2} b^{4} c^{3} d^{3} + 3 \, a^{3} b^{3} c^{2} d^{4} - a^{4} b^{2} c d^{5} + {\left(b^{6} c^{3} d^{3} - 3 \, a b^{5} c^{2} d^{4} + 3 \, a^{2} b^{4} c d^{5} - a^{3} b^{3} d^{6}\right)} x^{2} + {\left(b^{6} c^{4} d^{2} - 2 \, a b^{5} c^{3} d^{3} + 2 \, a^{3} b^{3} c d^{5} - a^{4} b^{2} d^{6}\right)} x}"," ",0,"(a*b^3*c^4 - a^2*b^2*c^3*d + a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^4 - a*b^3*c^3*d + a^3*b*c*d^3 - a^4*d^4)*x + (3*a^3*b*c^2*d^2 - a^4*c*d^3 + (3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + (3*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3 - a^4*d^4)*x)*log(b*x + a) + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + (b^4*c^3*d - 3*a*b^3*c^2*d^2)*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2)*x)*log(d*x + c))/(a*b^5*c^4*d^2 - 3*a^2*b^4*c^3*d^3 + 3*a^3*b^3*c^2*d^4 - a^4*b^2*c*d^5 + (b^6*c^3*d^3 - 3*a*b^5*c^2*d^4 + 3*a^2*b^4*c*d^5 - a^3*b^3*d^6)*x^2 + (b^6*c^4*d^2 - 2*a*b^5*c^3*d^3 + 2*a^3*b^3*c*d^5 - a^4*b^2*d^6)*x)","B",0
284,1,303,0,0.925417," ","integrate(x^2/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a b^{2} c^{3} - 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 + 2 \, {\left(a b^{2} c d^{2} x^{2} + a^{2} b c^{2} d + {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(a b^{2} c d^{2} x^{2} + a^{2} b c^{2} d + {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{4} c^{4} d - 3 \, a^{2} b^{3} c^{3} d^{2} + 3 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4} + {\left(b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} + 3 \, a^{2} b^{3} c d^{4} - a^{3} b^{2} d^{5}\right)} x^{2} + {\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} + 2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x}"," ",0,"-(a*b^2*c^3 - 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 + 2*(a*b^2*c*d^2*x^2 + a^2*b*c^2*d + (a*b^2*c^2*d + a^2*b*c*d^2)*x)*log(b*x + a) - 2*(a*b^2*c*d^2*x^2 + a^2*b*c^2*d + (a*b^2*c^2*d + a^2*b*c*d^2)*x)*log(d*x + c))/(a*b^4*c^4*d - 3*a^2*b^3*c^3*d^2 + 3*a^3*b^2*c^2*d^3 - a^4*b*c*d^4 + (b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 + 3*a^2*b^3*c*d^4 - a^3*b^2*d^5)*x^2 + (b^5*c^4*d - 2*a*b^4*c^3*d^2 + 2*a^3*b^2*c*d^4 - a^4*b*d^5)*x)","B",0
285,1,283,0,1.011767," ","integrate(x/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, a b c^{2} - 2 \, a^{2} c d + {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x + {\left(a b c^{2} + a^{2} c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2} + {\left(b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} x\right)} \log\left(b x + a\right) - {\left(a b c^{2} + a^{2} c d + {\left(b^{2} c d + a b d^{2}\right)} x^{2} + {\left(b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x}"," ",0,"(2*a*b*c^2 - 2*a^2*c*d + (b^2*c^2 - a^2*d^2)*x + (a*b*c^2 + a^2*c*d + (b^2*c*d + a*b*d^2)*x^2 + (b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)*log(b*x + a) - (a*b*c^2 + a^2*c*d + (b^2*c*d + a*b*d^2)*x^2 + (b^2*c^2 + 2*a*b*c*d + a^2*d^2)*x)*log(d*x + c))/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x)","B",0
286,1,241,0,1.090434," ","integrate(1/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} - a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x}"," ",0,"-(b^2*c^2 - a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a) - 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c))/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x)","B",0
287,1,524,0,12.704066," ","integrate(1/x/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{a b^{3} c^{4} - a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(a b^{3} c^{3} d - a^{3} b c d^{3}\right)} x - {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2}\right)} x\right)} \log\left(b x + a\right) - {\left(3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c^{2} d^{2} + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x\right)} \log\left(d x + c\right) + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x\right)} \log\left(x\right)}{a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3} + {\left(a^{2} b^{4} c^{5} d - 3 \, a^{3} b^{3} c^{4} d^{2} + 3 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4}\right)} x^{2} + {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x}"," ",0,"(a*b^3*c^4 - a^2*b^2*c^3*d + a^3*b*c^2*d^2 - a^4*c*d^3 + (a*b^3*c^3*d - a^3*b*c*d^3)*x - (a*b^3*c^4 - 3*a^2*b^2*c^3*d + (b^4*c^3*d - 3*a*b^3*c^2*d^2)*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2)*x)*log(b*x + a) - (3*a^3*b*c^2*d^2 - a^4*c*d^3 + (3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + (3*a^2*b^2*c^2*d^2 + 2*a^3*b*c*d^3 - a^4*d^4)*x)*log(d*x + c) + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x)*log(x))/(a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3 + (a^2*b^4*c^5*d - 3*a^3*b^3*c^4*d^2 + 3*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4)*x^2 + (a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x)","B",0
288,1,653,0,35.496420," ","integrate(1/x^2/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} b^{3} c^{5} - 3 \, a^{3} b^{2} c^{4} d + 3 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + 2 \, {\left(a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - a^{4} b c d^{4}\right)} x^{2} + {\left(2 \, a b^{4} c^{5} - 3 \, a^{2} b^{3} c^{4} d + 3 \, a^{4} b c^{2} d^{3} - 2 \, a^{5} c d^{4}\right)} x - 2 \, {\left({\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2}\right)} x^{3} + {\left(b^{5} c^{5} - a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2}\right)} x^{2} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{3} + {\left(2 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} - a^{5} d^{5}\right)} x^{2} + {\left(2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left({\left(b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} + 2 \, a^{3} b^{2} c d^{4} - a^{4} b d^{5}\right)} x^{3} + {\left(b^{5} c^{5} - a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} - a^{5} d^{5}\right)} x^{2} + {\left(a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d + 2 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x\right)} \log\left(x\right)}{{\left(a^{3} b^{4} c^{6} d - 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - a^{6} b c^{3} d^{4}\right)} x^{3} + {\left(a^{3} b^{4} c^{7} - 2 \, a^{4} b^{3} c^{6} d + 2 \, a^{6} b c^{4} d^{3} - a^{7} c^{3} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{7} - 3 \, a^{5} b^{2} c^{6} d + 3 \, a^{6} b c^{5} d^{2} - a^{7} c^{4} d^{3}\right)} x}"," ",0,"-(a^2*b^3*c^5 - 3*a^3*b^2*c^4*d + 3*a^4*b*c^3*d^2 - a^5*c^2*d^3 + 2*(a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - a^4*b*c*d^4)*x^2 + (2*a*b^4*c^5 - 3*a^2*b^3*c^4*d + 3*a^4*b*c^2*d^3 - 2*a^5*c*d^4)*x - 2*((b^5*c^4*d - 2*a*b^4*c^3*d^2)*x^3 + (b^5*c^5 - a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2)*x^2 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d)*x)*log(b*x + a) - 2*((2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^3 + (2*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 - a^5*d^5)*x^2 + (2*a^4*b*c^2*d^3 - a^5*c*d^4)*x)*log(d*x + c) + 2*((b^5*c^4*d - 2*a*b^4*c^3*d^2 + 2*a^3*b^2*c*d^4 - a^4*b*d^5)*x^3 + (b^5*c^5 - a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 - a^5*d^5)*x^2 + (a*b^4*c^5 - 2*a^2*b^3*c^4*d + 2*a^4*b*c^2*d^3 - a^5*c*d^4)*x)*log(x))/((a^3*b^4*c^6*d - 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - a^6*b*c^3*d^4)*x^3 + (a^3*b^4*c^7 - 2*a^4*b^3*c^6*d + 2*a^6*b*c^4*d^3 - a^7*c^3*d^4)*x^2 + (a^4*b^3*c^7 - 3*a^5*b^2*c^6*d + 3*a^6*b*c^5*d^2 - a^7*c^4*d^3)*x)","B",0
289,1,750,0,78.827647," ","integrate(1/x^3/(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a^{3} b^{3} c^{6} - 3 \, a^{4} b^{2} c^{5} d + 3 \, a^{5} b c^{4} d^{2} - a^{6} c^{3} d^{3} - 2 \, {\left(3 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2} + 5 \, a^{4} b^{2} c^{2} d^{4} - 3 \, a^{5} b c d^{5}\right)} x^{3} - {\left(6 \, a b^{5} c^{6} - 7 \, a^{2} b^{4} c^{5} d - 5 \, a^{3} b^{3} c^{4} d^{2} + 5 \, a^{4} b^{2} c^{3} d^{3} + 7 \, a^{5} b c^{2} d^{4} - 6 \, a^{6} c d^{5}\right)} x^{2} - 3 \, {\left(a^{2} b^{4} c^{6} - 2 \, a^{3} b^{3} c^{5} d + 2 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4}\right)} x + 2 \, {\left({\left(3 \, b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2}\right)} x^{4} + {\left(3 \, b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2}\right)} x^{3} + {\left(3 \, a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d\right)} x^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(5 \, a^{4} b^{2} c d^{5} - 3 \, a^{5} b d^{6}\right)} x^{4} + {\left(5 \, a^{4} b^{2} c^{2} d^{4} + 2 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} + {\left(5 \, a^{5} b c^{2} d^{4} - 3 \, a^{6} c d^{5}\right)} x^{2}\right)} \log\left(d x + c\right) - 2 \, {\left({\left(3 \, b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 5 \, a^{4} b^{2} c d^{5} - 3 \, a^{5} b d^{6}\right)} x^{4} + {\left(3 \, b^{6} c^{6} - 2 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2} + 5 \, a^{4} b^{2} c^{2} d^{4} + 2 \, a^{5} b c d^{5} - 3 \, a^{6} d^{6}\right)} x^{3} + {\left(3 \, a b^{5} c^{6} - 5 \, a^{2} b^{4} c^{5} d + 5 \, a^{5} b c^{2} d^{4} - 3 \, a^{6} c d^{5}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{4} c^{7} d - 3 \, a^{5} b^{3} c^{6} d^{2} + 3 \, a^{6} b^{2} c^{5} d^{3} - a^{7} b c^{4} d^{4}\right)} x^{4} + {\left(a^{4} b^{4} c^{8} - 2 \, a^{5} b^{3} c^{7} d + 2 \, a^{7} b c^{5} d^{3} - a^{8} c^{4} d^{4}\right)} x^{3} + {\left(a^{5} b^{3} c^{8} - 3 \, a^{6} b^{2} c^{7} d + 3 \, a^{7} b c^{6} d^{2} - a^{8} c^{5} d^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*(a^3*b^3*c^6 - 3*a^4*b^2*c^5*d + 3*a^5*b*c^4*d^2 - a^6*c^3*d^3 - 2*(3*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2 + 5*a^4*b^2*c^2*d^4 - 3*a^5*b*c*d^5)*x^3 - (6*a*b^5*c^6 - 7*a^2*b^4*c^5*d - 5*a^3*b^3*c^4*d^2 + 5*a^4*b^2*c^3*d^3 + 7*a^5*b*c^2*d^4 - 6*a^6*c*d^5)*x^2 - 3*(a^2*b^4*c^6 - 2*a^3*b^3*c^5*d + 2*a^5*b*c^3*d^3 - a^6*c^2*d^4)*x + 2*((3*b^6*c^5*d - 5*a*b^5*c^4*d^2)*x^4 + (3*b^6*c^6 - 2*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2)*x^3 + (3*a*b^5*c^6 - 5*a^2*b^4*c^5*d)*x^2)*log(b*x + a) + 2*((5*a^4*b^2*c*d^5 - 3*a^5*b*d^6)*x^4 + (5*a^4*b^2*c^2*d^4 + 2*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 + (5*a^5*b*c^2*d^4 - 3*a^6*c*d^5)*x^2)*log(d*x + c) - 2*((3*b^6*c^5*d - 5*a*b^5*c^4*d^2 + 5*a^4*b^2*c*d^5 - 3*a^5*b*d^6)*x^4 + (3*b^6*c^6 - 2*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2 + 5*a^4*b^2*c^2*d^4 + 2*a^5*b*c*d^5 - 3*a^6*d^6)*x^3 + (3*a*b^5*c^6 - 5*a^2*b^4*c^5*d + 5*a^5*b*c^2*d^4 - 3*a^6*c*d^5)*x^2)*log(x))/((a^4*b^4*c^7*d - 3*a^5*b^3*c^6*d^2 + 3*a^6*b^2*c^5*d^3 - a^7*b*c^4*d^4)*x^4 + (a^4*b^4*c^8 - 2*a^5*b^3*c^7*d + 2*a^7*b*c^5*d^3 - a^8*c^4*d^4)*x^3 + (a^5*b^3*c^8 - 3*a^6*b^2*c^7*d + 3*a^7*b*c^6*d^2 - a^8*c^5*d^3)*x^2)","B",0
290,1,1201,0,1.302181," ","integrate(x^7/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{27 \, a b^{7} c^{9} - 66 \, a^{2} b^{6} c^{8} d + 39 \, a^{3} b^{5} c^{7} d^{2} - 6 \, a^{7} b c^{3} d^{6} + 6 \, a^{8} c^{2} d^{7} - 2 \, {\left(b^{8} c^{4} d^{5} - 4 \, a b^{7} c^{3} d^{6} + 6 \, a^{2} b^{6} c^{2} d^{7} - 4 \, a^{3} b^{5} c d^{8} + a^{4} b^{4} d^{9}\right)} x^{6} + {\left(5 \, b^{8} c^{5} d^{4} - 16 \, a b^{7} c^{4} d^{5} + 14 \, a^{2} b^{6} c^{3} d^{6} + 4 \, a^{3} b^{5} c^{2} d^{7} - 11 \, a^{4} b^{4} c d^{8} + 4 \, a^{5} b^{3} d^{9}\right)} x^{5} - {\left(20 \, b^{8} c^{6} d^{3} - 61 \, a b^{7} c^{5} d^{4} + 56 \, a^{2} b^{6} c^{4} d^{5} - 14 \, a^{3} b^{5} c^{3} d^{6} + 16 \, a^{4} b^{4} c^{2} d^{7} - 29 \, a^{5} b^{3} c d^{8} + 12 \, a^{6} b^{2} d^{9}\right)} x^{4} - {\left(63 \, b^{8} c^{7} d^{2} - 166 \, a b^{7} c^{6} d^{3} + 94 \, a^{2} b^{6} c^{5} d^{4} + 42 \, a^{3} b^{5} c^{4} d^{5} + 7 \, a^{4} b^{4} c^{3} d^{6} - 46 \, a^{5} b^{3} c^{2} d^{7} - 12 \, a^{6} b^{2} c d^{8} + 18 \, a^{7} b d^{9}\right)} x^{3} - 3 \, {\left(2 \, b^{8} c^{8} d + 9 \, a b^{7} c^{7} d^{2} - 46 \, a^{2} b^{6} c^{6} d^{3} + 50 \, a^{3} b^{5} c^{5} d^{4} - 7 \, a^{5} b^{3} c^{3} d^{6} - 20 \, a^{6} b^{2} c^{2} d^{7} + 14 \, a^{7} b c d^{8} - 2 \, a^{8} d^{9}\right)} x^{2} + 3 \, {\left(9 \, b^{8} c^{9} - 24 \, a b^{7} c^{8} d + 25 \, a^{2} b^{6} c^{7} d^{2} - 16 \, a^{3} b^{5} c^{6} d^{3} + 12 \, a^{6} b^{2} c^{3} d^{6} - 10 \, a^{7} b c^{2} d^{7} + 4 \, a^{8} c d^{8}\right)} x - 6 \, {\left(7 \, a^{7} b c^{3} d^{6} - 4 \, a^{8} c^{2} d^{7} + {\left(7 \, a^{6} b^{2} c d^{8} - 4 \, a^{7} b d^{9}\right)} x^{3} + {\left(14 \, a^{6} b^{2} c^{2} d^{7} - a^{7} b c d^{8} - 4 \, a^{8} d^{9}\right)} x^{2} + {\left(7 \, a^{6} b^{2} c^{3} d^{6} + 10 \, a^{7} b c^{2} d^{7} - 8 \, a^{8} c d^{8}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(10 \, a b^{7} c^{9} - 28 \, a^{2} b^{6} c^{8} d + 21 \, a^{3} b^{5} c^{7} d^{2} + {\left(10 \, b^{8} c^{7} d^{2} - 28 \, a b^{7} c^{6} d^{3} + 21 \, a^{2} b^{6} c^{5} d^{4}\right)} x^{3} + {\left(20 \, b^{8} c^{8} d - 46 \, a b^{7} c^{7} d^{2} + 14 \, a^{2} b^{6} c^{6} d^{3} + 21 \, a^{3} b^{5} c^{5} d^{4}\right)} x^{2} + {\left(10 \, b^{8} c^{9} - 8 \, a b^{7} c^{8} d - 35 \, a^{2} b^{6} c^{7} d^{2} + 42 \, a^{3} b^{5} c^{6} d^{3}\right)} x\right)} \log\left(d x + c\right)}{6 \, {\left(a b^{9} c^{6} d^{6} - 4 \, a^{2} b^{8} c^{5} d^{7} + 6 \, a^{3} b^{7} c^{4} d^{8} - 4 \, a^{4} b^{6} c^{3} d^{9} + a^{5} b^{5} c^{2} d^{10} + {\left(b^{10} c^{4} d^{8} - 4 \, a b^{9} c^{3} d^{9} + 6 \, a^{2} b^{8} c^{2} d^{10} - 4 \, a^{3} b^{7} c d^{11} + a^{4} b^{6} d^{12}\right)} x^{3} + {\left(2 \, b^{10} c^{5} d^{7} - 7 \, a b^{9} c^{4} d^{8} + 8 \, a^{2} b^{8} c^{3} d^{9} - 2 \, a^{3} b^{7} c^{2} d^{10} - 2 \, a^{4} b^{6} c d^{11} + a^{5} b^{5} d^{12}\right)} x^{2} + {\left(b^{10} c^{6} d^{6} - 2 \, a b^{9} c^{5} d^{7} - 2 \, a^{2} b^{8} c^{4} d^{8} + 8 \, a^{3} b^{7} c^{3} d^{9} - 7 \, a^{4} b^{6} c^{2} d^{10} + 2 \, a^{5} b^{5} c d^{11}\right)} x\right)}}"," ",0,"-1/6*(27*a*b^7*c^9 - 66*a^2*b^6*c^8*d + 39*a^3*b^5*c^7*d^2 - 6*a^7*b*c^3*d^6 + 6*a^8*c^2*d^7 - 2*(b^8*c^4*d^5 - 4*a*b^7*c^3*d^6 + 6*a^2*b^6*c^2*d^7 - 4*a^3*b^5*c*d^8 + a^4*b^4*d^9)*x^6 + (5*b^8*c^5*d^4 - 16*a*b^7*c^4*d^5 + 14*a^2*b^6*c^3*d^6 + 4*a^3*b^5*c^2*d^7 - 11*a^4*b^4*c*d^8 + 4*a^5*b^3*d^9)*x^5 - (20*b^8*c^6*d^3 - 61*a*b^7*c^5*d^4 + 56*a^2*b^6*c^4*d^5 - 14*a^3*b^5*c^3*d^6 + 16*a^4*b^4*c^2*d^7 - 29*a^5*b^3*c*d^8 + 12*a^6*b^2*d^9)*x^4 - (63*b^8*c^7*d^2 - 166*a*b^7*c^6*d^3 + 94*a^2*b^6*c^5*d^4 + 42*a^3*b^5*c^4*d^5 + 7*a^4*b^4*c^3*d^6 - 46*a^5*b^3*c^2*d^7 - 12*a^6*b^2*c*d^8 + 18*a^7*b*d^9)*x^3 - 3*(2*b^8*c^8*d + 9*a*b^7*c^7*d^2 - 46*a^2*b^6*c^6*d^3 + 50*a^3*b^5*c^5*d^4 - 7*a^5*b^3*c^3*d^6 - 20*a^6*b^2*c^2*d^7 + 14*a^7*b*c*d^8 - 2*a^8*d^9)*x^2 + 3*(9*b^8*c^9 - 24*a*b^7*c^8*d + 25*a^2*b^6*c^7*d^2 - 16*a^3*b^5*c^6*d^3 + 12*a^6*b^2*c^3*d^6 - 10*a^7*b*c^2*d^7 + 4*a^8*c*d^8)*x - 6*(7*a^7*b*c^3*d^6 - 4*a^8*c^2*d^7 + (7*a^6*b^2*c*d^8 - 4*a^7*b*d^9)*x^3 + (14*a^6*b^2*c^2*d^7 - a^7*b*c*d^8 - 4*a^8*d^9)*x^2 + (7*a^6*b^2*c^3*d^6 + 10*a^7*b*c^2*d^7 - 8*a^8*c*d^8)*x)*log(b*x + a) + 6*(10*a*b^7*c^9 - 28*a^2*b^6*c^8*d + 21*a^3*b^5*c^7*d^2 + (10*b^8*c^7*d^2 - 28*a*b^7*c^6*d^3 + 21*a^2*b^6*c^5*d^4)*x^3 + (20*b^8*c^8*d - 46*a*b^7*c^7*d^2 + 14*a^2*b^6*c^6*d^3 + 21*a^3*b^5*c^5*d^4)*x^2 + (10*b^8*c^9 - 8*a*b^7*c^8*d - 35*a^2*b^6*c^7*d^2 + 42*a^3*b^5*c^6*d^3)*x)*log(d*x + c))/(a*b^9*c^6*d^6 - 4*a^2*b^8*c^5*d^7 + 6*a^3*b^7*c^4*d^8 - 4*a^4*b^6*c^3*d^9 + a^5*b^5*c^2*d^10 + (b^10*c^4*d^8 - 4*a*b^9*c^3*d^9 + 6*a^2*b^8*c^2*d^10 - 4*a^3*b^7*c*d^11 + a^4*b^6*d^12)*x^3 + (2*b^10*c^5*d^7 - 7*a*b^9*c^4*d^8 + 8*a^2*b^8*c^3*d^9 - 2*a^3*b^7*c^2*d^10 - 2*a^4*b^6*c*d^11 + a^5*b^5*d^12)*x^2 + (b^10*c^6*d^6 - 2*a*b^9*c^5*d^7 - 2*a^2*b^8*c^4*d^8 + 8*a^3*b^7*c^3*d^9 - 7*a^4*b^6*c^2*d^10 + 2*a^5*b^5*c*d^11)*x)","B",0
291,1,1081,0,1.604254," ","integrate(x^6/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{7 \, a b^{6} c^{8} - 18 \, a^{2} b^{5} c^{7} d + 11 \, a^{3} b^{4} c^{6} d^{2} - 2 \, a^{6} b c^{3} d^{5} + 2 \, a^{7} c^{2} d^{6} + {\left(b^{7} c^{4} d^{4} - 4 \, a b^{6} c^{3} d^{5} + 6 \, a^{2} b^{5} c^{2} d^{6} - 4 \, a^{3} b^{4} c d^{7} + a^{4} b^{3} d^{8}\right)} x^{5} - {\left(4 \, b^{7} c^{5} d^{3} - 13 \, a b^{6} c^{4} d^{4} + 12 \, a^{2} b^{5} c^{3} d^{5} + 2 \, a^{3} b^{4} c^{2} d^{6} - 8 \, a^{4} b^{3} c d^{7} + 3 \, a^{5} b^{2} d^{8}\right)} x^{4} - {\left(11 \, b^{7} c^{6} d^{2} - 32 \, a b^{6} c^{5} d^{3} + 22 \, a^{2} b^{5} c^{4} d^{4} + 12 \, a^{3} b^{4} c^{3} d^{5} - 13 \, a^{4} b^{3} c^{2} d^{6} - 4 \, a^{5} b^{2} c d^{7} + 4 \, a^{6} b d^{8}\right)} x^{3} + {\left(2 \, b^{7} c^{7} d - 11 \, a b^{6} c^{6} d^{2} + 28 \, a^{2} b^{5} c^{5} d^{3} - 34 \, a^{3} b^{4} c^{4} d^{4} + 6 \, a^{4} b^{3} c^{3} d^{5} + 17 \, a^{5} b^{2} c^{2} d^{6} - 10 \, a^{6} b c d^{7} + 2 \, a^{7} d^{8}\right)} x^{2} + {\left(7 \, b^{7} c^{8} - 16 \, a b^{6} c^{7} d + 11 \, a^{2} b^{5} c^{6} d^{2} - 8 \, a^{3} b^{4} c^{5} d^{3} + 10 \, a^{5} b^{2} c^{3} d^{5} - 8 \, a^{6} b c^{2} d^{6} + 4 \, a^{7} c d^{7}\right)} x - 6 \, {\left(2 \, a^{6} b c^{3} d^{5} - a^{7} c^{2} d^{6} + {\left(2 \, a^{5} b^{2} c d^{7} - a^{6} b d^{8}\right)} x^{3} + {\left(4 \, a^{5} b^{2} c^{2} d^{6} - a^{7} d^{8}\right)} x^{2} + {\left(2 \, a^{5} b^{2} c^{3} d^{5} + 3 \, a^{6} b c^{2} d^{6} - 2 \, a^{7} c d^{7}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(2 \, a b^{6} c^{8} - 6 \, a^{2} b^{5} c^{7} d + 5 \, a^{3} b^{4} c^{6} d^{2} + {\left(2 \, b^{7} c^{6} d^{2} - 6 \, a b^{6} c^{5} d^{3} + 5 \, a^{2} b^{5} c^{4} d^{4}\right)} x^{3} + {\left(4 \, b^{7} c^{7} d - 10 \, a b^{6} c^{6} d^{2} + 4 \, a^{2} b^{5} c^{5} d^{3} + 5 \, a^{3} b^{4} c^{4} d^{4}\right)} x^{2} + {\left(2 \, b^{7} c^{8} - 2 \, a b^{6} c^{7} d - 7 \, a^{2} b^{5} c^{6} d^{2} + 10 \, a^{3} b^{4} c^{5} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{8} c^{6} d^{5} - 4 \, a^{2} b^{7} c^{5} d^{6} + 6 \, a^{3} b^{6} c^{4} d^{7} - 4 \, a^{4} b^{5} c^{3} d^{8} + a^{5} b^{4} c^{2} d^{9} + {\left(b^{9} c^{4} d^{7} - 4 \, a b^{8} c^{3} d^{8} + 6 \, a^{2} b^{7} c^{2} d^{9} - 4 \, a^{3} b^{6} c d^{10} + a^{4} b^{5} d^{11}\right)} x^{3} + {\left(2 \, b^{9} c^{5} d^{6} - 7 \, a b^{8} c^{4} d^{7} + 8 \, a^{2} b^{7} c^{3} d^{8} - 2 \, a^{3} b^{6} c^{2} d^{9} - 2 \, a^{4} b^{5} c d^{10} + a^{5} b^{4} d^{11}\right)} x^{2} + {\left(b^{9} c^{6} d^{5} - 2 \, a b^{8} c^{5} d^{6} - 2 \, a^{2} b^{7} c^{4} d^{7} + 8 \, a^{3} b^{6} c^{3} d^{8} - 7 \, a^{4} b^{5} c^{2} d^{9} + 2 \, a^{5} b^{4} c d^{10}\right)} x\right)}}"," ",0,"1/2*(7*a*b^6*c^8 - 18*a^2*b^5*c^7*d + 11*a^3*b^4*c^6*d^2 - 2*a^6*b*c^3*d^5 + 2*a^7*c^2*d^6 + (b^7*c^4*d^4 - 4*a*b^6*c^3*d^5 + 6*a^2*b^5*c^2*d^6 - 4*a^3*b^4*c*d^7 + a^4*b^3*d^8)*x^5 - (4*b^7*c^5*d^3 - 13*a*b^6*c^4*d^4 + 12*a^2*b^5*c^3*d^5 + 2*a^3*b^4*c^2*d^6 - 8*a^4*b^3*c*d^7 + 3*a^5*b^2*d^8)*x^4 - (11*b^7*c^6*d^2 - 32*a*b^6*c^5*d^3 + 22*a^2*b^5*c^4*d^4 + 12*a^3*b^4*c^3*d^5 - 13*a^4*b^3*c^2*d^6 - 4*a^5*b^2*c*d^7 + 4*a^6*b*d^8)*x^3 + (2*b^7*c^7*d - 11*a*b^6*c^6*d^2 + 28*a^2*b^5*c^5*d^3 - 34*a^3*b^4*c^4*d^4 + 6*a^4*b^3*c^3*d^5 + 17*a^5*b^2*c^2*d^6 - 10*a^6*b*c*d^7 + 2*a^7*d^8)*x^2 + (7*b^7*c^8 - 16*a*b^6*c^7*d + 11*a^2*b^5*c^6*d^2 - 8*a^3*b^4*c^5*d^3 + 10*a^5*b^2*c^3*d^5 - 8*a^6*b*c^2*d^6 + 4*a^7*c*d^7)*x - 6*(2*a^6*b*c^3*d^5 - a^7*c^2*d^6 + (2*a^5*b^2*c*d^7 - a^6*b*d^8)*x^3 + (4*a^5*b^2*c^2*d^6 - a^7*d^8)*x^2 + (2*a^5*b^2*c^3*d^5 + 3*a^6*b*c^2*d^6 - 2*a^7*c*d^7)*x)*log(b*x + a) + 6*(2*a*b^6*c^8 - 6*a^2*b^5*c^7*d + 5*a^3*b^4*c^6*d^2 + (2*b^7*c^6*d^2 - 6*a*b^6*c^5*d^3 + 5*a^2*b^5*c^4*d^4)*x^3 + (4*b^7*c^7*d - 10*a*b^6*c^6*d^2 + 4*a^2*b^5*c^5*d^3 + 5*a^3*b^4*c^4*d^4)*x^2 + (2*b^7*c^8 - 2*a*b^6*c^7*d - 7*a^2*b^5*c^6*d^2 + 10*a^3*b^4*c^5*d^3)*x)*log(d*x + c))/(a*b^8*c^6*d^5 - 4*a^2*b^7*c^5*d^6 + 6*a^3*b^6*c^4*d^7 - 4*a^4*b^5*c^3*d^8 + a^5*b^4*c^2*d^9 + (b^9*c^4*d^7 - 4*a*b^8*c^3*d^8 + 6*a^2*b^7*c^2*d^9 - 4*a^3*b^6*c*d^10 + a^4*b^5*d^11)*x^3 + (2*b^9*c^5*d^6 - 7*a*b^8*c^4*d^7 + 8*a^2*b^7*c^3*d^8 - 2*a^3*b^6*c^2*d^9 - 2*a^4*b^5*c*d^10 + a^5*b^4*d^11)*x^2 + (b^9*c^6*d^5 - 2*a*b^8*c^5*d^6 - 2*a^2*b^7*c^4*d^7 + 8*a^3*b^6*c^3*d^8 - 7*a^4*b^5*c^2*d^9 + 2*a^5*b^4*c*d^10)*x)","B",0
292,1,981,0,1.192996," ","integrate(x^5/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{5 \, a b^{5} c^{7} - 14 \, a^{2} b^{4} c^{6} d + 9 \, a^{3} b^{3} c^{5} d^{2} - 2 \, a^{5} b c^{3} d^{4} + 2 \, a^{6} c^{2} d^{5} - 2 \, {\left(b^{6} c^{4} d^{3} - 4 \, a b^{5} c^{3} d^{4} + 6 \, a^{2} b^{4} c^{2} d^{5} - 4 \, a^{3} b^{3} c d^{6} + a^{4} b^{2} d^{7}\right)} x^{4} - 2 \, {\left(2 \, b^{6} c^{5} d^{2} - 7 \, a b^{5} c^{4} d^{3} + 8 \, a^{2} b^{4} c^{3} d^{4} - 2 \, a^{3} b^{3} c^{2} d^{5} - 2 \, a^{4} b^{2} c d^{6} + a^{5} b d^{7}\right)} x^{3} + 2 \, {\left(2 \, b^{6} c^{6} d - 6 \, a b^{5} c^{5} d^{2} + 7 \, a^{2} b^{4} c^{4} d^{3} - 8 \, a^{3} b^{3} c^{3} d^{4} + 7 \, a^{4} b^{2} c^{2} d^{5} - 3 \, a^{5} b c d^{6} + a^{6} d^{7}\right)} x^{2} + {\left(5 \, b^{6} c^{7} - 10 \, a b^{5} c^{6} d + a^{2} b^{4} c^{5} d^{2} - 2 \, a^{3} b^{3} c^{4} d^{3} + 8 \, a^{4} b^{2} c^{3} d^{4} - 6 \, a^{5} b c^{2} d^{5} + 4 \, a^{6} c d^{6}\right)} x - 2 \, {\left(5 \, a^{5} b c^{3} d^{4} - 2 \, a^{6} c^{2} d^{5} + {\left(5 \, a^{4} b^{2} c d^{6} - 2 \, a^{5} b d^{7}\right)} x^{3} + {\left(10 \, a^{4} b^{2} c^{2} d^{5} + a^{5} b c d^{6} - 2 \, a^{6} d^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{2} c^{3} d^{4} + 8 \, a^{5} b c^{2} d^{5} - 4 \, a^{6} c d^{6}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, a b^{5} c^{7} - 10 \, a^{2} b^{4} c^{6} d + 10 \, a^{3} b^{3} c^{5} d^{2} + {\left(3 \, b^{6} c^{5} d^{2} - 10 \, a b^{5} c^{4} d^{3} + 10 \, a^{2} b^{4} c^{3} d^{4}\right)} x^{3} + {\left(6 \, b^{6} c^{6} d - 17 \, a b^{5} c^{5} d^{2} + 10 \, a^{2} b^{4} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{3} d^{4}\right)} x^{2} + {\left(3 \, b^{6} c^{7} - 4 \, a b^{5} c^{6} d - 10 \, a^{2} b^{4} c^{5} d^{2} + 20 \, a^{3} b^{3} c^{4} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{7} c^{6} d^{4} - 4 \, a^{2} b^{6} c^{5} d^{5} + 6 \, a^{3} b^{5} c^{4} d^{6} - 4 \, a^{4} b^{4} c^{3} d^{7} + a^{5} b^{3} c^{2} d^{8} + {\left(b^{8} c^{4} d^{6} - 4 \, a b^{7} c^{3} d^{7} + 6 \, a^{2} b^{6} c^{2} d^{8} - 4 \, a^{3} b^{5} c d^{9} + a^{4} b^{4} d^{10}\right)} x^{3} + {\left(2 \, b^{8} c^{5} d^{5} - 7 \, a b^{7} c^{4} d^{6} + 8 \, a^{2} b^{6} c^{3} d^{7} - 2 \, a^{3} b^{5} c^{2} d^{8} - 2 \, a^{4} b^{4} c d^{9} + a^{5} b^{3} d^{10}\right)} x^{2} + {\left(b^{8} c^{6} d^{4} - 2 \, a b^{7} c^{5} d^{5} - 2 \, a^{2} b^{6} c^{4} d^{6} + 8 \, a^{3} b^{5} c^{3} d^{7} - 7 \, a^{4} b^{4} c^{2} d^{8} + 2 \, a^{5} b^{3} c d^{9}\right)} x\right)}}"," ",0,"-1/2*(5*a*b^5*c^7 - 14*a^2*b^4*c^6*d + 9*a^3*b^3*c^5*d^2 - 2*a^5*b*c^3*d^4 + 2*a^6*c^2*d^5 - 2*(b^6*c^4*d^3 - 4*a*b^5*c^3*d^4 + 6*a^2*b^4*c^2*d^5 - 4*a^3*b^3*c*d^6 + a^4*b^2*d^7)*x^4 - 2*(2*b^6*c^5*d^2 - 7*a*b^5*c^4*d^3 + 8*a^2*b^4*c^3*d^4 - 2*a^3*b^3*c^2*d^5 - 2*a^4*b^2*c*d^6 + a^5*b*d^7)*x^3 + 2*(2*b^6*c^6*d - 6*a*b^5*c^5*d^2 + 7*a^2*b^4*c^4*d^3 - 8*a^3*b^3*c^3*d^4 + 7*a^4*b^2*c^2*d^5 - 3*a^5*b*c*d^6 + a^6*d^7)*x^2 + (5*b^6*c^7 - 10*a*b^5*c^6*d + a^2*b^4*c^5*d^2 - 2*a^3*b^3*c^4*d^3 + 8*a^4*b^2*c^3*d^4 - 6*a^5*b*c^2*d^5 + 4*a^6*c*d^6)*x - 2*(5*a^5*b*c^3*d^4 - 2*a^6*c^2*d^5 + (5*a^4*b^2*c*d^6 - 2*a^5*b*d^7)*x^3 + (10*a^4*b^2*c^2*d^5 + a^5*b*c*d^6 - 2*a^6*d^7)*x^2 + (5*a^4*b^2*c^3*d^4 + 8*a^5*b*c^2*d^5 - 4*a^6*c*d^6)*x)*log(b*x + a) + 2*(3*a*b^5*c^7 - 10*a^2*b^4*c^6*d + 10*a^3*b^3*c^5*d^2 + (3*b^6*c^5*d^2 - 10*a*b^5*c^4*d^3 + 10*a^2*b^4*c^3*d^4)*x^3 + (6*b^6*c^6*d - 17*a*b^5*c^5*d^2 + 10*a^2*b^4*c^4*d^3 + 10*a^3*b^3*c^3*d^4)*x^2 + (3*b^6*c^7 - 4*a*b^5*c^6*d - 10*a^2*b^4*c^5*d^2 + 20*a^3*b^3*c^4*d^3)*x)*log(d*x + c))/(a*b^7*c^6*d^4 - 4*a^2*b^6*c^5*d^5 + 6*a^3*b^5*c^4*d^6 - 4*a^4*b^4*c^3*d^7 + a^5*b^3*c^2*d^8 + (b^8*c^4*d^6 - 4*a*b^7*c^3*d^7 + 6*a^2*b^6*c^2*d^8 - 4*a^3*b^5*c*d^9 + a^4*b^4*d^10)*x^3 + (2*b^8*c^5*d^5 - 7*a*b^7*c^4*d^6 + 8*a^2*b^6*c^3*d^7 - 2*a^3*b^5*c^2*d^8 - 2*a^4*b^4*c*d^9 + a^5*b^3*d^10)*x^2 + (b^8*c^6*d^4 - 2*a*b^7*c^5*d^5 - 2*a^2*b^6*c^4*d^6 + 8*a^3*b^5*c^3*d^7 - 7*a^4*b^4*c^2*d^8 + 2*a^5*b^3*c*d^9)*x)","B",0
293,1,797,0,0.874718," ","integrate(x^4/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, a b^{4} c^{6} - 10 \, a^{2} b^{3} c^{5} d + 7 \, a^{3} b^{2} c^{4} d^{2} - 2 \, a^{4} b c^{3} d^{3} + 2 \, a^{5} c^{2} d^{4} + 2 \, {\left(2 \, b^{5} c^{5} d - 6 \, a b^{4} c^{4} d^{2} + 4 \, a^{2} b^{3} c^{3} d^{3} - a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(3 \, b^{5} c^{6} - 6 \, a b^{4} c^{5} d - 5 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 4 \, a^{4} b c^{2} d^{4} + 4 \, a^{5} c d^{5}\right)} x - 2 \, {\left(4 \, a^{4} b c^{3} d^{3} - a^{5} c^{2} d^{4} + {\left(4 \, a^{3} b^{2} c d^{5} - a^{4} b d^{6}\right)} x^{3} + {\left(8 \, a^{3} b^{2} c^{2} d^{4} + 2 \, a^{4} b c d^{5} - a^{5} d^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{2} c^{3} d^{3} + 7 \, a^{4} b c^{2} d^{4} - 2 \, a^{5} c d^{5}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} + 6 \, a^{3} b^{2} c^{2} d^{4}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 12 \, a^{3} b^{2} c^{3} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{6} c^{6} d^{3} - 4 \, a^{2} b^{5} c^{5} d^{4} + 6 \, a^{3} b^{4} c^{4} d^{5} - 4 \, a^{4} b^{3} c^{3} d^{6} + a^{5} b^{2} c^{2} d^{7} + {\left(b^{7} c^{4} d^{5} - 4 \, a b^{6} c^{3} d^{6} + 6 \, a^{2} b^{5} c^{2} d^{7} - 4 \, a^{3} b^{4} c d^{8} + a^{4} b^{3} d^{9}\right)} x^{3} + {\left(2 \, b^{7} c^{5} d^{4} - 7 \, a b^{6} c^{4} d^{5} + 8 \, a^{2} b^{5} c^{3} d^{6} - 2 \, a^{3} b^{4} c^{2} d^{7} - 2 \, a^{4} b^{3} c d^{8} + a^{5} b^{2} d^{9}\right)} x^{2} + {\left(b^{7} c^{6} d^{3} - 2 \, a b^{6} c^{5} d^{4} - 2 \, a^{2} b^{5} c^{4} d^{5} + 8 \, a^{3} b^{4} c^{3} d^{6} - 7 \, a^{4} b^{3} c^{2} d^{7} + 2 \, a^{5} b^{2} c d^{8}\right)} x\right)}}"," ",0,"1/2*(3*a*b^4*c^6 - 10*a^2*b^3*c^5*d + 7*a^3*b^2*c^4*d^2 - 2*a^4*b*c^3*d^3 + 2*a^5*c^2*d^4 + 2*(2*b^5*c^5*d - 6*a*b^4*c^4*d^2 + 4*a^2*b^3*c^3*d^3 - a^4*b*c*d^5 + a^5*d^6)*x^2 + (3*b^5*c^6 - 6*a*b^4*c^5*d - 5*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 4*a^4*b*c^2*d^4 + 4*a^5*c*d^5)*x - 2*(4*a^4*b*c^3*d^3 - a^5*c^2*d^4 + (4*a^3*b^2*c*d^5 - a^4*b*d^6)*x^3 + (8*a^3*b^2*c^2*d^4 + 2*a^4*b*c*d^5 - a^5*d^6)*x^2 + (4*a^3*b^2*c^3*d^3 + 7*a^4*b*c^2*d^4 - 2*a^5*c*d^5)*x)*log(b*x + a) + 2*(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 + 6*a^3*b^2*c^2*d^4)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 12*a^3*b^2*c^3*d^3)*x)*log(d*x + c))/(a*b^6*c^6*d^3 - 4*a^2*b^5*c^5*d^4 + 6*a^3*b^4*c^4*d^5 - 4*a^4*b^3*c^3*d^6 + a^5*b^2*c^2*d^7 + (b^7*c^4*d^5 - 4*a*b^6*c^3*d^6 + 6*a^2*b^5*c^2*d^7 - 4*a^3*b^4*c*d^8 + a^4*b^3*d^9)*x^3 + (2*b^7*c^5*d^4 - 7*a*b^6*c^4*d^5 + 8*a^2*b^5*c^3*d^6 - 2*a^3*b^4*c^2*d^7 - 2*a^4*b^3*c*d^8 + a^5*b^2*d^9)*x^2 + (b^7*c^6*d^3 - 2*a*b^6*c^5*d^4 - 2*a^2*b^5*c^4*d^5 + 8*a^3*b^4*c^3*d^6 - 7*a^4*b^3*c^2*d^7 + 2*a^5*b^2*c*d^8)*x)","B",0
294,1,621,0,1.215362," ","integrate(x^3/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a b^{3} c^{5} - 6 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} + 2 \, a^{4} c^{2} d^{3} + 2 \, {\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} - a^{3} b c d^{4} + a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - 4 \, a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 2 \, a^{3} b c^{2} d^{3} + 4 \, a^{4} c d^{4}\right)} x - 6 \, {\left(a^{2} b^{2} c d^{4} x^{3} + a^{3} b c^{3} d^{2} + {\left(2 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4}\right)} x^{2} + {\left(a^{2} b^{2} c^{3} d^{2} + 2 \, a^{3} b c^{2} d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(a^{2} b^{2} c d^{4} x^{3} + a^{3} b c^{3} d^{2} + {\left(2 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4}\right)} x^{2} + {\left(a^{2} b^{2} c^{3} d^{2} + 2 \, a^{3} b c^{2} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{5} c^{6} d^{2} - 4 \, a^{2} b^{4} c^{5} d^{3} + 6 \, a^{3} b^{3} c^{4} d^{4} - 4 \, a^{4} b^{2} c^{3} d^{5} + a^{5} b c^{2} d^{6} + {\left(b^{6} c^{4} d^{4} - 4 \, a b^{5} c^{3} d^{5} + 6 \, a^{2} b^{4} c^{2} d^{6} - 4 \, a^{3} b^{3} c d^{7} + a^{4} b^{2} d^{8}\right)} x^{3} + {\left(2 \, b^{6} c^{5} d^{3} - 7 \, a b^{5} c^{4} d^{4} + 8 \, a^{2} b^{4} c^{3} d^{5} - 2 \, a^{3} b^{3} c^{2} d^{6} - 2 \, a^{4} b^{2} c d^{7} + a^{5} b d^{8}\right)} x^{2} + {\left(b^{6} c^{6} d^{2} - 2 \, a b^{5} c^{5} d^{3} - 2 \, a^{2} b^{4} c^{4} d^{4} + 8 \, a^{3} b^{3} c^{3} d^{5} - 7 \, a^{4} b^{2} c^{2} d^{6} + 2 \, a^{5} b c d^{7}\right)} x\right)}}"," ",0,"-1/2*(a*b^3*c^5 - 6*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 + 2*a^4*c^2*d^3 + 2*(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 - a^3*b*c*d^4 + a^4*d^5)*x^2 + (b^4*c^5 - 4*a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 2*a^3*b*c^2*d^3 + 4*a^4*c*d^4)*x - 6*(a^2*b^2*c*d^4*x^3 + a^3*b*c^3*d^2 + (2*a^2*b^2*c^2*d^3 + a^3*b*c*d^4)*x^2 + (a^2*b^2*c^3*d^2 + 2*a^3*b*c^2*d^3)*x)*log(b*x + a) + 6*(a^2*b^2*c*d^4*x^3 + a^3*b*c^3*d^2 + (2*a^2*b^2*c^2*d^3 + a^3*b*c*d^4)*x^2 + (a^2*b^2*c^3*d^2 + 2*a^3*b*c^2*d^3)*x)*log(d*x + c))/(a*b^5*c^6*d^2 - 4*a^2*b^4*c^5*d^3 + 6*a^3*b^3*c^4*d^4 - 4*a^4*b^2*c^3*d^5 + a^5*b*c^2*d^6 + (b^6*c^4*d^4 - 4*a*b^5*c^3*d^5 + 6*a^2*b^4*c^2*d^6 - 4*a^3*b^3*c*d^7 + a^4*b^2*d^8)*x^3 + (2*b^6*c^5*d^3 - 7*a*b^5*c^4*d^4 + 8*a^2*b^4*c^3*d^5 - 2*a^3*b^3*c^2*d^6 - 2*a^4*b^2*c*d^7 + a^5*b*d^8)*x^2 + (b^6*c^6*d^2 - 2*a*b^5*c^5*d^3 - 2*a^2*b^4*c^4*d^4 + 8*a^3*b^3*c^3*d^5 - 7*a^4*b^2*c^2*d^6 + 2*a^5*b*c*d^7)*x)","B",0
295,1,617,0,1.197583," ","integrate(x^2/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a b^{2} c^{4} + 4 \, a^{2} b c^{3} d - 5 \, a^{3} c^{2} d^{2} + 2 \, {\left(2 \, a b^{2} c^{2} d^{2} - a^{2} b c d^{3} - a^{3} d^{4}\right)} x^{2} + {\left(b^{3} c^{4} + 2 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} - 8 \, a^{3} c d^{3}\right)} x + 2 \, {\left(2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3} + {\left(4 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{2} + {\left(2 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, a^{2} b c^{3} d + a^{3} c^{2} d^{2} + {\left(2 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} x^{3} + {\left(4 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x^{2} + {\left(2 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{4} c^{6} d - 4 \, a^{2} b^{3} c^{5} d^{2} + 6 \, a^{3} b^{2} c^{4} d^{3} - 4 \, a^{4} b c^{3} d^{4} + a^{5} c^{2} d^{5} + {\left(b^{5} c^{4} d^{3} - 4 \, a b^{4} c^{3} d^{4} + 6 \, a^{2} b^{3} c^{2} d^{5} - 4 \, a^{3} b^{2} c d^{6} + a^{4} b d^{7}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d^{2} - 7 \, a b^{4} c^{4} d^{3} + 8 \, a^{2} b^{3} c^{3} d^{4} - 2 \, a^{3} b^{2} c^{2} d^{5} - 2 \, a^{4} b c d^{6} + a^{5} d^{7}\right)} x^{2} + {\left(b^{5} c^{6} d - 2 \, a b^{4} c^{5} d^{2} - 2 \, a^{2} b^{3} c^{4} d^{3} + 8 \, a^{3} b^{2} c^{3} d^{4} - 7 \, a^{4} b c^{2} d^{5} + 2 \, a^{5} c d^{6}\right)} x\right)}}"," ",0,"-1/2*(a*b^2*c^4 + 4*a^2*b*c^3*d - 5*a^3*c^2*d^2 + 2*(2*a*b^2*c^2*d^2 - a^2*b*c*d^3 - a^3*d^4)*x^2 + (b^3*c^4 + 2*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 - 8*a^3*c*d^3)*x + 2*(2*a^2*b*c^3*d + a^3*c^2*d^2 + (2*a*b^2*c*d^3 + a^2*b*d^4)*x^3 + (4*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 + a^3*d^4)*x^2 + (2*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x)*log(b*x + a) - 2*(2*a^2*b*c^3*d + a^3*c^2*d^2 + (2*a*b^2*c*d^3 + a^2*b*d^4)*x^3 + (4*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 + a^3*d^4)*x^2 + (2*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*x)*log(d*x + c))/(a*b^4*c^6*d - 4*a^2*b^3*c^5*d^2 + 6*a^3*b^2*c^4*d^3 - 4*a^4*b*c^3*d^4 + a^5*c^2*d^5 + (b^5*c^4*d^3 - 4*a*b^4*c^3*d^4 + 6*a^2*b^3*c^2*d^5 - 4*a^3*b^2*c*d^6 + a^4*b*d^7)*x^3 + (2*b^5*c^5*d^2 - 7*a*b^4*c^4*d^3 + 8*a^2*b^3*c^3*d^4 - 2*a^3*b^2*c^2*d^5 - 2*a^4*b*c*d^6 + a^5*d^7)*x^2 + (b^5*c^6*d - 2*a*b^4*c^5*d^2 - 2*a^2*b^3*c^4*d^3 + 8*a^3*b^2*c^3*d^4 - 7*a^4*b*c^2*d^5 + 2*a^5*c*d^6)*x)","B",0
296,1,586,0,1.088261," ","integrate(x/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{5 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d - a^{3} c d^{2} + 2 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} x^{2} + {\left(3 \, b^{3} c^{3} + 4 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} x + 2 \, {\left(a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{3} + {\left(2 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} + 4 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{3} + {\left(2 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} + 4 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x\right)}}"," ",0,"1/2*(5*a*b^2*c^3 - 4*a^2*b*c^2*d - a^3*c*d^2 + 2*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*x^2 + (3*b^3*c^3 + 4*a*b^2*c^2*d - 5*a^2*b*c*d^2 - 2*a^3*d^3)*x + 2*(a*b^2*c^3 + 2*a^2*b*c^2*d + (b^3*c*d^2 + 2*a*b^2*d^3)*x^3 + (2*b^3*c^2*d + 5*a*b^2*c*d^2 + 2*a^2*b*d^3)*x^2 + (b^3*c^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)*x)*log(b*x + a) - 2*(a*b^2*c^3 + 2*a^2*b*c^2*d + (b^3*c*d^2 + 2*a*b^2*d^3)*x^3 + (2*b^3*c^2*d + 5*a*b^2*c*d^2 + 2*a^2*b*d^3)*x^2 + (b^3*c^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)*x)*log(d*x + c))/(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x)","B",0
297,1,495,0,1.117420," ","integrate(1/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x\right)}}"," ",0,"-1/2*(2*b^3*c^3 + 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + a^3*d^3 + 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c))/(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x)","B",0
298,1,1044,0,46.621439," ","integrate(1/x/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, a b^{4} c^{6} - 2 \, a^{2} b^{3} c^{5} d + 7 \, a^{3} b^{2} c^{4} d^{2} - 10 \, a^{4} b c^{3} d^{3} + 3 \, a^{5} c^{2} d^{4} + 2 \, {\left(a b^{4} c^{4} d^{2} + 2 \, a^{2} b^{3} c^{3} d^{3} - 4 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5}\right)} x^{2} + {\left(4 \, a b^{4} c^{5} d + 3 \, a^{2} b^{3} c^{4} d^{2} - 4 \, a^{3} b^{2} c^{3} d^{3} - 5 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x - 2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} - 4 \, a^{2} b^{3} c^{3} d^{3}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 8 \, a^{2} b^{3} c^{4} d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{3} + {\left(12 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(6 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{4} c^{9} - 4 \, a^{4} b^{3} c^{8} d + 6 \, a^{5} b^{2} c^{7} d^{2} - 4 \, a^{6} b c^{6} d^{3} + a^{7} c^{5} d^{4} + {\left(a^{2} b^{5} c^{7} d^{2} - 4 \, a^{3} b^{4} c^{6} d^{3} + 6 \, a^{4} b^{3} c^{5} d^{4} - 4 \, a^{5} b^{2} c^{4} d^{5} + a^{6} b c^{3} d^{6}\right)} x^{3} + {\left(2 \, a^{2} b^{5} c^{8} d - 7 \, a^{3} b^{4} c^{7} d^{2} + 8 \, a^{4} b^{3} c^{6} d^{3} - 2 \, a^{5} b^{2} c^{5} d^{4} - 2 \, a^{6} b c^{4} d^{5} + a^{7} c^{3} d^{6}\right)} x^{2} + {\left(a^{2} b^{5} c^{9} - 2 \, a^{3} b^{4} c^{8} d - 2 \, a^{4} b^{3} c^{7} d^{2} + 8 \, a^{5} b^{2} c^{6} d^{3} - 7 \, a^{6} b c^{5} d^{4} + 2 \, a^{7} c^{4} d^{5}\right)} x\right)}}"," ",0,"1/2*(2*a*b^4*c^6 - 2*a^2*b^3*c^5*d + 7*a^3*b^2*c^4*d^2 - 10*a^4*b*c^3*d^3 + 3*a^5*c^2*d^4 + 2*(a*b^4*c^4*d^2 + 2*a^2*b^3*c^3*d^3 - 4*a^3*b^2*c^2*d^4 + a^4*b*c*d^5)*x^2 + (4*a*b^4*c^5*d + 3*a^2*b^3*c^4*d^2 - 4*a^3*b^2*c^3*d^3 - 5*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x - 2*(a*b^4*c^6 - 4*a^2*b^3*c^5*d + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 - 4*a^2*b^3*c^3*d^3)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 8*a^2*b^3*c^4*d^2)*x)*log(b*x + a) - 2*(6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^3 + (12*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^2 + (6*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x)*log(d*x + c) + 2*(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x)*log(x))/(a^3*b^4*c^9 - 4*a^4*b^3*c^8*d + 6*a^5*b^2*c^7*d^2 - 4*a^6*b*c^6*d^3 + a^7*c^5*d^4 + (a^2*b^5*c^7*d^2 - 4*a^3*b^4*c^6*d^3 + 6*a^4*b^3*c^5*d^4 - 4*a^5*b^2*c^4*d^5 + a^6*b*c^3*d^6)*x^3 + (2*a^2*b^5*c^8*d - 7*a^3*b^4*c^7*d^2 + 8*a^4*b^3*c^6*d^3 - 2*a^5*b^2*c^5*d^4 - 2*a^6*b*c^4*d^5 + a^7*c^3*d^6)*x^2 + (a^2*b^5*c^9 - 2*a^3*b^4*c^8*d - 2*a^4*b^3*c^7*d^2 + 8*a^5*b^2*c^6*d^3 - 7*a^6*b*c^5*d^4 + 2*a^7*c^4*d^5)*x)","B",0
299,1,1213,0,177.327836," ","integrate(1/x^2/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b^{4} c^{7} - 8 \, a^{3} b^{3} c^{6} d + 12 \, a^{4} b^{2} c^{5} d^{2} - 8 \, a^{5} b c^{4} d^{3} + 2 \, a^{6} c^{3} d^{4} + 2 \, {\left(2 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} + 3 \, a^{5} b c d^{6}\right)} x^{3} + {\left(8 \, a b^{5} c^{6} d - 18 \, a^{2} b^{4} c^{5} d^{2} + 25 \, a^{3} b^{3} c^{4} d^{3} - 10 \, a^{4} b^{2} c^{3} d^{4} - 11 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{2} + {\left(4 \, a b^{5} c^{7} - 6 \, a^{2} b^{4} c^{6} d - 4 \, a^{3} b^{3} c^{5} d^{2} + 25 \, a^{4} b^{2} c^{4} d^{3} - 28 \, a^{5} b c^{3} d^{4} + 9 \, a^{6} c^{2} d^{5}\right)} x - 2 \, {\left({\left(2 \, b^{6} c^{5} d^{2} - 5 \, a b^{5} c^{4} d^{3}\right)} x^{4} + {\left(4 \, b^{6} c^{6} d - 8 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3}\right)} x^{3} + {\left(2 \, b^{6} c^{7} - a b^{5} c^{6} d - 10 \, a^{2} b^{4} c^{5} d^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{7} - 5 \, a^{2} b^{4} c^{6} d\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(10 \, a^{3} b^{3} c^{2} d^{5} - 10 \, a^{4} b^{2} c d^{6} + 3 \, a^{5} b d^{7}\right)} x^{4} + {\left(20 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} - 4 \, a^{5} b c d^{6} + 3 \, a^{6} d^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{3} c^{4} d^{3} + 10 \, a^{4} b^{2} c^{3} d^{4} - 17 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{2} + {\left(10 \, a^{4} b^{2} c^{4} d^{3} - 10 \, a^{5} b c^{3} d^{4} + 3 \, a^{6} c^{2} d^{5}\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left({\left(2 \, b^{6} c^{5} d^{2} - 5 \, a b^{5} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{2} d^{5} - 10 \, a^{4} b^{2} c d^{6} + 3 \, a^{5} b d^{7}\right)} x^{4} + {\left(4 \, b^{6} c^{6} d - 8 \, a b^{5} c^{5} d^{2} - 5 \, a^{2} b^{4} c^{4} d^{3} + 20 \, a^{3} b^{3} c^{3} d^{4} - 10 \, a^{4} b^{2} c^{2} d^{5} - 4 \, a^{5} b c d^{6} + 3 \, a^{6} d^{7}\right)} x^{3} + {\left(2 \, b^{6} c^{7} - a b^{5} c^{6} d - 10 \, a^{2} b^{4} c^{5} d^{2} + 10 \, a^{3} b^{3} c^{4} d^{3} + 10 \, a^{4} b^{2} c^{3} d^{4} - 17 \, a^{5} b c^{2} d^{5} + 6 \, a^{6} c d^{6}\right)} x^{2} + {\left(2 \, a b^{5} c^{7} - 5 \, a^{2} b^{4} c^{6} d + 10 \, a^{4} b^{2} c^{4} d^{3} - 10 \, a^{5} b c^{3} d^{4} + 3 \, a^{6} c^{2} d^{5}\right)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{3} b^{5} c^{8} d^{2} - 4 \, a^{4} b^{4} c^{7} d^{3} + 6 \, a^{5} b^{3} c^{6} d^{4} - 4 \, a^{6} b^{2} c^{5} d^{5} + a^{7} b c^{4} d^{6}\right)} x^{4} + {\left(2 \, a^{3} b^{5} c^{9} d - 7 \, a^{4} b^{4} c^{8} d^{2} + 8 \, a^{5} b^{3} c^{7} d^{3} - 2 \, a^{6} b^{2} c^{6} d^{4} - 2 \, a^{7} b c^{5} d^{5} + a^{8} c^{4} d^{6}\right)} x^{3} + {\left(a^{3} b^{5} c^{10} - 2 \, a^{4} b^{4} c^{9} d - 2 \, a^{5} b^{3} c^{8} d^{2} + 8 \, a^{6} b^{2} c^{7} d^{3} - 7 \, a^{7} b c^{6} d^{4} + 2 \, a^{8} c^{5} d^{5}\right)} x^{2} + {\left(a^{4} b^{4} c^{10} - 4 \, a^{5} b^{3} c^{9} d + 6 \, a^{6} b^{2} c^{8} d^{2} - 4 \, a^{7} b c^{7} d^{3} + a^{8} c^{6} d^{4}\right)} x\right)}}"," ",0,"-1/2*(2*a^2*b^4*c^7 - 8*a^3*b^3*c^6*d + 12*a^4*b^2*c^5*d^2 - 8*a^5*b*c^4*d^3 + 2*a^6*c^3*d^4 + 2*(2*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3 + 10*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 + 3*a^5*b*c*d^6)*x^3 + (8*a*b^5*c^6*d - 18*a^2*b^4*c^5*d^2 + 25*a^3*b^3*c^4*d^3 - 10*a^4*b^2*c^3*d^4 - 11*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^2 + (4*a*b^5*c^7 - 6*a^2*b^4*c^6*d - 4*a^3*b^3*c^5*d^2 + 25*a^4*b^2*c^4*d^3 - 28*a^5*b*c^3*d^4 + 9*a^6*c^2*d^5)*x - 2*((2*b^6*c^5*d^2 - 5*a*b^5*c^4*d^3)*x^4 + (4*b^6*c^6*d - 8*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3)*x^3 + (2*b^6*c^7 - a*b^5*c^6*d - 10*a^2*b^4*c^5*d^2)*x^2 + (2*a*b^5*c^7 - 5*a^2*b^4*c^6*d)*x)*log(b*x + a) - 2*((10*a^3*b^3*c^2*d^5 - 10*a^4*b^2*c*d^6 + 3*a^5*b*d^7)*x^4 + (20*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 - 4*a^5*b*c*d^6 + 3*a^6*d^7)*x^3 + (10*a^3*b^3*c^4*d^3 + 10*a^4*b^2*c^3*d^4 - 17*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^2 + (10*a^4*b^2*c^4*d^3 - 10*a^5*b*c^3*d^4 + 3*a^6*c^2*d^5)*x)*log(d*x + c) + 2*((2*b^6*c^5*d^2 - 5*a*b^5*c^4*d^3 + 10*a^3*b^3*c^2*d^5 - 10*a^4*b^2*c*d^6 + 3*a^5*b*d^7)*x^4 + (4*b^6*c^6*d - 8*a*b^5*c^5*d^2 - 5*a^2*b^4*c^4*d^3 + 20*a^3*b^3*c^3*d^4 - 10*a^4*b^2*c^2*d^5 - 4*a^5*b*c*d^6 + 3*a^6*d^7)*x^3 + (2*b^6*c^7 - a*b^5*c^6*d - 10*a^2*b^4*c^5*d^2 + 10*a^3*b^3*c^4*d^3 + 10*a^4*b^2*c^3*d^4 - 17*a^5*b*c^2*d^5 + 6*a^6*c*d^6)*x^2 + (2*a*b^5*c^7 - 5*a^2*b^4*c^6*d + 10*a^4*b^2*c^4*d^3 - 10*a^5*b*c^3*d^4 + 3*a^6*c^2*d^5)*x)*log(x))/((a^3*b^5*c^8*d^2 - 4*a^4*b^4*c^7*d^3 + 6*a^5*b^3*c^6*d^4 - 4*a^6*b^2*c^5*d^5 + a^7*b*c^4*d^6)*x^4 + (2*a^3*b^5*c^9*d - 7*a^4*b^4*c^8*d^2 + 8*a^5*b^3*c^7*d^3 - 2*a^6*b^2*c^6*d^4 - 2*a^7*b*c^5*d^5 + a^8*c^4*d^6)*x^3 + (a^3*b^5*c^10 - 2*a^4*b^4*c^9*d - 2*a^5*b^3*c^8*d^2 + 8*a^6*b^2*c^7*d^3 - 7*a^7*b*c^6*d^4 + 2*a^8*c^5*d^5)*x^2 + (a^4*b^4*c^10 - 4*a^5*b^3*c^9*d + 6*a^6*b^2*c^8*d^2 - 4*a^7*b*c^7*d^3 + a^8*c^6*d^4)*x)","B",0
300,-1,0,0,0.000000," ","integrate(1/x^3/(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,1,425,0,1.644308," ","integrate(x^3*(d*x+c)^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{6} d^{3} x^{6} - 10 \, a^{3} b^{3} c^{3} + 42 \, a^{4} b^{2} c^{2} d - 54 \, a^{5} b c d^{2} + 22 \, a^{6} d^{3} + 2 \, {\left(2 \, b^{6} c d^{2} - a b^{5} d^{3}\right)} x^{5} + {\left(6 \, b^{6} c^{2} d - 10 \, a b^{5} c d^{2} + 5 \, a^{2} b^{4} d^{3}\right)} x^{4} + 4 \, {\left(b^{6} c^{3} - 6 \, a b^{5} c^{2} d + 10 \, a^{2} b^{4} c d^{2} - 5 \, a^{3} b^{3} d^{3}\right)} x^{3} + 2 \, {\left(4 \, a b^{5} c^{3} - 33 \, a^{2} b^{4} c^{2} d + 63 \, a^{3} b^{3} c d^{2} - 34 \, a^{4} b^{2} d^{3}\right)} x^{2} - 4 \, {\left(2 \, a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d - 3 \, a^{4} b^{2} c d^{2} + 4 \, a^{5} b d^{3}\right)} x - 12 \, {\left(a^{3} b^{3} c^{3} - 6 \, a^{4} b^{2} c^{2} d + 10 \, a^{5} b c d^{2} - 5 \, a^{6} d^{3} + {\left(a b^{5} c^{3} - 6 \, a^{2} b^{4} c^{2} d + 10 \, a^{3} b^{3} c d^{2} - 5 \, a^{4} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a^{2} b^{4} c^{3} - 6 \, a^{3} b^{3} c^{2} d + 10 \, a^{4} b^{2} c d^{2} - 5 \, a^{5} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{4 \, {\left(b^{9} x^{2} + 2 \, a b^{8} x + a^{2} b^{7}\right)}}"," ",0,"1/4*(b^6*d^3*x^6 - 10*a^3*b^3*c^3 + 42*a^4*b^2*c^2*d - 54*a^5*b*c*d^2 + 22*a^6*d^3 + 2*(2*b^6*c*d^2 - a*b^5*d^3)*x^5 + (6*b^6*c^2*d - 10*a*b^5*c*d^2 + 5*a^2*b^4*d^3)*x^4 + 4*(b^6*c^3 - 6*a*b^5*c^2*d + 10*a^2*b^4*c*d^2 - 5*a^3*b^3*d^3)*x^3 + 2*(4*a*b^5*c^3 - 33*a^2*b^4*c^2*d + 63*a^3*b^3*c*d^2 - 34*a^4*b^2*d^3)*x^2 - 4*(2*a^2*b^4*c^3 - 3*a^3*b^3*c^2*d - 3*a^4*b^2*c*d^2 + 4*a^5*b*d^3)*x - 12*(a^3*b^3*c^3 - 6*a^4*b^2*c^2*d + 10*a^5*b*c*d^2 - 5*a^6*d^3 + (a*b^5*c^3 - 6*a^2*b^4*c^2*d + 10*a^3*b^3*c*d^2 - 5*a^4*b^2*d^3)*x^2 + 2*(a^2*b^4*c^3 - 6*a^3*b^3*c^2*d + 10*a^4*b^2*c*d^2 - 5*a^5*b*d^3)*x)*log(b*x + a))/(b^9*x^2 + 2*a*b^8*x + a^2*b^7)","B",0
302,1,361,0,1.713202," ","integrate(x^2*(d*x+c)^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} d^{3} x^{5} + 9 \, a^{2} b^{3} c^{3} - 45 \, a^{3} b^{2} c^{2} d + 63 \, a^{4} b c d^{2} - 27 \, a^{5} d^{3} + {\left(9 \, b^{5} c d^{2} - 5 \, a b^{4} d^{3}\right)} x^{4} + 2 \, {\left(9 \, b^{5} c^{2} d - 18 \, a b^{4} c d^{2} + 10 \, a^{2} b^{3} d^{3}\right)} x^{3} + 9 \, {\left(4 \, a b^{4} c^{2} d - 11 \, a^{2} b^{3} c d^{2} + 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{4} c^{3} - 6 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x + 6 \, {\left(a^{2} b^{3} c^{3} - 9 \, a^{3} b^{2} c^{2} d + 18 \, a^{4} b c d^{2} - 10 \, a^{5} d^{3} + {\left(b^{5} c^{3} - 9 \, a b^{4} c^{2} d + 18 \, a^{2} b^{3} c d^{2} - 10 \, a^{3} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} - 9 \, a^{2} b^{3} c^{2} d + 18 \, a^{3} b^{2} c d^{2} - 10 \, a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"1/6*(2*b^5*d^3*x^5 + 9*a^2*b^3*c^3 - 45*a^3*b^2*c^2*d + 63*a^4*b*c*d^2 - 27*a^5*d^3 + (9*b^5*c*d^2 - 5*a*b^4*d^3)*x^4 + 2*(9*b^5*c^2*d - 18*a*b^4*c*d^2 + 10*a^2*b^3*d^3)*x^3 + 9*(4*a*b^4*c^2*d - 11*a^2*b^3*c*d^2 + 7*a^3*b^2*d^3)*x^2 + 6*(2*a*b^4*c^3 - 6*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x + 6*(a^2*b^3*c^3 - 9*a^3*b^2*c^2*d + 18*a^4*b*c*d^2 - 10*a^5*d^3 + (b^5*c^3 - 9*a*b^4*c^2*d + 18*a^2*b^3*c*d^2 - 10*a^3*b^2*d^3)*x^2 + 2*(a*b^4*c^3 - 9*a^2*b^3*c^2*d + 18*a^3*b^2*c*d^2 - 10*a^4*b*d^3)*x)*log(b*x + a))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","B",0
303,1,274,0,1.504603," ","integrate(x*(d*x+c)^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{4} d^{3} x^{4} - a b^{3} c^{3} + 9 \, a^{2} b^{2} c^{2} d - 15 \, a^{3} b c d^{2} + 7 \, a^{4} d^{3} + 2 \, {\left(3 \, b^{4} c d^{2} - 2 \, a b^{3} d^{3}\right)} x^{3} + {\left(12 \, a b^{3} c d^{2} - 11 \, a^{2} b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{4} c^{3} - 6 \, a b^{3} c^{2} d + 6 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x + 6 \, {\left(a^{2} b^{2} c^{2} d - 3 \, a^{3} b c d^{2} + 2 \, a^{4} d^{3} + {\left(b^{4} c^{2} d - 3 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d - 3 \, a^{2} b^{2} c d^{2} + 2 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(b^4*d^3*x^4 - a*b^3*c^3 + 9*a^2*b^2*c^2*d - 15*a^3*b*c*d^2 + 7*a^4*d^3 + 2*(3*b^4*c*d^2 - 2*a*b^3*d^3)*x^3 + (12*a*b^3*c*d^2 - 11*a^2*b^2*d^3)*x^2 - 2*(b^4*c^3 - 6*a*b^3*c^2*d + 6*a^2*b^2*c*d^2 - a^3*b*d^3)*x + 6*(a^2*b^2*c^2*d - 3*a^3*b*c*d^2 + 2*a^4*d^3 + (b^4*c^2*d - 3*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*x^2 + 2*(a*b^3*c^2*d - 3*a^2*b^2*c*d^2 + 2*a^3*b*d^3)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","B",0
304,1,188,0,1.613647," ","integrate((d*x+c)^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 4 \, a b^{2} d^{3} x^{2} - b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3} - 2 \, {\left(3 \, b^{3} c^{2} d - 6 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x + 6 \, {\left(a^{2} b c d^{2} - a^{3} d^{3} + {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{2} c d^{2} - a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*d^3*x^3 + 4*a*b^2*d^3*x^2 - b^3*c^3 - 3*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 5*a^3*d^3 - 2*(3*b^3*c^2*d - 6*a*b^2*c*d^2 + 2*a^2*b*d^3)*x + 6*(a^2*b*c*d^2 - a^3*d^3 + (b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(a*b^2*c*d^2 - a^2*b*d^3)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","B",0
305,1,212,0,1.749957," ","integrate((d*x+c)^3/x/(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + 3 \, a^{5} d^{3} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x - 2 \, {\left(a^{2} b^{3} c^{3} - a^{5} d^{3} + {\left(b^{5} c^{3} - a^{3} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} - a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(b^{5} c^{3} x^{2} + 2 \, a b^{4} c^{3} x + a^{2} b^{3} c^{3}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{5} x^{2} + 2 \, a^{4} b^{4} x + a^{5} b^{3}\right)}}"," ",0,"1/2*(3*a^2*b^3*c^3 - 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + 3*a^5*d^3 + 2*(a*b^4*c^3 - 3*a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x - 2*(a^2*b^3*c^3 - a^5*d^3 + (b^5*c^3 - a^3*b^2*d^3)*x^2 + 2*(a*b^4*c^3 - a^4*b*d^3)*x)*log(b*x + a) + 2*(b^5*c^3*x^2 + 2*a*b^4*c^3*x + a^2*b^3*c^3)*log(x))/(a^3*b^5*x^2 + 2*a^4*b^4*x + a^5*b^3)","B",0
306,1,284,0,1.417322," ","integrate((d*x+c)^3/x^2/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} b^{2} c^{3} + 2 \, {\left(3 \, a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + a^{4} b d^{3}\right)} x^{2} + {\left(9 \, a^{2} b^{3} c^{3} - 9 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} + a^{5} d^{3}\right)} x - 6 \, {\left({\left(b^{5} c^{3} - a b^{4} c^{2} d\right)} x^{3} + 2 \, {\left(a b^{4} c^{3} - a^{2} b^{3} c^{2} d\right)} x^{2} + {\left(a^{2} b^{3} c^{3} - a^{3} b^{2} c^{2} d\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left({\left(b^{5} c^{3} - a b^{4} c^{2} d\right)} x^{3} + 2 \, {\left(a b^{4} c^{3} - a^{2} b^{3} c^{2} d\right)} x^{2} + {\left(a^{2} b^{3} c^{3} - a^{3} b^{2} c^{2} d\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{4} x^{3} + 2 \, a^{5} b^{3} x^{2} + a^{6} b^{2} x\right)}}"," ",0,"-1/2*(2*a^3*b^2*c^3 + 2*(3*a*b^4*c^3 - 3*a^2*b^3*c^2*d + a^4*b*d^3)*x^2 + (9*a^2*b^3*c^3 - 9*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 + a^5*d^3)*x - 6*((b^5*c^3 - a*b^4*c^2*d)*x^3 + 2*(a*b^4*c^3 - a^2*b^3*c^2*d)*x^2 + (a^2*b^3*c^3 - a^3*b^2*c^2*d)*x)*log(b*x + a) + 6*((b^5*c^3 - a*b^4*c^2*d)*x^3 + 2*(a*b^4*c^3 - a^2*b^3*c^2*d)*x^2 + (a^2*b^3*c^3 - a^3*b^2*c^2*d)*x)*log(x))/(a^4*b^4*x^3 + 2*a^5*b^3*x^2 + a^6*b^2*x)","B",0
307,1,385,0,1.589044," ","integrate((d*x+c)^3/x^3/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{a^{4} b c^{3} - 6 \, {\left(2 \, a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x^{3} - {\left(18 \, a^{2} b^{3} c^{3} - 27 \, a^{3} b^{2} c^{2} d + 9 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{2} - 2 \, {\left(2 \, a^{3} b^{2} c^{3} - 3 \, a^{4} b c^{2} d\right)} x + 6 \, {\left({\left(2 \, b^{5} c^{3} - 3 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x^{3} + {\left(2 \, a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{2}\right)} \log\left(b x + a\right) - 6 \, {\left({\left(2 \, b^{5} c^{3} - 3 \, a b^{4} c^{2} d + a^{2} b^{3} c d^{2}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + a^{3} b^{2} c d^{2}\right)} x^{3} + {\left(2 \, a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + a^{4} b c d^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{3} x^{4} + 2 \, a^{6} b^{2} x^{3} + a^{7} b x^{2}\right)}}"," ",0,"-1/2*(a^4*b*c^3 - 6*(2*a*b^4*c^3 - 3*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x^3 - (18*a^2*b^3*c^3 - 27*a^3*b^2*c^2*d + 9*a^4*b*c*d^2 - a^5*d^3)*x^2 - 2*(2*a^3*b^2*c^3 - 3*a^4*b*c^2*d)*x + 6*((2*b^5*c^3 - 3*a*b^4*c^2*d + a^2*b^3*c*d^2)*x^4 + 2*(2*a*b^4*c^3 - 3*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x^3 + (2*a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^2)*log(b*x + a) - 6*((2*b^5*c^3 - 3*a*b^4*c^2*d + a^2*b^3*c*d^2)*x^4 + 2*(2*a*b^4*c^3 - 3*a^2*b^3*c^2*d + a^3*b^2*c*d^2)*x^3 + (2*a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + a^4*b*c*d^2)*x^2)*log(x))/(a^5*b^3*x^4 + 2*a^6*b^2*x^3 + a^7*b*x^2)","B",0
308,1,487,0,1.714916," ","integrate((d*x+c)^3/x^4/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, a^{5} c^{3} + 6 \, {\left(10 \, a b^{4} c^{3} - 18 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} + 9 \, {\left(10 \, a^{2} b^{3} c^{3} - 18 \, a^{3} b^{2} c^{2} d + 9 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{3} + 2 \, {\left(10 \, a^{3} b^{2} c^{3} - 18 \, a^{4} b c^{2} d + 9 \, a^{5} c d^{2}\right)} x^{2} - {\left(5 \, a^{4} b c^{3} - 9 \, a^{5} c^{2} d\right)} x - 6 \, {\left({\left(10 \, b^{5} c^{3} - 18 \, a b^{4} c^{2} d + 9 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} + 2 \, {\left(10 \, a b^{4} c^{3} - 18 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} + {\left(10 \, a^{2} b^{3} c^{3} - 18 \, a^{3} b^{2} c^{2} d + 9 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{3}\right)} \log\left(b x + a\right) + 6 \, {\left({\left(10 \, b^{5} c^{3} - 18 \, a b^{4} c^{2} d + 9 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} + 2 \, {\left(10 \, a b^{4} c^{3} - 18 \, a^{2} b^{3} c^{2} d + 9 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} + {\left(10 \, a^{2} b^{3} c^{3} - 18 \, a^{3} b^{2} c^{2} d + 9 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{3}\right)} \log\left(x\right)}{6 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}"," ",0,"-1/6*(2*a^5*c^3 + 6*(10*a*b^4*c^3 - 18*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 + 9*(10*a^2*b^3*c^3 - 18*a^3*b^2*c^2*d + 9*a^4*b*c*d^2 - a^5*d^3)*x^3 + 2*(10*a^3*b^2*c^3 - 18*a^4*b*c^2*d + 9*a^5*c*d^2)*x^2 - (5*a^4*b*c^3 - 9*a^5*c^2*d)*x - 6*((10*b^5*c^3 - 18*a*b^4*c^2*d + 9*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5 + 2*(10*a*b^4*c^3 - 18*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 + (10*a^2*b^3*c^3 - 18*a^3*b^2*c^2*d + 9*a^4*b*c*d^2 - a^5*d^3)*x^3)*log(b*x + a) + 6*((10*b^5*c^3 - 18*a*b^4*c^2*d + 9*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5 + 2*(10*a*b^4*c^3 - 18*a^2*b^3*c^2*d + 9*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 + (10*a^2*b^3*c^3 - 18*a^3*b^2*c^2*d + 9*a^4*b*c*d^2 - a^5*d^3)*x^3)*log(x))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3)","B",0
309,1,1567,0,2.183484," ","integrate(x^7/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{7 \, a^{2} b^{7} c^{9} - 20 \, a^{3} b^{6} c^{8} d + 13 \, a^{4} b^{5} c^{7} d^{2} - 13 \, a^{7} b^{2} c^{4} d^{5} + 20 \, a^{8} b c^{3} d^{6} - 7 \, a^{9} c^{2} d^{7} + {\left(b^{9} c^{5} d^{4} - 5 \, a b^{8} c^{4} d^{5} + 10 \, a^{2} b^{7} c^{3} d^{6} - 10 \, a^{3} b^{6} c^{2} d^{7} + 5 \, a^{4} b^{5} c d^{8} - a^{5} b^{4} d^{9}\right)} x^{6} - 4 \, {\left(b^{9} c^{6} d^{3} - 4 \, a b^{8} c^{5} d^{4} + 5 \, a^{2} b^{7} c^{4} d^{5} - 5 \, a^{4} b^{5} c^{2} d^{7} + 4 \, a^{5} b^{4} c d^{8} - a^{6} b^{3} d^{9}\right)} x^{5} - {\left(11 \, b^{9} c^{7} d^{2} - 35 \, a b^{8} c^{6} d^{3} + 21 \, a^{2} b^{7} c^{5} d^{4} + 35 \, a^{3} b^{6} c^{4} d^{5} - 35 \, a^{4} b^{5} c^{3} d^{6} - 21 \, a^{5} b^{4} c^{2} d^{7} + 35 \, a^{6} b^{3} c d^{8} - 11 \, a^{7} b^{2} d^{9}\right)} x^{4} + 2 \, {\left(b^{9} c^{8} d - 10 \, a b^{8} c^{7} d^{2} + 33 \, a^{2} b^{7} c^{6} d^{3} - 43 \, a^{3} b^{6} c^{5} d^{4} + 43 \, a^{5} b^{4} c^{3} d^{6} - 33 \, a^{6} b^{3} c^{2} d^{7} + 10 \, a^{7} b^{2} c d^{8} - a^{8} b d^{9}\right)} x^{3} + {\left(7 \, b^{9} c^{9} - 16 \, a b^{8} c^{8} d + 6 \, a^{2} b^{7} c^{7} d^{2} + 11 \, a^{3} b^{6} c^{6} d^{3} - 50 \, a^{4} b^{5} c^{5} d^{4} + 50 \, a^{5} b^{4} c^{4} d^{5} - 11 \, a^{6} b^{3} c^{3} d^{6} - 6 \, a^{7} b^{2} c^{2} d^{7} + 16 \, a^{8} b c d^{8} - 7 \, a^{9} d^{9}\right)} x^{2} + 2 \, {\left(7 \, a b^{8} c^{9} - 19 \, a^{2} b^{7} c^{8} d + 14 \, a^{3} b^{6} c^{7} d^{2} - 8 \, a^{4} b^{5} c^{6} d^{3} + 8 \, a^{6} b^{3} c^{4} d^{5} - 14 \, a^{7} b^{2} c^{3} d^{6} + 19 \, a^{8} b c^{2} d^{7} - 7 \, a^{9} c d^{8}\right)} x - 6 \, {\left(7 \, a^{7} b^{2} c^{4} d^{5} - 7 \, a^{8} b c^{3} d^{6} + 2 \, a^{9} c^{2} d^{7} + {\left(7 \, a^{5} b^{4} c^{2} d^{7} - 7 \, a^{6} b^{3} c d^{8} + 2 \, a^{7} b^{2} d^{9}\right)} x^{4} + 2 \, {\left(7 \, a^{5} b^{4} c^{3} d^{6} - 5 \, a^{7} b^{2} c d^{8} + 2 \, a^{8} b d^{9}\right)} x^{3} + {\left(7 \, a^{5} b^{4} c^{4} d^{5} + 21 \, a^{6} b^{3} c^{3} d^{6} - 19 \, a^{7} b^{2} c^{2} d^{7} + a^{8} b c d^{8} + 2 \, a^{9} d^{9}\right)} x^{2} + 2 \, {\left(7 \, a^{6} b^{3} c^{4} d^{5} - 5 \, a^{8} b c^{2} d^{7} + 2 \, a^{9} c d^{8}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(2 \, a^{2} b^{7} c^{9} - 7 \, a^{3} b^{6} c^{8} d + 7 \, a^{4} b^{5} c^{7} d^{2} + {\left(2 \, b^{9} c^{7} d^{2} - 7 \, a b^{8} c^{6} d^{3} + 7 \, a^{2} b^{7} c^{5} d^{4}\right)} x^{4} + 2 \, {\left(2 \, b^{9} c^{8} d - 5 \, a b^{8} c^{7} d^{2} + 7 \, a^{3} b^{6} c^{5} d^{4}\right)} x^{3} + {\left(2 \, b^{9} c^{9} + a b^{8} c^{8} d - 19 \, a^{2} b^{7} c^{7} d^{2} + 21 \, a^{3} b^{6} c^{6} d^{3} + 7 \, a^{4} b^{5} c^{5} d^{4}\right)} x^{2} + 2 \, {\left(2 \, a b^{8} c^{9} - 5 \, a^{2} b^{7} c^{8} d + 7 \, a^{4} b^{5} c^{6} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{10} c^{7} d^{5} - 5 \, a^{3} b^{9} c^{6} d^{6} + 10 \, a^{4} b^{8} c^{5} d^{7} - 10 \, a^{5} b^{7} c^{4} d^{8} + 5 \, a^{6} b^{6} c^{3} d^{9} - a^{7} b^{5} c^{2} d^{10} + {\left(b^{12} c^{5} d^{7} - 5 \, a b^{11} c^{4} d^{8} + 10 \, a^{2} b^{10} c^{3} d^{9} - 10 \, a^{3} b^{9} c^{2} d^{10} + 5 \, a^{4} b^{8} c d^{11} - a^{5} b^{7} d^{12}\right)} x^{4} + 2 \, {\left(b^{12} c^{6} d^{6} - 4 \, a b^{11} c^{5} d^{7} + 5 \, a^{2} b^{10} c^{4} d^{8} - 5 \, a^{4} b^{8} c^{2} d^{10} + 4 \, a^{5} b^{7} c d^{11} - a^{6} b^{6} d^{12}\right)} x^{3} + {\left(b^{12} c^{7} d^{5} - a b^{11} c^{6} d^{6} - 9 \, a^{2} b^{10} c^{5} d^{7} + 25 \, a^{3} b^{9} c^{4} d^{8} - 25 \, a^{4} b^{8} c^{3} d^{9} + 9 \, a^{5} b^{7} c^{2} d^{10} + a^{6} b^{6} c d^{11} - a^{7} b^{5} d^{12}\right)} x^{2} + 2 \, {\left(a b^{11} c^{7} d^{5} - 4 \, a^{2} b^{10} c^{6} d^{6} + 5 \, a^{3} b^{9} c^{5} d^{7} - 5 \, a^{5} b^{7} c^{3} d^{9} + 4 \, a^{6} b^{6} c^{2} d^{10} - a^{7} b^{5} c d^{11}\right)} x\right)}}"," ",0,"1/2*(7*a^2*b^7*c^9 - 20*a^3*b^6*c^8*d + 13*a^4*b^5*c^7*d^2 - 13*a^7*b^2*c^4*d^5 + 20*a^8*b*c^3*d^6 - 7*a^9*c^2*d^7 + (b^9*c^5*d^4 - 5*a*b^8*c^4*d^5 + 10*a^2*b^7*c^3*d^6 - 10*a^3*b^6*c^2*d^7 + 5*a^4*b^5*c*d^8 - a^5*b^4*d^9)*x^6 - 4*(b^9*c^6*d^3 - 4*a*b^8*c^5*d^4 + 5*a^2*b^7*c^4*d^5 - 5*a^4*b^5*c^2*d^7 + 4*a^5*b^4*c*d^8 - a^6*b^3*d^9)*x^5 - (11*b^9*c^7*d^2 - 35*a*b^8*c^6*d^3 + 21*a^2*b^7*c^5*d^4 + 35*a^3*b^6*c^4*d^5 - 35*a^4*b^5*c^3*d^6 - 21*a^5*b^4*c^2*d^7 + 35*a^6*b^3*c*d^8 - 11*a^7*b^2*d^9)*x^4 + 2*(b^9*c^8*d - 10*a*b^8*c^7*d^2 + 33*a^2*b^7*c^6*d^3 - 43*a^3*b^6*c^5*d^4 + 43*a^5*b^4*c^3*d^6 - 33*a^6*b^3*c^2*d^7 + 10*a^7*b^2*c*d^8 - a^8*b*d^9)*x^3 + (7*b^9*c^9 - 16*a*b^8*c^8*d + 6*a^2*b^7*c^7*d^2 + 11*a^3*b^6*c^6*d^3 - 50*a^4*b^5*c^5*d^4 + 50*a^5*b^4*c^4*d^5 - 11*a^6*b^3*c^3*d^6 - 6*a^7*b^2*c^2*d^7 + 16*a^8*b*c*d^8 - 7*a^9*d^9)*x^2 + 2*(7*a*b^8*c^9 - 19*a^2*b^7*c^8*d + 14*a^3*b^6*c^7*d^2 - 8*a^4*b^5*c^6*d^3 + 8*a^6*b^3*c^4*d^5 - 14*a^7*b^2*c^3*d^6 + 19*a^8*b*c^2*d^7 - 7*a^9*c*d^8)*x - 6*(7*a^7*b^2*c^4*d^5 - 7*a^8*b*c^3*d^6 + 2*a^9*c^2*d^7 + (7*a^5*b^4*c^2*d^7 - 7*a^6*b^3*c*d^8 + 2*a^7*b^2*d^9)*x^4 + 2*(7*a^5*b^4*c^3*d^6 - 5*a^7*b^2*c*d^8 + 2*a^8*b*d^9)*x^3 + (7*a^5*b^4*c^4*d^5 + 21*a^6*b^3*c^3*d^6 - 19*a^7*b^2*c^2*d^7 + a^8*b*c*d^8 + 2*a^9*d^9)*x^2 + 2*(7*a^6*b^3*c^4*d^5 - 5*a^8*b*c^2*d^7 + 2*a^9*c*d^8)*x)*log(b*x + a) + 6*(2*a^2*b^7*c^9 - 7*a^3*b^6*c^8*d + 7*a^4*b^5*c^7*d^2 + (2*b^9*c^7*d^2 - 7*a*b^8*c^6*d^3 + 7*a^2*b^7*c^5*d^4)*x^4 + 2*(2*b^9*c^8*d - 5*a*b^8*c^7*d^2 + 7*a^3*b^6*c^5*d^4)*x^3 + (2*b^9*c^9 + a*b^8*c^8*d - 19*a^2*b^7*c^7*d^2 + 21*a^3*b^6*c^6*d^3 + 7*a^4*b^5*c^5*d^4)*x^2 + 2*(2*a*b^8*c^9 - 5*a^2*b^7*c^8*d + 7*a^4*b^5*c^6*d^3)*x)*log(d*x + c))/(a^2*b^10*c^7*d^5 - 5*a^3*b^9*c^6*d^6 + 10*a^4*b^8*c^5*d^7 - 10*a^5*b^7*c^4*d^8 + 5*a^6*b^6*c^3*d^9 - a^7*b^5*c^2*d^10 + (b^12*c^5*d^7 - 5*a*b^11*c^4*d^8 + 10*a^2*b^10*c^3*d^9 - 10*a^3*b^9*c^2*d^10 + 5*a^4*b^8*c*d^11 - a^5*b^7*d^12)*x^4 + 2*(b^12*c^6*d^6 - 4*a*b^11*c^5*d^7 + 5*a^2*b^10*c^4*d^8 - 5*a^4*b^8*c^2*d^10 + 4*a^5*b^7*c*d^11 - a^6*b^6*d^12)*x^3 + (b^12*c^7*d^5 - a*b^11*c^6*d^6 - 9*a^2*b^10*c^5*d^7 + 25*a^3*b^9*c^4*d^8 - 25*a^4*b^8*c^3*d^9 + 9*a^5*b^7*c^2*d^10 + a^6*b^6*c*d^11 - a^7*b^5*d^12)*x^2 + 2*(a*b^11*c^7*d^5 - 4*a^2*b^10*c^6*d^6 + 5*a^3*b^9*c^5*d^7 - 5*a^5*b^7*c^3*d^9 + 4*a^6*b^6*c^2*d^10 - a^7*b^5*c*d^11)*x)","B",0
310,1,1457,0,1.959438," ","integrate(x^6/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{5 \, a^{2} b^{6} c^{8} - 16 \, a^{3} b^{5} c^{7} d + 11 \, a^{4} b^{4} c^{6} d^{2} - 11 \, a^{6} b^{2} c^{4} d^{4} + 16 \, a^{7} b c^{3} d^{5} - 5 \, a^{8} c^{2} d^{6} - 2 \, {\left(b^{8} c^{5} d^{3} - 5 \, a b^{7} c^{4} d^{4} + 10 \, a^{2} b^{6} c^{3} d^{5} - 10 \, a^{3} b^{5} c^{2} d^{6} + 5 \, a^{4} b^{4} c d^{7} - a^{5} b^{3} d^{8}\right)} x^{5} - 4 \, {\left(b^{8} c^{6} d^{2} - 4 \, a b^{7} c^{5} d^{3} + 5 \, a^{2} b^{6} c^{4} d^{4} - 5 \, a^{4} b^{4} c^{2} d^{6} + 4 \, a^{5} b^{3} c d^{7} - a^{6} b^{2} d^{8}\right)} x^{4} + 2 \, {\left(2 \, b^{8} c^{7} d - 8 \, a b^{7} c^{6} d^{2} + 15 \, a^{2} b^{6} c^{5} d^{3} - 25 \, a^{3} b^{5} c^{4} d^{4} + 25 \, a^{4} b^{4} c^{3} d^{5} - 15 \, a^{5} b^{3} c^{2} d^{6} + 8 \, a^{6} b^{2} c d^{7} - 2 \, a^{7} b d^{8}\right)} x^{3} + {\left(5 \, b^{8} c^{8} - 8 \, a b^{7} c^{7} d - 9 \, a^{2} b^{6} c^{6} d^{2} + 4 \, a^{3} b^{5} c^{5} d^{3} - 4 \, a^{5} b^{3} c^{3} d^{5} + 9 \, a^{6} b^{2} c^{2} d^{6} + 8 \, a^{7} b c d^{7} - 5 \, a^{8} d^{8}\right)} x^{2} + 2 \, {\left(5 \, a b^{7} c^{8} - 14 \, a^{2} b^{6} c^{7} d + 7 \, a^{3} b^{5} c^{6} d^{2} - 4 \, a^{4} b^{4} c^{5} d^{3} + 4 \, a^{5} b^{3} c^{4} d^{4} - 7 \, a^{6} b^{2} c^{3} d^{5} + 14 \, a^{7} b c^{2} d^{6} - 5 \, a^{8} c d^{7}\right)} x - 6 \, {\left(5 \, a^{6} b^{2} c^{4} d^{4} - 4 \, a^{7} b c^{3} d^{5} + a^{8} c^{2} d^{6} + {\left(5 \, a^{4} b^{4} c^{2} d^{6} - 4 \, a^{5} b^{3} c d^{7} + a^{6} b^{2} d^{8}\right)} x^{4} + 2 \, {\left(5 \, a^{4} b^{4} c^{3} d^{5} + a^{5} b^{3} c^{2} d^{6} - 3 \, a^{6} b^{2} c d^{7} + a^{7} b d^{8}\right)} x^{3} + {\left(5 \, a^{4} b^{4} c^{4} d^{4} + 16 \, a^{5} b^{3} c^{3} d^{5} - 10 \, a^{6} b^{2} c^{2} d^{6} + a^{8} d^{8}\right)} x^{2} + 2 \, {\left(5 \, a^{5} b^{3} c^{4} d^{4} + a^{6} b^{2} c^{3} d^{5} - 3 \, a^{7} b c^{2} d^{6} + a^{8} c d^{7}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(a^{2} b^{6} c^{8} - 4 \, a^{3} b^{5} c^{7} d + 5 \, a^{4} b^{4} c^{6} d^{2} + {\left(b^{8} c^{6} d^{2} - 4 \, a b^{7} c^{5} d^{3} + 5 \, a^{2} b^{6} c^{4} d^{4}\right)} x^{4} + 2 \, {\left(b^{8} c^{7} d - 3 \, a b^{7} c^{6} d^{2} + a^{2} b^{6} c^{5} d^{3} + 5 \, a^{3} b^{5} c^{4} d^{4}\right)} x^{3} + {\left(b^{8} c^{8} - 10 \, a^{2} b^{6} c^{6} d^{2} + 16 \, a^{3} b^{5} c^{5} d^{3} + 5 \, a^{4} b^{4} c^{4} d^{4}\right)} x^{2} + 2 \, {\left(a b^{7} c^{8} - 3 \, a^{2} b^{6} c^{7} d + a^{3} b^{5} c^{6} d^{2} + 5 \, a^{4} b^{4} c^{5} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{9} c^{7} d^{4} - 5 \, a^{3} b^{8} c^{6} d^{5} + 10 \, a^{4} b^{7} c^{5} d^{6} - 10 \, a^{5} b^{6} c^{4} d^{7} + 5 \, a^{6} b^{5} c^{3} d^{8} - a^{7} b^{4} c^{2} d^{9} + {\left(b^{11} c^{5} d^{6} - 5 \, a b^{10} c^{4} d^{7} + 10 \, a^{2} b^{9} c^{3} d^{8} - 10 \, a^{3} b^{8} c^{2} d^{9} + 5 \, a^{4} b^{7} c d^{10} - a^{5} b^{6} d^{11}\right)} x^{4} + 2 \, {\left(b^{11} c^{6} d^{5} - 4 \, a b^{10} c^{5} d^{6} + 5 \, a^{2} b^{9} c^{4} d^{7} - 5 \, a^{4} b^{7} c^{2} d^{9} + 4 \, a^{5} b^{6} c d^{10} - a^{6} b^{5} d^{11}\right)} x^{3} + {\left(b^{11} c^{7} d^{4} - a b^{10} c^{6} d^{5} - 9 \, a^{2} b^{9} c^{5} d^{6} + 25 \, a^{3} b^{8} c^{4} d^{7} - 25 \, a^{4} b^{7} c^{3} d^{8} + 9 \, a^{5} b^{6} c^{2} d^{9} + a^{6} b^{5} c d^{10} - a^{7} b^{4} d^{11}\right)} x^{2} + 2 \, {\left(a b^{10} c^{7} d^{4} - 4 \, a^{2} b^{9} c^{6} d^{5} + 5 \, a^{3} b^{8} c^{5} d^{6} - 5 \, a^{5} b^{6} c^{3} d^{8} + 4 \, a^{6} b^{5} c^{2} d^{9} - a^{7} b^{4} c d^{10}\right)} x\right)}}"," ",0,"-1/2*(5*a^2*b^6*c^8 - 16*a^3*b^5*c^7*d + 11*a^4*b^4*c^6*d^2 - 11*a^6*b^2*c^4*d^4 + 16*a^7*b*c^3*d^5 - 5*a^8*c^2*d^6 - 2*(b^8*c^5*d^3 - 5*a*b^7*c^4*d^4 + 10*a^2*b^6*c^3*d^5 - 10*a^3*b^5*c^2*d^6 + 5*a^4*b^4*c*d^7 - a^5*b^3*d^8)*x^5 - 4*(b^8*c^6*d^2 - 4*a*b^7*c^5*d^3 + 5*a^2*b^6*c^4*d^4 - 5*a^4*b^4*c^2*d^6 + 4*a^5*b^3*c*d^7 - a^6*b^2*d^8)*x^4 + 2*(2*b^8*c^7*d - 8*a*b^7*c^6*d^2 + 15*a^2*b^6*c^5*d^3 - 25*a^3*b^5*c^4*d^4 + 25*a^4*b^4*c^3*d^5 - 15*a^5*b^3*c^2*d^6 + 8*a^6*b^2*c*d^7 - 2*a^7*b*d^8)*x^3 + (5*b^8*c^8 - 8*a*b^7*c^7*d - 9*a^2*b^6*c^6*d^2 + 4*a^3*b^5*c^5*d^3 - 4*a^5*b^3*c^3*d^5 + 9*a^6*b^2*c^2*d^6 + 8*a^7*b*c*d^7 - 5*a^8*d^8)*x^2 + 2*(5*a*b^7*c^8 - 14*a^2*b^6*c^7*d + 7*a^3*b^5*c^6*d^2 - 4*a^4*b^4*c^5*d^3 + 4*a^5*b^3*c^4*d^4 - 7*a^6*b^2*c^3*d^5 + 14*a^7*b*c^2*d^6 - 5*a^8*c*d^7)*x - 6*(5*a^6*b^2*c^4*d^4 - 4*a^7*b*c^3*d^5 + a^8*c^2*d^6 + (5*a^4*b^4*c^2*d^6 - 4*a^5*b^3*c*d^7 + a^6*b^2*d^8)*x^4 + 2*(5*a^4*b^4*c^3*d^5 + a^5*b^3*c^2*d^6 - 3*a^6*b^2*c*d^7 + a^7*b*d^8)*x^3 + (5*a^4*b^4*c^4*d^4 + 16*a^5*b^3*c^3*d^5 - 10*a^6*b^2*c^2*d^6 + a^8*d^8)*x^2 + 2*(5*a^5*b^3*c^4*d^4 + a^6*b^2*c^3*d^5 - 3*a^7*b*c^2*d^6 + a^8*c*d^7)*x)*log(b*x + a) + 6*(a^2*b^6*c^8 - 4*a^3*b^5*c^7*d + 5*a^4*b^4*c^6*d^2 + (b^8*c^6*d^2 - 4*a*b^7*c^5*d^3 + 5*a^2*b^6*c^4*d^4)*x^4 + 2*(b^8*c^7*d - 3*a*b^7*c^6*d^2 + a^2*b^6*c^5*d^3 + 5*a^3*b^5*c^4*d^4)*x^3 + (b^8*c^8 - 10*a^2*b^6*c^6*d^2 + 16*a^3*b^5*c^5*d^3 + 5*a^4*b^4*c^4*d^4)*x^2 + 2*(a*b^7*c^8 - 3*a^2*b^6*c^7*d + a^3*b^5*c^6*d^2 + 5*a^4*b^4*c^5*d^3)*x)*log(d*x + c))/(a^2*b^9*c^7*d^4 - 5*a^3*b^8*c^6*d^5 + 10*a^4*b^7*c^5*d^6 - 10*a^5*b^6*c^4*d^7 + 5*a^6*b^5*c^3*d^8 - a^7*b^4*c^2*d^9 + (b^11*c^5*d^6 - 5*a*b^10*c^4*d^7 + 10*a^2*b^9*c^3*d^8 - 10*a^3*b^8*c^2*d^9 + 5*a^4*b^7*c*d^10 - a^5*b^6*d^11)*x^4 + 2*(b^11*c^6*d^5 - 4*a*b^10*c^5*d^6 + 5*a^2*b^9*c^4*d^7 - 5*a^4*b^7*c^2*d^9 + 4*a^5*b^6*c*d^10 - a^6*b^5*d^11)*x^3 + (b^11*c^7*d^4 - a*b^10*c^6*d^5 - 9*a^2*b^9*c^5*d^6 + 25*a^3*b^8*c^4*d^7 - 25*a^4*b^7*c^3*d^8 + 9*a^5*b^6*c^2*d^9 + a^6*b^5*c*d^10 - a^7*b^4*d^11)*x^2 + 2*(a*b^10*c^7*d^4 - 4*a^2*b^9*c^6*d^5 + 5*a^3*b^8*c^5*d^6 - 5*a^5*b^6*c^3*d^8 + 4*a^6*b^5*c^2*d^9 - a^7*b^4*c*d^10)*x)","B",0
311,1,1267,0,1.061123," ","integrate(x^5/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{5} c^{7} - 12 \, a^{3} b^{4} c^{6} d + 9 \, a^{4} b^{3} c^{5} d^{2} - 9 \, a^{5} b^{2} c^{4} d^{3} + 12 \, a^{6} b c^{3} d^{4} - 3 \, a^{7} c^{2} d^{5} + 2 \, {\left(2 \, b^{7} c^{6} d - 7 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 7 \, a^{5} b^{2} c d^{6} - 2 \, a^{6} b d^{7}\right)} x^{3} + {\left(3 \, b^{7} c^{7} - 4 \, a b^{6} c^{6} d - 19 \, a^{2} b^{5} c^{5} d^{2} + 20 \, a^{3} b^{4} c^{4} d^{3} - 20 \, a^{4} b^{3} c^{3} d^{4} + 19 \, a^{5} b^{2} c^{2} d^{5} + 4 \, a^{6} b c d^{6} - 3 \, a^{7} d^{7}\right)} x^{2} + 2 \, {\left(3 \, a b^{6} c^{7} - 10 \, a^{2} b^{5} c^{6} d + 2 \, a^{3} b^{4} c^{5} d^{2} - 2 \, a^{5} b^{2} c^{3} d^{4} + 10 \, a^{6} b c^{2} d^{5} - 3 \, a^{7} c d^{6}\right)} x - 2 \, {\left(10 \, a^{5} b^{2} c^{4} d^{3} - 5 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5} + {\left(10 \, a^{3} b^{4} c^{2} d^{5} - 5 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} d^{4} + 5 \, a^{4} b^{3} c^{2} d^{5} - 4 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} - a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{2} + 2 \, {\left(10 \, a^{4} b^{3} c^{4} d^{3} + 5 \, a^{5} b^{2} c^{3} d^{4} - 4 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} + 10 \, a^{3} b^{4} c^{3} d^{4}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 35 \, a^{3} b^{4} c^{4} d^{3} + 10 \, a^{4} b^{3} c^{3} d^{4}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} + 10 \, a^{4} b^{3} c^{4} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{8} c^{7} d^{3} - 5 \, a^{3} b^{7} c^{6} d^{4} + 10 \, a^{4} b^{6} c^{5} d^{5} - 10 \, a^{5} b^{5} c^{4} d^{6} + 5 \, a^{6} b^{4} c^{3} d^{7} - a^{7} b^{3} c^{2} d^{8} + {\left(b^{10} c^{5} d^{5} - 5 \, a b^{9} c^{4} d^{6} + 10 \, a^{2} b^{8} c^{3} d^{7} - 10 \, a^{3} b^{7} c^{2} d^{8} + 5 \, a^{4} b^{6} c d^{9} - a^{5} b^{5} d^{10}\right)} x^{4} + 2 \, {\left(b^{10} c^{6} d^{4} - 4 \, a b^{9} c^{5} d^{5} + 5 \, a^{2} b^{8} c^{4} d^{6} - 5 \, a^{4} b^{6} c^{2} d^{8} + 4 \, a^{5} b^{5} c d^{9} - a^{6} b^{4} d^{10}\right)} x^{3} + {\left(b^{10} c^{7} d^{3} - a b^{9} c^{6} d^{4} - 9 \, a^{2} b^{8} c^{5} d^{5} + 25 \, a^{3} b^{7} c^{4} d^{6} - 25 \, a^{4} b^{6} c^{3} d^{7} + 9 \, a^{5} b^{5} c^{2} d^{8} + a^{6} b^{4} c d^{9} - a^{7} b^{3} d^{10}\right)} x^{2} + 2 \, {\left(a b^{9} c^{7} d^{3} - 4 \, a^{2} b^{8} c^{6} d^{4} + 5 \, a^{3} b^{7} c^{5} d^{5} - 5 \, a^{5} b^{5} c^{3} d^{7} + 4 \, a^{6} b^{4} c^{2} d^{8} - a^{7} b^{3} c d^{9}\right)} x\right)}}"," ",0,"1/2*(3*a^2*b^5*c^7 - 12*a^3*b^4*c^6*d + 9*a^4*b^3*c^5*d^2 - 9*a^5*b^2*c^4*d^3 + 12*a^6*b*c^3*d^4 - 3*a^7*c^2*d^5 + 2*(2*b^7*c^6*d - 7*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 7*a^5*b^2*c*d^6 - 2*a^6*b*d^7)*x^3 + (3*b^7*c^7 - 4*a*b^6*c^6*d - 19*a^2*b^5*c^5*d^2 + 20*a^3*b^4*c^4*d^3 - 20*a^4*b^3*c^3*d^4 + 19*a^5*b^2*c^2*d^5 + 4*a^6*b*c*d^6 - 3*a^7*d^7)*x^2 + 2*(3*a*b^6*c^7 - 10*a^2*b^5*c^6*d + 2*a^3*b^4*c^5*d^2 - 2*a^5*b^2*c^3*d^4 + 10*a^6*b*c^2*d^5 - 3*a^7*c*d^6)*x - 2*(10*a^5*b^2*c^4*d^3 - 5*a^6*b*c^3*d^4 + a^7*c^2*d^5 + (10*a^3*b^4*c^2*d^5 - 5*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^4 + 2*(10*a^3*b^4*c^3*d^4 + 5*a^4*b^3*c^2*d^5 - 4*a^5*b^2*c*d^6 + a^6*b*d^7)*x^3 + (10*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 - a^6*b*c*d^6 + a^7*d^7)*x^2 + 2*(10*a^4*b^3*c^4*d^3 + 5*a^5*b^2*c^3*d^4 - 4*a^6*b*c^2*d^5 + a^7*c*d^6)*x)*log(b*x + a) + 2*(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 + 10*a^3*b^4*c^3*d^4)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 + 10*a^4*b^3*c^3*d^4)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 + 10*a^4*b^3*c^4*d^3)*x)*log(d*x + c))/(a^2*b^8*c^7*d^3 - 5*a^3*b^7*c^6*d^4 + 10*a^4*b^6*c^5*d^5 - 10*a^5*b^5*c^4*d^6 + 5*a^6*b^4*c^3*d^7 - a^7*b^3*c^2*d^8 + (b^10*c^5*d^5 - 5*a*b^9*c^4*d^6 + 10*a^2*b^8*c^3*d^7 - 10*a^3*b^7*c^2*d^8 + 5*a^4*b^6*c*d^9 - a^5*b^5*d^10)*x^4 + 2*(b^10*c^6*d^4 - 4*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 - 5*a^4*b^6*c^2*d^8 + 4*a^5*b^5*c*d^9 - a^6*b^4*d^10)*x^3 + (b^10*c^7*d^3 - a*b^9*c^6*d^4 - 9*a^2*b^8*c^5*d^5 + 25*a^3*b^7*c^4*d^6 - 25*a^4*b^6*c^3*d^7 + 9*a^5*b^5*c^2*d^8 + a^6*b^4*c*d^9 - a^7*b^3*d^10)*x^2 + 2*(a*b^9*c^7*d^3 - 4*a^2*b^8*c^6*d^4 + 5*a^3*b^7*c^5*d^5 - 5*a^5*b^5*c^3*d^7 + 4*a^6*b^4*c^2*d^8 - a^7*b^3*c*d^9)*x)","B",0
312,1,985,0,1.497282," ","integrate(x^4/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a^{2} b^{4} c^{6} - 8 \, a^{3} b^{3} c^{5} d + 8 \, a^{5} b c^{3} d^{3} - a^{6} c^{2} d^{4} + 2 \, {\left(b^{6} c^{5} d - 5 \, a b^{5} c^{4} d^{2} + 4 \, a^{2} b^{4} c^{3} d^{3} - 4 \, a^{3} b^{3} c^{2} d^{4} + 5 \, a^{4} b^{2} c d^{5} - a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 4 \, a b^{5} c^{5} d - 13 \, a^{2} b^{4} c^{4} d^{2} + 13 \, a^{4} b^{2} c^{2} d^{4} + 4 \, a^{5} b c d^{5} - a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 7 \, a^{2} b^{4} c^{5} d - 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} + 7 \, a^{5} b c^{2} d^{4} - a^{6} c d^{5}\right)} x - 12 \, {\left(a^{2} b^{4} c^{2} d^{4} x^{4} + a^{4} b^{2} c^{4} d^{2} + 2 \, {\left(a^{2} b^{4} c^{3} d^{3} + a^{3} b^{3} c^{2} d^{4}\right)} x^{3} + {\left(a^{2} b^{4} c^{4} d^{2} + 4 \, a^{3} b^{3} c^{3} d^{3} + a^{4} b^{2} c^{2} d^{4}\right)} x^{2} + 2 \, {\left(a^{3} b^{3} c^{4} d^{2} + a^{4} b^{2} c^{3} d^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(a^{2} b^{4} c^{2} d^{4} x^{4} + a^{4} b^{2} c^{4} d^{2} + 2 \, {\left(a^{2} b^{4} c^{3} d^{3} + a^{3} b^{3} c^{2} d^{4}\right)} x^{3} + {\left(a^{2} b^{4} c^{4} d^{2} + 4 \, a^{3} b^{3} c^{3} d^{3} + a^{4} b^{2} c^{2} d^{4}\right)} x^{2} + 2 \, {\left(a^{3} b^{3} c^{4} d^{2} + a^{4} b^{2} c^{3} d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{7} c^{7} d^{2} - 5 \, a^{3} b^{6} c^{6} d^{3} + 10 \, a^{4} b^{5} c^{5} d^{4} - 10 \, a^{5} b^{4} c^{4} d^{5} + 5 \, a^{6} b^{3} c^{3} d^{6} - a^{7} b^{2} c^{2} d^{7} + {\left(b^{9} c^{5} d^{4} - 5 \, a b^{8} c^{4} d^{5} + 10 \, a^{2} b^{7} c^{3} d^{6} - 10 \, a^{3} b^{6} c^{2} d^{7} + 5 \, a^{4} b^{5} c d^{8} - a^{5} b^{4} d^{9}\right)} x^{4} + 2 \, {\left(b^{9} c^{6} d^{3} - 4 \, a b^{8} c^{5} d^{4} + 5 \, a^{2} b^{7} c^{4} d^{5} - 5 \, a^{4} b^{5} c^{2} d^{7} + 4 \, a^{5} b^{4} c d^{8} - a^{6} b^{3} d^{9}\right)} x^{3} + {\left(b^{9} c^{7} d^{2} - a b^{8} c^{6} d^{3} - 9 \, a^{2} b^{7} c^{5} d^{4} + 25 \, a^{3} b^{6} c^{4} d^{5} - 25 \, a^{4} b^{5} c^{3} d^{6} + 9 \, a^{5} b^{4} c^{2} d^{7} + a^{6} b^{3} c d^{8} - a^{7} b^{2} d^{9}\right)} x^{2} + 2 \, {\left(a b^{8} c^{7} d^{2} - 4 \, a^{2} b^{7} c^{6} d^{3} + 5 \, a^{3} b^{6} c^{5} d^{4} - 5 \, a^{5} b^{4} c^{3} d^{6} + 4 \, a^{6} b^{3} c^{2} d^{7} - a^{7} b^{2} c d^{8}\right)} x\right)}}"," ",0,"-1/2*(a^2*b^4*c^6 - 8*a^3*b^3*c^5*d + 8*a^5*b*c^3*d^3 - a^6*c^2*d^4 + 2*(b^6*c^5*d - 5*a*b^5*c^4*d^2 + 4*a^2*b^4*c^3*d^3 - 4*a^3*b^3*c^2*d^4 + 5*a^4*b^2*c*d^5 - a^5*b*d^6)*x^3 + (b^6*c^6 - 4*a*b^5*c^5*d - 13*a^2*b^4*c^4*d^2 + 13*a^4*b^2*c^2*d^4 + 4*a^5*b*c*d^5 - a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 7*a^2*b^4*c^5*d - 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 + 7*a^5*b*c^2*d^4 - a^6*c*d^5)*x - 12*(a^2*b^4*c^2*d^4*x^4 + a^4*b^2*c^4*d^2 + 2*(a^2*b^4*c^3*d^3 + a^3*b^3*c^2*d^4)*x^3 + (a^2*b^4*c^4*d^2 + 4*a^3*b^3*c^3*d^3 + a^4*b^2*c^2*d^4)*x^2 + 2*(a^3*b^3*c^4*d^2 + a^4*b^2*c^3*d^3)*x)*log(b*x + a) + 12*(a^2*b^4*c^2*d^4*x^4 + a^4*b^2*c^4*d^2 + 2*(a^2*b^4*c^3*d^3 + a^3*b^3*c^2*d^4)*x^3 + (a^2*b^4*c^4*d^2 + 4*a^3*b^3*c^3*d^3 + a^4*b^2*c^2*d^4)*x^2 + 2*(a^3*b^3*c^4*d^2 + a^4*b^2*c^3*d^3)*x)*log(d*x + c))/(a^2*b^7*c^7*d^2 - 5*a^3*b^6*c^6*d^3 + 10*a^4*b^5*c^5*d^4 - 10*a^5*b^4*c^4*d^5 + 5*a^6*b^3*c^3*d^6 - a^7*b^2*c^2*d^7 + (b^9*c^5*d^4 - 5*a*b^8*c^4*d^5 + 10*a^2*b^7*c^3*d^6 - 10*a^3*b^6*c^2*d^7 + 5*a^4*b^5*c*d^8 - a^5*b^4*d^9)*x^4 + 2*(b^9*c^6*d^3 - 4*a*b^8*c^5*d^4 + 5*a^2*b^7*c^4*d^5 - 5*a^4*b^5*c^2*d^7 + 4*a^5*b^4*c*d^8 - a^6*b^3*d^9)*x^3 + (b^9*c^7*d^2 - a*b^8*c^6*d^3 - 9*a^2*b^7*c^5*d^4 + 25*a^3*b^6*c^4*d^5 - 25*a^4*b^5*c^3*d^6 + 9*a^5*b^4*c^2*d^7 + a^6*b^3*c*d^8 - a^7*b^2*d^9)*x^2 + 2*(a*b^8*c^7*d^2 - 4*a^2*b^7*c^6*d^3 + 5*a^3*b^6*c^5*d^4 - 5*a^5*b^4*c^3*d^6 + 4*a^6*b^3*c^2*d^7 - a^7*b^2*c*d^8)*x)","B",0
313,1,991,0,1.691834," ","integrate(x^3/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a^{2} b^{3} c^{5} + 9 \, a^{3} b^{2} c^{4} d - 9 \, a^{4} b c^{3} d^{2} - a^{5} c^{2} d^{3} + 6 \, {\left(a b^{4} c^{3} d^{2} - a^{3} b^{2} c d^{4}\right)} x^{3} + {\left(b^{5} c^{5} + 4 \, a b^{4} c^{4} d + 19 \, a^{2} b^{3} c^{3} d^{2} - 19 \, a^{3} b^{2} c^{2} d^{3} - 4 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} x^{2} + 2 \, {\left(a b^{4} c^{5} + 7 \, a^{2} b^{3} c^{4} d - 7 \, a^{4} b c^{2} d^{3} - a^{5} c d^{4}\right)} x + 6 \, {\left(a^{3} b^{2} c^{4} d + a^{4} b c^{3} d^{2} + {\left(a b^{4} c^{2} d^{3} + a^{2} b^{3} c d^{4}\right)} x^{4} + 2 \, {\left(a b^{4} c^{3} d^{2} + 2 \, a^{2} b^{3} c^{2} d^{3} + a^{3} b^{2} c d^{4}\right)} x^{3} + {\left(a b^{4} c^{4} d + 5 \, a^{2} b^{3} c^{3} d^{2} + 5 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4}\right)} x^{2} + 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\right)} \log\left(b x + a\right) - 6 \, {\left(a^{3} b^{2} c^{4} d + a^{4} b c^{3} d^{2} + {\left(a b^{4} c^{2} d^{3} + a^{2} b^{3} c d^{4}\right)} x^{4} + 2 \, {\left(a b^{4} c^{3} d^{2} + 2 \, a^{2} b^{3} c^{2} d^{3} + a^{3} b^{2} c d^{4}\right)} x^{3} + {\left(a b^{4} c^{4} d + 5 \, a^{2} b^{3} c^{3} d^{2} + 5 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4}\right)} x^{2} + 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\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{6} c^{7} d - 5 \, a^{3} b^{5} c^{6} d^{2} + 10 \, a^{4} b^{4} c^{5} d^{3} - 10 \, a^{5} b^{3} c^{4} d^{4} + 5 \, a^{6} b^{2} c^{3} d^{5} - a^{7} b c^{2} d^{6} + {\left(b^{8} c^{5} d^{3} - 5 \, a b^{7} c^{4} d^{4} + 10 \, a^{2} b^{6} c^{3} d^{5} - 10 \, a^{3} b^{5} c^{2} d^{6} + 5 \, a^{4} b^{4} c d^{7} - a^{5} b^{3} d^{8}\right)} x^{4} + 2 \, {\left(b^{8} c^{6} d^{2} - 4 \, a b^{7} c^{5} d^{3} + 5 \, a^{2} b^{6} c^{4} d^{4} - 5 \, a^{4} b^{4} c^{2} d^{6} + 4 \, a^{5} b^{3} c d^{7} - a^{6} b^{2} d^{8}\right)} x^{3} + {\left(b^{8} c^{7} d - a b^{7} c^{6} d^{2} - 9 \, a^{2} b^{6} c^{5} d^{3} + 25 \, a^{3} b^{5} c^{4} d^{4} - 25 \, a^{4} b^{4} c^{3} d^{5} + 9 \, a^{5} b^{3} c^{2} d^{6} + a^{6} b^{2} c d^{7} - a^{7} b d^{8}\right)} x^{2} + 2 \, {\left(a b^{7} c^{7} d - 4 \, a^{2} b^{6} c^{6} d^{2} + 5 \, a^{3} b^{5} c^{5} d^{3} - 5 \, a^{5} b^{3} c^{3} d^{5} + 4 \, a^{6} b^{2} c^{2} d^{6} - a^{7} b c d^{7}\right)} x\right)}}"," ",0,"-1/2*(a^2*b^3*c^5 + 9*a^3*b^2*c^4*d - 9*a^4*b*c^3*d^2 - a^5*c^2*d^3 + 6*(a*b^4*c^3*d^2 - a^3*b^2*c*d^4)*x^3 + (b^5*c^5 + 4*a*b^4*c^4*d + 19*a^2*b^3*c^3*d^2 - 19*a^3*b^2*c^2*d^3 - 4*a^4*b*c*d^4 - a^5*d^5)*x^2 + 2*(a*b^4*c^5 + 7*a^2*b^3*c^4*d - 7*a^4*b*c^2*d^3 - a^5*c*d^4)*x + 6*(a^3*b^2*c^4*d + a^4*b*c^3*d^2 + (a*b^4*c^2*d^3 + a^2*b^3*c*d^4)*x^4 + 2*(a*b^4*c^3*d^2 + 2*a^2*b^3*c^2*d^3 + a^3*b^2*c*d^4)*x^3 + (a*b^4*c^4*d + 5*a^2*b^3*c^3*d^2 + 5*a^3*b^2*c^2*d^3 + a^4*b*c*d^4)*x^2 + 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)*log(b*x + a) - 6*(a^3*b^2*c^4*d + a^4*b*c^3*d^2 + (a*b^4*c^2*d^3 + a^2*b^3*c*d^4)*x^4 + 2*(a*b^4*c^3*d^2 + 2*a^2*b^3*c^2*d^3 + a^3*b^2*c*d^4)*x^3 + (a*b^4*c^4*d + 5*a^2*b^3*c^3*d^2 + 5*a^3*b^2*c^2*d^3 + a^4*b*c*d^4)*x^2 + 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)*log(d*x + c))/(a^2*b^6*c^7*d - 5*a^3*b^5*c^6*d^2 + 10*a^4*b^4*c^5*d^3 - 10*a^5*b^3*c^4*d^4 + 5*a^6*b^2*c^3*d^5 - a^7*b*c^2*d^6 + (b^8*c^5*d^3 - 5*a*b^7*c^4*d^4 + 10*a^2*b^6*c^3*d^5 - 10*a^3*b^5*c^2*d^6 + 5*a^4*b^4*c*d^7 - a^5*b^3*d^8)*x^4 + 2*(b^8*c^6*d^2 - 4*a*b^7*c^5*d^3 + 5*a^2*b^6*c^4*d^4 - 5*a^4*b^4*c^2*d^6 + 4*a^5*b^3*c*d^7 - a^6*b^2*d^8)*x^3 + (b^8*c^7*d - a*b^7*c^6*d^2 - 9*a^2*b^6*c^5*d^3 + 25*a^3*b^5*c^4*d^4 - 25*a^4*b^4*c^3*d^5 + 9*a^5*b^3*c^2*d^6 + a^6*b^2*c*d^7 - a^7*b*d^8)*x^2 + 2*(a*b^7*c^7*d - 4*a^2*b^6*c^6*d^2 + 5*a^3*b^5*c^5*d^3 - 5*a^5*b^3*c^3*d^5 + 4*a^6*b^2*c^2*d^6 - a^7*b*c*d^7)*x)","B",0
314,1,990,0,1.700996," ","integrate(x^2/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{6 \, a^{2} b^{2} c^{4} - 6 \, a^{4} c^{2} d^{2} + 2 \, {\left(b^{4} c^{3} d + 3 \, a b^{3} c^{2} d^{2} - 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{3} + 3 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x^{2} + 2 \, {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} - 5 \, a^{4} c d^{3}\right)} x + 2 \, {\left(a^{2} b^{2} c^{4} + 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{4} c^{3} d + 5 \, a b^{3} c^{2} d^{2} + 5 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{3} + {\left(b^{4} c^{4} + 8 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{4} + 5 \, a^{2} b^{2} c^{3} d + 5 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(a^{2} b^{2} c^{4} + 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{4} + 2 \, {\left(b^{4} c^{3} d + 5 \, a b^{3} c^{2} d^{2} + 5 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{3} + {\left(b^{4} c^{4} + 8 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{4} + 5 \, a^{2} b^{2} c^{3} d + 5 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x\right)}}"," ",0,"1/2*(6*a^2*b^2*c^4 - 6*a^4*c^2*d^2 + 2*(b^4*c^3*d + 3*a*b^3*c^2*d^2 - 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x^3 + 3*(b^4*c^4 + 4*a*b^3*c^3*d - 4*a^3*b*c*d^3 - a^4*d^4)*x^2 + 2*(5*a*b^3*c^4 + 3*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 - 5*a^4*c*d^3)*x + 2*(a^2*b^2*c^4 + 4*a^3*b*c^3*d + a^4*c^2*d^2 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^4 + 2*(b^4*c^3*d + 5*a*b^3*c^2*d^2 + 5*a^2*b^2*c*d^3 + a^3*b*d^4)*x^3 + (b^4*c^4 + 8*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 + a^4*d^4)*x^2 + 2*(a*b^3*c^4 + 5*a^2*b^2*c^3*d + 5*a^3*b*c^2*d^2 + a^4*c*d^3)*x)*log(b*x + a) - 2*(a^2*b^2*c^4 + 4*a^3*b*c^3*d + a^4*c^2*d^2 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^4 + 2*(b^4*c^3*d + 5*a*b^3*c^2*d^2 + 5*a^2*b^2*c*d^3 + a^3*b*d^4)*x^3 + (b^4*c^4 + 8*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 + a^4*d^4)*x^2 + 2*(a*b^3*c^4 + 5*a^2*b^2*c^3*d + 5*a^3*b*c^2*d^2 + a^4*c*d^3)*x)*log(d*x + c))/(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*x)","B",0
315,1,891,0,1.571748," ","integrate(x/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a b^{3} c^{4} + 9 \, a^{2} b^{2} c^{3} d - 9 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 9 \, {\left(b^{4} c^{3} d + a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x^{2} + 2 \, {\left(b^{4} c^{4} + 7 \, a b^{3} c^{3} d - 7 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x + 6 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2} + {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{3} + {\left(b^{4} c^{3} d + 5 \, a b^{3} c^{2} d^{2} + 5 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2} + {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{3} + {\left(b^{4} c^{3} d + 5 \, a b^{3} c^{2} d^{2} + 5 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{3} d + 2 \, a^{2} b^{2} c^{2} d^{2} + a^{3} b c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x\right)}}"," ",0,"-1/2*(a*b^3*c^4 + 9*a^2*b^2*c^3*d - 9*a^3*b*c^2*d^2 - a^4*c*d^3 + 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 9*(b^4*c^3*d + a*b^3*c^2*d^2 - a^2*b^2*c*d^3 - a^3*b*d^4)*x^2 + 2*(b^4*c^4 + 7*a*b^3*c^3*d - 7*a^3*b*c*d^3 - a^4*d^4)*x + 6*(a^2*b^2*c^3*d + a^3*b*c^2*d^2 + (b^4*c*d^3 + a*b^3*d^4)*x^4 + 2*(b^4*c^2*d^2 + 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^3 + (b^4*c^3*d + 5*a*b^3*c^2*d^2 + 5*a^2*b^2*c*d^3 + a^3*b*d^4)*x^2 + 2*(a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x)*log(b*x + a) - 6*(a^2*b^2*c^3*d + a^3*b*c^2*d^2 + (b^4*c*d^3 + a*b^3*d^4)*x^4 + 2*(b^4*c^2*d^2 + 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^3 + (b^4*c^3*d + 5*a*b^3*c^2*d^2 + 5*a^2*b^2*c*d^3 + a^3*b*d^4)*x^2 + 2*(a*b^3*c^3*d + 2*a^2*b^2*c^2*d^2 + a^3*b*c*d^3)*x)*log(d*x + c))/(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*x)","B",0
316,1,760,0,1.034704," ","integrate(1/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 8 \, a^{3} b c d^{3} - a^{4} d^{4} - 12 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} - 18 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x - 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x\right)}}"," ",0,"-1/2*(b^4*c^4 - 8*a*b^3*c^3*d + 8*a^3*b*c*d^3 - a^4*d^4 - 12*(b^4*c*d^3 - a*b^3*d^4)*x^3 - 18*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 - a^3*b*d^4)*x - 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c))/(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*x)","B",0
317,1,1630,0,176.780869," ","integrate(1/x/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{5} c^{7} - 12 \, a^{3} b^{4} c^{6} d + 9 \, a^{4} b^{3} c^{5} d^{2} - 9 \, a^{5} b^{2} c^{4} d^{3} + 12 \, a^{6} b c^{3} d^{4} - 3 \, a^{7} c^{2} d^{5} + 2 \, {\left(a b^{6} c^{5} d^{2} - 5 \, a^{2} b^{5} c^{4} d^{3} + 5 \, a^{4} b^{3} c^{2} d^{5} - a^{5} b^{2} c d^{6}\right)} x^{3} + {\left(4 \, a b^{6} c^{6} d - 17 \, a^{2} b^{5} c^{5} d^{2} - 5 \, a^{3} b^{4} c^{4} d^{3} + 5 \, a^{4} b^{3} c^{3} d^{4} + 17 \, a^{5} b^{2} c^{2} d^{5} - 4 \, a^{6} b c d^{6}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 2 \, a^{2} b^{5} c^{6} d - 8 \, a^{3} b^{4} c^{5} d^{2} + 8 \, a^{5} b^{2} c^{3} d^{4} + 2 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x - 2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} + 10 \, a^{3} b^{4} c^{3} d^{4}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 35 \, a^{3} b^{4} c^{4} d^{3} + 10 \, a^{4} b^{3} c^{3} d^{4}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} + 10 \, a^{4} b^{3} c^{4} d^{3}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(10 \, a^{5} b^{2} c^{4} d^{3} - 5 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5} + {\left(10 \, a^{3} b^{4} c^{2} d^{5} - 5 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(10 \, a^{3} b^{4} c^{3} d^{4} + 5 \, a^{4} b^{3} c^{2} d^{5} - 4 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{4} c^{4} d^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} - a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{2} + 2 \, {\left(10 \, a^{4} b^{3} c^{4} d^{3} + 5 \, a^{5} b^{2} c^{3} d^{4} - 4 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{5} c^{10} - 5 \, a^{6} b^{4} c^{9} d + 10 \, a^{7} b^{3} c^{8} d^{2} - 10 \, a^{8} b^{2} c^{7} d^{3} + 5 \, a^{9} b c^{6} d^{4} - a^{10} c^{5} d^{5} + {\left(a^{3} b^{7} c^{8} d^{2} - 5 \, a^{4} b^{6} c^{7} d^{3} + 10 \, a^{5} b^{5} c^{6} d^{4} - 10 \, a^{6} b^{4} c^{5} d^{5} + 5 \, a^{7} b^{3} c^{4} d^{6} - a^{8} b^{2} c^{3} d^{7}\right)} x^{4} + 2 \, {\left(a^{3} b^{7} c^{9} d - 4 \, a^{4} b^{6} c^{8} d^{2} + 5 \, a^{5} b^{5} c^{7} d^{3} - 5 \, a^{7} b^{3} c^{5} d^{5} + 4 \, a^{8} b^{2} c^{4} d^{6} - a^{9} b c^{3} d^{7}\right)} x^{3} + {\left(a^{3} b^{7} c^{10} - a^{4} b^{6} c^{9} d - 9 \, a^{5} b^{5} c^{8} d^{2} + 25 \, a^{6} b^{4} c^{7} d^{3} - 25 \, a^{7} b^{3} c^{6} d^{4} + 9 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6} - a^{10} c^{3} d^{7}\right)} x^{2} + 2 \, {\left(a^{4} b^{6} c^{10} - 4 \, a^{5} b^{5} c^{9} d + 5 \, a^{6} b^{4} c^{8} d^{2} - 5 \, a^{8} b^{2} c^{6} d^{4} + 4 \, a^{9} b c^{5} d^{5} - a^{10} c^{4} d^{6}\right)} x\right)}}"," ",0,"1/2*(3*a^2*b^5*c^7 - 12*a^3*b^4*c^6*d + 9*a^4*b^3*c^5*d^2 - 9*a^5*b^2*c^4*d^3 + 12*a^6*b*c^3*d^4 - 3*a^7*c^2*d^5 + 2*(a*b^6*c^5*d^2 - 5*a^2*b^5*c^4*d^3 + 5*a^4*b^3*c^2*d^5 - a^5*b^2*c*d^6)*x^3 + (4*a*b^6*c^6*d - 17*a^2*b^5*c^5*d^2 - 5*a^3*b^4*c^4*d^3 + 5*a^4*b^3*c^3*d^4 + 17*a^5*b^2*c^2*d^5 - 4*a^6*b*c*d^6)*x^2 + 2*(a*b^6*c^7 - 2*a^2*b^5*c^6*d - 8*a^3*b^4*c^5*d^2 + 8*a^5*b^2*c^3*d^4 + 2*a^6*b*c^2*d^5 - a^7*c*d^6)*x - 2*(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 + 10*a^3*b^4*c^3*d^4)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 + 10*a^4*b^3*c^3*d^4)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 + 10*a^4*b^3*c^4*d^3)*x)*log(b*x + a) + 2*(10*a^5*b^2*c^4*d^3 - 5*a^6*b*c^3*d^4 + a^7*c^2*d^5 + (10*a^3*b^4*c^2*d^5 - 5*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^4 + 2*(10*a^3*b^4*c^3*d^4 + 5*a^4*b^3*c^2*d^5 - 4*a^5*b^2*c*d^6 + a^6*b*d^7)*x^3 + (10*a^3*b^4*c^4*d^3 + 35*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 - a^6*b*c*d^6 + a^7*d^7)*x^2 + 2*(10*a^4*b^3*c^4*d^3 + 5*a^5*b^2*c^3*d^4 - 4*a^6*b*c^2*d^5 + a^7*c*d^6)*x)*log(d*x + c) + 2*(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*x)*log(x))/(a^5*b^5*c^10 - 5*a^6*b^4*c^9*d + 10*a^7*b^3*c^8*d^2 - 10*a^8*b^2*c^7*d^3 + 5*a^9*b*c^6*d^4 - a^10*c^5*d^5 + (a^3*b^7*c^8*d^2 - 5*a^4*b^6*c^7*d^3 + 10*a^5*b^5*c^6*d^4 - 10*a^6*b^4*c^5*d^5 + 5*a^7*b^3*c^4*d^6 - a^8*b^2*c^3*d^7)*x^4 + 2*(a^3*b^7*c^9*d - 4*a^4*b^6*c^8*d^2 + 5*a^5*b^5*c^7*d^3 - 5*a^7*b^3*c^5*d^5 + 4*a^8*b^2*c^4*d^6 - a^9*b*c^3*d^7)*x^3 + (a^3*b^7*c^10 - a^4*b^6*c^9*d - 9*a^5*b^5*c^8*d^2 + 25*a^6*b^4*c^7*d^3 - 25*a^7*b^3*c^6*d^4 + 9*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6 - a^10*c^3*d^7)*x^2 + 2*(a^4*b^6*c^10 - 4*a^5*b^5*c^9*d + 5*a^6*b^4*c^8*d^2 - 5*a^8*b^2*c^6*d^4 + 4*a^9*b*c^5*d^5 - a^10*c^4*d^6)*x)","B",0
318,-1,0,0,0.000000," ","integrate(1/x^2/(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,32,0,1.022537," ","integrate(x^(7/2)*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{2}{1287} \, {\left(99 \, B b x^{6} + 143 \, A a x^{4} + 117 \, {\left(B a + A b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/1287*(99*B*b*x^6 + 143*A*a*x^4 + 117*(B*a + A*b)*x^5)*sqrt(x)","A",0
320,1,32,0,1.255053," ","integrate(x^(5/2)*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{2}{693} \, {\left(63 \, B b x^{5} + 99 \, A a x^{3} + 77 \, {\left(B a + A b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/693*(63*B*b*x^5 + 99*A*a*x^3 + 77*(B*a + A*b)*x^4)*sqrt(x)","A",0
321,1,32,0,0.965443," ","integrate(x^(3/2)*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b x^{4} + 63 \, A a x^{2} + 45 \, {\left(B a + A b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/315*(35*B*b*x^4 + 63*A*a*x^2 + 45*(B*a + A*b)*x^3)*sqrt(x)","A",0
322,1,30,0,0.986619," ","integrate((b*x+a)*(B*x+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B b x^{3} + 35 \, A a x + 21 \, {\left(B a + A b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/105*(15*B*b*x^3 + 35*A*a*x + 21*(B*a + A*b)*x^2)*sqrt(x)","A",0
323,1,27,0,0.717791," ","integrate((b*x+a)*(B*x+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, B b x^{2} + 15 \, A a + 5 \, {\left(B a + A b\right)} x\right)} \sqrt{x}"," ",0,"2/15*(3*B*b*x^2 + 15*A*a + 5*(B*a + A*b)*x)*sqrt(x)","A",0
324,1,26,0,1.119081," ","integrate((b*x+a)*(B*x+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x^{2} - 3 \, A a + 3 \, {\left(B a + A b\right)} x\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(B*b*x^2 - 3*A*a + 3*(B*a + A*b)*x)/sqrt(x)","A",0
325,1,27,0,1.056641," ","integrate((b*x+a)*(B*x+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b x^{2} - A a - 3 \, {\left(B a + A b\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(3*B*b*x^2 - A*a - 3*(B*a + A*b)*x)/x^(3/2)","A",0
326,1,27,0,0.916862," ","integrate((b*x+a)*(B*x+A)/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B b x^{2} + 3 \, A a + 5 \, {\left(B a + A b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*B*b*x^2 + 3*A*a + 5*(B*a + A*b)*x)/x^(5/2)","A",0
327,1,56,0,0.728776," ","integrate(x^(7/2)*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, B b^{2} x^{7} + 715 \, A a^{2} x^{4} + 495 \, {\left(2 \, B a b + A b^{2}\right)} x^{6} + 585 \, {\left(B a^{2} + 2 \, A a b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/6435*(429*B*b^2*x^7 + 715*A*a^2*x^4 + 495*(2*B*a*b + A*b^2)*x^6 + 585*(B*a^2 + 2*A*a*b)*x^5)*sqrt(x)","A",0
328,1,56,0,0.964161," ","integrate(x^(5/2)*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{2}{9009} \, {\left(693 \, B b^{2} x^{6} + 1287 \, A a^{2} x^{3} + 819 \, {\left(2 \, B a b + A b^{2}\right)} x^{5} + 1001 \, {\left(B a^{2} + 2 \, A a b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/9009*(693*B*b^2*x^6 + 1287*A*a^2*x^3 + 819*(2*B*a*b + A*b^2)*x^5 + 1001*(B*a^2 + 2*A*a*b)*x^4)*sqrt(x)","A",0
329,1,56,0,0.676065," ","integrate(x^(3/2)*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B b^{2} x^{5} + 693 \, A a^{2} x^{2} + 385 \, {\left(2 \, B a b + A b^{2}\right)} x^{4} + 495 \, {\left(B a^{2} + 2 \, A a b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*b^2*x^5 + 693*A*a^2*x^2 + 385*(2*B*a*b + A*b^2)*x^4 + 495*(B*a^2 + 2*A*a*b)*x^3)*sqrt(x)","A",0
330,1,54,0,0.692194," ","integrate((b*x+a)^2*(B*x+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b^{2} x^{4} + 105 \, A a^{2} x + 45 \, {\left(2 \, B a b + A b^{2}\right)} x^{3} + 63 \, {\left(B a^{2} + 2 \, A a b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/315*(35*B*b^2*x^4 + 105*A*a^2*x + 45*(2*B*a*b + A*b^2)*x^3 + 63*(B*a^2 + 2*A*a*b)*x^2)*sqrt(x)","A",0
331,1,51,0,0.860374," ","integrate((b*x+a)^2*(B*x+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, B b^{2} x^{3} + 105 \, A a^{2} + 21 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)} \sqrt{x}"," ",0,"2/105*(15*B*b^2*x^3 + 105*A*a^2 + 21*(2*B*a*b + A*b^2)*x^2 + 35*(B*a^2 + 2*A*a*b)*x)*sqrt(x)","A",0
332,1,51,0,0.988785," ","integrate((b*x+a)^2*(B*x+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{3} - 15 \, A a^{2} + 5 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{15 \, \sqrt{x}}"," ",0,"2/15*(3*B*b^2*x^3 - 15*A*a^2 + 5*(2*B*a*b + A*b^2)*x^2 + 15*(B*a^2 + 2*A*a*b)*x)/sqrt(x)","A",0
333,1,50,0,0.927524," ","integrate((b*x+a)^2*(B*x+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} x^{3} - A a^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 3 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(B*b^2*x^3 - A*a^2 + 3*(2*B*a*b + A*b^2)*x^2 - 3*(B*a^2 + 2*A*a*b)*x)/x^(3/2)","A",0
334,1,51,0,0.719271," ","integrate((b*x+a)^2*(B*x+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} x^{3} - 3 \, A a^{2} - 15 \, {\left(2 \, B a b + A b^{2}\right)} x^{2} - 5 \, {\left(B a^{2} + 2 \, A a b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(15*B*b^2*x^3 - 3*A*a^2 - 15*(2*B*a*b + A*b^2)*x^2 - 5*(B*a^2 + 2*A*a*b)*x)/x^(5/2)","A",0
335,1,78,0,0.865592," ","integrate(x^(7/2)*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{2}{109395} \, {\left(6435 \, B b^{3} x^{8} + 12155 \, A a^{3} x^{4} + 7293 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{7} + 25245 \, {\left(B a^{2} b + A a b^{2}\right)} x^{6} + 9945 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{5}\right)} \sqrt{x}"," ",0,"2/109395*(6435*B*b^3*x^8 + 12155*A*a^3*x^4 + 7293*(3*B*a*b^2 + A*b^3)*x^7 + 25245*(B*a^2*b + A*a*b^2)*x^6 + 9945*(B*a^3 + 3*A*a^2*b)*x^5)*sqrt(x)","A",0
336,1,78,0,0.677681," ","integrate(x^(5/2)*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{2}{45045} \, {\left(3003 \, B b^{3} x^{7} + 6435 \, A a^{3} x^{3} + 3465 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{6} + 12285 \, {\left(B a^{2} b + A a b^{2}\right)} x^{5} + 5005 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{4}\right)} \sqrt{x}"," ",0,"2/45045*(3003*B*b^3*x^7 + 6435*A*a^3*x^3 + 3465*(3*B*a*b^2 + A*b^3)*x^6 + 12285*(B*a^2*b + A*a*b^2)*x^5 + 5005*(B*a^3 + 3*A*a^2*b)*x^4)*sqrt(x)","A",0
337,1,78,0,1.021111," ","integrate(x^(3/2)*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{2}{15015} \, {\left(1155 \, B b^{3} x^{6} + 3003 \, A a^{3} x^{2} + 1365 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{5} + 5005 \, {\left(B a^{2} b + A a b^{2}\right)} x^{4} + 2145 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{3}\right)} \sqrt{x}"," ",0,"2/15015*(1155*B*b^3*x^6 + 3003*A*a^3*x^2 + 1365*(3*B*a*b^2 + A*b^3)*x^5 + 5005*(B*a^2*b + A*a*b^2)*x^4 + 2145*(B*a^3 + 3*A*a^2*b)*x^3)*sqrt(x)","A",0
338,1,76,0,0.874825," ","integrate((b*x+a)^3*(B*x+A)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{3465} \, {\left(315 \, B b^{3} x^{5} + 1155 \, A a^{3} x + 385 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{4} + 1485 \, {\left(B a^{2} b + A a b^{2}\right)} x^{3} + 693 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x^{2}\right)} \sqrt{x}"," ",0,"2/3465*(315*B*b^3*x^5 + 1155*A*a^3*x + 385*(3*B*a*b^2 + A*b^3)*x^4 + 1485*(B*a^2*b + A*a*b^2)*x^3 + 693*(B*a^3 + 3*A*a^2*b)*x^2)*sqrt(x)","A",0
339,1,73,0,0.954105," ","integrate((b*x+a)^3*(B*x+A)/x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, B b^{3} x^{4} + 315 \, A a^{3} + 45 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 189 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)} \sqrt{x}"," ",0,"2/315*(35*B*b^3*x^4 + 315*A*a^3 + 45*(3*B*a*b^2 + A*b^3)*x^3 + 189*(B*a^2*b + A*a*b^2)*x^2 + 105*(B*a^3 + 3*A*a^2*b)*x)*sqrt(x)","A",0
340,1,73,0,0.857135," ","integrate((b*x+a)^3*(B*x+A)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{4} - 35 \, A a^{3} + 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 35 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{35 \, \sqrt{x}}"," ",0,"2/35*(5*B*b^3*x^4 - 35*A*a^3 + 7*(3*B*a*b^2 + A*b^3)*x^3 + 35*(B*a^2*b + A*a*b^2)*x^2 + 35*(B*a^3 + 3*A*a^2*b)*x)/sqrt(x)","A",0
341,1,73,0,0.740644," ","integrate((b*x+a)^3*(B*x+A)/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} x^{4} - 5 \, A a^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} + 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 15 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{15 \, x^{\frac{3}{2}}}"," ",0,"2/15*(3*B*b^3*x^4 - 5*A*a^3 + 5*(3*B*a*b^2 + A*b^3)*x^3 + 45*(B*a^2*b + A*a*b^2)*x^2 - 15*(B*a^3 + 3*A*a^2*b)*x)/x^(3/2)","A",0
342,1,73,0,0.856133," ","integrate((b*x+a)^3*(B*x+A)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{4} - 3 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} x^{3} - 45 \, {\left(B a^{2} b + A a b^{2}\right)} x^{2} - 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} x\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"2/15*(5*B*b^3*x^4 - 3*A*a^3 + 15*(3*B*a*b^2 + A*b^3)*x^3 - 45*(B*a^2*b + A*a*b^2)*x^2 - 5*(B*a^3 + 3*A*a^2*b)*x)/x^(5/2)","A",0
343,1,37,0,1.012748," ","integrate((2-3*x)^3*x^(1/2)/(1+x)^2,x, algorithm=""fricas"")","\frac{2875 \, {\left(x + 1\right)} \arctan\left(\sqrt{x}\right) - {\left(54 \, x^{3} - 306 \, x^{2} + 1890 \, x + 2875\right)} \sqrt{x}}{5 \, {\left(x + 1\right)}}"," ",0,"1/5*(2875*(x + 1)*arctan(sqrt(x)) - (54*x^3 - 306*x^2 + 1890*x + 2875)*sqrt(x))/(x + 1)","A",0
344,1,276,0,0.953570," ","integrate(x^(7/2)*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(35 \, B b^{4} x^{4} + 315 \, B a^{4} - 315 \, A a^{3} b - 45 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 63 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{315 \, b^{5}}, -\frac{2 \, {\left(315 \, {\left(B a^{4} - A a^{3} b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(35 \, B b^{4} x^{4} + 315 \, B a^{4} - 315 \, A a^{3} b - 45 \, {\left(B a b^{3} - A b^{4}\right)} x^{3} + 63 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{2} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x\right)} \sqrt{x}\right)}}{315 \, b^{5}}\right]"," ",0,"[-1/315*(315*(B*a^4 - A*a^3*b)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(35*B*b^4*x^4 + 315*B*a^4 - 315*A*a^3*b - 45*(B*a*b^3 - A*b^4)*x^3 + 63*(B*a^2*b^2 - A*a*b^3)*x^2 - 105*(B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/b^5, -2/315*(315*(B*a^4 - A*a^3*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (35*B*b^4*x^4 + 315*B*a^4 - 315*A*a^3*b - 45*(B*a*b^3 - A*b^4)*x^3 + 63*(B*a^2*b^2 - A*a*b^3)*x^2 - 105*(B*a^3*b - A*a^2*b^2)*x)*sqrt(x))/b^5]","A",0
345,1,229,0,0.973416," ","integrate(x^(5/2)*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(15 \, B b^{3} x^{3} - 105 \, B a^{3} + 105 \, A a^{2} b - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}}{105 \, b^{4}}, \frac{2 \, {\left(105 \, {\left(B a^{3} - A a^{2} b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(15 \, B b^{3} x^{3} - 105 \, B a^{3} + 105 \, A a^{2} b - 21 \, {\left(B a b^{2} - A b^{3}\right)} x^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{x}\right)}}{105 \, b^{4}}\right]"," ",0,"[-1/105*(105*(B*a^3 - A*a^2*b)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(15*B*b^3*x^3 - 105*B*a^3 + 105*A*a^2*b - 21*(B*a*b^2 - A*b^3)*x^2 + 35*(B*a^2*b - A*a*b^2)*x)*sqrt(x))/b^4, 2/105*(105*(B*a^3 - A*a^2*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (15*B*b^3*x^3 - 105*B*a^3 + 105*A*a^2*b - 21*(B*a*b^2 - A*b^3)*x^2 + 35*(B*a^2*b - A*a*b^2)*x)*sqrt(x))/b^4]","A",0
346,1,180,0,0.792817," ","integrate(x^(3/2)*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{2} - A a b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} x^{2} + 15 \, B a^{2} - 15 \, A a b - 5 \, {\left(B a b - A b^{2}\right)} x\right)} \sqrt{x}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, {\left(B a^{2} - A a b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(3 \, B b^{2} x^{2} + 15 \, B a^{2} - 15 \, A a b - 5 \, {\left(B a b - A b^{2}\right)} x\right)} \sqrt{x}\right)}}{15 \, b^{3}}\right]"," ",0,"[-1/15*(15*(B*a^2 - A*a*b)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(3*B*b^2*x^2 + 15*B*a^2 - 15*A*a*b - 5*(B*a*b - A*b^2)*x)*sqrt(x))/b^3, -2/15*(15*(B*a^2 - A*a*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (3*B*b^2*x^2 + 15*B*a^2 - 15*A*a*b - 5*(B*a*b - A*b^2)*x)*sqrt(x))/b^3]","A",0
347,1,129,0,0.757766," ","integrate((B*x+A)*x^(1/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(B b x - 3 \, B a + 3 \, A b\right)} \sqrt{x}}{3 \, b^{2}}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(B b x - 3 \, B a + 3 \, A b\right)} \sqrt{x}\right)}}{3 \, b^{2}}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(B*b*x - 3*B*a + 3*A*b)*sqrt(x))/b^2, 2/3*(3*(B*a - A*b)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (B*b*x - 3*B*a + 3*A*b)*sqrt(x))/b^2]","A",0
348,1,102,0,1.142026," ","integrate((B*x+A)/(b*x+a)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, B a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{a b^{2}}, \frac{2 \, {\left(B a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)\right)}}{a b^{2}}\right]"," ",0,"[(2*B*a*b*sqrt(x) + (B*a - A*b)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a*b^2), 2*(B*a*b*sqrt(x) + (B*a - A*b)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))))/(a*b^2)]","A",0
349,1,112,0,0.751067," ","integrate((B*x+A)/x^(3/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{2 \, A a b \sqrt{x} - {\left(B a - A b\right)} \sqrt{-a b} x \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{a^{2} b x}, -\frac{2 \, {\left(A a b \sqrt{x} + {\left(B a - A b\right)} \sqrt{a b} x \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)\right)}}{a^{2} b x}\right]"," ",0,"[-(2*A*a*b*sqrt(x) - (B*a - A*b)*sqrt(-a*b)*x*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a^2*b*x), -2*(A*a*b*sqrt(x) + (B*a - A*b)*sqrt(a*b)*x*arctan(sqrt(a*b)/(b*sqrt(x))))/(a^2*b*x)]","A",0
350,1,146,0,1.032917," ","integrate((B*x+A)/x^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} x^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(A a + 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}}{3 \, a^{2} x^{2}}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} x^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(A a + 3 \, {\left(B a - A b\right)} x\right)} \sqrt{x}\right)}}{3 \, a^{2} x^{2}}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*x^2*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(A*a + 3*(B*a - A*b)*x)*sqrt(x))/(a^2*x^2), 2/3*(3*(B*a - A*b)*x^2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (A*a + 3*(B*a - A*b)*x)*sqrt(x))/(a^2*x^2)]","A",0
351,1,195,0,0.891138," ","integrate((B*x+A)/x^(7/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a b - A b^{2}\right)} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(3 \, A a^{2} - 15 \, {\left(B a b - A b^{2}\right)} x^{2} + 5 \, {\left(B a^{2} - A a b\right)} x\right)} \sqrt{x}}{15 \, a^{3} x^{3}}, -\frac{2 \, {\left(15 \, {\left(B a b - A b^{2}\right)} x^{3} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(3 \, A a^{2} - 15 \, {\left(B a b - A b^{2}\right)} x^{2} + 5 \, {\left(B a^{2} - A a b\right)} x\right)} \sqrt{x}\right)}}{15 \, a^{3} x^{3}}\right]"," ",0,"[-1/15*(15*(B*a*b - A*b^2)*x^3*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(3*A*a^2 - 15*(B*a*b - A*b^2)*x^2 + 5*(B*a^2 - A*a*b)*x)*sqrt(x))/(a^3*x^3), -2/15*(15*(B*a*b - A*b^2)*x^3*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (3*A*a^2 - 15*(B*a*b - A*b^2)*x^2 + 5*(B*a^2 - A*a*b)*x)*sqrt(x))/(a^3*x^3)]","A",0
352,1,246,0,1.114866," ","integrate((B*x+A)/x^(9/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a b^{2} - A b^{3}\right)} x^{4} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(15 \, A a^{3} + 105 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x\right)} \sqrt{x}}{105 \, a^{4} x^{4}}, \frac{2 \, {\left(105 \, {\left(B a b^{2} - A b^{3}\right)} x^{4} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(15 \, A a^{3} + 105 \, {\left(B a b^{2} - A b^{3}\right)} x^{3} - 35 \, {\left(B a^{2} b - A a b^{2}\right)} x^{2} + 21 \, {\left(B a^{3} - A a^{2} b\right)} x\right)} \sqrt{x}\right)}}{105 \, a^{4} x^{4}}\right]"," ",0,"[-1/105*(105*(B*a*b^2 - A*b^3)*x^4*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(15*A*a^3 + 105*(B*a*b^2 - A*b^3)*x^3 - 35*(B*a^2*b - A*a*b^2)*x^2 + 21*(B*a^3 - A*a^2*b)*x)*sqrt(x))/(a^4*x^4), 2/105*(105*(B*a*b^2 - A*b^3)*x^4*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (15*A*a^3 + 105*(B*a*b^2 - A*b^3)*x^3 - 35*(B*a^2*b - A*a*b^2)*x^2 + 21*(B*a^3 - A*a^2*b)*x)*sqrt(x))/(a^4*x^4)]","A",0
353,1,291,0,1.019573," ","integrate((B*x+A)/x^(11/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(B a b^{3} - A b^{4}\right)} x^{5} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(35 \, A a^{4} - 315 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} + 105 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{3} - 63 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x^{2} + 45 \, {\left(B a^{4} - A a^{3} b\right)} x\right)} \sqrt{x}}{315 \, a^{5} x^{5}}, -\frac{2 \, {\left(315 \, {\left(B a b^{3} - A b^{4}\right)} x^{5} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(35 \, A a^{4} - 315 \, {\left(B a b^{3} - A b^{4}\right)} x^{4} + 105 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} x^{3} - 63 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} x^{2} + 45 \, {\left(B a^{4} - A a^{3} b\right)} x\right)} \sqrt{x}\right)}}{315 \, a^{5} x^{5}}\right]"," ",0,"[-1/315*(315*(B*a*b^3 - A*b^4)*x^5*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(35*A*a^4 - 315*(B*a*b^3 - A*b^4)*x^4 + 105*(B*a^2*b^2 - A*a*b^3)*x^3 - 63*(B*a^3*b - A*a^2*b^2)*x^2 + 45*(B*a^4 - A*a^3*b)*x)*sqrt(x))/(a^5*x^5), -2/315*(315*(B*a*b^3 - A*b^4)*x^5*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (35*A*a^4 - 315*(B*a*b^3 - A*b^4)*x^4 + 105*(B*a^2*b^2 - A*a*b^3)*x^3 - 63*(B*a^3*b - A*a^2*b^2)*x^2 + 45*(B*a^4 - A*a^3*b)*x)*sqrt(x))/(a^5*x^5)]","A",0
354,1,341,0,0.994533," ","integrate(x^(7/2)*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(30 \, B b^{4} x^{4} - 945 \, B a^{4} + 735 \, A a^{3} b - 6 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{210 \, {\left(b^{6} x + a b^{5}\right)}}, \frac{105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b + {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(30 \, B b^{4} x^{4} - 945 \, B a^{4} + 735 \, A a^{3} b - 6 \, {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{105 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[-1/210*(105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(30*B*b^4*x^4 - 945*B*a^4 + 735*A*a^3*b - 6*(9*B*a*b^3 - 7*A*b^4)*x^3 + 14*(9*B*a^2*b^2 - 7*A*a*b^3)*x^2 - 70*(9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(x))/(b^6*x + a*b^5), 1/105*(105*(9*B*a^4 - 7*A*a^3*b + (9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (30*B*b^4*x^4 - 945*B*a^4 + 735*A*a^3*b - 6*(9*B*a*b^3 - 7*A*b^4)*x^3 + 14*(9*B*a^2*b^2 - 7*A*a*b^3)*x^2 - 70*(9*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(x))/(b^6*x + a*b^5)]","A",0
355,1,290,0,0.827115," ","integrate(x^(5/2)*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(6 \, B b^{3} x^{3} + 105 \, B a^{3} - 75 \, A a^{2} b - 2 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{x}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(6 \, B b^{3} x^{3} + 105 \, B a^{3} - 75 \, A a^{2} b - 2 \, {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{x}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[-1/30*(15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(6*B*b^3*x^3 + 105*B*a^3 - 75*A*a^2*b - 2*(7*B*a*b^2 - 5*A*b^3)*x^2 + 10*(7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(x))/(b^5*x + a*b^4), -1/15*(15*(7*B*a^3 - 5*A*a^2*b + (7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (6*B*b^3*x^3 + 105*B*a^3 - 75*A*a^2*b - 2*(7*B*a*b^2 - 5*A*b^3)*x^2 + 10*(7*B*a^2*b - 5*A*a*b^2)*x)*sqrt(x))/(b^5*x + a*b^4)]","A",0
356,1,231,0,1.102197," ","integrate(x^(3/2)*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(2 \, B b^{2} x^{2} - 15 \, B a^{2} + 9 \, A a b - 2 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{x}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, \frac{3 \, {\left(5 \, B a^{2} - 3 \, A a b + {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(2 \, B b^{2} x^{2} - 15 \, B a^{2} + 9 \, A a b - 2 \, {\left(5 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{x}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[-1/6*(3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(2*B*b^2*x^2 - 15*B*a^2 + 9*A*a*b - 2*(5*B*a*b - 3*A*b^2)*x)*sqrt(x))/(b^4*x + a*b^3), 1/3*(3*(5*B*a^2 - 3*A*a*b + (5*B*a*b - 3*A*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (2*B*b^2*x^2 - 15*B*a^2 + 9*A*a*b - 2*(5*B*a*b - 3*A*b^2)*x)*sqrt(x))/(b^4*x + a*b^3)]","A",0
357,1,198,0,1.102754," ","integrate((B*x+A)*x^(1/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(2 \, B a b^{2} x + 3 \, B a^{2} b - A a b^{2}\right)} \sqrt{x}}{2 \, {\left(a b^{4} x + a^{2} b^{3}\right)}}, \frac{{\left(3 \, B a^{2} - A a b + {\left(3 \, B a b - A b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(2 \, B a b^{2} x + 3 \, B a^{2} b - A a b^{2}\right)} \sqrt{x}}{a b^{4} x + a^{2} b^{3}}\right]"," ",0,"[1/2*((3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(2*B*a*b^2*x + 3*B*a^2*b - A*a*b^2)*sqrt(x))/(a*b^4*x + a^2*b^3), ((3*B*a^2 - A*a*b + (3*B*a*b - A*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (2*B*a*b^2*x + 3*B*a^2*b - A*a*b^2)*sqrt(x))/(a*b^4*x + a^2*b^3)]","A",0
358,1,177,0,1.148309," ","integrate((B*x+A)/(b*x+a)^2/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x}}{2 \, {\left(a^{2} b^{3} x + a^{3} b^{2}\right)}}, -\frac{{\left(B a^{2} + A a b + {\left(B a b + A b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(B a^{2} b - A a b^{2}\right)} \sqrt{x}}{a^{2} b^{3} x + a^{3} b^{2}}\right]"," ",0,"[-1/2*((B*a^2 + A*a*b + (B*a*b + A*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(B*a^2*b - A*a*b^2)*sqrt(x))/(a^2*b^3*x + a^3*b^2), -((B*a^2 + A*a*b + (B*a*b + A*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (B*a^2*b - A*a*b^2)*sqrt(x))/(a^2*b^3*x + a^3*b^2)]","A",0
359,1,215,0,1.200823," ","integrate((B*x+A)/x^(3/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{2 \, {\left(a^{3} b^{2} x^{2} + a^{4} b x\right)}}, -\frac{{\left({\left(B a b - 3 \, A b^{2}\right)} x^{2} + {\left(B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(2 \, A a^{2} b - {\left(B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{a^{3} b^{2} x^{2} + a^{4} b x}\right]"," ",0,"[1/2*(((B*a*b - 3*A*b^2)*x^2 + (B*a^2 - 3*A*a*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(a^3*b^2*x^2 + a^4*b*x), -(((B*a*b - 3*A*b^2)*x^2 + (B*a^2 - 3*A*a*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (2*A*a^2*b - (B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(a^3*b^2*x^2 + a^4*b*x)]","A",0
360,1,262,0,0.795426," ","integrate((B*x+A)/x^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(2 \, A a^{2} + 3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x\right)} \sqrt{x}}{6 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, B a b - 5 \, A b^{2}\right)} x^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(2 \, A a^{2} + 3 \, {\left(3 \, B a b - 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} x\right)} \sqrt{x}}{3 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}\right]"," ",0,"[-1/6*(3*((3*B*a*b - 5*A*b^2)*x^3 + (3*B*a^2 - 5*A*a*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(2*A*a^2 + 3*(3*B*a*b - 5*A*b^2)*x^2 + 2*(3*B*a^2 - 5*A*a*b)*x)*sqrt(x))/(a^3*b*x^3 + a^4*x^2), 1/3*(3*((3*B*a*b - 5*A*b^2)*x^3 + (3*B*a^2 - 5*A*a*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (2*A*a^2 + 3*(3*B*a*b - 5*A*b^2)*x^2 + 2*(3*B*a^2 - 5*A*a*b)*x)*sqrt(x))/(a^3*b*x^3 + a^4*x^2)]","A",0
361,1,319,0,1.137346," ","integrate((B*x+A)/x^(7/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(6 \, A a^{3} - 15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} - 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{30 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}, -\frac{15 \, {\left({\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(6 \, A a^{3} - 15 \, {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} - 10 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{15 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}\right]"," ",0,"[-1/30*(15*((5*B*a*b^2 - 7*A*b^3)*x^4 + (5*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(6*A*a^3 - 15*(5*B*a*b^2 - 7*A*b^3)*x^3 - 10*(5*B*a^2*b - 7*A*a*b^2)*x^2 + 2*(5*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b*x^4 + a^5*x^3), -1/15*(15*((5*B*a*b^2 - 7*A*b^3)*x^4 + (5*B*a^2*b - 7*A*a*b^2)*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (6*A*a^3 - 15*(5*B*a*b^2 - 7*A*b^3)*x^3 - 10*(5*B*a^2*b - 7*A*a*b^2)*x^2 + 2*(5*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b*x^4 + a^5*x^3)]","A",0
362,1,372,0,1.038120," ","integrate((B*x+A)/x^(9/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(30 \, A a^{4} + 105 \, {\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} + 70 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 14 \, {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(7 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{210 \, {\left(a^{5} b x^{5} + a^{6} x^{4}\right)}}, \frac{105 \, {\left({\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(30 \, A a^{4} + 105 \, {\left(7 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} + 70 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 14 \, {\left(7 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 6 \, {\left(7 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{105 \, {\left(a^{5} b x^{5} + a^{6} x^{4}\right)}}\right]"," ",0,"[-1/210*(105*((7*B*a*b^3 - 9*A*b^4)*x^5 + (7*B*a^2*b^2 - 9*A*a*b^3)*x^4)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(30*A*a^4 + 105*(7*B*a*b^3 - 9*A*b^4)*x^4 + 70*(7*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 14*(7*B*a^3*b - 9*A*a^2*b^2)*x^2 + 6*(7*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b*x^5 + a^6*x^4), 1/105*(105*((7*B*a*b^3 - 9*A*b^4)*x^5 + (7*B*a^2*b^2 - 9*A*a*b^3)*x^4)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (30*A*a^4 + 105*(7*B*a*b^3 - 9*A*b^4)*x^4 + 70*(7*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 14*(7*B*a^3*b - 9*A*a^2*b^2)*x^2 + 6*(7*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b*x^5 + a^6*x^4)]","A",0
363,1,408,0,0.979789," ","integrate(x^(7/2)*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(24 \, B b^{4} x^{4} + 945 \, B a^{4} - 525 \, A a^{3} b - 8 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{120 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 2 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(24 \, B b^{4} x^{4} + 945 \, B a^{4} - 525 \, A a^{3} b - 8 \, {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{60 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/120*(105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(24*B*b^4*x^4 + 945*B*a^4 - 525*A*a^3*b - 8*(9*B*a*b^3 - 5*A*b^4)*x^3 + 56*(9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 175*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/60*(105*(9*B*a^4 - 5*A*a^3*b + (9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 2*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (24*B*b^4*x^4 + 945*B*a^4 - 525*A*a^3*b - 8*(9*B*a*b^3 - 5*A*b^4)*x^3 + 56*(9*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 175*(9*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
364,1,349,0,1.117342," ","integrate(x^(5/2)*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b + {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) - 2 \, {\left(8 \, B b^{3} x^{3} - 105 \, B a^{3} + 45 \, A a^{2} b - 8 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} - 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b + {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(8 \, B b^{3} x^{3} - 105 \, B a^{3} + 45 \, A a^{2} b - 8 \, {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} x^{2} - 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} x\right)} \sqrt{x}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(15*(7*B*a^3 - 3*A*a^2*b + (7*B*a*b^2 - 3*A*b^3)*x^2 + 2*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) - 2*(8*B*b^3*x^3 - 105*B*a^3 + 45*A*a^2*b - 8*(7*B*a*b^2 - 3*A*b^3)*x^2 - 25*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/12*(15*(7*B*a^3 - 3*A*a^2*b + (7*B*a*b^2 - 3*A*b^3)*x^2 + 2*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (8*B*b^3*x^3 - 105*B*a^3 + 45*A*a^2*b - 8*(7*B*a*b^2 - 3*A*b^3)*x^2 - 25*(7*B*a^2*b - 3*A*a*b^2)*x)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
365,1,319,0,1.166768," ","integrate(x^(3/2)*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B a^{3} - A a^{2} b + {\left(5 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(8 \, B a b^{3} x^{2} + 15 \, B a^{3} b - 3 \, A a^{2} b^{2} + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a b^{6} x^{2} + 2 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}, \frac{3 \, {\left(5 \, B a^{3} - A a^{2} b + {\left(5 \, B a b^{2} - A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(8 \, B a b^{3} x^{2} + 15 \, B a^{3} b - 3 \, A a^{2} b^{2} + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a b^{6} x^{2} + 2 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}\right]"," ",0,"[1/8*(3*(5*B*a^3 - A*a^2*b + (5*B*a*b^2 - A*b^3)*x^2 + 2*(5*B*a^2*b - A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(8*B*a*b^3*x^2 + 15*B*a^3*b - 3*A*a^2*b^2 + 5*(5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a*b^6*x^2 + 2*a^2*b^5*x + a^3*b^4), 1/4*(3*(5*B*a^3 - A*a^2*b + (5*B*a*b^2 - A*b^3)*x^2 + 2*(5*B*a^2*b - A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (8*B*a*b^3*x^2 + 15*B*a^3*b - 3*A*a^2*b^2 + 5*(5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a*b^6*x^2 + 2*a^2*b^5*x + a^3*b^4)]","A",0
366,1,291,0,1.099993," ","integrate((B*x+A)*x^(1/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{3} + A a^{2} b + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(3 \, B a^{3} b + A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{5} x^{2} + 2 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}, -\frac{{\left(3 \, B a^{3} + A a^{2} b + {\left(3 \, B a b^{2} + A b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b + A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(3 \, B a^{3} b + A a^{2} b^{2} + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{2} b^{5} x^{2} + 2 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}\right]"," ",0,"[-1/8*((3*B*a^3 + A*a^2*b + (3*B*a*b^2 + A*b^3)*x^2 + 2*(3*B*a^2*b + A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(3*B*a^3*b + A*a^2*b^2 + (5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a^2*b^5*x^2 + 2*a^3*b^4*x + a^4*b^3), -1/4*((3*B*a^3 + A*a^2*b + (3*B*a*b^2 + A*b^3)*x^2 + 2*(3*B*a^2*b + A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (3*B*a^3*b + A*a^2*b^2 + (5*B*a^2*b^2 - A*a*b^3)*x)*sqrt(x))/(a^2*b^5*x^2 + 2*a^3*b^4*x + a^4*b^3)]","A",0
367,1,291,0,1.125364," ","integrate((B*x+A)/(b*x+a)^3/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{3} + 3 \, A a^{2} b + {\left(B a b^{2} + 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2} - {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}, -\frac{{\left(B a^{3} + 3 \, A a^{2} b + {\left(B a b^{2} + 3 \, A b^{3}\right)} x^{2} + 2 \, {\left(B a^{2} b + 3 \, A a b^{2}\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(B a^{3} b - 5 \, A a^{2} b^{2} - {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}\right]"," ",0,"[-1/8*((B*a^3 + 3*A*a^2*b + (B*a*b^2 + 3*A*b^3)*x^2 + 2*(B*a^2*b + 3*A*a*b^2)*x)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(B*a^3*b - 5*A*a^2*b^2 - (B*a^2*b^2 + 3*A*a*b^3)*x)*sqrt(x))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2), -1/4*((B*a^3 + 3*A*a^2*b + (B*a*b^2 + 3*A*b^3)*x^2 + 2*(B*a^2*b + 3*A*a*b^2)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (B*a^3*b - 5*A*a^2*b^2 - (B*a^2*b^2 + 3*A*a*b^3)*x)*sqrt(x))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2)]","A",0
368,1,331,0,0.734783," ","integrate((B*x+A)/x^(3/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{-a b} \log\left(\frac{b x - a + 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(8 \, A a^{3} b - 3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}, -\frac{3 \, {\left({\left(B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(8 \, A a^{3} b - 3 \, {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{x}}{4 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}\right]"," ",0,"[1/8*(3*((B*a*b^2 - 5*A*b^3)*x^3 + 2*(B*a^2*b - 5*A*a*b^2)*x^2 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(-a*b)*log((b*x - a + 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(8*A*a^3*b - 3*(B*a^2*b^2 - 5*A*a*b^3)*x^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x), -1/4*(3*((B*a*b^2 - 5*A*b^3)*x^3 + 2*(B*a^2*b - 5*A*a*b^2)*x^2 + (B*a^3 - 5*A*a^2*b)*x)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (8*A*a^3*b - 3*(B*a^2*b^2 - 5*A*a*b^3)*x^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(x))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x)]","A",0
369,1,380,0,1.067549," ","integrate((B*x+A)/x^(5/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(8 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{24 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{4} + 2 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(8 \, A a^{3} + 15 \, {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} x^{3} + 25 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} x^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} x\right)} \sqrt{x}}{12 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}\right]"," ",0,"[-1/24*(15*((3*B*a*b^2 - 7*A*b^3)*x^4 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^3 + (3*B*a^3 - 7*A*a^2*b)*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(8*A*a^3 + 15*(3*B*a*b^2 - 7*A*b^3)*x^3 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^2 + 8*(3*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2), 1/12*(15*((3*B*a*b^2 - 7*A*b^3)*x^4 + 2*(3*B*a^2*b - 7*A*a*b^2)*x^3 + (3*B*a^3 - 7*A*a^2*b)*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (8*A*a^3 + 15*(3*B*a*b^2 - 7*A*b^3)*x^3 + 25*(3*B*a^2*b - 7*A*a*b^2)*x^2 + 8*(3*B*a^3 - 7*A*a^2*b)*x)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)]","A",0
370,1,437,0,1.134970," ","integrate((B*x+A)/x^(7/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(24 \, A a^{4} - 105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} - 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{120 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}, -\frac{105 \, {\left({\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{5} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) + {\left(24 \, A a^{4} - 105 \, {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} x^{4} - 175 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{3} - 56 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} x\right)} \sqrt{x}}{60 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}\right]"," ",0,"[-1/120*(105*((5*B*a*b^3 - 9*A*b^4)*x^5 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^4 + (5*B*a^3*b - 9*A*a^2*b^2)*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(24*A*a^4 - 105*(5*B*a*b^3 - 9*A*b^4)*x^4 - 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^2 + 8*(5*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3), -1/60*(105*((5*B*a*b^3 - 9*A*b^4)*x^5 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*x^4 + (5*B*a^3*b - 9*A*a^2*b^2)*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) + (24*A*a^4 - 105*(5*B*a*b^3 - 9*A*b^4)*x^4 - 175*(5*B*a^2*b^2 - 9*A*a*b^3)*x^3 - 56*(5*B*a^3*b - 9*A*a^2*b^2)*x^2 + 8*(5*B*a^4 - 9*A*a^3*b)*x)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)]","A",0
371,1,607,0,1.046618," ","integrate(x^m*(b*x+a)^4*(B*x+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{4} m^{5} + 15 \, B b^{4} m^{4} + 85 \, B b^{4} m^{3} + 225 \, B b^{4} m^{2} + 274 \, B b^{4} m + 120 \, B b^{4}\right)} x^{6} + {\left({\left(4 \, B a b^{3} + A b^{4}\right)} m^{5} + 576 \, B a b^{3} + 144 \, A b^{4} + 16 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{4} + 95 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{3} + 260 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m^{2} + 324 \, {\left(4 \, B a b^{3} + A b^{4}\right)} m\right)} x^{5} + 2 \, {\left({\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{5} + 540 \, B a^{2} b^{2} + 360 \, A a b^{3} + 17 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{4} + 107 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{3} + 307 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m^{2} + 396 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} m\right)} x^{4} + 2 \, {\left({\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{5} + 480 \, B a^{3} b + 720 \, A a^{2} b^{2} + 18 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{4} + 121 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{3} + 372 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m^{2} + 508 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{4} + 4 \, A a^{3} b\right)} m^{5} + 360 \, B a^{4} + 1440 \, A a^{3} b + 19 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{4} + 137 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{3} + 461 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m^{2} + 702 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} m\right)} x^{2} + {\left(A a^{4} m^{5} + 20 \, A a^{4} m^{4} + 155 \, A a^{4} m^{3} + 580 \, A a^{4} m^{2} + 1044 \, A a^{4} m + 720 \, A a^{4}\right)} x\right)} x^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720}"," ",0,"((B*b^4*m^5 + 15*B*b^4*m^4 + 85*B*b^4*m^3 + 225*B*b^4*m^2 + 274*B*b^4*m + 120*B*b^4)*x^6 + ((4*B*a*b^3 + A*b^4)*m^5 + 576*B*a*b^3 + 144*A*b^4 + 16*(4*B*a*b^3 + A*b^4)*m^4 + 95*(4*B*a*b^3 + A*b^4)*m^3 + 260*(4*B*a*b^3 + A*b^4)*m^2 + 324*(4*B*a*b^3 + A*b^4)*m)*x^5 + 2*((3*B*a^2*b^2 + 2*A*a*b^3)*m^5 + 540*B*a^2*b^2 + 360*A*a*b^3 + 17*(3*B*a^2*b^2 + 2*A*a*b^3)*m^4 + 107*(3*B*a^2*b^2 + 2*A*a*b^3)*m^3 + 307*(3*B*a^2*b^2 + 2*A*a*b^3)*m^2 + 396*(3*B*a^2*b^2 + 2*A*a*b^3)*m)*x^4 + 2*((2*B*a^3*b + 3*A*a^2*b^2)*m^5 + 480*B*a^3*b + 720*A*a^2*b^2 + 18*(2*B*a^3*b + 3*A*a^2*b^2)*m^4 + 121*(2*B*a^3*b + 3*A*a^2*b^2)*m^3 + 372*(2*B*a^3*b + 3*A*a^2*b^2)*m^2 + 508*(2*B*a^3*b + 3*A*a^2*b^2)*m)*x^3 + ((B*a^4 + 4*A*a^3*b)*m^5 + 360*B*a^4 + 1440*A*a^3*b + 19*(B*a^4 + 4*A*a^3*b)*m^4 + 137*(B*a^4 + 4*A*a^3*b)*m^3 + 461*(B*a^4 + 4*A*a^3*b)*m^2 + 702*(B*a^4 + 4*A*a^3*b)*m)*x^2 + (A*a^4*m^5 + 20*A*a^4*m^4 + 155*A*a^4*m^3 + 580*A*a^4*m^2 + 1044*A*a^4*m + 720*A*a^4)*x)*x^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)","B",0
372,1,379,0,1.078948," ","integrate(x^m*(b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{3} m^{4} + 10 \, B b^{3} m^{3} + 35 \, B b^{3} m^{2} + 50 \, B b^{3} m + 24 \, B b^{3}\right)} x^{5} + {\left({\left(3 \, B a b^{2} + A b^{3}\right)} m^{4} + 90 \, B a b^{2} + 30 \, A b^{3} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m^{3} + 41 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m^{2} + 61 \, {\left(3 \, B a b^{2} + A b^{3}\right)} m\right)} x^{4} + 3 \, {\left({\left(B a^{2} b + A a b^{2}\right)} m^{4} + 40 \, B a^{2} b + 40 \, A a b^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} m^{3} + 49 \, {\left(B a^{2} b + A a b^{2}\right)} m^{2} + 78 \, {\left(B a^{2} b + A a b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{3} + 3 \, A a^{2} b\right)} m^{4} + 60 \, B a^{3} + 180 \, A a^{2} b + 13 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{3} + 59 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m^{2} + 107 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} m\right)} x^{2} + {\left(A a^{3} m^{4} + 14 \, A a^{3} m^{3} + 71 \, A a^{3} m^{2} + 154 \, A a^{3} m + 120 \, A a^{3}\right)} x\right)} x^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120}"," ",0,"((B*b^3*m^4 + 10*B*b^3*m^3 + 35*B*b^3*m^2 + 50*B*b^3*m + 24*B*b^3)*x^5 + ((3*B*a*b^2 + A*b^3)*m^4 + 90*B*a*b^2 + 30*A*b^3 + 11*(3*B*a*b^2 + A*b^3)*m^3 + 41*(3*B*a*b^2 + A*b^3)*m^2 + 61*(3*B*a*b^2 + A*b^3)*m)*x^4 + 3*((B*a^2*b + A*a*b^2)*m^4 + 40*B*a^2*b + 40*A*a*b^2 + 12*(B*a^2*b + A*a*b^2)*m^3 + 49*(B*a^2*b + A*a*b^2)*m^2 + 78*(B*a^2*b + A*a*b^2)*m)*x^3 + ((B*a^3 + 3*A*a^2*b)*m^4 + 60*B*a^3 + 180*A*a^2*b + 13*(B*a^3 + 3*A*a^2*b)*m^3 + 59*(B*a^3 + 3*A*a^2*b)*m^2 + 107*(B*a^3 + 3*A*a^2*b)*m)*x^2 + (A*a^3*m^4 + 14*A*a^3*m^3 + 71*A*a^3*m^2 + 154*A*a^3*m + 120*A*a^3)*x)*x^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)","B",0
373,1,215,0,0.826201," ","integrate(x^m*(b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b^{2} m^{3} + 6 \, B b^{2} m^{2} + 11 \, B b^{2} m + 6 \, B b^{2}\right)} x^{4} + {\left({\left(2 \, B a b + A b^{2}\right)} m^{3} + 16 \, B a b + 8 \, A b^{2} + 7 \, {\left(2 \, B a b + A b^{2}\right)} m^{2} + 14 \, {\left(2 \, B a b + A b^{2}\right)} m\right)} x^{3} + {\left({\left(B a^{2} + 2 \, A a b\right)} m^{3} + 12 \, B a^{2} + 24 \, A a b + 8 \, {\left(B a^{2} + 2 \, A a b\right)} m^{2} + 19 \, {\left(B a^{2} + 2 \, A a b\right)} m\right)} x^{2} + {\left(A a^{2} m^{3} + 9 \, A a^{2} m^{2} + 26 \, A a^{2} m + 24 \, A a^{2}\right)} x\right)} x^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"((B*b^2*m^3 + 6*B*b^2*m^2 + 11*B*b^2*m + 6*B*b^2)*x^4 + ((2*B*a*b + A*b^2)*m^3 + 16*B*a*b + 8*A*b^2 + 7*(2*B*a*b + A*b^2)*m^2 + 14*(2*B*a*b + A*b^2)*m)*x^3 + ((B*a^2 + 2*A*a*b)*m^3 + 12*B*a^2 + 24*A*a*b + 8*(B*a^2 + 2*A*a*b)*m^2 + 19*(B*a^2 + 2*A*a*b)*m)*x^2 + (A*a^2*m^3 + 9*A*a^2*m^2 + 26*A*a^2*m + 24*A*a^2)*x)*x^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
374,1,92,0,0.685568," ","integrate(x^m*(b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{{\left({\left(B b m^{2} + 3 \, B b m + 2 \, B b\right)} x^{3} + {\left({\left(B a + A b\right)} m^{2} + 3 \, B a + 3 \, A b + 4 \, {\left(B a + A b\right)} m\right)} x^{2} + {\left(A a m^{2} + 5 \, A a m + 6 \, A a\right)} x\right)} x^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6}"," ",0,"((B*b*m^2 + 3*B*b*m + 2*B*b)*x^3 + ((B*a + A*b)*m^2 + 3*B*a + 3*A*b + 4*(B*a + A*b)*m)*x^2 + (A*a*m^2 + 5*A*a*m + 6*A*a)*x)*x^m/(m^3 + 6*m^2 + 11*m + 6)","B",0
375,0,0,0,1.070185," ","integrate(x^m*(B*x+A)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} x^{m}}{b x + a}, x\right)"," ",0,"integral((B*x + A)*x^m/(b*x + a), x)","F",0
376,0,0,0,1.380963," ","integrate(x^m*(B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} x^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((B*x + A)*x^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
377,0,0,0,1.215111," ","integrate(x^m*(B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} x^{m}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral((B*x + A)*x^m/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
378,1,1623,0,1.362112," ","integrate(x^m*(b*x+a)^2*(d*x+c)^5,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} d^{5} m^{7} + 28 \, b^{2} d^{5} m^{6} + 322 \, b^{2} d^{5} m^{5} + 1960 \, b^{2} d^{5} m^{4} + 6769 \, b^{2} d^{5} m^{3} + 13132 \, b^{2} d^{5} m^{2} + 13068 \, b^{2} d^{5} m + 5040 \, b^{2} d^{5}\right)} x^{8} + {\left({\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{7} + 28800 \, b^{2} c d^{4} + 11520 \, a b d^{5} + 29 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{6} + 343 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{5} + 2135 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{4} + 7504 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{3} + 14756 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m^{2} + 14832 \, {\left(5 \, b^{2} c d^{4} + 2 \, a b d^{5}\right)} m\right)} x^{7} + {\left({\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{7} + 67200 \, b^{2} c^{2} d^{3} + 67200 \, a b c d^{4} + 6720 \, a^{2} d^{5} + 30 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{6} + 366 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{5} + 2340 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{4} + 8409 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{3} + 16830 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m^{2} + 17144 \, {\left(10 \, b^{2} c^{2} d^{3} + 10 \, a b c d^{4} + a^{2} d^{5}\right)} m\right)} x^{6} + 5 \, {\left({\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{7} + 16128 \, b^{2} c^{3} d^{2} + 32256 \, a b c^{2} d^{3} + 8064 \, a^{2} c d^{4} + 31 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{6} + 391 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{5} + 2581 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{4} + 9544 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{3} + 19564 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m^{2} + 20304 \, {\left(2 \, b^{2} c^{3} d^{2} + 4 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} m\right)} x^{5} + 5 \, {\left({\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{7} + 10080 \, b^{2} c^{4} d + 40320 \, a b c^{3} d^{2} + 20160 \, a^{2} c^{2} d^{3} + 32 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{6} + 418 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{5} + 2864 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{4} + 10993 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{3} + 23312 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m^{2} + 24876 \, {\left(b^{2} c^{4} d + 4 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} m\right)} x^{4} + {\left({\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{7} + 13440 \, b^{2} c^{5} + 134400 \, a b c^{4} d + 134400 \, a^{2} c^{3} d^{2} + 33 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{6} + 447 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{5} + 3195 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{4} + 12864 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{3} + 28692 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m^{2} + 32048 \, {\left(b^{2} c^{5} + 10 \, a b c^{4} d + 10 \, a^{2} c^{3} d^{2}\right)} m\right)} x^{3} + {\left({\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{7} + 40320 \, a b c^{5} + 100800 \, a^{2} c^{4} d + 34 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{6} + 478 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{5} + 3580 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{4} + 15289 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{3} + 36706 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m^{2} + 44712 \, {\left(2 \, a b c^{5} + 5 \, a^{2} c^{4} d\right)} m\right)} x^{2} + {\left(a^{2} c^{5} m^{7} + 35 \, a^{2} c^{5} m^{6} + 511 \, a^{2} c^{5} m^{5} + 4025 \, a^{2} c^{5} m^{4} + 18424 \, a^{2} c^{5} m^{3} + 48860 \, a^{2} c^{5} m^{2} + 69264 \, a^{2} c^{5} m + 40320 \, a^{2} c^{5}\right)} x\right)} x^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320}"," ",0,"((b^2*d^5*m^7 + 28*b^2*d^5*m^6 + 322*b^2*d^5*m^5 + 1960*b^2*d^5*m^4 + 6769*b^2*d^5*m^3 + 13132*b^2*d^5*m^2 + 13068*b^2*d^5*m + 5040*b^2*d^5)*x^8 + ((5*b^2*c*d^4 + 2*a*b*d^5)*m^7 + 28800*b^2*c*d^4 + 11520*a*b*d^5 + 29*(5*b^2*c*d^4 + 2*a*b*d^5)*m^6 + 343*(5*b^2*c*d^4 + 2*a*b*d^5)*m^5 + 2135*(5*b^2*c*d^4 + 2*a*b*d^5)*m^4 + 7504*(5*b^2*c*d^4 + 2*a*b*d^5)*m^3 + 14756*(5*b^2*c*d^4 + 2*a*b*d^5)*m^2 + 14832*(5*b^2*c*d^4 + 2*a*b*d^5)*m)*x^7 + ((10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^7 + 67200*b^2*c^2*d^3 + 67200*a*b*c*d^4 + 6720*a^2*d^5 + 30*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^6 + 366*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^5 + 2340*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^4 + 8409*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^3 + 16830*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m^2 + 17144*(10*b^2*c^2*d^3 + 10*a*b*c*d^4 + a^2*d^5)*m)*x^6 + 5*((2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^7 + 16128*b^2*c^3*d^2 + 32256*a*b*c^2*d^3 + 8064*a^2*c*d^4 + 31*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^6 + 391*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^5 + 2581*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^4 + 9544*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^3 + 19564*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m^2 + 20304*(2*b^2*c^3*d^2 + 4*a*b*c^2*d^3 + a^2*c*d^4)*m)*x^5 + 5*((b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^7 + 10080*b^2*c^4*d + 40320*a*b*c^3*d^2 + 20160*a^2*c^2*d^3 + 32*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^6 + 418*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^5 + 2864*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^4 + 10993*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^3 + 23312*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m^2 + 24876*(b^2*c^4*d + 4*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*m)*x^4 + ((b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^7 + 13440*b^2*c^5 + 134400*a*b*c^4*d + 134400*a^2*c^3*d^2 + 33*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^6 + 447*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^5 + 3195*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^4 + 12864*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^3 + 28692*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m^2 + 32048*(b^2*c^5 + 10*a*b*c^4*d + 10*a^2*c^3*d^2)*m)*x^3 + ((2*a*b*c^5 + 5*a^2*c^4*d)*m^7 + 40320*a*b*c^5 + 100800*a^2*c^4*d + 34*(2*a*b*c^5 + 5*a^2*c^4*d)*m^6 + 478*(2*a*b*c^5 + 5*a^2*c^4*d)*m^5 + 3580*(2*a*b*c^5 + 5*a^2*c^4*d)*m^4 + 15289*(2*a*b*c^5 + 5*a^2*c^4*d)*m^3 + 36706*(2*a*b*c^5 + 5*a^2*c^4*d)*m^2 + 44712*(2*a*b*c^5 + 5*a^2*c^4*d)*m)*x^2 + (a^2*c^5*m^7 + 35*a^2*c^5*m^6 + 511*a^2*c^5*m^5 + 4025*a^2*c^5*m^4 + 18424*a^2*c^5*m^3 + 48860*a^2*c^5*m^2 + 69264*a^2*c^5*m + 40320*a^2*c^5)*x)*x^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320)","B",0
379,0,0,0,1.255959," ","integrate(x^m*(d*x+c)^3/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} x^{m}}{b x + a}, x\right)"," ",0,"integral((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*x^m/(b*x + a), x)","F",0
380,0,0,0,1.163866," ","integrate(x^m*(d*x+c)^2/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} x^{m}}{b x + a}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*x^m/(b*x + a), x)","F",0
381,0,0,0,1.366278," ","integrate(x^m*(d*x+c)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} x^{m}}{b x + a}, x\right)"," ",0,"integral((d*x + c)*x^m/(b*x + a), x)","F",0
382,0,0,0,1.384582," ","integrate(x^m/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral(x^m/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
383,0,0,0,0.792804," ","integrate(x^m/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b d^{2} x^{3} + a c^{2} + {\left(2 \, b c d + a d^{2}\right)} x^{2} + {\left(b c^{2} + 2 \, a c d\right)} x}, x\right)"," ",0,"integral(x^m/(b*d^2*x^3 + a*c^2 + (2*b*c*d + a*d^2)*x^2 + (b*c^2 + 2*a*c*d)*x), x)","F",0
384,0,0,0,1.361710," ","integrate(x^m/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{b d^{3} x^{4} + a c^{3} + {\left(3 \, b c d^{2} + a d^{3}\right)} x^{3} + 3 \, {\left(b c^{2} d + a c d^{2}\right)} x^{2} + {\left(b c^{3} + 3 \, a c^{2} d\right)} x}, x\right)"," ",0,"integral(x^m/(b*d^3*x^4 + a*c^3 + (3*b*c*d^2 + a*d^3)*x^3 + 3*(b*c^2*d + a*c*d^2)*x^2 + (b*c^3 + 3*a*c^2*d)*x), x)","F",0
385,0,0,0,1.223129," ","integrate(b^2*x^m/(a*x^2+b)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{m}}{a^{2} x^{4} + 2 \, a b x^{2} + b^{2}}, x\right)"," ",0,"integral(b^2*x^m/(a^2*x^4 + 2*a*b*x^2 + b^2), x)","F",0
386,0,0,0,1.194241," ","integrate(x^m/(1-x*a^(1/2)/(-b)^(1/2))^2/(1+x*a^(1/2)/(-b)^(1/2))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{m}}{a^{2} x^{4} + 2 \, a b x^{2} + b^{2}}, x\right)"," ",0,"integral(b^2*x^m/(a^2*x^4 + 2*a*b*x^2 + b^2), x)","F",0
387,1,143,0,1.285842," ","integrate(x^4*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B b^{6} x^{6} - 1280 \, B a^{6} + 1664 \, A a^{5} b + 315 \, {\left(B a b^{5} + 13 \, A b^{6}\right)} x^{5} - 35 \, {\left(10 \, B a^{2} b^{4} - 13 \, A a b^{5}\right)} x^{4} + 40 \, {\left(10 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{3} - 48 \, {\left(10 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{2} + 64 \, {\left(10 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x\right)} \sqrt{b x + a}}{45045 \, b^{6}}"," ",0,"2/45045*(3465*B*b^6*x^6 - 1280*B*a^6 + 1664*A*a^5*b + 315*(B*a*b^5 + 13*A*b^6)*x^5 - 35*(10*B*a^2*b^4 - 13*A*a*b^5)*x^4 + 40*(10*B*a^3*b^3 - 13*A*a^2*b^4)*x^3 - 48*(10*B*a^4*b^2 - 13*A*a^3*b^3)*x^2 + 64*(10*B*a^5*b - 13*A*a^4*b^2)*x)*sqrt(b*x + a)/b^6","A",0
388,1,119,0,1.367629," ","integrate(x^3*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{5} x^{5} + 128 \, B a^{5} - 176 \, A a^{4} b + 35 \, {\left(B a b^{4} + 11 \, A b^{5}\right)} x^{4} - 5 \, {\left(8 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{2} - 8 \, {\left(8 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{3465 \, b^{5}}"," ",0,"2/3465*(315*B*b^5*x^5 + 128*B*a^5 - 176*A*a^4*b + 35*(B*a*b^4 + 11*A*b^5)*x^4 - 5*(8*B*a^2*b^3 - 11*A*a*b^4)*x^3 + 6*(8*B*a^3*b^2 - 11*A*a^2*b^3)*x^2 - 8*(8*B*a^4*b - 11*A*a^3*b^2)*x)*sqrt(b*x + a)/b^5","A",0
389,1,95,0,1.237780," ","integrate(x^2*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{4} - 16 \, B a^{4} + 24 \, A a^{3} b + 5 \, {\left(B a b^{3} + 9 \, A b^{4}\right)} x^{3} - 3 \, {\left(2 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{2} + 4 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{315 \, b^{4}}"," ",0,"2/315*(35*B*b^4*x^4 - 16*B*a^4 + 24*A*a^3*b + 5*(B*a*b^3 + 9*A*b^4)*x^3 - 3*(2*B*a^2*b^2 - 3*A*a*b^3)*x^2 + 4*(2*B*a^3*b - 3*A*a^2*b^2)*x)*sqrt(b*x + a)/b^4","A",0
390,1,71,0,1.241901," ","integrate(x*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{3} x^{3} + 8 \, B a^{3} - 14 \, A a^{2} b + 3 \, {\left(B a b^{2} + 7 \, A b^{3}\right)} x^{2} - {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}}{105 \, b^{3}}"," ",0,"2/105*(15*B*b^3*x^3 + 8*B*a^3 - 14*A*a^2*b + 3*(B*a*b^2 + 7*A*b^3)*x^2 - (4*B*a^2*b - 7*A*a*b^2)*x)*sqrt(b*x + a)/b^3","A",0
391,1,46,0,1.027814," ","integrate((B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{2} - 2 \, B a^{2} + 5 \, A a b + {\left(B a b + 5 \, A b^{2}\right)} x\right)} \sqrt{b x + a}}{15 \, b^{2}}"," ",0,"2/15*(3*B*b^2*x^2 - 2*B*a^2 + 5*A*a*b + (B*a*b + 5*A*b^2)*x)*sqrt(b*x + a)/b^2","A",0
392,1,111,0,1.196034," ","integrate((B*x+A)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, A \sqrt{a} b \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(B b x + B a + 3 \, A b\right)} \sqrt{b x + a}}{3 \, b}, \frac{2 \, {\left(3 \, A \sqrt{-a} b \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(B b x + B a + 3 \, A b\right)} \sqrt{b x + a}\right)}}{3 \, b}\right]"," ",0,"[1/3*(3*A*sqrt(a)*b*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(B*b*x + B*a + 3*A*b)*sqrt(b*x + a))/b, 2/3*(3*A*sqrt(-a)*b*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (B*b*x + B*a + 3*A*b)*sqrt(b*x + a))/b]","A",0
393,1,124,0,1.040890," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a + A b\right)} \sqrt{a} x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, B a x - A a\right)} \sqrt{b x + a}}{2 \, a x}, \frac{{\left(2 \, B a + A b\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, B a x - A a\right)} \sqrt{b x + a}}{a x}\right]"," ",0,"[1/2*((2*B*a + A*b)*sqrt(a)*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*B*a*x - A*a)*sqrt(b*x + a))/(a*x), ((2*B*a + A*b)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*B*a*x - A*a)*sqrt(b*x + a))/(a*x)]","A",0
394,1,158,0,1.399641," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{a} x^{2} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{b x + a}}{8 \, a^{2} x^{2}}, \frac{{\left(4 \, B a b - A b^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(2 \, A a^{2} + {\left(4 \, B a^{2} + A a b\right)} x\right)} \sqrt{b x + a}}{4 \, a^{2} x^{2}}\right]"," ",0,"[-1/8*((4*B*a*b - A*b^2)*sqrt(a)*x^2*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(b*x + a))/(a^2*x^2), 1/4*((4*B*a*b - A*b^2)*sqrt(-a)*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (2*A*a^2 + (4*B*a^2 + A*a*b)*x)*sqrt(b*x + a))/(a^2*x^2)]","A",0
395,1,209,0,1.323556," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} \sqrt{a} x^{3} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, A a^{3} + 3 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x\right)} \sqrt{b x + a}}{48 \, a^{3} x^{3}}, -\frac{3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(8 \, A a^{3} + 3 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + A a^{2} b\right)} x\right)} \sqrt{b x + a}}{24 \, a^{3} x^{3}}\right]"," ",0,"[-1/48*(3*(2*B*a*b^2 - A*b^3)*sqrt(a)*x^3*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*A*a^3 + 3*(2*B*a^2*b - A*a*b^2)*x^2 + 2*(6*B*a^3 + A*a^2*b)*x)*sqrt(b*x + a))/(a^3*x^3), -1/24*(3*(2*B*a*b^2 - A*b^3)*sqrt(-a)*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (8*A*a^3 + 3*(2*B*a^2*b - A*a*b^2)*x^2 + 2*(6*B*a^3 + A*a^2*b)*x)*sqrt(b*x + a))/(a^3*x^3)]","A",0
396,1,258,0,1.237007," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} \sqrt{a} x^{4} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{4} - 3 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{3} + 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x\right)} \sqrt{b x + a}}{384 \, a^{4} x^{4}}, \frac{3 \, {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(48 \, A a^{4} - 3 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{3} + 2 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + A a^{3} b\right)} x\right)} \sqrt{b x + a}}{192 \, a^{4} x^{4}}\right]"," ",0,"[-1/384*(3*(8*B*a*b^3 - 5*A*b^4)*sqrt(a)*x^4*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^4 - 3*(8*B*a^2*b^2 - 5*A*a*b^3)*x^3 + 2*(8*B*a^3*b - 5*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + A*a^3*b)*x)*sqrt(b*x + a))/(a^4*x^4), 1/192*(3*(8*B*a*b^3 - 5*A*b^4)*sqrt(-a)*x^4*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (48*A*a^4 - 3*(8*B*a^2*b^2 - 5*A*a*b^3)*x^3 + 2*(8*B*a^3*b - 5*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + A*a^3*b)*x)*sqrt(b*x + a))/(a^4*x^4)]","A",0
397,1,305,0,0.963082," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5}\right)} \sqrt{a} x^{5} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(384 \, A a^{5} + 15 \, {\left(10 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{4} - 10 \, {\left(10 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3840 \, a^{5} x^{5}}, -\frac{15 \, {\left(10 \, B a b^{4} - 7 \, A b^{5}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(384 \, A a^{5} + 15 \, {\left(10 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{4} - 10 \, {\left(10 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + A a^{4} b\right)} x\right)} \sqrt{b x + a}}{1920 \, a^{5} x^{5}}\right]"," ",0,"[-1/3840*(15*(10*B*a*b^4 - 7*A*b^5)*sqrt(a)*x^5*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(384*A*a^5 + 15*(10*B*a^2*b^3 - 7*A*a*b^4)*x^4 - 10*(10*B*a^3*b^2 - 7*A*a^2*b^3)*x^3 + 8*(10*B*a^4*b - 7*A*a^3*b^2)*x^2 + 48*(10*B*a^5 + A*a^4*b)*x)*sqrt(b*x + a))/(a^5*x^5), -1/1920*(15*(10*B*a*b^4 - 7*A*b^5)*sqrt(-a)*x^5*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (384*A*a^5 + 15*(10*B*a^2*b^3 - 7*A*a*b^4)*x^4 - 10*(10*B*a^3*b^2 - 7*A*a^2*b^3)*x^3 + 8*(10*B*a^4*b - 7*A*a^3*b^2)*x^2 + 48*(10*B*a^5 + A*a^4*b)*x)*sqrt(b*x + a))/(a^5*x^5)]","A",0
398,1,167,0,1.221170," ","integrate(x^4*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{7} x^{7} - 256 \, B a^{7} + 384 \, A a^{6} b + 231 \, {\left(16 \, B a b^{6} + 15 \, A b^{7}\right)} x^{6} + 63 \, {\left(B a^{2} b^{5} + 70 \, A a b^{6}\right)} x^{5} - 35 \, {\left(2 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5}\right)} x^{4} + 40 \, {\left(2 \, B a^{4} b^{3} - 3 \, A a^{3} b^{4}\right)} x^{3} - 48 \, {\left(2 \, B a^{5} b^{2} - 3 \, A a^{4} b^{3}\right)} x^{2} + 64 \, {\left(2 \, B a^{6} b - 3 \, A a^{5} b^{2}\right)} x\right)} \sqrt{b x + a}}{45045 \, b^{6}}"," ",0,"2/45045*(3003*B*b^7*x^7 - 256*B*a^7 + 384*A*a^6*b + 231*(16*B*a*b^6 + 15*A*b^7)*x^6 + 63*(B*a^2*b^5 + 70*A*a*b^6)*x^5 - 35*(2*B*a^3*b^4 - 3*A*a^2*b^5)*x^4 + 40*(2*B*a^4*b^3 - 3*A*a^3*b^4)*x^3 - 48*(2*B*a^5*b^2 - 3*A*a^4*b^3)*x^2 + 64*(2*B*a^6*b - 3*A*a^5*b^2)*x)*sqrt(b*x + a)/b^6","A",0
399,1,143,0,0.771673," ","integrate(x^3*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B b^{6} x^{6} + 128 \, B a^{6} - 208 \, A a^{5} b + 105 \, {\left(14 \, B a b^{5} + 13 \, A b^{6}\right)} x^{5} + 35 \, {\left(B a^{2} b^{4} + 52 \, A a b^{5}\right)} x^{4} - 5 \, {\left(8 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{2} - 8 \, {\left(8 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x\right)} \sqrt{b x + a}}{15015 \, b^{5}}"," ",0,"2/15015*(1155*B*b^6*x^6 + 128*B*a^6 - 208*A*a^5*b + 105*(14*B*a*b^5 + 13*A*b^6)*x^5 + 35*(B*a^2*b^4 + 52*A*a*b^5)*x^4 - 5*(8*B*a^3*b^3 - 13*A*a^2*b^4)*x^3 + 6*(8*B*a^4*b^2 - 13*A*a^3*b^3)*x^2 - 8*(8*B*a^5*b - 13*A*a^4*b^2)*x)*sqrt(b*x + a)/b^5","A",0
400,1,120,0,1.101850," ","integrate(x^2*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{5} x^{5} - 48 \, B a^{5} + 88 \, A a^{4} b + 35 \, {\left(12 \, B a b^{4} + 11 \, A b^{5}\right)} x^{4} + 5 \, {\left(3 \, B a^{2} b^{3} + 110 \, A a b^{4}\right)} x^{3} - 3 \, {\left(6 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{2} + 4 \, {\left(6 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{3465 \, b^{4}}"," ",0,"2/3465*(315*B*b^5*x^5 - 48*B*a^5 + 88*A*a^4*b + 35*(12*B*a*b^4 + 11*A*b^5)*x^4 + 5*(3*B*a^2*b^3 + 110*A*a*b^4)*x^3 - 3*(6*B*a^3*b^2 - 11*A*a^2*b^3)*x^2 + 4*(6*B*a^4*b - 11*A*a^3*b^2)*x)*sqrt(b*x + a)/b^4","A",0
401,1,95,0,1.321372," ","integrate(x*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{4} + 8 \, B a^{4} - 18 \, A a^{3} b + 5 \, {\left(10 \, B a b^{3} + 9 \, A b^{4}\right)} x^{3} + 3 \, {\left(B a^{2} b^{2} + 24 \, A a b^{3}\right)} x^{2} - {\left(4 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{315 \, b^{3}}"," ",0,"2/315*(35*B*b^4*x^4 + 8*B*a^4 - 18*A*a^3*b + 5*(10*B*a*b^3 + 9*A*b^4)*x^3 + 3*(B*a^2*b^2 + 24*A*a*b^3)*x^2 - (4*B*a^3*b - 9*A*a^2*b^2)*x)*sqrt(b*x + a)/b^3","A",0
402,1,69,0,1.223428," ","integrate((b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} x^{3} - 2 \, B a^{3} + 7 \, A a^{2} b + {\left(8 \, B a b^{2} + 7 \, A b^{3}\right)} x^{2} + {\left(B a^{2} b + 14 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}}{35 \, b^{2}}"," ",0,"2/35*(5*B*b^3*x^3 - 2*B*a^3 + 7*A*a^2*b + (8*B*a*b^2 + 7*A*b^3)*x^2 + (B*a^2*b + 14*A*a*b^2)*x)*sqrt(b*x + a)/b^2","B",0
403,1,158,0,1.074181," ","integrate((b*x+a)^(3/2)*(B*x+A)/x,x, algorithm=""fricas"")","\left[\frac{15 \, A a^{\frac{3}{2}} b \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, B b^{2} x^{2} + 3 \, B a^{2} + 20 \, A a b + {\left(6 \, B a b + 5 \, A b^{2}\right)} x\right)} \sqrt{b x + a}}{15 \, b}, \frac{2 \, {\left(15 \, A \sqrt{-a} a b \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, B b^{2} x^{2} + 3 \, B a^{2} + 20 \, A a b + {\left(6 \, B a b + 5 \, A b^{2}\right)} x\right)} \sqrt{b x + a}\right)}}{15 \, b}\right]"," ",0,"[1/15*(15*A*a^(3/2)*b*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*B*b^2*x^2 + 3*B*a^2 + 20*A*a*b + (6*B*a*b + 5*A*b^2)*x)*sqrt(b*x + a))/b, 2/15*(15*A*sqrt(-a)*a*b*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*B*b^2*x^2 + 3*B*a^2 + 20*A*a*b + (6*B*a*b + 5*A*b^2)*x)*sqrt(b*x + a))/b]","A",0
404,1,151,0,1.690837," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{a} x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, B b x^{2} - 3 \, A a + 2 \, {\left(4 \, B a + 3 \, A b\right)} x\right)} \sqrt{b x + a}}{6 \, x}, \frac{3 \, {\left(2 \, B a + 3 \, A b\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, B b x^{2} - 3 \, A a + 2 \, {\left(4 \, B a + 3 \, A b\right)} x\right)} \sqrt{b x + a}}{3 \, x}\right]"," ",0,"[1/6*(3*(2*B*a + 3*A*b)*sqrt(a)*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*B*b*x^2 - 3*A*a + 2*(4*B*a + 3*A*b)*x)*sqrt(b*x + a))/x, 1/3*(3*(2*B*a + 3*A*b)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*B*b*x^2 - 3*A*a + 2*(4*B*a + 3*A*b)*x)*sqrt(b*x + a))/x]","A",0
405,1,177,0,1.592773," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{a} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, B a b x^{2} - 2 \, A a^{2} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x\right)} \sqrt{b x + a}}{8 \, a x^{2}}, \frac{3 \, {\left(4 \, B a b + A b^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(8 \, B a b x^{2} - 2 \, A a^{2} - {\left(4 \, B a^{2} + 5 \, A a b\right)} x\right)} \sqrt{b x + a}}{4 \, a x^{2}}\right]"," ",0,"[1/8*(3*(4*B*a*b + A*b^2)*sqrt(a)*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*B*a*b*x^2 - 2*A*a^2 - (4*B*a^2 + 5*A*a*b)*x)*sqrt(b*x + a))/(a*x^2), 1/4*(3*(4*B*a*b + A*b^2)*sqrt(-a)*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (8*B*a*b*x^2 - 2*A*a^2 - (4*B*a^2 + 5*A*a*b)*x)*sqrt(b*x + a))/(a*x^2)]","A",0
406,1,210,0,1.483132," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B a b^{2} - A b^{3}\right)} \sqrt{a} x^{3} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, A a^{3} + 3 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{48 \, a^{2} x^{3}}, \frac{3 \, {\left(6 \, B a b^{2} - A b^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(8 \, A a^{3} + 3 \, {\left(10 \, B a^{2} b + A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} + 7 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{24 \, a^{2} x^{3}}\right]"," ",0,"[-1/48*(3*(6*B*a*b^2 - A*b^3)*sqrt(a)*x^3*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*A*a^3 + 3*(10*B*a^2*b + A*a*b^2)*x^2 + 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(b*x + a))/(a^2*x^3), 1/24*(3*(6*B*a*b^2 - A*b^3)*sqrt(-a)*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (8*A*a^3 + 3*(10*B*a^2*b + A*a*b^2)*x^2 + 2*(6*B*a^3 + 7*A*a^2*b)*x)*sqrt(b*x + a))/(a^2*x^3)]","A",0
407,1,259,0,1.291895," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4}\right)} \sqrt{a} x^{4} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{4} + 3 \, {\left(8 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{384 \, a^{3} x^{4}}, -\frac{3 \, {\left(8 \, B a b^{3} - 3 \, A b^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(48 \, A a^{4} + 3 \, {\left(8 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} x^{3} + 2 \, {\left(56 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 9 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{192 \, a^{3} x^{4}}\right]"," ",0,"[-1/384*(3*(8*B*a*b^3 - 3*A*b^4)*sqrt(a)*x^4*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^4 + 3*(8*B*a^2*b^2 - 3*A*a*b^3)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(b*x + a))/(a^3*x^4), -1/192*(3*(8*B*a*b^3 - 3*A*b^4)*sqrt(-a)*x^4*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (48*A*a^4 + 3*(8*B*a^2*b^2 - 3*A*a*b^3)*x^3 + 2*(56*B*a^3*b + 3*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + 9*A*a^3*b)*x)*sqrt(b*x + a))/(a^3*x^4)]","A",0
408,1,306,0,1.417155," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{4} - A b^{5}\right)} \sqrt{a} x^{5} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(128 \, A a^{5} - 15 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} x^{4} + 10 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2}\right)} x^{2} + 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{1280 \, a^{4} x^{5}}, \frac{15 \, {\left(2 \, B a b^{4} - A b^{5}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(128 \, A a^{5} - 15 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} x^{4} + 10 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(30 \, B a^{4} b + A a^{3} b^{2}\right)} x^{2} + 16 \, {\left(10 \, B a^{5} + 11 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{640 \, a^{4} x^{5}}\right]"," ",0,"[-1/1280*(15*(2*B*a*b^4 - A*b^5)*sqrt(a)*x^5*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(128*A*a^5 - 15*(2*B*a^2*b^3 - A*a*b^4)*x^4 + 10*(2*B*a^3*b^2 - A*a^2*b^3)*x^3 + 8*(30*B*a^4*b + A*a^3*b^2)*x^2 + 16*(10*B*a^5 + 11*A*a^4*b)*x)*sqrt(b*x + a))/(a^4*x^5), 1/640*(15*(2*B*a*b^4 - A*b^5)*sqrt(-a)*x^5*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (128*A*a^5 - 15*(2*B*a^2*b^3 - A*a*b^4)*x^4 + 10*(2*B*a^3*b^2 - A*a^2*b^3)*x^3 + 8*(30*B*a^4*b + A*a^3*b^2)*x^2 + 16*(10*B*a^5 + 11*A*a^4*b)*x)*sqrt(b*x + a))/(a^4*x^5)]","A",0
409,1,353,0,1.353088," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^7,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, B a b^{5} - 7 \, A b^{6}\right)} \sqrt{a} x^{6} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(1280 \, A a^{6} + 15 \, {\left(12 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} x^{5} - 10 \, {\left(12 \, B a^{3} b^{3} - 7 \, A a^{2} b^{4}\right)} x^{4} + 8 \, {\left(12 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3}\right)} x^{3} + 48 \, {\left(44 \, B a^{5} b + A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 13 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{15360 \, a^{5} x^{6}}, -\frac{15 \, {\left(12 \, B a b^{5} - 7 \, A b^{6}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(1280 \, A a^{6} + 15 \, {\left(12 \, B a^{2} b^{4} - 7 \, A a b^{5}\right)} x^{5} - 10 \, {\left(12 \, B a^{3} b^{3} - 7 \, A a^{2} b^{4}\right)} x^{4} + 8 \, {\left(12 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3}\right)} x^{3} + 48 \, {\left(44 \, B a^{5} b + A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 13 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{7680 \, a^{5} x^{6}}\right]"," ",0,"[-1/15360*(15*(12*B*a*b^5 - 7*A*b^6)*sqrt(a)*x^6*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(1280*A*a^6 + 15*(12*B*a^2*b^4 - 7*A*a*b^5)*x^5 - 10*(12*B*a^3*b^3 - 7*A*a^2*b^4)*x^4 + 8*(12*B*a^4*b^2 - 7*A*a^3*b^3)*x^3 + 48*(44*B*a^5*b + A*a^4*b^2)*x^2 + 128*(12*B*a^6 + 13*A*a^5*b)*x)*sqrt(b*x + a))/(a^5*x^6), -1/7680*(15*(12*B*a*b^5 - 7*A*b^6)*sqrt(-a)*x^6*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (1280*A*a^6 + 15*(12*B*a^2*b^4 - 7*A*a*b^5)*x^5 - 10*(12*B*a^3*b^3 - 7*A*a^2*b^4)*x^4 + 8*(12*B*a^4*b^2 - 7*A*a^3*b^3)*x^3 + 48*(44*B*a^5*b + A*a^4*b^2)*x^2 + 128*(12*B*a^6 + 13*A*a^5*b)*x)*sqrt(b*x + a))/(a^5*x^6)]","A",0
410,1,192,0,1.309931," ","integrate(x^4*(b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(45045 \, B b^{8} x^{8} - 1280 \, B a^{8} + 2176 \, A a^{7} b + 3003 \, {\left(35 \, B a b^{7} + 17 \, A b^{8}\right)} x^{7} + 231 \, {\left(275 \, B a^{2} b^{6} + 527 \, A a b^{7}\right)} x^{6} + 63 \, {\left(5 \, B a^{3} b^{5} + 1207 \, A a^{2} b^{6}\right)} x^{5} - 35 \, {\left(10 \, B a^{4} b^{4} - 17 \, A a^{3} b^{5}\right)} x^{4} + 40 \, {\left(10 \, B a^{5} b^{3} - 17 \, A a^{4} b^{4}\right)} x^{3} - 48 \, {\left(10 \, B a^{6} b^{2} - 17 \, A a^{5} b^{3}\right)} x^{2} + 64 \, {\left(10 \, B a^{7} b - 17 \, A a^{6} b^{2}\right)} x\right)} \sqrt{b x + a}}{765765 \, b^{6}}"," ",0,"2/765765*(45045*B*b^8*x^8 - 1280*B*a^8 + 2176*A*a^7*b + 3003*(35*B*a*b^7 + 17*A*b^8)*x^7 + 231*(275*B*a^2*b^6 + 527*A*a*b^7)*x^6 + 63*(5*B*a^3*b^5 + 1207*A*a^2*b^6)*x^5 - 35*(10*B*a^4*b^4 - 17*A*a^3*b^5)*x^4 + 40*(10*B*a^5*b^3 - 17*A*a^4*b^4)*x^3 - 48*(10*B*a^6*b^2 - 17*A*a^5*b^3)*x^2 + 64*(10*B*a^7*b - 17*A*a^6*b^2)*x)*sqrt(b*x + a)/b^6","A",0
411,1,167,0,1.144526," ","integrate(x^3*(b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{7} x^{7} + 128 \, B a^{7} - 240 \, A a^{6} b + 231 \, {\left(31 \, B a b^{6} + 15 \, A b^{7}\right)} x^{6} + 63 \, {\left(71 \, B a^{2} b^{5} + 135 \, A a b^{6}\right)} x^{5} + 35 \, {\left(B a^{3} b^{4} + 159 \, A a^{2} b^{5}\right)} x^{4} - 5 \, {\left(8 \, B a^{4} b^{3} - 15 \, A a^{3} b^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3}\right)} x^{2} - 8 \, {\left(8 \, B a^{6} b - 15 \, A a^{5} b^{2}\right)} x\right)} \sqrt{b x + a}}{45045 \, b^{5}}"," ",0,"2/45045*(3003*B*b^7*x^7 + 128*B*a^7 - 240*A*a^6*b + 231*(31*B*a*b^6 + 15*A*b^7)*x^6 + 63*(71*B*a^2*b^5 + 135*A*a*b^6)*x^5 + 35*(B*a^3*b^4 + 159*A*a^2*b^5)*x^4 - 5*(8*B*a^4*b^3 - 15*A*a^3*b^4)*x^3 + 6*(8*B*a^5*b^2 - 15*A*a^4*b^3)*x^2 - 8*(8*B*a^6*b - 15*A*a^5*b^2)*x)*sqrt(b*x + a)/b^5","A",0
412,1,143,0,1.201310," ","integrate(x^2*(b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B b^{6} x^{6} - 48 \, B a^{6} + 104 \, A a^{5} b + 63 \, {\left(27 \, B a b^{5} + 13 \, A b^{6}\right)} x^{5} + 7 \, {\left(159 \, B a^{2} b^{4} + 299 \, A a b^{5}\right)} x^{4} + {\left(15 \, B a^{3} b^{3} + 1469 \, A a^{2} b^{4}\right)} x^{3} - 3 \, {\left(6 \, B a^{4} b^{2} - 13 \, A a^{3} b^{3}\right)} x^{2} + 4 \, {\left(6 \, B a^{5} b - 13 \, A a^{4} b^{2}\right)} x\right)} \sqrt{b x + a}}{9009 \, b^{4}}"," ",0,"2/9009*(693*B*b^6*x^6 - 48*B*a^6 + 104*A*a^5*b + 63*(27*B*a*b^5 + 13*A*b^6)*x^5 + 7*(159*B*a^2*b^4 + 299*A*a*b^5)*x^4 + (15*B*a^3*b^3 + 1469*A*a^2*b^4)*x^3 - 3*(6*B*a^4*b^2 - 13*A*a^3*b^3)*x^2 + 4*(6*B*a^5*b - 13*A*a^4*b^2)*x)*sqrt(b*x + a)/b^4","A",0
413,1,118,0,1.112674," ","integrate(x*(b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b^{5} x^{5} + 8 \, B a^{5} - 22 \, A a^{4} b + 7 \, {\left(23 \, B a b^{4} + 11 \, A b^{5}\right)} x^{4} + {\left(113 \, B a^{2} b^{3} + 209 \, A a b^{4}\right)} x^{3} + 3 \, {\left(B a^{3} b^{2} + 55 \, A a^{2} b^{3}\right)} x^{2} - {\left(4 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{693 \, b^{3}}"," ",0,"2/693*(63*B*b^5*x^5 + 8*B*a^5 - 22*A*a^4*b + 7*(23*B*a*b^4 + 11*A*b^5)*x^4 + (113*B*a^2*b^3 + 209*A*a*b^4)*x^3 + 3*(B*a^3*b^2 + 55*A*a^2*b^3)*x^2 - (4*B*a^4*b - 11*A*a^3*b^2)*x)*sqrt(b*x + a)/b^3","B",0
414,1,93,0,1.222539," ","integrate((b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, B b^{4} x^{4} - 2 \, B a^{4} + 9 \, A a^{3} b + {\left(19 \, B a b^{3} + 9 \, A b^{4}\right)} x^{3} + 3 \, {\left(5 \, B a^{2} b^{2} + 9 \, A a b^{3}\right)} x^{2} + {\left(B a^{3} b + 27 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{63 \, b^{2}}"," ",0,"2/63*(7*B*b^4*x^4 - 2*B*a^4 + 9*A*a^3*b + (19*B*a*b^3 + 9*A*b^4)*x^3 + 3*(5*B*a^2*b^2 + 9*A*a*b^3)*x^2 + (B*a^3*b + 27*A*a^2*b^2)*x)*sqrt(b*x + a)/b^2","B",0
415,1,208,0,1.502833," ","integrate((b*x+a)^(5/2)*(B*x+A)/x,x, algorithm=""fricas"")","\left[\frac{105 \, A a^{\frac{5}{2}} b \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(15 \, B b^{3} x^{3} + 15 \, B a^{3} + 161 \, A a^{2} b + 3 \, {\left(15 \, B a b^{2} + 7 \, A b^{3}\right)} x^{2} + {\left(45 \, B a^{2} b + 77 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}}{105 \, b}, \frac{2 \, {\left(105 \, A \sqrt{-a} a^{2} b \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, B b^{3} x^{3} + 15 \, B a^{3} + 161 \, A a^{2} b + 3 \, {\left(15 \, B a b^{2} + 7 \, A b^{3}\right)} x^{2} + {\left(45 \, B a^{2} b + 77 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}\right)}}{105 \, b}\right]"," ",0,"[1/105*(105*A*a^(5/2)*b*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(15*B*b^3*x^3 + 15*B*a^3 + 161*A*a^2*b + 3*(15*B*a*b^2 + 7*A*b^3)*x^2 + (45*B*a^2*b + 77*A*a*b^2)*x)*sqrt(b*x + a))/b, 2/105*(105*A*sqrt(-a)*a^2*b*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*B*b^3*x^3 + 15*B*a^3 + 161*A*a^2*b + 3*(15*B*a*b^2 + 7*A*b^3)*x^2 + (45*B*a^2*b + 77*A*a*b^2)*x)*sqrt(b*x + a))/b]","A",0
416,1,205,0,1.419715," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{a} x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(6 \, B b^{2} x^{3} - 15 \, A a^{2} + 2 \, {\left(11 \, B a b + 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(23 \, B a^{2} + 35 \, A a b\right)} x\right)} \sqrt{b x + a}}{30 \, x}, \frac{15 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(6 \, B b^{2} x^{3} - 15 \, A a^{2} + 2 \, {\left(11 \, B a b + 5 \, A b^{2}\right)} x^{2} + 2 \, {\left(23 \, B a^{2} + 35 \, A a b\right)} x\right)} \sqrt{b x + a}}{15 \, x}\right]"," ",0,"[1/30*(15*(2*B*a^2 + 5*A*a*b)*sqrt(a)*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(6*B*b^2*x^3 - 15*A*a^2 + 2*(11*B*a*b + 5*A*b^2)*x^2 + 2*(23*B*a^2 + 35*A*a*b)*x)*sqrt(b*x + a))/x, 1/15*(15*(2*B*a^2 + 5*A*a*b)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (6*B*b^2*x^3 - 15*A*a^2 + 2*(11*B*a*b + 5*A*b^2)*x^2 + 2*(23*B*a^2 + 35*A*a*b)*x)*sqrt(b*x + a))/x]","A",0
417,1,209,0,1.406483," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} \sqrt{a} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, B b^{2} x^{3} - 6 \, A a^{2} + 8 \, {\left(7 \, B a b + 3 \, A b^{2}\right)} x^{2} - 3 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} x\right)} \sqrt{b x + a}}{24 \, x^{2}}, \frac{15 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(8 \, B b^{2} x^{3} - 6 \, A a^{2} + 8 \, {\left(7 \, B a b + 3 \, A b^{2}\right)} x^{2} - 3 \, {\left(4 \, B a^{2} + 9 \, A a b\right)} x\right)} \sqrt{b x + a}}{12 \, x^{2}}\right]"," ",0,"[1/24*(15*(4*B*a*b + 3*A*b^2)*sqrt(a)*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*B*b^2*x^3 - 6*A*a^2 + 8*(7*B*a*b + 3*A*b^2)*x^2 - 3*(4*B*a^2 + 9*A*a*b)*x)*sqrt(b*x + a))/x^2, 1/12*(15*(4*B*a*b + 3*A*b^2)*sqrt(-a)*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (8*B*b^2*x^3 - 6*A*a^2 + 8*(7*B*a*b + 3*A*b^2)*x^2 - 3*(4*B*a^2 + 9*A*a*b)*x)*sqrt(b*x + a))/x^2]","A",0
418,1,229,0,1.235078," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(6 \, B a b^{2} + A b^{3}\right)} \sqrt{a} x^{3} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, B a b^{2} x^{3} - 8 \, A a^{3} - 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{48 \, a x^{3}}, \frac{15 \, {\left(6 \, B a b^{2} + A b^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(48 \, B a b^{2} x^{3} - 8 \, A a^{3} - 3 \, {\left(18 \, B a^{2} b + 11 \, A a b^{2}\right)} x^{2} - 2 \, {\left(6 \, B a^{3} + 13 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{24 \, a x^{3}}\right]"," ",0,"[1/48*(15*(6*B*a*b^2 + A*b^3)*sqrt(a)*x^3*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*B*a*b^2*x^3 - 8*A*a^3 - 3*(18*B*a^2*b + 11*A*a*b^2)*x^2 - 2*(6*B*a^3 + 13*A*a^2*b)*x)*sqrt(b*x + a))/(a*x^3), 1/24*(15*(6*B*a*b^2 + A*b^3)*sqrt(-a)*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (48*B*a*b^2*x^3 - 8*A*a^3 - 3*(18*B*a^2*b + 11*A*a*b^2)*x^2 - 2*(6*B*a^3 + 13*A*a^2*b)*x)*sqrt(b*x + a))/(a*x^3)]","A",0
419,1,260,0,1.270262," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^5,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, B a b^{3} - A b^{4}\right)} \sqrt{a} x^{4} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{4} + 3 \, {\left(88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{3} + 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{384 \, a^{2} x^{4}}, \frac{15 \, {\left(8 \, B a b^{3} - A b^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(48 \, A a^{4} + 3 \, {\left(88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} x^{3} + 2 \, {\left(104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} + 17 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{192 \, a^{2} x^{4}}\right]"," ",0,"[-1/384*(15*(8*B*a*b^3 - A*b^4)*sqrt(a)*x^4*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^4 + 3*(88*B*a^2*b^2 + 5*A*a*b^3)*x^3 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(b*x + a))/(a^2*x^4), 1/192*(15*(8*B*a*b^3 - A*b^4)*sqrt(-a)*x^4*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (48*A*a^4 + 3*(88*B*a^2*b^2 + 5*A*a*b^3)*x^3 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^2 + 8*(8*B*a^4 + 17*A*a^3*b)*x)*sqrt(b*x + a))/(a^2*x^4)]","A",0
420,1,307,0,1.838869," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5}\right)} \sqrt{a} x^{5} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(384 \, A a^{5} + 15 \, {\left(10 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} + 10 \, {\left(118 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3840 \, a^{3} x^{5}}, -\frac{15 \, {\left(10 \, B a b^{4} - 3 \, A b^{5}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(384 \, A a^{5} + 15 \, {\left(10 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} + 10 \, {\left(118 \, B a^{3} b^{2} + 3 \, A a^{2} b^{3}\right)} x^{3} + 8 \, {\left(170 \, B a^{4} b + 93 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} + 21 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{1920 \, a^{3} x^{5}}\right]"," ",0,"[-1/3840*(15*(10*B*a*b^4 - 3*A*b^5)*sqrt(a)*x^5*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(384*A*a^5 + 15*(10*B*a^2*b^3 - 3*A*a*b^4)*x^4 + 10*(118*B*a^3*b^2 + 3*A*a^2*b^3)*x^3 + 8*(170*B*a^4*b + 93*A*a^3*b^2)*x^2 + 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(b*x + a))/(a^3*x^5), -1/1920*(15*(10*B*a*b^4 - 3*A*b^5)*sqrt(-a)*x^5*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (384*A*a^5 + 15*(10*B*a^2*b^3 - 3*A*a*b^4)*x^4 + 10*(118*B*a^3*b^2 + 3*A*a^2*b^3)*x^3 + 8*(170*B*a^4*b + 93*A*a^3*b^2)*x^2 + 48*(10*B*a^5 + 21*A*a^4*b)*x)*sqrt(b*x + a))/(a^3*x^5)]","A",0
421,1,356,0,0.966702," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^7,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6}\right)} \sqrt{a} x^{6} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(1280 \, A a^{6} - 15 \, {\left(12 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{5} + 10 \, {\left(12 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3}\right)} x^{3} + 144 \, {\left(28 \, B a^{5} b + 15 \, A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{15360 \, a^{4} x^{6}}, \frac{15 \, {\left(12 \, B a b^{5} - 5 \, A b^{6}\right)} \sqrt{-a} x^{6} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(1280 \, A a^{6} - 15 \, {\left(12 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} x^{5} + 10 \, {\left(12 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} x^{4} + 8 \, {\left(372 \, B a^{4} b^{2} + 5 \, A a^{3} b^{3}\right)} x^{3} + 144 \, {\left(28 \, B a^{5} b + 15 \, A a^{4} b^{2}\right)} x^{2} + 128 \, {\left(12 \, B a^{6} + 25 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{7680 \, a^{4} x^{6}}\right]"," ",0,"[-1/15360*(15*(12*B*a*b^5 - 5*A*b^6)*sqrt(a)*x^6*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(1280*A*a^6 - 15*(12*B*a^2*b^4 - 5*A*a*b^5)*x^5 + 10*(12*B*a^3*b^3 - 5*A*a^2*b^4)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3)*x^3 + 144*(28*B*a^5*b + 15*A*a^4*b^2)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(b*x + a))/(a^4*x^6), 1/7680*(15*(12*B*a*b^5 - 5*A*b^6)*sqrt(-a)*x^6*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (1280*A*a^6 - 15*(12*B*a^2*b^4 - 5*A*a*b^5)*x^5 + 10*(12*B*a^3*b^3 - 5*A*a^2*b^4)*x^4 + 8*(372*B*a^4*b^2 + 5*A*a^3*b^3)*x^3 + 144*(28*B*a^5*b + 15*A*a^4*b^2)*x^2 + 128*(12*B*a^6 + 25*A*a^5*b)*x)*sqrt(b*x + a))/(a^4*x^6)]","A",0
422,1,401,0,1.319896," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^8,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(2 \, B a b^{6} - A b^{7}\right)} \sqrt{a} x^{7} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3072 \, A a^{7} + 105 \, {\left(2 \, B a^{2} b^{5} - A a b^{6}\right)} x^{6} - 70 \, {\left(2 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} x^{5} + 56 \, {\left(2 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{4} + 48 \, {\left(126 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} x^{3} + 128 \, {\left(70 \, B a^{6} b + 37 \, A a^{5} b^{2}\right)} x^{2} + 256 \, {\left(14 \, B a^{7} + 29 \, A a^{6} b\right)} x\right)} \sqrt{b x + a}}{43008 \, a^{5} x^{7}}, -\frac{105 \, {\left(2 \, B a b^{6} - A b^{7}\right)} \sqrt{-a} x^{7} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3072 \, A a^{7} + 105 \, {\left(2 \, B a^{2} b^{5} - A a b^{6}\right)} x^{6} - 70 \, {\left(2 \, B a^{3} b^{4} - A a^{2} b^{5}\right)} x^{5} + 56 \, {\left(2 \, B a^{4} b^{3} - A a^{3} b^{4}\right)} x^{4} + 48 \, {\left(126 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} x^{3} + 128 \, {\left(70 \, B a^{6} b + 37 \, A a^{5} b^{2}\right)} x^{2} + 256 \, {\left(14 \, B a^{7} + 29 \, A a^{6} b\right)} x\right)} \sqrt{b x + a}}{21504 \, a^{5} x^{7}}\right]"," ",0,"[-1/43008*(105*(2*B*a*b^6 - A*b^7)*sqrt(a)*x^7*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3072*A*a^7 + 105*(2*B*a^2*b^5 - A*a*b^6)*x^6 - 70*(2*B*a^3*b^4 - A*a^2*b^5)*x^5 + 56*(2*B*a^4*b^3 - A*a^3*b^4)*x^4 + 48*(126*B*a^5*b^2 + A*a^4*b^3)*x^3 + 128*(70*B*a^6*b + 37*A*a^5*b^2)*x^2 + 256*(14*B*a^7 + 29*A*a^6*b)*x)*sqrt(b*x + a))/(a^5*x^7), -1/21504*(105*(2*B*a*b^6 - A*b^7)*sqrt(-a)*x^7*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3072*A*a^7 + 105*(2*B*a^2*b^5 - A*a*b^6)*x^6 - 70*(2*B*a^3*b^4 - A*a^2*b^5)*x^5 + 56*(2*B*a^4*b^3 - A*a^3*b^4)*x^4 + 48*(126*B*a^5*b^2 + A*a^4*b^3)*x^3 + 128*(70*B*a^6*b + 37*A*a^5*b^2)*x^2 + 256*(14*B*a^7 + 29*A*a^6*b)*x)*sqrt(b*x + a))/(a^5*x^7)]","A",0
423,1,120,0,1.393746," ","integrate(x^4*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{5} x^{5} - 1280 \, B a^{5} + 1408 \, A a^{4} b - 35 \, {\left(10 \, B a b^{4} - 11 \, A b^{5}\right)} x^{4} + 40 \, {\left(10 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} x^{3} - 48 \, {\left(10 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} x^{2} + 64 \, {\left(10 \, B a^{4} b - 11 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{3465 \, b^{6}}"," ",0,"2/3465*(315*B*b^5*x^5 - 1280*B*a^5 + 1408*A*a^4*b - 35*(10*B*a*b^4 - 11*A*b^5)*x^4 + 40*(10*B*a^2*b^3 - 11*A*a*b^4)*x^3 - 48*(10*B*a^3*b^2 - 11*A*a^2*b^3)*x^2 + 64*(10*B*a^4*b - 11*A*a^3*b^2)*x)*sqrt(b*x + a)/b^6","A",0
424,1,96,0,0.804457," ","integrate(x^3*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{4} x^{4} + 128 \, B a^{4} - 144 \, A a^{3} b - 5 \, {\left(8 \, B a b^{3} - 9 \, A b^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} x^{2} - 8 \, {\left(8 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{315 \, b^{5}}"," ",0,"2/315*(35*B*b^4*x^4 + 128*B*a^4 - 144*A*a^3*b - 5*(8*B*a*b^3 - 9*A*b^4)*x^3 + 6*(8*B*a^2*b^2 - 9*A*a*b^3)*x^2 - 8*(8*B*a^3*b - 9*A*a^2*b^2)*x)*sqrt(b*x + a)/b^5","A",0
425,1,72,0,1.168145," ","integrate(x^2*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{3} x^{3} - 48 \, B a^{3} + 56 \, A a^{2} b - 3 \, {\left(6 \, B a b^{2} - 7 \, A b^{3}\right)} x^{2} + 4 \, {\left(6 \, B a^{2} b - 7 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}}{105 \, b^{4}}"," ",0,"2/105*(15*B*b^3*x^3 - 48*B*a^3 + 56*A*a^2*b - 3*(6*B*a*b^2 - 7*A*b^3)*x^2 + 4*(6*B*a^2*b - 7*A*a*b^2)*x)*sqrt(b*x + a)/b^4","A",0
426,1,48,0,0.630945," ","integrate(x*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{2} + 8 \, B a^{2} - 10 \, A a b - {\left(4 \, B a b - 5 \, A b^{2}\right)} x\right)} \sqrt{b x + a}}{15 \, b^{3}}"," ",0,"2/15*(3*B*b^2*x^2 + 8*B*a^2 - 10*A*a*b - (4*B*a*b - 5*A*b^2)*x)*sqrt(b*x + a)/b^3","A",0
427,1,25,0,1.148596," ","integrate((B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x - 2 \, B a + 3 \, A b\right)} \sqrt{b x + a}}{3 \, b^{2}}"," ",0,"2/3*(B*b*x - 2*B*a + 3*A*b)*sqrt(b*x + a)/b^2","A",0
428,1,94,0,0.886471," ","integrate((B*x+A)/x/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{A \sqrt{a} b \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} B a}{a b}, \frac{2 \, {\left(A \sqrt{-a} b \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \sqrt{b x + a} B a\right)}}{a b}\right]"," ",0,"[(A*sqrt(a)*b*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*B*a)/(a*b), 2*(A*sqrt(-a)*b*arctan(sqrt(b*x + a)*sqrt(-a)/a) + sqrt(b*x + a)*B*a)/(a*b)]","A",0
429,1,111,0,0.884807," ","integrate((B*x+A)/x^2/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a - A b\right)} \sqrt{a} x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} A a}{2 \, a^{2} x}, \frac{{\left(2 \, B a - A b\right)} \sqrt{-a} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{b x + a} A a}{a^{2} x}\right]"," ",0,"[-1/2*((2*B*a - A*b)*sqrt(a)*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*A*a)/(a^2*x), ((2*B*a - A*b)*sqrt(-a)*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(b*x + a)*A*a)/(a^2*x)]","A",0
430,1,159,0,1.239311," ","integrate((B*x+A)/x^3/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{a} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{b x + a}}{8 \, a^{3} x^{2}}, -\frac{{\left(4 \, B a b - 3 \, A b^{2}\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, A a^{2} + {\left(4 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{b x + a}}{4 \, a^{3} x^{2}}\right]"," ",0,"[-1/8*((4*B*a*b - 3*A*b^2)*sqrt(a)*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x)*sqrt(b*x + a))/(a^3*x^2), -1/4*((4*B*a*b - 3*A*b^2)*sqrt(-a)*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*A*a^2 + (4*B*a^2 - 3*A*a*b)*x)*sqrt(b*x + a))/(a^3*x^2)]","A",0
431,1,212,0,1.312282," ","integrate((B*x+A)/x^4/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} \sqrt{a} x^{3} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, A a^{3} - 3 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{48 \, a^{4} x^{3}}, \frac{3 \, {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} \sqrt{-a} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(8 \, A a^{3} - 3 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{24 \, a^{4} x^{3}}\right]"," ",0,"[-1/48*(3*(6*B*a*b^2 - 5*A*b^3)*sqrt(a)*x^3*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*A*a^3 - 3*(6*B*a^2*b - 5*A*a*b^2)*x^2 + 2*(6*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*x^3), 1/24*(3*(6*B*a*b^2 - 5*A*b^3)*sqrt(-a)*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (8*A*a^3 - 3*(6*B*a^2*b - 5*A*a*b^2)*x^2 + 2*(6*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*x^3)]","A",0
432,1,259,0,1.386586," ","integrate((B*x+A)/x^5/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(8 \, B a b^{3} - 7 \, A b^{4}\right)} \sqrt{a} x^{4} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{4} + 15 \, {\left(8 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} - 10 \, {\left(8 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{384 \, a^{5} x^{4}}, -\frac{15 \, {\left(8 \, B a b^{3} - 7 \, A b^{4}\right)} \sqrt{-a} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(48 \, A a^{4} + 15 \, {\left(8 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} - 10 \, {\left(8 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{192 \, a^{5} x^{4}}\right]"," ",0,"[-1/384*(15*(8*B*a*b^3 - 7*A*b^4)*sqrt(a)*x^4*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^4 + 15*(8*B*a^2*b^2 - 7*A*a*b^3)*x^3 - 10*(8*B*a^3*b - 7*A*a^2*b^2)*x^2 + 8*(8*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*x^4), -1/192*(15*(8*B*a*b^3 - 7*A*b^4)*sqrt(-a)*x^4*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (48*A*a^4 + 15*(8*B*a^2*b^2 - 7*A*a*b^3)*x^3 - 10*(8*B*a^3*b - 7*A*a^2*b^2)*x^2 + 8*(8*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*x^4)]","A",0
433,1,308,0,1.134620," ","integrate((B*x+A)/x^6/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(10 \, B a b^{4} - 9 \, A b^{5}\right)} \sqrt{a} x^{5} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(384 \, A a^{5} - 105 \, {\left(10 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 70 \, {\left(10 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} - 56 \, {\left(10 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3840 \, a^{6} x^{5}}, \frac{105 \, {\left(10 \, B a b^{4} - 9 \, A b^{5}\right)} \sqrt{-a} x^{5} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(384 \, A a^{5} - 105 \, {\left(10 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 70 \, {\left(10 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} - 56 \, {\left(10 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + 48 \, {\left(10 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{1920 \, a^{6} x^{5}}\right]"," ",0,"[-1/3840*(105*(10*B*a*b^4 - 9*A*b^5)*sqrt(a)*x^5*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(384*A*a^5 - 105*(10*B*a^2*b^3 - 9*A*a*b^4)*x^4 + 70*(10*B*a^3*b^2 - 9*A*a^2*b^3)*x^3 - 56*(10*B*a^4*b - 9*A*a^3*b^2)*x^2 + 48*(10*B*a^5 - 9*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*x^5), 1/1920*(105*(10*B*a*b^4 - 9*A*b^5)*sqrt(-a)*x^5*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (384*A*a^5 - 105*(10*B*a^2*b^3 - 9*A*a*b^4)*x^4 + 70*(10*B*a^3*b^2 - 9*A*a^2*b^3)*x^3 - 56*(10*B*a^4*b - 9*A*a^3*b^2)*x^2 + 48*(10*B*a^5 - 9*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*x^5)]","A",0
434,1,130,0,0.999504," ","integrate(x^4*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{5} x^{5} + 1280 \, B a^{5} - 1152 \, A a^{4} b - 5 \, {\left(10 \, B a b^{4} - 9 \, A b^{5}\right)} x^{4} + 8 \, {\left(10 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{3} - 16 \, {\left(10 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{2} + 64 \, {\left(10 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{315 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"2/315*(35*B*b^5*x^5 + 1280*B*a^5 - 1152*A*a^4*b - 5*(10*B*a*b^4 - 9*A*b^5)*x^4 + 8*(10*B*a^2*b^3 - 9*A*a*b^4)*x^3 - 16*(10*B*a^3*b^2 - 9*A*a^2*b^3)*x^2 + 64*(10*B*a^4*b - 9*A*a^3*b^2)*x)*sqrt(b*x + a)/(b^7*x + a*b^6)","A",0
435,1,106,0,1.180351," ","integrate(x^3*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{4} x^{4} - 128 \, B a^{4} + 112 \, A a^{3} b - {\left(8 \, B a b^{3} - 7 \, A b^{4}\right)} x^{3} + 2 \, {\left(8 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{2} - 8 \, {\left(8 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{35 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"2/35*(5*B*b^4*x^4 - 128*B*a^4 + 112*A*a^3*b - (8*B*a*b^3 - 7*A*b^4)*x^3 + 2*(8*B*a^2*b^2 - 7*A*a*b^3)*x^2 - 8*(8*B*a^3*b - 7*A*a^2*b^2)*x)*sqrt(b*x + a)/(b^6*x + a*b^5)","A",0
436,1,82,0,1.047404," ","integrate(x^2*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} x^{3} + 48 \, B a^{3} - 40 \, A a^{2} b - {\left(6 \, B a b^{2} - 5 \, A b^{3}\right)} x^{2} + 4 \, {\left(6 \, B a^{2} b - 5 \, A a b^{2}\right)} x\right)} \sqrt{b x + a}}{15 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"2/15*(3*B*b^3*x^3 + 48*B*a^3 - 40*A*a^2*b - (6*B*a*b^2 - 5*A*b^3)*x^2 + 4*(6*B*a^2*b - 5*A*a*b^2)*x)*sqrt(b*x + a)/(b^5*x + a*b^4)","A",0
437,1,57,0,1.116241," ","integrate(x*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} x^{2} - 8 \, B a^{2} + 6 \, A a b - {\left(4 \, B a b - 3 \, A b^{2}\right)} x\right)} \sqrt{b x + a}}{3 \, {\left(b^{4} x + a b^{3}\right)}}"," ",0,"2/3*(B*b^2*x^2 - 8*B*a^2 + 6*A*a*b - (4*B*a*b - 3*A*b^2)*x)*sqrt(b*x + a)/(b^4*x + a*b^3)","A",0
438,1,35,0,1.177525," ","integrate((B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b x + 2 \, B a - A b\right)} \sqrt{b x + a}}{b^{3} x + a b^{2}}"," ",0,"2*(B*b*x + 2*B*a - A*b)*sqrt(b*x + a)/(b^3*x + a*b^2)","A",0
439,1,151,0,1.355115," ","integrate((B*x+A)/x/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(A b^{2} x + A a b\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(B a^{2} - A a b\right)} \sqrt{b x + a}}{a^{2} b^{2} x + a^{3} b}, \frac{2 \, {\left({\left(A b^{2} x + A a b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(B a^{2} - A a b\right)} \sqrt{b x + a}\right)}}{a^{2} b^{2} x + a^{3} b}\right]"," ",0,"[((A*b^2*x + A*a*b)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(B*a^2 - A*a*b)*sqrt(b*x + a))/(a^2*b^2*x + a^3*b), 2*((A*b^2*x + A*a*b)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (B*a^2 - A*a*b)*sqrt(b*x + a))/(a^2*b^2*x + a^3*b)]","A",0
440,1,211,0,1.378309," ","integrate((B*x+A)/x^2/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{2} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(A a^{2} - {\left(2 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{b x + a}}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}, \frac{{\left({\left(2 \, B a b - 3 \, A b^{2}\right)} x^{2} + {\left(2 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(A a^{2} - {\left(2 \, B a^{2} - 3 \, A a b\right)} x\right)} \sqrt{b x + a}}{a^{3} b x^{2} + a^{4} x}\right]"," ",0,"[-1/2*(((2*B*a*b - 3*A*b^2)*x^2 + (2*B*a^2 - 3*A*a*b)*x)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(A*a^2 - (2*B*a^2 - 3*A*a*b)*x)*sqrt(b*x + a))/(a^3*b*x^2 + a^4*x), (((2*B*a*b - 3*A*b^2)*x^2 + (2*B*a^2 - 3*A*a*b)*x)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (A*a^2 - (2*B*a^2 - 3*A*a*b)*x)*sqrt(b*x + a))/(a^3*b*x^2 + a^4*x)]","A",0
441,1,275,0,1.407149," ","integrate((B*x+A)/x^3/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{3} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, A a^{3} + 3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{8 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}, -\frac{3 \, {\left({\left(4 \, B a b^{2} - 5 \, A b^{3}\right)} x^{3} + {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, A a^{3} + 3 \, {\left(4 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(4 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{4 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}\right]"," ",0,"[-1/8*(3*((4*B*a*b^2 - 5*A*b^3)*x^3 + (4*B*a^2*b - 5*A*a*b^2)*x^2)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*A*a^3 + 3*(4*B*a^2*b - 5*A*a*b^2)*x^2 + (4*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*b*x^3 + a^5*x^2), -1/4*(3*((4*B*a*b^2 - 5*A*b^3)*x^3 + (4*B*a^2*b - 5*A*a*b^2)*x^2)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*A*a^3 + 3*(4*B*a^2*b - 5*A*a*b^2)*x^2 + (4*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*b*x^3 + a^5*x^2)]","A",0
442,1,330,0,1.255334," ","integrate((B*x+A)/x^4/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(6 \, B a b^{3} - 7 \, A b^{4}\right)} x^{4} + {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3}\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, A a^{4} - 15 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} - 5 \, {\left(6 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{48 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}, \frac{15 \, {\left({\left(6 \, B a b^{3} - 7 \, A b^{4}\right)} x^{4} + {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(8 \, A a^{4} - 15 \, {\left(6 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} - 5 \, {\left(6 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 2 \, {\left(6 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{24 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}\right]"," ",0,"[-1/48*(15*((6*B*a*b^3 - 7*A*b^4)*x^4 + (6*B*a^2*b^2 - 7*A*a*b^3)*x^3)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*A*a^4 - 15*(6*B*a^2*b^2 - 7*A*a*b^3)*x^3 - 5*(6*B*a^3*b - 7*A*a^2*b^2)*x^2 + 2*(6*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*b*x^4 + a^6*x^3), 1/24*(15*((6*B*a*b^3 - 7*A*b^4)*x^4 + (6*B*a^2*b^2 - 7*A*a*b^3)*x^3)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (8*A*a^4 - 15*(6*B*a^2*b^2 - 7*A*a*b^3)*x^3 - 5*(6*B*a^3*b - 7*A*a^2*b^2)*x^2 + 2*(6*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*b*x^4 + a^6*x^3)]","A",0
443,1,377,0,0.967318," ","integrate((B*x+A)/x^5/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(8 \, B a b^{4} - 9 \, A b^{5}\right)} x^{5} + {\left(8 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{5} + 105 \, {\left(8 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 35 \, {\left(8 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} - 14 \, {\left(8 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{384 \, {\left(a^{6} b x^{5} + a^{7} x^{4}\right)}}, -\frac{105 \, {\left({\left(8 \, B a b^{4} - 9 \, A b^{5}\right)} x^{5} + {\left(8 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(48 \, A a^{5} + 105 \, {\left(8 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} x^{4} + 35 \, {\left(8 \, B a^{3} b^{2} - 9 \, A a^{2} b^{3}\right)} x^{3} - 14 \, {\left(8 \, B a^{4} b - 9 \, A a^{3} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{5} - 9 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{192 \, {\left(a^{6} b x^{5} + a^{7} x^{4}\right)}}\right]"," ",0,"[-1/384*(105*((8*B*a*b^4 - 9*A*b^5)*x^5 + (8*B*a^2*b^3 - 9*A*a*b^4)*x^4)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^5 + 105*(8*B*a^2*b^3 - 9*A*a*b^4)*x^4 + 35*(8*B*a^3*b^2 - 9*A*a^2*b^3)*x^3 - 14*(8*B*a^4*b - 9*A*a^3*b^2)*x^2 + 8*(8*B*a^5 - 9*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*b*x^5 + a^7*x^4), -1/192*(105*((8*B*a*b^4 - 9*A*b^5)*x^5 + (8*B*a^2*b^3 - 9*A*a*b^4)*x^4)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (48*A*a^5 + 105*(8*B*a^2*b^3 - 9*A*a*b^4)*x^4 + 35*(8*B*a^3*b^2 - 9*A*a^2*b^3)*x^3 - 14*(8*B*a^4*b - 9*A*a^3*b^2)*x^2 + 8*(8*B*a^5 - 9*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*b*x^5 + a^7*x^4)]","A",0
444,1,141,0,1.328783," ","integrate(x^4*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{5} x^{5} - 1280 \, B a^{5} + 896 \, A a^{4} b - 3 \, {\left(10 \, B a b^{4} - 7 \, A b^{5}\right)} x^{4} + 8 \, {\left(10 \, B a^{2} b^{3} - 7 \, A a b^{4}\right)} x^{3} - 48 \, {\left(10 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\right)} x^{2} - 192 \, {\left(10 \, B a^{4} b - 7 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b x + a}}{105 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"2/105*(15*B*b^5*x^5 - 1280*B*a^5 + 896*A*a^4*b - 3*(10*B*a*b^4 - 7*A*b^5)*x^4 + 8*(10*B*a^2*b^3 - 7*A*a*b^4)*x^3 - 48*(10*B*a^3*b^2 - 7*A*a^2*b^3)*x^2 - 192*(10*B*a^4*b - 7*A*a^3*b^2)*x)*sqrt(b*x + a)/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","A",0
445,1,117,0,1.211425," ","integrate(x^3*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{4} x^{4} + 128 \, B a^{4} - 80 \, A a^{3} b - {\left(8 \, B a b^{3} - 5 \, A b^{4}\right)} x^{3} + 6 \, {\left(8 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} x^{2} + 24 \, {\left(8 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b x + a}}{15 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"2/15*(3*B*b^4*x^4 + 128*B*a^4 - 80*A*a^3*b - (8*B*a*b^3 - 5*A*b^4)*x^3 + 6*(8*B*a^2*b^2 - 5*A*a*b^3)*x^2 + 24*(8*B*a^3*b - 5*A*a^2*b^2)*x)*sqrt(b*x + a)/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
446,1,92,0,1.251554," ","integrate(x^2*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{3} x^{3} - 16 \, B a^{3} + 8 \, A a^{2} b - 3 \, {\left(2 \, B a b^{2} - A b^{3}\right)} x^{2} - 12 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} x\right)} \sqrt{b x + a}}{3 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"2/3*(B*b^3*x^3 - 16*B*a^3 + 8*A*a^2*b - 3*(2*B*a*b^2 - A*b^3)*x^2 - 12*(2*B*a^2*b - A*a*b^2)*x)*sqrt(b*x + a)/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
447,1,69,0,1.249418," ","integrate(x*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} x^{2} + 8 \, B a^{2} - 2 \, A a b + 3 \, {\left(4 \, B a b - A b^{2}\right)} x\right)} \sqrt{b x + a}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"2/3*(3*B*b^2*x^2 + 8*B*a^2 - 2*A*a*b + 3*(4*B*a*b - A*b^2)*x)*sqrt(b*x + a)/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
448,1,46,0,0.783638," ","integrate((B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B b x + 2 \, B a + A b\right)} \sqrt{b x + a}}{3 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-2/3*(3*B*b*x + 2*B*a + A*b)*sqrt(b*x + a)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
449,1,221,0,1.306897," ","integrate((B*x+A)/x/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, A a b^{2} x - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x + a}}{3 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}, \frac{2 \, {\left(3 \, {\left(A b^{3} x^{2} + 2 \, A a b^{2} x + A a^{2} b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, A a b^{2} x - B a^{3} + 4 \, A a^{2} b\right)} \sqrt{b x + a}\right)}}{3 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}\right]"," ",0,"[1/3*(3*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*A*a*b^2*x - B*a^3 + 4*A*a^2*b)*sqrt(b*x + a))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b), 2/3*(3*(A*b^3*x^2 + 2*A*a*b^2*x + A*a^2*b)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*A*a*b^2*x - B*a^3 + 4*A*a^2*b)*sqrt(b*x + a))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b)]","A",0
450,1,330,0,1.465002," ","integrate((B*x+A)/x^2/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, A a^{3} - 3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} - 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{6 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}, \frac{3 \, {\left({\left(2 \, B a b^{2} - 5 \, A b^{3}\right)} x^{3} + 2 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} + {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(3 \, A a^{3} - 3 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} x^{2} - 4 \, {\left(2 \, B a^{3} - 5 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{3 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}\right]"," ",0,"[-1/6*(3*((2*B*a*b^2 - 5*A*b^3)*x^3 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^2 + (2*B*a^3 - 5*A*a^2*b)*x)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*A*a^3 - 3*(2*B*a^2*b - 5*A*a*b^2)*x^2 - 4*(2*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x), 1/3*(3*((2*B*a*b^2 - 5*A*b^3)*x^3 + 2*(2*B*a^2*b - 5*A*a*b^2)*x^2 + (2*B*a^3 - 5*A*a^2*b)*x)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (3*A*a^3 - 3*(2*B*a^2*b - 5*A*a*b^2)*x^2 - 4*(2*B*a^3 - 5*A*a^2*b)*x)*sqrt(b*x + a))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)]","A",0
451,1,395,0,1.427911," ","integrate((B*x+A)/x^3/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, B a b^{3} - 7 \, A b^{4}\right)} x^{4} + 2 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(6 \, A a^{4} + 15 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + 20 \, {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 3 \, {\left(4 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{24 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}, -\frac{15 \, {\left({\left(4 \, B a b^{3} - 7 \, A b^{4}\right)} x^{4} + 2 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(6 \, A a^{4} + 15 \, {\left(4 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} x^{3} + 20 \, {\left(4 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} x^{2} + 3 \, {\left(4 \, B a^{4} - 7 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{12 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}\right]"," ",0,"[-1/24*(15*((4*B*a*b^3 - 7*A*b^4)*x^4 + 2*(4*B*a^2*b^2 - 7*A*a*b^3)*x^3 + (4*B*a^3*b - 7*A*a^2*b^2)*x^2)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(6*A*a^4 + 15*(4*B*a^2*b^2 - 7*A*a*b^3)*x^3 + 20*(4*B*a^3*b - 7*A*a^2*b^2)*x^2 + 3*(4*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2), -1/12*(15*((4*B*a*b^3 - 7*A*b^4)*x^4 + 2*(4*B*a^2*b^2 - 7*A*a*b^3)*x^3 + (4*B*a^3*b - 7*A*a^2*b^2)*x^2)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (6*A*a^4 + 15*(4*B*a^2*b^2 - 7*A*a*b^3)*x^3 + 20*(4*B*a^3*b - 7*A*a^2*b^2)*x^2 + 3*(4*B*a^4 - 7*A*a^3*b)*x)*sqrt(b*x + a))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)]","A",0
452,1,448,0,1.379392," ","integrate((B*x+A)/x^4/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(2 \, B a b^{4} - 3 \, A b^{5}\right)} x^{5} + 2 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} + {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, A a^{5} - 105 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} - 140 \, {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{3} - 21 \, {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x^{2} + 6 \, {\left(2 \, B a^{5} - 3 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{48 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}, \frac{105 \, {\left({\left(2 \, B a b^{4} - 3 \, A b^{5}\right)} x^{5} + 2 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} + {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(8 \, A a^{5} - 105 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} x^{4} - 140 \, {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} x^{3} - 21 \, {\left(2 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} x^{2} + 6 \, {\left(2 \, B a^{5} - 3 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{24 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}\right]"," ",0,"[-1/48*(105*((2*B*a*b^4 - 3*A*b^5)*x^5 + 2*(2*B*a^2*b^3 - 3*A*a*b^4)*x^4 + (2*B*a^3*b^2 - 3*A*a^2*b^3)*x^3)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*A*a^5 - 105*(2*B*a^2*b^3 - 3*A*a*b^4)*x^4 - 140*(2*B*a^3*b^2 - 3*A*a^2*b^3)*x^3 - 21*(2*B*a^4*b - 3*A*a^3*b^2)*x^2 + 6*(2*B*a^5 - 3*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3), 1/24*(105*((2*B*a*b^4 - 3*A*b^5)*x^5 + 2*(2*B*a^2*b^3 - 3*A*a*b^4)*x^4 + (2*B*a^3*b^2 - 3*A*a^2*b^3)*x^3)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (8*A*a^5 - 105*(2*B*a^2*b^3 - 3*A*a*b^4)*x^4 - 140*(2*B*a^3*b^2 - 3*A*a^2*b^3)*x^3 - 21*(2*B*a^4*b - 3*A*a^3*b^2)*x^2 + 6*(2*B*a^5 - 3*A*a^4*b)*x)*sqrt(b*x + a))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3)]","A",0
453,1,495,0,1.287812," ","integrate((B*x+A)/x^5/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left({\left(8 \, B a b^{5} - 11 \, A b^{6}\right)} x^{6} + 2 \, {\left(8 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + {\left(8 \, B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(48 \, A a^{6} + 315 \, {\left(8 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + 420 \, {\left(8 \, B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4} + 63 \, {\left(8 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{3} - 18 \, {\left(8 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{6} - 11 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{384 \, {\left(a^{7} b^{2} x^{6} + 2 \, a^{8} b x^{5} + a^{9} x^{4}\right)}}, -\frac{315 \, {\left({\left(8 \, B a b^{5} - 11 \, A b^{6}\right)} x^{6} + 2 \, {\left(8 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + {\left(8 \, B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(48 \, A a^{6} + 315 \, {\left(8 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} x^{5} + 420 \, {\left(8 \, B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} x^{4} + 63 \, {\left(8 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} x^{3} - 18 \, {\left(8 \, B a^{5} b - 11 \, A a^{4} b^{2}\right)} x^{2} + 8 \, {\left(8 \, B a^{6} - 11 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{192 \, {\left(a^{7} b^{2} x^{6} + 2 \, a^{8} b x^{5} + a^{9} x^{4}\right)}}\right]"," ",0,"[-1/384*(315*((8*B*a*b^5 - 11*A*b^6)*x^6 + 2*(8*B*a^2*b^4 - 11*A*a*b^5)*x^5 + (8*B*a^3*b^3 - 11*A*a^2*b^4)*x^4)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(48*A*a^6 + 315*(8*B*a^2*b^4 - 11*A*a*b^5)*x^5 + 420*(8*B*a^3*b^3 - 11*A*a^2*b^4)*x^4 + 63*(8*B*a^4*b^2 - 11*A*a^3*b^3)*x^3 - 18*(8*B*a^5*b - 11*A*a^4*b^2)*x^2 + 8*(8*B*a^6 - 11*A*a^5*b)*x)*sqrt(b*x + a))/(a^7*b^2*x^6 + 2*a^8*b*x^5 + a^9*x^4), -1/192*(315*((8*B*a*b^5 - 11*A*b^6)*x^6 + 2*(8*B*a^2*b^4 - 11*A*a*b^5)*x^5 + (8*B*a^3*b^3 - 11*A*a^2*b^4)*x^4)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (48*A*a^6 + 315*(8*B*a^2*b^4 - 11*A*a*b^5)*x^5 + 420*(8*B*a^3*b^3 - 11*A*a^2*b^4)*x^4 + 63*(8*B*a^4*b^2 - 11*A*a^3*b^3)*x^3 - 18*(8*B*a^5*b - 11*A*a^4*b^2)*x^2 + 8*(8*B*a^6 - 11*A*a^5*b)*x)*sqrt(b*x + a))/(a^7*b^2*x^6 + 2*a^8*b*x^5 + a^9*x^4)]","A",0
454,1,158,0,1.305810," ","integrate((b*x+a)^2/x^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a b c d - a^{2} d^{2}\right)} \sqrt{c} x \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, b^{2} c^{2} x - a^{2} c d\right)} \sqrt{d x + c}}{2 \, c^{2} d x}, \frac{{\left(4 \, a b c d - a^{2} d^{2}\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(2 \, b^{2} c^{2} x - a^{2} c d\right)} \sqrt{d x + c}}{c^{2} d x}\right]"," ",0,"[-1/2*((4*a*b*c*d - a^2*d^2)*sqrt(c)*x*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*b^2*c^2*x - a^2*c*d)*sqrt(d*x + c))/(c^2*d*x), ((4*a*b*c*d - a^2*d^2)*sqrt(-c)*x*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (2*b^2*c^2*x - a^2*c*d)*sqrt(d*x + c))/(c^2*d*x)]","A",0
455,1,713,0,1.111011," ","integrate(x^3*(d*x+c)^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(a^{3} b^{2} c^{2} d^{3} - 2 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(315 \, b^{5} d^{5} x^{5} + 40 \, b^{5} c^{5} + 110 \, a b^{4} c^{4} d + 495 \, a^{2} b^{3} c^{3} d^{2} - 5313 \, a^{3} b^{2} c^{2} d^{3} + 8085 \, a^{4} b c d^{4} - 3465 \, a^{5} d^{5} + 35 \, {\left(23 \, b^{5} c d^{4} - 11 \, a b^{4} d^{5}\right)} x^{4} + 5 \, {\left(113 \, b^{5} c^{2} d^{3} - 209 \, a b^{4} c d^{4} + 99 \, a^{2} b^{3} d^{5}\right)} x^{3} + 3 \, {\left(5 \, b^{5} c^{3} d^{2} - 275 \, a b^{4} c^{2} d^{3} + 495 \, a^{2} b^{3} c d^{4} - 231 \, a^{3} b^{2} d^{5}\right)} x^{2} - {\left(20 \, b^{5} c^{4} d + 55 \, a b^{4} c^{3} d^{2} - 1485 \, a^{2} b^{3} c^{2} d^{3} + 2541 \, a^{3} b^{2} c d^{4} - 1155 \, a^{4} b d^{5}\right)} x\right)} \sqrt{d x + c}}{3465 \, b^{6} d^{3}}, \frac{2 \, {\left(3465 \, {\left(a^{3} b^{2} c^{2} d^{3} - 2 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(315 \, b^{5} d^{5} x^{5} + 40 \, b^{5} c^{5} + 110 \, a b^{4} c^{4} d + 495 \, a^{2} b^{3} c^{3} d^{2} - 5313 \, a^{3} b^{2} c^{2} d^{3} + 8085 \, a^{4} b c d^{4} - 3465 \, a^{5} d^{5} + 35 \, {\left(23 \, b^{5} c d^{4} - 11 \, a b^{4} d^{5}\right)} x^{4} + 5 \, {\left(113 \, b^{5} c^{2} d^{3} - 209 \, a b^{4} c d^{4} + 99 \, a^{2} b^{3} d^{5}\right)} x^{3} + 3 \, {\left(5 \, b^{5} c^{3} d^{2} - 275 \, a b^{4} c^{2} d^{3} + 495 \, a^{2} b^{3} c d^{4} - 231 \, a^{3} b^{2} d^{5}\right)} x^{2} - {\left(20 \, b^{5} c^{4} d + 55 \, a b^{4} c^{3} d^{2} - 1485 \, a^{2} b^{3} c^{2} d^{3} + 2541 \, a^{3} b^{2} c d^{4} - 1155 \, a^{4} b d^{5}\right)} x\right)} \sqrt{d x + c}\right)}}{3465 \, b^{6} d^{3}}\right]"," ",0,"[1/3465*(3465*(a^3*b^2*c^2*d^3 - 2*a^4*b*c*d^4 + a^5*d^5)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(315*b^5*d^5*x^5 + 40*b^5*c^5 + 110*a*b^4*c^4*d + 495*a^2*b^3*c^3*d^2 - 5313*a^3*b^2*c^2*d^3 + 8085*a^4*b*c*d^4 - 3465*a^5*d^5 + 35*(23*b^5*c*d^4 - 11*a*b^4*d^5)*x^4 + 5*(113*b^5*c^2*d^3 - 209*a*b^4*c*d^4 + 99*a^2*b^3*d^5)*x^3 + 3*(5*b^5*c^3*d^2 - 275*a*b^4*c^2*d^3 + 495*a^2*b^3*c*d^4 - 231*a^3*b^2*d^5)*x^2 - (20*b^5*c^4*d + 55*a*b^4*c^3*d^2 - 1485*a^2*b^3*c^2*d^3 + 2541*a^3*b^2*c*d^4 - 1155*a^4*b*d^5)*x)*sqrt(d*x + c))/(b^6*d^3), 2/3465*(3465*(a^3*b^2*c^2*d^3 - 2*a^4*b*c*d^4 + a^5*d^5)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (315*b^5*d^5*x^5 + 40*b^5*c^5 + 110*a*b^4*c^4*d + 495*a^2*b^3*c^3*d^2 - 5313*a^3*b^2*c^2*d^3 + 8085*a^4*b*c*d^4 - 3465*a^5*d^5 + 35*(23*b^5*c*d^4 - 11*a*b^4*d^5)*x^4 + 5*(113*b^5*c^2*d^3 - 209*a*b^4*c*d^4 + 99*a^2*b^3*d^5)*x^3 + 3*(5*b^5*c^3*d^2 - 275*a*b^4*c^2*d^3 + 495*a^2*b^3*c*d^4 - 231*a^3*b^2*d^5)*x^2 - (20*b^5*c^4*d + 55*a*b^4*c^3*d^2 - 1485*a^2*b^3*c^2*d^3 + 2541*a^3*b^2*c*d^4 - 1155*a^4*b*d^5)*x)*sqrt(d*x + c))/(b^6*d^3)]","A",0
456,1,552,0,1.210022," ","integrate(x^2*(d*x+c)^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} b^{2} c^{2} d^{2} - 2 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(35 \, b^{4} d^{4} x^{4} - 10 \, b^{4} c^{4} - 45 \, a b^{3} c^{3} d + 483 \, a^{2} b^{2} c^{2} d^{2} - 735 \, a^{3} b c d^{3} + 315 \, a^{4} d^{4} + 5 \, {\left(19 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(25 \, b^{4} c^{2} d^{2} - 45 \, a b^{3} c d^{3} + 21 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(5 \, b^{4} c^{3} d - 135 \, a b^{3} c^{2} d^{2} + 231 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x + c}}{315 \, b^{5} d^{2}}, -\frac{2 \, {\left(315 \, {\left(a^{2} b^{2} c^{2} d^{2} - 2 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(35 \, b^{4} d^{4} x^{4} - 10 \, b^{4} c^{4} - 45 \, a b^{3} c^{3} d + 483 \, a^{2} b^{2} c^{2} d^{2} - 735 \, a^{3} b c d^{3} + 315 \, a^{4} d^{4} + 5 \, {\left(19 \, b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(25 \, b^{4} c^{2} d^{2} - 45 \, a b^{3} c d^{3} + 21 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(5 \, b^{4} c^{3} d - 135 \, a b^{3} c^{2} d^{2} + 231 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4}\right)} x\right)} \sqrt{d x + c}\right)}}{315 \, b^{5} d^{2}}\right]"," ",0,"[1/315*(315*(a^2*b^2*c^2*d^2 - 2*a^3*b*c*d^3 + a^4*d^4)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(35*b^4*d^4*x^4 - 10*b^4*c^4 - 45*a*b^3*c^3*d + 483*a^2*b^2*c^2*d^2 - 735*a^3*b*c*d^3 + 315*a^4*d^4 + 5*(19*b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 3*(25*b^4*c^2*d^2 - 45*a*b^3*c*d^3 + 21*a^2*b^2*d^4)*x^2 + (5*b^4*c^3*d - 135*a*b^3*c^2*d^2 + 231*a^2*b^2*c*d^3 - 105*a^3*b*d^4)*x)*sqrt(d*x + c))/(b^5*d^2), -2/315*(315*(a^2*b^2*c^2*d^2 - 2*a^3*b*c*d^3 + a^4*d^4)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (35*b^4*d^4*x^4 - 10*b^4*c^4 - 45*a*b^3*c^3*d + 483*a^2*b^2*c^2*d^2 - 735*a^3*b*c*d^3 + 315*a^4*d^4 + 5*(19*b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 3*(25*b^4*c^2*d^2 - 45*a*b^3*c*d^3 + 21*a^2*b^2*d^4)*x^2 + (5*b^4*c^3*d - 135*a*b^3*c^2*d^2 + 231*a^2*b^2*c*d^3 - 105*a^3*b*d^4)*x)*sqrt(d*x + c))/(b^5*d^2)]","A",0
457,1,411,0,1.327566," ","integrate(x*(d*x+c)^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(15 \, b^{3} d^{3} x^{3} + 15 \, b^{3} c^{3} - 161 \, a b^{2} c^{2} d + 245 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + 3 \, {\left(15 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(45 \, b^{3} c^{2} d - 77 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x + c}}{105 \, b^{4} d}, \frac{2 \, {\left(105 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(15 \, b^{3} d^{3} x^{3} + 15 \, b^{3} c^{3} - 161 \, a b^{2} c^{2} d + 245 \, a^{2} b c d^{2} - 105 \, a^{3} d^{3} + 3 \, {\left(15 \, b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(45 \, b^{3} c^{2} d - 77 \, a b^{2} c d^{2} + 35 \, a^{2} b d^{3}\right)} x\right)} \sqrt{d x + c}\right)}}{105 \, b^{4} d}\right]"," ",0,"[1/105*(105*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(15*b^3*d^3*x^3 + 15*b^3*c^3 - 161*a*b^2*c^2*d + 245*a^2*b*c*d^2 - 105*a^3*d^3 + 3*(15*b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + (45*b^3*c^2*d - 77*a*b^2*c*d^2 + 35*a^2*b*d^3)*x)*sqrt(d*x + c))/(b^4*d), 2/105*(105*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (15*b^3*d^3*x^3 + 15*b^3*c^3 - 161*a*b^2*c^2*d + 245*a^2*b*c*d^2 - 105*a^3*d^3 + 3*(15*b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + (45*b^3*c^2*d - 77*a*b^2*c*d^2 + 35*a^2*b*d^3)*x)*sqrt(d*x + c))/(b^4*d)]","A",0
458,1,290,0,1.312542," ","integrate((d*x+c)^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 23 \, b^{2} c^{2} - 35 \, a b c d + 15 \, a^{2} d^{2} + {\left(11 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(3 \, b^{2} d^{2} x^{2} + 23 \, b^{2} c^{2} - 35 \, a b c d + 15 \, a^{2} d^{2} + {\left(11 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{d x + c}\right)}}{15 \, b^{3}}\right]"," ",0,"[1/15*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(3*b^2*d^2*x^2 + 23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + (11*b^2*c*d - 5*a*b*d^2)*x)*sqrt(d*x + c))/b^3, -2/15*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (3*b^2*d^2*x^2 + 23*b^2*c^2 - 35*a*b*c*d + 15*a^2*d^2 + (11*b^2*c*d - 5*a*b*d^2)*x)*sqrt(d*x + c))/b^3]","A",0
459,1,598,0,1.933885," ","integrate((d*x+c)^(5/2)/x/(b*x+a),x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} c^{\frac{5}{2}} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a b d^{2} x + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x + c}}{3 \, a b^{2}}, \frac{3 \, b^{2} c^{\frac{5}{2}} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 6 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + 2 \, {\left(a b d^{2} x + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x + c}}{3 \, a b^{2}}, \frac{6 \, b^{2} \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a b d^{2} x + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x + c}}{3 \, a b^{2}}, \frac{2 \, {\left(3 \, b^{2} \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(a b d^{2} x + 7 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{d x + c}\right)}}{3 \, a b^{2}}\right]"," ",0,"[1/3*(3*b^2*c^(5/2)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a*b*d^2*x + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x + c))/(a*b^2), 1/3*(3*b^2*c^(5/2)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 6*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + 2*(a*b*d^2*x + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x + c))/(a*b^2), 1/3*(6*b^2*sqrt(-c)*c^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a*b*d^2*x + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x + c))/(a*b^2), 2/3*(3*b^2*sqrt(-c)*c^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (a*b*d^2*x + 7*a*b*c*d - 3*a^2*d^2)*sqrt(d*x + c))/(a*b^2)]","A",0
460,1,638,0,1.879369," ","integrate((d*x+c)^(5/2)/x^2/(b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{c} x \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(2 \, a^{2} d^{2} x - a b c^{2}\right)} \sqrt{d x + c}}{2 \, a^{2} b x}, -\frac{4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{c} x \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{2} d^{2} x - a b c^{2}\right)} \sqrt{d x + c}}{2 \, a^{2} b x}, -\frac{{\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - {\left(2 \, a^{2} d^{2} x - a b c^{2}\right)} \sqrt{d x + c}}{a^{2} b x}, -\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(2 \, b^{2} c^{2} - 5 \, a b c d\right)} \sqrt{-c} x \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(2 \, a^{2} d^{2} x - a b c^{2}\right)} \sqrt{d x + c}}{a^{2} b x}\right]"," ",0,"[1/2*(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - (2*b^2*c^2 - 5*a*b*c*d)*sqrt(c)*x*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(2*a^2*d^2*x - a*b*c^2)*sqrt(d*x + c))/(a^2*b*x), -1/2*(4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (2*b^2*c^2 - 5*a*b*c*d)*sqrt(c)*x*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^2*d^2*x - a*b*c^2)*sqrt(d*x + c))/(a^2*b*x), -((2*b^2*c^2 - 5*a*b*c*d)*sqrt(-c)*x*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - (2*a^2*d^2*x - a*b*c^2)*sqrt(d*x + c))/(a^2*b*x), -(2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (2*b^2*c^2 - 5*a*b*c*d)*sqrt(-c)*x*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (2*a^2*d^2*x - a*b*c^2)*sqrt(d*x + c))/(a^2*b*x)]","A",0
461,1,713,0,1.988496," ","integrate((d*x+c)^(5/2)/x^3/(b*x+a),x, algorithm=""fricas"")","\left[\frac{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + {\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{c} x^{2} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(4 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{d x + c}}{8 \, a^{3} x^{2}}, \frac{16 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{c} x^{2} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(4 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{d x + c}}{8 \, a^{3} x^{2}}, \frac{{\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - {\left(2 \, a^{2} c^{2} - {\left(4 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{d x + c}}{4 \, a^{3} x^{2}}, \frac{8 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(8 \, b^{2} c^{2} - 20 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(2 \, a^{2} c^{2} - {\left(4 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{d x + c}}{4 \, a^{3} x^{2}}\right]"," ",0,"[1/8*(8*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + (8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(c)*x^2*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^2*c^2 - (4*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(d*x + c))/(a^3*x^2), 1/8*(16*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(c)*x^2*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^2*c^2 - (4*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(d*x + c))/(a^3*x^2), 1/4*((8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(-c)*x^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 4*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - (2*a^2*c^2 - (4*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(d*x + c))/(a^3*x^2), 1/4*(8*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*x^2*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (8*b^2*c^2 - 20*a*b*c*d + 15*a^2*d^2)*sqrt(-c)*x^2*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (2*a^2*c^2 - (4*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(d*x + c))/(a^3*x^2)]","A",0
462,1,930,0,2.087342," ","integrate((d*x+c)^(5/2)/x^4/(b*x+a),x, algorithm=""fricas"")","\left[\frac{48 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{b^{2} c - a b d} x^{3} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) - 3 \, {\left(16 \, b^{3} c^{3} - 40 \, a b^{2} c^{2} d + 30 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{c} x^{3} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(8 \, a^{3} c^{3} + 3 \, {\left(8 \, a b^{2} c^{3} - 18 \, a^{2} b c^{2} d + 11 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(6 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{d x + c}}{48 \, a^{4} c x^{3}}, \frac{96 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{-b^{2} c + a b d} x^{3} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 3 \, {\left(16 \, b^{3} c^{3} - 40 \, a b^{2} c^{2} d + 30 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{c} x^{3} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(8 \, a^{3} c^{3} + 3 \, {\left(8 \, a b^{2} c^{3} - 18 \, a^{2} b c^{2} d + 11 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(6 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{d x + c}}{48 \, a^{4} c x^{3}}, -\frac{3 \, {\left(16 \, b^{3} c^{3} - 40 \, a b^{2} c^{2} d + 30 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 24 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{b^{2} c - a b d} x^{3} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + {\left(8 \, a^{3} c^{3} + 3 \, {\left(8 \, a b^{2} c^{3} - 18 \, a^{2} b c^{2} d + 11 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(6 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{d x + c}}{24 \, a^{4} c x^{3}}, \frac{48 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{-b^{2} c + a b d} x^{3} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 3 \, {\left(16 \, b^{3} c^{3} - 40 \, a b^{2} c^{2} d + 30 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(8 \, a^{3} c^{3} + 3 \, {\left(8 \, a b^{2} c^{3} - 18 \, a^{2} b c^{2} d + 11 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(6 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{d x + c}}{24 \, a^{4} c x^{3}}\right]"," ",0,"[1/48*(48*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(b^2*c - a*b*d)*x^3*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) - 3*(16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(c)*x^3*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(8*a^3*c^3 + 3*(8*a*b^2*c^3 - 18*a^2*b*c^2*d + 11*a^3*c*d^2)*x^2 - 2*(6*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(d*x + c))/(a^4*c*x^3), 1/48*(96*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(-b^2*c + a*b*d)*x^3*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 3*(16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(c)*x^3*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(8*a^3*c^3 + 3*(8*a*b^2*c^3 - 18*a^2*b*c^2*d + 11*a^3*c*d^2)*x^2 - 2*(6*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(d*x + c))/(a^4*c*x^3), -1/24*(3*(16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-c)*x^3*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 24*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(b^2*c - a*b*d)*x^3*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + (8*a^3*c^3 + 3*(8*a*b^2*c^3 - 18*a^2*b*c^2*d + 11*a^3*c*d^2)*x^2 - 2*(6*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(d*x + c))/(a^4*c*x^3), 1/24*(48*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(-b^2*c + a*b*d)*x^3*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 3*(16*b^3*c^3 - 40*a*b^2*c^2*d + 30*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-c)*x^3*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (8*a^3*c^3 + 3*(8*a*b^2*c^3 - 18*a^2*b*c^2*d + 11*a^3*c*d^2)*x^2 - 2*(6*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(d*x + c))/(a^4*c*x^3)]","A",0
463,-1,0,0,0.000000," ","integrate(1/x^(1/3)/(d*x+4*c)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,-1,0,0,0.000000," ","integrate(1/x^(1/3)/(-d*x+8*c)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,1,798,0,1.866949," ","integrate((d*x+c)^(1/2)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + a}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(2 \, a b c x + a^{2} c\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b c x^{2} + a^{4} c x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(2 \, a b c x + a^{2} c\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b c x^{2} + a^{4} c x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + a}\right) + 2 \, {\left(2 \, a b c x + a^{2} c\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b c x^{2} + a^{4} c x\right)}}, -\frac{{\left({\left(4 \, b^{2} c^{2} - 3 \, a b c d\right)} x^{2} + {\left(4 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(2 \, a b c x + a^{2} c\right)} \sqrt{d x + c}}{a^{3} b c x^{2} + a^{4} c x}\right]"," ",0,"[-1/2*(((4*b^2*c^2 - 3*a*b*c*d)*x^2 + (4*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d + 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + ((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(2*a*b*c*x + a^2*c)*sqrt(d*x + c))/(a^3*b*c*x^2 + a^4*c*x), -1/2*(2*((4*b^2*c^2 - 3*a*b*c*d)*x^2 + (4*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) + ((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(2*a*b*c*x + a^2*c)*sqrt(d*x + c))/(a^3*b*c*x^2 + a^4*c*x), -1/2*(2*((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + ((4*b^2*c^2 - 3*a*b*c*d)*x^2 + (4*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d + 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + 2*(2*a*b*c*x + a^2*c)*sqrt(d*x + c))/(a^3*b*c*x^2 + a^4*c*x), -(((4*b^2*c^2 - 3*a*b*c*d)*x^2 + (4*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) + ((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (2*a*b*c*x + a^2*c)*sqrt(d*x + c))/(a^3*b*c*x^2 + a^4*c*x)]","A",0
466,1,624,0,2.084928," ","integrate((d*x+c)^(3/2)/x/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(b^{2} c x + a b c\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}, \frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(b^{2} c x + a b c\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + {\left(a b c - a^{2} d\right)} \sqrt{d x + c}}{a^{2} b^{2} x + a^{3} b}, \frac{4 \, {\left(b^{2} c x + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a b c - a^{2} d\right)} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}, \frac{{\left(2 \, a b c + a^{2} d + {\left(2 \, b^{2} c + a b d\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + 2 \, {\left(b^{2} c x + a b c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(a b c - a^{2} d\right)} \sqrt{d x + c}}{a^{2} b^{2} x + a^{3} b}\right]"," ",0,"[1/2*((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(b^2*c*x + a*b*c)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a*b*c - a^2*d)*sqrt(d*x + c))/(a^2*b^2*x + a^3*b), ((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (b^2*c*x + a*b*c)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + (a*b*c - a^2*d)*sqrt(d*x + c))/(a^2*b^2*x + a^3*b), 1/2*(4*(b^2*c*x + a*b*c)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a*b*c - a^2*d)*sqrt(d*x + c))/(a^2*b^2*x + a^3*b), ((2*a*b*c + a^2*d + (2*b^2*c + a*b*d)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + 2*(b^2*c*x + a*b*c)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (a*b*c - a^2*d)*sqrt(d*x + c))/(a^2*b^2*x + a^3*b)]","A",0
467,1,770,0,1.800116," ","integrate((d*x+c)^(3/2)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{2} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + 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^{2} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{2} c - 3 \, a b d\right)} x^{2} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}, -\frac{{\left({\left(4 \, b^{2} c - a b d\right)} x^{2} + {\left(4 \, a b c - a^{2} d\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + 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^{2} + {\left(4 \, a b c - 3 \, a^{2} d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(a^{2} c + {\left(2 \, a b c - a^{2} d\right)} x\right)} \sqrt{d x + c}}{a^{3} b x^{2} + a^{4} x}\right]"," ",0,"[-1/2*(((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + ((4*b^2*c - 3*a*b*d)*x^2 + (4*a*b*c - 3*a^2*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a^2*c + (2*a*b*c - a^2*d)*x)*sqrt(d*x + c))/(a^3*b*x^2 + a^4*x), -1/2*(2*((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^2*c - 3*a*b*d)*x^2 + (4*a*b*c - 3*a^2*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a^2*c + (2*a*b*c - a^2*d)*x)*sqrt(d*x + c))/(a^3*b*x^2 + a^4*x), -1/2*(2*((4*b^2*c - 3*a*b*d)*x^2 + (4*a*b*c - 3*a^2*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + ((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a^2*c + (2*a*b*c - a^2*d)*x)*sqrt(d*x + c))/(a^3*b*x^2 + a^4*x), -(((4*b^2*c - a*b*d)*x^2 + (4*a*b*c - a^2*d)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^2*c - 3*a*b*d)*x^2 + (4*a*b*c - 3*a^2*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (a^2*c + (2*a*b*c - a^2*d)*x)*sqrt(d*x + c))/(a^3*b*x^2 + a^4*x)]","A",0
468,1,788,0,1.083186," ","integrate(x^3*(d*x+c)^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(6 \, a^{3} b^{2} c^{2} d^{2} - 17 \, a^{4} b c d^{3} + 11 \, a^{5} d^{4} + {\left(6 \, a^{2} b^{3} c^{2} d^{2} - 17 \, a^{3} b^{2} c d^{3} + 11 \, a^{4} b d^{4}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(70 \, b^{5} d^{4} x^{5} - 20 \, a b^{4} c^{4} - 180 \, a^{2} b^{3} c^{3} d + 3213 \, a^{3} b^{2} c^{2} d^{2} - 6510 \, a^{4} b c d^{3} + 3465 \, a^{5} d^{4} + 10 \, {\left(19 \, b^{5} c d^{3} - 11 \, a b^{4} d^{4}\right)} x^{4} + 2 \, {\left(75 \, b^{5} c^{2} d^{2} - 175 \, a b^{4} c d^{3} + 99 \, a^{2} b^{3} d^{4}\right)} x^{3} + 2 \, {\left(5 \, b^{5} c^{3} d - 195 \, a b^{4} c^{2} d^{2} + 423 \, a^{2} b^{3} c d^{3} - 231 \, a^{3} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(10 \, b^{5} c^{4} + 85 \, a b^{4} c^{3} d - 1179 \, a^{2} b^{3} c^{2} d^{2} + 2247 \, a^{3} b^{2} c d^{3} - 1155 \, a^{4} b d^{4}\right)} x\right)} \sqrt{d x + c}}{630 \, {\left(b^{7} d^{2} x + a b^{6} d^{2}\right)}}, -\frac{315 \, {\left(6 \, a^{3} b^{2} c^{2} d^{2} - 17 \, a^{4} b c d^{3} + 11 \, a^{5} d^{4} + {\left(6 \, a^{2} b^{3} c^{2} d^{2} - 17 \, a^{3} b^{2} c d^{3} + 11 \, a^{4} b d^{4}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(70 \, b^{5} d^{4} x^{5} - 20 \, a b^{4} c^{4} - 180 \, a^{2} b^{3} c^{3} d + 3213 \, a^{3} b^{2} c^{2} d^{2} - 6510 \, a^{4} b c d^{3} + 3465 \, a^{5} d^{4} + 10 \, {\left(19 \, b^{5} c d^{3} - 11 \, a b^{4} d^{4}\right)} x^{4} + 2 \, {\left(75 \, b^{5} c^{2} d^{2} - 175 \, a b^{4} c d^{3} + 99 \, a^{2} b^{3} d^{4}\right)} x^{3} + 2 \, {\left(5 \, b^{5} c^{3} d - 195 \, a b^{4} c^{2} d^{2} + 423 \, a^{2} b^{3} c d^{3} - 231 \, a^{3} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(10 \, b^{5} c^{4} + 85 \, a b^{4} c^{3} d - 1179 \, a^{2} b^{3} c^{2} d^{2} + 2247 \, a^{3} b^{2} c d^{3} - 1155 \, a^{4} b d^{4}\right)} x\right)} \sqrt{d x + c}}{315 \, {\left(b^{7} d^{2} x + a b^{6} d^{2}\right)}}\right]"," ",0,"[1/630*(315*(6*a^3*b^2*c^2*d^2 - 17*a^4*b*c*d^3 + 11*a^5*d^4 + (6*a^2*b^3*c^2*d^2 - 17*a^3*b^2*c*d^3 + 11*a^4*b*d^4)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(70*b^5*d^4*x^5 - 20*a*b^4*c^4 - 180*a^2*b^3*c^3*d + 3213*a^3*b^2*c^2*d^2 - 6510*a^4*b*c*d^3 + 3465*a^5*d^4 + 10*(19*b^5*c*d^3 - 11*a*b^4*d^4)*x^4 + 2*(75*b^5*c^2*d^2 - 175*a*b^4*c*d^3 + 99*a^2*b^3*d^4)*x^3 + 2*(5*b^5*c^3*d - 195*a*b^4*c^2*d^2 + 423*a^2*b^3*c*d^3 - 231*a^3*b^2*d^4)*x^2 - 2*(10*b^5*c^4 + 85*a*b^4*c^3*d - 1179*a^2*b^3*c^2*d^2 + 2247*a^3*b^2*c*d^3 - 1155*a^4*b*d^4)*x)*sqrt(d*x + c))/(b^7*d^2*x + a*b^6*d^2), -1/315*(315*(6*a^3*b^2*c^2*d^2 - 17*a^4*b*c*d^3 + 11*a^5*d^4 + (6*a^2*b^3*c^2*d^2 - 17*a^3*b^2*c*d^3 + 11*a^4*b*d^4)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (70*b^5*d^4*x^5 - 20*a*b^4*c^4 - 180*a^2*b^3*c^3*d + 3213*a^3*b^2*c^2*d^2 - 6510*a^4*b*c*d^3 + 3465*a^5*d^4 + 10*(19*b^5*c*d^3 - 11*a*b^4*d^4)*x^4 + 2*(75*b^5*c^2*d^2 - 175*a*b^4*c*d^3 + 99*a^2*b^3*d^4)*x^3 + 2*(5*b^5*c^3*d - 195*a*b^4*c^2*d^2 + 423*a^2*b^3*c*d^3 - 231*a^3*b^2*d^4)*x^2 - 2*(10*b^5*c^4 + 85*a*b^4*c^3*d - 1179*a^2*b^3*c^2*d^2 + 2247*a^3*b^2*c*d^3 - 1155*a^4*b*d^4)*x)*sqrt(d*x + c))/(b^7*d^2*x + a*b^6*d^2)]","B",0
469,1,607,0,2.197048," ","integrate(x^2*(d*x+c)^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, a^{2} b^{2} c^{2} d - 13 \, a^{3} b c d^{2} + 9 \, a^{4} d^{3} + {\left(4 \, a b^{3} c^{2} d - 13 \, a^{2} b^{2} c d^{2} + 9 \, a^{3} b d^{3}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(30 \, b^{4} d^{3} x^{4} + 30 \, a b^{3} c^{3} - 749 \, a^{2} b^{2} c^{2} d + 1680 \, a^{3} b c d^{2} - 945 \, a^{4} d^{3} + 18 \, {\left(5 \, b^{4} c d^{2} - 3 \, a b^{3} d^{3}\right)} x^{3} + 2 \, {\left(45 \, b^{4} c^{2} d - 109 \, a b^{3} c d^{2} + 63 \, a^{2} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(15 \, b^{4} c^{3} - 277 \, a b^{3} c^{2} d + 581 \, a^{2} b^{2} c d^{2} - 315 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x + c}}{210 \, {\left(b^{6} d x + a b^{5} d\right)}}, \frac{105 \, {\left(4 \, a^{2} b^{2} c^{2} d - 13 \, a^{3} b c d^{2} + 9 \, a^{4} d^{3} + {\left(4 \, a b^{3} c^{2} d - 13 \, a^{2} b^{2} c d^{2} + 9 \, a^{3} b d^{3}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(30 \, b^{4} d^{3} x^{4} + 30 \, a b^{3} c^{3} - 749 \, a^{2} b^{2} c^{2} d + 1680 \, a^{3} b c d^{2} - 945 \, a^{4} d^{3} + 18 \, {\left(5 \, b^{4} c d^{2} - 3 \, a b^{3} d^{3}\right)} x^{3} + 2 \, {\left(45 \, b^{4} c^{2} d - 109 \, a b^{3} c d^{2} + 63 \, a^{2} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(15 \, b^{4} c^{3} - 277 \, a b^{3} c^{2} d + 581 \, a^{2} b^{2} c d^{2} - 315 \, a^{3} b d^{3}\right)} x\right)} \sqrt{d x + c}}{105 \, {\left(b^{6} d x + a b^{5} d\right)}}\right]"," ",0,"[1/210*(105*(4*a^2*b^2*c^2*d - 13*a^3*b*c*d^2 + 9*a^4*d^3 + (4*a*b^3*c^2*d - 13*a^2*b^2*c*d^2 + 9*a^3*b*d^3)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(30*b^4*d^3*x^4 + 30*a*b^3*c^3 - 749*a^2*b^2*c^2*d + 1680*a^3*b*c*d^2 - 945*a^4*d^3 + 18*(5*b^4*c*d^2 - 3*a*b^3*d^3)*x^3 + 2*(45*b^4*c^2*d - 109*a*b^3*c*d^2 + 63*a^2*b^2*d^3)*x^2 + 2*(15*b^4*c^3 - 277*a*b^3*c^2*d + 581*a^2*b^2*c*d^2 - 315*a^3*b*d^3)*x)*sqrt(d*x + c))/(b^6*d*x + a*b^5*d), 1/105*(105*(4*a^2*b^2*c^2*d - 13*a^3*b*c*d^2 + 9*a^4*d^3 + (4*a*b^3*c^2*d - 13*a^2*b^2*c*d^2 + 9*a^3*b*d^3)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (30*b^4*d^3*x^4 + 30*a*b^3*c^3 - 749*a^2*b^2*c^2*d + 1680*a^3*b*c*d^2 - 945*a^4*d^3 + 18*(5*b^4*c*d^2 - 3*a*b^3*d^3)*x^3 + 2*(45*b^4*c^2*d - 109*a*b^3*c*d^2 + 63*a^2*b^2*d^3)*x^2 + 2*(15*b^4*c^3 - 277*a*b^3*c^2*d + 581*a^2*b^2*c*d^2 - 315*a^3*b*d^3)*x)*sqrt(d*x + c))/(b^6*d*x + a*b^5*d)]","A",0
470,1,450,0,1.459000," ","integrate(x*(d*x+c)^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(2 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} - 9 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(6 \, b^{3} d^{2} x^{3} + 61 \, a b^{2} c^{2} - 170 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(11 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(23 \, b^{3} c^{2} - 59 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x + c}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(2 \, a b^{2} c^{2} - 9 \, a^{2} b c d + 7 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} - 9 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(6 \, b^{3} d^{2} x^{3} + 61 \, a b^{2} c^{2} - 170 \, a^{2} b c d + 105 \, a^{3} d^{2} + 2 \, {\left(11 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(23 \, b^{3} c^{2} - 59 \, a b^{2} c d + 35 \, a^{2} b d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[1/30*(15*(2*a*b^2*c^2 - 9*a^2*b*c*d + 7*a^3*d^2 + (2*b^3*c^2 - 9*a*b^2*c*d + 7*a^2*b*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(6*b^3*d^2*x^3 + 61*a*b^2*c^2 - 170*a^2*b*c*d + 105*a^3*d^2 + 2*(11*b^3*c*d - 7*a*b^2*d^2)*x^2 + 2*(23*b^3*c^2 - 59*a*b^2*c*d + 35*a^2*b*d^2)*x)*sqrt(d*x + c))/(b^5*x + a*b^4), -1/15*(15*(2*a*b^2*c^2 - 9*a^2*b*c*d + 7*a^3*d^2 + (2*b^3*c^2 - 9*a*b^2*c*d + 7*a^2*b*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (6*b^3*d^2*x^3 + 61*a*b^2*c^2 - 170*a^2*b*c*d + 105*a^3*d^2 + 2*(11*b^3*c*d - 7*a*b^2*d^2)*x^2 + 2*(23*b^3*c^2 - 59*a*b^2*c*d + 35*a^2*b*d^2)*x)*sqrt(d*x + c))/(b^5*x + a*b^4)]","A",0
471,1,330,0,2.050391," ","integrate((d*x+c)^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c^{2} + 20 \, a b c d - 15 \, a^{2} d^{2} + 2 \, {\left(7 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{d x + c}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{15 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) - {\left(2 \, b^{2} d^{2} x^{2} - 3 \, b^{2} c^{2} + 20 \, a b c d - 15 \, a^{2} d^{2} + 2 \, {\left(7 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[-1/6*(15*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - 2*(2*b^2*d^2*x^2 - 3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 2*(7*b^2*c*d - 5*a*b*d^2)*x)*sqrt(d*x + c))/(b^4*x + a*b^3), -1/3*(15*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) - (2*b^2*d^2*x^2 - 3*b^2*c^2 + 20*a*b*c*d - 15*a^2*d^2 + 2*(7*b^2*c*d - 5*a*b*d^2)*x)*sqrt(d*x + c))/(b^4*x + a*b^3)]","A",0
472,1,865,0,1.918529," ","integrate((d*x+c)^(5/2)/x/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - 2 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{2} b d^{2} x + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{3} x + a^{3} b^{2}\right)}}, \frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + {\left(2 \, a^{2} b d^{2} x + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x + c}}{a^{2} b^{3} x + a^{3} b^{2}}, \frac{4 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(2 \, a^{2} b d^{2} x + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{3} x + a^{3} b^{2}\right)}}, \frac{{\left(2 \, a b^{2} c^{2} + a^{2} b c d - 3 \, a^{3} d^{2} + {\left(2 \, b^{3} c^{2} + a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + 2 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(2 \, a^{2} b d^{2} x + a b^{2} c^{2} - 2 \, a^{2} b c d + 3 \, a^{3} d^{2}\right)} \sqrt{d x + c}}{a^{2} b^{3} x + a^{3} b^{2}}\right]"," ",0,"[-1/2*((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - 2*(b^3*c^2*x + a*b^2*c^2)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^2*b*d^2*x + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x + c))/(a^2*b^3*x + a^3*b^2), ((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (b^3*c^2*x + a*b^2*c^2)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + (2*a^2*b*d^2*x + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x + c))/(a^2*b^3*x + a^3*b^2), 1/2*(4*(b^3*c^2*x + a*b^2*c^2)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(2*a^2*b*d^2*x + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x + c))/(a^2*b^3*x + a^3*b^2), ((2*a*b^2*c^2 + a^2*b*c*d - 3*a^3*d^2 + (2*b^3*c^2 + a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + 2*(b^3*c^2*x + a*b^2*c^2)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (2*a^2*b*d^2*x + a*b^2*c^2 - 2*a^2*b*c*d + 3*a^3*d^2)*sqrt(d*x + c))/(a^2*b^3*x + a^3*b^2)]","A",0
473,1,1002,0,2.028096," ","integrate((d*x+c)^(5/2)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b^{2} x^{2} + a^{4} b x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b^{2} x^{2} + a^{4} b x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b^{2} x^{2} + a^{4} b x\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(a^{2} b c^{2} + {\left(2 \, a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x\right)} \sqrt{d x + c}}{a^{3} b^{2} x^{2} + a^{4} b x}\right]"," ",0,"[-1/2*(((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + ((4*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)*sqrt(d*x + c))/(a^3*b^2*x^2 + a^4*b*x), -1/2*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)*sqrt(d*x + c))/(a^3*b^2*x^2 + a^4*b*x), -1/2*(2*((4*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)*sqrt(d*x + c))/(a^3*b^2*x^2 + a^4*b*x), -(((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((4*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (4*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (a^2*b*c^2 + (2*a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x)*sqrt(d*x + c))/(a^3*b^2*x^2 + a^4*b*x)]","A",0
474,1,1173,0,1.910869," ","integrate((d*x+c)^(5/2)/x^3/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left({\left(6 \, b^{3} c^{2} - 7 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(6 \, a b^{2} c^{2} - 7 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + {\left({\left(24 \, b^{3} c^{2} - 40 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} x^{3} + {\left(24 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{3} c^{2} - {\left(12 \, a b^{2} c^{2} - 17 \, a^{2} b c d + 4 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{2} b c^{2} - 3 \, a^{3} c d\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}, \frac{8 \, {\left({\left(6 \, b^{3} c^{2} - 7 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(6 \, a b^{2} c^{2} - 7 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(24 \, b^{3} c^{2} - 40 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} x^{3} + {\left(24 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(2 \, a^{3} c^{2} - {\left(12 \, a b^{2} c^{2} - 17 \, a^{2} b c d + 4 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{2} b c^{2} - 3 \, a^{3} c d\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}, \frac{{\left({\left(24 \, b^{3} c^{2} - 40 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} x^{3} + {\left(24 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 2 \, {\left({\left(6 \, b^{3} c^{2} - 7 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(6 \, a b^{2} c^{2} - 7 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) - {\left(2 \, a^{3} c^{2} - {\left(12 \, a b^{2} c^{2} - 17 \, a^{2} b c d + 4 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{2} b c^{2} - 3 \, a^{3} c d\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}, \frac{4 \, {\left({\left(6 \, b^{3} c^{2} - 7 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(6 \, a b^{2} c^{2} - 7 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left({\left(24 \, b^{3} c^{2} - 40 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} x^{3} + {\left(24 \, a b^{2} c^{2} - 40 \, a^{2} b c d + 15 \, a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(2 \, a^{3} c^{2} - {\left(12 \, a b^{2} c^{2} - 17 \, a^{2} b c d + 4 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{2} b c^{2} - 3 \, a^{3} c d\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}\right]"," ",0,"[1/8*(4*((6*b^3*c^2 - 7*a*b^2*c*d + a^2*b*d^2)*x^3 + (6*a*b^2*c^2 - 7*a^2*b*c*d + a^3*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + ((24*b^3*c^2 - 40*a*b^2*c*d + 15*a^2*b*d^2)*x^3 + (24*a*b^2*c^2 - 40*a^2*b*c*d + 15*a^3*d^2)*x^2)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^3*c^2 - (12*a*b^2*c^2 - 17*a^2*b*c*d + 4*a^3*d^2)*x^2 - 3*(2*a^2*b*c^2 - 3*a^3*c*d)*x)*sqrt(d*x + c))/(a^4*b*x^3 + a^5*x^2), 1/8*(8*((6*b^3*c^2 - 7*a*b^2*c*d + a^2*b*d^2)*x^3 + (6*a*b^2*c^2 - 7*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((24*b^3*c^2 - 40*a*b^2*c*d + 15*a^2*b*d^2)*x^3 + (24*a*b^2*c^2 - 40*a^2*b*c*d + 15*a^3*d^2)*x^2)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(2*a^3*c^2 - (12*a*b^2*c^2 - 17*a^2*b*c*d + 4*a^3*d^2)*x^2 - 3*(2*a^2*b*c^2 - 3*a^3*c*d)*x)*sqrt(d*x + c))/(a^4*b*x^3 + a^5*x^2), 1/4*(((24*b^3*c^2 - 40*a*b^2*c*d + 15*a^2*b*d^2)*x^3 + (24*a*b^2*c^2 - 40*a^2*b*c*d + 15*a^3*d^2)*x^2)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 2*((6*b^3*c^2 - 7*a*b^2*c*d + a^2*b*d^2)*x^3 + (6*a*b^2*c^2 - 7*a^2*b*c*d + a^3*d^2)*x^2)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) - (2*a^3*c^2 - (12*a*b^2*c^2 - 17*a^2*b*c*d + 4*a^3*d^2)*x^2 - 3*(2*a^2*b*c^2 - 3*a^3*c*d)*x)*sqrt(d*x + c))/(a^4*b*x^3 + a^5*x^2), 1/4*(4*((6*b^3*c^2 - 7*a*b^2*c*d + a^2*b*d^2)*x^3 + (6*a*b^2*c^2 - 7*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + ((24*b^3*c^2 - 40*a*b^2*c*d + 15*a^2*b*d^2)*x^3 + (24*a*b^2*c^2 - 40*a^2*b*c*d + 15*a^3*d^2)*x^2)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (2*a^3*c^2 - (12*a*b^2*c^2 - 17*a^2*b*c*d + 4*a^3*d^2)*x^2 - 3*(2*a^2*b*c^2 - 3*a^3*c*d)*x)*sqrt(d*x + c))/(a^4*b*x^3 + a^5*x^2)]","A",0
475,1,1482,0,2.297306," ","integrate((d*x+c)^(5/2)/x^4/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{24 \, {\left({\left(8 \, b^{3} c^{3} - 11 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2}\right)} x^{4} + {\left(8 \, a b^{2} c^{3} - 11 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) - 3 \, {\left({\left(64 \, b^{4} c^{3} - 120 \, a b^{3} c^{2} d + 60 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4} + {\left(64 \, a b^{3} c^{3} - 120 \, a^{2} b^{2} c^{2} d + 60 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(8 \, a^{4} c^{3} + 3 \, {\left(32 \, a b^{3} c^{3} - 52 \, a^{2} b^{2} c^{2} d + 19 \, a^{3} b c d^{2}\right)} x^{3} + {\left(48 \, a^{2} b^{2} c^{3} - 82 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(8 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{d x + c}}{48 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}, \frac{48 \, {\left({\left(8 \, b^{3} c^{3} - 11 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2}\right)} x^{4} + {\left(8 \, a b^{2} c^{3} - 11 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 3 \, {\left({\left(64 \, b^{4} c^{3} - 120 \, a b^{3} c^{2} d + 60 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4} + {\left(64 \, a b^{3} c^{3} - 120 \, a^{2} b^{2} c^{2} d + 60 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} x^{3}\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(8 \, a^{4} c^{3} + 3 \, {\left(32 \, a b^{3} c^{3} - 52 \, a^{2} b^{2} c^{2} d + 19 \, a^{3} b c d^{2}\right)} x^{3} + {\left(48 \, a^{2} b^{2} c^{3} - 82 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(8 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{d x + c}}{48 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}, -\frac{3 \, {\left({\left(64 \, b^{4} c^{3} - 120 \, a b^{3} c^{2} d + 60 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4} + {\left(64 \, a b^{3} c^{3} - 120 \, a^{2} b^{2} c^{2} d + 60 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 12 \, {\left({\left(8 \, b^{3} c^{3} - 11 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2}\right)} x^{4} + {\left(8 \, a b^{2} c^{3} - 11 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + {\left(8 \, a^{4} c^{3} + 3 \, {\left(32 \, a b^{3} c^{3} - 52 \, a^{2} b^{2} c^{2} d + 19 \, a^{3} b c d^{2}\right)} x^{3} + {\left(48 \, a^{2} b^{2} c^{3} - 82 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(8 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{d x + c}}{24 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}, \frac{24 \, {\left({\left(8 \, b^{3} c^{3} - 11 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2}\right)} x^{4} + {\left(8 \, a b^{2} c^{3} - 11 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 3 \, {\left({\left(64 \, b^{4} c^{3} - 120 \, a b^{3} c^{2} d + 60 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x^{4} + {\left(64 \, a b^{3} c^{3} - 120 \, a^{2} b^{2} c^{2} d + 60 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} x^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(8 \, a^{4} c^{3} + 3 \, {\left(32 \, a b^{3} c^{3} - 52 \, a^{2} b^{2} c^{2} d + 19 \, a^{3} b c d^{2}\right)} x^{3} + {\left(48 \, a^{2} b^{2} c^{3} - 82 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(8 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{d x + c}}{24 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}\right]"," ",0,"[1/48*(24*((8*b^3*c^3 - 11*a*b^2*c^2*d + 3*a^2*b*c*d^2)*x^4 + (8*a*b^2*c^3 - 11*a^2*b*c^2*d + 3*a^3*c*d^2)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) - 3*((64*b^4*c^3 - 120*a*b^3*c^2*d + 60*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4 + (64*a*b^3*c^3 - 120*a^2*b^2*c^2*d + 60*a^3*b*c*d^2 - 5*a^4*d^3)*x^3)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(8*a^4*c^3 + 3*(32*a*b^3*c^3 - 52*a^2*b^2*c^2*d + 19*a^3*b*c*d^2)*x^3 + (48*a^2*b^2*c^3 - 82*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(8*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3), 1/48*(48*((8*b^3*c^3 - 11*a*b^2*c^2*d + 3*a^2*b*c*d^2)*x^4 + (8*a*b^2*c^3 - 11*a^2*b*c^2*d + 3*a^3*c*d^2)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 3*((64*b^4*c^3 - 120*a*b^3*c^2*d + 60*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4 + (64*a*b^3*c^3 - 120*a^2*b^2*c^2*d + 60*a^3*b*c*d^2 - 5*a^4*d^3)*x^3)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(8*a^4*c^3 + 3*(32*a*b^3*c^3 - 52*a^2*b^2*c^2*d + 19*a^3*b*c*d^2)*x^3 + (48*a^2*b^2*c^3 - 82*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(8*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3), -1/24*(3*((64*b^4*c^3 - 120*a*b^3*c^2*d + 60*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4 + (64*a*b^3*c^3 - 120*a^2*b^2*c^2*d + 60*a^3*b*c*d^2 - 5*a^4*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 12*((8*b^3*c^3 - 11*a*b^2*c^2*d + 3*a^2*b*c*d^2)*x^4 + (8*a*b^2*c^3 - 11*a^2*b*c^2*d + 3*a^3*c*d^2)*x^3)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + (8*a^4*c^3 + 3*(32*a*b^3*c^3 - 52*a^2*b^2*c^2*d + 19*a^3*b*c*d^2)*x^3 + (48*a^2*b^2*c^3 - 82*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(8*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3), 1/24*(24*((8*b^3*c^3 - 11*a*b^2*c^2*d + 3*a^2*b*c*d^2)*x^4 + (8*a*b^2*c^3 - 11*a^2*b*c^2*d + 3*a^3*c*d^2)*x^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 3*((64*b^4*c^3 - 120*a*b^3*c^2*d + 60*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x^4 + (64*a*b^3*c^3 - 120*a^2*b^2*c^2*d + 60*a^3*b*c*d^2 - 5*a^4*d^3)*x^3)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (8*a^4*c^3 + 3*(32*a*b^3*c^3 - 52*a^2*b^2*c^2*d + 19*a^3*b*c*d^2)*x^3 + (48*a^2*b^2*c^3 - 82*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(8*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3)]","A",0
476,1,1164,0,2.099433," ","integrate(1/x^2/(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{2} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + a}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\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\right)} \sqrt{d x + c}}{2 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{2} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{2} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) - {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\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\right)} \sqrt{d x + c}}{2 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{2} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{2} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + 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\right)} \sqrt{d x + c}}{2 \, {\left({\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{2} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x\right)}}, -\frac{{\left({\left(4 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d\right)} x^{2} + {\left(4 \, a b^{2} c^{3} - 5 \, a^{2} b c^{2} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) + {\left({\left(4 \, b^{3} c^{2} - 3 \, a b^{2} c d - a^{2} b d^{2}\right)} x^{2} + {\left(4 \, a b^{2} c^{2} - 3 \, a^{2} b c d - a^{3} d^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + 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\right)} \sqrt{d x + c}}{{\left(a^{3} b^{2} c^{3} - a^{4} b c^{2} d\right)} x^{2} + {\left(a^{4} b c^{3} - a^{5} c^{2} d\right)} x}\right]"," ",0,"[1/2*(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^2 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d - 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt(d*x + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^2 + (a^4*b*c^3 - a^5*c^2*d)*x), -1/2*(2*((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^2 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) - ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt(d*x + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^2 + (a^4*b*c^3 - a^5*c^2*d)*x), -1/2*(2*((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - ((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^2 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d - 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + 2*(a^2*b*c^2 - a^3*c*d + (2*a*b^2*c^2 - a^2*b*c*d)*x)*sqrt(d*x + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^2 + (a^4*b*c^3 - a^5*c^2*d)*x), -(((4*b^3*c^3 - 5*a*b^2*c^2*d)*x^2 + (4*a*b^2*c^3 - 5*a^2*b*c^2*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) + ((4*b^3*c^2 - 3*a*b^2*c*d - a^2*b*d^2)*x^2 + (4*a*b^2*c^2 - 3*a^2*b*c*d - a^3*d^2)*x)*sqrt(-c)*arctan(sqrt(d*x + 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)*sqrt(d*x + c))/((a^3*b^2*c^3 - a^4*b*c^2*d)*x^2 + (a^4*b*c^3 - a^5*c^2*d)*x)]","A",0
477,1,2312,0,3.263242," ","integrate(1/x^2/(b*x+a)^2/(d*x+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^{3} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + 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^{3} + {\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^{2} + {\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\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\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^{2} + {\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\right)} \sqrt{d x + c}}{2 \, {\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^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{3} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + 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^{3} + {\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^{2} + {\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\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\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^{2} + {\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\right)} \sqrt{d x + c}}{2 \, {\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^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x\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^{3} + {\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^{2} + {\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\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{3} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + 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^{2} + {\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\right)} \sqrt{d x + c}}{2 \, {\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^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x\right)}}, -\frac{{\left({\left(4 \, b^{4} c^{4} d - 7 \, a b^{3} c^{3} d^{2}\right)} x^{3} + {\left(4 \, b^{4} c^{5} - 3 \, a b^{3} c^{4} d - 7 \, a^{2} b^{2} c^{3} d^{2}\right)} x^{2} + {\left(4 \, a b^{3} c^{5} - 7 \, a^{2} b^{2} c^{4} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + 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^{3} + {\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^{2} + {\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\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + 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^{2} + {\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\right)} \sqrt{d x + c}}{{\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^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x}\right]"," ",0,"[-1/2*(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^3 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^2 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d + 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + 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^3 + (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^2 + (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)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 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^2 + (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)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x), -1/2*(2*((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^3 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^2 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + 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^3 + (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^2 + (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)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 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^2 + (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)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x), -1/2*(2*((4*b^4*c^3*d - 5*a*b^3*c^2*d^2 - 2*a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x^3 + (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^2 + (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)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + ((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^3 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^2 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d + 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + 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^2 + (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)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x), -(((4*b^4*c^4*d - 7*a*b^3*c^3*d^2)*x^3 + (4*b^4*c^5 - 3*a*b^3*c^4*d - 7*a^2*b^2*c^3*d^2)*x^2 + (4*a*b^3*c^5 - 7*a^2*b^2*c^4*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + 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^3 + (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^2 + (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)*sqrt(-c)*arctan(sqrt(d*x + 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^2 + (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)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x)]","B",0
478,1,3872,0,9.605396," ","integrate(1/x^2/(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{4} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{3} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{2} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + a}\right) + 3 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{3} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{d x + c}}{6 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}, -\frac{6 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{4} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{3} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{2} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) - 3 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{c} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{3} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{d x + c}}{6 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}, -\frac{6 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - 3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{4} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{3} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{2} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x\right)} \sqrt{\frac{b}{b c - a d}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, {\left(b c - a d\right)} \sqrt{d x + c} \sqrt{\frac{b}{b c - a d}}}{b x + a}\right) + 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{3} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{d x + c}}{6 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}, -\frac{3 \, {\left({\left(4 \, b^{5} c^{5} d^{2} - 9 \, a b^{4} c^{4} d^{3}\right)} x^{4} + {\left(8 \, b^{5} c^{6} d - 14 \, a b^{4} c^{5} d^{2} - 9 \, a^{2} b^{3} c^{4} d^{3}\right)} x^{3} + {\left(4 \, b^{5} c^{7} - a b^{4} c^{6} d - 18 \, a^{2} b^{3} c^{5} d^{2}\right)} x^{2} + {\left(4 \, a b^{4} c^{7} - 9 \, a^{2} b^{3} c^{6} d\right)} x\right)} \sqrt{-\frac{b}{b c - a d}} \arctan\left(-\frac{{\left(b c - a d\right)} \sqrt{d x + c} \sqrt{-\frac{b}{b c - a d}}}{b d x + b c}\right) + 3 \, {\left({\left(4 \, b^{5} c^{4} d^{2} - 7 \, a b^{4} c^{3} d^{3} - 3 \, a^{2} b^{3} c^{2} d^{4} + 11 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(8 \, b^{5} c^{5} d - 10 \, a b^{4} c^{4} d^{2} - 13 \, a^{2} b^{3} c^{3} d^{3} + 19 \, a^{3} b^{2} c^{2} d^{4} + a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(4 \, b^{5} c^{6} + a b^{4} c^{5} d - 17 \, a^{2} b^{3} c^{4} d^{2} + 5 \, a^{3} b^{2} c^{3} d^{3} + 17 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(4 \, a b^{4} c^{6} - 7 \, a^{2} b^{3} c^{5} d - 3 \, a^{3} b^{2} c^{4} d^{2} + 11 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + 3 \, {\left(2 \, a b^{4} c^{4} d^{2} - 3 \, a^{2} b^{3} c^{3} d^{3} + 11 \, a^{3} b^{2} c^{2} d^{4} - 5 \, a^{4} b c d^{5}\right)} x^{3} + {\left(12 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 35 \, a^{3} b^{2} c^{3} d^{3} + 13 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(6 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 41 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{d x + c}}{3 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^4 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^3 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^2 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d - 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + 3*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^3 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x), -1/6*(6*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^4 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^3 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^2 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) - 3*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(c)*log((d*x + 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^3 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x), -1/6*(6*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - 3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^4 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^3 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^2 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x)*sqrt(b/(b*c - a*d))*log((b*d*x + 2*b*c - a*d - 2*(b*c - a*d)*sqrt(d*x + c)*sqrt(b/(b*c - a*d)))/(b*x + a)) + 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^3 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x), -1/3*(3*((4*b^5*c^5*d^2 - 9*a*b^4*c^4*d^3)*x^4 + (8*b^5*c^6*d - 14*a*b^4*c^5*d^2 - 9*a^2*b^3*c^4*d^3)*x^3 + (4*b^5*c^7 - a*b^4*c^6*d - 18*a^2*b^3*c^5*d^2)*x^2 + (4*a*b^4*c^7 - 9*a^2*b^3*c^6*d)*x)*sqrt(-b/(b*c - a*d))*arctan(-(b*c - a*d)*sqrt(d*x + c)*sqrt(-b/(b*c - a*d))/(b*d*x + b*c)) + 3*((4*b^5*c^4*d^2 - 7*a*b^4*c^3*d^3 - 3*a^2*b^3*c^2*d^4 + 11*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (8*b^5*c^5*d - 10*a*b^4*c^4*d^2 - 13*a^2*b^3*c^3*d^3 + 19*a^3*b^2*c^2*d^4 + a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (4*b^5*c^6 + a*b^4*c^5*d - 17*a^2*b^3*c^4*d^2 + 5*a^3*b^2*c^3*d^3 + 17*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (4*a*b^4*c^6 - 7*a^2*b^3*c^5*d - 3*a^3*b^2*c^4*d^2 + 11*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + 3*(2*a*b^4*c^4*d^2 - 3*a^2*b^3*c^3*d^3 + 11*a^3*b^2*c^2*d^4 - 5*a^4*b*c*d^5)*x^3 + (12*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 35*a^3*b^2*c^3*d^3 + 13*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (6*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 41*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x)]","B",0
479,1,295,0,1.470119," ","integrate(x^(5/2)*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(384 \, B b^{5} x^{4} - 105 \, B a^{4} b + 150 \, A a^{3} b^{2} + 48 \, {\left(B a b^{4} + 10 \, A b^{5}\right)} x^{3} - 8 \, {\left(7 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3840 \, b^{5}}, -\frac{15 \, {\left(7 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(384 \, B b^{5} x^{4} - 105 \, B a^{4} b + 150 \, A a^{3} b^{2} + 48 \, {\left(B a b^{4} + 10 \, A b^{5}\right)} x^{3} - 8 \, {\left(7 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{1920 \, b^{5}}\right]"," ",0,"[-1/3840*(15*(7*B*a^5 - 10*A*a^4*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(384*B*b^5*x^4 - 105*B*a^4*b + 150*A*a^3*b^2 + 48*(B*a*b^4 + 10*A*b^5)*x^3 - 8*(7*B*a^2*b^3 - 10*A*a*b^4)*x^2 + 10*(7*B*a^3*b^2 - 10*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5, -1/1920*(15*(7*B*a^5 - 10*A*a^4*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (384*B*b^5*x^4 - 105*B*a^4*b + 150*A*a^3*b^2 + 48*(B*a*b^4 + 10*A*b^5)*x^3 - 8*(7*B*a^2*b^3 - 10*A*a*b^4)*x^2 + 10*(7*B*a^3*b^2 - 10*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5]","A",0
480,1,246,0,1.898976," ","integrate(x^(3/2)*(B*x+A)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(48 \, B b^{4} x^{3} + 15 \, B a^{3} b - 24 \, A a^{2} b^{2} + 8 \, {\left(B a b^{3} + 8 \, A b^{4}\right)} x^{2} - 2 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{384 \, b^{4}}, \frac{3 \, {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(48 \, B b^{4} x^{3} + 15 \, B a^{3} b - 24 \, A a^{2} b^{2} + 8 \, {\left(B a b^{3} + 8 \, A b^{4}\right)} x^{2} - 2 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{192 \, b^{4}}\right]"," ",0,"[-1/384*(3*(5*B*a^4 - 8*A*a^3*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(48*B*b^4*x^3 + 15*B*a^3*b - 24*A*a^2*b^2 + 8*(B*a*b^3 + 8*A*b^4)*x^2 - 2*(5*B*a^2*b^2 - 8*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4, 1/192*(3*(5*B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (48*B*b^4*x^3 + 15*B*a^3*b - 24*A*a^2*b^2 + 8*(B*a*b^3 + 8*A*b^4)*x^2 - 2*(5*B*a^2*b^2 - 8*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4]","A",0
481,1,197,0,1.878667," ","integrate((B*x+A)*x^(1/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(8 \, B b^{3} x^{2} - 3 \, B a^{2} b + 6 \, A a b^{2} + 2 \, {\left(B a b^{2} + 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{3}}, -\frac{3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(8 \, B b^{3} x^{2} - 3 \, B a^{2} b + 6 \, A a b^{2} + 2 \, {\left(B a b^{2} + 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{3}}\right]"," ",0,"[-1/48*(3*(B*a^3 - 2*A*a^2*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(8*B*b^3*x^2 - 3*B*a^2*b + 6*A*a*b^2 + 2*(B*a*b^2 + 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3, -1/24*(3*(B*a^3 - 2*A*a^2*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (8*B*b^3*x^2 - 3*B*a^2*b + 6*A*a*b^2 + 2*(B*a*b^2 + 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
482,1,146,0,1.810364," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(2 \, B b^{2} x + B a b + 4 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b^{2}}, \frac{{\left(B a^{2} - 4 \, A a b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(2 \, B b^{2} x + B a b + 4 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b^{2}}\right]"," ",0,"[-1/8*((B*a^2 - 4*A*a*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(2*B*b^2*x + B*a*b + 4*A*b^2)*sqrt(b*x + a)*sqrt(x))/b^2, 1/4*((B*a^2 - 4*A*a*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (2*B*b^2*x + B*a*b + 4*A*b^2)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
483,1,131,0,1.557880," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B a + 2 \, A b\right)} \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(B b x - 2 \, A b\right)} \sqrt{b x + a} \sqrt{x}}{2 \, b x}, -\frac{{\left(B a + 2 \, A b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(B b x - 2 \, A b\right)} \sqrt{b x + a} \sqrt{x}}{b x}\right]"," ",0,"[1/2*((B*a + 2*A*b)*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(B*b*x - 2*A*b)*sqrt(b*x + a)*sqrt(x))/(b*x), -((B*a + 2*A*b)*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (B*b*x - 2*A*b)*sqrt(b*x + a)*sqrt(x))/(b*x)]","A",0
484,1,134,0,1.438117," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, B a \sqrt{b} x^{2} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(A a + {\left(3 \, B a + A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, a x^{2}}, -\frac{2 \, {\left(3 \, B a \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(A a + {\left(3 \, B a + A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}\right)}}{3 \, a x^{2}}\right]"," ",0,"[1/3*(3*B*a*sqrt(b)*x^2*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(A*a + (3*B*a + A*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^2), -2/3*(3*B*a*sqrt(-b)*x^2*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (A*a + (3*B*a + A*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^2)]","A",0
485,1,51,0,1.697799," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{2} + {\left(5 \, B a b - 2 \, A b^{2}\right)} x^{2} + {\left(5 \, B a^{2} + A a b\right)} x\right)} \sqrt{b x + a}}{15 \, a^{2} x^{\frac{5}{2}}}"," ",0,"-2/15*(3*A*a^2 + (5*B*a*b - 2*A*b^2)*x^2 + (5*B*a^2 + A*a*b)*x)*sqrt(b*x + a)/(a^2*x^(5/2))","A",0
486,1,76,0,1.318979," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A a^{3} - 2 \, {\left(7 \, B a b^{2} - 4 \, A b^{3}\right)} x^{3} + {\left(7 \, B a^{2} b - 4 \, A a b^{2}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} + A a^{2} b\right)} x\right)} \sqrt{b x + a}}{105 \, a^{3} x^{\frac{7}{2}}}"," ",0,"-2/105*(15*A*a^3 - 2*(7*B*a*b^2 - 4*A*b^3)*x^3 + (7*B*a^2*b - 4*A*a*b^2)*x^2 + 3*(7*B*a^3 + A*a^2*b)*x)*sqrt(b*x + a)/(a^3*x^(7/2))","A",0
487,1,101,0,1.443904," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A a^{4} + 8 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} x^{4} - 4 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} x^{3} + 3 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} x^{2} + 5 \, {\left(9 \, B a^{4} + A a^{3} b\right)} x\right)} \sqrt{b x + a}}{315 \, a^{4} x^{\frac{9}{2}}}"," ",0,"-2/315*(35*A*a^4 + 8*(3*B*a*b^3 - 2*A*b^4)*x^4 - 4*(3*B*a^2*b^2 - 2*A*a*b^3)*x^3 + 3*(3*B*a^3*b - 2*A*a^2*b^2)*x^2 + 5*(9*B*a^4 + A*a^3*b)*x)*sqrt(b*x + a)/(a^4*x^(9/2))","A",0
488,1,125,0,1.435790," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A a^{5} - 16 \, {\left(11 \, B a b^{4} - 8 \, A b^{5}\right)} x^{5} + 8 \, {\left(11 \, B a^{2} b^{3} - 8 \, A a b^{4}\right)} x^{4} - 6 \, {\left(11 \, B a^{3} b^{2} - 8 \, A a^{2} b^{3}\right)} x^{3} + 5 \, {\left(11 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} x^{2} + 35 \, {\left(11 \, B a^{5} + A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3465 \, a^{5} x^{\frac{11}{2}}}"," ",0,"-2/3465*(315*A*a^5 - 16*(11*B*a*b^4 - 8*A*b^5)*x^5 + 8*(11*B*a^2*b^3 - 8*A*a*b^4)*x^4 - 6*(11*B*a^3*b^2 - 8*A*a^2*b^3)*x^3 + 5*(11*B*a^4*b - 8*A*a^3*b^2)*x^2 + 35*(11*B*a^5 + A*a^4*b)*x)*sqrt(b*x + a)/(a^5*x^(11/2))","A",0
489,1,149,0,0.898533," ","integrate((B*x+A)*(b*x+a)^(1/2)/x^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3465 \, A a^{6} + 128 \, {\left(13 \, B a b^{5} - 10 \, A b^{6}\right)} x^{6} - 64 \, {\left(13 \, B a^{2} b^{4} - 10 \, A a b^{5}\right)} x^{5} + 48 \, {\left(13 \, B a^{3} b^{3} - 10 \, A a^{2} b^{4}\right)} x^{4} - 40 \, {\left(13 \, B a^{4} b^{2} - 10 \, A a^{3} b^{3}\right)} x^{3} + 35 \, {\left(13 \, B a^{5} b - 10 \, A a^{4} b^{2}\right)} x^{2} + 315 \, {\left(13 \, B a^{6} + A a^{5} b\right)} x\right)} \sqrt{b x + a}}{45045 \, a^{6} x^{\frac{13}{2}}}"," ",0,"-2/45045*(3465*A*a^6 + 128*(13*B*a*b^5 - 10*A*b^6)*x^6 - 64*(13*B*a^2*b^4 - 10*A*a*b^5)*x^5 + 48*(13*B*a^3*b^3 - 10*A*a^2*b^4)*x^4 - 40*(13*B*a^4*b^2 - 10*A*a^3*b^3)*x^3 + 35*(13*B*a^5*b - 10*A*a^4*b^2)*x^2 + 315*(13*B*a^6 + A*a^5*b)*x)*sqrt(b*x + a)/(a^6*x^(13/2))","A",0
490,1,343,0,1.887950," ","integrate(x^(5/2)*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(1280 \, B b^{6} x^{5} - 105 \, B a^{5} b + 180 \, A a^{4} b^{2} + 128 \, {\left(13 \, B a b^{5} + 12 \, A b^{6}\right)} x^{4} + 48 \, {\left(B a^{2} b^{4} + 44 \, A a b^{5}\right)} x^{3} - 8 \, {\left(7 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15360 \, b^{5}}, -\frac{15 \, {\left(7 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(1280 \, B b^{6} x^{5} - 105 \, B a^{5} b + 180 \, A a^{4} b^{2} + 128 \, {\left(13 \, B a b^{5} + 12 \, A b^{6}\right)} x^{4} + 48 \, {\left(B a^{2} b^{4} + 44 \, A a b^{5}\right)} x^{3} - 8 \, {\left(7 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{7680 \, b^{5}}\right]"," ",0,"[-1/15360*(15*(7*B*a^6 - 12*A*a^5*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(1280*B*b^6*x^5 - 105*B*a^5*b + 180*A*a^4*b^2 + 128*(13*B*a*b^5 + 12*A*b^6)*x^4 + 48*(B*a^2*b^4 + 44*A*a*b^5)*x^3 - 8*(7*B*a^3*b^3 - 12*A*a^2*b^4)*x^2 + 10*(7*B*a^4*b^2 - 12*A*a^3*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5, -1/7680*(15*(7*B*a^6 - 12*A*a^5*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (1280*B*b^6*x^5 - 105*B*a^5*b + 180*A*a^4*b^2 + 128*(13*B*a*b^5 + 12*A*b^6)*x^4 + 48*(B*a^2*b^4 + 44*A*a*b^5)*x^3 - 8*(7*B*a^3*b^3 - 12*A*a^2*b^4)*x^2 + 10*(7*B*a^4*b^2 - 12*A*a^3*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5]","A",0
491,1,290,0,1.259680," ","integrate(x^(3/2)*(b*x+a)^(3/2)*(B*x+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{5} - 2 \, A a^{4} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(128 \, B b^{5} x^{4} + 15 \, B a^{4} b - 30 \, A a^{3} b^{2} + 16 \, {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} x^{3} + 8 \, {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} x^{2} - 10 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{1280 \, b^{4}}, \frac{15 \, {\left(B a^{5} - 2 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(128 \, B b^{5} x^{4} + 15 \, B a^{4} b - 30 \, A a^{3} b^{2} + 16 \, {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} x^{3} + 8 \, {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} x^{2} - 10 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{640 \, b^{4}}\right]"," ",0,"[-1/1280*(15*(B*a^5 - 2*A*a^4*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(128*B*b^5*x^4 + 15*B*a^4*b - 30*A*a^3*b^2 + 16*(11*B*a*b^4 + 10*A*b^5)*x^3 + 8*(B*a^2*b^3 + 30*A*a*b^4)*x^2 - 10*(B*a^3*b^2 - 2*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4, 1/640*(15*(B*a^5 - 2*A*a^4*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (128*B*b^5*x^4 + 15*B*a^4*b - 30*A*a^3*b^2 + 16*(11*B*a*b^4 + 10*A*b^5)*x^3 + 8*(B*a^2*b^3 + 30*A*a*b^4)*x^2 - 10*(B*a^3*b^2 - 2*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4]","A",0
492,1,249,0,1.500921," ","integrate((b*x+a)^(3/2)*(B*x+A)*x^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(48 \, B b^{4} x^{3} - 9 \, B a^{3} b + 24 \, A a^{2} b^{2} + 8 \, {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{384 \, b^{3}}, -\frac{3 \, {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(48 \, B b^{4} x^{3} - 9 \, B a^{3} b + 24 \, A a^{2} b^{2} + 8 \, {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} x^{2} + 2 \, {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{192 \, b^{3}}\right]"," ",0,"[-1/384*(3*(3*B*a^4 - 8*A*a^3*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(48*B*b^4*x^3 - 9*B*a^3*b + 24*A*a^2*b^2 + 8*(9*B*a*b^3 + 8*A*b^4)*x^2 + 2*(3*B*a^2*b^2 + 56*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3, -1/192*(3*(3*B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (48*B*b^4*x^3 - 9*B*a^3*b + 24*A*a^2*b^2 + 8*(9*B*a*b^3 + 8*A*b^4)*x^2 + 2*(3*B*a^2*b^2 + 56*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
493,1,198,0,2.032274," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(8 \, B b^{3} x^{2} + 3 \, B a^{2} b + 30 \, A a b^{2} + 2 \, {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{2}}, \frac{3 \, {\left(B a^{3} - 6 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, B b^{3} x^{2} + 3 \, B a^{2} b + 30 \, A a b^{2} + 2 \, {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{2}}\right]"," ",0,"[-1/48*(3*(B*a^3 - 6*A*a^2*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(8*B*b^3*x^2 + 3*B*a^2*b + 30*A*a*b^2 + 2*(7*B*a*b^2 + 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^2, 1/24*(3*(B*a^3 - 6*A*a^2*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*B*b^3*x^2 + 3*B*a^2*b + 30*A*a*b^2 + 2*(7*B*a*b^2 + 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
494,1,179,0,1.429204," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, B b^{2} x^{2} - 8 \, A a b + {\left(5 \, B a b + 4 \, A b^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b x}, -\frac{3 \, {\left(B a^{2} + 4 \, A a b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, B b^{2} x^{2} - 8 \, A a b + {\left(5 \, B a b + 4 \, A b^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b x}\right]"," ",0,"[1/8*(3*(B*a^2 + 4*A*a*b)*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*B*b^2*x^2 - 8*A*a*b + (5*B*a*b + 4*A*b^2)*x)*sqrt(b*x + a)*sqrt(x))/(b*x), -1/4*(3*(B*a^2 + 4*A*a*b)*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*B*b^2*x^2 - 8*A*a*b + (5*B*a*b + 4*A*b^2)*x)*sqrt(b*x + a)*sqrt(x))/(b*x)]","A",0
495,1,163,0,1.321420," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B a + 2 \, A b\right)} \sqrt{b} x^{2} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(3 \, B b x^{2} - 2 \, A a - 2 \, {\left(3 \, B a + 4 \, A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{6 \, x^{2}}, -\frac{3 \, {\left(3 \, B a + 2 \, A b\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(3 \, B b x^{2} - 2 \, A a - 2 \, {\left(3 \, B a + 4 \, A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, x^{2}}\right]"," ",0,"[1/6*(3*(3*B*a + 2*A*b)*sqrt(b)*x^2*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(3*B*b*x^2 - 2*A*a - 2*(3*B*a + 4*A*b)*x)*sqrt(b*x + a)*sqrt(x))/x^2, -1/3*(3*(3*B*a + 2*A*b)*sqrt(-b)*x^2*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (3*B*b*x^2 - 2*A*a - 2*(3*B*a + 4*A*b)*x)*sqrt(b*x + a)*sqrt(x))/x^2]","A",0
496,1,181,0,1.169505," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, B a b^{\frac{3}{2}} x^{3} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(3 \, A a^{2} + {\left(20 \, B a b + 3 \, A b^{2}\right)} x^{2} + {\left(5 \, B a^{2} + 6 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15 \, a x^{3}}, -\frac{2 \, {\left(15 \, B a \sqrt{-b} b x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(3 \, A a^{2} + {\left(20 \, B a b + 3 \, A b^{2}\right)} x^{2} + {\left(5 \, B a^{2} + 6 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}\right)}}{15 \, a x^{3}}\right]"," ",0,"[1/15*(15*B*a*b^(3/2)*x^3*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(3*A*a^2 + (20*B*a*b + 3*A*b^2)*x^2 + (5*B*a^2 + 6*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^3), -2/15*(15*B*a*sqrt(-b)*b*x^3*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (3*A*a^2 + (20*B*a*b + 3*A*b^2)*x^2 + (5*B*a^2 + 6*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^3)]","A",0
497,1,74,0,1.665317," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A a^{3} + {\left(7 \, B a b^{2} - 2 \, A b^{3}\right)} x^{3} + {\left(14 \, B a^{2} b + A a b^{2}\right)} x^{2} + {\left(7 \, B a^{3} + 8 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{35 \, a^{2} x^{\frac{7}{2}}}"," ",0,"-2/35*(5*A*a^3 + (7*B*a*b^2 - 2*A*b^3)*x^3 + (14*B*a^2*b + A*a*b^2)*x^2 + (7*B*a^3 + 8*A*a^2*b)*x)*sqrt(b*x + a)/(a^2*x^(7/2))","A",0
498,1,100,0,1.201636," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A a^{4} - 2 \, {\left(9 \, B a b^{3} - 4 \, A b^{4}\right)} x^{4} + {\left(9 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{3} + 3 \, {\left(24 \, B a^{3} b + A a^{2} b^{2}\right)} x^{2} + 5 \, {\left(9 \, B a^{4} + 10 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{315 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-2/315*(35*A*a^4 - 2*(9*B*a*b^3 - 4*A*b^4)*x^4 + (9*B*a^2*b^2 - 4*A*a*b^3)*x^3 + 3*(24*B*a^3*b + A*a^2*b^2)*x^2 + 5*(9*B*a^4 + 10*A*a^3*b)*x)*sqrt(b*x + a)/(a^3*x^(9/2))","A",0
499,1,126,0,1.441259," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A a^{5} + 8 \, {\left(11 \, B a b^{4} - 6 \, A b^{5}\right)} x^{5} - 4 \, {\left(11 \, B a^{2} b^{3} - 6 \, A a b^{4}\right)} x^{4} + 3 \, {\left(11 \, B a^{3} b^{2} - 6 \, A a^{2} b^{3}\right)} x^{3} + 5 \, {\left(110 \, B a^{4} b + 3 \, A a^{3} b^{2}\right)} x^{2} + 35 \, {\left(11 \, B a^{5} + 12 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3465 \, a^{4} x^{\frac{11}{2}}}"," ",0,"-2/3465*(315*A*a^5 + 8*(11*B*a*b^4 - 6*A*b^5)*x^5 - 4*(11*B*a^2*b^3 - 6*A*a*b^4)*x^4 + 3*(11*B*a^3*b^2 - 6*A*a^2*b^3)*x^3 + 5*(110*B*a^4*b + 3*A*a^3*b^2)*x^2 + 35*(11*B*a^5 + 12*A*a^4*b)*x)*sqrt(b*x + a)/(a^4*x^(11/2))","A",0
500,1,149,0,1.520941," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, A a^{6} - 16 \, {\left(13 \, B a b^{5} - 8 \, A b^{6}\right)} x^{6} + 8 \, {\left(13 \, B a^{2} b^{4} - 8 \, A a b^{5}\right)} x^{5} - 6 \, {\left(13 \, B a^{3} b^{3} - 8 \, A a^{2} b^{4}\right)} x^{4} + 5 \, {\left(13 \, B a^{4} b^{2} - 8 \, A a^{3} b^{3}\right)} x^{3} + 35 \, {\left(52 \, B a^{5} b + A a^{4} b^{2}\right)} x^{2} + 105 \, {\left(13 \, B a^{6} + 14 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{15015 \, a^{5} x^{\frac{13}{2}}}"," ",0,"-2/15015*(1155*A*a^6 - 16*(13*B*a*b^5 - 8*A*b^6)*x^6 + 8*(13*B*a^2*b^4 - 8*A*a*b^5)*x^5 - 6*(13*B*a^3*b^3 - 8*A*a^2*b^4)*x^4 + 5*(13*B*a^4*b^2 - 8*A*a^3*b^3)*x^3 + 35*(52*B*a^5*b + A*a^4*b^2)*x^2 + 105*(13*B*a^6 + 14*A*a^5*b)*x)*sqrt(b*x + a)/(a^5*x^(13/2))","A",0
501,1,173,0,1.588948," ","integrate((b*x+a)^(3/2)*(B*x+A)/x^(17/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, A a^{7} + 128 \, {\left(3 \, B a b^{6} - 2 \, A b^{7}\right)} x^{7} - 64 \, {\left(3 \, B a^{2} b^{5} - 2 \, A a b^{6}\right)} x^{6} + 48 \, {\left(3 \, B a^{3} b^{4} - 2 \, A a^{2} b^{5}\right)} x^{5} - 40 \, {\left(3 \, B a^{4} b^{3} - 2 \, A a^{3} b^{4}\right)} x^{4} + 35 \, {\left(3 \, B a^{5} b^{2} - 2 \, A a^{4} b^{3}\right)} x^{3} + 63 \, {\left(70 \, B a^{6} b + A a^{5} b^{2}\right)} x^{2} + 231 \, {\left(15 \, B a^{7} + 16 \, A a^{6} b\right)} x\right)} \sqrt{b x + a}}{45045 \, a^{6} x^{\frac{15}{2}}}"," ",0,"-2/45045*(3003*A*a^7 + 128*(3*B*a*b^6 - 2*A*b^7)*x^7 - 64*(3*B*a^2*b^5 - 2*A*a*b^6)*x^6 + 48*(3*B*a^3*b^4 - 2*A*a^2*b^5)*x^5 - 40*(3*B*a^4*b^3 - 2*A*a^3*b^4)*x^4 + 35*(3*B*a^5*b^2 - 2*A*a^4*b^3)*x^3 + 63*(70*B*a^6*b + A*a^5*b^2)*x^2 + 231*(15*B*a^7 + 16*A*a^6*b)*x)*sqrt(b*x + a)/(a^6*x^(15/2))","A",0
502,1,344,0,1.807349," ","integrate(x^(3/2)*(b*x+a)^(5/2)*(B*x+A),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(1280 \, B b^{6} x^{5} + 75 \, B a^{5} b - 180 \, A a^{4} b^{2} + 128 \, {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} x^{4} + 144 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} x^{3} + 8 \, {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} x^{2} - 10 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15360 \, b^{4}}, \frac{15 \, {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(1280 \, B b^{6} x^{5} + 75 \, B a^{5} b - 180 \, A a^{4} b^{2} + 128 \, {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} x^{4} + 144 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} x^{3} + 8 \, {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} x^{2} - 10 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{7680 \, b^{4}}\right]"," ",0,"[-1/15360*(15*(5*B*a^6 - 12*A*a^5*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(1280*B*b^6*x^5 + 75*B*a^5*b - 180*A*a^4*b^2 + 128*(25*B*a*b^5 + 12*A*b^6)*x^4 + 144*(15*B*a^2*b^4 + 28*A*a*b^5)*x^3 + 8*(5*B*a^3*b^3 + 372*A*a^2*b^4)*x^2 - 10*(5*B*a^4*b^2 - 12*A*a^3*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4, 1/7680*(15*(5*B*a^6 - 12*A*a^5*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (1280*B*b^6*x^5 + 75*B*a^5*b - 180*A*a^4*b^2 + 128*(25*B*a*b^5 + 12*A*b^6)*x^4 + 144*(15*B*a^2*b^4 + 28*A*a*b^5)*x^3 + 8*(5*B*a^3*b^3 + 372*A*a^2*b^4)*x^2 - 10*(5*B*a^4*b^2 - 12*A*a^3*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4]","A",0
503,1,297,0,1.313928," ","integrate((b*x+a)^(5/2)*(B*x+A)*x^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(384 \, B b^{5} x^{4} - 45 \, B a^{4} b + 150 \, A a^{3} b^{2} + 48 \, {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} x^{3} + 8 \, {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} x^{2} + 10 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3840 \, b^{3}}, -\frac{15 \, {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(384 \, B b^{5} x^{4} - 45 \, B a^{4} b + 150 \, A a^{3} b^{2} + 48 \, {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} x^{3} + 8 \, {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} x^{2} + 10 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{1920 \, b^{3}}\right]"," ",0,"[-1/3840*(15*(3*B*a^5 - 10*A*a^4*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(384*B*b^5*x^4 - 45*B*a^4*b + 150*A*a^3*b^2 + 48*(21*B*a*b^4 + 10*A*b^5)*x^3 + 8*(93*B*a^2*b^3 + 170*A*a*b^4)*x^2 + 10*(3*B*a^3*b^2 + 118*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3, -1/1920*(15*(3*B*a^5 - 10*A*a^4*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (384*B*b^5*x^4 - 45*B*a^4*b + 150*A*a^3*b^2 + 48*(21*B*a*b^4 + 10*A*b^5)*x^3 + 8*(93*B*a^2*b^3 + 170*A*a*b^4)*x^2 + 10*(3*B*a^3*b^2 + 118*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
504,1,246,0,1.554044," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(48 \, B b^{4} x^{3} + 15 \, B a^{3} b + 264 \, A a^{2} b^{2} + 8 \, {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} x^{2} + 2 \, {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{384 \, b^{2}}, \frac{15 \, {\left(B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(48 \, B b^{4} x^{3} + 15 \, B a^{3} b + 264 \, A a^{2} b^{2} + 8 \, {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} x^{2} + 2 \, {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{192 \, b^{2}}\right]"," ",0,"[-1/384*(15*(B*a^4 - 8*A*a^3*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(48*B*b^4*x^3 + 15*B*a^3*b + 264*A*a^2*b^2 + 8*(17*B*a*b^3 + 8*A*b^4)*x^2 + 2*(59*B*a^2*b^2 + 104*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^2, 1/192*(15*(B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (48*B*b^4*x^3 + 15*B*a^3*b + 264*A*a^2*b^2 + 8*(17*B*a*b^3 + 8*A*b^4)*x^2 + 2*(59*B*a^2*b^2 + 104*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
505,1,233,0,1.709570," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, B b^{3} x^{3} - 48 \, A a^{2} b + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{2} + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b x}, -\frac{15 \, {\left(B a^{3} + 6 \, A a^{2} b\right)} \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(8 \, B b^{3} x^{3} - 48 \, A a^{2} b + 2 \, {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} x^{2} + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b x}\right]"," ",0,"[1/48*(15*(B*a^3 + 6*A*a^2*b)*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*B*b^3*x^3 - 48*A*a^2*b + 2*(13*B*a*b^2 + 6*A*b^3)*x^2 + 3*(11*B*a^2*b + 18*A*a*b^2)*x)*sqrt(b*x + a)*sqrt(x))/(b*x), -1/24*(15*(B*a^3 + 6*A*a^2*b)*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (8*B*b^3*x^3 - 48*A*a^2*b + 2*(13*B*a*b^2 + 6*A*b^3)*x^2 + 3*(11*B*a^2*b + 18*A*a*b^2)*x)*sqrt(b*x + a)*sqrt(x))/(b*x)]","A",0
506,1,217,0,1.436320," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, B a^{2} + 4 \, A a b\right)} \sqrt{b} x^{2} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(6 \, B b^{2} x^{3} - 8 \, A a^{2} + 3 \, {\left(9 \, B a b + 4 \, A b^{2}\right)} x^{2} - 8 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, x^{2}}, -\frac{15 \, {\left(3 \, B a^{2} + 4 \, A a b\right)} \sqrt{-b} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(6 \, B b^{2} x^{3} - 8 \, A a^{2} + 3 \, {\left(9 \, B a b + 4 \, A b^{2}\right)} x^{2} - 8 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{12 \, x^{2}}\right]"," ",0,"[1/24*(15*(3*B*a^2 + 4*A*a*b)*sqrt(b)*x^2*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(6*B*b^2*x^3 - 8*A*a^2 + 3*(9*B*a*b + 4*A*b^2)*x^2 - 8*(3*B*a^2 + 7*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/x^2, -1/12*(15*(3*B*a^2 + 4*A*a*b)*sqrt(-b)*x^2*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (6*B*b^2*x^3 - 8*A*a^2 + 3*(9*B*a*b + 4*A*b^2)*x^2 - 8*(3*B*a^2 + 7*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/x^2]","A",0
507,1,217,0,2.196463," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} \sqrt{b} x^{3} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(15 \, B b^{2} x^{3} - 6 \, A a^{2} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} x^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{30 \, x^{3}}, -\frac{15 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} \sqrt{-b} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(15 \, B b^{2} x^{3} - 6 \, A a^{2} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} x^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15 \, x^{3}}\right]"," ",0,"[1/30*(15*(5*B*a*b + 2*A*b^2)*sqrt(b)*x^3*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(15*B*b^2*x^3 - 6*A*a^2 - 2*(35*B*a*b + 23*A*b^2)*x^2 - 2*(5*B*a^2 + 11*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/x^3, -1/15*(15*(5*B*a*b + 2*A*b^2)*sqrt(-b)*x^3*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (15*B*b^2*x^3 - 6*A*a^2 - 2*(35*B*a*b + 23*A*b^2)*x^2 - 2*(5*B*a^2 + 11*A*a*b)*x)*sqrt(b*x + a)*sqrt(x))/x^3]","A",0
508,1,231,0,0.939199," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, B a b^{\frac{5}{2}} x^{4} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(15 \, A a^{3} + {\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} x^{3} + {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{105 \, a x^{4}}, -\frac{2 \, {\left(105 \, B a \sqrt{-b} b^{2} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(15 \, A a^{3} + {\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} x^{3} + {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}\right)}}{105 \, a x^{4}}\right]"," ",0,"[1/105*(105*B*a*b^(5/2)*x^4*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(15*A*a^3 + (161*B*a*b^2 + 15*A*b^3)*x^3 + (77*B*a^2*b + 45*A*a*b^2)*x^2 + 3*(7*B*a^3 + 15*A*a^2*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^4), -2/105*(105*B*a*sqrt(-b)*b^2*x^4*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (15*A*a^3 + (161*B*a*b^2 + 15*A*b^3)*x^3 + (77*B*a^2*b + 45*A*a*b^2)*x^2 + 3*(7*B*a^3 + 15*A*a^2*b)*x)*sqrt(b*x + a)*sqrt(x))/(a*x^4)]","A",0
509,1,98,0,1.648095," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, A a^{4} + {\left(9 \, B a b^{3} - 2 \, A b^{4}\right)} x^{4} + {\left(27 \, B a^{2} b^{2} + A a b^{3}\right)} x^{3} + 3 \, {\left(9 \, B a^{3} b + 5 \, A a^{2} b^{2}\right)} x^{2} + {\left(9 \, B a^{4} + 19 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{63 \, a^{2} x^{\frac{9}{2}}}"," ",0,"-2/63*(7*A*a^4 + (9*B*a*b^3 - 2*A*b^4)*x^4 + (27*B*a^2*b^2 + A*a*b^3)*x^3 + 3*(9*B*a^3*b + 5*A*a^2*b^2)*x^2 + (9*B*a^4 + 19*A*a^3*b)*x)*sqrt(b*x + a)/(a^2*x^(9/2))","B",0
510,1,123,0,1.642755," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(63 \, A a^{5} - 2 \, {\left(11 \, B a b^{4} - 4 \, A b^{5}\right)} x^{5} + {\left(11 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} x^{4} + 3 \, {\left(55 \, B a^{3} b^{2} + A a^{2} b^{3}\right)} x^{3} + {\left(209 \, B a^{4} b + 113 \, A a^{3} b^{2}\right)} x^{2} + 7 \, {\left(11 \, B a^{5} + 23 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{693 \, a^{3} x^{\frac{11}{2}}}"," ",0,"-2/693*(63*A*a^5 - 2*(11*B*a*b^4 - 4*A*b^5)*x^5 + (11*B*a^2*b^3 - 4*A*a*b^4)*x^4 + 3*(55*B*a^3*b^2 + A*a^2*b^3)*x^3 + (209*B*a^4*b + 113*A*a^3*b^2)*x^2 + 7*(11*B*a^5 + 23*A*a^4*b)*x)*sqrt(b*x + a)/(a^3*x^(11/2))","A",0
511,1,149,0,1.632548," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(693 \, A a^{6} + 8 \, {\left(13 \, B a b^{5} - 6 \, A b^{6}\right)} x^{6} - 4 \, {\left(13 \, B a^{2} b^{4} - 6 \, A a b^{5}\right)} x^{5} + 3 \, {\left(13 \, B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} x^{4} + {\left(1469 \, B a^{4} b^{2} + 15 \, A a^{3} b^{3}\right)} x^{3} + 7 \, {\left(299 \, B a^{5} b + 159 \, A a^{4} b^{2}\right)} x^{2} + 63 \, {\left(13 \, B a^{6} + 27 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{9009 \, a^{4} x^{\frac{13}{2}}}"," ",0,"-2/9009*(693*A*a^6 + 8*(13*B*a*b^5 - 6*A*b^6)*x^6 - 4*(13*B*a^2*b^4 - 6*A*a*b^5)*x^5 + 3*(13*B*a^3*b^3 - 6*A*a^2*b^4)*x^4 + (1469*B*a^4*b^2 + 15*A*a^3*b^3)*x^3 + 7*(299*B*a^5*b + 159*A*a^4*b^2)*x^2 + 63*(13*B*a^6 + 27*A*a^5*b)*x)*sqrt(b*x + a)/(a^4*x^(13/2))","A",0
512,1,173,0,1.602477," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(17/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, A a^{7} - 16 \, {\left(15 \, B a b^{6} - 8 \, A b^{7}\right)} x^{7} + 8 \, {\left(15 \, B a^{2} b^{5} - 8 \, A a b^{6}\right)} x^{6} - 6 \, {\left(15 \, B a^{3} b^{4} - 8 \, A a^{2} b^{5}\right)} x^{5} + 5 \, {\left(15 \, B a^{4} b^{3} - 8 \, A a^{3} b^{4}\right)} x^{4} + 35 \, {\left(159 \, B a^{5} b^{2} + A a^{4} b^{3}\right)} x^{3} + 63 \, {\left(135 \, B a^{6} b + 71 \, A a^{5} b^{2}\right)} x^{2} + 231 \, {\left(15 \, B a^{7} + 31 \, A a^{6} b\right)} x\right)} \sqrt{b x + a}}{45045 \, a^{5} x^{\frac{15}{2}}}"," ",0,"-2/45045*(3003*A*a^7 - 16*(15*B*a*b^6 - 8*A*b^7)*x^7 + 8*(15*B*a^2*b^5 - 8*A*a*b^6)*x^6 - 6*(15*B*a^3*b^4 - 8*A*a^2*b^5)*x^5 + 5*(15*B*a^4*b^3 - 8*A*a^3*b^4)*x^4 + 35*(159*B*a^5*b^2 + A*a^4*b^3)*x^3 + 63*(135*B*a^6*b + 71*A*a^5*b^2)*x^2 + 231*(15*B*a^7 + 31*A*a^6*b)*x)*sqrt(b*x + a)/(a^5*x^(15/2))","A",0
513,1,198,0,1.668752," ","integrate((b*x+a)^(5/2)*(B*x+A)/x^(19/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(45045 \, A a^{8} + 128 \, {\left(17 \, B a b^{7} - 10 \, A b^{8}\right)} x^{8} - 64 \, {\left(17 \, B a^{2} b^{6} - 10 \, A a b^{7}\right)} x^{7} + 48 \, {\left(17 \, B a^{3} b^{5} - 10 \, A a^{2} b^{6}\right)} x^{6} - 40 \, {\left(17 \, B a^{4} b^{4} - 10 \, A a^{3} b^{5}\right)} x^{5} + 35 \, {\left(17 \, B a^{5} b^{3} - 10 \, A a^{4} b^{4}\right)} x^{4} + 63 \, {\left(1207 \, B a^{6} b^{2} + 5 \, A a^{5} b^{3}\right)} x^{3} + 231 \, {\left(527 \, B a^{7} b + 275 \, A a^{6} b^{2}\right)} x^{2} + 3003 \, {\left(17 \, B a^{8} + 35 \, A a^{7} b\right)} x\right)} \sqrt{b x + a}}{765765 \, a^{6} x^{\frac{17}{2}}}"," ",0,"-2/765765*(45045*A*a^8 + 128*(17*B*a*b^7 - 10*A*b^8)*x^8 - 64*(17*B*a^2*b^6 - 10*A*a*b^7)*x^7 + 48*(17*B*a^3*b^5 - 10*A*a^2*b^6)*x^6 - 40*(17*B*a^4*b^4 - 10*A*a^3*b^5)*x^5 + 35*(17*B*a^5*b^3 - 10*A*a^4*b^4)*x^4 + 63*(1207*B*a^6*b^2 + 5*A*a^5*b^3)*x^3 + 231*(527*B*a^7*b + 275*A*a^6*b^2)*x^2 + 3003*(17*B*a^8 + 35*A*a^7*b)*x)*sqrt(b*x + a)/(a^6*x^(17/2))","A",0
514,1,296,0,1.709506," ","integrate(x^(7/2)*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(384 \, B b^{5} x^{4} + 945 \, B a^{4} b - 1050 \, A a^{3} b^{2} - 48 \, {\left(9 \, B a b^{4} - 10 \, A b^{5}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3840 \, b^{6}}, \frac{105 \, {\left(9 \, B a^{5} - 10 \, A a^{4} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(384 \, B b^{5} x^{4} + 945 \, B a^{4} b - 1050 \, A a^{3} b^{2} - 48 \, {\left(9 \, B a b^{4} - 10 \, A b^{5}\right)} x^{3} + 56 \, {\left(9 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{2} - 70 \, {\left(9 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{1920 \, b^{6}}\right]"," ",0,"[-1/3840*(105*(9*B*a^5 - 10*A*a^4*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(384*B*b^5*x^4 + 945*B*a^4*b - 1050*A*a^3*b^2 - 48*(9*B*a*b^4 - 10*A*b^5)*x^3 + 56*(9*B*a^2*b^3 - 10*A*a*b^4)*x^2 - 70*(9*B*a^3*b^2 - 10*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^6, 1/1920*(105*(9*B*a^5 - 10*A*a^4*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (384*B*b^5*x^4 + 945*B*a^4*b - 1050*A*a^3*b^2 - 48*(9*B*a*b^4 - 10*A*b^5)*x^3 + 56*(9*B*a^2*b^3 - 10*A*a*b^4)*x^2 - 70*(9*B*a^3*b^2 - 10*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^6]","A",0
515,1,249,0,1.746188," ","integrate(x^(5/2)*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(48 \, B b^{4} x^{3} - 105 \, B a^{3} b + 120 \, A a^{2} b^{2} - 8 \, {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{384 \, b^{5}}, -\frac{15 \, {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(48 \, B b^{4} x^{3} - 105 \, B a^{3} b + 120 \, A a^{2} b^{2} - 8 \, {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} x^{2} + 10 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{192 \, b^{5}}\right]"," ",0,"[-1/384*(15*(7*B*a^4 - 8*A*a^3*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(48*B*b^4*x^3 - 105*B*a^3*b + 120*A*a^2*b^2 - 8*(7*B*a*b^3 - 8*A*b^4)*x^2 + 10*(7*B*a^2*b^2 - 8*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5, -1/192*(15*(7*B*a^4 - 8*A*a^3*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (48*B*b^4*x^3 - 105*B*a^3*b + 120*A*a^2*b^2 - 8*(7*B*a*b^3 - 8*A*b^4)*x^2 + 10*(7*B*a^2*b^2 - 8*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^5]","A",0
516,1,200,0,1.587768," ","integrate(x^(3/2)*(B*x+A)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(8 \, B b^{3} x^{2} + 15 \, B a^{2} b - 18 \, A a b^{2} - 2 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{4}}, \frac{3 \, {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, B b^{3} x^{2} + 15 \, B a^{2} b - 18 \, A a b^{2} - 2 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{4}}\right]"," ",0,"[-1/48*(3*(5*B*a^3 - 6*A*a^2*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(8*B*b^3*x^2 + 15*B*a^2*b - 18*A*a*b^2 - 2*(5*B*a*b^2 - 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4, 1/24*(3*(5*B*a^3 - 6*A*a^2*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*B*b^3*x^2 + 15*B*a^2*b - 18*A*a*b^2 - 2*(5*B*a*b^2 - 6*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/b^4]","A",0
517,1,151,0,0.925352," ","integrate((B*x+A)*x^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(2 \, B b^{2} x - 3 \, B a b + 4 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b^{3}}, -\frac{{\left(3 \, B a^{2} - 4 \, A a b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, B b^{2} x - 3 \, B a b + 4 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b^{3}}\right]"," ",0,"[-1/8*((3*B*a^2 - 4*A*a*b)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(2*B*b^2*x - 3*B*a*b + 4*A*b^2)*sqrt(b*x + a)*sqrt(x))/b^3, -1/4*((3*B*a^2 - 4*A*a*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*B*b^2*x - 3*B*a*b + 4*A*b^2)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
518,1,108,0,1.548530," ","integrate((B*x+A)/x^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b x + a} B b \sqrt{x} - {\left(B a - 2 \, A b\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right)}{2 \, b^{2}}, \frac{\sqrt{b x + a} B b \sqrt{x} + {\left(B a - 2 \, A b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right)}{b^{2}}\right]"," ",0,"[1/2*(2*sqrt(b*x + a)*B*b*sqrt(x) - (B*a - 2*A*b)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a))/b^2, (sqrt(b*x + a)*B*b*sqrt(x) + (B*a - 2*A*b)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))))/b^2]","A",0
519,1,109,0,1.367539," ","integrate((B*x+A)/x^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{B a \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, \sqrt{b x + a} A b \sqrt{x}}{a b x}, -\frac{2 \, {\left(B a \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + \sqrt{b x + a} A b \sqrt{x}\right)}}{a b x}\right]"," ",0,"[(B*a*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*sqrt(b*x + a)*A*b*sqrt(x))/(a*b*x), -2*(B*a*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + sqrt(b*x + a)*A*b*sqrt(x))/(a*b*x)]","A",0
520,1,30,0,1.475538," ","integrate((B*x+A)/x^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a + {\left(3 \, B a - 2 \, A b\right)} x\right)} \sqrt{b x + a}}{3 \, a^{2} x^{\frac{3}{2}}}"," ",0,"-2/3*(A*a + (3*B*a - 2*A*b)*x)*sqrt(b*x + a)/(a^2*x^(3/2))","A",0
521,1,53,0,1.105485," ","integrate((B*x+A)/x^(7/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{2} - 2 \, {\left(5 \, B a b - 4 \, A b^{2}\right)} x^{2} + {\left(5 \, B a^{2} - 4 \, A a b\right)} x\right)} \sqrt{b x + a}}{15 \, a^{3} x^{\frac{5}{2}}}"," ",0,"-2/15*(3*A*a^2 - 2*(5*B*a*b - 4*A*b^2)*x^2 + (5*B*a^2 - 4*A*a*b)*x)*sqrt(b*x + a)/(a^3*x^(5/2))","A",0
522,1,78,0,1.343103," ","integrate((B*x+A)/x^(9/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A a^{3} + 8 \, {\left(7 \, B a b^{2} - 6 \, A b^{3}\right)} x^{3} - 4 \, {\left(7 \, B a^{2} b - 6 \, A a b^{2}\right)} x^{2} + 3 \, {\left(7 \, B a^{3} - 6 \, A a^{2} b\right)} x\right)} \sqrt{b x + a}}{105 \, a^{4} x^{\frac{7}{2}}}"," ",0,"-2/105*(15*A*a^3 + 8*(7*B*a*b^2 - 6*A*b^3)*x^3 - 4*(7*B*a^2*b - 6*A*a*b^2)*x^2 + 3*(7*B*a^3 - 6*A*a^2*b)*x)*sqrt(b*x + a)/(a^4*x^(7/2))","A",0
523,1,102,0,1.622050," ","integrate((B*x+A)/x^(11/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A a^{4} - 16 \, {\left(9 \, B a b^{3} - 8 \, A b^{4}\right)} x^{4} + 8 \, {\left(9 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{3} - 6 \, {\left(9 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{2} + 5 \, {\left(9 \, B a^{4} - 8 \, A a^{3} b\right)} x\right)} \sqrt{b x + a}}{315 \, a^{5} x^{\frac{9}{2}}}"," ",0,"-2/315*(35*A*a^4 - 16*(9*B*a*b^3 - 8*A*b^4)*x^4 + 8*(9*B*a^2*b^2 - 8*A*a*b^3)*x^3 - 6*(9*B*a^3*b - 8*A*a^2*b^2)*x^2 + 5*(9*B*a^4 - 8*A*a^3*b)*x)*sqrt(b*x + a)/(a^5*x^(9/2))","A",0
524,1,126,0,1.677320," ","integrate((B*x+A)/x^(13/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, A a^{5} + 128 \, {\left(11 \, B a b^{4} - 10 \, A b^{5}\right)} x^{5} - 64 \, {\left(11 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{4} + 48 \, {\left(11 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x^{3} - 40 \, {\left(11 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} x^{2} + 35 \, {\left(11 \, B a^{5} - 10 \, A a^{4} b\right)} x\right)} \sqrt{b x + a}}{3465 \, a^{6} x^{\frac{11}{2}}}"," ",0,"-2/3465*(315*A*a^5 + 128*(11*B*a*b^4 - 10*A*b^5)*x^5 - 64*(11*B*a^2*b^3 - 10*A*a*b^4)*x^4 + 48*(11*B*a^3*b^2 - 10*A*a^2*b^3)*x^3 - 40*(11*B*a^4*b - 10*A*a^3*b^2)*x^2 + 35*(11*B*a^5 - 10*A*a^4*b)*x)*sqrt(b*x + a)/(a^6*x^(11/2))","A",0
525,1,150,0,1.687175," ","integrate((B*x+A)/x^(15/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(693 \, A a^{6} - 256 \, {\left(13 \, B a b^{5} - 12 \, A b^{6}\right)} x^{6} + 128 \, {\left(13 \, B a^{2} b^{4} - 12 \, A a b^{5}\right)} x^{5} - 96 \, {\left(13 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} x^{4} + 80 \, {\left(13 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x^{3} - 70 \, {\left(13 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} x^{2} + 63 \, {\left(13 \, B a^{6} - 12 \, A a^{5} b\right)} x\right)} \sqrt{b x + a}}{9009 \, a^{7} x^{\frac{13}{2}}}"," ",0,"-2/9009*(693*A*a^6 - 256*(13*B*a*b^5 - 12*A*b^6)*x^6 + 128*(13*B*a^2*b^4 - 12*A*a*b^5)*x^5 - 96*(13*B*a^3*b^3 - 12*A*a^2*b^4)*x^4 + 80*(13*B*a^4*b^2 - 12*A*a^3*b^3)*x^3 - 70*(13*B*a^5*b - 12*A*a^4*b^2)*x^2 + 63*(13*B*a^6 - 12*A*a^5*b)*x)*sqrt(b*x + a)/(a^7*x^(13/2))","A",0
526,1,355,0,1.688505," ","integrate(x^(7/2)*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, B a^{5} - 8 \, A a^{4} b + {\left(9 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(48 \, B b^{5} x^{4} - 945 \, B a^{4} b + 840 \, A a^{3} b^{2} - 8 \, {\left(9 \, B a b^{4} - 8 \, A b^{5}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{3} - 8 \, A a b^{4}\right)} x^{2} - 35 \, {\left(9 \, B a^{3} b^{2} - 8 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{384 \, {\left(b^{7} x + a b^{6}\right)}}, -\frac{105 \, {\left(9 \, B a^{5} - 8 \, A a^{4} b + {\left(9 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(48 \, B b^{5} x^{4} - 945 \, B a^{4} b + 840 \, A a^{3} b^{2} - 8 \, {\left(9 \, B a b^{4} - 8 \, A b^{5}\right)} x^{3} + 14 \, {\left(9 \, B a^{2} b^{3} - 8 \, A a b^{4}\right)} x^{2} - 35 \, {\left(9 \, B a^{3} b^{2} - 8 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{192 \, {\left(b^{7} x + a b^{6}\right)}}\right]"," ",0,"[-1/384*(105*(9*B*a^5 - 8*A*a^4*b + (9*B*a^4*b - 8*A*a^3*b^2)*x)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(48*B*b^5*x^4 - 945*B*a^4*b + 840*A*a^3*b^2 - 8*(9*B*a*b^4 - 8*A*b^5)*x^3 + 14*(9*B*a^2*b^3 - 8*A*a*b^4)*x^2 - 35*(9*B*a^3*b^2 - 8*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^7*x + a*b^6), -1/192*(105*(9*B*a^5 - 8*A*a^4*b + (9*B*a^4*b - 8*A*a^3*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (48*B*b^5*x^4 - 945*B*a^4*b + 840*A*a^3*b^2 - 8*(9*B*a*b^4 - 8*A*b^5)*x^3 + 14*(9*B*a^2*b^3 - 8*A*a*b^4)*x^2 - 35*(9*B*a^3*b^2 - 8*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^7*x + a*b^6)]","A",0
527,1,306,0,1.678217," ","integrate(x^(5/2)*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{4} - 6 \, A a^{3} b + {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(8 \, B b^{4} x^{3} + 105 \, B a^{3} b - 90 \, A a^{2} b^{2} - 2 \, {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} x^{2} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, {\left(b^{6} x + a b^{5}\right)}}, \frac{15 \, {\left(7 \, B a^{4} - 6 \, A a^{3} b + {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, B b^{4} x^{3} + 105 \, B a^{3} b - 90 \, A a^{2} b^{2} - 2 \, {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} x^{2} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[-1/48*(15*(7*B*a^4 - 6*A*a^3*b + (7*B*a^3*b - 6*A*a^2*b^2)*x)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(8*B*b^4*x^3 + 105*B*a^3*b - 90*A*a^2*b^2 - 2*(7*B*a*b^3 - 6*A*b^4)*x^2 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^6*x + a*b^5), 1/24*(15*(7*B*a^4 - 6*A*a^3*b + (7*B*a^3*b - 6*A*a^2*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*B*b^4*x^3 + 105*B*a^3*b - 90*A*a^2*b^2 - 2*(7*B*a*b^3 - 6*A*b^4)*x^2 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^6*x + a*b^5)]","A",0
528,1,255,0,1.437171," ","integrate(x^(3/2)*(B*x+A)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{3} - 4 \, A a^{2} b + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(2 \, B b^{3} x^{2} - 15 \, B a^{2} b + 12 \, A a b^{2} - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{8 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{3 \, {\left(5 \, B a^{3} - 4 \, A a^{2} b + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, B b^{3} x^{2} - 15 \, B a^{2} b + 12 \, A a b^{2} - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{4 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[-1/8*(3*(5*B*a^3 - 4*A*a^2*b + (5*B*a^2*b - 4*A*a*b^2)*x)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(2*B*b^3*x^2 - 15*B*a^2*b + 12*A*a*b^2 - (5*B*a*b^2 - 4*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^5*x + a*b^4), -1/4*(3*(5*B*a^3 - 4*A*a^2*b + (5*B*a^2*b - 4*A*a*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*B*b^3*x^2 - 15*B*a^2*b + 12*A*a*b^2 - (5*B*a*b^2 - 4*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^5*x + a*b^4)]","A",0
529,1,195,0,1.439924," ","integrate((B*x+A)*x^(1/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a^{2} - 2 \, A a b + {\left(3 \, B a b - 2 \, A b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(B b^{2} x + 3 \, B a b - 2 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{2 \, {\left(b^{4} x + a b^{3}\right)}}, \frac{{\left(3 \, B a^{2} - 2 \, A a b + {\left(3 \, B a b - 2 \, A b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(B b^{2} x + 3 \, B a b - 2 \, A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{b^{4} x + a b^{3}}\right]"," ",0,"[-1/2*((3*B*a^2 - 2*A*a*b + (3*B*a*b - 2*A*b^2)*x)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(B*b^2*x + 3*B*a*b - 2*A*b^2)*sqrt(b*x + a)*sqrt(x))/(b^4*x + a*b^3), ((3*B*a^2 - 2*A*a*b + (3*B*a*b - 2*A*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (B*b^2*x + 3*B*a*b - 2*A*b^2)*sqrt(b*x + a)*sqrt(x))/(b^4*x + a*b^3)]","A",0
530,1,157,0,0.809783," ","integrate((B*x+A)/(b*x+a)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B a b x + B a^{2}\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(B a b - A b^{2}\right)} \sqrt{b x + a} \sqrt{x}}{a b^{3} x + a^{2} b^{2}}, -\frac{2 \, {\left({\left(B a b x + B a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(B a b - A b^{2}\right)} \sqrt{b x + a} \sqrt{x}\right)}}{a b^{3} x + a^{2} b^{2}}\right]"," ",0,"[((B*a*b*x + B*a^2)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(B*a*b - A*b^2)*sqrt(b*x + a)*sqrt(x))/(a*b^3*x + a^2*b^2), -2*((B*a*b*x + B*a^2)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (B*a*b - A*b^2)*sqrt(b*x + a)*sqrt(x))/(a*b^3*x + a^2*b^2)]","A",0
531,1,43,0,1.298746," ","integrate((B*x+A)/x^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a - {\left(B a - 2 \, A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{a^{2} b x^{2} + a^{3} x}"," ",0,"-2*(A*a - (B*a - 2*A*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^2*b*x^2 + a^3*x)","A",0
532,1,67,0,1.517110," ","integrate((B*x+A)/x^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a^{2} + 2 \, {\left(3 \, B a b - 4 \, A b^{2}\right)} x^{2} + {\left(3 \, B a^{2} - 4 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}"," ",0,"-2/3*(A*a^2 + 2*(3*B*a*b - 4*A*b^2)*x^2 + (3*B*a^2 - 4*A*a*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^3*b*x^3 + a^4*x^2)","A",0
533,1,92,0,1.446767," ","integrate((B*x+A)/x^(7/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{3} - 8 \, {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} x^{3} - 4 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} x^{2} + {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}"," ",0,"-2/15*(3*A*a^3 - 8*(5*B*a*b^2 - 6*A*b^3)*x^3 - 4*(5*B*a^2*b - 6*A*a*b^2)*x^2 + (5*B*a^3 - 6*A*a^2*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^4*b*x^4 + a^5*x^3)","A",0
534,1,116,0,1.463504," ","integrate((B*x+A)/x^(9/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A a^{4} + 16 \, {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} x^{4} + 8 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{3} - 2 \, {\left(7 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{2} + {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{35 \, {\left(a^{5} b x^{5} + a^{6} x^{4}\right)}}"," ",0,"-2/35*(5*A*a^4 + 16*(7*B*a*b^3 - 8*A*b^4)*x^4 + 8*(7*B*a^2*b^2 - 8*A*a*b^3)*x^3 - 2*(7*B*a^3*b - 8*A*a^2*b^2)*x^2 + (7*B*a^4 - 8*A*a^3*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^5*b*x^5 + a^6*x^4)","A",0
535,1,141,0,1.351452," ","integrate((B*x+A)/x^(11/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, A a^{5} - 128 \, {\left(9 \, B a b^{4} - 10 \, A b^{5}\right)} x^{5} - 64 \, {\left(9 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{4} + 16 \, {\left(9 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x^{3} - 8 \, {\left(9 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} x^{2} + 5 \, {\left(9 \, B a^{5} - 10 \, A a^{4} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{315 \, {\left(a^{6} b x^{6} + a^{7} x^{5}\right)}}"," ",0,"-2/315*(35*A*a^5 - 128*(9*B*a*b^4 - 10*A*b^5)*x^5 - 64*(9*B*a^2*b^3 - 10*A*a*b^4)*x^4 + 16*(9*B*a^3*b^2 - 10*A*a^2*b^3)*x^3 - 8*(9*B*a^4*b - 10*A*a^3*b^2)*x^2 + 5*(9*B*a^5 - 10*A*a^4*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^6*b*x^6 + a^7*x^5)","A",0
536,1,165,0,1.318828," ","integrate((B*x+A)/x^(13/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(63 \, A a^{6} + 256 \, {\left(11 \, B a b^{5} - 12 \, A b^{6}\right)} x^{6} + 128 \, {\left(11 \, B a^{2} b^{4} - 12 \, A a b^{5}\right)} x^{5} - 32 \, {\left(11 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} x^{4} + 16 \, {\left(11 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} x^{3} - 10 \, {\left(11 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} x^{2} + 7 \, {\left(11 \, B a^{6} - 12 \, A a^{5} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{693 \, {\left(a^{7} b x^{7} + a^{8} x^{6}\right)}}"," ",0,"-2/693*(63*A*a^6 + 256*(11*B*a*b^5 - 12*A*b^6)*x^6 + 128*(11*B*a^2*b^4 - 12*A*a*b^5)*x^5 - 32*(11*B*a^3*b^3 - 12*A*a^2*b^4)*x^4 + 16*(11*B*a^4*b^2 - 12*A*a^3*b^3)*x^3 - 10*(11*B*a^5*b - 12*A*a^4*b^2)*x^2 + 7*(11*B*a^6 - 12*A*a^5*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^7*b*x^7 + a^8*x^6)","A",0
537,1,424,0,1.543160," ","integrate(x^(7/2)*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(3 \, B a^{5} - 2 \, A a^{4} b + {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(8 \, B b^{5} x^{4} + 315 \, B a^{4} b - 210 \, A a^{3} b^{2} - 6 \, {\left(3 \, B a b^{4} - 2 \, A b^{5}\right)} x^{3} + 21 \, {\left(3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} x^{2} + 140 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{48 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}, \frac{105 \, {\left(3 \, B a^{5} - 2 \, A a^{4} b + {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x^{2} + 2 \, {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, B b^{5} x^{4} + 315 \, B a^{4} b - 210 \, A a^{3} b^{2} - 6 \, {\left(3 \, B a b^{4} - 2 \, A b^{5}\right)} x^{3} + 21 \, {\left(3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} x^{2} + 140 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}\right]"," ",0,"[-1/48*(105*(3*B*a^5 - 2*A*a^4*b + (3*B*a^3*b^2 - 2*A*a^2*b^3)*x^2 + 2*(3*B*a^4*b - 2*A*a^3*b^2)*x)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(8*B*b^5*x^4 + 315*B*a^4*b - 210*A*a^3*b^2 - 6*(3*B*a*b^4 - 2*A*b^5)*x^3 + 21*(3*B*a^2*b^3 - 2*A*a*b^4)*x^2 + 140*(3*B*a^3*b^2 - 2*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6), 1/24*(105*(3*B*a^5 - 2*A*a^4*b + (3*B*a^3*b^2 - 2*A*a^2*b^3)*x^2 + 2*(3*B*a^4*b - 2*A*a^3*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*B*b^5*x^4 + 315*B*a^4*b - 210*A*a^3*b^2 - 6*(3*B*a*b^4 - 2*A*b^5)*x^3 + 21*(3*B*a^2*b^3 - 2*A*a*b^4)*x^2 + 140*(3*B*a^3*b^2 - 2*A*a^2*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)]","A",0
538,1,373,0,1.697622," ","integrate(x^(5/2)*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B a^{4} - 4 \, A a^{3} b + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(6 \, B b^{4} x^{3} - 105 \, B a^{3} b + 60 \, A a^{2} b^{2} - 3 \, {\left(7 \, B a b^{3} - 4 \, A b^{4}\right)} x^{2} - 20 \, {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{24 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{15 \, {\left(7 \, B a^{4} - 4 \, A a^{3} b + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x^{2} + 2 \, {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(6 \, B b^{4} x^{3} - 105 \, B a^{3} b + 60 \, A a^{2} b^{2} - 3 \, {\left(7 \, B a b^{3} - 4 \, A b^{4}\right)} x^{2} - 20 \, {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{12 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/24*(15*(7*B*a^4 - 4*A*a^3*b + (7*B*a^2*b^2 - 4*A*a*b^3)*x^2 + 2*(7*B*a^3*b - 4*A*a^2*b^2)*x)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(6*B*b^4*x^3 - 105*B*a^3*b + 60*A*a^2*b^2 - 3*(7*B*a*b^3 - 4*A*b^4)*x^2 - 20*(7*B*a^2*b^2 - 4*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/12*(15*(7*B*a^4 - 4*A*a^3*b + (7*B*a^2*b^2 - 4*A*a*b^3)*x^2 + 2*(7*B*a^3*b - 4*A*a^2*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (6*B*b^4*x^3 - 105*B*a^3*b + 60*A*a^2*b^2 - 3*(7*B*a*b^3 - 4*A*b^4)*x^2 - 20*(7*B*a^2*b^2 - 4*A*a*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
539,1,314,0,1.306822," ","integrate(x^(3/2)*(B*x+A)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{3} - 2 \, A a^{2} b + {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(3 \, B b^{3} x^{2} + 15 \, B a^{2} b - 6 \, A a b^{2} + 4 \, {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{6 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{3 \, {\left(5 \, B a^{3} - 2 \, A a^{2} b + {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x^{2} + 2 \, {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(3 \, B b^{3} x^{2} + 15 \, B a^{2} b - 6 \, A a b^{2} + 4 \, {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/6*(3*(5*B*a^3 - 2*A*a^2*b + (5*B*a*b^2 - 2*A*b^3)*x^2 + 2*(5*B*a^2*b - 2*A*a*b^2)*x)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(3*B*b^3*x^2 + 15*B*a^2*b - 6*A*a*b^2 + 4*(5*B*a*b^2 - 2*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/3*(3*(5*B*a^3 - 2*A*a^2*b + (5*B*a*b^2 - 2*A*b^3)*x^2 + 2*(5*B*a^2*b - 2*A*a*b^2)*x)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (3*B*b^3*x^2 + 15*B*a^2*b - 6*A*a*b^2 + 4*(5*B*a*b^2 - 2*A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
540,1,232,0,0.869482," ","integrate((B*x+A)*x^(1/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b^{2} x^{2} + 2 \, B a^{2} b x + B a^{3}\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(3 \, B a^{2} b + {\left(4 \, B a b^{2} - A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a b^{5} x^{2} + 2 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}, -\frac{2 \, {\left(3 \, {\left(B a b^{2} x^{2} + 2 \, B a^{2} b x + B a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(3 \, B a^{2} b + {\left(4 \, B a b^{2} - A b^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{x}\right)}}{3 \, {\left(a b^{5} x^{2} + 2 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}\right]"," ",0,"[1/3*(3*(B*a*b^2*x^2 + 2*B*a^2*b*x + B*a^3)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(3*B*a^2*b + (4*B*a*b^2 - A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(a*b^5*x^2 + 2*a^2*b^4*x + a^3*b^3), -2/3*(3*(B*a*b^2*x^2 + 2*B*a^2*b*x + B*a^3)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (3*B*a^2*b + (4*B*a*b^2 - A*b^3)*x)*sqrt(b*x + a)*sqrt(x))/(a*b^5*x^2 + 2*a^2*b^4*x + a^3*b^3)]","A",0
541,1,50,0,1.539492," ","integrate((B*x+A)/(b*x+a)^(5/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a + {\left(B a + 2 \, A b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)}}"," ",0,"2/3*(3*A*a + (B*a + 2*A*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^2*b^2*x^2 + 2*a^3*b*x + a^4)","A",0
542,1,76,0,1.476471," ","integrate((B*x+A)/x^(3/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{2} - 2 \, {\left(B a b - 4 \, A b^{2}\right)} x^{2} - 3 \, {\left(B a^{2} - 4 \, A a b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}"," ",0,"-2/3*(3*A*a^2 - 2*(B*a*b - 4*A*b^2)*x^2 - 3*(B*a^2 - 4*A*a*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x)","A",0
543,1,100,0,0.771513," ","integrate((B*x+A)/x^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a^{3} + 8 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} x^{3} + 12 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} x^{2} + 3 \, {\left(B a^{3} - 2 \, A a^{2} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}"," ",0,"-2/3*(A*a^3 + 8*(B*a*b^2 - 2*A*b^3)*x^3 + 12*(B*a^2*b - 2*A*a*b^2)*x^2 + 3*(B*a^3 - 2*A*a^2*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)","A",0
544,1,127,0,1.247633," ","integrate((B*x+A)/x^(7/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{4} - 16 \, {\left(5 \, B a b^{3} - 8 \, A b^{4}\right)} x^{4} - 24 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} x^{3} - 6 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} x^{2} + {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{15 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}"," ",0,"-2/15*(3*A*a^4 - 16*(5*B*a*b^3 - 8*A*b^4)*x^4 - 24*(5*B*a^2*b^2 - 8*A*a*b^3)*x^3 - 6*(5*B*a^3*b - 8*A*a^2*b^2)*x^2 + (5*B*a^4 - 8*A*a^3*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)","A",0
545,1,152,0,1.208032," ","integrate((B*x+A)/x^(9/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A a^{5} + 128 \, {\left(7 \, B a b^{4} - 10 \, A b^{5}\right)} x^{5} + 192 \, {\left(7 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} x^{4} + 48 \, {\left(7 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} x^{3} - 8 \, {\left(7 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} x^{2} + 3 \, {\left(7 \, B a^{5} - 10 \, A a^{4} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{105 \, {\left(a^{6} b^{2} x^{6} + 2 \, a^{7} b x^{5} + a^{8} x^{4}\right)}}"," ",0,"-2/105*(15*A*a^5 + 128*(7*B*a*b^4 - 10*A*b^5)*x^5 + 192*(7*B*a^2*b^3 - 10*A*a*b^4)*x^4 + 48*(7*B*a^3*b^2 - 10*A*a^2*b^3)*x^3 - 8*(7*B*a^4*b - 10*A*a^3*b^2)*x^2 + 3*(7*B*a^5 - 10*A*a^4*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^6*b^2*x^6 + 2*a^7*b*x^5 + a^8*x^4)","A",0
546,1,176,0,0.696731," ","integrate((B*x+A)/x^(11/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, A a^{6} - 256 \, {\left(3 \, B a b^{5} - 4 \, A b^{6}\right)} x^{6} - 384 \, {\left(3 \, B a^{2} b^{4} - 4 \, A a b^{5}\right)} x^{5} - 96 \, {\left(3 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} x^{4} + 16 \, {\left(3 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3}\right)} x^{3} - 6 \, {\left(3 \, B a^{5} b - 4 \, A a^{4} b^{2}\right)} x^{2} + 3 \, {\left(3 \, B a^{6} - 4 \, A a^{5} b\right)} x\right)} \sqrt{b x + a} \sqrt{x}}{63 \, {\left(a^{7} b^{2} x^{7} + 2 \, a^{8} b x^{6} + a^{9} x^{5}\right)}}"," ",0,"-2/63*(7*A*a^6 - 256*(3*B*a*b^5 - 4*A*b^6)*x^6 - 384*(3*B*a^2*b^4 - 4*A*a*b^5)*x^5 - 96*(3*B*a^3*b^3 - 4*A*a^2*b^4)*x^4 + 16*(3*B*a^4*b^2 - 4*A*a^3*b^3)*x^3 - 6*(3*B*a^5*b - 4*A*a^4*b^2)*x^2 + 3*(3*B*a^6 - 4*A*a^5*b)*x)*sqrt(b*x + a)*sqrt(x)/(a^7*b^2*x^7 + 2*a^8*b*x^6 + a^9*x^5)","A",0
547,1,702,0,1.134077," ","integrate(x^3*(b*x+a)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 2 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 40 \, a b^{4} c^{3} d^{2} + 34 \, a^{2} b^{3} c^{2} d^{3} + 40 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + 7 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 11 \, a b^{4} c^{2} d^{3} - 11 \, a^{2} b^{3} c d^{4} + 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{5} d^{5}}, -\frac{15 \, {\left(7 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 2 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 40 \, a b^{4} c^{3} d^{2} + 34 \, a^{2} b^{3} c^{2} d^{3} + 40 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + 7 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 11 \, a b^{4} c^{2} d^{3} - 11 \, a^{2} b^{3} c d^{4} + 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{5} d^{5}}\right]"," ",0,"[1/7680*(15*(7*b^5*c^5 - 5*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 2*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 40*a*b^4*c^3*d^2 + 34*a^2*b^3*c^2*d^3 + 40*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(b^5*c*d^4 + a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 2*a*b^4*c*d^4 + 7*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 11*a*b^4*c^2*d^3 - 11*a^2*b^3*c*d^4 + 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5), -1/3840*(15*(7*b^5*c^5 - 5*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 2*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 40*a*b^4*c^3*d^2 + 34*a^2*b^3*c^2*d^3 + 40*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(b^5*c*d^4 + a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 2*a*b^4*c*d^4 + 7*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 11*a*b^4*c^2*d^3 - 11*a^2*b^3*c*d^4 + 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5)]","A",0
548,1,542,0,1.878813," ","integrate(x^2*(b*x+a)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 5 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} - 7 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{4} d^{4}}, \frac{3 \, {\left(5 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 5 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} - 7 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{4} d^{4}}\right]"," ",0,"[1/768*(3*(5*b^4*c^4 - 4*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 5*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 7*a*b^3*c^2*d^2 - 7*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(b^4*c*d^3 + a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 2*a*b^3*c*d^3 + 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4), 1/384*(3*(5*b^4*c^4 - 4*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 5*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 7*a*b^3*c^2*d^2 - 7*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(b^4*c*d^3 + a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 2*a*b^3*c*d^3 + 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4)]","A",0
549,1,406,0,1.047890," ","integrate(x*(b*x+a)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{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} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{3} d^{3}}, -\frac{3 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{3} d^{3}}\right]"," ",0,"[1/96*(3*(b^3*c^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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), -1/48*(3*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3)]","A",0
550,1,300,0,1.197087," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2} d^{2}}, \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2} d^{2}}\right]"," ",0,"[1/16*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2), 1/8*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2)]","A",0
551,1,822,0,2.055475," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a c} b d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{4 \, b d}, \frac{\sqrt{a c} b d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} b d - {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{2 \, b d}, \frac{4 \, \sqrt{-a c} b d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{4 \, b d}, \frac{2 \, \sqrt{-a c} b d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} b d - {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{2 \, b d}\right]"," ",0,"[1/4*(2*sqrt(a*c)*b*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b*d), 1/2*(sqrt(a*c)*b*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 2*sqrt(b*x + a)*sqrt(d*x + c)*b*d - (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b*d), 1/4*(4*sqrt(-a*c)*b*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 4*sqrt(b*x + a)*sqrt(d*x + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b*d), 1/2*(2*sqrt(-a*c)*b*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*b*d - (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b*d)]","B",0
552,1,842,0,1.547291," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{b d} a c x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \sqrt{a c} {\left(b c + a d\right)} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c} a c}{4 \, a c x}, -\frac{4 \, \sqrt{-b d} a c x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - \sqrt{a c} {\left(b c + a d\right)} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} a c}{4 \, a c x}, \frac{\sqrt{b d} a c x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \sqrt{-a c} {\left(b c + a d\right)} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, \sqrt{b x + a} \sqrt{d x + c} a c}{2 \, a c x}, -\frac{2 \, \sqrt{-b d} a c x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - \sqrt{-a c} {\left(b c + a d\right)} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} a c}{2 \, a c x}\right]"," ",0,"[1/4*(2*sqrt(b*d)*a*c*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + sqrt(a*c)*(b*c + a*d)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c*x), -1/4*(4*sqrt(-b*d)*a*c*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - sqrt(a*c)*(b*c + a*d)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c*x), 1/2*(sqrt(b*d)*a*c*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + sqrt(-a*c)*(b*c + a*d)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c*x), -1/2*(2*sqrt(-b*d)*a*c*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - sqrt(-a*c)*(b*c + a*d)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c*x)]","B",0
553,1,326,0,1.379348," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} c^{2} x^{2}}, -\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} c^{2} x^{2}}\right]"," ",0,"[1/16*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^2), -1/8*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(2*a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^2)]","A",0
554,1,434,0,2.352676," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{3} c^{3} x^{3}}, \frac{3 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{3} c^{3} x^{3}}\right]"," ",0,"[1/96*(3*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 - (3*a*b^2*c^3 - 2*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^3), 1/48*(3*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 - (3*a*b^2*c^3 - 2*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^3)]","A",0
555,1,568,0,7.183901," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 5 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d - 7 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{4} c^{4} x^{4}}, -\frac{3 \, {\left(5 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + 5 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 7 \, a^{2} b^{2} c^{3} d - 7 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{4} c^{4} x^{4}}\right]"," ",0,"[1/768*(3*(5*b^4*c^4 - 4*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 5*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 + (15*a*b^3*c^4 - 7*a^2*b^2*c^3*d - 7*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 2*a^3*b*c^3*d + 5*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^4), -1/384*(3*(5*b^4*c^4 - 4*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + 5*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 - 7*a^2*b^2*c^3*d - 7*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 2*a^3*b*c^3*d + 5*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^4)]","A",0
556,1,730,0,17.262894," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 2 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 40 \, a^{2} b^{3} c^{4} d - 34 \, a^{3} b^{2} c^{3} d^{2} - 40 \, a^{4} b c^{2} d^{3} + 105 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 11 \, a^{3} b^{2} c^{4} d - 11 \, a^{4} b c^{3} d^{2} + 35 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{5} c^{5} x^{5}}, \frac{15 \, {\left(7 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 2 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 40 \, a^{2} b^{3} c^{4} d - 34 \, a^{3} b^{2} c^{3} d^{2} - 40 \, a^{4} b c^{2} d^{3} + 105 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 11 \, a^{3} b^{2} c^{4} d - 11 \, a^{4} b c^{3} d^{2} + 35 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 2 \, a^{4} b c^{4} d + 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{5} c^{5} x^{5}}\right]"," ",0,"[1/7680*(15*(7*b^5*c^5 - 5*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 2*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(384*a^5*c^5 - (105*a*b^4*c^5 - 40*a^2*b^3*c^4*d - 34*a^3*b^2*c^3*d^2 - 40*a^4*b*c^2*d^3 + 105*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 11*a^3*b^2*c^4*d - 11*a^4*b*c^3*d^2 + 35*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 2*a^4*b*c^4*d + 7*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^5*x^5), 1/3840*(15*(7*b^5*c^5 - 5*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 2*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(384*a^5*c^5 - (105*a*b^4*c^5 - 40*a^2*b^3*c^4*d - 34*a^3*b^2*c^3*d^2 - 40*a^4*b*c^2*d^3 + 105*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 11*a^3*b^2*c^4*d - 11*a^4*b*c^3*d^2 + 35*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 2*a^4*b*c^4*d + 7*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^5*x^5)]","A",0
557,1,704,0,1.474508," ","integrate(x^2*(d*x+c)^(3/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 7 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{4} + 45 \, b^{5} c^{4} d - 30 \, a b^{4} c^{3} d^{2} - 36 \, a^{2} b^{3} c^{2} d^{3} + 190 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(11 \, b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(3 \, b^{5} c^{2} d^{3} + 12 \, a b^{4} c d^{4} - 7 \, a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(15 \, b^{5} c^{3} d^{2} - 9 \, a b^{4} c^{2} d^{3} + 61 \, a^{2} b^{3} c d^{4} - 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{5} d^{4}}, \frac{15 \, {\left(3 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 7 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{4} + 45 \, b^{5} c^{4} d - 30 \, a b^{4} c^{3} d^{2} - 36 \, a^{2} b^{3} c^{2} d^{3} + 190 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(11 \, b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(3 \, b^{5} c^{2} d^{3} + 12 \, a b^{4} c d^{4} - 7 \, a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(15 \, b^{5} c^{3} d^{2} - 9 \, a b^{4} c^{2} d^{3} + 61 \, a^{2} b^{3} c d^{4} - 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{5} d^{4}}\right]"," ",0,"[-1/7680*(15*(3*b^5*c^5 - 3*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 7*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(384*b^5*d^5*x^4 + 45*b^5*c^4*d - 30*a*b^4*c^3*d^2 - 36*a^2*b^3*c^2*d^3 + 190*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(11*b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(3*b^5*c^2*d^3 + 12*a*b^4*c*d^4 - 7*a^2*b^3*d^5)*x^2 - 2*(15*b^5*c^3*d^2 - 9*a*b^4*c^2*d^3 + 61*a^2*b^3*c*d^4 - 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^4), 1/3840*(15*(3*b^5*c^5 - 3*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 7*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(384*b^5*d^5*x^4 + 45*b^5*c^4*d - 30*a*b^4*c^3*d^2 - 36*a^2*b^3*c^2*d^3 + 190*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(11*b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(3*b^5*c^2*d^3 + 12*a*b^4*c*d^4 - 7*a^2*b^3*d^5)*x^2 - 2*(15*b^5*c^3*d^2 - 9*a*b^4*c^2*d^3 + 61*a^2*b^3*c*d^4 - 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^4)]","A",0
558,1,544,0,1.321242," ","integrate(x*(d*x+c)^(3/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 9 \, a b^{3} c^{2} d^{2} - 31 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 10 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{4} d^{3}}, -\frac{3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 9 \, a b^{3} c^{2} d^{2} - 31 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 10 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{4} d^{3}}\right]"," ",0,"[-1/768*(3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 9*a*b^3*c^2*d^2 - 31*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 10*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3), -1/384*(3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 9*a*b^3*c^2*d^2 - 31*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 10*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3)]","A",0
559,1,410,0,1.377971," ","integrate((b*x+a)^(1/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(7 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{3} d^{2}}, \frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(7 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{3} d^{2}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 8*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(7*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2), 1/48*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 8*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(7*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2)]","A",0
560,1,985,0,6.355393," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{a c} b^{2} c d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2} d}, \frac{4 \, \sqrt{a c} b^{2} c d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2} d}, \frac{16 \, \sqrt{-a c} b^{2} c d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2} d}, \frac{8 \, \sqrt{-a c} b^{2} c d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2} d}\right]"," ",0,"[1/16*(8*sqrt(a*c)*b^2*c*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + 5*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d), 1/8*(4*sqrt(a*c)*b^2*c*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + 5*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d), 1/16*(16*sqrt(-a*c)*b^2*c*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + 5*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d), 1/8*(8*sqrt(-a*c)*b^2*c*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + 5*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d)]","A",0
561,1,893,0,2.790779," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b c + a d\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(b c + 3 \, a d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} {\left(d x - c\right)}}{4 \, x}, -\frac{2 \, {\left(3 \, b c + a d\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - {\left(b c + 3 \, a d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c} {\left(d x - c\right)}}{4 \, x}, \frac{2 \, {\left(b c + 3 \, a d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + {\left(3 \, b c + a d\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} {\left(d x - c\right)}}{4 \, x}, \frac{{\left(b c + 3 \, a d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(3 \, b c + a d\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} {\left(d x - c\right)}}{2 \, x}\right]"," ",0,"[1/4*((3*b*c + a*d)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + (b*c + 3*a*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*(d*x - c))/x, -1/4*(2*(3*b*c + a*d)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - (b*c + 3*a*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*sqrt(d*x + c)*(d*x - c))/x, 1/4*(2*(b*c + 3*a*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + (3*b*c + a*d)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*sqrt(d*x + c)*(d*x - c))/x, 1/2*((b*c + 3*a*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (3*b*c + a*d)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*(d*x - c))/x]","A",0
562,1,1023,0,4.067642," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{b d} a^{2} c d x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} c x^{2}}, -\frac{16 \, \sqrt{-b d} a^{2} c d x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} c x^{2}}, \frac{4 \, \sqrt{b d} a^{2} c d x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} c x^{2}}, -\frac{8 \, \sqrt{-b d} a^{2} c d x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} + 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} c x^{2}}\right]"," ",0,"[1/16*(8*sqrt(b*d)*a^2*c*d*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 + (a*b*c^2 + 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^2), -1/16*(16*sqrt(-b*d)*a^2*c*d*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c^2 + (a*b*c^2 + 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^2), 1/8*(4*sqrt(b*d)*a^2*c*d*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 + (a*b*c^2 + 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^2), -1/8*(8*sqrt(-b*d)*a^2*c*d*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(2*a^2*c^2 + (a*b*c^2 + 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^2)]","A",0
563,1,438,0,2.316217," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{3} c^{2} x^{3}}, \frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{3} c^{2} x^{3}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 - (3*a*b^2*c^3 - 8*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^3), 1/48*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 - (3*a*b^2*c^3 - 8*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^3)]","A",0
564,1,570,0,7.784504," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 31 \, a^{2} b^{2} c^{3} d + 9 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d - 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{4} c^{3} x^{4}}, -\frac{3 \, {\left(5 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 31 \, a^{2} b^{2} c^{3} d + 9 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d - 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{4} c^{3} x^{4}}\right]"," ",0,"[-1/768*(3*(5*b^4*c^4 - 12*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 + (15*a*b^3*c^4 - 31*a^2*b^2*c^3*d + 9*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 10*a^3*b*c^3*d - 3*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^4), -1/384*(3*(5*b^4*c^4 - 12*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 - 31*a^2*b^2*c^3*d + 9*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 10*a^3*b*c^3*d - 3*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^4)]","A",0
565,1,732,0,18.211428," ","integrate((d*x+c)^(3/2)*(b*x+a)^(1/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{5} c^{5} - 15 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 190 \, a^{2} b^{3} c^{4} d + 36 \, a^{3} b^{2} c^{3} d^{2} + 30 \, a^{4} b c^{2} d^{3} - 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 61 \, a^{3} b^{2} c^{4} d + 9 \, a^{4} b c^{3} d^{2} - 15 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 12 \, a^{4} b c^{4} d - 3 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + 11 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{5} c^{4} x^{5}}, \frac{15 \, {\left(7 \, b^{5} c^{5} - 15 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 190 \, a^{2} b^{3} c^{4} d + 36 \, a^{3} b^{2} c^{3} d^{2} + 30 \, a^{4} b c^{2} d^{3} - 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 61 \, a^{3} b^{2} c^{4} d + 9 \, a^{4} b c^{3} d^{2} - 15 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 12 \, a^{4} b c^{4} d - 3 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + 11 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{5} c^{4} x^{5}}\right]"," ",0,"[-1/7680*(15*(7*b^5*c^5 - 15*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(384*a^5*c^5 - (105*a*b^4*c^5 - 190*a^2*b^3*c^4*d + 36*a^3*b^2*c^3*d^2 + 30*a^4*b*c^2*d^3 - 45*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 61*a^3*b^2*c^4*d + 9*a^4*b*c^3*d^2 - 15*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 12*a^4*b*c^4*d - 3*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + 11*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^4*x^5), 1/3840*(15*(7*b^5*c^5 - 15*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(384*a^5*c^5 - (105*a*b^4*c^5 - 190*a^2*b^3*c^4*d + 36*a^3*b^2*c^3*d^2 + 30*a^4*b*c^2*d^3 - 45*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 61*a^3*b^2*c^4*d + 9*a^4*b*c^3*d^2 - 15*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 12*a^4*b*c^4*d - 3*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + 11*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^4*x^5)]","A",0
566,1,892,0,1.771150," ","integrate(x^2*(d*x+c)^(5/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, b^{6} c^{6} - 6 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 75 \, a^{4} b^{2} c^{2} d^{4} - 70 \, a^{5} b c d^{5} + 21 \, a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(1280 \, b^{6} d^{6} x^{5} + 75 \, b^{6} c^{5} d - 65 \, a b^{5} c^{4} d^{2} - 90 \, a^{2} b^{4} c^{3} d^{3} + 838 \, a^{3} b^{3} c^{2} d^{4} - 945 \, a^{4} b^{2} c d^{5} + 315 \, a^{5} b d^{6} + 128 \, {\left(25 \, b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(135 \, b^{6} c^{2} d^{4} + 26 \, a b^{5} c d^{5} - 9 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(5 \, b^{6} c^{3} d^{3} + 51 \, a b^{5} c^{2} d^{4} - 61 \, a^{2} b^{4} c d^{5} + 21 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(25 \, b^{6} c^{4} d^{2} - 20 \, a b^{5} c^{3} d^{3} + 262 \, a^{2} b^{4} c^{2} d^{4} - 308 \, a^{3} b^{3} c d^{5} + 105 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, b^{6} d^{4}}, \frac{15 \, {\left(5 \, b^{6} c^{6} - 6 \, a b^{5} c^{5} d - 5 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 75 \, a^{4} b^{2} c^{2} d^{4} - 70 \, a^{5} b c d^{5} + 21 \, a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, b^{6} d^{6} x^{5} + 75 \, b^{6} c^{5} d - 65 \, a b^{5} c^{4} d^{2} - 90 \, a^{2} b^{4} c^{3} d^{3} + 838 \, a^{3} b^{3} c^{2} d^{4} - 945 \, a^{4} b^{2} c d^{5} + 315 \, a^{5} b d^{6} + 128 \, {\left(25 \, b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(135 \, b^{6} c^{2} d^{4} + 26 \, a b^{5} c d^{5} - 9 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(5 \, b^{6} c^{3} d^{3} + 51 \, a b^{5} c^{2} d^{4} - 61 \, a^{2} b^{4} c d^{5} + 21 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(25 \, b^{6} c^{4} d^{2} - 20 \, a b^{5} c^{3} d^{3} + 262 \, a^{2} b^{4} c^{2} d^{4} - 308 \, a^{3} b^{3} c d^{5} + 105 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, b^{6} d^{4}}\right]"," ",0,"[1/30720*(15*(5*b^6*c^6 - 6*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 75*a^4*b^2*c^2*d^4 - 70*a^5*b*c*d^5 + 21*a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(1280*b^6*d^6*x^5 + 75*b^6*c^5*d - 65*a*b^5*c^4*d^2 - 90*a^2*b^4*c^3*d^3 + 838*a^3*b^3*c^2*d^4 - 945*a^4*b^2*c*d^5 + 315*a^5*b*d^6 + 128*(25*b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(135*b^6*c^2*d^4 + 26*a*b^5*c*d^5 - 9*a^2*b^4*d^6)*x^3 + 8*(5*b^6*c^3*d^3 + 51*a*b^5*c^2*d^4 - 61*a^2*b^4*c*d^5 + 21*a^3*b^3*d^6)*x^2 - 2*(25*b^6*c^4*d^2 - 20*a*b^5*c^3*d^3 + 262*a^2*b^4*c^2*d^4 - 308*a^3*b^3*c*d^5 + 105*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^4), 1/15360*(15*(5*b^6*c^6 - 6*a*b^5*c^5*d - 5*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 75*a^4*b^2*c^2*d^4 - 70*a^5*b*c*d^5 + 21*a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(1280*b^6*d^6*x^5 + 75*b^6*c^5*d - 65*a*b^5*c^4*d^2 - 90*a^2*b^4*c^3*d^3 + 838*a^3*b^3*c^2*d^4 - 945*a^4*b^2*c*d^5 + 315*a^5*b*d^6 + 128*(25*b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(135*b^6*c^2*d^4 + 26*a*b^5*c*d^5 - 9*a^2*b^4*d^6)*x^3 + 8*(5*b^6*c^3*d^3 + 51*a*b^5*c^2*d^4 - 61*a^2*b^4*c*d^5 + 21*a^3*b^3*d^6)*x^2 - 2*(25*b^6*c^4*d^2 - 20*a*b^5*c^3*d^3 + 262*a^2*b^4*c^2*d^4 - 308*a^3*b^3*c*d^5 + 105*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^4)]","A",0
567,1,704,0,1.614692," ","integrate(x*(d*x+c)^(5/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 10 \, a^{2} b^{3} c^{3} d^{2} + 30 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 60 \, a b^{4} c^{3} d^{2} - 346 \, a^{2} b^{3} c^{2} d^{3} + 340 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(21 \, b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 22 \, a b^{4} c d^{4} - 7 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 109 \, a b^{4} c^{2} d^{3} - 111 \, a^{2} b^{3} c d^{4} + 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{5} d^{3}}, -\frac{15 \, {\left(3 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 10 \, a^{2} b^{3} c^{3} d^{2} + 30 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 60 \, a b^{4} c^{3} d^{2} - 346 \, a^{2} b^{3} c^{2} d^{3} + 340 \, a^{3} b^{2} c d^{4} - 105 \, a^{4} b d^{5} + 48 \, {\left(21 \, b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 22 \, a b^{4} c d^{4} - 7 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 109 \, a b^{4} c^{2} d^{3} - 111 \, a^{2} b^{3} c d^{4} + 35 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{5} d^{3}}\right]"," ",0,"[1/7680*(15*(3*b^5*c^5 - 5*a*b^4*c^4*d - 10*a^2*b^3*c^3*d^2 + 30*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 60*a*b^4*c^3*d^2 - 346*a^2*b^3*c^2*d^3 + 340*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(21*b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 22*a*b^4*c*d^4 - 7*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 109*a*b^4*c^2*d^3 - 111*a^2*b^3*c*d^4 + 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^3), -1/3840*(15*(3*b^5*c^5 - 5*a*b^4*c^4*d - 10*a^2*b^3*c^3*d^2 + 30*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 60*a*b^4*c^3*d^2 - 346*a^2*b^3*c^2*d^3 + 340*a^3*b^2*c*d^4 - 105*a^4*b*d^5 + 48*(21*b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 22*a*b^4*c*d^4 - 7*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 109*a*b^4*c^2*d^3 - 111*a^2*b^3*c*d^4 + 35*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^3)]","A",0
568,1,540,0,1.777035," ","integrate((b*x+a)^(1/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 73 \, a b^{3} c^{2} d^{2} - 55 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 18 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{4} d^{2}}, \frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 73 \, a b^{3} c^{2} d^{2} - 55 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 18 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{4} d^{2}}\right]"," ",0,"[1/768*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 73*a*b^3*c^2*d^2 - 55*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(17*b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 18*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^2), 1/384*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 73*a*b^3*c^2*d^2 - 55*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(17*b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 18*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^2)]","A",0
569,1,1197,0,19.509059," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{a c} b^{3} c^{2} d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{3} d}, \frac{24 \, \sqrt{a c} b^{3} c^{2} d \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{3} d}, \frac{96 \, \sqrt{-a c} b^{3} c^{2} d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{3} d}, \frac{48 \, \sqrt{-a c} b^{3} c^{2} d \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{3} d}\right]"," ",0,"[1/96*(48*sqrt(a*c)*b^3*c^2*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 33*b^3*c^2*d + 14*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(13*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d), 1/48*(24*sqrt(a*c)*b^3*c^2*d*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 33*b^3*c^2*d + 14*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(13*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d), 1/96*(96*sqrt(-a*c)*b^3*c^2*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 33*b^3*c^2*d + 14*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(13*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d), 1/48*(48*sqrt(-a*c)*b^3*c^2*d*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 33*b^3*c^2*d + 14*a*b^2*c*d^2 - 3*a^2*b*d^3 + 2*(13*b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d)]","A",0
570,1,1079,0,10.365695," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{{\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, b d^{2} x^{2} - 4 \, b c^{2} + {\left(9 \, b c d + a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b x}, -\frac{{\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 2 \, {\left(2 \, b d^{2} x^{2} - 4 \, b c^{2} + {\left(9 \, b c d + a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b x}, \frac{8 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b d^{2} x^{2} - 4 \, b c^{2} + {\left(9 \, b c d + a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b x}, \frac{4 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b d^{2} x^{2} - 4 \, b c^{2} + {\left(9 \, b c d + a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b x}\right]"," ",0,"[-1/16*((15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(b^2*c^2 + 5*a*b*c*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*b*d^2*x^2 - 4*b*c^2 + (9*b*c*d + a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*x), -1/8*((15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(b^2*c^2 + 5*a*b*c*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 2*(2*b*d^2*x^2 - 4*b*c^2 + (9*b*c*d + a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*x), 1/16*(8*(b^2*c^2 + 5*a*b*c*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b*d^2*x^2 - 4*b*c^2 + (9*b*c*d + a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*x), 1/8*(4*(b^2*c^2 + 5*a*b*c*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(2*b*d^2*x^2 - 4*b*c^2 + (9*b*c*d + a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*x)]","A",0
571,1,1094,0,8.061491," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, a d^{2} x^{2} - 2 \, a c^{2} - {\left(b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a x^{2}}, -\frac{8 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(4 \, a d^{2} x^{2} - 2 \, a c^{2} - {\left(b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a x^{2}}, -\frac{{\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 2 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(4 \, a d^{2} x^{2} - 2 \, a c^{2} - {\left(b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a x^{2}}, -\frac{{\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 4 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(4 \, a d^{2} x^{2} - 2 \, a c^{2} - {\left(b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a x^{2}}\right]"," ",0,"[1/16*(4*(5*a*b*c*d + a^2*d^2)*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - (b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*a*d^2*x^2 - 2*a*c^2 - (b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*x^2), -1/16*(8*(5*a*b*c*d + a^2*d^2)*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + (b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(4*a*d^2*x^2 - 2*a*c^2 - (b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*x^2), -1/8*((b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 2*(5*a*b*c*d + a^2*d^2)*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(4*a*d^2*x^2 - 2*a*c^2 - (b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*x^2), -1/8*((b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 4*(5*a*b*c*d + a^2*d^2)*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(4*a*d^2*x^2 - 2*a*c^2 - (b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*x^2)]","A",0
572,1,1245,0,9.000590," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{b d} a^{3} c d^{2} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 14 \, a^{2} b c^{2} d - 33 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{3} c x^{3}}, -\frac{96 \, \sqrt{-b d} a^{3} c d^{2} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 14 \, a^{2} b c^{2} d - 33 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{3} c x^{3}}, \frac{24 \, \sqrt{b d} a^{3} c d^{2} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 14 \, a^{2} b c^{2} d - 33 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{3} c x^{3}}, -\frac{48 \, \sqrt{-b d} a^{3} c d^{2} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} - 14 \, a^{2} b c^{2} d - 33 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{3} c x^{3}}\right]"," ",0,"[1/96*(48*sqrt(b*d)*a^3*c*d^2*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 - (3*a*b^2*c^3 - 14*a^2*b*c^2*d - 33*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^3), -1/96*(96*sqrt(-b*d)*a^3*c*d^2*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 - (3*a*b^2*c^3 - 14*a^2*b*c^2*d - 33*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^3), 1/48*(24*sqrt(b*d)*a^3*c*d^2*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 - (3*a*b^2*c^3 - 14*a^2*b*c^2*d - 33*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^3), -1/48*(48*sqrt(-b*d)*a^3*c*d^2*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 - (3*a*b^2*c^3 - 14*a^2*b*c^2*d - 33*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^3)]","A",0
573,1,566,0,7.998018," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 73 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 18 \, a^{3} b c^{3} d - 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{4} c^{2} x^{4}}, -\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 73 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} - 18 \, a^{3} b c^{3} d - 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{4} c^{2} x^{4}}\right]"," ",0,"[1/768*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 + (15*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 73*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 18*a^3*b*c^3*d - 59*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^2*x^4), -1/384*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 73*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 - 18*a^3*b*c^3*d - 59*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^2*x^4)]","A",0
574,1,732,0,19.449508," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 340 \, a^{2} b^{3} c^{4} d + 346 \, a^{3} b^{2} c^{3} d^{2} - 60 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 111 \, a^{3} b^{2} c^{4} d + 109 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 22 \, a^{4} b c^{4} d - 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + 21 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{5} c^{3} x^{5}}, \frac{15 \, {\left(7 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(384 \, a^{5} c^{5} - {\left(105 \, a b^{4} c^{5} - 340 \, a^{2} b^{3} c^{4} d + 346 \, a^{3} b^{2} c^{3} d^{2} - 60 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(35 \, a^{2} b^{3} c^{5} - 111 \, a^{3} b^{2} c^{4} d + 109 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} - 8 \, {\left(7 \, a^{3} b^{2} c^{5} - 22 \, a^{4} b c^{4} d - 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(a^{4} b c^{5} + 21 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{5} c^{3} x^{5}}\right]"," ",0,"[1/7680*(15*(7*b^5*c^5 - 25*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(384*a^5*c^5 - (105*a*b^4*c^5 - 340*a^2*b^3*c^4*d + 346*a^3*b^2*c^3*d^2 - 60*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 111*a^3*b^2*c^4*d + 109*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 22*a^4*b*c^4*d - 93*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + 21*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^3*x^5), 1/3840*(15*(7*b^5*c^5 - 25*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(384*a^5*c^5 - (105*a*b^4*c^5 - 340*a^2*b^3*c^4*d + 346*a^3*b^2*c^3*d^2 - 60*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(35*a^2*b^3*c^5 - 111*a^3*b^2*c^4*d + 109*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 - 8*(7*a^3*b^2*c^5 - 22*a^4*b*c^4*d - 93*a^5*c^3*d^2)*x^2 + 48*(a^4*b*c^5 + 21*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^3*x^5)]","A",0
575,1,918,0,43.408312," ","integrate((d*x+c)^(5/2)*(b*x+a)^(1/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right)} \sqrt{a c} x^{6} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(1280 \, a^{6} c^{6} + {\left(315 \, a b^{5} c^{6} - 945 \, a^{2} b^{4} c^{5} d + 838 \, a^{3} b^{3} c^{4} d^{2} - 90 \, a^{4} b^{2} c^{3} d^{3} - 65 \, a^{5} b c^{2} d^{4} + 75 \, a^{6} c d^{5}\right)} x^{5} - 2 \, {\left(105 \, a^{2} b^{4} c^{6} - 308 \, a^{3} b^{3} c^{5} d + 262 \, a^{4} b^{2} c^{4} d^{2} - 20 \, a^{5} b c^{3} d^{3} + 25 \, a^{6} c^{2} d^{4}\right)} x^{4} + 8 \, {\left(21 \, a^{3} b^{3} c^{6} - 61 \, a^{4} b^{2} c^{5} d + 51 \, a^{5} b c^{4} d^{2} + 5 \, a^{6} c^{3} d^{3}\right)} x^{3} - 16 \, {\left(9 \, a^{4} b^{2} c^{6} - 26 \, a^{5} b c^{5} d - 135 \, a^{6} c^{4} d^{2}\right)} x^{2} + 128 \, {\left(a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, a^{6} c^{4} x^{6}}, -\frac{15 \, {\left(21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right)} \sqrt{-a c} x^{6} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(1280 \, a^{6} c^{6} + {\left(315 \, a b^{5} c^{6} - 945 \, a^{2} b^{4} c^{5} d + 838 \, a^{3} b^{3} c^{4} d^{2} - 90 \, a^{4} b^{2} c^{3} d^{3} - 65 \, a^{5} b c^{2} d^{4} + 75 \, a^{6} c d^{5}\right)} x^{5} - 2 \, {\left(105 \, a^{2} b^{4} c^{6} - 308 \, a^{3} b^{3} c^{5} d + 262 \, a^{4} b^{2} c^{4} d^{2} - 20 \, a^{5} b c^{3} d^{3} + 25 \, a^{6} c^{2} d^{4}\right)} x^{4} + 8 \, {\left(21 \, a^{3} b^{3} c^{6} - 61 \, a^{4} b^{2} c^{5} d + 51 \, a^{5} b c^{4} d^{2} + 5 \, a^{6} c^{3} d^{3}\right)} x^{3} - 16 \, {\left(9 \, a^{4} b^{2} c^{6} - 26 \, a^{5} b c^{5} d - 135 \, a^{6} c^{4} d^{2}\right)} x^{2} + 128 \, {\left(a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, a^{6} c^{4} x^{6}}\right]"," ",0,"[1/30720*(15*(21*b^6*c^6 - 70*a*b^5*c^5*d + 75*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 5*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + 5*a^6*d^6)*sqrt(a*c)*x^6*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(1280*a^6*c^6 + (315*a*b^5*c^6 - 945*a^2*b^4*c^5*d + 838*a^3*b^3*c^4*d^2 - 90*a^4*b^2*c^3*d^3 - 65*a^5*b*c^2*d^4 + 75*a^6*c*d^5)*x^5 - 2*(105*a^2*b^4*c^6 - 308*a^3*b^3*c^5*d + 262*a^4*b^2*c^4*d^2 - 20*a^5*b*c^3*d^3 + 25*a^6*c^2*d^4)*x^4 + 8*(21*a^3*b^3*c^6 - 61*a^4*b^2*c^5*d + 51*a^5*b*c^4*d^2 + 5*a^6*c^3*d^3)*x^3 - 16*(9*a^4*b^2*c^6 - 26*a^5*b*c^5*d - 135*a^6*c^4*d^2)*x^2 + 128*(a^5*b*c^6 + 25*a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*c^4*x^6), -1/15360*(15*(21*b^6*c^6 - 70*a*b^5*c^5*d + 75*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 5*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + 5*a^6*d^6)*sqrt(-a*c)*x^6*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(1280*a^6*c^6 + (315*a*b^5*c^6 - 945*a^2*b^4*c^5*d + 838*a^3*b^3*c^4*d^2 - 90*a^4*b^2*c^3*d^3 - 65*a^5*b*c^2*d^4 + 75*a^6*c*d^5)*x^5 - 2*(105*a^2*b^4*c^6 - 308*a^3*b^3*c^5*d + 262*a^4*b^2*c^4*d^2 - 20*a^5*b*c^3*d^3 + 25*a^6*c^2*d^4)*x^4 + 8*(21*a^3*b^3*c^6 - 61*a^4*b^2*c^5*d + 51*a^5*b*c^4*d^2 + 5*a^6*c^3*d^3)*x^3 - 16*(9*a^4*b^2*c^6 - 26*a^5*b*c^5*d - 135*a^6*c^4*d^2)*x^2 + 128*(a^5*b*c^6 + 25*a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*c^4*x^6)]","A",0
576,1,546,0,1.595076," ","integrate(x^3*(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(35 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 105 \, b^{4} c^{3} d + 25 \, a b^{3} c^{2} d^{2} + 17 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 6 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{4} d^{5}}, -\frac{3 \, {\left(35 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 105 \, b^{4} c^{3} d + 25 \, a b^{3} c^{2} d^{2} + 17 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} - 8 \, {\left(7 \, b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{2} d^{2} - 6 \, a b^{3} c d^{3} - 5 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{4} d^{5}}\right]"," ",0,"[-1/768*(3*(35*b^4*c^4 - 20*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^4*x^3 - 105*b^4*c^3*d + 25*a*b^3*c^2*d^2 + 17*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - a*b^3*d^4)*x^2 + 2*(35*b^4*c^2*d^2 - 6*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5), -1/384*(3*(35*b^4*c^4 - 20*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^4*x^3 - 105*b^4*c^3*d + 25*a*b^3*c^2*d^2 + 17*a^2*b^2*c*d^3 + 15*a^3*b*d^4 - 8*(7*b^4*c*d^3 - a*b^3*d^4)*x^2 + 2*(35*b^4*c^2*d^2 - 6*a*b^3*c*d^3 - 5*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5)]","A",0
577,1,414,0,1.356238," ","integrate(x^2*(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{3} d^{4}}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{3} d^{4}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 + 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4), 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*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4)]","A",0
578,1,306,0,1.425388," ","integrate(x*(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2} d^{3}}, -\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d + a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2} d^{3}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(2*b^2*d^2*x - 3*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3), -1/8*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^2*x - 3*b^2*c*d + a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3)]","A",0
579,1,235,0,1.402333," ","integrate((b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x + a} \sqrt{d x + c} b d - {\left(b c - a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{4 \, b d^{2}}, \frac{2 \, \sqrt{b x + a} \sqrt{d x + c} b d + {\left(b c - a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{2 \, b d^{2}}\right]"," ",0,"[1/4*(4*sqrt(b*x + a)*sqrt(d*x + c)*b*d - (b*c - a*d)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b*d^2), 1/2*(2*sqrt(b*x + a)*sqrt(d*x + c)*b*d + (b*c - a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b*d^2)]","A",0
580,1,711,0,1.518900," ","integrate((b*x+a)^(1/2)/x/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \frac{1}{2} \, \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right), -\sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right), \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right), \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right)\right]"," ",0,"[1/2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 1/2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2), -sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 1/2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2), sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 1/2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x), sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x))]","B",0
581,1,252,0,1.789318," ","integrate((b*x+a)^(1/2)/x^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a c} {\left(b c - a d\right)} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} a c}{4 \, a c^{2} x}, \frac{\sqrt{-a c} {\left(b c - a d\right)} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, \sqrt{b x + a} \sqrt{d x + c} a c}{2 \, a c^{2} x}\right]"," ",0,"[-1/4*(sqrt(a*c)*(b*c - a*d)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c^2*x), 1/2*(sqrt(-a*c)*(b*c - a*d)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a*c^2*x)]","A",0
582,1,330,0,1.965036," ","integrate((b*x+a)^(1/2)/x^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} c^{3} x^{2}}, -\frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{2} + {\left(a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} c^{3} x^{2}}\right]"," ",0,"[-1/16*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c^2 + (a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^2), -1/8*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(2*a^2*c^2 + (a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^2)]","A",0
583,1,436,0,3.184143," ","integrate((b*x+a)^(1/2)/x^4/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 4 \, a^{2} b c^{2} d - 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{3} c^{4} x^{3}}, \frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 4 \, a^{2} b c^{2} d - 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{3} c^{4} x^{3}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 - (3*a*b^2*c^3 + 4*a^2*b*c^2*d - 15*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^3), 1/48*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 - (3*a*b^2*c^3 + 4*a^2*b*c^2*d - 15*a^3*c*d^2)*x^2 + 2*(a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^3)]","A",0
584,1,570,0,11.632418," ","integrate((b*x+a)^(1/2)/x^5/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 35 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 17 \, a^{2} b^{2} c^{3} d + 25 \, a^{3} b c^{2} d^{2} - 105 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} + 6 \, a^{3} b c^{3} d - 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{4} c^{5} x^{4}}, -\frac{3 \, {\left(5 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 35 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 17 \, a^{2} b^{2} c^{3} d + 25 \, a^{3} b c^{2} d^{2} - 105 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(5 \, a^{2} b^{2} c^{4} + 6 \, a^{3} b c^{3} d - 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{4} c^{5} x^{4}}\right]"," ",0,"[-1/768*(3*(5*b^4*c^4 + 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 35*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 + (15*a*b^3*c^4 + 17*a^2*b^2*c^3*d + 25*a^3*b*c^2*d^2 - 105*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 + 6*a^3*b*c^3*d - 35*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^5*x^4), -1/384*(3*(5*b^4*c^4 + 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 35*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 + 17*a^2*b^2*c^3*d + 25*a^3*b*c^2*d^2 - 105*a^4*c*d^3)*x^3 - 2*(5*a^2*b^2*c^4 + 6*a^3*b*c^3*d - 35*a^4*c^2*d^2)*x^2 + 8*(a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^5*x^4)]","A",0
585,1,444,0,1.395917," ","integrate(x^2*(b*x+a)^(1/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(15 \, b^{2} c^{3} - 6 \, a b c^{2} d - a^{2} c d^{2} + {\left(15 \, b^{2} c^{2} d - 6 \, a b c d^{2} - a^{2} d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(2 \, b^{2} d^{3} x^{2} - 15 \, b^{2} c^{2} d + a b c d^{2} - {\left(5 \, b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}, -\frac{{\left(15 \, b^{2} c^{3} - 6 \, a b c^{2} d - a^{2} c d^{2} + {\left(15 \, b^{2} c^{2} d - 6 \, a b c d^{2} - a^{2} d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{3} x^{2} - 15 \, b^{2} c^{2} d + a b c d^{2} - {\left(5 \, b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}\right]"," ",0,"[-1/16*((15*b^2*c^3 - 6*a*b*c^2*d - a^2*c*d^2 + (15*b^2*c^2*d - 6*a*b*c*d^2 - a^2*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(2*b^2*d^3*x^2 - 15*b^2*c^2*d + a*b*c*d^2 - (5*b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^5*x + b^2*c*d^4), -1/8*((15*b^2*c^3 - 6*a*b*c^2*d - a^2*c*d^2 + (15*b^2*c^2*d - 6*a*b*c*d^2 - a^2*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^3*x^2 - 15*b^2*c^2*d + a*b*c*d^2 - (5*b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^5*x + b^2*c*d^4)]","A",0
586,1,308,0,1.367664," ","integrate(x*(b*x+a)^(1/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(b d^{2} x + 3 \, b c d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(b d^{4} x + b c d^{3}\right)}}, \frac{{\left(3 \, b c^{2} - a c d + {\left(3 \, b c d - a d^{2}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(b d^{2} x + 3 \, b c d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b d^{4} x + b c d^{3}\right)}}\right]"," ",0,"[-1/4*((3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(b*d^2*x + 3*b*c*d)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^4*x + b*c*d^3), 1/2*((3*b*c^2 - a*c*d + (3*b*c*d - a*d^2)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(b*d^2*x + 3*b*c*d)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^4*x + b*c*d^3)]","A",0
587,1,241,0,1.064577," ","integrate((b*x+a)^(1/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d x + c\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(d^{2} x + c d\right)}}, -\frac{{\left(d x + c\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c}}{d^{2} x + c d}\right]"," ",0,"[1/2*((d*x + c)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*sqrt(b*x + a)*sqrt(d*x + c))/(d^2*x + c*d), -((d*x + c)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c))/(d^2*x + c*d)]","B",0
588,1,248,0,1.585573," ","integrate((b*x+a)^(1/2)/x/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(d x + c\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d x + c^{2}\right)}}, \frac{{\left(d x + c\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c}}{c d x + c^{2}}\right]"," ",0,"[1/2*((d*x + c)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x + c^2), ((d*x + c)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x + c^2)]","B",0
589,1,330,0,1.932138," ","integrate((b*x+a)^(1/2)/x^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b c d - 3 \, a d^{2}\right)} x^{2} + {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a c d x + a c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a c^{3} d x^{2} + a c^{4} x\right)}}, \frac{{\left({\left(b c d - 3 \, a d^{2}\right)} x^{2} + {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(3 \, a c d x + a c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a c^{3} d x^{2} + a c^{4} x\right)}}\right]"," ",0,"[-1/4*(((b*c*d - 3*a*d^2)*x^2 + (b*c^2 - 3*a*c*d)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a*c*d*x + a*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*d*x^2 + a*c^4*x), 1/2*(((b*c*d - 3*a*d^2)*x^2 + (b*c^2 - 3*a*c*d)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(3*a*c*d*x + a*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*d*x^2 + a*c^4*x)]","A",0
590,1,474,0,3.282050," ","integrate((b*x+a)^(1/2)/x^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b^{2} c^{2} d + 6 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2} + {\left(a b c^{3} - 5 \, a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(a^{2} c^{4} d x^{3} + a^{2} c^{5} x^{2}\right)}}, -\frac{{\left({\left(b^{2} c^{2} d + 6 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} + 6 \, a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{3} + {\left(a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2} + {\left(a b c^{3} - 5 \, a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(a^{2} c^{4} d x^{3} + a^{2} c^{5} x^{2}\right)}}\right]"," ",0,"[-1/16*(((b^2*c^2*d + 6*a*b*c*d^2 - 15*a^2*d^3)*x^3 + (b^2*c^3 + 6*a*b*c^2*d - 15*a^2*c*d^2)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c^3 + (a*b*c^2*d - 15*a^2*c*d^2)*x^2 + (a*b*c^3 - 5*a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*d*x^3 + a^2*c^5*x^2), -1/8*(((b^2*c^2*d + 6*a*b*c*d^2 - 15*a^2*d^3)*x^3 + (b^2*c^3 + 6*a*b*c^2*d - 15*a^2*c*d^2)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(2*a^2*c^3 + (a*b*c^2*d - 15*a^2*c*d^2)*x^2 + (a*b*c^3 - 5*a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*d*x^3 + a^2*c^5*x^2)]","A",0
591,1,866,0,2.504185," ","integrate(x^3*(b*x+a)^(1/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(35 \, b^{3} c^{5} - 45 \, a b^{2} c^{4} d + 9 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(35 \, b^{3} c^{3} d^{2} - 45 \, a b^{2} c^{2} d^{3} + 9 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{3} c^{4} d - 45 \, a b^{2} c^{3} d^{2} + 9 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(105 \, b^{3} c^{4} d - 100 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - 6 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x^{3} + 3 \, {\left(7 \, b^{3} c^{2} d^{3} - 8 \, a b^{2} c d^{4} + a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(70 \, b^{3} c^{3} d^{2} - 69 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{3} c^{3} d^{5} - a b^{2} c^{2} d^{6} + {\left(b^{3} c d^{7} - a b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{3} c^{2} d^{6} - a b^{2} c d^{7}\right)} x\right)}}, -\frac{3 \, {\left(35 \, b^{3} c^{5} - 45 \, a b^{2} c^{4} d + 9 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(35 \, b^{3} c^{3} d^{2} - 45 \, a b^{2} c^{2} d^{3} + 9 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{3} c^{4} d - 45 \, a b^{2} c^{3} d^{2} + 9 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(105 \, b^{3} c^{4} d - 100 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - 6 \, {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x^{3} + 3 \, {\left(7 \, b^{3} c^{2} d^{3} - 8 \, a b^{2} c d^{4} + a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(70 \, b^{3} c^{3} d^{2} - 69 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(b^{3} c^{3} d^{5} - a b^{2} c^{2} d^{6} + {\left(b^{3} c d^{7} - a b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{3} c^{2} d^{6} - a b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(35*b^3*c^5 - 45*a*b^2*c^4*d + 9*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (35*b^3*c^3*d^2 - 45*a*b^2*c^2*d^3 + 9*a^2*b*c*d^4 + a^3*d^5)*x^2 + 2*(35*b^3*c^4*d - 45*a*b^2*c^3*d^2 + 9*a^2*b*c^2*d^3 + a^3*c*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(105*b^3*c^4*d - 100*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - 6*(b^3*c*d^4 - a*b^2*d^5)*x^3 + 3*(7*b^3*c^2*d^3 - 8*a*b^2*c*d^4 + a^2*b*d^5)*x^2 + 2*(70*b^3*c^3*d^2 - 69*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^3*d^5 - a*b^2*c^2*d^6 + (b^3*c*d^7 - a*b^2*d^8)*x^2 + 2*(b^3*c^2*d^6 - a*b^2*c*d^7)*x), -1/24*(3*(35*b^3*c^5 - 45*a*b^2*c^4*d + 9*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (35*b^3*c^3*d^2 - 45*a*b^2*c^2*d^3 + 9*a^2*b*c*d^4 + a^3*d^5)*x^2 + 2*(35*b^3*c^4*d - 45*a*b^2*c^3*d^2 + 9*a^2*b*c^2*d^3 + a^3*c*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(105*b^3*c^4*d - 100*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - 6*(b^3*c*d^4 - a*b^2*d^5)*x^3 + 3*(7*b^3*c^2*d^3 - 8*a*b^2*c*d^4 + a^2*b*d^5)*x^2 + 2*(70*b^3*c^3*d^2 - 69*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^3*d^5 - a*b^2*c^2*d^6 + (b^3*c*d^7 - a*b^2*d^8)*x^2 + 2*(b^3*c^2*d^6 - a*b^2*c*d^7)*x)]","B",0
592,1,640,0,1.891422," ","integrate(x^2*(b*x+a)^(1/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{2} c^{4} - 6 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(5 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(5 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(15 \, b^{2} c^{3} d - 13 \, a b c^{2} d^{2} + 3 \, {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2} + 2 \, {\left(10 \, b^{2} c^{2} d^{2} - 9 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(b^{2} c^{3} d^{4} - a b c^{2} d^{5} + {\left(b^{2} c d^{6} - a b d^{7}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d^{5} - a b c d^{6}\right)} x\right)}}, \frac{3 \, {\left(5 \, b^{2} c^{4} - 6 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(5 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(5 \, b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, b^{2} c^{3} d - 13 \, a b c^{2} d^{2} + 3 \, {\left(b^{2} c d^{3} - a b d^{4}\right)} x^{2} + 2 \, {\left(10 \, b^{2} c^{2} d^{2} - 9 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b^{2} c^{3} d^{4} - a b c^{2} d^{5} + {\left(b^{2} c d^{6} - a b d^{7}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d^{5} - a b c d^{6}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*(5*b^2*c^4 - 6*a*b*c^3*d + a^2*c^2*d^2 + (5*b^2*c^2*d^2 - 6*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(5*b^2*c^3*d - 6*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(15*b^2*c^3*d - 13*a*b*c^2*d^2 + 3*(b^2*c*d^3 - a*b*d^4)*x^2 + 2*(10*b^2*c^2*d^2 - 9*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*c^3*d^4 - a*b*c^2*d^5 + (b^2*c*d^6 - a*b*d^7)*x^2 + 2*(b^2*c^2*d^5 - a*b*c*d^6)*x), 1/6*(3*(5*b^2*c^4 - 6*a*b*c^3*d + a^2*c^2*d^2 + (5*b^2*c^2*d^2 - 6*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(5*b^2*c^3*d - 6*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*b^2*c^3*d - 13*a*b*c^2*d^2 + 3*(b^2*c*d^3 - a*b*d^4)*x^2 + 2*(10*b^2*c^2*d^2 - 9*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*c^3*d^4 - a*b*c^2*d^5 + (b^2*c*d^6 - a*b*d^7)*x^2 + 2*(b^2*c^2*d^5 - a*b*c*d^6)*x)]","B",0
593,1,469,0,1.734959," ","integrate(x*(b*x+a)^(1/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c d^{2} - a d^{3}\right)} x^{2} + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b c^{2} - 2 \, a c d + {\left(4 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b c^{3} d^{2} - a c^{2} d^{3} + {\left(b c d^{4} - a d^{5}\right)} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} x\right)}}, -\frac{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c d^{2} - a d^{3}\right)} x^{2} + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(3 \, b c^{2} - 2 \, a c d + {\left(4 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(b c^{3} d^{2} - a c^{2} d^{3} + {\left(b c d^{4} - a d^{5}\right)} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(b*c^3 - a*c^2*d + (b*c*d^2 - a*d^3)*x^2 + 2*(b*c^2*d - a*c*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b*c^2 - 2*a*c*d + (4*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*c^3*d^2 - a*c^2*d^3 + (b*c*d^4 - a*d^5)*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*x), -1/3*(3*(b*c^3 - a*c^2*d + (b*c*d^2 - a*d^3)*x^2 + 2*(b*c^2*d - a*c*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(3*b*c^2 - 2*a*c*d + (4*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*c^3*d^2 - a*c^2*d^3 + (b*c*d^4 - a*d^5)*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*x)]","B",0
594,1,65,0,1.598819," ","integrate((b*x+a)^(1/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x + a\right)}^{\frac{3}{2}} \sqrt{d x + c}}{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c d^{2} - a d^{3}\right)} x^{2} + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x\right)}}"," ",0,"2/3*(b*x + a)^(3/2)*sqrt(d*x + c)/(b*c^3 - a*c^2*d + (b*c*d^2 - a*d^3)*x^2 + 2*(b*c^2*d - a*c*d^2)*x)","B",0
595,1,479,0,2.281052," ","integrate((b*x+a)^(1/2)/x/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c d^{2} - a d^{3}\right)} x^{2} + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, b c^{2} - 4 \, a c d + {\left(2 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b c^{5} - a c^{4} d + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b c^{4} d - a c^{3} d^{2}\right)} x\right)}}, \frac{3 \, {\left(b c^{3} - a c^{2} d + {\left(b c d^{2} - a d^{3}\right)} x^{2} + 2 \, {\left(b c^{2} d - a c d^{2}\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, {\left(3 \, b c^{2} - 4 \, a c d + {\left(2 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(b c^{5} - a c^{4} d + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} x^{2} + 2 \, {\left(b c^{4} d - a c^{3} d^{2}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(b*c^3 - a*c^2*d + (b*c*d^2 - a*d^3)*x^2 + 2*(b*c^2*d - a*c*d^2)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*b*c^2 - 4*a*c*d + (2*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*c^5 - a*c^4*d + (b*c^3*d^2 - a*c^2*d^3)*x^2 + 2*(b*c^4*d - a*c^3*d^2)*x), 1/3*(3*(b*c^3 - a*c^2*d + (b*c*d^2 - a*d^3)*x^2 + 2*(b*c^2*d - a*c*d^2)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*(3*b*c^2 - 4*a*c*d + (2*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*c^5 - a*c^4*d + (b*c^3*d^2 - a*c^2*d^3)*x^2 + 2*(b*c^4*d - a*c^3*d^2)*x)]","B",0
596,1,670,0,2.890685," ","integrate((b*x+a)^(1/2)/x^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{3} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{2} + {\left(b^{2} c^{4} - 6 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a b c^{4} - 3 \, a^{2} c^{3} d + {\left(13 \, a b c^{2} d^{2} - 15 \, a^{2} c d^{3}\right)} x^{2} + 2 \, {\left(9 \, a b c^{3} d - 10 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left({\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3}\right)} x^{3} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x^{2} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x\right)}}, \frac{3 \, {\left({\left(b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 5 \, a^{2} d^{4}\right)} x^{3} + 2 \, {\left(b^{2} c^{3} d - 6 \, a b c^{2} d^{2} + 5 \, a^{2} c d^{3}\right)} x^{2} + {\left(b^{2} c^{4} - 6 \, a b c^{3} d + 5 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(3 \, a b c^{4} - 3 \, a^{2} c^{3} d + {\left(13 \, a b c^{2} d^{2} - 15 \, a^{2} c d^{3}\right)} x^{2} + 2 \, {\left(9 \, a b c^{3} d - 10 \, a^{2} c^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left({\left(a b c^{5} d^{2} - a^{2} c^{4} d^{3}\right)} x^{3} + 2 \, {\left(a b c^{6} d - a^{2} c^{5} d^{2}\right)} x^{2} + {\left(a b c^{7} - a^{2} c^{6} d\right)} x\right)}}\right]"," ",0,"[-1/12*(3*((b^2*c^2*d^2 - 6*a*b*c*d^3 + 5*a^2*d^4)*x^3 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^2 + (b^2*c^4 - 6*a*b*c^3*d + 5*a^2*c^2*d^2)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a*b*c^4 - 3*a^2*c^3*d + (13*a*b*c^2*d^2 - 15*a^2*c*d^3)*x^2 + 2*(9*a*b*c^3*d - 10*a^2*c^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a*b*c^5*d^2 - a^2*c^4*d^3)*x^3 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x^2 + (a*b*c^7 - a^2*c^6*d)*x), 1/6*(3*((b^2*c^2*d^2 - 6*a*b*c*d^3 + 5*a^2*d^4)*x^3 + 2*(b^2*c^3*d - 6*a*b*c^2*d^2 + 5*a^2*c*d^3)*x^2 + (b^2*c^4 - 6*a*b*c^3*d + 5*a^2*c^2*d^2)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(3*a*b*c^4 - 3*a^2*c^3*d + (13*a*b*c^2*d^2 - 15*a^2*c*d^3)*x^2 + 2*(9*a*b*c^3*d - 10*a^2*c^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a*b*c^5*d^2 - a^2*c^4*d^3)*x^3 + 2*(a*b*c^6*d - a^2*c^5*d^2)*x^2 + (a*b*c^7 - a^2*c^6*d)*x)]","B",0
597,1,904,0,7.834148," ","integrate((b*x+a)^(1/2)/x^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{3} c^{3} d^{2} + 9 \, a b^{2} c^{2} d^{3} - 45 \, a^{2} b c d^{4} + 35 \, a^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 45 \, a^{2} b c^{2} d^{3} + 35 \, a^{3} c d^{4}\right)} x^{3} + {\left(b^{3} c^{5} + 9 \, a b^{2} c^{4} d - 45 \, a^{2} b c^{3} d^{2} + 35 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(6 \, a^{2} b c^{5} - 6 \, a^{3} c^{4} d + {\left(3 \, a b^{2} c^{3} d^{2} - 100 \, a^{2} b c^{2} d^{3} + 105 \, a^{3} c d^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{2} c^{4} d - 69 \, a^{2} b c^{3} d^{2} + 70 \, a^{3} c^{2} d^{3}\right)} x^{2} + 3 \, {\left(a b^{2} c^{5} - 8 \, a^{2} b c^{4} d + 7 \, a^{3} c^{3} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left({\left(a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3}\right)} x^{4} + 2 \, {\left(a^{2} b c^{7} d - a^{3} c^{6} d^{2}\right)} x^{3} + {\left(a^{2} b c^{8} - a^{3} c^{7} d\right)} x^{2}\right)}}, -\frac{3 \, {\left({\left(b^{3} c^{3} d^{2} + 9 \, a b^{2} c^{2} d^{3} - 45 \, a^{2} b c d^{4} + 35 \, a^{3} d^{5}\right)} x^{4} + 2 \, {\left(b^{3} c^{4} d + 9 \, a b^{2} c^{3} d^{2} - 45 \, a^{2} b c^{2} d^{3} + 35 \, a^{3} c d^{4}\right)} x^{3} + {\left(b^{3} c^{5} + 9 \, a b^{2} c^{4} d - 45 \, a^{2} b c^{3} d^{2} + 35 \, a^{3} c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(6 \, a^{2} b c^{5} - 6 \, a^{3} c^{4} d + {\left(3 \, a b^{2} c^{3} d^{2} - 100 \, a^{2} b c^{2} d^{3} + 105 \, a^{3} c d^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{2} c^{4} d - 69 \, a^{2} b c^{3} d^{2} + 70 \, a^{3} c^{2} d^{3}\right)} x^{2} + 3 \, {\left(a b^{2} c^{5} - 8 \, a^{2} b c^{4} d + 7 \, a^{3} c^{3} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left({\left(a^{2} b c^{6} d^{2} - a^{3} c^{5} d^{3}\right)} x^{4} + 2 \, {\left(a^{2} b c^{7} d - a^{3} c^{6} d^{2}\right)} x^{3} + {\left(a^{2} b c^{8} - a^{3} c^{7} d\right)} x^{2}\right)}}\right]"," ",0,"[-1/48*(3*((b^3*c^3*d^2 + 9*a*b^2*c^2*d^3 - 45*a^2*b*c*d^4 + 35*a^3*d^5)*x^4 + 2*(b^3*c^4*d + 9*a*b^2*c^3*d^2 - 45*a^2*b*c^2*d^3 + 35*a^3*c*d^4)*x^3 + (b^3*c^5 + 9*a*b^2*c^4*d - 45*a^2*b*c^3*d^2 + 35*a^3*c^2*d^3)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(6*a^2*b*c^5 - 6*a^3*c^4*d + (3*a*b^2*c^3*d^2 - 100*a^2*b*c^2*d^3 + 105*a^3*c*d^4)*x^3 + 2*(3*a*b^2*c^4*d - 69*a^2*b*c^3*d^2 + 70*a^3*c^2*d^3)*x^2 + 3*(a*b^2*c^5 - 8*a^2*b*c^4*d + 7*a^3*c^3*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b*c^6*d^2 - a^3*c^5*d^3)*x^4 + 2*(a^2*b*c^7*d - a^3*c^6*d^2)*x^3 + (a^2*b*c^8 - a^3*c^7*d)*x^2), -1/24*(3*((b^3*c^3*d^2 + 9*a*b^2*c^2*d^3 - 45*a^2*b*c*d^4 + 35*a^3*d^5)*x^4 + 2*(b^3*c^4*d + 9*a*b^2*c^3*d^2 - 45*a^2*b*c^2*d^3 + 35*a^3*c*d^4)*x^3 + (b^3*c^5 + 9*a*b^2*c^4*d - 45*a^2*b*c^3*d^2 + 35*a^3*c^2*d^3)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(6*a^2*b*c^5 - 6*a^3*c^4*d + (3*a*b^2*c^3*d^2 - 100*a^2*b*c^2*d^3 + 105*a^3*c*d^4)*x^3 + 2*(3*a*b^2*c^4*d - 69*a^2*b*c^3*d^2 + 70*a^3*c^2*d^3)*x^2 + 3*(a*b^2*c^5 - 8*a^2*b*c^4*d + 7*a^3*c^3*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b*c^6*d^2 - a^3*c^5*d^3)*x^4 + 2*(a^2*b*c^7*d - a^3*c^6*d^2)*x^3 + (a^2*b*c^8 - a^3*c^7*d)*x^2)]","B",0
598,1,704,0,1.562751," ","integrate(x^2*(b*x+a)^(3/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{5} c^{5} - 15 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 190 \, a b^{4} c^{3} d^{2} - 36 \, a^{2} b^{3} c^{2} d^{3} - 30 \, a^{3} b^{2} c d^{4} + 45 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + 11 \, a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 12 \, a b^{4} c d^{4} - 3 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 61 \, a b^{4} c^{2} d^{3} + 9 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{4} d^{5}}, -\frac{15 \, {\left(7 \, b^{5} c^{5} - 15 \, a b^{4} c^{4} d + 6 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} + 3 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 190 \, a b^{4} c^{3} d^{2} - 36 \, a^{2} b^{3} c^{2} d^{3} - 30 \, a^{3} b^{2} c d^{4} + 45 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + 11 \, a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 12 \, a b^{4} c d^{4} - 3 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 61 \, a b^{4} c^{2} d^{3} + 9 \, a^{2} b^{3} c d^{4} - 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{4} d^{5}}\right]"," ",0,"[-1/7680*(15*(7*b^5*c^5 - 15*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 190*a*b^4*c^3*d^2 - 36*a^2*b^3*c^2*d^3 - 30*a^3*b^2*c*d^4 + 45*a^4*b*d^5 + 48*(b^5*c*d^4 + 11*a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 12*a*b^4*c*d^4 - 3*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 61*a*b^4*c^2*d^3 + 9*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5), -1/3840*(15*(7*b^5*c^5 - 15*a*b^4*c^4*d + 6*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 + 3*a^4*b*c*d^4 - 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 190*a*b^4*c^3*d^2 - 36*a^2*b^3*c^2*d^3 - 30*a^3*b^2*c*d^4 + 45*a^4*b*d^5 + 48*(b^5*c*d^4 + 11*a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 12*a*b^4*c*d^4 - 3*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 61*a*b^4*c^2*d^3 + 9*a^2*b^3*c*d^4 - 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5)]","A",0
599,1,544,0,1.497039," ","integrate(x*(b*x+a)^(3/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d + 6 \, 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} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 31 \, a b^{3} c^{2} d^{2} + 9 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} - 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{3} d^{4}}, \frac{3 \, {\left(5 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 31 \, a b^{3} c^{2} d^{2} + 9 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} - 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{3} d^{4}}\right]"," ",0,"[-1/768*(3*(5*b^4*c^4 - 12*a*b^3*c^3*d + 6*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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 31*a*b^3*c^2*d^2 + 9*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(b^4*c*d^3 + 9*a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 10*a*b^3*c*d^3 - 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4), 1/384*(3*(5*b^4*c^4 - 12*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 31*a*b^3*c^2*d^2 + 9*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(b^4*c*d^3 + 9*a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 10*a*b^3*c*d^3 - 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4)]","A",0
600,1,410,0,1.554004," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d^{3}}, -\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d^{3}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 8*a*b^2*c*d^2 + 3*a^2*b*d^3 + 2*(b^3*c*d^2 + 7*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3), -1/48*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 8*a*b^2*c*d^2 + 3*a^2*b*d^3 + 2*(b^3*c*d^2 + 7*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3)]","A",0
601,1,979,0,6.039935," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{a c} a b d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b d^{2}}, \frac{4 \, \sqrt{a c} a b d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b d^{2}}, \frac{16 \, \sqrt{-a c} a b d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b d^{2}}, \frac{8 \, \sqrt{-a c} a b d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b d^{2}}\right]"," ",0,"[1/16*(8*sqrt(a*c)*a*b*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2), 1/8*(4*sqrt(a*c)*a*b*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2), 1/16*(16*sqrt(-a*c)*a*b*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2), 1/8*(8*sqrt(-a*c)*a*b*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2)]","A",0
602,1,893,0,3.041223," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(b c + 3 \, a d\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(3 \, b c + a d\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} {\left(b x - a\right)} \sqrt{d x + c}}{4 \, x}, -\frac{2 \, {\left(b c + 3 \, a d\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(3 \, b c + a d\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} {\left(b x - a\right)} \sqrt{d x + c}}{4 \, x}, \frac{2 \, {\left(3 \, b c + a d\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b c + 3 \, a d\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} {\left(b x - a\right)} \sqrt{d x + c}}{4 \, x}, \frac{{\left(3 \, b c + a d\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(b c + 3 \, a d\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} {\left(b x - a\right)} \sqrt{d x + c}}{2 \, x}\right]"," ",0,"[1/4*((b*c + 3*a*d)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (3*b*c + a*d)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*(b*x - a)*sqrt(d*x + c))/x, -1/4*(2*(b*c + 3*a*d)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (3*b*c + a*d)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*(b*x - a)*sqrt(d*x + c))/x, 1/4*(2*(3*b*c + a*d)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b*c + 3*a*d)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*(b*x - a)*sqrt(d*x + c))/x, 1/2*((3*b*c + a*d)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (b*c + 3*a*d)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*sqrt(b*x + a)*(b*x - a)*sqrt(d*x + c))/x]","A",0
603,1,1027,0,3.640643," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{8 \, \sqrt{b d} a b c^{2} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a c^{2} x^{2}}, -\frac{16 \, \sqrt{-b d} a b c^{2} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a c^{2} x^{2}}, \frac{4 \, \sqrt{b d} a b c^{2} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a c^{2} x^{2}}, -\frac{8 \, \sqrt{-b d} a b c^{2} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a c^{2} x^{2}}\right]"," ",0,"[1/16*(8*sqrt(b*d)*a*b*c^2*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 + (5*a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^2), -1/16*(16*sqrt(-b*d)*a*b*c^2*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c^2 + (5*a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^2), 1/8*(4*sqrt(b*d)*a*b*c^2*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 + (5*a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^2), -1/8*(8*sqrt(-b*d)*a*b*c^2*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - (3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(2*a^2*c^2 + (5*a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^2)]","A",0
604,1,436,0,1.714001," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 8 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(7 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c^{3} x^{3}}, -\frac{3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 8 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(7 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c^{3} x^{3}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (3*a*b^2*c^3 + 8*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(7*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^3), -1/48*(3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (3*a*b^2*c^3 + 8*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(7*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^3)]","A",0
605,1,572,0,7.666046," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 9 \, a^{2} b^{2} c^{3} d + 31 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 10 \, a^{3} b c^{3} d - 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{3} c^{4} x^{4}}, \frac{3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 9 \, a^{2} b^{2} c^{3} d + 31 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 10 \, a^{3} b c^{3} d - 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{3} c^{4} x^{4}}\right]"," ",0,"[-1/768*(3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 - (9*a*b^3*c^4 - 9*a^2*b^2*c^3*d + 31*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 10*a^3*b*c^3*d - 5*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^4), 1/384*(3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 - (9*a*b^3*c^4 - 9*a^2*b^2*c^3*d + 31*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 10*a^3*b*c^3*d - 5*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^4)]","A",0
606,1,730,0,18.405114," ","integrate((b*x+a)^(3/2)*(d*x+c)^(1/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 7 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(384 \, a^{5} c^{5} + {\left(45 \, a b^{4} c^{5} - 30 \, a^{2} b^{3} c^{4} d - 36 \, a^{3} b^{2} c^{3} d^{2} + 190 \, a^{4} b c^{2} d^{3} - 105 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(15 \, a^{2} b^{3} c^{5} - 9 \, a^{3} b^{2} c^{4} d + 61 \, a^{4} b c^{3} d^{2} - 35 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(3 \, a^{3} b^{2} c^{5} + 12 \, a^{4} b c^{4} d - 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(11 \, a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{4} c^{5} x^{5}}, -\frac{15 \, {\left(3 \, b^{5} c^{5} - 3 \, a b^{4} c^{4} d - 2 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 7 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(384 \, a^{5} c^{5} + {\left(45 \, a b^{4} c^{5} - 30 \, a^{2} b^{3} c^{4} d - 36 \, a^{3} b^{2} c^{3} d^{2} + 190 \, a^{4} b c^{2} d^{3} - 105 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(15 \, a^{2} b^{3} c^{5} - 9 \, a^{3} b^{2} c^{4} d + 61 \, a^{4} b c^{3} d^{2} - 35 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(3 \, a^{3} b^{2} c^{5} + 12 \, a^{4} b c^{4} d - 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(11 \, a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{4} c^{5} x^{5}}\right]"," ",0,"[-1/7680*(15*(3*b^5*c^5 - 3*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 7*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(384*a^5*c^5 + (45*a*b^4*c^5 - 30*a^2*b^3*c^4*d - 36*a^3*b^2*c^3*d^2 + 190*a^4*b*c^2*d^3 - 105*a^5*c*d^4)*x^4 - 2*(15*a^2*b^3*c^5 - 9*a^3*b^2*c^4*d + 61*a^4*b*c^3*d^2 - 35*a^5*c^2*d^3)*x^3 + 8*(3*a^3*b^2*c^5 + 12*a^4*b*c^4*d - 7*a^5*c^3*d^2)*x^2 + 48*(11*a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^5*x^5), -1/3840*(15*(3*b^5*c^5 - 3*a*b^4*c^4*d - 2*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 7*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(384*a^5*c^5 + (45*a*b^4*c^5 - 30*a^2*b^3*c^4*d - 36*a^3*b^2*c^3*d^2 + 190*a^4*b*c^2*d^3 - 105*a^5*c*d^4)*x^4 - 2*(15*a^2*b^3*c^5 - 9*a^3*b^2*c^4*d + 61*a^4*b*c^3*d^2 - 35*a^5*c^2*d^3)*x^3 + 8*(3*a^3*b^2*c^5 + 12*a^4*b*c^4*d - 7*a^5*c^3*d^2)*x^2 + 48*(11*a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^5*x^5)]","A",0
607,1,890,0,1.024651," ","integrate(x^2*(b*x+a)^(3/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{6} c^{6} - 18 \, a b^{5} c^{5} d + 9 \, a^{2} b^{4} c^{4} d^{2} + 4 \, a^{3} b^{3} c^{3} d^{3} + 9 \, a^{4} b^{2} c^{2} d^{4} - 18 \, a^{5} b c d^{5} + 7 \, a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(1280 \, b^{6} d^{6} x^{5} - 105 \, b^{6} c^{5} d + 235 \, a b^{5} c^{4} d^{2} - 66 \, a^{2} b^{4} c^{3} d^{3} - 66 \, a^{3} b^{3} c^{2} d^{4} + 235 \, a^{4} b^{2} c d^{5} - 105 \, a^{5} b d^{6} + 1664 \, {\left(b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(3 \, b^{6} c^{2} d^{4} + 146 \, a b^{5} c d^{5} + 3 \, a^{2} b^{4} d^{6}\right)} x^{3} - 8 \, {\left(7 \, b^{6} c^{3} d^{3} - 15 \, a b^{5} c^{2} d^{4} - 15 \, a^{2} b^{4} c d^{5} + 7 \, a^{3} b^{3} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{6} c^{4} d^{2} - 76 \, a b^{5} c^{3} d^{3} + 18 \, a^{2} b^{4} c^{2} d^{4} - 76 \, a^{3} b^{3} c d^{5} + 35 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, b^{5} d^{5}}, -\frac{15 \, {\left(7 \, b^{6} c^{6} - 18 \, a b^{5} c^{5} d + 9 \, a^{2} b^{4} c^{4} d^{2} + 4 \, a^{3} b^{3} c^{3} d^{3} + 9 \, a^{4} b^{2} c^{2} d^{4} - 18 \, a^{5} b c d^{5} + 7 \, a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(1280 \, b^{6} d^{6} x^{5} - 105 \, b^{6} c^{5} d + 235 \, a b^{5} c^{4} d^{2} - 66 \, a^{2} b^{4} c^{3} d^{3} - 66 \, a^{3} b^{3} c^{2} d^{4} + 235 \, a^{4} b^{2} c d^{5} - 105 \, a^{5} b d^{6} + 1664 \, {\left(b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(3 \, b^{6} c^{2} d^{4} + 146 \, a b^{5} c d^{5} + 3 \, a^{2} b^{4} d^{6}\right)} x^{3} - 8 \, {\left(7 \, b^{6} c^{3} d^{3} - 15 \, a b^{5} c^{2} d^{4} - 15 \, a^{2} b^{4} c d^{5} + 7 \, a^{3} b^{3} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{6} c^{4} d^{2} - 76 \, a b^{5} c^{3} d^{3} + 18 \, a^{2} b^{4} c^{2} d^{4} - 76 \, a^{3} b^{3} c d^{5} + 35 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, b^{5} d^{5}}\right]"," ",0,"[1/30720*(15*(7*b^6*c^6 - 18*a*b^5*c^5*d + 9*a^2*b^4*c^4*d^2 + 4*a^3*b^3*c^3*d^3 + 9*a^4*b^2*c^2*d^4 - 18*a^5*b*c*d^5 + 7*a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(1280*b^6*d^6*x^5 - 105*b^6*c^5*d + 235*a*b^5*c^4*d^2 - 66*a^2*b^4*c^3*d^3 - 66*a^3*b^3*c^2*d^4 + 235*a^4*b^2*c*d^5 - 105*a^5*b*d^6 + 1664*(b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(3*b^6*c^2*d^4 + 146*a*b^5*c*d^5 + 3*a^2*b^4*d^6)*x^3 - 8*(7*b^6*c^3*d^3 - 15*a*b^5*c^2*d^4 - 15*a^2*b^4*c*d^5 + 7*a^3*b^3*d^6)*x^2 + 2*(35*b^6*c^4*d^2 - 76*a*b^5*c^3*d^3 + 18*a^2*b^4*c^2*d^4 - 76*a^3*b^3*c*d^5 + 35*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5), -1/15360*(15*(7*b^6*c^6 - 18*a*b^5*c^5*d + 9*a^2*b^4*c^4*d^2 + 4*a^3*b^3*c^3*d^3 + 9*a^4*b^2*c^2*d^4 - 18*a^5*b*c*d^5 + 7*a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(1280*b^6*d^6*x^5 - 105*b^6*c^5*d + 235*a*b^5*c^4*d^2 - 66*a^2*b^4*c^3*d^3 - 66*a^3*b^3*c^2*d^4 + 235*a^4*b^2*c*d^5 - 105*a^5*b*d^6 + 1664*(b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(3*b^6*c^2*d^4 + 146*a*b^5*c*d^5 + 3*a^2*b^4*d^6)*x^3 - 8*(7*b^6*c^3*d^3 - 15*a*b^5*c^2*d^4 - 15*a^2*b^4*c*d^5 + 7*a^3*b^3*d^6)*x^2 + 2*(35*b^6*c^4*d^2 - 76*a*b^5*c^3*d^3 + 18*a^2*b^4*c^2*d^4 - 76*a^3*b^3*c*d^5 + 35*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5)]","A",0
608,1,694,0,1.539532," ","integrate(x*(b*x+a)^(3/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - 3 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(128 \, b^{5} d^{5} x^{4} + 15 \, b^{5} c^{4} d - 40 \, a b^{4} c^{3} d^{2} + 18 \, a^{2} b^{3} c^{2} d^{3} - 40 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5} + 176 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(b^{5} c^{2} d^{3} + 34 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(5 \, b^{5} c^{3} d^{2} - 13 \, a b^{4} c^{2} d^{3} - 13 \, a^{2} b^{3} c d^{4} + 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, b^{4} d^{4}}, \frac{15 \, {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - 3 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(128 \, b^{5} d^{5} x^{4} + 15 \, b^{5} c^{4} d - 40 \, a b^{4} c^{3} d^{2} + 18 \, a^{2} b^{3} c^{2} d^{3} - 40 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5} + 176 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(b^{5} c^{2} d^{3} + 34 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(5 \, b^{5} c^{3} d^{2} - 13 \, a b^{4} c^{2} d^{3} - 13 \, a^{2} b^{3} c d^{4} + 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, b^{4} d^{4}}\right]"," ",0,"[1/2560*(15*(b^5*c^5 - 3*a*b^4*c^4*d + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a^4*b*c*d^4 + a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(128*b^5*d^5*x^4 + 15*b^5*c^4*d - 40*a*b^4*c^3*d^2 + 18*a^2*b^3*c^2*d^3 - 40*a^3*b^2*c*d^4 + 15*a^4*b*d^5 + 176*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(b^5*c^2*d^3 + 34*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 - 2*(5*b^5*c^3*d^2 - 13*a*b^4*c^2*d^3 - 13*a^2*b^3*c*d^4 + 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4), 1/1280*(15*(b^5*c^5 - 3*a*b^4*c^4*d + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a^4*b*c*d^4 + a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(128*b^5*d^5*x^4 + 15*b^5*c^4*d - 40*a*b^4*c^3*d^2 + 18*a^2*b^3*c^2*d^3 - 40*a^3*b^2*c*d^4 + 15*a^4*b*d^5 + 176*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(b^5*c^2*d^3 + 34*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 - 2*(5*b^5*c^3*d^2 - 13*a*b^4*c^2*d^3 - 13*a^2*b^3*c*d^4 + 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4)]","A",0
609,1,534,0,1.358769," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(16 \, b^{4} d^{4} x^{3} - 3 \, b^{4} c^{3} d + 11 \, a b^{3} c^{2} d^{2} + 11 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4} + 24 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(b^{4} c^{2} d^{2} + 22 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{256 \, b^{3} d^{3}}, -\frac{3 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(16 \, b^{4} d^{4} x^{3} - 3 \, b^{4} c^{3} d + 11 \, a b^{3} c^{2} d^{2} + 11 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4} + 24 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(b^{4} c^{2} d^{2} + 22 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{128 \, b^{3} d^{3}}\right]"," ",0,"[1/256*(3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(16*b^4*d^4*x^3 - 3*b^4*c^3*d + 11*a*b^3*c^2*d^2 + 11*a^2*b^2*c*d^3 - 3*a^3*b*d^4 + 24*(b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(b^4*c^2*d^2 + 22*a*b^3*c*d^3 + a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), -1/128*(3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(16*b^4*d^4*x^3 - 3*b^4*c^3*d + 11*a*b^3*c^2*d^2 + 11*a^2*b^2*c*d^3 - 3*a^3*b*d^4 + 24*(b^4*c*d^3 + a*b^3*d^4)*x^2 + 2*(b^4*c^2*d^2 + 22*a*b^3*c*d^3 + a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3)]","A",0
610,1,1193,0,17.407955," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{a c} a b^{2} c d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 38 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 14 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d^{2}}, \frac{24 \, \sqrt{a c} a b^{2} c d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 38 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 14 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d^{2}}, \frac{96 \, \sqrt{-a c} a b^{2} c d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 38 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 14 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d^{2}}, \frac{48 \, \sqrt{-a c} a b^{2} c d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d + 38 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3} + 14 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d^{2}}\right]"," ",0,"[1/96*(48*sqrt(a*c)*a*b^2*c*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 38*a*b^2*c*d^2 + 3*a^2*b*d^3 + 14*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2), 1/48*(24*sqrt(a*c)*a*b^2*c*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 38*a*b^2*c*d^2 + 3*a^2*b*d^3 + 14*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2), 1/96*(96*sqrt(-a*c)*a*b^2*c*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 38*a*b^2*c*d^2 + 3*a^2*b*d^3 + 14*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2), 1/48*(48*sqrt(-a*c)*a*b^2*c*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 3*b^3*c^2*d + 38*a*b^2*c*d^2 + 3*a^2*b*d^3 + 14*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2)]","A",0
611,1,1073,0,5.045966," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 12 \, {\left(b^{2} c d + a b d^{2}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 4 \, a b c d + 5 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b d x}, -\frac{3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 6 \, {\left(b^{2} c d + a b d^{2}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 4 \, a b c d + 5 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b d x}, \frac{24 \, {\left(b^{2} c d + a b d^{2}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 4 \, a b c d + 5 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b d x}, \frac{12 \, {\left(b^{2} c d + a b d^{2}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 4 \, a b c d + 5 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b d x}\right]"," ",0,"[1/16*(3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 12*(b^2*c*d + a*b*d^2)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*b^2*d^2*x^2 - 4*a*b*c*d + 5*(b^2*c*d + a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x), -1/8*(3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 6*(b^2*c*d + a*b*d^2)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 2*(2*b^2*d^2*x^2 - 4*a*b*c*d + 5*(b^2*c*d + a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x), 1/16*(24*(b^2*c*d + a*b*d^2)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x^2 - 4*a*b*c*d + 5*(b^2*c*d + a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x), 1/8*(12*(b^2*c*d + a*b*d^2)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x^2 - 4*a*b*c*d + 5*(b^2*c*d + a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x)]","A",0
612,1,1089,0,4.321476," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a b c^{2} + a^{2} c d\right)} \sqrt{b d} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, a b c d x^{2} - 2 \, a^{2} c^{2} - 5 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a c x^{2}}, -\frac{24 \, {\left(a b c^{2} + a^{2} c d\right)} \sqrt{-b d} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(4 \, a b c d x^{2} - 2 \, a^{2} c^{2} - 5 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a c x^{2}}, \frac{3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 6 \, {\left(a b c^{2} + a^{2} c d\right)} \sqrt{b d} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 2 \, {\left(4 \, a b c d x^{2} - 2 \, a^{2} c^{2} - 5 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a c x^{2}}, \frac{3 \, {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 12 \, {\left(a b c^{2} + a^{2} c d\right)} \sqrt{-b d} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(4 \, a b c d x^{2} - 2 \, a^{2} c^{2} - 5 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a c x^{2}}\right]"," ",0,"[1/16*(12*(a*b*c^2 + a^2*c*d)*sqrt(b*d)*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*a*b*c*d*x^2 - 2*a^2*c^2 - 5*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^2), -1/16*(24*(a*b*c^2 + a^2*c*d)*sqrt(-b*d)*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(4*a*b*c*d*x^2 - 2*a^2*c^2 - 5*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^2), 1/8*(3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 6*(a*b*c^2 + a^2*c*d)*sqrt(b*d)*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 2*(4*a*b*c*d*x^2 - 2*a^2*c^2 - 5*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^2), 1/8*(3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 12*(a*b*c^2 + a^2*c*d)*sqrt(-b*d)*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(4*a*b*c*d*x^2 - 2*a^2*c^2 - 5*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^2)]","A",0
613,1,1237,0,7.777646," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{b d} a^{2} b c^{2} d x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 38 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c^{2} x^{3}}, -\frac{96 \, \sqrt{-b d} a^{2} b c^{2} d x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 38 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c^{2} x^{3}}, \frac{24 \, \sqrt{b d} a^{2} b c^{2} d x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 38 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c^{2} x^{3}}, -\frac{48 \, \sqrt{-b d} a^{2} b c^{2} d x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} + 38 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c^{2} x^{3}}\right]"," ",0,"[1/96*(48*sqrt(b*d)*a^2*b*c^2*d*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 + (3*a*b^2*c^3 + 38*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 14*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^3), -1/96*(96*sqrt(-b*d)*a^2*b*c^2*d*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (3*a*b^2*c^3 + 38*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 14*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^3), 1/48*(24*sqrt(b*d)*a^2*b*c^2*d*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 + (3*a*b^2*c^3 + 38*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 14*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^3), -1/48*(48*sqrt(-b*d)*a^2*b*c^2*d*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (3*a*b^2*c^3 + 38*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 + 14*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^3)]","A",0
614,1,562,0,7.273401," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(16 \, a^{4} c^{4} - {\left(3 \, a b^{3} c^{4} - 11 \, a^{2} b^{2} c^{3} d - 11 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} c^{4} + 22 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{2} + 24 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{256 \, a^{3} c^{3} x^{4}}, \frac{3 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(16 \, a^{4} c^{4} - {\left(3 \, a b^{3} c^{4} - 11 \, a^{2} b^{2} c^{3} d - 11 \, a^{3} b c^{2} d^{2} + 3 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} c^{4} + 22 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} x^{2} + 24 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{128 \, a^{3} c^{3} x^{4}}\right]"," ",0,"[1/256*(3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(16*a^4*c^4 - (3*a*b^3*c^4 - 11*a^2*b^2*c^3*d - 11*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3 + 2*(a^2*b^2*c^4 + 22*a^3*b*c^3*d + a^4*c^2*d^2)*x^2 + 24*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^4), 1/128*(3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(16*a^4*c^4 - (3*a*b^3*c^4 - 11*a^2*b^2*c^3*d - 11*a^3*b*c^2*d^2 + 3*a^4*c*d^3)*x^3 + 2*(a^2*b^2*c^4 + 22*a^3*b*c^3*d + a^4*c^2*d^2)*x^2 + 24*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^4)]","A",0
615,1,720,0,18.457534," ","integrate((b*x+a)^(3/2)*(d*x+c)^(3/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - 3 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(128 \, a^{5} c^{5} + {\left(15 \, a b^{4} c^{5} - 40 \, a^{2} b^{3} c^{4} d + 18 \, a^{3} b^{2} c^{3} d^{2} - 40 \, a^{4} b c^{2} d^{3} + 15 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{5} - 13 \, a^{3} b^{2} c^{4} d - 13 \, a^{4} b c^{3} d^{2} + 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(a^{3} b^{2} c^{5} + 34 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{2} + 176 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, a^{4} c^{4} x^{5}}, -\frac{15 \, {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 2 \, a^{2} b^{3} c^{3} d^{2} + 2 \, a^{3} b^{2} c^{2} d^{3} - 3 \, a^{4} b c d^{4} + a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(128 \, a^{5} c^{5} + {\left(15 \, a b^{4} c^{5} - 40 \, a^{2} b^{3} c^{4} d + 18 \, a^{3} b^{2} c^{3} d^{2} - 40 \, a^{4} b c^{2} d^{3} + 15 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{5} - 13 \, a^{3} b^{2} c^{4} d - 13 \, a^{4} b c^{3} d^{2} + 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(a^{3} b^{2} c^{5} + 34 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{2} + 176 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, a^{4} c^{4} x^{5}}\right]"," ",0,"[1/2560*(15*(b^5*c^5 - 3*a*b^4*c^4*d + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a^4*b*c*d^4 + a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(128*a^5*c^5 + (15*a*b^4*c^5 - 40*a^2*b^3*c^4*d + 18*a^3*b^2*c^3*d^2 - 40*a^4*b*c^2*d^3 + 15*a^5*c*d^4)*x^4 - 2*(5*a^2*b^3*c^5 - 13*a^3*b^2*c^4*d - 13*a^4*b*c^3*d^2 + 5*a^5*c^2*d^3)*x^3 + 8*(a^3*b^2*c^5 + 34*a^4*b*c^4*d + a^5*c^3*d^2)*x^2 + 176*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^5), -1/1280*(15*(b^5*c^5 - 3*a*b^4*c^4*d + 2*a^2*b^3*c^3*d^2 + 2*a^3*b^2*c^2*d^3 - 3*a^4*b*c*d^4 + a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(128*a^5*c^5 + (15*a*b^4*c^5 - 40*a^2*b^3*c^4*d + 18*a^3*b^2*c^3*d^2 - 40*a^4*b*c^2*d^3 + 15*a^5*c*d^4)*x^4 - 2*(5*a^2*b^3*c^5 - 13*a^3*b^2*c^4*d - 13*a^4*b*c^3*d^2 + 5*a^5*c^2*d^3)*x^3 + 8*(a^3*b^2*c^5 + 34*a^4*b*c^4*d + a^5*c^3*d^2)*x^2 + 176*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^5)]","A",0
616,1,1110,0,1.510979," ","integrate(x^2*(b*x+a)^(3/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(5 \, b^{7} c^{7} - 15 \, a b^{6} c^{6} d + 9 \, a^{2} b^{5} c^{5} d^{2} + 5 \, a^{3} b^{4} c^{4} d^{3} + 15 \, a^{4} b^{3} c^{3} d^{4} - 45 \, a^{5} b^{2} c^{2} d^{5} + 35 \, a^{6} b c d^{6} - 9 \, a^{7} d^{7}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(15360 \, b^{7} d^{7} x^{6} - 525 \, b^{7} c^{6} d + 1400 \, a b^{6} c^{5} d^{2} - 525 \, a^{2} b^{5} c^{4} d^{3} - 600 \, a^{3} b^{4} c^{3} d^{4} + 3689 \, a^{4} b^{3} c^{2} d^{5} - 3360 \, a^{5} b^{2} c d^{6} + 945 \, a^{6} b d^{7} + 1280 \, {\left(29 \, b^{7} c d^{6} + 15 \, a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(185 \, b^{7} c^{2} d^{5} + 380 \, a b^{6} c d^{6} + 3 \, a^{2} b^{5} d^{7}\right)} x^{4} + 16 \, {\left(15 \, b^{7} c^{3} d^{4} + 2095 \, a b^{6} c^{2} d^{5} + 93 \, a^{2} b^{5} c d^{6} - 27 \, a^{3} b^{4} d^{7}\right)} x^{3} - 8 \, {\left(35 \, b^{7} c^{4} d^{3} - 90 \, a b^{6} c^{3} d^{4} - 228 \, a^{2} b^{5} c^{2} d^{5} + 218 \, a^{3} b^{4} c d^{6} - 63 \, a^{4} b^{3} d^{7}\right)} x^{2} + 2 \, {\left(175 \, b^{7} c^{5} d^{2} - 455 \, a b^{6} c^{4} d^{3} + 150 \, a^{2} b^{5} c^{3} d^{4} - 1166 \, a^{3} b^{4} c^{2} d^{5} + 1099 \, a^{4} b^{3} c d^{6} - 315 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{430080 \, b^{6} d^{5}}, -\frac{105 \, {\left(5 \, b^{7} c^{7} - 15 \, a b^{6} c^{6} d + 9 \, a^{2} b^{5} c^{5} d^{2} + 5 \, a^{3} b^{4} c^{4} d^{3} + 15 \, a^{4} b^{3} c^{3} d^{4} - 45 \, a^{5} b^{2} c^{2} d^{5} + 35 \, a^{6} b c d^{6} - 9 \, a^{7} d^{7}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(15360 \, b^{7} d^{7} x^{6} - 525 \, b^{7} c^{6} d + 1400 \, a b^{6} c^{5} d^{2} - 525 \, a^{2} b^{5} c^{4} d^{3} - 600 \, a^{3} b^{4} c^{3} d^{4} + 3689 \, a^{4} b^{3} c^{2} d^{5} - 3360 \, a^{5} b^{2} c d^{6} + 945 \, a^{6} b d^{7} + 1280 \, {\left(29 \, b^{7} c d^{6} + 15 \, a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(185 \, b^{7} c^{2} d^{5} + 380 \, a b^{6} c d^{6} + 3 \, a^{2} b^{5} d^{7}\right)} x^{4} + 16 \, {\left(15 \, b^{7} c^{3} d^{4} + 2095 \, a b^{6} c^{2} d^{5} + 93 \, a^{2} b^{5} c d^{6} - 27 \, a^{3} b^{4} d^{7}\right)} x^{3} - 8 \, {\left(35 \, b^{7} c^{4} d^{3} - 90 \, a b^{6} c^{3} d^{4} - 228 \, a^{2} b^{5} c^{2} d^{5} + 218 \, a^{3} b^{4} c d^{6} - 63 \, a^{4} b^{3} d^{7}\right)} x^{2} + 2 \, {\left(175 \, b^{7} c^{5} d^{2} - 455 \, a b^{6} c^{4} d^{3} + 150 \, a^{2} b^{5} c^{3} d^{4} - 1166 \, a^{3} b^{4} c^{2} d^{5} + 1099 \, a^{4} b^{3} c d^{6} - 315 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{215040 \, b^{6} d^{5}}\right]"," ",0,"[-1/430080*(105*(5*b^7*c^7 - 15*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 + 5*a^3*b^4*c^4*d^3 + 15*a^4*b^3*c^3*d^4 - 45*a^5*b^2*c^2*d^5 + 35*a^6*b*c*d^6 - 9*a^7*d^7)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(15360*b^7*d^7*x^6 - 525*b^7*c^6*d + 1400*a*b^6*c^5*d^2 - 525*a^2*b^5*c^4*d^3 - 600*a^3*b^4*c^3*d^4 + 3689*a^4*b^3*c^2*d^5 - 3360*a^5*b^2*c*d^6 + 945*a^6*b*d^7 + 1280*(29*b^7*c*d^6 + 15*a*b^6*d^7)*x^5 + 128*(185*b^7*c^2*d^5 + 380*a*b^6*c*d^6 + 3*a^2*b^5*d^7)*x^4 + 16*(15*b^7*c^3*d^4 + 2095*a*b^6*c^2*d^5 + 93*a^2*b^5*c*d^6 - 27*a^3*b^4*d^7)*x^3 - 8*(35*b^7*c^4*d^3 - 90*a*b^6*c^3*d^4 - 228*a^2*b^5*c^2*d^5 + 218*a^3*b^4*c*d^6 - 63*a^4*b^3*d^7)*x^2 + 2*(175*b^7*c^5*d^2 - 455*a*b^6*c^4*d^3 + 150*a^2*b^5*c^3*d^4 - 1166*a^3*b^4*c^2*d^5 + 1099*a^4*b^3*c*d^6 - 315*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^5), -1/215040*(105*(5*b^7*c^7 - 15*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 + 5*a^3*b^4*c^4*d^3 + 15*a^4*b^3*c^3*d^4 - 45*a^5*b^2*c^2*d^5 + 35*a^6*b*c*d^6 - 9*a^7*d^7)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(15360*b^7*d^7*x^6 - 525*b^7*c^6*d + 1400*a*b^6*c^5*d^2 - 525*a^2*b^5*c^4*d^3 - 600*a^3*b^4*c^3*d^4 + 3689*a^4*b^3*c^2*d^5 - 3360*a^5*b^2*c*d^6 + 945*a^6*b*d^7 + 1280*(29*b^7*c*d^6 + 15*a*b^6*d^7)*x^5 + 128*(185*b^7*c^2*d^5 + 380*a*b^6*c*d^6 + 3*a^2*b^5*d^7)*x^4 + 16*(15*b^7*c^3*d^4 + 2095*a*b^6*c^2*d^5 + 93*a^2*b^5*c*d^6 - 27*a^3*b^4*d^7)*x^3 - 8*(35*b^7*c^4*d^3 - 90*a*b^6*c^3*d^4 - 228*a^2*b^5*c^2*d^5 + 218*a^3*b^4*c*d^6 - 63*a^4*b^3*d^7)*x^2 + 2*(175*b^7*c^5*d^2 - 455*a*b^6*c^4*d^3 + 150*a^2*b^5*c^3*d^4 - 1166*a^3*b^4*c^2*d^5 + 1099*a^4*b^3*c*d^6 - 315*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^5)]","A",0
617,1,894,0,1.278985," ","integrate(x*(b*x+a)^(3/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(5 \, b^{6} c^{6} - 18 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} + 20 \, a^{3} b^{3} c^{3} d^{3} - 45 \, a^{4} b^{2} c^{2} d^{4} + 30 \, a^{5} b c d^{5} - 7 \, a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(1280 \, b^{6} d^{6} x^{5} + 75 \, b^{6} c^{5} d - 245 \, a b^{5} c^{4} d^{2} + 150 \, a^{2} b^{4} c^{3} d^{3} - 546 \, a^{3} b^{3} c^{2} d^{4} + 415 \, a^{4} b^{2} c d^{5} - 105 \, a^{5} b d^{6} + 128 \, {\left(25 \, b^{6} c d^{5} + 13 \, a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(135 \, b^{6} c^{2} d^{4} + 278 \, a b^{5} c d^{5} + 3 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(5 \, b^{6} c^{3} d^{3} + 423 \, a b^{5} c^{2} d^{4} + 27 \, a^{2} b^{4} c d^{5} - 7 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(25 \, b^{6} c^{4} d^{2} - 80 \, a b^{5} c^{3} d^{3} - 174 \, a^{2} b^{4} c^{2} d^{4} + 136 \, a^{3} b^{3} c d^{5} - 35 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, b^{5} d^{4}}, \frac{15 \, {\left(5 \, b^{6} c^{6} - 18 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} + 20 \, a^{3} b^{3} c^{3} d^{3} - 45 \, a^{4} b^{2} c^{2} d^{4} + 30 \, a^{5} b c d^{5} - 7 \, a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, b^{6} d^{6} x^{5} + 75 \, b^{6} c^{5} d - 245 \, a b^{5} c^{4} d^{2} + 150 \, a^{2} b^{4} c^{3} d^{3} - 546 \, a^{3} b^{3} c^{2} d^{4} + 415 \, a^{4} b^{2} c d^{5} - 105 \, a^{5} b d^{6} + 128 \, {\left(25 \, b^{6} c d^{5} + 13 \, a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(135 \, b^{6} c^{2} d^{4} + 278 \, a b^{5} c d^{5} + 3 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(5 \, b^{6} c^{3} d^{3} + 423 \, a b^{5} c^{2} d^{4} + 27 \, a^{2} b^{4} c d^{5} - 7 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(25 \, b^{6} c^{4} d^{2} - 80 \, a b^{5} c^{3} d^{3} - 174 \, a^{2} b^{4} c^{2} d^{4} + 136 \, a^{3} b^{3} c d^{5} - 35 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, b^{5} d^{4}}\right]"," ",0,"[-1/30720*(15*(5*b^6*c^6 - 18*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 + 20*a^3*b^3*c^3*d^3 - 45*a^4*b^2*c^2*d^4 + 30*a^5*b*c*d^5 - 7*a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(1280*b^6*d^6*x^5 + 75*b^6*c^5*d - 245*a*b^5*c^4*d^2 + 150*a^2*b^4*c^3*d^3 - 546*a^3*b^3*c^2*d^4 + 415*a^4*b^2*c*d^5 - 105*a^5*b*d^6 + 128*(25*b^6*c*d^5 + 13*a*b^5*d^6)*x^4 + 16*(135*b^6*c^2*d^4 + 278*a*b^5*c*d^5 + 3*a^2*b^4*d^6)*x^3 + 8*(5*b^6*c^3*d^3 + 423*a*b^5*c^2*d^4 + 27*a^2*b^4*c*d^5 - 7*a^3*b^3*d^6)*x^2 - 2*(25*b^6*c^4*d^2 - 80*a*b^5*c^3*d^3 - 174*a^2*b^4*c^2*d^4 + 136*a^3*b^3*c*d^5 - 35*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^4), 1/15360*(15*(5*b^6*c^6 - 18*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 + 20*a^3*b^3*c^3*d^3 - 45*a^4*b^2*c^2*d^4 + 30*a^5*b*c*d^5 - 7*a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(1280*b^6*d^6*x^5 + 75*b^6*c^5*d - 245*a*b^5*c^4*d^2 + 150*a^2*b^4*c^3*d^3 - 546*a^3*b^3*c^2*d^4 + 415*a^4*b^2*c*d^5 - 105*a^5*b*d^6 + 128*(25*b^6*c*d^5 + 13*a*b^5*d^6)*x^4 + 16*(135*b^6*c^2*d^4 + 278*a*b^5*c*d^5 + 3*a^2*b^4*d^6)*x^3 + 8*(5*b^6*c^3*d^3 + 423*a*b^5*c^2*d^4 + 27*a^2*b^4*c*d^5 - 7*a^3*b^3*d^6)*x^2 - 2*(25*b^6*c^4*d^2 - 80*a*b^5*c^3*d^3 - 174*a^2*b^4*c^2*d^4 + 136*a^3*b^3*c*d^5 - 35*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^4)]","A",0
618,1,702,0,1.447501," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(128 \, b^{5} d^{5} x^{4} - 15 \, b^{5} c^{4} d + 70 \, a b^{4} c^{3} d^{2} + 128 \, a^{2} b^{3} c^{2} d^{3} - 70 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5} + 16 \, {\left(21 \, b^{5} c d^{4} + 11 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(31 \, b^{5} c^{2} d^{3} + 64 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(5 \, b^{5} c^{3} d^{2} + 233 \, a b^{4} c^{2} d^{3} + 23 \, a^{2} b^{3} c d^{4} - 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, b^{4} d^{3}}, -\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(128 \, b^{5} d^{5} x^{4} - 15 \, b^{5} c^{4} d + 70 \, a b^{4} c^{3} d^{2} + 128 \, a^{2} b^{3} c^{2} d^{3} - 70 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5} + 16 \, {\left(21 \, b^{5} c d^{4} + 11 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(31 \, b^{5} c^{2} d^{3} + 64 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(5 \, b^{5} c^{3} d^{2} + 233 \, a b^{4} c^{2} d^{3} + 23 \, a^{2} b^{3} c d^{4} - 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, b^{4} d^{3}}\right]"," ",0,"[-1/2560*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(128*b^5*d^5*x^4 - 15*b^5*c^4*d + 70*a*b^4*c^3*d^2 + 128*a^2*b^3*c^2*d^3 - 70*a^3*b^2*c*d^4 + 15*a^4*b*d^5 + 16*(21*b^5*c*d^4 + 11*a*b^4*d^5)*x^3 + 8*(31*b^5*c^2*d^3 + 64*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 + 2*(5*b^5*c^3*d^2 + 233*a*b^4*c^2*d^3 + 23*a^2*b^3*c*d^4 - 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3), -1/1280*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(128*b^5*d^5*x^4 - 15*b^5*c^4*d + 70*a*b^4*c^3*d^2 + 128*a^2*b^3*c^2*d^3 - 70*a^3*b^2*c*d^4 + 15*a^4*b*d^5 + 16*(21*b^5*c*d^4 + 11*a*b^4*d^5)*x^3 + 8*(31*b^5*c^2*d^3 + 64*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 + 2*(5*b^5*c^3*d^2 + 233*a*b^4*c^2*d^3 + 23*a^2*b^3*c*d^4 - 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3)]","A",0
619,1,1481,0,53.421237," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{a c} a b^{3} c^{2} d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 337 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{3} d^{2}}, \frac{192 \, \sqrt{a c} a b^{3} c^{2} d^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 337 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{3} d^{2}}, \frac{768 \, \sqrt{-a c} a b^{3} c^{2} d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 337 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{3} d^{2}}, \frac{384 \, \sqrt{-a c} a b^{3} c^{2} d^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d + 337 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} - 9 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} + 9 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{3} d^{2}}\right]"," ",0,"[1/768*(384*sqrt(a*c)*a*b^3*c^2*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 337*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(17*b^4*c*d^3 + 9*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2), 1/384*(192*sqrt(a*c)*a*b^3*c^2*d^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 337*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(17*b^4*c*d^3 + 9*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2), 1/768*(768*sqrt(-a*c)*a*b^3*c^2*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 337*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(17*b^4*c*d^3 + 9*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2), 1/384*(384*sqrt(-a*c)*a*b^3*c^2*d^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d + 337*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 - 9*a^3*b*d^4 + 8*(17*b^4*c*d^3 + 9*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2)]","A",0
620,1,1337,0,21.231804," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 24 \, {\left(3 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a b^{2} c^{2} d + 2 \, {\left(13 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(33 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d x}, -\frac{3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 12 \, {\left(3 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a b^{2} c^{2} d + 2 \, {\left(13 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(33 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d x}, \frac{48 \, {\left(3 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a b^{2} c^{2} d + 2 \, {\left(13 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(33 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d x}, \frac{24 \, {\left(3 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a b^{2} c^{2} d + 2 \, {\left(13 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} x^{2} + {\left(33 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d x}\right]"," ",0,"[-1/96*(3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 24*(3*b^3*c^2*d + 5*a*b^2*c*d^2)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*b^3*d^3*x^3 - 24*a*b^2*c^2*d + 2*(13*b^3*c*d^2 + 7*a*b^2*d^3)*x^2 + (33*b^3*c^2*d + 68*a*b^2*c*d^2 + 3*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d*x), -1/48*(3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 12*(3*b^3*c^2*d + 5*a*b^2*c*d^2)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 2*(8*b^3*d^3*x^3 - 24*a*b^2*c^2*d + 2*(13*b^3*c*d^2 + 7*a*b^2*d^3)*x^2 + (33*b^3*c^2*d + 68*a*b^2*c*d^2 + 3*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d*x), 1/96*(48*(3*b^3*c^2*d + 5*a*b^2*c*d^2)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^3 - 24*a*b^2*c^2*d + 2*(13*b^3*c*d^2 + 7*a*b^2*d^3)*x^2 + (33*b^3*c^2*d + 68*a*b^2*c*d^2 + 3*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d*x), 1/48*(24*(3*b^3*c^2*d + 5*a*b^2*c*d^2)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^3 - 24*a*b^2*c^2*d + 2*(13*b^3*c*d^2 + 7*a*b^2*d^3)*x^2 + (33*b^3*c^2*d + 68*a*b^2*c*d^2 + 3*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d*x)]","A",0
621,1,1185,0,11.273105," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, b d^{2} x^{3} - 2 \, a c^{2} + {\left(9 \, b c d + 5 \, a d^{2}\right)} x^{2} - {\left(5 \, b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, -\frac{6 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, b d^{2} x^{3} - 2 \, a c^{2} + {\left(9 \, b c d + 5 \, a d^{2}\right)} x^{2} - {\left(5 \, b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, \frac{6 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b d^{2} x^{3} - 2 \, a c^{2} + {\left(9 \, b c d + 5 \, a d^{2}\right)} x^{2} - {\left(5 \, b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, \frac{3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b d^{2} x^{3} - 2 \, a c^{2} + {\left(9 \, b c d + 5 \, a d^{2}\right)} x^{2} - {\left(5 \, b c^{2} + 9 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, x^{2}}\right]"," ",0,"[1/16*(3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*b*d^2*x^3 - 2*a*c^2 + (9*b*c*d + 5*a*d^2)*x^2 - (5*b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, -1/16*(6*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*b*d^2*x^3 - 2*a*c^2 + (9*b*c*d + 5*a*d^2)*x^2 - (5*b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, 1/16*(6*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b*d^2*x^3 - 2*a*c^2 + (9*b*c*d + 5*a*d^2)*x^2 - (5*b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, 1/8*(3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(2*b*d^2*x^3 - 2*a*c^2 + (9*b*c*d + 5*a*d^2)*x^2 - (5*b*c^2 + 9*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2]","A",0
622,1,1353,0,12.549368," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{24 \, {\left(5 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(24 \, a^{2} b c d^{2} x^{3} - 8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c x^{3}}, -\frac{48 \, {\left(5 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(24 \, a^{2} b c d^{2} x^{3} - 8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c x^{3}}, -\frac{3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 12 \, {\left(5 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(24 \, a^{2} b c d^{2} x^{3} - 8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c x^{3}}, -\frac{3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 24 \, {\left(5 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(24 \, a^{2} b c d^{2} x^{3} - 8 \, a^{3} c^{3} - {\left(3 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{2} b c^{3} + 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c x^{3}}\right]"," ",0,"[1/96*(24*(5*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(24*a^2*b*c*d^2*x^3 - 8*a^3*c^3 - (3*a*b^2*c^3 + 68*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(7*a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^3), -1/96*(48*(5*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(24*a^2*b*c*d^2*x^3 - 8*a^3*c^3 - (3*a*b^2*c^3 + 68*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(7*a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^3), -1/48*(3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 12*(5*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(24*a^2*b*c*d^2*x^3 - 8*a^3*c^3 - (3*a*b^2*c^3 + 68*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(7*a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^3), -1/48*(3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 24*(5*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(24*a^2*b*c*d^2*x^3 - 8*a^3*c^3 - (3*a*b^2*c^3 + 68*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(7*a^2*b*c^3 + 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c*x^3)]","A",0
623,1,1529,0,28.920717," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{b d} a^{3} b c^{2} d^{2} x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d - 337 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{3} c^{2} x^{4}}, -\frac{768 \, \sqrt{-b d} a^{3} b c^{2} d^{2} x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d - 337 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{3} c^{2} x^{4}}, \frac{192 \, \sqrt{b d} a^{3} b c^{2} d^{2} x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d - 337 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{3} c^{2} x^{4}}, -\frac{384 \, \sqrt{-b d} a^{3} b c^{2} d^{2} x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d - 337 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{3} c^{2} x^{4}}\right]"," ",0,"[1/768*(384*sqrt(b*d)*a^3*b*c^2*d^2*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 - (9*a*b^3*c^4 - 57*a^2*b^2*c^3*d - 337*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^4), -1/768*(768*sqrt(-b*d)*a^3*b*c^2*d^2*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 - (9*a*b^3*c^4 - 57*a^2*b^2*c^3*d - 337*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^4), 1/384*(192*sqrt(b*d)*a^3*b*c^2*d^2*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 - (9*a*b^3*c^4 - 57*a^2*b^2*c^3*d - 337*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^4), -1/384*(384*sqrt(-b*d)*a^3*b*c^2*d^2*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 - (9*a*b^3*c^4 - 57*a^2*b^2*c^3*d - 337*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 + 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^4)]","A",0
624,1,728,0,18.819711," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(128 \, a^{5} c^{5} + {\left(15 \, a b^{4} c^{5} - 70 \, a^{2} b^{3} c^{4} d + 128 \, a^{3} b^{2} c^{3} d^{2} + 70 \, a^{4} b c^{2} d^{3} - 15 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{5} - 23 \, a^{3} b^{2} c^{4} d - 233 \, a^{4} b c^{3} d^{2} - 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(a^{3} b^{2} c^{5} + 64 \, a^{4} b c^{4} d + 31 \, a^{5} c^{3} d^{2}\right)} x^{2} + 16 \, {\left(11 \, a^{4} b c^{5} + 21 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, a^{4} c^{3} x^{5}}, -\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(128 \, a^{5} c^{5} + {\left(15 \, a b^{4} c^{5} - 70 \, a^{2} b^{3} c^{4} d + 128 \, a^{3} b^{2} c^{3} d^{2} + 70 \, a^{4} b c^{2} d^{3} - 15 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(5 \, a^{2} b^{3} c^{5} - 23 \, a^{3} b^{2} c^{4} d - 233 \, a^{4} b c^{3} d^{2} - 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(a^{3} b^{2} c^{5} + 64 \, a^{4} b c^{4} d + 31 \, a^{5} c^{3} d^{2}\right)} x^{2} + 16 \, {\left(11 \, a^{4} b c^{5} + 21 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, a^{4} c^{3} x^{5}}\right]"," ",0,"[-1/2560*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(128*a^5*c^5 + (15*a*b^4*c^5 - 70*a^2*b^3*c^4*d + 128*a^3*b^2*c^3*d^2 + 70*a^4*b*c^2*d^3 - 15*a^5*c*d^4)*x^4 - 2*(5*a^2*b^3*c^5 - 23*a^3*b^2*c^4*d - 233*a^4*b*c^3*d^2 - 5*a^5*c^2*d^3)*x^3 + 8*(a^3*b^2*c^5 + 64*a^4*b*c^4*d + 31*a^5*c^3*d^2)*x^2 + 16*(11*a^4*b*c^5 + 21*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^5), -1/1280*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(128*a^5*c^5 + (15*a*b^4*c^5 - 70*a^2*b^3*c^4*d + 128*a^3*b^2*c^3*d^2 + 70*a^4*b*c^2*d^3 - 15*a^5*c*d^4)*x^4 - 2*(5*a^2*b^3*c^5 - 23*a^3*b^2*c^4*d - 233*a^4*b*c^3*d^2 - 5*a^5*c^2*d^3)*x^3 + 8*(a^3*b^2*c^5 + 64*a^4*b*c^4*d + 31*a^5*c^3*d^2)*x^2 + 16*(11*a^4*b*c^5 + 21*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^5)]","A",0
625,1,922,0,43.128505," ","integrate((b*x+a)^(3/2)*(d*x+c)^(5/2)/x^7,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 45 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} + 18 \, a^{5} b c d^{5} - 5 \, a^{6} d^{6}\right)} \sqrt{a c} x^{6} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(1280 \, a^{6} c^{6} - {\left(105 \, a b^{5} c^{6} - 415 \, a^{2} b^{4} c^{5} d + 546 \, a^{3} b^{3} c^{4} d^{2} - 150 \, a^{4} b^{2} c^{3} d^{3} + 245 \, a^{5} b c^{2} d^{4} - 75 \, a^{6} c d^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{2} b^{4} c^{6} - 136 \, a^{3} b^{3} c^{5} d + 174 \, a^{4} b^{2} c^{4} d^{2} + 80 \, a^{5} b c^{3} d^{3} - 25 \, a^{6} c^{2} d^{4}\right)} x^{4} - 8 \, {\left(7 \, a^{3} b^{3} c^{6} - 27 \, a^{4} b^{2} c^{5} d - 423 \, a^{5} b c^{4} d^{2} - 5 \, a^{6} c^{3} d^{3}\right)} x^{3} + 16 \, {\left(3 \, a^{4} b^{2} c^{6} + 278 \, a^{5} b c^{5} d + 135 \, a^{6} c^{4} d^{2}\right)} x^{2} + 128 \, {\left(13 \, a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, a^{5} c^{4} x^{6}}, \frac{15 \, {\left(7 \, b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 45 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} + 18 \, a^{5} b c d^{5} - 5 \, a^{6} d^{6}\right)} \sqrt{-a c} x^{6} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(1280 \, a^{6} c^{6} - {\left(105 \, a b^{5} c^{6} - 415 \, a^{2} b^{4} c^{5} d + 546 \, a^{3} b^{3} c^{4} d^{2} - 150 \, a^{4} b^{2} c^{3} d^{3} + 245 \, a^{5} b c^{2} d^{4} - 75 \, a^{6} c d^{5}\right)} x^{5} + 2 \, {\left(35 \, a^{2} b^{4} c^{6} - 136 \, a^{3} b^{3} c^{5} d + 174 \, a^{4} b^{2} c^{4} d^{2} + 80 \, a^{5} b c^{3} d^{3} - 25 \, a^{6} c^{2} d^{4}\right)} x^{4} - 8 \, {\left(7 \, a^{3} b^{3} c^{6} - 27 \, a^{4} b^{2} c^{5} d - 423 \, a^{5} b c^{4} d^{2} - 5 \, a^{6} c^{3} d^{3}\right)} x^{3} + 16 \, {\left(3 \, a^{4} b^{2} c^{6} + 278 \, a^{5} b c^{5} d + 135 \, a^{6} c^{4} d^{2}\right)} x^{2} + 128 \, {\left(13 \, a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, a^{5} c^{4} x^{6}}\right]"," ",0,"[-1/30720*(15*(7*b^6*c^6 - 30*a*b^5*c^5*d + 45*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 15*a^4*b^2*c^2*d^4 + 18*a^5*b*c*d^5 - 5*a^6*d^6)*sqrt(a*c)*x^6*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(1280*a^6*c^6 - (105*a*b^5*c^6 - 415*a^2*b^4*c^5*d + 546*a^3*b^3*c^4*d^2 - 150*a^4*b^2*c^3*d^3 + 245*a^5*b*c^2*d^4 - 75*a^6*c*d^5)*x^5 + 2*(35*a^2*b^4*c^6 - 136*a^3*b^3*c^5*d + 174*a^4*b^2*c^4*d^2 + 80*a^5*b*c^3*d^3 - 25*a^6*c^2*d^4)*x^4 - 8*(7*a^3*b^3*c^6 - 27*a^4*b^2*c^5*d - 423*a^5*b*c^4*d^2 - 5*a^6*c^3*d^3)*x^3 + 16*(3*a^4*b^2*c^6 + 278*a^5*b*c^5*d + 135*a^6*c^4*d^2)*x^2 + 128*(13*a^5*b*c^6 + 25*a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^4*x^6), 1/15360*(15*(7*b^6*c^6 - 30*a*b^5*c^5*d + 45*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 15*a^4*b^2*c^2*d^4 + 18*a^5*b*c*d^5 - 5*a^6*d^6)*sqrt(-a*c)*x^6*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(1280*a^6*c^6 - (105*a*b^5*c^6 - 415*a^2*b^4*c^5*d + 546*a^3*b^3*c^4*d^2 - 150*a^4*b^2*c^3*d^3 + 245*a^5*b*c^2*d^4 - 75*a^6*c*d^5)*x^5 + 2*(35*a^2*b^4*c^6 - 136*a^3*b^3*c^5*d + 174*a^4*b^2*c^4*d^2 + 80*a^5*b*c^3*d^3 - 25*a^6*c^2*d^4)*x^4 - 8*(7*a^3*b^3*c^6 - 27*a^4*b^2*c^5*d - 423*a^5*b*c^4*d^2 - 5*a^6*c^3*d^3)*x^3 + 16*(3*a^4*b^2*c^6 + 278*a^5*b*c^5*d + 135*a^6*c^4*d^2)*x^2 + 128*(13*a^5*b*c^6 + 25*a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^4*x^6)]","A",0
626,1,546,0,1.660418," ","integrate(x^2*(b*x+a)^(3/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 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} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{3} d^{5}}, -\frac{3 \, {\left(35 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + 3 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 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} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{3} d^{5}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 - 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 + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^5), -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*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^4*x^3 - 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 + 2*(35*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^5)]","A",0
627,1,412,0,1.398772," ","integrate(x*(b*x+a)^(3/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{2} d^{4}}, \frac{3 \, {\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{2} d^{4}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^4), 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*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^4)]","A",0
628,1,306,0,1.157586," ","integrate((b*x+a)^(3/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b d^{3}}, -\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d + 5 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b d^{3}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x - 3*b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3), -1/8*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^2*x - 3*b^2*c*d + 5*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3)]","A",0
629,1,838,0,3.872480," ","integrate((b*x+a)^(3/2)/x/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a d \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(b c - 3 \, a d\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} b}{4 \, d}, \frac{a d \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + {\left(b c - 3 \, a d\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} b}{2 \, d}, \frac{4 \, a d \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(b c - 3 \, a d\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} b}{4 \, d}, \frac{2 \, a d \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b c - 3 \, a d\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} b}{2 \, d}\right]"," ",0,"[1/4*(2*a*d*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (b*c - 3*a*d)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*sqrt(d*x + c)*b)/d, 1/2*(a*d*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + (b*c - 3*a*d)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*b)/d, 1/4*(4*a*d*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (b*c - 3*a*d)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*sqrt(d*x + c)*b)/d, 1/2*(2*a*d*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b*c - 3*a*d)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*b)/d]","B",0
630,1,862,0,3.102804," ","integrate((b*x+a)^(3/2)/x^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(3 \, b c - a d\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c} a}{4 \, c x}, -\frac{4 \, b c x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + {\left(3 \, b c - a d\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} a}{4 \, c x}, \frac{b c x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(3 \, b c - a d\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, \sqrt{b x + a} \sqrt{d x + c} a}{2 \, c x}, -\frac{2 \, b c x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(3 \, b c - a d\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} a}{2 \, c x}\right]"," ",0,"[1/4*(2*b*c*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - (3*b*c - a*d)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*sqrt(d*x + c)*a)/(c*x), -1/4*(4*b*c*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + (3*b*c - a*d)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*a)/(c*x), 1/2*(b*c*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (3*b*c - a*d)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*sqrt(b*x + a)*sqrt(d*x + c)*a)/(c*x), -1/2*(2*b*c*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (3*b*c - a*d)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*a)/(c*x)]","B",0
631,1,332,0,1.876843," ","integrate((b*x+a)^(3/2)/x^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a c^{3} x^{2}}, \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} + {\left(5 \, a b c^{2} - 3 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a c^{3} x^{2}}\right]"," ",0,"[1/16*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 + (5*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^2), 1/8*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 + (5*a*b*c^2 - 3*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^2)]","A",0
632,1,438,0,3.409144," ","integrate((b*x+a)^(3/2)/x^4/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} - 22 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(7 \, a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{2} c^{4} x^{3}}, -\frac{3 \, {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(3 \, a b^{2} c^{3} - 22 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(7 \, a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{2} c^{4} x^{3}}\right]"," ",0,"[1/96*(3*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 + (3*a*b^2*c^3 - 22*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 + 2*(7*a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*x^3), -1/48*(3*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (3*a*b^2*c^3 - 22*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 + 2*(7*a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*x^3)]","A",0
633,1,574,0,10.979717," ","integrate((b*x+a)^(3/2)/x^5/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} + 15 \, a^{2} b^{2} c^{3} d - 145 \, a^{3} b c^{2} d^{2} + 105 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} - 46 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{3} c^{5} x^{4}}, \frac{3 \, {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} - {\left(9 \, a b^{3} c^{4} + 15 \, a^{2} b^{2} c^{3} d - 145 \, a^{3} b c^{2} d^{2} + 105 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} - 46 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(9 \, a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{3} c^{5} x^{4}}\right]"," ",0,"[1/768*(3*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 - (9*a*b^3*c^4 + 15*a^2*b^2*c^3*d - 145*a^3*b*c^2*d^2 + 105*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 - 46*a^3*b*c^3*d + 35*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^5*x^4), 1/384*(3*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 - (9*a*b^3*c^4 + 15*a^2*b^2*c^3*d - 145*a^3*b*c^2*d^2 + 105*a^4*c*d^3)*x^3 + 2*(3*a^2*b^2*c^4 - 46*a^3*b*c^3*d + 35*a^4*c^2*d^2)*x^2 + 8*(9*a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^5*x^4)]","A",0
634,1,600,0,1.859914," ","integrate(x^2*(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{3} c^{4} - 45 \, a b^{2} c^{3} d + 9 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3} + {\left(35 \, b^{3} c^{3} d - 45 \, a b^{2} c^{2} d^{2} + 9 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{4} x^{3} + 105 \, b^{3} c^{3} d - 100 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 14 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{2} + {\left(35 \, b^{3} c^{2} d^{2} - 38 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b^{2} d^{6} x + b^{2} c d^{5}\right)}}, \frac{3 \, {\left(35 \, b^{3} c^{4} - 45 \, a b^{2} c^{3} d + 9 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3} + {\left(35 \, b^{3} c^{3} d - 45 \, a b^{2} c^{2} d^{2} + 9 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{4} x^{3} + 105 \, b^{3} c^{3} d - 100 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 14 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{2} + {\left(35 \, b^{3} c^{2} d^{2} - 38 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{2} d^{6} x + b^{2} c d^{5}\right)}}\right]"," ",0,"[1/96*(3*(35*b^3*c^4 - 45*a*b^2*c^3*d + 9*a^2*b*c^2*d^2 + a^3*c*d^3 + (35*b^3*c^3*d - 45*a*b^2*c^2*d^2 + 9*a^2*b*c*d^3 + a^3*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^4*x^3 + 105*b^3*c^3*d - 100*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 14*(b^3*c*d^3 - a*b^2*d^4)*x^2 + (35*b^3*c^2*d^2 - 38*a*b^2*c*d^3 + 3*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^6*x + b^2*c*d^5), 1/48*(3*(35*b^3*c^4 - 45*a*b^2*c^3*d + 9*a^2*b*c^2*d^2 + a^3*c*d^3 + (35*b^3*c^3*d - 45*a*b^2*c^2*d^2 + 9*a^2*b*c*d^3 + a^3*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^4*x^3 + 105*b^3*c^3*d - 100*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 14*(b^3*c*d^3 - a*b^2*d^4)*x^2 + (35*b^3*c^2*d^2 - 38*a*b^2*c*d^3 + 3*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^6*x + b^2*c*d^5)]","A",0
635,1,434,0,1.744742," ","integrate(x*(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{2} c^{3} - 6 \, a b c^{2} d + a^{2} c d^{2} + {\left(5 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{3} x^{2} - 15 \, b^{2} c^{2} d + 13 \, a b c d^{2} - 5 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(b d^{5} x + b c d^{4}\right)}}, -\frac{3 \, {\left(5 \, b^{2} c^{3} - 6 \, a b c^{2} d + a^{2} c d^{2} + {\left(5 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{3} x^{2} - 15 \, b^{2} c^{2} d + 13 \, a b c d^{2} - 5 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(b d^{5} x + b c d^{4}\right)}}\right]"," ",0,"[1/16*(3*(5*b^2*c^3 - 6*a*b*c^2*d + a^2*c*d^2 + (5*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^3*x^2 - 15*b^2*c^2*d + 13*a*b*c*d^2 - 5*(b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^5*x + b*c*d^4), -1/8*(3*(5*b^2*c^3 - 6*a*b*c^2*d + a^2*c*d^2 + (5*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^3*x^2 - 15*b^2*c^2*d + 13*a*b*c*d^2 - 5*(b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^5*x + b*c*d^4)]","A",0
636,1,311,0,1.817435," ","integrate((b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(b d x + 3 \, b c - 2 \, a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(d^{3} x + c d^{2}\right)}}, \frac{3 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(b d x + 3 \, b c - 2 \, a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(d^{3} x + c d^{2}\right)}}\right]"," ",0,"[-1/4*(3*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(b*d*x + 3*b*c - 2*a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(d^3*x + c*d^2), 1/2*(3*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(b*d*x + 3*b*c - 2*a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(d^3*x + c*d^2)]","A",0
637,1,956,0,3.526853," ","integrate((b*x+a)^(3/2)/x/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c d x + b c^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(a d^{2} x + a c d\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d^{2} x + c^{2} d\right)}}, -\frac{2 \, {\left(b c d x + b c^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(a d^{2} x + a c d\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d^{2} x + c^{2} d\right)}}, \frac{2 \, {\left(a d^{2} x + a c d\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b c d x + b c^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d^{2} x + c^{2} d\right)}}, \frac{{\left(a d^{2} x + a c d\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(b c d x + b c^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 2 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{c d^{2} x + c^{2} d}\right]"," ",0,"[1/2*((b*c*d*x + b*c^2)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (a*d^2*x + a*c*d)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^2*x + c^2*d), -1/2*(2*(b*c*d*x + b*c^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (a*d^2*x + a*c*d)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^2*x + c^2*d), 1/2*(2*(a*d^2*x + a*c*d)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b*c*d*x + b*c^2)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^2*x + c^2*d), ((a*d^2*x + a*c*d)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (b*c*d*x + b*c^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 2*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^2*x + c^2*d)]","B",0
638,1,343,0,2.512599," ","integrate((b*x+a)^(3/2)/x^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b c d - a d^{2}\right)} x^{2} + {\left(b c^{2} - a c d\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(a c - {\left(2 \, b c - 3 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(c^{2} d x^{2} + c^{3} x\right)}}, \frac{3 \, {\left({\left(b c d - a d^{2}\right)} x^{2} + {\left(b c^{2} - a c d\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(a c - {\left(2 \, b c - 3 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c^{2} d x^{2} + c^{3} x\right)}}\right]"," ",0,"[-1/4*(3*((b*c*d - a*d^2)*x^2 + (b*c^2 - a*c*d)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(a*c - (2*b*c - 3*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d*x^2 + c^3*x), 1/2*(3*((b*c*d - a*d^2)*x^2 + (b*c^2 - a*c*d)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(a*c - (2*b*c - 3*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d*x^2 + c^3*x)]","A",0
639,1,472,0,3.606622," ","integrate((b*x+a)^(3/2)/x^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{2} c^{2} d - 6 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} - 6 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{3} + {\left(13 \, a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2} + 5 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(a c^{4} d x^{3} + a c^{5} x^{2}\right)}}, \frac{3 \, {\left({\left(b^{2} c^{2} d - 6 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} - 6 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{3} + {\left(13 \, a b c^{2} d - 15 \, a^{2} c d^{2}\right)} x^{2} + 5 \, {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(a c^{4} d x^{3} + a c^{5} x^{2}\right)}}\right]"," ",0,"[1/16*(3*((b^2*c^2*d - 6*a*b*c*d^2 + 5*a^2*d^3)*x^3 + (b^2*c^3 - 6*a*b*c^2*d + 5*a^2*c*d^2)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^3 + (13*a*b*c^2*d - 15*a^2*c*d^2)*x^2 + 5*(a*b*c^3 - a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^4*d*x^3 + a*c^5*x^2), 1/8*(3*((b^2*c^2*d - 6*a*b*c*d^2 + 5*a^2*d^3)*x^3 + (b^2*c^3 - 6*a*b*c^2*d + 5*a^2*c*d^2)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^3 + (13*a*b*c^2*d - 15*a^2*c*d^2)*x^2 + 5*(a*b*c^3 - a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^4*d*x^3 + a*c^5*x^2)]","A",0
640,1,638,0,9.405825," ","integrate((b*x+a)^(3/2)/x^4/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c^{3} d + 9 \, a b^{2} c^{2} d^{2} - 45 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 9 \, a b^{2} c^{3} d - 45 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{4} + {\left(3 \, a b^{2} c^{3} d - 100 \, a^{2} b c^{2} d^{2} + 105 \, a^{3} c d^{3}\right)} x^{3} + {\left(3 \, a b^{2} c^{4} - 38 \, a^{2} b c^{3} d + 35 \, a^{3} c^{2} d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{4} - a^{3} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a^{2} c^{5} d x^{4} + a^{2} c^{6} x^{3}\right)}}, -\frac{3 \, {\left({\left(b^{3} c^{3} d + 9 \, a b^{2} c^{2} d^{2} - 45 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} + 9 \, a b^{2} c^{3} d - 45 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{4} + {\left(3 \, a b^{2} c^{3} d - 100 \, a^{2} b c^{2} d^{2} + 105 \, a^{3} c d^{3}\right)} x^{3} + {\left(3 \, a b^{2} c^{4} - 38 \, a^{2} b c^{3} d + 35 \, a^{3} c^{2} d^{2}\right)} x^{2} + 14 \, {\left(a^{2} b c^{4} - a^{3} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{2} c^{5} d x^{4} + a^{2} c^{6} x^{3}\right)}}\right]"," ",0,"[1/96*(3*((b^3*c^3*d + 9*a*b^2*c^2*d^2 - 45*a^2*b*c*d^3 + 35*a^3*d^4)*x^4 + (b^3*c^4 + 9*a*b^2*c^3*d - 45*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^4 + (3*a*b^2*c^3*d - 100*a^2*b*c^2*d^2 + 105*a^3*c*d^3)*x^3 + (3*a*b^2*c^4 - 38*a^2*b*c^3*d + 35*a^3*c^2*d^2)*x^2 + 14*(a^2*b*c^4 - a^3*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^5*d*x^4 + a^2*c^6*x^3), -1/48*(3*((b^3*c^3*d + 9*a*b^2*c^2*d^2 - 45*a^2*b*c*d^3 + 35*a^3*d^4)*x^4 + (b^3*c^4 + 9*a*b^2*c^3*d - 45*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^4 + (3*a*b^2*c^3*d - 100*a^2*b*c^2*d^2 + 105*a^3*c*d^3)*x^3 + (3*a*b^2*c^4 - 38*a^2*b*c^3*d + 35*a^3*c^2*d^2)*x^2 + 14*(a^2*b*c^4 - a^3*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^5*d*x^4 + a^2*c^6*x^3)]","A",0
641,1,594,0,3.202554," ","integrate(x^2*(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{2} c^{4} - 30 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(6 \, b^{2} d^{4} x^{3} - 105 \, b^{2} c^{3} d + 55 \, a b c^{2} d^{2} - 3 \, {\left(7 \, b^{2} c d^{3} - 5 \, a b d^{4}\right)} x^{2} - 2 \, {\left(70 \, b^{2} c^{2} d^{2} - 39 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b d^{7} x^{2} + 2 \, b c d^{6} x + b c^{2} d^{5}\right)}}, -\frac{3 \, {\left(35 \, b^{2} c^{4} - 30 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(35 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{2} + 2 \, {\left(35 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(6 \, b^{2} d^{4} x^{3} - 105 \, b^{2} c^{3} d + 55 \, a b c^{2} d^{2} - 3 \, {\left(7 \, b^{2} c d^{3} - 5 \, a b d^{4}\right)} x^{2} - 2 \, {\left(70 \, b^{2} c^{2} d^{2} - 39 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(b d^{7} x^{2} + 2 \, b c d^{6} x + b c^{2} d^{5}\right)}}\right]"," ",0,"[1/48*(3*(35*b^2*c^4 - 30*a*b*c^3*d + 3*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 30*a*b*c*d^3 + 3*a^2*d^4)*x^2 + 2*(35*b^2*c^3*d - 30*a*b*c^2*d^2 + 3*a^2*c*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(6*b^2*d^4*x^3 - 105*b^2*c^3*d + 55*a*b*c^2*d^2 - 3*(7*b^2*c*d^3 - 5*a*b*d^4)*x^2 - 2*(70*b^2*c^2*d^2 - 39*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^7*x^2 + 2*b*c*d^6*x + b*c^2*d^5), -1/24*(3*(35*b^2*c^4 - 30*a*b*c^3*d + 3*a^2*c^2*d^2 + (35*b^2*c^2*d^2 - 30*a*b*c*d^3 + 3*a^2*d^4)*x^2 + 2*(35*b^2*c^3*d - 30*a*b*c^2*d^2 + 3*a^2*c*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(6*b^2*d^4*x^3 - 105*b^2*c^3*d + 55*a*b*c^2*d^2 - 3*(7*b^2*c*d^3 - 5*a*b*d^4)*x^2 - 2*(70*b^2*c^2*d^2 - 39*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^7*x^2 + 2*b*c*d^6*x + b*c^2*d^5)]","A",0
642,1,431,0,2.067725," ","integrate(x*(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, b c^{3} - 3 \, a c^{2} d + {\left(5 \, b c d^{2} - 3 \, a d^{3}\right)} x^{2} + 2 \, {\left(5 \, b c^{2} d - 3 \, a c d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b d^{2} x^{2} + 15 \, b c^{2} - 4 \, a c d + 2 \, {\left(10 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}, \frac{3 \, {\left(5 \, b c^{3} - 3 \, a c^{2} d + {\left(5 \, b c d^{2} - 3 \, a d^{3}\right)} x^{2} + 2 \, {\left(5 \, b c^{2} d - 3 \, a c d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(3 \, b d^{2} x^{2} + 15 \, b c^{2} - 4 \, a c d + 2 \, {\left(10 \, b c d - 3 \, a d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}\right]"," ",0,"[-1/12*(3*(5*b*c^3 - 3*a*c^2*d + (5*b*c*d^2 - 3*a*d^3)*x^2 + 2*(5*b*c^2*d - 3*a*c*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b*d^2*x^2 + 15*b*c^2 - 4*a*c*d + 2*(10*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3), 1/6*(3*(5*b*c^3 - 3*a*c^2*d + (5*b*c*d^2 - 3*a*d^3)*x^2 + 2*(5*b*c^2*d - 3*a*c*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(3*b*d^2*x^2 + 15*b*c^2 - 4*a*c*d + 2*(10*b*c*d - 3*a*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)]","A",0
643,1,325,0,1.929348," ","integrate((b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(4 \, b d x + 3 \, b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}, -\frac{3 \, {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(4 \, b d x + 3 \, b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}\right]"," ",0,"[1/6*(3*(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(4*b*d*x + 3*b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2), -1/3*(3*(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(4*b*d*x + 3*b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)]","B",0
644,1,337,0,2.250159," ","integrate((b*x+a)^(3/2)/x/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, a c + {\left(b c + 3 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{2} d^{2} x^{2} + 2 \, c^{3} d x + c^{4}\right)}}, \frac{3 \, {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, {\left(4 \, a c + {\left(b c + 3 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(c^{2} d^{2} x^{2} + 2 \, c^{3} d x + c^{4}\right)}}\right]"," ",0,"[1/6*(3*(a*d^2*x^2 + 2*a*c*d*x + a*c^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*a*c + (b*c + 3*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + 2*c^3*d*x + c^4), 1/3*(3*(a*d^2*x^2 + 2*a*c*d*x + a*c^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*(4*a*c + (b*c + 3*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + 2*c^3*d*x + c^4)]","B",0
645,1,463,0,3.888073," ","integrate((b*x+a)^(3/2)/x^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(3 \, b c d^{2} - 5 \, a d^{3}\right)} x^{3} + 2 \, {\left(3 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2} + {\left(3 \, b c^{3} - 5 \, a c^{2} d\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a c^{2} - {\left(4 \, b c d - 15 \, a d^{2}\right)} x^{2} - 2 \, {\left(3 \, b c^{2} - 10 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(c^{3} d^{2} x^{3} + 2 \, c^{4} d x^{2} + c^{5} x\right)}}, \frac{3 \, {\left({\left(3 \, b c d^{2} - 5 \, a d^{3}\right)} x^{3} + 2 \, {\left(3 \, b c^{2} d - 5 \, a c d^{2}\right)} x^{2} + {\left(3 \, b c^{3} - 5 \, a c^{2} d\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(3 \, a c^{2} - {\left(4 \, b c d - 15 \, a d^{2}\right)} x^{2} - 2 \, {\left(3 \, b c^{2} - 10 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{3} d^{2} x^{3} + 2 \, c^{4} d x^{2} + c^{5} x\right)}}\right]"," ",0,"[-1/12*(3*((3*b*c*d^2 - 5*a*d^3)*x^3 + 2*(3*b*c^2*d - 5*a*c*d^2)*x^2 + (3*b*c^3 - 5*a*c^2*d)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a*c^2 - (4*b*c*d - 15*a*d^2)*x^2 - 2*(3*b*c^2 - 10*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d^2*x^3 + 2*c^4*d*x^2 + c^5*x), 1/6*(3*((3*b*c*d^2 - 5*a*d^3)*x^3 + 2*(3*b*c^2*d - 5*a*c*d^2)*x^2 + (3*b*c^3 - 5*a*c^2*d)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(3*a*c^2 - (4*b*c*d - 15*a*d^2)*x^2 - 2*(3*b*c^2 - 10*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d^2*x^3 + 2*c^4*d*x^2 + c^5*x)]","A",0
646,1,634,0,10.419908," ","integrate((b*x+a)^(3/2)/x^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{4} - 30 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{2} c^{4} + 5 \, {\left(11 \, a b c^{2} d^{2} - 21 \, a^{2} c d^{3}\right)} x^{3} + 2 \, {\left(39 \, a b c^{3} d - 70 \, a^{2} c^{2} d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a c^{5} d^{2} x^{4} + 2 \, a c^{6} d x^{3} + a c^{7} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 30 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d - 30 \, a b c^{2} d^{2} + 35 \, a^{2} c d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{4} - 30 \, a b c^{3} d + 35 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{2} c^{4} + 5 \, {\left(11 \, a b c^{2} d^{2} - 21 \, a^{2} c d^{3}\right)} x^{3} + 2 \, {\left(39 \, a b c^{3} d - 70 \, a^{2} c^{2} d^{2}\right)} x^{2} + 3 \, {\left(5 \, a b c^{4} - 7 \, a^{2} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(a c^{5} d^{2} x^{4} + 2 \, a c^{6} d x^{3} + a c^{7} x^{2}\right)}}\right]"," ",0,"[1/48*(3*((3*b^2*c^2*d^2 - 30*a*b*c*d^3 + 35*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d - 30*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^3 + (3*b^2*c^4 - 30*a*b*c^3*d + 35*a^2*c^2*d^2)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^2*c^4 + 5*(11*a*b*c^2*d^2 - 21*a^2*c*d^3)*x^3 + 2*(39*a*b*c^3*d - 70*a^2*c^2*d^2)*x^2 + 3*(5*a*b*c^4 - 7*a^2*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^5*d^2*x^4 + 2*a*c^6*d*x^3 + a*c^7*x^2), 1/24*(3*((3*b^2*c^2*d^2 - 30*a*b*c*d^3 + 35*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d - 30*a*b*c^2*d^2 + 35*a^2*c*d^3)*x^3 + (3*b^2*c^4 - 30*a*b*c^3*d + 35*a^2*c^2*d^2)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(6*a^2*c^4 + 5*(11*a*b*c^2*d^2 - 21*a^2*c*d^3)*x^3 + 2*(39*a*b*c^3*d - 70*a^2*c^2*d^2)*x^2 + 3*(5*a*b*c^4 - 7*a^2*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^5*d^2*x^4 + 2*a*c^6*d*x^3 + a*c^7*x^2)]","A",0
647,1,892,0,1.211075," ","integrate(x^2*(b*x+a)^(5/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(1280 \, b^{6} d^{6} x^{5} + 315 \, b^{6} c^{5} d - 945 \, a b^{5} c^{4} d^{2} + 838 \, a^{2} b^{4} c^{3} d^{3} - 90 \, a^{3} b^{3} c^{2} d^{4} - 65 \, a^{4} b^{2} c d^{5} + 75 \, a^{5} b d^{6} + 128 \, {\left(b^{6} c d^{5} + 25 \, a b^{5} d^{6}\right)} x^{4} - 16 \, {\left(9 \, b^{6} c^{2} d^{4} - 26 \, a b^{5} c d^{5} - 135 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(21 \, b^{6} c^{3} d^{3} - 61 \, a b^{5} c^{2} d^{4} + 51 \, a^{2} b^{4} c d^{5} + 5 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(105 \, b^{6} c^{4} d^{2} - 308 \, a b^{5} c^{3} d^{3} + 262 \, a^{2} b^{4} c^{2} d^{4} - 20 \, a^{3} b^{3} c d^{5} + 25 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, b^{4} d^{6}}, \frac{15 \, {\left(21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, b^{6} d^{6} x^{5} + 315 \, b^{6} c^{5} d - 945 \, a b^{5} c^{4} d^{2} + 838 \, a^{2} b^{4} c^{3} d^{3} - 90 \, a^{3} b^{3} c^{2} d^{4} - 65 \, a^{4} b^{2} c d^{5} + 75 \, a^{5} b d^{6} + 128 \, {\left(b^{6} c d^{5} + 25 \, a b^{5} d^{6}\right)} x^{4} - 16 \, {\left(9 \, b^{6} c^{2} d^{4} - 26 \, a b^{5} c d^{5} - 135 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(21 \, b^{6} c^{3} d^{3} - 61 \, a b^{5} c^{2} d^{4} + 51 \, a^{2} b^{4} c d^{5} + 5 \, a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(105 \, b^{6} c^{4} d^{2} - 308 \, a b^{5} c^{3} d^{3} + 262 \, a^{2} b^{4} c^{2} d^{4} - 20 \, a^{3} b^{3} c d^{5} + 25 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, b^{4} d^{6}}\right]"," ",0,"[1/30720*(15*(21*b^6*c^6 - 70*a*b^5*c^5*d + 75*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 5*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + 5*a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(1280*b^6*d^6*x^5 + 315*b^6*c^5*d - 945*a*b^5*c^4*d^2 + 838*a^2*b^4*c^3*d^3 - 90*a^3*b^3*c^2*d^4 - 65*a^4*b^2*c*d^5 + 75*a^5*b*d^6 + 128*(b^6*c*d^5 + 25*a*b^5*d^6)*x^4 - 16*(9*b^6*c^2*d^4 - 26*a*b^5*c*d^5 - 135*a^2*b^4*d^6)*x^3 + 8*(21*b^6*c^3*d^3 - 61*a*b^5*c^2*d^4 + 51*a^2*b^4*c*d^5 + 5*a^3*b^3*d^6)*x^2 - 2*(105*b^6*c^4*d^2 - 308*a*b^5*c^3*d^3 + 262*a^2*b^4*c^2*d^4 - 20*a^3*b^3*c*d^5 + 25*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^6), 1/15360*(15*(21*b^6*c^6 - 70*a*b^5*c^5*d + 75*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 5*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + 5*a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(1280*b^6*d^6*x^5 + 315*b^6*c^5*d - 945*a*b^5*c^4*d^2 + 838*a^2*b^4*c^3*d^3 - 90*a^3*b^3*c^2*d^4 - 65*a^4*b^2*c*d^5 + 75*a^5*b*d^6 + 128*(b^6*c*d^5 + 25*a*b^5*d^6)*x^4 - 16*(9*b^6*c^2*d^4 - 26*a*b^5*c*d^5 - 135*a^2*b^4*d^6)*x^3 + 8*(21*b^6*c^3*d^3 - 61*a*b^5*c^2*d^4 + 51*a^2*b^4*c*d^5 + 5*a^3*b^3*d^6)*x^2 - 2*(105*b^6*c^4*d^2 - 308*a*b^5*c^3*d^3 + 262*a^2*b^4*c^2*d^4 - 20*a^3*b^3*c*d^5 + 25*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^6)]","A",0
648,1,704,0,1.744852," ","integrate(x*(b*x+a)^(5/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 10 \, 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} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 340 \, a b^{4} c^{3} d^{2} - 346 \, a^{2} b^{3} c^{2} d^{3} + 60 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + 21 \, a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 22 \, a b^{4} c d^{4} - 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 111 \, a b^{4} c^{2} d^{3} + 109 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{3} d^{5}}, -\frac{15 \, {\left(7 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 105 \, b^{5} c^{4} d + 340 \, a b^{4} c^{3} d^{2} - 346 \, a^{2} b^{3} c^{2} d^{3} + 60 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 48 \, {\left(b^{5} c d^{4} + 21 \, a b^{4} d^{5}\right)} x^{3} - 8 \, {\left(7 \, b^{5} c^{2} d^{3} - 22 \, a b^{4} c d^{4} - 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(35 \, b^{5} c^{3} d^{2} - 111 \, a b^{4} c^{2} d^{3} + 109 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{3} d^{5}}\right]"," ",0,"[1/7680*(15*(7*b^5*c^5 - 25*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 10*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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 340*a*b^4*c^3*d^2 - 346*a^2*b^3*c^2*d^3 + 60*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 48*(b^5*c*d^4 + 21*a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 22*a*b^4*c*d^4 - 93*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 111*a*b^4*c^2*d^3 + 109*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^5), -1/3840*(15*(7*b^5*c^5 - 25*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 - 5*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^5*d^5*x^4 - 105*b^5*c^4*d + 340*a*b^4*c^3*d^2 - 346*a^2*b^3*c^2*d^3 + 60*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 48*(b^5*c*d^4 + 21*a*b^4*d^5)*x^3 - 8*(7*b^5*c^2*d^3 - 22*a*b^4*c*d^4 - 93*a^2*b^3*d^5)*x^2 + 2*(35*b^5*c^3*d^2 - 111*a*b^4*c^2*d^3 + 109*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^5)]","A",0
649,1,540,0,1.450320," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 55 \, a b^{3} c^{2} d^{2} + 73 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 18 \, a b^{3} c d^{3} - 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{4}}, \frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 55 \, a b^{3} c^{2} d^{2} + 73 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} d^{2} - 18 \, a b^{3} c d^{3} - 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{4}}\right]"," ",0,"[1/768*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 55*a*b^3*c^2*d^2 + 73*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(b^4*c*d^3 + 17*a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 18*a*b^3*c*d^3 - 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^4), 1/384*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 55*a*b^3*c^2*d^2 + 73*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(b^4*c*d^3 + 17*a*b^3*d^4)*x^2 - 2*(5*b^4*c^2*d^2 - 18*a*b^3*c*d^3 - 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^4)]","A",0
650,1,1197,0,19.887812," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{a c} a^{2} b d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d^{3}}, \frac{24 \, \sqrt{a c} a^{2} b d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d^{3}}, \frac{96 \, \sqrt{-a c} a^{2} b d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d^{3}}, \frac{48 \, \sqrt{-a c} a^{2} b d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d^{3}}\right]"," ",0,"[1/96*(48*sqrt(a*c)*a^2*b*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 14*a*b^2*c*d^2 + 33*a^2*b*d^3 + 2*(b^3*c*d^2 + 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3), 1/48*(24*sqrt(a*c)*a^2*b*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 14*a*b^2*c*d^2 + 33*a^2*b*d^3 + 2*(b^3*c*d^2 + 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3), 1/96*(96*sqrt(-a*c)*a^2*b*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 14*a*b^2*c*d^2 + 33*a^2*b*d^3 + 2*(b^3*c*d^2 + 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3), 1/48*(48*sqrt(-a*c)*a^2*b*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(b^3*c^3 - 5*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 - 3*b^3*c^2*d + 14*a*b^2*c*d^2 + 33*a^2*b*d^3 + 2*(b^3*c*d^2 + 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^3)]","A",0
651,1,1074,0,9.750548," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, b^{2} d x^{2} - 4 \, a^{2} d + {\left(b^{2} c + 9 \, a b d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, d x}, \frac{{\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 2 \, {\left(2 \, b^{2} d x^{2} - 4 \, a^{2} d + {\left(b^{2} c + 9 \, a b d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, d x}, \frac{8 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d x^{2} - 4 \, a^{2} d + {\left(b^{2} c + 9 \, a b d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, d x}, \frac{4 \, {\left(5 \, a b c d + a^{2} d^{2}\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d x^{2} - 4 \, a^{2} d + {\left(b^{2} c + 9 \, a b d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, d x}\right]"," ",0,"[-1/16*((b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(5*a*b*c*d + a^2*d^2)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*b^2*d*x^2 - 4*a^2*d + (b^2*c + 9*a*b*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d*x), 1/8*((b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(5*a*b*c*d + a^2*d^2)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 2*(2*b^2*d*x^2 - 4*a^2*d + (b^2*c + 9*a*b*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d*x), 1/16*(8*(5*a*b*c*d + a^2*d^2)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d*x^2 - 4*a^2*d + (b^2*c + 9*a*b*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d*x), 1/8*(4*(5*a*b*c*d + a^2*d^2)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b^2*c^2 - 10*a*b*c*d - 15*a^2*d^2)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(2*b^2*d*x^2 - 4*a^2*d + (b^2*c + 9*a*b*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d*x)]","A",0
652,1,1098,0,7.034372," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, b^{2} c x^{2} - 2 \, a^{2} c - {\left(9 \, a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, c x^{2}}, -\frac{8 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + {\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(4 \, b^{2} c x^{2} - 2 \, a^{2} c - {\left(9 \, a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, c x^{2}}, \frac{{\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 2 \, {\left(4 \, b^{2} c x^{2} - 2 \, a^{2} c - {\left(9 \, a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, c x^{2}}, \frac{{\left(15 \, b^{2} c^{2} + 10 \, a b c d - a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 4 \, {\left(b^{2} c^{2} + 5 \, a b c d\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(4 \, b^{2} c x^{2} - 2 \, a^{2} c - {\left(9 \, a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, c x^{2}}\right]"," ",0,"[1/16*(4*(b^2*c^2 + 5*a*b*c*d)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - (15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*b^2*c*x^2 - 2*a^2*c - (9*a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c*x^2), -1/16*(8*(b^2*c^2 + 5*a*b*c*d)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + (15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(4*b^2*c*x^2 - 2*a^2*c - (9*a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c*x^2), 1/8*((15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*(b^2*c^2 + 5*a*b*c*d)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 2*(4*b^2*c*x^2 - 2*a^2*c - (9*a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c*x^2), 1/8*((15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 4*(b^2*c^2 + 5*a*b*c*d)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(4*b^2*c*x^2 - 2*a^2*c - (9*a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c*x^2)]","A",0
653,1,1241,0,8.531143," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{48 \, \sqrt{b d} a b^{2} c^{3} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c^{3} x^{3}}, -\frac{96 \, \sqrt{-b d} a b^{2} c^{3} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c^{3} x^{3}}, \frac{24 \, \sqrt{b d} a b^{2} c^{3} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c^{3} x^{3}}, -\frac{48 \, \sqrt{-b d} a b^{2} c^{3} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 5 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c^{3} x^{3}}\right]"," ",0,"[1/96*(48*sqrt(b*d)*a*b^2*c^3*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 + (33*a*b^2*c^3 + 14*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^3), -1/96*(96*sqrt(-b*d)*a*b^2*c^3*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (33*a*b^2*c^3 + 14*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^3), 1/48*(24*sqrt(b*d)*a*b^2*c^3*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 + (33*a*b^2*c^3 + 14*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^3), -1/48*(48*sqrt(-b*d)*a*b^2*c^3*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 3*(5*b^3*c^3 + 15*a*b^2*c^2*d - 5*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (33*a*b^2*c^3 + 14*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^3*x^3)]","A",0
654,1,566,0,7.587955," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 73 \, a^{2} b^{2} c^{3} d - 55 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 18 \, a^{3} b c^{3} d - 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{4} x^{4}}, -\frac{15 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 73 \, a^{2} b^{2} c^{3} d - 55 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 18 \, a^{3} b c^{3} d - 5 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{4} x^{4}}\right]"," ",0,"[1/768*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 + (15*a*b^3*c^4 + 73*a^2*b^2*c^3*d - 55*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 18*a^3*b*c^3*d - 5*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*x^4), -1/384*(15*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 + 73*a^2*b^2*c^3*d - 55*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 18*a^3*b*c^3*d - 5*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^4*x^4)]","A",0
655,1,732,0,19.054713," ","integrate((b*x+a)^(5/2)*(d*x+c)^(1/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 10 \, a^{2} b^{3} c^{3} d^{2} + 30 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 60 \, a^{2} b^{3} c^{4} d + 346 \, a^{3} b^{2} c^{3} d^{2} - 340 \, a^{4} b c^{2} d^{3} + 105 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 109 \, a^{3} b^{2} c^{4} d - 111 \, a^{4} b c^{3} d^{2} + 35 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 22 \, a^{4} b c^{4} d - 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(21 \, a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{3} c^{5} x^{5}}, \frac{15 \, {\left(3 \, b^{5} c^{5} - 5 \, a b^{4} c^{4} d - 10 \, a^{2} b^{3} c^{3} d^{2} + 30 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 7 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 60 \, a^{2} b^{3} c^{4} d + 346 \, a^{3} b^{2} c^{3} d^{2} - 340 \, a^{4} b c^{2} d^{3} + 105 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 109 \, a^{3} b^{2} c^{4} d - 111 \, a^{4} b c^{3} d^{2} + 35 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 22 \, a^{4} b c^{4} d - 7 \, a^{5} c^{3} d^{2}\right)} x^{2} + 48 \, {\left(21 \, a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{3} c^{5} x^{5}}\right]"," ",0,"[1/7680*(15*(3*b^5*c^5 - 5*a*b^4*c^4*d - 10*a^2*b^3*c^3*d^2 + 30*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(384*a^5*c^5 - (45*a*b^4*c^5 - 60*a^2*b^3*c^4*d + 346*a^3*b^2*c^3*d^2 - 340*a^4*b*c^2*d^3 + 105*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 109*a^3*b^2*c^4*d - 111*a^4*b*c^3*d^2 + 35*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 22*a^4*b*c^4*d - 7*a^5*c^3*d^2)*x^2 + 48*(21*a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^5*x^5), 1/3840*(15*(3*b^5*c^5 - 5*a*b^4*c^4*d - 10*a^2*b^3*c^3*d^2 + 30*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 7*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(384*a^5*c^5 - (45*a*b^4*c^5 - 60*a^2*b^3*c^4*d + 346*a^3*b^2*c^3*d^2 - 340*a^4*b*c^2*d^3 + 105*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 109*a^3*b^2*c^4*d - 111*a^4*b*c^3*d^2 + 35*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 22*a^4*b*c^4*d - 7*a^5*c^3*d^2)*x^2 + 48*(21*a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^5*x^5)]","A",0
656,1,1110,0,1.562500," ","integrate(x^2*(b*x+a)^(5/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(9 \, b^{7} c^{7} - 35 \, a b^{6} c^{6} d + 45 \, a^{2} b^{5} c^{5} d^{2} - 15 \, a^{3} b^{4} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + 15 \, a^{6} b c d^{6} - 5 \, a^{7} d^{7}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(15360 \, b^{7} d^{7} x^{6} + 945 \, b^{7} c^{6} d - 3360 \, a b^{6} c^{5} d^{2} + 3689 \, a^{2} b^{5} c^{4} d^{3} - 600 \, a^{3} b^{4} c^{3} d^{4} - 525 \, a^{4} b^{3} c^{2} d^{5} + 1400 \, a^{5} b^{2} c d^{6} - 525 \, a^{6} b d^{7} + 1280 \, {\left(15 \, b^{7} c d^{6} + 29 \, a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(3 \, b^{7} c^{2} d^{5} + 380 \, a b^{6} c d^{6} + 185 \, a^{2} b^{5} d^{7}\right)} x^{4} - 16 \, {\left(27 \, b^{7} c^{3} d^{4} - 93 \, a b^{6} c^{2} d^{5} - 2095 \, a^{2} b^{5} c d^{6} - 15 \, a^{3} b^{4} d^{7}\right)} x^{3} + 8 \, {\left(63 \, b^{7} c^{4} d^{3} - 218 \, a b^{6} c^{3} d^{4} + 228 \, a^{2} b^{5} c^{2} d^{5} + 90 \, a^{3} b^{4} c d^{6} - 35 \, a^{4} b^{3} d^{7}\right)} x^{2} - 2 \, {\left(315 \, b^{7} c^{5} d^{2} - 1099 \, a b^{6} c^{4} d^{3} + 1166 \, a^{2} b^{5} c^{3} d^{4} - 150 \, a^{3} b^{4} c^{2} d^{5} + 455 \, a^{4} b^{3} c d^{6} - 175 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{430080 \, b^{5} d^{6}}, \frac{105 \, {\left(9 \, b^{7} c^{7} - 35 \, a b^{6} c^{6} d + 45 \, a^{2} b^{5} c^{5} d^{2} - 15 \, a^{3} b^{4} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + 15 \, a^{6} b c d^{6} - 5 \, a^{7} d^{7}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15360 \, b^{7} d^{7} x^{6} + 945 \, b^{7} c^{6} d - 3360 \, a b^{6} c^{5} d^{2} + 3689 \, a^{2} b^{5} c^{4} d^{3} - 600 \, a^{3} b^{4} c^{3} d^{4} - 525 \, a^{4} b^{3} c^{2} d^{5} + 1400 \, a^{5} b^{2} c d^{6} - 525 \, a^{6} b d^{7} + 1280 \, {\left(15 \, b^{7} c d^{6} + 29 \, a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(3 \, b^{7} c^{2} d^{5} + 380 \, a b^{6} c d^{6} + 185 \, a^{2} b^{5} d^{7}\right)} x^{4} - 16 \, {\left(27 \, b^{7} c^{3} d^{4} - 93 \, a b^{6} c^{2} d^{5} - 2095 \, a^{2} b^{5} c d^{6} - 15 \, a^{3} b^{4} d^{7}\right)} x^{3} + 8 \, {\left(63 \, b^{7} c^{4} d^{3} - 218 \, a b^{6} c^{3} d^{4} + 228 \, a^{2} b^{5} c^{2} d^{5} + 90 \, a^{3} b^{4} c d^{6} - 35 \, a^{4} b^{3} d^{7}\right)} x^{2} - 2 \, {\left(315 \, b^{7} c^{5} d^{2} - 1099 \, a b^{6} c^{4} d^{3} + 1166 \, a^{2} b^{5} c^{3} d^{4} - 150 \, a^{3} b^{4} c^{2} d^{5} + 455 \, a^{4} b^{3} c d^{6} - 175 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{215040 \, b^{5} d^{6}}\right]"," ",0,"[-1/430080*(105*(9*b^7*c^7 - 35*a*b^6*c^6*d + 45*a^2*b^5*c^5*d^2 - 15*a^3*b^4*c^4*d^3 - 5*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + 15*a^6*b*c*d^6 - 5*a^7*d^7)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(15360*b^7*d^7*x^6 + 945*b^7*c^6*d - 3360*a*b^6*c^5*d^2 + 3689*a^2*b^5*c^4*d^3 - 600*a^3*b^4*c^3*d^4 - 525*a^4*b^3*c^2*d^5 + 1400*a^5*b^2*c*d^6 - 525*a^6*b*d^7 + 1280*(15*b^7*c*d^6 + 29*a*b^6*d^7)*x^5 + 128*(3*b^7*c^2*d^5 + 380*a*b^6*c*d^6 + 185*a^2*b^5*d^7)*x^4 - 16*(27*b^7*c^3*d^4 - 93*a*b^6*c^2*d^5 - 2095*a^2*b^5*c*d^6 - 15*a^3*b^4*d^7)*x^3 + 8*(63*b^7*c^4*d^3 - 218*a*b^6*c^3*d^4 + 228*a^2*b^5*c^2*d^5 + 90*a^3*b^4*c*d^6 - 35*a^4*b^3*d^7)*x^2 - 2*(315*b^7*c^5*d^2 - 1099*a*b^6*c^4*d^3 + 1166*a^2*b^5*c^3*d^4 - 150*a^3*b^4*c^2*d^5 + 455*a^4*b^3*c*d^6 - 175*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^6), 1/215040*(105*(9*b^7*c^7 - 35*a*b^6*c^6*d + 45*a^2*b^5*c^5*d^2 - 15*a^3*b^4*c^4*d^3 - 5*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + 15*a^6*b*c*d^6 - 5*a^7*d^7)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15360*b^7*d^7*x^6 + 945*b^7*c^6*d - 3360*a*b^6*c^5*d^2 + 3689*a^2*b^5*c^4*d^3 - 600*a^3*b^4*c^3*d^4 - 525*a^4*b^3*c^2*d^5 + 1400*a^5*b^2*c*d^6 - 525*a^6*b*d^7 + 1280*(15*b^7*c*d^6 + 29*a*b^6*d^7)*x^5 + 128*(3*b^7*c^2*d^5 + 380*a*b^6*c*d^6 + 185*a^2*b^5*d^7)*x^4 - 16*(27*b^7*c^3*d^4 - 93*a*b^6*c^2*d^5 - 2095*a^2*b^5*c*d^6 - 15*a^3*b^4*d^7)*x^3 + 8*(63*b^7*c^4*d^3 - 218*a*b^6*c^3*d^4 + 228*a^2*b^5*c^2*d^5 + 90*a^3*b^4*c*d^6 - 35*a^4*b^3*d^7)*x^2 - 2*(315*b^7*c^5*d^2 - 1099*a*b^6*c^4*d^3 + 1166*a^2*b^5*c^3*d^4 - 150*a^3*b^4*c^2*d^5 + 455*a^4*b^3*c*d^6 - 175*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^6)]","A",0
657,1,894,0,1.603091," ","integrate(x*(b*x+a)^(5/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 45 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} + 18 \, a^{5} b c d^{5} - 5 \, a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(1280 \, b^{6} d^{6} x^{5} - 105 \, b^{6} c^{5} d + 415 \, a b^{5} c^{4} d^{2} - 546 \, a^{2} b^{4} c^{3} d^{3} + 150 \, a^{3} b^{3} c^{2} d^{4} - 245 \, a^{4} b^{2} c d^{5} + 75 \, a^{5} b d^{6} + 128 \, {\left(13 \, b^{6} c d^{5} + 25 \, a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(3 \, b^{6} c^{2} d^{4} + 278 \, a b^{5} c d^{5} + 135 \, a^{2} b^{4} d^{6}\right)} x^{3} - 8 \, {\left(7 \, b^{6} c^{3} d^{3} - 27 \, a b^{5} c^{2} d^{4} - 423 \, a^{2} b^{4} c d^{5} - 5 \, a^{3} b^{3} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{6} c^{4} d^{2} - 136 \, a b^{5} c^{3} d^{3} + 174 \, a^{2} b^{4} c^{2} d^{4} + 80 \, a^{3} b^{3} c d^{5} - 25 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{30720 \, b^{4} d^{5}}, -\frac{15 \, {\left(7 \, b^{6} c^{6} - 30 \, a b^{5} c^{5} d + 45 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} + 18 \, a^{5} b c d^{5} - 5 \, a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(1280 \, b^{6} d^{6} x^{5} - 105 \, b^{6} c^{5} d + 415 \, a b^{5} c^{4} d^{2} - 546 \, a^{2} b^{4} c^{3} d^{3} + 150 \, a^{3} b^{3} c^{2} d^{4} - 245 \, a^{4} b^{2} c d^{5} + 75 \, a^{5} b d^{6} + 128 \, {\left(13 \, b^{6} c d^{5} + 25 \, a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(3 \, b^{6} c^{2} d^{4} + 278 \, a b^{5} c d^{5} + 135 \, a^{2} b^{4} d^{6}\right)} x^{3} - 8 \, {\left(7 \, b^{6} c^{3} d^{3} - 27 \, a b^{5} c^{2} d^{4} - 423 \, a^{2} b^{4} c d^{5} - 5 \, a^{3} b^{3} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{6} c^{4} d^{2} - 136 \, a b^{5} c^{3} d^{3} + 174 \, a^{2} b^{4} c^{2} d^{4} + 80 \, a^{3} b^{3} c d^{5} - 25 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{15360 \, b^{4} d^{5}}\right]"," ",0,"[-1/30720*(15*(7*b^6*c^6 - 30*a*b^5*c^5*d + 45*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 15*a^4*b^2*c^2*d^4 + 18*a^5*b*c*d^5 - 5*a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(1280*b^6*d^6*x^5 - 105*b^6*c^5*d + 415*a*b^5*c^4*d^2 - 546*a^2*b^4*c^3*d^3 + 150*a^3*b^3*c^2*d^4 - 245*a^4*b^2*c*d^5 + 75*a^5*b*d^6 + 128*(13*b^6*c*d^5 + 25*a*b^5*d^6)*x^4 + 16*(3*b^6*c^2*d^4 + 278*a*b^5*c*d^5 + 135*a^2*b^4*d^6)*x^3 - 8*(7*b^6*c^3*d^3 - 27*a*b^5*c^2*d^4 - 423*a^2*b^4*c*d^5 - 5*a^3*b^3*d^6)*x^2 + 2*(35*b^6*c^4*d^2 - 136*a*b^5*c^3*d^3 + 174*a^2*b^4*c^2*d^4 + 80*a^3*b^3*c*d^5 - 25*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5), -1/15360*(15*(7*b^6*c^6 - 30*a*b^5*c^5*d + 45*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 - 15*a^4*b^2*c^2*d^4 + 18*a^5*b*c*d^5 - 5*a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(1280*b^6*d^6*x^5 - 105*b^6*c^5*d + 415*a*b^5*c^4*d^2 - 546*a^2*b^4*c^3*d^3 + 150*a^3*b^3*c^2*d^4 - 245*a^4*b^2*c*d^5 + 75*a^5*b*d^6 + 128*(13*b^6*c*d^5 + 25*a*b^5*d^6)*x^4 + 16*(3*b^6*c^2*d^4 + 278*a*b^5*c*d^5 + 135*a^2*b^4*d^6)*x^3 - 8*(7*b^6*c^3*d^3 - 27*a*b^5*c^2*d^4 - 423*a^2*b^4*c*d^5 - 5*a^3*b^3*d^6)*x^2 + 2*(35*b^6*c^4*d^2 - 136*a*b^5*c^3*d^3 + 174*a^2*b^4*c^2*d^4 + 80*a^3*b^3*c*d^5 - 25*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^5)]","A",0
658,1,702,0,1.151445," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(128 \, b^{5} d^{5} x^{4} + 15 \, b^{5} c^{4} d - 70 \, a b^{4} c^{3} d^{2} + 128 \, a^{2} b^{3} c^{2} d^{3} + 70 \, a^{3} b^{2} c d^{4} - 15 \, a^{4} b d^{5} + 16 \, {\left(11 \, b^{5} c d^{4} + 21 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(b^{5} c^{2} d^{3} + 64 \, a b^{4} c d^{4} + 31 \, a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(5 \, b^{5} c^{3} d^{2} - 23 \, a b^{4} c^{2} d^{3} - 233 \, a^{2} b^{3} c d^{4} - 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, b^{3} d^{4}}, \frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(128 \, b^{5} d^{5} x^{4} + 15 \, b^{5} c^{4} d - 70 \, a b^{4} c^{3} d^{2} + 128 \, a^{2} b^{3} c^{2} d^{3} + 70 \, a^{3} b^{2} c d^{4} - 15 \, a^{4} b d^{5} + 16 \, {\left(11 \, b^{5} c d^{4} + 21 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(b^{5} c^{2} d^{3} + 64 \, a b^{4} c d^{4} + 31 \, a^{2} b^{3} d^{5}\right)} x^{2} - 2 \, {\left(5 \, b^{5} c^{3} d^{2} - 23 \, a b^{4} c^{2} d^{3} - 233 \, a^{2} b^{3} c d^{4} - 5 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, b^{3} d^{4}}\right]"," ",0,"[-1/2560*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(128*b^5*d^5*x^4 + 15*b^5*c^4*d - 70*a*b^4*c^3*d^2 + 128*a^2*b^3*c^2*d^3 + 70*a^3*b^2*c*d^4 - 15*a^4*b*d^5 + 16*(11*b^5*c*d^4 + 21*a*b^4*d^5)*x^3 + 8*(b^5*c^2*d^3 + 64*a*b^4*c*d^4 + 31*a^2*b^3*d^5)*x^2 - 2*(5*b^5*c^3*d^2 - 23*a*b^4*c^2*d^3 - 233*a^2*b^3*c*d^4 - 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4), 1/1280*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(128*b^5*d^5*x^4 + 15*b^5*c^4*d - 70*a*b^4*c^3*d^2 + 128*a^2*b^3*c^2*d^3 + 70*a^3*b^2*c*d^4 - 15*a^4*b*d^5 + 16*(11*b^5*c*d^4 + 21*a*b^4*d^5)*x^3 + 8*(b^5*c^2*d^3 + 64*a*b^4*c*d^4 + 31*a^2*b^3*d^5)*x^2 - 2*(5*b^5*c^3*d^2 - 23*a*b^4*c^2*d^3 - 233*a^2*b^3*c*d^4 - 5*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^4)]","A",0
659,1,1481,0,44.022832," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{a c} a^{2} b^{2} c d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 57 \, a b^{3} c^{2} d^{2} + 337 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{3}}, \frac{192 \, \sqrt{a c} a^{2} b^{2} c d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 57 \, a b^{3} c^{2} d^{2} + 337 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{3}}, \frac{768 \, \sqrt{-a c} a^{2} b^{2} c d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 57 \, a b^{3} c^{2} d^{2} + 337 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{3}}, \frac{384 \, \sqrt{-a c} a^{2} b^{2} c d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(3 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 90 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 5 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d + 57 \, a b^{3} c^{2} d^{2} + 337 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} + 17 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 122 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{3}}\right]"," ",0,"[1/768*(384*sqrt(a*c)*a^2*b^2*c*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 57*a*b^3*c^2*d^2 + 337*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + 17*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3), 1/384*(192*sqrt(a*c)*a^2*b^2*c*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 57*a*b^3*c^2*d^2 + 337*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + 17*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3), 1/768*(768*sqrt(-a*c)*a^2*b^2*c*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 57*a*b^3*c^2*d^2 + 337*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + 17*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3), 1/384*(384*sqrt(-a*c)*a^2*b^2*c*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(3*b^4*c^4 - 20*a*b^3*c^3*d + 90*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 5*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 - 9*b^4*c^3*d + 57*a*b^3*c^2*d^2 + 337*a^2*b^2*c*d^3 + 15*a^3*b*d^4 + 8*(9*b^4*c*d^3 + 17*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 + 122*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^3)]","A",0
660,1,1333,0,12.726096," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 24 \, {\left(5 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a^{2} b c d^{2} + 2 \, {\left(7 \, b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x^{2} + {\left(3 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d^{2} x}, \frac{3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 12 \, {\left(5 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a^{2} b c d^{2} + 2 \, {\left(7 \, b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x^{2} + {\left(3 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d^{2} x}, \frac{48 \, {\left(5 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a^{2} b c d^{2} + 2 \, {\left(7 \, b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x^{2} + {\left(3 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d^{2} x}, \frac{24 \, {\left(5 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 3 \, {\left(b^{3} c^{3} - 15 \, a b^{2} c^{2} d - 45 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{3} - 24 \, a^{2} b c d^{2} + 2 \, {\left(7 \, b^{3} c d^{2} + 13 \, a b^{2} d^{3}\right)} x^{2} + {\left(3 \, b^{3} c^{2} d + 68 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d^{2} x}\right]"," ",0,"[-1/96*(3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 24*(5*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*b^3*d^3*x^3 - 24*a^2*b*c*d^2 + 2*(7*b^3*c*d^2 + 13*a*b^2*d^3)*x^2 + (3*b^3*c^2*d + 68*a*b^2*c*d^2 + 33*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2*x), 1/48*(3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 12*(5*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 2*(8*b^3*d^3*x^3 - 24*a^2*b*c*d^2 + 2*(7*b^3*c*d^2 + 13*a*b^2*d^3)*x^2 + (3*b^3*c^2*d + 68*a*b^2*c*d^2 + 33*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2*x), 1/96*(48*(5*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^3 - 24*a^2*b*c*d^2 + 2*(7*b^3*c*d^2 + 13*a*b^2*d^3)*x^2 + (3*b^3*c^2*d + 68*a*b^2*c*d^2 + 33*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2*x), 1/48*(24*(5*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 3*(b^3*c^3 - 15*a*b^2*c^2*d - 45*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^3 - 24*a^2*b*c*d^2 + 2*(7*b^3*c*d^2 + 13*a*b^2*d^3)*x^2 + (3*b^3*c^2*d + 68*a*b^2*c*d^2 + 33*a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^2*x)]","A",0
661,1,1185,0,5.964820," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, b^{2} d x^{3} - 2 \, a^{2} c + {\left(5 \, b^{2} c + 9 \, a b d\right)} x^{2} - {\left(9 \, a b c + 5 \, a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, -\frac{6 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, b^{2} d x^{3} - 2 \, a^{2} c + {\left(5 \, b^{2} c + 9 \, a b d\right)} x^{2} - {\left(9 \, a b c + 5 \, a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, \frac{6 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d x^{3} - 2 \, a^{2} c + {\left(5 \, b^{2} c + 9 \, a b d\right)} x^{2} - {\left(9 \, a b c + 5 \, a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, x^{2}}, \frac{3 \, {\left(5 \, b^{2} c^{2} + 10 \, a b c d + a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 3 \, {\left(b^{2} c^{2} + 10 \, a b c d + 5 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d x^{3} - 2 \, a^{2} c + {\left(5 \, b^{2} c + 9 \, a b d\right)} x^{2} - {\left(9 \, a b c + 5 \, a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, x^{2}}\right]"," ",0,"[1/16*(3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*b^2*d*x^3 - 2*a^2*c + (5*b^2*c + 9*a*b*d)*x^2 - (9*a*b*c + 5*a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, -1/16*(6*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*b^2*d*x^3 - 2*a^2*c + (5*b^2*c + 9*a*b*d)*x^2 - (9*a*b*c + 5*a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, 1/16*(6*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d*x^3 - 2*a^2*c + (5*b^2*c + 9*a*b*d)*x^2 - (9*a*b*c + 5*a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2, 1/8*(3*(5*b^2*c^2 + 10*a*b*c*d + a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 3*(b^2*c^2 + 10*a*b*c*d + 5*a^2*d^2)*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(2*b^2*d*x^3 - 2*a^2*c + (5*b^2*c + 9*a*b*d)*x^2 - (9*a*b*c + 5*a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/x^2]","A",0
662,1,1357,0,6.898497," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{24 \, {\left(3 \, a b^{2} c^{3} + 5 \, a^{2} b c^{2} d\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(24 \, a b^{2} c^{2} d x^{3} - 8 \, a^{3} c^{3} - {\left(33 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(13 \, a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c^{2} x^{3}}, -\frac{48 \, {\left(3 \, a b^{2} c^{3} + 5 \, a^{2} b c^{2} d\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(24 \, a b^{2} c^{2} d x^{3} - 8 \, a^{3} c^{3} - {\left(33 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(13 \, a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c^{2} x^{3}}, \frac{3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 12 \, {\left(3 \, a b^{2} c^{3} + 5 \, a^{2} b c^{2} d\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 2 \, {\left(24 \, a b^{2} c^{2} d x^{3} - 8 \, a^{3} c^{3} - {\left(33 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(13 \, a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c^{2} x^{3}}, \frac{3 \, {\left(5 \, b^{3} c^{3} + 45 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 24 \, {\left(3 \, a b^{2} c^{3} + 5 \, a^{2} b c^{2} d\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(24 \, a b^{2} c^{2} d x^{3} - 8 \, a^{3} c^{3} - {\left(33 \, a b^{2} c^{3} + 68 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(13 \, a^{2} b c^{3} + 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c^{2} x^{3}}\right]"," ",0,"[1/96*(24*(3*a*b^2*c^3 + 5*a^2*b*c^2*d)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(24*a*b^2*c^2*d*x^3 - 8*a^3*c^3 - (33*a*b^2*c^3 + 68*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(13*a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^3), -1/96*(48*(3*a*b^2*c^3 + 5*a^2*b*c^2*d)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(24*a*b^2*c^2*d*x^3 - 8*a^3*c^3 - (33*a*b^2*c^3 + 68*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(13*a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^3), 1/48*(3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 12*(3*a*b^2*c^3 + 5*a^2*b*c^2*d)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 2*(24*a*b^2*c^2*d*x^3 - 8*a^3*c^3 - (33*a*b^2*c^3 + 68*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(13*a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^3), 1/48*(3*(5*b^3*c^3 + 45*a*b^2*c^2*d + 15*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 24*(3*a*b^2*c^3 + 5*a^2*b*c^2*d)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(24*a*b^2*c^2*d*x^3 - 8*a^3*c^3 - (33*a*b^2*c^3 + 68*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(13*a^2*b*c^3 + 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^2*x^3)]","A",0
663,1,1525,0,17.018758," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x^5,x, algorithm=""fricas"")","\left[\frac{384 \, \sqrt{b d} a^{2} b^{2} c^{3} d x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 337 \, a^{2} b^{2} c^{3} d + 57 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{3} x^{4}}, -\frac{768 \, \sqrt{-b d} a^{2} b^{2} c^{3} d x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 337 \, a^{2} b^{2} c^{3} d + 57 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{3} x^{4}}, \frac{192 \, \sqrt{b d} a^{2} b^{2} c^{3} d x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 337 \, a^{2} b^{2} c^{3} d + 57 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{3} x^{4}}, -\frac{384 \, \sqrt{-b d} a^{2} b^{2} c^{3} d x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 3 \, {\left(5 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} + 337 \, a^{2} b^{2} c^{3} d + 57 \, a^{3} b c^{2} d^{2} - 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 122 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} + 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{3} x^{4}}\right]"," ",0,"[1/768*(384*sqrt(b*d)*a^2*b^2*c^3*d*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 + (15*a*b^3*c^4 + 337*a^2*b^2*c^3*d + 57*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^4), -1/768*(768*sqrt(-b*d)*a^2*b^2*c^3*d*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 + (15*a*b^3*c^4 + 337*a^2*b^2*c^3*d + 57*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^4), 1/384*(192*sqrt(b*d)*a^2*b^2*c^3*d*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 + (15*a*b^3*c^4 + 337*a^2*b^2*c^3*d + 57*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^4), -1/384*(384*sqrt(-b*d)*a^2*b^2*c^3*d*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 3*(5*b^4*c^4 - 60*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 3*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 + 337*a^2*b^2*c^3*d + 57*a^3*b*c^2*d^2 - 9*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 + 122*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 + 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^3*x^4)]","A",0
664,1,730,0,12.657552," ","integrate((b*x+a)^(5/2)*(d*x+c)^(3/2)/x^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(128 \, a^{5} c^{5} - {\left(15 \, a b^{4} c^{5} - 70 \, a^{2} b^{3} c^{4} d - 128 \, a^{3} b^{2} c^{3} d^{2} + 70 \, a^{4} b c^{2} d^{3} - 15 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(5 \, a^{2} b^{3} c^{5} + 233 \, a^{3} b^{2} c^{4} d + 23 \, a^{4} b c^{3} d^{2} - 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(31 \, a^{3} b^{2} c^{5} + 64 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{2} + 16 \, {\left(21 \, a^{4} b c^{5} + 11 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, a^{3} c^{4} x^{5}}, \frac{15 \, {\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(128 \, a^{5} c^{5} - {\left(15 \, a b^{4} c^{5} - 70 \, a^{2} b^{3} c^{4} d - 128 \, a^{3} b^{2} c^{3} d^{2} + 70 \, a^{4} b c^{2} d^{3} - 15 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(5 \, a^{2} b^{3} c^{5} + 233 \, a^{3} b^{2} c^{4} d + 23 \, a^{4} b c^{3} d^{2} - 5 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(31 \, a^{3} b^{2} c^{5} + 64 \, a^{4} b c^{4} d + a^{5} c^{3} d^{2}\right)} x^{2} + 16 \, {\left(21 \, a^{4} b c^{5} + 11 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, a^{3} c^{4} x^{5}}\right]"," ",0,"[-1/2560*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(128*a^5*c^5 - (15*a*b^4*c^5 - 70*a^2*b^3*c^4*d - 128*a^3*b^2*c^3*d^2 + 70*a^4*b*c^2*d^3 - 15*a^5*c*d^4)*x^4 + 2*(5*a^2*b^3*c^5 + 233*a^3*b^2*c^4*d + 23*a^4*b*c^3*d^2 - 5*a^5*c^2*d^3)*x^3 + 8*(31*a^3*b^2*c^5 + 64*a^4*b*c^4*d + a^5*c^3*d^2)*x^2 + 16*(21*a^4*b*c^5 + 11*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^5), 1/1280*(15*(b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(128*a^5*c^5 - (15*a*b^4*c^5 - 70*a^2*b^3*c^4*d - 128*a^3*b^2*c^3*d^2 + 70*a^4*b*c^2*d^3 - 15*a^5*c*d^4)*x^4 + 2*(5*a^2*b^3*c^5 + 233*a^3*b^2*c^4*d + 23*a^4*b*c^3*d^2 - 5*a^5*c^2*d^3)*x^3 + 8*(31*a^3*b^2*c^5 + 64*a^4*b*c^4*d + a^5*c^3*d^2)*x^2 + 16*(21*a^4*b*c^5 + 11*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^4*x^5)]","A",0
665,1,1102,0,1.107513," ","integrate(x*(b*x+a)^(5/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{7} c^{7} - 5 \, a b^{6} c^{6} d + 9 \, a^{2} b^{5} c^{5} d^{2} - 5 \, a^{3} b^{4} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} - 5 \, a^{6} b c d^{6} + a^{7} d^{7}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(3072 \, b^{7} d^{7} x^{6} - 105 \, b^{7} c^{6} d + 490 \, a b^{6} c^{5} d^{2} - 791 \, a^{2} b^{5} c^{4} d^{3} + 300 \, a^{3} b^{4} c^{3} d^{4} - 791 \, a^{4} b^{3} c^{2} d^{5} + 490 \, a^{5} b^{2} c d^{6} - 105 \, a^{6} b d^{7} + 7424 \, {\left(b^{7} c d^{6} + a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(37 \, b^{7} c^{2} d^{5} + 146 \, a b^{6} c d^{6} + 37 \, a^{2} b^{5} d^{7}\right)} x^{4} + 16 \, {\left(3 \, b^{7} c^{3} d^{4} + 797 \, a b^{6} c^{2} d^{5} + 797 \, a^{2} b^{5} c d^{6} + 3 \, a^{3} b^{4} d^{7}\right)} x^{3} - 8 \, {\left(7 \, b^{7} c^{4} d^{3} - 32 \, a b^{6} c^{3} d^{4} - 1230 \, a^{2} b^{5} c^{2} d^{5} - 32 \, a^{3} b^{4} c d^{6} + 7 \, a^{4} b^{3} d^{7}\right)} x^{2} + 2 \, {\left(35 \, b^{7} c^{5} d^{2} - 161 \, a b^{6} c^{4} d^{3} + 254 \, a^{2} b^{5} c^{3} d^{4} + 254 \, a^{3} b^{4} c^{2} d^{5} - 161 \, a^{4} b^{3} c d^{6} + 35 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{86016 \, b^{5} d^{5}}, -\frac{105 \, {\left(b^{7} c^{7} - 5 \, a b^{6} c^{6} d + 9 \, a^{2} b^{5} c^{5} d^{2} - 5 \, a^{3} b^{4} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} - 5 \, a^{6} b c d^{6} + a^{7} d^{7}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(3072 \, b^{7} d^{7} x^{6} - 105 \, b^{7} c^{6} d + 490 \, a b^{6} c^{5} d^{2} - 791 \, a^{2} b^{5} c^{4} d^{3} + 300 \, a^{3} b^{4} c^{3} d^{4} - 791 \, a^{4} b^{3} c^{2} d^{5} + 490 \, a^{5} b^{2} c d^{6} - 105 \, a^{6} b d^{7} + 7424 \, {\left(b^{7} c d^{6} + a b^{6} d^{7}\right)} x^{5} + 128 \, {\left(37 \, b^{7} c^{2} d^{5} + 146 \, a b^{6} c d^{6} + 37 \, a^{2} b^{5} d^{7}\right)} x^{4} + 16 \, {\left(3 \, b^{7} c^{3} d^{4} + 797 \, a b^{6} c^{2} d^{5} + 797 \, a^{2} b^{5} c d^{6} + 3 \, a^{3} b^{4} d^{7}\right)} x^{3} - 8 \, {\left(7 \, b^{7} c^{4} d^{3} - 32 \, a b^{6} c^{3} d^{4} - 1230 \, a^{2} b^{5} c^{2} d^{5} - 32 \, a^{3} b^{4} c d^{6} + 7 \, a^{4} b^{3} d^{7}\right)} x^{2} + 2 \, {\left(35 \, b^{7} c^{5} d^{2} - 161 \, a b^{6} c^{4} d^{3} + 254 \, a^{2} b^{5} c^{3} d^{4} + 254 \, a^{3} b^{4} c^{2} d^{5} - 161 \, a^{4} b^{3} c d^{6} + 35 \, a^{5} b^{2} d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{43008 \, b^{5} d^{5}}\right]"," ",0,"[1/86016*(105*(b^7*c^7 - 5*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 - 5*a^3*b^4*c^4*d^3 - 5*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 - 5*a^6*b*c*d^6 + a^7*d^7)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(3072*b^7*d^7*x^6 - 105*b^7*c^6*d + 490*a*b^6*c^5*d^2 - 791*a^2*b^5*c^4*d^3 + 300*a^3*b^4*c^3*d^4 - 791*a^4*b^3*c^2*d^5 + 490*a^5*b^2*c*d^6 - 105*a^6*b*d^7 + 7424*(b^7*c*d^6 + a*b^6*d^7)*x^5 + 128*(37*b^7*c^2*d^5 + 146*a*b^6*c*d^6 + 37*a^2*b^5*d^7)*x^4 + 16*(3*b^7*c^3*d^4 + 797*a*b^6*c^2*d^5 + 797*a^2*b^5*c*d^6 + 3*a^3*b^4*d^7)*x^3 - 8*(7*b^7*c^4*d^3 - 32*a*b^6*c^3*d^4 - 1230*a^2*b^5*c^2*d^5 - 32*a^3*b^4*c*d^6 + 7*a^4*b^3*d^7)*x^2 + 2*(35*b^7*c^5*d^2 - 161*a*b^6*c^4*d^3 + 254*a^2*b^5*c^3*d^4 + 254*a^3*b^4*c^2*d^5 - 161*a^4*b^3*c*d^6 + 35*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5), -1/43008*(105*(b^7*c^7 - 5*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 - 5*a^3*b^4*c^4*d^3 - 5*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 - 5*a^6*b*c*d^6 + a^7*d^7)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(3072*b^7*d^7*x^6 - 105*b^7*c^6*d + 490*a*b^6*c^5*d^2 - 791*a^2*b^5*c^4*d^3 + 300*a^3*b^4*c^3*d^4 - 791*a^4*b^3*c^2*d^5 + 490*a^5*b^2*c*d^6 - 105*a^6*b*d^7 + 7424*(b^7*c*d^6 + a*b^6*d^7)*x^5 + 128*(37*b^7*c^2*d^5 + 146*a*b^6*c*d^6 + 37*a^2*b^5*d^7)*x^4 + 16*(3*b^7*c^3*d^4 + 797*a*b^6*c^2*d^5 + 797*a^2*b^5*c*d^6 + 3*a^3*b^4*d^7)*x^3 - 8*(7*b^7*c^4*d^3 - 32*a*b^6*c^3*d^4 - 1230*a^2*b^5*c^2*d^5 - 32*a^3*b^4*c*d^6 + 7*a^4*b^3*d^7)*x^2 + 2*(35*b^7*c^5*d^2 - 161*a*b^6*c^4*d^3 + 254*a^2*b^5*c^3*d^4 + 254*a^3*b^4*c^2*d^5 - 161*a^4*b^3*c*d^6 + 35*a^5*b^2*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^5)]","A",0
666,1,882,0,0.984637," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(256 \, b^{6} d^{6} x^{5} + 15 \, b^{6} c^{5} d - 85 \, a b^{5} c^{4} d^{2} + 198 \, a^{2} b^{4} c^{3} d^{3} + 198 \, a^{3} b^{3} c^{2} d^{4} - 85 \, a^{4} b^{2} c d^{5} + 15 \, a^{5} b d^{6} + 640 \, {\left(b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(27 \, b^{6} c^{2} d^{4} + 106 \, a b^{5} c d^{5} + 27 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(b^{6} c^{3} d^{3} + 159 \, a b^{5} c^{2} d^{4} + 159 \, a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(5 \, b^{6} c^{4} d^{2} - 28 \, a b^{5} c^{3} d^{3} - 594 \, a^{2} b^{4} c^{2} d^{4} - 28 \, a^{3} b^{3} c d^{5} + 5 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6144 \, b^{4} d^{4}}, \frac{15 \, {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(256 \, b^{6} d^{6} x^{5} + 15 \, b^{6} c^{5} d - 85 \, a b^{5} c^{4} d^{2} + 198 \, a^{2} b^{4} c^{3} d^{3} + 198 \, a^{3} b^{3} c^{2} d^{4} - 85 \, a^{4} b^{2} c d^{5} + 15 \, a^{5} b d^{6} + 640 \, {\left(b^{6} c d^{5} + a b^{5} d^{6}\right)} x^{4} + 16 \, {\left(27 \, b^{6} c^{2} d^{4} + 106 \, a b^{5} c d^{5} + 27 \, a^{2} b^{4} d^{6}\right)} x^{3} + 8 \, {\left(b^{6} c^{3} d^{3} + 159 \, a b^{5} c^{2} d^{4} + 159 \, a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6}\right)} x^{2} - 2 \, {\left(5 \, b^{6} c^{4} d^{2} - 28 \, a b^{5} c^{3} d^{3} - 594 \, a^{2} b^{4} c^{2} d^{4} - 28 \, a^{3} b^{3} c d^{5} + 5 \, a^{4} b^{2} d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3072 \, b^{4} d^{4}}\right]"," ",0,"[1/6144*(15*(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(256*b^6*d^6*x^5 + 15*b^6*c^5*d - 85*a*b^5*c^4*d^2 + 198*a^2*b^4*c^3*d^3 + 198*a^3*b^3*c^2*d^4 - 85*a^4*b^2*c*d^5 + 15*a^5*b*d^6 + 640*(b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(27*b^6*c^2*d^4 + 106*a*b^5*c*d^5 + 27*a^2*b^4*d^6)*x^3 + 8*(b^6*c^3*d^3 + 159*a*b^5*c^2*d^4 + 159*a^2*b^4*c*d^5 + a^3*b^3*d^6)*x^2 - 2*(5*b^6*c^4*d^2 - 28*a*b^5*c^3*d^3 - 594*a^2*b^4*c^2*d^4 - 28*a^3*b^3*c*d^5 + 5*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4), 1/3072*(15*(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(256*b^6*d^6*x^5 + 15*b^6*c^5*d - 85*a*b^5*c^4*d^2 + 198*a^2*b^4*c^3*d^3 + 198*a^3*b^3*c^2*d^4 - 85*a^4*b^2*c*d^5 + 15*a^5*b*d^6 + 640*(b^6*c*d^5 + a*b^5*d^6)*x^4 + 16*(27*b^6*c^2*d^4 + 106*a*b^5*c*d^5 + 27*a^2*b^4*d^6)*x^3 + 8*(b^6*c^3*d^3 + 159*a*b^5*c^2*d^4 + 159*a^2*b^4*c*d^5 + a^3*b^3*d^6)*x^2 - 2*(5*b^6*c^4*d^2 - 28*a*b^5*c^3*d^3 - 594*a^2*b^4*c^2*d^4 - 28*a^3*b^3*c*d^5 + 5*a^4*b^2*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4)]","B",0
667,1,1801,0,140.550973," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{3840 \, \sqrt{a c} a^{2} b^{3} c^{2} d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 360 \, a b^{4} c^{3} d^{2} + 3754 \, a^{2} b^{3} c^{2} d^{3} + 360 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 1008 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 362 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 1289 \, a b^{4} c^{2} d^{3} + 1289 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{3} d^{3}}, \frac{1920 \, \sqrt{a c} a^{2} b^{3} c^{2} d^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 360 \, a b^{4} c^{3} d^{2} + 3754 \, a^{2} b^{3} c^{2} d^{3} + 360 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 1008 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 362 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 1289 \, a b^{4} c^{2} d^{3} + 1289 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{3} d^{3}}, \frac{7680 \, \sqrt{-a c} a^{2} b^{3} c^{2} d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 360 \, a b^{4} c^{3} d^{2} + 3754 \, a^{2} b^{3} c^{2} d^{3} + 360 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 1008 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 362 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 1289 \, a b^{4} c^{2} d^{3} + 1289 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{3} d^{3}}, \frac{3840 \, \sqrt{-a c} a^{2} b^{3} c^{2} d^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d + 360 \, a b^{4} c^{3} d^{2} + 3754 \, a^{2} b^{3} c^{2} d^{3} + 360 \, a^{3} b^{2} c d^{4} - 45 \, a^{4} b d^{5} + 1008 \, {\left(b^{5} c d^{4} + a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} + 362 \, a b^{4} c d^{4} + 93 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} + 1289 \, a b^{4} c^{2} d^{3} + 1289 \, a^{2} b^{3} c d^{4} + 15 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{3} d^{3}}\right]"," ",0,"[1/7680*(3840*sqrt(a*c)*a^2*b^3*c^2*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 360*a*b^4*c^3*d^2 + 3754*a^2*b^3*c^2*d^3 + 360*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 1008*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 362*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 1289*a*b^4*c^2*d^3 + 1289*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), 1/3840*(1920*sqrt(a*c)*a^2*b^3*c^2*d^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 360*a*b^4*c^3*d^2 + 3754*a^2*b^3*c^2*d^3 + 360*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 1008*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 362*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 1289*a*b^4*c^2*d^3 + 1289*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), 1/7680*(7680*sqrt(-a*c)*a^2*b^3*c^2*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 360*a*b^4*c^3*d^2 + 3754*a^2*b^3*c^2*d^3 + 360*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 1008*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 362*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 1289*a*b^4*c^2*d^3 + 1289*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), 1/3840*(3840*sqrt(-a*c)*a^2*b^3*c^2*d^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(384*b^5*d^5*x^4 - 45*b^5*c^4*d + 360*a*b^4*c^3*d^2 + 3754*a^2*b^3*c^2*d^3 + 360*a^3*b^2*c*d^4 - 45*a^4*b*d^5 + 1008*(b^5*c*d^4 + a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 + 362*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 + 1289*a*b^4*c^2*d^3 + 1289*a^2*b^3*c*d^4 + 15*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3)]","A",0
668,1,1613,0,39.503903," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 960 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{4} - 192 \, a^{2} b^{2} c^{2} d^{2} + 136 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(15 \, b^{4} c^{3} d + 601 \, a b^{3} c^{2} d^{2} + 601 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{2} x}, \frac{15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 480 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} \sqrt{a c} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{4} - 192 \, a^{2} b^{2} c^{2} d^{2} + 136 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(15 \, b^{4} c^{3} d + 601 \, a b^{3} c^{2} d^{2} + 601 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{2} x}, \frac{1920 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{b d} x \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{4} - 192 \, a^{2} b^{2} c^{2} d^{2} + 136 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(15 \, b^{4} c^{3} d + 601 \, a b^{3} c^{2} d^{2} + 601 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{2} x}, \frac{960 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} \sqrt{-a c} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-b d} x \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{4} - 192 \, a^{2} b^{2} c^{2} d^{2} + 136 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} + 59 \, a^{2} b^{2} d^{4}\right)} x^{2} + {\left(15 \, b^{4} c^{3} d + 601 \, a b^{3} c^{2} d^{2} + 601 \, a^{2} b^{2} c d^{3} + 15 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{2} x}\right]"," ",0,"[1/768*(15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 960*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*b^4*d^4*x^4 - 192*a^2*b^2*c^2*d^2 + 136*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 2*(59*b^4*c^2*d^2 + 226*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2 + (15*b^4*c^3*d + 601*a*b^3*c^2*d^2 + 601*a^2*b^2*c*d^3 + 15*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2*x), 1/384*(15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 480*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*sqrt(a*c)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 2*(48*b^4*d^4*x^4 - 192*a^2*b^2*c^2*d^2 + 136*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 2*(59*b^4*c^2*d^2 + 226*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2 + (15*b^4*c^3*d + 601*a*b^3*c^2*d^2 + 601*a^2*b^2*c*d^3 + 15*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2*x), 1/768*(1920*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(b*d)*x*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^4 - 192*a^2*b^2*c^2*d^2 + 136*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 2*(59*b^4*c^2*d^2 + 226*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2 + (15*b^4*c^3*d + 601*a*b^3*c^2*d^2 + 601*a^2*b^2*c*d^3 + 15*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2*x), 1/384*(960*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*sqrt(-a*c)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(-b*d)*x*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^4 - 192*a^2*b^2*c^2*d^2 + 136*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 2*(59*b^4*c^2*d^2 + 226*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x^2 + (15*b^4*c^3*d + 601*a*b^3*c^2*d^2 + 601*a^2*b^2*c*d^3 + 15*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^2*x)]","A",0
669,1,1469,0,23.191265," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 30 \, {\left(3 \, b^{3} c^{2} d + 10 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{4} - 12 \, a^{2} b c^{2} d + 26 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{3} + {\left(33 \, b^{3} c^{2} d + 122 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x^{2} - 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d x^{2}}, -\frac{15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 15 \, {\left(3 \, b^{3} c^{2} d + 10 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{4} - 12 \, a^{2} b c^{2} d + 26 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{3} + {\left(33 \, b^{3} c^{2} d + 122 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x^{2} - 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d x^{2}}, \frac{60 \, {\left(3 \, b^{3} c^{2} d + 10 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{b d} x^{2} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{4} - 12 \, a^{2} b c^{2} d + 26 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{3} + {\left(33 \, b^{3} c^{2} d + 122 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x^{2} - 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d x^{2}}, \frac{30 \, {\left(3 \, b^{3} c^{2} d + 10 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-b d} x^{2} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{4} - 12 \, a^{2} b c^{2} d + 26 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{3} + {\left(33 \, b^{3} c^{2} d + 122 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3}\right)} x^{2} - 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d x^{2}}\right]"," ",0,"[1/96*(15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 30*(3*b^3*c^2*d + 10*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*b^3*d^3*x^4 - 12*a^2*b*c^2*d + 26*(b^3*c*d^2 + a*b^2*d^3)*x^3 + (33*b^3*c^2*d + 122*a*b^2*c*d^2 + 33*a^2*b*d^3)*x^2 - 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x^2), -1/48*(15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 15*(3*b^3*c^2*d + 10*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 2*(8*b^3*d^3*x^4 - 12*a^2*b*c^2*d + 26*(b^3*c*d^2 + a*b^2*d^3)*x^3 + (33*b^3*c^2*d + 122*a*b^2*c*d^2 + 33*a^2*b*d^3)*x^2 - 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x^2), 1/96*(60*(3*b^3*c^2*d + 10*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(b*d)*x^2*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^4 - 12*a^2*b*c^2*d + 26*(b^3*c*d^2 + a*b^2*d^3)*x^3 + (33*b^3*c^2*d + 122*a*b^2*c*d^2 + 33*a^2*b*d^3)*x^2 - 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x^2), 1/48*(30*(3*b^3*c^2*d + 10*a*b^2*c*d^2 + 3*a^2*b*d^3)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(-b*d)*x^2*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^4 - 12*a^2*b*c^2*d + 26*(b^3*c*d^2 + a*b^2*d^3)*x^3 + (33*b^3*c^2*d + 122*a*b^2*c*d^2 + 33*a^2*b*d^3)*x^2 - 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d*x^2)]","A",0
670,1,1473,0,14.593387," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{30 \, {\left(3 \, a b^{2} c^{3} + 10 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(12 \, a b^{2} c d^{2} x^{4} - 8 \, a^{3} c^{3} + 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x^{3} - {\left(33 \, a b^{2} c^{3} + 122 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 26 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c x^{3}}, -\frac{60 \, {\left(3 \, a b^{2} c^{3} + 10 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(12 \, a b^{2} c d^{2} x^{4} - 8 \, a^{3} c^{3} + 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x^{3} - {\left(33 \, a b^{2} c^{3} + 122 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 26 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c x^{3}}, \frac{15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 15 \, {\left(3 \, a b^{2} c^{3} + 10 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{b d} x^{3} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 2 \, {\left(12 \, a b^{2} c d^{2} x^{4} - 8 \, a^{3} c^{3} + 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x^{3} - {\left(33 \, a b^{2} c^{3} + 122 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 26 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c x^{3}}, \frac{15 \, {\left(b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 30 \, {\left(3 \, a b^{2} c^{3} + 10 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} \sqrt{-b d} x^{3} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(12 \, a b^{2} c d^{2} x^{4} - 8 \, a^{3} c^{3} + 54 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x^{3} - {\left(33 \, a b^{2} c^{3} + 122 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 26 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c x^{3}}\right]"," ",0,"[1/96*(30*(3*a*b^2*c^3 + 10*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(12*a*b^2*c*d^2*x^4 - 8*a^3*c^3 + 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x^3 - (33*a*b^2*c^3 + 122*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 26*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^3), -1/96*(60*(3*a*b^2*c^3 + 10*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(12*a*b^2*c*d^2*x^4 - 8*a^3*c^3 + 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x^3 - (33*a*b^2*c^3 + 122*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 26*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^3), 1/48*(15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 15*(3*a*b^2*c^3 + 10*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(b*d)*x^3*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 2*(12*a*b^2*c*d^2*x^4 - 8*a^3*c^3 + 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x^3 - (33*a*b^2*c^3 + 122*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 26*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^3), 1/48*(15*(b^3*c^3 + 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 + a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 30*(3*a*b^2*c^3 + 10*a^2*b*c^2*d + 3*a^3*c*d^2)*sqrt(-b*d)*x^3*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(12*a*b^2*c*d^2*x^4 - 8*a^3*c^3 + 54*(a*b^2*c^2*d + a^2*b*c*d^2)*x^3 - (33*a*b^2*c^3 + 122*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 26*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c*x^3)]","A",0
671,1,1633,0,28.122196," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{960 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2}\right)} \sqrt{b d} x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(192 \, a^{2} b^{2} c^{2} d^{2} x^{4} - 48 \, a^{4} c^{4} - {\left(15 \, a b^{3} c^{4} + 601 \, a^{2} b^{2} c^{3} d + 601 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 226 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 136 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{2} x^{4}}, -\frac{1920 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2}\right)} \sqrt{-b d} x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(192 \, a^{2} b^{2} c^{2} d^{2} x^{4} - 48 \, a^{4} c^{4} - {\left(15 \, a b^{3} c^{4} + 601 \, a^{2} b^{2} c^{3} d + 601 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 226 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 136 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{2} x^{4}}, -\frac{15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 480 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2}\right)} \sqrt{b d} x^{4} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(192 \, a^{2} b^{2} c^{2} d^{2} x^{4} - 48 \, a^{4} c^{4} - {\left(15 \, a b^{3} c^{4} + 601 \, a^{2} b^{2} c^{3} d + 601 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 226 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 136 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{2} x^{4}}, -\frac{15 \, {\left(b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 90 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 960 \, {\left(a^{2} b^{2} c^{3} d + a^{3} b c^{2} d^{2}\right)} \sqrt{-b d} x^{4} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(192 \, a^{2} b^{2} c^{2} d^{2} x^{4} - 48 \, a^{4} c^{4} - {\left(15 \, a b^{3} c^{4} + 601 \, a^{2} b^{2} c^{3} d + 601 \, a^{3} b c^{2} d^{2} + 15 \, a^{4} c d^{3}\right)} x^{3} - 2 \, {\left(59 \, a^{2} b^{2} c^{4} + 226 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 136 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{2} x^{4}}\right]"," ",0,"[1/768*(960*(a^2*b^2*c^3*d + a^3*b*c^2*d^2)*sqrt(b*d)*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(192*a^2*b^2*c^2*d^2*x^4 - 48*a^4*c^4 - (15*a*b^3*c^4 + 601*a^2*b^2*c^3*d + 601*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(59*a^2*b^2*c^4 + 226*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 136*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^4), -1/768*(1920*(a^2*b^2*c^3*d + a^3*b*c^2*d^2)*sqrt(-b*d)*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(192*a^2*b^2*c^2*d^2*x^4 - 48*a^4*c^4 - (15*a*b^3*c^4 + 601*a^2*b^2*c^3*d + 601*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(59*a^2*b^2*c^4 + 226*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 136*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^4), -1/384*(15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 480*(a^2*b^2*c^3*d + a^3*b*c^2*d^2)*sqrt(b*d)*x^4*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(192*a^2*b^2*c^2*d^2*x^4 - 48*a^4*c^4 - (15*a*b^3*c^4 + 601*a^2*b^2*c^3*d + 601*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(59*a^2*b^2*c^4 + 226*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 136*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^4), -1/384*(15*(b^4*c^4 - 20*a*b^3*c^3*d - 90*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 960*(a^2*b^2*c^3*d + a^3*b*c^2*d^2)*sqrt(-b*d)*x^4*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(192*a^2*b^2*c^2*d^2*x^4 - 48*a^4*c^4 - (15*a*b^3*c^4 + 601*a^2*b^2*c^3*d + 601*a^3*b*c^2*d^2 + 15*a^4*c*d^3)*x^3 - 2*(59*a^2*b^2*c^4 + 226*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 136*(a^3*b*c^4 + a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^2*x^4)]","A",0
672,1,1849,0,60.262130," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{3840 \, \sqrt{b d} a^{3} b^{2} c^{3} d^{2} x^{5} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 360 \, a^{2} b^{3} c^{4} d - 3754 \, a^{3} b^{2} c^{3} d^{2} - 360 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 1289 \, a^{3} b^{2} c^{4} d + 1289 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 362 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 1008 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{3} c^{3} x^{5}}, -\frac{7680 \, \sqrt{-b d} a^{3} b^{2} c^{3} d^{2} x^{5} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 360 \, a^{2} b^{3} c^{4} d - 3754 \, a^{3} b^{2} c^{3} d^{2} - 360 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 1289 \, a^{3} b^{2} c^{4} d + 1289 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 362 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 1008 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{3} c^{3} x^{5}}, \frac{1920 \, \sqrt{b d} a^{3} b^{2} c^{3} d^{2} x^{5} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 360 \, a^{2} b^{3} c^{4} d - 3754 \, a^{3} b^{2} c^{3} d^{2} - 360 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 1289 \, a^{3} b^{2} c^{4} d + 1289 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 362 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 1008 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{3} c^{3} x^{5}}, -\frac{3840 \, \sqrt{-b d} a^{3} b^{2} c^{3} d^{2} x^{5} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 15 \, {\left(3 \, b^{5} c^{5} - 25 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} + 150 \, a^{3} b^{2} c^{2} d^{3} - 25 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5}\right)} \sqrt{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(384 \, a^{5} c^{5} - {\left(45 \, a b^{4} c^{5} - 360 \, a^{2} b^{3} c^{4} d - 3754 \, a^{3} b^{2} c^{3} d^{2} - 360 \, a^{4} b c^{2} d^{3} + 45 \, a^{5} c d^{4}\right)} x^{4} + 2 \, {\left(15 \, a^{2} b^{3} c^{5} + 1289 \, a^{3} b^{2} c^{4} d + 1289 \, a^{4} b c^{3} d^{2} + 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(93 \, a^{3} b^{2} c^{5} + 362 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} + 1008 \, {\left(a^{4} b c^{5} + a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{3} c^{3} x^{5}}\right]"," ",0,"[1/7680*(3840*sqrt(b*d)*a^3*b^2*c^3*d^2*x^5*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(384*a^5*c^5 - (45*a*b^4*c^5 - 360*a^2*b^3*c^4*d - 3754*a^3*b^2*c^3*d^2 - 360*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 1289*a^3*b^2*c^4*d + 1289*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 362*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 + 1008*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^5), -1/7680*(7680*sqrt(-b*d)*a^3*b^2*c^3*d^2*x^5*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(384*a^5*c^5 - (45*a*b^4*c^5 - 360*a^2*b^3*c^4*d - 3754*a^3*b^2*c^3*d^2 - 360*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 1289*a^3*b^2*c^4*d + 1289*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 362*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 + 1008*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^5), 1/3840*(1920*sqrt(b*d)*a^3*b^2*c^3*d^2*x^5*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(384*a^5*c^5 - (45*a*b^4*c^5 - 360*a^2*b^3*c^4*d - 3754*a^3*b^2*c^3*d^2 - 360*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 1289*a^3*b^2*c^4*d + 1289*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 362*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 + 1008*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^5), -1/3840*(3840*sqrt(-b*d)*a^3*b^2*c^3*d^2*x^5*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 15*(3*b^5*c^5 - 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 - 25*a^4*b*c*d^4 + 3*a^5*d^5)*sqrt(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(384*a^5*c^5 - (45*a*b^4*c^5 - 360*a^2*b^3*c^4*d - 3754*a^3*b^2*c^3*d^2 - 360*a^4*b*c^2*d^3 + 45*a^5*c*d^4)*x^4 + 2*(15*a^2*b^3*c^5 + 1289*a^3*b^2*c^4*d + 1289*a^4*b*c^3*d^2 + 15*a^5*c^2*d^3)*x^3 + 8*(93*a^3*b^2*c^5 + 362*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 + 1008*(a^4*b*c^5 + a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^5)]","A",0
673,1,908,0,39.620906," ","integrate((b*x+a)^(5/2)*(d*x+c)^(5/2)/x^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{a c} x^{6} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(256 \, a^{6} c^{6} + {\left(15 \, a b^{5} c^{6} - 85 \, a^{2} b^{4} c^{5} d + 198 \, a^{3} b^{3} c^{4} d^{2} + 198 \, a^{4} b^{2} c^{3} d^{3} - 85 \, a^{5} b c^{2} d^{4} + 15 \, a^{6} c d^{5}\right)} x^{5} - 2 \, {\left(5 \, a^{2} b^{4} c^{6} - 28 \, a^{3} b^{3} c^{5} d - 594 \, a^{4} b^{2} c^{4} d^{2} - 28 \, a^{5} b c^{3} d^{3} + 5 \, a^{6} c^{2} d^{4}\right)} x^{4} + 8 \, {\left(a^{3} b^{3} c^{6} + 159 \, a^{4} b^{2} c^{5} d + 159 \, a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{3} + 16 \, {\left(27 \, a^{4} b^{2} c^{6} + 106 \, a^{5} b c^{5} d + 27 \, a^{6} c^{4} d^{2}\right)} x^{2} + 640 \, {\left(a^{5} b c^{6} + a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6144 \, a^{4} c^{4} x^{6}}, -\frac{15 \, {\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} \sqrt{-a c} x^{6} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(256 \, a^{6} c^{6} + {\left(15 \, a b^{5} c^{6} - 85 \, a^{2} b^{4} c^{5} d + 198 \, a^{3} b^{3} c^{4} d^{2} + 198 \, a^{4} b^{2} c^{3} d^{3} - 85 \, a^{5} b c^{2} d^{4} + 15 \, a^{6} c d^{5}\right)} x^{5} - 2 \, {\left(5 \, a^{2} b^{4} c^{6} - 28 \, a^{3} b^{3} c^{5} d - 594 \, a^{4} b^{2} c^{4} d^{2} - 28 \, a^{5} b c^{3} d^{3} + 5 \, a^{6} c^{2} d^{4}\right)} x^{4} + 8 \, {\left(a^{3} b^{3} c^{6} + 159 \, a^{4} b^{2} c^{5} d + 159 \, a^{5} b c^{4} d^{2} + a^{6} c^{3} d^{3}\right)} x^{3} + 16 \, {\left(27 \, a^{4} b^{2} c^{6} + 106 \, a^{5} b c^{5} d + 27 \, a^{6} c^{4} d^{2}\right)} x^{2} + 640 \, {\left(a^{5} b c^{6} + a^{6} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3072 \, a^{4} c^{4} x^{6}}\right]"," ",0,"[1/6144*(15*(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(a*c)*x^6*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(256*a^6*c^6 + (15*a*b^5*c^6 - 85*a^2*b^4*c^5*d + 198*a^3*b^3*c^4*d^2 + 198*a^4*b^2*c^3*d^3 - 85*a^5*b*c^2*d^4 + 15*a^6*c*d^5)*x^5 - 2*(5*a^2*b^4*c^6 - 28*a^3*b^3*c^5*d - 594*a^4*b^2*c^4*d^2 - 28*a^5*b*c^3*d^3 + 5*a^6*c^2*d^4)*x^4 + 8*(a^3*b^3*c^6 + 159*a^4*b^2*c^5*d + 159*a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^3 + 16*(27*a^4*b^2*c^6 + 106*a^5*b*c^5*d + 27*a^6*c^4*d^2)*x^2 + 640*(a^5*b*c^6 + a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^6), -1/3072*(15*(b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*sqrt(-a*c)*x^6*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(256*a^6*c^6 + (15*a*b^5*c^6 - 85*a^2*b^4*c^5*d + 198*a^3*b^3*c^4*d^2 + 198*a^4*b^2*c^3*d^3 - 85*a^5*b*c^2*d^4 + 15*a^6*c*d^5)*x^5 - 2*(5*a^2*b^4*c^6 - 28*a^3*b^3*c^5*d - 594*a^4*b^2*c^4*d^2 - 28*a^5*b*c^3*d^3 + 5*a^6*c^2*d^4)*x^4 + 8*(a^3*b^3*c^6 + 159*a^4*b^2*c^5*d + 159*a^5*b*c^4*d^2 + a^6*c^3*d^3)*x^3 + 16*(27*a^4*b^2*c^6 + 106*a^5*b*c^5*d + 27*a^6*c^4*d^2)*x^2 + 640*(a^5*b*c^6 + a^6*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^6)]","A",0
674,1,706,0,1.506369," ","integrate(x^2*(b*x+a)^(5/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{4} + 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} + 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} - 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{3} d^{6}}, \frac{15 \, {\left(63 \, b^{5} c^{5} - 175 \, a b^{4} c^{4} d + 150 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} - 5 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(384 \, b^{5} d^{5} x^{4} + 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} + 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} - 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{3} d^{6}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(384*b^5*d^5*x^4 + 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 + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 - 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^6), 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*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(384*b^5*d^5*x^4 + 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 + 8*(63*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 93*a^2*b^3*d^5)*x^2 - 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)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^6)]","A",0
675,1,546,0,1.622897," ","integrate(x*(b*x+a)^(5/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 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} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{2} d^{5}}, -\frac{15 \, {\left(7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 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} + 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{2} d^{5}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^4*x^3 - 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 + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^5), -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*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^4*x^3 - 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 + 2*(35*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 59*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^5)]","A",0
676,1,412,0,1.388686," ","integrate((b*x+a)^(5/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 15 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b d^{4}}, \frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 15 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 33 \, a^{2} b d^{3} - 2 \, {\left(5 \, b^{3} c d^{2} - 13 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b d^{4}}\right]"," ",0,"[-1/96*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 + 15*b^3*c^2*d - 40*a*b^2*c*d^2 + 33*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^4), 1/48*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 15*b^3*c^2*d - 40*a*b^2*c*d^2 + 33*a^2*b*d^3 - 2*(5*b^3*c*d^2 - 13*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^4)]","A",0
677,1,987,0,8.730652," ","integrate((b*x+a)^(5/2)/x/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} d^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d x - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, d^{2}}, \frac{4 \, a^{2} d^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d x - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, d^{2}}, \frac{16 \, a^{2} d^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d x - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, d^{2}}, \frac{8 \, a^{2} d^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d x - 3 \, b^{2} c + 9 \, a b d\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, d^{2}}\right]"," ",0,"[1/16*(8*a^2*d^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d*x - 3*b^2*c + 9*a*b*d)*sqrt(b*x + a)*sqrt(d*x + c))/d^2, 1/8*(4*a^2*d^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(2*b^2*d*x - 3*b^2*c + 9*a*b*d)*sqrt(b*x + a)*sqrt(d*x + c))/d^2, 1/16*(16*a^2*d^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d*x - 3*b^2*c + 9*a*b*d)*sqrt(b*x + a)*sqrt(d*x + c))/d^2, 1/8*(8*a^2*d^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(2*b^2*d*x - 3*b^2*c + 9*a*b*d)*sqrt(b*x + a)*sqrt(d*x + c))/d^2]","A",0
678,1,993,0,6.635226," ","integrate((b*x+a)^(5/2)/x^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(b^{2} c x - a^{2} d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, c d x}, \frac{2 \, {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(b^{2} c x - a^{2} d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, c d x}, \frac{2 \, {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(b^{2} c x - a^{2} d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, c d x}, \frac{{\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(b^{2} c x - a^{2} d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, c d x}\right]"," ",0,"[-1/4*((b^2*c^2 - 5*a*b*c*d)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (5*a*b*c*d - a^2*d^2)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(b^2*c*x - a^2*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x), 1/4*(2*(b^2*c^2 - 5*a*b*c*d)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (5*a*b*c*d - a^2*d^2)*x*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(b^2*c*x - a^2*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x), 1/4*(2*(5*a*b*c*d - a^2*d^2)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (b^2*c^2 - 5*a*b*c*d)*x*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(b^2*c*x - a^2*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x), 1/2*((5*a*b*c*d - a^2*d^2)*x*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b^2*c^2 - 5*a*b*c*d)*x*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(b^2*c*x - a^2*d)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d*x)]","A",0
679,1,1035,0,6.138186," ","integrate((b*x+a)^(5/2)/x^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, b^{2} c^{2} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, c^{2} x^{2}}, -\frac{16 \, b^{2} c^{2} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, c^{2} x^{2}}, \frac{4 \, b^{2} c^{2} x^{2} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, c^{2} x^{2}}, -\frac{8 \, b^{2} c^{2} x^{2} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} c + 3 \, {\left(3 \, a b c - a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, c^{2} x^{2}}\right]"," ",0,"[1/16*(8*b^2*c^2*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*x^2), -1/16*(16*b^2*c^2*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^2*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*x^2), 1/8*(4*b^2*c^2*x^2*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*x^2), -1/8*(8*b^2*c^2*x^2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*x^2*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 2*(2*a^2*c + 3*(3*a*b*c - a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*x^2)]","A",0
680,1,438,0,3.030194," ","integrate((b*x+a)^(5/2)/x^4/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} - 40 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a c^{4} x^{3}}, \frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{3} + {\left(33 \, a b^{2} c^{3} - 40 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{3} - 5 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a c^{4} x^{3}}\right]"," ",0,"[-1/96*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (33*a*b^2*c^3 - 40*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^4*x^3), 1/48*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^3 + (33*a*b^2*c^3 - 40*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 + 2*(13*a^2*b*c^3 - 5*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^4*x^3)]","A",0
681,1,570,0,10.443402," ","integrate((b*x+a)^(5/2)/x^5/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \sqrt{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 191 \, a^{2} b^{2} c^{3} d + 265 \, a^{3} b c^{2} d^{2} - 105 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} - 86 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{2} c^{5} x^{4}}, -\frac{15 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \sqrt{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{4} + {\left(15 \, a b^{3} c^{4} - 191 \, a^{2} b^{2} c^{3} d + 265 \, a^{3} b c^{2} d^{2} - 105 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{4} - 86 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{4} - 7 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{2} c^{5} x^{4}}\right]"," ",0,"[-1/768*(15*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*sqrt(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 + (15*a*b^3*c^4 - 191*a^2*b^2*c^3*d + 265*a^3*b*c^2*d^2 - 105*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 - 86*a^3*b*c^3*d + 35*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^5*x^4), -1/384*(15*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*sqrt(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^4 + (15*a*b^3*c^4 - 191*a^2*b^2*c^3*d + 265*a^3*b*c^2*d^2 - 105*a^4*c*d^3)*x^3 + 2*(59*a^2*b^2*c^4 - 86*a^3*b*c^3*d + 35*a^4*c^2*d^2)*x^2 + 8*(17*a^3*b*c^4 - 7*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^5*x^4)]","A",0
682,1,796,0,2.514368," ","integrate(x^2*(b*x+a)^(5/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(63 \, b^{4} c^{5} - 140 \, a b^{3} c^{4} d + 90 \, a^{2} b^{2} c^{3} d^{2} - 12 \, a^{3} b c^{2} d^{3} - a^{4} c d^{4} + {\left(63 \, b^{4} c^{4} d - 140 \, a b^{3} c^{3} d^{2} + 90 \, a^{2} b^{2} c^{2} d^{3} - 12 \, a^{3} b c d^{4} - a^{4} d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{5} x^{4} - 945 \, b^{4} c^{4} d + 1785 \, a b^{3} c^{3} d^{2} - 839 \, a^{2} b^{2} c^{2} d^{3} + 15 \, a^{3} b c d^{4} - 8 \, {\left(9 \, b^{4} c d^{4} - 17 \, a b^{3} d^{5}\right)} x^{3} + 2 \, {\left(63 \, b^{4} c^{2} d^{3} - 122 \, a b^{3} c d^{4} + 59 \, a^{2} b^{2} d^{5}\right)} x^{2} - {\left(315 \, b^{4} c^{3} d^{2} - 637 \, a b^{3} c^{2} d^{3} + 337 \, a^{2} b^{2} c d^{4} - 15 \, a^{3} b d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(b^{2} d^{7} x + b^{2} c d^{6}\right)}}, -\frac{15 \, {\left(63 \, b^{4} c^{5} - 140 \, a b^{3} c^{4} d + 90 \, a^{2} b^{2} c^{3} d^{2} - 12 \, a^{3} b c^{2} d^{3} - a^{4} c d^{4} + {\left(63 \, b^{4} c^{4} d - 140 \, a b^{3} c^{3} d^{2} + 90 \, a^{2} b^{2} c^{2} d^{3} - 12 \, a^{3} b c d^{4} - a^{4} d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{5} x^{4} - 945 \, b^{4} c^{4} d + 1785 \, a b^{3} c^{3} d^{2} - 839 \, a^{2} b^{2} c^{2} d^{3} + 15 \, a^{3} b c d^{4} - 8 \, {\left(9 \, b^{4} c d^{4} - 17 \, a b^{3} d^{5}\right)} x^{3} + 2 \, {\left(63 \, b^{4} c^{2} d^{3} - 122 \, a b^{3} c d^{4} + 59 \, a^{2} b^{2} d^{5}\right)} x^{2} - {\left(315 \, b^{4} c^{3} d^{2} - 637 \, a b^{3} c^{2} d^{3} + 337 \, a^{2} b^{2} c d^{4} - 15 \, a^{3} b d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(b^{2} d^{7} x + b^{2} c d^{6}\right)}}\right]"," ",0,"[-1/768*(15*(63*b^4*c^5 - 140*a*b^3*c^4*d + 90*a^2*b^2*c^3*d^2 - 12*a^3*b*c^2*d^3 - a^4*c*d^4 + (63*b^4*c^4*d - 140*a*b^3*c^3*d^2 + 90*a^2*b^2*c^2*d^3 - 12*a^3*b*c*d^4 - a^4*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^5*x^4 - 945*b^4*c^4*d + 1785*a*b^3*c^3*d^2 - 839*a^2*b^2*c^2*d^3 + 15*a^3*b*c*d^4 - 8*(9*b^4*c*d^4 - 17*a*b^3*d^5)*x^3 + 2*(63*b^4*c^2*d^3 - 122*a*b^3*c*d^4 + 59*a^2*b^2*d^5)*x^2 - (315*b^4*c^3*d^2 - 637*a*b^3*c^2*d^3 + 337*a^2*b^2*c*d^4 - 15*a^3*b*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^7*x + b^2*c*d^6), -1/384*(15*(63*b^4*c^5 - 140*a*b^3*c^4*d + 90*a^2*b^2*c^3*d^2 - 12*a^3*b*c^2*d^3 - a^4*c*d^4 + (63*b^4*c^4*d - 140*a*b^3*c^3*d^2 + 90*a^2*b^2*c^2*d^3 - 12*a^3*b*c*d^4 - a^4*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^5*x^4 - 945*b^4*c^4*d + 1785*a*b^3*c^3*d^2 - 839*a^2*b^2*c^2*d^3 + 15*a^3*b*c*d^4 - 8*(9*b^4*c*d^4 - 17*a*b^3*d^5)*x^3 + 2*(63*b^4*c^2*d^3 - 122*a*b^3*c*d^4 + 59*a^2*b^2*d^5)*x^2 - (315*b^4*c^3*d^2 - 637*a*b^3*c^2*d^3 + 337*a^2*b^2*c*d^4 - 15*a^3*b*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^7*x + b^2*c*d^6)]","A",0
683,1,598,0,1.843154," ","integrate(x*(b*x+a)^(5/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, b^{3} c^{4} - 15 \, a b^{2} c^{3} d + 9 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3} + {\left(7 \, b^{3} c^{3} d - 15 \, a b^{2} c^{2} d^{2} + 9 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{4} x^{3} + 105 \, b^{3} c^{3} d - 190 \, a b^{2} c^{2} d^{2} + 81 \, a^{2} b c d^{3} - 2 \, {\left(7 \, b^{3} c d^{3} - 13 \, a b^{2} d^{4}\right)} x^{2} + {\left(35 \, b^{3} c^{2} d^{2} - 68 \, a b^{2} c d^{3} + 33 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b d^{6} x + b c d^{5}\right)}}, \frac{15 \, {\left(7 \, b^{3} c^{4} - 15 \, a b^{2} c^{3} d + 9 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3} + {\left(7 \, b^{3} c^{3} d - 15 \, a b^{2} c^{2} d^{2} + 9 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{4} x^{3} + 105 \, b^{3} c^{3} d - 190 \, a b^{2} c^{2} d^{2} + 81 \, a^{2} b c d^{3} - 2 \, {\left(7 \, b^{3} c d^{3} - 13 \, a b^{2} d^{4}\right)} x^{2} + {\left(35 \, b^{3} c^{2} d^{2} - 68 \, a b^{2} c d^{3} + 33 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b d^{6} x + b c d^{5}\right)}}\right]"," ",0,"[-1/96*(15*(7*b^3*c^4 - 15*a*b^2*c^3*d + 9*a^2*b*c^2*d^2 - a^3*c*d^3 + (7*b^3*c^3*d - 15*a*b^2*c^2*d^2 + 9*a^2*b*c*d^3 - a^3*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^4*x^3 + 105*b^3*c^3*d - 190*a*b^2*c^2*d^2 + 81*a^2*b*c*d^3 - 2*(7*b^3*c*d^3 - 13*a*b^2*d^4)*x^2 + (35*b^3*c^2*d^2 - 68*a*b^2*c*d^3 + 33*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^6*x + b*c*d^5), 1/48*(15*(7*b^3*c^4 - 15*a*b^2*c^3*d + 9*a^2*b*c^2*d^2 - a^3*c*d^3 + (7*b^3*c^3*d - 15*a*b^2*c^2*d^2 + 9*a^2*b*c*d^3 - a^3*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^4*x^3 + 105*b^3*c^3*d - 190*a*b^2*c^2*d^2 + 81*a^2*b*c*d^3 - 2*(7*b^3*c*d^3 - 13*a*b^2*d^4)*x^2 + (35*b^3*c^2*d^2 - 68*a*b^2*c*d^3 + 33*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^6*x + b*c*d^5)]","A",0
684,1,441,0,1.353551," ","integrate((b*x+a)^(5/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 15 \, b^{2} c^{2} + 25 \, a b c d - 8 \, a^{2} d^{2} - {\left(5 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(d^{4} x + c d^{3}\right)}}, -\frac{15 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 15 \, b^{2} c^{2} + 25 \, a b c d - 8 \, a^{2} d^{2} - {\left(5 \, b^{2} c d - 9 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(d^{4} x + c d^{3}\right)}}\right]"," ",0,"[1/16*(15*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x^2 - 15*b^2*c^2 + 25*a*b*c*d - 8*a^2*d^2 - (5*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^4*x + c*d^3), -1/8*(15*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 2*(2*b^2*d^2*x^2 - 15*b^2*c^2 + 25*a*b*c*d - 8*a^2*d^2 - (5*b^2*c*d - 9*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^4*x + c*d^3)]","A",0
685,1,1181,0,5.108507," ","integrate((b*x+a)^(5/2)/x/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(b^{2} c d x + 3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(c d^{3} x + c^{2} d^{2}\right)}}, \frac{{\left(3 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 2 \, {\left(b^{2} c d x + 3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d^{3} x + c^{2} d^{2}\right)}}, \frac{4 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(b^{2} c d x + 3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(c d^{3} x + c^{2} d^{2}\right)}}, \frac{2 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(3 \, b^{2} c^{3} - 5 \, a b c^{2} d + {\left(3 \, b^{2} c^{2} d - 5 \, a b c d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(b^{2} c d x + 3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c d^{3} x + c^{2} d^{2}\right)}}\right]"," ",0,"[-1/4*((3*b^2*c^3 - 5*a*b*c^2*d + (3*b^2*c^2*d - 5*a*b*c*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(a^2*d^3*x + a^2*c*d^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(b^2*c*d*x + 3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^3*x + c^2*d^2), 1/2*((3*b^2*c^3 - 5*a*b*c^2*d + (3*b^2*c^2*d - 5*a*b*c*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + (a^2*d^3*x + a^2*c*d^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 2*(b^2*c*d*x + 3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^3*x + c^2*d^2), 1/4*(4*(a^2*d^3*x + a^2*c*d^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - (3*b^2*c^3 - 5*a*b*c^2*d + (3*b^2*c^2*d - 5*a*b*c*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(b^2*c*d*x + 3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^3*x + c^2*d^2), 1/2*(2*(a^2*d^3*x + a^2*c*d^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (3*b^2*c^3 - 5*a*b*c^2*d + (3*b^2*c^2*d - 5*a*b*c*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(b^2*c*d*x + 3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(c*d^3*x + c^2*d^2)]","B",0
686,1,1233,0,5.650340," ","integrate((b*x+a)^(5/2)/x^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{2} d x^{2} + b^{2} c^{3} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a^{2} c d + {\left(2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(c^{2} d^{2} x^{2} + c^{3} d x\right)}}, -\frac{4 \, {\left(b^{2} c^{2} d x^{2} + b^{2} c^{3} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + {\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(a^{2} c d + {\left(2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(c^{2} d^{2} x^{2} + c^{3} d x\right)}}, \frac{{\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + {\left(b^{2} c^{2} d x^{2} + b^{2} c^{3} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(a^{2} c d + {\left(2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c^{2} d^{2} x^{2} + c^{3} d x\right)}}, \frac{{\left({\left(5 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(5 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(b^{2} c^{2} d x^{2} + b^{2} c^{3} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 2 \, {\left(a^{2} c d + {\left(2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(c^{2} d^{2} x^{2} + c^{3} d x\right)}}\right]"," ",0,"[1/4*(2*(b^2*c^2*d*x^2 + b^2*c^3*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - ((5*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a^2*c*d + (2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + c^3*d*x), -1/4*(4*(b^2*c^2*d*x^2 + b^2*c^3*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + ((5*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(a^2*c*d + (2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + c^3*d*x), 1/2*(((5*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + (b^2*c^2*d*x^2 + b^2*c^3*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(a^2*c*d + (2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + c^3*d*x), 1/2*(((5*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (5*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(b^2*c^2*d*x^2 + b^2*c^3*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 2*(a^2*c*d + (2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^2*x^2 + c^3*d*x)]","B",0
687,1,479,0,3.075614," ","integrate((b*x+a)^(5/2)/x^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} - {\left(8 \, b^{2} c^{2} - 25 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} + {\left(9 \, a b c^{2} - 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(c^{3} d x^{3} + c^{4} x^{2}\right)}}, \frac{15 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x^{3} + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(8 \, b^{2} c^{2} - 25 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} + {\left(9 \, a b c^{2} - 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(c^{3} d x^{3} + c^{4} x^{2}\right)}}\right]"," ",0,"[1/16*(15*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^3 + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 - (8*b^2*c^2 - 25*a*b*c*d + 15*a^2*d^2)*x^2 + (9*a*b*c^2 - 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d*x^3 + c^4*x^2), 1/8*(15*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x^3 + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*x^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(2*a^2*c^2 - (8*b^2*c^2 - 25*a*b*c*d + 15*a^2*d^2)*x^2 + (9*a*b*c^2 - 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d*x^3 + c^4*x^2)]","A",0
688,1,632,0,9.119046," ","integrate((b*x+a)^(5/2)/x^4/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{3} c^{3} d - 9 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} - 7 \, a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} - 9 \, a b^{2} c^{3} d + 15 \, a^{2} b c^{2} d^{2} - 7 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{4} + {\left(81 \, a b^{2} c^{3} d - 190 \, a^{2} b c^{2} d^{2} + 105 \, a^{3} c d^{3}\right)} x^{3} + {\left(33 \, a b^{2} c^{4} - 68 \, a^{2} b c^{3} d + 35 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{4} - 7 \, a^{3} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a c^{5} d x^{4} + a c^{6} x^{3}\right)}}, \frac{15 \, {\left({\left(b^{3} c^{3} d - 9 \, a b^{2} c^{2} d^{2} + 15 \, a^{2} b c d^{3} - 7 \, a^{3} d^{4}\right)} x^{4} + {\left(b^{3} c^{4} - 9 \, a b^{2} c^{3} d + 15 \, a^{2} b c^{2} d^{2} - 7 \, a^{3} c d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{4} + {\left(81 \, a b^{2} c^{3} d - 190 \, a^{2} b c^{2} d^{2} + 105 \, a^{3} c d^{3}\right)} x^{3} + {\left(33 \, a b^{2} c^{4} - 68 \, a^{2} b c^{3} d + 35 \, a^{3} c^{2} d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{4} - 7 \, a^{3} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a c^{5} d x^{4} + a c^{6} x^{3}\right)}}\right]"," ",0,"[-1/96*(15*((b^3*c^3*d - 9*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 - 7*a^3*d^4)*x^4 + (b^3*c^4 - 9*a*b^2*c^3*d + 15*a^2*b*c^2*d^2 - 7*a^3*c*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^4 + (81*a*b^2*c^3*d - 190*a^2*b*c^2*d^2 + 105*a^3*c*d^3)*x^3 + (33*a*b^2*c^4 - 68*a^2*b*c^3*d + 35*a^3*c^2*d^2)*x^2 + 2*(13*a^2*b*c^4 - 7*a^3*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^5*d*x^4 + a*c^6*x^3), 1/48*(15*((b^3*c^3*d - 9*a*b^2*c^2*d^2 + 15*a^2*b*c*d^3 - 7*a^3*d^4)*x^4 + (b^3*c^4 - 9*a*b^2*c^3*d + 15*a^2*b*c^2*d^2 - 7*a^3*c*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^4 + (81*a*b^2*c^3*d - 190*a^2*b*c^2*d^2 + 105*a^3*c*d^3)*x^3 + (33*a*b^2*c^4 - 68*a^2*b*c^3*d + 35*a^3*c^2*d^2)*x^2 + 2*(13*a^2*b*c^4 - 7*a^3*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^5*d*x^4 + a*c^6*x^3)]","A",0
689,1,828,0,19.868774," ","integrate((b*x+a)^(5/2)/x^5/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{4} c^{4} d + 12 \, a b^{3} c^{3} d^{2} - 90 \, a^{2} b^{2} c^{2} d^{3} + 140 \, a^{3} b c d^{4} - 63 \, a^{4} d^{5}\right)} x^{5} + {\left(b^{4} c^{5} + 12 \, a b^{3} c^{4} d - 90 \, a^{2} b^{2} c^{3} d^{2} + 140 \, a^{3} b c^{2} d^{3} - 63 \, a^{4} c d^{4}\right)} x^{4}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{5} + {\left(15 \, a b^{3} c^{4} d - 839 \, a^{2} b^{2} c^{3} d^{2} + 1785 \, a^{3} b c^{2} d^{3} - 945 \, a^{4} c d^{4}\right)} x^{4} + {\left(15 \, a b^{3} c^{5} - 337 \, a^{2} b^{2} c^{4} d + 637 \, a^{3} b c^{3} d^{2} - 315 \, a^{4} c^{2} d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{5} - 122 \, a^{3} b c^{4} d + 63 \, a^{4} c^{3} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{5} - 9 \, a^{4} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(a^{2} c^{6} d x^{5} + a^{2} c^{7} x^{4}\right)}}, -\frac{15 \, {\left({\left(b^{4} c^{4} d + 12 \, a b^{3} c^{3} d^{2} - 90 \, a^{2} b^{2} c^{2} d^{3} + 140 \, a^{3} b c d^{4} - 63 \, a^{4} d^{5}\right)} x^{5} + {\left(b^{4} c^{5} + 12 \, a b^{3} c^{4} d - 90 \, a^{2} b^{2} c^{3} d^{2} + 140 \, a^{3} b c^{2} d^{3} - 63 \, a^{4} c d^{4}\right)} x^{4}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{5} + {\left(15 \, a b^{3} c^{4} d - 839 \, a^{2} b^{2} c^{3} d^{2} + 1785 \, a^{3} b c^{2} d^{3} - 945 \, a^{4} c d^{4}\right)} x^{4} + {\left(15 \, a b^{3} c^{5} - 337 \, a^{2} b^{2} c^{4} d + 637 \, a^{3} b c^{3} d^{2} - 315 \, a^{4} c^{2} d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{5} - 122 \, a^{3} b c^{4} d + 63 \, a^{4} c^{3} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{5} - 9 \, a^{4} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(a^{2} c^{6} d x^{5} + a^{2} c^{7} x^{4}\right)}}\right]"," ",0,"[-1/768*(15*((b^4*c^4*d + 12*a*b^3*c^3*d^2 - 90*a^2*b^2*c^2*d^3 + 140*a^3*b*c*d^4 - 63*a^4*d^5)*x^5 + (b^4*c^5 + 12*a*b^3*c^4*d - 90*a^2*b^2*c^3*d^2 + 140*a^3*b*c^2*d^3 - 63*a^4*c*d^4)*x^4)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^5 + (15*a*b^3*c^4*d - 839*a^2*b^2*c^3*d^2 + 1785*a^3*b*c^2*d^3 - 945*a^4*c*d^4)*x^4 + (15*a*b^3*c^5 - 337*a^2*b^2*c^4*d + 637*a^3*b*c^3*d^2 - 315*a^4*c^2*d^3)*x^3 + 2*(59*a^2*b^2*c^5 - 122*a^3*b*c^4*d + 63*a^4*c^3*d^2)*x^2 + 8*(17*a^3*b*c^5 - 9*a^4*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^6*d*x^5 + a^2*c^7*x^4), -1/384*(15*((b^4*c^4*d + 12*a*b^3*c^3*d^2 - 90*a^2*b^2*c^2*d^3 + 140*a^3*b*c*d^4 - 63*a^4*d^5)*x^5 + (b^4*c^5 + 12*a*b^3*c^4*d - 90*a^2*b^2*c^3*d^2 + 140*a^3*b*c^2*d^3 - 63*a^4*c*d^4)*x^4)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^5 + (15*a*b^3*c^4*d - 839*a^2*b^2*c^3*d^2 + 1785*a^3*b*c^2*d^3 - 945*a^4*c*d^4)*x^4 + (15*a*b^3*c^5 - 337*a^2*b^2*c^4*d + 637*a^3*b*c^3*d^2 - 315*a^4*c^2*d^3)*x^3 + 2*(59*a^2*b^2*c^5 - 122*a^3*b*c^4*d + 63*a^4*c^3*d^2)*x^2 + 8*(17*a^3*b*c^5 - 9*a^4*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^6*d*x^5 + a^2*c^7*x^4)]","A",0
690,1,1066,0,4.888782," ","integrate(x^3*(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(231 \, b^{4} c^{6} - 420 \, a b^{3} c^{5} d + 210 \, a^{2} b^{2} c^{4} d^{2} - 20 \, a^{3} b c^{3} d^{3} - a^{4} c^{2} d^{4} + {\left(231 \, b^{4} c^{4} d^{2} - 420 \, a b^{3} c^{3} d^{3} + 210 \, a^{2} b^{2} c^{2} d^{4} - 20 \, a^{3} b c d^{5} - a^{4} d^{6}\right)} x^{2} + 2 \, {\left(231 \, b^{4} c^{5} d - 420 \, a b^{3} c^{4} d^{2} + 210 \, a^{2} b^{2} c^{3} d^{3} - 20 \, a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{6} x^{5} - 3465 \, b^{4} c^{5} d + 5145 \, a b^{3} c^{4} d^{2} - 1743 \, a^{2} b^{2} c^{3} d^{3} + 15 \, a^{3} b c^{2} d^{4} - 8 \, {\left(11 \, b^{4} c d^{5} - 17 \, a b^{3} d^{6}\right)} x^{4} + 2 \, {\left(99 \, b^{4} c^{2} d^{4} - 158 \, a b^{3} c d^{5} + 59 \, a^{2} b^{2} d^{6}\right)} x^{3} - 3 \, {\left(231 \, b^{4} c^{3} d^{3} - 387 \, a b^{3} c^{2} d^{4} + 161 \, a^{2} b^{2} c d^{5} - 5 \, a^{3} b d^{6}\right)} x^{2} - 6 \, {\left(770 \, b^{4} c^{4} d^{2} - 1169 \, a b^{3} c^{3} d^{3} + 412 \, a^{2} b^{2} c^{2} d^{4} - 5 \, a^{3} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(b^{2} d^{9} x^{2} + 2 \, b^{2} c d^{8} x + b^{2} c^{2} d^{7}\right)}}, -\frac{15 \, {\left(231 \, b^{4} c^{6} - 420 \, a b^{3} c^{5} d + 210 \, a^{2} b^{2} c^{4} d^{2} - 20 \, a^{3} b c^{3} d^{3} - a^{4} c^{2} d^{4} + {\left(231 \, b^{4} c^{4} d^{2} - 420 \, a b^{3} c^{3} d^{3} + 210 \, a^{2} b^{2} c^{2} d^{4} - 20 \, a^{3} b c d^{5} - a^{4} d^{6}\right)} x^{2} + 2 \, {\left(231 \, b^{4} c^{5} d - 420 \, a b^{3} c^{4} d^{2} + 210 \, a^{2} b^{2} c^{3} d^{3} - 20 \, a^{3} b c^{2} d^{4} - a^{4} c d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{6} x^{5} - 3465 \, b^{4} c^{5} d + 5145 \, a b^{3} c^{4} d^{2} - 1743 \, a^{2} b^{2} c^{3} d^{3} + 15 \, a^{3} b c^{2} d^{4} - 8 \, {\left(11 \, b^{4} c d^{5} - 17 \, a b^{3} d^{6}\right)} x^{4} + 2 \, {\left(99 \, b^{4} c^{2} d^{4} - 158 \, a b^{3} c d^{5} + 59 \, a^{2} b^{2} d^{6}\right)} x^{3} - 3 \, {\left(231 \, b^{4} c^{3} d^{3} - 387 \, a b^{3} c^{2} d^{4} + 161 \, a^{2} b^{2} c d^{5} - 5 \, a^{3} b d^{6}\right)} x^{2} - 6 \, {\left(770 \, b^{4} c^{4} d^{2} - 1169 \, a b^{3} c^{3} d^{3} + 412 \, a^{2} b^{2} c^{2} d^{4} - 5 \, a^{3} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(b^{2} d^{9} x^{2} + 2 \, b^{2} c d^{8} x + b^{2} c^{2} d^{7}\right)}}\right]"," ",0,"[-1/768*(15*(231*b^4*c^6 - 420*a*b^3*c^5*d + 210*a^2*b^2*c^4*d^2 - 20*a^3*b*c^3*d^3 - a^4*c^2*d^4 + (231*b^4*c^4*d^2 - 420*a*b^3*c^3*d^3 + 210*a^2*b^2*c^2*d^4 - 20*a^3*b*c*d^5 - a^4*d^6)*x^2 + 2*(231*b^4*c^5*d - 420*a*b^3*c^4*d^2 + 210*a^2*b^2*c^3*d^3 - 20*a^3*b*c^2*d^4 - a^4*c*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^6*x^5 - 3465*b^4*c^5*d + 5145*a*b^3*c^4*d^2 - 1743*a^2*b^2*c^3*d^3 + 15*a^3*b*c^2*d^4 - 8*(11*b^4*c*d^5 - 17*a*b^3*d^6)*x^4 + 2*(99*b^4*c^2*d^4 - 158*a*b^3*c*d^5 + 59*a^2*b^2*d^6)*x^3 - 3*(231*b^4*c^3*d^3 - 387*a*b^3*c^2*d^4 + 161*a^2*b^2*c*d^5 - 5*a^3*b*d^6)*x^2 - 6*(770*b^4*c^4*d^2 - 1169*a*b^3*c^3*d^3 + 412*a^2*b^2*c^2*d^4 - 5*a^3*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^9*x^2 + 2*b^2*c*d^8*x + b^2*c^2*d^7), -1/384*(15*(231*b^4*c^6 - 420*a*b^3*c^5*d + 210*a^2*b^2*c^4*d^2 - 20*a^3*b*c^3*d^3 - a^4*c^2*d^4 + (231*b^4*c^4*d^2 - 420*a*b^3*c^3*d^3 + 210*a^2*b^2*c^2*d^4 - 20*a^3*b*c*d^5 - a^4*d^6)*x^2 + 2*(231*b^4*c^5*d - 420*a*b^3*c^4*d^2 + 210*a^2*b^2*c^3*d^3 - 20*a^3*b*c^2*d^4 - a^4*c*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^6*x^5 - 3465*b^4*c^5*d + 5145*a*b^3*c^4*d^2 - 1743*a^2*b^2*c^3*d^3 + 15*a^3*b*c^2*d^4 - 8*(11*b^4*c*d^5 - 17*a*b^3*d^6)*x^4 + 2*(99*b^4*c^2*d^4 - 158*a*b^3*c*d^5 + 59*a^2*b^2*d^6)*x^3 - 3*(231*b^4*c^3*d^3 - 387*a*b^3*c^2*d^4 + 161*a^2*b^2*c*d^5 - 5*a^3*b*d^6)*x^2 - 6*(770*b^4*c^4*d^2 - 1169*a*b^3*c^3*d^3 + 412*a^2*b^2*c^2*d^4 - 5*a^3*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^2*d^9*x^2 + 2*b^2*c*d^8*x + b^2*c^2*d^7)]","A",0
691,1,810,0,3.324090," ","integrate(x^2*(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(21 \, b^{3} c^{5} - 35 \, a b^{2} c^{4} d + 15 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(21 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 15 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{2} + 2 \, {\left(21 \, b^{3} c^{4} d - 35 \, a b^{2} c^{3} d^{2} + 15 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{5} x^{4} + 315 \, b^{3} c^{4} d - 420 \, a b^{2} c^{3} d^{2} + 113 \, a^{2} b c^{2} d^{3} - 2 \, {\left(9 \, b^{3} c d^{4} - 13 \, a b^{2} d^{5}\right)} x^{3} + 3 \, {\left(21 \, b^{3} c^{2} d^{3} - 32 \, a b^{2} c d^{4} + 11 \, a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(210 \, b^{3} c^{3} d^{2} - 287 \, a b^{2} c^{2} d^{3} + 81 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b d^{8} x^{2} + 2 \, b c d^{7} x + b c^{2} d^{6}\right)}}, \frac{15 \, {\left(21 \, b^{3} c^{5} - 35 \, a b^{2} c^{4} d + 15 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(21 \, b^{3} c^{3} d^{2} - 35 \, a b^{2} c^{2} d^{3} + 15 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{2} + 2 \, {\left(21 \, b^{3} c^{4} d - 35 \, a b^{2} c^{3} d^{2} + 15 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{5} x^{4} + 315 \, b^{3} c^{4} d - 420 \, a b^{2} c^{3} d^{2} + 113 \, a^{2} b c^{2} d^{3} - 2 \, {\left(9 \, b^{3} c d^{4} - 13 \, a b^{2} d^{5}\right)} x^{3} + 3 \, {\left(21 \, b^{3} c^{2} d^{3} - 32 \, a b^{2} c d^{4} + 11 \, a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(210 \, b^{3} c^{3} d^{2} - 287 \, a b^{2} c^{2} d^{3} + 81 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b d^{8} x^{2} + 2 \, b c d^{7} x + b c^{2} d^{6}\right)}}\right]"," ",0,"[-1/96*(15*(21*b^3*c^5 - 35*a*b^2*c^4*d + 15*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (21*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 15*a^2*b*c*d^4 - a^3*d^5)*x^2 + 2*(21*b^3*c^4*d - 35*a*b^2*c^3*d^2 + 15*a^2*b*c^2*d^3 - a^3*c*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^5*x^4 + 315*b^3*c^4*d - 420*a*b^2*c^3*d^2 + 113*a^2*b*c^2*d^3 - 2*(9*b^3*c*d^4 - 13*a*b^2*d^5)*x^3 + 3*(21*b^3*c^2*d^3 - 32*a*b^2*c*d^4 + 11*a^2*b*d^5)*x^2 + 2*(210*b^3*c^3*d^2 - 287*a*b^2*c^2*d^3 + 81*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^8*x^2 + 2*b*c*d^7*x + b*c^2*d^6), 1/48*(15*(21*b^3*c^5 - 35*a*b^2*c^4*d + 15*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (21*b^3*c^3*d^2 - 35*a*b^2*c^2*d^3 + 15*a^2*b*c*d^4 - a^3*d^5)*x^2 + 2*(21*b^3*c^4*d - 35*a*b^2*c^3*d^2 + 15*a^2*b*c^2*d^3 - a^3*c*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^5*x^4 + 315*b^3*c^4*d - 420*a*b^2*c^3*d^2 + 113*a^2*b*c^2*d^3 - 2*(9*b^3*c*d^4 - 13*a*b^2*d^5)*x^3 + 3*(21*b^3*c^2*d^3 - 32*a*b^2*c*d^4 + 11*a^2*b*d^5)*x^2 + 2*(210*b^3*c^3*d^2 - 287*a*b^2*c^2*d^3 + 81*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b*d^8*x^2 + 2*b*c*d^7*x + b*c^2*d^6)]","A",0
692,1,619,0,2.194032," ","integrate(x*(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{2} + 2 \, {\left(7 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(6 \, b^{2} d^{3} x^{3} - 105 \, b^{2} c^{3} + 115 \, a b c^{2} d - 16 \, a^{2} c d^{2} - 3 \, {\left(7 \, b^{2} c d^{2} - 9 \, a b d^{3}\right)} x^{2} - 2 \, {\left(70 \, b^{2} c^{2} d - 79 \, a b c d^{2} + 12 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(d^{6} x^{2} + 2 \, c d^{5} x + c^{2} d^{4}\right)}}, -\frac{15 \, {\left(7 \, b^{2} c^{4} - 10 \, a b c^{3} d + 3 \, a^{2} c^{2} d^{2} + {\left(7 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} x^{2} + 2 \, {\left(7 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 2 \, {\left(6 \, b^{2} d^{3} x^{3} - 105 \, b^{2} c^{3} + 115 \, a b c^{2} d - 16 \, a^{2} c d^{2} - 3 \, {\left(7 \, b^{2} c d^{2} - 9 \, a b d^{3}\right)} x^{2} - 2 \, {\left(70 \, b^{2} c^{2} d - 79 \, a b c d^{2} + 12 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(d^{6} x^{2} + 2 \, c d^{5} x + c^{2} d^{4}\right)}}\right]"," ",0,"[1/48*(15*(7*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^2 + 2*(7*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(6*b^2*d^3*x^3 - 105*b^2*c^3 + 115*a*b*c^2*d - 16*a^2*c*d^2 - 3*(7*b^2*c*d^2 - 9*a*b*d^3)*x^2 - 2*(70*b^2*c^2*d - 79*a*b*c*d^2 + 12*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^6*x^2 + 2*c*d^5*x + c^2*d^4), -1/24*(15*(7*b^2*c^4 - 10*a*b*c^3*d + 3*a^2*c^2*d^2 + (7*b^2*c^2*d^2 - 10*a*b*c*d^3 + 3*a^2*d^4)*x^2 + 2*(7*b^2*c^3*d - 10*a*b*c^2*d^2 + 3*a^2*c*d^3)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 2*(6*b^2*d^3*x^3 - 105*b^2*c^3 + 115*a*b*c^2*d - 16*a^2*c*d^2 - 3*(7*b^2*c*d^2 - 9*a*b*d^3)*x^2 - 2*(70*b^2*c^2*d - 79*a*b*c*d^2 + 12*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^6*x^2 + 2*c*d^5*x + c^2*d^4)]","A",0
693,1,475,0,1.897524," ","integrate((b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} c^{3} - a b c^{2} d + {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} x\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b^{2} d^{2} x^{2} + 15 \, b^{2} c^{2} - 10 \, a b c d - 2 \, a^{2} d^{2} + 2 \, {\left(10 \, b^{2} c d - 7 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}, \frac{15 \, {\left(b^{2} c^{3} - a b c^{2} d + {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} x\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 15 \, b^{2} c^{2} - 10 \, a b c d - 2 \, a^{2} d^{2} + 2 \, {\left(10 \, b^{2} c d - 7 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}\right]"," ",0,"[-1/12*(15*(b^2*c^3 - a*b*c^2*d + (b^2*c*d^2 - a*b*d^3)*x^2 + 2*(b^2*c^2*d - a*b*c*d^2)*x)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b^2*d^2*x^2 + 15*b^2*c^2 - 10*a*b*c*d - 2*a^2*d^2 + 2*(10*b^2*c*d - 7*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3), 1/6*(15*(b^2*c^3 - a*b*c^2*d + (b^2*c*d^2 - a*b*d^3)*x^2 + 2*(b^2*c^2*d - a*b*c*d^2)*x)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) + 2*(3*b^2*d^2*x^2 + 15*b^2*c^2 - 10*a*b*c*d - 2*a^2*d^2 + 2*(10*b^2*c*d - 7*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)]","B",0
694,1,1361,0,5.169717," ","integrate((b*x+a)^(5/2)/x/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(3 \, b^{2} c^{3} + a b c^{2} d - 4 \, a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - a b c d^{2} - 3 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{2} d^{4} x^{2} + 2 \, c^{3} d^{3} x + c^{4} d^{2}\right)}}, -\frac{6 \, {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 3 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, b^{2} c^{3} + a b c^{2} d - 4 \, a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - a b c d^{2} - 3 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{2} d^{4} x^{2} + 2 \, c^{3} d^{3} x + c^{4} d^{2}\right)}}, \frac{6 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) + 3 \, {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b^{2} c^{3} + a b c^{2} d - 4 \, a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - a b c d^{2} - 3 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{2} d^{4} x^{2} + 2 \, c^{3} d^{3} x + c^{4} d^{2}\right)}}, \frac{3 \, {\left(a^{2} d^{4} x^{2} + 2 \, a^{2} c d^{3} x + a^{2} c^{2} d^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 3 \, {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - 2 \, {\left(3 \, b^{2} c^{3} + a b c^{2} d - 4 \, a^{2} c d^{2} + {\left(4 \, b^{2} c^{2} d - a b c d^{2} - 3 \, a^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(c^{2} d^{4} x^{2} + 2 \, c^{3} d^{3} x + c^{4} d^{2}\right)}}\right]"," ",0,"[1/6*(3*(b^2*c^2*d^2*x^2 + 2*b^2*c^3*d*x + b^2*c^4)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(3*b^2*c^3 + a*b*c^2*d - 4*a^2*c*d^2 + (4*b^2*c^2*d - a*b*c*d^2 - 3*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^4*x^2 + 2*c^3*d^3*x + c^4*d^2), -1/6*(6*(b^2*c^2*d^2*x^2 + 2*b^2*c^3*d*x + b^2*c^4)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 3*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*b^2*c^3 + a*b*c^2*d - 4*a^2*c*d^2 + (4*b^2*c^2*d - a*b*c*d^2 - 3*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^4*x^2 + 2*c^3*d^3*x + c^4*d^2), 1/6*(6*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) + 3*(b^2*c^2*d^2*x^2 + 2*b^2*c^3*d*x + b^2*c^4)*sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b^2*c^3 + a*b*c^2*d - 4*a^2*c*d^2 + (4*b^2*c^2*d - a*b*c*d^2 - 3*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^4*x^2 + 2*c^3*d^3*x + c^4*d^2), 1/3*(3*(a^2*d^4*x^2 + 2*a^2*c*d^3*x + a^2*c^2*d^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 3*(b^2*c^2*d^2*x^2 + 2*b^2*c^3*d*x + b^2*c^4)*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - 2*(3*b^2*c^3 + a*b*c^2*d - 4*a^2*c*d^2 + (4*b^2*c^2*d - a*b*c*d^2 - 3*a^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^2*d^4*x^2 + 2*c^3*d^3*x + c^4*d^2)]","B",0
695,1,507,0,2.756583," ","integrate((b*x+a)^(5/2)/x^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(a b c d^{2} - a^{2} d^{3}\right)} x^{3} + 2 \, {\left(a b c^{2} d - a^{2} c d^{2}\right)} x^{2} + {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a^{2} c^{2} - {\left(2 \, b^{2} c^{2} + 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} - 2 \, {\left(7 \, a b c^{2} - 10 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(c^{3} d^{2} x^{3} + 2 \, c^{4} d x^{2} + c^{5} x\right)}}, \frac{15 \, {\left({\left(a b c d^{2} - a^{2} d^{3}\right)} x^{3} + 2 \, {\left(a b c^{2} d - a^{2} c d^{2}\right)} x^{2} + {\left(a b c^{3} - a^{2} c^{2} d\right)} x\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(3 \, a^{2} c^{2} - {\left(2 \, b^{2} c^{2} + 10 \, a b c d - 15 \, a^{2} d^{2}\right)} x^{2} - 2 \, {\left(7 \, a b c^{2} - 10 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(c^{3} d^{2} x^{3} + 2 \, c^{4} d x^{2} + c^{5} x\right)}}\right]"," ",0,"[-1/12*(15*((a*b*c*d^2 - a^2*d^3)*x^3 + 2*(a*b*c^2*d - a^2*c*d^2)*x^2 + (a*b*c^3 - a^2*c^2*d)*x)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a^2*c^2 - (2*b^2*c^2 + 10*a*b*c*d - 15*a^2*d^2)*x^2 - 2*(7*a*b*c^2 - 10*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d^2*x^3 + 2*c^4*d*x^2 + c^5*x), 1/6*(15*((a*b*c*d^2 - a^2*d^3)*x^3 + 2*(a*b*c^2*d - a^2*c*d^2)*x^2 + (a*b*c^3 - a^2*c^2*d)*x)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(3*a^2*c^2 - (2*b^2*c^2 + 10*a*b*c*d - 15*a^2*d^2)*x^2 - 2*(7*a*b*c^2 - 10*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^3*d^2*x^3 + 2*c^4*d*x^2 + c^5*x)]","B",0
696,1,659,0,8.566191," ","integrate((b*x+a)^(5/2)/x^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 7 \, a^{2} c d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{4} - 10 \, a b c^{3} d + 7 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{\frac{a}{c}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} + {\left(b c^{2} + a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a}{c}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{2} c^{3} - {\left(16 \, b^{2} c^{2} d - 115 \, a b c d^{2} + 105 \, a^{2} d^{3}\right)} x^{3} - 2 \, {\left(12 \, b^{2} c^{3} - 79 \, a b c^{2} d + 70 \, a^{2} c d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b c^{3} - 7 \, a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(c^{4} d^{2} x^{4} + 2 \, c^{5} d x^{3} + c^{6} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, b^{2} c^{2} d^{2} - 10 \, a b c d^{3} + 7 \, a^{2} d^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{2} c^{3} d - 10 \, a b c^{2} d^{2} + 7 \, a^{2} c d^{3}\right)} x^{3} + {\left(3 \, b^{2} c^{4} - 10 \, a b c^{3} d + 7 \, a^{2} c^{2} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{a}{c}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{a}{c}}}{2 \, {\left(a b d x^{2} + a^{2} c + {\left(a b c + a^{2} d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{2} c^{3} - {\left(16 \, b^{2} c^{2} d - 115 \, a b c d^{2} + 105 \, a^{2} d^{3}\right)} x^{3} - 2 \, {\left(12 \, b^{2} c^{3} - 79 \, a b c^{2} d + 70 \, a^{2} c d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b c^{3} - 7 \, a^{2} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(c^{4} d^{2} x^{4} + 2 \, c^{5} d x^{3} + c^{6} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((3*b^2*c^2*d^2 - 10*a*b*c*d^3 + 7*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d - 10*a*b*c^2*d^2 + 7*a^2*c*d^3)*x^3 + (3*b^2*c^4 - 10*a*b*c^3*d + 7*a^2*c^2*d^2)*x^2)*sqrt(a/c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c^2 + (b*c^2 + a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(a/c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^2*c^3 - (16*b^2*c^2*d - 115*a*b*c*d^2 + 105*a^2*d^3)*x^3 - 2*(12*b^2*c^3 - 79*a*b*c^2*d + 70*a^2*c*d^2)*x^2 + 3*(9*a*b*c^3 - 7*a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^4*d^2*x^4 + 2*c^5*d*x^3 + c^6*x^2), 1/24*(15*((3*b^2*c^2*d^2 - 10*a*b*c*d^3 + 7*a^2*d^4)*x^4 + 2*(3*b^2*c^3*d - 10*a*b*c^2*d^2 + 7*a^2*c*d^3)*x^3 + (3*b^2*c^4 - 10*a*b*c^3*d + 7*a^2*c^2*d^2)*x^2)*sqrt(-a/c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-a/c)/(a*b*d*x^2 + a^2*c + (a*b*c + a^2*d)*x)) - 2*(6*a^2*c^3 - (16*b^2*c^2*d - 115*a*b*c*d^2 + 105*a^2*d^3)*x^3 - 2*(12*b^2*c^3 - 79*a*b*c^2*d + 70*a^2*c*d^2)*x^2 + 3*(9*a*b*c^3 - 7*a^2*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(c^4*d^2*x^4 + 2*c^5*d*x^3 + c^6*x^2)]","A",0
697,1,842,0,19.030474," ","integrate((b*x+a)^(5/2)/x^4/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} + 35 \, a^{2} b c d^{4} - 21 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(b^{3} c^{4} d - 15 \, a b^{2} c^{3} d^{2} + 35 \, a^{2} b c^{2} d^{3} - 21 \, a^{3} c d^{4}\right)} x^{4} + {\left(b^{3} c^{5} - 15 \, a b^{2} c^{4} d + 35 \, a^{2} b c^{3} d^{2} - 21 \, a^{3} c^{2} d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{5} + {\left(113 \, a b^{2} c^{3} d^{2} - 420 \, a^{2} b c^{2} d^{3} + 315 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(81 \, a b^{2} c^{4} d - 287 \, a^{2} b c^{3} d^{2} + 210 \, a^{3} c^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, a b^{2} c^{5} - 32 \, a^{2} b c^{4} d + 21 \, a^{3} c^{3} d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{5} - 9 \, a^{3} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a c^{6} d^{2} x^{5} + 2 \, a c^{7} d x^{4} + a c^{8} x^{3}\right)}}, \frac{15 \, {\left({\left(b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} + 35 \, a^{2} b c d^{4} - 21 \, a^{3} d^{5}\right)} x^{5} + 2 \, {\left(b^{3} c^{4} d - 15 \, a b^{2} c^{3} d^{2} + 35 \, a^{2} b c^{2} d^{3} - 21 \, a^{3} c d^{4}\right)} x^{4} + {\left(b^{3} c^{5} - 15 \, a b^{2} c^{4} d + 35 \, a^{2} b c^{3} d^{2} - 21 \, a^{3} c^{2} d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(8 \, a^{3} c^{5} + {\left(113 \, a b^{2} c^{3} d^{2} - 420 \, a^{2} b c^{2} d^{3} + 315 \, a^{3} c d^{4}\right)} x^{4} + 2 \, {\left(81 \, a b^{2} c^{4} d - 287 \, a^{2} b c^{3} d^{2} + 210 \, a^{3} c^{2} d^{3}\right)} x^{3} + 3 \, {\left(11 \, a b^{2} c^{5} - 32 \, a^{2} b c^{4} d + 21 \, a^{3} c^{3} d^{2}\right)} x^{2} + 2 \, {\left(13 \, a^{2} b c^{5} - 9 \, a^{3} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a c^{6} d^{2} x^{5} + 2 \, a c^{7} d x^{4} + a c^{8} x^{3}\right)}}\right]"," ",0,"[-1/96*(15*((b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 + 35*a^2*b*c*d^4 - 21*a^3*d^5)*x^5 + 2*(b^3*c^4*d - 15*a*b^2*c^3*d^2 + 35*a^2*b*c^2*d^3 - 21*a^3*c*d^4)*x^4 + (b^3*c^5 - 15*a*b^2*c^4*d + 35*a^2*b*c^3*d^2 - 21*a^3*c^2*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^5 + (113*a*b^2*c^3*d^2 - 420*a^2*b*c^2*d^3 + 315*a^3*c*d^4)*x^4 + 2*(81*a*b^2*c^4*d - 287*a^2*b*c^3*d^2 + 210*a^3*c^2*d^3)*x^3 + 3*(11*a*b^2*c^5 - 32*a^2*b*c^4*d + 21*a^3*c^3*d^2)*x^2 + 2*(13*a^2*b*c^5 - 9*a^3*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^6*d^2*x^5 + 2*a*c^7*d*x^4 + a*c^8*x^3), 1/48*(15*((b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 + 35*a^2*b*c*d^4 - 21*a^3*d^5)*x^5 + 2*(b^3*c^4*d - 15*a*b^2*c^3*d^2 + 35*a^2*b*c^2*d^3 - 21*a^3*c*d^4)*x^4 + (b^3*c^5 - 15*a*b^2*c^4*d + 35*a^2*b*c^3*d^2 - 21*a^3*c^2*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(8*a^3*c^5 + (113*a*b^2*c^3*d^2 - 420*a^2*b*c^2*d^3 + 315*a^3*c*d^4)*x^4 + 2*(81*a*b^2*c^4*d - 287*a^2*b*c^3*d^2 + 210*a^3*c^2*d^3)*x^3 + 3*(11*a*b^2*c^5 - 32*a^2*b*c^4*d + 21*a^3*c^3*d^2)*x^2 + 2*(13*a^2*b*c^5 - 9*a^3*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*c^6*d^2*x^5 + 2*a*c^7*d*x^4 + a*c^8*x^3)]","A",0
698,1,1100,0,50.435734," ","integrate((b*x+a)^(5/2)/x^5/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{4} c^{4} d^{2} + 20 \, a b^{3} c^{3} d^{3} - 210 \, a^{2} b^{2} c^{2} d^{4} + 420 \, a^{3} b c d^{5} - 231 \, a^{4} d^{6}\right)} x^{6} + 2 \, {\left(b^{4} c^{5} d + 20 \, a b^{3} c^{4} d^{2} - 210 \, a^{2} b^{2} c^{3} d^{3} + 420 \, a^{3} b c^{2} d^{4} - 231 \, a^{4} c d^{5}\right)} x^{5} + {\left(b^{4} c^{6} + 20 \, a b^{3} c^{5} d - 210 \, a^{2} b^{2} c^{4} d^{2} + 420 \, a^{3} b c^{3} d^{3} - 231 \, a^{4} c^{2} d^{4}\right)} x^{4}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{6} + 3 \, {\left(5 \, a b^{3} c^{4} d^{2} - 581 \, a^{2} b^{2} c^{3} d^{3} + 1715 \, a^{3} b c^{2} d^{4} - 1155 \, a^{4} c d^{5}\right)} x^{5} + 6 \, {\left(5 \, a b^{3} c^{5} d - 412 \, a^{2} b^{2} c^{4} d^{2} + 1169 \, a^{3} b c^{3} d^{3} - 770 \, a^{4} c^{2} d^{4}\right)} x^{4} + 3 \, {\left(5 \, a b^{3} c^{6} - 161 \, a^{2} b^{2} c^{5} d + 387 \, a^{3} b c^{4} d^{2} - 231 \, a^{4} c^{3} d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{6} - 158 \, a^{3} b c^{5} d + 99 \, a^{4} c^{4} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{6} - 11 \, a^{4} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(a^{2} c^{7} d^{2} x^{6} + 2 \, a^{2} c^{8} d x^{5} + a^{2} c^{9} x^{4}\right)}}, -\frac{15 \, {\left({\left(b^{4} c^{4} d^{2} + 20 \, a b^{3} c^{3} d^{3} - 210 \, a^{2} b^{2} c^{2} d^{4} + 420 \, a^{3} b c d^{5} - 231 \, a^{4} d^{6}\right)} x^{6} + 2 \, {\left(b^{4} c^{5} d + 20 \, a b^{3} c^{4} d^{2} - 210 \, a^{2} b^{2} c^{3} d^{3} + 420 \, a^{3} b c^{2} d^{4} - 231 \, a^{4} c d^{5}\right)} x^{5} + {\left(b^{4} c^{6} + 20 \, a b^{3} c^{5} d - 210 \, a^{2} b^{2} c^{4} d^{2} + 420 \, a^{3} b c^{3} d^{3} - 231 \, a^{4} c^{2} d^{4}\right)} x^{4}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(48 \, a^{4} c^{6} + 3 \, {\left(5 \, a b^{3} c^{4} d^{2} - 581 \, a^{2} b^{2} c^{3} d^{3} + 1715 \, a^{3} b c^{2} d^{4} - 1155 \, a^{4} c d^{5}\right)} x^{5} + 6 \, {\left(5 \, a b^{3} c^{5} d - 412 \, a^{2} b^{2} c^{4} d^{2} + 1169 \, a^{3} b c^{3} d^{3} - 770 \, a^{4} c^{2} d^{4}\right)} x^{4} + 3 \, {\left(5 \, a b^{3} c^{6} - 161 \, a^{2} b^{2} c^{5} d + 387 \, a^{3} b c^{4} d^{2} - 231 \, a^{4} c^{3} d^{3}\right)} x^{3} + 2 \, {\left(59 \, a^{2} b^{2} c^{6} - 158 \, a^{3} b c^{5} d + 99 \, a^{4} c^{4} d^{2}\right)} x^{2} + 8 \, {\left(17 \, a^{3} b c^{6} - 11 \, a^{4} c^{5} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(a^{2} c^{7} d^{2} x^{6} + 2 \, a^{2} c^{8} d x^{5} + a^{2} c^{9} x^{4}\right)}}\right]"," ",0,"[-1/768*(15*((b^4*c^4*d^2 + 20*a*b^3*c^3*d^3 - 210*a^2*b^2*c^2*d^4 + 420*a^3*b*c*d^5 - 231*a^4*d^6)*x^6 + 2*(b^4*c^5*d + 20*a*b^3*c^4*d^2 - 210*a^2*b^2*c^3*d^3 + 420*a^3*b*c^2*d^4 - 231*a^4*c*d^5)*x^5 + (b^4*c^6 + 20*a*b^3*c^5*d - 210*a^2*b^2*c^4*d^2 + 420*a^3*b*c^3*d^3 - 231*a^4*c^2*d^4)*x^4)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^6 + 3*(5*a*b^3*c^4*d^2 - 581*a^2*b^2*c^3*d^3 + 1715*a^3*b*c^2*d^4 - 1155*a^4*c*d^5)*x^5 + 6*(5*a*b^3*c^5*d - 412*a^2*b^2*c^4*d^2 + 1169*a^3*b*c^3*d^3 - 770*a^4*c^2*d^4)*x^4 + 3*(5*a*b^3*c^6 - 161*a^2*b^2*c^5*d + 387*a^3*b*c^4*d^2 - 231*a^4*c^3*d^3)*x^3 + 2*(59*a^2*b^2*c^6 - 158*a^3*b*c^5*d + 99*a^4*c^4*d^2)*x^2 + 8*(17*a^3*b*c^6 - 11*a^4*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^7*d^2*x^6 + 2*a^2*c^8*d*x^5 + a^2*c^9*x^4), -1/384*(15*((b^4*c^4*d^2 + 20*a*b^3*c^3*d^3 - 210*a^2*b^2*c^2*d^4 + 420*a^3*b*c*d^5 - 231*a^4*d^6)*x^6 + 2*(b^4*c^5*d + 20*a*b^3*c^4*d^2 - 210*a^2*b^2*c^3*d^3 + 420*a^3*b*c^2*d^4 - 231*a^4*c*d^5)*x^5 + (b^4*c^6 + 20*a*b^3*c^5*d - 210*a^2*b^2*c^4*d^2 + 420*a^3*b*c^3*d^3 - 231*a^4*c^2*d^4)*x^4)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(48*a^4*c^6 + 3*(5*a*b^3*c^4*d^2 - 581*a^2*b^2*c^3*d^3 + 1715*a^3*b*c^2*d^4 - 1155*a^4*c*d^5)*x^5 + 6*(5*a*b^3*c^5*d - 412*a^2*b^2*c^4*d^2 + 1169*a^3*b*c^3*d^3 - 770*a^4*c^2*d^4)*x^4 + 3*(5*a*b^3*c^6 - 161*a^2*b^2*c^5*d + 387*a^3*b*c^4*d^2 - 231*a^4*c^3*d^3)*x^3 + 2*(59*a^2*b^2*c^6 - 158*a^3*b*c^5*d + 99*a^4*c^4*d^2)*x^2 + 8*(17*a^3*b*c^6 - 11*a^4*c^5*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*c^7*d^2*x^6 + 2*a^2*c^8*d*x^5 + a^2*c^9*x^4)]","A",0
699,1,408,0,1.357703," ","integrate(x^2*(d*x+c)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{4} d^{3}}, -\frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{2} - 3 \, b^{3} c^{2} d - 4 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{4} d^{3}}\right]"," ",0,"[-1/96*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 - 3*b^3*c^2*d - 4*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3), -1/48*(3*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^3*d^3*x^2 - 3*b^3*c^2*d - 4*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^3)]","A",0
700,1,304,0,1.287914," ","integrate(x*(d*x+c)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(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} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{3} d^{2}}, \frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b^{2} d^{2} x + b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{3} d^{2}}\right]"," ",0,"[-1/16*((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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(2*b^2*d^2*x + b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2), 1/8*((b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(2*b^2*d^2*x + b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^2)]","A",0
701,1,236,0,1.351811," ","integrate((d*x+c)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x + a} \sqrt{d x + c} b d - {\left(b c - a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{4 \, b^{2} d}, \frac{2 \, \sqrt{b x + a} \sqrt{d x + c} b d - {\left(b c - a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{2 \, b^{2} d}\right]"," ",0,"[1/4*(4*sqrt(b*x + a)*sqrt(d*x + c)*b*d - (b*c - a*d)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b^2*d), 1/2*(2*sqrt(b*x + a)*sqrt(d*x + c)*b*d - (b*c - a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b^2*d)]","A",0
702,1,711,0,1.535470," ","integrate((d*x+c)^(1/2)/x/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \frac{1}{2} \, \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right), -\sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right), \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + \frac{1}{2} \, \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right), \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right)\right]"," ",0,"[1/2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 1/2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2), -sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 1/2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2), sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 1/2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x), sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x))]","B",0
703,1,252,0,1.324130," ","integrate((d*x+c)^(1/2)/x^2/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{a c} {\left(b c - a d\right)} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} a c}{4 \, a^{2} c x}, -\frac{\sqrt{-a c} {\left(b c - a d\right)} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} a c}{2 \, a^{2} c x}\right]"," ",0,"[-1/4*(sqrt(a*c)*(b*c - a*d)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a^2*c*x), -1/2*(sqrt(-a*c)*(b*c - a*d)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a^2*c*x)]","A",0
704,1,336,0,1.635716," ","integrate((d*x+c)^(1/2)/x^3/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a^{2} c^{2} - {\left(3 \, a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{3} c^{2} x^{2}}, \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(3 \, a b c^{2} - a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{3} c^{2} x^{2}}\right]"," ",0,"[-1/16*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a^2*c^2 - (3*a*b*c^2 - a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^2), 1/8*((3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 - (3*a*b*c^2 - a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^2*x^2)]","A",0
705,1,440,0,2.320184," ","integrate((d*x+c)^(1/2)/x^4/(b*x+a)^(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{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{4} c^{3} x^{3}}, -\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{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 4 \, a^{2} b c^{2} d - 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{4} c^{3} x^{3}}\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(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (15*a*b^2*c^3 - 4*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^3), -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(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (15*a*b^2*c^3 - 4*a^2*b*c^2*d - 3*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^3*x^3)]","A",0
706,1,546,0,1.418705," ","integrate(x^2*(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} + 145 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{5} d^{3}}, -\frac{3 \, {\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b^{4} d^{4} x^{3} - 9 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} + 145 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4} + 8 \, {\left(9 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} - 46 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{5} d^{3}}\right]"," ",0,"[1/768*(3*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(48*b^4*d^4*x^3 - 9*b^4*c^3*d - 15*a*b^3*c^2*d^2 + 145*a^2*b^2*c*d^3 - 105*a^3*b*d^4 + 8*(9*b^4*c*d^3 - 7*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^3), -1/384*(3*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(48*b^4*d^4*x^3 - 9*b^4*c^3*d - 15*a*b^3*c^2*d^2 + 145*a^2*b^2*c*d^3 - 105*a^3*b*d^4 + 8*(9*b^4*c*d^3 - 7*a*b^3*d^4)*x^2 + 2*(3*b^4*c^2*d^2 - 46*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^3)]","A",0
707,1,412,0,1.384895," ","integrate(x*(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(7 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{4} d^{2}}, \frac{3 \, {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 3 \, b^{3} c^{2} d - 22 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(7 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{4} d^{2}}\right]"," ",0,"[1/96*(3*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 3*b^3*c^2*d - 22*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(7*b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^2), 1/48*(3*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 3*b^3*c^2*d - 22*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(7*b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^2)]","A",0
708,1,306,0,1.451876," ","integrate((d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{3} d}, -\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x + 5 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{3} d}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x + 5*b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d), -1/8*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^2*x + 5*b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d)]","A",0
709,1,844,0,3.050245," ","integrate((d*x+c)^(3/2)/x/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(3 \, b c - a d\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} d}{4 \, b}, \frac{b c \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(3 \, b c - a d\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} d}{2 \, b}, \frac{4 \, b c \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(3 \, b c - a d\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} d}{4 \, b}, \frac{2 \, b c \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(3 \, b c - a d\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} d}{2 \, b}\right]"," ",0,"[1/4*(2*b*c*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (3*b*c - a*d)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*sqrt(d*x + c)*d)/b, 1/2*(b*c*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (3*b*c - a*d)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*d)/b, 1/4*(4*b*c*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (3*b*c - a*d)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*sqrt(b*x + a)*sqrt(d*x + c)*d)/b, 1/2*(2*b*c*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (3*b*c - a*d)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*d)/b]","B",0
710,1,858,0,2.569687," ","integrate((d*x+c)^(3/2)/x^2/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a d x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(b c - 3 \, a d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c} c}{4 \, a x}, -\frac{4 \, a d x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + {\left(b c - 3 \, a d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, \sqrt{b x + a} \sqrt{d x + c} c}{4 \, a x}, \frac{a d x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left(b c - 3 \, a d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 2 \, \sqrt{b x + a} \sqrt{d x + c} c}{2 \, a x}, -\frac{2 \, a d x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + {\left(b c - 3 \, a d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} c}{2 \, a x}\right]"," ",0,"[1/4*(2*a*d*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - (b*c - 3*a*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*sqrt(d*x + c)*c)/(a*x), -1/4*(4*a*d*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + (b*c - 3*a*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*sqrt(b*x + a)*sqrt(d*x + c)*c)/(a*x), 1/2*(a*d*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - (b*c - 3*a*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 2*sqrt(b*x + a)*sqrt(d*x + c)*c)/(a*x), -1/2*(2*a*d*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + (b*c - 3*a*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*c)/(a*x)]","B",0
711,1,334,0,1.222636," ","integrate((d*x+c)^(3/2)/x^3/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} - {\left(3 \, a b c^{2} - 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{3} c x^{2}}, \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(3 \, a b c^{2} - 5 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{3} c x^{2}}\right]"," ",0,"[1/16*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 - (3*a*b*c^2 - 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^2), 1/8*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 - (3*a*b*c^2 - 5*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c*x^2)]","A",0
712,1,438,0,2.271949," ","integrate((d*x+c)^(3/2)/x^4/(b*x+a)^(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{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 22 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{4} c^{2} x^{3}}, -\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{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 22 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - 7 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{4} c^{2} x^{3}}\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(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 + (15*a*b^2*c^3 - 22*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^2*x^3), -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(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (15*a*b^2*c^3 - 22*a^2*b*c^2*d + 3*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - 7*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^2*x^3)]","A",0
713,1,574,0,6.879429," ","integrate((d*x+c)^(3/2)/x^5/(b*x+a)^(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{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(48 \, a^{4} c^{4} - {\left(105 \, a b^{3} c^{4} - 145 \, a^{2} b^{2} c^{3} d + 15 \, a^{3} b c^{2} d^{2} + 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(35 \, a^{2} b^{2} c^{4} - 46 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(7 \, a^{3} b c^{4} - 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{5} c^{3} x^{4}}, \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{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} - {\left(105 \, a b^{3} c^{4} - 145 \, a^{2} b^{2} c^{3} d + 15 \, a^{3} b c^{2} d^{2} + 9 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(35 \, a^{2} b^{2} c^{4} - 46 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(7 \, a^{3} b c^{4} - 9 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{5} c^{3} x^{4}}\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(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(48*a^4*c^4 - (105*a*b^3*c^4 - 145*a^2*b^2*c^3*d + 15*a^3*b*c^2*d^2 + 9*a^4*c*d^3)*x^3 + 2*(35*a^2*b^2*c^4 - 46*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 - 8*(7*a^3*b*c^4 - 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^3*x^4), 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(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 - (105*a*b^3*c^4 - 145*a^2*b^2*c^3*d + 15*a^3*b*c^2*d^2 + 9*a^4*c*d^3)*x^3 + 2*(35*a^2*b^2*c^4 - 46*a^3*b*c^3*d + 3*a^4*c^2*d^2)*x^2 - 8*(7*a^3*b*c^4 - 9*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^3*x^4)]","A",0
714,1,706,0,1.460203," ","integrate(x^2*(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 150 \, a^{3} b^{2} c^{2} d^{3} + 175 \, a^{4} b c d^{4} - 63 \, a^{5} d^{5}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d - 90 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 2310 \, a^{3} b^{2} c d^{4} + 945 \, a^{4} b d^{5} + 144 \, {\left(7 \, b^{5} c d^{4} - 3 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 63 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} - 481 \, a b^{4} c^{2} d^{3} + 749 \, a^{2} b^{3} c d^{4} - 315 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, b^{6} d^{3}}, -\frac{15 \, {\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 150 \, a^{3} b^{2} c^{2} d^{3} + 175 \, a^{4} b c d^{4} - 63 \, a^{5} d^{5}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{5} d^{5} x^{4} - 45 \, b^{5} c^{4} d - 90 \, a b^{4} c^{3} d^{2} + 1564 \, a^{2} b^{3} c^{2} d^{3} - 2310 \, a^{3} b^{2} c d^{4} + 945 \, a^{4} b d^{5} + 144 \, {\left(7 \, b^{5} c d^{4} - 3 \, a b^{4} d^{5}\right)} x^{3} + 8 \, {\left(93 \, b^{5} c^{2} d^{3} - 148 \, a b^{4} c d^{4} + 63 \, a^{2} b^{3} d^{5}\right)} x^{2} + 2 \, {\left(15 \, b^{5} c^{3} d^{2} - 481 \, a b^{4} c^{2} d^{3} + 749 \, a^{2} b^{3} c d^{4} - 315 \, a^{3} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, b^{6} d^{3}}\right]"," ",0,"[-1/7680*(15*(3*b^5*c^5 + 5*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 150*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 - 63*a^5*d^5)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(384*b^5*d^5*x^4 - 45*b^5*c^4*d - 90*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 2310*a^3*b^2*c*d^4 + 945*a^4*b*d^5 + 144*(7*b^5*c*d^4 - 3*a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 63*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 - 481*a*b^4*c^2*d^3 + 749*a^2*b^3*c*d^4 - 315*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^3), -1/3840*(15*(3*b^5*c^5 + 5*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 150*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 - 63*a^5*d^5)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^5*d^5*x^4 - 45*b^5*c^4*d - 90*a*b^4*c^3*d^2 + 1564*a^2*b^3*c^2*d^3 - 2310*a^3*b^2*c*d^4 + 945*a^4*b*d^5 + 144*(7*b^5*c*d^4 - 3*a*b^4*d^5)*x^3 + 8*(93*b^5*c^2*d^3 - 148*a*b^4*c*d^4 + 63*a^2*b^3*d^5)*x^2 + 2*(15*b^5*c^3*d^2 - 481*a*b^4*c^2*d^3 + 749*a^2*b^3*c*d^4 - 315*a^3*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^3)]","A",0
715,1,544,0,1.480941," ","integrate(x*(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 191 \, a b^{3} c^{2} d^{2} + 265 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, b^{5} d^{2}}, \frac{15 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{4} d^{4} x^{3} + 15 \, b^{4} c^{3} d - 191 \, a b^{3} c^{2} d^{2} + 265 \, a^{2} b^{2} c d^{3} - 105 \, a^{3} b d^{4} + 8 \, {\left(17 \, b^{4} c d^{3} - 7 \, a b^{3} d^{4}\right)} x^{2} + 2 \, {\left(59 \, b^{4} c^{2} d^{2} - 86 \, a b^{3} c d^{3} + 35 \, a^{2} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, b^{5} d^{2}}\right]"," ",0,"[-1/768*(15*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 191*a*b^3*c^2*d^2 + 265*a^2*b^2*c*d^3 - 105*a^3*b*d^4 + 8*(17*b^4*c*d^3 - 7*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^2), 1/384*(15*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^4*d^4*x^3 + 15*b^4*c^3*d - 191*a*b^3*c^2*d^2 + 265*a^2*b^2*c*d^3 - 105*a^3*b*d^4 + 8*(17*b^4*c*d^3 - 7*a*b^3*d^4)*x^2 + 2*(59*b^4*c^2*d^2 - 86*a*b^3*c*d^3 + 35*a^2*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d^2)]","A",0
716,1,412,0,0.818601," ","integrate((d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{4} d}, -\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 33 \, b^{3} c^{2} d - 40 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} + 2 \, {\left(13 \, b^{3} c d^{2} - 5 \, a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{4} d}\right]"," ",0,"[-1/96*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^3*d^3*x^2 + 33*b^3*c^2*d - 40*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(13*b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d), -1/48*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^3*d^3*x^2 + 33*b^3*c^2*d - 40*a*b^2*c*d^2 + 15*a^2*b*d^3 + 2*(13*b^3*c*d^2 - 5*a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d)]","A",0
717,1,987,0,8.486013," ","integrate((d*x+c)^(5/2)/x/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, b^{2} c^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b d^{2} x + 9 \, b c d - 3 \, a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2}}, \frac{4 \, b^{2} c^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b d^{2} x + 9 \, b c d - 3 \, a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2}}, \frac{16 \, b^{2} c^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b d^{2} x + 9 \, b c d - 3 \, a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{2}}, \frac{8 \, b^{2} c^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(15 \, b^{2} c^{2} - 10 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, b d^{2} x + 9 \, b c d - 3 \, a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{2}}\right]"," ",0,"[1/16*(8*b^2*c^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b*d^2*x + 9*b*c*d - 3*a*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/b^2, 1/8*(4*b^2*c^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(2*b*d^2*x + 9*b*c*d - 3*a*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/b^2, 1/16*(16*b^2*c^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b*d^2*x + 9*b*c*d - 3*a*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/b^2, 1/8*(8*b^2*c^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(2*b*d^2*x + 9*b*c*d - 3*a*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/b^2]","A",0
718,1,991,0,6.896377," ","integrate((d*x+c)^(5/2)/x^2/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a d^{2} x - b c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, a b x}, -\frac{2 \, {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a d^{2} x - b c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, a b x}, -\frac{2 \, {\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(a d^{2} x - b c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, a b x}, -\frac{{\left(b^{2} c^{2} - 5 \, a b c d\right)} x \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + {\left(5 \, a b c d - a^{2} d^{2}\right)} x \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(a d^{2} x - b c^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, a b x}\right]"," ",0,"[-1/4*((5*a*b*c*d - a^2*d^2)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + (b^2*c^2 - 5*a*b*c*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a*d^2*x - b*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b*x), -1/4*(2*(5*a*b*c*d - a^2*d^2)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + (b^2*c^2 - 5*a*b*c*d)*x*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a*d^2*x - b*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b*x), -1/4*(2*(b^2*c^2 - 5*a*b*c*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + (5*a*b*c*d - a^2*d^2)*x*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(a*d^2*x - b*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b*x), -1/2*((b^2*c^2 - 5*a*b*c*d)*x*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + (5*a*b*c*d - a^2*d^2)*x*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(a*d^2*x - b*c^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b*x)]","A",0
719,1,1031,0,5.658824," ","integrate((d*x+c)^(5/2)/x^3/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} d^{2} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a c^{2} - 3 \, {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} x^{2}}, -\frac{16 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(2 \, a c^{2} - 3 \, {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{2} x^{2}}, \frac{4 \, a^{2} d^{2} x^{2} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a c^{2} - 3 \, {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} x^{2}}, -\frac{8 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - {\left(3 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2}\right)} x^{2} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 2 \, {\left(2 \, a c^{2} - 3 \, {\left(b c^{2} - 3 \, a c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{2} x^{2}}\right]"," ",0,"[1/16*(8*a^2*d^2*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a*c^2 - 3*(b*c^2 - 3*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*x^2), -1/16*(16*a^2*d^2*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*x^2*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(2*a*c^2 - 3*(b*c^2 - 3*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*x^2), 1/8*(4*a^2*d^2*x^2*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 2*(2*a*c^2 - 3*(b*c^2 - 3*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*x^2), -1/8*(8*a^2*d^2*x^2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - (3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*x^2*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 2*(2*a*c^2 - 3*(b*c^2 - 3*a*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*x^2)]","A",0
720,1,438,0,1.886218," ","integrate((d*x+c)^(5/2)/x^4/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 40 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{4} c x^{3}}, -\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} - 40 \, a^{2} b c^{2} d + 33 \, a^{3} c d^{2}\right)} x^{2} - 2 \, {\left(5 \, a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{4} c x^{3}}\right]"," ",0,"[-1/96*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^3*c^3 + (15*a*b^2*c^3 - 40*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c*x^3), -1/48*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (15*a*b^2*c^3 - 40*a^2*b*c^2*d + 33*a^3*c*d^2)*x^2 - 2*(5*a^2*b*c^3 - 13*a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c*x^3)]","A",0
721,1,574,0,6.590488," ","integrate((d*x+c)^(5/2)/x^5/(b*x+a)^(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{a c} x^{4} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{4} c^{4} - {\left(105 \, a b^{3} c^{4} - 265 \, a^{2} b^{2} c^{3} d + 191 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(35 \, a^{2} b^{2} c^{4} - 86 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(7 \, a^{3} b c^{4} - 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, a^{5} c^{2} x^{4}}, \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{-a c} x^{4} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{4} c^{4} - {\left(105 \, a b^{3} c^{4} - 265 \, a^{2} b^{2} c^{3} d + 191 \, a^{3} b c^{2} d^{2} - 15 \, a^{4} c d^{3}\right)} x^{3} + 2 \, {\left(35 \, a^{2} b^{2} c^{4} - 86 \, a^{3} b c^{3} d + 59 \, a^{4} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(7 \, a^{3} b c^{4} - 17 \, a^{4} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, a^{5} c^{2} x^{4}}\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(a*c)*x^4*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^4*c^4 - (105*a*b^3*c^4 - 265*a^2*b^2*c^3*d + 191*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(35*a^2*b^2*c^4 - 86*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 8*(7*a^3*b*c^4 - 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^2*x^4), 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(-a*c)*x^4*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^4*c^4 - (105*a*b^3*c^4 - 265*a^2*b^2*c^3*d + 191*a^3*b*c^2*d^2 - 15*a^4*c*d^3)*x^3 + 2*(35*a^2*b^2*c^4 - 86*a^3*b*c^3*d + 59*a^4*c^2*d^2)*x^2 - 8*(7*a^3*b*c^4 - 17*a^4*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*c^2*x^4)]","A",0
722,1,732,0,15.605558," ","integrate((d*x+c)^(5/2)/x^6/(b*x+a)^(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{a c} x^{5} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(384 \, a^{5} c^{5} + {\left(945 \, a b^{4} c^{5} - 2310 \, a^{2} b^{3} c^{4} d + 1564 \, a^{3} b^{2} c^{3} d^{2} - 90 \, a^{4} b c^{2} d^{3} - 45 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(315 \, a^{2} b^{3} c^{5} - 749 \, a^{3} b^{2} c^{4} d + 481 \, a^{4} b c^{3} d^{2} - 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(63 \, a^{3} b^{2} c^{5} - 148 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} - 144 \, {\left(3 \, a^{4} b c^{5} - 7 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, a^{6} c^{3} x^{5}}, -\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{-a c} x^{5} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(384 \, a^{5} c^{5} + {\left(945 \, a b^{4} c^{5} - 2310 \, a^{2} b^{3} c^{4} d + 1564 \, a^{3} b^{2} c^{3} d^{2} - 90 \, a^{4} b c^{2} d^{3} - 45 \, a^{5} c d^{4}\right)} x^{4} - 2 \, {\left(315 \, a^{2} b^{3} c^{5} - 749 \, a^{3} b^{2} c^{4} d + 481 \, a^{4} b c^{3} d^{2} - 15 \, a^{5} c^{2} d^{3}\right)} x^{3} + 8 \, {\left(63 \, a^{3} b^{2} c^{5} - 148 \, a^{4} b c^{4} d + 93 \, a^{5} c^{3} d^{2}\right)} x^{2} - 144 \, {\left(3 \, a^{4} b c^{5} - 7 \, a^{5} c^{4} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, a^{6} c^{3} x^{5}}\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(a*c)*x^5*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(384*a^5*c^5 + (945*a*b^4*c^5 - 2310*a^2*b^3*c^4*d + 1564*a^3*b^2*c^3*d^2 - 90*a^4*b*c^2*d^3 - 45*a^5*c*d^4)*x^4 - 2*(315*a^2*b^3*c^5 - 749*a^3*b^2*c^4*d + 481*a^4*b*c^3*d^2 - 15*a^5*c^2*d^3)*x^3 + 8*(63*a^3*b^2*c^5 - 148*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 - 144*(3*a^4*b*c^5 - 7*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*c^3*x^5), -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(-a*c)*x^5*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(384*a^5*c^5 + (945*a*b^4*c^5 - 2310*a^2*b^3*c^4*d + 1564*a^3*b^2*c^3*d^2 - 90*a^4*b*c^2*d^3 - 45*a^5*c*d^4)*x^4 - 2*(315*a^2*b^3*c^5 - 749*a^3*b^2*c^4*d + 481*a^4*b*c^3*d^2 - 15*a^5*c^2*d^3)*x^3 + 8*(63*a^3*b^2*c^5 - 148*a^4*b*c^4*d + 93*a^5*c^3*d^2)*x^2 - 144*(3*a^4*b*c^5 - 7*a^5*c^4*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*c^3*x^5)]","A",0
723,1,62,0,1.199777," ","integrate(x^4*(1+x)^(3/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{240} \, {\left(40 \, x^{5} + 96 \, x^{4} + 110 \, x^{3} + 128 \, x^{2} + 165 \, x + 256\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{11}{8} \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/240*(40*x^5 + 96*x^4 + 110*x^3 + 128*x^2 + 165*x + 256)*sqrt(x + 1)*sqrt(-x + 1) - 11/8*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
724,1,57,0,1.317735," ","integrate(x^3*(1+x)^(3/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{20} \, {\left(4 \, x^{4} + 10 \, x^{3} + 12 \, x^{2} + 15 \, x + 24\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{3}{2} \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/20*(4*x^4 + 10*x^3 + 12*x^2 + 15*x + 24)*sqrt(x + 1)*sqrt(-x + 1) - 3/2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
725,1,52,0,1.149788," ","integrate(x^2*(1+x)^(3/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{24} \, {\left(6 \, x^{3} + 16 \, x^{2} + 21 \, x + 32\right)} \sqrt{x + 1} \sqrt{-x + 1} - \frac{7}{4} \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/24*(6*x^3 + 16*x^2 + 21*x + 32)*sqrt(x + 1)*sqrt(-x + 1) - 7/4*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
726,1,45,0,1.380642," ","integrate(x*(1+x)^(3/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(x^{2} + 3 \, x + 5\right)} \sqrt{x + 1} \sqrt{-x + 1} - 2 \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/3*(x^2 + 3*x + 5)*sqrt(x + 1)*sqrt(-x + 1) - 2*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
727,1,40,0,1.057804," ","integrate((1+x)^(3/2)/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x + 4\right)} \sqrt{x + 1} \sqrt{-x + 1} - 3 \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-1/2*(x + 4)*sqrt(x + 1)*sqrt(-x + 1) - 3*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
728,1,57,0,1.196552," ","integrate((1+x)^(3/2)/x/(1-x)^(1/2),x, algorithm=""fricas"")","-\sqrt{x + 1} \sqrt{-x + 1} - 4 \, \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)"," ",0,"-sqrt(x + 1)*sqrt(-x + 1) - 4*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x)","A",0
729,1,65,0,0.860194," ","integrate((1+x)^(3/2)/x^2/(1-x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, x \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - 2 \, x \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + \sqrt{x + 1} \sqrt{-x + 1}}{x}"," ",0,"-(2*x*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - 2*x*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + sqrt(x + 1)*sqrt(-x + 1))/x","A",0
730,1,50,0,1.326722," ","integrate((1+x)^(3/2)/x^3/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{2} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - {\left(4 \, x + 1\right)} \sqrt{x + 1} \sqrt{-x + 1}}{2 \, x^{2}}"," ",0,"1/2*(3*x^2*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - (4*x + 1)*sqrt(x + 1)*sqrt(-x + 1))/x^2","A",0
731,1,55,0,1.338275," ","integrate((1+x)^(3/2)/x^4/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{3 \, x^{3} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - {\left(5 \, x^{2} + 3 \, x + 1\right)} \sqrt{x + 1} \sqrt{-x + 1}}{3 \, x^{3}}"," ",0,"1/3*(3*x^3*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - (5*x^2 + 3*x + 1)*sqrt(x + 1)*sqrt(-x + 1))/x^3","A",0
732,1,60,0,1.252093," ","integrate((1+x)^(3/2)/x^5/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{21 \, x^{4} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - {\left(32 \, x^{3} + 21 \, x^{2} + 16 \, x + 6\right)} \sqrt{x + 1} \sqrt{-x + 1}}{24 \, x^{4}}"," ",0,"1/24*(21*x^4*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - (32*x^3 + 21*x^2 + 16*x + 6)*sqrt(x + 1)*sqrt(-x + 1))/x^4","A",0
733,1,410,0,1.684900," ","integrate(x^3/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{3} d^{3} x^{2} + 15 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} - 10 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, b^{4} d^{4}}, \frac{3 \, {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{3} d^{3} x^{2} + 15 \, b^{3} c^{2} d + 14 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3} - 10 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, b^{4} d^{4}}\right]"," ",0,"[1/96*(3*(5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^3*d^3*x^2 + 15*b^3*c^2*d + 14*a*b^2*c*d^2 + 15*a^2*b*d^3 - 10*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4), 1/48*(3*(5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^3*d^3*x^2 + 15*b^3*c^2*d + 14*a*b^2*c*d^2 + 15*a^2*b*d^3 - 10*(b^3*c*d^2 + a*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*d^4)]","A",0
734,1,308,0,1.305877," ","integrate(x^2/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, b^{3} d^{3}}, -\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x - 3 \, b^{2} c d - 3 \, a b d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, b^{3} d^{3}}\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 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3), -1/8*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^2*d^2*x - 3*b^2*c*d - 3*a*b*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*d^3)]","A",0
735,1,232,0,1.050661," ","integrate(x/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x + a} \sqrt{d x + c} b d + {\left(b c + a d\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{4 \, b^{2} d^{2}}, \frac{2 \, \sqrt{b x + a} \sqrt{d x + c} b d + {\left(b c + a d\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{2 \, b^{2} d^{2}}\right]"," ",0,"[1/4*(4*sqrt(b*x + a)*sqrt(d*x + c)*b*d + (b*c + a*d)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b^2*d^2), 1/2*(2*sqrt(b*x + a)*sqrt(d*x + c)*b*d + (b*c + a*d)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b^2*d^2)]","A",0
736,1,178,0,1.324174," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{2 \, b d}, -\frac{\sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{b d}\right]"," ",0,"[1/2*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x)/(b*d), -sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x))/(b*d)]","B",0
737,1,187,0,1.394977," ","integrate(1/x/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right)}{2 \, a c}, \frac{\sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right)}{a c}\right]"," ",0,"[1/2*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2)/(a*c), sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x))/(a*c)]","B",0
738,1,250,0,1.177438," ","integrate(1/x^2/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} {\left(b c + a d\right)} x \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, \sqrt{b x + a} \sqrt{d x + c} a c}{4 \, a^{2} c^{2} x}, -\frac{\sqrt{-a c} {\left(b c + a d\right)} x \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, \sqrt{b x + a} \sqrt{d x + c} a c}{2 \, a^{2} c^{2} x}\right]"," ",0,"[1/4*(sqrt(a*c)*(b*c + a*d)*x*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a^2*c^2*x), -1/2*(sqrt(-a*c)*(b*c + a*d)*x*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*sqrt(b*x + a)*sqrt(d*x + c)*a*c)/(a^2*c^2*x)]","A",0
739,1,332,0,1.834606," ","integrate(1/x^3/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{a c} x^{2} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} - 3 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, a^{3} c^{3} x^{2}}, \frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{-a c} x^{2} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - 3 \, {\left(a b c^{2} + a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, a^{3} c^{3} x^{2}}\right]"," ",0,"[1/16*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(a*c)*x^2*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 - 3*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^2), 1/8*((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*sqrt(-a*c)*x^2*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*c^2 - 3*(a*b*c^2 + a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*c^3*x^2)]","A",0
740,1,436,0,2.313941," ","integrate(1/x^4/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{a c} x^{3} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} - 10 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, a^{4} c^{4} x^{3}}, -\frac{3 \, {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \sqrt{-a c} x^{3} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} c^{3} + {\left(15 \, a b^{2} c^{3} + 14 \, a^{2} b c^{2} d + 15 \, a^{3} c d^{2}\right)} x^{2} - 10 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, a^{4} c^{4} x^{3}}\right]"," ",0,"[1/96*(3*(5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(a*c)*x^3*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^3*c^3 + (15*a*b^2*c^3 + 14*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 - 10*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^3), -1/48*(3*(5*b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 5*a^3*d^3)*sqrt(-a*c)*x^3*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^3*c^3 + (15*a*b^2*c^3 + 14*a^2*b*c^2*d + 15*a^3*c*d^2)*x^2 - 10*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*c^4*x^3)]","A",0
741,1,630,0,1.493813," ","integrate(x^3/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - a^{2} b c^{2} d^{2} - a^{3} c d^{3} + {\left(5 \, b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} - a^{2} b c d^{3} - a^{3} d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(15 \, b^{3} c^{3} d - 4 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} - 2 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{2} + {\left(5 \, b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(b^{4} c^{2} d^{4} - a b^{3} c d^{5} + {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)} x\right)}}, -\frac{3 \, {\left(5 \, b^{3} c^{4} - 3 \, a b^{2} c^{3} d - a^{2} b c^{2} d^{2} - a^{3} c d^{3} + {\left(5 \, b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} - a^{2} b c d^{3} - a^{3} d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, b^{3} c^{3} d - 4 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} - 2 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} x^{2} + {\left(5 \, b^{3} c^{2} d^{2} - 2 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(b^{4} c^{2} d^{4} - a b^{3} c d^{5} + {\left(b^{4} c d^{5} - a b^{3} d^{6}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(5*b^3*c^4 - 3*a*b^2*c^3*d - a^2*b*c^2*d^2 - a^3*c*d^3 + (5*b^3*c^3*d - 3*a*b^2*c^2*d^2 - a^2*b*c*d^3 - a^3*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(15*b^3*c^3*d - 4*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 - 2*(b^3*c*d^3 - a*b^2*d^4)*x^2 + (5*b^3*c^2*d^2 - 2*a*b^2*c*d^3 - 3*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*c^2*d^4 - a*b^3*c*d^5 + (b^4*c*d^5 - a*b^3*d^6)*x), -1/8*(3*(5*b^3*c^4 - 3*a*b^2*c^3*d - a^2*b*c^2*d^2 - a^3*c*d^3 + (5*b^3*c^3*d - 3*a*b^2*c^2*d^2 - a^2*b*c*d^3 - a^3*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*b^3*c^3*d - 4*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 - 2*(b^3*c*d^3 - a*b^2*d^4)*x^2 + (5*b^3*c^2*d^2 - 2*a*b^2*c*d^3 - 3*a^2*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*c^2*d^4 - a*b^3*c*d^5 + (b^4*c*d^5 - a*b^3*d^6)*x)]","B",0
742,1,468,0,1.522261," ","integrate(x^2/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(3 \, b^{2} c^{2} d - a b c d^{2} + {\left(b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(b^{3} c^{2} d^{3} - a b^{2} c d^{4} + {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x\right)}}, \frac{{\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2} + {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, b^{2} c^{2} d - a b c d^{2} + {\left(b^{2} c d^{2} - a b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{3} c^{2} d^{3} - a b^{2} c d^{4} + {\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} x\right)}}\right]"," ",0,"[1/4*((3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(3*b^2*c^2*d - a*b*c*d^2 + (b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^2*d^3 - a*b^2*c*d^4 + (b^3*c*d^4 - a*b^2*d^5)*x), 1/2*((3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2 + (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(3*b^2*c^2*d - a*b*c*d^2 + (b^2*c*d^2 - a*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^2*d^3 - a*b^2*c*d^4 + (b^3*c*d^4 - a*b^2*d^5)*x)]","B",0
743,1,335,0,1.876276," ","integrate(x/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{b x + a} \sqrt{d x + c} b c d - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{2 \, {\left(b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x\right)}}, -\frac{2 \, \sqrt{b x + a} \sqrt{d x + c} b c d + {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right)}{b^{2} c^{2} d^{2} - a b c d^{3} + {\left(b^{2} c d^{3} - a b d^{4}\right)} x}\right]"," ",0,"[-1/2*(4*sqrt(b*x + a)*sqrt(d*x + c)*b*c*d - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x), -(2*sqrt(b*x + a)*sqrt(d*x + c)*b*c*d + (b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)))/(b^2*c^2*d^2 - a*b*c*d^3 + (b^2*c*d^3 - a*b*d^4)*x)]","B",0
744,1,42,0,1.380449," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x + a} \sqrt{d x + c}}{b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x}"," ",0,"2*sqrt(b*x + a)*sqrt(d*x + c)/(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)","A",0
745,1,346,0,2.088339," ","integrate(1/x/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{b x + a} \sqrt{d x + c} a c d - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right)}{2 \, {\left(a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x\right)}}, -\frac{2 \, \sqrt{b x + a} \sqrt{d x + c} a c d - {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right)}{a b c^{4} - a^{2} c^{3} d + {\left(a b c^{3} d - a^{2} c^{2} d^{2}\right)} x}\right]"," ",0,"[-1/2*(4*sqrt(b*x + a)*sqrt(d*x + c)*a*c*d - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x), -(2*sqrt(b*x + a)*sqrt(d*x + c)*a*c*d - (b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)))/(a*b*c^4 - a^2*c^3*d + (a*b*c^3*d - a^2*c^2*d^2)*x)]","B",0
746,1,492,0,2.354222," ","integrate(1/x^2/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c^{2} d + 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a b c^{3} - a^{2} c^{2} d + {\left(a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x\right)}}, -\frac{{\left({\left(b^{2} c^{2} d + 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x^{2} + {\left(b^{2} c^{3} + 2 \, a b c^{2} d - 3 \, a^{2} c d^{2}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\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\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left({\left(a^{2} b c^{4} d - a^{3} c^{3} d^{2}\right)} x^{2} + {\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} x\right)}}\right]"," ",0,"[1/4*(((b^2*c^2*d + 2*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (b^2*c^3 + 2*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^2 + (a^2*b*c^5 - a^3*c^4*d)*x), -1/2*(((b^2*c^2*d + 2*a*b*c*d^2 - 3*a^2*d^3)*x^2 + (b^2*c^3 + 2*a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(a*b*c^3 - a^2*c^2*d + (a*b*c^2*d - 3*a^2*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b*c^4*d - a^3*c^3*d^2)*x^2 + (a^2*b*c^5 - a^3*c^4*d)*x)]","B",0
747,1,664,0,3.379702," ","integrate(1/x^3/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c^{3} d + a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{3} + {\left(b^{3} c^{4} + a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} b c^{4} - 2 \, a^{3} c^{3} d - {\left(3 \, a b^{2} c^{3} d + 4 \, a^{2} b c^{2} d^{2} - 15 \, a^{3} c d^{3}\right)} x^{2} - {\left(3 \, a b^{2} c^{4} + 2 \, a^{2} b c^{3} d - 5 \, a^{3} c^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left({\left(a^{3} b c^{5} d - a^{4} c^{4} d^{2}\right)} x^{3} + {\left(a^{3} b c^{6} - a^{4} c^{5} d\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(b^{3} c^{3} d + a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 5 \, a^{3} d^{4}\right)} x^{3} + {\left(b^{3} c^{4} + a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} b c^{4} - 2 \, a^{3} c^{3} d - {\left(3 \, a b^{2} c^{3} d + 4 \, a^{2} b c^{2} d^{2} - 15 \, a^{3} c d^{3}\right)} x^{2} - {\left(3 \, a b^{2} c^{4} + 2 \, a^{2} b c^{3} d - 5 \, a^{3} c^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left({\left(a^{3} b c^{5} d - a^{4} c^{4} d^{2}\right)} x^{3} + {\left(a^{3} b c^{6} - a^{4} c^{5} d\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(3*((b^3*c^3*d + a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 5*a^3*d^4)*x^3 + (b^3*c^4 + a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*b*c^4 - 2*a^3*c^3*d - (3*a*b^2*c^3*d + 4*a^2*b*c^2*d^2 - 15*a^3*c*d^3)*x^2 - (3*a*b^2*c^4 + 2*a^2*b*c^3*d - 5*a^3*c^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b*c^5*d - a^4*c^4*d^2)*x^3 + (a^3*b*c^6 - a^4*c^5*d)*x^2), 1/8*(3*((b^3*c^3*d + a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 5*a^3*d^4)*x^3 + (b^3*c^4 + a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^2*b*c^4 - 2*a^3*c^3*d - (3*a*b^2*c^3*d + 4*a^2*b*c^2*d^2 - 15*a^3*c*d^3)*x^2 - (3*a*b^2*c^4 + 2*a^2*b*c^3*d - 5*a^3*c^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b*c^5*d - a^4*c^4*d^2)*x^3 + (a^3*b*c^6 - a^4*c^5*d)*x^2)]","A",0
748,1,1144,0,2.898040," ","integrate(x^4/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, b^{4} c^{6} - 60 \, a b^{3} c^{5} d + 18 \, a^{2} b^{2} c^{4} d^{2} + 4 \, a^{3} b c^{3} d^{3} + 3 \, a^{4} c^{2} d^{4} + {\left(35 \, b^{4} c^{4} d^{2} - 60 \, a b^{3} c^{3} d^{3} + 18 \, a^{2} b^{2} c^{2} d^{4} + 4 \, a^{3} b c d^{5} + 3 \, a^{4} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{5} d - 60 \, a b^{3} c^{4} d^{2} + 18 \, a^{2} b^{2} c^{3} d^{3} + 4 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(105 \, b^{4} c^{5} d - 145 \, a b^{3} c^{4} d^{2} + 15 \, a^{2} b^{2} c^{3} d^{3} + 9 \, a^{3} b c^{2} d^{4} - 6 \, {\left(b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} + a^{2} b^{2} d^{6}\right)} x^{3} + 3 \, {\left(7 \, b^{4} c^{3} d^{3} - 11 \, a b^{3} c^{2} d^{4} + a^{2} b^{2} c d^{5} + 3 \, a^{3} b d^{6}\right)} x^{2} + 2 \, {\left(70 \, b^{4} c^{4} d^{2} - 99 \, a b^{3} c^{3} d^{3} + 12 \, a^{2} b^{2} c^{2} d^{4} + 9 \, a^{3} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{5} c^{4} d^{5} - 2 \, a b^{4} c^{3} d^{6} + a^{2} b^{3} c^{2} d^{7} + {\left(b^{5} c^{2} d^{7} - 2 \, a b^{4} c d^{8} + a^{2} b^{3} d^{9}\right)} x^{2} + 2 \, {\left(b^{5} c^{3} d^{6} - 2 \, a b^{4} c^{2} d^{7} + a^{2} b^{3} c d^{8}\right)} x\right)}}, -\frac{3 \, {\left(35 \, b^{4} c^{6} - 60 \, a b^{3} c^{5} d + 18 \, a^{2} b^{2} c^{4} d^{2} + 4 \, a^{3} b c^{3} d^{3} + 3 \, a^{4} c^{2} d^{4} + {\left(35 \, b^{4} c^{4} d^{2} - 60 \, a b^{3} c^{3} d^{3} + 18 \, a^{2} b^{2} c^{2} d^{4} + 4 \, a^{3} b c d^{5} + 3 \, a^{4} d^{6}\right)} x^{2} + 2 \, {\left(35 \, b^{4} c^{5} d - 60 \, a b^{3} c^{4} d^{2} + 18 \, a^{2} b^{2} c^{3} d^{3} + 4 \, a^{3} b c^{2} d^{4} + 3 \, a^{4} c d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(105 \, b^{4} c^{5} d - 145 \, a b^{3} c^{4} d^{2} + 15 \, a^{2} b^{2} c^{3} d^{3} + 9 \, a^{3} b c^{2} d^{4} - 6 \, {\left(b^{4} c^{2} d^{4} - 2 \, a b^{3} c d^{5} + a^{2} b^{2} d^{6}\right)} x^{3} + 3 \, {\left(7 \, b^{4} c^{3} d^{3} - 11 \, a b^{3} c^{2} d^{4} + a^{2} b^{2} c d^{5} + 3 \, a^{3} b d^{6}\right)} x^{2} + 2 \, {\left(70 \, b^{4} c^{4} d^{2} - 99 \, a b^{3} c^{3} d^{3} + 12 \, a^{2} b^{2} c^{2} d^{4} + 9 \, a^{3} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(b^{5} c^{4} d^{5} - 2 \, a b^{4} c^{3} d^{6} + a^{2} b^{3} c^{2} d^{7} + {\left(b^{5} c^{2} d^{7} - 2 \, a b^{4} c d^{8} + a^{2} b^{3} d^{9}\right)} x^{2} + 2 \, {\left(b^{5} c^{3} d^{6} - 2 \, a b^{4} c^{2} d^{7} + a^{2} b^{3} c d^{8}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(35*b^4*c^6 - 60*a*b^3*c^5*d + 18*a^2*b^2*c^4*d^2 + 4*a^3*b*c^3*d^3 + 3*a^4*c^2*d^4 + (35*b^4*c^4*d^2 - 60*a*b^3*c^3*d^3 + 18*a^2*b^2*c^2*d^4 + 4*a^3*b*c*d^5 + 3*a^4*d^6)*x^2 + 2*(35*b^4*c^5*d - 60*a*b^3*c^4*d^2 + 18*a^2*b^2*c^3*d^3 + 4*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(105*b^4*c^5*d - 145*a*b^3*c^4*d^2 + 15*a^2*b^2*c^3*d^3 + 9*a^3*b*c^2*d^4 - 6*(b^4*c^2*d^4 - 2*a*b^3*c*d^5 + a^2*b^2*d^6)*x^3 + 3*(7*b^4*c^3*d^3 - 11*a*b^3*c^2*d^4 + a^2*b^2*c*d^5 + 3*a^3*b*d^6)*x^2 + 2*(70*b^4*c^4*d^2 - 99*a*b^3*c^3*d^3 + 12*a^2*b^2*c^2*d^4 + 9*a^3*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*c^4*d^5 - 2*a*b^4*c^3*d^6 + a^2*b^3*c^2*d^7 + (b^5*c^2*d^7 - 2*a*b^4*c*d^8 + a^2*b^3*d^9)*x^2 + 2*(b^5*c^3*d^6 - 2*a*b^4*c^2*d^7 + a^2*b^3*c*d^8)*x), -1/24*(3*(35*b^4*c^6 - 60*a*b^3*c^5*d + 18*a^2*b^2*c^4*d^2 + 4*a^3*b*c^3*d^3 + 3*a^4*c^2*d^4 + (35*b^4*c^4*d^2 - 60*a*b^3*c^3*d^3 + 18*a^2*b^2*c^2*d^4 + 4*a^3*b*c*d^5 + 3*a^4*d^6)*x^2 + 2*(35*b^4*c^5*d - 60*a*b^3*c^4*d^2 + 18*a^2*b^2*c^3*d^3 + 4*a^3*b*c^2*d^4 + 3*a^4*c*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(105*b^4*c^5*d - 145*a*b^3*c^4*d^2 + 15*a^2*b^2*c^3*d^3 + 9*a^3*b*c^2*d^4 - 6*(b^4*c^2*d^4 - 2*a*b^3*c*d^5 + a^2*b^2*d^6)*x^3 + 3*(7*b^4*c^3*d^3 - 11*a*b^3*c^2*d^4 + a^2*b^2*c*d^5 + 3*a^3*b*d^6)*x^2 + 2*(70*b^4*c^4*d^2 - 99*a*b^3*c^3*d^3 + 12*a^2*b^2*c^2*d^4 + 9*a^3*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*c^4*d^5 - 2*a*b^4*c^3*d^6 + a^2*b^3*c^2*d^7 + (b^5*c^2*d^7 - 2*a*b^4*c*d^8 + a^2*b^3*d^9)*x^2 + 2*(b^5*c^3*d^6 - 2*a*b^4*c^2*d^7 + a^2*b^3*c*d^8)*x)]","B",0
749,1,896,0,2.024273," ","integrate(x^3/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, b^{3} c^{5} - 9 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(5 \, b^{3} c^{3} d^{2} - 9 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{2} + 2 \, {\left(5 \, b^{3} c^{4} d - 9 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(15 \, b^{3} c^{4} d - 22 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} + 3 \, {\left(b^{3} c^{2} d^{3} - 2 \, a b^{2} c d^{4} + a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(10 \, b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(b^{4} c^{4} d^{4} - 2 \, a b^{3} c^{3} d^{5} + a^{2} b^{2} c^{2} d^{6} + {\left(b^{4} c^{2} d^{6} - 2 \, a b^{3} c d^{7} + a^{2} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{4} c^{3} d^{5} - 2 \, a b^{3} c^{2} d^{6} + a^{2} b^{2} c d^{7}\right)} x\right)}}, \frac{3 \, {\left(5 \, b^{3} c^{5} - 9 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} + a^{3} c^{2} d^{3} + {\left(5 \, b^{3} c^{3} d^{2} - 9 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} + a^{3} d^{5}\right)} x^{2} + 2 \, {\left(5 \, b^{3} c^{4} d - 9 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} + a^{3} c d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, b^{3} c^{4} d - 22 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} + 3 \, {\left(b^{3} c^{2} d^{3} - 2 \, a b^{2} c d^{4} + a^{2} b d^{5}\right)} x^{2} + 2 \, {\left(10 \, b^{3} c^{3} d^{2} - 15 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b^{4} c^{4} d^{4} - 2 \, a b^{3} c^{3} d^{5} + a^{2} b^{2} c^{2} d^{6} + {\left(b^{4} c^{2} d^{6} - 2 \, a b^{3} c d^{7} + a^{2} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{4} c^{3} d^{5} - 2 \, a b^{3} c^{2} d^{6} + a^{2} b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[1/12*(3*(5*b^3*c^5 - 9*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 + a^3*d^5)*x^2 + 2*(5*b^3*c^4*d - 9*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(15*b^3*c^4*d - 22*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 + 3*(b^3*c^2*d^3 - 2*a*b^2*c*d^4 + a^2*b*d^5)*x^2 + 2*(10*b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*c^4*d^4 - 2*a*b^3*c^3*d^5 + a^2*b^2*c^2*d^6 + (b^4*c^2*d^6 - 2*a*b^3*c*d^7 + a^2*b^2*d^8)*x^2 + 2*(b^4*c^3*d^5 - 2*a*b^3*c^2*d^6 + a^2*b^2*c*d^7)*x), 1/6*(3*(5*b^3*c^5 - 9*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 + a^3*c^2*d^3 + (5*b^3*c^3*d^2 - 9*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 + a^3*d^5)*x^2 + 2*(5*b^3*c^4*d - 9*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 + a^3*c*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*b^3*c^4*d - 22*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 + 3*(b^3*c^2*d^3 - 2*a*b^2*c*d^4 + a^2*b*d^5)*x^2 + 2*(10*b^3*c^3*d^2 - 15*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*c^4*d^4 - 2*a*b^3*c^3*d^5 + a^2*b^2*c^2*d^6 + (b^4*c^2*d^6 - 2*a*b^3*c*d^7 + a^2*b^2*d^8)*x^2 + 2*(b^4*c^3*d^5 - 2*a*b^3*c^2*d^6 + a^2*b^2*c*d^7)*x)]","B",0
750,1,670,0,1.854402," ","integrate(x^2/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b^{2} c^{3} d - 5 \, a b c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{2} d^{2} - 3 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b^{3} c^{4} d^{3} - 2 \, a b^{2} c^{3} d^{4} + a^{2} b c^{2} d^{5} + {\left(b^{3} c^{2} d^{5} - 2 \, a b^{2} c d^{6} + a^{2} b d^{7}\right)} x^{2} + 2 \, {\left(b^{3} c^{3} d^{4} - 2 \, a b^{2} c^{2} d^{5} + a^{2} b c d^{6}\right)} x\right)}}, -\frac{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, b^{2} c^{3} d - 5 \, a b c^{2} d^{2} + 2 \, {\left(2 \, b^{2} c^{2} d^{2} - 3 \, a b c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(b^{3} c^{4} d^{3} - 2 \, a b^{2} c^{3} d^{4} + a^{2} b c^{2} d^{5} + {\left(b^{3} c^{2} d^{5} - 2 \, a b^{2} c d^{6} + a^{2} b d^{7}\right)} x^{2} + 2 \, {\left(b^{3} c^{3} d^{4} - 2 \, a b^{2} c^{2} d^{5} + a^{2} b c d^{6}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b^2*c^3*d - 5*a*b*c^2*d^2 + 2*(2*b^2*c^2*d^2 - 3*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^4*d^3 - 2*a*b^2*c^3*d^4 + a^2*b*c^2*d^5 + (b^3*c^2*d^5 - 2*a*b^2*c*d^6 + a^2*b*d^7)*x^2 + 2*(b^3*c^3*d^4 - 2*a*b^2*c^2*d^5 + a^2*b*c*d^6)*x), -1/3*(3*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(3*b^2*c^3*d - 5*a*b*c^2*d^2 + 2*(2*b^2*c^2*d^2 - 3*a*b*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*c^4*d^3 - 2*a*b^2*c^3*d^4 + a^2*b*c^2*d^5 + (b^3*c^2*d^5 - 2*a*b^2*c*d^6 + a^2*b*d^7)*x^2 + 2*(b^3*c^3*d^4 - 2*a*b^2*c^2*d^5 + a^2*b*c*d^6)*x)]","B",0
751,1,120,0,1.677632," ","integrate(x/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a c - {\left(b c - 3 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)}}"," ",0,"-2/3*(2*a*c - (b*c - 3*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)","A",0
752,1,118,0,1.678883," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b d x + 3 \, b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)}}"," ",0,"2/3*(2*b*d*x + 3*b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)","B",0
753,1,678,0,2.390612," ","integrate(1/x/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + {\left(5 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{2} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a b c^{3} d - 4 \, a^{2} c^{2} d^{2} + {\left(5 \, a b c^{2} d^{2} - 3 \, a^{2} c d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a b^{2} c^{7} - 2 \, a^{2} b c^{6} d + a^{3} c^{5} d^{2} + {\left(a b^{2} c^{5} d^{2} - 2 \, a^{2} b c^{4} d^{3} + a^{3} c^{3} d^{4}\right)} x^{2} + 2 \, {\left(a b^{2} c^{6} d - 2 \, a^{2} b c^{5} d^{2} + a^{3} c^{4} d^{3}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a*b*c^3*d - 4*a^2*c^2*d^2 + (5*a*b*c^2*d^2 - 3*a^2*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^2 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x), 1/3*(3*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2 + (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(6*a*b*c^3*d - 4*a^2*c^2*d^2 + (5*a*b*c^2*d^2 - 3*a^2*c*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*c^7 - 2*a^2*b*c^6*d + a^3*c^5*d^2 + (a*b^2*c^5*d^2 - 2*a^2*b*c^4*d^3 + a^3*c^3*d^4)*x^2 + 2*(a*b^2*c^6*d - 2*a^2*b*c^5*d^2 + a^3*c^4*d^3)*x)]","B",0
754,1,928,0,3.755695," ","integrate(1/x^2/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c^{3} d^{2} + 3 \, a b^{2} c^{2} d^{3} - 9 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{3} + 2 \, {\left(b^{3} c^{4} d + 3 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{2} + {\left(b^{3} c^{5} + 3 \, a b^{2} c^{4} d - 9 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + {\left(3 \, a b^{2} c^{3} d^{2} - 22 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{4} d - 15 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{2} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{3} c^{3} d^{2} + 3 \, a b^{2} c^{2} d^{3} - 9 \, a^{2} b c d^{4} + 5 \, a^{3} d^{5}\right)} x^{3} + 2 \, {\left(b^{3} c^{4} d + 3 \, a b^{2} c^{3} d^{2} - 9 \, a^{2} b c^{2} d^{3} + 5 \, a^{3} c d^{4}\right)} x^{2} + {\left(b^{3} c^{5} + 3 \, a b^{2} c^{4} d - 9 \, a^{2} b c^{3} d^{2} + 5 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a b^{2} c^{5} - 6 \, a^{2} b c^{4} d + 3 \, a^{3} c^{3} d^{2} + {\left(3 \, a b^{2} c^{3} d^{2} - 22 \, a^{2} b c^{2} d^{3} + 15 \, a^{3} c d^{4}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{4} d - 15 \, a^{2} b c^{3} d^{2} + 10 \, a^{3} c^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left({\left(a^{2} b^{2} c^{6} d^{2} - 2 \, a^{3} b c^{5} d^{3} + a^{4} c^{4} d^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} c^{7} d - 2 \, a^{3} b c^{6} d^{2} + a^{4} c^{5} d^{3}\right)} x^{2} + {\left(a^{2} b^{2} c^{8} - 2 \, a^{3} b c^{7} d + a^{4} c^{6} d^{2}\right)} x\right)}}\right]"," ",0,"[1/12*(3*((b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 - 9*a^2*b*c*d^4 + 5*a^3*d^5)*x^3 + 2*(b^3*c^4*d + 3*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^2 + (b^3*c^5 + 3*a*b^2*c^4*d - 9*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + (3*a*b^2*c^3*d^2 - 22*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^2 + 2*(3*a*b^2*c^4*d - 15*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^3 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^2 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x), -1/6*(3*((b^3*c^3*d^2 + 3*a*b^2*c^2*d^3 - 9*a^2*b*c*d^4 + 5*a^3*d^5)*x^3 + 2*(b^3*c^4*d + 3*a*b^2*c^3*d^2 - 9*a^2*b*c^2*d^3 + 5*a^3*c*d^4)*x^2 + (b^3*c^5 + 3*a*b^2*c^4*d - 9*a^2*b*c^3*d^2 + 5*a^3*c^2*d^3)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(3*a*b^2*c^5 - 6*a^2*b*c^4*d + 3*a^3*c^3*d^2 + (3*a*b^2*c^3*d^2 - 22*a^2*b*c^2*d^3 + 15*a^3*c*d^4)*x^2 + 2*(3*a*b^2*c^4*d - 15*a^2*b*c^3*d^2 + 10*a^3*c^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^2*b^2*c^6*d^2 - 2*a^3*b*c^5*d^3 + a^4*c^4*d^4)*x^3 + 2*(a^2*b^2*c^7*d - 2*a^3*b*c^6*d^2 + a^4*c^5*d^3)*x^2 + (a^2*b^2*c^8 - 2*a^3*b*c^7*d + a^4*c^6*d^2)*x)]","B",0
755,1,1186,0,9.615977," ","integrate(1/x^3/(d*x+c)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, b^{4} c^{4} d^{2} + 4 \, a b^{3} c^{3} d^{3} + 18 \, a^{2} b^{2} c^{2} d^{4} - 60 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{4} + 2 \, {\left(3 \, b^{4} c^{5} d + 4 \, a b^{3} c^{4} d^{2} + 18 \, a^{2} b^{2} c^{3} d^{3} - 60 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{3} + {\left(3 \, b^{4} c^{6} + 4 \, a b^{3} c^{5} d + 18 \, a^{2} b^{2} c^{4} d^{2} - 60 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{2} b^{2} c^{6} - 12 \, a^{3} b c^{5} d + 6 \, a^{4} c^{4} d^{2} - {\left(9 \, a b^{3} c^{4} d^{2} + 15 \, a^{2} b^{2} c^{3} d^{3} - 145 \, a^{3} b c^{2} d^{4} + 105 \, a^{4} c d^{5}\right)} x^{3} - 2 \, {\left(9 \, a b^{3} c^{5} d + 12 \, a^{2} b^{2} c^{4} d^{2} - 99 \, a^{3} b c^{3} d^{3} + 70 \, a^{4} c^{2} d^{4}\right)} x^{2} - 3 \, {\left(3 \, a b^{3} c^{6} + a^{2} b^{2} c^{5} d - 11 \, a^{3} b c^{4} d^{2} + 7 \, a^{4} c^{3} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left({\left(a^{3} b^{2} c^{7} d^{2} - 2 \, a^{4} b c^{6} d^{3} + a^{5} c^{5} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{2} c^{8} d - 2 \, a^{4} b c^{7} d^{2} + a^{5} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{2} c^{9} - 2 \, a^{4} b c^{8} d + a^{5} c^{7} d^{2}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(3 \, b^{4} c^{4} d^{2} + 4 \, a b^{3} c^{3} d^{3} + 18 \, a^{2} b^{2} c^{2} d^{4} - 60 \, a^{3} b c d^{5} + 35 \, a^{4} d^{6}\right)} x^{4} + 2 \, {\left(3 \, b^{4} c^{5} d + 4 \, a b^{3} c^{4} d^{2} + 18 \, a^{2} b^{2} c^{3} d^{3} - 60 \, a^{3} b c^{2} d^{4} + 35 \, a^{4} c d^{5}\right)} x^{3} + {\left(3 \, b^{4} c^{6} + 4 \, a b^{3} c^{5} d + 18 \, a^{2} b^{2} c^{4} d^{2} - 60 \, a^{3} b c^{3} d^{3} + 35 \, a^{4} c^{2} d^{4}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{2} b^{2} c^{6} - 12 \, a^{3} b c^{5} d + 6 \, a^{4} c^{4} d^{2} - {\left(9 \, a b^{3} c^{4} d^{2} + 15 \, a^{2} b^{2} c^{3} d^{3} - 145 \, a^{3} b c^{2} d^{4} + 105 \, a^{4} c d^{5}\right)} x^{3} - 2 \, {\left(9 \, a b^{3} c^{5} d + 12 \, a^{2} b^{2} c^{4} d^{2} - 99 \, a^{3} b c^{3} d^{3} + 70 \, a^{4} c^{2} d^{4}\right)} x^{2} - 3 \, {\left(3 \, a b^{3} c^{6} + a^{2} b^{2} c^{5} d - 11 \, a^{3} b c^{4} d^{2} + 7 \, a^{4} c^{3} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left({\left(a^{3} b^{2} c^{7} d^{2} - 2 \, a^{4} b c^{6} d^{3} + a^{5} c^{5} d^{4}\right)} x^{4} + 2 \, {\left(a^{3} b^{2} c^{8} d - 2 \, a^{4} b c^{7} d^{2} + a^{5} c^{6} d^{3}\right)} x^{3} + {\left(a^{3} b^{2} c^{9} - 2 \, a^{4} b c^{8} d + a^{5} c^{7} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/48*(3*((3*b^4*c^4*d^2 + 4*a*b^3*c^3*d^3 + 18*a^2*b^2*c^2*d^4 - 60*a^3*b*c*d^5 + 35*a^4*d^6)*x^4 + 2*(3*b^4*c^5*d + 4*a*b^3*c^4*d^2 + 18*a^2*b^2*c^3*d^3 - 60*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^3 + (3*b^4*c^6 + 4*a*b^3*c^5*d + 18*a^2*b^2*c^4*d^2 - 60*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^2*b^2*c^6 - 12*a^3*b*c^5*d + 6*a^4*c^4*d^2 - (9*a*b^3*c^4*d^2 + 15*a^2*b^2*c^3*d^3 - 145*a^3*b*c^2*d^4 + 105*a^4*c*d^5)*x^3 - 2*(9*a*b^3*c^5*d + 12*a^2*b^2*c^4*d^2 - 99*a^3*b*c^3*d^3 + 70*a^4*c^2*d^4)*x^2 - 3*(3*a*b^3*c^6 + a^2*b^2*c^5*d - 11*a^3*b*c^4*d^2 + 7*a^4*c^3*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b^2*c^7*d^2 - 2*a^4*b*c^6*d^3 + a^5*c^5*d^4)*x^4 + 2*(a^3*b^2*c^8*d - 2*a^4*b*c^7*d^2 + a^5*c^6*d^3)*x^3 + (a^3*b^2*c^9 - 2*a^4*b*c^8*d + a^5*c^7*d^2)*x^2), 1/24*(3*((3*b^4*c^4*d^2 + 4*a*b^3*c^3*d^3 + 18*a^2*b^2*c^2*d^4 - 60*a^3*b*c*d^5 + 35*a^4*d^6)*x^4 + 2*(3*b^4*c^5*d + 4*a*b^3*c^4*d^2 + 18*a^2*b^2*c^3*d^3 - 60*a^3*b*c^2*d^4 + 35*a^4*c*d^5)*x^3 + (3*b^4*c^6 + 4*a*b^3*c^5*d + 18*a^2*b^2*c^4*d^2 - 60*a^3*b*c^3*d^3 + 35*a^4*c^2*d^4)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(6*a^2*b^2*c^6 - 12*a^3*b*c^5*d + 6*a^4*c^4*d^2 - (9*a*b^3*c^4*d^2 + 15*a^2*b^2*c^3*d^3 - 145*a^3*b*c^2*d^4 + 105*a^4*c*d^5)*x^3 - 2*(9*a*b^3*c^5*d + 12*a^2*b^2*c^4*d^2 - 99*a^3*b*c^3*d^3 + 70*a^4*c^2*d^4)*x^2 - 3*(3*a*b^3*c^6 + a^2*b^2*c^5*d - 11*a^3*b*c^4*d^2 + 7*a^4*c^3*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b^2*c^7*d^2 - 2*a^4*b*c^6*d^3 + a^5*c^5*d^4)*x^4 + 2*(a^3*b^2*c^8*d - 2*a^4*b*c^7*d^2 + a^5*c^6*d^3)*x^3 + (a^3*b^2*c^9 - 2*a^4*b*c^8*d + a^5*c^7*d^2)*x^2)]","B",0
756,1,23,0,1.108553," ","integrate(1/x/(c*x)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x + a} \sqrt{c x}}{a c x}"," ",0,"-2*sqrt(b*x + a)*sqrt(c*x)/(a*c*x)","A",0
757,1,110,0,1.375514," ","integrate(1/x/(b*x+a)^(1/2)/(-b*c*x+a*c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{b^{2} c x^{2} - 2 \, a^{2} c + 2 \, \sqrt{-b c x + a c} \sqrt{b x + a} a \sqrt{c}}{x^{2}}\right)}{2 \, a \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{-b c x + a c} \sqrt{b x + a} a \sqrt{-c}}{b^{2} c x^{2} - a^{2} c}\right)}{a c}\right]"," ",0,"[1/2*log(-(b^2*c*x^2 - 2*a^2*c + 2*sqrt(-b*c*x + a*c)*sqrt(b*x + a)*a*sqrt(c))/x^2)/(a*sqrt(c)), -sqrt(-c)*arctan(sqrt(-b*c*x + a*c)*sqrt(b*x + a)*a*sqrt(-c)/(b^2*c*x^2 - a^2*c))/(a*c)]","A",0
758,1,180,0,1.191677," ","integrate(1/x/(-b*x-a+1)^(1/2)/(b*x+a+1)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + 1} \log\left(\frac{{\left(2 \, a^{2} - 1\right)} b^{2} x^{2} + 2 \, a^{4} + 4 \, {\left(a^{3} - a\right)} b x + 2 \, {\left(a b x + a^{2} - 1\right)} \sqrt{-a^{2} + 1} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} - 4 \, a^{2} + 2}{x^{2}}\right)}{2 \, {\left(a^{2} - 1\right)}}, \frac{\arctan\left(\frac{{\left(a b x + a^{2} - 1\right)} \sqrt{a^{2} - 1} \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}{{\left(a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 2 \, {\left(a^{3} - a\right)} b x - 2 \, a^{2} + 1}\right)}{\sqrt{a^{2} - 1}}\right]"," ",0,"[-1/2*sqrt(-a^2 + 1)*log(((2*a^2 - 1)*b^2*x^2 + 2*a^4 + 4*(a^3 - a)*b*x + 2*(a*b*x + a^2 - 1)*sqrt(-a^2 + 1)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) - 4*a^2 + 2)/x^2)/(a^2 - 1), arctan((a*b*x + a^2 - 1)*sqrt(a^2 - 1)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)/((a^2 - 1)*b^2*x^2 + a^4 + 2*(a^3 - a)*b*x - 2*a^2 + 1))/sqrt(a^2 - 1)]","A",0
759,1,788,0,2.403939," ","integrate(x^3*(d*x+c)^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{4} c^{4} + 4 \, a^{2} b^{3} c^{3} d + 30 \, a^{3} b^{2} c^{2} d^{2} - 140 \, a^{4} b c d^{3} + 105 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 4 \, a b^{4} c^{3} d + 30 \, a^{2} b^{3} c^{2} d^{2} - 140 \, a^{3} b^{2} c d^{3} + 105 \, a^{4} b d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(16 \, b^{5} d^{4} x^{4} - 3 \, a b^{4} c^{3} d - 13 \, a^{2} b^{3} c^{2} d^{2} + 315 \, a^{3} b^{2} c d^{3} - 315 \, a^{4} b d^{4} + 24 \, {\left(b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{3} + 2 \, {\left(b^{5} c^{2} d^{2} - 22 \, a b^{4} c d^{3} + 21 \, a^{2} b^{3} d^{4}\right)} x^{2} - {\left(3 \, b^{5} c^{3} d + 11 \, a b^{4} c^{2} d^{2} - 119 \, a^{2} b^{3} c d^{3} + 105 \, a^{3} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{256 \, {\left(b^{7} d^{3} x + a b^{6} d^{3}\right)}}, -\frac{3 \, {\left(a b^{4} c^{4} + 4 \, a^{2} b^{3} c^{3} d + 30 \, a^{3} b^{2} c^{2} d^{2} - 140 \, a^{4} b c d^{3} + 105 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 4 \, a b^{4} c^{3} d + 30 \, a^{2} b^{3} c^{2} d^{2} - 140 \, a^{3} b^{2} c d^{3} + 105 \, a^{4} b d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(16 \, b^{5} d^{4} x^{4} - 3 \, a b^{4} c^{3} d - 13 \, a^{2} b^{3} c^{2} d^{2} + 315 \, a^{3} b^{2} c d^{3} - 315 \, a^{4} b d^{4} + 24 \, {\left(b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{3} + 2 \, {\left(b^{5} c^{2} d^{2} - 22 \, a b^{4} c d^{3} + 21 \, a^{2} b^{3} d^{4}\right)} x^{2} - {\left(3 \, b^{5} c^{3} d + 11 \, a b^{4} c^{2} d^{2} - 119 \, a^{2} b^{3} c d^{3} + 105 \, a^{3} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{128 \, {\left(b^{7} d^{3} x + a b^{6} d^{3}\right)}}\right]"," ",0,"[1/256*(3*(a*b^4*c^4 + 4*a^2*b^3*c^3*d + 30*a^3*b^2*c^2*d^2 - 140*a^4*b*c*d^3 + 105*a^5*d^4 + (b^5*c^4 + 4*a*b^4*c^3*d + 30*a^2*b^3*c^2*d^2 - 140*a^3*b^2*c*d^3 + 105*a^4*b*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(16*b^5*d^4*x^4 - 3*a*b^4*c^3*d - 13*a^2*b^3*c^2*d^2 + 315*a^3*b^2*c*d^3 - 315*a^4*b*d^4 + 24*(b^5*c*d^3 - a*b^4*d^4)*x^3 + 2*(b^5*c^2*d^2 - 22*a*b^4*c*d^3 + 21*a^2*b^3*d^4)*x^2 - (3*b^5*c^3*d + 11*a*b^4*c^2*d^2 - 119*a^2*b^3*c*d^3 + 105*a^3*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^7*d^3*x + a*b^6*d^3), -1/128*(3*(a*b^4*c^4 + 4*a^2*b^3*c^3*d + 30*a^3*b^2*c^2*d^2 - 140*a^4*b*c*d^3 + 105*a^5*d^4 + (b^5*c^4 + 4*a*b^4*c^3*d + 30*a^2*b^3*c^2*d^2 - 140*a^3*b^2*c*d^3 + 105*a^4*b*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(16*b^5*d^4*x^4 - 3*a*b^4*c^3*d - 13*a^2*b^3*c^2*d^2 + 315*a^3*b^2*c*d^3 - 315*a^4*b*d^4 + 24*(b^5*c*d^3 - a*b^4*d^4)*x^3 + 2*(b^5*c^2*d^2 - 22*a*b^4*c*d^3 + 21*a^2*b^3*d^4)*x^2 - (3*b^5*c^3*d + 11*a*b^4*c^2*d^2 - 119*a^2*b^3*c*d^3 + 105*a^3*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^7*d^3*x + a*b^6*d^3)]","A",0
760,1,600,0,1.921783," ","integrate(x^2*(d*x+c)^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} c^{3} + 9 \, a^{2} b^{2} c^{2} d - 45 \, a^{3} b c d^{2} + 35 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 9 \, a b^{3} c^{2} d - 45 \, a^{2} b^{2} c d^{2} + 35 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(8 \, b^{4} d^{3} x^{3} + 3 \, a b^{3} c^{2} d - 100 \, a^{2} b^{2} c d^{2} + 105 \, a^{3} b d^{3} + 14 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{2} d - 38 \, a b^{3} c d^{2} + 35 \, a^{2} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b^{6} d^{2} x + a b^{5} d^{2}\right)}}, \frac{3 \, {\left(a b^{3} c^{3} + 9 \, a^{2} b^{2} c^{2} d - 45 \, a^{3} b c d^{2} + 35 \, a^{4} d^{3} + {\left(b^{4} c^{3} + 9 \, a b^{3} c^{2} d - 45 \, a^{2} b^{2} c d^{2} + 35 \, a^{3} b d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, b^{4} d^{3} x^{3} + 3 \, a b^{3} c^{2} d - 100 \, a^{2} b^{2} c d^{2} + 105 \, a^{3} b d^{3} + 14 \, {\left(b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{2} + {\left(3 \, b^{4} c^{2} d - 38 \, a b^{3} c d^{2} + 35 \, a^{2} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{6} d^{2} x + a b^{5} d^{2}\right)}}\right]"," ",0,"[1/96*(3*(a*b^3*c^3 + 9*a^2*b^2*c^2*d - 45*a^3*b*c*d^2 + 35*a^4*d^3 + (b^4*c^3 + 9*a*b^3*c^2*d - 45*a^2*b^2*c*d^2 + 35*a^3*b*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(8*b^4*d^3*x^3 + 3*a*b^3*c^2*d - 100*a^2*b^2*c*d^2 + 105*a^3*b*d^3 + 14*(b^4*c*d^2 - a*b^3*d^3)*x^2 + (3*b^4*c^2*d - 38*a*b^3*c*d^2 + 35*a^2*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^2*x + a*b^5*d^2), 1/48*(3*(a*b^3*c^3 + 9*a^2*b^2*c^2*d - 45*a^3*b*c*d^2 + 35*a^4*d^3 + (b^4*c^3 + 9*a*b^3*c^2*d - 45*a^2*b^2*c*d^2 + 35*a^3*b*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(8*b^4*d^3*x^3 + 3*a*b^3*c^2*d - 100*a^2*b^2*c*d^2 + 105*a^3*b*d^3 + 14*(b^4*c*d^2 - a*b^3*d^3)*x^2 + (3*b^4*c^2*d - 38*a*b^3*c*d^2 + 35*a^2*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d^2*x + a*b^5*d^2)]","A",0
761,1,434,0,1.586817," ","integrate(x*(d*x+c)^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{3} d^{2} x^{2} + 13 \, a b^{2} c d - 15 \, a^{2} b d^{2} + 5 \, {\left(b^{3} c d - a b^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(b^{5} d x + a b^{4} d\right)}}, -\frac{3 \, {\left(a b^{2} c^{2} - 6 \, a^{2} b c d + 5 \, a^{3} d^{2} + {\left(b^{3} c^{2} - 6 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{3} d^{2} x^{2} + 13 \, a b^{2} c d - 15 \, a^{2} b d^{2} + 5 \, {\left(b^{3} c d - a b^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(b^{5} d x + a b^{4} d\right)}}\right]"," ",0,"[1/16*(3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^3*d^2*x^2 + 13*a*b^2*c*d - 15*a^2*b*d^2 + 5*(b^3*c*d - a*b^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d*x + a*b^4*d), -1/8*(3*(a*b^2*c^2 - 6*a^2*b*c*d + 5*a^3*d^2 + (b^3*c^2 - 6*a*b^2*c*d + 5*a^2*b*d^2)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(2*b^3*d^2*x^2 + 13*a*b^2*c*d - 15*a^2*b*d^2 + 5*(b^3*c*d - a*b^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*d*x + a*b^4*d)]","A",0
762,1,311,0,1.497030," ","integrate((d*x+c)^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(b d x - 2 \, b c + 3 \, a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(b^{3} x + a b^{2}\right)}}, -\frac{3 \, {\left(a b c - a^{2} d + {\left(b^{2} c - a b d\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(b d x - 2 \, b c + 3 \, a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{3} x + a b^{2}\right)}}\right]"," ",0,"[-1/4*(3*(a*b*c - a^2*d + (b^2*c - a*b*d)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(b*d*x - 2*b*c + 3*a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*x + a*b^2), -1/2*(3*(a*b*c - a^2*d + (b^2*c - a*b*d)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(b*d*x - 2*b*c + 3*a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(b^3*x + a*b^2)]","A",0
763,1,956,0,2.682168," ","integrate((d*x+c)^(3/2)/x/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b d x + a^{2} d\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + {\left(b^{2} c x + a b c\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{2} x + a^{2} b\right)}}, -\frac{2 \, {\left(a b d x + a^{2} d\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - {\left(b^{2} c x + a b c\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{2} x + a^{2} b\right)}}, \frac{2 \, {\left(b^{2} c x + a b c\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + {\left(a b d x + a^{2} d\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{2} x + a^{2} b\right)}}, \frac{{\left(b^{2} c x + a b c\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(a b d x + a^{2} d\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(b c - a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{a b^{2} x + a^{2} b}\right]"," ",0,"[1/2*((a*b*d*x + a^2*d)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + (b^2*c*x + a*b*c)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*x + a^2*b), -1/2*(2*(a*b*d*x + a^2*d)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - (b^2*c*x + a*b*c)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*x + a^2*b), 1/2*(2*(b^2*c*x + a*b*c)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + (a*b*d*x + a^2*d)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*x + a^2*b), ((b^2*c*x + a*b*c)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (a*b*d*x + a^2*d)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(b*c - a*d)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^2*x + a^2*b)]","B",0
764,1,341,0,1.752315," ","integrate((d*x+c)^(3/2)/x^2/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{2} c - a b d\right)} x^{2} + {\left(a b c - a^{2} d\right)} x\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(a c + {\left(3 \, b c - 2 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a^{2} b x^{2} + a^{3} x\right)}}, -\frac{3 \, {\left({\left(b^{2} c - a b d\right)} x^{2} + {\left(a b c - a^{2} d\right)} x\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 2 \, {\left(a c + {\left(3 \, b c - 2 \, a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a^{2} b x^{2} + a^{3} x\right)}}\right]"," ",0,"[-1/4*(3*((b^2*c - a*b*d)*x^2 + (a*b*c - a^2*d)*x)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(a*c + (3*b*c - 2*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b*x^2 + a^3*x), -1/2*(3*((b^2*c - a*b*d)*x^2 + (a*b*c - a^2*d)*x)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 2*(a*c + (3*b*c - 2*a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b*x^2 + a^3*x)]","A",0
765,1,474,0,2.303488," ","integrate((d*x+c)^(3/2)/x^3/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{3} c^{2} - {\left(15 \, a b^{2} c^{2} - 13 \, a^{2} b c d\right)} x^{2} - 5 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(a^{4} b c x^{3} + a^{5} c x^{2}\right)}}, \frac{3 \, {\left({\left(5 \, b^{3} c^{2} - 6 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(5 \, a b^{2} c^{2} - 6 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} c^{2} - {\left(15 \, a b^{2} c^{2} - 13 \, a^{2} b c d\right)} x^{2} - 5 \, {\left(a^{2} b c^{2} - a^{3} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(a^{4} b c x^{3} + a^{5} c x^{2}\right)}}\right]"," ",0,"[1/16*(3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^3 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^3*c^2 - (15*a*b^2*c^2 - 13*a^2*b*c*d)*x^2 - 5*(a^2*b*c^2 - a^3*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*b*c*x^3 + a^5*c*x^2), 1/8*(3*((5*b^3*c^2 - 6*a*b^2*c*d + a^2*b*d^2)*x^3 + (5*a*b^2*c^2 - 6*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^3*c^2 - (15*a*b^2*c^2 - 13*a^2*b*c*d)*x^2 - 5*(a^2*b*c^2 - a^3*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*b*c*x^3 + a^5*c*x^2)]","A",0
766,1,638,0,5.789598," ","integrate((d*x+c)^(3/2)/x^4/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(35 \, b^{4} c^{3} - 45 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{4} + {\left(35 \, a b^{3} c^{3} - 45 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(8 \, a^{4} c^{3} + {\left(105 \, a b^{3} c^{3} - 100 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{3} - 38 \, a^{3} b c^{2} d + 3 \, a^{4} c d^{2}\right)} x^{2} - 14 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a^{5} b c^{2} x^{4} + a^{6} c^{2} x^{3}\right)}}, -\frac{3 \, {\left({\left(35 \, b^{4} c^{3} - 45 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} + a^{3} b d^{3}\right)} x^{4} + {\left(35 \, a b^{3} c^{3} - 45 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{4} c^{3} + {\left(105 \, a b^{3} c^{3} - 100 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{3} - 38 \, a^{3} b c^{2} d + 3 \, a^{4} c d^{2}\right)} x^{2} - 14 \, {\left(a^{3} b c^{3} - a^{4} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{5} b c^{2} x^{4} + a^{6} c^{2} x^{3}\right)}}\right]"," ",0,"[1/96*(3*((35*b^4*c^3 - 45*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 + a^3*b*d^3)*x^4 + (35*a*b^3*c^3 - 45*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 + a^4*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(8*a^4*c^3 + (105*a*b^3*c^3 - 100*a^2*b^2*c^2*d + 3*a^3*b*c*d^2)*x^3 + (35*a^2*b^2*c^3 - 38*a^3*b*c^2*d + 3*a^4*c*d^2)*x^2 - 14*(a^3*b*c^3 - a^4*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b*c^2*x^4 + a^6*c^2*x^3), -1/48*(3*((35*b^4*c^3 - 45*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 + a^3*b*d^3)*x^4 + (35*a*b^3*c^3 - 45*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 + a^4*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^4*c^3 + (105*a*b^3*c^3 - 100*a^2*b^2*c^2*d + 3*a^3*b*c*d^2)*x^3 + (35*a^2*b^2*c^3 - 38*a^3*b*c^2*d + 3*a^4*c*d^2)*x^2 - 14*(a^3*b*c^3 - a^4*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b*c^2*x^4 + a^6*c^2*x^3)]","A",0
767,1,1008,0,2.712200," ","integrate(x^3*(d*x+c)^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d + 50 \, a^{3} b^{3} c^{3} d^{2} - 350 \, a^{4} b^{2} c^{2} d^{3} + 525 \, a^{5} b c d^{4} - 231 \, a^{6} d^{5} + {\left(b^{6} c^{5} + 5 \, a b^{5} c^{4} d + 50 \, a^{2} b^{4} c^{3} d^{2} - 350 \, a^{3} b^{3} c^{2} d^{3} + 525 \, a^{4} b^{2} c d^{4} - 231 \, a^{5} b d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(128 \, b^{6} d^{5} x^{5} - 15 \, a b^{5} c^{4} d - 80 \, a^{2} b^{4} c^{3} d^{2} + 3318 \, a^{3} b^{3} c^{2} d^{3} - 6720 \, a^{4} b^{2} c d^{4} + 3465 \, a^{5} b d^{5} + 16 \, {\left(21 \, b^{6} c d^{4} - 11 \, a b^{5} d^{5}\right)} x^{4} + 8 \, {\left(31 \, b^{6} c^{2} d^{3} - 64 \, a b^{5} c d^{4} + 33 \, a^{2} b^{4} d^{5}\right)} x^{3} + 2 \, {\left(5 \, b^{6} c^{3} d^{2} - 233 \, a b^{5} c^{2} d^{3} + 459 \, a^{2} b^{4} c d^{4} - 231 \, a^{3} b^{3} d^{5}\right)} x^{2} - {\left(15 \, b^{6} c^{4} d + 70 \, a b^{5} c^{3} d^{2} - 1324 \, a^{2} b^{4} c^{2} d^{3} + 2394 \, a^{3} b^{3} c d^{4} - 1155 \, a^{4} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2560 \, {\left(b^{8} d^{3} x + a b^{7} d^{3}\right)}}, -\frac{15 \, {\left(a b^{5} c^{5} + 5 \, a^{2} b^{4} c^{4} d + 50 \, a^{3} b^{3} c^{3} d^{2} - 350 \, a^{4} b^{2} c^{2} d^{3} + 525 \, a^{5} b c d^{4} - 231 \, a^{6} d^{5} + {\left(b^{6} c^{5} + 5 \, a b^{5} c^{4} d + 50 \, a^{2} b^{4} c^{3} d^{2} - 350 \, a^{3} b^{3} c^{2} d^{3} + 525 \, a^{4} b^{2} c d^{4} - 231 \, a^{5} b d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(128 \, b^{6} d^{5} x^{5} - 15 \, a b^{5} c^{4} d - 80 \, a^{2} b^{4} c^{3} d^{2} + 3318 \, a^{3} b^{3} c^{2} d^{3} - 6720 \, a^{4} b^{2} c d^{4} + 3465 \, a^{5} b d^{5} + 16 \, {\left(21 \, b^{6} c d^{4} - 11 \, a b^{5} d^{5}\right)} x^{4} + 8 \, {\left(31 \, b^{6} c^{2} d^{3} - 64 \, a b^{5} c d^{4} + 33 \, a^{2} b^{4} d^{5}\right)} x^{3} + 2 \, {\left(5 \, b^{6} c^{3} d^{2} - 233 \, a b^{5} c^{2} d^{3} + 459 \, a^{2} b^{4} c d^{4} - 231 \, a^{3} b^{3} d^{5}\right)} x^{2} - {\left(15 \, b^{6} c^{4} d + 70 \, a b^{5} c^{3} d^{2} - 1324 \, a^{2} b^{4} c^{2} d^{3} + 2394 \, a^{3} b^{3} c d^{4} - 1155 \, a^{4} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{1280 \, {\left(b^{8} d^{3} x + a b^{7} d^{3}\right)}}\right]"," ",0,"[-1/2560*(15*(a*b^5*c^5 + 5*a^2*b^4*c^4*d + 50*a^3*b^3*c^3*d^2 - 350*a^4*b^2*c^2*d^3 + 525*a^5*b*c*d^4 - 231*a^6*d^5 + (b^6*c^5 + 5*a*b^5*c^4*d + 50*a^2*b^4*c^3*d^2 - 350*a^3*b^3*c^2*d^3 + 525*a^4*b^2*c*d^4 - 231*a^5*b*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(128*b^6*d^5*x^5 - 15*a*b^5*c^4*d - 80*a^2*b^4*c^3*d^2 + 3318*a^3*b^3*c^2*d^3 - 6720*a^4*b^2*c*d^4 + 3465*a^5*b*d^5 + 16*(21*b^6*c*d^4 - 11*a*b^5*d^5)*x^4 + 8*(31*b^6*c^2*d^3 - 64*a*b^5*c*d^4 + 33*a^2*b^4*d^5)*x^3 + 2*(5*b^6*c^3*d^2 - 233*a*b^5*c^2*d^3 + 459*a^2*b^4*c*d^4 - 231*a^3*b^3*d^5)*x^2 - (15*b^6*c^4*d + 70*a*b^5*c^3*d^2 - 1324*a^2*b^4*c^2*d^3 + 2394*a^3*b^3*c*d^4 - 1155*a^4*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^8*d^3*x + a*b^7*d^3), -1/1280*(15*(a*b^5*c^5 + 5*a^2*b^4*c^4*d + 50*a^3*b^3*c^3*d^2 - 350*a^4*b^2*c^2*d^3 + 525*a^5*b*c*d^4 - 231*a^6*d^5 + (b^6*c^5 + 5*a*b^5*c^4*d + 50*a^2*b^4*c^3*d^2 - 350*a^3*b^3*c^2*d^3 + 525*a^4*b^2*c*d^4 - 231*a^5*b*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(128*b^6*d^5*x^5 - 15*a*b^5*c^4*d - 80*a^2*b^4*c^3*d^2 + 3318*a^3*b^3*c^2*d^3 - 6720*a^4*b^2*c*d^4 + 3465*a^5*b*d^5 + 16*(21*b^6*c*d^4 - 11*a*b^5*d^5)*x^4 + 8*(31*b^6*c^2*d^3 - 64*a*b^5*c*d^4 + 33*a^2*b^4*d^5)*x^3 + 2*(5*b^6*c^3*d^2 - 233*a*b^5*c^2*d^3 + 459*a^2*b^4*c*d^4 - 231*a^3*b^3*d^5)*x^2 - (15*b^6*c^4*d + 70*a*b^5*c^3*d^2 - 1324*a^2*b^4*c^2*d^3 + 2394*a^3*b^3*c*d^4 - 1155*a^4*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^8*d^3*x + a*b^7*d^3)]","A",0
768,1,790,0,2.053064," ","integrate(x^2*(d*x+c)^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b^{4} c^{4} + 12 \, a^{2} b^{3} c^{3} d - 90 \, a^{3} b^{2} c^{2} d^{2} + 140 \, a^{4} b c d^{3} - 63 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 12 \, a b^{4} c^{3} d - 90 \, a^{2} b^{3} c^{2} d^{2} + 140 \, a^{3} b^{2} c d^{3} - 63 \, a^{4} b d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{5} d^{4} x^{4} + 15 \, a b^{4} c^{3} d - 839 \, a^{2} b^{3} c^{2} d^{2} + 1785 \, a^{3} b^{2} c d^{3} - 945 \, a^{4} b d^{4} + 8 \, {\left(17 \, b^{5} c d^{3} - 9 \, a b^{4} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{5} c^{2} d^{2} - 122 \, a b^{4} c d^{3} + 63 \, a^{2} b^{3} d^{4}\right)} x^{2} + {\left(15 \, b^{5} c^{3} d - 337 \, a b^{4} c^{2} d^{2} + 637 \, a^{2} b^{3} c d^{3} - 315 \, a^{3} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(b^{7} d^{2} x + a b^{6} d^{2}\right)}}, \frac{15 \, {\left(a b^{4} c^{4} + 12 \, a^{2} b^{3} c^{3} d - 90 \, a^{3} b^{2} c^{2} d^{2} + 140 \, a^{4} b c d^{3} - 63 \, a^{5} d^{4} + {\left(b^{5} c^{4} + 12 \, a b^{4} c^{3} d - 90 \, a^{2} b^{3} c^{2} d^{2} + 140 \, a^{3} b^{2} c d^{3} - 63 \, a^{4} b d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{5} d^{4} x^{4} + 15 \, a b^{4} c^{3} d - 839 \, a^{2} b^{3} c^{2} d^{2} + 1785 \, a^{3} b^{2} c d^{3} - 945 \, a^{4} b d^{4} + 8 \, {\left(17 \, b^{5} c d^{3} - 9 \, a b^{4} d^{4}\right)} x^{3} + 2 \, {\left(59 \, b^{5} c^{2} d^{2} - 122 \, a b^{4} c d^{3} + 63 \, a^{2} b^{3} d^{4}\right)} x^{2} + {\left(15 \, b^{5} c^{3} d - 337 \, a b^{4} c^{2} d^{2} + 637 \, a^{2} b^{3} c d^{3} - 315 \, a^{3} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(b^{7} d^{2} x + a b^{6} d^{2}\right)}}\right]"," ",0,"[-1/768*(15*(a*b^4*c^4 + 12*a^2*b^3*c^3*d - 90*a^3*b^2*c^2*d^2 + 140*a^4*b*c*d^3 - 63*a^5*d^4 + (b^5*c^4 + 12*a*b^4*c^3*d - 90*a^2*b^3*c^2*d^2 + 140*a^3*b^2*c*d^3 - 63*a^4*b*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^5*d^4*x^4 + 15*a*b^4*c^3*d - 839*a^2*b^3*c^2*d^2 + 1785*a^3*b^2*c*d^3 - 945*a^4*b*d^4 + 8*(17*b^5*c*d^3 - 9*a*b^4*d^4)*x^3 + 2*(59*b^5*c^2*d^2 - 122*a*b^4*c*d^3 + 63*a^2*b^3*d^4)*x^2 + (15*b^5*c^3*d - 337*a*b^4*c^2*d^2 + 637*a^2*b^3*c*d^3 - 315*a^3*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^7*d^2*x + a*b^6*d^2), 1/384*(15*(a*b^4*c^4 + 12*a^2*b^3*c^3*d - 90*a^3*b^2*c^2*d^2 + 140*a^4*b*c*d^3 - 63*a^5*d^4 + (b^5*c^4 + 12*a*b^4*c^3*d - 90*a^2*b^3*c^2*d^2 + 140*a^3*b^2*c*d^3 - 63*a^4*b*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^5*d^4*x^4 + 15*a*b^4*c^3*d - 839*a^2*b^3*c^2*d^2 + 1785*a^3*b^2*c*d^3 - 945*a^4*b*d^4 + 8*(17*b^5*c*d^3 - 9*a*b^4*d^4)*x^3 + 2*(59*b^5*c^2*d^2 - 122*a*b^4*c*d^3 + 63*a^2*b^3*d^4)*x^2 + (15*b^5*c^3*d - 337*a*b^4*c^2*d^2 + 637*a^2*b^3*c*d^3 - 315*a^3*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^7*d^2*x + a*b^6*d^2)]","A",0
769,1,594,0,1.469195," ","integrate(x*(d*x+c)^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 15 \, a^{3} b c d^{2} - 7 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 15 \, a^{2} b^{2} c d^{2} - 7 \, a^{3} b d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{4} d^{3} x^{3} + 81 \, a b^{3} c^{2} d - 190 \, a^{2} b^{2} c d^{2} + 105 \, a^{3} b d^{3} + 2 \, {\left(13 \, b^{4} c d^{2} - 7 \, a b^{3} d^{3}\right)} x^{2} + {\left(33 \, b^{4} c^{2} d - 68 \, a b^{3} c d^{2} + 35 \, a^{2} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b^{6} d x + a b^{5} d\right)}}, -\frac{15 \, {\left(a b^{3} c^{3} - 9 \, a^{2} b^{2} c^{2} d + 15 \, a^{3} b c d^{2} - 7 \, a^{4} d^{3} + {\left(b^{4} c^{3} - 9 \, a b^{3} c^{2} d + 15 \, a^{2} b^{2} c d^{2} - 7 \, a^{3} b d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{4} d^{3} x^{3} + 81 \, a b^{3} c^{2} d - 190 \, a^{2} b^{2} c d^{2} + 105 \, a^{3} b d^{3} + 2 \, {\left(13 \, b^{4} c d^{2} - 7 \, a b^{3} d^{3}\right)} x^{2} + {\left(33 \, b^{4} c^{2} d - 68 \, a b^{3} c d^{2} + 35 \, a^{2} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{6} d x + a b^{5} d\right)}}\right]"," ",0,"[-1/96*(15*(a*b^3*c^3 - 9*a^2*b^2*c^2*d + 15*a^3*b*c*d^2 - 7*a^4*d^3 + (b^4*c^3 - 9*a*b^3*c^2*d + 15*a^2*b^2*c*d^2 - 7*a^3*b*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^4*d^3*x^3 + 81*a*b^3*c^2*d - 190*a^2*b^2*c*d^2 + 105*a^3*b*d^3 + 2*(13*b^4*c*d^2 - 7*a*b^3*d^3)*x^2 + (33*b^4*c^2*d - 68*a*b^3*c*d^2 + 35*a^2*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d*x + a*b^5*d), -1/48*(15*(a*b^3*c^3 - 9*a^2*b^2*c^2*d + 15*a^3*b*c*d^2 - 7*a^4*d^3 + (b^4*c^3 - 9*a*b^3*c^2*d + 15*a^2*b^2*c*d^2 - 7*a^3*b*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^4*d^3*x^3 + 81*a*b^3*c^2*d - 190*a^2*b^2*c*d^2 + 105*a^3*b*d^3 + 2*(13*b^4*c*d^2 - 7*a*b^3*d^3)*x^2 + (33*b^4*c^2*d - 68*a*b^3*c*d^2 + 35*a^2*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*d*x + a*b^5*d)]","A",0
770,1,439,0,1.497718," ","integrate((d*x+c)^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(2 \, b^{2} d^{2} x^{2} - 8 \, b^{2} c^{2} + 25 \, a b c d - 15 \, a^{2} d^{2} + {\left(9 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{15 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b^{2} d^{2} x^{2} - 8 \, b^{2} c^{2} + 25 \, a b c d - 15 \, a^{2} d^{2} + {\left(9 \, b^{2} c d - 5 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[1/16*(15*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(2*b^2*d^2*x^2 - 8*b^2*c^2 + 25*a*b*c*d - 15*a^2*d^2 + (9*b^2*c*d - 5*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*x + a*b^3), -1/8*(15*(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(2*b^2*d^2*x^2 - 8*b^2*c^2 + 25*a*b*c*d - 15*a^2*d^2 + (9*b^2*c*d - 5*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^4*x + a*b^3)]","A",0
771,1,1183,0,6.671277," ","integrate((d*x+c)^(5/2)/x/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(5 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 2 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a b d^{2} x + 2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a b^{3} x + a^{2} b^{2}\right)}}, -\frac{{\left(5 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 2 \, {\left(a b d^{2} x + 2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{3} x + a^{2} b^{2}\right)}}, \frac{4 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(5 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(a b d^{2} x + 2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a b^{3} x + a^{2} b^{2}\right)}}, \frac{2 \, {\left(b^{3} c^{2} x + a b^{2} c^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(5 \, a^{2} b c d - 3 \, a^{3} d^{2} + {\left(5 \, a b^{2} c d - 3 \, a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(a b d^{2} x + 2 \, b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{3} x + a^{2} b^{2}\right)}}\right]"," ",0,"[-1/4*((5*a^2*b*c*d - 3*a^3*d^2 + (5*a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 2*(b^3*c^2*x + a*b^2*c^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a*b*d^2*x + 2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^3*x + a^2*b^2), -1/2*((5*a^2*b*c*d - 3*a^3*d^2 + (5*a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - (b^3*c^2*x + a*b^2*c^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 2*(a*b*d^2*x + 2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^3*x + a^2*b^2), 1/4*(4*(b^3*c^2*x + a*b^2*c^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (5*a^2*b*c*d - 3*a^3*d^2 + (5*a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(a*b*d^2*x + 2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^3*x + a^2*b^2), 1/2*(2*(b^3*c^2*x + a*b^2*c^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (5*a^2*b*c*d - 3*a^3*d^2 + (5*a*b^2*c*d - 3*a^2*b*d^2)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(a*b*d^2*x + 2*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^3*x + a^2*b^2)]","B",0
772,1,1234,0,6.154101," ","integrate((d*x+c)^(5/2)/x^2/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a b c^{2} + {\left(3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b x\right)}}, -\frac{4 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + {\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(a b c^{2} + {\left(3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a^{2} b^{2} x^{2} + a^{3} b x\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 2 \, {\left(a b c^{2} + {\left(3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b x\right)}}, -\frac{{\left({\left(3 \, b^{3} c^{2} - 5 \, a b^{2} c d\right)} x^{2} + {\left(3 \, a b^{2} c^{2} - 5 \, a^{2} b c d\right)} x\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 2 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(a b c^{2} + {\left(3 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a^{2} b^{2} x^{2} + a^{3} b x\right)}}\right]"," ",0,"[1/4*(2*(a^2*b*d^2*x^2 + a^3*d^2*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - ((3*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a*b*c^2 + (3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^2*x^2 + a^3*b*x), -1/4*(4*(a^2*b*d^2*x^2 + a^3*d^2*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + ((3*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(a*b*c^2 + (3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^2*x^2 + a^3*b*x), -1/2*(((3*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - (a^2*b*d^2*x^2 + a^3*d^2*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 2*(a*b*c^2 + (3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^2*x^2 + a^3*b*x), -1/2*(((3*b^3*c^2 - 5*a*b^2*c*d)*x^2 + (3*a*b^2*c^2 - 5*a^2*b*c*d)*x)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 2*(a^2*b*d^2*x^2 + a^3*d^2*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(a*b*c^2 + (3*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^2*x^2 + a^3*b*x)]","B",0
773,1,481,0,2.442111," ","integrate((d*x+c)^(5/2)/x^3/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{2} c^{2} - {\left(15 \, b^{2} c^{2} - 25 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{2} - {\left(5 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}, \frac{15 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x^{3} + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{2} c^{2} - {\left(15 \, b^{2} c^{2} - 25 \, a b c d + 8 \, a^{2} d^{2}\right)} x^{2} - {\left(5 \, a b c^{2} - 9 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}\right]"," ",0,"[1/16*(15*((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3 + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^2*c^2 - (15*b^2*c^2 - 25*a*b*c*d + 8*a^2*d^2)*x^2 - (5*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b*x^3 + a^4*x^2), 1/8*(15*((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x^3 + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*x^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 2*(2*a^2*c^2 - (15*b^2*c^2 - 25*a*b*c*d + 8*a^2*d^2)*x^2 - (5*a*b*c^2 - 9*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b*x^3 + a^4*x^2)]","A",0
774,1,636,0,5.954708," ","integrate((d*x+c)^(5/2)/x^4/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(7 \, b^{4} c^{3} - 15 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} + {\left(7 \, a b^{3} c^{3} - 15 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{4} c^{3} + {\left(105 \, a b^{3} c^{3} - 190 \, a^{2} b^{2} c^{2} d + 81 \, a^{3} b c d^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{3} - 68 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}, -\frac{15 \, {\left({\left(7 \, b^{4} c^{3} - 15 \, a b^{3} c^{2} d + 9 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x^{4} + {\left(7 \, a b^{3} c^{3} - 15 \, a^{2} b^{2} c^{2} d + 9 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{4} c^{3} + {\left(105 \, a b^{3} c^{3} - 190 \, a^{2} b^{2} c^{2} d + 81 \, a^{3} b c d^{2}\right)} x^{3} + {\left(35 \, a^{2} b^{2} c^{3} - 68 \, a^{3} b c^{2} d + 33 \, a^{4} c d^{2}\right)} x^{2} - 2 \, {\left(7 \, a^{3} b c^{3} - 13 \, a^{4} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{5} b c x^{4} + a^{6} c x^{3}\right)}}\right]"," ",0,"[-1/96*(15*((7*b^4*c^3 - 15*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4 + (7*a*b^3*c^3 - 15*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 - a^4*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^4*c^3 + (105*a*b^3*c^3 - 190*a^2*b^2*c^2*d + 81*a^3*b*c*d^2)*x^3 + (35*a^2*b^2*c^3 - 68*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(7*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3), -1/48*(15*((7*b^4*c^3 - 15*a*b^3*c^2*d + 9*a^2*b^2*c*d^2 - a^3*b*d^3)*x^4 + (7*a*b^3*c^3 - 15*a^2*b^2*c^2*d + 9*a^3*b*c*d^2 - a^4*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^4*c^3 + (105*a*b^3*c^3 - 190*a^2*b^2*c^2*d + 81*a^3*b*c*d^2)*x^3 + (35*a^2*b^2*c^3 - 68*a^3*b*c^2*d + 33*a^4*c*d^2)*x^2 - 2*(7*a^3*b*c^3 - 13*a^4*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b*c*x^4 + a^6*c*x^3)]","A",0
775,1,836,0,13.616876," ","integrate((d*x+c)^(5/2)/x^5/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(63 \, b^{5} c^{4} - 140 \, a b^{4} c^{3} d + 90 \, a^{2} b^{3} c^{2} d^{2} - 12 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{5} + {\left(63 \, a b^{4} c^{4} - 140 \, a^{2} b^{3} c^{3} d + 90 \, a^{3} b^{2} c^{2} d^{2} - 12 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{4}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{5} c^{4} - {\left(945 \, a b^{4} c^{4} - 1785 \, a^{2} b^{3} c^{3} d + 839 \, a^{3} b^{2} c^{2} d^{2} - 15 \, a^{4} b c d^{3}\right)} x^{4} - {\left(315 \, a^{2} b^{3} c^{4} - 637 \, a^{3} b^{2} c^{3} d + 337 \, a^{4} b c^{2} d^{2} - 15 \, a^{5} c d^{3}\right)} x^{3} + 2 \, {\left(63 \, a^{3} b^{2} c^{4} - 122 \, a^{4} b c^{3} d + 59 \, a^{5} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(9 \, a^{4} b c^{4} - 17 \, a^{5} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(a^{6} b c^{2} x^{5} + a^{7} c^{2} x^{4}\right)}}, \frac{15 \, {\left({\left(63 \, b^{5} c^{4} - 140 \, a b^{4} c^{3} d + 90 \, a^{2} b^{3} c^{2} d^{2} - 12 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x^{5} + {\left(63 \, a b^{4} c^{4} - 140 \, a^{2} b^{3} c^{3} d + 90 \, a^{3} b^{2} c^{2} d^{2} - 12 \, a^{4} b c d^{3} - a^{5} d^{4}\right)} x^{4}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{5} c^{4} - {\left(945 \, a b^{4} c^{4} - 1785 \, a^{2} b^{3} c^{3} d + 839 \, a^{3} b^{2} c^{2} d^{2} - 15 \, a^{4} b c d^{3}\right)} x^{4} - {\left(315 \, a^{2} b^{3} c^{4} - 637 \, a^{3} b^{2} c^{3} d + 337 \, a^{4} b c^{2} d^{2} - 15 \, a^{5} c d^{3}\right)} x^{3} + 2 \, {\left(63 \, a^{3} b^{2} c^{4} - 122 \, a^{4} b c^{3} d + 59 \, a^{5} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(9 \, a^{4} b c^{4} - 17 \, a^{5} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(a^{6} b c^{2} x^{5} + a^{7} c^{2} x^{4}\right)}}\right]"," ",0,"[-1/768*(15*((63*b^5*c^4 - 140*a*b^4*c^3*d + 90*a^2*b^3*c^2*d^2 - 12*a^3*b^2*c*d^3 - a^4*b*d^4)*x^5 + (63*a*b^4*c^4 - 140*a^2*b^3*c^3*d + 90*a^3*b^2*c^2*d^2 - 12*a^4*b*c*d^3 - a^5*d^4)*x^4)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^5*c^4 - (945*a*b^4*c^4 - 1785*a^2*b^3*c^3*d + 839*a^3*b^2*c^2*d^2 - 15*a^4*b*c*d^3)*x^4 - (315*a^2*b^3*c^4 - 637*a^3*b^2*c^3*d + 337*a^4*b*c^2*d^2 - 15*a^5*c*d^3)*x^3 + 2*(63*a^3*b^2*c^4 - 122*a^4*b*c^3*d + 59*a^5*c^2*d^2)*x^2 - 8*(9*a^4*b*c^4 - 17*a^5*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*b*c^2*x^5 + a^7*c^2*x^4), 1/384*(15*((63*b^5*c^4 - 140*a*b^4*c^3*d + 90*a^2*b^3*c^2*d^2 - 12*a^3*b^2*c*d^3 - a^4*b*d^4)*x^5 + (63*a*b^4*c^4 - 140*a^2*b^3*c^3*d + 90*a^3*b^2*c^2*d^2 - 12*a^4*b*c*d^3 - a^5*d^4)*x^4)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^5*c^4 - (945*a*b^4*c^4 - 1785*a^2*b^3*c^3*d + 839*a^3*b^2*c^2*d^2 - 15*a^4*b*c*d^3)*x^4 - (315*a^2*b^3*c^4 - 637*a^3*b^2*c^3*d + 337*a^4*b*c^2*d^2 - 15*a^5*c*d^3)*x^3 + 2*(63*a^3*b^2*c^4 - 122*a^4*b*c^3*d + 59*a^5*c^2*d^2)*x^2 - 8*(9*a^4*b*c^4 - 17*a^5*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*b*c^2*x^5 + a^7*c^2*x^4)]","A",0
776,1,1200,0,3.033251," ","integrate(x^4/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, a b^{4} c^{5} - 4 \, a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} - 4 \, a^{4} b c^{2} d^{3} + 5 \, a^{5} c d^{4} + {\left(5 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} - 4 \, a^{3} b^{2} c d^{4} + 5 \, a^{4} b d^{5}\right)} x^{2} + {\left(5 \, b^{5} c^{5} + a b^{4} c^{4} d - 6 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} + 5 \, a^{5} d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(15 \, a b^{4} c^{4} d - 7 \, a^{2} b^{3} c^{3} d^{2} - 7 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 2 \, {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{3} + 5 \, {\left(b^{5} c^{3} d^{2} - a b^{4} c^{2} d^{3} - a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(15 \, b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} - 10 \, a^{2} b^{3} c^{2} d^{3} - 2 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left(a b^{6} c^{3} d^{4} - 2 \, a^{2} b^{5} c^{2} d^{5} + a^{3} b^{4} c d^{6} + {\left(b^{7} c^{2} d^{5} - 2 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right)} x^{2} + {\left(b^{7} c^{3} d^{4} - a b^{6} c^{2} d^{5} - a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right)} x\right)}}, -\frac{3 \, {\left(5 \, a b^{4} c^{5} - 4 \, a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} - 4 \, a^{4} b c^{2} d^{3} + 5 \, a^{5} c d^{4} + {\left(5 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} - 4 \, a^{3} b^{2} c d^{4} + 5 \, a^{4} b d^{5}\right)} x^{2} + {\left(5 \, b^{5} c^{5} + a b^{4} c^{4} d - 6 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} + 5 \, a^{5} d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, a b^{4} c^{4} d - 7 \, a^{2} b^{3} c^{3} d^{2} - 7 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4} - 2 \, {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{3} + 5 \, {\left(b^{5} c^{3} d^{2} - a b^{4} c^{2} d^{3} - a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(15 \, b^{5} c^{4} d - 2 \, a b^{4} c^{3} d^{2} - 10 \, a^{2} b^{3} c^{2} d^{3} - 2 \, a^{3} b^{2} c d^{4} + 15 \, a^{4} b d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left(a b^{6} c^{3} d^{4} - 2 \, a^{2} b^{5} c^{2} d^{5} + a^{3} b^{4} c d^{6} + {\left(b^{7} c^{2} d^{5} - 2 \, a b^{6} c d^{6} + a^{2} b^{5} d^{7}\right)} x^{2} + {\left(b^{7} c^{3} d^{4} - a b^{6} c^{2} d^{5} - a^{2} b^{5} c d^{6} + a^{3} b^{4} d^{7}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(5*a*b^4*c^5 - 4*a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 - 4*a^4*b*c^2*d^3 + 5*a^5*c*d^4 + (5*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 - 4*a^3*b^2*c*d^4 + 5*a^4*b*d^5)*x^2 + (5*b^5*c^5 + a*b^4*c^4*d - 6*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 + 5*a^5*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(15*a*b^4*c^4*d - 7*a^2*b^3*c^3*d^2 - 7*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 2*(b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^3 + 5*(b^5*c^3*d^2 - a*b^4*c^2*d^3 - a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (15*b^5*c^4*d - 2*a*b^4*c^3*d^2 - 10*a^2*b^3*c^2*d^3 - 2*a^3*b^2*c*d^4 + 15*a^4*b*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^6*c^3*d^4 - 2*a^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + (b^7*c^2*d^5 - 2*a*b^6*c*d^6 + a^2*b^5*d^7)*x^2 + (b^7*c^3*d^4 - a*b^6*c^2*d^5 - a^2*b^5*c*d^6 + a^3*b^4*d^7)*x), -1/8*(3*(5*a*b^4*c^5 - 4*a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 - 4*a^4*b*c^2*d^3 + 5*a^5*c*d^4 + (5*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 - 4*a^3*b^2*c*d^4 + 5*a^4*b*d^5)*x^2 + (5*b^5*c^5 + a*b^4*c^4*d - 6*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 + 5*a^5*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*a*b^4*c^4*d - 7*a^2*b^3*c^3*d^2 - 7*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4 - 2*(b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^3 + 5*(b^5*c^3*d^2 - a*b^4*c^2*d^3 - a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (15*b^5*c^4*d - 2*a*b^4*c^3*d^2 - 10*a^2*b^3*c^2*d^3 - 2*a^3*b^2*c*d^4 + 15*a^4*b*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^6*c^3*d^4 - 2*a^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + (b^7*c^2*d^5 - 2*a*b^6*c*d^6 + a^2*b^5*d^7)*x^2 + (b^7*c^3*d^4 - a*b^6*c^2*d^5 - a^2*b^5*c*d^6 + a^3*b^4*d^7)*x)]","B",0
777,1,910,0,1.412621," ","integrate(x^3/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3} + {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{4} d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left(a b^{5} c^{3} d^{3} - 2 \, a^{2} b^{4} c^{2} d^{4} + a^{3} b^{3} c d^{5} + {\left(b^{6} c^{2} d^{4} - 2 \, a b^{5} c d^{5} + a^{2} b^{4} d^{6}\right)} x^{2} + {\left(b^{6} c^{3} d^{3} - a b^{5} c^{2} d^{4} - a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6}\right)} x\right)}}, \frac{3 \, {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3} + {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{2} + {\left(b^{4} c^{4} - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{4} d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + 3 \, a^{3} b d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{5} c^{3} d^{3} - 2 \, a^{2} b^{4} c^{2} d^{4} + a^{3} b^{3} c d^{5} + {\left(b^{6} c^{2} d^{4} - 2 \, a b^{5} c d^{5} + a^{2} b^{4} d^{6}\right)} x^{2} + {\left(b^{6} c^{3} d^{3} - a b^{5} c^{2} d^{4} - a^{2} b^{4} c d^{5} + a^{3} b^{3} d^{6}\right)} x\right)}}\right]"," ",0,"[1/4*(3*(a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3 + (b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x^2 + (b^4*c^4 - 2*a^2*b^2*c^2*d^2 + a^4*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^5*c^3*d^3 - 2*a^2*b^4*c^2*d^4 + a^3*b^3*c*d^5 + (b^6*c^2*d^4 - 2*a*b^5*c*d^5 + a^2*b^4*d^6)*x^2 + (b^6*c^3*d^3 - a*b^5*c^2*d^4 - a^2*b^4*c*d^5 + a^3*b^3*d^6)*x), 1/2*(3*(a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3 + (b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x^2 + (b^4*c^4 - 2*a^2*b^2*c^2*d^2 + a^4*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + 3*a^3*b*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^5*c^3*d^3 - 2*a^2*b^4*c^2*d^4 + a^3*b^3*c*d^5 + (b^6*c^2*d^4 - 2*a*b^5*c*d^5 + a^2*b^4*d^6)*x^2 + (b^6*c^3*d^3 - a*b^5*c^2*d^4 - a^2*b^4*c*d^5 + a^3*b^3*d^6)*x)]","B",0
778,1,710,0,1.906535," ","integrate(x^2/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2} + {\left(b^{3} c^{2} d + a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} + a^{3} b^{2} c d^{4} + {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} + {\left(b^{5} c^{3} d^{2} - a b^{4} c^{2} d^{3} - a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x\right)}}, -\frac{{\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(a b^{2} c^{2} d + a^{2} b c d^{2} + {\left(b^{3} c^{2} d + a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} + a^{3} b^{2} c d^{4} + {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} x^{2} + {\left(b^{5} c^{3} d^{2} - a b^{4} c^{2} d^{3} - a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x}\right]"," ",0,"[1/2*((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(a*b^2*c^2*d + a^2*b*c*d^2 + (b^3*c^2*d + a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 + a^3*b^2*c*d^4 + (b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 + (b^5*c^3*d^2 - a*b^4*c^2*d^3 - a^2*b^3*c*d^4 + a^3*b^2*d^5)*x), -((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(a*b^2*c^2*d + a^2*b*c*d^2 + (b^3*c^2*d + a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 + a^3*b^2*c*d^4 + (b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*x^2 + (b^5*c^3*d^2 - a*b^4*c^2*d^3 - a^2*b^3*c*d^4 + a^3*b^2*d^5)*x)]","B",0
779,1,127,0,1.151874," ","integrate(x/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x}"," ",0,"2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)","A",0
780,1,125,0,1.404060," ","integrate(1/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c}}{a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x}"," ",0,"-2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)","B",0
781,1,719,0,2.260851," ","integrate(1/x/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(a b^{2} c^{3} + a^{3} c d^{2} + {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\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^{2} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x\right)}}, \frac{{\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(a b^{2} c^{3} + a^{3} c d^{2} + {\left(a b^{2} c^{2} d + a^{2} b c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{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^{2} + {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x}\right]"," ",0,"[1/2*((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(a*b^2*c^3 + a^3*c*d^2 + (a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + 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^2 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x), ((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(a*b^2*c^3 + a^3*c*d^2 + (a*b^2*c^2*d + a^2*b*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + 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^2 + (a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x)]","B",0
782,1,940,0,3.397777," ","integrate(1/x^2/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{3} + {\left(b^{4} c^{4} - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{4} d^{4}\right)} x^{2} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{2} + {\left(3 \, 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{4 \, {\left({\left(a^{3} b^{3} c^{5} d - 2 \, a^{4} b^{2} c^{4} d^{2} + a^{5} b c^{3} d^{3}\right)} x^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x^{3} + {\left(b^{4} c^{4} - 2 \, a^{2} b^{2} c^{2} d^{2} + a^{4} d^{4}\right)} x^{2} + {\left(a b^{3} c^{4} - a^{2} b^{2} c^{3} d - a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2} + {\left(3 \, a b^{3} c^{3} d - 2 \, a^{2} b^{2} c^{2} d^{2} + 3 \, a^{3} b c d^{3}\right)} x^{2} + {\left(3 \, 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\right)} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\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^{3} + {\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^{2} + {\left(a^{4} b^{2} c^{6} - 2 \, a^{5} b c^{5} d + a^{6} c^{4} d^{2}\right)} x\right)}}\right]"," ",0,"[1/4*(3*((b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x^3 + (b^4*c^4 - 2*a^2*b^2*c^2*d^2 + a^4*d^4)*x^2 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^2 + (3*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)*sqrt(b*x + a)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x), -1/2*(3*((b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x^3 + (b^4*c^4 - 2*a^2*b^2*c^2*d^2 + a^4*d^4)*x^2 + (a*b^3*c^4 - a^2*b^2*c^3*d - a^3*b*c^2*d^2 + a^4*c*d^3)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2 + (3*a*b^3*c^3*d - 2*a^2*b^2*c^2*d^2 + 3*a^3*b*c*d^3)*x^2 + (3*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)*sqrt(b*x + a)*sqrt(d*x + 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^3 + (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^2 + (a^4*b^2*c^6 - 2*a^5*b*c^5*d + a^6*c^4*d^2)*x)]","B",0
783,1,1244,0,10.115912," ","integrate(1/x^3/(b*x+a)^(3/2)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} - 4 \, a^{3} b^{2} c d^{4} + 5 \, a^{4} b d^{5}\right)} x^{4} + {\left(5 \, b^{5} c^{5} + a b^{4} c^{4} d - 6 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} + 5 \, a^{5} d^{5}\right)} x^{3} + {\left(5 \, a b^{4} c^{5} - 4 \, a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} - 4 \, a^{4} b c^{2} d^{3} + 5 \, a^{5} c d^{4}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(2 \, a^{3} b^{2} c^{5} - 4 \, a^{4} b c^{4} d + 2 \, a^{5} c^{3} d^{2} - {\left(15 \, a b^{4} c^{4} d - 7 \, a^{2} b^{3} c^{3} d^{2} - 7 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4}\right)} x^{3} - {\left(15 \, a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d - 10 \, a^{3} b^{2} c^{3} d^{2} - 2 \, a^{4} b c^{2} d^{3} + 15 \, a^{5} c d^{4}\right)} x^{2} - 5 \, {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{16 \, {\left({\left(a^{4} b^{3} c^{6} d - 2 \, a^{5} b^{2} c^{5} d^{2} + a^{6} b c^{4} d^{3}\right)} x^{4} + {\left(a^{4} b^{3} c^{7} - a^{5} b^{2} c^{6} d - a^{6} b c^{5} d^{2} + a^{7} c^{4} d^{3}\right)} x^{3} + {\left(a^{5} b^{2} c^{7} - 2 \, a^{6} b c^{6} d + a^{7} c^{5} d^{2}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(5 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 2 \, a^{2} b^{3} c^{2} d^{3} - 4 \, a^{3} b^{2} c d^{4} + 5 \, a^{4} b d^{5}\right)} x^{4} + {\left(5 \, b^{5} c^{5} + a b^{4} c^{4} d - 6 \, a^{2} b^{3} c^{3} d^{2} - 6 \, a^{3} b^{2} c^{2} d^{3} + a^{4} b c d^{4} + 5 \, a^{5} d^{5}\right)} x^{3} + {\left(5 \, a b^{4} c^{5} - 4 \, a^{2} b^{3} c^{4} d - 2 \, a^{3} b^{2} c^{3} d^{2} - 4 \, a^{4} b c^{2} d^{3} + 5 \, a^{5} c d^{4}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(2 \, a^{3} b^{2} c^{5} - 4 \, a^{4} b c^{4} d + 2 \, a^{5} c^{3} d^{2} - {\left(15 \, a b^{4} c^{4} d - 7 \, a^{2} b^{3} c^{3} d^{2} - 7 \, a^{3} b^{2} c^{2} d^{3} + 15 \, a^{4} b c d^{4}\right)} x^{3} - {\left(15 \, a b^{4} c^{5} - 2 \, a^{2} b^{3} c^{4} d - 10 \, a^{3} b^{2} c^{3} d^{2} - 2 \, a^{4} b c^{2} d^{3} + 15 \, a^{5} c d^{4}\right)} x^{2} - 5 \, {\left(a^{2} b^{3} c^{5} - a^{3} b^{2} c^{4} d - a^{4} b c^{3} d^{2} + a^{5} c^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{8 \, {\left({\left(a^{4} b^{3} c^{6} d - 2 \, a^{5} b^{2} c^{5} d^{2} + a^{6} b c^{4} d^{3}\right)} x^{4} + {\left(a^{4} b^{3} c^{7} - a^{5} b^{2} c^{6} d - a^{6} b c^{5} d^{2} + a^{7} c^{4} d^{3}\right)} x^{3} + {\left(a^{5} b^{2} c^{7} - 2 \, a^{6} b c^{6} d + a^{7} c^{5} d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(3*((5*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 - 4*a^3*b^2*c*d^4 + 5*a^4*b*d^5)*x^4 + (5*b^5*c^5 + a*b^4*c^4*d - 6*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 + 5*a^5*d^5)*x^3 + (5*a*b^4*c^5 - 4*a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 - 4*a^4*b*c^2*d^3 + 5*a^5*c*d^4)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(2*a^3*b^2*c^5 - 4*a^4*b*c^4*d + 2*a^5*c^3*d^2 - (15*a*b^4*c^4*d - 7*a^2*b^3*c^3*d^2 - 7*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4)*x^3 - (15*a*b^4*c^5 - 2*a^2*b^3*c^4*d - 10*a^3*b^2*c^3*d^2 - 2*a^4*b*c^2*d^3 + 15*a^5*c*d^4)*x^2 - 5*(a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^3*c^6*d - 2*a^5*b^2*c^5*d^2 + a^6*b*c^4*d^3)*x^4 + (a^4*b^3*c^7 - a^5*b^2*c^6*d - a^6*b*c^5*d^2 + a^7*c^4*d^3)*x^3 + (a^5*b^2*c^7 - 2*a^6*b*c^6*d + a^7*c^5*d^2)*x^2), 1/8*(3*((5*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 2*a^2*b^3*c^2*d^3 - 4*a^3*b^2*c*d^4 + 5*a^4*b*d^5)*x^4 + (5*b^5*c^5 + a*b^4*c^4*d - 6*a^2*b^3*c^3*d^2 - 6*a^3*b^2*c^2*d^3 + a^4*b*c*d^4 + 5*a^5*d^5)*x^3 + (5*a*b^4*c^5 - 4*a^2*b^3*c^4*d - 2*a^3*b^2*c^3*d^2 - 4*a^4*b*c^2*d^3 + 5*a^5*c*d^4)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(2*a^3*b^2*c^5 - 4*a^4*b*c^4*d + 2*a^5*c^3*d^2 - (15*a*b^4*c^4*d - 7*a^2*b^3*c^3*d^2 - 7*a^3*b^2*c^2*d^3 + 15*a^4*b*c*d^4)*x^3 - (15*a*b^4*c^5 - 2*a^2*b^3*c^4*d - 10*a^3*b^2*c^3*d^2 - 2*a^4*b*c^2*d^3 + 15*a^5*c*d^4)*x^2 - 5*(a^2*b^3*c^5 - a^3*b^2*c^4*d - a^4*b*c^3*d^2 + a^5*c^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^3*c^6*d - 2*a^5*b^2*c^5*d^2 + a^6*b*c^4*d^3)*x^4 + (a^4*b^3*c^7 - a^5*b^2*c^6*d - a^6*b*c^5*d^2 + a^7*c^4*d^3)*x^3 + (a^5*b^2*c^7 - 2*a^6*b*c^6*d + a^7*c^5*d^2)*x^2)]","B",0
784,1,1960,0,6.729401," ","integrate(x^5/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, a b^{5} c^{7} - 15 \, a^{2} b^{4} c^{6} d + 6 \, a^{3} b^{3} c^{5} d^{2} + 2 \, a^{4} b^{2} c^{4} d^{3} + 3 \, a^{5} b c^{3} d^{4} - 3 \, a^{6} c^{2} d^{5} + {\left(7 \, b^{6} c^{5} d^{2} - 15 \, a b^{5} c^{4} d^{3} + 6 \, a^{2} b^{4} c^{3} d^{4} + 2 \, a^{3} b^{3} c^{2} d^{5} + 3 \, a^{4} b^{2} c d^{6} - 3 \, a^{5} b d^{7}\right)} x^{3} + {\left(14 \, b^{6} c^{6} d - 23 \, a b^{5} c^{5} d^{2} - 3 \, a^{2} b^{4} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{3} d^{4} + 8 \, a^{4} b^{2} c^{2} d^{5} - 3 \, a^{5} b c d^{6} - 3 \, a^{6} d^{7}\right)} x^{2} + {\left(7 \, b^{6} c^{7} - a b^{5} c^{6} d - 24 \, a^{2} b^{4} c^{5} d^{2} + 14 \, a^{3} b^{3} c^{4} d^{3} + 7 \, a^{4} b^{2} c^{3} d^{4} + 3 \, a^{5} b c^{2} d^{5} - 6 \, a^{6} c d^{6}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(105 \, a b^{5} c^{6} d - 190 \, a^{2} b^{4} c^{5} d^{2} + 36 \, a^{3} b^{3} c^{4} d^{3} + 30 \, a^{4} b^{2} c^{3} d^{4} - 45 \, a^{5} b c^{2} d^{5} - 6 \, {\left(b^{6} c^{3} d^{4} - 3 \, a b^{5} c^{2} d^{5} + 3 \, a^{2} b^{4} c d^{6} - a^{3} b^{3} d^{7}\right)} x^{4} + 3 \, {\left(7 \, b^{6} c^{4} d^{3} - 16 \, a b^{5} c^{3} d^{4} + 6 \, a^{2} b^{4} c^{2} d^{5} + 8 \, a^{3} b^{3} c d^{6} - 5 \, a^{4} b^{2} d^{7}\right)} x^{3} + {\left(140 \, b^{6} c^{5} d^{2} - 237 \, a b^{5} c^{4} d^{3} + 12 \, a^{2} b^{4} c^{3} d^{4} + 66 \, a^{3} b^{3} c^{2} d^{5} - 45 \, a^{5} b d^{7}\right)} x^{2} + {\left(105 \, b^{6} c^{6} d - 50 \, a b^{5} c^{5} d^{2} - 222 \, a^{2} b^{4} c^{4} d^{3} + 84 \, a^{3} b^{3} c^{3} d^{4} + 45 \, a^{4} b^{2} c^{2} d^{5} - 90 \, a^{5} b c d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a b^{7} c^{5} d^{5} - 3 \, a^{2} b^{6} c^{4} d^{6} + 3 \, a^{3} b^{5} c^{3} d^{7} - a^{4} b^{4} c^{2} d^{8} + {\left(b^{8} c^{3} d^{7} - 3 \, a b^{7} c^{2} d^{8} + 3 \, a^{2} b^{6} c d^{9} - a^{3} b^{5} d^{10}\right)} x^{3} + {\left(2 \, b^{8} c^{4} d^{6} - 5 \, a b^{7} c^{3} d^{7} + 3 \, a^{2} b^{6} c^{2} d^{8} + a^{3} b^{5} c d^{9} - a^{4} b^{4} d^{10}\right)} x^{2} + {\left(b^{8} c^{5} d^{5} - a b^{7} c^{4} d^{6} - 3 \, a^{2} b^{6} c^{3} d^{7} + 5 \, a^{3} b^{5} c^{2} d^{8} - 2 \, a^{4} b^{4} c d^{9}\right)} x\right)}}, -\frac{15 \, {\left(7 \, a b^{5} c^{7} - 15 \, a^{2} b^{4} c^{6} d + 6 \, a^{3} b^{3} c^{5} d^{2} + 2 \, a^{4} b^{2} c^{4} d^{3} + 3 \, a^{5} b c^{3} d^{4} - 3 \, a^{6} c^{2} d^{5} + {\left(7 \, b^{6} c^{5} d^{2} - 15 \, a b^{5} c^{4} d^{3} + 6 \, a^{2} b^{4} c^{3} d^{4} + 2 \, a^{3} b^{3} c^{2} d^{5} + 3 \, a^{4} b^{2} c d^{6} - 3 \, a^{5} b d^{7}\right)} x^{3} + {\left(14 \, b^{6} c^{6} d - 23 \, a b^{5} c^{5} d^{2} - 3 \, a^{2} b^{4} c^{4} d^{3} + 10 \, a^{3} b^{3} c^{3} d^{4} + 8 \, a^{4} b^{2} c^{2} d^{5} - 3 \, a^{5} b c d^{6} - 3 \, a^{6} d^{7}\right)} x^{2} + {\left(7 \, b^{6} c^{7} - a b^{5} c^{6} d - 24 \, a^{2} b^{4} c^{5} d^{2} + 14 \, a^{3} b^{3} c^{4} d^{3} + 7 \, a^{4} b^{2} c^{3} d^{4} + 3 \, a^{5} b c^{2} d^{5} - 6 \, a^{6} c d^{6}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(105 \, a b^{5} c^{6} d - 190 \, a^{2} b^{4} c^{5} d^{2} + 36 \, a^{3} b^{3} c^{4} d^{3} + 30 \, a^{4} b^{2} c^{3} d^{4} - 45 \, a^{5} b c^{2} d^{5} - 6 \, {\left(b^{6} c^{3} d^{4} - 3 \, a b^{5} c^{2} d^{5} + 3 \, a^{2} b^{4} c d^{6} - a^{3} b^{3} d^{7}\right)} x^{4} + 3 \, {\left(7 \, b^{6} c^{4} d^{3} - 16 \, a b^{5} c^{3} d^{4} + 6 \, a^{2} b^{4} c^{2} d^{5} + 8 \, a^{3} b^{3} c d^{6} - 5 \, a^{4} b^{2} d^{7}\right)} x^{3} + {\left(140 \, b^{6} c^{5} d^{2} - 237 \, a b^{5} c^{4} d^{3} + 12 \, a^{2} b^{4} c^{3} d^{4} + 66 \, a^{3} b^{3} c^{2} d^{5} - 45 \, a^{5} b d^{7}\right)} x^{2} + {\left(105 \, b^{6} c^{6} d - 50 \, a b^{5} c^{5} d^{2} - 222 \, a^{2} b^{4} c^{4} d^{3} + 84 \, a^{3} b^{3} c^{3} d^{4} + 45 \, a^{4} b^{2} c^{2} d^{5} - 90 \, a^{5} b c d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(a b^{7} c^{5} d^{5} - 3 \, a^{2} b^{6} c^{4} d^{6} + 3 \, a^{3} b^{5} c^{3} d^{7} - a^{4} b^{4} c^{2} d^{8} + {\left(b^{8} c^{3} d^{7} - 3 \, a b^{7} c^{2} d^{8} + 3 \, a^{2} b^{6} c d^{9} - a^{3} b^{5} d^{10}\right)} x^{3} + {\left(2 \, b^{8} c^{4} d^{6} - 5 \, a b^{7} c^{3} d^{7} + 3 \, a^{2} b^{6} c^{2} d^{8} + a^{3} b^{5} c d^{9} - a^{4} b^{4} d^{10}\right)} x^{2} + {\left(b^{8} c^{5} d^{5} - a b^{7} c^{4} d^{6} - 3 \, a^{2} b^{6} c^{3} d^{7} + 5 \, a^{3} b^{5} c^{2} d^{8} - 2 \, a^{4} b^{4} c d^{9}\right)} x\right)}}\right]"," ",0,"[1/48*(15*(7*a*b^5*c^7 - 15*a^2*b^4*c^6*d + 6*a^3*b^3*c^5*d^2 + 2*a^4*b^2*c^4*d^3 + 3*a^5*b*c^3*d^4 - 3*a^6*c^2*d^5 + (7*b^6*c^5*d^2 - 15*a*b^5*c^4*d^3 + 6*a^2*b^4*c^3*d^4 + 2*a^3*b^3*c^2*d^5 + 3*a^4*b^2*c*d^6 - 3*a^5*b*d^7)*x^3 + (14*b^6*c^6*d - 23*a*b^5*c^5*d^2 - 3*a^2*b^4*c^4*d^3 + 10*a^3*b^3*c^3*d^4 + 8*a^4*b^2*c^2*d^5 - 3*a^5*b*c*d^6 - 3*a^6*d^7)*x^2 + (7*b^6*c^7 - a*b^5*c^6*d - 24*a^2*b^4*c^5*d^2 + 14*a^3*b^3*c^4*d^3 + 7*a^4*b^2*c^3*d^4 + 3*a^5*b*c^2*d^5 - 6*a^6*c*d^6)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(105*a*b^5*c^6*d - 190*a^2*b^4*c^5*d^2 + 36*a^3*b^3*c^4*d^3 + 30*a^4*b^2*c^3*d^4 - 45*a^5*b*c^2*d^5 - 6*(b^6*c^3*d^4 - 3*a*b^5*c^2*d^5 + 3*a^2*b^4*c*d^6 - a^3*b^3*d^7)*x^4 + 3*(7*b^6*c^4*d^3 - 16*a*b^5*c^3*d^4 + 6*a^2*b^4*c^2*d^5 + 8*a^3*b^3*c*d^6 - 5*a^4*b^2*d^7)*x^3 + (140*b^6*c^5*d^2 - 237*a*b^5*c^4*d^3 + 12*a^2*b^4*c^3*d^4 + 66*a^3*b^3*c^2*d^5 - 45*a^5*b*d^7)*x^2 + (105*b^6*c^6*d - 50*a*b^5*c^5*d^2 - 222*a^2*b^4*c^4*d^3 + 84*a^3*b^3*c^3*d^4 + 45*a^4*b^2*c^2*d^5 - 90*a^5*b*c*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^7*c^5*d^5 - 3*a^2*b^6*c^4*d^6 + 3*a^3*b^5*c^3*d^7 - a^4*b^4*c^2*d^8 + (b^8*c^3*d^7 - 3*a*b^7*c^2*d^8 + 3*a^2*b^6*c*d^9 - a^3*b^5*d^10)*x^3 + (2*b^8*c^4*d^6 - 5*a*b^7*c^3*d^7 + 3*a^2*b^6*c^2*d^8 + a^3*b^5*c*d^9 - a^4*b^4*d^10)*x^2 + (b^8*c^5*d^5 - a*b^7*c^4*d^6 - 3*a^2*b^6*c^3*d^7 + 5*a^3*b^5*c^2*d^8 - 2*a^4*b^4*c*d^9)*x), -1/24*(15*(7*a*b^5*c^7 - 15*a^2*b^4*c^6*d + 6*a^3*b^3*c^5*d^2 + 2*a^4*b^2*c^4*d^3 + 3*a^5*b*c^3*d^4 - 3*a^6*c^2*d^5 + (7*b^6*c^5*d^2 - 15*a*b^5*c^4*d^3 + 6*a^2*b^4*c^3*d^4 + 2*a^3*b^3*c^2*d^5 + 3*a^4*b^2*c*d^6 - 3*a^5*b*d^7)*x^3 + (14*b^6*c^6*d - 23*a*b^5*c^5*d^2 - 3*a^2*b^4*c^4*d^3 + 10*a^3*b^3*c^3*d^4 + 8*a^4*b^2*c^2*d^5 - 3*a^5*b*c*d^6 - 3*a^6*d^7)*x^2 + (7*b^6*c^7 - a*b^5*c^6*d - 24*a^2*b^4*c^5*d^2 + 14*a^3*b^3*c^4*d^3 + 7*a^4*b^2*c^3*d^4 + 3*a^5*b*c^2*d^5 - 6*a^6*c*d^6)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(105*a*b^5*c^6*d - 190*a^2*b^4*c^5*d^2 + 36*a^3*b^3*c^4*d^3 + 30*a^4*b^2*c^3*d^4 - 45*a^5*b*c^2*d^5 - 6*(b^6*c^3*d^4 - 3*a*b^5*c^2*d^5 + 3*a^2*b^4*c*d^6 - a^3*b^3*d^7)*x^4 + 3*(7*b^6*c^4*d^3 - 16*a*b^5*c^3*d^4 + 6*a^2*b^4*c^2*d^5 + 8*a^3*b^3*c*d^6 - 5*a^4*b^2*d^7)*x^3 + (140*b^6*c^5*d^2 - 237*a*b^5*c^4*d^3 + 12*a^2*b^4*c^3*d^4 + 66*a^3*b^3*c^2*d^5 - 45*a^5*b*d^7)*x^2 + (105*b^6*c^6*d - 50*a*b^5*c^5*d^2 - 222*a^2*b^4*c^4*d^3 + 84*a^3*b^3*c^3*d^4 + 45*a^4*b^2*c^2*d^5 - 90*a^5*b*c*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^7*c^5*d^5 - 3*a^2*b^6*c^4*d^6 + 3*a^3*b^5*c^3*d^7 - a^4*b^4*c^2*d^8 + (b^8*c^3*d^7 - 3*a*b^7*c^2*d^8 + 3*a^2*b^6*c*d^9 - a^3*b^5*d^10)*x^3 + (2*b^8*c^4*d^6 - 5*a*b^7*c^3*d^7 + 3*a^2*b^6*c^2*d^8 + a^3*b^5*c*d^9 - a^4*b^4*d^10)*x^2 + (b^8*c^5*d^5 - a*b^7*c^4*d^6 - 3*a^2*b^6*c^3*d^7 + 5*a^3*b^5*c^2*d^8 - 2*a^4*b^4*c*d^9)*x)]","B",0
785,1,1628,0,2.814618," ","integrate(x^4/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, a b^{4} c^{6} - 12 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} + 4 \, a^{4} b c^{3} d^{3} - 3 \, a^{5} c^{2} d^{4} + {\left(5 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} + 4 \, a^{3} b^{2} c d^{5} - 3 \, a^{4} b d^{6}\right)} x^{3} + {\left(10 \, b^{5} c^{5} d - 19 \, a b^{4} c^{4} d^{2} + 14 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} - 3 \, a^{5} d^{6}\right)} x^{2} + {\left(5 \, b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 18 \, a^{2} b^{3} c^{4} d^{2} + 16 \, a^{3} b^{2} c^{3} d^{3} + 5 \, a^{4} b c^{2} d^{4} - 6 \, a^{5} c d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(15 \, a b^{4} c^{5} d - 31 \, a^{2} b^{3} c^{4} d^{2} + 9 \, a^{3} b^{2} c^{3} d^{3} - 9 \, a^{4} b c^{2} d^{4} + 3 \, {\left(b^{5} c^{3} d^{3} - 3 \, a b^{4} c^{2} d^{4} + 3 \, a^{2} b^{3} c d^{5} - a^{3} b^{2} d^{6}\right)} x^{3} + {\left(20 \, b^{5} c^{4} d^{2} - 39 \, a b^{4} c^{3} d^{3} + 9 \, a^{2} b^{3} c^{2} d^{4} + 3 \, a^{3} b^{2} c d^{5} - 9 \, a^{4} b d^{6}\right)} x^{2} + {\left(15 \, b^{5} c^{5} d - 11 \, a b^{4} c^{4} d^{2} - 33 \, a^{2} b^{3} c^{3} d^{3} + 15 \, a^{3} b^{2} c^{2} d^{4} - 18 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(a b^{6} c^{5} d^{4} - 3 \, a^{2} b^{5} c^{4} d^{5} + 3 \, a^{3} b^{4} c^{3} d^{6} - a^{4} b^{3} c^{2} d^{7} + {\left(b^{7} c^{3} d^{6} - 3 \, a b^{6} c^{2} d^{7} + 3 \, a^{2} b^{5} c d^{8} - a^{3} b^{4} d^{9}\right)} x^{3} + {\left(2 \, b^{7} c^{4} d^{5} - 5 \, a b^{6} c^{3} d^{6} + 3 \, a^{2} b^{5} c^{2} d^{7} + a^{3} b^{4} c d^{8} - a^{4} b^{3} d^{9}\right)} x^{2} + {\left(b^{7} c^{5} d^{4} - a b^{6} c^{4} d^{5} - 3 \, a^{2} b^{5} c^{3} d^{6} + 5 \, a^{3} b^{4} c^{2} d^{7} - 2 \, a^{4} b^{3} c d^{8}\right)} x\right)}}, \frac{3 \, {\left(5 \, a b^{4} c^{6} - 12 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} + 4 \, a^{4} b c^{3} d^{3} - 3 \, a^{5} c^{2} d^{4} + {\left(5 \, b^{5} c^{4} d^{2} - 12 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} + 4 \, a^{3} b^{2} c d^{5} - 3 \, a^{4} b d^{6}\right)} x^{3} + {\left(10 \, b^{5} c^{5} d - 19 \, a b^{4} c^{4} d^{2} + 14 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} - 3 \, a^{5} d^{6}\right)} x^{2} + {\left(5 \, b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 18 \, a^{2} b^{3} c^{4} d^{2} + 16 \, a^{3} b^{2} c^{3} d^{3} + 5 \, a^{4} b c^{2} d^{4} - 6 \, a^{5} c d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, a b^{4} c^{5} d - 31 \, a^{2} b^{3} c^{4} d^{2} + 9 \, a^{3} b^{2} c^{3} d^{3} - 9 \, a^{4} b c^{2} d^{4} + 3 \, {\left(b^{5} c^{3} d^{3} - 3 \, a b^{4} c^{2} d^{4} + 3 \, a^{2} b^{3} c d^{5} - a^{3} b^{2} d^{6}\right)} x^{3} + {\left(20 \, b^{5} c^{4} d^{2} - 39 \, a b^{4} c^{3} d^{3} + 9 \, a^{2} b^{3} c^{2} d^{4} + 3 \, a^{3} b^{2} c d^{5} - 9 \, a^{4} b d^{6}\right)} x^{2} + {\left(15 \, b^{5} c^{5} d - 11 \, a b^{4} c^{4} d^{2} - 33 \, a^{2} b^{3} c^{3} d^{3} + 15 \, a^{3} b^{2} c^{2} d^{4} - 18 \, a^{4} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a b^{6} c^{5} d^{4} - 3 \, a^{2} b^{5} c^{4} d^{5} + 3 \, a^{3} b^{4} c^{3} d^{6} - a^{4} b^{3} c^{2} d^{7} + {\left(b^{7} c^{3} d^{6} - 3 \, a b^{6} c^{2} d^{7} + 3 \, a^{2} b^{5} c d^{8} - a^{3} b^{4} d^{9}\right)} x^{3} + {\left(2 \, b^{7} c^{4} d^{5} - 5 \, a b^{6} c^{3} d^{6} + 3 \, a^{2} b^{5} c^{2} d^{7} + a^{3} b^{4} c d^{8} - a^{4} b^{3} d^{9}\right)} x^{2} + {\left(b^{7} c^{5} d^{4} - a b^{6} c^{4} d^{5} - 3 \, a^{2} b^{5} c^{3} d^{6} + 5 \, a^{3} b^{4} c^{2} d^{7} - 2 \, a^{4} b^{3} c d^{8}\right)} x\right)}}\right]"," ",0,"[1/12*(3*(5*a*b^4*c^6 - 12*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 + 4*a^4*b*c^3*d^3 - 3*a^5*c^2*d^4 + (5*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 + 4*a^3*b^2*c*d^5 - 3*a^4*b*d^6)*x^3 + (10*b^5*c^5*d - 19*a*b^4*c^4*d^2 + 14*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 - 3*a^5*d^6)*x^2 + (5*b^5*c^6 - 2*a*b^4*c^5*d - 18*a^2*b^3*c^4*d^2 + 16*a^3*b^2*c^3*d^3 + 5*a^4*b*c^2*d^4 - 6*a^5*c*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(15*a*b^4*c^5*d - 31*a^2*b^3*c^4*d^2 + 9*a^3*b^2*c^3*d^3 - 9*a^4*b*c^2*d^4 + 3*(b^5*c^3*d^3 - 3*a*b^4*c^2*d^4 + 3*a^2*b^3*c*d^5 - a^3*b^2*d^6)*x^3 + (20*b^5*c^4*d^2 - 39*a*b^4*c^3*d^3 + 9*a^2*b^3*c^2*d^4 + 3*a^3*b^2*c*d^5 - 9*a^4*b*d^6)*x^2 + (15*b^5*c^5*d - 11*a*b^4*c^4*d^2 - 33*a^2*b^3*c^3*d^3 + 15*a^3*b^2*c^2*d^4 - 18*a^4*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^6*c^5*d^4 - 3*a^2*b^5*c^4*d^5 + 3*a^3*b^4*c^3*d^6 - a^4*b^3*c^2*d^7 + (b^7*c^3*d^6 - 3*a*b^6*c^2*d^7 + 3*a^2*b^5*c*d^8 - a^3*b^4*d^9)*x^3 + (2*b^7*c^4*d^5 - 5*a*b^6*c^3*d^6 + 3*a^2*b^5*c^2*d^7 + a^3*b^4*c*d^8 - a^4*b^3*d^9)*x^2 + (b^7*c^5*d^4 - a*b^6*c^4*d^5 - 3*a^2*b^5*c^3*d^6 + 5*a^3*b^4*c^2*d^7 - 2*a^4*b^3*c*d^8)*x), 1/6*(3*(5*a*b^4*c^6 - 12*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 + 4*a^4*b*c^3*d^3 - 3*a^5*c^2*d^4 + (5*b^5*c^4*d^2 - 12*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 + 4*a^3*b^2*c*d^5 - 3*a^4*b*d^6)*x^3 + (10*b^5*c^5*d - 19*a*b^4*c^4*d^2 + 14*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 - 3*a^5*d^6)*x^2 + (5*b^5*c^6 - 2*a*b^4*c^5*d - 18*a^2*b^3*c^4*d^2 + 16*a^3*b^2*c^3*d^3 + 5*a^4*b*c^2*d^4 - 6*a^5*c*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*a*b^4*c^5*d - 31*a^2*b^3*c^4*d^2 + 9*a^3*b^2*c^3*d^3 - 9*a^4*b*c^2*d^4 + 3*(b^5*c^3*d^3 - 3*a*b^4*c^2*d^4 + 3*a^2*b^3*c*d^5 - a^3*b^2*d^6)*x^3 + (20*b^5*c^4*d^2 - 39*a*b^4*c^3*d^3 + 9*a^2*b^3*c^2*d^4 + 3*a^3*b^2*c*d^5 - 9*a^4*b*d^6)*x^2 + (15*b^5*c^5*d - 11*a*b^4*c^4*d^2 - 33*a^2*b^3*c^3*d^3 + 15*a^3*b^2*c^2*d^4 - 18*a^4*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^6*c^5*d^4 - 3*a^2*b^5*c^4*d^5 + 3*a^3*b^4*c^3*d^6 - a^4*b^3*c^2*d^7 + (b^7*c^3*d^6 - 3*a*b^6*c^2*d^7 + 3*a^2*b^5*c*d^8 - a^3*b^4*d^9)*x^3 + (2*b^7*c^4*d^5 - 5*a*b^6*c^3*d^6 + 3*a^2*b^5*c^2*d^7 + a^3*b^4*c*d^8 - a^4*b^3*d^9)*x^2 + (b^7*c^5*d^4 - a*b^6*c^4*d^5 - 3*a^2*b^5*c^3*d^6 + 5*a^3*b^4*c^2*d^7 - 2*a^4*b^3*c*d^8)*x)]","B",0
786,1,1326,0,3.768018," ","integrate(x^3/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, a b^{3} c^{4} d - 8 \, a^{2} b^{2} c^{3} d^{2} - 3 \, a^{3} b c^{2} d^{3} + {\left(4 \, b^{4} c^{3} d^{2} - 9 \, a b^{3} c^{2} d^{3} - 3 \, a^{3} b d^{5}\right)} x^{2} + {\left(3 \, b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} - 9 \, a^{2} b^{2} c^{2} d^{3} - 6 \, a^{3} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a b^{5} c^{5} d^{3} - 3 \, a^{2} b^{4} c^{4} d^{4} + 3 \, a^{3} b^{3} c^{3} d^{5} - a^{4} b^{2} c^{2} d^{6} + {\left(b^{6} c^{3} d^{5} - 3 \, a b^{5} c^{2} d^{6} + 3 \, a^{2} b^{4} c d^{7} - a^{3} b^{3} d^{8}\right)} x^{3} + {\left(2 \, b^{6} c^{4} d^{4} - 5 \, a b^{5} c^{3} d^{5} + 3 \, a^{2} b^{4} c^{2} d^{6} + a^{3} b^{3} c d^{7} - a^{4} b^{2} d^{8}\right)} x^{2} + {\left(b^{6} c^{5} d^{3} - a b^{5} c^{4} d^{4} - 3 \, a^{2} b^{4} c^{3} d^{5} + 5 \, a^{3} b^{3} c^{2} d^{6} - 2 \, a^{4} b^{2} c d^{7}\right)} x\right)}}, -\frac{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, a b^{3} c^{4} d - 8 \, a^{2} b^{2} c^{3} d^{2} - 3 \, a^{3} b c^{2} d^{3} + {\left(4 \, b^{4} c^{3} d^{2} - 9 \, a b^{3} c^{2} d^{3} - 3 \, a^{3} b d^{5}\right)} x^{2} + {\left(3 \, b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} - 9 \, a^{2} b^{2} c^{2} d^{3} - 6 \, a^{3} b c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a b^{5} c^{5} d^{3} - 3 \, a^{2} b^{4} c^{4} d^{4} + 3 \, a^{3} b^{3} c^{3} d^{5} - a^{4} b^{2} c^{2} d^{6} + {\left(b^{6} c^{3} d^{5} - 3 \, a b^{5} c^{2} d^{6} + 3 \, a^{2} b^{4} c d^{7} - a^{3} b^{3} d^{8}\right)} x^{3} + {\left(2 \, b^{6} c^{4} d^{4} - 5 \, a b^{5} c^{3} d^{5} + 3 \, a^{2} b^{4} c^{2} d^{6} + a^{3} b^{3} c d^{7} - a^{4} b^{2} d^{8}\right)} x^{2} + {\left(b^{6} c^{5} d^{3} - a b^{5} c^{4} d^{4} - 3 \, a^{2} b^{4} c^{3} d^{5} + 5 \, a^{3} b^{3} c^{2} d^{6} - 2 \, a^{4} b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*a*b^3*c^4*d - 8*a^2*b^2*c^3*d^2 - 3*a^3*b*c^2*d^3 + (4*b^4*c^3*d^2 - 9*a*b^3*c^2*d^3 - 3*a^3*b*d^5)*x^2 + (3*b^4*c^4*d - 4*a*b^3*c^3*d^2 - 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^5*c^5*d^3 - 3*a^2*b^4*c^4*d^4 + 3*a^3*b^3*c^3*d^5 - a^4*b^2*c^2*d^6 + (b^6*c^3*d^5 - 3*a*b^5*c^2*d^6 + 3*a^2*b^4*c*d^7 - a^3*b^3*d^8)*x^3 + (2*b^6*c^4*d^4 - 5*a*b^5*c^3*d^5 + 3*a^2*b^4*c^2*d^6 + a^3*b^3*c*d^7 - a^4*b^2*d^8)*x^2 + (b^6*c^5*d^3 - a*b^5*c^4*d^4 - 3*a^2*b^4*c^3*d^5 + 5*a^3*b^3*c^2*d^6 - 2*a^4*b^2*c*d^7)*x), -1/3*(3*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(3*a*b^3*c^4*d - 8*a^2*b^2*c^3*d^2 - 3*a^3*b*c^2*d^3 + (4*b^4*c^3*d^2 - 9*a*b^3*c^2*d^3 - 3*a^3*b*d^5)*x^2 + (3*b^4*c^4*d - 4*a*b^3*c^3*d^2 - 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a*b^5*c^5*d^3 - 3*a^2*b^4*c^4*d^4 + 3*a^3*b^3*c^3*d^5 - a^4*b^2*c^2*d^6 + (b^6*c^3*d^5 - 3*a*b^5*c^2*d^6 + 3*a^2*b^4*c*d^7 - a^3*b^3*d^8)*x^3 + (2*b^6*c^4*d^4 - 5*a*b^5*c^3*d^5 + 3*a^2*b^4*c^2*d^6 + a^3*b^3*c*d^7 - a^4*b^2*d^8)*x^2 + (b^6*c^5*d^3 - a*b^5*c^4*d^4 - 3*a^2*b^4*c^3*d^5 + 5*a^3*b^3*c^2*d^6 - 2*a^4*b^2*c*d^7)*x)]","B",0
787,1,275,0,2.842240," ","integrate(x^2/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a^{2} c^{2} - {\left(b^{2} c^{2} - 6 \, a b c d - 3 \, a^{2} d^{2}\right)} x^{2} + 4 \, {\left(a b c^{2} + 3 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)}}"," ",0,"-2/3*(8*a^2*c^2 - (b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*x^2 + 4*(a*b*c^2 + 3*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)","B",0
788,1,281,0,2.499213," ","integrate(x/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6 \, a b c^{2} + 2 \, a^{2} c d + 2 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x^{2} + {\left(3 \, b^{2} c^{2} + 10 \, a b c d + 3 \, a^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)}}"," ",0,"2/3*(6*a*b*c^2 + 2*a^2*c*d + 2*(b^2*c*d + 3*a*b*d^2)*x^2 + (3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)","B",0
789,1,273,0,2.331161," ","integrate(1/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{2} d^{2} x^{2} + 3 \, b^{2} c^{2} + 6 \, a b c d - a^{2} d^{2} + 4 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)}}"," ",0,"-2/3*(8*b^2*d^2*x^2 + 3*b^2*c^2 + 6*a*b*c*d - a^2*d^2 + 4*(3*b^2*c*d + a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)","B",0
790,1,1336,0,4.763833," ","integrate(1/x/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a b^{3} c^{5} + 9 \, a^{3} b c^{3} d^{2} - 4 \, a^{4} c^{2} d^{3} + {\left(3 \, a b^{3} c^{3} d^{2} + 8 \, a^{2} b^{2} c^{2} d^{3} - 3 \, a^{3} b c d^{4}\right)} x^{2} + {\left(6 \, a b^{3} c^{4} d + 9 \, a^{2} b^{2} c^{3} d^{2} + 4 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{3} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{2} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x\right)}}, \frac{3 \, {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3} + {\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a b^{3} c^{5} + 9 \, a^{3} b c^{3} d^{2} - 4 \, a^{4} c^{2} d^{3} + {\left(3 \, a b^{3} c^{3} d^{2} + 8 \, a^{2} b^{2} c^{2} d^{3} - 3 \, a^{3} b c d^{4}\right)} x^{2} + {\left(6 \, a b^{3} c^{4} d + 9 \, a^{2} b^{2} c^{3} d^{2} + 4 \, a^{3} b c^{2} d^{3} - 3 \, a^{4} c d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{3} b^{3} c^{8} - 3 \, a^{4} b^{2} c^{7} d + 3 \, a^{5} b c^{6} d^{2} - a^{6} c^{5} d^{3} + {\left(a^{2} b^{4} c^{6} d^{2} - 3 \, a^{3} b^{3} c^{5} d^{3} + 3 \, a^{4} b^{2} c^{4} d^{4} - a^{5} b c^{3} d^{5}\right)} x^{3} + {\left(2 \, a^{2} b^{4} c^{7} d - 5 \, a^{3} b^{3} c^{6} d^{2} + 3 \, a^{4} b^{2} c^{5} d^{3} + a^{5} b c^{4} d^{4} - a^{6} c^{3} d^{5}\right)} x^{2} + {\left(a^{2} b^{4} c^{8} - a^{3} b^{3} c^{7} d - 3 \, a^{4} b^{2} c^{6} d^{2} + 5 \, a^{5} b c^{5} d^{3} - 2 \, a^{6} c^{4} d^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a*b^3*c^5 + 9*a^3*b*c^3*d^2 - 4*a^4*c^2*d^3 + (3*a*b^3*c^3*d^2 + 8*a^2*b^2*c^2*d^3 - 3*a^3*b*c*d^4)*x^2 + (6*a*b^3*c^4*d + 9*a^2*b^2*c^3*d^2 + 4*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^3 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^2 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x), 1/3*(3*(a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3 + (b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(3*a*b^3*c^5 + 9*a^3*b*c^3*d^2 - 4*a^4*c^2*d^3 + (3*a*b^3*c^3*d^2 + 8*a^2*b^2*c^2*d^3 - 3*a^3*b*c*d^4)*x^2 + (6*a*b^3*c^4*d + 9*a^2*b^2*c^3*d^2 + 4*a^3*b*c^2*d^3 - 3*a^4*c*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b^3*c^8 - 3*a^4*b^2*c^7*d + 3*a^5*b*c^6*d^2 - a^6*c^5*d^3 + (a^2*b^4*c^6*d^2 - 3*a^3*b^3*c^5*d^3 + 3*a^4*b^2*c^4*d^4 - a^5*b*c^3*d^5)*x^3 + (2*a^2*b^4*c^7*d - 5*a^3*b^3*c^6*d^2 + 3*a^4*b^2*c^5*d^3 + a^5*b*c^4*d^4 - a^6*c^3*d^5)*x^2 + (a^2*b^4*c^8 - a^3*b^3*c^7*d - 3*a^4*b^2*c^6*d^2 + 5*a^5*b*c^5*d^3 - 2*a^6*c^4*d^4)*x)]","B",0
791,1,1658,0,13.486432," ","integrate(1/x^2/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(3 \, b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} - 6 \, a^{2} b^{3} c^{2} d^{4} + 12 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(6 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 16 \, a^{2} b^{3} c^{3} d^{3} + 18 \, a^{3} b^{2} c^{2} d^{4} + 2 \, a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(3 \, b^{5} c^{6} + 2 \, a b^{4} c^{5} d - 14 \, a^{2} b^{3} c^{4} d^{2} + 19 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(3 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 6 \, a^{3} b^{2} c^{4} d^{2} + 12 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + {\left(9 \, a b^{4} c^{4} d^{2} - 9 \, a^{2} b^{3} c^{3} d^{3} + 31 \, a^{3} b^{2} c^{2} d^{4} - 15 \, a^{4} b c d^{5}\right)} x^{3} + {\left(18 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 33 \, a^{3} b^{2} c^{3} d^{3} + 11 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(9 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 39 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}, -\frac{3 \, {\left({\left(3 \, b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} - 6 \, a^{2} b^{3} c^{2} d^{4} + 12 \, a^{3} b^{2} c d^{5} - 5 \, a^{4} b d^{6}\right)} x^{4} + {\left(6 \, b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} - 16 \, a^{2} b^{3} c^{3} d^{3} + 18 \, a^{3} b^{2} c^{2} d^{4} + 2 \, a^{4} b c d^{5} - 5 \, a^{5} d^{6}\right)} x^{3} + {\left(3 \, b^{5} c^{6} + 2 \, a b^{4} c^{5} d - 14 \, a^{2} b^{3} c^{4} d^{2} + 19 \, a^{4} b c^{2} d^{4} - 10 \, a^{5} c d^{5}\right)} x^{2} + {\left(3 \, a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d - 6 \, a^{3} b^{2} c^{4} d^{2} + 12 \, a^{4} b c^{3} d^{3} - 5 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a^{2} b^{3} c^{6} - 9 \, a^{3} b^{2} c^{5} d + 9 \, a^{4} b c^{4} d^{2} - 3 \, a^{5} c^{3} d^{3} + {\left(9 \, a b^{4} c^{4} d^{2} - 9 \, a^{2} b^{3} c^{3} d^{3} + 31 \, a^{3} b^{2} c^{2} d^{4} - 15 \, a^{4} b c d^{5}\right)} x^{3} + {\left(18 \, a b^{4} c^{5} d - 15 \, a^{2} b^{3} c^{4} d^{2} + 33 \, a^{3} b^{2} c^{3} d^{3} + 11 \, a^{4} b c^{2} d^{4} - 15 \, a^{5} c d^{5}\right)} x^{2} + {\left(9 \, a b^{4} c^{6} - 3 \, a^{2} b^{3} c^{5} d - 9 \, a^{3} b^{2} c^{4} d^{2} + 39 \, a^{4} b c^{3} d^{3} - 20 \, a^{5} c^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left({\left(a^{3} b^{4} c^{7} d^{2} - 3 \, a^{4} b^{3} c^{6} d^{3} + 3 \, a^{5} b^{2} c^{5} d^{4} - a^{6} b c^{4} d^{5}\right)} x^{4} + {\left(2 \, a^{3} b^{4} c^{8} d - 5 \, a^{4} b^{3} c^{7} d^{2} + 3 \, a^{5} b^{2} c^{6} d^{3} + a^{6} b c^{5} d^{4} - a^{7} c^{4} d^{5}\right)} x^{3} + {\left(a^{3} b^{4} c^{9} - a^{4} b^{3} c^{8} d - 3 \, a^{5} b^{2} c^{7} d^{2} + 5 \, a^{6} b c^{6} d^{3} - 2 \, a^{7} c^{5} d^{4}\right)} x^{2} + {\left(a^{4} b^{3} c^{9} - 3 \, a^{5} b^{2} c^{8} d + 3 \, a^{6} b c^{7} d^{2} - a^{7} c^{6} d^{3}\right)} x\right)}}\right]"," ",0,"[1/12*(3*((3*b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 - 6*a^2*b^3*c^2*d^4 + 12*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (6*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 16*a^2*b^3*c^3*d^3 + 18*a^3*b^2*c^2*d^4 + 2*a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (3*b^5*c^6 + 2*a*b^4*c^5*d - 14*a^2*b^3*c^4*d^2 + 19*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (3*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 6*a^3*b^2*c^4*d^2 + 12*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + (9*a*b^4*c^4*d^2 - 9*a^2*b^3*c^3*d^3 + 31*a^3*b^2*c^2*d^4 - 15*a^4*b*c*d^5)*x^3 + (18*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 33*a^3*b^2*c^3*d^3 + 11*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (9*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 39*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x), -1/6*(3*((3*b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 - 6*a^2*b^3*c^2*d^4 + 12*a^3*b^2*c*d^5 - 5*a^4*b*d^6)*x^4 + (6*b^5*c^5*d - 5*a*b^4*c^4*d^2 - 16*a^2*b^3*c^3*d^3 + 18*a^3*b^2*c^2*d^4 + 2*a^4*b*c*d^5 - 5*a^5*d^6)*x^3 + (3*b^5*c^6 + 2*a*b^4*c^5*d - 14*a^2*b^3*c^4*d^2 + 19*a^4*b*c^2*d^4 - 10*a^5*c*d^5)*x^2 + (3*a*b^4*c^6 - 4*a^2*b^3*c^5*d - 6*a^3*b^2*c^4*d^2 + 12*a^4*b*c^3*d^3 - 5*a^5*c^2*d^4)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(3*a^2*b^3*c^6 - 9*a^3*b^2*c^5*d + 9*a^4*b*c^4*d^2 - 3*a^5*c^3*d^3 + (9*a*b^4*c^4*d^2 - 9*a^2*b^3*c^3*d^3 + 31*a^3*b^2*c^2*d^4 - 15*a^4*b*c*d^5)*x^3 + (18*a*b^4*c^5*d - 15*a^2*b^3*c^4*d^2 + 33*a^3*b^2*c^3*d^3 + 11*a^4*b*c^2*d^4 - 15*a^5*c*d^5)*x^2 + (9*a*b^4*c^6 - 3*a^2*b^3*c^5*d - 9*a^3*b^2*c^4*d^2 + 39*a^4*b*c^3*d^3 - 20*a^5*c^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^3*b^4*c^7*d^2 - 3*a^4*b^3*c^6*d^3 + 3*a^5*b^2*c^5*d^4 - a^6*b*c^4*d^5)*x^4 + (2*a^3*b^4*c^8*d - 5*a^4*b^3*c^7*d^2 + 3*a^5*b^2*c^6*d^3 + a^6*b*c^5*d^4 - a^7*c^4*d^5)*x^3 + (a^3*b^4*c^9 - a^4*b^3*c^8*d - 3*a^5*b^2*c^7*d^2 + 5*a^6*b*c^6*d^3 - 2*a^7*c^5*d^4)*x^2 + (a^4*b^3*c^9 - 3*a^5*b^2*c^8*d + 3*a^6*b*c^7*d^2 - a^7*c^6*d^3)*x)]","B",0
792,1,2002,0,28.231081," ","integrate(1/x^3/(b*x+a)^(3/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(3 \, b^{6} c^{5} d^{2} - 3 \, a b^{5} c^{4} d^{3} - 2 \, a^{2} b^{4} c^{3} d^{4} - 6 \, a^{3} b^{3} c^{2} d^{5} + 15 \, a^{4} b^{2} c d^{6} - 7 \, a^{5} b d^{7}\right)} x^{5} + {\left(6 \, b^{6} c^{6} d - 3 \, a b^{5} c^{5} d^{2} - 7 \, a^{2} b^{4} c^{4} d^{3} - 14 \, a^{3} b^{3} c^{3} d^{4} + 24 \, a^{4} b^{2} c^{2} d^{5} + a^{5} b c d^{6} - 7 \, a^{6} d^{7}\right)} x^{4} + {\left(3 \, b^{6} c^{7} + 3 \, a b^{5} c^{6} d - 8 \, a^{2} b^{4} c^{5} d^{2} - 10 \, a^{3} b^{3} c^{4} d^{3} + 3 \, a^{4} b^{2} c^{3} d^{4} + 23 \, a^{5} b c^{2} d^{5} - 14 \, a^{6} c d^{6}\right)} x^{3} + {\left(3 \, a b^{5} c^{7} - 3 \, a^{2} b^{4} c^{6} d - 2 \, a^{3} b^{3} c^{5} d^{2} - 6 \, a^{4} b^{2} c^{4} d^{3} + 15 \, a^{5} b c^{3} d^{4} - 7 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{3} b^{3} c^{7} - 18 \, a^{4} b^{2} c^{6} d + 18 \, a^{5} b c^{5} d^{2} - 6 \, a^{6} c^{4} d^{3} - {\left(45 \, a b^{5} c^{5} d^{2} - 30 \, a^{2} b^{4} c^{4} d^{3} - 36 \, a^{3} b^{3} c^{3} d^{4} + 190 \, a^{4} b^{2} c^{2} d^{5} - 105 \, a^{5} b c d^{6}\right)} x^{4} - {\left(90 \, a b^{5} c^{6} d - 45 \, a^{2} b^{4} c^{5} d^{2} - 84 \, a^{3} b^{3} c^{4} d^{3} + 222 \, a^{4} b^{2} c^{3} d^{4} + 50 \, a^{5} b c^{2} d^{5} - 105 \, a^{6} c d^{6}\right)} x^{3} - {\left(45 \, a b^{5} c^{7} - 66 \, a^{3} b^{3} c^{5} d^{2} - 12 \, a^{4} b^{2} c^{4} d^{3} + 237 \, a^{5} b c^{3} d^{4} - 140 \, a^{6} c^{2} d^{5}\right)} x^{2} - 3 \, {\left(5 \, a^{2} b^{4} c^{7} - 8 \, a^{3} b^{3} c^{6} d - 6 \, a^{4} b^{2} c^{5} d^{2} + 16 \, a^{5} b c^{4} d^{3} - 7 \, a^{6} c^{3} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left({\left(a^{4} b^{4} c^{8} d^{2} - 3 \, a^{5} b^{3} c^{7} d^{3} + 3 \, a^{6} b^{2} c^{6} d^{4} - a^{7} b c^{5} d^{5}\right)} x^{5} + {\left(2 \, a^{4} b^{4} c^{9} d - 5 \, a^{5} b^{3} c^{8} d^{2} + 3 \, a^{6} b^{2} c^{7} d^{3} + a^{7} b c^{6} d^{4} - a^{8} c^{5} d^{5}\right)} x^{4} + {\left(a^{4} b^{4} c^{10} - a^{5} b^{3} c^{9} d - 3 \, a^{6} b^{2} c^{8} d^{2} + 5 \, a^{7} b c^{7} d^{3} - 2 \, a^{8} c^{6} d^{4}\right)} x^{3} + {\left(a^{5} b^{3} c^{10} - 3 \, a^{6} b^{2} c^{9} d + 3 \, a^{7} b c^{8} d^{2} - a^{8} c^{7} d^{3}\right)} x^{2}\right)}}, \frac{15 \, {\left({\left(3 \, b^{6} c^{5} d^{2} - 3 \, a b^{5} c^{4} d^{3} - 2 \, a^{2} b^{4} c^{3} d^{4} - 6 \, a^{3} b^{3} c^{2} d^{5} + 15 \, a^{4} b^{2} c d^{6} - 7 \, a^{5} b d^{7}\right)} x^{5} + {\left(6 \, b^{6} c^{6} d - 3 \, a b^{5} c^{5} d^{2} - 7 \, a^{2} b^{4} c^{4} d^{3} - 14 \, a^{3} b^{3} c^{3} d^{4} + 24 \, a^{4} b^{2} c^{2} d^{5} + a^{5} b c d^{6} - 7 \, a^{6} d^{7}\right)} x^{4} + {\left(3 \, b^{6} c^{7} + 3 \, a b^{5} c^{6} d - 8 \, a^{2} b^{4} c^{5} d^{2} - 10 \, a^{3} b^{3} c^{4} d^{3} + 3 \, a^{4} b^{2} c^{3} d^{4} + 23 \, a^{5} b c^{2} d^{5} - 14 \, a^{6} c d^{6}\right)} x^{3} + {\left(3 \, a b^{5} c^{7} - 3 \, a^{2} b^{4} c^{6} d - 2 \, a^{3} b^{3} c^{5} d^{2} - 6 \, a^{4} b^{2} c^{4} d^{3} + 15 \, a^{5} b c^{3} d^{4} - 7 \, a^{6} c^{2} d^{5}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{3} b^{3} c^{7} - 18 \, a^{4} b^{2} c^{6} d + 18 \, a^{5} b c^{5} d^{2} - 6 \, a^{6} c^{4} d^{3} - {\left(45 \, a b^{5} c^{5} d^{2} - 30 \, a^{2} b^{4} c^{4} d^{3} - 36 \, a^{3} b^{3} c^{3} d^{4} + 190 \, a^{4} b^{2} c^{2} d^{5} - 105 \, a^{5} b c d^{6}\right)} x^{4} - {\left(90 \, a b^{5} c^{6} d - 45 \, a^{2} b^{4} c^{5} d^{2} - 84 \, a^{3} b^{3} c^{4} d^{3} + 222 \, a^{4} b^{2} c^{3} d^{4} + 50 \, a^{5} b c^{2} d^{5} - 105 \, a^{6} c d^{6}\right)} x^{3} - {\left(45 \, a b^{5} c^{7} - 66 \, a^{3} b^{3} c^{5} d^{2} - 12 \, a^{4} b^{2} c^{4} d^{3} + 237 \, a^{5} b c^{3} d^{4} - 140 \, a^{6} c^{2} d^{5}\right)} x^{2} - 3 \, {\left(5 \, a^{2} b^{4} c^{7} - 8 \, a^{3} b^{3} c^{6} d - 6 \, a^{4} b^{2} c^{5} d^{2} + 16 \, a^{5} b c^{4} d^{3} - 7 \, a^{6} c^{3} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left({\left(a^{4} b^{4} c^{8} d^{2} - 3 \, a^{5} b^{3} c^{7} d^{3} + 3 \, a^{6} b^{2} c^{6} d^{4} - a^{7} b c^{5} d^{5}\right)} x^{5} + {\left(2 \, a^{4} b^{4} c^{9} d - 5 \, a^{5} b^{3} c^{8} d^{2} + 3 \, a^{6} b^{2} c^{7} d^{3} + a^{7} b c^{6} d^{4} - a^{8} c^{5} d^{5}\right)} x^{4} + {\left(a^{4} b^{4} c^{10} - a^{5} b^{3} c^{9} d - 3 \, a^{6} b^{2} c^{8} d^{2} + 5 \, a^{7} b c^{7} d^{3} - 2 \, a^{8} c^{6} d^{4}\right)} x^{3} + {\left(a^{5} b^{3} c^{10} - 3 \, a^{6} b^{2} c^{9} d + 3 \, a^{7} b c^{8} d^{2} - a^{8} c^{7} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((3*b^6*c^5*d^2 - 3*a*b^5*c^4*d^3 - 2*a^2*b^4*c^3*d^4 - 6*a^3*b^3*c^2*d^5 + 15*a^4*b^2*c*d^6 - 7*a^5*b*d^7)*x^5 + (6*b^6*c^6*d - 3*a*b^5*c^5*d^2 - 7*a^2*b^4*c^4*d^3 - 14*a^3*b^3*c^3*d^4 + 24*a^4*b^2*c^2*d^5 + a^5*b*c*d^6 - 7*a^6*d^7)*x^4 + (3*b^6*c^7 + 3*a*b^5*c^6*d - 8*a^2*b^4*c^5*d^2 - 10*a^3*b^3*c^4*d^3 + 3*a^4*b^2*c^3*d^4 + 23*a^5*b*c^2*d^5 - 14*a^6*c*d^6)*x^3 + (3*a*b^5*c^7 - 3*a^2*b^4*c^6*d - 2*a^3*b^3*c^5*d^2 - 6*a^4*b^2*c^4*d^3 + 15*a^5*b*c^3*d^4 - 7*a^6*c^2*d^5)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^3*b^3*c^7 - 18*a^4*b^2*c^6*d + 18*a^5*b*c^5*d^2 - 6*a^6*c^4*d^3 - (45*a*b^5*c^5*d^2 - 30*a^2*b^4*c^4*d^3 - 36*a^3*b^3*c^3*d^4 + 190*a^4*b^2*c^2*d^5 - 105*a^5*b*c*d^6)*x^4 - (90*a*b^5*c^6*d - 45*a^2*b^4*c^5*d^2 - 84*a^3*b^3*c^4*d^3 + 222*a^4*b^2*c^3*d^4 + 50*a^5*b*c^2*d^5 - 105*a^6*c*d^6)*x^3 - (45*a*b^5*c^7 - 66*a^3*b^3*c^5*d^2 - 12*a^4*b^2*c^4*d^3 + 237*a^5*b*c^3*d^4 - 140*a^6*c^2*d^5)*x^2 - 3*(5*a^2*b^4*c^7 - 8*a^3*b^3*c^6*d - 6*a^4*b^2*c^5*d^2 + 16*a^5*b*c^4*d^3 - 7*a^6*c^3*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^4*c^8*d^2 - 3*a^5*b^3*c^7*d^3 + 3*a^6*b^2*c^6*d^4 - a^7*b*c^5*d^5)*x^5 + (2*a^4*b^4*c^9*d - 5*a^5*b^3*c^8*d^2 + 3*a^6*b^2*c^7*d^3 + a^7*b*c^6*d^4 - a^8*c^5*d^5)*x^4 + (a^4*b^4*c^10 - a^5*b^3*c^9*d - 3*a^6*b^2*c^8*d^2 + 5*a^7*b*c^7*d^3 - 2*a^8*c^6*d^4)*x^3 + (a^5*b^3*c^10 - 3*a^6*b^2*c^9*d + 3*a^7*b*c^8*d^2 - a^8*c^7*d^3)*x^2), 1/24*(15*((3*b^6*c^5*d^2 - 3*a*b^5*c^4*d^3 - 2*a^2*b^4*c^3*d^4 - 6*a^3*b^3*c^2*d^5 + 15*a^4*b^2*c*d^6 - 7*a^5*b*d^7)*x^5 + (6*b^6*c^6*d - 3*a*b^5*c^5*d^2 - 7*a^2*b^4*c^4*d^3 - 14*a^3*b^3*c^3*d^4 + 24*a^4*b^2*c^2*d^5 + a^5*b*c*d^6 - 7*a^6*d^7)*x^4 + (3*b^6*c^7 + 3*a*b^5*c^6*d - 8*a^2*b^4*c^5*d^2 - 10*a^3*b^3*c^4*d^3 + 3*a^4*b^2*c^3*d^4 + 23*a^5*b*c^2*d^5 - 14*a^6*c*d^6)*x^3 + (3*a*b^5*c^7 - 3*a^2*b^4*c^6*d - 2*a^3*b^3*c^5*d^2 - 6*a^4*b^2*c^4*d^3 + 15*a^5*b*c^3*d^4 - 7*a^6*c^2*d^5)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(6*a^3*b^3*c^7 - 18*a^4*b^2*c^6*d + 18*a^5*b*c^5*d^2 - 6*a^6*c^4*d^3 - (45*a*b^5*c^5*d^2 - 30*a^2*b^4*c^4*d^3 - 36*a^3*b^3*c^3*d^4 + 190*a^4*b^2*c^2*d^5 - 105*a^5*b*c*d^6)*x^4 - (90*a*b^5*c^6*d - 45*a^2*b^4*c^5*d^2 - 84*a^3*b^3*c^4*d^3 + 222*a^4*b^2*c^3*d^4 + 50*a^5*b*c^2*d^5 - 105*a^6*c*d^6)*x^3 - (45*a*b^5*c^7 - 66*a^3*b^3*c^5*d^2 - 12*a^4*b^2*c^4*d^3 + 237*a^5*b*c^3*d^4 - 140*a^6*c^2*d^5)*x^2 - 3*(5*a^2*b^4*c^7 - 8*a^3*b^3*c^6*d - 6*a^4*b^2*c^5*d^2 + 16*a^5*b*c^4*d^3 - 7*a^6*c^3*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^4*c^8*d^2 - 3*a^5*b^3*c^7*d^3 + 3*a^6*b^2*c^6*d^4 - a^7*b*c^5*d^5)*x^5 + (2*a^4*b^4*c^9*d - 5*a^5*b^3*c^8*d^2 + 3*a^6*b^2*c^7*d^3 + a^7*b*c^6*d^4 - a^8*c^5*d^5)*x^4 + (a^4*b^4*c^10 - a^5*b^3*c^9*d - 3*a^6*b^2*c^8*d^2 + 5*a^7*b*c^7*d^3 - 2*a^8*c^6*d^4)*x^3 + (a^5*b^3*c^10 - 3*a^6*b^2*c^9*d + 3*a^7*b*c^8*d^2 - a^8*c^7*d^3)*x^2)]","B",0
793,1,1338,0,4.992255," ","integrate(x^4*(d*x+c)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, a^{2} b^{5} c^{5} + 25 \, a^{3} b^{4} c^{4} d + 350 \, a^{4} b^{3} c^{3} d^{2} - 3150 \, a^{5} b^{2} c^{2} d^{3} + 5775 \, a^{6} b c d^{4} - 3003 \, a^{7} d^{5} + {\left(3 \, b^{7} c^{5} + 25 \, a b^{6} c^{4} d + 350 \, a^{2} b^{5} c^{3} d^{2} - 3150 \, a^{3} b^{4} c^{2} d^{3} + 5775 \, a^{4} b^{3} c d^{4} - 3003 \, a^{5} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(3 \, a b^{6} c^{5} + 25 \, a^{2} b^{5} c^{4} d + 350 \, a^{3} b^{4} c^{3} d^{2} - 3150 \, a^{4} b^{3} c^{2} d^{3} + 5775 \, a^{5} b^{2} c d^{4} - 3003 \, a^{6} b d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(384 \, b^{7} d^{5} x^{6} - 45 \, a^{2} b^{5} c^{4} d - 390 \, a^{3} b^{4} c^{3} d^{2} + 27384 \, a^{4} b^{3} c^{2} d^{3} - 71610 \, a^{5} b^{2} c d^{4} + 45045 \, a^{6} b d^{5} + 48 \, {\left(21 \, b^{7} c d^{4} - 13 \, a b^{6} d^{5}\right)} x^{5} + 8 \, {\left(93 \, b^{7} c^{2} d^{3} - 236 \, a b^{6} c d^{4} + 143 \, a^{2} b^{5} d^{5}\right)} x^{4} + 2 \, {\left(15 \, b^{7} c^{3} d^{2} - 917 \, a b^{6} c^{2} d^{3} + 2189 \, a^{2} b^{5} c d^{4} - 1287 \, a^{3} b^{4} d^{5}\right)} x^{3} - 3 \, {\left(15 \, b^{7} c^{4} d + 110 \, a b^{6} c^{3} d^{2} - 2468 \, a^{2} b^{5} c^{2} d^{3} + 5346 \, a^{3} b^{4} c d^{4} - 3003 \, a^{4} b^{3} d^{5}\right)} x^{2} - 6 \, {\left(15 \, a b^{6} c^{4} d + 125 \, a^{2} b^{5} c^{3} d^{2} - 6441 \, a^{3} b^{4} c^{2} d^{3} + 16247 \, a^{4} b^{3} c d^{4} - 10010 \, a^{5} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{7680 \, {\left(b^{10} d^{3} x^{2} + 2 \, a b^{9} d^{3} x + a^{2} b^{8} d^{3}\right)}}, -\frac{15 \, {\left(3 \, a^{2} b^{5} c^{5} + 25 \, a^{3} b^{4} c^{4} d + 350 \, a^{4} b^{3} c^{3} d^{2} - 3150 \, a^{5} b^{2} c^{2} d^{3} + 5775 \, a^{6} b c d^{4} - 3003 \, a^{7} d^{5} + {\left(3 \, b^{7} c^{5} + 25 \, a b^{6} c^{4} d + 350 \, a^{2} b^{5} c^{3} d^{2} - 3150 \, a^{3} b^{4} c^{2} d^{3} + 5775 \, a^{4} b^{3} c d^{4} - 3003 \, a^{5} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(3 \, a b^{6} c^{5} + 25 \, a^{2} b^{5} c^{4} d + 350 \, a^{3} b^{4} c^{3} d^{2} - 3150 \, a^{4} b^{3} c^{2} d^{3} + 5775 \, a^{5} b^{2} c d^{4} - 3003 \, a^{6} b d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, b^{7} d^{5} x^{6} - 45 \, a^{2} b^{5} c^{4} d - 390 \, a^{3} b^{4} c^{3} d^{2} + 27384 \, a^{4} b^{3} c^{2} d^{3} - 71610 \, a^{5} b^{2} c d^{4} + 45045 \, a^{6} b d^{5} + 48 \, {\left(21 \, b^{7} c d^{4} - 13 \, a b^{6} d^{5}\right)} x^{5} + 8 \, {\left(93 \, b^{7} c^{2} d^{3} - 236 \, a b^{6} c d^{4} + 143 \, a^{2} b^{5} d^{5}\right)} x^{4} + 2 \, {\left(15 \, b^{7} c^{3} d^{2} - 917 \, a b^{6} c^{2} d^{3} + 2189 \, a^{2} b^{5} c d^{4} - 1287 \, a^{3} b^{4} d^{5}\right)} x^{3} - 3 \, {\left(15 \, b^{7} c^{4} d + 110 \, a b^{6} c^{3} d^{2} - 2468 \, a^{2} b^{5} c^{2} d^{3} + 5346 \, a^{3} b^{4} c d^{4} - 3003 \, a^{4} b^{3} d^{5}\right)} x^{2} - 6 \, {\left(15 \, a b^{6} c^{4} d + 125 \, a^{2} b^{5} c^{3} d^{2} - 6441 \, a^{3} b^{4} c^{2} d^{3} + 16247 \, a^{4} b^{3} c d^{4} - 10010 \, a^{5} b^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3840 \, {\left(b^{10} d^{3} x^{2} + 2 \, a b^{9} d^{3} x + a^{2} b^{8} d^{3}\right)}}\right]"," ",0,"[-1/7680*(15*(3*a^2*b^5*c^5 + 25*a^3*b^4*c^4*d + 350*a^4*b^3*c^3*d^2 - 3150*a^5*b^2*c^2*d^3 + 5775*a^6*b*c*d^4 - 3003*a^7*d^5 + (3*b^7*c^5 + 25*a*b^6*c^4*d + 350*a^2*b^5*c^3*d^2 - 3150*a^3*b^4*c^2*d^3 + 5775*a^4*b^3*c*d^4 - 3003*a^5*b^2*d^5)*x^2 + 2*(3*a*b^6*c^5 + 25*a^2*b^5*c^4*d + 350*a^3*b^4*c^3*d^2 - 3150*a^4*b^3*c^2*d^3 + 5775*a^5*b^2*c*d^4 - 3003*a^6*b*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(384*b^7*d^5*x^6 - 45*a^2*b^5*c^4*d - 390*a^3*b^4*c^3*d^2 + 27384*a^4*b^3*c^2*d^3 - 71610*a^5*b^2*c*d^4 + 45045*a^6*b*d^5 + 48*(21*b^7*c*d^4 - 13*a*b^6*d^5)*x^5 + 8*(93*b^7*c^2*d^3 - 236*a*b^6*c*d^4 + 143*a^2*b^5*d^5)*x^4 + 2*(15*b^7*c^3*d^2 - 917*a*b^6*c^2*d^3 + 2189*a^2*b^5*c*d^4 - 1287*a^3*b^4*d^5)*x^3 - 3*(15*b^7*c^4*d + 110*a*b^6*c^3*d^2 - 2468*a^2*b^5*c^2*d^3 + 5346*a^3*b^4*c*d^4 - 3003*a^4*b^3*d^5)*x^2 - 6*(15*a*b^6*c^4*d + 125*a^2*b^5*c^3*d^2 - 6441*a^3*b^4*c^2*d^3 + 16247*a^4*b^3*c*d^4 - 10010*a^5*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^10*d^3*x^2 + 2*a*b^9*d^3*x + a^2*b^8*d^3), -1/3840*(15*(3*a^2*b^5*c^5 + 25*a^3*b^4*c^4*d + 350*a^4*b^3*c^3*d^2 - 3150*a^5*b^2*c^2*d^3 + 5775*a^6*b*c*d^4 - 3003*a^7*d^5 + (3*b^7*c^5 + 25*a*b^6*c^4*d + 350*a^2*b^5*c^3*d^2 - 3150*a^3*b^4*c^2*d^3 + 5775*a^4*b^3*c*d^4 - 3003*a^5*b^2*d^5)*x^2 + 2*(3*a*b^6*c^5 + 25*a^2*b^5*c^4*d + 350*a^3*b^4*c^3*d^2 - 3150*a^4*b^3*c^2*d^3 + 5775*a^5*b^2*c*d^4 - 3003*a^6*b*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(384*b^7*d^5*x^6 - 45*a^2*b^5*c^4*d - 390*a^3*b^4*c^3*d^2 + 27384*a^4*b^3*c^2*d^3 - 71610*a^5*b^2*c*d^4 + 45045*a^6*b*d^5 + 48*(21*b^7*c*d^4 - 13*a*b^6*d^5)*x^5 + 8*(93*b^7*c^2*d^3 - 236*a*b^6*c*d^4 + 143*a^2*b^5*d^5)*x^4 + 2*(15*b^7*c^3*d^2 - 917*a*b^6*c^2*d^3 + 2189*a^2*b^5*c*d^4 - 1287*a^3*b^4*d^5)*x^3 - 3*(15*b^7*c^4*d + 110*a*b^6*c^3*d^2 - 2468*a^2*b^5*c^2*d^3 + 5346*a^3*b^4*c*d^4 - 3003*a^4*b^3*d^5)*x^2 - 6*(15*a*b^6*c^4*d + 125*a^2*b^5*c^3*d^2 - 6441*a^3*b^4*c^2*d^3 + 16247*a^4*b^3*c*d^4 - 10010*a^5*b^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^10*d^3*x^2 + 2*a*b^9*d^3*x + a^2*b^8*d^3)]","A",0
794,1,1060,0,3.385812," ","integrate(x^3*(d*x+c)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a^{2} b^{4} c^{4} + 20 \, a^{3} b^{3} c^{3} d - 210 \, a^{4} b^{2} c^{2} d^{2} + 420 \, a^{5} b c d^{3} - 231 \, a^{6} d^{4} + {\left(b^{6} c^{4} + 20 \, a b^{5} c^{3} d - 210 \, a^{2} b^{4} c^{2} d^{2} + 420 \, a^{3} b^{3} c d^{3} - 231 \, a^{4} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} + 20 \, a^{2} b^{4} c^{3} d - 210 \, a^{3} b^{3} c^{2} d^{2} + 420 \, a^{4} b^{2} c d^{3} - 231 \, a^{5} b d^{4}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(48 \, b^{6} d^{4} x^{5} + 15 \, a^{2} b^{4} c^{3} d - 1743 \, a^{3} b^{3} c^{2} d^{2} + 5145 \, a^{4} b^{2} c d^{3} - 3465 \, a^{5} b d^{4} + 8 \, {\left(17 \, b^{6} c d^{3} - 11 \, a b^{5} d^{4}\right)} x^{4} + 2 \, {\left(59 \, b^{6} c^{2} d^{2} - 158 \, a b^{5} c d^{3} + 99 \, a^{2} b^{4} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{6} c^{3} d - 161 \, a b^{5} c^{2} d^{2} + 387 \, a^{2} b^{4} c d^{3} - 231 \, a^{3} b^{3} d^{4}\right)} x^{2} + 6 \, {\left(5 \, a b^{5} c^{3} d - 412 \, a^{2} b^{4} c^{2} d^{2} + 1169 \, a^{3} b^{3} c d^{3} - 770 \, a^{4} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(b^{9} d^{2} x^{2} + 2 \, a b^{8} d^{2} x + a^{2} b^{7} d^{2}\right)}}, \frac{15 \, {\left(a^{2} b^{4} c^{4} + 20 \, a^{3} b^{3} c^{3} d - 210 \, a^{4} b^{2} c^{2} d^{2} + 420 \, a^{5} b c d^{3} - 231 \, a^{6} d^{4} + {\left(b^{6} c^{4} + 20 \, a b^{5} c^{3} d - 210 \, a^{2} b^{4} c^{2} d^{2} + 420 \, a^{3} b^{3} c d^{3} - 231 \, a^{4} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} + 20 \, a^{2} b^{4} c^{3} d - 210 \, a^{3} b^{3} c^{2} d^{2} + 420 \, a^{4} b^{2} c d^{3} - 231 \, a^{5} b d^{4}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, b^{6} d^{4} x^{5} + 15 \, a^{2} b^{4} c^{3} d - 1743 \, a^{3} b^{3} c^{2} d^{2} + 5145 \, a^{4} b^{2} c d^{3} - 3465 \, a^{5} b d^{4} + 8 \, {\left(17 \, b^{6} c d^{3} - 11 \, a b^{5} d^{4}\right)} x^{4} + 2 \, {\left(59 \, b^{6} c^{2} d^{2} - 158 \, a b^{5} c d^{3} + 99 \, a^{2} b^{4} d^{4}\right)} x^{3} + 3 \, {\left(5 \, b^{6} c^{3} d - 161 \, a b^{5} c^{2} d^{2} + 387 \, a^{2} b^{4} c d^{3} - 231 \, a^{3} b^{3} d^{4}\right)} x^{2} + 6 \, {\left(5 \, a b^{5} c^{3} d - 412 \, a^{2} b^{4} c^{2} d^{2} + 1169 \, a^{3} b^{3} c d^{3} - 770 \, a^{4} b^{2} d^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(b^{9} d^{2} x^{2} + 2 \, a b^{8} d^{2} x + a^{2} b^{7} d^{2}\right)}}\right]"," ",0,"[-1/768*(15*(a^2*b^4*c^4 + 20*a^3*b^3*c^3*d - 210*a^4*b^2*c^2*d^2 + 420*a^5*b*c*d^3 - 231*a^6*d^4 + (b^6*c^4 + 20*a*b^5*c^3*d - 210*a^2*b^4*c^2*d^2 + 420*a^3*b^3*c*d^3 - 231*a^4*b^2*d^4)*x^2 + 2*(a*b^5*c^4 + 20*a^2*b^4*c^3*d - 210*a^3*b^3*c^2*d^2 + 420*a^4*b^2*c*d^3 - 231*a^5*b*d^4)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(48*b^6*d^4*x^5 + 15*a^2*b^4*c^3*d - 1743*a^3*b^3*c^2*d^2 + 5145*a^4*b^2*c*d^3 - 3465*a^5*b*d^4 + 8*(17*b^6*c*d^3 - 11*a*b^5*d^4)*x^4 + 2*(59*b^6*c^2*d^2 - 158*a*b^5*c*d^3 + 99*a^2*b^4*d^4)*x^3 + 3*(5*b^6*c^3*d - 161*a*b^5*c^2*d^2 + 387*a^2*b^4*c*d^3 - 231*a^3*b^3*d^4)*x^2 + 6*(5*a*b^5*c^3*d - 412*a^2*b^4*c^2*d^2 + 1169*a^3*b^3*c*d^3 - 770*a^4*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^9*d^2*x^2 + 2*a*b^8*d^2*x + a^2*b^7*d^2), 1/384*(15*(a^2*b^4*c^4 + 20*a^3*b^3*c^3*d - 210*a^4*b^2*c^2*d^2 + 420*a^5*b*c*d^3 - 231*a^6*d^4 + (b^6*c^4 + 20*a*b^5*c^3*d - 210*a^2*b^4*c^2*d^2 + 420*a^3*b^3*c*d^3 - 231*a^4*b^2*d^4)*x^2 + 2*(a*b^5*c^4 + 20*a^2*b^4*c^3*d - 210*a^3*b^3*c^2*d^2 + 420*a^4*b^2*c*d^3 - 231*a^5*b*d^4)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(48*b^6*d^4*x^5 + 15*a^2*b^4*c^3*d - 1743*a^3*b^3*c^2*d^2 + 5145*a^4*b^2*c*d^3 - 3465*a^5*b*d^4 + 8*(17*b^6*c*d^3 - 11*a*b^5*d^4)*x^4 + 2*(59*b^6*c^2*d^2 - 158*a*b^5*c*d^3 + 99*a^2*b^4*d^4)*x^3 + 3*(5*b^6*c^3*d - 161*a*b^5*c^2*d^2 + 387*a^2*b^4*c*d^3 - 231*a^3*b^3*d^4)*x^2 + 6*(5*a*b^5*c^3*d - 412*a^2*b^4*c^2*d^2 + 1169*a^3*b^3*c*d^3 - 770*a^4*b^2*d^4)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^9*d^2*x^2 + 2*a*b^8*d^2*x + a^2*b^7*d^2)]","A",0
795,1,804,0,3.290260," ","integrate(x^2*(d*x+c)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a^{2} b^{3} c^{3} - 15 \, a^{3} b^{2} c^{2} d + 35 \, a^{4} b c d^{2} - 21 \, a^{5} d^{3} + {\left(b^{5} c^{3} - 15 \, a b^{4} c^{2} d + 35 \, a^{2} b^{3} c d^{2} - 21 \, a^{3} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} - 15 \, a^{2} b^{3} c^{2} d + 35 \, a^{3} b^{2} c d^{2} - 21 \, a^{4} b d^{3}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(8 \, b^{5} d^{3} x^{4} + 113 \, a^{2} b^{3} c^{2} d - 420 \, a^{3} b^{2} c d^{2} + 315 \, a^{4} b d^{3} + 2 \, {\left(13 \, b^{5} c d^{2} - 9 \, a b^{4} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{5} c^{2} d - 32 \, a b^{4} c d^{2} + 21 \, a^{2} b^{3} d^{3}\right)} x^{2} + 2 \, {\left(81 \, a b^{4} c^{2} d - 287 \, a^{2} b^{3} c d^{2} + 210 \, a^{3} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(b^{8} d x^{2} + 2 \, a b^{7} d x + a^{2} b^{6} d\right)}}, -\frac{15 \, {\left(a^{2} b^{3} c^{3} - 15 \, a^{3} b^{2} c^{2} d + 35 \, a^{4} b c d^{2} - 21 \, a^{5} d^{3} + {\left(b^{5} c^{3} - 15 \, a b^{4} c^{2} d + 35 \, a^{2} b^{3} c d^{2} - 21 \, a^{3} b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} - 15 \, a^{2} b^{3} c^{2} d + 35 \, a^{3} b^{2} c d^{2} - 21 \, a^{4} b d^{3}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b^{5} d^{3} x^{4} + 113 \, a^{2} b^{3} c^{2} d - 420 \, a^{3} b^{2} c d^{2} + 315 \, a^{4} b d^{3} + 2 \, {\left(13 \, b^{5} c d^{2} - 9 \, a b^{4} d^{3}\right)} x^{3} + 3 \, {\left(11 \, b^{5} c^{2} d - 32 \, a b^{4} c d^{2} + 21 \, a^{2} b^{3} d^{3}\right)} x^{2} + 2 \, {\left(81 \, a b^{4} c^{2} d - 287 \, a^{2} b^{3} c d^{2} + 210 \, a^{3} b^{2} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{8} d x^{2} + 2 \, a b^{7} d x + a^{2} b^{6} d\right)}}\right]"," ",0,"[-1/96*(15*(a^2*b^3*c^3 - 15*a^3*b^2*c^2*d + 35*a^4*b*c*d^2 - 21*a^5*d^3 + (b^5*c^3 - 15*a*b^4*c^2*d + 35*a^2*b^3*c*d^2 - 21*a^3*b^2*d^3)*x^2 + 2*(a*b^4*c^3 - 15*a^2*b^3*c^2*d + 35*a^3*b^2*c*d^2 - 21*a^4*b*d^3)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(8*b^5*d^3*x^4 + 113*a^2*b^3*c^2*d - 420*a^3*b^2*c*d^2 + 315*a^4*b*d^3 + 2*(13*b^5*c*d^2 - 9*a*b^4*d^3)*x^3 + 3*(11*b^5*c^2*d - 32*a*b^4*c*d^2 + 21*a^2*b^3*d^3)*x^2 + 2*(81*a*b^4*c^2*d - 287*a^2*b^3*c*d^2 + 210*a^3*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^8*d*x^2 + 2*a*b^7*d*x + a^2*b^6*d), -1/48*(15*(a^2*b^3*c^3 - 15*a^3*b^2*c^2*d + 35*a^4*b*c*d^2 - 21*a^5*d^3 + (b^5*c^3 - 15*a*b^4*c^2*d + 35*a^2*b^3*c*d^2 - 21*a^3*b^2*d^3)*x^2 + 2*(a*b^4*c^3 - 15*a^2*b^3*c^2*d + 35*a^3*b^2*c*d^2 - 21*a^4*b*d^3)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 2*(8*b^5*d^3*x^4 + 113*a^2*b^3*c^2*d - 420*a^3*b^2*c*d^2 + 315*a^4*b*d^3 + 2*(13*b^5*c*d^2 - 9*a*b^4*d^3)*x^3 + 3*(11*b^5*c^2*d - 32*a*b^4*c*d^2 + 21*a^2*b^3*d^3)*x^2 + 2*(81*a*b^4*c^2*d - 287*a^2*b^3*c*d^2 + 210*a^3*b^2*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^8*d*x^2 + 2*a*b^7*d*x + a^2*b^6*d)]","A",0
796,1,619,0,2.392176," ","integrate(x*(d*x+c)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 7 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 7 \, a^{3} b d^{2}\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(6 \, b^{3} d^{2} x^{3} - 16 \, a b^{2} c^{2} + 115 \, a^{2} b c d - 105 \, a^{3} d^{2} + 3 \, {\left(9 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{2} - 2 \, {\left(12 \, b^{3} c^{2} - 79 \, a b^{2} c d + 70 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{15 \, {\left(3 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 7 \, a^{4} d^{2} + {\left(3 \, b^{4} c^{2} - 10 \, a b^{3} c d + 7 \, a^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 7 \, a^{3} b d^{2}\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(6 \, b^{3} d^{2} x^{3} - 16 \, a b^{2} c^{2} + 115 \, a^{2} b c d - 105 \, a^{3} d^{2} + 3 \, {\left(9 \, b^{3} c d - 7 \, a b^{2} d^{2}\right)} x^{2} - 2 \, {\left(12 \, b^{3} c^{2} - 79 \, a b^{2} c d + 70 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[1/48*(15*(3*a^2*b^2*c^2 - 10*a^3*b*c*d + 7*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^2 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 7*a^3*b*d^2)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(6*b^3*d^2*x^3 - 16*a*b^2*c^2 + 115*a^2*b*c*d - 105*a^3*d^2 + 3*(9*b^3*c*d - 7*a*b^2*d^2)*x^2 - 2*(12*b^3*c^2 - 79*a*b^2*c*d + 70*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/24*(15*(3*a^2*b^2*c^2 - 10*a^3*b*c*d + 7*a^4*d^2 + (3*b^4*c^2 - 10*a*b^3*c*d + 7*a^2*b^2*d^2)*x^2 + 2*(3*a*b^3*c^2 - 10*a^2*b^2*c*d + 7*a^3*b*d^2)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(6*b^3*d^2*x^3 - 16*a*b^2*c^2 + 115*a^2*b*c*d - 105*a^3*d^2 + 3*(9*b^3*c*d - 7*a*b^2*d^2)*x^2 - 2*(12*b^3*c^2 - 79*a*b^2*c*d + 70*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
797,1,475,0,1.998008," ","integrate((d*x+c)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a^{2} b c d - a^{3} d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, b^{2} d^{2} x^{2} - 2 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2} - 2 \, {\left(7 \, b^{2} c d - 10 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{15 \, {\left(a^{2} b c d - a^{3} d^{2} + {\left(b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} - 2 \, b^{2} c^{2} - 10 \, a b c d + 15 \, a^{2} d^{2} - 2 \, {\left(7 \, b^{2} c d - 10 \, a b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[-1/12*(15*(a^2*b*c*d - a^3*d^2 + (b^3*c*d - a*b^2*d^2)*x^2 + 2*(a*b^2*c*d - a^2*b*d^2)*x)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*b^2*d^2*x^2 - 2*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2 - 2*(7*b^2*c*d - 10*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -1/6*(15*(a^2*b*c*d - a^3*d^2 + (b^3*c*d - a*b^2*d^2)*x^2 + 2*(a*b^2*c*d - a^2*b*d^2)*x)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 2*(3*b^2*d^2*x^2 - 2*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2 - 2*(7*b^2*c*d - 10*a*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","B",0
798,1,1361,0,5.934772," ","integrate((d*x+c)^(5/2)/x/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{3} b d^{2} x + a^{4} d^{2}\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 3 \, {\left(b^{4} c^{2} x^{2} + 2 \, a b^{3} c^{2} x + a^{2} b^{2} c^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}, -\frac{6 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{3} b d^{2} x + a^{4} d^{2}\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - 3 \, {\left(b^{4} c^{2} x^{2} + 2 \, a b^{3} c^{2} x + a^{2} b^{2} c^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}, \frac{6 \, {\left(b^{4} c^{2} x^{2} + 2 \, a b^{3} c^{2} x + a^{2} b^{2} c^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 3 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{3} b d^{2} x + a^{4} d^{2}\right)} \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}, \frac{3 \, {\left(b^{4} c^{2} x^{2} + 2 \, a b^{3} c^{2} x + a^{2} b^{2} c^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 3 \, {\left(a^{2} b^{2} d^{2} x^{2} + 2 \, a^{3} b d^{2} x + a^{4} d^{2}\right)} \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) + 2 \, {\left(4 \, a b^{2} c^{2} - a^{2} b c d - 3 \, a^{3} d^{2} + {\left(3 \, b^{3} c^{2} + a b^{2} c d - 4 \, a^{2} b d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}\right]"," ",0,"[1/6*(3*(a^2*b^2*d^2*x^2 + 2*a^3*b*d^2*x + a^4*d^2)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 3*(b^4*c^2*x^2 + 2*a*b^3*c^2*x + a^2*b^2*c^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2), -1/6*(6*(a^2*b^2*d^2*x^2 + 2*a^3*b*d^2*x + a^4*d^2)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - 3*(b^4*c^2*x^2 + 2*a*b^3*c^2*x + a^2*b^2*c^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2), 1/6*(6*(b^4*c^2*x^2 + 2*a*b^3*c^2*x + a^2*b^2*c^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 3*(a^2*b^2*d^2*x^2 + 2*a^3*b*d^2*x + a^4*d^2)*sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2), 1/3*(3*(b^4*c^2*x^2 + 2*a*b^3*c^2*x + a^2*b^2*c^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 3*(a^2*b^2*d^2*x^2 + 2*a^3*b*d^2*x + a^4*d^2)*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) + 2*(4*a*b^2*c^2 - a^2*b*c*d - 3*a^3*d^2 + (3*b^3*c^2 + a*b^2*c*d - 4*a^2*b*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2)]","B",0
799,1,505,0,2.697938," ","integrate((d*x+c)^(5/2)/x^2/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{3} + 2 \, {\left(a b^{2} c^{2} - a^{2} b c d\right)} x^{2} + {\left(a^{2} b c^{2} - a^{3} c d\right)} x\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(3 \, a^{2} c^{2} + {\left(15 \, b^{2} c^{2} - 10 \, a b c d - 2 \, a^{2} d^{2}\right)} x^{2} + 2 \, {\left(10 \, a b c^{2} - 7 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}, -\frac{15 \, {\left({\left(b^{3} c^{2} - a b^{2} c d\right)} x^{3} + 2 \, {\left(a b^{2} c^{2} - a^{2} b c d\right)} x^{2} + {\left(a^{2} b c^{2} - a^{3} c d\right)} x\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a^{2} c^{2} + {\left(15 \, b^{2} c^{2} - 10 \, a b c d - 2 \, a^{2} d^{2}\right)} x^{2} + 2 \, {\left(10 \, a b c^{2} - 7 \, a^{2} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}\right]"," ",0,"[-1/12*(15*((b^3*c^2 - a*b^2*c*d)*x^3 + 2*(a*b^2*c^2 - a^2*b*c*d)*x^2 + (a^2*b*c^2 - a^3*c*d)*x)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(3*a^2*c^2 + (15*b^2*c^2 - 10*a*b*c*d - 2*a^2*d^2)*x^2 + 2*(10*a*b*c^2 - 7*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x), -1/6*(15*((b^3*c^2 - a*b^2*c*d)*x^3 + 2*(a*b^2*c^2 - a^2*b*c*d)*x^2 + (a^2*b*c^2 - a^3*c*d)*x)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) + 2*(3*a^2*c^2 + (15*b^2*c^2 - 10*a*b*c*d - 2*a^2*d^2)*x^2 + 2*(10*a*b*c^2 - 7*a^2*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x)]","B",0
800,1,659,0,5.628458," ","integrate((d*x+c)^(5/2)/x^3/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(7 \, b^{4} c^{2} - 10 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(7 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x^{3} + {\left(7 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 3 \, a^{4} d^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{a}} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c + {\left(a b c + a^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{c}{a}} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{3} c^{2} - {\left(105 \, b^{3} c^{2} - 115 \, a b^{2} c d + 16 \, a^{2} b d^{2}\right)} x^{3} - 2 \, {\left(70 \, a b^{2} c^{2} - 79 \, a^{2} b c d + 12 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(7 \, a^{2} b c^{2} - 9 \, a^{3} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}, \frac{15 \, {\left({\left(7 \, b^{4} c^{2} - 10 \, a b^{3} c d + 3 \, a^{2} b^{2} d^{2}\right)} x^{4} + 2 \, {\left(7 \, a b^{3} c^{2} - 10 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} x^{3} + {\left(7 \, a^{2} b^{2} c^{2} - 10 \, a^{3} b c d + 3 \, a^{4} d^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{a}} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{c}{a}}}{2 \, {\left(b c d x^{2} + a c^{2} + {\left(b c^{2} + a c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{3} c^{2} - {\left(105 \, b^{3} c^{2} - 115 \, a b^{2} c d + 16 \, a^{2} b d^{2}\right)} x^{3} - 2 \, {\left(70 \, a b^{2} c^{2} - 79 \, a^{2} b c d + 12 \, a^{3} d^{2}\right)} x^{2} - 3 \, {\left(7 \, a^{2} b c^{2} - 9 \, a^{3} c d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((7*b^4*c^2 - 10*a*b^3*c*d + 3*a^2*b^2*d^2)*x^4 + 2*(7*a*b^3*c^2 - 10*a^2*b^2*c*d + 3*a^3*b*d^2)*x^3 + (7*a^2*b^2*c^2 - 10*a^3*b*c*d + 3*a^4*d^2)*x^2)*sqrt(c/a)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a^2*c + (a*b*c + a^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(c/a) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^3*c^2 - (105*b^3*c^2 - 115*a*b^2*c*d + 16*a^2*b*d^2)*x^3 - 2*(70*a*b^2*c^2 - 79*a^2*b*c*d + 12*a^3*d^2)*x^2 - 3*(7*a^2*b*c^2 - 9*a^3*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2), 1/24*(15*((7*b^4*c^2 - 10*a*b^3*c*d + 3*a^2*b^2*d^2)*x^4 + 2*(7*a*b^3*c^2 - 10*a^2*b^2*c*d + 3*a^3*b*d^2)*x^3 + (7*a^2*b^2*c^2 - 10*a^3*b*c*d + 3*a^4*d^2)*x^2)*sqrt(-c/a)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-c/a)/(b*c*d*x^2 + a*c^2 + (b*c^2 + a*c*d)*x)) - 2*(6*a^3*c^2 - (105*b^3*c^2 - 115*a*b^2*c*d + 16*a^2*b*d^2)*x^3 - 2*(70*a*b^2*c^2 - 79*a^2*b*c*d + 12*a^3*d^2)*x^2 - 3*(7*a^2*b*c^2 - 9*a^3*c*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)]","A",0
801,1,848,0,12.234025," ","integrate((d*x+c)^(5/2)/x^4/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(21 \, b^{5} c^{3} - 35 \, a b^{4} c^{2} d + 15 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} + 2 \, {\left(21 \, a b^{4} c^{3} - 35 \, a^{2} b^{3} c^{2} d + 15 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} + {\left(21 \, a^{2} b^{3} c^{3} - 35 \, a^{3} b^{2} c^{2} d + 15 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{3}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(8 \, a^{5} c^{3} + {\left(315 \, a b^{4} c^{3} - 420 \, a^{2} b^{3} c^{2} d + 113 \, a^{3} b^{2} c d^{2}\right)} x^{4} + 2 \, {\left(210 \, a^{2} b^{3} c^{3} - 287 \, a^{3} b^{2} c^{2} d + 81 \, a^{4} b c d^{2}\right)} x^{3} + 3 \, {\left(21 \, a^{3} b^{2} c^{3} - 32 \, a^{4} b c^{2} d + 11 \, a^{5} c d^{2}\right)} x^{2} - 2 \, {\left(9 \, a^{4} b c^{3} - 13 \, a^{5} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{96 \, {\left(a^{6} b^{2} c x^{5} + 2 \, a^{7} b c x^{4} + a^{8} c x^{3}\right)}}, -\frac{15 \, {\left({\left(21 \, b^{5} c^{3} - 35 \, a b^{4} c^{2} d + 15 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} x^{5} + 2 \, {\left(21 \, a b^{4} c^{3} - 35 \, a^{2} b^{3} c^{2} d + 15 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x^{4} + {\left(21 \, a^{2} b^{3} c^{3} - 35 \, a^{3} b^{2} c^{2} d + 15 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} x^{3}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{5} c^{3} + {\left(315 \, a b^{4} c^{3} - 420 \, a^{2} b^{3} c^{2} d + 113 \, a^{3} b^{2} c d^{2}\right)} x^{4} + 2 \, {\left(210 \, a^{2} b^{3} c^{3} - 287 \, a^{3} b^{2} c^{2} d + 81 \, a^{4} b c d^{2}\right)} x^{3} + 3 \, {\left(21 \, a^{3} b^{2} c^{3} - 32 \, a^{4} b c^{2} d + 11 \, a^{5} c d^{2}\right)} x^{2} - 2 \, {\left(9 \, a^{4} b c^{3} - 13 \, a^{5} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{6} b^{2} c x^{5} + 2 \, a^{7} b c x^{4} + a^{8} c x^{3}\right)}}\right]"," ",0,"[-1/96*(15*((21*b^5*c^3 - 35*a*b^4*c^2*d + 15*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5 + 2*(21*a*b^4*c^3 - 35*a^2*b^3*c^2*d + 15*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 + (21*a^2*b^3*c^3 - 35*a^3*b^2*c^2*d + 15*a^4*b*c*d^2 - a^5*d^3)*x^3)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(8*a^5*c^3 + (315*a*b^4*c^3 - 420*a^2*b^3*c^2*d + 113*a^3*b^2*c*d^2)*x^4 + 2*(210*a^2*b^3*c^3 - 287*a^3*b^2*c^2*d + 81*a^4*b*c*d^2)*x^3 + 3*(21*a^3*b^2*c^3 - 32*a^4*b*c^2*d + 11*a^5*c*d^2)*x^2 - 2*(9*a^4*b*c^3 - 13*a^5*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*b^2*c*x^5 + 2*a^7*b*c*x^4 + a^8*c*x^3), -1/48*(15*((21*b^5*c^3 - 35*a*b^4*c^2*d + 15*a^2*b^3*c*d^2 - a^3*b^2*d^3)*x^5 + 2*(21*a*b^4*c^3 - 35*a^2*b^3*c^2*d + 15*a^3*b^2*c*d^2 - a^4*b*d^3)*x^4 + (21*a^2*b^3*c^3 - 35*a^3*b^2*c^2*d + 15*a^4*b*c*d^2 - a^5*d^3)*x^3)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(8*a^5*c^3 + (315*a*b^4*c^3 - 420*a^2*b^3*c^2*d + 113*a^3*b^2*c*d^2)*x^4 + 2*(210*a^2*b^3*c^3 - 287*a^3*b^2*c^2*d + 81*a^4*b*c*d^2)*x^3 + 3*(21*a^3*b^2*c^3 - 32*a^4*b*c^2*d + 11*a^5*c*d^2)*x^2 - 2*(9*a^4*b*c^3 - 13*a^5*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^6*b^2*c*x^5 + 2*a^7*b*c*x^4 + a^8*c*x^3)]","A",0
802,1,1106,0,35.875383," ","integrate((d*x+c)^(5/2)/x^5/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(231 \, b^{6} c^{4} - 420 \, a b^{5} c^{3} d + 210 \, a^{2} b^{4} c^{2} d^{2} - 20 \, a^{3} b^{3} c d^{3} - a^{4} b^{2} d^{4}\right)} x^{6} + 2 \, {\left(231 \, a b^{5} c^{4} - 420 \, a^{2} b^{4} c^{3} d + 210 \, a^{3} b^{3} c^{2} d^{2} - 20 \, a^{4} b^{2} c d^{3} - a^{5} b d^{4}\right)} x^{5} + {\left(231 \, a^{2} b^{4} c^{4} - 420 \, a^{3} b^{3} c^{3} d + 210 \, a^{4} b^{2} c^{2} d^{2} - 20 \, a^{5} b c d^{3} - a^{6} d^{4}\right)} x^{4}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(48 \, a^{6} c^{4} - 3 \, {\left(1155 \, a b^{5} c^{4} - 1715 \, a^{2} b^{4} c^{3} d + 581 \, a^{3} b^{3} c^{2} d^{2} - 5 \, a^{4} b^{2} c d^{3}\right)} x^{5} - 6 \, {\left(770 \, a^{2} b^{4} c^{4} - 1169 \, a^{3} b^{3} c^{3} d + 412 \, a^{4} b^{2} c^{2} d^{2} - 5 \, a^{5} b c d^{3}\right)} x^{4} - 3 \, {\left(231 \, a^{3} b^{3} c^{4} - 387 \, a^{4} b^{2} c^{3} d + 161 \, a^{5} b c^{2} d^{2} - 5 \, a^{6} c d^{3}\right)} x^{3} + 2 \, {\left(99 \, a^{4} b^{2} c^{4} - 158 \, a^{5} b c^{3} d + 59 \, a^{6} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(11 \, a^{5} b c^{4} - 17 \, a^{6} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{768 \, {\left(a^{7} b^{2} c^{2} x^{6} + 2 \, a^{8} b c^{2} x^{5} + a^{9} c^{2} x^{4}\right)}}, \frac{15 \, {\left({\left(231 \, b^{6} c^{4} - 420 \, a b^{5} c^{3} d + 210 \, a^{2} b^{4} c^{2} d^{2} - 20 \, a^{3} b^{3} c d^{3} - a^{4} b^{2} d^{4}\right)} x^{6} + 2 \, {\left(231 \, a b^{5} c^{4} - 420 \, a^{2} b^{4} c^{3} d + 210 \, a^{3} b^{3} c^{2} d^{2} - 20 \, a^{4} b^{2} c d^{3} - a^{5} b d^{4}\right)} x^{5} + {\left(231 \, a^{2} b^{4} c^{4} - 420 \, a^{3} b^{3} c^{3} d + 210 \, a^{4} b^{2} c^{2} d^{2} - 20 \, a^{5} b c d^{3} - a^{6} d^{4}\right)} x^{4}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(48 \, a^{6} c^{4} - 3 \, {\left(1155 \, a b^{5} c^{4} - 1715 \, a^{2} b^{4} c^{3} d + 581 \, a^{3} b^{3} c^{2} d^{2} - 5 \, a^{4} b^{2} c d^{3}\right)} x^{5} - 6 \, {\left(770 \, a^{2} b^{4} c^{4} - 1169 \, a^{3} b^{3} c^{3} d + 412 \, a^{4} b^{2} c^{2} d^{2} - 5 \, a^{5} b c d^{3}\right)} x^{4} - 3 \, {\left(231 \, a^{3} b^{3} c^{4} - 387 \, a^{4} b^{2} c^{3} d + 161 \, a^{5} b c^{2} d^{2} - 5 \, a^{6} c d^{3}\right)} x^{3} + 2 \, {\left(99 \, a^{4} b^{2} c^{4} - 158 \, a^{5} b c^{3} d + 59 \, a^{6} c^{2} d^{2}\right)} x^{2} - 8 \, {\left(11 \, a^{5} b c^{4} - 17 \, a^{6} c^{3} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{384 \, {\left(a^{7} b^{2} c^{2} x^{6} + 2 \, a^{8} b c^{2} x^{5} + a^{9} c^{2} x^{4}\right)}}\right]"," ",0,"[-1/768*(15*((231*b^6*c^4 - 420*a*b^5*c^3*d + 210*a^2*b^4*c^2*d^2 - 20*a^3*b^3*c*d^3 - a^4*b^2*d^4)*x^6 + 2*(231*a*b^5*c^4 - 420*a^2*b^4*c^3*d + 210*a^3*b^3*c^2*d^2 - 20*a^4*b^2*c*d^3 - a^5*b*d^4)*x^5 + (231*a^2*b^4*c^4 - 420*a^3*b^3*c^3*d + 210*a^4*b^2*c^2*d^2 - 20*a^5*b*c*d^3 - a^6*d^4)*x^4)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(48*a^6*c^4 - 3*(1155*a*b^5*c^4 - 1715*a^2*b^4*c^3*d + 581*a^3*b^3*c^2*d^2 - 5*a^4*b^2*c*d^3)*x^5 - 6*(770*a^2*b^4*c^4 - 1169*a^3*b^3*c^3*d + 412*a^4*b^2*c^2*d^2 - 5*a^5*b*c*d^3)*x^4 - 3*(231*a^3*b^3*c^4 - 387*a^4*b^2*c^3*d + 161*a^5*b*c^2*d^2 - 5*a^6*c*d^3)*x^3 + 2*(99*a^4*b^2*c^4 - 158*a^5*b*c^3*d + 59*a^6*c^2*d^2)*x^2 - 8*(11*a^5*b*c^4 - 17*a^6*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^7*b^2*c^2*x^6 + 2*a^8*b*c^2*x^5 + a^9*c^2*x^4), 1/384*(15*((231*b^6*c^4 - 420*a*b^5*c^3*d + 210*a^2*b^4*c^2*d^2 - 20*a^3*b^3*c*d^3 - a^4*b^2*d^4)*x^6 + 2*(231*a*b^5*c^4 - 420*a^2*b^4*c^3*d + 210*a^3*b^3*c^2*d^2 - 20*a^4*b^2*c*d^3 - a^5*b*d^4)*x^5 + (231*a^2*b^4*c^4 - 420*a^3*b^3*c^3*d + 210*a^4*b^2*c^2*d^2 - 20*a^5*b*c*d^3 - a^6*d^4)*x^4)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(48*a^6*c^4 - 3*(1155*a*b^5*c^4 - 1715*a^2*b^4*c^3*d + 581*a^3*b^3*c^2*d^2 - 5*a^4*b^2*c*d^3)*x^5 - 6*(770*a^2*b^4*c^4 - 1169*a^3*b^3*c^3*d + 412*a^4*b^2*c^2*d^2 - 5*a^5*b*c*d^3)*x^4 - 3*(231*a^3*b^3*c^4 - 387*a^4*b^2*c^3*d + 161*a^5*b*c^2*d^2 - 5*a^6*c*d^3)*x^3 + 2*(99*a^4*b^2*c^4 - 158*a^5*b*c^3*d + 59*a^6*c^2*d^2)*x^2 - 8*(11*a^5*b*c^4 - 17*a^6*c^3*d)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^7*b^2*c^2*x^6 + 2*a^8*b*c^2*x^5 + a^9*c^2*x^4)]","A",0
803,1,670,0,1.876343," ","integrate(x^2/(b*x+a)^(5/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3} + {\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} x\right)}}, -\frac{3 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2} + {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) - 2 \, {\left(5 \, a^{2} b^{2} c d - 3 \, a^{3} b d^{2} + 2 \, {\left(3 \, a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{5} c^{2} d - 2 \, a^{3} b^{4} c d^{2} + a^{4} b^{3} d^{3} + {\left(b^{7} c^{2} d - 2 \, a b^{6} c d^{2} + a^{2} b^{5} d^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{2} d - 2 \, a^{2} b^{5} c d^{2} + a^{3} b^{4} d^{3}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 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)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3 + (b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*x^2 + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*x), -1/3*(3*(a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2 + (b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) - 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)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^5*c^2*d - 2*a^3*b^4*c*d^2 + a^4*b^3*d^3 + (b^7*c^2*d - 2*a*b^6*c*d^2 + a^2*b^5*d^3)*x^2 + 2*(a*b^6*c^2*d - 2*a^2*b^5*c*d^2 + a^3*b^4*d^3)*x)]","B",0
804,1,2954,0,12.171493," ","integrate(x^6/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, a^{2} b^{6} c^{8} - 18 \, a^{3} b^{5} c^{7} d + 9 \, a^{4} b^{4} c^{6} d^{2} + 4 \, a^{5} b^{3} c^{5} d^{3} + 9 \, a^{6} b^{2} c^{4} d^{4} - 18 \, a^{7} b c^{3} d^{5} + 7 \, a^{8} c^{2} d^{6} + {\left(7 \, b^{8} c^{6} d^{2} - 18 \, a b^{7} c^{5} d^{3} + 9 \, a^{2} b^{6} c^{4} d^{4} + 4 \, a^{3} b^{5} c^{3} d^{5} + 9 \, a^{4} b^{4} c^{2} d^{6} - 18 \, a^{5} b^{3} c d^{7} + 7 \, a^{6} b^{2} d^{8}\right)} x^{4} + 2 \, {\left(7 \, b^{8} c^{7} d - 11 \, a b^{7} c^{6} d^{2} - 9 \, a^{2} b^{6} c^{5} d^{3} + 13 \, a^{3} b^{5} c^{4} d^{4} + 13 \, a^{4} b^{4} c^{3} d^{5} - 9 \, a^{5} b^{3} c^{2} d^{6} - 11 \, a^{6} b^{2} c d^{7} + 7 \, a^{7} b d^{8}\right)} x^{3} + {\left(7 \, b^{8} c^{8} + 10 \, a b^{7} c^{7} d - 56 \, a^{2} b^{6} c^{6} d^{2} + 22 \, a^{3} b^{5} c^{5} d^{3} + 34 \, a^{4} b^{4} c^{4} d^{4} + 22 \, a^{5} b^{3} c^{3} d^{5} - 56 \, a^{6} b^{2} c^{2} d^{6} + 10 \, a^{7} b c d^{7} + 7 \, a^{8} d^{8}\right)} x^{2} + 2 \, {\left(7 \, a b^{7} c^{8} - 11 \, a^{2} b^{6} c^{7} d - 9 \, a^{3} b^{5} c^{6} d^{2} + 13 \, a^{4} b^{4} c^{5} d^{3} + 13 \, a^{5} b^{3} c^{4} d^{4} - 9 \, a^{6} b^{2} c^{3} d^{5} - 11 \, a^{7} b c^{2} d^{6} + 7 \, a^{8} c d^{7}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(105 \, a^{2} b^{6} c^{7} d - 235 \, a^{3} b^{5} c^{6} d^{2} + 66 \, a^{4} b^{4} c^{5} d^{3} + 66 \, a^{5} b^{3} c^{4} d^{4} - 235 \, a^{6} b^{2} c^{3} d^{5} + 105 \, a^{7} b c^{2} d^{6} - 6 \, {\left(b^{8} c^{4} d^{4} - 4 \, a b^{7} c^{3} d^{5} + 6 \, a^{2} b^{6} c^{2} d^{6} - 4 \, a^{3} b^{5} c d^{7} + a^{4} b^{4} d^{8}\right)} x^{5} + 21 \, {\left(b^{8} c^{5} d^{3} - 3 \, a b^{7} c^{4} d^{4} + 2 \, a^{2} b^{6} c^{3} d^{5} + 2 \, a^{3} b^{5} c^{2} d^{6} - 3 \, a^{4} b^{4} c d^{7} + a^{5} b^{3} d^{8}\right)} x^{4} + 4 \, {\left(35 \, b^{8} c^{6} d^{2} - 69 \, a b^{7} c^{5} d^{3} - 3 \, a^{2} b^{6} c^{4} d^{4} + 42 \, a^{3} b^{5} c^{3} d^{5} - 3 \, a^{4} b^{4} c^{2} d^{6} - 69 \, a^{5} b^{3} c d^{7} + 35 \, a^{6} b^{2} d^{8}\right)} x^{3} + 3 \, {\left(35 \, b^{8} c^{7} d + 15 \, a b^{7} c^{6} d^{2} - 183 \, a^{2} b^{6} c^{5} d^{3} + 69 \, a^{3} b^{5} c^{4} d^{4} + 69 \, a^{4} b^{4} c^{3} d^{5} - 183 \, a^{5} b^{3} c^{2} d^{6} + 15 \, a^{6} b^{2} c d^{7} + 35 \, a^{7} b d^{8}\right)} x^{2} + 6 \, {\left(35 \, a b^{7} c^{7} d - 55 \, a^{2} b^{6} c^{6} d^{2} - 31 \, a^{3} b^{5} c^{5} d^{3} + 38 \, a^{4} b^{4} c^{4} d^{4} - 31 \, a^{5} b^{3} c^{3} d^{5} - 55 \, a^{6} b^{2} c^{2} d^{6} + 35 \, a^{7} b c d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left(a^{2} b^{9} c^{6} d^{5} - 4 \, a^{3} b^{8} c^{5} d^{6} + 6 \, a^{4} b^{7} c^{4} d^{7} - 4 \, a^{5} b^{6} c^{3} d^{8} + a^{6} b^{5} c^{2} d^{9} + {\left(b^{11} c^{4} d^{7} - 4 \, a b^{10} c^{3} d^{8} + 6 \, a^{2} b^{9} c^{2} d^{9} - 4 \, a^{3} b^{8} c d^{10} + a^{4} b^{7} d^{11}\right)} x^{4} + 2 \, {\left(b^{11} c^{5} d^{6} - 3 \, a b^{10} c^{4} d^{7} + 2 \, a^{2} b^{9} c^{3} d^{8} + 2 \, a^{3} b^{8} c^{2} d^{9} - 3 \, a^{4} b^{7} c d^{10} + a^{5} b^{6} d^{11}\right)} x^{3} + {\left(b^{11} c^{6} d^{5} - 9 \, a^{2} b^{9} c^{4} d^{7} + 16 \, a^{3} b^{8} c^{3} d^{8} - 9 \, a^{4} b^{7} c^{2} d^{9} + a^{6} b^{5} d^{11}\right)} x^{2} + 2 \, {\left(a b^{10} c^{6} d^{5} - 3 \, a^{2} b^{9} c^{5} d^{6} + 2 \, a^{3} b^{8} c^{4} d^{7} + 2 \, a^{4} b^{7} c^{3} d^{8} - 3 \, a^{5} b^{6} c^{2} d^{9} + a^{6} b^{5} c d^{10}\right)} x\right)}}, -\frac{15 \, {\left(7 \, a^{2} b^{6} c^{8} - 18 \, a^{3} b^{5} c^{7} d + 9 \, a^{4} b^{4} c^{6} d^{2} + 4 \, a^{5} b^{3} c^{5} d^{3} + 9 \, a^{6} b^{2} c^{4} d^{4} - 18 \, a^{7} b c^{3} d^{5} + 7 \, a^{8} c^{2} d^{6} + {\left(7 \, b^{8} c^{6} d^{2} - 18 \, a b^{7} c^{5} d^{3} + 9 \, a^{2} b^{6} c^{4} d^{4} + 4 \, a^{3} b^{5} c^{3} d^{5} + 9 \, a^{4} b^{4} c^{2} d^{6} - 18 \, a^{5} b^{3} c d^{7} + 7 \, a^{6} b^{2} d^{8}\right)} x^{4} + 2 \, {\left(7 \, b^{8} c^{7} d - 11 \, a b^{7} c^{6} d^{2} - 9 \, a^{2} b^{6} c^{5} d^{3} + 13 \, a^{3} b^{5} c^{4} d^{4} + 13 \, a^{4} b^{4} c^{3} d^{5} - 9 \, a^{5} b^{3} c^{2} d^{6} - 11 \, a^{6} b^{2} c d^{7} + 7 \, a^{7} b d^{8}\right)} x^{3} + {\left(7 \, b^{8} c^{8} + 10 \, a b^{7} c^{7} d - 56 \, a^{2} b^{6} c^{6} d^{2} + 22 \, a^{3} b^{5} c^{5} d^{3} + 34 \, a^{4} b^{4} c^{4} d^{4} + 22 \, a^{5} b^{3} c^{3} d^{5} - 56 \, a^{6} b^{2} c^{2} d^{6} + 10 \, a^{7} b c d^{7} + 7 \, a^{8} d^{8}\right)} x^{2} + 2 \, {\left(7 \, a b^{7} c^{8} - 11 \, a^{2} b^{6} c^{7} d - 9 \, a^{3} b^{5} c^{6} d^{2} + 13 \, a^{4} b^{4} c^{5} d^{3} + 13 \, a^{5} b^{3} c^{4} d^{4} - 9 \, a^{6} b^{2} c^{3} d^{5} - 11 \, a^{7} b c^{2} d^{6} + 7 \, a^{8} c d^{7}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(105 \, a^{2} b^{6} c^{7} d - 235 \, a^{3} b^{5} c^{6} d^{2} + 66 \, a^{4} b^{4} c^{5} d^{3} + 66 \, a^{5} b^{3} c^{4} d^{4} - 235 \, a^{6} b^{2} c^{3} d^{5} + 105 \, a^{7} b c^{2} d^{6} - 6 \, {\left(b^{8} c^{4} d^{4} - 4 \, a b^{7} c^{3} d^{5} + 6 \, a^{2} b^{6} c^{2} d^{6} - 4 \, a^{3} b^{5} c d^{7} + a^{4} b^{4} d^{8}\right)} x^{5} + 21 \, {\left(b^{8} c^{5} d^{3} - 3 \, a b^{7} c^{4} d^{4} + 2 \, a^{2} b^{6} c^{3} d^{5} + 2 \, a^{3} b^{5} c^{2} d^{6} - 3 \, a^{4} b^{4} c d^{7} + a^{5} b^{3} d^{8}\right)} x^{4} + 4 \, {\left(35 \, b^{8} c^{6} d^{2} - 69 \, a b^{7} c^{5} d^{3} - 3 \, a^{2} b^{6} c^{4} d^{4} + 42 \, a^{3} b^{5} c^{3} d^{5} - 3 \, a^{4} b^{4} c^{2} d^{6} - 69 \, a^{5} b^{3} c d^{7} + 35 \, a^{6} b^{2} d^{8}\right)} x^{3} + 3 \, {\left(35 \, b^{8} c^{7} d + 15 \, a b^{7} c^{6} d^{2} - 183 \, a^{2} b^{6} c^{5} d^{3} + 69 \, a^{3} b^{5} c^{4} d^{4} + 69 \, a^{4} b^{4} c^{3} d^{5} - 183 \, a^{5} b^{3} c^{2} d^{6} + 15 \, a^{6} b^{2} c d^{7} + 35 \, a^{7} b d^{8}\right)} x^{2} + 6 \, {\left(35 \, a b^{7} c^{7} d - 55 \, a^{2} b^{6} c^{6} d^{2} - 31 \, a^{3} b^{5} c^{5} d^{3} + 38 \, a^{4} b^{4} c^{4} d^{4} - 31 \, a^{5} b^{3} c^{3} d^{5} - 55 \, a^{6} b^{2} c^{2} d^{6} + 35 \, a^{7} b c d^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left(a^{2} b^{9} c^{6} d^{5} - 4 \, a^{3} b^{8} c^{5} d^{6} + 6 \, a^{4} b^{7} c^{4} d^{7} - 4 \, a^{5} b^{6} c^{3} d^{8} + a^{6} b^{5} c^{2} d^{9} + {\left(b^{11} c^{4} d^{7} - 4 \, a b^{10} c^{3} d^{8} + 6 \, a^{2} b^{9} c^{2} d^{9} - 4 \, a^{3} b^{8} c d^{10} + a^{4} b^{7} d^{11}\right)} x^{4} + 2 \, {\left(b^{11} c^{5} d^{6} - 3 \, a b^{10} c^{4} d^{7} + 2 \, a^{2} b^{9} c^{3} d^{8} + 2 \, a^{3} b^{8} c^{2} d^{9} - 3 \, a^{4} b^{7} c d^{10} + a^{5} b^{6} d^{11}\right)} x^{3} + {\left(b^{11} c^{6} d^{5} - 9 \, a^{2} b^{9} c^{4} d^{7} + 16 \, a^{3} b^{8} c^{3} d^{8} - 9 \, a^{4} b^{7} c^{2} d^{9} + a^{6} b^{5} d^{11}\right)} x^{2} + 2 \, {\left(a b^{10} c^{6} d^{5} - 3 \, a^{2} b^{9} c^{5} d^{6} + 2 \, a^{3} b^{8} c^{4} d^{7} + 2 \, a^{4} b^{7} c^{3} d^{8} - 3 \, a^{5} b^{6} c^{2} d^{9} + a^{6} b^{5} c d^{10}\right)} x\right)}}\right]"," ",0,"[1/48*(15*(7*a^2*b^6*c^8 - 18*a^3*b^5*c^7*d + 9*a^4*b^4*c^6*d^2 + 4*a^5*b^3*c^5*d^3 + 9*a^6*b^2*c^4*d^4 - 18*a^7*b*c^3*d^5 + 7*a^8*c^2*d^6 + (7*b^8*c^6*d^2 - 18*a*b^7*c^5*d^3 + 9*a^2*b^6*c^4*d^4 + 4*a^3*b^5*c^3*d^5 + 9*a^4*b^4*c^2*d^6 - 18*a^5*b^3*c*d^7 + 7*a^6*b^2*d^8)*x^4 + 2*(7*b^8*c^7*d - 11*a*b^7*c^6*d^2 - 9*a^2*b^6*c^5*d^3 + 13*a^3*b^5*c^4*d^4 + 13*a^4*b^4*c^3*d^5 - 9*a^5*b^3*c^2*d^6 - 11*a^6*b^2*c*d^7 + 7*a^7*b*d^8)*x^3 + (7*b^8*c^8 + 10*a*b^7*c^7*d - 56*a^2*b^6*c^6*d^2 + 22*a^3*b^5*c^5*d^3 + 34*a^4*b^4*c^4*d^4 + 22*a^5*b^3*c^3*d^5 - 56*a^6*b^2*c^2*d^6 + 10*a^7*b*c*d^7 + 7*a^8*d^8)*x^2 + 2*(7*a*b^7*c^8 - 11*a^2*b^6*c^7*d - 9*a^3*b^5*c^6*d^2 + 13*a^4*b^4*c^5*d^3 + 13*a^5*b^3*c^4*d^4 - 9*a^6*b^2*c^3*d^5 - 11*a^7*b*c^2*d^6 + 7*a^8*c*d^7)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(105*a^2*b^6*c^7*d - 235*a^3*b^5*c^6*d^2 + 66*a^4*b^4*c^5*d^3 + 66*a^5*b^3*c^4*d^4 - 235*a^6*b^2*c^3*d^5 + 105*a^7*b*c^2*d^6 - 6*(b^8*c^4*d^4 - 4*a*b^7*c^3*d^5 + 6*a^2*b^6*c^2*d^6 - 4*a^3*b^5*c*d^7 + a^4*b^4*d^8)*x^5 + 21*(b^8*c^5*d^3 - 3*a*b^7*c^4*d^4 + 2*a^2*b^6*c^3*d^5 + 2*a^3*b^5*c^2*d^6 - 3*a^4*b^4*c*d^7 + a^5*b^3*d^8)*x^4 + 4*(35*b^8*c^6*d^2 - 69*a*b^7*c^5*d^3 - 3*a^2*b^6*c^4*d^4 + 42*a^3*b^5*c^3*d^5 - 3*a^4*b^4*c^2*d^6 - 69*a^5*b^3*c*d^7 + 35*a^6*b^2*d^8)*x^3 + 3*(35*b^8*c^7*d + 15*a*b^7*c^6*d^2 - 183*a^2*b^6*c^5*d^3 + 69*a^3*b^5*c^4*d^4 + 69*a^4*b^4*c^3*d^5 - 183*a^5*b^3*c^2*d^6 + 15*a^6*b^2*c*d^7 + 35*a^7*b*d^8)*x^2 + 6*(35*a*b^7*c^7*d - 55*a^2*b^6*c^6*d^2 - 31*a^3*b^5*c^5*d^3 + 38*a^4*b^4*c^4*d^4 - 31*a^5*b^3*c^3*d^5 - 55*a^6*b^2*c^2*d^6 + 35*a^7*b*c*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^9*c^6*d^5 - 4*a^3*b^8*c^5*d^6 + 6*a^4*b^7*c^4*d^7 - 4*a^5*b^6*c^3*d^8 + a^6*b^5*c^2*d^9 + (b^11*c^4*d^7 - 4*a*b^10*c^3*d^8 + 6*a^2*b^9*c^2*d^9 - 4*a^3*b^8*c*d^10 + a^4*b^7*d^11)*x^4 + 2*(b^11*c^5*d^6 - 3*a*b^10*c^4*d^7 + 2*a^2*b^9*c^3*d^8 + 2*a^3*b^8*c^2*d^9 - 3*a^4*b^7*c*d^10 + a^5*b^6*d^11)*x^3 + (b^11*c^6*d^5 - 9*a^2*b^9*c^4*d^7 + 16*a^3*b^8*c^3*d^8 - 9*a^4*b^7*c^2*d^9 + a^6*b^5*d^11)*x^2 + 2*(a*b^10*c^6*d^5 - 3*a^2*b^9*c^5*d^6 + 2*a^3*b^8*c^4*d^7 + 2*a^4*b^7*c^3*d^8 - 3*a^5*b^6*c^2*d^9 + a^6*b^5*c*d^10)*x), -1/24*(15*(7*a^2*b^6*c^8 - 18*a^3*b^5*c^7*d + 9*a^4*b^4*c^6*d^2 + 4*a^5*b^3*c^5*d^3 + 9*a^6*b^2*c^4*d^4 - 18*a^7*b*c^3*d^5 + 7*a^8*c^2*d^6 + (7*b^8*c^6*d^2 - 18*a*b^7*c^5*d^3 + 9*a^2*b^6*c^4*d^4 + 4*a^3*b^5*c^3*d^5 + 9*a^4*b^4*c^2*d^6 - 18*a^5*b^3*c*d^7 + 7*a^6*b^2*d^8)*x^4 + 2*(7*b^8*c^7*d - 11*a*b^7*c^6*d^2 - 9*a^2*b^6*c^5*d^3 + 13*a^3*b^5*c^4*d^4 + 13*a^4*b^4*c^3*d^5 - 9*a^5*b^3*c^2*d^6 - 11*a^6*b^2*c*d^7 + 7*a^7*b*d^8)*x^3 + (7*b^8*c^8 + 10*a*b^7*c^7*d - 56*a^2*b^6*c^6*d^2 + 22*a^3*b^5*c^5*d^3 + 34*a^4*b^4*c^4*d^4 + 22*a^5*b^3*c^3*d^5 - 56*a^6*b^2*c^2*d^6 + 10*a^7*b*c*d^7 + 7*a^8*d^8)*x^2 + 2*(7*a*b^7*c^8 - 11*a^2*b^6*c^7*d - 9*a^3*b^5*c^6*d^2 + 13*a^4*b^4*c^5*d^3 + 13*a^5*b^3*c^4*d^4 - 9*a^6*b^2*c^3*d^5 - 11*a^7*b*c^2*d^6 + 7*a^8*c*d^7)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(105*a^2*b^6*c^7*d - 235*a^3*b^5*c^6*d^2 + 66*a^4*b^4*c^5*d^3 + 66*a^5*b^3*c^4*d^4 - 235*a^6*b^2*c^3*d^5 + 105*a^7*b*c^2*d^6 - 6*(b^8*c^4*d^4 - 4*a*b^7*c^3*d^5 + 6*a^2*b^6*c^2*d^6 - 4*a^3*b^5*c*d^7 + a^4*b^4*d^8)*x^5 + 21*(b^8*c^5*d^3 - 3*a*b^7*c^4*d^4 + 2*a^2*b^6*c^3*d^5 + 2*a^3*b^5*c^2*d^6 - 3*a^4*b^4*c*d^7 + a^5*b^3*d^8)*x^4 + 4*(35*b^8*c^6*d^2 - 69*a*b^7*c^5*d^3 - 3*a^2*b^6*c^4*d^4 + 42*a^3*b^5*c^3*d^5 - 3*a^4*b^4*c^2*d^6 - 69*a^5*b^3*c*d^7 + 35*a^6*b^2*d^8)*x^3 + 3*(35*b^8*c^7*d + 15*a*b^7*c^6*d^2 - 183*a^2*b^6*c^5*d^3 + 69*a^3*b^5*c^4*d^4 + 69*a^4*b^4*c^3*d^5 - 183*a^5*b^3*c^2*d^6 + 15*a^6*b^2*c*d^7 + 35*a^7*b*d^8)*x^2 + 6*(35*a*b^7*c^7*d - 55*a^2*b^6*c^6*d^2 - 31*a^3*b^5*c^5*d^3 + 38*a^4*b^4*c^4*d^4 - 31*a^5*b^3*c^3*d^5 - 55*a^6*b^2*c^2*d^6 + 35*a^7*b*c*d^7)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^9*c^6*d^5 - 4*a^3*b^8*c^5*d^6 + 6*a^4*b^7*c^4*d^7 - 4*a^5*b^6*c^3*d^8 + a^6*b^5*c^2*d^9 + (b^11*c^4*d^7 - 4*a*b^10*c^3*d^8 + 6*a^2*b^9*c^2*d^9 - 4*a^3*b^8*c*d^10 + a^4*b^7*d^11)*x^4 + 2*(b^11*c^5*d^6 - 3*a*b^10*c^4*d^7 + 2*a^2*b^9*c^3*d^8 + 2*a^3*b^8*c^2*d^9 - 3*a^4*b^7*c*d^10 + a^5*b^6*d^11)*x^3 + (b^11*c^6*d^5 - 9*a^2*b^9*c^4*d^7 + 16*a^3*b^8*c^3*d^8 - 9*a^4*b^7*c^2*d^9 + a^6*b^5*d^11)*x^2 + 2*(a*b^10*c^6*d^5 - 3*a^2*b^9*c^5*d^6 + 2*a^3*b^8*c^4*d^7 + 2*a^4*b^7*c^3*d^8 - 3*a^5*b^6*c^2*d^9 + a^6*b^5*c*d^10)*x)]","B",0
805,1,2474,0,5.773830," ","integrate(x^5/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b^{5} c^{7} - 3 \, a^{3} b^{4} c^{6} d + 2 \, a^{4} b^{3} c^{5} d^{2} + 2 \, a^{5} b^{2} c^{4} d^{3} - 3 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 3 \, a b^{6} c^{4} d^{3} + 2 \, a^{2} b^{5} c^{3} d^{4} + 2 \, a^{3} b^{4} c^{2} d^{5} - 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 2 \, a b^{6} c^{5} d^{2} - a^{2} b^{5} c^{4} d^{3} + 4 \, a^{3} b^{4} c^{3} d^{4} - a^{4} b^{3} c^{2} d^{5} - 2 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} + a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 7 \, a^{3} b^{4} c^{4} d^{3} + 7 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 2 \, a^{2} b^{5} c^{6} d - a^{3} b^{4} c^{5} d^{2} + 4 \, a^{4} b^{3} c^{4} d^{3} - a^{5} b^{2} c^{3} d^{4} - 2 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} - 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + 4 \, {\left(15 \, a^{2} b^{5} c^{6} d - 40 \, a^{3} b^{4} c^{5} d^{2} + 18 \, a^{4} b^{3} c^{4} d^{3} - 40 \, a^{5} b^{2} c^{3} d^{4} + 15 \, a^{6} b c^{2} d^{5} + 3 \, {\left(b^{7} c^{4} d^{3} - 4 \, a b^{6} c^{3} d^{4} + 6 \, a^{2} b^{5} c^{2} d^{5} - 4 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right)} x^{4} + 4 \, {\left(5 \, b^{7} c^{5} d^{2} - 12 \, a b^{6} c^{4} d^{3} + 3 \, a^{2} b^{5} c^{3} d^{4} + 3 \, a^{3} b^{4} c^{2} d^{5} - 12 \, a^{4} b^{3} c d^{6} + 5 \, a^{5} b^{2} d^{7}\right)} x^{3} + 3 \, {\left(5 \, b^{7} c^{6} d - 29 \, a^{2} b^{5} c^{4} d^{3} + 16 \, a^{3} b^{4} c^{3} d^{4} - 29 \, a^{4} b^{3} c^{2} d^{5} + 5 \, a^{6} b d^{7}\right)} x^{2} + 6 \, {\left(5 \, a b^{6} c^{6} d - 10 \, a^{2} b^{5} c^{5} d^{2} - 3 \, a^{3} b^{4} c^{4} d^{3} - 3 \, a^{4} b^{3} c^{3} d^{4} - 10 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left(a^{2} b^{8} c^{6} d^{4} - 4 \, a^{3} b^{7} c^{5} d^{5} + 6 \, a^{4} b^{6} c^{4} d^{6} - 4 \, a^{5} b^{5} c^{3} d^{7} + a^{6} b^{4} c^{2} d^{8} + {\left(b^{10} c^{4} d^{6} - 4 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} - 4 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right)} x^{4} + 2 \, {\left(b^{10} c^{5} d^{5} - 3 \, a b^{9} c^{4} d^{6} + 2 \, a^{2} b^{8} c^{3} d^{7} + 2 \, a^{3} b^{7} c^{2} d^{8} - 3 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right)} x^{3} + {\left(b^{10} c^{6} d^{4} - 9 \, a^{2} b^{8} c^{4} d^{6} + 16 \, a^{3} b^{7} c^{3} d^{7} - 9 \, a^{4} b^{6} c^{2} d^{8} + a^{6} b^{4} d^{10}\right)} x^{2} + 2 \, {\left(a b^{9} c^{6} d^{4} - 3 \, a^{2} b^{8} c^{5} d^{5} + 2 \, a^{3} b^{7} c^{4} d^{6} + 2 \, a^{4} b^{6} c^{3} d^{7} - 3 \, a^{5} b^{5} c^{2} d^{8} + a^{6} b^{4} c d^{9}\right)} x\right)}}, \frac{15 \, {\left(a^{2} b^{5} c^{7} - 3 \, a^{3} b^{4} c^{6} d + 2 \, a^{4} b^{3} c^{5} d^{2} + 2 \, a^{5} b^{2} c^{4} d^{3} - 3 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 3 \, a b^{6} c^{4} d^{3} + 2 \, a^{2} b^{5} c^{3} d^{4} + 2 \, a^{3} b^{4} c^{2} d^{5} - 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 2 \, a b^{6} c^{5} d^{2} - a^{2} b^{5} c^{4} d^{3} + 4 \, a^{3} b^{4} c^{3} d^{4} - a^{4} b^{3} c^{2} d^{5} - 2 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} + a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 7 \, a^{3} b^{4} c^{4} d^{3} + 7 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 2 \, a^{2} b^{5} c^{6} d - a^{3} b^{4} c^{5} d^{2} + 4 \, a^{4} b^{3} c^{4} d^{3} - a^{5} b^{2} c^{3} d^{4} - 2 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(15 \, a^{2} b^{5} c^{6} d - 40 \, a^{3} b^{4} c^{5} d^{2} + 18 \, a^{4} b^{3} c^{4} d^{3} - 40 \, a^{5} b^{2} c^{3} d^{4} + 15 \, a^{6} b c^{2} d^{5} + 3 \, {\left(b^{7} c^{4} d^{3} - 4 \, a b^{6} c^{3} d^{4} + 6 \, a^{2} b^{5} c^{2} d^{5} - 4 \, a^{3} b^{4} c d^{6} + a^{4} b^{3} d^{7}\right)} x^{4} + 4 \, {\left(5 \, b^{7} c^{5} d^{2} - 12 \, a b^{6} c^{4} d^{3} + 3 \, a^{2} b^{5} c^{3} d^{4} + 3 \, a^{3} b^{4} c^{2} d^{5} - 12 \, a^{4} b^{3} c d^{6} + 5 \, a^{5} b^{2} d^{7}\right)} x^{3} + 3 \, {\left(5 \, b^{7} c^{6} d - 29 \, a^{2} b^{5} c^{4} d^{3} + 16 \, a^{3} b^{4} c^{3} d^{4} - 29 \, a^{4} b^{3} c^{2} d^{5} + 5 \, a^{6} b d^{7}\right)} x^{2} + 6 \, {\left(5 \, a b^{6} c^{6} d - 10 \, a^{2} b^{5} c^{5} d^{2} - 3 \, a^{3} b^{4} c^{4} d^{3} - 3 \, a^{4} b^{3} c^{3} d^{4} - 10 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{8} c^{6} d^{4} - 4 \, a^{3} b^{7} c^{5} d^{5} + 6 \, a^{4} b^{6} c^{4} d^{6} - 4 \, a^{5} b^{5} c^{3} d^{7} + a^{6} b^{4} c^{2} d^{8} + {\left(b^{10} c^{4} d^{6} - 4 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} - 4 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right)} x^{4} + 2 \, {\left(b^{10} c^{5} d^{5} - 3 \, a b^{9} c^{4} d^{6} + 2 \, a^{2} b^{8} c^{3} d^{7} + 2 \, a^{3} b^{7} c^{2} d^{8} - 3 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right)} x^{3} + {\left(b^{10} c^{6} d^{4} - 9 \, a^{2} b^{8} c^{4} d^{6} + 16 \, a^{3} b^{7} c^{3} d^{7} - 9 \, a^{4} b^{6} c^{2} d^{8} + a^{6} b^{4} d^{10}\right)} x^{2} + 2 \, {\left(a b^{9} c^{6} d^{4} - 3 \, a^{2} b^{8} c^{5} d^{5} + 2 \, a^{3} b^{7} c^{4} d^{6} + 2 \, a^{4} b^{6} c^{3} d^{7} - 3 \, a^{5} b^{5} c^{2} d^{8} + a^{6} b^{4} c d^{9}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5 + (b^7*c^5*d^2 - 3*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 3*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 2*a*b^6*c^5*d^2 - a^2*b^5*c^4*d^3 + 4*a^3*b^4*c^3*d^4 - a^4*b^3*c^2*d^5 - 2*a^5*b^2*c*d^6 + a^6*b*d^7)*x^3 + (b^7*c^7 + a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 7*a^3*b^4*c^4*d^3 + 7*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 2*a^2*b^5*c^6*d - a^3*b^4*c^5*d^2 + 4*a^4*b^3*c^4*d^3 - a^5*b^2*c^3*d^4 - 2*a^6*b*c^2*d^5 + a^7*c*d^6)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 - 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) + 4*(15*a^2*b^5*c^6*d - 40*a^3*b^4*c^5*d^2 + 18*a^4*b^3*c^4*d^3 - 40*a^5*b^2*c^3*d^4 + 15*a^6*b*c^2*d^5 + 3*(b^7*c^4*d^3 - 4*a*b^6*c^3*d^4 + 6*a^2*b^5*c^2*d^5 - 4*a^3*b^4*c*d^6 + a^4*b^3*d^7)*x^4 + 4*(5*b^7*c^5*d^2 - 12*a*b^6*c^4*d^3 + 3*a^2*b^5*c^3*d^4 + 3*a^3*b^4*c^2*d^5 - 12*a^4*b^3*c*d^6 + 5*a^5*b^2*d^7)*x^3 + 3*(5*b^7*c^6*d - 29*a^2*b^5*c^4*d^3 + 16*a^3*b^4*c^3*d^4 - 29*a^4*b^3*c^2*d^5 + 5*a^6*b*d^7)*x^2 + 6*(5*a*b^6*c^6*d - 10*a^2*b^5*c^5*d^2 - 3*a^3*b^4*c^4*d^3 - 3*a^4*b^3*c^3*d^4 - 10*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^8*c^6*d^4 - 4*a^3*b^7*c^5*d^5 + 6*a^4*b^6*c^4*d^6 - 4*a^5*b^5*c^3*d^7 + a^6*b^4*c^2*d^8 + (b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^4 + 2*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^3 + (b^10*c^6*d^4 - 9*a^2*b^8*c^4*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4*b^6*c^2*d^8 + a^6*b^4*d^10)*x^2 + 2*(a*b^9*c^6*d^4 - 3*a^2*b^8*c^5*d^5 + 2*a^3*b^7*c^4*d^6 + 2*a^4*b^6*c^3*d^7 - 3*a^5*b^5*c^2*d^8 + a^6*b^4*c*d^9)*x), 1/6*(15*(a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5 + (b^7*c^5*d^2 - 3*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 3*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 2*a*b^6*c^5*d^2 - a^2*b^5*c^4*d^3 + 4*a^3*b^4*c^3*d^4 - a^4*b^3*c^2*d^5 - 2*a^5*b^2*c*d^6 + a^6*b*d^7)*x^3 + (b^7*c^7 + a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 7*a^3*b^4*c^4*d^3 + 7*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 2*a^2*b^5*c^6*d - a^3*b^4*c^5*d^2 + 4*a^4*b^3*c^4*d^3 - a^5*b^2*c^3*d^4 - 2*a^6*b*c^2*d^5 + a^7*c*d^6)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(15*a^2*b^5*c^6*d - 40*a^3*b^4*c^5*d^2 + 18*a^4*b^3*c^4*d^3 - 40*a^5*b^2*c^3*d^4 + 15*a^6*b*c^2*d^5 + 3*(b^7*c^4*d^3 - 4*a*b^6*c^3*d^4 + 6*a^2*b^5*c^2*d^5 - 4*a^3*b^4*c*d^6 + a^4*b^3*d^7)*x^4 + 4*(5*b^7*c^5*d^2 - 12*a*b^6*c^4*d^3 + 3*a^2*b^5*c^3*d^4 + 3*a^3*b^4*c^2*d^5 - 12*a^4*b^3*c*d^6 + 5*a^5*b^2*d^7)*x^3 + 3*(5*b^7*c^6*d - 29*a^2*b^5*c^4*d^3 + 16*a^3*b^4*c^3*d^4 - 29*a^4*b^3*c^2*d^5 + 5*a^6*b*d^7)*x^2 + 6*(5*a*b^6*c^6*d - 10*a^2*b^5*c^5*d^2 - 3*a^3*b^4*c^4*d^3 - 3*a^4*b^3*c^3*d^4 - 10*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^8*c^6*d^4 - 4*a^3*b^7*c^5*d^5 + 6*a^4*b^6*c^4*d^6 - 4*a^5*b^5*c^3*d^7 + a^6*b^4*c^2*d^8 + (b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^4 + 2*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^3 + (b^10*c^6*d^4 - 9*a^2*b^8*c^4*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4*b^6*c^2*d^8 + a^6*b^4*d^10)*x^2 + 2*(a*b^9*c^6*d^4 - 3*a^2*b^8*c^5*d^5 + 2*a^3*b^7*c^4*d^6 + 2*a^4*b^6*c^3*d^7 - 3*a^5*b^5*c^2*d^8 + a^6*b^4*c*d^9)*x)]","B",0
806,1,2066,0,4.246526," ","integrate(x^4/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{b d} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d x + b c + a d\right)} \sqrt{b d} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) - 4 \, {\left(3 \, a^{2} b^{4} c^{5} d - 11 \, a^{3} b^{3} c^{4} d^{2} - 11 \, a^{4} b^{2} c^{3} d^{3} + 3 \, a^{5} b c^{2} d^{4} + 4 \, {\left(b^{6} c^{4} d^{2} - 3 \, a b^{5} c^{3} d^{3} - 3 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{3} + 3 \, {\left(b^{6} c^{5} d - a b^{5} c^{4} d^{2} - 8 \, a^{2} b^{4} c^{3} d^{3} - 8 \, a^{3} b^{3} c^{2} d^{4} - a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{2} + 6 \, {\left(a b^{5} c^{5} d - 3 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} - 3 \, a^{4} b^{2} c^{2} d^{4} + a^{5} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{2} b^{7} c^{6} d^{3} - 4 \, a^{3} b^{6} c^{5} d^{4} + 6 \, a^{4} b^{5} c^{4} d^{5} - 4 \, a^{5} b^{4} c^{3} d^{6} + a^{6} b^{3} c^{2} d^{7} + {\left(b^{9} c^{4} d^{5} - 4 \, a b^{8} c^{3} d^{6} + 6 \, a^{2} b^{7} c^{2} d^{7} - 4 \, a^{3} b^{6} c d^{8} + a^{4} b^{5} d^{9}\right)} x^{4} + 2 \, {\left(b^{9} c^{5} d^{4} - 3 \, a b^{8} c^{4} d^{5} + 2 \, a^{2} b^{7} c^{3} d^{6} + 2 \, a^{3} b^{6} c^{2} d^{7} - 3 \, a^{4} b^{5} c d^{8} + a^{5} b^{4} d^{9}\right)} x^{3} + {\left(b^{9} c^{6} d^{3} - 9 \, a^{2} b^{7} c^{4} d^{5} + 16 \, a^{3} b^{6} c^{3} d^{6} - 9 \, a^{4} b^{5} c^{2} d^{7} + a^{6} b^{3} d^{9}\right)} x^{2} + 2 \, {\left(a b^{8} c^{6} d^{3} - 3 \, a^{2} b^{7} c^{5} d^{4} + 2 \, a^{3} b^{6} c^{4} d^{5} + 2 \, a^{4} b^{5} c^{3} d^{6} - 3 \, a^{5} b^{4} c^{2} d^{7} + a^{6} b^{3} c d^{8}\right)} x\right)}}, -\frac{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{-b d} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{-b d} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, a^{2} b^{4} c^{5} d - 11 \, a^{3} b^{3} c^{4} d^{2} - 11 \, a^{4} b^{2} c^{3} d^{3} + 3 \, a^{5} b c^{2} d^{4} + 4 \, {\left(b^{6} c^{4} d^{2} - 3 \, a b^{5} c^{3} d^{3} - 3 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{3} + 3 \, {\left(b^{6} c^{5} d - a b^{5} c^{4} d^{2} - 8 \, a^{2} b^{4} c^{3} d^{3} - 8 \, a^{3} b^{3} c^{2} d^{4} - a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{2} + 6 \, {\left(a b^{5} c^{5} d - 3 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} - 3 \, a^{4} b^{2} c^{2} d^{4} + a^{5} b c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{7} c^{6} d^{3} - 4 \, a^{3} b^{6} c^{5} d^{4} + 6 \, a^{4} b^{5} c^{4} d^{5} - 4 \, a^{5} b^{4} c^{3} d^{6} + a^{6} b^{3} c^{2} d^{7} + {\left(b^{9} c^{4} d^{5} - 4 \, a b^{8} c^{3} d^{6} + 6 \, a^{2} b^{7} c^{2} d^{7} - 4 \, a^{3} b^{6} c d^{8} + a^{4} b^{5} d^{9}\right)} x^{4} + 2 \, {\left(b^{9} c^{5} d^{4} - 3 \, a b^{8} c^{4} d^{5} + 2 \, a^{2} b^{7} c^{3} d^{6} + 2 \, a^{3} b^{6} c^{2} d^{7} - 3 \, a^{4} b^{5} c d^{8} + a^{5} b^{4} d^{9}\right)} x^{3} + {\left(b^{9} c^{6} d^{3} - 9 \, a^{2} b^{7} c^{4} d^{5} + 16 \, a^{3} b^{6} c^{3} d^{6} - 9 \, a^{4} b^{5} c^{2} d^{7} + a^{6} b^{3} d^{9}\right)} x^{2} + 2 \, {\left(a b^{8} c^{6} d^{3} - 3 \, a^{2} b^{7} c^{5} d^{4} + 2 \, a^{3} b^{6} c^{4} d^{5} + 2 \, a^{4} b^{5} c^{3} d^{6} - 3 \, a^{5} b^{4} c^{2} d^{7} + a^{6} b^{3} c d^{8}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(b*d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d*x + b*c + a*d)*sqrt(b*d)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(b^2*c*d + a*b*d^2)*x) - 4*(3*a^2*b^4*c^5*d - 11*a^3*b^3*c^4*d^2 - 11*a^4*b^2*c^3*d^3 + 3*a^5*b*c^2*d^4 + 4*(b^6*c^4*d^2 - 3*a*b^5*c^3*d^3 - 3*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^3 + 3*(b^6*c^5*d - a*b^5*c^4*d^2 - 8*a^2*b^4*c^3*d^3 - 8*a^3*b^3*c^2*d^4 - a^4*b^2*c*d^5 + a^5*b*d^6)*x^2 + 6*(a*b^5*c^5*d - 3*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 - 3*a^4*b^2*c^2*d^4 + a^5*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^7*c^6*d^3 - 4*a^3*b^6*c^5*d^4 + 6*a^4*b^5*c^4*d^5 - 4*a^5*b^4*c^3*d^6 + a^6*b^3*c^2*d^7 + (b^9*c^4*d^5 - 4*a*b^8*c^3*d^6 + 6*a^2*b^7*c^2*d^7 - 4*a^3*b^6*c*d^8 + a^4*b^5*d^9)*x^4 + 2*(b^9*c^5*d^4 - 3*a*b^8*c^4*d^5 + 2*a^2*b^7*c^3*d^6 + 2*a^3*b^6*c^2*d^7 - 3*a^4*b^5*c*d^8 + a^5*b^4*d^9)*x^3 + (b^9*c^6*d^3 - 9*a^2*b^7*c^4*d^5 + 16*a^3*b^6*c^3*d^6 - 9*a^4*b^5*c^2*d^7 + a^6*b^3*d^9)*x^2 + 2*(a*b^8*c^6*d^3 - 3*a^2*b^7*c^5*d^4 + 2*a^3*b^6*c^4*d^5 + 2*a^4*b^5*c^3*d^6 - 3*a^5*b^4*c^2*d^7 + a^6*b^3*c*d^8)*x), -1/3*(3*(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(-b*d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(-b*d)*sqrt(b*x + a)*sqrt(d*x + c)/(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)) + 2*(3*a^2*b^4*c^5*d - 11*a^3*b^3*c^4*d^2 - 11*a^4*b^2*c^3*d^3 + 3*a^5*b*c^2*d^4 + 4*(b^6*c^4*d^2 - 3*a*b^5*c^3*d^3 - 3*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^3 + 3*(b^6*c^5*d - a*b^5*c^4*d^2 - 8*a^2*b^4*c^3*d^3 - 8*a^3*b^3*c^2*d^4 - a^4*b^2*c*d^5 + a^5*b*d^6)*x^2 + 6*(a*b^5*c^5*d - 3*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 - 3*a^4*b^2*c^2*d^4 + a^5*b*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^2*b^7*c^6*d^3 - 4*a^3*b^6*c^5*d^4 + 6*a^4*b^5*c^4*d^5 - 4*a^5*b^4*c^3*d^6 + a^6*b^3*c^2*d^7 + (b^9*c^4*d^5 - 4*a*b^8*c^3*d^6 + 6*a^2*b^7*c^2*d^7 - 4*a^3*b^6*c*d^8 + a^4*b^5*d^9)*x^4 + 2*(b^9*c^5*d^4 - 3*a*b^8*c^4*d^5 + 2*a^2*b^7*c^3*d^6 + 2*a^3*b^6*c^2*d^7 - 3*a^4*b^5*c*d^8 + a^5*b^4*d^9)*x^3 + (b^9*c^6*d^3 - 9*a^2*b^7*c^4*d^5 + 16*a^3*b^6*c^3*d^6 - 9*a^4*b^5*c^2*d^7 + a^6*b^3*d^9)*x^2 + 2*(a*b^8*c^6*d^3 - 3*a^2*b^7*c^5*d^4 + 2*a^3*b^6*c^4*d^5 + 2*a^4*b^5*c^3*d^6 - 3*a^5*b^4*c^2*d^7 + a^6*b^3*c*d^8)*x)]","B",0
807,1,448,0,3.550961," ","integrate(x^3/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, a^{3} c^{3} - {\left(b^{3} c^{3} - 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{3} + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} x^{2} + 24 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)}}"," ",0,"-2/3*(16*a^3*c^3 - (b^3*c^3 - 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + a^3*d^3)*x^3 + 6*(a*b^2*c^3 + 6*a^2*b*c^2*d + a^3*c*d^2)*x^2 + 24*(a^2*b*c^3 + a^3*c^2*d)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)","B",0
808,1,468,0,3.373564," ","integrate(x^2/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} b c^{3} + 8 \, a^{3} c^{2} d + 2 \, {\left(b^{3} c^{2} d + 6 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{3} + 3 \, {\left(b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} x^{2} + 12 \, {\left(a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)}}"," ",0,"2/3*(8*a^2*b*c^3 + 8*a^3*c^2*d + 2*(b^3*c^2*d + 6*a*b^2*c*d^2 + a^2*b*d^3)*x^3 + 3*(b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 + a^3*d^3)*x^2 + 12*(a*b^2*c^3 + 2*a^2*b*c^2*d + a^3*c*d^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)","B",0
809,1,468,0,3.636133," ","integrate(x/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a b^{2} c^{3} + 12 \, a^{2} b c^{2} d + 2 \, a^{3} c d^{2} + 8 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{3} + 12 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)}}"," ",0,"-2/3*(2*a*b^2*c^3 + 12*a^2*b*c^2*d + 2*a^3*c*d^2 + 8*(b^3*c*d^2 + a*b^2*d^3)*x^3 + 12*(b^3*c^2*d + 2*a*b^2*c*d^2 + a^2*b*d^3)*x^2 + 3*(b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 + a^3*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)","B",0
810,1,447,0,4.155084," ","integrate(1/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - a^{3} d^{3} + 24 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{2} d + 6 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)}}"," ",0,"2/3*(16*b^3*d^3*x^3 - b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 - a^3*d^3 + 24*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 6*(b^3*c^2*d + 6*a*b^2*c*d^2 + a^2*b*d^3)*x)*sqrt(b*x + a)*sqrt(d*x + c)/(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)","B",0
811,1,2078,0,13.020141," ","integrate(1/x/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) + 4 \, {\left(4 \, a^{2} b^{4} c^{6} - 12 \, a^{3} b^{3} c^{5} d - 12 \, a^{5} b c^{3} d^{3} + 4 \, a^{6} c^{2} d^{4} + {\left(3 \, a b^{5} c^{4} d^{2} - 11 \, a^{2} b^{4} c^{3} d^{3} - 11 \, a^{3} b^{3} c^{2} d^{4} + 3 \, a^{4} b^{2} c d^{5}\right)} x^{3} + 6 \, {\left(a b^{5} c^{5} d - 3 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} - 3 \, a^{4} b^{2} c^{2} d^{4} + a^{5} b c d^{5}\right)} x^{2} + 3 \, {\left(a b^{5} c^{6} - a^{2} b^{4} c^{5} d - 8 \, a^{3} b^{3} c^{4} d^{2} - 8 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left(a^{5} b^{4} c^{9} - 4 \, a^{6} b^{3} c^{8} d + 6 \, a^{7} b^{2} c^{7} d^{2} - 4 \, a^{8} b c^{6} d^{3} + a^{9} c^{5} d^{4} + {\left(a^{3} b^{6} c^{7} d^{2} - 4 \, a^{4} b^{5} c^{6} d^{3} + 6 \, a^{5} b^{4} c^{5} d^{4} - 4 \, a^{6} b^{3} c^{4} d^{5} + a^{7} b^{2} c^{3} d^{6}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{8} d - 3 \, a^{4} b^{5} c^{7} d^{2} + 2 \, a^{5} b^{4} c^{6} d^{3} + 2 \, a^{6} b^{3} c^{5} d^{4} - 3 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6}\right)} x^{3} + {\left(a^{3} b^{6} c^{9} - 9 \, a^{5} b^{4} c^{7} d^{2} + 16 \, a^{6} b^{3} c^{6} d^{3} - 9 \, a^{7} b^{2} c^{5} d^{4} + a^{9} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{9} - 3 \, a^{5} b^{4} c^{8} d + 2 \, a^{6} b^{3} c^{7} d^{2} + 2 \, a^{7} b^{2} c^{6} d^{3} - 3 \, a^{8} b c^{5} d^{4} + a^{9} c^{4} d^{5}\right)} x\right)}}, \frac{3 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} + {\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(4 \, a^{2} b^{4} c^{6} - 12 \, a^{3} b^{3} c^{5} d - 12 \, a^{5} b c^{3} d^{3} + 4 \, a^{6} c^{2} d^{4} + {\left(3 \, a b^{5} c^{4} d^{2} - 11 \, a^{2} b^{4} c^{3} d^{3} - 11 \, a^{3} b^{3} c^{2} d^{4} + 3 \, a^{4} b^{2} c d^{5}\right)} x^{3} + 6 \, {\left(a b^{5} c^{5} d - 3 \, a^{2} b^{4} c^{4} d^{2} - 4 \, a^{3} b^{3} c^{3} d^{3} - 3 \, a^{4} b^{2} c^{2} d^{4} + a^{5} b c d^{5}\right)} x^{2} + 3 \, {\left(a b^{5} c^{6} - a^{2} b^{4} c^{5} d - 8 \, a^{3} b^{3} c^{4} d^{2} - 8 \, a^{4} b^{2} c^{3} d^{3} - a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{3 \, {\left(a^{5} b^{4} c^{9} - 4 \, a^{6} b^{3} c^{8} d + 6 \, a^{7} b^{2} c^{7} d^{2} - 4 \, a^{8} b c^{6} d^{3} + a^{9} c^{5} d^{4} + {\left(a^{3} b^{6} c^{7} d^{2} - 4 \, a^{4} b^{5} c^{6} d^{3} + 6 \, a^{5} b^{4} c^{5} d^{4} - 4 \, a^{6} b^{3} c^{4} d^{5} + a^{7} b^{2} c^{3} d^{6}\right)} x^{4} + 2 \, {\left(a^{3} b^{6} c^{8} d - 3 \, a^{4} b^{5} c^{7} d^{2} + 2 \, a^{5} b^{4} c^{6} d^{3} + 2 \, a^{6} b^{3} c^{5} d^{4} - 3 \, a^{7} b^{2} c^{4} d^{5} + a^{8} b c^{3} d^{6}\right)} x^{3} + {\left(a^{3} b^{6} c^{9} - 9 \, a^{5} b^{4} c^{7} d^{2} + 16 \, a^{6} b^{3} c^{6} d^{3} - 9 \, a^{7} b^{2} c^{5} d^{4} + a^{9} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{9} - 3 \, a^{5} b^{4} c^{8} d + 2 \, a^{6} b^{3} c^{7} d^{2} + 2 \, a^{7} b^{2} c^{6} d^{3} - 3 \, a^{8} b c^{5} d^{4} + a^{9} c^{4} d^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) + 4*(4*a^2*b^4*c^6 - 12*a^3*b^3*c^5*d - 12*a^5*b*c^3*d^3 + 4*a^6*c^2*d^4 + (3*a*b^5*c^4*d^2 - 11*a^2*b^4*c^3*d^3 - 11*a^3*b^3*c^2*d^4 + 3*a^4*b^2*c*d^5)*x^3 + 6*(a*b^5*c^5*d - 3*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 - 3*a^4*b^2*c^2*d^4 + a^5*b*c*d^5)*x^2 + 3*(a*b^5*c^6 - a^2*b^4*c^5*d - 8*a^3*b^3*c^4*d^2 - 8*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b^4*c^9 - 4*a^6*b^3*c^8*d + 6*a^7*b^2*c^7*d^2 - 4*a^8*b*c^6*d^3 + a^9*c^5*d^4 + (a^3*b^6*c^7*d^2 - 4*a^4*b^5*c^6*d^3 + 6*a^5*b^4*c^5*d^4 - 4*a^6*b^3*c^4*d^5 + a^7*b^2*c^3*d^6)*x^4 + 2*(a^3*b^6*c^8*d - 3*a^4*b^5*c^7*d^2 + 2*a^5*b^4*c^6*d^3 + 2*a^6*b^3*c^5*d^4 - 3*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6)*x^3 + (a^3*b^6*c^9 - 9*a^5*b^4*c^7*d^2 + 16*a^6*b^3*c^6*d^3 - 9*a^7*b^2*c^5*d^4 + a^9*c^3*d^6)*x^2 + 2*(a^4*b^5*c^9 - 3*a^5*b^4*c^8*d + 2*a^6*b^3*c^7*d^2 + 2*a^7*b^2*c^6*d^3 - 3*a^8*b*c^5*d^4 + a^9*c^4*d^5)*x), 1/3*(3*(a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4 + (b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(4*a^2*b^4*c^6 - 12*a^3*b^3*c^5*d - 12*a^5*b*c^3*d^3 + 4*a^6*c^2*d^4 + (3*a*b^5*c^4*d^2 - 11*a^2*b^4*c^3*d^3 - 11*a^3*b^3*c^2*d^4 + 3*a^4*b^2*c*d^5)*x^3 + 6*(a*b^5*c^5*d - 3*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 - 3*a^4*b^2*c^2*d^4 + a^5*b*c*d^5)*x^2 + 3*(a*b^5*c^6 - a^2*b^4*c^5*d - 8*a^3*b^3*c^4*d^2 - 8*a^4*b^2*c^3*d^3 - a^5*b*c^2*d^4 + a^6*c*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/(a^5*b^4*c^9 - 4*a^6*b^3*c^8*d + 6*a^7*b^2*c^7*d^2 - 4*a^8*b*c^6*d^3 + a^9*c^5*d^4 + (a^3*b^6*c^7*d^2 - 4*a^4*b^5*c^6*d^3 + 6*a^5*b^4*c^5*d^4 - 4*a^6*b^3*c^4*d^5 + a^7*b^2*c^3*d^6)*x^4 + 2*(a^3*b^6*c^8*d - 3*a^4*b^5*c^7*d^2 + 2*a^5*b^4*c^6*d^3 + 2*a^6*b^3*c^5*d^4 - 3*a^7*b^2*c^4*d^5 + a^8*b*c^3*d^6)*x^3 + (a^3*b^6*c^9 - 9*a^5*b^4*c^7*d^2 + 16*a^6*b^3*c^6*d^3 - 9*a^7*b^2*c^5*d^4 + a^9*c^3*d^6)*x^2 + 2*(a^4*b^5*c^9 - 3*a^5*b^4*c^8*d + 2*a^6*b^3*c^7*d^2 + 2*a^7*b^2*c^6*d^3 - 3*a^8*b*c^5*d^4 + a^9*c^4*d^5)*x)]","B",0
812,1,2506,0,36.505306," ","integrate(1/x^2/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(b^{7} c^{5} d^{2} - 3 \, a b^{6} c^{4} d^{3} + 2 \, a^{2} b^{5} c^{3} d^{4} + 2 \, a^{3} b^{4} c^{2} d^{5} - 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{5} + 2 \, {\left(b^{7} c^{6} d - 2 \, a b^{6} c^{5} d^{2} - a^{2} b^{5} c^{4} d^{3} + 4 \, a^{3} b^{4} c^{3} d^{4} - a^{4} b^{3} c^{2} d^{5} - 2 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{4} + {\left(b^{7} c^{7} + a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 7 \, a^{3} b^{4} c^{4} d^{3} + 7 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{3} + 2 \, {\left(a b^{6} c^{7} - 2 \, a^{2} b^{5} c^{6} d - a^{3} b^{4} c^{5} d^{2} + 4 \, a^{4} b^{3} c^{4} d^{3} - a^{5} b^{2} c^{3} d^{4} - 2 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x^{2} + {\left(a^{2} b^{5} c^{7} - 3 \, a^{3} b^{4} c^{6} d + 2 \, a^{4} b^{3} c^{5} d^{2} + 2 \, a^{5} b^{2} c^{4} d^{3} - 3 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5}\right)} x\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} + 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(3 \, a^{3} b^{4} c^{7} - 12 \, a^{4} b^{3} c^{6} d + 18 \, a^{5} b^{2} c^{5} d^{2} - 12 \, a^{6} b c^{4} d^{3} + 3 \, a^{7} c^{3} d^{4} + {\left(15 \, a b^{6} c^{5} d^{2} - 40 \, a^{2} b^{5} c^{4} d^{3} + 18 \, a^{3} b^{4} c^{3} d^{4} - 40 \, a^{4} b^{3} c^{2} d^{5} + 15 \, a^{5} b^{2} c d^{6}\right)} x^{4} + 6 \, {\left(5 \, a b^{6} c^{6} d - 10 \, a^{2} b^{5} c^{5} d^{2} - 3 \, a^{3} b^{4} c^{4} d^{3} - 3 \, a^{4} b^{3} c^{3} d^{4} - 10 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6}\right)} x^{3} + 3 \, {\left(5 \, a b^{6} c^{7} - 29 \, a^{3} b^{4} c^{5} d^{2} + 16 \, a^{4} b^{3} c^{4} d^{3} - 29 \, a^{5} b^{2} c^{3} d^{4} + 5 \, a^{7} c d^{6}\right)} x^{2} + 4 \, {\left(5 \, a^{2} b^{5} c^{7} - 12 \, a^{3} b^{4} c^{6} d + 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - 12 \, a^{6} b c^{3} d^{4} + 5 \, a^{7} c^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{12 \, {\left({\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6}\right)} x^{5} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x^{4} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{3} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{2} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x\right)}}, -\frac{15 \, {\left({\left(b^{7} c^{5} d^{2} - 3 \, a b^{6} c^{4} d^{3} + 2 \, a^{2} b^{5} c^{3} d^{4} + 2 \, a^{3} b^{4} c^{2} d^{5} - 3 \, a^{4} b^{3} c d^{6} + a^{5} b^{2} d^{7}\right)} x^{5} + 2 \, {\left(b^{7} c^{6} d - 2 \, a b^{6} c^{5} d^{2} - a^{2} b^{5} c^{4} d^{3} + 4 \, a^{3} b^{4} c^{3} d^{4} - a^{4} b^{3} c^{2} d^{5} - 2 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right)} x^{4} + {\left(b^{7} c^{7} + a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 7 \, a^{3} b^{4} c^{4} d^{3} + 7 \, a^{4} b^{3} c^{3} d^{4} - 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + a^{7} d^{7}\right)} x^{3} + 2 \, {\left(a b^{6} c^{7} - 2 \, a^{2} b^{5} c^{6} d - a^{3} b^{4} c^{5} d^{2} + 4 \, a^{4} b^{3} c^{4} d^{3} - a^{5} b^{2} c^{3} d^{4} - 2 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right)} x^{2} + {\left(a^{2} b^{5} c^{7} - 3 \, a^{3} b^{4} c^{6} d + 2 \, a^{4} b^{3} c^{5} d^{2} + 2 \, a^{5} b^{2} c^{4} d^{3} - 3 \, a^{6} b c^{3} d^{4} + a^{7} c^{2} d^{5}\right)} x\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) + 2 \, {\left(3 \, a^{3} b^{4} c^{7} - 12 \, a^{4} b^{3} c^{6} d + 18 \, a^{5} b^{2} c^{5} d^{2} - 12 \, a^{6} b c^{4} d^{3} + 3 \, a^{7} c^{3} d^{4} + {\left(15 \, a b^{6} c^{5} d^{2} - 40 \, a^{2} b^{5} c^{4} d^{3} + 18 \, a^{3} b^{4} c^{3} d^{4} - 40 \, a^{4} b^{3} c^{2} d^{5} + 15 \, a^{5} b^{2} c d^{6}\right)} x^{4} + 6 \, {\left(5 \, a b^{6} c^{6} d - 10 \, a^{2} b^{5} c^{5} d^{2} - 3 \, a^{3} b^{4} c^{4} d^{3} - 3 \, a^{4} b^{3} c^{3} d^{4} - 10 \, a^{5} b^{2} c^{2} d^{5} + 5 \, a^{6} b c d^{6}\right)} x^{3} + 3 \, {\left(5 \, a b^{6} c^{7} - 29 \, a^{3} b^{4} c^{5} d^{2} + 16 \, a^{4} b^{3} c^{4} d^{3} - 29 \, a^{5} b^{2} c^{3} d^{4} + 5 \, a^{7} c d^{6}\right)} x^{2} + 4 \, {\left(5 \, a^{2} b^{5} c^{7} - 12 \, a^{3} b^{4} c^{6} d + 3 \, a^{4} b^{3} c^{5} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{3} - 12 \, a^{6} b c^{3} d^{4} + 5 \, a^{7} c^{2} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{6 \, {\left({\left(a^{4} b^{6} c^{8} d^{2} - 4 \, a^{5} b^{5} c^{7} d^{3} + 6 \, a^{6} b^{4} c^{6} d^{4} - 4 \, a^{7} b^{3} c^{5} d^{5} + a^{8} b^{2} c^{4} d^{6}\right)} x^{5} + 2 \, {\left(a^{4} b^{6} c^{9} d - 3 \, a^{5} b^{5} c^{8} d^{2} + 2 \, a^{6} b^{4} c^{7} d^{3} + 2 \, a^{7} b^{3} c^{6} d^{4} - 3 \, a^{8} b^{2} c^{5} d^{5} + a^{9} b c^{4} d^{6}\right)} x^{4} + {\left(a^{4} b^{6} c^{10} - 9 \, a^{6} b^{4} c^{8} d^{2} + 16 \, a^{7} b^{3} c^{7} d^{3} - 9 \, a^{8} b^{2} c^{6} d^{4} + a^{10} c^{4} d^{6}\right)} x^{3} + 2 \, {\left(a^{5} b^{5} c^{10} - 3 \, a^{6} b^{4} c^{9} d + 2 \, a^{7} b^{3} c^{8} d^{2} + 2 \, a^{8} b^{2} c^{7} d^{3} - 3 \, a^{9} b c^{6} d^{4} + a^{10} c^{5} d^{5}\right)} x^{2} + {\left(a^{6} b^{4} c^{10} - 4 \, a^{7} b^{3} c^{9} d + 6 \, a^{8} b^{2} c^{8} d^{2} - 4 \, a^{9} b c^{7} d^{3} + a^{10} c^{6} d^{4}\right)} x\right)}}\right]"," ",0,"[1/12*(15*((b^7*c^5*d^2 - 3*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 3*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^5 + 2*(b^7*c^6*d - 2*a*b^6*c^5*d^2 - a^2*b^5*c^4*d^3 + 4*a^3*b^4*c^3*d^4 - a^4*b^3*c^2*d^5 - 2*a^5*b^2*c*d^6 + a^6*b*d^7)*x^4 + (b^7*c^7 + a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 7*a^3*b^4*c^4*d^3 + 7*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + a^7*d^7)*x^3 + 2*(a*b^6*c^7 - 2*a^2*b^5*c^6*d - a^3*b^4*c^5*d^2 + 4*a^4*b^3*c^4*d^3 - a^5*b^2*c^3*d^4 - 2*a^6*b*c^2*d^5 + a^7*c*d^6)*x^2 + (a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*x)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 + 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(3*a^3*b^4*c^7 - 12*a^4*b^3*c^6*d + 18*a^5*b^2*c^5*d^2 - 12*a^6*b*c^4*d^3 + 3*a^7*c^3*d^4 + (15*a*b^6*c^5*d^2 - 40*a^2*b^5*c^4*d^3 + 18*a^3*b^4*c^3*d^4 - 40*a^4*b^3*c^2*d^5 + 15*a^5*b^2*c*d^6)*x^4 + 6*(5*a*b^6*c^6*d - 10*a^2*b^5*c^5*d^2 - 3*a^3*b^4*c^4*d^3 - 3*a^4*b^3*c^3*d^4 - 10*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6)*x^3 + 3*(5*a*b^6*c^7 - 29*a^3*b^4*c^5*d^2 + 16*a^4*b^3*c^4*d^3 - 29*a^5*b^2*c^3*d^4 + 5*a^7*c*d^6)*x^2 + 4*(5*a^2*b^5*c^7 - 12*a^3*b^4*c^6*d + 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - 12*a^6*b*c^3*d^4 + 5*a^7*c^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6)*x^5 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x^4 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^3 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^2 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x), -1/6*(15*((b^7*c^5*d^2 - 3*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 3*a^4*b^3*c*d^6 + a^5*b^2*d^7)*x^5 + 2*(b^7*c^6*d - 2*a*b^6*c^5*d^2 - a^2*b^5*c^4*d^3 + 4*a^3*b^4*c^3*d^4 - a^4*b^3*c^2*d^5 - 2*a^5*b^2*c*d^6 + a^6*b*d^7)*x^4 + (b^7*c^7 + a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 7*a^3*b^4*c^4*d^3 + 7*a^4*b^3*c^3*d^4 - 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + a^7*d^7)*x^3 + 2*(a*b^6*c^7 - 2*a^2*b^5*c^6*d - a^3*b^4*c^5*d^2 + 4*a^4*b^3*c^4*d^3 - a^5*b^2*c^3*d^4 - 2*a^6*b*c^2*d^5 + a^7*c*d^6)*x^2 + (a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*x)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) + 2*(3*a^3*b^4*c^7 - 12*a^4*b^3*c^6*d + 18*a^5*b^2*c^5*d^2 - 12*a^6*b*c^4*d^3 + 3*a^7*c^3*d^4 + (15*a*b^6*c^5*d^2 - 40*a^2*b^5*c^4*d^3 + 18*a^3*b^4*c^3*d^4 - 40*a^4*b^3*c^2*d^5 + 15*a^5*b^2*c*d^6)*x^4 + 6*(5*a*b^6*c^6*d - 10*a^2*b^5*c^5*d^2 - 3*a^3*b^4*c^4*d^3 - 3*a^4*b^3*c^3*d^4 - 10*a^5*b^2*c^2*d^5 + 5*a^6*b*c*d^6)*x^3 + 3*(5*a*b^6*c^7 - 29*a^3*b^4*c^5*d^2 + 16*a^4*b^3*c^4*d^3 - 29*a^5*b^2*c^3*d^4 + 5*a^7*c*d^6)*x^2 + 4*(5*a^2*b^5*c^7 - 12*a^3*b^4*c^6*d + 3*a^4*b^3*c^5*d^2 + 3*a^5*b^2*c^4*d^3 - 12*a^6*b*c^3*d^4 + 5*a^7*c^2*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^4*b^6*c^8*d^2 - 4*a^5*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6)*x^5 + 2*(a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*x^4 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*x^3 + 2*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*x^2 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*x)]","B",0
813,1,2996,0,76.739504," ","integrate(1/x^3/(b*x+a)^(5/2)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(7 \, b^{8} c^{6} d^{2} - 18 \, a b^{7} c^{5} d^{3} + 9 \, a^{2} b^{6} c^{4} d^{4} + 4 \, a^{3} b^{5} c^{3} d^{5} + 9 \, a^{4} b^{4} c^{2} d^{6} - 18 \, a^{5} b^{3} c d^{7} + 7 \, a^{6} b^{2} d^{8}\right)} x^{6} + 2 \, {\left(7 \, b^{8} c^{7} d - 11 \, a b^{7} c^{6} d^{2} - 9 \, a^{2} b^{6} c^{5} d^{3} + 13 \, a^{3} b^{5} c^{4} d^{4} + 13 \, a^{4} b^{4} c^{3} d^{5} - 9 \, a^{5} b^{3} c^{2} d^{6} - 11 \, a^{6} b^{2} c d^{7} + 7 \, a^{7} b d^{8}\right)} x^{5} + {\left(7 \, b^{8} c^{8} + 10 \, a b^{7} c^{7} d - 56 \, a^{2} b^{6} c^{6} d^{2} + 22 \, a^{3} b^{5} c^{5} d^{3} + 34 \, a^{4} b^{4} c^{4} d^{4} + 22 \, a^{5} b^{3} c^{3} d^{5} - 56 \, a^{6} b^{2} c^{2} d^{6} + 10 \, a^{7} b c d^{7} + 7 \, a^{8} d^{8}\right)} x^{4} + 2 \, {\left(7 \, a b^{7} c^{8} - 11 \, a^{2} b^{6} c^{7} d - 9 \, a^{3} b^{5} c^{6} d^{2} + 13 \, a^{4} b^{4} c^{5} d^{3} + 13 \, a^{5} b^{3} c^{4} d^{4} - 9 \, a^{6} b^{2} c^{3} d^{5} - 11 \, a^{7} b c^{2} d^{6} + 7 \, a^{8} c d^{7}\right)} x^{3} + {\left(7 \, a^{2} b^{6} c^{8} - 18 \, a^{3} b^{5} c^{7} d + 9 \, a^{4} b^{4} c^{6} d^{2} + 4 \, a^{5} b^{3} c^{5} d^{3} + 9 \, a^{6} b^{2} c^{4} d^{4} - 18 \, a^{7} b c^{3} d^{5} + 7 \, a^{8} c^{2} d^{6}\right)} x^{2}\right)} \sqrt{a c} \log\left(\frac{8 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{a c} \sqrt{b x + a} \sqrt{d x + c} + 8 \, {\left(a b c^{2} + a^{2} c d\right)} x}{x^{2}}\right) - 4 \, {\left(6 \, a^{4} b^{4} c^{8} - 24 \, a^{5} b^{3} c^{7} d + 36 \, a^{6} b^{2} c^{6} d^{2} - 24 \, a^{7} b c^{5} d^{3} + 6 \, a^{8} c^{4} d^{4} - {\left(105 \, a b^{7} c^{6} d^{2} - 235 \, a^{2} b^{6} c^{5} d^{3} + 66 \, a^{3} b^{5} c^{4} d^{4} + 66 \, a^{4} b^{4} c^{3} d^{5} - 235 \, a^{5} b^{3} c^{2} d^{6} + 105 \, a^{6} b^{2} c d^{7}\right)} x^{5} - 6 \, {\left(35 \, a b^{7} c^{7} d - 55 \, a^{2} b^{6} c^{6} d^{2} - 31 \, a^{3} b^{5} c^{5} d^{3} + 38 \, a^{4} b^{4} c^{4} d^{4} - 31 \, a^{5} b^{3} c^{3} d^{5} - 55 \, a^{6} b^{2} c^{2} d^{6} + 35 \, a^{7} b c d^{7}\right)} x^{4} - 3 \, {\left(35 \, a b^{7} c^{8} + 15 \, a^{2} b^{6} c^{7} d - 183 \, a^{3} b^{5} c^{6} d^{2} + 69 \, a^{4} b^{4} c^{5} d^{3} + 69 \, a^{5} b^{3} c^{4} d^{4} - 183 \, a^{6} b^{2} c^{3} d^{5} + 15 \, a^{7} b c^{2} d^{6} + 35 \, a^{8} c d^{7}\right)} x^{3} - 4 \, {\left(35 \, a^{2} b^{6} c^{8} - 69 \, a^{3} b^{5} c^{7} d - 3 \, a^{4} b^{4} c^{6} d^{2} + 42 \, a^{5} b^{3} c^{5} d^{3} - 3 \, a^{6} b^{2} c^{4} d^{4} - 69 \, a^{7} b c^{3} d^{5} + 35 \, a^{8} c^{2} d^{6}\right)} x^{2} - 21 \, {\left(a^{3} b^{5} c^{8} - 3 \, a^{4} b^{4} c^{7} d + 2 \, a^{5} b^{3} c^{6} d^{2} + 2 \, a^{6} b^{2} c^{5} d^{3} - 3 \, a^{7} b c^{4} d^{4} + a^{8} c^{3} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{48 \, {\left({\left(a^{5} b^{6} c^{9} d^{2} - 4 \, a^{6} b^{5} c^{8} d^{3} + 6 \, a^{7} b^{4} c^{7} d^{4} - 4 \, a^{8} b^{3} c^{6} d^{5} + a^{9} b^{2} c^{5} d^{6}\right)} x^{6} + 2 \, {\left(a^{5} b^{6} c^{10} d - 3 \, a^{6} b^{5} c^{9} d^{2} + 2 \, a^{7} b^{4} c^{8} d^{3} + 2 \, a^{8} b^{3} c^{7} d^{4} - 3 \, a^{9} b^{2} c^{6} d^{5} + a^{10} b c^{5} d^{6}\right)} x^{5} + {\left(a^{5} b^{6} c^{11} - 9 \, a^{7} b^{4} c^{9} d^{2} + 16 \, a^{8} b^{3} c^{8} d^{3} - 9 \, a^{9} b^{2} c^{7} d^{4} + a^{11} c^{5} d^{6}\right)} x^{4} + 2 \, {\left(a^{6} b^{5} c^{11} - 3 \, a^{7} b^{4} c^{10} d + 2 \, a^{8} b^{3} c^{9} d^{2} + 2 \, a^{9} b^{2} c^{8} d^{3} - 3 \, a^{10} b c^{7} d^{4} + a^{11} c^{6} d^{5}\right)} x^{3} + {\left(a^{7} b^{4} c^{11} - 4 \, a^{8} b^{3} c^{10} d + 6 \, a^{9} b^{2} c^{9} d^{2} - 4 \, a^{10} b c^{8} d^{3} + a^{11} c^{7} d^{4}\right)} x^{2}\right)}}, \frac{15 \, {\left({\left(7 \, b^{8} c^{6} d^{2} - 18 \, a b^{7} c^{5} d^{3} + 9 \, a^{2} b^{6} c^{4} d^{4} + 4 \, a^{3} b^{5} c^{3} d^{5} + 9 \, a^{4} b^{4} c^{2} d^{6} - 18 \, a^{5} b^{3} c d^{7} + 7 \, a^{6} b^{2} d^{8}\right)} x^{6} + 2 \, {\left(7 \, b^{8} c^{7} d - 11 \, a b^{7} c^{6} d^{2} - 9 \, a^{2} b^{6} c^{5} d^{3} + 13 \, a^{3} b^{5} c^{4} d^{4} + 13 \, a^{4} b^{4} c^{3} d^{5} - 9 \, a^{5} b^{3} c^{2} d^{6} - 11 \, a^{6} b^{2} c d^{7} + 7 \, a^{7} b d^{8}\right)} x^{5} + {\left(7 \, b^{8} c^{8} + 10 \, a b^{7} c^{7} d - 56 \, a^{2} b^{6} c^{6} d^{2} + 22 \, a^{3} b^{5} c^{5} d^{3} + 34 \, a^{4} b^{4} c^{4} d^{4} + 22 \, a^{5} b^{3} c^{3} d^{5} - 56 \, a^{6} b^{2} c^{2} d^{6} + 10 \, a^{7} b c d^{7} + 7 \, a^{8} d^{8}\right)} x^{4} + 2 \, {\left(7 \, a b^{7} c^{8} - 11 \, a^{2} b^{6} c^{7} d - 9 \, a^{3} b^{5} c^{6} d^{2} + 13 \, a^{4} b^{4} c^{5} d^{3} + 13 \, a^{5} b^{3} c^{4} d^{4} - 9 \, a^{6} b^{2} c^{3} d^{5} - 11 \, a^{7} b c^{2} d^{6} + 7 \, a^{8} c d^{7}\right)} x^{3} + {\left(7 \, a^{2} b^{6} c^{8} - 18 \, a^{3} b^{5} c^{7} d + 9 \, a^{4} b^{4} c^{6} d^{2} + 4 \, a^{5} b^{3} c^{5} d^{3} + 9 \, a^{6} b^{2} c^{4} d^{4} - 18 \, a^{7} b c^{3} d^{5} + 7 \, a^{8} c^{2} d^{6}\right)} x^{2}\right)} \sqrt{-a c} \arctan\left(\frac{{\left(2 \, a c + {\left(b c + a d\right)} x\right)} \sqrt{-a c} \sqrt{b x + a} \sqrt{d x + c}}{2 \, {\left(a b c d x^{2} + a^{2} c^{2} + {\left(a b c^{2} + a^{2} c d\right)} x\right)}}\right) - 2 \, {\left(6 \, a^{4} b^{4} c^{8} - 24 \, a^{5} b^{3} c^{7} d + 36 \, a^{6} b^{2} c^{6} d^{2} - 24 \, a^{7} b c^{5} d^{3} + 6 \, a^{8} c^{4} d^{4} - {\left(105 \, a b^{7} c^{6} d^{2} - 235 \, a^{2} b^{6} c^{5} d^{3} + 66 \, a^{3} b^{5} c^{4} d^{4} + 66 \, a^{4} b^{4} c^{3} d^{5} - 235 \, a^{5} b^{3} c^{2} d^{6} + 105 \, a^{6} b^{2} c d^{7}\right)} x^{5} - 6 \, {\left(35 \, a b^{7} c^{7} d - 55 \, a^{2} b^{6} c^{6} d^{2} - 31 \, a^{3} b^{5} c^{5} d^{3} + 38 \, a^{4} b^{4} c^{4} d^{4} - 31 \, a^{5} b^{3} c^{3} d^{5} - 55 \, a^{6} b^{2} c^{2} d^{6} + 35 \, a^{7} b c d^{7}\right)} x^{4} - 3 \, {\left(35 \, a b^{7} c^{8} + 15 \, a^{2} b^{6} c^{7} d - 183 \, a^{3} b^{5} c^{6} d^{2} + 69 \, a^{4} b^{4} c^{5} d^{3} + 69 \, a^{5} b^{3} c^{4} d^{4} - 183 \, a^{6} b^{2} c^{3} d^{5} + 15 \, a^{7} b c^{2} d^{6} + 35 \, a^{8} c d^{7}\right)} x^{3} - 4 \, {\left(35 \, a^{2} b^{6} c^{8} - 69 \, a^{3} b^{5} c^{7} d - 3 \, a^{4} b^{4} c^{6} d^{2} + 42 \, a^{5} b^{3} c^{5} d^{3} - 3 \, a^{6} b^{2} c^{4} d^{4} - 69 \, a^{7} b c^{3} d^{5} + 35 \, a^{8} c^{2} d^{6}\right)} x^{2} - 21 \, {\left(a^{3} b^{5} c^{8} - 3 \, a^{4} b^{4} c^{7} d + 2 \, a^{5} b^{3} c^{6} d^{2} + 2 \, a^{6} b^{2} c^{5} d^{3} - 3 \, a^{7} b c^{4} d^{4} + a^{8} c^{3} d^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c}}{24 \, {\left({\left(a^{5} b^{6} c^{9} d^{2} - 4 \, a^{6} b^{5} c^{8} d^{3} + 6 \, a^{7} b^{4} c^{7} d^{4} - 4 \, a^{8} b^{3} c^{6} d^{5} + a^{9} b^{2} c^{5} d^{6}\right)} x^{6} + 2 \, {\left(a^{5} b^{6} c^{10} d - 3 \, a^{6} b^{5} c^{9} d^{2} + 2 \, a^{7} b^{4} c^{8} d^{3} + 2 \, a^{8} b^{3} c^{7} d^{4} - 3 \, a^{9} b^{2} c^{6} d^{5} + a^{10} b c^{5} d^{6}\right)} x^{5} + {\left(a^{5} b^{6} c^{11} - 9 \, a^{7} b^{4} c^{9} d^{2} + 16 \, a^{8} b^{3} c^{8} d^{3} - 9 \, a^{9} b^{2} c^{7} d^{4} + a^{11} c^{5} d^{6}\right)} x^{4} + 2 \, {\left(a^{6} b^{5} c^{11} - 3 \, a^{7} b^{4} c^{10} d + 2 \, a^{8} b^{3} c^{9} d^{2} + 2 \, a^{9} b^{2} c^{8} d^{3} - 3 \, a^{10} b c^{7} d^{4} + a^{11} c^{6} d^{5}\right)} x^{3} + {\left(a^{7} b^{4} c^{11} - 4 \, a^{8} b^{3} c^{10} d + 6 \, a^{9} b^{2} c^{9} d^{2} - 4 \, a^{10} b c^{8} d^{3} + a^{11} c^{7} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/48*(15*((7*b^8*c^6*d^2 - 18*a*b^7*c^5*d^3 + 9*a^2*b^6*c^4*d^4 + 4*a^3*b^5*c^3*d^5 + 9*a^4*b^4*c^2*d^6 - 18*a^5*b^3*c*d^7 + 7*a^6*b^2*d^8)*x^6 + 2*(7*b^8*c^7*d - 11*a*b^7*c^6*d^2 - 9*a^2*b^6*c^5*d^3 + 13*a^3*b^5*c^4*d^4 + 13*a^4*b^4*c^3*d^5 - 9*a^5*b^3*c^2*d^6 - 11*a^6*b^2*c*d^7 + 7*a^7*b*d^8)*x^5 + (7*b^8*c^8 + 10*a*b^7*c^7*d - 56*a^2*b^6*c^6*d^2 + 22*a^3*b^5*c^5*d^3 + 34*a^4*b^4*c^4*d^4 + 22*a^5*b^3*c^3*d^5 - 56*a^6*b^2*c^2*d^6 + 10*a^7*b*c*d^7 + 7*a^8*d^8)*x^4 + 2*(7*a*b^7*c^8 - 11*a^2*b^6*c^7*d - 9*a^3*b^5*c^6*d^2 + 13*a^4*b^4*c^5*d^3 + 13*a^5*b^3*c^4*d^4 - 9*a^6*b^2*c^3*d^5 - 11*a^7*b*c^2*d^6 + 7*a^8*c*d^7)*x^3 + (7*a^2*b^6*c^8 - 18*a^3*b^5*c^7*d + 9*a^4*b^4*c^6*d^2 + 4*a^5*b^3*c^5*d^3 + 9*a^6*b^2*c^4*d^4 - 18*a^7*b*c^3*d^5 + 7*a^8*c^2*d^6)*x^2)*sqrt(a*c)*log((8*a^2*c^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^2 - 4*(2*a*c + (b*c + a*d)*x)*sqrt(a*c)*sqrt(b*x + a)*sqrt(d*x + c) + 8*(a*b*c^2 + a^2*c*d)*x)/x^2) - 4*(6*a^4*b^4*c^8 - 24*a^5*b^3*c^7*d + 36*a^6*b^2*c^6*d^2 - 24*a^7*b*c^5*d^3 + 6*a^8*c^4*d^4 - (105*a*b^7*c^6*d^2 - 235*a^2*b^6*c^5*d^3 + 66*a^3*b^5*c^4*d^4 + 66*a^4*b^4*c^3*d^5 - 235*a^5*b^3*c^2*d^6 + 105*a^6*b^2*c*d^7)*x^5 - 6*(35*a*b^7*c^7*d - 55*a^2*b^6*c^6*d^2 - 31*a^3*b^5*c^5*d^3 + 38*a^4*b^4*c^4*d^4 - 31*a^5*b^3*c^3*d^5 - 55*a^6*b^2*c^2*d^6 + 35*a^7*b*c*d^7)*x^4 - 3*(35*a*b^7*c^8 + 15*a^2*b^6*c^7*d - 183*a^3*b^5*c^6*d^2 + 69*a^4*b^4*c^5*d^3 + 69*a^5*b^3*c^4*d^4 - 183*a^6*b^2*c^3*d^5 + 15*a^7*b*c^2*d^6 + 35*a^8*c*d^7)*x^3 - 4*(35*a^2*b^6*c^8 - 69*a^3*b^5*c^7*d - 3*a^4*b^4*c^6*d^2 + 42*a^5*b^3*c^5*d^3 - 3*a^6*b^2*c^4*d^4 - 69*a^7*b*c^3*d^5 + 35*a^8*c^2*d^6)*x^2 - 21*(a^3*b^5*c^8 - 3*a^4*b^4*c^7*d + 2*a^5*b^3*c^6*d^2 + 2*a^6*b^2*c^5*d^3 - 3*a^7*b*c^4*d^4 + a^8*c^3*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^5*b^6*c^9*d^2 - 4*a^6*b^5*c^8*d^3 + 6*a^7*b^4*c^7*d^4 - 4*a^8*b^3*c^6*d^5 + a^9*b^2*c^5*d^6)*x^6 + 2*(a^5*b^6*c^10*d - 3*a^6*b^5*c^9*d^2 + 2*a^7*b^4*c^8*d^3 + 2*a^8*b^3*c^7*d^4 - 3*a^9*b^2*c^6*d^5 + a^10*b*c^5*d^6)*x^5 + (a^5*b^6*c^11 - 9*a^7*b^4*c^9*d^2 + 16*a^8*b^3*c^8*d^3 - 9*a^9*b^2*c^7*d^4 + a^11*c^5*d^6)*x^4 + 2*(a^6*b^5*c^11 - 3*a^7*b^4*c^10*d + 2*a^8*b^3*c^9*d^2 + 2*a^9*b^2*c^8*d^3 - 3*a^10*b*c^7*d^4 + a^11*c^6*d^5)*x^3 + (a^7*b^4*c^11 - 4*a^8*b^3*c^10*d + 6*a^9*b^2*c^9*d^2 - 4*a^10*b*c^8*d^3 + a^11*c^7*d^4)*x^2), 1/24*(15*((7*b^8*c^6*d^2 - 18*a*b^7*c^5*d^3 + 9*a^2*b^6*c^4*d^4 + 4*a^3*b^5*c^3*d^5 + 9*a^4*b^4*c^2*d^6 - 18*a^5*b^3*c*d^7 + 7*a^6*b^2*d^8)*x^6 + 2*(7*b^8*c^7*d - 11*a*b^7*c^6*d^2 - 9*a^2*b^6*c^5*d^3 + 13*a^3*b^5*c^4*d^4 + 13*a^4*b^4*c^3*d^5 - 9*a^5*b^3*c^2*d^6 - 11*a^6*b^2*c*d^7 + 7*a^7*b*d^8)*x^5 + (7*b^8*c^8 + 10*a*b^7*c^7*d - 56*a^2*b^6*c^6*d^2 + 22*a^3*b^5*c^5*d^3 + 34*a^4*b^4*c^4*d^4 + 22*a^5*b^3*c^3*d^5 - 56*a^6*b^2*c^2*d^6 + 10*a^7*b*c*d^7 + 7*a^8*d^8)*x^4 + 2*(7*a*b^7*c^8 - 11*a^2*b^6*c^7*d - 9*a^3*b^5*c^6*d^2 + 13*a^4*b^4*c^5*d^3 + 13*a^5*b^3*c^4*d^4 - 9*a^6*b^2*c^3*d^5 - 11*a^7*b*c^2*d^6 + 7*a^8*c*d^7)*x^3 + (7*a^2*b^6*c^8 - 18*a^3*b^5*c^7*d + 9*a^4*b^4*c^6*d^2 + 4*a^5*b^3*c^5*d^3 + 9*a^6*b^2*c^4*d^4 - 18*a^7*b*c^3*d^5 + 7*a^8*c^2*d^6)*x^2)*sqrt(-a*c)*arctan(1/2*(2*a*c + (b*c + a*d)*x)*sqrt(-a*c)*sqrt(b*x + a)*sqrt(d*x + c)/(a*b*c*d*x^2 + a^2*c^2 + (a*b*c^2 + a^2*c*d)*x)) - 2*(6*a^4*b^4*c^8 - 24*a^5*b^3*c^7*d + 36*a^6*b^2*c^6*d^2 - 24*a^7*b*c^5*d^3 + 6*a^8*c^4*d^4 - (105*a*b^7*c^6*d^2 - 235*a^2*b^6*c^5*d^3 + 66*a^3*b^5*c^4*d^4 + 66*a^4*b^4*c^3*d^5 - 235*a^5*b^3*c^2*d^6 + 105*a^6*b^2*c*d^7)*x^5 - 6*(35*a*b^7*c^7*d - 55*a^2*b^6*c^6*d^2 - 31*a^3*b^5*c^5*d^3 + 38*a^4*b^4*c^4*d^4 - 31*a^5*b^3*c^3*d^5 - 55*a^6*b^2*c^2*d^6 + 35*a^7*b*c*d^7)*x^4 - 3*(35*a*b^7*c^8 + 15*a^2*b^6*c^7*d - 183*a^3*b^5*c^6*d^2 + 69*a^4*b^4*c^5*d^3 + 69*a^5*b^3*c^4*d^4 - 183*a^6*b^2*c^3*d^5 + 15*a^7*b*c^2*d^6 + 35*a^8*c*d^7)*x^3 - 4*(35*a^2*b^6*c^8 - 69*a^3*b^5*c^7*d - 3*a^4*b^4*c^6*d^2 + 42*a^5*b^3*c^5*d^3 - 3*a^6*b^2*c^4*d^4 - 69*a^7*b*c^3*d^5 + 35*a^8*c^2*d^6)*x^2 - 21*(a^3*b^5*c^8 - 3*a^4*b^4*c^7*d + 2*a^5*b^3*c^6*d^2 + 2*a^6*b^2*c^5*d^3 - 3*a^7*b*c^4*d^4 + a^8*c^3*d^5)*x)*sqrt(b*x + a)*sqrt(d*x + c))/((a^5*b^6*c^9*d^2 - 4*a^6*b^5*c^8*d^3 + 6*a^7*b^4*c^7*d^4 - 4*a^8*b^3*c^6*d^5 + a^9*b^2*c^5*d^6)*x^6 + 2*(a^5*b^6*c^10*d - 3*a^6*b^5*c^9*d^2 + 2*a^7*b^4*c^8*d^3 + 2*a^8*b^3*c^7*d^4 - 3*a^9*b^2*c^6*d^5 + a^10*b*c^5*d^6)*x^5 + (a^5*b^6*c^11 - 9*a^7*b^4*c^9*d^2 + 16*a^8*b^3*c^8*d^3 - 9*a^9*b^2*c^7*d^4 + a^11*c^5*d^6)*x^4 + 2*(a^6*b^5*c^11 - 3*a^7*b^4*c^10*d + 2*a^8*b^3*c^9*d^2 + 2*a^9*b^2*c^8*d^3 - 3*a^10*b*c^7*d^4 + a^11*c^6*d^5)*x^3 + (a^7*b^4*c^11 - 4*a^8*b^3*c^10*d + 6*a^9*b^2*c^9*d^2 - 4*a^10*b*c^8*d^3 + a^11*c^7*d^4)*x^2)]","B",0
814,1,1,0,1.071460," ","integrate(x^2*(b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
815,1,1,0,1.978612," ","integrate(x*(b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
816,1,1,0,1.390515," ","integrate((b*x+a)^(1/2)/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
817,1,1,0,1.428818," ","integrate((b*x+a)^(1/2)/x/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
818,1,1,0,1.591140," ","integrate((b*x+a)^(1/2)/x^2/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
819,1,1,0,1.539566," ","integrate((b*x+a)^(1/2)/x^3/(-b*x-a)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
820,1,42,0,1.820086," ","integrate((b*x+a)^(1/2)/(x^m)/(-b*x-a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x + a} \sqrt{-b x - a} x}{{\left(a m + {\left(b m - b\right)} x - a\right)} x^{m}}"," ",0,"sqrt(b*x + a)*sqrt(-b*x - a)*x/((a*m + (b*m - b)*x - a)*x^m)","A",0
821,1,9,0,1.743021," ","integrate(x^2*(b*x+a)^n/((-b*x-a)^n),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \cos\left(\pi n\right)"," ",0,"1/3*x^3*cos(pi*n)","A",0
822,1,9,0,1.555810," ","integrate(x*(b*x+a)^n/((-b*x-a)^n),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \cos\left(\pi n\right)"," ",0,"1/2*x^2*cos(pi*n)","A",0
823,1,6,0,2.628649," ","integrate((b*x+a)^n/((-b*x-a)^n),x, algorithm=""fricas"")","x \cos\left(\pi n\right)"," ",0,"x*cos(pi*n)","A",0
824,1,7,0,2.053024," ","integrate((b*x+a)^n/x/((-b*x-a)^n),x, algorithm=""fricas"")","\cos\left(\pi n\right) \log\left(x\right)"," ",0,"cos(pi*n)*log(x)","A",0
825,1,9,0,0.999646," ","integrate((b*x+a)^n/x^2/((-b*x-a)^n),x, algorithm=""fricas"")","-\frac{\cos\left(\pi n\right)}{x}"," ",0,"-cos(pi*n)/x","A",0
826,1,9,0,1.142115," ","integrate((b*x+a)^n/x^3/((-b*x-a)^n),x, algorithm=""fricas"")","-\frac{\cos\left(\pi n\right)}{2 \, x^{2}}"," ",0,"-1/2*cos(pi*n)/x^2","A",0
827,1,17,0,1.639791," ","integrate((b*x+a)^n/(x^m)/((-b*x-a)^n),x, algorithm=""fricas"")","-\frac{x \cos\left(\pi n\right)}{{\left(m - 1\right)} x^{m}}"," ",0,"-x*cos(pi*n)/((m - 1)*x^m)","A",0
828,1,80,0,0.787095," ","integrate(x^3*(1+x)^(1/2)/(1-x)^(5/2),x, algorithm=""fricas"")","-\frac{52 \, x^{2} + {\left(3 \, x^{3} + 12 \, x^{2} - 71 \, x + 52\right)} \sqrt{x + 1} \sqrt{-x + 1} + 66 \, {\left(x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - 104 \, x + 52}{6 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/6*(52*x^2 + (3*x^3 + 12*x^2 - 71*x + 52)*sqrt(x + 1)*sqrt(-x + 1) + 66*(x^2 - 2*x + 1)*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - 104*x + 52)/(x^2 - 2*x + 1)","A",0
829,1,75,0,0.799668," ","integrate(x^2*(1+x)^(1/2)/(1-x)^(5/2),x, algorithm=""fricas"")","-\frac{14 \, x^{2} + {\left(3 \, x^{2} - 19 \, x + 14\right)} \sqrt{x + 1} \sqrt{-x + 1} + 18 \, {\left(x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - 28 \, x + 14}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/3*(14*x^2 + (3*x^2 - 19*x + 14)*sqrt(x + 1)*sqrt(-x + 1) + 18*(x^2 - 2*x + 1)*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - 28*x + 14)/(x^2 - 2*x + 1)","A",0
830,1,71,0,1.572711," ","integrate(x*(1+x)^(1/2)/(1-x)^(5/2),x, algorithm=""fricas"")","-\frac{5 \, x^{2} - {\left(7 \, x - 5\right)} \sqrt{x + 1} \sqrt{-x + 1} + 6 \, {\left(x^{2} - 2 \, x + 1\right)} \arctan\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - 10 \, x + 5}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/3*(5*x^2 - (7*x - 5)*sqrt(x + 1)*sqrt(-x + 1) + 6*(x^2 - 2*x + 1)*arctan((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - 10*x + 5)/(x^2 - 2*x + 1)","B",0
831,1,33,0,1.385952," ","integrate((1+x)^(1/2)/(1-x)^(5/2),x, algorithm=""fricas"")","\frac{x^{2} + {\left(x + 1\right)}^{\frac{3}{2}} \sqrt{-x + 1} - 2 \, x + 1}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/3*(x^2 + (x + 1)^(3/2)*sqrt(-x + 1) - 2*x + 1)/(x^2 - 2*x + 1)","B",0
832,1,31,0,1.379843," ","integrate((1+x)^(1/2)/(-1+x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(x + 1\right)}^{\frac{3}{2}} \sqrt{x - 1} + x^{2} - 2 \, x + 1}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"-1/3*((x + 1)^(3/2)*sqrt(x - 1) + x^2 - 2*x + 1)/(x^2 - 2*x + 1)","B",0
833,1,71,0,0.907916," ","integrate((1+x)^(1/2)/(1-x)^(5/2)/x,x, algorithm=""fricas"")","\frac{7 \, x^{2} - {\left(5 \, x - 7\right)} \sqrt{x + 1} \sqrt{-x + 1} + 3 \, {\left(x^{2} - 2 \, x + 1\right)} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) - 14 \, x + 7}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/3*(7*x^2 - (5*x - 7)*sqrt(x + 1)*sqrt(-x + 1) + 3*(x^2 - 2*x + 1)*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) - 14*x + 7)/(x^2 - 2*x + 1)","A",0
834,1,84,0,1.475098," ","integrate((1+x)^(1/2)/(1-x)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{13 \, x^{3} - 26 \, x^{2} - {\left(14 \, x^{2} - 19 \, x + 3\right)} \sqrt{x + 1} \sqrt{-x + 1} + 9 \, {\left(x^{3} - 2 \, x^{2} + x\right)} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right) + 13 \, x}{3 \, {\left(x^{3} - 2 \, x^{2} + x\right)}}"," ",0,"1/3*(13*x^3 - 26*x^2 - (14*x^2 - 19*x + 3)*sqrt(x + 1)*sqrt(-x + 1) + 9*(x^3 - 2*x^2 + x)*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x) + 13*x)/(x^3 - 2*x^2 + x)","A",0
835,1,95,0,1.482754," ","integrate((1+x)^(1/2)/(1-x)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{38 \, x^{4} - 76 \, x^{3} + 38 \, x^{2} - {\left(52 \, x^{3} - 71 \, x^{2} + 12 \, x + 3\right)} \sqrt{x + 1} \sqrt{-x + 1} + 33 \, {\left(x^{4} - 2 \, x^{3} + x^{2}\right)} \log\left(\frac{\sqrt{x + 1} \sqrt{-x + 1} - 1}{x}\right)}{6 \, {\left(x^{4} - 2 \, x^{3} + x^{2}\right)}}"," ",0,"1/6*(38*x^4 - 76*x^3 + 38*x^2 - (52*x^3 - 71*x^2 + 12*x + 3)*sqrt(x + 1)*sqrt(-x + 1) + 33*(x^4 - 2*x^3 + x^2)*log((sqrt(x + 1)*sqrt(-x + 1) - 1)/x))/(x^4 - 2*x^3 + x^2)","A",0
836,1,32,0,1.358070," ","integrate(x^2/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{x + 1} \sqrt{x - 1} x - \frac{1}{2} \, \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"1/2*sqrt(x + 1)*sqrt(x - 1)*x - 1/2*log(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
837,1,11,0,1.389183," ","integrate(x/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\sqrt{x + 1} \sqrt{x - 1}"," ",0,"sqrt(x + 1)*sqrt(x - 1)","A",0
838,1,18,0,1.022991," ","integrate(1/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","-\log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"-log(sqrt(x + 1)*sqrt(x - 1) - x)","B",0
839,1,18,0,1.587058," ","integrate(1/x/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"2*arctan(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
840,1,17,0,1.510278," ","integrate(1/x^2/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{x + 1} \sqrt{x - 1} + x}{x}"," ",0,"(sqrt(x + 1)*sqrt(x - 1) + x)/x","A",0
841,1,40,0,1.577404," ","integrate(x^2*(-1+x)^(1/2)*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, {\left(2 \, x^{3} - x\right)} \sqrt{x + 1} \sqrt{x - 1} + \frac{1}{8} \, \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"1/8*(2*x^3 - x)*sqrt(x + 1)*sqrt(x - 1) + 1/8*log(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
842,1,17,0,1.339165," ","integrate(x*(-1+x)^(1/2)*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{2} - 1\right)} \sqrt{x + 1} \sqrt{x - 1}"," ",0,"1/3*(x^2 - 1)*sqrt(x + 1)*sqrt(x - 1)","A",0
843,1,32,0,1.661681," ","integrate((-1+x)^(1/2)*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{x + 1} \sqrt{x - 1} x + \frac{1}{2} \, \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"1/2*sqrt(x + 1)*sqrt(x - 1)*x + 1/2*log(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
844,1,30,0,1.425416," ","integrate((-1+x)^(1/2)*(1+x)^(1/2)/x,x, algorithm=""fricas"")","\sqrt{x + 1} \sqrt{x - 1} - 2 \, \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right)"," ",0,"sqrt(x + 1)*sqrt(x - 1) - 2*arctan(sqrt(x + 1)*sqrt(x - 1) - x)","A",0
845,1,36,0,1.344476," ","integrate((-1+x)^(1/2)*(1+x)^(1/2)/x^2,x, algorithm=""fricas"")","-\frac{x \log\left(\sqrt{x + 1} \sqrt{x - 1} - x\right) + \sqrt{x + 1} \sqrt{x - 1} + x}{x}"," ",0,"-(x*log(sqrt(x + 1)*sqrt(x - 1) - x) + sqrt(x + 1)*sqrt(x - 1) + x)/x","A",0
846,1,23,0,1.395003," ","integrate(1/(1+2*x)^(1/2)/(3+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\sqrt{2 \, x + 3} \sqrt{2 \, x + 1} - 2 \, x - 2\right)"," ",0,"-1/2*log(sqrt(2*x + 3)*sqrt(2*x + 1) - 2*x - 2)","A",0
847,1,46,0,1.382708," ","integrate(1/x/(-2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(\frac{\sqrt{3} \sqrt{2} \sqrt{5 \, x + 3} \sqrt{3 \, x - 2} {\left(x + 12\right)}}{12 \, {\left(15 \, x^{2} - x - 6\right)}}\right)"," ",0,"-1/6*sqrt(3)*sqrt(2)*arctan(1/12*sqrt(3)*sqrt(2)*sqrt(5*x + 3)*sqrt(3*x - 2)*(x + 12)/(15*x^2 - x - 6))","A",0
848,1,44,0,1.326752," ","integrate(1/(-1+x)^(3/2)/x/(1+x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(x^{2} - 1\right)} \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right) + \sqrt{x + 1} \sqrt{x - 1}}{x^{2} - 1}"," ",0,"-(2*(x^2 - 1)*arctan(sqrt(x + 1)*sqrt(x - 1) - x) + sqrt(x + 1)*sqrt(x - 1))/(x^2 - 1)","A",0
849,1,19,0,1.451042," ","integrate(x*(1-x)^(1/2)*(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{2} - 1\right)} \sqrt{x + 1} \sqrt{-x + 1}"," ",0,"1/3*(x^2 - 1)*sqrt(x + 1)*sqrt(-x + 1)","A",0
850,1,82,0,1.180312," ","integrate(x^3*(2+3*x)^(3/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{212336640} \, {\left(106168320 \, x^{5} + 94666752 \, x^{4} + 4119552 \, x^{3} - 1849728 \, x^{2} + 1089592 \, x - 881613\right)} \sqrt{4 \, x + 1} \sqrt{3 \, x + 2} + \frac{1067875}{1019215872} \, \sqrt{3} \log\left(8 \, \sqrt{3} {\left(24 \, x + 11\right)} \sqrt{4 \, x + 1} \sqrt{3 \, x + 2} + 1152 \, x^{2} + 1056 \, x + 217\right)"," ",0,"1/212336640*(106168320*x^5 + 94666752*x^4 + 4119552*x^3 - 1849728*x^2 + 1089592*x - 881613)*sqrt(4*x + 1)*sqrt(3*x + 2) + 1067875/1019215872*sqrt(3)*log(8*sqrt(3)*(24*x + 11)*sqrt(4*x + 1)*sqrt(3*x + 2) + 1152*x^2 + 1056*x + 217)","A",0
851,1,31,0,1.359195," ","integrate(1/(b*x+a-1)^(1/2)/(b*x+a+1)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(-b x + \sqrt{b x + a + 1} \sqrt{b x + a - 1} - a\right)}{b}"," ",0,"-log(-b*x + sqrt(b*x + a + 1)*sqrt(b*x + a - 1) - a)/b","A",0
852,0,0,0,1.659201," ","integrate(1/x^(1/2)/(-b*x+a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x + a} \sqrt{-b x + a} \sqrt{x}}{b^{2} x^{3} - a^{2} x}, x\right)"," ",0,"integral(-sqrt(b*x + a)*sqrt(-b*x + a)*sqrt(x)/(b^2*x^3 - a^2*x), x)","F",0
853,0,0,0,1.458041," ","integrate(1/(-x)^(1/2)/(-b*x+a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{-b x + a} \sqrt{-x}}{b^{2} x^{3} - a^{2} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(-b*x + a)*sqrt(-x)/(b^2*x^3 - a^2*x), x)","F",0
854,0,0,0,1.420827," ","integrate(1/(e*x)^(1/2)/(-b*x+a)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x + a} \sqrt{-b x + a} \sqrt{e x}}{b^{2} e x^{3} - a^{2} e x}, x\right)"," ",0,"integral(-sqrt(b*x + a)*sqrt(-b*x + a)*sqrt(e*x)/(b^2*e*x^3 - a^2*e*x), x)","F",0
855,0,0,0,1.538606," ","integrate(1/x^(1/2)/(-b*x+2)^(1/2)/(b*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x + 2} \sqrt{-b x + 2} \sqrt{x}}{b^{2} x^{3} - 4 \, x}, x\right)"," ",0,"integral(-sqrt(b*x + 2)*sqrt(-b*x + 2)*sqrt(x)/(b^2*x^3 - 4*x), x)","F",0
856,0,0,0,1.302443," ","integrate(1/(-x)^(1/2)/(-b*x+2)^(1/2)/(b*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + 2} \sqrt{-b x + 2} \sqrt{-x}}{b^{2} x^{3} - 4 \, x}, x\right)"," ",0,"integral(sqrt(b*x + 2)*sqrt(-b*x + 2)*sqrt(-x)/(b^2*x^3 - 4*x), x)","F",0
857,0,0,0,1.590788," ","integrate(1/(e*x)^(1/2)/(-b*x+2)^(1/2)/(b*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x + 2} \sqrt{-b x + 2} \sqrt{e x}}{b^{2} e x^{3} - 4 \, e x}, x\right)"," ",0,"integral(-sqrt(b*x + 2)*sqrt(-b*x + 2)*sqrt(e*x)/(b^2*e*x^3 - 4*e*x), x)","F",0
858,0,0,0,1.295888," ","integrate(1/(2-3*x)^(1/2)/x^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x + 2} \sqrt{x} \sqrt{-3 \, x + 2}}{9 \, x^{3} - 4 \, x}, x\right)"," ",0,"integral(-sqrt(3*x + 2)*sqrt(x)*sqrt(-3*x + 2)/(9*x^3 - 4*x), x)","F",0
859,0,0,0,1.565882," ","integrate(1/(2-3*x)^(1/2)/(-x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x} \sqrt{3 \, x + 2} \sqrt{-3 \, x + 2}}{9 \, x^{3} - 4 \, x}, x\right)"," ",0,"integral(sqrt(-x)*sqrt(3*x + 2)*sqrt(-3*x + 2)/(9*x^3 - 4*x), x)","F",0
860,0,0,0,1.329911," ","integrate(1/(2-3*x)^(1/2)/(e*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} \sqrt{3 \, x + 2} \sqrt{-3 \, x + 2}}{9 \, e x^{3} - 4 \, e x}, x\right)"," ",0,"integral(-sqrt(e*x)*sqrt(3*x + 2)*sqrt(-3*x + 2)/(9*e*x^3 - 4*e*x), x)","F",0
861,0,0,0,1.446716," ","integrate(1/(1-x)^(1/2)/x^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 1} \sqrt{x} \sqrt{-x + 1}}{x^{3} - x}, x\right)"," ",0,"integral(-sqrt(x + 1)*sqrt(x)*sqrt(-x + 1)/(x^3 - x), x)","F",0
862,0,0,0,1.395402," ","integrate(1/(1+x)^(1/2)/(-x^2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + x} \sqrt{x + 1}}{x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-x^2 + x)*sqrt(x + 1)/(x^3 - x), x)","F",0
863,0,0,0,1.391231," ","integrate(1/(b*x)^(1/2)/(-c*x+1)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x} \sqrt{c x + 1} \sqrt{-c x + 1}}{b c^{2} x^{3} - b x}, x\right)"," ",0,"integral(-sqrt(b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(b*c^2*x^3 - b*x), x)","F",0
864,0,0,0,1.386592," ","integrate(1/(b*x)^(1/2)/(-c*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x} \sqrt{-c x + 1} \sqrt{d x + 1}}{b c d x^{3} + {\left(b c - b d\right)} x^{2} - b x}, x\right)"," ",0,"integral(-sqrt(b*x)*sqrt(-c*x + 1)*sqrt(d*x + 1)/(b*c*d*x^3 + (b*c - b*d)*x^2 - b*x), x)","F",0
865,0,0,0,1.368884," ","integrate((1+x)^(1/2)/(1-x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 1} \sqrt{x} \sqrt{-x + 1}}{x^{2} - x}, x\right)"," ",0,"integral(-sqrt(x + 1)*sqrt(x)*sqrt(-x + 1)/(x^2 - x), x)","F",0
866,0,0,0,1.720812," ","integrate((1+x)^(1/2)/(-x^2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + x} \sqrt{x + 1}}{x^{2} - x}, x\right)"," ",0,"integral(-sqrt(-x^2 + x)*sqrt(x + 1)/(x^2 - x), x)","F",0
867,0,0,0,1.478121," ","integrate((c*x+1)^(1/2)/(b*x)^(1/2)/(-c*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x} \sqrt{c x + 1} \sqrt{-c x + 1}}{b c x^{2} - b x}, x\right)"," ",0,"integral(-sqrt(b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(b*c*x^2 - b*x), x)","F",0
868,0,0,0,1.441431," ","integrate((c*x+1)^(1/2)/(b*x)^(1/2)/(-d*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b x} \sqrt{c x + 1} \sqrt{-d x + 1}}{b d x^{2} - b x}, x\right)"," ",0,"integral(-sqrt(b*x)*sqrt(c*x + 1)*sqrt(-d*x + 1)/(b*d*x^2 - b*x), x)","F",0
869,0,0,0,1.369858," ","integrate((1-x)^(1/2)/x^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x + 1} \sqrt{x} \sqrt{-x + 1}}{x^{2} + x}, x\right)"," ",0,"integral(sqrt(x + 1)*sqrt(x)*sqrt(-x + 1)/(x^2 + x), x)","F",0
870,0,0,0,0.884495," ","integrate((-1+1/x)^(1/2)*(1/x)^(1/2)*x^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-\frac{x - 1}{x}}}{\sqrt{x + 1}}, x\right)"," ",0,"integral(sqrt(-(x - 1)/x)/sqrt(x + 1), x)","F",0
871,0,0,0,1.464325," ","integrate((-c*x+1)^(1/2)/(b*x)^(1/2)/(c*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x} \sqrt{c x + 1} \sqrt{-c x + 1}}{b c x^{2} + b x}, x\right)"," ",0,"integral(sqrt(b*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(b*c*x^2 + b*x), x)","F",0
872,0,0,0,1.550586," ","integrate((-c*x+1)^(1/2)/(b*x)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x} \sqrt{-c x + 1} \sqrt{d x + 1}}{b d x^{2} + b x}, x\right)"," ",0,"integral(sqrt(b*x)*sqrt(-c*x + 1)*sqrt(d*x + 1)/(b*d*x^2 + b*x), x)","F",0
873,0,0,0,1.361794," ","integrate(1/(2-3*x)^(1/2)/x^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{x} \sqrt{-3 \, x + 2}}{3 \, e x^{3} + {\left(3 \, d - 2 \, e\right)} x^{2} - 2 \, d x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(x)*sqrt(-3*x + 2)/(3*e*x^3 + (3*d - 2*e)*x^2 - 2*d*x), x)","F",0
874,0,0,0,1.148425," ","integrate((e*x+d)^(1/2)/(2-3*x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{x} \sqrt{-3 \, x + 2}}{3 \, x^{2} - 2 \, x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(x)*sqrt(-3*x + 2)/(3*x^2 - 2*x), x)","F",0
875,0,0,0,1.317385," ","integrate(x^4/(1-x)^(1/3)/(2-x)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{2} - 3 \, x + 2}, x\right)"," ",0,"integral(x^4*(-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^2 - 3*x + 2), x)","F",0
876,0,0,0,0.923476," ","integrate(x^3/(1-x)^(1/3)/(2-x)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{2} - 3 \, x + 2}, x\right)"," ",0,"integral(x^3*(-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^2 - 3*x + 2), x)","F",0
877,0,0,0,1.435356," ","integrate(x^2/(1-x)^(1/3)/(2-x)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{2} - 3 \, x + 2}, x\right)"," ",0,"integral(x^2*(-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^2 - 3*x + 2), x)","F",0
878,0,0,0,1.760236," ","integrate(x/(1-x)^(1/3)/(2-x)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{2} - 3 \, x + 2}, x\right)"," ",0,"integral(x*(-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^2 - 3*x + 2), x)","F",0
879,0,0,0,0.800614," ","integrate(1/(1-x)^(1/3)/(2-x)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{2} - 3 \, x + 2}, x\right)"," ",0,"integral((-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^2 - 3*x + 2), x)","F",0
880,1,296,0,5.749304," ","integrate(1/(1-x)^(1/3)/(2-x)^(1/3)/x,x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{1}{6}} {\left(24 \cdot 2^{\frac{1}{6}} {\left(x^{4} - 36 \, x^{3} + 180 \, x^{2} - 288 \, x + 144\right)} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}} - 12 \, \sqrt{2} {\left(x^{5} - 14 \, x^{4} + 36 \, x^{3} - 24 \, x^{2}\right)} {\left(-x + 2\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{1}{3}} + 2^{\frac{5}{6}} {\left(x^{6} - 72 \, x^{5} + 792 \, x^{4} - 3168 \, x^{3} + 5904 \, x^{2} - 5184 \, x + 1728\right)}\right)}}{6 \, {\left(x^{6} - 432 \, x^{4} + 2592 \, x^{3} - 5616 \, x^{2} + 5184 \, x - 1728\right)}}\right) + \frac{1}{12} \cdot 2^{\frac{2}{3}} \log\left(\frac{2^{\frac{1}{3}} x^{2} + 6 \cdot 2^{\frac{2}{3}} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}} + 6 \, {\left(x - 2\right)} {\left(-x + 2\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{1}{3}}}{x^{2}}\right) - \frac{1}{24} \cdot 2^{\frac{2}{3}} \log\left(\frac{24 \, {\left(x^{2} - 6 \, x + 6\right)} {\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}} - 6 \cdot 2^{\frac{1}{3}} {\left(x^{3} - 14 \, x^{2} + 36 \, x - 24\right)} {\left(-x + 2\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{1}{3}} + 2^{\frac{2}{3}} {\left(x^{4} - 36 \, x^{3} + 180 \, x^{2} - 288 \, x + 144\right)}}{x^{4}}\right)"," ",0,"1/12*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(1/6)*(24*2^(1/6)*(x^4 - 36*x^3 + 180*x^2 - 288*x + 144)*(-x + 2)^(2/3)*(-x + 1)^(2/3) - 12*sqrt(2)*(x^5 - 14*x^4 + 36*x^3 - 24*x^2)*(-x + 2)^(1/3)*(-x + 1)^(1/3) + 2^(5/6)*(x^6 - 72*x^5 + 792*x^4 - 3168*x^3 + 5904*x^2 - 5184*x + 1728))/(x^6 - 432*x^4 + 2592*x^3 - 5616*x^2 + 5184*x - 1728)) + 1/12*2^(2/3)*log((2^(1/3)*x^2 + 6*2^(2/3)*(-x + 2)^(2/3)*(-x + 1)^(2/3) + 6*(x - 2)*(-x + 2)^(1/3)*(-x + 1)^(1/3))/x^2) - 1/24*2^(2/3)*log((24*(x^2 - 6*x + 6)*(-x + 2)^(2/3)*(-x + 1)^(2/3) - 6*2^(1/3)*(x^3 - 14*x^2 + 36*x - 24)*(-x + 2)^(1/3)*(-x + 1)^(1/3) + 2^(2/3)*(x^4 - 36*x^3 + 180*x^2 - 288*x + 144))/x^4)","B",0
881,0,0,0,5.342804," ","integrate(1/(1-x)^(1/3)/(2-x)^(1/3)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{4} - 3 \, x^{3} + 2 \, x^{2}}, x\right)"," ",0,"integral((-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^4 - 3*x^3 + 2*x^2), x)","F",0
882,0,0,0,4.859179," ","integrate(1/(1-x)^(1/3)/(2-x)^(1/3)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 2\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}{x^{5} - 3 \, x^{4} + 2 \, x^{3}}, x\right)"," ",0,"integral((-x + 2)^(2/3)*(-x + 1)^(2/3)/(x^5 - 3*x^4 + 2*x^3), x)","F",0
883,1,2864,0,3.130323," ","integrate(x^3*(b*x+a)^(1/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{12 \, b^{3} d^{4} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(195 \, b^{15} c^{4} d^{13} - 60 \, a b^{14} c^{3} d^{14} - 30 \, a^{2} b^{13} c^{2} d^{15} - 28 \, a^{3} b^{12} c d^{16} - 77 \, a^{4} b^{11} d^{17}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{3}{4}} + {\left(b^{11} d^{14} x + b^{11} c d^{13}\right)} \sqrt{\frac{{\left(38025 \, b^{8} c^{8} - 23400 \, a b^{7} c^{7} d - 8100 \, a^{2} b^{6} c^{6} d^{2} - 7320 \, a^{3} b^{5} c^{5} d^{3} - 25770 \, a^{4} b^{4} c^{4} d^{4} + 10920 \, a^{5} b^{3} c^{3} d^{5} + 5404 \, a^{6} b^{2} c^{2} d^{6} + 4312 \, a^{7} b c d^{7} + 5929 \, a^{8} d^{8}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{8} d^{9} x + b^{8} c d^{8}\right)} \sqrt{\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}}}{d x + c}} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{3}{4}}}{1445900625 \, b^{16} c^{17} - 1779570000 \, a b^{15} c^{16} d - 68445000 \, a^{2} b^{14} c^{15} d^{2} - 177606000 \, a^{3} b^{13} c^{14} d^{3} - 1551622500 \, a^{4} b^{12} c^{13} d^{4} + 2155086000 \, a^{5} b^{11} c^{12} d^{5} + 370974600 \, a^{6} b^{10} c^{11} d^{6} + 275389200 \, a^{7} b^{9} c^{10} d^{7} + 665778150 \, a^{8} b^{8} c^{9} d^{8} - 989262960 \, a^{9} b^{7} c^{8} d^{9} - 318453240 \, a^{10} b^{6} c^{7} d^{10} - 191017680 \, a^{11} b^{5} c^{6} d^{11} - 182203364 \, a^{12} b^{4} c^{5} d^{12} + 176093456 \, a^{13} b^{3} c^{4} d^{13} + 82673976 \, a^{14} b^{2} c^{3} d^{14} + 51131696 \, a^{15} b c^{2} d^{15} + 35153041 \, a^{16} c d^{16} + {\left(1445900625 \, b^{16} c^{16} d - 1779570000 \, a b^{15} c^{15} d^{2} - 68445000 \, a^{2} b^{14} c^{14} d^{3} - 177606000 \, a^{3} b^{13} c^{13} d^{4} - 1551622500 \, a^{4} b^{12} c^{12} d^{5} + 2155086000 \, a^{5} b^{11} c^{11} d^{6} + 370974600 \, a^{6} b^{10} c^{10} d^{7} + 275389200 \, a^{7} b^{9} c^{9} d^{8} + 665778150 \, a^{8} b^{8} c^{8} d^{9} - 989262960 \, a^{9} b^{7} c^{7} d^{10} - 318453240 \, a^{10} b^{6} c^{6} d^{11} - 191017680 \, a^{11} b^{5} c^{5} d^{12} - 182203364 \, a^{12} b^{4} c^{4} d^{13} + 176093456 \, a^{13} b^{3} c^{3} d^{14} + 82673976 \, a^{14} b^{2} c^{2} d^{15} + 51131696 \, a^{15} b c d^{16} + 35153041 \, a^{16} d^{17}\right)} x}\right) + 3 \, b^{3} d^{4} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(195 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} - 28 \, a^{3} b c d^{3} - 77 \, a^{4} d^{4}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{4} d^{5} x + b^{4} c d^{4}\right)} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{1}{4}}}{d x + c}\right) - 3 \, b^{3} d^{4} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(195 \, b^{4} c^{4} - 60 \, a b^{3} c^{3} d - 30 \, a^{2} b^{2} c^{2} d^{2} - 28 \, a^{3} b c d^{3} - 77 \, a^{4} d^{4}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{4} d^{5} x + b^{4} c d^{4}\right)} \left(\frac{1445900625 \, b^{16} c^{16} - 1779570000 \, a b^{15} c^{15} d - 68445000 \, a^{2} b^{14} c^{14} d^{2} - 177606000 \, a^{3} b^{13} c^{13} d^{3} - 1551622500 \, a^{4} b^{12} c^{12} d^{4} + 2155086000 \, a^{5} b^{11} c^{11} d^{5} + 370974600 \, a^{6} b^{10} c^{10} d^{6} + 275389200 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} - 989262960 \, a^{9} b^{7} c^{7} d^{9} - 318453240 \, a^{10} b^{6} c^{6} d^{10} - 191017680 \, a^{11} b^{5} c^{5} d^{11} - 182203364 \, a^{12} b^{4} c^{4} d^{12} + 176093456 \, a^{13} b^{3} c^{3} d^{13} + 82673976 \, a^{14} b^{2} c^{2} d^{14} + 51131696 \, a^{15} b c d^{15} + 35153041 \, a^{16} d^{16}}{b^{15} d^{17}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(384 \, b^{3} d^{3} x^{3} - 585 \, b^{3} c^{3} + 63 \, a b^{2} c^{2} d + 61 \, a^{2} b c d^{2} + 77 \, a^{3} d^{3} - 32 \, {\left(13 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(117 \, b^{3} c^{2} d - 10 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{6144 \, b^{3} d^{4}}"," ",0,"1/6144*(12*b^3*d^4*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(1/4)*arctan(((195*b^15*c^4*d^13 - 60*a*b^14*c^3*d^14 - 30*a^2*b^13*c^2*d^15 - 28*a^3*b^12*c*d^16 - 77*a^4*b^11*d^17)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(3/4) + (b^11*d^14*x + b^11*c*d^13)*sqrt(((38025*b^8*c^8 - 23400*a*b^7*c^7*d - 8100*a^2*b^6*c^6*d^2 - 7320*a^3*b^5*c^5*d^3 - 25770*a^4*b^4*c^4*d^4 + 10920*a^5*b^3*c^3*d^5 + 5404*a^6*b^2*c^2*d^6 + 4312*a^7*b*c*d^7 + 5929*a^8*d^8)*sqrt(b*x + a)*sqrt(d*x + c) + (b^8*d^9*x + b^8*c*d^8)*sqrt((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17)))/(d*x + c))*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(3/4))/(1445900625*b^16*c^17 - 1779570000*a*b^15*c^16*d - 68445000*a^2*b^14*c^15*d^2 - 177606000*a^3*b^13*c^14*d^3 - 1551622500*a^4*b^12*c^13*d^4 + 2155086000*a^5*b^11*c^12*d^5 + 370974600*a^6*b^10*c^11*d^6 + 275389200*a^7*b^9*c^10*d^7 + 665778150*a^8*b^8*c^9*d^8 - 989262960*a^9*b^7*c^8*d^9 - 318453240*a^10*b^6*c^7*d^10 - 191017680*a^11*b^5*c^6*d^11 - 182203364*a^12*b^4*c^5*d^12 + 176093456*a^13*b^3*c^4*d^13 + 82673976*a^14*b^2*c^3*d^14 + 51131696*a^15*b*c^2*d^15 + 35153041*a^16*c*d^16 + (1445900625*b^16*c^16*d - 1779570000*a*b^15*c^15*d^2 - 68445000*a^2*b^14*c^14*d^3 - 177606000*a^3*b^13*c^13*d^4 - 1551622500*a^4*b^12*c^12*d^5 + 2155086000*a^5*b^11*c^11*d^6 + 370974600*a^6*b^10*c^10*d^7 + 275389200*a^7*b^9*c^9*d^8 + 665778150*a^8*b^8*c^8*d^9 - 989262960*a^9*b^7*c^7*d^10 - 318453240*a^10*b^6*c^6*d^11 - 191017680*a^11*b^5*c^5*d^12 - 182203364*a^12*b^4*c^4*d^13 + 176093456*a^13*b^3*c^3*d^14 + 82673976*a^14*b^2*c^2*d^15 + 51131696*a^15*b*c*d^16 + 35153041*a^16*d^17)*x)) + 3*b^3*d^4*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(1/4)*log(-((195*b^4*c^4 - 60*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 - 28*a^3*b*c*d^3 - 77*a^4*d^4)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^4*d^5*x + b^4*c*d^4)*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(1/4))/(d*x + c)) - 3*b^3*d^4*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(1/4)*log(-((195*b^4*c^4 - 60*a*b^3*c^3*d - 30*a^2*b^2*c^2*d^2 - 28*a^3*b*c*d^3 - 77*a^4*d^4)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^4*d^5*x + b^4*c*d^4)*((1445900625*b^16*c^16 - 1779570000*a*b^15*c^15*d - 68445000*a^2*b^14*c^14*d^2 - 177606000*a^3*b^13*c^13*d^3 - 1551622500*a^4*b^12*c^12*d^4 + 2155086000*a^5*b^11*c^11*d^5 + 370974600*a^6*b^10*c^10*d^6 + 275389200*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 - 989262960*a^9*b^7*c^7*d^9 - 318453240*a^10*b^6*c^6*d^10 - 191017680*a^11*b^5*c^5*d^11 - 182203364*a^12*b^4*c^4*d^12 + 176093456*a^13*b^3*c^3*d^13 + 82673976*a^14*b^2*c^2*d^14 + 51131696*a^15*b*c*d^15 + 35153041*a^16*d^16)/(b^15*d^17))^(1/4))/(d*x + c)) + 4*(384*b^3*d^3*x^3 - 585*b^3*c^3 + 63*a*b^2*c^2*d + 61*a^2*b*c*d^2 + 77*a^3*d^3 - 32*(13*b^3*c*d^2 - a*b^2*d^3)*x^2 + 4*(117*b^3*c^2*d - 10*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b^3*d^4)","B",0
884,1,2182,0,1.694215," ","integrate(x^2*(b*x+a)^(1/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{12 \, b^{2} d^{3} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(15 \, b^{11} c^{3} d^{10} - 5 \, a b^{10} c^{2} d^{11} - 3 \, a^{2} b^{9} c d^{12} - 7 \, a^{3} b^{8} d^{13}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{3}{4}} + {\left(b^{8} d^{11} x + b^{8} c d^{10}\right)} \sqrt{\frac{{\left(225 \, b^{6} c^{6} - 150 \, a b^{5} c^{5} d - 65 \, a^{2} b^{4} c^{4} d^{2} - 180 \, a^{3} b^{3} c^{3} d^{3} + 79 \, a^{4} b^{2} c^{2} d^{4} + 42 \, a^{5} b c d^{5} + 49 \, a^{6} d^{6}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{6} d^{7} x + b^{6} c d^{6}\right)} \sqrt{\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}}}{d x + c}} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{3}{4}}}{50625 \, b^{12} c^{13} - 67500 \, a b^{11} c^{12} d - 6750 \, a^{2} b^{10} c^{11} d^{2} - 61500 \, a^{3} b^{9} c^{10} d^{3} + 93775 \, a^{4} b^{8} c^{9} d^{4} + 18600 \, a^{5} b^{7} c^{8} d^{5} + 31580 \, a^{6} b^{6} c^{7} d^{6} - 48600 \, a^{7} b^{5} c^{6} d^{7} - 15249 \, a^{8} b^{4} c^{5} d^{8} - 11004 \, a^{9} b^{3} c^{4} d^{9} + 9506 \, a^{10} b^{2} c^{3} d^{10} + 4116 \, a^{11} b c^{2} d^{11} + 2401 \, a^{12} c d^{12} + {\left(50625 \, b^{12} c^{12} d - 67500 \, a b^{11} c^{11} d^{2} - 6750 \, a^{2} b^{10} c^{10} d^{3} - 61500 \, a^{3} b^{9} c^{9} d^{4} + 93775 \, a^{4} b^{8} c^{8} d^{5} + 18600 \, a^{5} b^{7} c^{7} d^{6} + 31580 \, a^{6} b^{6} c^{6} d^{7} - 48600 \, a^{7} b^{5} c^{5} d^{8} - 15249 \, a^{8} b^{4} c^{4} d^{9} - 11004 \, a^{9} b^{3} c^{3} d^{10} + 9506 \, a^{10} b^{2} c^{2} d^{11} + 4116 \, a^{11} b c d^{12} + 2401 \, a^{12} d^{13}\right)} x}\right) + 3 \, b^{2} d^{3} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(15 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 7 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{3} d^{4} x + b^{3} c d^{3}\right)} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) - 3 \, b^{2} d^{3} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(15 \, b^{3} c^{3} - 5 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 7 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{3} d^{4} x + b^{3} c d^{3}\right)} \left(\frac{50625 \, b^{12} c^{12} - 67500 \, a b^{11} c^{11} d - 6750 \, a^{2} b^{10} c^{10} d^{2} - 61500 \, a^{3} b^{9} c^{9} d^{3} + 93775 \, a^{4} b^{8} c^{8} d^{4} + 18600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} - 48600 \, a^{7} b^{5} c^{5} d^{7} - 15249 \, a^{8} b^{4} c^{4} d^{8} - 11004 \, a^{9} b^{3} c^{3} d^{9} + 9506 \, a^{10} b^{2} c^{2} d^{10} + 4116 \, a^{11} b c d^{11} + 2401 \, a^{12} d^{12}}{b^{11} d^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(32 \, b^{2} d^{2} x^{2} + 45 \, b^{2} c^{2} - 6 \, a b c d - 7 \, a^{2} d^{2} - 4 \, {\left(9 \, b^{2} c d - a b d^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{384 \, b^{2} d^{3}}"," ",0,"-1/384*(12*b^2*d^3*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(1/4)*arctan(((15*b^11*c^3*d^10 - 5*a*b^10*c^2*d^11 - 3*a^2*b^9*c*d^12 - 7*a^3*b^8*d^13)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(3/4) + (b^8*d^11*x + b^8*c*d^10)*sqrt(((225*b^6*c^6 - 150*a*b^5*c^5*d - 65*a^2*b^4*c^4*d^2 - 180*a^3*b^3*c^3*d^3 + 79*a^4*b^2*c^2*d^4 + 42*a^5*b*c*d^5 + 49*a^6*d^6)*sqrt(b*x + a)*sqrt(d*x + c) + (b^6*d^7*x + b^6*c*d^6)*sqrt((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13)))/(d*x + c))*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(3/4))/(50625*b^12*c^13 - 67500*a*b^11*c^12*d - 6750*a^2*b^10*c^11*d^2 - 61500*a^3*b^9*c^10*d^3 + 93775*a^4*b^8*c^9*d^4 + 18600*a^5*b^7*c^8*d^5 + 31580*a^6*b^6*c^7*d^6 - 48600*a^7*b^5*c^6*d^7 - 15249*a^8*b^4*c^5*d^8 - 11004*a^9*b^3*c^4*d^9 + 9506*a^10*b^2*c^3*d^10 + 4116*a^11*b*c^2*d^11 + 2401*a^12*c*d^12 + (50625*b^12*c^12*d - 67500*a*b^11*c^11*d^2 - 6750*a^2*b^10*c^10*d^3 - 61500*a^3*b^9*c^9*d^4 + 93775*a^4*b^8*c^8*d^5 + 18600*a^5*b^7*c^7*d^6 + 31580*a^6*b^6*c^6*d^7 - 48600*a^7*b^5*c^5*d^8 - 15249*a^8*b^4*c^4*d^9 - 11004*a^9*b^3*c^3*d^10 + 9506*a^10*b^2*c^2*d^11 + 4116*a^11*b*c*d^12 + 2401*a^12*d^13)*x)) + 3*b^2*d^3*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(1/4)*log(-((15*b^3*c^3 - 5*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 7*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^3*d^4*x + b^3*c*d^3)*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(1/4))/(d*x + c)) - 3*b^2*d^3*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(1/4)*log(-((15*b^3*c^3 - 5*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 7*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^3*d^4*x + b^3*c*d^3)*((50625*b^12*c^12 - 67500*a*b^11*c^11*d - 6750*a^2*b^10*c^10*d^2 - 61500*a^3*b^9*c^9*d^3 + 93775*a^4*b^8*c^8*d^4 + 18600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 - 48600*a^7*b^5*c^5*d^7 - 15249*a^8*b^4*c^4*d^8 - 11004*a^9*b^3*c^3*d^9 + 9506*a^10*b^2*c^2*d^10 + 4116*a^11*b*c*d^11 + 2401*a^12*d^12)/(b^11*d^13))^(1/4))/(d*x + c)) - 4*(32*b^2*d^2*x^2 + 45*b^2*c^2 - 6*a*b*c*d - 7*a^2*d^2 - 4*(9*b^2*c*d - a*b*d^2)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b^2*d^3)","B",0
885,1,1506,0,1.723758," ","integrate(x*(b*x+a)^(1/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{4 \, b d^{2} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(5 \, b^{7} c^{2} d^{7} - 2 \, a b^{6} c d^{8} - 3 \, a^{2} b^{5} d^{9}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{3}{4}} + {\left(b^{5} d^{8} x + b^{5} c d^{7}\right)} \sqrt{\frac{{\left(25 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{4} d^{5} x + b^{4} c d^{4}\right)} \sqrt{\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}}}{d x + c}} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{3}{4}}}{625 \, b^{8} c^{9} - 1000 \, a b^{7} c^{8} d - 900 \, a^{2} b^{6} c^{7} d^{2} + 1640 \, a^{3} b^{5} c^{6} d^{3} + 646 \, a^{4} b^{4} c^{5} d^{4} - 984 \, a^{5} b^{3} c^{4} d^{5} - 324 \, a^{6} b^{2} c^{3} d^{6} + 216 \, a^{7} b c^{2} d^{7} + 81 \, a^{8} c d^{8} + {\left(625 \, b^{8} c^{8} d - 1000 \, a b^{7} c^{7} d^{2} - 900 \, a^{2} b^{6} c^{6} d^{3} + 1640 \, a^{3} b^{5} c^{5} d^{4} + 646 \, a^{4} b^{4} c^{4} d^{5} - 984 \, a^{5} b^{3} c^{3} d^{6} - 324 \, a^{6} b^{2} c^{2} d^{7} + 216 \, a^{7} b c d^{8} + 81 \, a^{8} d^{9}\right)} x}\right) + b d^{2} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) - b d^{2} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(5 \, b^{2} c^{2} - 2 \, a b c d - 3 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \left(\frac{625 \, b^{8} c^{8} - 1000 \, a b^{7} c^{7} d - 900 \, a^{2} b^{6} c^{6} d^{2} + 1640 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} - 984 \, a^{5} b^{3} c^{3} d^{5} - 324 \, a^{6} b^{2} c^{2} d^{6} + 216 \, a^{7} b c d^{7} + 81 \, a^{8} d^{8}}{b^{7} d^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(4 \, b d x - 5 \, b c + a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{32 \, b d^{2}}"," ",0,"1/32*(4*b*d^2*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(1/4)*arctan(((5*b^7*c^2*d^7 - 2*a*b^6*c*d^8 - 3*a^2*b^5*d^9)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(3/4) + (b^5*d^8*x + b^5*c*d^7)*sqrt(((25*b^4*c^4 - 20*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + 9*a^4*d^4)*sqrt(b*x + a)*sqrt(d*x + c) + (b^4*d^5*x + b^4*c*d^4)*sqrt((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9)))/(d*x + c))*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(3/4))/(625*b^8*c^9 - 1000*a*b^7*c^8*d - 900*a^2*b^6*c^7*d^2 + 1640*a^3*b^5*c^6*d^3 + 646*a^4*b^4*c^5*d^4 - 984*a^5*b^3*c^4*d^5 - 324*a^6*b^2*c^3*d^6 + 216*a^7*b*c^2*d^7 + 81*a^8*c*d^8 + (625*b^8*c^8*d - 1000*a*b^7*c^7*d^2 - 900*a^2*b^6*c^6*d^3 + 1640*a^3*b^5*c^5*d^4 + 646*a^4*b^4*c^4*d^5 - 984*a^5*b^3*c^3*d^6 - 324*a^6*b^2*c^2*d^7 + 216*a^7*b*c*d^8 + 81*a^8*d^9)*x)) + b*d^2*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(1/4)*log(-((5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^2*d^3*x + b^2*c*d^2)*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(1/4))/(d*x + c)) - b*d^2*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(1/4)*log(-((5*b^2*c^2 - 2*a*b*c*d - 3*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^2*d^3*x + b^2*c*d^2)*((625*b^8*c^8 - 1000*a*b^7*c^7*d - 900*a^2*b^6*c^6*d^2 + 1640*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 - 984*a^5*b^3*c^3*d^5 - 324*a^6*b^2*c^2*d^6 + 216*a^7*b*c*d^7 + 81*a^8*d^8)/(b^7*d^9))^(1/4))/(d*x + c)) + 4*(4*b*d*x - 5*b*c + a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b*d^2)","B",0
886,1,814,0,1.634038," ","integrate((b*x+a)^(1/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, d \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{3} c d^{4} - a b^{2} d^{5}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{3}{4}} + {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)} \sqrt{\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \sqrt{\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}}}{d x + c}} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{3}{4}}}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4} + {\left(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)} x}\right) + d \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b c - a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b d^{2} x + b c d\right)} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) - d \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b c - a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b d^{2} x + b c d\right)} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{b^{3} d^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{4 \, d}"," ",0,"-1/4*(4*d*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(1/4)*arctan(((b^3*c*d^4 - a*b^2*d^5)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(3/4) + (b^2*d^5*x + b^2*c*d^4)*sqrt(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c) + (b^2*d^3*x + b^2*c*d^2)*sqrt((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5)))/(d*x + c))*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(3/4))/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4 + (b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*x)) + d*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(1/4)*log(-((b*c - a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b*d^2*x + b*c*d)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(1/4))/(d*x + c)) - d*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(1/4)*log(-((b*c - a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b*d^2*x + b*c*d)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(b^3*d^5))^(1/4))/(d*x + c)) - 4*(b*x + a)^(1/4)*(d*x + c)^(3/4))/d","B",0
887,1,396,0,1.683709," ","integrate((b*x+a)^(1/4)/x/(d*x+c)^(1/4),x, algorithm=""fricas"")","4 \, \left(\frac{a}{c}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} c \left(\frac{a}{c}\right)^{\frac{3}{4}} - {\left(c d x + c^{2}\right)} \sqrt{\frac{{\left(d x + c\right)} \sqrt{\frac{a}{c}} + \sqrt{b x + a} \sqrt{d x + c}}{d x + c}} \left(\frac{a}{c}\right)^{\frac{3}{4}}}{a d x + a c}\right) - 4 \, \left(\frac{b}{d}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} d \left(\frac{b}{d}\right)^{\frac{3}{4}} - {\left(d^{2} x + c d\right)} \sqrt{\frac{{\left(d x + c\right)} \sqrt{\frac{b}{d}} + \sqrt{b x + a} \sqrt{d x + c}}{d x + c}} \left(\frac{b}{d}\right)^{\frac{3}{4}}}{b d x + b c}\right) - \left(\frac{a}{c}\right)^{\frac{1}{4}} \log\left(\frac{{\left(d x + c\right)} \left(\frac{a}{c}\right)^{\frac{1}{4}} + {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right) + \left(\frac{a}{c}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(d x + c\right)} \left(\frac{a}{c}\right)^{\frac{1}{4}} - {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right) + \left(\frac{b}{d}\right)^{\frac{1}{4}} \log\left(\frac{{\left(d x + c\right)} \left(\frac{b}{d}\right)^{\frac{1}{4}} + {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right) - \left(\frac{b}{d}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(d x + c\right)} \left(\frac{b}{d}\right)^{\frac{1}{4}} - {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right)"," ",0,"4*(a/c)^(1/4)*arctan(-((b*x + a)^(1/4)*(d*x + c)^(3/4)*c*(a/c)^(3/4) - (c*d*x + c^2)*sqrt(((d*x + c)*sqrt(a/c) + sqrt(b*x + a)*sqrt(d*x + c))/(d*x + c))*(a/c)^(3/4))/(a*d*x + a*c)) - 4*(b/d)^(1/4)*arctan(-((b*x + a)^(1/4)*(d*x + c)^(3/4)*d*(b/d)^(3/4) - (d^2*x + c*d)*sqrt(((d*x + c)*sqrt(b/d) + sqrt(b*x + a)*sqrt(d*x + c))/(d*x + c))*(b/d)^(3/4))/(b*d*x + b*c)) - (a/c)^(1/4)*log(((d*x + c)*(a/c)^(1/4) + (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c)) + (a/c)^(1/4)*log(-((d*x + c)*(a/c)^(1/4) - (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c)) + (b/d)^(1/4)*log(((d*x + c)*(b/d)^(1/4) + (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c)) - (b/d)^(1/4)*log(-((d*x + c)*(b/d)^(1/4) - (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c))","B",0
888,1,820,0,1.574350," ","integrate((b*x+a)^(1/4)/x^2/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, c x \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(a^{2} b c^{5} - a^{3} c^{4} d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{3}{4}} + {\left(a^{2} c^{4} d x + a^{2} c^{5}\right)} \sqrt{\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{2} c^{2} d x + a^{2} c^{3}\right)} \sqrt{\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}}}{d x + c}} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{3}{4}}}{b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4} + {\left(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)} x}\right) + c x \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b c - a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a c d x + a c^{2}\right)} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) - c x \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b c - a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a c d x + a c^{2}\right)} \left(\frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{3} c^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{4 \, c x}"," ",0,"-1/4*(4*c*x*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(1/4)*arctan(((a^2*b*c^5 - a^3*c^4*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(3/4) + (a^2*c^4*d*x + a^2*c^5)*sqrt(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c) + (a^2*c^2*d*x + a^2*c^3)*sqrt((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5)))/(d*x + c))*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(3/4))/(b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4 + (b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*x)) + c*x*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(1/4)*log(-((b*c - a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a*c*d*x + a*c^2)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(1/4))/(d*x + c)) - c*x*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(1/4)*log(-((b*c - a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a*c*d*x + a*c^2)*((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/(a^3*c^5))^(1/4))/(d*x + c)) + 4*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(c*x)","B",0
889,1,1520,0,1.216207," ","integrate((b*x+a)^(1/4)/x^3/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{4 \, a c^{2} x^{2} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(3 \, a^{5} b^{2} c^{9} + 2 \, a^{6} b c^{8} d - 5 \, a^{7} c^{7} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{3}{4}} + {\left(a^{5} c^{7} d x + a^{5} c^{8}\right)} \sqrt{\frac{{\left(9 \, b^{4} c^{4} + 12 \, a b^{3} c^{3} d - 26 \, a^{2} b^{2} c^{2} d^{2} - 20 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{4} c^{4} d x + a^{4} c^{5}\right)} \sqrt{\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}}}{d x + c}} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{3}{4}}}{81 \, b^{8} c^{9} + 216 \, a b^{7} c^{8} d - 324 \, a^{2} b^{6} c^{7} d^{2} - 984 \, a^{3} b^{5} c^{6} d^{3} + 646 \, a^{4} b^{4} c^{5} d^{4} + 1640 \, a^{5} b^{3} c^{4} d^{5} - 900 \, a^{6} b^{2} c^{3} d^{6} - 1000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8} + {\left(81 \, b^{8} c^{8} d + 216 \, a b^{7} c^{7} d^{2} - 324 \, a^{2} b^{6} c^{6} d^{3} - 984 \, a^{3} b^{5} c^{5} d^{4} + 646 \, a^{4} b^{4} c^{4} d^{5} + 1640 \, a^{5} b^{3} c^{3} d^{6} - 900 \, a^{6} b^{2} c^{2} d^{7} - 1000 \, a^{7} b c d^{8} + 625 \, a^{8} d^{9}\right)} x}\right) + a c^{2} x^{2} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{2} c^{2} d x + a^{2} c^{3}\right)} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) - a c^{2} x^{2} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d - 5 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{2} c^{2} d x + a^{2} c^{3}\right)} \left(\frac{81 \, b^{8} c^{8} + 216 \, a b^{7} c^{7} d - 324 \, a^{2} b^{6} c^{6} d^{2} - 984 \, a^{3} b^{5} c^{5} d^{3} + 646 \, a^{4} b^{4} c^{4} d^{4} + 1640 \, a^{5} b^{3} c^{3} d^{5} - 900 \, a^{6} b^{2} c^{2} d^{6} - 1000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{7} c^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(4 \, a c + {\left(b c - 5 \, a d\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{32 \, a c^{2} x^{2}}"," ",0,"1/32*(4*a*c^2*x^2*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(1/4)*arctan(((3*a^5*b^2*c^9 + 2*a^6*b*c^8*d - 5*a^7*c^7*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(3/4) + (a^5*c^7*d*x + a^5*c^8)*sqrt(((9*b^4*c^4 + 12*a*b^3*c^3*d - 26*a^2*b^2*c^2*d^2 - 20*a^3*b*c*d^3 + 25*a^4*d^4)*sqrt(b*x + a)*sqrt(d*x + c) + (a^4*c^4*d*x + a^4*c^5)*sqrt((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9)))/(d*x + c))*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(3/4))/(81*b^8*c^9 + 216*a*b^7*c^8*d - 324*a^2*b^6*c^7*d^2 - 984*a^3*b^5*c^6*d^3 + 646*a^4*b^4*c^5*d^4 + 1640*a^5*b^3*c^4*d^5 - 900*a^6*b^2*c^3*d^6 - 1000*a^7*b*c^2*d^7 + 625*a^8*c*d^8 + (81*b^8*c^8*d + 216*a*b^7*c^7*d^2 - 324*a^2*b^6*c^6*d^3 - 984*a^3*b^5*c^5*d^4 + 646*a^4*b^4*c^4*d^5 + 1640*a^5*b^3*c^3*d^6 - 900*a^6*b^2*c^2*d^7 - 1000*a^7*b*c*d^8 + 625*a^8*d^9)*x)) + a*c^2*x^2*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(1/4)*log(-((3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^2*c^2*d*x + a^2*c^3)*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(1/4))/(d*x + c)) - a*c^2*x^2*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(1/4)*log(-((3*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^2*c^2*d*x + a^2*c^3)*((81*b^8*c^8 + 216*a*b^7*c^7*d - 324*a^2*b^6*c^6*d^2 - 984*a^3*b^5*c^5*d^3 + 646*a^4*b^4*c^4*d^4 + 1640*a^5*b^3*c^3*d^5 - 900*a^6*b^2*c^2*d^6 - 1000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^7*c^9))^(1/4))/(d*x + c)) - 4*(4*a*c + (b*c - 5*a*d)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a*c^2*x^2)","B",0
890,1,2196,0,2.231790," ","integrate((b*x+a)^(1/4)/x^4/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{12 \, a^{2} c^{3} x^{3} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(7 \, a^{8} b^{3} c^{13} + 3 \, a^{9} b^{2} c^{12} d + 5 \, a^{10} b c^{11} d^{2} - 15 \, a^{11} c^{10} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{3}{4}} + {\left(a^{8} c^{10} d x + a^{8} c^{11}\right)} \sqrt{\frac{{\left(49 \, b^{6} c^{6} + 42 \, a b^{5} c^{5} d + 79 \, a^{2} b^{4} c^{4} d^{2} - 180 \, a^{3} b^{3} c^{3} d^{3} - 65 \, a^{4} b^{2} c^{2} d^{4} - 150 \, a^{5} b c d^{5} + 225 \, a^{6} d^{6}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{6} c^{6} d x + a^{6} c^{7}\right)} \sqrt{\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}}}{d x + c}} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{3}{4}}}{2401 \, b^{12} c^{13} + 4116 \, a b^{11} c^{12} d + 9506 \, a^{2} b^{10} c^{11} d^{2} - 11004 \, a^{3} b^{9} c^{10} d^{3} - 15249 \, a^{4} b^{8} c^{9} d^{4} - 48600 \, a^{5} b^{7} c^{8} d^{5} + 31580 \, a^{6} b^{6} c^{7} d^{6} + 18600 \, a^{7} b^{5} c^{6} d^{7} + 93775 \, a^{8} b^{4} c^{5} d^{8} - 61500 \, a^{9} b^{3} c^{4} d^{9} - 6750 \, a^{10} b^{2} c^{3} d^{10} - 67500 \, a^{11} b c^{2} d^{11} + 50625 \, a^{12} c d^{12} + {\left(2401 \, b^{12} c^{12} d + 4116 \, a b^{11} c^{11} d^{2} + 9506 \, a^{2} b^{10} c^{10} d^{3} - 11004 \, a^{3} b^{9} c^{9} d^{4} - 15249 \, a^{4} b^{8} c^{8} d^{5} - 48600 \, a^{5} b^{7} c^{7} d^{6} + 31580 \, a^{6} b^{6} c^{6} d^{7} + 18600 \, a^{7} b^{5} c^{5} d^{8} + 93775 \, a^{8} b^{4} c^{4} d^{9} - 61500 \, a^{9} b^{3} c^{3} d^{10} - 6750 \, a^{10} b^{2} c^{2} d^{11} - 67500 \, a^{11} b c d^{12} + 50625 \, a^{12} d^{13}\right)} x}\right) + 3 \, a^{2} c^{3} x^{3} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(7 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 5 \, a^{2} b c d^{2} - 15 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{3} c^{3} d x + a^{3} c^{4}\right)} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) - 3 \, a^{2} c^{3} x^{3} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(7 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 5 \, a^{2} b c d^{2} - 15 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{3} c^{3} d x + a^{3} c^{4}\right)} \left(\frac{2401 \, b^{12} c^{12} + 4116 \, a b^{11} c^{11} d + 9506 \, a^{2} b^{10} c^{10} d^{2} - 11004 \, a^{3} b^{9} c^{9} d^{3} - 15249 \, a^{4} b^{8} c^{8} d^{4} - 48600 \, a^{5} b^{7} c^{7} d^{5} + 31580 \, a^{6} b^{6} c^{6} d^{6} + 18600 \, a^{7} b^{5} c^{5} d^{7} + 93775 \, a^{8} b^{4} c^{4} d^{8} - 61500 \, a^{9} b^{3} c^{3} d^{9} - 6750 \, a^{10} b^{2} c^{2} d^{10} - 67500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{11} c^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(32 \, a^{2} c^{2} - {\left(7 \, b^{2} c^{2} + 6 \, a b c d - 45 \, a^{2} d^{2}\right)} x^{2} + 4 \, {\left(a b c^{2} - 9 \, a^{2} c d\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{384 \, a^{2} c^{3} x^{3}}"," ",0,"-1/384*(12*a^2*c^3*x^3*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(1/4)*arctan(((7*a^8*b^3*c^13 + 3*a^9*b^2*c^12*d + 5*a^10*b*c^11*d^2 - 15*a^11*c^10*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(3/4) + (a^8*c^10*d*x + a^8*c^11)*sqrt(((49*b^6*c^6 + 42*a*b^5*c^5*d + 79*a^2*b^4*c^4*d^2 - 180*a^3*b^3*c^3*d^3 - 65*a^4*b^2*c^2*d^4 - 150*a^5*b*c*d^5 + 225*a^6*d^6)*sqrt(b*x + a)*sqrt(d*x + c) + (a^6*c^6*d*x + a^6*c^7)*sqrt((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13)))/(d*x + c))*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(3/4))/(2401*b^12*c^13 + 4116*a*b^11*c^12*d + 9506*a^2*b^10*c^11*d^2 - 11004*a^3*b^9*c^10*d^3 - 15249*a^4*b^8*c^9*d^4 - 48600*a^5*b^7*c^8*d^5 + 31580*a^6*b^6*c^7*d^6 + 18600*a^7*b^5*c^6*d^7 + 93775*a^8*b^4*c^5*d^8 - 61500*a^9*b^3*c^4*d^9 - 6750*a^10*b^2*c^3*d^10 - 67500*a^11*b*c^2*d^11 + 50625*a^12*c*d^12 + (2401*b^12*c^12*d + 4116*a*b^11*c^11*d^2 + 9506*a^2*b^10*c^10*d^3 - 11004*a^3*b^9*c^9*d^4 - 15249*a^4*b^8*c^8*d^5 - 48600*a^5*b^7*c^7*d^6 + 31580*a^6*b^6*c^6*d^7 + 18600*a^7*b^5*c^5*d^8 + 93775*a^8*b^4*c^4*d^9 - 61500*a^9*b^3*c^3*d^10 - 6750*a^10*b^2*c^2*d^11 - 67500*a^11*b*c*d^12 + 50625*a^12*d^13)*x)) + 3*a^2*c^3*x^3*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(1/4)*log(-((7*b^3*c^3 + 3*a*b^2*c^2*d + 5*a^2*b*c*d^2 - 15*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^3*c^3*d*x + a^3*c^4)*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(1/4))/(d*x + c)) - 3*a^2*c^3*x^3*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(1/4)*log(-((7*b^3*c^3 + 3*a*b^2*c^2*d + 5*a^2*b*c*d^2 - 15*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^3*c^3*d*x + a^3*c^4)*((2401*b^12*c^12 + 4116*a*b^11*c^11*d + 9506*a^2*b^10*c^10*d^2 - 11004*a^3*b^9*c^9*d^3 - 15249*a^4*b^8*c^8*d^4 - 48600*a^5*b^7*c^7*d^5 + 31580*a^6*b^6*c^6*d^6 + 18600*a^7*b^5*c^5*d^7 + 93775*a^8*b^4*c^4*d^8 - 61500*a^9*b^3*c^3*d^9 - 6750*a^10*b^2*c^2*d^10 - 67500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^11*c^13))^(1/4))/(d*x + c)) + 4*(32*a^2*c^2 - (7*b^2*c^2 + 6*a*b*c*d - 45*a^2*d^2)*x^2 + 4*(a*b*c^2 - 9*a^2*c*d)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a^2*c^3*x^3)","B",0
891,1,2877,0,3.423246," ","integrate((b*x+a)^(1/4)/x^5/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{12 \, a^{3} c^{4} x^{4} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(77 \, a^{11} b^{4} c^{17} + 28 \, a^{12} b^{3} c^{16} d + 30 \, a^{13} b^{2} c^{15} d^{2} + 60 \, a^{14} b c^{14} d^{3} - 195 \, a^{15} c^{13} d^{4}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{3}{4}} + {\left(a^{11} c^{13} d x + a^{11} c^{14}\right)} \sqrt{\frac{{\left(5929 \, b^{8} c^{8} + 4312 \, a b^{7} c^{7} d + 5404 \, a^{2} b^{6} c^{6} d^{2} + 10920 \, a^{3} b^{5} c^{5} d^{3} - 25770 \, a^{4} b^{4} c^{4} d^{4} - 7320 \, a^{5} b^{3} c^{3} d^{5} - 8100 \, a^{6} b^{2} c^{2} d^{6} - 23400 \, a^{7} b c d^{7} + 38025 \, a^{8} d^{8}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{8} c^{8} d x + a^{8} c^{9}\right)} \sqrt{\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}}}{d x + c}} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{3}{4}}}{35153041 \, b^{16} c^{17} + 51131696 \, a b^{15} c^{16} d + 82673976 \, a^{2} b^{14} c^{15} d^{2} + 176093456 \, a^{3} b^{13} c^{14} d^{3} - 182203364 \, a^{4} b^{12} c^{13} d^{4} - 191017680 \, a^{5} b^{11} c^{12} d^{5} - 318453240 \, a^{6} b^{10} c^{11} d^{6} - 989262960 \, a^{7} b^{9} c^{10} d^{7} + 665778150 \, a^{8} b^{8} c^{9} d^{8} + 275389200 \, a^{9} b^{7} c^{8} d^{9} + 370974600 \, a^{10} b^{6} c^{7} d^{10} + 2155086000 \, a^{11} b^{5} c^{6} d^{11} - 1551622500 \, a^{12} b^{4} c^{5} d^{12} - 177606000 \, a^{13} b^{3} c^{4} d^{13} - 68445000 \, a^{14} b^{2} c^{3} d^{14} - 1779570000 \, a^{15} b c^{2} d^{15} + 1445900625 \, a^{16} c d^{16} + {\left(35153041 \, b^{16} c^{16} d + 51131696 \, a b^{15} c^{15} d^{2} + 82673976 \, a^{2} b^{14} c^{14} d^{3} + 176093456 \, a^{3} b^{13} c^{13} d^{4} - 182203364 \, a^{4} b^{12} c^{12} d^{5} - 191017680 \, a^{5} b^{11} c^{11} d^{6} - 318453240 \, a^{6} b^{10} c^{10} d^{7} - 989262960 \, a^{7} b^{9} c^{9} d^{8} + 665778150 \, a^{8} b^{8} c^{8} d^{9} + 275389200 \, a^{9} b^{7} c^{7} d^{10} + 370974600 \, a^{10} b^{6} c^{6} d^{11} + 2155086000 \, a^{11} b^{5} c^{5} d^{12} - 1551622500 \, a^{12} b^{4} c^{4} d^{13} - 177606000 \, a^{13} b^{3} c^{3} d^{14} - 68445000 \, a^{14} b^{2} c^{2} d^{15} - 1779570000 \, a^{15} b c d^{16} + 1445900625 \, a^{16} d^{17}\right)} x}\right) + 3 \, a^{3} c^{4} x^{4} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(77 \, b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 195 \, a^{4} d^{4}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{4} c^{4} d x + a^{4} c^{5}\right)} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{1}{4}}}{d x + c}\right) - 3 \, a^{3} c^{4} x^{4} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(77 \, b^{4} c^{4} + 28 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} - 195 \, a^{4} d^{4}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{4} c^{4} d x + a^{4} c^{5}\right)} \left(\frac{35153041 \, b^{16} c^{16} + 51131696 \, a b^{15} c^{15} d + 82673976 \, a^{2} b^{14} c^{14} d^{2} + 176093456 \, a^{3} b^{13} c^{13} d^{3} - 182203364 \, a^{4} b^{12} c^{12} d^{4} - 191017680 \, a^{5} b^{11} c^{11} d^{5} - 318453240 \, a^{6} b^{10} c^{10} d^{6} - 989262960 \, a^{7} b^{9} c^{9} d^{7} + 665778150 \, a^{8} b^{8} c^{8} d^{8} + 275389200 \, a^{9} b^{7} c^{7} d^{9} + 370974600 \, a^{10} b^{6} c^{6} d^{10} + 2155086000 \, a^{11} b^{5} c^{5} d^{11} - 1551622500 \, a^{12} b^{4} c^{4} d^{12} - 177606000 \, a^{13} b^{3} c^{3} d^{13} - 68445000 \, a^{14} b^{2} c^{2} d^{14} - 1779570000 \, a^{15} b c d^{15} + 1445900625 \, a^{16} d^{16}}{a^{15} c^{17}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(384 \, a^{3} c^{3} + {\left(77 \, b^{3} c^{3} + 61 \, a b^{2} c^{2} d + 63 \, a^{2} b c d^{2} - 585 \, a^{3} d^{3}\right)} x^{3} - 4 \, {\left(11 \, a b^{2} c^{3} + 10 \, a^{2} b c^{2} d - 117 \, a^{3} c d^{2}\right)} x^{2} + 32 \, {\left(a^{2} b c^{3} - 13 \, a^{3} c^{2} d\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{6144 \, a^{3} c^{4} x^{4}}"," ",0,"1/6144*(12*a^3*c^4*x^4*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(1/4)*arctan(((77*a^11*b^4*c^17 + 28*a^12*b^3*c^16*d + 30*a^13*b^2*c^15*d^2 + 60*a^14*b*c^14*d^3 - 195*a^15*c^13*d^4)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(3/4) + (a^11*c^13*d*x + a^11*c^14)*sqrt(((5929*b^8*c^8 + 4312*a*b^7*c^7*d + 5404*a^2*b^6*c^6*d^2 + 10920*a^3*b^5*c^5*d^3 - 25770*a^4*b^4*c^4*d^4 - 7320*a^5*b^3*c^3*d^5 - 8100*a^6*b^2*c^2*d^6 - 23400*a^7*b*c*d^7 + 38025*a^8*d^8)*sqrt(b*x + a)*sqrt(d*x + c) + (a^8*c^8*d*x + a^8*c^9)*sqrt((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17)))/(d*x + c))*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(3/4))/(35153041*b^16*c^17 + 51131696*a*b^15*c^16*d + 82673976*a^2*b^14*c^15*d^2 + 176093456*a^3*b^13*c^14*d^3 - 182203364*a^4*b^12*c^13*d^4 - 191017680*a^5*b^11*c^12*d^5 - 318453240*a^6*b^10*c^11*d^6 - 989262960*a^7*b^9*c^10*d^7 + 665778150*a^8*b^8*c^9*d^8 + 275389200*a^9*b^7*c^8*d^9 + 370974600*a^10*b^6*c^7*d^10 + 2155086000*a^11*b^5*c^6*d^11 - 1551622500*a^12*b^4*c^5*d^12 - 177606000*a^13*b^3*c^4*d^13 - 68445000*a^14*b^2*c^3*d^14 - 1779570000*a^15*b*c^2*d^15 + 1445900625*a^16*c*d^16 + (35153041*b^16*c^16*d + 51131696*a*b^15*c^15*d^2 + 82673976*a^2*b^14*c^14*d^3 + 176093456*a^3*b^13*c^13*d^4 - 182203364*a^4*b^12*c^12*d^5 - 191017680*a^5*b^11*c^11*d^6 - 318453240*a^6*b^10*c^10*d^7 - 989262960*a^7*b^9*c^9*d^8 + 665778150*a^8*b^8*c^8*d^9 + 275389200*a^9*b^7*c^7*d^10 + 370974600*a^10*b^6*c^6*d^11 + 2155086000*a^11*b^5*c^5*d^12 - 1551622500*a^12*b^4*c^4*d^13 - 177606000*a^13*b^3*c^3*d^14 - 68445000*a^14*b^2*c^2*d^15 - 1779570000*a^15*b*c*d^16 + 1445900625*a^16*d^17)*x)) + 3*a^3*c^4*x^4*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(1/4)*log(-((77*b^4*c^4 + 28*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 195*a^4*d^4)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^4*c^4*d*x + a^4*c^5)*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(1/4))/(d*x + c)) - 3*a^3*c^4*x^4*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(1/4)*log(-((77*b^4*c^4 + 28*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 - 195*a^4*d^4)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^4*c^4*d*x + a^4*c^5)*((35153041*b^16*c^16 + 51131696*a*b^15*c^15*d + 82673976*a^2*b^14*c^14*d^2 + 176093456*a^3*b^13*c^13*d^3 - 182203364*a^4*b^12*c^12*d^4 - 191017680*a^5*b^11*c^11*d^5 - 318453240*a^6*b^10*c^10*d^6 - 989262960*a^7*b^9*c^9*d^7 + 665778150*a^8*b^8*c^8*d^8 + 275389200*a^9*b^7*c^7*d^9 + 370974600*a^10*b^6*c^6*d^10 + 2155086000*a^11*b^5*c^5*d^11 - 1551622500*a^12*b^4*c^4*d^12 - 177606000*a^13*b^3*c^3*d^13 - 68445000*a^14*b^2*c^2*d^14 - 1779570000*a^15*b*c*d^15 + 1445900625*a^16*d^16)/(a^15*c^17))^(1/4))/(d*x + c)) - 4*(384*a^3*c^3 + (77*b^3*c^3 + 61*a*b^2*c^2*d + 63*a^2*b*c*d^2 - 585*a^3*d^3)*x^3 - 4*(11*a*b^2*c^3 + 10*a^2*b*c^2*d - 117*a^3*c*d^2)*x^2 + 32*(a^2*b*c^3 - 13*a^3*c^2*d)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a^3*c^4*x^4)","B",0
892,1,282,0,1.259322," ","integrate(x^2*(1+x)^(1/4)/(1-x)^(1/4),x, algorithm=""fricas"")","-\frac{1}{24} \, {\left(8 \, x^{2} + 10 \, x + 11\right)} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + \frac{3}{8} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + 1}{x - 1}\right) + \frac{3}{8} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{-\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - 1}{x - 1}\right) - \frac{3}{32} \, \sqrt{2} \log\left(\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x - 1}\right) + \frac{3}{32} \, \sqrt{2} \log\left(-\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1\right)}}{x - 1}\right)"," ",0,"-1/24*(8*x^2 + 10*x + 11)*(x + 1)^(1/4)*(-x + 1)^(3/4) + 3/8*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt((sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + 1)/(x - 1)) + 3/8*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt(-(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - 1)/(x - 1)) - 3/32*sqrt(2)*log(4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) + 3/32*sqrt(2)*log(-4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1))","A",0
893,1,277,0,1.363456," ","integrate(x*(1+x)^(1/4)/(1-x)^(1/4),x, algorithm=""fricas"")","-\frac{1}{4} \, {\left(2 \, x + 3\right)} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + 1}{x - 1}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{-\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - 1}{x - 1}\right) - \frac{1}{16} \, \sqrt{2} \log\left(\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x - 1}\right) + \frac{1}{16} \, \sqrt{2} \log\left(-\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1\right)}}{x - 1}\right)"," ",0,"-1/4*(2*x + 3)*(x + 1)^(1/4)*(-x + 1)^(3/4) + 1/4*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt((sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + 1)/(x - 1)) + 1/4*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt(-(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - 1)/(x - 1)) - 1/16*sqrt(2)*log(4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) + 1/16*sqrt(2)*log(-4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1))","A",0
894,1,270,0,1.616547," ","integrate((1+x)^(1/4)/(1-x)^(1/4),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + 1}{x - 1}\right) + \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{-\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - 1}{x - 1}\right) - \frac{1}{4} \, \sqrt{2} \log\left(\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x - 1}\right) + \frac{1}{4} \, \sqrt{2} \log\left(-\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1\right)}}{x - 1}\right) - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}"," ",0,"sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt((sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + 1)/(x - 1)) + sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt(-(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - 1)/(x - 1)) - 1/4*sqrt(2)*log(4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) + 1/4*sqrt(2)*log(-4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) - (x + 1)^(1/4)*(-x + 1)^(3/4)","A",0
895,1,329,0,1.401319," ","integrate((1+x)^(1/4)/(1-x)^(1/4)/x,x, algorithm=""fricas"")","2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + 1}{x - 1}\right) + 2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)} \sqrt{-\frac{\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1}{x - 1}} - \sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - 1}{x - 1}\right) - \frac{1}{2} \, \sqrt{2} \log\left(\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + x - \sqrt{x + 1} \sqrt{-x + 1} - 1\right)}}{x - 1}\right) + \frac{1}{2} \, \sqrt{2} \log\left(-\frac{4 \, {\left(\sqrt{2} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - x + \sqrt{x + 1} \sqrt{-x + 1} + 1\right)}}{x - 1}\right) + 2 \, \arctan\left(\frac{{\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x - 1}\right) + \log\left(\frac{x + {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - \log\left(-\frac{x - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right)"," ",0,"2*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt((sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + 1)/(x - 1)) + 2*sqrt(2)*arctan((sqrt(2)*(x - 1)*sqrt(-(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) - sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - 1)/(x - 1)) - 1/2*sqrt(2)*log(4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) + x - sqrt(x + 1)*sqrt(-x + 1) - 1)/(x - 1)) + 1/2*sqrt(2)*log(-4*(sqrt(2)*(x + 1)^(1/4)*(-x + 1)^(3/4) - x + sqrt(x + 1)*sqrt(-x + 1) + 1)/(x - 1)) + 2*arctan((x + 1)^(1/4)*(-x + 1)^(3/4)/(x - 1)) + log((x + (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - log(-(x - (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1))","B",0
896,1,95,0,0.903718," ","integrate((1+x)^(1/4)/(1-x)^(1/4)/x^2,x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(\frac{{\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x - 1}\right) + x \log\left(\frac{x + {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - x \log\left(-\frac{x - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 2 \, {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{2 \, x}"," ",0,"1/2*(2*x*arctan((x + 1)^(1/4)*(-x + 1)^(3/4)/(x - 1)) + x*log((x + (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - x*log(-(x - (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 2*(x + 1)^(1/4)*(-x + 1)^(3/4))/x","A",0
897,1,106,0,0.775782," ","integrate((1+x)^(1/4)/(1-x)^(1/4)/x^3,x, algorithm=""fricas"")","\frac{2 \, x^{2} \arctan\left(\frac{{\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x - 1}\right) + x^{2} \log\left(\frac{x + {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - x^{2} \log\left(-\frac{x - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 2 \, {\left(3 \, x + 2\right)} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{8 \, x^{2}}"," ",0,"1/8*(2*x^2*arctan((x + 1)^(1/4)*(-x + 1)^(3/4)/(x - 1)) + x^2*log((x + (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - x^2*log(-(x - (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 2*(3*x + 2)*(x + 1)^(1/4)*(-x + 1)^(3/4))/x^2","A",0
898,1,112,0,1.376657," ","integrate((1+x)^(1/4)/(1-x)^(1/4)/x^4,x, algorithm=""fricas"")","\frac{18 \, x^{3} \arctan\left(\frac{{\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x - 1}\right) + 9 \, x^{3} \log\left(\frac{x + {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 9 \, x^{3} \log\left(-\frac{x - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 2 \, {\left(11 \, x^{2} + 10 \, x + 8\right)} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{48 \, x^{3}}"," ",0,"1/48*(18*x^3*arctan((x + 1)^(1/4)*(-x + 1)^(3/4)/(x - 1)) + 9*x^3*log((x + (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 9*x^3*log(-(x - (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 2*(11*x^2 + 10*x + 8)*(x + 1)^(1/4)*(-x + 1)^(3/4))/x^3","A",0
899,1,117,0,1.443488," ","integrate((1+x)^(1/4)/(1-x)^(1/4)/x^5,x, algorithm=""fricas"")","\frac{66 \, x^{4} \arctan\left(\frac{{\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x - 1}\right) + 33 \, x^{4} \log\left(\frac{x + {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 33 \, x^{4} \log\left(-\frac{x - {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - 1}{x - 1}\right) - 2 \, {\left(83 \, x^{3} + 58 \, x^{2} + 56 \, x + 48\right)} {\left(x + 1\right)}^{\frac{1}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{384 \, x^{4}}"," ",0,"1/384*(66*x^4*arctan((x + 1)^(1/4)*(-x + 1)^(3/4)/(x - 1)) + 33*x^4*log((x + (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 33*x^4*log(-(x - (x + 1)^(1/4)*(-x + 1)^(3/4) - 1)/(x - 1)) - 2*(83*x^3 + 58*x^2 + 56*x + 48)*(x + 1)^(1/4)*(-x + 1)^(3/4))/x^4","A",0
900,1,2182,0,1.816227," ","integrate(x^3/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{12 \, b^{3} d^{3} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(15 \, b^{14} c^{3} d^{10} + 15 \, a b^{13} c^{2} d^{11} + 21 \, a^{2} b^{12} c d^{12} + 77 \, a^{3} b^{11} d^{13}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{3}{4}} - {\left(b^{11} d^{11} x + b^{11} c d^{10}\right)} \sqrt{\frac{{\left(225 \, b^{6} c^{6} + 450 \, a b^{5} c^{5} d + 855 \, a^{2} b^{4} c^{4} d^{2} + 2940 \, a^{3} b^{3} c^{3} d^{3} + 2751 \, a^{4} b^{2} c^{2} d^{4} + 3234 \, a^{5} b c d^{5} + 5929 \, a^{6} d^{6}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{8} d^{7} x + b^{8} c d^{6}\right)} \sqrt{\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}}}{d x + c}} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{3}{4}}}{50625 \, b^{12} c^{13} + 202500 \, a b^{11} c^{12} d + 587250 \, a^{2} b^{10} c^{11} d^{2} + 2092500 \, a^{3} b^{9} c^{10} d^{3} + 4614975 \, a^{4} b^{8} c^{9} d^{4} + 8958600 \, a^{5} b^{7} c^{8} d^{5} + 18926460 \, a^{6} b^{6} c^{7} d^{6} + 27042120 \, a^{7} b^{5} c^{6} d^{7} + 36722511 \, a^{8} b^{4} c^{5} d^{8} + 52655988 \, a^{9} b^{3} c^{4} d^{9} + 43080114 \, a^{10} b^{2} c^{3} d^{10} + 38348772 \, a^{11} b c^{2} d^{11} + 35153041 \, a^{12} c d^{12} + {\left(50625 \, b^{12} c^{12} d + 202500 \, a b^{11} c^{11} d^{2} + 587250 \, a^{2} b^{10} c^{10} d^{3} + 2092500 \, a^{3} b^{9} c^{9} d^{4} + 4614975 \, a^{4} b^{8} c^{8} d^{5} + 8958600 \, a^{5} b^{7} c^{7} d^{6} + 18926460 \, a^{6} b^{6} c^{6} d^{7} + 27042120 \, a^{7} b^{5} c^{5} d^{8} + 36722511 \, a^{8} b^{4} c^{4} d^{9} + 52655988 \, a^{9} b^{3} c^{3} d^{10} + 43080114 \, a^{10} b^{2} c^{2} d^{11} + 38348772 \, a^{11} b c d^{12} + 35153041 \, a^{12} d^{13}\right)} x}\right) - 3 \, b^{3} d^{3} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(15 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 21 \, a^{2} b c d^{2} + 77 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{4} d^{4} x + b^{4} c d^{3}\right)} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) + 3 \, b^{3} d^{3} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(15 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 21 \, a^{2} b c d^{2} + 77 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{4} d^{4} x + b^{4} c d^{3}\right)} \left(\frac{50625 \, b^{12} c^{12} + 202500 \, a b^{11} c^{11} d + 587250 \, a^{2} b^{10} c^{10} d^{2} + 2092500 \, a^{3} b^{9} c^{9} d^{3} + 4614975 \, a^{4} b^{8} c^{8} d^{4} + 8958600 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 27042120 \, a^{7} b^{5} c^{5} d^{7} + 36722511 \, a^{8} b^{4} c^{4} d^{8} + 52655988 \, a^{9} b^{3} c^{3} d^{9} + 43080114 \, a^{10} b^{2} c^{2} d^{10} + 38348772 \, a^{11} b c d^{11} + 35153041 \, a^{12} d^{12}}{b^{15} d^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(32 \, b^{2} d^{2} x^{2} + 45 \, b^{2} c^{2} + 54 \, a b c d + 77 \, a^{2} d^{2} - 4 \, {\left(9 \, b^{2} c d + 11 \, a b d^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{384 \, b^{3} d^{3}}"," ",0,"1/384*(12*b^3*d^3*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(1/4)*arctan(-((15*b^14*c^3*d^10 + 15*a*b^13*c^2*d^11 + 21*a^2*b^12*c*d^12 + 77*a^3*b^11*d^13)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(3/4) - (b^11*d^11*x + b^11*c*d^10)*sqrt(((225*b^6*c^6 + 450*a*b^5*c^5*d + 855*a^2*b^4*c^4*d^2 + 2940*a^3*b^3*c^3*d^3 + 2751*a^4*b^2*c^2*d^4 + 3234*a^5*b*c*d^5 + 5929*a^6*d^6)*sqrt(b*x + a)*sqrt(d*x + c) + (b^8*d^7*x + b^8*c*d^6)*sqrt((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13)))/(d*x + c))*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(3/4))/(50625*b^12*c^13 + 202500*a*b^11*c^12*d + 587250*a^2*b^10*c^11*d^2 + 2092500*a^3*b^9*c^10*d^3 + 4614975*a^4*b^8*c^9*d^4 + 8958600*a^5*b^7*c^8*d^5 + 18926460*a^6*b^6*c^7*d^6 + 27042120*a^7*b^5*c^6*d^7 + 36722511*a^8*b^4*c^5*d^8 + 52655988*a^9*b^3*c^4*d^9 + 43080114*a^10*b^2*c^3*d^10 + 38348772*a^11*b*c^2*d^11 + 35153041*a^12*c*d^12 + (50625*b^12*c^12*d + 202500*a*b^11*c^11*d^2 + 587250*a^2*b^10*c^10*d^3 + 2092500*a^3*b^9*c^9*d^4 + 4614975*a^4*b^8*c^8*d^5 + 8958600*a^5*b^7*c^7*d^6 + 18926460*a^6*b^6*c^6*d^7 + 27042120*a^7*b^5*c^5*d^8 + 36722511*a^8*b^4*c^4*d^9 + 52655988*a^9*b^3*c^3*d^10 + 43080114*a^10*b^2*c^2*d^11 + 38348772*a^11*b*c*d^12 + 35153041*a^12*d^13)*x)) - 3*b^3*d^3*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(1/4)*log(((15*b^3*c^3 + 15*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 77*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^4*d^4*x + b^4*c*d^3)*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(1/4))/(d*x + c)) + 3*b^3*d^3*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(1/4)*log(((15*b^3*c^3 + 15*a*b^2*c^2*d + 21*a^2*b*c*d^2 + 77*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^4*d^4*x + b^4*c*d^3)*((50625*b^12*c^12 + 202500*a*b^11*c^11*d + 587250*a^2*b^10*c^10*d^2 + 2092500*a^3*b^9*c^9*d^3 + 4614975*a^4*b^8*c^8*d^4 + 8958600*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 27042120*a^7*b^5*c^5*d^7 + 36722511*a^8*b^4*c^4*d^8 + 52655988*a^9*b^3*c^3*d^9 + 43080114*a^10*b^2*c^2*d^10 + 38348772*a^11*b*c*d^11 + 35153041*a^12*d^12)/(b^15*d^13))^(1/4))/(d*x + c)) + 4*(32*b^2*d^2*x^2 + 45*b^2*c^2 + 54*a*b*c*d + 77*a^2*d^2 - 4*(9*b^2*c*d + 11*a*b*d^2)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b^3*d^3)","B",0
901,1,1513,0,1.396821," ","integrate(x^2/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, b^{2} d^{2} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(5 \, b^{10} c^{2} d^{7} + 6 \, a b^{9} c d^{8} + 21 \, a^{2} b^{8} d^{9}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{3}{4}} - {\left(b^{8} d^{8} x + b^{8} c d^{7}\right)} \sqrt{\frac{{\left(25 \, b^{4} c^{4} + 60 \, a b^{3} c^{3} d + 246 \, a^{2} b^{2} c^{2} d^{2} + 252 \, a^{3} b c d^{3} + 441 \, a^{4} d^{4}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{6} d^{5} x + b^{6} c d^{4}\right)} \sqrt{\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}}}{d x + c}} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{3}{4}}}{625 \, b^{8} c^{9} + 3000 \, a b^{7} c^{8} d + 15900 \, a^{2} b^{6} c^{7} d^{2} + 42120 \, a^{3} b^{5} c^{6} d^{3} + 112806 \, a^{4} b^{4} c^{5} d^{4} + 176904 \, a^{5} b^{3} c^{4} d^{5} + 280476 \, a^{6} b^{2} c^{3} d^{6} + 222264 \, a^{7} b c^{2} d^{7} + 194481 \, a^{8} c d^{8} + {\left(625 \, b^{8} c^{8} d + 3000 \, a b^{7} c^{7} d^{2} + 15900 \, a^{2} b^{6} c^{6} d^{3} + 42120 \, a^{3} b^{5} c^{5} d^{4} + 112806 \, a^{4} b^{4} c^{4} d^{5} + 176904 \, a^{5} b^{3} c^{3} d^{6} + 280476 \, a^{6} b^{2} c^{2} d^{7} + 222264 \, a^{7} b c d^{8} + 194481 \, a^{8} d^{9}\right)} x}\right) - b^{2} d^{2} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{3} d^{3} x + b^{3} c d^{2}\right)} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) + b^{2} d^{2} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(5 \, b^{2} c^{2} + 6 \, a b c d + 21 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{3} d^{3} x + b^{3} c d^{2}\right)} \left(\frac{625 \, b^{8} c^{8} + 3000 \, a b^{7} c^{7} d + 15900 \, a^{2} b^{6} c^{6} d^{2} + 42120 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 176904 \, a^{5} b^{3} c^{3} d^{5} + 280476 \, a^{6} b^{2} c^{2} d^{6} + 222264 \, a^{7} b c d^{7} + 194481 \, a^{8} d^{8}}{b^{11} d^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(4 \, b d x - 5 \, b c - 7 \, a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{32 \, b^{2} d^{2}}"," ",0,"-1/32*(4*b^2*d^2*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(1/4)*arctan(-((5*b^10*c^2*d^7 + 6*a*b^9*c*d^8 + 21*a^2*b^8*d^9)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(3/4) - (b^8*d^8*x + b^8*c*d^7)*sqrt(((25*b^4*c^4 + 60*a*b^3*c^3*d + 246*a^2*b^2*c^2*d^2 + 252*a^3*b*c*d^3 + 441*a^4*d^4)*sqrt(b*x + a)*sqrt(d*x + c) + (b^6*d^5*x + b^6*c*d^4)*sqrt((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9)))/(d*x + c))*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(3/4))/(625*b^8*c^9 + 3000*a*b^7*c^8*d + 15900*a^2*b^6*c^7*d^2 + 42120*a^3*b^5*c^6*d^3 + 112806*a^4*b^4*c^5*d^4 + 176904*a^5*b^3*c^4*d^5 + 280476*a^6*b^2*c^3*d^6 + 222264*a^7*b*c^2*d^7 + 194481*a^8*c*d^8 + (625*b^8*c^8*d + 3000*a*b^7*c^7*d^2 + 15900*a^2*b^6*c^6*d^3 + 42120*a^3*b^5*c^5*d^4 + 112806*a^4*b^4*c^4*d^5 + 176904*a^5*b^3*c^3*d^6 + 280476*a^6*b^2*c^2*d^7 + 222264*a^7*b*c*d^8 + 194481*a^8*d^9)*x)) - b^2*d^2*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(1/4)*log(((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^3*d^3*x + b^3*c*d^2)*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(1/4))/(d*x + c)) + b^2*d^2*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(1/4)*log(((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^3*d^3*x + b^3*c*d^2)*((625*b^8*c^8 + 3000*a*b^7*c^7*d + 15900*a^2*b^6*c^6*d^2 + 42120*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 176904*a^5*b^3*c^3*d^5 + 280476*a^6*b^2*c^2*d^6 + 222264*a^7*b*c*d^7 + 194481*a^8*d^8)/(b^11*d^9))^(1/4))/(d*x + c)) - 4*(4*b*d*x - 5*b*c - 7*a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b^2*d^2)","B",0
902,1,839,0,1.589828," ","integrate(x/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{4 \, b d \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{6} c d^{4} + 3 \, a b^{5} d^{5}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{3}{4}} - {\left(b^{5} d^{5} x + b^{5} c d^{4}\right)} \sqrt{\frac{{\left(b^{2} c^{2} + 6 \, a b c d + 9 \, a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(b^{4} d^{3} x + b^{4} c d^{2}\right)} \sqrt{\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}}}{d x + c}} \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{3}{4}}}{b^{4} c^{5} + 12 \, a b^{3} c^{4} d + 54 \, a^{2} b^{2} c^{3} d^{2} + 108 \, a^{3} b c^{2} d^{3} + 81 \, a^{4} c d^{4} + {\left(b^{4} c^{4} d + 12 \, a b^{3} c^{3} d^{2} + 54 \, a^{2} b^{2} c^{2} d^{3} + 108 \, a^{3} b c d^{4} + 81 \, a^{4} d^{5}\right)} x}\right) - b d \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b c + 3 \, a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(b^{2} d^{2} x + b^{2} c d\right)} \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) + b d \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b c + 3 \, a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(b^{2} d^{2} x + b^{2} c d\right)} \left(\frac{b^{4} c^{4} + 12 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 108 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}}{b^{7} d^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{4 \, b d}"," ",0,"1/4*(4*b*d*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(1/4)*arctan(-((b^6*c*d^4 + 3*a*b^5*d^5)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(3/4) - (b^5*d^5*x + b^5*c*d^4)*sqrt(((b^2*c^2 + 6*a*b*c*d + 9*a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c) + (b^4*d^3*x + b^4*c*d^2)*sqrt((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5)))/(d*x + c))*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(3/4))/(b^4*c^5 + 12*a*b^3*c^4*d + 54*a^2*b^2*c^3*d^2 + 108*a^3*b*c^2*d^3 + 81*a^4*c*d^4 + (b^4*c^4*d + 12*a*b^3*c^3*d^2 + 54*a^2*b^2*c^2*d^3 + 108*a^3*b*c*d^4 + 81*a^4*d^5)*x)) - b*d*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(1/4)*log(((b*c + 3*a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (b^2*d^2*x + b^2*c*d)*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(1/4))/(d*x + c)) + b*d*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(1/4)*log(((b*c + 3*a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (b^2*d^2*x + b^2*c*d)*((b^4*c^4 + 12*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 108*a^3*b*c*d^3 + 81*a^4*d^4)/(b^7*d^5))^(1/4))/(d*x + c)) + 4*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(b*d)","B",0
903,1,234,0,0.816491," ","integrate(1/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-4 \, \left(\frac{1}{b^{3} d}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} b^{2} d \left(\frac{1}{b^{3} d}\right)^{\frac{3}{4}} - {\left(b^{2} d^{2} x + b^{2} c d\right)} \sqrt{\frac{{\left(b^{2} d x + b^{2} c\right)} \sqrt{\frac{1}{b^{3} d}} + \sqrt{b x + a} \sqrt{d x + c}}{d x + c}} \left(\frac{1}{b^{3} d}\right)^{\frac{3}{4}}}{d x + c}\right) + \left(\frac{1}{b^{3} d}\right)^{\frac{1}{4}} \log\left(\frac{{\left(b d x + b c\right)} \left(\frac{1}{b^{3} d}\right)^{\frac{1}{4}} + {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right) - \left(\frac{1}{b^{3} d}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(b d x + b c\right)} \left(\frac{1}{b^{3} d}\right)^{\frac{1}{4}} - {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right)"," ",0,"-4*(1/(b^3*d))^(1/4)*arctan(-((b*x + a)^(1/4)*(d*x + c)^(3/4)*b^2*d*(1/(b^3*d))^(3/4) - (b^2*d^2*x + b^2*c*d)*sqrt(((b^2*d*x + b^2*c)*sqrt(1/(b^3*d)) + sqrt(b*x + a)*sqrt(d*x + c))/(d*x + c))*(1/(b^3*d))^(3/4))/(d*x + c)) + (1/(b^3*d))^(1/4)*log(((b*d*x + b*c)*(1/(b^3*d))^(1/4) + (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c)) - (1/(b^3*d))^(1/4)*log(-((b*d*x + b*c)*(1/(b^3*d))^(1/4) - (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c))","B",0
904,1,234,0,1.445579," ","integrate(1/x/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","4 \, \left(\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} a^{2} c \left(\frac{1}{a^{3} c}\right)^{\frac{3}{4}} - {\left(a^{2} c d x + a^{2} c^{2}\right)} \sqrt{\frac{{\left(a^{2} d x + a^{2} c\right)} \sqrt{\frac{1}{a^{3} c}} + \sqrt{b x + a} \sqrt{d x + c}}{d x + c}} \left(\frac{1}{a^{3} c}\right)^{\frac{3}{4}}}{d x + c}\right) - \left(\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(\frac{{\left(a d x + a c\right)} \left(\frac{1}{a^{3} c}\right)^{\frac{1}{4}} + {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right) + \left(\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(-\frac{{\left(a d x + a c\right)} \left(\frac{1}{a^{3} c}\right)^{\frac{1}{4}} - {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{d x + c}\right)"," ",0,"4*(1/(a^3*c))^(1/4)*arctan(-((b*x + a)^(1/4)*(d*x + c)^(3/4)*a^2*c*(1/(a^3*c))^(3/4) - (a^2*c*d*x + a^2*c^2)*sqrt(((a^2*d*x + a^2*c)*sqrt(1/(a^3*c)) + sqrt(b*x + a)*sqrt(d*x + c))/(d*x + c))*(1/(a^3*c))^(3/4))/(d*x + c)) - (1/(a^3*c))^(1/4)*log(((a*d*x + a*c)*(1/(a^3*c))^(1/4) + (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c)) + (1/(a^3*c))^(1/4)*log(-((a*d*x + a*c)*(1/(a^3*c))^(1/4) - (b*x + a)^(1/4)*(d*x + c)^(3/4))/(d*x + c))","B",0
905,1,845,0,1.591109," ","integrate(1/x^2/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{4 \, a c x \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(3 \, a^{5} b c^{5} + a^{6} c^{4} d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{3}{4}} - {\left(a^{5} c^{4} d x + a^{5} c^{5}\right)} \sqrt{\frac{{\left(9 \, b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{4} c^{2} d x + a^{4} c^{3}\right)} \sqrt{\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}}}{d x + c}} \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{3}{4}}}{81 \, b^{4} c^{5} + 108 \, a b^{3} c^{4} d + 54 \, a^{2} b^{2} c^{3} d^{2} + 12 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4} + {\left(81 \, b^{4} c^{4} d + 108 \, a b^{3} c^{3} d^{2} + 54 \, a^{2} b^{2} c^{2} d^{3} + 12 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} x}\right) - a c x \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(3 \, b c + a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{2} c d x + a^{2} c^{2}\right)} \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) + a c x \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(3 \, b c + a d\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{2} c d x + a^{2} c^{2}\right)} \left(\frac{81 \, b^{4} c^{4} + 108 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} + a^{4} d^{4}}{a^{7} c^{5}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{4 \, a c x}"," ",0,"-1/4*(4*a*c*x*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(1/4)*arctan(-((3*a^5*b*c^5 + a^6*c^4*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(3/4) - (a^5*c^4*d*x + a^5*c^5)*sqrt(((9*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*sqrt(b*x + a)*sqrt(d*x + c) + (a^4*c^2*d*x + a^4*c^3)*sqrt((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5)))/(d*x + c))*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(3/4))/(81*b^4*c^5 + 108*a*b^3*c^4*d + 54*a^2*b^2*c^3*d^2 + 12*a^3*b*c^2*d^3 + a^4*c*d^4 + (81*b^4*c^4*d + 108*a*b^3*c^3*d^2 + 54*a^2*b^2*c^2*d^3 + 12*a^3*b*c*d^4 + a^4*d^5)*x)) - a*c*x*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(1/4)*log(((3*b*c + a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^2*c*d*x + a^2*c^2)*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(1/4))/(d*x + c)) + a*c*x*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(1/4)*log(((3*b*c + a*d)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^2*c*d*x + a^2*c^2)*((81*b^4*c^4 + 108*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 + a^4*d^4)/(a^7*c^5))^(1/4))/(d*x + c)) + 4*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a*c*x)","B",0
906,1,1528,0,1.831770," ","integrate(1/x^3/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x^{2} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(21 \, a^{8} b^{2} c^{9} + 6 \, a^{9} b c^{8} d + 5 \, a^{10} c^{7} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{3}{4}} - {\left(a^{8} c^{7} d x + a^{8} c^{8}\right)} \sqrt{\frac{{\left(441 \, b^{4} c^{4} + 252 \, a b^{3} c^{3} d + 246 \, a^{2} b^{2} c^{2} d^{2} + 60 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{6} c^{4} d x + a^{6} c^{5}\right)} \sqrt{\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}}}{d x + c}} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{3}{4}}}{194481 \, b^{8} c^{9} + 222264 \, a b^{7} c^{8} d + 280476 \, a^{2} b^{6} c^{7} d^{2} + 176904 \, a^{3} b^{5} c^{6} d^{3} + 112806 \, a^{4} b^{4} c^{5} d^{4} + 42120 \, a^{5} b^{3} c^{4} d^{5} + 15900 \, a^{6} b^{2} c^{3} d^{6} + 3000 \, a^{7} b c^{2} d^{7} + 625 \, a^{8} c d^{8} + {\left(194481 \, b^{8} c^{8} d + 222264 \, a b^{7} c^{7} d^{2} + 280476 \, a^{2} b^{6} c^{6} d^{3} + 176904 \, a^{3} b^{5} c^{5} d^{4} + 112806 \, a^{4} b^{4} c^{4} d^{5} + 42120 \, a^{5} b^{3} c^{3} d^{6} + 15900 \, a^{6} b^{2} c^{2} d^{7} + 3000 \, a^{7} b c d^{8} + 625 \, a^{8} d^{9}\right)} x}\right) - a^{2} c^{2} x^{2} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(21 \, b^{2} c^{2} + 6 \, a b c d + 5 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{3} c^{2} d x + a^{3} c^{3}\right)} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) + a^{2} c^{2} x^{2} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(21 \, b^{2} c^{2} + 6 \, a b c d + 5 \, a^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{3} c^{2} d x + a^{3} c^{3}\right)} \left(\frac{194481 \, b^{8} c^{8} + 222264 \, a b^{7} c^{7} d + 280476 \, a^{2} b^{6} c^{6} d^{2} + 176904 \, a^{3} b^{5} c^{5} d^{3} + 112806 \, a^{4} b^{4} c^{4} d^{4} + 42120 \, a^{5} b^{3} c^{3} d^{5} + 15900 \, a^{6} b^{2} c^{2} d^{6} + 3000 \, a^{7} b c d^{7} + 625 \, a^{8} d^{8}}{a^{11} c^{9}}\right)^{\frac{1}{4}}}{d x + c}\right) - 4 \, {\left(4 \, a c - {\left(7 \, b c + 5 \, a d\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{32 \, a^{2} c^{2} x^{2}}"," ",0,"1/32*(4*a^2*c^2*x^2*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(1/4)*arctan(-((21*a^8*b^2*c^9 + 6*a^9*b*c^8*d + 5*a^10*c^7*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(3/4) - (a^8*c^7*d*x + a^8*c^8)*sqrt(((441*b^4*c^4 + 252*a*b^3*c^3*d + 246*a^2*b^2*c^2*d^2 + 60*a^3*b*c*d^3 + 25*a^4*d^4)*sqrt(b*x + a)*sqrt(d*x + c) + (a^6*c^4*d*x + a^6*c^5)*sqrt((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9)))/(d*x + c))*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(3/4))/(194481*b^8*c^9 + 222264*a*b^7*c^8*d + 280476*a^2*b^6*c^7*d^2 + 176904*a^3*b^5*c^6*d^3 + 112806*a^4*b^4*c^5*d^4 + 42120*a^5*b^3*c^4*d^5 + 15900*a^6*b^2*c^3*d^6 + 3000*a^7*b*c^2*d^7 + 625*a^8*c*d^8 + (194481*b^8*c^8*d + 222264*a*b^7*c^7*d^2 + 280476*a^2*b^6*c^6*d^3 + 176904*a^3*b^5*c^5*d^4 + 112806*a^4*b^4*c^4*d^5 + 42120*a^5*b^3*c^3*d^6 + 15900*a^6*b^2*c^2*d^7 + 3000*a^7*b*c*d^8 + 625*a^8*d^9)*x)) - a^2*c^2*x^2*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(1/4)*log(((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^3*c^2*d*x + a^3*c^3)*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(1/4))/(d*x + c)) + a^2*c^2*x^2*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(1/4)*log(((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^3*c^2*d*x + a^3*c^3)*((194481*b^8*c^8 + 222264*a*b^7*c^7*d + 280476*a^2*b^6*c^6*d^2 + 176904*a^3*b^5*c^5*d^3 + 112806*a^4*b^4*c^4*d^4 + 42120*a^5*b^3*c^3*d^5 + 15900*a^6*b^2*c^2*d^6 + 3000*a^7*b*c*d^7 + 625*a^8*d^8)/(a^11*c^9))^(1/4))/(d*x + c)) - 4*(4*a*c - (7*b*c + 5*a*d)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a^2*c^2*x^2)","B",0
907,1,2196,0,2.306409," ","integrate(1/x^4/(b*x+a)^(3/4)/(d*x+c)^(1/4),x, algorithm=""fricas"")","-\frac{12 \, a^{3} c^{3} x^{3} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(77 \, a^{11} b^{3} c^{13} + 21 \, a^{12} b^{2} c^{12} d + 15 \, a^{13} b c^{11} d^{2} + 15 \, a^{14} c^{10} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{3}{4}} - {\left(a^{11} c^{10} d x + a^{11} c^{11}\right)} \sqrt{\frac{{\left(5929 \, b^{6} c^{6} + 3234 \, a b^{5} c^{5} d + 2751 \, a^{2} b^{4} c^{4} d^{2} + 2940 \, a^{3} b^{3} c^{3} d^{3} + 855 \, a^{4} b^{2} c^{2} d^{4} + 450 \, a^{5} b c d^{5} + 225 \, a^{6} d^{6}\right)} \sqrt{b x + a} \sqrt{d x + c} + {\left(a^{8} c^{6} d x + a^{8} c^{7}\right)} \sqrt{\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}}}{d x + c}} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{3}{4}}}{35153041 \, b^{12} c^{13} + 38348772 \, a b^{11} c^{12} d + 43080114 \, a^{2} b^{10} c^{11} d^{2} + 52655988 \, a^{3} b^{9} c^{10} d^{3} + 36722511 \, a^{4} b^{8} c^{9} d^{4} + 27042120 \, a^{5} b^{7} c^{8} d^{5} + 18926460 \, a^{6} b^{6} c^{7} d^{6} + 8958600 \, a^{7} b^{5} c^{6} d^{7} + 4614975 \, a^{8} b^{4} c^{5} d^{8} + 2092500 \, a^{9} b^{3} c^{4} d^{9} + 587250 \, a^{10} b^{2} c^{3} d^{10} + 202500 \, a^{11} b c^{2} d^{11} + 50625 \, a^{12} c d^{12} + {\left(35153041 \, b^{12} c^{12} d + 38348772 \, a b^{11} c^{11} d^{2} + 43080114 \, a^{2} b^{10} c^{10} d^{3} + 52655988 \, a^{3} b^{9} c^{9} d^{4} + 36722511 \, a^{4} b^{8} c^{8} d^{5} + 27042120 \, a^{5} b^{7} c^{7} d^{6} + 18926460 \, a^{6} b^{6} c^{6} d^{7} + 8958600 \, a^{7} b^{5} c^{5} d^{8} + 4614975 \, a^{8} b^{4} c^{4} d^{9} + 2092500 \, a^{9} b^{3} c^{3} d^{10} + 587250 \, a^{10} b^{2} c^{2} d^{11} + 202500 \, a^{11} b c d^{12} + 50625 \, a^{12} d^{13}\right)} x}\right) - 3 \, a^{3} c^{3} x^{3} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(77 \, b^{3} c^{3} + 21 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 15 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} + {\left(a^{4} c^{3} d x + a^{4} c^{4}\right)} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) + 3 \, a^{3} c^{3} x^{3} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{1}{4}} \log\left(\frac{{\left(77 \, b^{3} c^{3} + 21 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 15 \, a^{3} d^{3}\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}} - {\left(a^{4} c^{3} d x + a^{4} c^{4}\right)} \left(\frac{35153041 \, b^{12} c^{12} + 38348772 \, a b^{11} c^{11} d + 43080114 \, a^{2} b^{10} c^{10} d^{2} + 52655988 \, a^{3} b^{9} c^{9} d^{3} + 36722511 \, a^{4} b^{8} c^{8} d^{4} + 27042120 \, a^{5} b^{7} c^{7} d^{5} + 18926460 \, a^{6} b^{6} c^{6} d^{6} + 8958600 \, a^{7} b^{5} c^{5} d^{7} + 4614975 \, a^{8} b^{4} c^{4} d^{8} + 2092500 \, a^{9} b^{3} c^{3} d^{9} + 587250 \, a^{10} b^{2} c^{2} d^{10} + 202500 \, a^{11} b c d^{11} + 50625 \, a^{12} d^{12}}{a^{15} c^{13}}\right)^{\frac{1}{4}}}{d x + c}\right) + 4 \, {\left(32 \, a^{2} c^{2} + {\left(77 \, b^{2} c^{2} + 54 \, a b c d + 45 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(11 \, a b c^{2} + 9 \, a^{2} c d\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{4}} {\left(d x + c\right)}^{\frac{3}{4}}}{384 \, a^{3} c^{3} x^{3}}"," ",0,"-1/384*(12*a^3*c^3*x^3*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(1/4)*arctan(-((77*a^11*b^3*c^13 + 21*a^12*b^2*c^12*d + 15*a^13*b*c^11*d^2 + 15*a^14*c^10*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4)*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(3/4) - (a^11*c^10*d*x + a^11*c^11)*sqrt(((5929*b^6*c^6 + 3234*a*b^5*c^5*d + 2751*a^2*b^4*c^4*d^2 + 2940*a^3*b^3*c^3*d^3 + 855*a^4*b^2*c^2*d^4 + 450*a^5*b*c*d^5 + 225*a^6*d^6)*sqrt(b*x + a)*sqrt(d*x + c) + (a^8*c^6*d*x + a^8*c^7)*sqrt((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13)))/(d*x + c))*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(3/4))/(35153041*b^12*c^13 + 38348772*a*b^11*c^12*d + 43080114*a^2*b^10*c^11*d^2 + 52655988*a^3*b^9*c^10*d^3 + 36722511*a^4*b^8*c^9*d^4 + 27042120*a^5*b^7*c^8*d^5 + 18926460*a^6*b^6*c^7*d^6 + 8958600*a^7*b^5*c^6*d^7 + 4614975*a^8*b^4*c^5*d^8 + 2092500*a^9*b^3*c^4*d^9 + 587250*a^10*b^2*c^3*d^10 + 202500*a^11*b*c^2*d^11 + 50625*a^12*c*d^12 + (35153041*b^12*c^12*d + 38348772*a*b^11*c^11*d^2 + 43080114*a^2*b^10*c^10*d^3 + 52655988*a^3*b^9*c^9*d^4 + 36722511*a^4*b^8*c^8*d^5 + 27042120*a^5*b^7*c^7*d^6 + 18926460*a^6*b^6*c^6*d^7 + 8958600*a^7*b^5*c^5*d^8 + 4614975*a^8*b^4*c^4*d^9 + 2092500*a^9*b^3*c^3*d^10 + 587250*a^10*b^2*c^2*d^11 + 202500*a^11*b*c*d^12 + 50625*a^12*d^13)*x)) - 3*a^3*c^3*x^3*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(1/4)*log(((77*b^3*c^3 + 21*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 15*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) + (a^4*c^3*d*x + a^4*c^4)*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(1/4))/(d*x + c)) + 3*a^3*c^3*x^3*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(1/4)*log(((77*b^3*c^3 + 21*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 15*a^3*d^3)*(b*x + a)^(1/4)*(d*x + c)^(3/4) - (a^4*c^3*d*x + a^4*c^4)*((35153041*b^12*c^12 + 38348772*a*b^11*c^11*d + 43080114*a^2*b^10*c^10*d^2 + 52655988*a^3*b^9*c^9*d^3 + 36722511*a^4*b^8*c^8*d^4 + 27042120*a^5*b^7*c^7*d^5 + 18926460*a^6*b^6*c^6*d^6 + 8958600*a^7*b^5*c^5*d^7 + 4614975*a^8*b^4*c^4*d^8 + 2092500*a^9*b^3*c^3*d^9 + 587250*a^10*b^2*c^2*d^10 + 202500*a^11*b*c*d^11 + 50625*a^12*d^12)/(a^15*c^13))^(1/4))/(d*x + c)) + 4*(32*a^2*c^2 + (77*b^2*c^2 + 54*a*b*c*d + 45*a^2*d^2)*x^2 - 4*(11*a*b*c^2 + 9*a^2*c*d)*x)*(b*x + a)^(1/4)*(d*x + c)^(3/4))/(a^3*c^3*x^3)","B",0
908,1,478,0,1.291466," ","integrate((e*x)^(3/2)/(1-x)^(1/4)/(1+x)^(1/4),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + \frac{1}{4} \, \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \arctan\left(-\frac{e^{6} x^{2} - e^{6} + \sqrt{2} {\left(e^{6}\right)}^{\frac{3}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - \sqrt{2} {\left(e^{6}\right)}^{\frac{3}{4}} {\left(x^{2} - 1\right)} \sqrt{-\frac{e^{3} \sqrt{x + 1} x \sqrt{-x + 1} - \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - \sqrt{e^{6}} {\left(x^{2} - 1\right)}}{x^{2} - 1}}}{e^{6} x^{2} - e^{6}}\right) + \frac{1}{4} \, \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \arctan\left(\frac{e^{6} x^{2} - e^{6} - \sqrt{2} {\left(e^{6}\right)}^{\frac{3}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} + \sqrt{2} {\left(e^{6}\right)}^{\frac{3}{4}} {\left(x^{2} - 1\right)} \sqrt{-\frac{e^{3} \sqrt{x + 1} x \sqrt{-x + 1} + \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - \sqrt{e^{6}} {\left(x^{2} - 1\right)}}{x^{2} - 1}}}{e^{6} x^{2} - e^{6}}\right) + \frac{1}{16} \, \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \log\left(-\frac{e^{3} \sqrt{x + 1} x \sqrt{-x + 1} + \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - \sqrt{e^{6}} {\left(x^{2} - 1\right)}}{x^{2} - 1}\right) - \frac{1}{16} \, \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \log\left(-\frac{e^{3} \sqrt{x + 1} x \sqrt{-x + 1} - \sqrt{2} {\left(e^{6}\right)}^{\frac{1}{4}} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} - \sqrt{e^{6}} {\left(x^{2} - 1\right)}}{x^{2} - 1}\right)"," ",0,"-1/2*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) + 1/4*sqrt(2)*(e^6)^(1/4)*arctan(-(e^6*x^2 - e^6 + sqrt(2)*(e^6)^(3/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) - sqrt(2)*(e^6)^(3/4)*(x^2 - 1)*sqrt(-(e^3*sqrt(x + 1)*x*sqrt(-x + 1) - sqrt(2)*(e^6)^(1/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) - sqrt(e^6)*(x^2 - 1))/(x^2 - 1)))/(e^6*x^2 - e^6)) + 1/4*sqrt(2)*(e^6)^(1/4)*arctan((e^6*x^2 - e^6 - sqrt(2)*(e^6)^(3/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) + sqrt(2)*(e^6)^(3/4)*(x^2 - 1)*sqrt(-(e^3*sqrt(x + 1)*x*sqrt(-x + 1) + sqrt(2)*(e^6)^(1/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) - sqrt(e^6)*(x^2 - 1))/(x^2 - 1)))/(e^6*x^2 - e^6)) + 1/16*sqrt(2)*(e^6)^(1/4)*log(-(e^3*sqrt(x + 1)*x*sqrt(-x + 1) + sqrt(2)*(e^6)^(1/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) - sqrt(e^6)*(x^2 - 1))/(x^2 - 1)) - 1/16*sqrt(2)*(e^6)^(1/4)*log(-(e^3*sqrt(x + 1)*x*sqrt(-x + 1) - sqrt(2)*(e^6)^(1/4)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4) - sqrt(e^6)*(x^2 - 1))/(x^2 - 1))","B",0
909,1,455,0,1.593009," ","integrate(1/(1-x)^(1/4)/(e*x)^(1/2)/(1+x)^(1/4),x, algorithm=""fricas"")","\sqrt{2} \frac{1}{e^{2}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{3}{4}} - \sqrt{2} {\left(e x^{2} - e\right)} \sqrt{-\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{1}{4}} + e \sqrt{x + 1} x \sqrt{-x + 1} - {\left(e^{2} x^{2} - e^{2}\right)} \sqrt{\frac{1}{e^{2}}}}{x^{2} - 1}} \frac{1}{e^{2}}^{\frac{3}{4}} - x^{2} + 1}{x^{2} - 1}\right) + \sqrt{2} \frac{1}{e^{2}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{3}{4}} - \sqrt{2} {\left(e x^{2} - e\right)} \sqrt{\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{1}{4}} - e \sqrt{x + 1} x \sqrt{-x + 1} + {\left(e^{2} x^{2} - e^{2}\right)} \sqrt{\frac{1}{e^{2}}}}{x^{2} - 1}} \frac{1}{e^{2}}^{\frac{3}{4}} + x^{2} - 1}{x^{2} - 1}\right) + \frac{1}{4} \, \sqrt{2} \frac{1}{e^{2}}^{\frac{1}{4}} \log\left(-\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{1}{4}} + e \sqrt{x + 1} x \sqrt{-x + 1} - {\left(e^{2} x^{2} - e^{2}\right)} \sqrt{\frac{1}{e^{2}}}}{x^{2} - 1}\right) - \frac{1}{4} \, \sqrt{2} \frac{1}{e^{2}}^{\frac{1}{4}} \log\left(\frac{\sqrt{2} \sqrt{e x} e {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}} \frac{1}{e^{2}}^{\frac{1}{4}} - e \sqrt{x + 1} x \sqrt{-x + 1} + {\left(e^{2} x^{2} - e^{2}\right)} \sqrt{\frac{1}{e^{2}}}}{x^{2} - 1}\right)"," ",0,"sqrt(2)*(e^(-2))^(1/4)*arctan(-(sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(3/4) - sqrt(2)*(e*x^2 - e)*sqrt(-(sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(1/4) + e*sqrt(x + 1)*x*sqrt(-x + 1) - (e^2*x^2 - e^2)*sqrt(e^(-2)))/(x^2 - 1))*(e^(-2))^(3/4) - x^2 + 1)/(x^2 - 1)) + sqrt(2)*(e^(-2))^(1/4)*arctan(-(sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(3/4) - sqrt(2)*(e*x^2 - e)*sqrt((sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(1/4) - e*sqrt(x + 1)*x*sqrt(-x + 1) + (e^2*x^2 - e^2)*sqrt(e^(-2)))/(x^2 - 1))*(e^(-2))^(3/4) + x^2 - 1)/(x^2 - 1)) + 1/4*sqrt(2)*(e^(-2))^(1/4)*log(-(sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(1/4) + e*sqrt(x + 1)*x*sqrt(-x + 1) - (e^2*x^2 - e^2)*sqrt(e^(-2)))/(x^2 - 1)) - 1/4*sqrt(2)*(e^(-2))^(1/4)*log((sqrt(2)*sqrt(e*x)*e*(x + 1)^(3/4)*(-x + 1)^(3/4)*(e^(-2))^(1/4) - e*sqrt(x + 1)*x*sqrt(-x + 1) + (e^2*x^2 - e^2)*sqrt(e^(-2)))/(x^2 - 1))","B",0
910,1,25,0,1.393980," ","integrate(1/(1-x)^(1/4)/(e*x)^(5/2)/(1+x)^(1/4),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{3 \, e^{3} x^{2}}"," ",0,"-2/3*sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^3*x^2)","A",0
911,1,32,0,1.316420," ","integrate(1/(1-x)^(1/4)/(e*x)^(9/2)/(1+x)^(1/4),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x} {\left(4 \, x^{2} + 3\right)} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{21 \, e^{5} x^{4}}"," ",0,"-2/21*sqrt(e*x)*(4*x^2 + 3)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^5*x^4)","A",0
912,1,37,0,1.103533," ","integrate(1/(1-x)^(1/4)/(e*x)^(13/2)/(1+x)^(1/4),x, algorithm=""fricas"")","-\frac{2 \, {\left(32 \, x^{4} + 24 \, x^{2} + 21\right)} \sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{231 \, e^{7} x^{6}}"," ",0,"-2/231*(32*x^4 + 24*x^2 + 21)*sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^7*x^6)","A",0
913,0,0,0,0.962505," ","integrate((e*x)^(5/2)/(1-x)^(1/4)/(1+x)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} e^{2} {\left(x + 1\right)}^{\frac{3}{4}} x^{2} {\left(-x + 1\right)}^{\frac{3}{4}}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(e*x)*e^2*(x + 1)^(3/4)*x^2*(-x + 1)^(3/4)/(x^2 - 1), x)","F",0
914,0,0,0,0.894818," ","integrate((e*x)^(1/2)/(1-x)^(1/4)/(1+x)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(x^2 - 1), x)","F",0
915,0,0,0,1.140078," ","integrate(1/(1-x)^(1/4)/(e*x)^(3/2)/(1+x)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{e^{2} x^{4} - e^{2} x^{2}}, x\right)"," ",0,"integral(-sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^2*x^4 - e^2*x^2), x)","F",0
916,0,0,0,0.819468," ","integrate(1/(1-x)^(1/4)/(e*x)^(7/2)/(1+x)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{e^{4} x^{6} - e^{4} x^{4}}, x\right)"," ",0,"integral(-sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^4*x^6 - e^4*x^4), x)","F",0
917,0,0,0,1.051688," ","integrate(1/(1-x)^(1/4)/(e*x)^(11/2)/(1+x)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x} {\left(x + 1\right)}^{\frac{3}{4}} {\left(-x + 1\right)}^{\frac{3}{4}}}{e^{6} x^{8} - e^{6} x^{6}}, x\right)"," ",0,"integral(-sqrt(e*x)*(x + 1)^(3/4)*(-x + 1)^(3/4)/(e^6*x^8 - e^6*x^6), x)","F",0
918,1,251,0,1.139975," ","integrate(x^2*(b*x+a)^n*(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b c n + 8 \, a^{3} b c - 6 \, a^{4} d + {\left(b^{4} d n^{3} + 6 \, b^{4} d n^{2} + 11 \, b^{4} d n + 6 \, b^{4} d\right)} x^{4} + {\left(8 \, b^{4} c + {\left(b^{4} c + a b^{3} d\right)} n^{3} + {\left(7 \, b^{4} c + 3 \, a b^{3} d\right)} n^{2} + 2 \, {\left(7 \, b^{4} c + a b^{3} d\right)} n\right)} x^{3} + {\left(a b^{3} c n^{3} + {\left(5 \, a b^{3} c - 3 \, a^{2} b^{2} d\right)} n^{2} + {\left(4 \, a b^{3} c - 3 \, a^{2} b^{2} d\right)} n\right)} x^{2} - 2 \, {\left(a^{2} b^{2} c n^{2} + {\left(4 \, a^{2} b^{2} c - 3 \, a^{3} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"(2*a^3*b*c*n + 8*a^3*b*c - 6*a^4*d + (b^4*d*n^3 + 6*b^4*d*n^2 + 11*b^4*d*n + 6*b^4*d)*x^4 + (8*b^4*c + (b^4*c + a*b^3*d)*n^3 + (7*b^4*c + 3*a*b^3*d)*n^2 + 2*(7*b^4*c + a*b^3*d)*n)*x^3 + (a*b^3*c*n^3 + (5*a*b^3*c - 3*a^2*b^2*d)*n^2 + (4*a*b^3*c - 3*a^2*b^2*d)*n)*x^2 - 2*(a^2*b^2*c*n^2 + (4*a^2*b^2*c - 3*a^3*b*d)*n)*x)*(b*x + a)^n/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
919,1,159,0,1.282471," ","integrate(x*(b*x+a)^n*(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(a^{2} b c n + 3 \, a^{2} b c - 2 \, a^{3} d - {\left(b^{3} d n^{2} + 3 \, b^{3} d n + 2 \, b^{3} d\right)} x^{3} - {\left(3 \, b^{3} c + {\left(b^{3} c + a b^{2} d\right)} n^{2} + {\left(4 \, b^{3} c + a b^{2} d\right)} n\right)} x^{2} - {\left(a b^{2} c n^{2} + {\left(3 \, a b^{2} c - 2 \, a^{2} b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}}"," ",0,"-(a^2*b*c*n + 3*a^2*b*c - 2*a^3*d - (b^3*d*n^2 + 3*b^3*d*n + 2*b^3*d)*x^3 - (3*b^3*c + (b^3*c + a*b^2*d)*n^2 + (4*b^3*c + a*b^2*d)*n)*x^2 - (a*b^2*c*n^2 + (3*a*b^2*c - 2*a^2*b*d)*n)*x)*(b*x + a)^n/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","B",0
920,1,83,0,1.468822," ","integrate((b*x+a)^n*(d*x+c),x, algorithm=""fricas"")","\frac{{\left(a b c n + 2 \, a b c - a^{2} d + {\left(b^{2} d n + b^{2} d\right)} x^{2} + {\left(2 \, b^{2} c + {\left(b^{2} c + a b d\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{2} n^{2} + 3 \, b^{2} n + 2 \, b^{2}}"," ",0,"(a*b*c*n + 2*a*b*c - a^2*d + (b^2*d*n + b^2*d)*x^2 + (2*b^2*c + (b^2*c + a*b*d)*n)*x)*(b*x + a)^n/(b^2*n^2 + 3*b^2*n + 2*b^2)","A",0
921,0,0,0,1.401981," ","integrate((b*x+a)^n*(d*x+c)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d*x + c)*(b*x + a)^n/x, x)","F",0
922,0,0,0,1.480603," ","integrate((b*x+a)^n*(d*x+c)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(b x + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral((d*x + c)*(b*x + a)^n/x^2, x)","F",0
923,1,584,0,1.238470," ","integrate(x^2*(b*x+a)^n*(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{2} c^{2} n^{2} + 40 \, a^{3} b^{2} c^{2} - 60 \, a^{4} b c d + 24 \, a^{5} d^{2} + {\left(b^{5} d^{2} n^{4} + 10 \, b^{5} d^{2} n^{3} + 35 \, b^{5} d^{2} n^{2} + 50 \, b^{5} d^{2} n + 24 \, b^{5} d^{2}\right)} x^{5} + {\left(60 \, b^{5} c d + {\left(2 \, b^{5} c d + a b^{4} d^{2}\right)} n^{4} + 2 \, {\left(11 \, b^{5} c d + 3 \, a b^{4} d^{2}\right)} n^{3} + {\left(82 \, b^{5} c d + 11 \, a b^{4} d^{2}\right)} n^{2} + 2 \, {\left(61 \, b^{5} c d + 3 \, a b^{4} d^{2}\right)} n\right)} x^{4} + {\left(40 \, b^{5} c^{2} + {\left(b^{5} c^{2} + 2 \, a b^{4} c d\right)} n^{4} + 4 \, {\left(3 \, b^{5} c^{2} + 4 \, a b^{4} c d - a^{2} b^{3} d^{2}\right)} n^{3} + {\left(49 \, b^{5} c^{2} + 34 \, a b^{4} c d - 12 \, a^{2} b^{3} d^{2}\right)} n^{2} + 2 \, {\left(39 \, b^{5} c^{2} + 10 \, a b^{4} c d - 4 \, a^{2} b^{3} d^{2}\right)} n\right)} x^{3} + {\left(a b^{4} c^{2} n^{4} + 2 \, {\left(5 \, a b^{4} c^{2} - 3 \, a^{2} b^{3} c d\right)} n^{3} + {\left(29 \, a b^{4} c^{2} - 36 \, a^{2} b^{3} c d + 12 \, a^{3} b^{2} d^{2}\right)} n^{2} + 2 \, {\left(10 \, a b^{4} c^{2} - 15 \, a^{2} b^{3} c d + 6 \, a^{3} b^{2} d^{2}\right)} n\right)} x^{2} + 6 \, {\left(3 \, a^{3} b^{2} c^{2} - 2 \, a^{4} b c d\right)} n - 2 \, {\left(a^{2} b^{3} c^{2} n^{3} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d\right)} n^{2} + 2 \, {\left(10 \, a^{2} b^{3} c^{2} - 15 \, a^{3} b^{2} c d + 6 \, a^{4} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"(2*a^3*b^2*c^2*n^2 + 40*a^3*b^2*c^2 - 60*a^4*b*c*d + 24*a^5*d^2 + (b^5*d^2*n^4 + 10*b^5*d^2*n^3 + 35*b^5*d^2*n^2 + 50*b^5*d^2*n + 24*b^5*d^2)*x^5 + (60*b^5*c*d + (2*b^5*c*d + a*b^4*d^2)*n^4 + 2*(11*b^5*c*d + 3*a*b^4*d^2)*n^3 + (82*b^5*c*d + 11*a*b^4*d^2)*n^2 + 2*(61*b^5*c*d + 3*a*b^4*d^2)*n)*x^4 + (40*b^5*c^2 + (b^5*c^2 + 2*a*b^4*c*d)*n^4 + 4*(3*b^5*c^2 + 4*a*b^4*c*d - a^2*b^3*d^2)*n^3 + (49*b^5*c^2 + 34*a*b^4*c*d - 12*a^2*b^3*d^2)*n^2 + 2*(39*b^5*c^2 + 10*a*b^4*c*d - 4*a^2*b^3*d^2)*n)*x^3 + (a*b^4*c^2*n^4 + 2*(5*a*b^4*c^2 - 3*a^2*b^3*c*d)*n^3 + (29*a*b^4*c^2 - 36*a^2*b^3*c*d + 12*a^3*b^2*d^2)*n^2 + 2*(10*a*b^4*c^2 - 15*a^2*b^3*c*d + 6*a^3*b^2*d^2)*n)*x^2 + 6*(3*a^3*b^2*c^2 - 2*a^4*b*c*d)*n - 2*(a^2*b^3*c^2*n^3 + 3*(3*a^2*b^3*c^2 - 2*a^3*b^2*c*d)*n^2 + 2*(10*a^2*b^3*c^2 - 15*a^3*b^2*c*d + 6*a^4*b*d^2)*n)*x)*(b*x + a)^n/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
924,1,393,0,1.496107," ","integrate(x*(b*x+a)^n*(d*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{2} c^{2} n^{2} + 12 \, a^{2} b^{2} c^{2} - 16 \, a^{3} b c d + 6 \, a^{4} d^{2} - {\left(b^{4} d^{2} n^{3} + 6 \, b^{4} d^{2} n^{2} + 11 \, b^{4} d^{2} n + 6 \, b^{4} d^{2}\right)} x^{4} - {\left(16 \, b^{4} c d + {\left(2 \, b^{4} c d + a b^{3} d^{2}\right)} n^{3} + {\left(14 \, b^{4} c d + 3 \, a b^{3} d^{2}\right)} n^{2} + 2 \, {\left(14 \, b^{4} c d + a b^{3} d^{2}\right)} n\right)} x^{3} - {\left(12 \, b^{4} c^{2} + {\left(b^{4} c^{2} + 2 \, a b^{3} c d\right)} n^{3} + {\left(8 \, b^{4} c^{2} + 10 \, a b^{3} c d - 3 \, a^{2} b^{2} d^{2}\right)} n^{2} + {\left(19 \, b^{4} c^{2} + 8 \, a b^{3} c d - 3 \, a^{2} b^{2} d^{2}\right)} n\right)} x^{2} + {\left(7 \, a^{2} b^{2} c^{2} - 4 \, a^{3} b c d\right)} n - {\left(a b^{3} c^{2} n^{3} + {\left(7 \, a b^{3} c^{2} - 4 \, a^{2} b^{2} c d\right)} n^{2} + 2 \, {\left(6 \, a b^{3} c^{2} - 8 \, a^{2} b^{2} c d + 3 \, a^{3} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"-(a^2*b^2*c^2*n^2 + 12*a^2*b^2*c^2 - 16*a^3*b*c*d + 6*a^4*d^2 - (b^4*d^2*n^3 + 6*b^4*d^2*n^2 + 11*b^4*d^2*n + 6*b^4*d^2)*x^4 - (16*b^4*c*d + (2*b^4*c*d + a*b^3*d^2)*n^3 + (14*b^4*c*d + 3*a*b^3*d^2)*n^2 + 2*(14*b^4*c*d + a*b^3*d^2)*n)*x^3 - (12*b^4*c^2 + (b^4*c^2 + 2*a*b^3*c*d)*n^3 + (8*b^4*c^2 + 10*a*b^3*c*d - 3*a^2*b^2*d^2)*n^2 + (19*b^4*c^2 + 8*a*b^3*c*d - 3*a^2*b^2*d^2)*n)*x^2 + (7*a^2*b^2*c^2 - 4*a^3*b*c*d)*n - (a*b^3*c^2*n^3 + (7*a*b^3*c^2 - 4*a^2*b^2*c*d)*n^2 + 2*(6*a*b^3*c^2 - 8*a^2*b^2*c*d + 3*a^3*b*d^2)*n)*x)*(b*x + a)^n/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
925,1,235,0,1.257466," ","integrate((b*x+a)^n*(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(a b^{2} c^{2} n^{2} + 6 \, a b^{2} c^{2} - 6 \, a^{2} b c d + 2 \, a^{3} d^{2} + {\left(b^{3} d^{2} n^{2} + 3 \, b^{3} d^{2} n + 2 \, b^{3} d^{2}\right)} x^{3} + {\left(6 \, b^{3} c d + {\left(2 \, b^{3} c d + a b^{2} d^{2}\right)} n^{2} + {\left(8 \, b^{3} c d + a b^{2} d^{2}\right)} n\right)} x^{2} + {\left(5 \, a b^{2} c^{2} - 2 \, a^{2} b c d\right)} n + {\left(6 \, b^{3} c^{2} + {\left(b^{3} c^{2} + 2 \, a b^{2} c d\right)} n^{2} + {\left(5 \, b^{3} c^{2} + 6 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}}"," ",0,"(a*b^2*c^2*n^2 + 6*a*b^2*c^2 - 6*a^2*b*c*d + 2*a^3*d^2 + (b^3*d^2*n^2 + 3*b^3*d^2*n + 2*b^3*d^2)*x^3 + (6*b^3*c*d + (2*b^3*c*d + a*b^2*d^2)*n^2 + (8*b^3*c*d + a*b^2*d^2)*n)*x^2 + (5*a*b^2*c^2 - 2*a^2*b*c*d)*n + (6*b^3*c^2 + (b^3*c^2 + 2*a*b^2*c*d)*n^2 + (5*b^3*c^2 + 6*a*b^2*c*d - 2*a^2*b*d^2)*n)*x)*(b*x + a)^n/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","B",0
926,0,0,0,1.265676," ","integrate((b*x+a)^n*(d*x+c)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*(b*x + a)^n/x, x)","F",0
927,0,0,0,1.422611," ","integrate((b*x+a)^n*(d*x+c)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} {\left(b x + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*(b*x + a)^n/x^2, x)","F",0
928,0,0,0,1.458645," ","integrate((b*x+a)^n*(d*x+c)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} {\left(b x + a\right)}^{n}}{x^{3}}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*(b*x + a)^n/x^3, x)","F",0
929,0,0,0,1.339584," ","integrate((b*x+a)^n*(d*x+c)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} {\left(b x + a\right)}^{n}}{x^{4}}, x\right)"," ",0,"integral((d^2*x^2 + 2*c*d*x + c^2)*(b*x + a)^n/x^4, x)","F",0
930,1,1075,0,1.482077," ","integrate(x^2*(b*x+a)^n*(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} b^{3} c^{3} n^{3} + 240 \, a^{3} b^{3} c^{3} - 540 \, a^{4} b^{2} c^{2} d + 432 \, a^{5} b c d^{2} - 120 \, a^{6} d^{3} + {\left(b^{6} d^{3} n^{5} + 15 \, b^{6} d^{3} n^{4} + 85 \, b^{6} d^{3} n^{3} + 225 \, b^{6} d^{3} n^{2} + 274 \, b^{6} d^{3} n + 120 \, b^{6} d^{3}\right)} x^{6} + {\left(432 \, b^{6} c d^{2} + {\left(3 \, b^{6} c d^{2} + a b^{5} d^{3}\right)} n^{5} + 2 \, {\left(24 \, b^{6} c d^{2} + 5 \, a b^{5} d^{3}\right)} n^{4} + 5 \, {\left(57 \, b^{6} c d^{2} + 7 \, a b^{5} d^{3}\right)} n^{3} + 10 \, {\left(78 \, b^{6} c d^{2} + 5 \, a b^{5} d^{3}\right)} n^{2} + 12 \, {\left(81 \, b^{6} c d^{2} + 2 \, a b^{5} d^{3}\right)} n\right)} x^{5} + {\left(540 \, b^{6} c^{2} d + 3 \, {\left(b^{6} c^{2} d + a b^{5} c d^{2}\right)} n^{5} + {\left(51 \, b^{6} c^{2} d + 36 \, a b^{5} c d^{2} - 5 \, a^{2} b^{4} d^{3}\right)} n^{4} + 3 \, {\left(107 \, b^{6} c^{2} d + 47 \, a b^{5} c d^{2} - 10 \, a^{2} b^{4} d^{3}\right)} n^{3} + {\left(921 \, b^{6} c^{2} d + 216 \, a b^{5} c d^{2} - 55 \, a^{2} b^{4} d^{3}\right)} n^{2} + 6 \, {\left(198 \, b^{6} c^{2} d + 18 \, a b^{5} c d^{2} - 5 \, a^{2} b^{4} d^{3}\right)} n\right)} x^{4} + {\left(240 \, b^{6} c^{3} + {\left(b^{6} c^{3} + 3 \, a b^{5} c^{2} d\right)} n^{5} + 6 \, {\left(3 \, b^{6} c^{3} + 7 \, a b^{5} c^{2} d - 2 \, a^{2} b^{4} c d^{2}\right)} n^{4} + {\left(121 \, b^{6} c^{3} + 195 \, a b^{5} c^{2} d - 108 \, a^{2} b^{4} c d^{2} + 20 \, a^{3} b^{3} d^{3}\right)} n^{3} + 12 \, {\left(31 \, b^{6} c^{3} + 28 \, a b^{5} c^{2} d - 20 \, a^{2} b^{4} c d^{2} + 5 \, a^{3} b^{3} d^{3}\right)} n^{2} + 4 \, {\left(127 \, b^{6} c^{3} + 45 \, a b^{5} c^{2} d - 36 \, a^{2} b^{4} c d^{2} + 10 \, a^{3} b^{3} d^{3}\right)} n\right)} x^{3} + 6 \, {\left(5 \, a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d\right)} n^{2} + {\left(a b^{5} c^{3} n^{5} + {\left(16 \, a b^{5} c^{3} - 9 \, a^{2} b^{4} c^{2} d\right)} n^{4} + {\left(89 \, a b^{5} c^{3} - 108 \, a^{2} b^{4} c^{2} d + 36 \, a^{3} b^{3} c d^{2}\right)} n^{3} + {\left(194 \, a b^{5} c^{3} - 369 \, a^{2} b^{4} c^{2} d + 252 \, a^{3} b^{3} c d^{2} - 60 \, a^{4} b^{2} d^{3}\right)} n^{2} + 6 \, {\left(20 \, a b^{5} c^{3} - 45 \, a^{2} b^{4} c^{2} d + 36 \, a^{3} b^{3} c d^{2} - 10 \, a^{4} b^{2} d^{3}\right)} n\right)} x^{2} + 2 \, {\left(74 \, a^{3} b^{3} c^{3} - 99 \, a^{4} b^{2} c^{2} d + 36 \, a^{5} b c d^{2}\right)} n - 2 \, {\left(a^{2} b^{4} c^{3} n^{4} + 3 \, {\left(5 \, a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d\right)} n^{3} + {\left(74 \, a^{2} b^{4} c^{3} - 99 \, a^{3} b^{3} c^{2} d + 36 \, a^{4} b^{2} c d^{2}\right)} n^{2} + 6 \, {\left(20 \, a^{2} b^{4} c^{3} - 45 \, a^{3} b^{3} c^{2} d + 36 \, a^{4} b^{2} c d^{2} - 10 \, a^{5} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{6} n^{6} + 21 \, b^{6} n^{5} + 175 \, b^{6} n^{4} + 735 \, b^{6} n^{3} + 1624 \, b^{6} n^{2} + 1764 \, b^{6} n + 720 \, b^{6}}"," ",0,"(2*a^3*b^3*c^3*n^3 + 240*a^3*b^3*c^3 - 540*a^4*b^2*c^2*d + 432*a^5*b*c*d^2 - 120*a^6*d^3 + (b^6*d^3*n^5 + 15*b^6*d^3*n^4 + 85*b^6*d^3*n^3 + 225*b^6*d^3*n^2 + 274*b^6*d^3*n + 120*b^6*d^3)*x^6 + (432*b^6*c*d^2 + (3*b^6*c*d^2 + a*b^5*d^3)*n^5 + 2*(24*b^6*c*d^2 + 5*a*b^5*d^3)*n^4 + 5*(57*b^6*c*d^2 + 7*a*b^5*d^3)*n^3 + 10*(78*b^6*c*d^2 + 5*a*b^5*d^3)*n^2 + 12*(81*b^6*c*d^2 + 2*a*b^5*d^3)*n)*x^5 + (540*b^6*c^2*d + 3*(b^6*c^2*d + a*b^5*c*d^2)*n^5 + (51*b^6*c^2*d + 36*a*b^5*c*d^2 - 5*a^2*b^4*d^3)*n^4 + 3*(107*b^6*c^2*d + 47*a*b^5*c*d^2 - 10*a^2*b^4*d^3)*n^3 + (921*b^6*c^2*d + 216*a*b^5*c*d^2 - 55*a^2*b^4*d^3)*n^2 + 6*(198*b^6*c^2*d + 18*a*b^5*c*d^2 - 5*a^2*b^4*d^3)*n)*x^4 + (240*b^6*c^3 + (b^6*c^3 + 3*a*b^5*c^2*d)*n^5 + 6*(3*b^6*c^3 + 7*a*b^5*c^2*d - 2*a^2*b^4*c*d^2)*n^4 + (121*b^6*c^3 + 195*a*b^5*c^2*d - 108*a^2*b^4*c*d^2 + 20*a^3*b^3*d^3)*n^3 + 12*(31*b^6*c^3 + 28*a*b^5*c^2*d - 20*a^2*b^4*c*d^2 + 5*a^3*b^3*d^3)*n^2 + 4*(127*b^6*c^3 + 45*a*b^5*c^2*d - 36*a^2*b^4*c*d^2 + 10*a^3*b^3*d^3)*n)*x^3 + 6*(5*a^3*b^3*c^3 - 3*a^4*b^2*c^2*d)*n^2 + (a*b^5*c^3*n^5 + (16*a*b^5*c^3 - 9*a^2*b^4*c^2*d)*n^4 + (89*a*b^5*c^3 - 108*a^2*b^4*c^2*d + 36*a^3*b^3*c*d^2)*n^3 + (194*a*b^5*c^3 - 369*a^2*b^4*c^2*d + 252*a^3*b^3*c*d^2 - 60*a^4*b^2*d^3)*n^2 + 6*(20*a*b^5*c^3 - 45*a^2*b^4*c^2*d + 36*a^3*b^3*c*d^2 - 10*a^4*b^2*d^3)*n)*x^2 + 2*(74*a^3*b^3*c^3 - 99*a^4*b^2*c^2*d + 36*a^5*b*c*d^2)*n - 2*(a^2*b^4*c^3*n^4 + 3*(5*a^2*b^4*c^3 - 3*a^3*b^3*c^2*d)*n^3 + (74*a^2*b^4*c^3 - 99*a^3*b^3*c^2*d + 36*a^4*b^2*c*d^2)*n^2 + 6*(20*a^2*b^4*c^3 - 45*a^3*b^3*c^2*d + 36*a^4*b^2*c*d^2 - 10*a^5*b*d^3)*n)*x)*(b*x + a)^n/(b^6*n^6 + 21*b^6*n^5 + 175*b^6*n^4 + 735*b^6*n^3 + 1624*b^6*n^2 + 1764*b^6*n + 720*b^6)","B",0
931,1,766,0,1.451416," ","integrate(x*(b*x+a)^n*(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} b^{3} c^{3} n^{3} + 60 \, a^{2} b^{3} c^{3} - 120 \, a^{3} b^{2} c^{2} d + 90 \, a^{4} b c d^{2} - 24 \, a^{5} d^{3} - {\left(b^{5} d^{3} n^{4} + 10 \, b^{5} d^{3} n^{3} + 35 \, b^{5} d^{3} n^{2} + 50 \, b^{5} d^{3} n + 24 \, b^{5} d^{3}\right)} x^{5} - {\left(90 \, b^{5} c d^{2} + {\left(3 \, b^{5} c d^{2} + a b^{4} d^{3}\right)} n^{4} + 3 \, {\left(11 \, b^{5} c d^{2} + 2 \, a b^{4} d^{3}\right)} n^{3} + {\left(123 \, b^{5} c d^{2} + 11 \, a b^{4} d^{3}\right)} n^{2} + 3 \, {\left(61 \, b^{5} c d^{2} + 2 \, a b^{4} d^{3}\right)} n\right)} x^{4} - {\left(120 \, b^{5} c^{2} d + 3 \, {\left(b^{5} c^{2} d + a b^{4} c d^{2}\right)} n^{4} + 4 \, {\left(9 \, b^{5} c^{2} d + 6 \, a b^{4} c d^{2} - a^{2} b^{3} d^{3}\right)} n^{3} + 3 \, {\left(49 \, b^{5} c^{2} d + 17 \, a b^{4} c d^{2} - 4 \, a^{2} b^{3} d^{3}\right)} n^{2} + 2 \, {\left(117 \, b^{5} c^{2} d + 15 \, a b^{4} c d^{2} - 4 \, a^{2} b^{3} d^{3}\right)} n\right)} x^{3} + 6 \, {\left(2 \, a^{2} b^{3} c^{3} - a^{3} b^{2} c^{2} d\right)} n^{2} - {\left(60 \, b^{5} c^{3} + {\left(b^{5} c^{3} + 3 \, a b^{4} c^{2} d\right)} n^{4} + {\left(13 \, b^{5} c^{3} + 30 \, a b^{4} c^{2} d - 9 \, a^{2} b^{3} c d^{2}\right)} n^{3} + {\left(59 \, b^{5} c^{3} + 87 \, a b^{4} c^{2} d - 54 \, a^{2} b^{3} c d^{2} + 12 \, a^{3} b^{2} d^{3}\right)} n^{2} + {\left(107 \, b^{5} c^{3} + 60 \, a b^{4} c^{2} d - 45 \, a^{2} b^{3} c d^{2} + 12 \, a^{3} b^{2} d^{3}\right)} n\right)} x^{2} + {\left(47 \, a^{2} b^{3} c^{3} - 54 \, a^{3} b^{2} c^{2} d + 18 \, a^{4} b c d^{2}\right)} n - {\left(a b^{4} c^{3} n^{4} + 6 \, {\left(2 \, a b^{4} c^{3} - a^{2} b^{3} c^{2} d\right)} n^{3} + {\left(47 \, a b^{4} c^{3} - 54 \, a^{2} b^{3} c^{2} d + 18 \, a^{3} b^{2} c d^{2}\right)} n^{2} + 6 \, {\left(10 \, a b^{4} c^{3} - 20 \, a^{2} b^{3} c^{2} d + 15 \, a^{3} b^{2} c d^{2} - 4 \, a^{4} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"-(a^2*b^3*c^3*n^3 + 60*a^2*b^3*c^3 - 120*a^3*b^2*c^2*d + 90*a^4*b*c*d^2 - 24*a^5*d^3 - (b^5*d^3*n^4 + 10*b^5*d^3*n^3 + 35*b^5*d^3*n^2 + 50*b^5*d^3*n + 24*b^5*d^3)*x^5 - (90*b^5*c*d^2 + (3*b^5*c*d^2 + a*b^4*d^3)*n^4 + 3*(11*b^5*c*d^2 + 2*a*b^4*d^3)*n^3 + (123*b^5*c*d^2 + 11*a*b^4*d^3)*n^2 + 3*(61*b^5*c*d^2 + 2*a*b^4*d^3)*n)*x^4 - (120*b^5*c^2*d + 3*(b^5*c^2*d + a*b^4*c*d^2)*n^4 + 4*(9*b^5*c^2*d + 6*a*b^4*c*d^2 - a^2*b^3*d^3)*n^3 + 3*(49*b^5*c^2*d + 17*a*b^4*c*d^2 - 4*a^2*b^3*d^3)*n^2 + 2*(117*b^5*c^2*d + 15*a*b^4*c*d^2 - 4*a^2*b^3*d^3)*n)*x^3 + 6*(2*a^2*b^3*c^3 - a^3*b^2*c^2*d)*n^2 - (60*b^5*c^3 + (b^5*c^3 + 3*a*b^4*c^2*d)*n^4 + (13*b^5*c^3 + 30*a*b^4*c^2*d - 9*a^2*b^3*c*d^2)*n^3 + (59*b^5*c^3 + 87*a*b^4*c^2*d - 54*a^2*b^3*c*d^2 + 12*a^3*b^2*d^3)*n^2 + (107*b^5*c^3 + 60*a*b^4*c^2*d - 45*a^2*b^3*c*d^2 + 12*a^3*b^2*d^3)*n)*x^2 + (47*a^2*b^3*c^3 - 54*a^3*b^2*c^2*d + 18*a^4*b*c*d^2)*n - (a*b^4*c^3*n^4 + 6*(2*a*b^4*c^3 - a^2*b^3*c^2*d)*n^3 + (47*a*b^4*c^3 - 54*a^2*b^3*c^2*d + 18*a^3*b^2*c*d^2)*n^2 + 6*(10*a*b^4*c^3 - 20*a^2*b^3*c^2*d + 15*a^3*b^2*c*d^2 - 4*a^4*b*d^3)*n)*x)*(b*x + a)^n/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
932,1,497,0,1.930505," ","integrate((b*x+a)^n*(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(a b^{3} c^{3} n^{3} + 24 \, a b^{3} c^{3} - 36 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} - 6 \, a^{4} d^{3} + {\left(b^{4} d^{3} n^{3} + 6 \, b^{4} d^{3} n^{2} + 11 \, b^{4} d^{3} n + 6 \, b^{4} d^{3}\right)} x^{4} + {\left(24 \, b^{4} c d^{2} + {\left(3 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} n^{3} + 3 \, {\left(7 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} n^{2} + 2 \, {\left(21 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} n\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c^{3} - a^{2} b^{2} c^{2} d\right)} n^{2} + 3 \, {\left(12 \, b^{4} c^{2} d + {\left(b^{4} c^{2} d + a b^{3} c d^{2}\right)} n^{3} + {\left(8 \, b^{4} c^{2} d + 5 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} n^{2} + {\left(19 \, b^{4} c^{2} d + 4 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} n\right)} x^{2} + {\left(26 \, a b^{3} c^{3} - 21 \, a^{2} b^{2} c^{2} d + 6 \, a^{3} b c d^{2}\right)} n + {\left(24 \, b^{4} c^{3} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2} d\right)} n^{3} + 3 \, {\left(3 \, b^{4} c^{3} + 7 \, a b^{3} c^{2} d - 2 \, a^{2} b^{2} c d^{2}\right)} n^{2} + 2 \, {\left(13 \, b^{4} c^{3} + 18 \, a b^{3} c^{2} d - 12 \, a^{2} b^{2} c d^{2} + 3 \, a^{3} b d^{3}\right)} n\right)} x\right)} {\left(b x + a\right)}^{n}}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"(a*b^3*c^3*n^3 + 24*a*b^3*c^3 - 36*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 - 6*a^4*d^3 + (b^4*d^3*n^3 + 6*b^4*d^3*n^2 + 11*b^4*d^3*n + 6*b^4*d^3)*x^4 + (24*b^4*c*d^2 + (3*b^4*c*d^2 + a*b^3*d^3)*n^3 + 3*(7*b^4*c*d^2 + a*b^3*d^3)*n^2 + 2*(21*b^4*c*d^2 + a*b^3*d^3)*n)*x^3 + 3*(3*a*b^3*c^3 - a^2*b^2*c^2*d)*n^2 + 3*(12*b^4*c^2*d + (b^4*c^2*d + a*b^3*c*d^2)*n^3 + (8*b^4*c^2*d + 5*a*b^3*c*d^2 - a^2*b^2*d^3)*n^2 + (19*b^4*c^2*d + 4*a*b^3*c*d^2 - a^2*b^2*d^3)*n)*x^2 + (26*a*b^3*c^3 - 21*a^2*b^2*c^2*d + 6*a^3*b*c*d^2)*n + (24*b^4*c^3 + (b^4*c^3 + 3*a*b^3*c^2*d)*n^3 + 3*(3*b^4*c^3 + 7*a*b^3*c^2*d - 2*a^2*b^2*c*d^2)*n^2 + 2*(13*b^4*c^3 + 18*a*b^3*c^2*d - 12*a^2*b^2*c*d^2 + 3*a^3*b*d^3)*n)*x)*(b*x + a)^n/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
933,0,0,0,1.123456," ","integrate((b*x+a)^n*(d*x+c)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} {\left(b x + a\right)}^{n}}{x}, x\right)"," ",0,"integral((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*(b*x + a)^n/x, x)","F",0
934,0,0,0,1.319019," ","integrate((b*x+a)^n*(d*x+c)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} {\left(b x + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*(b*x + a)^n/x^2, x)","F",0
935,0,0,0,1.516150," ","integrate((b*x+a)^n*(d*x+c)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} {\left(b x + a\right)}^{n}}{x^{3}}, x\right)"," ",0,"integral((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*(b*x + a)^n/x^3, x)","F",0
936,1,29,0,1.601195," ","integrate(x^(1+2*n)*(b*x+a)^n*(3*b*x+2*a),x, algorithm=""fricas"")","\frac{{\left(b x^{2} + a x\right)} {\left(b x + a\right)}^{n} x^{2 \, n + 1}}{n + 1}"," ",0,"(b*x^2 + a*x)*(b*x + a)^n*x^(2*n + 1)/(n + 1)","A",0
937,0,0,0,0.861618," ","integrate(x^2*(b*x+a)^n/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x^{2}}{d x + c}, x\right)"," ",0,"integral((b*x + a)^n*x^2/(d*x + c), x)","F",0
938,0,0,0,1.423145," ","integrate(x*(b*x+a)^n/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x}{d x + c}, x\right)"," ",0,"integral((b*x + a)^n*x/(d*x + c), x)","F",0
939,0,0,0,1.294661," ","integrate((b*x+a)^n/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d x + c}, x\right)"," ",0,"integral((b*x + a)^n/(d*x + c), x)","F",0
940,0,0,0,2.041307," ","integrate((b*x+a)^n/x/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d x^{2} + c x}, x\right)"," ",0,"integral((b*x + a)^n/(d*x^2 + c*x), x)","F",0
941,0,0,0,0.943674," ","integrate((b*x+a)^n/x^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d x^{3} + c x^{2}}, x\right)"," ",0,"integral((b*x + a)^n/(d*x^3 + c*x^2), x)","F",0
942,0,0,0,1.294552," ","integrate(x^3*(b*x+a)^n/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*x + a)^n*x^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
943,0,0,0,1.411455," ","integrate(x^2*(b*x+a)^n/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*x + a)^n*x^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
944,0,0,0,1.579692," ","integrate(x*(b*x+a)^n/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*x + a)^n*x/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
945,0,0,0,1.425315," ","integrate((b*x+a)^n/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*x + a)^n/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
946,0,0,0,1.648353," ","integrate((b*x+a)^n/x/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d^{2} x^{3} + 2 \, c d x^{2} + c^{2} x}, x\right)"," ",0,"integral((b*x + a)^n/(d^2*x^3 + 2*c*d*x^2 + c^2*x), x)","F",0
947,0,0,0,1.466688," ","integrate((b*x+a)^n/x^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{d^{2} x^{4} + 2 \, c d x^{3} + c^{2} x^{2}}, x\right)"," ",0,"integral((b*x + a)^n/(d^2*x^4 + 2*c*d*x^3 + c^2*x^2), x)","F",0
948,0,0,0,0.956163," ","integrate((b*x)^(5/2)*(d*x+c)^n*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} f^{2} x^{4} + 2 \, b^{2} e f x^{3} + b^{2} e^{2} x^{2}\right)} \sqrt{b x} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((b^2*f^2*x^4 + 2*b^2*e*f*x^3 + b^2*e^2*x^2)*sqrt(b*x)*(d*x + c)^n, x)","F",0
949,0,0,0,1.099629," ","integrate((b*x)^(5/2)*(d*x+c)^n*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} f x^{3} + b^{2} e x^{2}\right)} \sqrt{b x} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((b^2*f*x^3 + b^2*e*x^2)*sqrt(b*x)*(d*x + c)^n, x)","F",0
950,0,0,0,1.468838," ","integrate((b*x)^(5/2)*(d*x+c)^n/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x} {\left(d x + c\right)}^{n} b^{2} x^{2}}{f x + e}, x\right)"," ",0,"integral(sqrt(b*x)*(d*x + c)^n*b^2*x^2/(f*x + e), x)","F",0
951,0,0,0,1.262371," ","integrate((b*x)^(5/2)*(d*x+c)^n/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x} {\left(d x + c\right)}^{n} b^{2} x^{2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sqrt(b*x)*(d*x + c)^n*b^2*x^2/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
952,0,0,0,1.315475," ","integrate((b*x)^m*(d*x+c)^n*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} \left(b x\right)^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x)^m*(d*x + c)^n, x)","F",0
953,0,0,0,1.569708," ","integrate((b*x)^m*(d*x+c)^n*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} \left(b x\right)^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((f*x + e)*(b*x)^m*(d*x + c)^n, x)","F",0
954,0,0,0,0.898797," ","integrate((b*x)^m*(d*x+c)^n/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b x\right)^{m} {\left(d x + c\right)}^{n}}{f x + e}, x\right)"," ",0,"integral((b*x)^m*(d*x + c)^n/(f*x + e), x)","F",0
955,0,0,0,1.552165," ","integrate((b*x)^m*(d*x+c)^n/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(b x\right)^{m} {\left(d x + c\right)}^{n}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x)^m*(d*x + c)^n/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
956,0,0,0,1.843943," ","integrate((b*x)^m*(d*x+c)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(b x\right)^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
957,0,0,0,1.308349," ","integrate((e*x)^m*(-b*x+a)^(2+n)*(b*x+a)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{n} {\left(-b x + a\right)}^{n + 2} \left(e x\right)^{m}, x\right)"," ",0,"integral((b*x + a)^n*(-b*x + a)^(n + 2)*(e*x)^m, x)","F",0
958,0,0,0,0.987745," ","integrate(x^2*(b*x+a)^n*(d*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{n} {\left(d x + c\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*x + a)^n*(d*x + c)^p*x^2, x)","F",0
959,0,0,0,1.478093," ","integrate(x*(b*x+a)^n*(d*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{n} {\left(d x + c\right)}^{p} x, x\right)"," ",0,"integral((b*x + a)^n*(d*x + c)^p*x, x)","F",0
960,0,0,0,1.508662," ","integrate((b*x+a)^n*(d*x+c)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{n} {\left(d x + c\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^n*(d*x + c)^p, x)","F",0
961,0,0,0,1.717855," ","integrate((b*x+a)^n*(d*x+c)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} {\left(d x + c\right)}^{p}}{x}, x\right)"," ",0,"integral((b*x + a)^n*(d*x + c)^p/x, x)","F",0
962,0,0,0,1.342718," ","integrate((b*x+a)^n*(d*x+c)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} {\left(d x + c\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*x + a)^n*(d*x + c)^p/x^2, x)","F",0
963,0,0,0,2.342487," ","integrate((b*x)^(3/2)*(d*x+c)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p} b x, x\right)"," ",0,"integral(sqrt(b*x)*(d*x + c)^n*(f*x + e)^p*b*x, x)","F",0
964,0,0,0,1.218613," ","integrate((b*x)^(1/2)*(d*x+c)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral(sqrt(b*x)*(d*x + c)^n*(f*x + e)^p, x)","F",0
965,0,0,0,1.292743," ","integrate((d*x+c)^n*(f*x+e)^p/(b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}}{b x}, x\right)"," ",0,"integral(sqrt(b*x)*(d*x + c)^n*(f*x + e)^p/(b*x), x)","F",0
966,0,0,0,0.969599," ","integrate((b*x)^m*(d*x+pi)^n*(f*x+E)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\pi + d x\right)}^{n} \left(b x\right)^{m} {\left(f x + E\right)}^{p}, x\right)"," ",0,"integral((pi + d*x)^n*(b*x)^m*(f*x + E)^p, x)","F",0
967,0,0,0,1.157920," ","integrate((b*x)^m*(d*x+pi)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(\pi + d x\right)}^{n} \left(b x\right)^{m} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((pi + d*x)^n*(b*x)^m*(f*x + e)^p, x)","F",0
968,0,0,0,0.973857," ","integrate((b*x)^(5/2)*(d*x+pi)^n*(f*x+E)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x} {\left(\pi + d x\right)}^{n} {\left(f x + E\right)}^{p} b^{2} x^{2}, x\right)"," ",0,"integral(sqrt(b*x)*(pi + d*x)^n*(f*x + E)^p*b^2*x^2, x)","F",0
969,0,0,0,1.100551," ","integrate((b*x)^(5/2)*(d*x+pi)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x} {\left(\pi + d x\right)}^{n} {\left(f x + e\right)}^{p} b^{2} x^{2}, x\right)"," ",0,"integral(sqrt(b*x)*(pi + d*x)^n*(f*x + e)^p*b^2*x^2, x)","F",0
970,0,0,0,1.019699," ","integrate(x^3*(b*x+a)^n/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x^{3}}{{\left(d x + c\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)^n*x^3/(d*x + c)^n, x)","F",0
971,0,0,0,1.209104," ","integrate(x^2*(b*x+a)^n/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x^{2}}{{\left(d x + c\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)^n*x^2/(d*x + c)^n, x)","F",0
972,0,0,0,1.402189," ","integrate(x*(b*x+a)^n/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n} x}{{\left(d x + c\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)^n*x/(d*x + c)^n, x)","F",0
973,0,0,0,1.026596," ","integrate((b*x+a)^n/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{{\left(d x + c\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)^n/(d*x + c)^n, x)","F",0
974,0,0,0,1.029082," ","integrate((b*x+a)^n/x/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{{\left(d x + c\right)}^{n} x}, x\right)"," ",0,"integral((b*x + a)^n/((d*x + c)^n*x), x)","F",0
975,0,0,0,1.254913," ","integrate((b*x+a)^n/x^2/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{{\left(d x + c\right)}^{n} x^{2}}, x\right)"," ",0,"integral((b*x + a)^n/((d*x + c)^n*x^2), x)","F",0
976,0,0,0,0.986903," ","integrate((b*x+a)^n/x^3/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{{\left(d x + c\right)}^{n} x^{3}}, x\right)"," ",0,"integral((b*x + a)^n/((d*x + c)^n*x^3), x)","F",0
977,0,0,0,1.228606," ","integrate((b*x+a)^n/x^4/((d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n}}{{\left(d x + c\right)}^{n} x^{4}}, x\right)"," ",0,"integral((b*x + a)^n/((d*x + c)^n*x^4), x)","F",0
978,0,0,0,1.113755," ","integrate((1-x)^n*x^3/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} {\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n}}, x\right)"," ",0,"integral(x^3*(-x + 1)^n/(x + 1)^n, x)","F",0
979,0,0,0,1.301236," ","integrate((1-x)^n*x^2/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} {\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n}}, x\right)"," ",0,"integral(x^2*(-x + 1)^n/(x + 1)^n, x)","F",0
980,0,0,0,1.027124," ","integrate((1-x)^n*x/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x {\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n}}, x\right)"," ",0,"integral(x*(-x + 1)^n/(x + 1)^n, x)","F",0
981,0,0,0,1.108001," ","integrate((1-x)^n/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n}}, x\right)"," ",0,"integral((-x + 1)^n/(x + 1)^n, x)","F",0
982,0,0,0,0.987429," ","integrate((1-x)^n/x/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n} x}, x\right)"," ",0,"integral((-x + 1)^n/((x + 1)^n*x), x)","F",0
983,0,0,0,1.336100," ","integrate((1-x)^n/x^2/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n} x^{2}}, x\right)"," ",0,"integral((-x + 1)^n/((x + 1)^n*x^2), x)","F",0
984,0,0,0,0.814982," ","integrate((1-x)^n/x^3/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n} x^{3}}, x\right)"," ",0,"integral((-x + 1)^n/((x + 1)^n*x^3), x)","F",0
985,0,0,0,1.138192," ","integrate((1-x)^n/x^4/((1+x)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x + 1\right)}^{n}}{{\left(x + 1\right)}^{n} x^{4}}, x\right)"," ",0,"integral((-x + 1)^n/((x + 1)^n*x^4), x)","F",0
986,0,0,0,0.734306," ","integrate(x^m*(-a*x+1)^n*(a*x+1)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a x + 1\right)}^{n} {\left(-a x + 1\right)}^{n} x^{m}, x\right)"," ",0,"integral((a*x + 1)^n*(-a*x + 1)^n*x^m, x)","F",0
987,0,0,0,1.217043," ","integrate(x^m*(-a*x+1)^n*(2*a*x+2)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a x + 2\right)}^{n} {\left(-a x + 1\right)}^{n} x^{m}, x\right)"," ",0,"integral((2*a*x + 2)^n*(-a*x + 1)^n*x^m, x)","F",0
988,0,0,0,0.837441," ","integrate(x^m*(-a*x+2)^n*(a*x+2)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a x + 2\right)}^{n} {\left(-a x + 2\right)}^{n} x^{m}, x\right)"," ",0,"integral((a*x + 2)^n*(-a*x + 2)^n*x^m, x)","F",0
989,0,0,0,0.877212," ","integrate(x^m*(1-1/2*a*x)^n*(a*x+2)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a x + 2\right)}^{n} {\left(-\frac{1}{2} \, a x + 1\right)}^{n} x^{m}, x\right)"," ",0,"integral((a*x + 2)^n*(-1/2*a*x + 1)^n*x^m, x)","F",0
990,0,0,0,1.316426," ","integrate(x^m*(-2*a*x+3)^(2+n)*(4*a*x+6)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, a x + 6\right)}^{n} {\left(-2 \, a x + 3\right)}^{n + 2} x^{m}, x\right)"," ",0,"integral((4*a*x + 6)^n*(-2*a*x + 3)^(n + 2)*x^m, x)","F",0
991,0,0,0,1.247274," ","integrate(x^m*(-2*a*x+3)^(1+n)*(4*a*x+6)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, a x + 6\right)}^{n} {\left(-2 \, a x + 3\right)}^{n + 1} x^{m}, x\right)"," ",0,"integral((4*a*x + 6)^n*(-2*a*x + 3)^(n + 1)*x^m, x)","F",0
992,0,0,0,0.904481," ","integrate(x^m*(-2*a*x+3)^n*(4*a*x+6)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, a x + 6\right)}^{n} {\left(-2 \, a x + 3\right)}^{n} x^{m}, x\right)"," ",0,"integral((4*a*x + 6)^n*(-2*a*x + 3)^n*x^m, x)","F",0
993,0,0,0,1.246025," ","integrate(x^m*(-2*a*x+3)^(-1+n)*(4*a*x+6)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, a x + 6\right)}^{n} {\left(-2 \, a x + 3\right)}^{n - 1} x^{m}, x\right)"," ",0,"integral((4*a*x + 6)^n*(-2*a*x + 3)^(n - 1)*x^m, x)","F",0
994,0,0,0,1.179663," ","integrate(x^m*(-2*a*x+3)^(-2+n)*(4*a*x+6)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, a x + 6\right)}^{n} {\left(-2 \, a x + 3\right)}^{n - 2} x^{m}, x\right)"," ",0,"integral((4*a*x + 6)^n*(-2*a*x + 3)^(n - 2)*x^m, x)","F",0
995,0,0,0,1.320966," ","integrate(x^m*(b*x+a)^(1+n)*(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{n + 1} {\left(d x + c\right)}^{n} x^{m}, x\right)"," ",0,"integral((b*x + a)^(n + 1)*(d*x + c)^n*x^m, x)","F",0
996,0,0,0,1.127888," ","integrate((a-x)^m*(f*x)^p*(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{n} \left(f x\right)^{p} {\left(a - x\right)}^{m}, x\right)"," ",0,"integral((d*x + c)^n*(f*x)^p*(a - x)^m, x)","F",0
997,0,0,0,1.085565," ","integrate((1-x)^(-1/2+p)*(1+x)^(1/2+p)/((c*x)^(2+2*p)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x + 1\right)}^{p + \frac{1}{2}} {\left(-x + 1\right)}^{p - \frac{1}{2}}}{\left(c x\right)^{2 \, p + 2}}, x\right)"," ",0,"integral((x + 1)^(p + 1/2)*(-x + 1)^(p - 1/2)/(c*x)^(2*p + 2), x)","F",0
998,0,0,0,1.329377," ","integrate((1+x/a)^(1/2*n)/x^2/((1-x/a)^(1/2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\frac{a + x}{a}\right)^{\frac{1}{2} \, n}}{x^{2} \left(\frac{a - x}{a}\right)^{\frac{1}{2} \, n}}, x\right)"," ",0,"integral(((a + x)/a)^(1/2*n)/(x^2*((a - x)/a)^(1/2*n)), x)","F",0
999,0,0,0,1.073953," ","integrate((b*x)^(-2-2*m)*(-a*x+1)^m*(a*x+1)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a x + 1\right)}^{m} {\left(-a x + 1\right)}^{m} \left(b x\right)^{-2 \, m - 2}, x\right)"," ",0,"integral((a*x + 1)^m*(-a*x + 1)^m*(b*x)^(-2*m - 2), x)","F",0
1000,0,0,0,0.795542," ","integrate((a*x+1)^n/x/((-a*x+1)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)}^{n}}{{\left(-a x + 1\right)}^{n} x}, x\right)"," ",0,"integral((a*x + 1)^n/((-a*x + 1)^n*x), x)","F",0
1001,0,0,0,0.949921," ","integrate((-a*x+1)^(1-n)*(a*x+1)^(1+n)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a x + 1\right)}^{n + 1} {\left(-a x + 1\right)}^{-n + 1}}{x^{2}}, x\right)"," ",0,"integral((a*x + 1)^(n + 1)*(-a*x + 1)^(-n + 1)/x^2, x)","F",0
1002,1,67,0,1.007310," ","integrate(x^2/(-a*x+1)^7/(a*x+1)^4,x, algorithm=""fricas"")","\frac{3 \, a x - 1}{24 \, {\left(a^{12} x^{9} - 3 \, a^{11} x^{8} + 8 \, a^{9} x^{6} - 6 \, a^{8} x^{5} - 6 \, a^{7} x^{4} + 8 \, a^{6} x^{3} - 3 \, a^{4} x + a^{3}\right)}}"," ",0,"1/24*(3*a*x - 1)/(a^12*x^9 - 3*a^11*x^8 + 8*a^9*x^6 - 6*a^8*x^5 - 6*a^7*x^4 + 8*a^6*x^3 - 3*a^4*x + a^3)","B",0
1003,1,123,0,1.106189," ","integrate(x^2/(-a*x+1)^11/(a*x+1)^7,x, algorithm=""fricas"")","\frac{4 \, a x - 1}{60 \, {\left(a^{19} x^{16} - 4 \, a^{18} x^{15} + 20 \, a^{16} x^{13} - 20 \, a^{15} x^{12} - 36 \, a^{14} x^{11} + 64 \, a^{13} x^{10} + 20 \, a^{12} x^{9} - 90 \, a^{11} x^{8} + 20 \, a^{10} x^{7} + 64 \, a^{9} x^{6} - 36 \, a^{8} x^{5} - 20 \, a^{7} x^{4} + 20 \, a^{6} x^{3} - 4 \, a^{4} x + a^{3}\right)}}"," ",0,"1/60*(4*a*x - 1)/(a^19*x^16 - 4*a^18*x^15 + 20*a^16*x^13 - 20*a^15*x^12 - 36*a^14*x^11 + 64*a^13*x^10 + 20*a^12*x^9 - 90*a^11*x^8 + 20*a^10*x^7 + 64*a^9*x^6 - 36*a^8*x^5 - 20*a^7*x^4 + 20*a^6*x^3 - 4*a^4*x + a^3)","B",0
1004,1,197,0,1.263948," ","integrate(x^2/(-a*x+1)^16/(a*x+1)^11,x, algorithm=""fricas"")","-\frac{5 \, a x - 1}{120 \, {\left(a^{28} x^{25} - 5 \, a^{27} x^{24} + 40 \, a^{25} x^{22} - 50 \, a^{24} x^{21} - 126 \, a^{23} x^{20} + 280 \, a^{22} x^{19} + 160 \, a^{21} x^{18} - 765 \, a^{20} x^{17} + 105 \, a^{19} x^{16} + 1248 \, a^{18} x^{15} - 720 \, a^{17} x^{14} - 1260 \, a^{16} x^{13} + 1260 \, a^{15} x^{12} + 720 \, a^{14} x^{11} - 1248 \, a^{13} x^{10} - 105 \, a^{12} x^{9} + 765 \, a^{11} x^{8} - 160 \, a^{10} x^{7} - 280 \, a^{9} x^{6} + 126 \, a^{8} x^{5} + 50 \, a^{7} x^{4} - 40 \, a^{6} x^{3} + 5 \, a^{4} x - a^{3}\right)}}"," ",0,"-1/120*(5*a*x - 1)/(a^28*x^25 - 5*a^27*x^24 + 40*a^25*x^22 - 50*a^24*x^21 - 126*a^23*x^20 + 280*a^22*x^19 + 160*a^21*x^18 - 765*a^20*x^17 + 105*a^19*x^16 + 1248*a^18*x^15 - 720*a^17*x^14 - 1260*a^16*x^13 + 1260*a^15*x^12 + 720*a^14*x^11 - 1248*a^13*x^10 - 105*a^12*x^9 + 765*a^11*x^8 - 160*a^10*x^7 - 280*a^9*x^6 + 126*a^8*x^5 + 50*a^7*x^4 - 40*a^6*x^3 + 5*a^4*x - a^3)","B",0
1005,1,74,0,1.334537," ","integrate(x^2*(-a*x+1)^(-1-1/2*n*(1+n))*(a*x+1)^(-1-1/2*(-1+n)*n),x, algorithm=""fricas"")","-\frac{{\left(a^{3} n x^{3} - a^{2} x^{2} - a n x + 1\right)} {\left(a x + 1\right)}^{-\frac{1}{2} \, n^{2} + \frac{1}{2} \, n - 1} {\left(-a x + 1\right)}^{-\frac{1}{2} \, n^{2} - \frac{1}{2} \, n - 1}}{a^{3} n^{3} - a^{3} n}"," ",0,"-(a^3*n*x^3 - a^2*x^2 - a*n*x + 1)*(a*x + 1)^(-1/2*n^2 + 1/2*n - 1)*(-a*x + 1)^(-1/2*n^2 - 1/2*n - 1)/(a^3*n^3 - a^3*n)","A",0
1006,0,0,0,0.748030," ","integrate((b*x+a)^(1+n)/x/((-b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n + 1}}{{\left(-b x + a\right)}^{n} x}, x\right)"," ",0,"integral((b*x + a)^(n + 1)/((-b*x + a)^n*x), x)","F",0
1007,0,0,0,1.018867," ","integrate((b*x+a)^(1+n)/x^2/((-b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n + 1}}{{\left(-b x + a\right)}^{n} x^{2}}, x\right)"," ",0,"integral((b*x + a)^(n + 1)/((-b*x + a)^n*x^2), x)","F",0
1008,0,0,0,1.416596," ","integrate((b*x+a)^(1+n)/x^3/((-b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n + 1}}{{\left(-b x + a\right)}^{n} x^{3}}, x\right)"," ",0,"integral((b*x + a)^(n + 1)/((-b*x + a)^n*x^3), x)","F",0
1009,0,0,0,1.347874," ","integrate((b*x+a)^(1+n)/x^4/((-b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n + 1}}{{\left(-b x + a\right)}^{n} x^{4}}, x\right)"," ",0,"integral((b*x + a)^(n + 1)/((-b*x + a)^n*x^4), x)","F",0
1010,0,0,0,0.742413," ","integrate((b*x+a)^(1+n)/x^5/((-b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{n + 1}}{{\left(-b x + a\right)}^{n} x^{5}}, x\right)"," ",0,"integral((b*x + a)^(n + 1)/((-b*x + a)^n*x^5), x)","F",0
1011,1,216,0,0.814258," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^4,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} b B + \frac{2}{3} x^{6} e^{3} d b B + \frac{1}{6} x^{6} e^{4} a B + \frac{1}{6} x^{6} e^{4} b A + \frac{6}{5} x^{5} e^{2} d^{2} b B + \frac{4}{5} x^{5} e^{3} d a B + \frac{4}{5} x^{5} e^{3} d b A + \frac{1}{5} x^{5} e^{4} a A + x^{4} e d^{3} b B + \frac{3}{2} x^{4} e^{2} d^{2} a B + \frac{3}{2} x^{4} e^{2} d^{2} b A + x^{4} e^{3} d a A + \frac{1}{3} x^{3} d^{4} b B + \frac{4}{3} x^{3} e d^{3} a B + \frac{4}{3} x^{3} e d^{3} b A + 2 x^{3} e^{2} d^{2} a A + \frac{1}{2} x^{2} d^{4} a B + \frac{1}{2} x^{2} d^{4} b A + 2 x^{2} e d^{3} a A + x d^{4} a A"," ",0,"1/7*x^7*e^4*b*B + 2/3*x^6*e^3*d*b*B + 1/6*x^6*e^4*a*B + 1/6*x^6*e^4*b*A + 6/5*x^5*e^2*d^2*b*B + 4/5*x^5*e^3*d*a*B + 4/5*x^5*e^3*d*b*A + 1/5*x^5*e^4*a*A + x^4*e*d^3*b*B + 3/2*x^4*e^2*d^2*a*B + 3/2*x^4*e^2*d^2*b*A + x^4*e^3*d*a*A + 1/3*x^3*d^4*b*B + 4/3*x^3*e*d^3*a*B + 4/3*x^3*e*d^3*b*A + 2*x^3*e^2*d^2*a*A + 1/2*x^2*d^4*a*B + 1/2*x^2*d^4*b*A + 2*x^2*e*d^3*a*A + x*d^4*a*A","B",0
1012,1,163,0,1.040309," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} b B + \frac{3}{5} x^{5} e^{2} d b B + \frac{1}{5} x^{5} e^{3} a B + \frac{1}{5} x^{5} e^{3} b A + \frac{3}{4} x^{4} e d^{2} b B + \frac{3}{4} x^{4} e^{2} d a B + \frac{3}{4} x^{4} e^{2} d b A + \frac{1}{4} x^{4} e^{3} a A + \frac{1}{3} x^{3} d^{3} b B + x^{3} e d^{2} a B + x^{3} e d^{2} b A + x^{3} e^{2} d a A + \frac{1}{2} x^{2} d^{3} a B + \frac{1}{2} x^{2} d^{3} b A + \frac{3}{2} x^{2} e d^{2} a A + x d^{3} a A"," ",0,"1/6*x^6*e^3*b*B + 3/5*x^5*e^2*d*b*B + 1/5*x^5*e^3*a*B + 1/5*x^5*e^3*b*A + 3/4*x^4*e*d^2*b*B + 3/4*x^4*e^2*d*a*B + 3/4*x^4*e^2*d*b*A + 1/4*x^4*e^3*a*A + 1/3*x^3*d^3*b*B + x^3*e*d^2*a*B + x^3*e*d^2*b*A + x^3*e^2*d*a*A + 1/2*x^2*d^3*a*B + 1/2*x^2*d^3*b*A + 3/2*x^2*e*d^2*a*A + x*d^3*a*A","B",0
1013,1,113,0,0.936511," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} b B + \frac{1}{2} x^{4} e d b B + \frac{1}{4} x^{4} e^{2} a B + \frac{1}{4} x^{4} e^{2} b A + \frac{1}{3} x^{3} d^{2} b B + \frac{2}{3} x^{3} e d a B + \frac{2}{3} x^{3} e d b A + \frac{1}{3} x^{3} e^{2} a A + \frac{1}{2} x^{2} d^{2} a B + \frac{1}{2} x^{2} d^{2} b A + x^{2} e d a A + x d^{2} a A"," ",0,"1/5*x^5*e^2*b*B + 1/2*x^4*e*d*b*B + 1/4*x^4*e^2*a*B + 1/4*x^4*e^2*b*A + 1/3*x^3*d^2*b*B + 2/3*x^3*e*d*a*B + 2/3*x^3*e*d*b*A + 1/3*x^3*e^2*a*A + 1/2*x^2*d^2*a*B + 1/2*x^2*d^2*b*A + x^2*e*d*a*A + x*d^2*a*A","A",0
1014,1,62,0,0.592073," ","integrate((b*x+a)*(B*x+A)*(e*x+d),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e b B + \frac{1}{3} x^{3} d b B + \frac{1}{3} x^{3} e a B + \frac{1}{3} x^{3} e b A + \frac{1}{2} x^{2} d a B + \frac{1}{2} x^{2} d b A + \frac{1}{2} x^{2} e a A + x d a A"," ",0,"1/4*x^4*e*b*B + 1/3*x^3*d*b*B + 1/3*x^3*e*a*B + 1/3*x^3*e*b*A + 1/2*x^2*d*a*B + 1/2*x^2*d*b*A + 1/2*x^2*e*a*A + x*d*a*A","A",0
1015,1,26,0,1.002482," ","integrate((b*x+a)*(B*x+A),x, algorithm=""fricas"")","\frac{1}{3} x^{3} b B + \frac{1}{2} x^{2} a B + \frac{1}{2} x^{2} b A + x a A"," ",0,"1/3*x^3*b*B + 1/2*x^2*a*B + 1/2*x^2*b*A + x*a*A","A",0
1016,1,68,0,1.142946," ","integrate((b*x+a)*(B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{B b e^{2} x^{2} - 2 \, {\left(B b d e - {\left(B a + A b\right)} e^{2}\right)} x + 2 \, {\left(B b d^{2} + A a e^{2} - {\left(B a + A b\right)} d e\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(B*b*e^2*x^2 - 2*(B*b*d*e - (B*a + A*b)*e^2)*x + 2*(B*b*d^2 + A*a*e^2 - (B*a + A*b)*d*e)*log(e*x + d))/e^3","A",0
1017,1,102,0,1.087778," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B b e^{2} x^{2} + B b d e x - B b d^{2} - A a e^{2} + {\left(B a + A b\right)} d e - {\left(2 \, B b d^{2} - {\left(B a + A b\right)} d e + {\left(2 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(B*b*e^2*x^2 + B*b*d*e*x - B*b*d^2 - A*a*e^2 + (B*a + A*b)*d*e - (2*B*b*d^2 - (B*a + A*b)*d*e + (2*B*b*d*e - (B*a + A*b)*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
1018,1,105,0,1.371009," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, B b d^{2} - A a e^{2} - {\left(B a + A b\right)} d e + 2 \, {\left(2 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x + 2 \, {\left(B b e^{2} x^{2} + 2 \, B b d e x + B b d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*B*b*d^2 - A*a*e^2 - (B*a + A*b)*d*e + 2*(2*B*b*d*e - (B*a + A*b)*e^2)*x + 2*(B*b*e^2*x^2 + 2*B*b*d*e*x + B*b*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1019,1,93,0,1.323970," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{6 \, B b e^{2} x^{2} + 2 \, B b d^{2} + 2 \, A a e^{2} + {\left(B a + A b\right)} d e + 3 \, {\left(2 \, B b d e + {\left(B a + A b\right)} e^{2}\right)} x}{6 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/6*(6*B*b*e^2*x^2 + 2*B*b*d^2 + 2*A*a*e^2 + (B*a + A*b)*d*e + 3*(2*B*b*d*e + (B*a + A*b)*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1020,1,102,0,1.318278," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, B b e^{2} x^{2} + B b d^{2} + 3 \, A a e^{2} + {\left(B a + A b\right)} d e + 4 \, {\left(B b d e + {\left(B a + A b\right)} e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*B*b*e^2*x^2 + B*b*d^2 + 3*A*a*e^2 + (B*a + A*b)*d*e + 4*(B*b*d*e + (B*a + A*b)*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1021,1,117,0,1.267037," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{20 \, B b e^{2} x^{2} + 2 \, B b d^{2} + 12 \, A a e^{2} + 3 \, {\left(B a + A b\right)} d e + 5 \, {\left(2 \, B b d e + 3 \, {\left(B a + A b\right)} e^{2}\right)} x}{60 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/60*(20*B*b*e^2*x^2 + 2*B*b*d^2 + 12*A*a*e^2 + 3*(B*a + A*b)*d*e + 5*(2*B*b*d*e + 3*(B*a + A*b)*e^2)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
1022,1,374,0,1.238597," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^4,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} b^{2} B + \frac{4}{7} x^{7} e^{3} d b^{2} B + \frac{2}{7} x^{7} e^{4} b a B + \frac{1}{7} x^{7} e^{4} b^{2} A + x^{6} e^{2} d^{2} b^{2} B + \frac{4}{3} x^{6} e^{3} d b a B + \frac{1}{6} x^{6} e^{4} a^{2} B + \frac{2}{3} x^{6} e^{3} d b^{2} A + \frac{1}{3} x^{6} e^{4} b a A + \frac{4}{5} x^{5} e d^{3} b^{2} B + \frac{12}{5} x^{5} e^{2} d^{2} b a B + \frac{4}{5} x^{5} e^{3} d a^{2} B + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} A + \frac{8}{5} x^{5} e^{3} d b a A + \frac{1}{5} x^{5} e^{4} a^{2} A + \frac{1}{4} x^{4} d^{4} b^{2} B + 2 x^{4} e d^{3} b a B + \frac{3}{2} x^{4} e^{2} d^{2} a^{2} B + x^{4} e d^{3} b^{2} A + 3 x^{4} e^{2} d^{2} b a A + x^{4} e^{3} d a^{2} A + \frac{2}{3} x^{3} d^{4} b a B + \frac{4}{3} x^{3} e d^{3} a^{2} B + \frac{1}{3} x^{3} d^{4} b^{2} A + \frac{8}{3} x^{3} e d^{3} b a A + 2 x^{3} e^{2} d^{2} a^{2} A + \frac{1}{2} x^{2} d^{4} a^{2} B + x^{2} d^{4} b a A + 2 x^{2} e d^{3} a^{2} A + x d^{4} a^{2} A"," ",0,"1/8*x^8*e^4*b^2*B + 4/7*x^7*e^3*d*b^2*B + 2/7*x^7*e^4*b*a*B + 1/7*x^7*e^4*b^2*A + x^6*e^2*d^2*b^2*B + 4/3*x^6*e^3*d*b*a*B + 1/6*x^6*e^4*a^2*B + 2/3*x^6*e^3*d*b^2*A + 1/3*x^6*e^4*b*a*A + 4/5*x^5*e*d^3*b^2*B + 12/5*x^5*e^2*d^2*b*a*B + 4/5*x^5*e^3*d*a^2*B + 6/5*x^5*e^2*d^2*b^2*A + 8/5*x^5*e^3*d*b*a*A + 1/5*x^5*e^4*a^2*A + 1/4*x^4*d^4*b^2*B + 2*x^4*e*d^3*b*a*B + 3/2*x^4*e^2*d^2*a^2*B + x^4*e*d^3*b^2*A + 3*x^4*e^2*d^2*b*a*A + x^4*e^3*d*a^2*A + 2/3*x^3*d^4*b*a*B + 4/3*x^3*e*d^3*a^2*B + 1/3*x^3*d^4*b^2*A + 8/3*x^3*e*d^3*b*a*A + 2*x^3*e^2*d^2*a^2*A + 1/2*x^2*d^4*a^2*B + x^2*d^4*b*a*A + 2*x^2*e*d^3*a^2*A + x*d^4*a^2*A","B",0
1023,1,287,0,0.705300," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} b^{2} B + \frac{1}{2} x^{6} e^{2} d b^{2} B + \frac{1}{3} x^{6} e^{3} b a B + \frac{1}{6} x^{6} e^{3} b^{2} A + \frac{3}{5} x^{5} e d^{2} b^{2} B + \frac{6}{5} x^{5} e^{2} d b a B + \frac{1}{5} x^{5} e^{3} a^{2} B + \frac{3}{5} x^{5} e^{2} d b^{2} A + \frac{2}{5} x^{5} e^{3} b a A + \frac{1}{4} x^{4} d^{3} b^{2} B + \frac{3}{2} x^{4} e d^{2} b a B + \frac{3}{4} x^{4} e^{2} d a^{2} B + \frac{3}{4} x^{4} e d^{2} b^{2} A + \frac{3}{2} x^{4} e^{2} d b a A + \frac{1}{4} x^{4} e^{3} a^{2} A + \frac{2}{3} x^{3} d^{3} b a B + x^{3} e d^{2} a^{2} B + \frac{1}{3} x^{3} d^{3} b^{2} A + 2 x^{3} e d^{2} b a A + x^{3} e^{2} d a^{2} A + \frac{1}{2} x^{2} d^{3} a^{2} B + x^{2} d^{3} b a A + \frac{3}{2} x^{2} e d^{2} a^{2} A + x d^{3} a^{2} A"," ",0,"1/7*x^7*e^3*b^2*B + 1/2*x^6*e^2*d*b^2*B + 1/3*x^6*e^3*b*a*B + 1/6*x^6*e^3*b^2*A + 3/5*x^5*e*d^2*b^2*B + 6/5*x^5*e^2*d*b*a*B + 1/5*x^5*e^3*a^2*B + 3/5*x^5*e^2*d*b^2*A + 2/5*x^5*e^3*b*a*A + 1/4*x^4*d^3*b^2*B + 3/2*x^4*e*d^2*b*a*B + 3/4*x^4*e^2*d*a^2*B + 3/4*x^4*e*d^2*b^2*A + 3/2*x^4*e^2*d*b*a*A + 1/4*x^4*e^3*a^2*A + 2/3*x^3*d^3*b*a*B + x^3*e*d^2*a^2*B + 1/3*x^3*d^3*b^2*A + 2*x^3*e*d^2*b*a*A + x^3*e^2*d*a^2*A + 1/2*x^2*d^3*a^2*B + x^2*d^3*b*a*A + 3/2*x^2*e*d^2*a^2*A + x*d^3*a^2*A","B",0
1024,1,199,0,1.015769," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{2} b^{2} B + \frac{2}{5} x^{5} e d b^{2} B + \frac{2}{5} x^{5} e^{2} b a B + \frac{1}{5} x^{5} e^{2} b^{2} A + \frac{1}{4} x^{4} d^{2} b^{2} B + x^{4} e d b a B + \frac{1}{4} x^{4} e^{2} a^{2} B + \frac{1}{2} x^{4} e d b^{2} A + \frac{1}{2} x^{4} e^{2} b a A + \frac{2}{3} x^{3} d^{2} b a B + \frac{2}{3} x^{3} e d a^{2} B + \frac{1}{3} x^{3} d^{2} b^{2} A + \frac{4}{3} x^{3} e d b a A + \frac{1}{3} x^{3} e^{2} a^{2} A + \frac{1}{2} x^{2} d^{2} a^{2} B + x^{2} d^{2} b a A + x^{2} e d a^{2} A + x d^{2} a^{2} A"," ",0,"1/6*x^6*e^2*b^2*B + 2/5*x^5*e*d*b^2*B + 2/5*x^5*e^2*b*a*B + 1/5*x^5*e^2*b^2*A + 1/4*x^4*d^2*b^2*B + x^4*e*d*b*a*B + 1/4*x^4*e^2*a^2*B + 1/2*x^4*e*d*b^2*A + 1/2*x^4*e^2*b*a*A + 2/3*x^3*d^2*b*a*B + 2/3*x^3*e*d*a^2*B + 1/3*x^3*d^2*b^2*A + 4/3*x^3*e*d*b*a*A + 1/3*x^3*e^2*a^2*A + 1/2*x^2*d^2*a^2*B + x^2*d^2*b*a*A + x^2*e*d*a^2*A + x*d^2*a^2*A","A",0
1025,1,113,0,1.107457," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e b^{2} B + \frac{1}{4} x^{4} d b^{2} B + \frac{1}{2} x^{4} e b a B + \frac{1}{4} x^{4} e b^{2} A + \frac{2}{3} x^{3} d b a B + \frac{1}{3} x^{3} e a^{2} B + \frac{1}{3} x^{3} d b^{2} A + \frac{2}{3} x^{3} e b a A + \frac{1}{2} x^{2} d a^{2} B + x^{2} d b a A + \frac{1}{2} x^{2} e a^{2} A + x d a^{2} A"," ",0,"1/5*x^5*e*b^2*B + 1/4*x^4*d*b^2*B + 1/2*x^4*e*b*a*B + 1/4*x^4*e*b^2*A + 2/3*x^3*d*b*a*B + 1/3*x^3*e*a^2*B + 1/3*x^3*d*b^2*A + 2/3*x^3*e*b*a*A + 1/2*x^2*d*a^2*B + x^2*d*b*a*A + 1/2*x^2*e*a^2*A + x*d*a^2*A","A",0
1026,1,49,0,1.191627," ","integrate((b*x+a)^2*(B*x+A),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b^{2} B + \frac{2}{3} x^{3} b a B + \frac{1}{3} x^{3} b^{2} A + \frac{1}{2} x^{2} a^{2} B + x^{2} b a A + x a^{2} A"," ",0,"1/4*x^4*b^2*B + 2/3*x^3*b*a*B + 1/3*x^3*b^2*A + 1/2*x^2*a^2*B + x^2*b*a*A + x*a^2*A","A",0
1027,1,153,0,1.216761," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, B b^{2} e^{3} x^{3} - 3 \, {\left(B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x - 6 \, {\left(B b^{2} d^{3} - A a^{2} e^{3} - {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*B*b^2*e^3*x^3 - 3*(B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 6*(B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x - 6*(B*b^2*d^3 - A*a^2*e^3 - (2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2)*log(e*x + d))/e^4","A",0
1028,1,238,0,1.136919," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{B b^{2} e^{3} x^{3} + 2 \, B b^{2} d^{3} - 2 \, A a^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - {\left(3 \, B b^{2} d e^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} - 2 \, {\left(2 \, B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2}\right)} x + 2 \, {\left(3 \, B b^{2} d^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + {\left(3 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(B*b^2*e^3*x^3 + 2*B*b^2*d^3 - 2*A*a^2*e^3 - 2*(2*B*a*b + A*b^2)*d^2*e + 2*(B*a^2 + 2*A*a*b)*d*e^2 - (3*B*b^2*d*e^2 - 2*(2*B*a*b + A*b^2)*e^3)*x^2 - 2*(2*B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2)*x + 2*(3*B*b^2*d^3 - 2*(2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2 + (3*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","B",0
1029,1,247,0,1.406847," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{2} e^{3} x^{3} + 4 \, B b^{2} d e^{2} x^{2} - 5 \, B b^{2} d^{3} - A a^{2} e^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 2 \, {\left(2 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x - 2 \, {\left(3 \, B b^{2} d^{3} - {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(3 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(3 \, B b^{2} d^{2} e - {\left(2 \, B a b + A b^{2}\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*B*b^2*e^3*x^3 + 4*B*b^2*d*e^2*x^2 - 5*B*b^2*d^3 - A*a^2*e^3 + 3*(2*B*a*b + A*b^2)*d^2*e - (B*a^2 + 2*A*a*b)*d*e^2 - 2*(2*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x - 2*(3*B*b^2*d^3 - (2*B*a*b + A*b^2)*d^2*e + (3*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 2*(3*B*b^2*d^2*e - (2*B*a*b + A*b^2)*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","B",0
1030,1,221,0,1.308349," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, B b^{2} d^{3} - 2 \, A a^{2} e^{3} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 6 \, {\left(3 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(9 \, B b^{2} d^{2} e - 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} - {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x + 6 \, {\left(B b^{2} e^{3} x^{3} + 3 \, B b^{2} d e^{2} x^{2} + 3 \, B b^{2} d^{2} e x + B b^{2} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*B*b^2*d^3 - 2*A*a^2*e^3 - 2*(2*B*a*b + A*b^2)*d^2*e - (B*a^2 + 2*A*a*b)*d*e^2 + 6*(3*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 3*(9*B*b^2*d^2*e - 2*(2*B*a*b + A*b^2)*d*e^2 - (B*a^2 + 2*A*a*b)*e^3)*x + 6*(B*b^2*e^3*x^3 + 3*B*b^2*d*e^2*x^2 + 3*B*b^2*d^2*e*x + B*b^2*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","B",0
1031,1,187,0,0.825302," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{12 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 3 \, A a^{2} e^{3} + {\left(2 \, B a b + A b^{2}\right)} d^{2} e + {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 6 \, {\left(3 \, B b^{2} d e^{2} + {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 4 \, {\left(3 \, B b^{2} d^{2} e + {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{12 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/12*(12*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 3*A*a^2*e^3 + (2*B*a*b + A*b^2)*d^2*e + (B*a^2 + 2*A*a*b)*d*e^2 + 6*(3*B*b^2*d*e^2 + (2*B*a*b + A*b^2)*e^3)*x^2 + 4*(3*B*b^2*d^2*e + (2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","B",0
1032,1,203,0,1.111006," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 12 \, A a^{2} e^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 3 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 10 \, {\left(3 \, B b^{2} d e^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 5 \, {\left(3 \, B b^{2} d^{2} e + 2 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{60 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/60*(30*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 12*A*a^2*e^3 + 2*(2*B*a*b + A*b^2)*d^2*e + 3*(B*a^2 + 2*A*a*b)*d*e^2 + 10*(3*B*b^2*d*e^2 + 2*(2*B*a*b + A*b^2)*e^3)*x^2 + 5*(3*B*b^2*d^2*e + 2*(2*B*a*b + A*b^2)*d*e^2 + 3*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
1033,1,208,0,1.189783," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, B b^{2} e^{3} x^{3} + B b^{2} d^{3} + 10 \, A a^{2} e^{3} + {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 15 \, {\left(B b^{2} d e^{2} + {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 6 \, {\left(B b^{2} d^{2} e + {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*B*b^2*e^3*x^3 + B*b^2*d^3 + 10*A*a^2*e^3 + (2*B*a*b + A*b^2)*d^2*e + 2*(B*a^2 + 2*A*a*b)*d*e^2 + 15*(B*b^2*d*e^2 + (2*B*a*b + A*b^2)*e^3)*x^2 + 6*(B*b^2*d^2*e + (2*B*a*b + A*b^2)*d*e^2 + 2*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
1034,1,225,0,1.393704," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{105 \, B b^{2} e^{3} x^{3} + 3 \, B b^{2} d^{3} + 60 \, A a^{2} e^{3} + 4 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 10 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 21 \, {\left(3 \, B b^{2} d e^{2} + 4 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 7 \, {\left(3 \, B b^{2} d^{2} e + 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 10 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x}{420 \, {\left(e^{11} x^{7} + 7 \, d e^{10} x^{6} + 21 \, d^{2} e^{9} x^{5} + 35 \, d^{3} e^{8} x^{4} + 35 \, d^{4} e^{7} x^{3} + 21 \, d^{5} e^{6} x^{2} + 7 \, d^{6} e^{5} x + d^{7} e^{4}\right)}}"," ",0,"-1/420*(105*B*b^2*e^3*x^3 + 3*B*b^2*d^3 + 60*A*a^2*e^3 + 4*(2*B*a*b + A*b^2)*d^2*e + 10*(B*a^2 + 2*A*a*b)*d*e^2 + 21*(3*B*b^2*d*e^2 + 4*(2*B*a*b + A*b^2)*e^3)*x^2 + 7*(3*B*b^2*d^2*e + 4*(2*B*a*b + A*b^2)*d*e^2 + 10*(B*a^2 + 2*A*a*b)*e^3)*x)/(e^11*x^7 + 7*d*e^10*x^6 + 21*d^2*e^9*x^5 + 35*d^3*e^8*x^4 + 35*d^4*e^7*x^3 + 21*d^5*e^6*x^2 + 7*d^6*e^5*x + d^7*e^4)","B",0
1035,1,658,0,0.860368," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^5,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{5} b^{3} B + \frac{5}{9} x^{9} e^{4} d b^{3} B + \frac{1}{3} x^{9} e^{5} b^{2} a B + \frac{1}{9} x^{9} e^{5} b^{3} A + \frac{5}{4} x^{8} e^{3} d^{2} b^{3} B + \frac{15}{8} x^{8} e^{4} d b^{2} a B + \frac{3}{8} x^{8} e^{5} b a^{2} B + \frac{5}{8} x^{8} e^{4} d b^{3} A + \frac{3}{8} x^{8} e^{5} b^{2} a A + \frac{10}{7} x^{7} e^{2} d^{3} b^{3} B + \frac{30}{7} x^{7} e^{3} d^{2} b^{2} a B + \frac{15}{7} x^{7} e^{4} d b a^{2} B + \frac{1}{7} x^{7} e^{5} a^{3} B + \frac{10}{7} x^{7} e^{3} d^{2} b^{3} A + \frac{15}{7} x^{7} e^{4} d b^{2} a A + \frac{3}{7} x^{7} e^{5} b a^{2} A + \frac{5}{6} x^{6} e d^{4} b^{3} B + 5 x^{6} e^{2} d^{3} b^{2} a B + 5 x^{6} e^{3} d^{2} b a^{2} B + \frac{5}{6} x^{6} e^{4} d a^{3} B + \frac{5}{3} x^{6} e^{2} d^{3} b^{3} A + 5 x^{6} e^{3} d^{2} b^{2} a A + \frac{5}{2} x^{6} e^{4} d b a^{2} A + \frac{1}{6} x^{6} e^{5} a^{3} A + \frac{1}{5} x^{5} d^{5} b^{3} B + 3 x^{5} e d^{4} b^{2} a B + 6 x^{5} e^{2} d^{3} b a^{2} B + 2 x^{5} e^{3} d^{2} a^{3} B + x^{5} e d^{4} b^{3} A + 6 x^{5} e^{2} d^{3} b^{2} a A + 6 x^{5} e^{3} d^{2} b a^{2} A + x^{5} e^{4} d a^{3} A + \frac{3}{4} x^{4} d^{5} b^{2} a B + \frac{15}{4} x^{4} e d^{4} b a^{2} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{3} B + \frac{1}{4} x^{4} d^{5} b^{3} A + \frac{15}{4} x^{4} e d^{4} b^{2} a A + \frac{15}{2} x^{4} e^{2} d^{3} b a^{2} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{3} A + x^{3} d^{5} b a^{2} B + \frac{5}{3} x^{3} e d^{4} a^{3} B + x^{3} d^{5} b^{2} a A + 5 x^{3} e d^{4} b a^{2} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{3} A + \frac{1}{2} x^{2} d^{5} a^{3} B + \frac{3}{2} x^{2} d^{5} b a^{2} A + \frac{5}{2} x^{2} e d^{4} a^{3} A + x d^{5} a^{3} A"," ",0,"1/10*x^10*e^5*b^3*B + 5/9*x^9*e^4*d*b^3*B + 1/3*x^9*e^5*b^2*a*B + 1/9*x^9*e^5*b^3*A + 5/4*x^8*e^3*d^2*b^3*B + 15/8*x^8*e^4*d*b^2*a*B + 3/8*x^8*e^5*b*a^2*B + 5/8*x^8*e^4*d*b^3*A + 3/8*x^8*e^5*b^2*a*A + 10/7*x^7*e^2*d^3*b^3*B + 30/7*x^7*e^3*d^2*b^2*a*B + 15/7*x^7*e^4*d*b*a^2*B + 1/7*x^7*e^5*a^3*B + 10/7*x^7*e^3*d^2*b^3*A + 15/7*x^7*e^4*d*b^2*a*A + 3/7*x^7*e^5*b*a^2*A + 5/6*x^6*e*d^4*b^3*B + 5*x^6*e^2*d^3*b^2*a*B + 5*x^6*e^3*d^2*b*a^2*B + 5/6*x^6*e^4*d*a^3*B + 5/3*x^6*e^2*d^3*b^3*A + 5*x^6*e^3*d^2*b^2*a*A + 5/2*x^6*e^4*d*b*a^2*A + 1/6*x^6*e^5*a^3*A + 1/5*x^5*d^5*b^3*B + 3*x^5*e*d^4*b^2*a*B + 6*x^5*e^2*d^3*b*a^2*B + 2*x^5*e^3*d^2*a^3*B + x^5*e*d^4*b^3*A + 6*x^5*e^2*d^3*b^2*a*A + 6*x^5*e^3*d^2*b*a^2*A + x^5*e^4*d*a^3*A + 3/4*x^4*d^5*b^2*a*B + 15/4*x^4*e*d^4*b*a^2*B + 5/2*x^4*e^2*d^3*a^3*B + 1/4*x^4*d^5*b^3*A + 15/4*x^4*e*d^4*b^2*a*A + 15/2*x^4*e^2*d^3*b*a^2*A + 5/2*x^4*e^3*d^2*a^3*A + x^3*d^5*b*a^2*B + 5/3*x^3*e*d^4*a^3*B + x^3*d^5*b^2*a*A + 5*x^3*e*d^4*b*a^2*A + 10/3*x^3*e^2*d^3*a^3*A + 1/2*x^2*d^5*a^3*B + 3/2*x^2*d^5*b*a^2*A + 5/2*x^2*e*d^4*a^3*A + x*d^5*a^3*A","B",0
1036,1,534,0,1.002991," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^4,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{4} b^{3} B + \frac{1}{2} x^{8} e^{3} d b^{3} B + \frac{3}{8} x^{8} e^{4} b^{2} a B + \frac{1}{8} x^{8} e^{4} b^{3} A + \frac{6}{7} x^{7} e^{2} d^{2} b^{3} B + \frac{12}{7} x^{7} e^{3} d b^{2} a B + \frac{3}{7} x^{7} e^{4} b a^{2} B + \frac{4}{7} x^{7} e^{3} d b^{3} A + \frac{3}{7} x^{7} e^{4} b^{2} a A + \frac{2}{3} x^{6} e d^{3} b^{3} B + 3 x^{6} e^{2} d^{2} b^{2} a B + 2 x^{6} e^{3} d b a^{2} B + \frac{1}{6} x^{6} e^{4} a^{3} B + x^{6} e^{2} d^{2} b^{3} A + 2 x^{6} e^{3} d b^{2} a A + \frac{1}{2} x^{6} e^{4} b a^{2} A + \frac{1}{5} x^{5} d^{4} b^{3} B + \frac{12}{5} x^{5} e d^{3} b^{2} a B + \frac{18}{5} x^{5} e^{2} d^{2} b a^{2} B + \frac{4}{5} x^{5} e^{3} d a^{3} B + \frac{4}{5} x^{5} e d^{3} b^{3} A + \frac{18}{5} x^{5} e^{2} d^{2} b^{2} a A + \frac{12}{5} x^{5} e^{3} d b a^{2} A + \frac{1}{5} x^{5} e^{4} a^{3} A + \frac{3}{4} x^{4} d^{4} b^{2} a B + 3 x^{4} e d^{3} b a^{2} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{3} B + \frac{1}{4} x^{4} d^{4} b^{3} A + 3 x^{4} e d^{3} b^{2} a A + \frac{9}{2} x^{4} e^{2} d^{2} b a^{2} A + x^{4} e^{3} d a^{3} A + x^{3} d^{4} b a^{2} B + \frac{4}{3} x^{3} e d^{3} a^{3} B + x^{3} d^{4} b^{2} a A + 4 x^{3} e d^{3} b a^{2} A + 2 x^{3} e^{2} d^{2} a^{3} A + \frac{1}{2} x^{2} d^{4} a^{3} B + \frac{3}{2} x^{2} d^{4} b a^{2} A + 2 x^{2} e d^{3} a^{3} A + x d^{4} a^{3} A"," ",0,"1/9*x^9*e^4*b^3*B + 1/2*x^8*e^3*d*b^3*B + 3/8*x^8*e^4*b^2*a*B + 1/8*x^8*e^4*b^3*A + 6/7*x^7*e^2*d^2*b^3*B + 12/7*x^7*e^3*d*b^2*a*B + 3/7*x^7*e^4*b*a^2*B + 4/7*x^7*e^3*d*b^3*A + 3/7*x^7*e^4*b^2*a*A + 2/3*x^6*e*d^3*b^3*B + 3*x^6*e^2*d^2*b^2*a*B + 2*x^6*e^3*d*b*a^2*B + 1/6*x^6*e^4*a^3*B + x^6*e^2*d^2*b^3*A + 2*x^6*e^3*d*b^2*a*A + 1/2*x^6*e^4*b*a^2*A + 1/5*x^5*d^4*b^3*B + 12/5*x^5*e*d^3*b^2*a*B + 18/5*x^5*e^2*d^2*b*a^2*B + 4/5*x^5*e^3*d*a^3*B + 4/5*x^5*e*d^3*b^3*A + 18/5*x^5*e^2*d^2*b^2*a*A + 12/5*x^5*e^3*d*b*a^2*A + 1/5*x^5*e^4*a^3*A + 3/4*x^4*d^4*b^2*a*B + 3*x^4*e*d^3*b*a^2*B + 3/2*x^4*e^2*d^2*a^3*B + 1/4*x^4*d^4*b^3*A + 3*x^4*e*d^3*b^2*a*A + 9/2*x^4*e^2*d^2*b*a^2*A + x^4*e^3*d*a^3*A + x^3*d^4*b*a^2*B + 4/3*x^3*e*d^3*a^3*B + x^3*d^4*b^2*a*A + 4*x^3*e*d^3*b*a^2*A + 2*x^3*e^2*d^2*a^3*A + 1/2*x^2*d^4*a^3*B + 3/2*x^2*d^4*b*a^2*A + 2*x^2*e*d^3*a^3*A + x*d^4*a^3*A","B",0
1037,1,410,0,1.036365," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} b^{3} B + \frac{3}{7} x^{7} e^{2} d b^{3} B + \frac{3}{7} x^{7} e^{3} b^{2} a B + \frac{1}{7} x^{7} e^{3} b^{3} A + \frac{1}{2} x^{6} e d^{2} b^{3} B + \frac{3}{2} x^{6} e^{2} d b^{2} a B + \frac{1}{2} x^{6} e^{3} b a^{2} B + \frac{1}{2} x^{6} e^{2} d b^{3} A + \frac{1}{2} x^{6} e^{3} b^{2} a A + \frac{1}{5} x^{5} d^{3} b^{3} B + \frac{9}{5} x^{5} e d^{2} b^{2} a B + \frac{9}{5} x^{5} e^{2} d b a^{2} B + \frac{1}{5} x^{5} e^{3} a^{3} B + \frac{3}{5} x^{5} e d^{2} b^{3} A + \frac{9}{5} x^{5} e^{2} d b^{2} a A + \frac{3}{5} x^{5} e^{3} b a^{2} A + \frac{3}{4} x^{4} d^{3} b^{2} a B + \frac{9}{4} x^{4} e d^{2} b a^{2} B + \frac{3}{4} x^{4} e^{2} d a^{3} B + \frac{1}{4} x^{4} d^{3} b^{3} A + \frac{9}{4} x^{4} e d^{2} b^{2} a A + \frac{9}{4} x^{4} e^{2} d b a^{2} A + \frac{1}{4} x^{4} e^{3} a^{3} A + x^{3} d^{3} b a^{2} B + x^{3} e d^{2} a^{3} B + x^{3} d^{3} b^{2} a A + 3 x^{3} e d^{2} b a^{2} A + x^{3} e^{2} d a^{3} A + \frac{1}{2} x^{2} d^{3} a^{3} B + \frac{3}{2} x^{2} d^{3} b a^{2} A + \frac{3}{2} x^{2} e d^{2} a^{3} A + x d^{3} a^{3} A"," ",0,"1/8*x^8*e^3*b^3*B + 3/7*x^7*e^2*d*b^3*B + 3/7*x^7*e^3*b^2*a*B + 1/7*x^7*e^3*b^3*A + 1/2*x^6*e*d^2*b^3*B + 3/2*x^6*e^2*d*b^2*a*B + 1/2*x^6*e^3*b*a^2*B + 1/2*x^6*e^2*d*b^3*A + 1/2*x^6*e^3*b^2*a*A + 1/5*x^5*d^3*b^3*B + 9/5*x^5*e*d^2*b^2*a*B + 9/5*x^5*e^2*d*b*a^2*B + 1/5*x^5*e^3*a^3*B + 3/5*x^5*e*d^2*b^3*A + 9/5*x^5*e^2*d*b^2*a*A + 3/5*x^5*e^3*b*a^2*A + 3/4*x^4*d^3*b^2*a*B + 9/4*x^4*e*d^2*b*a^2*B + 3/4*x^4*e^2*d*a^3*B + 1/4*x^4*d^3*b^3*A + 9/4*x^4*e*d^2*b^2*a*A + 9/4*x^4*e^2*d*b*a^2*A + 1/4*x^4*e^3*a^3*A + x^3*d^3*b*a^2*B + x^3*e*d^2*a^3*B + x^3*d^3*b^2*a*A + 3*x^3*e*d^2*b*a^2*A + x^3*e^2*d*a^3*A + 1/2*x^2*d^3*a^3*B + 3/2*x^2*d^3*b*a^2*A + 3/2*x^2*e*d^2*a^3*A + x*d^3*a^3*A","B",0
1038,1,287,0,0.922620," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} b^{3} B + \frac{1}{3} x^{6} e d b^{3} B + \frac{1}{2} x^{6} e^{2} b^{2} a B + \frac{1}{6} x^{6} e^{2} b^{3} A + \frac{1}{5} x^{5} d^{2} b^{3} B + \frac{6}{5} x^{5} e d b^{2} a B + \frac{3}{5} x^{5} e^{2} b a^{2} B + \frac{2}{5} x^{5} e d b^{3} A + \frac{3}{5} x^{5} e^{2} b^{2} a A + \frac{3}{4} x^{4} d^{2} b^{2} a B + \frac{3}{2} x^{4} e d b a^{2} B + \frac{1}{4} x^{4} e^{2} a^{3} B + \frac{1}{4} x^{4} d^{2} b^{3} A + \frac{3}{2} x^{4} e d b^{2} a A + \frac{3}{4} x^{4} e^{2} b a^{2} A + x^{3} d^{2} b a^{2} B + \frac{2}{3} x^{3} e d a^{3} B + x^{3} d^{2} b^{2} a A + 2 x^{3} e d b a^{2} A + \frac{1}{3} x^{3} e^{2} a^{3} A + \frac{1}{2} x^{2} d^{2} a^{3} B + \frac{3}{2} x^{2} d^{2} b a^{2} A + x^{2} e d a^{3} A + x d^{2} a^{3} A"," ",0,"1/7*x^7*e^2*b^3*B + 1/3*x^6*e*d*b^3*B + 1/2*x^6*e^2*b^2*a*B + 1/6*x^6*e^2*b^3*A + 1/5*x^5*d^2*b^3*B + 6/5*x^5*e*d*b^2*a*B + 3/5*x^5*e^2*b*a^2*B + 2/5*x^5*e*d*b^3*A + 3/5*x^5*e^2*b^2*a*A + 3/4*x^4*d^2*b^2*a*B + 3/2*x^4*e*d*b*a^2*B + 1/4*x^4*e^2*a^3*B + 1/4*x^4*d^2*b^3*A + 3/2*x^4*e*d*b^2*a*A + 3/4*x^4*e^2*b*a^2*A + x^3*d^2*b*a^2*B + 2/3*x^3*e*d*a^3*B + x^3*d^2*b^2*a*A + 2*x^3*e*d*b*a^2*A + 1/3*x^3*e^2*a^3*A + 1/2*x^2*d^2*a^3*B + 3/2*x^2*d^2*b*a^2*A + x^2*e*d*a^3*A + x*d^2*a^3*A","B",0
1039,1,163,0,0.940693," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e b^{3} B + \frac{1}{5} x^{5} d b^{3} B + \frac{3}{5} x^{5} e b^{2} a B + \frac{1}{5} x^{5} e b^{3} A + \frac{3}{4} x^{4} d b^{2} a B + \frac{3}{4} x^{4} e b a^{2} B + \frac{1}{4} x^{4} d b^{3} A + \frac{3}{4} x^{4} e b^{2} a A + x^{3} d b a^{2} B + \frac{1}{3} x^{3} e a^{3} B + x^{3} d b^{2} a A + x^{3} e b a^{2} A + \frac{1}{2} x^{2} d a^{3} B + \frac{3}{2} x^{2} d b a^{2} A + \frac{1}{2} x^{2} e a^{3} A + x d a^{3} A"," ",0,"1/6*x^6*e*b^3*B + 1/5*x^5*d*b^3*B + 3/5*x^5*e*b^2*a*B + 1/5*x^5*e*b^3*A + 3/4*x^4*d*b^2*a*B + 3/4*x^4*e*b*a^2*B + 1/4*x^4*d*b^3*A + 3/4*x^4*e*b^2*a*A + x^3*d*b*a^2*B + 1/3*x^3*e*a^3*B + x^3*d*b^2*a*A + x^3*e*b*a^2*A + 1/2*x^2*d*a^3*B + 3/2*x^2*d*b*a^2*A + 1/2*x^2*e*a^3*A + x*d*a^3*A","B",0
1040,1,72,0,1.026590," ","integrate((b*x+a)^3*(B*x+A),x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{3} B + \frac{3}{4} x^{4} b^{2} a B + \frac{1}{4} x^{4} b^{3} A + x^{3} b a^{2} B + x^{3} b^{2} a A + \frac{1}{2} x^{2} a^{3} B + \frac{3}{2} x^{2} b a^{2} A + x a^{3} A"," ",0,"1/5*x^5*b^3*B + 3/4*x^4*b^2*a*B + 1/4*x^4*b^3*A + x^3*b*a^2*B + x^3*b^2*a*A + 1/2*x^2*a^3*B + 3/2*x^2*b*a^2*A + x*a^3*A","B",0
1041,1,260,0,1.241563," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, B b^{3} e^{4} x^{4} - 4 \, {\left(B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 6 \, {\left(B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 12 \, {\left(B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 12 \, {\left(B b^{3} d^{4} + A a^{3} e^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*B*b^3*e^4*x^4 - 4*(B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 6*(B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 - 12*(B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 12*(B*b^3*d^4 + A*a^3*e^4 - (3*B*a*b^2 + A*b^3)*d^3*e + 3*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3)*log(e*x + d))/e^5","B",0
1042,1,396,0,1.116212," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{4} x^{4} - 6 \, B b^{3} d^{4} - 6 \, A a^{3} e^{4} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 18 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(4 \, B b^{3} d e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(4 \, B b^{3} d^{2} e^{2} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(3 \, B b^{3} d^{3} e - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3}\right)} x - 6 \, {\left(4 \, B b^{3} d^{4} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + {\left(4 \, B b^{3} d^{3} e - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/6*(2*B*b^3*e^4*x^4 - 6*B*b^3*d^4 - 6*A*a^3*e^4 + 6*(3*B*a*b^2 + A*b^3)*d^3*e - 18*(B*a^2*b + A*a*b^2)*d^2*e^2 + 6*(B*a^3 + 3*A*a^2*b)*d*e^3 - (4*B*b^3*d*e^3 - 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(4*B*b^3*d^2*e^2 - 3*(3*B*a*b^2 + A*b^3)*d*e^3 + 6*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 6*(3*B*b^3*d^3*e - 2*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3)*x - 6*(4*B*b^3*d^4 - 3*(3*B*a*b^2 + A*b^3)*d^3*e + 6*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 + (4*B*b^3*d^3*e - 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x)*log(e*x + d))/(e^6*x + d*e^5)","B",0
1043,1,420,0,1.033868," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{B b^{3} e^{4} x^{4} + 7 \, B b^{3} d^{4} - A a^{3} e^{4} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 9 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 2 \, {\left(2 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} - {\left(11 \, B b^{3} d^{2} e^{2} - 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3}\right)} x^{2} + 2 \, {\left(B b^{3} d^{3} e - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 6 \, {\left(2 \, B b^{3} d^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + {\left(2 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + {\left(B a^{2} b + A a b^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(B*b^3*e^4*x^4 + 7*B*b^3*d^4 - A*a^3*e^4 - 5*(3*B*a*b^2 + A*b^3)*d^3*e + 9*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 - 2*(2*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 - (11*B*b^3*d^2*e^2 - 4*(3*B*a*b^2 + A*b^3)*d*e^3)*x^2 + 2*(B*b^3*d^3*e - 2*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 6*(2*B*b^3*d^4 - (3*B*a*b^2 + A*b^3)*d^3*e + (B*a^2*b + A*a*b^2)*d^2*e^2 + (2*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + (B*a^2*b + A*a*b^2)*e^4)*x^2 + 2*(2*B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2 + (B*a^2*b + A*a*b^2)*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","B",0
1044,1,406,0,1.143223," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{6 \, B b^{3} e^{4} x^{4} + 18 \, B b^{3} d e^{3} x^{3} - 26 \, B b^{3} d^{4} - 2 \, A a^{3} e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 18 \, {\left(B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 3 \, {\left(18 \, B b^{3} d^{3} e - 9 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x - 6 \, {\left(4 \, B b^{3} d^{4} - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + {\left(4 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(4 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(4 \, B b^{3} d^{3} e - {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/6*(6*B*b^3*e^4*x^4 + 18*B*b^3*d*e^3*x^3 - 26*B*b^3*d^4 - 2*A*a^3*e^4 + 11*(3*B*a*b^2 + A*b^3)*d^3*e - 6*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 - 18*(B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 + (B*a^2*b + A*a*b^2)*e^4)*x^2 - 3*(18*B*b^3*d^3*e - 9*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 6*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x - 6*(4*B*b^3*d^4 - (3*B*a*b^2 + A*b^3)*d^3*e + (4*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(4*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3)*x^2 + 3*(4*B*b^3*d^3*e - (3*B*a*b^2 + A*b^3)*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","B",0
1045,1,354,0,0.871148," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, B b^{3} d^{4} - 3 \, A a^{3} e^{4} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 12 \, {\left(4 \, B b^{3} d e^{3} - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 18 \, {\left(6 \, B b^{3} d^{2} e^{2} - {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} - {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 4 \, {\left(22 \, B b^{3} d^{3} e - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x + 12 \, {\left(B b^{3} e^{4} x^{4} + 4 \, B b^{3} d e^{3} x^{3} + 6 \, B b^{3} d^{2} e^{2} x^{2} + 4 \, B b^{3} d^{3} e x + B b^{3} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*B*b^3*d^4 - 3*A*a^3*e^4 - 3*(3*B*a*b^2 + A*b^3)*d^3*e - 3*(B*a^2*b + A*a*b^2)*d^2*e^2 - (B*a^3 + 3*A*a^2*b)*d*e^3 + 12*(4*B*b^3*d*e^3 - (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 18*(6*B*b^3*d^2*e^2 - (3*B*a*b^2 + A*b^3)*d*e^3 - (B*a^2*b + A*a*b^2)*e^4)*x^2 + 4*(22*B*b^3*d^3*e - 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 - 3*(B*a^2*b + A*a*b^2)*d*e^3 - (B*a^3 + 3*A*a^2*b)*e^4)*x + 12*(B*b^3*e^4*x^4 + 4*B*b^3*d*e^3*x^3 + 6*B*b^3*d^2*e^2*x^2 + 4*B*b^3*d^3*e*x + B*b^3*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","B",0
1046,1,304,0,0.757444," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{20 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 4 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 2 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 10 \, {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 10 \, {\left(4 \, B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 5 \, {\left(4 \, B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 2 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{20 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/20*(20*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 4*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 2*(B*a^2*b + A*a*b^2)*d^2*e^2 + (B*a^3 + 3*A*a^2*b)*d*e^3 + 10*(4*B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 10*(4*B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 2*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 5*(4*B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 2*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","B",0
1047,1,317,0,0.713016," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, B b^{3} e^{4} x^{4} + 2 \, B b^{3} d^{4} + 10 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 20 \, {\left(2 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 15 \, {\left(2 \, B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(2 \, B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{60 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/60*(30*B*b^3*e^4*x^4 + 2*B*b^3*d^4 + 10*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 3*(B*a^2*b + A*a*b^2)*d^2*e^2 + 2*(B*a^3 + 3*A*a^2*b)*d*e^3 + 20*(2*B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 15*(2*B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 6*(2*B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 3*(B*a^2*b + A*a*b^2)*d*e^3 + 2*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","B",0
1048,1,332,0,1.137337," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{140 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 60 \, A a^{3} e^{4} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 35 \, {\left(4 \, B b^{3} d e^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 21 \, {\left(4 \, B b^{3} d^{2} e^{2} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 7 \, {\left(4 \, B b^{3} d^{3} e + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{420 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/420*(140*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 60*A*a^3*e^4 + 3*(3*B*a*b^2 + A*b^3)*d^3*e + 12*(B*a^2*b + A*a*b^2)*d^2*e^2 + 10*(B*a^3 + 3*A*a^2*b)*d*e^3 + 35*(4*B*b^3*d*e^3 + 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 21*(4*B*b^3*d^2*e^2 + 3*(3*B*a*b^2 + A*b^3)*d*e^3 + 12*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 7*(4*B*b^3*d^3*e + 3*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 12*(B*a^2*b + A*a*b^2)*d*e^3 + 10*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","B",0
1049,1,335,0,1.198455," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{70 \, B b^{3} e^{4} x^{4} + B b^{3} d^{4} + 35 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 5 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 56 \, {\left(B b^{3} d e^{3} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 28 \, {\left(B b^{3} d^{2} e^{2} + {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 5 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 8 \, {\left(B b^{3} d^{3} e + {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 5 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{280 \, {\left(e^{13} x^{8} + 8 \, d e^{12} x^{7} + 28 \, d^{2} e^{11} x^{6} + 56 \, d^{3} e^{10} x^{5} + 70 \, d^{4} e^{9} x^{4} + 56 \, d^{5} e^{8} x^{3} + 28 \, d^{6} e^{7} x^{2} + 8 \, d^{7} e^{6} x + d^{8} e^{5}\right)}}"," ",0,"-1/280*(70*B*b^3*e^4*x^4 + B*b^3*d^4 + 35*A*a^3*e^4 + (3*B*a*b^2 + A*b^3)*d^3*e + 5*(B*a^2*b + A*a*b^2)*d^2*e^2 + 5*(B*a^3 + 3*A*a^2*b)*d*e^3 + 56*(B*b^3*d*e^3 + (3*B*a*b^2 + A*b^3)*e^4)*x^3 + 28*(B*b^3*d^2*e^2 + (3*B*a*b^2 + A*b^3)*d*e^3 + 5*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 8*(B*b^3*d^3*e + (3*B*a*b^2 + A*b^3)*d^2*e^2 + 5*(B*a^2*b + A*a*b^2)*d*e^3 + 5*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^13*x^8 + 8*d*e^12*x^7 + 28*d^2*e^11*x^6 + 56*d^3*e^10*x^5 + 70*d^4*e^9*x^4 + 56*d^5*e^8*x^3 + 28*d^6*e^7*x^2 + 8*d^7*e^6*x + d^8*e^5)","B",0
1050,1,354,0,0.592142," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{504 \, B b^{3} e^{4} x^{4} + 4 \, B b^{3} d^{4} + 280 \, A a^{3} e^{4} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} + 84 \, {\left(4 \, B b^{3} d e^{3} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 36 \, {\left(4 \, B b^{3} d^{2} e^{2} + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 30 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 9 \, {\left(4 \, B b^{3} d^{3} e + 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 30 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x}{2520 \, {\left(e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right)}}"," ",0,"-1/2520*(504*B*b^3*e^4*x^4 + 4*B*b^3*d^4 + 280*A*a^3*e^4 + 5*(3*B*a*b^2 + A*b^3)*d^3*e + 30*(B*a^2*b + A*a*b^2)*d^2*e^2 + 35*(B*a^3 + 3*A*a^2*b)*d*e^3 + 84*(4*B*b^3*d*e^3 + 5*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 36*(4*B*b^3*d^2*e^2 + 5*(3*B*a*b^2 + A*b^3)*d*e^3 + 30*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 9*(4*B*b^3*d^3*e + 5*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 30*(B*a^2*b + A*a*b^2)*d*e^3 + 35*(B*a^3 + 3*A*a^2*b)*e^4)*x)/(e^14*x^9 + 9*d*e^13*x^8 + 36*d^2*e^12*x^7 + 84*d^3*e^11*x^6 + 126*d^4*e^10*x^5 + 126*d^5*e^9*x^4 + 84*d^6*e^8*x^3 + 36*d^7*e^7*x^2 + 9*d^8*e^6*x + d^9*e^5)","B",0
1051,1,1943,0,1.132468," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^8,x, algorithm=""fricas"")","\frac{1}{16} x^{16} e^{8} b^{6} B + \frac{8}{15} x^{15} e^{7} d b^{6} B + \frac{2}{5} x^{15} e^{8} b^{5} a B + \frac{1}{15} x^{15} e^{8} b^{6} A + 2 x^{14} e^{6} d^{2} b^{6} B + \frac{24}{7} x^{14} e^{7} d b^{5} a B + \frac{15}{14} x^{14} e^{8} b^{4} a^{2} B + \frac{4}{7} x^{14} e^{7} d b^{6} A + \frac{3}{7} x^{14} e^{8} b^{5} a A + \frac{56}{13} x^{13} e^{5} d^{3} b^{6} B + \frac{168}{13} x^{13} e^{6} d^{2} b^{5} a B + \frac{120}{13} x^{13} e^{7} d b^{4} a^{2} B + \frac{20}{13} x^{13} e^{8} b^{3} a^{3} B + \frac{28}{13} x^{13} e^{6} d^{2} b^{6} A + \frac{48}{13} x^{13} e^{7} d b^{5} a A + \frac{15}{13} x^{13} e^{8} b^{4} a^{2} A + \frac{35}{6} x^{12} e^{4} d^{4} b^{6} B + 28 x^{12} e^{5} d^{3} b^{5} a B + 35 x^{12} e^{6} d^{2} b^{4} a^{2} B + \frac{40}{3} x^{12} e^{7} d b^{3} a^{3} B + \frac{5}{4} x^{12} e^{8} b^{2} a^{4} B + \frac{14}{3} x^{12} e^{5} d^{3} b^{6} A + 14 x^{12} e^{6} d^{2} b^{5} a A + 10 x^{12} e^{7} d b^{4} a^{2} A + \frac{5}{3} x^{12} e^{8} b^{3} a^{3} A + \frac{56}{11} x^{11} e^{3} d^{5} b^{6} B + \frac{420}{11} x^{11} e^{4} d^{4} b^{5} a B + \frac{840}{11} x^{11} e^{5} d^{3} b^{4} a^{2} B + \frac{560}{11} x^{11} e^{6} d^{2} b^{3} a^{3} B + \frac{120}{11} x^{11} e^{7} d b^{2} a^{4} B + \frac{6}{11} x^{11} e^{8} b a^{5} B + \frac{70}{11} x^{11} e^{4} d^{4} b^{6} A + \frac{336}{11} x^{11} e^{5} d^{3} b^{5} a A + \frac{420}{11} x^{11} e^{6} d^{2} b^{4} a^{2} A + \frac{160}{11} x^{11} e^{7} d b^{3} a^{3} A + \frac{15}{11} x^{11} e^{8} b^{2} a^{4} A + \frac{14}{5} x^{10} e^{2} d^{6} b^{6} B + \frac{168}{5} x^{10} e^{3} d^{5} b^{5} a B + 105 x^{10} e^{4} d^{4} b^{4} a^{2} B + 112 x^{10} e^{5} d^{3} b^{3} a^{3} B + 42 x^{10} e^{6} d^{2} b^{2} a^{4} B + \frac{24}{5} x^{10} e^{7} d b a^{5} B + \frac{1}{10} x^{10} e^{8} a^{6} B + \frac{28}{5} x^{10} e^{3} d^{5} b^{6} A + 42 x^{10} e^{4} d^{4} b^{5} a A + 84 x^{10} e^{5} d^{3} b^{4} a^{2} A + 56 x^{10} e^{6} d^{2} b^{3} a^{3} A + 12 x^{10} e^{7} d b^{2} a^{4} A + \frac{3}{5} x^{10} e^{8} b a^{5} A + \frac{8}{9} x^{9} e d^{7} b^{6} B + \frac{56}{3} x^{9} e^{2} d^{6} b^{5} a B + \frac{280}{3} x^{9} e^{3} d^{5} b^{4} a^{2} B + \frac{1400}{9} x^{9} e^{4} d^{4} b^{3} a^{3} B + \frac{280}{3} x^{9} e^{5} d^{3} b^{2} a^{4} B + \frac{56}{3} x^{9} e^{6} d^{2} b a^{5} B + \frac{8}{9} x^{9} e^{7} d a^{6} B + \frac{28}{9} x^{9} e^{2} d^{6} b^{6} A + \frac{112}{3} x^{9} e^{3} d^{5} b^{5} a A + \frac{350}{3} x^{9} e^{4} d^{4} b^{4} a^{2} A + \frac{1120}{9} x^{9} e^{5} d^{3} b^{3} a^{3} A + \frac{140}{3} x^{9} e^{6} d^{2} b^{2} a^{4} A + \frac{16}{3} x^{9} e^{7} d b a^{5} A + \frac{1}{9} x^{9} e^{8} a^{6} A + \frac{1}{8} x^{8} d^{8} b^{6} B + 6 x^{8} e d^{7} b^{5} a B + \frac{105}{2} x^{8} e^{2} d^{6} b^{4} a^{2} B + 140 x^{8} e^{3} d^{5} b^{3} a^{3} B + \frac{525}{4} x^{8} e^{4} d^{4} b^{2} a^{4} B + 42 x^{8} e^{5} d^{3} b a^{5} B + \frac{7}{2} x^{8} e^{6} d^{2} a^{6} B + x^{8} e d^{7} b^{6} A + 21 x^{8} e^{2} d^{6} b^{5} a A + 105 x^{8} e^{3} d^{5} b^{4} a^{2} A + 175 x^{8} e^{4} d^{4} b^{3} a^{3} A + 105 x^{8} e^{5} d^{3} b^{2} a^{4} A + 21 x^{8} e^{6} d^{2} b a^{5} A + x^{8} e^{7} d a^{6} A + \frac{6}{7} x^{7} d^{8} b^{5} a B + \frac{120}{7} x^{7} e d^{7} b^{4} a^{2} B + 80 x^{7} e^{2} d^{6} b^{3} a^{3} B + 120 x^{7} e^{3} d^{5} b^{2} a^{4} B + 60 x^{7} e^{4} d^{4} b a^{5} B + 8 x^{7} e^{5} d^{3} a^{6} B + \frac{1}{7} x^{7} d^{8} b^{6} A + \frac{48}{7} x^{7} e d^{7} b^{5} a A + 60 x^{7} e^{2} d^{6} b^{4} a^{2} A + 160 x^{7} e^{3} d^{5} b^{3} a^{3} A + 150 x^{7} e^{4} d^{4} b^{2} a^{4} A + 48 x^{7} e^{5} d^{3} b a^{5} A + 4 x^{7} e^{6} d^{2} a^{6} A + \frac{5}{2} x^{6} d^{8} b^{4} a^{2} B + \frac{80}{3} x^{6} e d^{7} b^{3} a^{3} B + 70 x^{6} e^{2} d^{6} b^{2} a^{4} B + 56 x^{6} e^{3} d^{5} b a^{5} B + \frac{35}{3} x^{6} e^{4} d^{4} a^{6} B + x^{6} d^{8} b^{5} a A + 20 x^{6} e d^{7} b^{4} a^{2} A + \frac{280}{3} x^{6} e^{2} d^{6} b^{3} a^{3} A + 140 x^{6} e^{3} d^{5} b^{2} a^{4} A + 70 x^{6} e^{4} d^{4} b a^{5} A + \frac{28}{3} x^{6} e^{5} d^{3} a^{6} A + 4 x^{5} d^{8} b^{3} a^{3} B + 24 x^{5} e d^{7} b^{2} a^{4} B + \frac{168}{5} x^{5} e^{2} d^{6} b a^{5} B + \frac{56}{5} x^{5} e^{3} d^{5} a^{6} B + 3 x^{5} d^{8} b^{4} a^{2} A + 32 x^{5} e d^{7} b^{3} a^{3} A + 84 x^{5} e^{2} d^{6} b^{2} a^{4} A + \frac{336}{5} x^{5} e^{3} d^{5} b a^{5} A + 14 x^{5} e^{4} d^{4} a^{6} A + \frac{15}{4} x^{4} d^{8} b^{2} a^{4} B + 12 x^{4} e d^{7} b a^{5} B + 7 x^{4} e^{2} d^{6} a^{6} B + 5 x^{4} d^{8} b^{3} a^{3} A + 30 x^{4} e d^{7} b^{2} a^{4} A + 42 x^{4} e^{2} d^{6} b a^{5} A + 14 x^{4} e^{3} d^{5} a^{6} A + 2 x^{3} d^{8} b a^{5} B + \frac{8}{3} x^{3} e d^{7} a^{6} B + 5 x^{3} d^{8} b^{2} a^{4} A + 16 x^{3} e d^{7} b a^{5} A + \frac{28}{3} x^{3} e^{2} d^{6} a^{6} A + \frac{1}{2} x^{2} d^{8} a^{6} B + 3 x^{2} d^{8} b a^{5} A + 4 x^{2} e d^{7} a^{6} A + x d^{8} a^{6} A"," ",0,"1/16*x^16*e^8*b^6*B + 8/15*x^15*e^7*d*b^6*B + 2/5*x^15*e^8*b^5*a*B + 1/15*x^15*e^8*b^6*A + 2*x^14*e^6*d^2*b^6*B + 24/7*x^14*e^7*d*b^5*a*B + 15/14*x^14*e^8*b^4*a^2*B + 4/7*x^14*e^7*d*b^6*A + 3/7*x^14*e^8*b^5*a*A + 56/13*x^13*e^5*d^3*b^6*B + 168/13*x^13*e^6*d^2*b^5*a*B + 120/13*x^13*e^7*d*b^4*a^2*B + 20/13*x^13*e^8*b^3*a^3*B + 28/13*x^13*e^6*d^2*b^6*A + 48/13*x^13*e^7*d*b^5*a*A + 15/13*x^13*e^8*b^4*a^2*A + 35/6*x^12*e^4*d^4*b^6*B + 28*x^12*e^5*d^3*b^5*a*B + 35*x^12*e^6*d^2*b^4*a^2*B + 40/3*x^12*e^7*d*b^3*a^3*B + 5/4*x^12*e^8*b^2*a^4*B + 14/3*x^12*e^5*d^3*b^6*A + 14*x^12*e^6*d^2*b^5*a*A + 10*x^12*e^7*d*b^4*a^2*A + 5/3*x^12*e^8*b^3*a^3*A + 56/11*x^11*e^3*d^5*b^6*B + 420/11*x^11*e^4*d^4*b^5*a*B + 840/11*x^11*e^5*d^3*b^4*a^2*B + 560/11*x^11*e^6*d^2*b^3*a^3*B + 120/11*x^11*e^7*d*b^2*a^4*B + 6/11*x^11*e^8*b*a^5*B + 70/11*x^11*e^4*d^4*b^6*A + 336/11*x^11*e^5*d^3*b^5*a*A + 420/11*x^11*e^6*d^2*b^4*a^2*A + 160/11*x^11*e^7*d*b^3*a^3*A + 15/11*x^11*e^8*b^2*a^4*A + 14/5*x^10*e^2*d^6*b^6*B + 168/5*x^10*e^3*d^5*b^5*a*B + 105*x^10*e^4*d^4*b^4*a^2*B + 112*x^10*e^5*d^3*b^3*a^3*B + 42*x^10*e^6*d^2*b^2*a^4*B + 24/5*x^10*e^7*d*b*a^5*B + 1/10*x^10*e^8*a^6*B + 28/5*x^10*e^3*d^5*b^6*A + 42*x^10*e^4*d^4*b^5*a*A + 84*x^10*e^5*d^3*b^4*a^2*A + 56*x^10*e^6*d^2*b^3*a^3*A + 12*x^10*e^7*d*b^2*a^4*A + 3/5*x^10*e^8*b*a^5*A + 8/9*x^9*e*d^7*b^6*B + 56/3*x^9*e^2*d^6*b^5*a*B + 280/3*x^9*e^3*d^5*b^4*a^2*B + 1400/9*x^9*e^4*d^4*b^3*a^3*B + 280/3*x^9*e^5*d^3*b^2*a^4*B + 56/3*x^9*e^6*d^2*b*a^5*B + 8/9*x^9*e^7*d*a^6*B + 28/9*x^9*e^2*d^6*b^6*A + 112/3*x^9*e^3*d^5*b^5*a*A + 350/3*x^9*e^4*d^4*b^4*a^2*A + 1120/9*x^9*e^5*d^3*b^3*a^3*A + 140/3*x^9*e^6*d^2*b^2*a^4*A + 16/3*x^9*e^7*d*b*a^5*A + 1/9*x^9*e^8*a^6*A + 1/8*x^8*d^8*b^6*B + 6*x^8*e*d^7*b^5*a*B + 105/2*x^8*e^2*d^6*b^4*a^2*B + 140*x^8*e^3*d^5*b^3*a^3*B + 525/4*x^8*e^4*d^4*b^2*a^4*B + 42*x^8*e^5*d^3*b*a^5*B + 7/2*x^8*e^6*d^2*a^6*B + x^8*e*d^7*b^6*A + 21*x^8*e^2*d^6*b^5*a*A + 105*x^8*e^3*d^5*b^4*a^2*A + 175*x^8*e^4*d^4*b^3*a^3*A + 105*x^8*e^5*d^3*b^2*a^4*A + 21*x^8*e^6*d^2*b*a^5*A + x^8*e^7*d*a^6*A + 6/7*x^7*d^8*b^5*a*B + 120/7*x^7*e*d^7*b^4*a^2*B + 80*x^7*e^2*d^6*b^3*a^3*B + 120*x^7*e^3*d^5*b^2*a^4*B + 60*x^7*e^4*d^4*b*a^5*B + 8*x^7*e^5*d^3*a^6*B + 1/7*x^7*d^8*b^6*A + 48/7*x^7*e*d^7*b^5*a*A + 60*x^7*e^2*d^6*b^4*a^2*A + 160*x^7*e^3*d^5*b^3*a^3*A + 150*x^7*e^4*d^4*b^2*a^4*A + 48*x^7*e^5*d^3*b*a^5*A + 4*x^7*e^6*d^2*a^6*A + 5/2*x^6*d^8*b^4*a^2*B + 80/3*x^6*e*d^7*b^3*a^3*B + 70*x^6*e^2*d^6*b^2*a^4*B + 56*x^6*e^3*d^5*b*a^5*B + 35/3*x^6*e^4*d^4*a^6*B + x^6*d^8*b^5*a*A + 20*x^6*e*d^7*b^4*a^2*A + 280/3*x^6*e^2*d^6*b^3*a^3*A + 140*x^6*e^3*d^5*b^2*a^4*A + 70*x^6*e^4*d^4*b*a^5*A + 28/3*x^6*e^5*d^3*a^6*A + 4*x^5*d^8*b^3*a^3*B + 24*x^5*e*d^7*b^2*a^4*B + 168/5*x^5*e^2*d^6*b*a^5*B + 56/5*x^5*e^3*d^5*a^6*B + 3*x^5*d^8*b^4*a^2*A + 32*x^5*e*d^7*b^3*a^3*A + 84*x^5*e^2*d^6*b^2*a^4*A + 336/5*x^5*e^3*d^5*b*a^5*A + 14*x^5*e^4*d^4*a^6*A + 15/4*x^4*d^8*b^2*a^4*B + 12*x^4*e*d^7*b*a^5*B + 7*x^4*e^2*d^6*a^6*B + 5*x^4*d^8*b^3*a^3*A + 30*x^4*e*d^7*b^2*a^4*A + 42*x^4*e^2*d^6*b*a^5*A + 14*x^4*e^3*d^5*a^6*A + 2*x^3*d^8*b*a^5*B + 8/3*x^3*e*d^7*a^6*B + 5*x^3*d^8*b^2*a^4*A + 16*x^3*e*d^7*b*a^5*A + 28/3*x^3*e^2*d^6*a^6*A + 1/2*x^2*d^8*a^6*B + 3*x^2*d^8*b*a^5*A + 4*x^2*e*d^7*a^6*A + x*d^8*a^6*A","B",0
1052,1,1712,0,1.052398," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^7,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{7} b^{6} B + \frac{1}{2} x^{14} e^{6} d b^{6} B + \frac{3}{7} x^{14} e^{7} b^{5} a B + \frac{1}{14} x^{14} e^{7} b^{6} A + \frac{21}{13} x^{13} e^{5} d^{2} b^{6} B + \frac{42}{13} x^{13} e^{6} d b^{5} a B + \frac{15}{13} x^{13} e^{7} b^{4} a^{2} B + \frac{7}{13} x^{13} e^{6} d b^{6} A + \frac{6}{13} x^{13} e^{7} b^{5} a A + \frac{35}{12} x^{12} e^{4} d^{3} b^{6} B + \frac{21}{2} x^{12} e^{5} d^{2} b^{5} a B + \frac{35}{4} x^{12} e^{6} d b^{4} a^{2} B + \frac{5}{3} x^{12} e^{7} b^{3} a^{3} B + \frac{7}{4} x^{12} e^{5} d^{2} b^{6} A + \frac{7}{2} x^{12} e^{6} d b^{5} a A + \frac{5}{4} x^{12} e^{7} b^{4} a^{2} A + \frac{35}{11} x^{11} e^{3} d^{4} b^{6} B + \frac{210}{11} x^{11} e^{4} d^{3} b^{5} a B + \frac{315}{11} x^{11} e^{5} d^{2} b^{4} a^{2} B + \frac{140}{11} x^{11} e^{6} d b^{3} a^{3} B + \frac{15}{11} x^{11} e^{7} b^{2} a^{4} B + \frac{35}{11} x^{11} e^{4} d^{3} b^{6} A + \frac{126}{11} x^{11} e^{5} d^{2} b^{5} a A + \frac{105}{11} x^{11} e^{6} d b^{4} a^{2} A + \frac{20}{11} x^{11} e^{7} b^{3} a^{3} A + \frac{21}{10} x^{10} e^{2} d^{5} b^{6} B + 21 x^{10} e^{3} d^{4} b^{5} a B + \frac{105}{2} x^{10} e^{4} d^{3} b^{4} a^{2} B + 42 x^{10} e^{5} d^{2} b^{3} a^{3} B + \frac{21}{2} x^{10} e^{6} d b^{2} a^{4} B + \frac{3}{5} x^{10} e^{7} b a^{5} B + \frac{7}{2} x^{10} e^{3} d^{4} b^{6} A + 21 x^{10} e^{4} d^{3} b^{5} a A + \frac{63}{2} x^{10} e^{5} d^{2} b^{4} a^{2} A + 14 x^{10} e^{6} d b^{3} a^{3} A + \frac{3}{2} x^{10} e^{7} b^{2} a^{4} A + \frac{7}{9} x^{9} e d^{6} b^{6} B + 14 x^{9} e^{2} d^{5} b^{5} a B + \frac{175}{3} x^{9} e^{3} d^{4} b^{4} a^{2} B + \frac{700}{9} x^{9} e^{4} d^{3} b^{3} a^{3} B + 35 x^{9} e^{5} d^{2} b^{2} a^{4} B + \frac{14}{3} x^{9} e^{6} d b a^{5} B + \frac{1}{9} x^{9} e^{7} a^{6} B + \frac{7}{3} x^{9} e^{2} d^{5} b^{6} A + \frac{70}{3} x^{9} e^{3} d^{4} b^{5} a A + \frac{175}{3} x^{9} e^{4} d^{3} b^{4} a^{2} A + \frac{140}{3} x^{9} e^{5} d^{2} b^{3} a^{3} A + \frac{35}{3} x^{9} e^{6} d b^{2} a^{4} A + \frac{2}{3} x^{9} e^{7} b a^{5} A + \frac{1}{8} x^{8} d^{7} b^{6} B + \frac{21}{4} x^{8} e d^{6} b^{5} a B + \frac{315}{8} x^{8} e^{2} d^{5} b^{4} a^{2} B + \frac{175}{2} x^{8} e^{3} d^{4} b^{3} a^{3} B + \frac{525}{8} x^{8} e^{4} d^{3} b^{2} a^{4} B + \frac{63}{4} x^{8} e^{5} d^{2} b a^{5} B + \frac{7}{8} x^{8} e^{6} d a^{6} B + \frac{7}{8} x^{8} e d^{6} b^{6} A + \frac{63}{4} x^{8} e^{2} d^{5} b^{5} a A + \frac{525}{8} x^{8} e^{3} d^{4} b^{4} a^{2} A + \frac{175}{2} x^{8} e^{4} d^{3} b^{3} a^{3} A + \frac{315}{8} x^{8} e^{5} d^{2} b^{2} a^{4} A + \frac{21}{4} x^{8} e^{6} d b a^{5} A + \frac{1}{8} x^{8} e^{7} a^{6} A + \frac{6}{7} x^{7} d^{7} b^{5} a B + 15 x^{7} e d^{6} b^{4} a^{2} B + 60 x^{7} e^{2} d^{5} b^{3} a^{3} B + 75 x^{7} e^{3} d^{4} b^{2} a^{4} B + 30 x^{7} e^{4} d^{3} b a^{5} B + 3 x^{7} e^{5} d^{2} a^{6} B + \frac{1}{7} x^{7} d^{7} b^{6} A + 6 x^{7} e d^{6} b^{5} a A + 45 x^{7} e^{2} d^{5} b^{4} a^{2} A + 100 x^{7} e^{3} d^{4} b^{3} a^{3} A + 75 x^{7} e^{4} d^{3} b^{2} a^{4} A + 18 x^{7} e^{5} d^{2} b a^{5} A + x^{7} e^{6} d a^{6} A + \frac{5}{2} x^{6} d^{7} b^{4} a^{2} B + \frac{70}{3} x^{6} e d^{6} b^{3} a^{3} B + \frac{105}{2} x^{6} e^{2} d^{5} b^{2} a^{4} B + 35 x^{6} e^{3} d^{4} b a^{5} B + \frac{35}{6} x^{6} e^{4} d^{3} a^{6} B + x^{6} d^{7} b^{5} a A + \frac{35}{2} x^{6} e d^{6} b^{4} a^{2} A + 70 x^{6} e^{2} d^{5} b^{3} a^{3} A + \frac{175}{2} x^{6} e^{3} d^{4} b^{2} a^{4} A + 35 x^{6} e^{4} d^{3} b a^{5} A + \frac{7}{2} x^{6} e^{5} d^{2} a^{6} A + 4 x^{5} d^{7} b^{3} a^{3} B + 21 x^{5} e d^{6} b^{2} a^{4} B + \frac{126}{5} x^{5} e^{2} d^{5} b a^{5} B + 7 x^{5} e^{3} d^{4} a^{6} B + 3 x^{5} d^{7} b^{4} a^{2} A + 28 x^{5} e d^{6} b^{3} a^{3} A + 63 x^{5} e^{2} d^{5} b^{2} a^{4} A + 42 x^{5} e^{3} d^{4} b a^{5} A + 7 x^{5} e^{4} d^{3} a^{6} A + \frac{15}{4} x^{4} d^{7} b^{2} a^{4} B + \frac{21}{2} x^{4} e d^{6} b a^{5} B + \frac{21}{4} x^{4} e^{2} d^{5} a^{6} B + 5 x^{4} d^{7} b^{3} a^{3} A + \frac{105}{4} x^{4} e d^{6} b^{2} a^{4} A + \frac{63}{2} x^{4} e^{2} d^{5} b a^{5} A + \frac{35}{4} x^{4} e^{3} d^{4} a^{6} A + 2 x^{3} d^{7} b a^{5} B + \frac{7}{3} x^{3} e d^{6} a^{6} B + 5 x^{3} d^{7} b^{2} a^{4} A + 14 x^{3} e d^{6} b a^{5} A + 7 x^{3} e^{2} d^{5} a^{6} A + \frac{1}{2} x^{2} d^{7} a^{6} B + 3 x^{2} d^{7} b a^{5} A + \frac{7}{2} x^{2} e d^{6} a^{6} A + x d^{7} a^{6} A"," ",0,"1/15*x^15*e^7*b^6*B + 1/2*x^14*e^6*d*b^6*B + 3/7*x^14*e^7*b^5*a*B + 1/14*x^14*e^7*b^6*A + 21/13*x^13*e^5*d^2*b^6*B + 42/13*x^13*e^6*d*b^5*a*B + 15/13*x^13*e^7*b^4*a^2*B + 7/13*x^13*e^6*d*b^6*A + 6/13*x^13*e^7*b^5*a*A + 35/12*x^12*e^4*d^3*b^6*B + 21/2*x^12*e^5*d^2*b^5*a*B + 35/4*x^12*e^6*d*b^4*a^2*B + 5/3*x^12*e^7*b^3*a^3*B + 7/4*x^12*e^5*d^2*b^6*A + 7/2*x^12*e^6*d*b^5*a*A + 5/4*x^12*e^7*b^4*a^2*A + 35/11*x^11*e^3*d^4*b^6*B + 210/11*x^11*e^4*d^3*b^5*a*B + 315/11*x^11*e^5*d^2*b^4*a^2*B + 140/11*x^11*e^6*d*b^3*a^3*B + 15/11*x^11*e^7*b^2*a^4*B + 35/11*x^11*e^4*d^3*b^6*A + 126/11*x^11*e^5*d^2*b^5*a*A + 105/11*x^11*e^6*d*b^4*a^2*A + 20/11*x^11*e^7*b^3*a^3*A + 21/10*x^10*e^2*d^5*b^6*B + 21*x^10*e^3*d^4*b^5*a*B + 105/2*x^10*e^4*d^3*b^4*a^2*B + 42*x^10*e^5*d^2*b^3*a^3*B + 21/2*x^10*e^6*d*b^2*a^4*B + 3/5*x^10*e^7*b*a^5*B + 7/2*x^10*e^3*d^4*b^6*A + 21*x^10*e^4*d^3*b^5*a*A + 63/2*x^10*e^5*d^2*b^4*a^2*A + 14*x^10*e^6*d*b^3*a^3*A + 3/2*x^10*e^7*b^2*a^4*A + 7/9*x^9*e*d^6*b^6*B + 14*x^9*e^2*d^5*b^5*a*B + 175/3*x^9*e^3*d^4*b^4*a^2*B + 700/9*x^9*e^4*d^3*b^3*a^3*B + 35*x^9*e^5*d^2*b^2*a^4*B + 14/3*x^9*e^6*d*b*a^5*B + 1/9*x^9*e^7*a^6*B + 7/3*x^9*e^2*d^5*b^6*A + 70/3*x^9*e^3*d^4*b^5*a*A + 175/3*x^9*e^4*d^3*b^4*a^2*A + 140/3*x^9*e^5*d^2*b^3*a^3*A + 35/3*x^9*e^6*d*b^2*a^4*A + 2/3*x^9*e^7*b*a^5*A + 1/8*x^8*d^7*b^6*B + 21/4*x^8*e*d^6*b^5*a*B + 315/8*x^8*e^2*d^5*b^4*a^2*B + 175/2*x^8*e^3*d^4*b^3*a^3*B + 525/8*x^8*e^4*d^3*b^2*a^4*B + 63/4*x^8*e^5*d^2*b*a^5*B + 7/8*x^8*e^6*d*a^6*B + 7/8*x^8*e*d^6*b^6*A + 63/4*x^8*e^2*d^5*b^5*a*A + 525/8*x^8*e^3*d^4*b^4*a^2*A + 175/2*x^8*e^4*d^3*b^3*a^3*A + 315/8*x^8*e^5*d^2*b^2*a^4*A + 21/4*x^8*e^6*d*b*a^5*A + 1/8*x^8*e^7*a^6*A + 6/7*x^7*d^7*b^5*a*B + 15*x^7*e*d^6*b^4*a^2*B + 60*x^7*e^2*d^5*b^3*a^3*B + 75*x^7*e^3*d^4*b^2*a^4*B + 30*x^7*e^4*d^3*b*a^5*B + 3*x^7*e^5*d^2*a^6*B + 1/7*x^7*d^7*b^6*A + 6*x^7*e*d^6*b^5*a*A + 45*x^7*e^2*d^5*b^4*a^2*A + 100*x^7*e^3*d^4*b^3*a^3*A + 75*x^7*e^4*d^3*b^2*a^4*A + 18*x^7*e^5*d^2*b*a^5*A + x^7*e^6*d*a^6*A + 5/2*x^6*d^7*b^4*a^2*B + 70/3*x^6*e*d^6*b^3*a^3*B + 105/2*x^6*e^2*d^5*b^2*a^4*B + 35*x^6*e^3*d^4*b*a^5*B + 35/6*x^6*e^4*d^3*a^6*B + x^6*d^7*b^5*a*A + 35/2*x^6*e*d^6*b^4*a^2*A + 70*x^6*e^2*d^5*b^3*a^3*A + 175/2*x^6*e^3*d^4*b^2*a^4*A + 35*x^6*e^4*d^3*b*a^5*A + 7/2*x^6*e^5*d^2*a^6*A + 4*x^5*d^7*b^3*a^3*B + 21*x^5*e*d^6*b^2*a^4*B + 126/5*x^5*e^2*d^5*b*a^5*B + 7*x^5*e^3*d^4*a^6*B + 3*x^5*d^7*b^4*a^2*A + 28*x^5*e*d^6*b^3*a^3*A + 63*x^5*e^2*d^5*b^2*a^4*A + 42*x^5*e^3*d^4*b*a^5*A + 7*x^5*e^4*d^3*a^6*A + 15/4*x^4*d^7*b^2*a^4*B + 21/2*x^4*e*d^6*b*a^5*B + 21/4*x^4*e^2*d^5*a^6*B + 5*x^4*d^7*b^3*a^3*A + 105/4*x^4*e*d^6*b^2*a^4*A + 63/2*x^4*e^2*d^5*b*a^5*A + 35/4*x^4*e^3*d^4*a^6*A + 2*x^3*d^7*b*a^5*B + 7/3*x^3*e*d^6*a^6*B + 5*x^3*d^7*b^2*a^4*A + 14*x^3*e*d^6*b*a^5*A + 7*x^3*e^2*d^5*a^6*A + 1/2*x^2*d^7*a^6*B + 3*x^2*d^7*b*a^5*A + 7/2*x^2*e*d^6*a^6*A + x*d^7*a^6*A","B",0
1053,1,1480,0,0.988565," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^6,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e^{6} b^{6} B + \frac{6}{13} x^{13} e^{5} d b^{6} B + \frac{6}{13} x^{13} e^{6} b^{5} a B + \frac{1}{13} x^{13} e^{6} b^{6} A + \frac{5}{4} x^{12} e^{4} d^{2} b^{6} B + 3 x^{12} e^{5} d b^{5} a B + \frac{5}{4} x^{12} e^{6} b^{4} a^{2} B + \frac{1}{2} x^{12} e^{5} d b^{6} A + \frac{1}{2} x^{12} e^{6} b^{5} a A + \frac{20}{11} x^{11} e^{3} d^{3} b^{6} B + \frac{90}{11} x^{11} e^{4} d^{2} b^{5} a B + \frac{90}{11} x^{11} e^{5} d b^{4} a^{2} B + \frac{20}{11} x^{11} e^{6} b^{3} a^{3} B + \frac{15}{11} x^{11} e^{4} d^{2} b^{6} A + \frac{36}{11} x^{11} e^{5} d b^{5} a A + \frac{15}{11} x^{11} e^{6} b^{4} a^{2} A + \frac{3}{2} x^{10} e^{2} d^{4} b^{6} B + 12 x^{10} e^{3} d^{3} b^{5} a B + \frac{45}{2} x^{10} e^{4} d^{2} b^{4} a^{2} B + 12 x^{10} e^{5} d b^{3} a^{3} B + \frac{3}{2} x^{10} e^{6} b^{2} a^{4} B + 2 x^{10} e^{3} d^{3} b^{6} A + 9 x^{10} e^{4} d^{2} b^{5} a A + 9 x^{10} e^{5} d b^{4} a^{2} A + 2 x^{10} e^{6} b^{3} a^{3} A + \frac{2}{3} x^{9} e d^{5} b^{6} B + 10 x^{9} e^{2} d^{4} b^{5} a B + \frac{100}{3} x^{9} e^{3} d^{3} b^{4} a^{2} B + \frac{100}{3} x^{9} e^{4} d^{2} b^{3} a^{3} B + 10 x^{9} e^{5} d b^{2} a^{4} B + \frac{2}{3} x^{9} e^{6} b a^{5} B + \frac{5}{3} x^{9} e^{2} d^{4} b^{6} A + \frac{40}{3} x^{9} e^{3} d^{3} b^{5} a A + 25 x^{9} e^{4} d^{2} b^{4} a^{2} A + \frac{40}{3} x^{9} e^{5} d b^{3} a^{3} A + \frac{5}{3} x^{9} e^{6} b^{2} a^{4} A + \frac{1}{8} x^{8} d^{6} b^{6} B + \frac{9}{2} x^{8} e d^{5} b^{5} a B + \frac{225}{8} x^{8} e^{2} d^{4} b^{4} a^{2} B + 50 x^{8} e^{3} d^{3} b^{3} a^{3} B + \frac{225}{8} x^{8} e^{4} d^{2} b^{2} a^{4} B + \frac{9}{2} x^{8} e^{5} d b a^{5} B + \frac{1}{8} x^{8} e^{6} a^{6} B + \frac{3}{4} x^{8} e d^{5} b^{6} A + \frac{45}{4} x^{8} e^{2} d^{4} b^{5} a A + \frac{75}{2} x^{8} e^{3} d^{3} b^{4} a^{2} A + \frac{75}{2} x^{8} e^{4} d^{2} b^{3} a^{3} A + \frac{45}{4} x^{8} e^{5} d b^{2} a^{4} A + \frac{3}{4} x^{8} e^{6} b a^{5} A + \frac{6}{7} x^{7} d^{6} b^{5} a B + \frac{90}{7} x^{7} e d^{5} b^{4} a^{2} B + \frac{300}{7} x^{7} e^{2} d^{4} b^{3} a^{3} B + \frac{300}{7} x^{7} e^{3} d^{3} b^{2} a^{4} B + \frac{90}{7} x^{7} e^{4} d^{2} b a^{5} B + \frac{6}{7} x^{7} e^{5} d a^{6} B + \frac{1}{7} x^{7} d^{6} b^{6} A + \frac{36}{7} x^{7} e d^{5} b^{5} a A + \frac{225}{7} x^{7} e^{2} d^{4} b^{4} a^{2} A + \frac{400}{7} x^{7} e^{3} d^{3} b^{3} a^{3} A + \frac{225}{7} x^{7} e^{4} d^{2} b^{2} a^{4} A + \frac{36}{7} x^{7} e^{5} d b a^{5} A + \frac{1}{7} x^{7} e^{6} a^{6} A + \frac{5}{2} x^{6} d^{6} b^{4} a^{2} B + 20 x^{6} e d^{5} b^{3} a^{3} B + \frac{75}{2} x^{6} e^{2} d^{4} b^{2} a^{4} B + 20 x^{6} e^{3} d^{3} b a^{5} B + \frac{5}{2} x^{6} e^{4} d^{2} a^{6} B + x^{6} d^{6} b^{5} a A + 15 x^{6} e d^{5} b^{4} a^{2} A + 50 x^{6} e^{2} d^{4} b^{3} a^{3} A + 50 x^{6} e^{3} d^{3} b^{2} a^{4} A + 15 x^{6} e^{4} d^{2} b a^{5} A + x^{6} e^{5} d a^{6} A + 4 x^{5} d^{6} b^{3} a^{3} B + 18 x^{5} e d^{5} b^{2} a^{4} B + 18 x^{5} e^{2} d^{4} b a^{5} B + 4 x^{5} e^{3} d^{3} a^{6} B + 3 x^{5} d^{6} b^{4} a^{2} A + 24 x^{5} e d^{5} b^{3} a^{3} A + 45 x^{5} e^{2} d^{4} b^{2} a^{4} A + 24 x^{5} e^{3} d^{3} b a^{5} A + 3 x^{5} e^{4} d^{2} a^{6} A + \frac{15}{4} x^{4} d^{6} b^{2} a^{4} B + 9 x^{4} e d^{5} b a^{5} B + \frac{15}{4} x^{4} e^{2} d^{4} a^{6} B + 5 x^{4} d^{6} b^{3} a^{3} A + \frac{45}{2} x^{4} e d^{5} b^{2} a^{4} A + \frac{45}{2} x^{4} e^{2} d^{4} b a^{5} A + 5 x^{4} e^{3} d^{3} a^{6} A + 2 x^{3} d^{6} b a^{5} B + 2 x^{3} e d^{5} a^{6} B + 5 x^{3} d^{6} b^{2} a^{4} A + 12 x^{3} e d^{5} b a^{5} A + 5 x^{3} e^{2} d^{4} a^{6} A + \frac{1}{2} x^{2} d^{6} a^{6} B + 3 x^{2} d^{6} b a^{5} A + 3 x^{2} e d^{5} a^{6} A + x d^{6} a^{6} A"," ",0,"1/14*x^14*e^6*b^6*B + 6/13*x^13*e^5*d*b^6*B + 6/13*x^13*e^6*b^5*a*B + 1/13*x^13*e^6*b^6*A + 5/4*x^12*e^4*d^2*b^6*B + 3*x^12*e^5*d*b^5*a*B + 5/4*x^12*e^6*b^4*a^2*B + 1/2*x^12*e^5*d*b^6*A + 1/2*x^12*e^6*b^5*a*A + 20/11*x^11*e^3*d^3*b^6*B + 90/11*x^11*e^4*d^2*b^5*a*B + 90/11*x^11*e^5*d*b^4*a^2*B + 20/11*x^11*e^6*b^3*a^3*B + 15/11*x^11*e^4*d^2*b^6*A + 36/11*x^11*e^5*d*b^5*a*A + 15/11*x^11*e^6*b^4*a^2*A + 3/2*x^10*e^2*d^4*b^6*B + 12*x^10*e^3*d^3*b^5*a*B + 45/2*x^10*e^4*d^2*b^4*a^2*B + 12*x^10*e^5*d*b^3*a^3*B + 3/2*x^10*e^6*b^2*a^4*B + 2*x^10*e^3*d^3*b^6*A + 9*x^10*e^4*d^2*b^5*a*A + 9*x^10*e^5*d*b^4*a^2*A + 2*x^10*e^6*b^3*a^3*A + 2/3*x^9*e*d^5*b^6*B + 10*x^9*e^2*d^4*b^5*a*B + 100/3*x^9*e^3*d^3*b^4*a^2*B + 100/3*x^9*e^4*d^2*b^3*a^3*B + 10*x^9*e^5*d*b^2*a^4*B + 2/3*x^9*e^6*b*a^5*B + 5/3*x^9*e^2*d^4*b^6*A + 40/3*x^9*e^3*d^3*b^5*a*A + 25*x^9*e^4*d^2*b^4*a^2*A + 40/3*x^9*e^5*d*b^3*a^3*A + 5/3*x^9*e^6*b^2*a^4*A + 1/8*x^8*d^6*b^6*B + 9/2*x^8*e*d^5*b^5*a*B + 225/8*x^8*e^2*d^4*b^4*a^2*B + 50*x^8*e^3*d^3*b^3*a^3*B + 225/8*x^8*e^4*d^2*b^2*a^4*B + 9/2*x^8*e^5*d*b*a^5*B + 1/8*x^8*e^6*a^6*B + 3/4*x^8*e*d^5*b^6*A + 45/4*x^8*e^2*d^4*b^5*a*A + 75/2*x^8*e^3*d^3*b^4*a^2*A + 75/2*x^8*e^4*d^2*b^3*a^3*A + 45/4*x^8*e^5*d*b^2*a^4*A + 3/4*x^8*e^6*b*a^5*A + 6/7*x^7*d^6*b^5*a*B + 90/7*x^7*e*d^5*b^4*a^2*B + 300/7*x^7*e^2*d^4*b^3*a^3*B + 300/7*x^7*e^3*d^3*b^2*a^4*B + 90/7*x^7*e^4*d^2*b*a^5*B + 6/7*x^7*e^5*d*a^6*B + 1/7*x^7*d^6*b^6*A + 36/7*x^7*e*d^5*b^5*a*A + 225/7*x^7*e^2*d^4*b^4*a^2*A + 400/7*x^7*e^3*d^3*b^3*a^3*A + 225/7*x^7*e^4*d^2*b^2*a^4*A + 36/7*x^7*e^5*d*b*a^5*A + 1/7*x^7*e^6*a^6*A + 5/2*x^6*d^6*b^4*a^2*B + 20*x^6*e*d^5*b^3*a^3*B + 75/2*x^6*e^2*d^4*b^2*a^4*B + 20*x^6*e^3*d^3*b*a^5*B + 5/2*x^6*e^4*d^2*a^6*B + x^6*d^6*b^5*a*A + 15*x^6*e*d^5*b^4*a^2*A + 50*x^6*e^2*d^4*b^3*a^3*A + 50*x^6*e^3*d^3*b^2*a^4*A + 15*x^6*e^4*d^2*b*a^5*A + x^6*e^5*d*a^6*A + 4*x^5*d^6*b^3*a^3*B + 18*x^5*e*d^5*b^2*a^4*B + 18*x^5*e^2*d^4*b*a^5*B + 4*x^5*e^3*d^3*a^6*B + 3*x^5*d^6*b^4*a^2*A + 24*x^5*e*d^5*b^3*a^3*A + 45*x^5*e^2*d^4*b^2*a^4*A + 24*x^5*e^3*d^3*b*a^5*A + 3*x^5*e^4*d^2*a^6*A + 15/4*x^4*d^6*b^2*a^4*B + 9*x^4*e*d^5*b*a^5*B + 15/4*x^4*e^2*d^4*a^6*B + 5*x^4*d^6*b^3*a^3*A + 45/2*x^4*e*d^5*b^2*a^4*A + 45/2*x^4*e^2*d^4*b*a^5*A + 5*x^4*e^3*d^3*a^6*A + 2*x^3*d^6*b*a^5*B + 2*x^3*e*d^5*a^6*B + 5*x^3*d^6*b^2*a^4*A + 12*x^3*e*d^5*b*a^5*A + 5*x^3*e^2*d^4*a^6*A + 1/2*x^2*d^6*a^6*B + 3*x^2*d^6*b*a^5*A + 3*x^2*e*d^5*a^6*A + x*d^6*a^6*A","B",0
1054,1,1246,0,0.855914," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^5,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{5} b^{6} B + \frac{5}{12} x^{12} e^{4} d b^{6} B + \frac{1}{2} x^{12} e^{5} b^{5} a B + \frac{1}{12} x^{12} e^{5} b^{6} A + \frac{10}{11} x^{11} e^{3} d^{2} b^{6} B + \frac{30}{11} x^{11} e^{4} d b^{5} a B + \frac{15}{11} x^{11} e^{5} b^{4} a^{2} B + \frac{5}{11} x^{11} e^{4} d b^{6} A + \frac{6}{11} x^{11} e^{5} b^{5} a A + x^{10} e^{2} d^{3} b^{6} B + 6 x^{10} e^{3} d^{2} b^{5} a B + \frac{15}{2} x^{10} e^{4} d b^{4} a^{2} B + 2 x^{10} e^{5} b^{3} a^{3} B + x^{10} e^{3} d^{2} b^{6} A + 3 x^{10} e^{4} d b^{5} a A + \frac{3}{2} x^{10} e^{5} b^{4} a^{2} A + \frac{5}{9} x^{9} e d^{4} b^{6} B + \frac{20}{3} x^{9} e^{2} d^{3} b^{5} a B + \frac{50}{3} x^{9} e^{3} d^{2} b^{4} a^{2} B + \frac{100}{9} x^{9} e^{4} d b^{3} a^{3} B + \frac{5}{3} x^{9} e^{5} b^{2} a^{4} B + \frac{10}{9} x^{9} e^{2} d^{3} b^{6} A + \frac{20}{3} x^{9} e^{3} d^{2} b^{5} a A + \frac{25}{3} x^{9} e^{4} d b^{4} a^{2} A + \frac{20}{9} x^{9} e^{5} b^{3} a^{3} A + \frac{1}{8} x^{8} d^{5} b^{6} B + \frac{15}{4} x^{8} e d^{4} b^{5} a B + \frac{75}{4} x^{8} e^{2} d^{3} b^{4} a^{2} B + 25 x^{8} e^{3} d^{2} b^{3} a^{3} B + \frac{75}{8} x^{8} e^{4} d b^{2} a^{4} B + \frac{3}{4} x^{8} e^{5} b a^{5} B + \frac{5}{8} x^{8} e d^{4} b^{6} A + \frac{15}{2} x^{8} e^{2} d^{3} b^{5} a A + \frac{75}{4} x^{8} e^{3} d^{2} b^{4} a^{2} A + \frac{25}{2} x^{8} e^{4} d b^{3} a^{3} A + \frac{15}{8} x^{8} e^{5} b^{2} a^{4} A + \frac{6}{7} x^{7} d^{5} b^{5} a B + \frac{75}{7} x^{7} e d^{4} b^{4} a^{2} B + \frac{200}{7} x^{7} e^{2} d^{3} b^{3} a^{3} B + \frac{150}{7} x^{7} e^{3} d^{2} b^{2} a^{4} B + \frac{30}{7} x^{7} e^{4} d b a^{5} B + \frac{1}{7} x^{7} e^{5} a^{6} B + \frac{1}{7} x^{7} d^{5} b^{6} A + \frac{30}{7} x^{7} e d^{4} b^{5} a A + \frac{150}{7} x^{7} e^{2} d^{3} b^{4} a^{2} A + \frac{200}{7} x^{7} e^{3} d^{2} b^{3} a^{3} A + \frac{75}{7} x^{7} e^{4} d b^{2} a^{4} A + \frac{6}{7} x^{7} e^{5} b a^{5} A + \frac{5}{2} x^{6} d^{5} b^{4} a^{2} B + \frac{50}{3} x^{6} e d^{4} b^{3} a^{3} B + 25 x^{6} e^{2} d^{3} b^{2} a^{4} B + 10 x^{6} e^{3} d^{2} b a^{5} B + \frac{5}{6} x^{6} e^{4} d a^{6} B + x^{6} d^{5} b^{5} a A + \frac{25}{2} x^{6} e d^{4} b^{4} a^{2} A + \frac{100}{3} x^{6} e^{2} d^{3} b^{3} a^{3} A + 25 x^{6} e^{3} d^{2} b^{2} a^{4} A + 5 x^{6} e^{4} d b a^{5} A + \frac{1}{6} x^{6} e^{5} a^{6} A + 4 x^{5} d^{5} b^{3} a^{3} B + 15 x^{5} e d^{4} b^{2} a^{4} B + 12 x^{5} e^{2} d^{3} b a^{5} B + 2 x^{5} e^{3} d^{2} a^{6} B + 3 x^{5} d^{5} b^{4} a^{2} A + 20 x^{5} e d^{4} b^{3} a^{3} A + 30 x^{5} e^{2} d^{3} b^{2} a^{4} A + 12 x^{5} e^{3} d^{2} b a^{5} A + x^{5} e^{4} d a^{6} A + \frac{15}{4} x^{4} d^{5} b^{2} a^{4} B + \frac{15}{2} x^{4} e d^{4} b a^{5} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{6} B + 5 x^{4} d^{5} b^{3} a^{3} A + \frac{75}{4} x^{4} e d^{4} b^{2} a^{4} A + 15 x^{4} e^{2} d^{3} b a^{5} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{6} A + 2 x^{3} d^{5} b a^{5} B + \frac{5}{3} x^{3} e d^{4} a^{6} B + 5 x^{3} d^{5} b^{2} a^{4} A + 10 x^{3} e d^{4} b a^{5} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{6} A + \frac{1}{2} x^{2} d^{5} a^{6} B + 3 x^{2} d^{5} b a^{5} A + \frac{5}{2} x^{2} e d^{4} a^{6} A + x d^{5} a^{6} A"," ",0,"1/13*x^13*e^5*b^6*B + 5/12*x^12*e^4*d*b^6*B + 1/2*x^12*e^5*b^5*a*B + 1/12*x^12*e^5*b^6*A + 10/11*x^11*e^3*d^2*b^6*B + 30/11*x^11*e^4*d*b^5*a*B + 15/11*x^11*e^5*b^4*a^2*B + 5/11*x^11*e^4*d*b^6*A + 6/11*x^11*e^5*b^5*a*A + x^10*e^2*d^3*b^6*B + 6*x^10*e^3*d^2*b^5*a*B + 15/2*x^10*e^4*d*b^4*a^2*B + 2*x^10*e^5*b^3*a^3*B + x^10*e^3*d^2*b^6*A + 3*x^10*e^4*d*b^5*a*A + 3/2*x^10*e^5*b^4*a^2*A + 5/9*x^9*e*d^4*b^6*B + 20/3*x^9*e^2*d^3*b^5*a*B + 50/3*x^9*e^3*d^2*b^4*a^2*B + 100/9*x^9*e^4*d*b^3*a^3*B + 5/3*x^9*e^5*b^2*a^4*B + 10/9*x^9*e^2*d^3*b^6*A + 20/3*x^9*e^3*d^2*b^5*a*A + 25/3*x^9*e^4*d*b^4*a^2*A + 20/9*x^9*e^5*b^3*a^3*A + 1/8*x^8*d^5*b^6*B + 15/4*x^8*e*d^4*b^5*a*B + 75/4*x^8*e^2*d^3*b^4*a^2*B + 25*x^8*e^3*d^2*b^3*a^3*B + 75/8*x^8*e^4*d*b^2*a^4*B + 3/4*x^8*e^5*b*a^5*B + 5/8*x^8*e*d^4*b^6*A + 15/2*x^8*e^2*d^3*b^5*a*A + 75/4*x^8*e^3*d^2*b^4*a^2*A + 25/2*x^8*e^4*d*b^3*a^3*A + 15/8*x^8*e^5*b^2*a^4*A + 6/7*x^7*d^5*b^5*a*B + 75/7*x^7*e*d^4*b^4*a^2*B + 200/7*x^7*e^2*d^3*b^3*a^3*B + 150/7*x^7*e^3*d^2*b^2*a^4*B + 30/7*x^7*e^4*d*b*a^5*B + 1/7*x^7*e^5*a^6*B + 1/7*x^7*d^5*b^6*A + 30/7*x^7*e*d^4*b^5*a*A + 150/7*x^7*e^2*d^3*b^4*a^2*A + 200/7*x^7*e^3*d^2*b^3*a^3*A + 75/7*x^7*e^4*d*b^2*a^4*A + 6/7*x^7*e^5*b*a^5*A + 5/2*x^6*d^5*b^4*a^2*B + 50/3*x^6*e*d^4*b^3*a^3*B + 25*x^6*e^2*d^3*b^2*a^4*B + 10*x^6*e^3*d^2*b*a^5*B + 5/6*x^6*e^4*d*a^6*B + x^6*d^5*b^5*a*A + 25/2*x^6*e*d^4*b^4*a^2*A + 100/3*x^6*e^2*d^3*b^3*a^3*A + 25*x^6*e^3*d^2*b^2*a^4*A + 5*x^6*e^4*d*b*a^5*A + 1/6*x^6*e^5*a^6*A + 4*x^5*d^5*b^3*a^3*B + 15*x^5*e*d^4*b^2*a^4*B + 12*x^5*e^2*d^3*b*a^5*B + 2*x^5*e^3*d^2*a^6*B + 3*x^5*d^5*b^4*a^2*A + 20*x^5*e*d^4*b^3*a^3*A + 30*x^5*e^2*d^3*b^2*a^4*A + 12*x^5*e^3*d^2*b*a^5*A + x^5*e^4*d*a^6*A + 15/4*x^4*d^5*b^2*a^4*B + 15/2*x^4*e*d^4*b*a^5*B + 5/2*x^4*e^2*d^3*a^6*B + 5*x^4*d^5*b^3*a^3*A + 75/4*x^4*e*d^4*b^2*a^4*A + 15*x^4*e^2*d^3*b*a^5*A + 5/2*x^4*e^3*d^2*a^6*A + 2*x^3*d^5*b*a^5*B + 5/3*x^3*e*d^4*a^6*B + 5*x^3*d^5*b^2*a^4*A + 10*x^3*e*d^4*b*a^5*A + 10/3*x^3*e^2*d^3*a^6*A + 1/2*x^2*d^5*a^6*B + 3*x^2*d^5*b*a^5*A + 5/2*x^2*e*d^4*a^6*A + x*d^5*a^6*A","B",0
1055,1,1015,0,1.797520," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^4,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{4} b^{6} B + \frac{4}{11} x^{11} e^{3} d b^{6} B + \frac{6}{11} x^{11} e^{4} b^{5} a B + \frac{1}{11} x^{11} e^{4} b^{6} A + \frac{3}{5} x^{10} e^{2} d^{2} b^{6} B + \frac{12}{5} x^{10} e^{3} d b^{5} a B + \frac{3}{2} x^{10} e^{4} b^{4} a^{2} B + \frac{2}{5} x^{10} e^{3} d b^{6} A + \frac{3}{5} x^{10} e^{4} b^{5} a A + \frac{4}{9} x^{9} e d^{3} b^{6} B + 4 x^{9} e^{2} d^{2} b^{5} a B + \frac{20}{3} x^{9} e^{3} d b^{4} a^{2} B + \frac{20}{9} x^{9} e^{4} b^{3} a^{3} B + \frac{2}{3} x^{9} e^{2} d^{2} b^{6} A + \frac{8}{3} x^{9} e^{3} d b^{5} a A + \frac{5}{3} x^{9} e^{4} b^{4} a^{2} A + \frac{1}{8} x^{8} d^{4} b^{6} B + 3 x^{8} e d^{3} b^{5} a B + \frac{45}{4} x^{8} e^{2} d^{2} b^{4} a^{2} B + 10 x^{8} e^{3} d b^{3} a^{3} B + \frac{15}{8} x^{8} e^{4} b^{2} a^{4} B + \frac{1}{2} x^{8} e d^{3} b^{6} A + \frac{9}{2} x^{8} e^{2} d^{2} b^{5} a A + \frac{15}{2} x^{8} e^{3} d b^{4} a^{2} A + \frac{5}{2} x^{8} e^{4} b^{3} a^{3} A + \frac{6}{7} x^{7} d^{4} b^{5} a B + \frac{60}{7} x^{7} e d^{3} b^{4} a^{2} B + \frac{120}{7} x^{7} e^{2} d^{2} b^{3} a^{3} B + \frac{60}{7} x^{7} e^{3} d b^{2} a^{4} B + \frac{6}{7} x^{7} e^{4} b a^{5} B + \frac{1}{7} x^{7} d^{4} b^{6} A + \frac{24}{7} x^{7} e d^{3} b^{5} a A + \frac{90}{7} x^{7} e^{2} d^{2} b^{4} a^{2} A + \frac{80}{7} x^{7} e^{3} d b^{3} a^{3} A + \frac{15}{7} x^{7} e^{4} b^{2} a^{4} A + \frac{5}{2} x^{6} d^{4} b^{4} a^{2} B + \frac{40}{3} x^{6} e d^{3} b^{3} a^{3} B + 15 x^{6} e^{2} d^{2} b^{2} a^{4} B + 4 x^{6} e^{3} d b a^{5} B + \frac{1}{6} x^{6} e^{4} a^{6} B + x^{6} d^{4} b^{5} a A + 10 x^{6} e d^{3} b^{4} a^{2} A + 20 x^{6} e^{2} d^{2} b^{3} a^{3} A + 10 x^{6} e^{3} d b^{2} a^{4} A + x^{6} e^{4} b a^{5} A + 4 x^{5} d^{4} b^{3} a^{3} B + 12 x^{5} e d^{3} b^{2} a^{4} B + \frac{36}{5} x^{5} e^{2} d^{2} b a^{5} B + \frac{4}{5} x^{5} e^{3} d a^{6} B + 3 x^{5} d^{4} b^{4} a^{2} A + 16 x^{5} e d^{3} b^{3} a^{3} A + 18 x^{5} e^{2} d^{2} b^{2} a^{4} A + \frac{24}{5} x^{5} e^{3} d b a^{5} A + \frac{1}{5} x^{5} e^{4} a^{6} A + \frac{15}{4} x^{4} d^{4} b^{2} a^{4} B + 6 x^{4} e d^{3} b a^{5} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{6} B + 5 x^{4} d^{4} b^{3} a^{3} A + 15 x^{4} e d^{3} b^{2} a^{4} A + 9 x^{4} e^{2} d^{2} b a^{5} A + x^{4} e^{3} d a^{6} A + 2 x^{3} d^{4} b a^{5} B + \frac{4}{3} x^{3} e d^{3} a^{6} B + 5 x^{3} d^{4} b^{2} a^{4} A + 8 x^{3} e d^{3} b a^{5} A + 2 x^{3} e^{2} d^{2} a^{6} A + \frac{1}{2} x^{2} d^{4} a^{6} B + 3 x^{2} d^{4} b a^{5} A + 2 x^{2} e d^{3} a^{6} A + x d^{4} a^{6} A"," ",0,"1/12*x^12*e^4*b^6*B + 4/11*x^11*e^3*d*b^6*B + 6/11*x^11*e^4*b^5*a*B + 1/11*x^11*e^4*b^6*A + 3/5*x^10*e^2*d^2*b^6*B + 12/5*x^10*e^3*d*b^5*a*B + 3/2*x^10*e^4*b^4*a^2*B + 2/5*x^10*e^3*d*b^6*A + 3/5*x^10*e^4*b^5*a*A + 4/9*x^9*e*d^3*b^6*B + 4*x^9*e^2*d^2*b^5*a*B + 20/3*x^9*e^3*d*b^4*a^2*B + 20/9*x^9*e^4*b^3*a^3*B + 2/3*x^9*e^2*d^2*b^6*A + 8/3*x^9*e^3*d*b^5*a*A + 5/3*x^9*e^4*b^4*a^2*A + 1/8*x^8*d^4*b^6*B + 3*x^8*e*d^3*b^5*a*B + 45/4*x^8*e^2*d^2*b^4*a^2*B + 10*x^8*e^3*d*b^3*a^3*B + 15/8*x^8*e^4*b^2*a^4*B + 1/2*x^8*e*d^3*b^6*A + 9/2*x^8*e^2*d^2*b^5*a*A + 15/2*x^8*e^3*d*b^4*a^2*A + 5/2*x^8*e^4*b^3*a^3*A + 6/7*x^7*d^4*b^5*a*B + 60/7*x^7*e*d^3*b^4*a^2*B + 120/7*x^7*e^2*d^2*b^3*a^3*B + 60/7*x^7*e^3*d*b^2*a^4*B + 6/7*x^7*e^4*b*a^5*B + 1/7*x^7*d^4*b^6*A + 24/7*x^7*e*d^3*b^5*a*A + 90/7*x^7*e^2*d^2*b^4*a^2*A + 80/7*x^7*e^3*d*b^3*a^3*A + 15/7*x^7*e^4*b^2*a^4*A + 5/2*x^6*d^4*b^4*a^2*B + 40/3*x^6*e*d^3*b^3*a^3*B + 15*x^6*e^2*d^2*b^2*a^4*B + 4*x^6*e^3*d*b*a^5*B + 1/6*x^6*e^4*a^6*B + x^6*d^4*b^5*a*A + 10*x^6*e*d^3*b^4*a^2*A + 20*x^6*e^2*d^2*b^3*a^3*A + 10*x^6*e^3*d*b^2*a^4*A + x^6*e^4*b*a^5*A + 4*x^5*d^4*b^3*a^3*B + 12*x^5*e*d^3*b^2*a^4*B + 36/5*x^5*e^2*d^2*b*a^5*B + 4/5*x^5*e^3*d*a^6*B + 3*x^5*d^4*b^4*a^2*A + 16*x^5*e*d^3*b^3*a^3*A + 18*x^5*e^2*d^2*b^2*a^4*A + 24/5*x^5*e^3*d*b*a^5*A + 1/5*x^5*e^4*a^6*A + 15/4*x^4*d^4*b^2*a^4*B + 6*x^4*e*d^3*b*a^5*B + 3/2*x^4*e^2*d^2*a^6*B + 5*x^4*d^4*b^3*a^3*A + 15*x^4*e*d^3*b^2*a^4*A + 9*x^4*e^2*d^2*b*a^5*A + x^4*e^3*d*a^6*A + 2*x^3*d^4*b*a^5*B + 4/3*x^3*e*d^3*a^6*B + 5*x^3*d^4*b^2*a^4*A + 8*x^3*e*d^3*b*a^5*A + 2*x^3*e^2*d^2*a^6*A + 1/2*x^2*d^4*a^6*B + 3*x^2*d^4*b*a^5*A + 2*x^2*e*d^3*a^6*A + x*d^4*a^6*A","B",0
1056,1,782,0,0.988943," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} b^{6} B + \frac{3}{10} x^{10} e^{2} d b^{6} B + \frac{3}{5} x^{10} e^{3} b^{5} a B + \frac{1}{10} x^{10} e^{3} b^{6} A + \frac{1}{3} x^{9} e d^{2} b^{6} B + 2 x^{9} e^{2} d b^{5} a B + \frac{5}{3} x^{9} e^{3} b^{4} a^{2} B + \frac{1}{3} x^{9} e^{2} d b^{6} A + \frac{2}{3} x^{9} e^{3} b^{5} a A + \frac{1}{8} x^{8} d^{3} b^{6} B + \frac{9}{4} x^{8} e d^{2} b^{5} a B + \frac{45}{8} x^{8} e^{2} d b^{4} a^{2} B + \frac{5}{2} x^{8} e^{3} b^{3} a^{3} B + \frac{3}{8} x^{8} e d^{2} b^{6} A + \frac{9}{4} x^{8} e^{2} d b^{5} a A + \frac{15}{8} x^{8} e^{3} b^{4} a^{2} A + \frac{6}{7} x^{7} d^{3} b^{5} a B + \frac{45}{7} x^{7} e d^{2} b^{4} a^{2} B + \frac{60}{7} x^{7} e^{2} d b^{3} a^{3} B + \frac{15}{7} x^{7} e^{3} b^{2} a^{4} B + \frac{1}{7} x^{7} d^{3} b^{6} A + \frac{18}{7} x^{7} e d^{2} b^{5} a A + \frac{45}{7} x^{7} e^{2} d b^{4} a^{2} A + \frac{20}{7} x^{7} e^{3} b^{3} a^{3} A + \frac{5}{2} x^{6} d^{3} b^{4} a^{2} B + 10 x^{6} e d^{2} b^{3} a^{3} B + \frac{15}{2} x^{6} e^{2} d b^{2} a^{4} B + x^{6} e^{3} b a^{5} B + x^{6} d^{3} b^{5} a A + \frac{15}{2} x^{6} e d^{2} b^{4} a^{2} A + 10 x^{6} e^{2} d b^{3} a^{3} A + \frac{5}{2} x^{6} e^{3} b^{2} a^{4} A + 4 x^{5} d^{3} b^{3} a^{3} B + 9 x^{5} e d^{2} b^{2} a^{4} B + \frac{18}{5} x^{5} e^{2} d b a^{5} B + \frac{1}{5} x^{5} e^{3} a^{6} B + 3 x^{5} d^{3} b^{4} a^{2} A + 12 x^{5} e d^{2} b^{3} a^{3} A + 9 x^{5} e^{2} d b^{2} a^{4} A + \frac{6}{5} x^{5} e^{3} b a^{5} A + \frac{15}{4} x^{4} d^{3} b^{2} a^{4} B + \frac{9}{2} x^{4} e d^{2} b a^{5} B + \frac{3}{4} x^{4} e^{2} d a^{6} B + 5 x^{4} d^{3} b^{3} a^{3} A + \frac{45}{4} x^{4} e d^{2} b^{2} a^{4} A + \frac{9}{2} x^{4} e^{2} d b a^{5} A + \frac{1}{4} x^{4} e^{3} a^{6} A + 2 x^{3} d^{3} b a^{5} B + x^{3} e d^{2} a^{6} B + 5 x^{3} d^{3} b^{2} a^{4} A + 6 x^{3} e d^{2} b a^{5} A + x^{3} e^{2} d a^{6} A + \frac{1}{2} x^{2} d^{3} a^{6} B + 3 x^{2} d^{3} b a^{5} A + \frac{3}{2} x^{2} e d^{2} a^{6} A + x d^{3} a^{6} A"," ",0,"1/11*x^11*e^3*b^6*B + 3/10*x^10*e^2*d*b^6*B + 3/5*x^10*e^3*b^5*a*B + 1/10*x^10*e^3*b^6*A + 1/3*x^9*e*d^2*b^6*B + 2*x^9*e^2*d*b^5*a*B + 5/3*x^9*e^3*b^4*a^2*B + 1/3*x^9*e^2*d*b^6*A + 2/3*x^9*e^3*b^5*a*A + 1/8*x^8*d^3*b^6*B + 9/4*x^8*e*d^2*b^5*a*B + 45/8*x^8*e^2*d*b^4*a^2*B + 5/2*x^8*e^3*b^3*a^3*B + 3/8*x^8*e*d^2*b^6*A + 9/4*x^8*e^2*d*b^5*a*A + 15/8*x^8*e^3*b^4*a^2*A + 6/7*x^7*d^3*b^5*a*B + 45/7*x^7*e*d^2*b^4*a^2*B + 60/7*x^7*e^2*d*b^3*a^3*B + 15/7*x^7*e^3*b^2*a^4*B + 1/7*x^7*d^3*b^6*A + 18/7*x^7*e*d^2*b^5*a*A + 45/7*x^7*e^2*d*b^4*a^2*A + 20/7*x^7*e^3*b^3*a^3*A + 5/2*x^6*d^3*b^4*a^2*B + 10*x^6*e*d^2*b^3*a^3*B + 15/2*x^6*e^2*d*b^2*a^4*B + x^6*e^3*b*a^5*B + x^6*d^3*b^5*a*A + 15/2*x^6*e*d^2*b^4*a^2*A + 10*x^6*e^2*d*b^3*a^3*A + 5/2*x^6*e^3*b^2*a^4*A + 4*x^5*d^3*b^3*a^3*B + 9*x^5*e*d^2*b^2*a^4*B + 18/5*x^5*e^2*d*b*a^5*B + 1/5*x^5*e^3*a^6*B + 3*x^5*d^3*b^4*a^2*A + 12*x^5*e*d^2*b^3*a^3*A + 9*x^5*e^2*d*b^2*a^4*A + 6/5*x^5*e^3*b*a^5*A + 15/4*x^4*d^3*b^2*a^4*B + 9/2*x^4*e*d^2*b*a^5*B + 3/4*x^4*e^2*d*a^6*B + 5*x^4*d^3*b^3*a^3*A + 45/4*x^4*e*d^2*b^2*a^4*A + 9/2*x^4*e^2*d*b*a^5*A + 1/4*x^4*e^3*a^6*A + 2*x^3*d^3*b*a^5*B + x^3*e*d^2*a^6*B + 5*x^3*d^3*b^2*a^4*A + 6*x^3*e*d^2*b*a^5*A + x^3*e^2*d*a^6*A + 1/2*x^2*d^3*a^6*B + 3*x^2*d^3*b*a^5*A + 3/2*x^2*e*d^2*a^6*A + x*d^3*a^6*A","B",0
1057,1,552,0,0.514337," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{2} b^{6} B + \frac{2}{9} x^{9} e d b^{6} B + \frac{2}{3} x^{9} e^{2} b^{5} a B + \frac{1}{9} x^{9} e^{2} b^{6} A + \frac{1}{8} x^{8} d^{2} b^{6} B + \frac{3}{2} x^{8} e d b^{5} a B + \frac{15}{8} x^{8} e^{2} b^{4} a^{2} B + \frac{1}{4} x^{8} e d b^{6} A + \frac{3}{4} x^{8} e^{2} b^{5} a A + \frac{6}{7} x^{7} d^{2} b^{5} a B + \frac{30}{7} x^{7} e d b^{4} a^{2} B + \frac{20}{7} x^{7} e^{2} b^{3} a^{3} B + \frac{1}{7} x^{7} d^{2} b^{6} A + \frac{12}{7} x^{7} e d b^{5} a A + \frac{15}{7} x^{7} e^{2} b^{4} a^{2} A + \frac{5}{2} x^{6} d^{2} b^{4} a^{2} B + \frac{20}{3} x^{6} e d b^{3} a^{3} B + \frac{5}{2} x^{6} e^{2} b^{2} a^{4} B + x^{6} d^{2} b^{5} a A + 5 x^{6} e d b^{4} a^{2} A + \frac{10}{3} x^{6} e^{2} b^{3} a^{3} A + 4 x^{5} d^{2} b^{3} a^{3} B + 6 x^{5} e d b^{2} a^{4} B + \frac{6}{5} x^{5} e^{2} b a^{5} B + 3 x^{5} d^{2} b^{4} a^{2} A + 8 x^{5} e d b^{3} a^{3} A + 3 x^{5} e^{2} b^{2} a^{4} A + \frac{15}{4} x^{4} d^{2} b^{2} a^{4} B + 3 x^{4} e d b a^{5} B + \frac{1}{4} x^{4} e^{2} a^{6} B + 5 x^{4} d^{2} b^{3} a^{3} A + \frac{15}{2} x^{4} e d b^{2} a^{4} A + \frac{3}{2} x^{4} e^{2} b a^{5} A + 2 x^{3} d^{2} b a^{5} B + \frac{2}{3} x^{3} e d a^{6} B + 5 x^{3} d^{2} b^{2} a^{4} A + 4 x^{3} e d b a^{5} A + \frac{1}{3} x^{3} e^{2} a^{6} A + \frac{1}{2} x^{2} d^{2} a^{6} B + 3 x^{2} d^{2} b a^{5} A + x^{2} e d a^{6} A + x d^{2} a^{6} A"," ",0,"1/10*x^10*e^2*b^6*B + 2/9*x^9*e*d*b^6*B + 2/3*x^9*e^2*b^5*a*B + 1/9*x^9*e^2*b^6*A + 1/8*x^8*d^2*b^6*B + 3/2*x^8*e*d*b^5*a*B + 15/8*x^8*e^2*b^4*a^2*B + 1/4*x^8*e*d*b^6*A + 3/4*x^8*e^2*b^5*a*A + 6/7*x^7*d^2*b^5*a*B + 30/7*x^7*e*d*b^4*a^2*B + 20/7*x^7*e^2*b^3*a^3*B + 1/7*x^7*d^2*b^6*A + 12/7*x^7*e*d*b^5*a*A + 15/7*x^7*e^2*b^4*a^2*A + 5/2*x^6*d^2*b^4*a^2*B + 20/3*x^6*e*d*b^3*a^3*B + 5/2*x^6*e^2*b^2*a^4*B + x^6*d^2*b^5*a*A + 5*x^6*e*d*b^4*a^2*A + 10/3*x^6*e^2*b^3*a^3*A + 4*x^5*d^2*b^3*a^3*B + 6*x^5*e*d*b^2*a^4*B + 6/5*x^5*e^2*b*a^5*B + 3*x^5*d^2*b^4*a^2*A + 8*x^5*e*d*b^3*a^3*A + 3*x^5*e^2*b^2*a^4*A + 15/4*x^4*d^2*b^2*a^4*B + 3*x^4*e*d*b*a^5*B + 1/4*x^4*e^2*a^6*B + 5*x^4*d^2*b^3*a^3*A + 15/2*x^4*e*d*b^2*a^4*A + 3/2*x^4*e^2*b*a^5*A + 2*x^3*d^2*b*a^5*B + 2/3*x^3*e*d*a^6*B + 5*x^3*d^2*b^2*a^4*A + 4*x^3*e*d*b*a^5*A + 1/3*x^3*e^2*a^6*A + 1/2*x^2*d^2*a^6*B + 3*x^2*d^2*b*a^5*A + x^2*e*d*a^6*A + x*d^2*a^6*A","B",0
1058,1,321,0,1.364151," ","integrate((b*x+a)^6*(B*x+A)*(e*x+d),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e b^{6} B + \frac{1}{8} x^{8} d b^{6} B + \frac{3}{4} x^{8} e b^{5} a B + \frac{1}{8} x^{8} e b^{6} A + \frac{6}{7} x^{7} d b^{5} a B + \frac{15}{7} x^{7} e b^{4} a^{2} B + \frac{1}{7} x^{7} d b^{6} A + \frac{6}{7} x^{7} e b^{5} a A + \frac{5}{2} x^{6} d b^{4} a^{2} B + \frac{10}{3} x^{6} e b^{3} a^{3} B + x^{6} d b^{5} a A + \frac{5}{2} x^{6} e b^{4} a^{2} A + 4 x^{5} d b^{3} a^{3} B + 3 x^{5} e b^{2} a^{4} B + 3 x^{5} d b^{4} a^{2} A + 4 x^{5} e b^{3} a^{3} A + \frac{15}{4} x^{4} d b^{2} a^{4} B + \frac{3}{2} x^{4} e b a^{5} B + 5 x^{4} d b^{3} a^{3} A + \frac{15}{4} x^{4} e b^{2} a^{4} A + 2 x^{3} d b a^{5} B + \frac{1}{3} x^{3} e a^{6} B + 5 x^{3} d b^{2} a^{4} A + 2 x^{3} e b a^{5} A + \frac{1}{2} x^{2} d a^{6} B + 3 x^{2} d b a^{5} A + \frac{1}{2} x^{2} e a^{6} A + x d a^{6} A"," ",0,"1/9*x^9*e*b^6*B + 1/8*x^8*d*b^6*B + 3/4*x^8*e*b^5*a*B + 1/8*x^8*e*b^6*A + 6/7*x^7*d*b^5*a*B + 15/7*x^7*e*b^4*a^2*B + 1/7*x^7*d*b^6*A + 6/7*x^7*e*b^5*a*A + 5/2*x^6*d*b^4*a^2*B + 10/3*x^6*e*b^3*a^3*B + x^6*d*b^5*a*A + 5/2*x^6*e*b^4*a^2*A + 4*x^5*d*b^3*a^3*B + 3*x^5*e*b^2*a^4*B + 3*x^5*d*b^4*a^2*A + 4*x^5*e*b^3*a^3*A + 15/4*x^4*d*b^2*a^4*B + 3/2*x^4*e*b*a^5*B + 5*x^4*d*b^3*a^3*A + 15/4*x^4*e*b^2*a^4*A + 2*x^3*d*b*a^5*B + 1/3*x^3*e*a^6*B + 5*x^3*d*b^2*a^4*A + 2*x^3*e*b*a^5*A + 1/2*x^2*d*a^6*B + 3*x^2*d*b*a^5*A + 1/2*x^2*e*a^6*A + x*d*a^6*A","B",0
1059,1,145,0,1.110631," ","integrate((b*x+a)^6*(B*x+A),x, algorithm=""fricas"")","\frac{1}{8} x^{8} b^{6} B + \frac{6}{7} x^{7} b^{5} a B + \frac{1}{7} x^{7} b^{6} A + \frac{5}{2} x^{6} b^{4} a^{2} B + x^{6} b^{5} a A + 4 x^{5} b^{3} a^{3} B + 3 x^{5} b^{4} a^{2} A + \frac{15}{4} x^{4} b^{2} a^{4} B + 5 x^{4} b^{3} a^{3} A + 2 x^{3} b a^{5} B + 5 x^{3} b^{2} a^{4} A + \frac{1}{2} x^{2} a^{6} B + 3 x^{2} b a^{5} A + x a^{6} A"," ",0,"1/8*x^8*b^6*B + 6/7*x^7*b^5*a*B + 1/7*x^7*b^6*A + 5/2*x^6*b^4*a^2*B + x^6*b^5*a*A + 4*x^5*b^3*a^3*B + 3*x^5*b^4*a^2*A + 15/4*x^4*b^2*a^4*B + 5*x^4*b^3*a^3*A + 2*x^3*b*a^5*B + 5*x^3*b^2*a^4*A + 1/2*x^2*a^6*B + 3*x^2*b*a^5*A + x*a^6*A","B",0
1060,1,763,0,0.819110," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{60 \, B b^{6} e^{7} x^{7} - 70 \, {\left(B b^{6} d e^{6} - {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 84 \, {\left(B b^{6} d^{2} e^{5} - {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 105 \, {\left(B b^{6} d^{3} e^{4} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 140 \, {\left(B b^{6} d^{4} e^{3} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 210 \, {\left(B b^{6} d^{5} e^{2} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 420 \, {\left(B b^{6} d^{6} e - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x - 420 \, {\left(B b^{6} d^{7} - A a^{6} e^{7} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6}\right)} \log\left(e x + d\right)}{420 \, e^{8}}"," ",0,"1/420*(60*B*b^6*e^7*x^7 - 70*(B*b^6*d*e^6 - (6*B*a*b^5 + A*b^6)*e^7)*x^6 + 84*(B*b^6*d^2*e^5 - (6*B*a*b^5 + A*b^6)*d*e^6 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 105*(B*b^6*d^3*e^4 - (6*B*a*b^5 + A*b^6)*d^2*e^5 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 140*(B*b^6*d^4*e^3 - (6*B*a*b^5 + A*b^6)*d^3*e^4 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 210*(B*b^6*d^5*e^2 - (6*B*a*b^5 + A*b^6)*d^4*e^3 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 420*(B*b^6*d^6*e - (6*B*a*b^5 + A*b^6)*d^5*e^2 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x - 420*(B*b^6*d^7 - A*a^6*e^7 - (6*B*a*b^5 + A*b^6)*d^6*e + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + (B*a^6 + 6*A*a^5*b)*d*e^6)*log(e*x + d))/e^8","B",0
1061,1,1067,0,1.560498," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{10 \, B b^{6} e^{7} x^{7} + 60 \, B b^{6} d^{7} - 60 \, A a^{6} e^{7} - 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 180 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 300 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 300 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 180 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 60 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 2 \, {\left(7 \, B b^{6} d e^{6} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B b^{6} d^{2} e^{5} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B b^{6} d^{3} e^{4} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 10 \, {\left(7 \, B b^{6} d^{4} e^{3} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 30 \, {\left(7 \, B b^{6} d^{5} e^{2} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} - 60 \, {\left(6 \, B b^{6} d^{6} e - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 12 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 15 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 10 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6}\right)} x + 60 \, {\left(7 \, B b^{6} d^{7} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + {\left(7 \, B b^{6} d^{6} e - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{9} x + d e^{8}\right)}}"," ",0,"1/60*(10*B*b^6*e^7*x^7 + 60*B*b^6*d^7 - 60*A*a^6*e^7 - 60*(6*B*a*b^5 + A*b^6)*d^6*e + 180*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 300*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 300*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 180*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 60*(B*a^6 + 6*A*a^5*b)*d*e^6 - 2*(7*B*b^6*d*e^6 - 6*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 3*(7*B*b^6*d^2*e^5 - 6*(6*B*a*b^5 + A*b^6)*d*e^6 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 5*(7*B*b^6*d^3*e^4 - 6*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 10*(7*B*b^6*d^4*e^3 - 6*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 30*(7*B*b^6*d^5*e^2 - 6*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 6*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 - 60*(6*B*b^6*d^6*e - 5*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 12*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 15*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 10*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6)*x + 60*(7*B*b^6*d^7 - 6*(6*B*a*b^5 + A*b^6)*d^6*e + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 6*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + (B*a^6 + 6*A*a^5*b)*d*e^6 + (7*B*b^6*d^6*e - 6*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 6*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x)*log(e*x + d))/(e^9*x + d*e^8)","B",0
1062,1,1177,0,1.945481," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, B b^{6} e^{7} x^{7} - 130 \, B b^{6} d^{7} - 10 \, A a^{6} e^{7} + 110 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 270 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 350 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 250 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 90 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 10 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - {\left(7 \, B b^{6} d e^{6} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 2 \, {\left(7 \, B b^{6} d^{2} e^{5} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 5 \, {\left(7 \, B b^{6} d^{3} e^{4} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 20 \, {\left(7 \, B b^{6} d^{4} e^{3} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 10 \, {\left(50 \, B b^{6} d^{5} e^{2} - 34 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 63 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 55 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 20 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6}\right)} x^{2} + 20 \, {\left(8 \, B b^{6} d^{6} e - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 5 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} - 10 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} - {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x - 60 \, {\left(7 \, B b^{6} d^{7} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + {\left(7 \, B b^{6} d^{5} e^{2} - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 2 \, {\left(7 \, B b^{6} d^{6} e - 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{10} x^{2} + 2 \, d e^{9} x + d^{2} e^{8}\right)}}"," ",0,"1/20*(4*B*b^6*e^7*x^7 - 130*B*b^6*d^7 - 10*A*a^6*e^7 + 110*(6*B*a*b^5 + A*b^6)*d^6*e - 270*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 350*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 250*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 90*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 10*(B*a^6 + 6*A*a^5*b)*d*e^6 - (7*B*b^6*d*e^6 - 5*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 2*(7*B*b^6*d^2*e^5 - 5*(6*B*a*b^5 + A*b^6)*d*e^6 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 5*(7*B*b^6*d^3*e^4 - 5*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 20*(7*B*b^6*d^4*e^3 - 5*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 10*(50*B*b^6*d^5*e^2 - 34*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 63*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 55*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 20*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6)*x^2 + 20*(8*B*b^6*d^6*e - 4*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 5*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 - 10*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 6*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 - (B*a^6 + 6*A*a^5*b)*e^7)*x - 60*(7*B*b^6*d^7 - 5*(6*B*a*b^5 + A*b^6)*d^6*e + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - (2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + (7*B*b^6*d^5*e^2 - 5*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - (2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 2*(7*B*b^6*d^6*e - 5*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - (2*B*a^5*b + 5*A*a^4*b^2)*d*e^6)*x)*log(e*x + d))/(e^10*x^2 + 2*d*e^9*x + d^2*e^8)","B",0
1063,1,1225,0,0.889286," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, B b^{6} e^{7} x^{7} + 214 \, B b^{6} d^{7} - 4 \, A a^{6} e^{7} - 148 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 282 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 260 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 110 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 12 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 2 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - {\left(7 \, B b^{6} d e^{6} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 3 \, {\left(7 \, B b^{6} d^{2} e^{5} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 15 \, {\left(7 \, B b^{6} d^{3} e^{4} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} - 2 \, {\left(278 \, B b^{6} d^{4} e^{3} - 146 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 189 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 90 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6}\right)} x^{3} - 6 \, {\left(68 \, B b^{6} d^{5} e^{2} - 26 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 9 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 30 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} - 30 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 6 \, {\left(37 \, B b^{6} d^{6} e - 34 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 81 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 90 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 45 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} - {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x + 60 \, {\left(7 \, B b^{6} d^{7} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + {\left(7 \, B b^{6} d^{4} e^{3} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 3 \, {\left(7 \, B b^{6} d^{5} e^{2} - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6}\right)} x^{2} + 3 \, {\left(7 \, B b^{6} d^{6} e - 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right)}}"," ",0,"1/12*(3*B*b^6*e^7*x^7 + 214*B*b^6*d^7 - 4*A*a^6*e^7 - 148*(6*B*a*b^5 + A*b^6)*d^6*e + 282*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 260*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 110*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 12*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 2*(B*a^6 + 6*A*a^5*b)*d*e^6 - (7*B*b^6*d*e^6 - 4*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 3*(7*B*b^6*d^2*e^5 - 4*(6*B*a*b^5 + A*b^6)*d*e^6 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 15*(7*B*b^6*d^3*e^4 - 4*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 - 2*(278*B*b^6*d^4*e^3 - 146*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 189*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 90*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6)*x^3 - 6*(68*B*b^6*d^5*e^2 - 26*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 9*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 30*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 - 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 6*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 6*(37*B*b^6*d^6*e - 34*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 81*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 90*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 45*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 6*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 - (B*a^6 + 6*A*a^5*b)*e^7)*x + 60*(7*B*b^6*d^7 - 4*(6*B*a*b^5 + A*b^6)*d^6*e + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + (7*B*b^6*d^4*e^3 - 4*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 3*(7*B*b^6*d^5*e^2 - 4*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6)*x^2 + 3*(7*B*b^6*d^6*e - 4*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5)*x)*log(e*x + d))/(e^11*x^3 + 3*d*e^10*x^2 + 3*d^2*e^9*x + d^3*e^8)","B",0
1064,1,1222,0,1.153660," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{4 \, B b^{6} e^{7} x^{7} - 319 \, B b^{6} d^{7} - 3 \, A a^{6} e^{7} + 171 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 231 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 125 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 2 \, {\left(7 \, B b^{6} d e^{6} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 12 \, {\left(7 \, B b^{6} d^{2} e^{5} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 4 \, {\left(139 \, B b^{6} d^{3} e^{4} - 51 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 36 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6}\right)} x^{4} + 4 \, {\left(136 \, B b^{6} d^{4} e^{3} - 24 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} - 36 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 60 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} - 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 6 \, {\left(74 \, B b^{6} d^{5} e^{2} - 66 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 126 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 90 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} - 4 \, {\left(214 \, B b^{6} d^{6} e - 126 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 186 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 110 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x - 60 \, {\left(7 \, B b^{6} d^{7} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + {\left(7 \, B b^{6} d^{3} e^{4} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 4 \, {\left(7 \, B b^{6} d^{4} e^{3} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6}\right)} x^{3} + 6 \, {\left(7 \, B b^{6} d^{5} e^{2} - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5}\right)} x^{2} + 4 \, {\left(7 \, B b^{6} d^{6} e - 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{12} x^{4} + 4 \, d e^{11} x^{3} + 6 \, d^{2} e^{10} x^{2} + 4 \, d^{3} e^{9} x + d^{4} e^{8}\right)}}"," ",0,"1/12*(4*B*b^6*e^7*x^7 - 319*B*b^6*d^7 - 3*A*a^6*e^7 + 171*(6*B*a*b^5 + A*b^6)*d^6*e - 231*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 125*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - (B*a^6 + 6*A*a^5*b)*d*e^6 - 2*(7*B*b^6*d*e^6 - 3*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 12*(7*B*b^6*d^2*e^5 - 3*(6*B*a*b^5 + A*b^6)*d*e^6 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 4*(139*B*b^6*d^3*e^4 - 51*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 36*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6)*x^4 + 4*(136*B*b^6*d^4*e^3 - 24*(6*B*a*b^5 + A*b^6)*d^3*e^4 - 36*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 60*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 - 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 6*(74*B*b^6*d^5*e^2 - 66*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 126*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 90*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 - 4*(214*B*b^6*d^6*e - 126*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 186*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 110*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x - 60*(7*B*b^6*d^7 - 3*(6*B*a*b^5 + A*b^6)*d^6*e + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + (7*B*b^6*d^3*e^4 - 3*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 4*(7*B*b^6*d^4*e^3 - 3*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6)*x^3 + 6*(7*B*b^6*d^5*e^2 - 3*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5)*x^2 + 4*(7*B*b^6*d^6*e - 3*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4)*x)*log(e*x + d))/(e^12*x^4 + 4*d*e^11*x^3 + 6*d^2*e^10*x^2 + 4*d^3*e^9*x + d^4*e^8)","B",0
1065,1,1157,0,2.314894," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, B b^{6} e^{7} x^{7} + 459 \, B b^{6} d^{7} - 4 \, A a^{6} e^{7} - 174 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 137 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 2 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 10 \, {\left(7 \, B b^{6} d e^{6} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} - 100 \, {\left(5 \, B b^{6} d^{2} e^{5} - {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6}\right)} x^{5} - 100 \, {\left(4 \, B b^{6} d^{3} e^{4} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} - 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 50 \, {\left(26 \, B b^{6} d^{4} e^{3} - 16 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 18 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} - {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 10 \, {\left(270 \, B b^{6} d^{5} e^{2} - 120 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 110 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} - 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 2 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 5 \, {\left(375 \, B b^{6} d^{6} e - 150 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 125 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} - 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 2 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} - {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x + 60 \, {\left(7 \, B b^{6} d^{7} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + {\left(7 \, B b^{6} d^{2} e^{5} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 5 \, {\left(7 \, B b^{6} d^{3} e^{4} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6}\right)} x^{4} + 10 \, {\left(7 \, B b^{6} d^{4} e^{3} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5}\right)} x^{3} + 10 \, {\left(7 \, B b^{6} d^{5} e^{2} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4}\right)} x^{2} + 5 \, {\left(7 \, B b^{6} d^{6} e - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{13} x^{5} + 5 \, d e^{12} x^{4} + 10 \, d^{2} e^{11} x^{3} + 10 \, d^{3} e^{10} x^{2} + 5 \, d^{4} e^{9} x + d^{5} e^{8}\right)}}"," ",0,"1/20*(10*B*b^6*e^7*x^7 + 459*B*b^6*d^7 - 4*A*a^6*e^7 - 174*(6*B*a*b^5 + A*b^6)*d^6*e + 137*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 2*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - (B*a^6 + 6*A*a^5*b)*d*e^6 - 10*(7*B*b^6*d*e^6 - 2*(6*B*a*b^5 + A*b^6)*e^7)*x^6 - 100*(5*B*b^6*d^2*e^5 - (6*B*a*b^5 + A*b^6)*d*e^6)*x^5 - 100*(4*B*b^6*d^3*e^4 + (6*B*a*b^5 + A*b^6)*d^2*e^5 - 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 50*(26*B*b^6*d^4*e^3 - 16*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 18*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 - (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 10*(270*B*b^6*d^5*e^2 - 120*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 110*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 - 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 2*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 5*(375*B*b^6*d^6*e - 150*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 125*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 - 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 2*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 - (B*a^6 + 6*A*a^5*b)*e^7)*x + 60*(7*B*b^6*d^7 - 2*(6*B*a*b^5 + A*b^6)*d^6*e + (5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + (7*B*b^6*d^2*e^5 - 2*(6*B*a*b^5 + A*b^6)*d*e^6 + (5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 5*(7*B*b^6*d^3*e^4 - 2*(6*B*a*b^5 + A*b^6)*d^2*e^5 + (5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6)*x^4 + 10*(7*B*b^6*d^4*e^3 - 2*(6*B*a*b^5 + A*b^6)*d^3*e^4 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5)*x^3 + 10*(7*B*b^6*d^5*e^2 - 2*(6*B*a*b^5 + A*b^6)*d^4*e^3 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4)*x^2 + 5*(7*B*b^6*d^6*e - 2*(6*B*a*b^5 + A*b^6)*d^5*e^2 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3)*x)*log(e*x + d))/(e^13*x^5 + 5*d*e^12*x^4 + 10*d^2*e^11*x^3 + 10*d^3*e^10*x^2 + 5*d^4*e^9*x + d^5*e^8)","B",0
1066,1,1063,0,1.409516," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{60 \, B b^{6} e^{7} x^{7} + 360 \, B b^{6} d e^{6} x^{6} - 669 \, B b^{6} d^{7} - 10 \, A a^{6} e^{7} + 147 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 2 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} - 180 \, {\left(2 \, B b^{6} d^{2} e^{5} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} - 150 \, {\left(27 \, B b^{6} d^{3} e^{4} - 9 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} - 100 \, {\left(82 \, B b^{6} d^{4} e^{3} - 22 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 2 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} - 15 \, {\left(515 \, B b^{6} d^{5} e^{2} - 125 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} - 6 \, {\left(599 \, B b^{6} d^{6} e - 137 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 3 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 2 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x - 60 \, {\left(7 \, B b^{6} d^{7} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + {\left(7 \, B b^{6} d e^{6} - {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 6 \, {\left(7 \, B b^{6} d^{2} e^{5} - {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6}\right)} x^{5} + 15 \, {\left(7 \, B b^{6} d^{3} e^{4} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5}\right)} x^{4} + 20 \, {\left(7 \, B b^{6} d^{4} e^{3} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4}\right)} x^{3} + 15 \, {\left(7 \, B b^{6} d^{5} e^{2} - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3}\right)} x^{2} + 6 \, {\left(7 \, B b^{6} d^{6} e - {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{14} x^{6} + 6 \, d e^{13} x^{5} + 15 \, d^{2} e^{12} x^{4} + 20 \, d^{3} e^{11} x^{3} + 15 \, d^{4} e^{10} x^{2} + 6 \, d^{5} e^{9} x + d^{6} e^{8}\right)}}"," ",0,"1/60*(60*B*b^6*e^7*x^7 + 360*B*b^6*d*e^6*x^6 - 669*B*b^6*d^7 - 10*A*a^6*e^7 + 147*(6*B*a*b^5 + A*b^6)*d^6*e - 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 3*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 2*(B*a^6 + 6*A*a^5*b)*d*e^6 - 180*(2*B*b^6*d^2*e^5 - 2*(6*B*a*b^5 + A*b^6)*d*e^6 + (5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 - 150*(27*B*b^6*d^3*e^4 - 9*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 - 100*(82*B*b^6*d^4*e^3 - 22*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 2*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 - 15*(515*B*b^6*d^5*e^2 - 125*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 - 6*(599*B*b^6*d^6*e - 137*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 3*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 2*(B*a^6 + 6*A*a^5*b)*e^7)*x - 60*(7*B*b^6*d^7 - (6*B*a*b^5 + A*b^6)*d^6*e + (7*B*b^6*d*e^6 - (6*B*a*b^5 + A*b^6)*e^7)*x^6 + 6*(7*B*b^6*d^2*e^5 - (6*B*a*b^5 + A*b^6)*d*e^6)*x^5 + 15*(7*B*b^6*d^3*e^4 - (6*B*a*b^5 + A*b^6)*d^2*e^5)*x^4 + 20*(7*B*b^6*d^4*e^3 - (6*B*a*b^5 + A*b^6)*d^3*e^4)*x^3 + 15*(7*B*b^6*d^5*e^2 - (6*B*a*b^5 + A*b^6)*d^4*e^3)*x^2 + 6*(7*B*b^6*d^6*e - (6*B*a*b^5 + A*b^6)*d^5*e^2)*x)*log(e*x + d))/(e^14*x^6 + 6*d*e^13*x^5 + 15*d^2*e^12*x^4 + 20*d^3*e^11*x^3 + 15*d^4*e^10*x^2 + 6*d^5*e^9*x + d^6*e^8)","B",0
1067,1,939,0,1.972440," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^8,x, algorithm=""fricas"")","\frac{1089 \, B b^{6} d^{7} - 60 \, A a^{6} e^{7} - 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e - 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} - 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} - 12 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} - 10 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 420 \, {\left(7 \, B b^{6} d e^{6} - {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 630 \, {\left(21 \, B b^{6} d^{2} e^{5} - 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} - {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 350 \, {\left(77 \, B b^{6} d^{3} e^{4} - 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} - 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} - 2 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 175 \, {\left(175 \, B b^{6} d^{4} e^{3} - 12 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} - 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} - 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} - 3 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 21 \, {\left(959 \, B b^{6} d^{5} e^{2} - 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} - 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} - 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} - 12 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 7 \, {\left(1029 \, B b^{6} d^{6} e - 60 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} - 30 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} - 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} - 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} - 12 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} - 10 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x + 420 \, {\left(B b^{6} e^{7} x^{7} + 7 \, B b^{6} d e^{6} x^{6} + 21 \, B b^{6} d^{2} e^{5} x^{5} + 35 \, B b^{6} d^{3} e^{4} x^{4} + 35 \, B b^{6} d^{4} e^{3} x^{3} + 21 \, B b^{6} d^{5} e^{2} x^{2} + 7 \, B b^{6} d^{6} e x + B b^{6} d^{7}\right)} \log\left(e x + d\right)}{420 \, {\left(e^{15} x^{7} + 7 \, d e^{14} x^{6} + 21 \, d^{2} e^{13} x^{5} + 35 \, d^{3} e^{12} x^{4} + 35 \, d^{4} e^{11} x^{3} + 21 \, d^{5} e^{10} x^{2} + 7 \, d^{6} e^{9} x + d^{7} e^{8}\right)}}"," ",0,"1/420*(1089*B*b^6*d^7 - 60*A*a^6*e^7 - 60*(6*B*a*b^5 + A*b^6)*d^6*e - 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 - 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 - 12*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 - 10*(B*a^6 + 6*A*a^5*b)*d*e^6 + 420*(7*B*b^6*d*e^6 - (6*B*a*b^5 + A*b^6)*e^7)*x^6 + 630*(21*B*b^6*d^2*e^5 - 2*(6*B*a*b^5 + A*b^6)*d*e^6 - (5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 350*(77*B*b^6*d^3*e^4 - 6*(6*B*a*b^5 + A*b^6)*d^2*e^5 - 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 - 2*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 175*(175*B*b^6*d^4*e^3 - 12*(6*B*a*b^5 + A*b^6)*d^3*e^4 - 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 - 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 - 3*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 21*(959*B*b^6*d^5*e^2 - 60*(6*B*a*b^5 + A*b^6)*d^4*e^3 - 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 - 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 - 12*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 7*(1029*B*b^6*d^6*e - 60*(6*B*a*b^5 + A*b^6)*d^5*e^2 - 30*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 - 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 - 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 - 12*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 - 10*(B*a^6 + 6*A*a^5*b)*e^7)*x + 420*(B*b^6*e^7*x^7 + 7*B*b^6*d*e^6*x^6 + 21*B*b^6*d^2*e^5*x^5 + 35*B*b^6*d^3*e^4*x^4 + 35*B*b^6*d^4*e^3*x^3 + 21*B*b^6*d^5*e^2*x^2 + 7*B*b^6*d^6*e*x + B*b^6*d^7)*log(e*x + d))/(e^15*x^7 + 7*d*e^14*x^6 + 21*d^2*e^13*x^5 + 35*d^3*e^12*x^4 + 35*d^4*e^11*x^3 + 21*d^5*e^10*x^2 + 7*d^6*e^9*x + d^7*e^8)","B",0
1068,1,823,0,1.385167," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{56 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 7 \, A a^{6} e^{7} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 28 \, {\left(7 \, B b^{6} d e^{6} + {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 56 \, {\left(7 \, B b^{6} d^{2} e^{5} + {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 70 \, {\left(7 \, B b^{6} d^{3} e^{4} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 56 \, {\left(7 \, B b^{6} d^{4} e^{3} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 28 \, {\left(7 \, B b^{6} d^{5} e^{2} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 8 \, {\left(7 \, B b^{6} d^{6} e + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{56 \, {\left(e^{16} x^{8} + 8 \, d e^{15} x^{7} + 28 \, d^{2} e^{14} x^{6} + 56 \, d^{3} e^{13} x^{5} + 70 \, d^{4} e^{12} x^{4} + 56 \, d^{5} e^{11} x^{3} + 28 \, d^{6} e^{10} x^{2} + 8 \, d^{7} e^{9} x + d^{8} e^{8}\right)}}"," ",0,"-1/56*(56*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 7*A*a^6*e^7 + (6*B*a*b^5 + A*b^6)*d^6*e + (5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + (2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + (B*a^6 + 6*A*a^5*b)*d*e^6 + 28*(7*B*b^6*d*e^6 + (6*B*a*b^5 + A*b^6)*e^7)*x^6 + 56*(7*B*b^6*d^2*e^5 + (6*B*a*b^5 + A*b^6)*d*e^6 + (5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 70*(7*B*b^6*d^3*e^4 + (6*B*a*b^5 + A*b^6)*d^2*e^5 + (5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 56*(7*B*b^6*d^4*e^3 + (6*B*a*b^5 + A*b^6)*d^3*e^4 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 28*(7*B*b^6*d^5*e^2 + (6*B*a*b^5 + A*b^6)*d^4*e^3 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + (2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 8*(7*B*b^6*d^6*e + (6*B*a*b^5 + A*b^6)*d^5*e^2 + (5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + (4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + (3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + (2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + (B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^16*x^8 + 8*d*e^15*x^7 + 28*d^2*e^14*x^6 + 56*d^3*e^13*x^5 + 70*d^4*e^12*x^4 + 56*d^5*e^11*x^3 + 28*d^6*e^10*x^2 + 8*d^7*e^9*x + d^8*e^8)","B",0
1069,1,861,0,1.375651," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{252 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 56 \, A a^{6} e^{7} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 7 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 84 \, {\left(7 \, B b^{6} d e^{6} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 126 \, {\left(7 \, B b^{6} d^{2} e^{5} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 126 \, {\left(7 \, B b^{6} d^{3} e^{4} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 84 \, {\left(7 \, B b^{6} d^{4} e^{3} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 36 \, {\left(7 \, B b^{6} d^{5} e^{2} + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 9 \, {\left(7 \, B b^{6} d^{6} e + 2 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 3 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 4 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 5 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 6 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 7 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{504 \, {\left(e^{17} x^{9} + 9 \, d e^{16} x^{8} + 36 \, d^{2} e^{15} x^{7} + 84 \, d^{3} e^{14} x^{6} + 126 \, d^{4} e^{13} x^{5} + 126 \, d^{5} e^{12} x^{4} + 84 \, d^{6} e^{11} x^{3} + 36 \, d^{7} e^{10} x^{2} + 9 \, d^{8} e^{9} x + d^{9} e^{8}\right)}}"," ",0,"-1/504*(252*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 56*A*a^6*e^7 + 2*(6*B*a*b^5 + A*b^6)*d^6*e + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 6*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 7*(B*a^6 + 6*A*a^5*b)*d*e^6 + 84*(7*B*b^6*d*e^6 + 2*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 126*(7*B*b^6*d^2*e^5 + 2*(6*B*a*b^5 + A*b^6)*d*e^6 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 126*(7*B*b^6*d^3*e^4 + 2*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 84*(7*B*b^6*d^4*e^3 + 2*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 36*(7*B*b^6*d^5*e^2 + 2*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 6*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 9*(7*B*b^6*d^6*e + 2*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 3*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 4*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 5*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 6*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 7*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^17*x^9 + 9*d*e^16*x^8 + 36*d^2*e^15*x^7 + 84*d^3*e^14*x^6 + 126*d^4*e^13*x^5 + 126*d^5*e^12*x^4 + 84*d^6*e^11*x^3 + 36*d^7*e^10*x^2 + 9*d^8*e^9*x + d^9*e^8)","B",0
1070,1,872,0,1.364239," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{840 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 252 \, A a^{6} e^{7} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 21 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 28 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 210 \, {\left(7 \, B b^{6} d e^{6} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 252 \, {\left(7 \, B b^{6} d^{2} e^{5} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 210 \, {\left(7 \, B b^{6} d^{3} e^{4} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 120 \, {\left(7 \, B b^{6} d^{4} e^{3} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 45 \, {\left(7 \, B b^{6} d^{5} e^{2} + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 21 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 10 \, {\left(7 \, B b^{6} d^{6} e + 3 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 6 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 10 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 15 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 21 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 28 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{2520 \, {\left(e^{18} x^{10} + 10 \, d e^{17} x^{9} + 45 \, d^{2} e^{16} x^{8} + 120 \, d^{3} e^{15} x^{7} + 210 \, d^{4} e^{14} x^{6} + 252 \, d^{5} e^{13} x^{5} + 210 \, d^{6} e^{12} x^{4} + 120 \, d^{7} e^{11} x^{3} + 45 \, d^{8} e^{10} x^{2} + 10 \, d^{9} e^{9} x + d^{10} e^{8}\right)}}"," ",0,"-1/2520*(840*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 252*A*a^6*e^7 + 3*(6*B*a*b^5 + A*b^6)*d^6*e + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 21*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 28*(B*a^6 + 6*A*a^5*b)*d*e^6 + 210*(7*B*b^6*d*e^6 + 3*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 252*(7*B*b^6*d^2*e^5 + 3*(6*B*a*b^5 + A*b^6)*d*e^6 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 210*(7*B*b^6*d^3*e^4 + 3*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 120*(7*B*b^6*d^4*e^3 + 3*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 45*(7*B*b^6*d^5*e^2 + 3*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 21*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 10*(7*B*b^6*d^6*e + 3*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 6*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 10*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 15*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 21*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 28*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^18*x^10 + 10*d*e^17*x^9 + 45*d^2*e^16*x^8 + 120*d^3*e^15*x^7 + 210*d^4*e^14*x^6 + 252*d^5*e^13*x^5 + 210*d^6*e^12*x^4 + 120*d^7*e^11*x^3 + 45*d^8*e^10*x^2 + 10*d^9*e^9*x + d^10*e^8)","B",0
1071,1,883,0,1.007245," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{2310 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 840 \, A a^{6} e^{7} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 35 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 56 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 84 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 462 \, {\left(7 \, B b^{6} d e^{6} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 462 \, {\left(7 \, B b^{6} d^{2} e^{5} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 330 \, {\left(7 \, B b^{6} d^{3} e^{4} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 165 \, {\left(7 \, B b^{6} d^{4} e^{3} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 35 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 55 \, {\left(7 \, B b^{6} d^{5} e^{2} + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 35 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 56 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 11 \, {\left(7 \, B b^{6} d^{6} e + 4 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 10 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 20 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 35 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 56 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 84 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{9240 \, {\left(e^{19} x^{11} + 11 \, d e^{18} x^{10} + 55 \, d^{2} e^{17} x^{9} + 165 \, d^{3} e^{16} x^{8} + 330 \, d^{4} e^{15} x^{7} + 462 \, d^{5} e^{14} x^{6} + 462 \, d^{6} e^{13} x^{5} + 330 \, d^{7} e^{12} x^{4} + 165 \, d^{8} e^{11} x^{3} + 55 \, d^{9} e^{10} x^{2} + 11 \, d^{10} e^{9} x + d^{11} e^{8}\right)}}"," ",0,"-1/9240*(2310*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 840*A*a^6*e^7 + 4*(6*B*a*b^5 + A*b^6)*d^6*e + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 84*(B*a^6 + 6*A*a^5*b)*d*e^6 + 462*(7*B*b^6*d*e^6 + 4*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 462*(7*B*b^6*d^2*e^5 + 4*(6*B*a*b^5 + A*b^6)*d*e^6 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 330*(7*B*b^6*d^3*e^4 + 4*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 165*(7*B*b^6*d^4*e^3 + 4*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 55*(7*B*b^6*d^5*e^2 + 4*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 11*(7*B*b^6*d^6*e + 4*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 84*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^19*x^11 + 11*d*e^18*x^10 + 55*d^2*e^17*x^9 + 165*d^3*e^16*x^8 + 330*d^4*e^15*x^7 + 462*d^5*e^14*x^6 + 462*d^6*e^13*x^5 + 330*d^7*e^12*x^4 + 165*d^8*e^11*x^3 + 55*d^9*e^10*x^2 + 11*d^10*e^9*x + d^11*e^8)","B",0
1072,1,894,0,1.182649," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{5544 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 2310 \, A a^{6} e^{7} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 35 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 70 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 126 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 210 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 924 \, {\left(7 \, B b^{6} d e^{6} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 792 \, {\left(7 \, B b^{6} d^{2} e^{5} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 495 \, {\left(7 \, B b^{6} d^{3} e^{4} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 35 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 220 \, {\left(7 \, B b^{6} d^{4} e^{3} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 35 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 70 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 66 \, {\left(7 \, B b^{6} d^{5} e^{2} + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 35 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 70 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 126 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 12 \, {\left(7 \, B b^{6} d^{6} e + 5 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 15 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 35 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 70 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 126 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 210 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{27720 \, {\left(e^{20} x^{12} + 12 \, d e^{19} x^{11} + 66 \, d^{2} e^{18} x^{10} + 220 \, d^{3} e^{17} x^{9} + 495 \, d^{4} e^{16} x^{8} + 792 \, d^{5} e^{15} x^{7} + 924 \, d^{6} e^{14} x^{6} + 792 \, d^{7} e^{13} x^{5} + 495 \, d^{8} e^{12} x^{4} + 220 \, d^{9} e^{11} x^{3} + 66 \, d^{10} e^{10} x^{2} + 12 \, d^{11} e^{9} x + d^{12} e^{8}\right)}}"," ",0,"-1/27720*(5544*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 2310*A*a^6*e^7 + 5*(6*B*a*b^5 + A*b^6)*d^6*e + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 35*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 70*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 126*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 210*(B*a^6 + 6*A*a^5*b)*d*e^6 + 924*(7*B*b^6*d*e^6 + 5*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 792*(7*B*b^6*d^2*e^5 + 5*(6*B*a*b^5 + A*b^6)*d*e^6 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 495*(7*B*b^6*d^3*e^4 + 5*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 35*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 220*(7*B*b^6*d^4*e^3 + 5*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 35*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 70*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 66*(7*B*b^6*d^5*e^2 + 5*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 35*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 70*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 126*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 12*(7*B*b^6*d^6*e + 5*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 15*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 35*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 70*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 126*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 210*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^20*x^12 + 12*d*e^19*x^11 + 66*d^2*e^18*x^10 + 220*d^3*e^17*x^9 + 495*d^4*e^16*x^8 + 792*d^5*e^15*x^7 + 924*d^6*e^14*x^6 + 792*d^7*e^13*x^5 + 495*d^8*e^12*x^4 + 220*d^9*e^11*x^3 + 66*d^10*e^10*x^2 + 12*d^11*e^9*x + d^12*e^8)","B",0
1073,1,905,0,1.283480," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^14,x, algorithm=""fricas"")","-\frac{12012 \, B b^{6} e^{7} x^{7} + 7 \, B b^{6} d^{7} + 5544 \, A a^{6} e^{7} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 56 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 126 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 252 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 462 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 1716 \, {\left(7 \, B b^{6} d e^{6} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 1287 \, {\left(7 \, B b^{6} d^{2} e^{5} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 715 \, {\left(7 \, B b^{6} d^{3} e^{4} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 56 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 286 \, {\left(7 \, B b^{6} d^{4} e^{3} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 56 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 126 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 78 \, {\left(7 \, B b^{6} d^{5} e^{2} + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 56 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 126 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 252 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 13 \, {\left(7 \, B b^{6} d^{6} e + 6 \, {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 21 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 56 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 126 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 252 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 462 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{72072 \, {\left(e^{21} x^{13} + 13 \, d e^{20} x^{12} + 78 \, d^{2} e^{19} x^{11} + 286 \, d^{3} e^{18} x^{10} + 715 \, d^{4} e^{17} x^{9} + 1287 \, d^{5} e^{16} x^{8} + 1716 \, d^{6} e^{15} x^{7} + 1716 \, d^{7} e^{14} x^{6} + 1287 \, d^{8} e^{13} x^{5} + 715 \, d^{9} e^{12} x^{4} + 286 \, d^{10} e^{11} x^{3} + 78 \, d^{11} e^{10} x^{2} + 13 \, d^{12} e^{9} x + d^{13} e^{8}\right)}}"," ",0,"-1/72072*(12012*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 5544*A*a^6*e^7 + 6*(6*B*a*b^5 + A*b^6)*d^6*e + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 56*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 126*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 252*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 462*(B*a^6 + 6*A*a^5*b)*d*e^6 + 1716*(7*B*b^6*d*e^6 + 6*(6*B*a*b^5 + A*b^6)*e^7)*x^6 + 1287*(7*B*b^6*d^2*e^5 + 6*(6*B*a*b^5 + A*b^6)*d*e^6 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 715*(7*B*b^6*d^3*e^4 + 6*(6*B*a*b^5 + A*b^6)*d^2*e^5 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 56*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 286*(7*B*b^6*d^4*e^3 + 6*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 56*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 126*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 78*(7*B*b^6*d^5*e^2 + 6*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 56*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 126*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 252*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 13*(7*B*b^6*d^6*e + 6*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 21*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 56*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 126*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 252*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 462*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^21*x^13 + 13*d*e^20*x^12 + 78*d^2*e^19*x^11 + 286*d^3*e^18*x^10 + 715*d^4*e^17*x^9 + 1287*d^5*e^16*x^8 + 1716*d^6*e^15*x^7 + 1716*d^7*e^14*x^6 + 1287*d^8*e^13*x^5 + 715*d^9*e^12*x^4 + 286*d^10*e^11*x^3 + 78*d^11*e^10*x^2 + 13*d^12*e^9*x + d^13*e^8)","B",0
1074,1,902,0,1.090283," ","integrate((b*x+a)^6*(B*x+A)/(e*x+d)^15,x, algorithm=""fricas"")","-\frac{3432 \, B b^{6} e^{7} x^{7} + B b^{6} d^{7} + 1716 \, A a^{6} e^{7} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{6} e + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{5} e^{2} + 12 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{4} e^{3} + 30 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{3} e^{4} + 66 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d^{2} e^{5} + 132 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} d e^{6} + 3003 \, {\left(B b^{6} d e^{6} + {\left(6 \, B a b^{5} + A b^{6}\right)} e^{7}\right)} x^{6} + 2002 \, {\left(B b^{6} d^{2} e^{5} + {\left(6 \, B a b^{5} + A b^{6}\right)} d e^{6} + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} e^{7}\right)} x^{5} + 1001 \, {\left(B b^{6} d^{3} e^{4} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{2} e^{5} + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d e^{6} + 12 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} e^{7}\right)} x^{4} + 364 \, {\left(B b^{6} d^{4} e^{3} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{3} e^{4} + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{2} e^{5} + 12 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d e^{6} + 30 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} e^{7}\right)} x^{3} + 91 \, {\left(B b^{6} d^{5} e^{2} + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{4} e^{3} + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{3} e^{4} + 12 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{2} e^{5} + 30 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d e^{6} + 66 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} e^{7}\right)} x^{2} + 14 \, {\left(B b^{6} d^{6} e + {\left(6 \, B a b^{5} + A b^{6}\right)} d^{5} e^{2} + 4 \, {\left(5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right)} d^{4} e^{3} + 12 \, {\left(4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right)} d^{3} e^{4} + 30 \, {\left(3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right)} d^{2} e^{5} + 66 \, {\left(2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right)} d e^{6} + 132 \, {\left(B a^{6} + 6 \, A a^{5} b\right)} e^{7}\right)} x}{24024 \, {\left(e^{22} x^{14} + 14 \, d e^{21} x^{13} + 91 \, d^{2} e^{20} x^{12} + 364 \, d^{3} e^{19} x^{11} + 1001 \, d^{4} e^{18} x^{10} + 2002 \, d^{5} e^{17} x^{9} + 3003 \, d^{6} e^{16} x^{8} + 3432 \, d^{7} e^{15} x^{7} + 3003 \, d^{8} e^{14} x^{6} + 2002 \, d^{9} e^{13} x^{5} + 1001 \, d^{10} e^{12} x^{4} + 364 \, d^{11} e^{11} x^{3} + 91 \, d^{12} e^{10} x^{2} + 14 \, d^{13} e^{9} x + d^{14} e^{8}\right)}}"," ",0,"-1/24024*(3432*B*b^6*e^7*x^7 + B*b^6*d^7 + 1716*A*a^6*e^7 + (6*B*a*b^5 + A*b^6)*d^6*e + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^4*e^3 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 66*(2*B*a^5*b + 5*A*a^4*b^2)*d^2*e^5 + 132*(B*a^6 + 6*A*a^5*b)*d*e^6 + 3003*(B*b^6*d*e^6 + (6*B*a*b^5 + A*b^6)*e^7)*x^6 + 2002*(B*b^6*d^2*e^5 + (6*B*a*b^5 + A*b^6)*d*e^6 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*e^7)*x^5 + 1001*(B*b^6*d^3*e^4 + (6*B*a*b^5 + A*b^6)*d^2*e^5 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4 + 364*(B*b^6*d^4*e^3 + (6*B*a*b^5 + A*b^6)*d^3*e^4 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^2*e^5 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*e^7)*x^3 + 91*(B*b^6*d^5*e^2 + (6*B*a*b^5 + A*b^6)*d^4*e^3 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 66*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 14*(B*b^6*d^6*e + (6*B*a*b^5 + A*b^6)*d^5*e^2 + 4*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 + 12*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 30*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5 + 66*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 132*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^22*x^14 + 14*d*e^21*x^13 + 91*d^2*e^20*x^12 + 364*d^3*e^19*x^11 + 1001*d^4*e^18*x^10 + 2002*d^5*e^17*x^9 + 3003*d^6*e^16*x^8 + 3432*d^7*e^15*x^7 + 3003*d^8*e^14*x^6 + 2002*d^9*e^13*x^5 + 1001*d^10*e^12*x^4 + 364*d^11*e^11*x^3 + 91*d^12*e^10*x^2 + 14*d^13*e^9*x + d^14*e^8)","B",0
1075,1,5039,0,0.946123," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^13,x, algorithm=""fricas"")","\frac{1}{25} x^{25} e^{13} b^{10} B + \frac{13}{24} x^{24} e^{12} d b^{10} B + \frac{5}{12} x^{24} e^{13} b^{9} a B + \frac{1}{24} x^{24} e^{13} b^{10} A + \frac{78}{23} x^{23} e^{11} d^{2} b^{10} B + \frac{130}{23} x^{23} e^{12} d b^{9} a B + \frac{45}{23} x^{23} e^{13} b^{8} a^{2} B + \frac{13}{23} x^{23} e^{12} d b^{10} A + \frac{10}{23} x^{23} e^{13} b^{9} a A + 13 x^{22} e^{10} d^{3} b^{10} B + \frac{390}{11} x^{22} e^{11} d^{2} b^{9} a B + \frac{585}{22} x^{22} e^{12} d b^{8} a^{2} B + \frac{60}{11} x^{22} e^{13} b^{7} a^{3} B + \frac{39}{11} x^{22} e^{11} d^{2} b^{10} A + \frac{65}{11} x^{22} e^{12} d b^{9} a A + \frac{45}{22} x^{22} e^{13} b^{8} a^{2} A + \frac{715}{21} x^{21} e^{9} d^{4} b^{10} B + \frac{2860}{21} x^{21} e^{10} d^{3} b^{9} a B + \frac{1170}{7} x^{21} e^{11} d^{2} b^{8} a^{2} B + \frac{520}{7} x^{21} e^{12} d b^{7} a^{3} B + 10 x^{21} e^{13} b^{6} a^{4} B + \frac{286}{21} x^{21} e^{10} d^{3} b^{10} A + \frac{260}{7} x^{21} e^{11} d^{2} b^{9} a A + \frac{195}{7} x^{21} e^{12} d b^{8} a^{2} A + \frac{40}{7} x^{21} e^{13} b^{7} a^{3} A + \frac{1287}{20} x^{20} e^{8} d^{5} b^{10} B + \frac{715}{2} x^{20} e^{9} d^{4} b^{9} a B + \frac{1287}{2} x^{20} e^{10} d^{3} b^{8} a^{2} B + 468 x^{20} e^{11} d^{2} b^{7} a^{3} B + \frac{273}{2} x^{20} e^{12} d b^{6} a^{4} B + \frac{63}{5} x^{20} e^{13} b^{5} a^{5} B + \frac{143}{4} x^{20} e^{9} d^{4} b^{10} A + 143 x^{20} e^{10} d^{3} b^{9} a A + \frac{351}{2} x^{20} e^{11} d^{2} b^{8} a^{2} A + 78 x^{20} e^{12} d b^{7} a^{3} A + \frac{21}{2} x^{20} e^{13} b^{6} a^{4} A + \frac{1716}{19} x^{19} e^{7} d^{6} b^{10} B + \frac{12870}{19} x^{19} e^{8} d^{5} b^{9} a B + \frac{32175}{19} x^{19} e^{9} d^{4} b^{8} a^{2} B + \frac{34320}{19} x^{19} e^{10} d^{3} b^{7} a^{3} B + \frac{16380}{19} x^{19} e^{11} d^{2} b^{6} a^{4} B + \frac{3276}{19} x^{19} e^{12} d b^{5} a^{5} B + \frac{210}{19} x^{19} e^{13} b^{4} a^{6} B + \frac{1287}{19} x^{19} e^{8} d^{5} b^{10} A + \frac{7150}{19} x^{19} e^{9} d^{4} b^{9} a A + \frac{12870}{19} x^{19} e^{10} d^{3} b^{8} a^{2} A + \frac{9360}{19} x^{19} e^{11} d^{2} b^{7} a^{3} A + \frac{2730}{19} x^{19} e^{12} d b^{6} a^{4} A + \frac{252}{19} x^{19} e^{13} b^{5} a^{5} A + \frac{286}{3} x^{18} e^{6} d^{7} b^{10} B + \frac{2860}{3} x^{18} e^{7} d^{6} b^{9} a B + \frac{6435}{2} x^{18} e^{8} d^{5} b^{8} a^{2} B + \frac{14300}{3} x^{18} e^{9} d^{4} b^{7} a^{3} B + \frac{10010}{3} x^{18} e^{10} d^{3} b^{6} a^{4} B + 1092 x^{18} e^{11} d^{2} b^{5} a^{5} B + \frac{455}{3} x^{18} e^{12} d b^{4} a^{6} B + \frac{20}{3} x^{18} e^{13} b^{3} a^{7} B + \frac{286}{3} x^{18} e^{7} d^{6} b^{10} A + 715 x^{18} e^{8} d^{5} b^{9} a A + \frac{3575}{2} x^{18} e^{9} d^{4} b^{8} a^{2} A + \frac{5720}{3} x^{18} e^{10} d^{3} b^{7} a^{3} A + 910 x^{18} e^{11} d^{2} b^{6} a^{4} A + 182 x^{18} e^{12} d b^{5} a^{5} A + \frac{35}{3} x^{18} e^{13} b^{4} a^{6} A + \frac{1287}{17} x^{17} e^{5} d^{8} b^{10} B + \frac{17160}{17} x^{17} e^{6} d^{7} b^{9} a B + \frac{77220}{17} x^{17} e^{7} d^{6} b^{8} a^{2} B + \frac{154440}{17} x^{17} e^{8} d^{5} b^{7} a^{3} B + \frac{150150}{17} x^{17} e^{9} d^{4} b^{6} a^{4} B + \frac{72072}{17} x^{17} e^{10} d^{3} b^{5} a^{5} B + \frac{16380}{17} x^{17} e^{11} d^{2} b^{4} a^{6} B + \frac{1560}{17} x^{17} e^{12} d b^{3} a^{7} B + \frac{45}{17} x^{17} e^{13} b^{2} a^{8} B + \frac{1716}{17} x^{17} e^{6} d^{7} b^{10} A + \frac{17160}{17} x^{17} e^{7} d^{6} b^{9} a A + \frac{57915}{17} x^{17} e^{8} d^{5} b^{8} a^{2} A + \frac{85800}{17} x^{17} e^{9} d^{4} b^{7} a^{3} A + \frac{60060}{17} x^{17} e^{10} d^{3} b^{6} a^{4} A + \frac{19656}{17} x^{17} e^{11} d^{2} b^{5} a^{5} A + \frac{2730}{17} x^{17} e^{12} d b^{4} a^{6} A + \frac{120}{17} x^{17} e^{13} b^{3} a^{7} A + \frac{715}{16} x^{16} e^{4} d^{9} b^{10} B + \frac{6435}{8} x^{16} e^{5} d^{8} b^{9} a B + \frac{19305}{4} x^{16} e^{6} d^{7} b^{8} a^{2} B + 12870 x^{16} e^{7} d^{6} b^{7} a^{3} B + \frac{135135}{8} x^{16} e^{8} d^{5} b^{6} a^{4} B + \frac{45045}{4} x^{16} e^{9} d^{4} b^{5} a^{5} B + \frac{15015}{4} x^{16} e^{10} d^{3} b^{4} a^{6} B + 585 x^{16} e^{11} d^{2} b^{3} a^{7} B + \frac{585}{16} x^{16} e^{12} d b^{2} a^{8} B + \frac{5}{8} x^{16} e^{13} b a^{9} B + \frac{1287}{16} x^{16} e^{5} d^{8} b^{10} A + \frac{2145}{2} x^{16} e^{6} d^{7} b^{9} a A + \frac{19305}{4} x^{16} e^{7} d^{6} b^{8} a^{2} A + \frac{19305}{2} x^{16} e^{8} d^{5} b^{7} a^{3} A + \frac{75075}{8} x^{16} e^{9} d^{4} b^{6} a^{4} A + \frac{9009}{2} x^{16} e^{10} d^{3} b^{5} a^{5} A + \frac{4095}{4} x^{16} e^{11} d^{2} b^{4} a^{6} A + \frac{195}{2} x^{16} e^{12} d b^{3} a^{7} A + \frac{45}{16} x^{16} e^{13} b^{2} a^{8} A + \frac{286}{15} x^{15} e^{3} d^{10} b^{10} B + \frac{1430}{3} x^{15} e^{4} d^{9} b^{9} a B + 3861 x^{15} e^{5} d^{8} b^{8} a^{2} B + 13728 x^{15} e^{6} d^{7} b^{7} a^{3} B + 24024 x^{15} e^{7} d^{6} b^{6} a^{4} B + \frac{108108}{5} x^{15} e^{8} d^{5} b^{5} a^{5} B + 10010 x^{15} e^{9} d^{4} b^{4} a^{6} B + 2288 x^{15} e^{10} d^{3} b^{3} a^{7} B + 234 x^{15} e^{11} d^{2} b^{2} a^{8} B + \frac{26}{3} x^{15} e^{12} d b a^{9} B + \frac{1}{15} x^{15} e^{13} a^{10} B + \frac{143}{3} x^{15} e^{4} d^{9} b^{10} A + 858 x^{15} e^{5} d^{8} b^{9} a A + 5148 x^{15} e^{6} d^{7} b^{8} a^{2} A + 13728 x^{15} e^{7} d^{6} b^{7} a^{3} A + 18018 x^{15} e^{8} d^{5} b^{6} a^{4} A + 12012 x^{15} e^{9} d^{4} b^{5} a^{5} A + 4004 x^{15} e^{10} d^{3} b^{4} a^{6} A + 624 x^{15} e^{11} d^{2} b^{3} a^{7} A + 39 x^{15} e^{12} d b^{2} a^{8} A + \frac{2}{3} x^{15} e^{13} b a^{9} A + \frac{39}{7} x^{14} e^{2} d^{11} b^{10} B + \frac{1430}{7} x^{14} e^{3} d^{10} b^{9} a B + \frac{32175}{14} x^{14} e^{4} d^{9} b^{8} a^{2} B + \frac{77220}{7} x^{14} e^{5} d^{8} b^{7} a^{3} B + 25740 x^{14} e^{6} d^{7} b^{6} a^{4} B + 30888 x^{14} e^{7} d^{6} b^{5} a^{5} B + 19305 x^{14} e^{8} d^{5} b^{4} a^{6} B + \frac{42900}{7} x^{14} e^{9} d^{4} b^{3} a^{7} B + \frac{6435}{7} x^{14} e^{10} d^{3} b^{2} a^{8} B + \frac{390}{7} x^{14} e^{11} d^{2} b a^{9} B + \frac{13}{14} x^{14} e^{12} d a^{10} B + \frac{143}{7} x^{14} e^{3} d^{10} b^{10} A + \frac{3575}{7} x^{14} e^{4} d^{9} b^{9} a A + \frac{57915}{14} x^{14} e^{5} d^{8} b^{8} a^{2} A + \frac{102960}{7} x^{14} e^{6} d^{7} b^{7} a^{3} A + 25740 x^{14} e^{7} d^{6} b^{6} a^{4} A + 23166 x^{14} e^{8} d^{5} b^{5} a^{5} A + 10725 x^{14} e^{9} d^{4} b^{4} a^{6} A + \frac{17160}{7} x^{14} e^{10} d^{3} b^{3} a^{7} A + \frac{1755}{7} x^{14} e^{11} d^{2} b^{2} a^{8} A + \frac{65}{7} x^{14} e^{12} d b a^{9} A + \frac{1}{14} x^{14} e^{13} a^{10} A + x^{13} e d^{12} b^{10} B + 60 x^{13} e^{2} d^{11} b^{9} a B + 990 x^{13} e^{3} d^{10} b^{8} a^{2} B + 6600 x^{13} e^{4} d^{9} b^{7} a^{3} B + 20790 x^{13} e^{5} d^{8} b^{6} a^{4} B + 33264 x^{13} e^{6} d^{7} b^{5} a^{5} B + 27720 x^{13} e^{7} d^{6} b^{4} a^{6} B + 11880 x^{13} e^{8} d^{5} b^{3} a^{7} B + 2475 x^{13} e^{9} d^{4} b^{2} a^{8} B + 220 x^{13} e^{10} d^{3} b a^{9} B + 6 x^{13} e^{11} d^{2} a^{10} B + 6 x^{13} e^{2} d^{11} b^{10} A + 220 x^{13} e^{3} d^{10} b^{9} a A + 2475 x^{13} e^{4} d^{9} b^{8} a^{2} A + 11880 x^{13} e^{5} d^{8} b^{7} a^{3} A + 27720 x^{13} e^{6} d^{7} b^{6} a^{4} A + 33264 x^{13} e^{7} d^{6} b^{5} a^{5} A + 20790 x^{13} e^{8} d^{5} b^{4} a^{6} A + 6600 x^{13} e^{9} d^{4} b^{3} a^{7} A + 990 x^{13} e^{10} d^{3} b^{2} a^{8} A + 60 x^{13} e^{11} d^{2} b a^{9} A + x^{13} e^{12} d a^{10} A + \frac{1}{12} x^{12} d^{13} b^{10} B + \frac{65}{6} x^{12} e d^{12} b^{9} a B + \frac{585}{2} x^{12} e^{2} d^{11} b^{8} a^{2} B + 2860 x^{12} e^{3} d^{10} b^{7} a^{3} B + \frac{25025}{2} x^{12} e^{4} d^{9} b^{6} a^{4} B + 27027 x^{12} e^{5} d^{8} b^{5} a^{5} B + 30030 x^{12} e^{6} d^{7} b^{4} a^{6} B + 17160 x^{12} e^{7} d^{6} b^{3} a^{7} B + \frac{19305}{4} x^{12} e^{8} d^{5} b^{2} a^{8} B + \frac{3575}{6} x^{12} e^{9} d^{4} b a^{9} B + \frac{143}{6} x^{12} e^{10} d^{3} a^{10} B + \frac{13}{12} x^{12} e d^{12} b^{10} A + 65 x^{12} e^{2} d^{11} b^{9} a A + \frac{2145}{2} x^{12} e^{3} d^{10} b^{8} a^{2} A + 7150 x^{12} e^{4} d^{9} b^{7} a^{3} A + \frac{45045}{2} x^{12} e^{5} d^{8} b^{6} a^{4} A + 36036 x^{12} e^{6} d^{7} b^{5} a^{5} A + 30030 x^{12} e^{7} d^{6} b^{4} a^{6} A + 12870 x^{12} e^{8} d^{5} b^{3} a^{7} A + \frac{10725}{4} x^{12} e^{9} d^{4} b^{2} a^{8} A + \frac{715}{3} x^{12} e^{10} d^{3} b a^{9} A + \frac{13}{2} x^{12} e^{11} d^{2} a^{10} A + \frac{10}{11} x^{11} d^{13} b^{9} a B + \frac{585}{11} x^{11} e d^{12} b^{8} a^{2} B + \frac{9360}{11} x^{11} e^{2} d^{11} b^{7} a^{3} B + 5460 x^{11} e^{3} d^{10} b^{6} a^{4} B + 16380 x^{11} e^{4} d^{9} b^{5} a^{5} B + 24570 x^{11} e^{5} d^{8} b^{4} a^{6} B + 18720 x^{11} e^{6} d^{7} b^{3} a^{7} B + 7020 x^{11} e^{7} d^{6} b^{2} a^{8} B + 1170 x^{11} e^{8} d^{5} b a^{9} B + 65 x^{11} e^{9} d^{4} a^{10} B + \frac{1}{11} x^{11} d^{13} b^{10} A + \frac{130}{11} x^{11} e d^{12} b^{9} a A + \frac{3510}{11} x^{11} e^{2} d^{11} b^{8} a^{2} A + 3120 x^{11} e^{3} d^{10} b^{7} a^{3} A + 13650 x^{11} e^{4} 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13/2*x^12*e^11*d^2*a^10*A + 10/11*x^11*d^13*b^9*a*B + 585/11*x^11*e*d^12*b^8*a^2*B + 9360/11*x^11*e^2*d^11*b^7*a^3*B + 5460*x^11*e^3*d^10*b^6*a^4*B + 16380*x^11*e^4*d^9*b^5*a^5*B + 24570*x^11*e^5*d^8*b^4*a^6*B + 18720*x^11*e^6*d^7*b^3*a^7*B + 7020*x^11*e^7*d^6*b^2*a^8*B + 1170*x^11*e^8*d^5*b*a^9*B + 65*x^11*e^9*d^4*a^10*B + 1/11*x^11*d^13*b^10*A + 130/11*x^11*e*d^12*b^9*a*A + 3510/11*x^11*e^2*d^11*b^8*a^2*A + 3120*x^11*e^3*d^10*b^7*a^3*A + 13650*x^11*e^4*d^9*b^6*a^4*A + 29484*x^11*e^5*d^8*b^5*a^5*A + 32760*x^11*e^6*d^7*b^4*a^6*A + 18720*x^11*e^7*d^6*b^3*a^7*A + 5265*x^11*e^8*d^5*b^2*a^8*A + 650*x^11*e^9*d^4*b*a^9*A + 26*x^11*e^10*d^3*a^10*A + 9/2*x^10*d^13*b^8*a^2*B + 156*x^10*e*d^12*b^7*a^3*B + 1638*x^10*e^2*d^11*b^6*a^4*B + 36036/5*x^10*e^3*d^10*b^5*a^5*B + 15015*x^10*e^4*d^9*b^4*a^6*B + 15444*x^10*e^5*d^8*b^3*a^7*B + 7722*x^10*e^6*d^7*b^2*a^8*B + 1716*x^10*e^7*d^6*b*a^9*B + 1287/10*x^10*e^8*d^5*a^10*B + x^10*d^13*b^9*a*A + 117/2*x^10*e*d^12*b^8*a^2*A + 936*x^10*e^2*d^11*b^7*a^3*A + 6006*x^10*e^3*d^10*b^6*a^4*A + 18018*x^10*e^4*d^9*b^5*a^5*A + 27027*x^10*e^5*d^8*b^4*a^6*A + 20592*x^10*e^6*d^7*b^3*a^7*A + 7722*x^10*e^7*d^6*b^2*a^8*A + 1287*x^10*e^8*d^5*b*a^9*A + 143/2*x^10*e^9*d^4*a^10*A + 40/3*x^9*d^13*b^7*a^3*B + 910/3*x^9*e*d^12*b^6*a^4*B + 2184*x^9*e^2*d^11*b^5*a^5*B + 20020/3*x^9*e^3*d^10*b^4*a^6*B + 28600/3*x^9*e^4*d^9*b^3*a^7*B + 6435*x^9*e^5*d^8*b^2*a^8*B + 5720/3*x^9*e^6*d^7*b*a^9*B + 572/3*x^9*e^7*d^6*a^10*B + 5*x^9*d^13*b^8*a^2*A + 520/3*x^9*e*d^12*b^7*a^3*A + 1820*x^9*e^2*d^11*b^6*a^4*A + 8008*x^9*e^3*d^10*b^5*a^5*A + 50050/3*x^9*e^4*d^9*b^4*a^6*A + 17160*x^9*e^5*d^8*b^3*a^7*A + 8580*x^9*e^6*d^7*b^2*a^8*A + 5720/3*x^9*e^7*d^6*b*a^9*A + 143*x^9*e^8*d^5*a^10*A + 105/4*x^8*d^13*b^6*a^4*B + 819/2*x^8*e*d^12*b^5*a^5*B + 4095/2*x^8*e^2*d^11*b^4*a^6*B + 4290*x^8*e^3*d^10*b^3*a^7*B + 32175/8*x^8*e^4*d^9*b^2*a^8*B + 6435/4*x^8*e^5*d^8*b*a^9*B + 429/2*x^8*e^6*d^7*a^10*B + 15*x^8*d^13*b^7*a^3*A + 1365/4*x^8*e*d^12*b^6*a^4*A + 2457*x^8*e^2*d^11*b^5*a^5*A + 15015/2*x^8*e^3*d^10*b^4*a^6*A + 10725*x^8*e^4*d^9*b^3*a^7*A + 57915/8*x^8*e^5*d^8*b^2*a^8*A + 2145*x^8*e^6*d^7*b*a^9*A + 429/2*x^8*e^7*d^6*a^10*A + 36*x^7*d^13*b^5*a^5*B + 390*x^7*e*d^12*b^4*a^6*B + 9360/7*x^7*e^2*d^11*b^3*a^7*B + 12870/7*x^7*e^3*d^10*b^2*a^8*B + 7150/7*x^7*e^4*d^9*b*a^9*B + 1287/7*x^7*e^5*d^8*a^10*B + 30*x^7*d^13*b^6*a^4*A + 468*x^7*e*d^12*b^5*a^5*A + 2340*x^7*e^2*d^11*b^4*a^6*A + 34320/7*x^7*e^3*d^10*b^3*a^7*A + 32175/7*x^7*e^4*d^9*b^2*a^8*A + 12870/7*x^7*e^5*d^8*b*a^9*A + 1716/7*x^7*e^6*d^7*a^10*A + 35*x^6*d^13*b^4*a^6*B + 260*x^6*e*d^12*b^3*a^7*B + 585*x^6*e^2*d^11*b^2*a^8*B + 1430/3*x^6*e^3*d^10*b*a^9*B + 715/6*x^6*e^4*d^9*a^10*B + 42*x^6*d^13*b^5*a^5*A + 455*x^6*e*d^12*b^4*a^6*A + 1560*x^6*e^2*d^11*b^3*a^7*A + 2145*x^6*e^3*d^10*b^2*a^8*A + 3575/3*x^6*e^4*d^9*b*a^9*A + 429/2*x^6*e^5*d^8*a^10*A + 24*x^5*d^13*b^3*a^7*B + 117*x^5*e*d^12*b^2*a^8*B + 156*x^5*e^2*d^11*b*a^9*B + 286/5*x^5*e^3*d^10*a^10*B + 42*x^5*d^13*b^4*a^6*A + 312*x^5*e*d^12*b^3*a^7*A + 702*x^5*e^2*d^11*b^2*a^8*A + 572*x^5*e^3*d^10*b*a^9*A + 143*x^5*e^4*d^9*a^10*A + 45/4*x^4*d^13*b^2*a^8*B + 65/2*x^4*e*d^12*b*a^9*B + 39/2*x^4*e^2*d^11*a^10*B + 30*x^4*d^13*b^3*a^7*A + 585/4*x^4*e*d^12*b^2*a^8*A + 195*x^4*e^2*d^11*b*a^9*A + 143/2*x^4*e^3*d^10*a^10*A + 10/3*x^3*d^13*b*a^9*B + 13/3*x^3*e*d^12*a^10*B + 15*x^3*d^13*b^2*a^8*A + 130/3*x^3*e*d^12*b*a^9*A + 26*x^3*e^2*d^11*a^10*A + 1/2*x^2*d^13*a^10*B + 5*x^2*d^13*b*a^9*A + 13/2*x^2*e*d^12*a^10*A + x*d^13*a^10*A","B",0
1076,1,4663,0,0.794823," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^12,x, algorithm=""fricas"")","\frac{1}{24} x^{24} e^{12} b^{10} B + \frac{12}{23} x^{23} e^{11} d b^{10} B + \frac{10}{23} x^{23} e^{12} b^{9} a B + \frac{1}{23} x^{23} e^{12} b^{10} A + 3 x^{22} e^{10} d^{2} b^{10} B + \frac{60}{11} x^{22} e^{11} d b^{9} a B + \frac{45}{22} x^{22} e^{12} b^{8} a^{2} B + \frac{6}{11} x^{22} e^{11} d b^{10} A + \frac{5}{11} x^{22} e^{12} b^{9} a A + \frac{220}{21} x^{21} e^{9} d^{3} b^{10} B + \frac{220}{7} x^{21} e^{10} d^{2} b^{9} a B + \frac{180}{7} x^{21} e^{11} d b^{8} a^{2} B + \frac{40}{7} x^{21} e^{12} b^{7} a^{3} B + \frac{22}{7} x^{21} e^{10} d^{2} b^{10} A + \frac{40}{7} x^{21} e^{11} d b^{9} a A + \frac{15}{7} x^{21} e^{12} b^{8} a^{2} A + \frac{99}{4} x^{20} e^{8} d^{4} b^{10} B + 110 x^{20} e^{9} d^{3} b^{9} a B + \frac{297}{2} x^{20} e^{10} d^{2} b^{8} a^{2} B + 72 x^{20} e^{11} d b^{7} a^{3} B + \frac{21}{2} x^{20} e^{12} b^{6} a^{4} B + 11 x^{20} e^{9} d^{3} b^{10} A + 33 x^{20} e^{10} d^{2} b^{9} a A + 27 x^{20} e^{11} d b^{8} a^{2} A + 6 x^{20} e^{12} b^{7} a^{3} A + \frac{792}{19} x^{19} e^{7} d^{5} b^{10} B + \frac{4950}{19} x^{19} e^{8} d^{4} b^{9} a B + \frac{9900}{19} x^{19} e^{9} d^{3} b^{8} a^{2} B + \frac{7920}{19} x^{19} e^{10} d^{2} b^{7} a^{3} B + \frac{2520}{19} x^{19} e^{11} d b^{6} a^{4} B + \frac{252}{19} x^{19} e^{12} b^{5} a^{5} B + \frac{495}{19} x^{19} e^{8} d^{4} b^{10} A + \frac{2200}{19} x^{19} e^{9} d^{3} b^{9} a A + \frac{2970}{19} x^{19} e^{10} d^{2} b^{8} a^{2} A + \frac{1440}{19} x^{19} e^{11} d b^{7} a^{3} A + \frac{210}{19} x^{19} e^{12} b^{6} a^{4} A + \frac{154}{3} x^{18} e^{6} d^{6} b^{10} B + 440 x^{18} e^{7} d^{5} b^{9} a B + \frac{2475}{2} x^{18} e^{8} d^{4} b^{8} a^{2} B + \frac{4400}{3} x^{18} e^{9} d^{3} b^{7} a^{3} B + 770 x^{18} e^{10} d^{2} b^{6} a^{4} B + 168 x^{18} e^{11} d b^{5} a^{5} B + \frac{35}{3} x^{18} e^{12} b^{4} a^{6} B + 44 x^{18} e^{7} d^{5} b^{10} A + 275 x^{18} e^{8} d^{4} b^{9} a A + 550 x^{18} e^{9} d^{3} b^{8} a^{2} A + 440 x^{18} e^{10} d^{2} b^{7} a^{3} A + 140 x^{18} e^{11} d b^{6} a^{4} A + 14 x^{18} e^{12} b^{5} a^{5} A + \frac{792}{17} x^{17} e^{5} d^{7} b^{10} B + \frac{9240}{17} x^{17} e^{6} d^{6} b^{9} a B + \frac{35640}{17} x^{17} e^{7} d^{5} b^{8} a^{2} B + \frac{59400}{17} x^{17} e^{8} d^{4} b^{7} a^{3} B + \frac{46200}{17} x^{17} e^{9} d^{3} b^{6} a^{4} B + \frac{16632}{17} x^{17} e^{10} d^{2} b^{5} a^{5} B + \frac{2520}{17} x^{17} e^{11} d b^{4} a^{6} B + \frac{120}{17} x^{17} e^{12} b^{3} a^{7} B + \frac{924}{17} x^{17} e^{6} d^{6} b^{10} A + \frac{7920}{17} x^{17} e^{7} d^{5} b^{9} a A + \frac{22275}{17} x^{17} e^{8} d^{4} b^{8} a^{2} A + \frac{26400}{17} x^{17} e^{9} d^{3} b^{7} a^{3} A + \frac{13860}{17} x^{17} e^{10} d^{2} b^{6} a^{4} A + \frac{3024}{17} x^{17} e^{11} d b^{5} a^{5} A + \frac{210}{17} x^{17} e^{12} b^{4} a^{6} A + \frac{495}{16} x^{16} e^{4} d^{8} b^{10} B + 495 x^{16} e^{5} d^{7} b^{9} a B + \frac{10395}{4} x^{16} e^{6} d^{6} b^{8} a^{2} B + 5940 x^{16} e^{7} d^{5} b^{7} a^{3} B + \frac{51975}{8} x^{16} e^{8} d^{4} b^{6} a^{4} B + 3465 x^{16} e^{9} d^{3} b^{5} a^{5} B + \frac{3465}{4} x^{16} e^{10} d^{2} b^{4} a^{6} B + 90 x^{16} e^{11} d b^{3} a^{7} B + \frac{45}{16} x^{16} e^{12} b^{2} a^{8} B + \frac{99}{2} x^{16} e^{5} d^{7} b^{10} A + \frac{1155}{2} x^{16} e^{6} d^{6} b^{9} a A + \frac{4455}{2} x^{16} e^{7} d^{5} b^{8} a^{2} A + \frac{7425}{2} x^{16} e^{8} d^{4} b^{7} a^{3} A + \frac{5775}{2} x^{16} e^{9} d^{3} b^{6} a^{4} A + \frac{2079}{2} x^{16} e^{10} d^{2} b^{5} a^{5} A + \frac{315}{2} x^{16} e^{11} d b^{4} a^{6} A + \frac{15}{2} x^{16} e^{12} b^{3} a^{7} A + \frac{44}{3} x^{15} e^{3} d^{9} b^{10} B + 330 x^{15} e^{4} d^{8} b^{9} a B + 2376 x^{15} e^{5} d^{7} b^{8} a^{2} B + 7392 x^{15} e^{6} d^{6} b^{7} a^{3} B + 11088 x^{15} e^{7} d^{5} b^{6} a^{4} B + 8316 x^{15} e^{8} d^{4} b^{5} a^{5} B + 3080 x^{15} e^{9} d^{3} b^{4} a^{6} B + 528 x^{15} e^{10} d^{2} b^{3} a^{7} B + 36 x^{15} e^{11} d b^{2} a^{8} B + \frac{2}{3} x^{15} e^{12} b a^{9} B + 33 x^{15} e^{4} d^{8} b^{10} A + 528 x^{15} e^{5} d^{7} b^{9} a A + 2772 x^{15} e^{6} d^{6} b^{8} a^{2} A + 6336 x^{15} e^{7} d^{5} b^{7} a^{3} A + 6930 x^{15} e^{8} d^{4} b^{6} a^{4} A + 3696 x^{15} e^{9} d^{3} b^{5} a^{5} A + 924 x^{15} e^{10} d^{2} b^{4} a^{6} A + 96 x^{15} e^{11} d b^{3} a^{7} A + 3 x^{15} e^{12} b^{2} a^{8} A + \frac{33}{7} x^{14} e^{2} d^{10} b^{10} B + \frac{1100}{7} x^{14} e^{3} d^{9} b^{9} a B + \frac{22275}{14} x^{14} e^{4} d^{8} b^{8} a^{2} B + \frac{47520}{7} x^{14} e^{5} d^{7} b^{7} a^{3} B + 13860 x^{14} e^{6} d^{6} b^{6} a^{4} B + 14256 x^{14} e^{7} d^{5} b^{5} a^{5} B + 7425 x^{14} e^{8} d^{4} b^{4} a^{6} B + \frac{13200}{7} x^{14} e^{9} d^{3} b^{3} a^{7} B + \frac{1485}{7} x^{14} e^{10} d^{2} b^{2} a^{8} B + \frac{60}{7} x^{14} e^{11} d b a^{9} B + \frac{1}{14} x^{14} e^{12} a^{10} B + \frac{110}{7} x^{14} e^{3} d^{9} b^{10} A + \frac{2475}{7} x^{14} e^{4} d^{8} b^{9} a A + \frac{17820}{7} x^{14} e^{5} d^{7} b^{8} a^{2} A + 7920 x^{14} e^{6} d^{6} b^{7} a^{3} A + 11880 x^{14} e^{7} d^{5} b^{6} a^{4} A + 8910 x^{14} e^{8} d^{4} b^{5} a^{5} A + 3300 x^{14} e^{9} d^{3} b^{4} a^{6} A + \frac{3960}{7} x^{14} e^{10} d^{2} b^{3} a^{7} A + \frac{270}{7} x^{14} e^{11} d b^{2} a^{8} A + \frac{5}{7} x^{14} e^{12} b a^{9} A + \frac{12}{13} x^{13} e d^{11} b^{10} B + \frac{660}{13} x^{13} e^{2} d^{10} b^{9} a B + \frac{9900}{13} x^{13} e^{3} d^{9} b^{8} a^{2} B + \frac{59400}{13} x^{13} e^{4} d^{8} b^{7} a^{3} B + \frac{166320}{13} x^{13} e^{5} d^{7} b^{6} a^{4} B + \frac{232848}{13} x^{13} e^{6} d^{6} b^{5} a^{5} B + \frac{166320}{13} x^{13} e^{7} d^{5} b^{4} a^{6} B + \frac{59400}{13} x^{13} e^{8} d^{4} b^{3} a^{7} B + \frac{9900}{13} x^{13} e^{9} d^{3} b^{2} a^{8} B + \frac{660}{13} x^{13} e^{10} d^{2} b a^{9} B + \frac{12}{13} x^{13} e^{11} d a^{10} B + \frac{66}{13} x^{13} e^{2} d^{10} b^{10} A + \frac{2200}{13} x^{13} e^{3} d^{9} b^{9} a A + \frac{22275}{13} x^{13} e^{4} d^{8} b^{8} a^{2} A + \frac{95040}{13} x^{13} e^{5} d^{7} b^{7} a^{3} A + \frac{194040}{13} x^{13} e^{6} d^{6} b^{6} a^{4} A + \frac{199584}{13} x^{13} e^{7} d^{5} b^{5} a^{5} A + \frac{103950}{13} x^{13} e^{8} d^{4} b^{4} a^{6} A + \frac{26400}{13} x^{13} e^{9} d^{3} b^{3} a^{7} A + \frac{2970}{13} x^{13} e^{10} d^{2} b^{2} a^{8} A + \frac{120}{13} x^{13} e^{11} d b a^{9} A + \frac{1}{13} x^{13} e^{12} a^{10} A + \frac{1}{12} x^{12} d^{12} b^{10} B + 10 x^{12} e d^{11} b^{9} a B + \frac{495}{2} x^{12} e^{2} d^{10} b^{8} a^{2} B + 2200 x^{12} e^{3} d^{9} b^{7} a^{3} B + \frac{17325}{2} x^{12} e^{4} d^{8} b^{6} a^{4} B + 16632 x^{12} e^{5} d^{7} b^{5} a^{5} B + 16170 x^{12} e^{6} d^{6} b^{4} a^{6} B + 7920 x^{12} e^{7} d^{5} b^{3} a^{7} B + \frac{7425}{4} x^{12} e^{8} d^{4} b^{2} a^{8} B + \frac{550}{3} x^{12} e^{9} d^{3} b a^{9} B + \frac{11}{2} x^{12} e^{10} d^{2} a^{10} B + x^{12} e d^{11} b^{10} A + 55 x^{12} e^{2} d^{10} b^{9} a A + 825 x^{12} e^{3} d^{9} b^{8} a^{2} A + 4950 x^{12} e^{4} d^{8} b^{7} a^{3} A + 13860 x^{12} e^{5} d^{7} b^{6} a^{4} A + 19404 x^{12} e^{6} d^{6} b^{5} a^{5} A + 13860 x^{12} e^{7} d^{5} b^{4} a^{6} A + 4950 x^{12} e^{8} d^{4} b^{3} a^{7} A + 825 x^{12} e^{9} d^{3} b^{2} a^{8} A + 55 x^{12} e^{10} d^{2} b a^{9} A + x^{12} e^{11} d a^{10} A + \frac{10}{11} x^{11} d^{12} b^{9} a B + \frac{540}{11} x^{11} e d^{11} b^{8} a^{2} B + 720 x^{11} e^{2} d^{10} b^{7} a^{3} B + 4200 x^{11} e^{3} d^{9} b^{6} a^{4} B + 11340 x^{11} e^{4} d^{8} b^{5} a^{5} B + 15120 x^{11} e^{5} d^{7} b^{4} a^{6} B + 10080 x^{11} e^{6} d^{6} b^{3} a^{7} B + 3240 x^{11} e^{7} d^{5} b^{2} a^{8} B + 450 x^{11} e^{8} d^{4} b a^{9} B + 20 x^{11} e^{9} d^{3} a^{10} B + \frac{1}{11} x^{11} d^{12} b^{10} A + \frac{120}{11} x^{11} e d^{11} b^{9} a A + 270 x^{11} e^{2} d^{10} b^{8} a^{2} A + 2400 x^{11} e^{3} d^{9} b^{7} a^{3} A + 9450 x^{11} e^{4} d^{8} b^{6} a^{4} A + 18144 x^{11} e^{5} d^{7} b^{5} a^{5} A + 17640 x^{11} e^{6} d^{6} b^{4} a^{6} A + 8640 x^{11} e^{7} d^{5} b^{3} a^{7} A + 2025 x^{11} e^{8} d^{4} b^{2} a^{8} A + 200 x^{11} e^{9} d^{3} b a^{9} A + 6 x^{11} e^{10} d^{2} a^{10} A + \frac{9}{2} x^{10} d^{12} b^{8} a^{2} B + 144 x^{10} e d^{11} b^{7} a^{3} B + 1386 x^{10} e^{2} d^{10} b^{6} a^{4} B + 5544 x^{10} e^{3} d^{9} b^{5} a^{5} B + 10395 x^{10} e^{4} d^{8} b^{4} a^{6} B + 9504 x^{10} e^{5} d^{7} b^{3} a^{7} B + 4158 x^{10} e^{6} d^{6} b^{2} a^{8} B + 792 x^{10} e^{7} d^{5} b a^{9} B + \frac{99}{2} x^{10} e^{8} d^{4} a^{10} B + x^{10} d^{12} b^{9} a A + 54 x^{10} e d^{11} b^{8} a^{2} A + 792 x^{10} e^{2} d^{10} b^{7} a^{3} A + 4620 x^{10} e^{3} d^{9} b^{6} a^{4} A + 12474 x^{10} e^{4} d^{8} b^{5} a^{5} A + 16632 x^{10} e^{5} d^{7} b^{4} a^{6} A + 11088 x^{10} e^{6} d^{6} b^{3} a^{7} A + 3564 x^{10} e^{7} d^{5} b^{2} a^{8} A + 495 x^{10} e^{8} d^{4} b a^{9} A + 22 x^{10} e^{9} d^{3} a^{10} A + \frac{40}{3} x^{9} d^{12} b^{7} a^{3} B + 280 x^{9} e d^{11} b^{6} a^{4} B + 1848 x^{9} e^{2} d^{10} b^{5} a^{5} B + \frac{15400}{3} x^{9} e^{3} d^{9} b^{4} a^{6} B + 6600 x^{9} e^{4} d^{8} b^{3} a^{7} B + 3960 x^{9} e^{5} d^{7} b^{2} a^{8} B + \frac{3080}{3} x^{9} e^{6} d^{6} b a^{9} B + 88 x^{9} e^{7} d^{5} a^{10} B + 5 x^{9} d^{12} b^{8} a^{2} A + 160 x^{9} e d^{11} b^{7} a^{3} A + 1540 x^{9} e^{2} d^{10} b^{6} a^{4} A + 6160 x^{9} e^{3} d^{9} b^{5} a^{5} A + 11550 x^{9} e^{4} d^{8} b^{4} a^{6} A + 10560 x^{9} e^{5} d^{7} b^{3} a^{7} A + 4620 x^{9} e^{6} d^{6} b^{2} a^{8} A + 880 x^{9} e^{7} d^{5} b a^{9} A + 55 x^{9} e^{8} d^{4} a^{10} A + \frac{105}{4} x^{8} d^{12} b^{6} a^{4} B + 378 x^{8} e d^{11} b^{5} a^{5} B + \frac{3465}{2} x^{8} e^{2} d^{10} b^{4} a^{6} B + 3300 x^{8} e^{3} d^{9} b^{3} a^{7} B + \frac{22275}{8} x^{8} e^{4} d^{8} b^{2} a^{8} B + 990 x^{8} e^{5} d^{7} b a^{9} B + \frac{231}{2} x^{8} e^{6} d^{6} a^{10} B + 15 x^{8} d^{12} b^{7} a^{3} A + 315 x^{8} e d^{11} b^{6} a^{4} A + 2079 x^{8} e^{2} d^{10} b^{5} a^{5} A + 5775 x^{8} e^{3} d^{9} b^{4} a^{6} A + 7425 x^{8} e^{4} d^{8} b^{3} a^{7} A + 4455 x^{8} e^{5} d^{7} b^{2} a^{8} A + 1155 x^{8} e^{6} d^{6} b a^{9} A + 99 x^{8} e^{7} d^{5} a^{10} A + 36 x^{7} d^{12} b^{5} a^{5} B + 360 x^{7} e d^{11} b^{4} a^{6} B + \frac{7920}{7} x^{7} e^{2} d^{10} b^{3} a^{7} B + \frac{9900}{7} x^{7} e^{3} d^{9} b^{2} a^{8} B + \frac{4950}{7} x^{7} e^{4} d^{8} b a^{9} B + \frac{792}{7} x^{7} e^{5} d^{7} a^{10} B + 30 x^{7} d^{12} b^{6} a^{4} A + 432 x^{7} e d^{11} b^{5} a^{5} A + 1980 x^{7} e^{2} d^{10} b^{4} a^{6} A + \frac{26400}{7} x^{7} e^{3} d^{9} b^{3} a^{7} A + \frac{22275}{7} x^{7} e^{4} d^{8} b^{2} a^{8} A + \frac{7920}{7} x^{7} e^{5} d^{7} b a^{9} A + 132 x^{7} e^{6} d^{6} a^{10} A + 35 x^{6} d^{12} b^{4} a^{6} B + 240 x^{6} e d^{11} b^{3} a^{7} B + 495 x^{6} e^{2} d^{10} b^{2} a^{8} B + \frac{1100}{3} x^{6} e^{3} d^{9} b a^{9} B + \frac{165}{2} x^{6} e^{4} d^{8} a^{10} B + 42 x^{6} d^{12} b^{5} a^{5} A + 420 x^{6} e d^{11} b^{4} a^{6} A + 1320 x^{6} e^{2} d^{10} b^{3} a^{7} A + 1650 x^{6} e^{3} d^{9} b^{2} a^{8} A + 825 x^{6} e^{4} d^{8} b a^{9} A + 132 x^{6} e^{5} d^{7} a^{10} A + 24 x^{5} d^{12} b^{3} a^{7} B + 108 x^{5} e d^{11} b^{2} a^{8} B + 132 x^{5} e^{2} d^{10} b a^{9} B + 44 x^{5} e^{3} d^{9} a^{10} B + 42 x^{5} d^{12} b^{4} a^{6} A + 288 x^{5} e d^{11} b^{3} a^{7} A + 594 x^{5} e^{2} d^{10} b^{2} a^{8} A + 440 x^{5} e^{3} d^{9} b a^{9} A + 99 x^{5} e^{4} d^{8} a^{10} A + \frac{45}{4} x^{4} d^{12} b^{2} a^{8} B + 30 x^{4} e d^{11} b a^{9} B + \frac{33}{2} x^{4} e^{2} d^{10} a^{10} B + 30 x^{4} d^{12} b^{3} a^{7} A + 135 x^{4} e d^{11} b^{2} a^{8} A + 165 x^{4} e^{2} d^{10} b a^{9} A + 55 x^{4} e^{3} d^{9} a^{10} A + \frac{10}{3} x^{3} d^{12} b a^{9} B + 4 x^{3} e d^{11} a^{10} B + 15 x^{3} d^{12} b^{2} a^{8} A + 40 x^{3} e d^{11} b a^{9} A + 22 x^{3} e^{2} d^{10} a^{10} A + \frac{1}{2} x^{2} d^{12} a^{10} B + 5 x^{2} d^{12} b a^{9} A + 6 x^{2} e d^{11} a^{10} A + x d^{12} a^{10} A"," ",0,"1/24*x^24*e^12*b^10*B + 12/23*x^23*e^11*d*b^10*B + 10/23*x^23*e^12*b^9*a*B + 1/23*x^23*e^12*b^10*A + 3*x^22*e^10*d^2*b^10*B + 60/11*x^22*e^11*d*b^9*a*B + 45/22*x^22*e^12*b^8*a^2*B + 6/11*x^22*e^11*d*b^10*A + 5/11*x^22*e^12*b^9*a*A + 220/21*x^21*e^9*d^3*b^10*B + 220/7*x^21*e^10*d^2*b^9*a*B + 180/7*x^21*e^11*d*b^8*a^2*B + 40/7*x^21*e^12*b^7*a^3*B + 22/7*x^21*e^10*d^2*b^10*A + 40/7*x^21*e^11*d*b^9*a*A + 15/7*x^21*e^12*b^8*a^2*A + 99/4*x^20*e^8*d^4*b^10*B + 110*x^20*e^9*d^3*b^9*a*B + 297/2*x^20*e^10*d^2*b^8*a^2*B + 72*x^20*e^11*d*b^7*a^3*B + 21/2*x^20*e^12*b^6*a^4*B + 11*x^20*e^9*d^3*b^10*A + 33*x^20*e^10*d^2*b^9*a*A + 27*x^20*e^11*d*b^8*a^2*A + 6*x^20*e^12*b^7*a^3*A + 792/19*x^19*e^7*d^5*b^10*B + 4950/19*x^19*e^8*d^4*b^9*a*B + 9900/19*x^19*e^9*d^3*b^8*a^2*B + 7920/19*x^19*e^10*d^2*b^7*a^3*B + 2520/19*x^19*e^11*d*b^6*a^4*B + 252/19*x^19*e^12*b^5*a^5*B + 495/19*x^19*e^8*d^4*b^10*A + 2200/19*x^19*e^9*d^3*b^9*a*A + 2970/19*x^19*e^10*d^2*b^8*a^2*A + 1440/19*x^19*e^11*d*b^7*a^3*A + 210/19*x^19*e^12*b^6*a^4*A + 154/3*x^18*e^6*d^6*b^10*B + 440*x^18*e^7*d^5*b^9*a*B + 2475/2*x^18*e^8*d^4*b^8*a^2*B + 4400/3*x^18*e^9*d^3*b^7*a^3*B + 770*x^18*e^10*d^2*b^6*a^4*B + 168*x^18*e^11*d*b^5*a^5*B + 35/3*x^18*e^12*b^4*a^6*B + 44*x^18*e^7*d^5*b^10*A + 275*x^18*e^8*d^4*b^9*a*A + 550*x^18*e^9*d^3*b^8*a^2*A + 440*x^18*e^10*d^2*b^7*a^3*A + 140*x^18*e^11*d*b^6*a^4*A + 14*x^18*e^12*b^5*a^5*A + 792/17*x^17*e^5*d^7*b^10*B + 9240/17*x^17*e^6*d^6*b^9*a*B + 35640/17*x^17*e^7*d^5*b^8*a^2*B + 59400/17*x^17*e^8*d^4*b^7*a^3*B + 46200/17*x^17*e^9*d^3*b^6*a^4*B + 16632/17*x^17*e^10*d^2*b^5*a^5*B + 2520/17*x^17*e^11*d*b^4*a^6*B + 120/17*x^17*e^12*b^3*a^7*B + 924/17*x^17*e^6*d^6*b^10*A + 7920/17*x^17*e^7*d^5*b^9*a*A + 22275/17*x^17*e^8*d^4*b^8*a^2*A + 26400/17*x^17*e^9*d^3*b^7*a^3*A + 13860/17*x^17*e^10*d^2*b^6*a^4*A + 3024/17*x^17*e^11*d*b^5*a^5*A + 210/17*x^17*e^12*b^4*a^6*A + 495/16*x^16*e^4*d^8*b^10*B + 495*x^16*e^5*d^7*b^9*a*B + 10395/4*x^16*e^6*d^6*b^8*a^2*B + 5940*x^16*e^7*d^5*b^7*a^3*B + 51975/8*x^16*e^8*d^4*b^6*a^4*B + 3465*x^16*e^9*d^3*b^5*a^5*B + 3465/4*x^16*e^10*d^2*b^4*a^6*B + 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4950/7*x^7*e^4*d^8*b*a^9*B + 792/7*x^7*e^5*d^7*a^10*B + 30*x^7*d^12*b^6*a^4*A + 432*x^7*e*d^11*b^5*a^5*A + 1980*x^7*e^2*d^10*b^4*a^6*A + 26400/7*x^7*e^3*d^9*b^3*a^7*A + 22275/7*x^7*e^4*d^8*b^2*a^8*A + 7920/7*x^7*e^5*d^7*b*a^9*A + 132*x^7*e^6*d^6*a^10*A + 35*x^6*d^12*b^4*a^6*B + 240*x^6*e*d^11*b^3*a^7*B + 495*x^6*e^2*d^10*b^2*a^8*B + 1100/3*x^6*e^3*d^9*b*a^9*B + 165/2*x^6*e^4*d^8*a^10*B + 42*x^6*d^12*b^5*a^5*A + 420*x^6*e*d^11*b^4*a^6*A + 1320*x^6*e^2*d^10*b^3*a^7*A + 1650*x^6*e^3*d^9*b^2*a^8*A + 825*x^6*e^4*d^8*b*a^9*A + 132*x^6*e^5*d^7*a^10*A + 24*x^5*d^12*b^3*a^7*B + 108*x^5*e*d^11*b^2*a^8*B + 132*x^5*e^2*d^10*b*a^9*B + 44*x^5*e^3*d^9*a^10*B + 42*x^5*d^12*b^4*a^6*A + 288*x^5*e*d^11*b^3*a^7*A + 594*x^5*e^2*d^10*b^2*a^8*A + 440*x^5*e^3*d^9*b*a^9*A + 99*x^5*e^4*d^8*a^10*A + 45/4*x^4*d^12*b^2*a^8*B + 30*x^4*e*d^11*b*a^9*B + 33/2*x^4*e^2*d^10*a^10*B + 30*x^4*d^12*b^3*a^7*A + 135*x^4*e*d^11*b^2*a^8*A + 165*x^4*e^2*d^10*b*a^9*A + 55*x^4*e^3*d^9*a^10*A + 10/3*x^3*d^12*b*a^9*B + 4*x^3*e*d^11*a^10*B + 15*x^3*d^12*b^2*a^8*A + 40*x^3*e*d^11*b*a^9*A + 22*x^3*e^2*d^10*a^10*A + 1/2*x^2*d^12*a^10*B + 5*x^2*d^12*b*a^9*A + 6*x^2*e*d^11*a^10*A + x*d^12*a^10*A","B",0
1077,1,4288,0,0.885496," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^11,x, algorithm=""fricas"")","\frac{1}{23} x^{23} e^{11} b^{10} B + \frac{1}{2} x^{22} e^{10} d b^{10} B + \frac{5}{11} x^{22} e^{11} b^{9} a B + \frac{1}{22} x^{22} e^{11} b^{10} A + \frac{55}{21} x^{21} e^{9} d^{2} b^{10} B + \frac{110}{21} x^{21} e^{10} d b^{9} a B + \frac{15}{7} x^{21} e^{11} b^{8} a^{2} B + \frac{11}{21} x^{21} e^{10} d b^{10} A + \frac{10}{21} x^{21} e^{11} b^{9} a A + \frac{33}{4} x^{20} e^{8} d^{3} b^{10} B + \frac{55}{2} x^{20} e^{9} d^{2} b^{9} a B + \frac{99}{4} x^{20} e^{10} d b^{8} a^{2} B + 6 x^{20} e^{11} b^{7} a^{3} B + \frac{11}{4} x^{20} e^{9} d^{2} b^{10} A + \frac{11}{2} x^{20} e^{10} d b^{9} a A + \frac{9}{4} x^{20} e^{11} b^{8} a^{2} A + \frac{330}{19} x^{19} e^{7} d^{4} b^{10} B + \frac{1650}{19} x^{19} e^{8} d^{3} b^{9} a B + \frac{2475}{19} x^{19} e^{9} d^{2} b^{8} a^{2} B + \frac{1320}{19} x^{19} e^{10} d b^{7} a^{3} B + \frac{210}{19} x^{19} e^{11} b^{6} a^{4} B + \frac{165}{19} x^{19} e^{8} d^{3} b^{10} A + \frac{550}{19} x^{19} e^{9} d^{2} b^{9} a A + \frac{495}{19} x^{19} e^{10} d b^{8} a^{2} A + \frac{120}{19} x^{19} e^{11} b^{7} a^{3} A + \frac{77}{3} x^{18} e^{6} d^{5} b^{10} B + \frac{550}{3} x^{18} e^{7} d^{4} b^{9} a B + \frac{825}{2} x^{18} e^{8} d^{3} b^{8} a^{2} B + \frac{1100}{3} x^{18} e^{9} d^{2} b^{7} a^{3} B + \frac{385}{3} x^{18} e^{10} d b^{6} a^{4} B + 14 x^{18} e^{11} b^{5} a^{5} B + \frac{55}{3} x^{18} e^{7} d^{4} b^{10} A + \frac{275}{3} x^{18} e^{8} d^{3} b^{9} a A + \frac{275}{2} x^{18} e^{9} d^{2} b^{8} a^{2} A + \frac{220}{3} x^{18} e^{10} d b^{7} a^{3} A + \frac{35}{3} x^{18} e^{11} b^{6} a^{4} A + \frac{462}{17} x^{17} e^{5} d^{6} b^{10} B + \frac{4620}{17} x^{17} e^{6} d^{5} b^{9} a B + \frac{14850}{17} x^{17} e^{7} d^{4} b^{8} a^{2} B + \frac{19800}{17} x^{17} e^{8} d^{3} b^{7} a^{3} B + \frac{11550}{17} x^{17} e^{9} d^{2} b^{6} a^{4} B + \frac{2772}{17} x^{17} e^{10} d b^{5} a^{5} B + \frac{210}{17} x^{17} e^{11} b^{4} a^{6} B + \frac{462}{17} x^{17} e^{6} d^{5} b^{10} A + \frac{3300}{17} x^{17} e^{7} d^{4} b^{9} a A + \frac{7425}{17} x^{17} e^{8} d^{3} b^{8} a^{2} A + \frac{6600}{17} x^{17} e^{9} d^{2} b^{7} a^{3} A + \frac{2310}{17} x^{17} e^{10} d b^{6} a^{4} A + \frac{252}{17} x^{17} e^{11} b^{5} a^{5} A + \frac{165}{8} x^{16} e^{4} d^{7} b^{10} B + \frac{1155}{4} x^{16} e^{5} d^{6} b^{9} a B + \frac{10395}{8} x^{16} e^{6} d^{5} b^{8} a^{2} B + 2475 x^{16} e^{7} d^{4} b^{7} a^{3} B + \frac{17325}{8} x^{16} e^{8} d^{3} b^{6} a^{4} B + \frac{3465}{4} x^{16} e^{9} d^{2} b^{5} a^{5} B + \frac{1155}{8} x^{16} e^{10} d b^{4} a^{6} B + \frac{15}{2} x^{16} e^{11} b^{3} a^{7} B + \frac{231}{8} x^{16} e^{5} d^{6} b^{10} A + \frac{1155}{4} x^{16} e^{6} d^{5} b^{9} a A + \frac{7425}{8} x^{16} e^{7} d^{4} b^{8} a^{2} A + \frac{2475}{2} x^{16} e^{8} d^{3} b^{7} a^{3} A + \frac{5775}{8} x^{16} e^{9} d^{2} b^{6} a^{4} A + \frac{693}{4} x^{16} e^{10} d b^{5} a^{5} A + \frac{105}{8} x^{16} e^{11} b^{4} a^{6} A + 11 x^{15} e^{3} d^{8} b^{10} B + 220 x^{15} e^{4} d^{7} b^{9} a B + 1386 x^{15} e^{5} d^{6} b^{8} a^{2} B + 3696 x^{15} e^{6} d^{5} b^{7} a^{3} B + 4620 x^{15} e^{7} d^{4} b^{6} a^{4} B + 2772 x^{15} e^{8} d^{3} b^{5} a^{5} B + 770 x^{15} e^{9} d^{2} b^{4} a^{6} B + 88 x^{15} e^{10} d b^{3} a^{7} B + 3 x^{15} e^{11} b^{2} a^{8} B + 22 x^{15} e^{4} d^{7} b^{10} A + 308 x^{15} e^{5} d^{6} b^{9} a A + 1386 x^{15} e^{6} d^{5} b^{8} a^{2} A + 2640 x^{15} e^{7} d^{4} b^{7} a^{3} A + 2310 x^{15} e^{8} d^{3} b^{6} a^{4} A + 924 x^{15} e^{9} d^{2} b^{5} a^{5} A + 154 x^{15} e^{10} d b^{4} a^{6} A + 8 x^{15} e^{11} b^{3} a^{7} A + \frac{55}{14} x^{14} e^{2} d^{9} b^{10} B + \frac{825}{7} x^{14} e^{3} d^{8} b^{9} a B + \frac{7425}{7} x^{14} e^{4} d^{7} b^{8} a^{2} B + 3960 x^{14} e^{5} d^{6} b^{7} a^{3} B + 6930 x^{14} e^{6} d^{5} b^{6} a^{4} B + 5940 x^{14} e^{7} d^{4} b^{5} a^{5} B + 2475 x^{14} e^{8} d^{3} b^{4} a^{6} B + \frac{3300}{7} x^{14} e^{9} d^{2} b^{3} a^{7} B + \frac{495}{14} x^{14} e^{10} d b^{2} a^{8} B + \frac{5}{7} x^{14} e^{11} b a^{9} B + \frac{165}{14} x^{14} e^{3} d^{8} b^{10} A + \frac{1650}{7} x^{14} e^{4} d^{7} b^{9} a A + 1485 x^{14} e^{5} d^{6} b^{8} a^{2} A + 3960 x^{14} e^{6} d^{5} b^{7} a^{3} A + 4950 x^{14} e^{7} d^{4} b^{6} a^{4} A + 2970 x^{14} e^{8} d^{3} b^{5} a^{5} A + 825 x^{14} e^{9} d^{2} b^{4} a^{6} A + \frac{660}{7} x^{14} e^{10} d b^{3} a^{7} A + \frac{45}{14} x^{14} e^{11} b^{2} a^{8} A + \frac{11}{13} x^{13} e d^{10} b^{10} B + \frac{550}{13} x^{13} e^{2} d^{9} b^{9} a B + \frac{7425}{13} x^{13} e^{3} d^{8} b^{8} a^{2} B + \frac{39600}{13} x^{13} e^{4} d^{7} b^{7} a^{3} B + \frac{97020}{13} x^{13} e^{5} d^{6} b^{6} a^{4} B + \frac{116424}{13} x^{13} e^{6} d^{5} b^{5} a^{5} B + \frac{69300}{13} x^{13} e^{7} d^{4} b^{4} a^{6} B + \frac{19800}{13} x^{13} e^{8} d^{3} b^{3} a^{7} B + \frac{2475}{13} x^{13} e^{9} d^{2} b^{2} a^{8} B + \frac{110}{13} x^{13} e^{10} d b a^{9} B + \frac{1}{13} x^{13} e^{11} a^{10} B + \frac{55}{13} x^{13} e^{2} d^{9} b^{10} A + \frac{1650}{13} x^{13} e^{3} d^{8} b^{9} a A + \frac{14850}{13} x^{13} e^{4} d^{7} b^{8} a^{2} A + \frac{55440}{13} x^{13} e^{5} d^{6} b^{7} a^{3} A + \frac{97020}{13} x^{13} e^{6} d^{5} b^{6} a^{4} A + \frac{83160}{13} x^{13} e^{7} d^{4} b^{5} a^{5} A + \frac{34650}{13} x^{13} e^{8} d^{3} b^{4} a^{6} A + \frac{6600}{13} x^{13} e^{9} d^{2} b^{3} a^{7} A + \frac{495}{13} x^{13} e^{10} d b^{2} a^{8} A + \frac{10}{13} x^{13} e^{11} b a^{9} A + \frac{1}{12} x^{12} d^{11} b^{10} B + \frac{55}{6} x^{12} e d^{10} b^{9} a B + \frac{825}{4} x^{12} e^{2} d^{9} b^{8} a^{2} B + 1650 x^{12} e^{3} d^{8} b^{7} a^{3} B + 5775 x^{12} e^{4} d^{7} b^{6} a^{4} B + 9702 x^{12} e^{5} d^{6} b^{5} a^{5} B + 8085 x^{12} e^{6} d^{5} b^{4} a^{6} B + 3300 x^{12} e^{7} d^{4} b^{3} a^{7} B + \frac{2475}{4} x^{12} e^{8} d^{3} b^{2} a^{8} B + \frac{275}{6} x^{12} e^{9} d^{2} b a^{9} B + \frac{11}{12} x^{12} e^{10} d a^{10} B + \frac{11}{12} x^{12} e d^{10} b^{10} A + \frac{275}{6} x^{12} e^{2} d^{9} b^{9} a A + \frac{2475}{4} x^{12} e^{3} d^{8} b^{8} a^{2} A + 3300 x^{12} e^{4} d^{7} b^{7} a^{3} A + 8085 x^{12} e^{5} d^{6} b^{6} a^{4} A + 9702 x^{12} e^{6} d^{5} b^{5} a^{5} A + 5775 x^{12} e^{7} d^{4} b^{4} a^{6} A + 1650 x^{12} e^{8} d^{3} b^{3} a^{7} A + \frac{825}{4} x^{12} e^{9} d^{2} b^{2} a^{8} A + \frac{55}{6} x^{12} e^{10} d b a^{9} A + \frac{1}{12} x^{12} e^{11} a^{10} A + \frac{10}{11} x^{11} d^{11} b^{9} a B + 45 x^{11} e d^{10} b^{8} a^{2} B + 600 x^{11} e^{2} d^{9} b^{7} a^{3} B + 3150 x^{11} e^{3} d^{8} b^{6} a^{4} B + 7560 x^{11} e^{4} d^{7} b^{5} a^{5} B + 8820 x^{11} e^{5} d^{6} b^{4} a^{6} B + 5040 x^{11} e^{6} d^{5} b^{3} a^{7} B + 1350 x^{11} e^{7} d^{4} b^{2} a^{8} B + 150 x^{11} e^{8} d^{3} b a^{9} B + 5 x^{11} e^{9} d^{2} a^{10} B + \frac{1}{11} x^{11} d^{11} b^{10} A + 10 x^{11} e d^{10} b^{9} a A + 225 x^{11} e^{2} d^{9} b^{8} a^{2} A + 1800 x^{11} e^{3} d^{8} b^{7} a^{3} A + 6300 x^{11} e^{4} d^{7} b^{6} a^{4} A + 10584 x^{11} e^{5} d^{6} b^{5} a^{5} A + 8820 x^{11} e^{6} d^{5} b^{4} a^{6} A + 3600 x^{11} e^{7} d^{4} b^{3} a^{7} A + 675 x^{11} e^{8} d^{3} b^{2} a^{8} A + 50 x^{11} e^{9} d^{2} b a^{9} A + x^{11} e^{10} d a^{10} A + \frac{9}{2} x^{10} d^{11} b^{8} a^{2} B + 132 x^{10} e d^{10} b^{7} a^{3} B + 1155 x^{10} e^{2} d^{9} b^{6} a^{4} B + 4158 x^{10} e^{3} d^{8} b^{5} a^{5} B + 6930 x^{10} e^{4} d^{7} b^{4} a^{6} B + 5544 x^{10} e^{5} d^{6} b^{3} a^{7} B + 2079 x^{10} e^{6} d^{5} b^{2} a^{8} B + 330 x^{10} e^{7} d^{4} b a^{9} B + \frac{33}{2} x^{10} e^{8} d^{3} a^{10} B + x^{10} d^{11} b^{9} a A + \frac{99}{2} x^{10} e d^{10} b^{8} a^{2} A + 660 x^{10} e^{2} d^{9} b^{7} a^{3} A + 3465 x^{10} e^{3} d^{8} b^{6} a^{4} A + 8316 x^{10} e^{4} d^{7} b^{5} a^{5} A + 9702 x^{10} e^{5} d^{6} b^{4} a^{6} A + 5544 x^{10} e^{6} d^{5} b^{3} a^{7} A + 1485 x^{10} e^{7} d^{4} b^{2} a^{8} A + 165 x^{10} e^{8} d^{3} b a^{9} A + \frac{11}{2} x^{10} e^{9} d^{2} a^{10} A + \frac{40}{3} x^{9} d^{11} b^{7} a^{3} B + \frac{770}{3} x^{9} e d^{10} b^{6} a^{4} B + 1540 x^{9} e^{2} d^{9} b^{5} a^{5} B + 3850 x^{9} e^{3} d^{8} b^{4} a^{6} B + 4400 x^{9} e^{4} d^{7} b^{3} a^{7} B + 2310 x^{9} e^{5} d^{6} b^{2} a^{8} B + \frac{1540}{3} x^{9} e^{6} d^{5} b a^{9} B + \frac{110}{3} x^{9} e^{7} d^{4} a^{10} B + 5 x^{9} d^{11} b^{8} a^{2} A + \frac{440}{3} x^{9} e d^{10} b^{7} a^{3} A + \frac{3850}{3} x^{9} e^{2} d^{9} b^{6} a^{4} A + 4620 x^{9} e^{3} d^{8} b^{5} a^{5} A + 7700 x^{9} e^{4} d^{7} b^{4} a^{6} A + 6160 x^{9} e^{5} d^{6} b^{3} a^{7} A + 2310 x^{9} e^{6} d^{5} b^{2} a^{8} A + \frac{1100}{3} x^{9} e^{7} d^{4} b a^{9} A + \frac{55}{3} x^{9} e^{8} d^{3} a^{10} A + \frac{105}{4} x^{8} d^{11} b^{6} a^{4} B + \frac{693}{2} x^{8} e d^{10} b^{5} a^{5} B + \frac{5775}{4} x^{8} e^{2} d^{9} b^{4} a^{6} B + 2475 x^{8} e^{3} d^{8} b^{3} a^{7} B + \frac{7425}{4} x^{8} e^{4} d^{7} b^{2} a^{8} B + \frac{1155}{2} x^{8} e^{5} d^{6} b a^{9} B + \frac{231}{4} x^{8} e^{6} d^{5} a^{10} B + 15 x^{8} d^{11} b^{7} a^{3} A + \frac{1155}{4} x^{8} e d^{10} b^{6} a^{4} A + \frac{3465}{2} x^{8} e^{2} d^{9} b^{5} a^{5} A + \frac{17325}{4} x^{8} e^{3} d^{8} b^{4} a^{6} A + 4950 x^{8} e^{4} d^{7} b^{3} a^{7} A + \frac{10395}{4} x^{8} e^{5} d^{6} b^{2} a^{8} A + \frac{1155}{2} x^{8} e^{6} d^{5} b a^{9} A + \frac{165}{4} x^{8} e^{7} d^{4} a^{10} A + 36 x^{7} d^{11} b^{5} a^{5} B + 330 x^{7} e d^{10} b^{4} a^{6} B + \frac{6600}{7} x^{7} e^{2} d^{9} b^{3} a^{7} B + \frac{7425}{7} x^{7} e^{3} d^{8} b^{2} a^{8} B + \frac{3300}{7} x^{7} e^{4} d^{7} b a^{9} B + 66 x^{7} e^{5} d^{6} a^{10} B + 30 x^{7} d^{11} b^{6} a^{4} A + 396 x^{7} e d^{10} b^{5} a^{5} A + 1650 x^{7} e^{2} d^{9} b^{4} a^{6} A + \frac{19800}{7} x^{7} e^{3} d^{8} b^{3} a^{7} A + \frac{14850}{7} x^{7} e^{4} d^{7} b^{2} a^{8} A + 660 x^{7} e^{5} d^{6} b a^{9} A + 66 x^{7} e^{6} d^{5} a^{10} A + 35 x^{6} d^{11} b^{4} a^{6} B + 220 x^{6} e d^{10} b^{3} a^{7} B + \frac{825}{2} x^{6} e^{2} d^{9} b^{2} a^{8} B + 275 x^{6} e^{3} d^{8} b a^{9} B + 55 x^{6} e^{4} d^{7} a^{10} B + 42 x^{6} d^{11} b^{5} a^{5} A + 385 x^{6} e d^{10} b^{4} a^{6} A + 1100 x^{6} e^{2} d^{9} b^{3} a^{7} A + \frac{2475}{2} x^{6} e^{3} d^{8} b^{2} a^{8} A + 550 x^{6} e^{4} d^{7} b a^{9} A + 77 x^{6} e^{5} d^{6} a^{10} A + 24 x^{5} d^{11} b^{3} a^{7} B + 99 x^{5} e d^{10} b^{2} a^{8} B + 110 x^{5} e^{2} d^{9} b a^{9} B + 33 x^{5} e^{3} d^{8} a^{10} B + 42 x^{5} d^{11} b^{4} a^{6} A + 264 x^{5} e d^{10} b^{3} a^{7} A + 495 x^{5} e^{2} d^{9} b^{2} a^{8} A + 330 x^{5} e^{3} d^{8} b a^{9} A + 66 x^{5} e^{4} d^{7} a^{10} A + \frac{45}{4} x^{4} d^{11} b^{2} a^{8} B + \frac{55}{2} x^{4} e d^{10} b a^{9} B + \frac{55}{4} x^{4} e^{2} d^{9} a^{10} B + 30 x^{4} d^{11} b^{3} a^{7} A + \frac{495}{4} x^{4} e d^{10} b^{2} a^{8} A + \frac{275}{2} x^{4} e^{2} d^{9} b a^{9} A + \frac{165}{4} x^{4} e^{3} d^{8} a^{10} A + \frac{10}{3} x^{3} d^{11} b a^{9} B + \frac{11}{3} x^{3} e d^{10} a^{10} B + 15 x^{3} d^{11} b^{2} a^{8} A + \frac{110}{3} x^{3} e d^{10} b a^{9} A + \frac{55}{3} x^{3} e^{2} d^{9} a^{10} A + \frac{1}{2} x^{2} d^{11} a^{10} B + 5 x^{2} d^{11} b a^{9} A + \frac{11}{2} x^{2} e d^{10} a^{10} A + x d^{11} a^{10} A"," ",0,"1/23*x^23*e^11*b^10*B + 1/2*x^22*e^10*d*b^10*B + 5/11*x^22*e^11*b^9*a*B + 1/22*x^22*e^11*b^10*A + 55/21*x^21*e^9*d^2*b^10*B + 110/21*x^21*e^10*d*b^9*a*B + 15/7*x^21*e^11*b^8*a^2*B + 11/21*x^21*e^10*d*b^10*A + 10/21*x^21*e^11*b^9*a*A + 33/4*x^20*e^8*d^3*b^10*B + 55/2*x^20*e^9*d^2*b^9*a*B + 99/4*x^20*e^10*d*b^8*a^2*B + 6*x^20*e^11*b^7*a^3*B + 11/4*x^20*e^9*d^2*b^10*A + 11/2*x^20*e^10*d*b^9*a*A + 9/4*x^20*e^11*b^8*a^2*A + 330/19*x^19*e^7*d^4*b^10*B + 1650/19*x^19*e^8*d^3*b^9*a*B + 2475/19*x^19*e^9*d^2*b^8*a^2*B + 1320/19*x^19*e^10*d*b^7*a^3*B + 210/19*x^19*e^11*b^6*a^4*B + 165/19*x^19*e^8*d^3*b^10*A + 550/19*x^19*e^9*d^2*b^9*a*A + 495/19*x^19*e^10*d*b^8*a^2*A + 120/19*x^19*e^11*b^7*a^3*A + 77/3*x^18*e^6*d^5*b^10*B + 550/3*x^18*e^7*d^4*b^9*a*B + 825/2*x^18*e^8*d^3*b^8*a^2*B + 1100/3*x^18*e^9*d^2*b^7*a^3*B + 385/3*x^18*e^10*d*b^6*a^4*B + 14*x^18*e^11*b^5*a^5*B + 55/3*x^18*e^7*d^4*b^10*A + 275/3*x^18*e^8*d^3*b^9*a*A + 275/2*x^18*e^9*d^2*b^8*a^2*A + 220/3*x^18*e^10*d*b^7*a^3*A + 35/3*x^18*e^11*b^6*a^4*A + 462/17*x^17*e^5*d^6*b^10*B + 4620/17*x^17*e^6*d^5*b^9*a*B + 14850/17*x^17*e^7*d^4*b^8*a^2*B + 19800/17*x^17*e^8*d^3*b^7*a^3*B + 11550/17*x^17*e^9*d^2*b^6*a^4*B + 2772/17*x^17*e^10*d*b^5*a^5*B + 210/17*x^17*e^11*b^4*a^6*B + 462/17*x^17*e^6*d^5*b^10*A + 3300/17*x^17*e^7*d^4*b^9*a*A + 7425/17*x^17*e^8*d^3*b^8*a^2*A + 6600/17*x^17*e^9*d^2*b^7*a^3*A + 2310/17*x^17*e^10*d*b^6*a^4*A + 252/17*x^17*e^11*b^5*a^5*A + 165/8*x^16*e^4*d^7*b^10*B + 1155/4*x^16*e^5*d^6*b^9*a*B + 10395/8*x^16*e^6*d^5*b^8*a^2*B + 2475*x^16*e^7*d^4*b^7*a^3*B + 17325/8*x^16*e^8*d^3*b^6*a^4*B + 3465/4*x^16*e^9*d^2*b^5*a^5*B + 1155/8*x^16*e^10*d*b^4*a^6*B + 15/2*x^16*e^11*b^3*a^7*B + 231/8*x^16*e^5*d^6*b^10*A + 1155/4*x^16*e^6*d^5*b^9*a*A + 7425/8*x^16*e^7*d^4*b^8*a^2*A + 2475/2*x^16*e^8*d^3*b^7*a^3*A + 5775/8*x^16*e^9*d^2*b^6*a^4*A + 693/4*x^16*e^10*d*b^5*a^5*A + 105/8*x^16*e^11*b^4*a^6*A + 11*x^15*e^3*d^8*b^10*B + 220*x^15*e^4*d^7*b^9*a*B + 1386*x^15*e^5*d^6*b^8*a^2*B + 3696*x^15*e^6*d^5*b^7*a^3*B + 4620*x^15*e^7*d^4*b^6*a^4*B + 2772*x^15*e^8*d^3*b^5*a^5*B + 770*x^15*e^9*d^2*b^4*a^6*B + 88*x^15*e^10*d*b^3*a^7*B + 3*x^15*e^11*b^2*a^8*B + 22*x^15*e^4*d^7*b^10*A + 308*x^15*e^5*d^6*b^9*a*A + 1386*x^15*e^6*d^5*b^8*a^2*A + 2640*x^15*e^7*d^4*b^7*a^3*A + 2310*x^15*e^8*d^3*b^6*a^4*A + 924*x^15*e^9*d^2*b^5*a^5*A + 154*x^15*e^10*d*b^4*a^6*A + 8*x^15*e^11*b^3*a^7*A + 55/14*x^14*e^2*d^9*b^10*B + 825/7*x^14*e^3*d^8*b^9*a*B + 7425/7*x^14*e^4*d^7*b^8*a^2*B + 3960*x^14*e^5*d^6*b^7*a^3*B + 6930*x^14*e^6*d^5*b^6*a^4*B + 5940*x^14*e^7*d^4*b^5*a^5*B + 2475*x^14*e^8*d^3*b^4*a^6*B + 3300/7*x^14*e^9*d^2*b^3*a^7*B + 495/14*x^14*e^10*d*b^2*a^8*B + 5/7*x^14*e^11*b*a^9*B + 165/14*x^14*e^3*d^8*b^10*A + 1650/7*x^14*e^4*d^7*b^9*a*A + 1485*x^14*e^5*d^6*b^8*a^2*A + 3960*x^14*e^6*d^5*b^7*a^3*A + 4950*x^14*e^7*d^4*b^6*a^4*A + 2970*x^14*e^8*d^3*b^5*a^5*A + 825*x^14*e^9*d^2*b^4*a^6*A + 660/7*x^14*e^10*d*b^3*a^7*A + 45/14*x^14*e^11*b^2*a^8*A + 11/13*x^13*e*d^10*b^10*B + 550/13*x^13*e^2*d^9*b^9*a*B + 7425/13*x^13*e^3*d^8*b^8*a^2*B + 39600/13*x^13*e^4*d^7*b^7*a^3*B + 97020/13*x^13*e^5*d^6*b^6*a^4*B + 116424/13*x^13*e^6*d^5*b^5*a^5*B + 69300/13*x^13*e^7*d^4*b^4*a^6*B + 19800/13*x^13*e^8*d^3*b^3*a^7*B + 2475/13*x^13*e^9*d^2*b^2*a^8*B + 110/13*x^13*e^10*d*b*a^9*B + 1/13*x^13*e^11*a^10*B + 55/13*x^13*e^2*d^9*b^10*A + 1650/13*x^13*e^3*d^8*b^9*a*A + 14850/13*x^13*e^4*d^7*b^8*a^2*A + 55440/13*x^13*e^5*d^6*b^7*a^3*A + 97020/13*x^13*e^6*d^5*b^6*a^4*A + 83160/13*x^13*e^7*d^4*b^5*a^5*A + 34650/13*x^13*e^8*d^3*b^4*a^6*A + 6600/13*x^13*e^9*d^2*b^3*a^7*A + 495/13*x^13*e^10*d*b^2*a^8*A + 10/13*x^13*e^11*b*a^9*A + 1/12*x^12*d^11*b^10*B + 55/6*x^12*e*d^10*b^9*a*B + 825/4*x^12*e^2*d^9*b^8*a^2*B + 1650*x^12*e^3*d^8*b^7*a^3*B + 5775*x^12*e^4*d^7*b^6*a^4*B + 9702*x^12*e^5*d^6*b^5*a^5*B + 8085*x^12*e^6*d^5*b^4*a^6*B + 3300*x^12*e^7*d^4*b^3*a^7*B + 2475/4*x^12*e^8*d^3*b^2*a^8*B + 275/6*x^12*e^9*d^2*b*a^9*B + 11/12*x^12*e^10*d*a^10*B + 11/12*x^12*e*d^10*b^10*A + 275/6*x^12*e^2*d^9*b^9*a*A + 2475/4*x^12*e^3*d^8*b^8*a^2*A + 3300*x^12*e^4*d^7*b^7*a^3*A + 8085*x^12*e^5*d^6*b^6*a^4*A + 9702*x^12*e^6*d^5*b^5*a^5*A + 5775*x^12*e^7*d^4*b^4*a^6*A + 1650*x^12*e^8*d^3*b^3*a^7*A + 825/4*x^12*e^9*d^2*b^2*a^8*A + 55/6*x^12*e^10*d*b*a^9*A + 1/12*x^12*e^11*a^10*A + 10/11*x^11*d^11*b^9*a*B + 45*x^11*e*d^10*b^8*a^2*B + 600*x^11*e^2*d^9*b^7*a^3*B + 3150*x^11*e^3*d^8*b^6*a^4*B + 7560*x^11*e^4*d^7*b^5*a^5*B + 8820*x^11*e^5*d^6*b^4*a^6*B + 5040*x^11*e^6*d^5*b^3*a^7*B + 1350*x^11*e^7*d^4*b^2*a^8*B + 150*x^11*e^8*d^3*b*a^9*B + 5*x^11*e^9*d^2*a^10*B + 1/11*x^11*d^11*b^10*A + 10*x^11*e*d^10*b^9*a*A + 225*x^11*e^2*d^9*b^8*a^2*A + 1800*x^11*e^3*d^8*b^7*a^3*A + 6300*x^11*e^4*d^7*b^6*a^4*A + 10584*x^11*e^5*d^6*b^5*a^5*A + 8820*x^11*e^6*d^5*b^4*a^6*A + 3600*x^11*e^7*d^4*b^3*a^7*A + 675*x^11*e^8*d^3*b^2*a^8*A + 50*x^11*e^9*d^2*b*a^9*A + x^11*e^10*d*a^10*A + 9/2*x^10*d^11*b^8*a^2*B + 132*x^10*e*d^10*b^7*a^3*B + 1155*x^10*e^2*d^9*b^6*a^4*B + 4158*x^10*e^3*d^8*b^5*a^5*B + 6930*x^10*e^4*d^7*b^4*a^6*B + 5544*x^10*e^5*d^6*b^3*a^7*B + 2079*x^10*e^6*d^5*b^2*a^8*B + 330*x^10*e^7*d^4*b*a^9*B + 33/2*x^10*e^8*d^3*a^10*B + x^10*d^11*b^9*a*A + 99/2*x^10*e*d^10*b^8*a^2*A + 660*x^10*e^2*d^9*b^7*a^3*A + 3465*x^10*e^3*d^8*b^6*a^4*A + 8316*x^10*e^4*d^7*b^5*a^5*A + 9702*x^10*e^5*d^6*b^4*a^6*A + 5544*x^10*e^6*d^5*b^3*a^7*A + 1485*x^10*e^7*d^4*b^2*a^8*A + 165*x^10*e^8*d^3*b*a^9*A + 11/2*x^10*e^9*d^2*a^10*A + 40/3*x^9*d^11*b^7*a^3*B + 770/3*x^9*e*d^10*b^6*a^4*B + 1540*x^9*e^2*d^9*b^5*a^5*B + 3850*x^9*e^3*d^8*b^4*a^6*B + 4400*x^9*e^4*d^7*b^3*a^7*B + 2310*x^9*e^5*d^6*b^2*a^8*B + 1540/3*x^9*e^6*d^5*b*a^9*B + 110/3*x^9*e^7*d^4*a^10*B + 5*x^9*d^11*b^8*a^2*A + 440/3*x^9*e*d^10*b^7*a^3*A + 3850/3*x^9*e^2*d^9*b^6*a^4*A + 4620*x^9*e^3*d^8*b^5*a^5*A + 7700*x^9*e^4*d^7*b^4*a^6*A + 6160*x^9*e^5*d^6*b^3*a^7*A + 2310*x^9*e^6*d^5*b^2*a^8*A + 1100/3*x^9*e^7*d^4*b*a^9*A + 55/3*x^9*e^8*d^3*a^10*A + 105/4*x^8*d^11*b^6*a^4*B + 693/2*x^8*e*d^10*b^5*a^5*B + 5775/4*x^8*e^2*d^9*b^4*a^6*B + 2475*x^8*e^3*d^8*b^3*a^7*B + 7425/4*x^8*e^4*d^7*b^2*a^8*B + 1155/2*x^8*e^5*d^6*b*a^9*B + 231/4*x^8*e^6*d^5*a^10*B + 15*x^8*d^11*b^7*a^3*A + 1155/4*x^8*e*d^10*b^6*a^4*A + 3465/2*x^8*e^2*d^9*b^5*a^5*A + 17325/4*x^8*e^3*d^8*b^4*a^6*A + 4950*x^8*e^4*d^7*b^3*a^7*A + 10395/4*x^8*e^5*d^6*b^2*a^8*A + 1155/2*x^8*e^6*d^5*b*a^9*A + 165/4*x^8*e^7*d^4*a^10*A + 36*x^7*d^11*b^5*a^5*B + 330*x^7*e*d^10*b^4*a^6*B + 6600/7*x^7*e^2*d^9*b^3*a^7*B + 7425/7*x^7*e^3*d^8*b^2*a^8*B + 3300/7*x^7*e^4*d^7*b*a^9*B + 66*x^7*e^5*d^6*a^10*B + 30*x^7*d^11*b^6*a^4*A + 396*x^7*e*d^10*b^5*a^5*A + 1650*x^7*e^2*d^9*b^4*a^6*A + 19800/7*x^7*e^3*d^8*b^3*a^7*A + 14850/7*x^7*e^4*d^7*b^2*a^8*A + 660*x^7*e^5*d^6*b*a^9*A + 66*x^7*e^6*d^5*a^10*A + 35*x^6*d^11*b^4*a^6*B + 220*x^6*e*d^10*b^3*a^7*B + 825/2*x^6*e^2*d^9*b^2*a^8*B + 275*x^6*e^3*d^8*b*a^9*B + 55*x^6*e^4*d^7*a^10*B + 42*x^6*d^11*b^5*a^5*A + 385*x^6*e*d^10*b^4*a^6*A + 1100*x^6*e^2*d^9*b^3*a^7*A + 2475/2*x^6*e^3*d^8*b^2*a^8*A + 550*x^6*e^4*d^7*b*a^9*A + 77*x^6*e^5*d^6*a^10*A + 24*x^5*d^11*b^3*a^7*B + 99*x^5*e*d^10*b^2*a^8*B + 110*x^5*e^2*d^9*b*a^9*B + 33*x^5*e^3*d^8*a^10*B + 42*x^5*d^11*b^4*a^6*A + 264*x^5*e*d^10*b^3*a^7*A + 495*x^5*e^2*d^9*b^2*a^8*A + 330*x^5*e^3*d^8*b*a^9*A + 66*x^5*e^4*d^7*a^10*A + 45/4*x^4*d^11*b^2*a^8*B + 55/2*x^4*e*d^10*b*a^9*B + 55/4*x^4*e^2*d^9*a^10*B + 30*x^4*d^11*b^3*a^7*A + 495/4*x^4*e*d^10*b^2*a^8*A + 275/2*x^4*e^2*d^9*b*a^9*A + 165/4*x^4*e^3*d^8*a^10*A + 10/3*x^3*d^11*b*a^9*B + 11/3*x^3*e*d^10*a^10*B + 15*x^3*d^11*b^2*a^8*A + 110/3*x^3*e*d^10*b*a^9*A + 55/3*x^3*e^2*d^9*a^10*A + 1/2*x^2*d^11*a^10*B + 5*x^2*d^11*b*a^9*A + 11/2*x^2*e*d^10*a^10*A + x*d^11*a^10*A","B",0
1078,1,3912,0,1.047069," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^10,x, algorithm=""fricas"")","\frac{1}{22} x^{22} e^{10} b^{10} B + \frac{10}{21} x^{21} e^{9} d b^{10} B + \frac{10}{21} x^{21} e^{10} b^{9} a B + \frac{1}{21} x^{21} e^{10} b^{10} A + \frac{9}{4} x^{20} e^{8} d^{2} b^{10} B + 5 x^{20} e^{9} d b^{9} a B + \frac{9}{4} x^{20} e^{10} b^{8} a^{2} B + \frac{1}{2} x^{20} e^{9} d b^{10} A + \frac{1}{2} x^{20} e^{10} b^{9} a A + \frac{120}{19} x^{19} e^{7} d^{3} b^{10} B + \frac{450}{19} x^{19} e^{8} d^{2} b^{9} a B + \frac{450}{19} x^{19} e^{9} d b^{8} a^{2} B + \frac{120}{19} x^{19} e^{10} b^{7} a^{3} B + \frac{45}{19} x^{19} e^{8} d^{2} b^{10} A + \frac{100}{19} x^{19} e^{9} d b^{9} a A + \frac{45}{19} x^{19} e^{10} b^{8} a^{2} A + \frac{35}{3} x^{18} e^{6} d^{4} b^{10} B + \frac{200}{3} x^{18} e^{7} d^{3} b^{9} a B + \frac{225}{2} x^{18} e^{8} d^{2} b^{8} a^{2} B + \frac{200}{3} x^{18} e^{9} d b^{7} a^{3} B + \frac{35}{3} x^{18} e^{10} b^{6} a^{4} B + \frac{20}{3} x^{18} e^{7} d^{3} b^{10} A + 25 x^{18} e^{8} d^{2} b^{9} a A + 25 x^{18} e^{9} d b^{8} a^{2} A + \frac{20}{3} x^{18} e^{10} b^{7} a^{3} A + \frac{252}{17} x^{17} e^{5} d^{5} b^{10} B + \frac{2100}{17} x^{17} e^{6} d^{4} b^{9} a B + \frac{5400}{17} x^{17} e^{7} d^{3} b^{8} a^{2} B + \frac{5400}{17} x^{17} e^{8} d^{2} b^{7} a^{3} B + \frac{2100}{17} x^{17} e^{9} d b^{6} a^{4} B + \frac{252}{17} x^{17} e^{10} b^{5} a^{5} B + \frac{210}{17} x^{17} e^{6} d^{4} b^{10} A + \frac{1200}{17} x^{17} e^{7} d^{3} b^{9} a A + \frac{2025}{17} x^{17} e^{8} d^{2} b^{8} a^{2} A + \frac{1200}{17} x^{17} e^{9} d b^{7} a^{3} A + \frac{210}{17} x^{17} e^{10} b^{6} a^{4} A + \frac{105}{8} x^{16} e^{4} d^{6} b^{10} B + \frac{315}{2} x^{16} e^{5} d^{5} b^{9} a B + \frac{4725}{8} x^{16} e^{6} d^{4} b^{8} a^{2} B + 900 x^{16} e^{7} d^{3} b^{7} a^{3} B + \frac{4725}{8} x^{16} e^{8} d^{2} b^{6} a^{4} B + \frac{315}{2} x^{16} e^{9} d b^{5} a^{5} B + \frac{105}{8} x^{16} e^{10} b^{4} a^{6} B + \frac{63}{4} x^{16} e^{5} d^{5} b^{10} A + \frac{525}{4} x^{16} e^{6} d^{4} b^{9} a A + \frac{675}{2} x^{16} e^{7} d^{3} b^{8} a^{2} A + \frac{675}{2} x^{16} e^{8} d^{2} b^{7} a^{3} A + \frac{525}{4} x^{16} e^{9} d b^{6} a^{4} A + \frac{63}{4} x^{16} e^{10} b^{5} a^{5} A + 8 x^{15} e^{3} d^{7} b^{10} B + 140 x^{15} e^{4} d^{6} b^{9} a B + 756 x^{15} e^{5} d^{5} b^{8} a^{2} B + 1680 x^{15} e^{6} d^{4} b^{7} a^{3} B + 1680 x^{15} e^{7} d^{3} b^{6} a^{4} B + 756 x^{15} e^{8} d^{2} b^{5} a^{5} B + 140 x^{15} e^{9} d b^{4} a^{6} B + 8 x^{15} e^{10} b^{3} a^{7} B + 14 x^{15} e^{4} d^{6} b^{10} A + 168 x^{15} e^{5} d^{5} b^{9} a A + 630 x^{15} e^{6} d^{4} b^{8} a^{2} A + 960 x^{15} e^{7} d^{3} b^{7} a^{3} A + 630 x^{15} e^{8} d^{2} b^{6} a^{4} A + 168 x^{15} e^{9} d b^{5} a^{5} A + 14 x^{15} e^{10} b^{4} a^{6} A + \frac{45}{14} x^{14} e^{2} d^{8} b^{10} B + \frac{600}{7} x^{14} e^{3} d^{7} b^{9} a B + 675 x^{14} e^{4} d^{6} b^{8} a^{2} B + 2160 x^{14} e^{5} d^{5} b^{7} a^{3} B + 3150 x^{14} e^{6} d^{4} b^{6} a^{4} B + 2160 x^{14} e^{7} d^{3} b^{5} a^{5} B + 675 x^{14} e^{8} d^{2} b^{4} a^{6} B + \frac{600}{7} x^{14} e^{9} d b^{3} a^{7} B + \frac{45}{14} x^{14} e^{10} b^{2} a^{8} B + \frac{60}{7} x^{14} e^{3} d^{7} b^{10} A + 150 x^{14} e^{4} d^{6} b^{9} a A + 810 x^{14} e^{5} d^{5} b^{8} a^{2} A + 1800 x^{14} e^{6} d^{4} b^{7} a^{3} A + 1800 x^{14} e^{7} d^{3} b^{6} a^{4} A + 810 x^{14} e^{8} d^{2} b^{5} a^{5} A + 150 x^{14} e^{9} d b^{4} a^{6} A + \frac{60}{7} x^{14} e^{10} b^{3} a^{7} A + \frac{10}{13} x^{13} e d^{9} b^{10} B + \frac{450}{13} x^{13} e^{2} d^{8} b^{9} a B + \frac{5400}{13} x^{13} e^{3} d^{7} b^{8} a^{2} B + \frac{25200}{13} x^{13} e^{4} d^{6} b^{7} a^{3} B + \frac{52920}{13} x^{13} e^{5} d^{5} b^{6} a^{4} B + \frac{52920}{13} x^{13} e^{6} d^{4} b^{5} a^{5} B + \frac{25200}{13} x^{13} e^{7} d^{3} b^{4} a^{6} B + \frac{5400}{13} x^{13} e^{8} d^{2} b^{3} a^{7} B + \frac{450}{13} x^{13} e^{9} d b^{2} a^{8} B + \frac{10}{13} x^{13} e^{10} b a^{9} B + \frac{45}{13} x^{13} e^{2} d^{8} b^{10} A + \frac{1200}{13} x^{13} e^{3} d^{7} b^{9} a A + \frac{9450}{13} x^{13} e^{4} d^{6} b^{8} a^{2} A + \frac{30240}{13} x^{13} e^{5} d^{5} b^{7} a^{3} A + \frac{44100}{13} x^{13} e^{6} d^{4} b^{6} a^{4} A + \frac{30240}{13} x^{13} e^{7} d^{3} b^{5} a^{5} A + \frac{9450}{13} x^{13} e^{8} d^{2} b^{4} a^{6} A + \frac{1200}{13} x^{13} e^{9} d b^{3} a^{7} A + \frac{45}{13} x^{13} e^{10} b^{2} a^{8} A + \frac{1}{12} x^{12} d^{10} b^{10} B + \frac{25}{3} x^{12} e d^{9} b^{9} a B + \frac{675}{4} x^{12} e^{2} d^{8} b^{8} a^{2} B + 1200 x^{12} e^{3} d^{7} b^{7} a^{3} B + 3675 x^{12} e^{4} d^{6} b^{6} a^{4} B + 5292 x^{12} e^{5} d^{5} b^{5} a^{5} B + 3675 x^{12} e^{6} d^{4} b^{4} a^{6} B + 1200 x^{12} e^{7} d^{3} b^{3} a^{7} B + \frac{675}{4} x^{12} e^{8} d^{2} b^{2} a^{8} B + \frac{25}{3} x^{12} e^{9} d b a^{9} B + \frac{1}{12} x^{12} e^{10} a^{10} B + \frac{5}{6} x^{12} e d^{9} b^{10} A + \frac{75}{2} x^{12} e^{2} d^{8} b^{9} a A + 450 x^{12} e^{3} d^{7} b^{8} a^{2} A + 2100 x^{12} e^{4} d^{6} b^{7} a^{3} A + 4410 x^{12} e^{5} d^{5} b^{6} a^{4} A + 4410 x^{12} e^{6} d^{4} b^{5} a^{5} A + 2100 x^{12} e^{7} d^{3} b^{4} a^{6} A + 450 x^{12} e^{8} d^{2} b^{3} a^{7} A + \frac{75}{2} x^{12} e^{9} d b^{2} a^{8} A + \frac{5}{6} x^{12} e^{10} b a^{9} A + \frac{10}{11} x^{11} d^{10} b^{9} a B + \frac{450}{11} x^{11} e d^{9} b^{8} a^{2} B + \frac{5400}{11} x^{11} e^{2} d^{8} b^{7} a^{3} B + \frac{25200}{11} x^{11} e^{3} d^{7} b^{6} a^{4} B + \frac{52920}{11} x^{11} e^{4} d^{6} b^{5} a^{5} B + \frac{52920}{11} x^{11} e^{5} d^{5} b^{4} a^{6} B + \frac{25200}{11} x^{11} e^{6} d^{4} b^{3} a^{7} B + \frac{5400}{11} x^{11} e^{7} d^{3} b^{2} a^{8} B + \frac{450}{11} x^{11} e^{8} d^{2} b a^{9} B + \frac{10}{11} x^{11} e^{9} d a^{10} B + \frac{1}{11} x^{11} d^{10} b^{10} A + \frac{100}{11} x^{11} e d^{9} b^{9} a A + \frac{2025}{11} x^{11} e^{2} d^{8} b^{8} a^{2} A + \frac{14400}{11} x^{11} e^{3} d^{7} b^{7} a^{3} A + \frac{44100}{11} x^{11} e^{4} d^{6} b^{6} a^{4} A + \frac{63504}{11} x^{11} e^{5} d^{5} b^{5} a^{5} A + \frac{44100}{11} x^{11} e^{6} d^{4} b^{4} a^{6} A + \frac{14400}{11} x^{11} e^{7} d^{3} b^{3} a^{7} A + \frac{2025}{11} x^{11} e^{8} d^{2} b^{2} a^{8} A + \frac{100}{11} x^{11} e^{9} d b a^{9} A + \frac{1}{11} x^{11} e^{10} a^{10} A + \frac{9}{2} x^{10} d^{10} b^{8} a^{2} B + 120 x^{10} e d^{9} b^{7} a^{3} B + 945 x^{10} e^{2} d^{8} b^{6} a^{4} B + 3024 x^{10} e^{3} d^{7} b^{5} a^{5} B + 4410 x^{10} e^{4} d^{6} b^{4} a^{6} B + 3024 x^{10} e^{5} d^{5} b^{3} a^{7} B + 945 x^{10} e^{6} d^{4} b^{2} a^{8} B + 120 x^{10} e^{7} d^{3} b a^{9} B + \frac{9}{2} x^{10} e^{8} d^{2} a^{10} B + x^{10} d^{10} b^{9} a A + 45 x^{10} e d^{9} b^{8} a^{2} A + 540 x^{10} e^{2} d^{8} b^{7} a^{3} A + 2520 x^{10} e^{3} d^{7} b^{6} a^{4} A + 5292 x^{10} e^{4} d^{6} b^{5} a^{5} A + 5292 x^{10} e^{5} d^{5} b^{4} a^{6} A + 2520 x^{10} e^{6} d^{4} b^{3} a^{7} A + 540 x^{10} e^{7} d^{3} b^{2} a^{8} A + 45 x^{10} e^{8} d^{2} b a^{9} A + x^{10} e^{9} d a^{10} A + \frac{40}{3} x^{9} d^{10} b^{7} a^{3} B + \frac{700}{3} x^{9} e d^{9} b^{6} a^{4} B + 1260 x^{9} e^{2} d^{8} b^{5} a^{5} B + 2800 x^{9} e^{3} d^{7} b^{4} a^{6} B + 2800 x^{9} e^{4} d^{6} b^{3} a^{7} B + 1260 x^{9} e^{5} d^{5} b^{2} a^{8} B + \frac{700}{3} x^{9} e^{6} d^{4} b a^{9} B + \frac{40}{3} x^{9} e^{7} d^{3} a^{10} B + 5 x^{9} d^{10} b^{8} a^{2} A + \frac{400}{3} x^{9} e d^{9} b^{7} a^{3} A + 1050 x^{9} e^{2} d^{8} b^{6} a^{4} A + 3360 x^{9} e^{3} d^{7} b^{5} a^{5} A + 4900 x^{9} e^{4} d^{6} b^{4} a^{6} A + 3360 x^{9} e^{5} d^{5} b^{3} a^{7} A + 1050 x^{9} e^{6} d^{4} b^{2} a^{8} A + \frac{400}{3} x^{9} e^{7} d^{3} b a^{9} A + 5 x^{9} e^{8} d^{2} a^{10} A + \frac{105}{4} x^{8} d^{10} b^{6} a^{4} B + 315 x^{8} e d^{9} b^{5} a^{5} B + \frac{4725}{4} x^{8} e^{2} d^{8} b^{4} a^{6} B + 1800 x^{8} e^{3} d^{7} b^{3} a^{7} B + \frac{4725}{4} x^{8} e^{4} d^{6} b^{2} a^{8} B + 315 x^{8} e^{5} d^{5} b a^{9} B + \frac{105}{4} x^{8} e^{6} d^{4} a^{10} B + 15 x^{8} d^{10} b^{7} a^{3} A + \frac{525}{2} x^{8} e d^{9} b^{6} a^{4} A + \frac{2835}{2} x^{8} e^{2} d^{8} b^{5} a^{5} A + 3150 x^{8} e^{3} d^{7} b^{4} a^{6} A + 3150 x^{8} e^{4} d^{6} b^{3} a^{7} A + \frac{2835}{2} x^{8} e^{5} d^{5} b^{2} a^{8} A + \frac{525}{2} x^{8} e^{6} d^{4} b a^{9} A + 15 x^{8} e^{7} d^{3} a^{10} A + 36 x^{7} d^{10} b^{5} a^{5} B + 300 x^{7} e d^{9} b^{4} a^{6} B + \frac{5400}{7} x^{7} e^{2} d^{8} b^{3} a^{7} B + \frac{5400}{7} x^{7} e^{3} d^{7} b^{2} a^{8} B + 300 x^{7} e^{4} d^{6} b a^{9} B + 36 x^{7} e^{5} d^{5} a^{10} B + 30 x^{7} d^{10} b^{6} a^{4} A + 360 x^{7} e d^{9} b^{5} a^{5} A + 1350 x^{7} e^{2} d^{8} b^{4} a^{6} A + \frac{14400}{7} x^{7} e^{3} d^{7} b^{3} a^{7} A + 1350 x^{7} e^{4} d^{6} b^{2} a^{8} A + 360 x^{7} e^{5} d^{5} b a^{9} A + 30 x^{7} e^{6} d^{4} a^{10} A + 35 x^{6} d^{10} b^{4} a^{6} B + 200 x^{6} e d^{9} b^{3} a^{7} B + \frac{675}{2} x^{6} e^{2} d^{8} b^{2} a^{8} B + 200 x^{6} e^{3} d^{7} b a^{9} B + 35 x^{6} e^{4} d^{6} a^{10} B + 42 x^{6} d^{10} b^{5} a^{5} A + 350 x^{6} e d^{9} b^{4} a^{6} A + 900 x^{6} e^{2} d^{8} b^{3} a^{7} A + 900 x^{6} e^{3} d^{7} b^{2} a^{8} A + 350 x^{6} e^{4} d^{6} b a^{9} A + 42 x^{6} e^{5} d^{5} a^{10} A + 24 x^{5} d^{10} b^{3} a^{7} B + 90 x^{5} e d^{9} b^{2} a^{8} B + 90 x^{5} e^{2} d^{8} b a^{9} B + 24 x^{5} e^{3} d^{7} a^{10} B + 42 x^{5} d^{10} b^{4} a^{6} A + 240 x^{5} e d^{9} b^{3} a^{7} A + 405 x^{5} e^{2} d^{8} b^{2} a^{8} A + 240 x^{5} e^{3} d^{7} b a^{9} A + 42 x^{5} e^{4} d^{6} a^{10} A + \frac{45}{4} x^{4} d^{10} b^{2} a^{8} B + 25 x^{4} e d^{9} b a^{9} B + \frac{45}{4} x^{4} e^{2} d^{8} a^{10} B + 30 x^{4} d^{10} b^{3} a^{7} A + \frac{225}{2} x^{4} e d^{9} b^{2} a^{8} A + \frac{225}{2} x^{4} e^{2} d^{8} b a^{9} A + 30 x^{4} e^{3} d^{7} a^{10} A + \frac{10}{3} x^{3} d^{10} b a^{9} B + \frac{10}{3} x^{3} e d^{9} a^{10} B + 15 x^{3} d^{10} b^{2} a^{8} A + \frac{100}{3} x^{3} e d^{9} b a^{9} A + 15 x^{3} e^{2} d^{8} a^{10} A + \frac{1}{2} x^{2} d^{10} a^{10} B + 5 x^{2} d^{10} b a^{9} A + 5 x^{2} e d^{9} a^{10} A + x d^{10} a^{10} A"," ",0,"1/22*x^22*e^10*b^10*B + 10/21*x^21*e^9*d*b^10*B + 10/21*x^21*e^10*b^9*a*B + 1/21*x^21*e^10*b^10*A + 9/4*x^20*e^8*d^2*b^10*B + 5*x^20*e^9*d*b^9*a*B + 9/4*x^20*e^10*b^8*a^2*B + 1/2*x^20*e^9*d*b^10*A + 1/2*x^20*e^10*b^9*a*A + 120/19*x^19*e^7*d^3*b^10*B + 450/19*x^19*e^8*d^2*b^9*a*B + 450/19*x^19*e^9*d*b^8*a^2*B + 120/19*x^19*e^10*b^7*a^3*B + 45/19*x^19*e^8*d^2*b^10*A + 100/19*x^19*e^9*d*b^9*a*A + 45/19*x^19*e^10*b^8*a^2*A + 35/3*x^18*e^6*d^4*b^10*B + 200/3*x^18*e^7*d^3*b^9*a*B + 225/2*x^18*e^8*d^2*b^8*a^2*B + 200/3*x^18*e^9*d*b^7*a^3*B + 35/3*x^18*e^10*b^6*a^4*B + 20/3*x^18*e^7*d^3*b^10*A + 25*x^18*e^8*d^2*b^9*a*A + 25*x^18*e^9*d*b^8*a^2*A + 20/3*x^18*e^10*b^7*a^3*A + 252/17*x^17*e^5*d^5*b^10*B + 2100/17*x^17*e^6*d^4*b^9*a*B + 5400/17*x^17*e^7*d^3*b^8*a^2*B + 5400/17*x^17*e^8*d^2*b^7*a^3*B + 2100/17*x^17*e^9*d*b^6*a^4*B + 252/17*x^17*e^10*b^5*a^5*B + 210/17*x^17*e^6*d^4*b^10*A + 1200/17*x^17*e^7*d^3*b^9*a*A + 2025/17*x^17*e^8*d^2*b^8*a^2*A + 1200/17*x^17*e^9*d*b^7*a^3*A + 210/17*x^17*e^10*b^6*a^4*A + 105/8*x^16*e^4*d^6*b^10*B + 315/2*x^16*e^5*d^5*b^9*a*B + 4725/8*x^16*e^6*d^4*b^8*a^2*B + 900*x^16*e^7*d^3*b^7*a^3*B + 4725/8*x^16*e^8*d^2*b^6*a^4*B + 315/2*x^16*e^9*d*b^5*a^5*B + 105/8*x^16*e^10*b^4*a^6*B + 63/4*x^16*e^5*d^5*b^10*A + 525/4*x^16*e^6*d^4*b^9*a*A + 675/2*x^16*e^7*d^3*b^8*a^2*A + 675/2*x^16*e^8*d^2*b^7*a^3*A + 525/4*x^16*e^9*d*b^6*a^4*A + 63/4*x^16*e^10*b^5*a^5*A + 8*x^15*e^3*d^7*b^10*B + 140*x^15*e^4*d^6*b^9*a*B + 756*x^15*e^5*d^5*b^8*a^2*B + 1680*x^15*e^6*d^4*b^7*a^3*B + 1680*x^15*e^7*d^3*b^6*a^4*B + 756*x^15*e^8*d^2*b^5*a^5*B + 140*x^15*e^9*d*b^4*a^6*B + 8*x^15*e^10*b^3*a^7*B + 14*x^15*e^4*d^6*b^10*A + 168*x^15*e^5*d^5*b^9*a*A + 630*x^15*e^6*d^4*b^8*a^2*A + 960*x^15*e^7*d^3*b^7*a^3*A + 630*x^15*e^8*d^2*b^6*a^4*A + 168*x^15*e^9*d*b^5*a^5*A + 14*x^15*e^10*b^4*a^6*A + 45/14*x^14*e^2*d^8*b^10*B + 600/7*x^14*e^3*d^7*b^9*a*B + 675*x^14*e^4*d^6*b^8*a^2*B + 2160*x^14*e^5*d^5*b^7*a^3*B + 3150*x^14*e^6*d^4*b^6*a^4*B + 2160*x^14*e^7*d^3*b^5*a^5*B + 675*x^14*e^8*d^2*b^4*a^6*B + 600/7*x^14*e^9*d*b^3*a^7*B + 45/14*x^14*e^10*b^2*a^8*B + 60/7*x^14*e^3*d^7*b^10*A + 150*x^14*e^4*d^6*b^9*a*A + 810*x^14*e^5*d^5*b^8*a^2*A + 1800*x^14*e^6*d^4*b^7*a^3*A + 1800*x^14*e^7*d^3*b^6*a^4*A + 810*x^14*e^8*d^2*b^5*a^5*A + 150*x^14*e^9*d*b^4*a^6*A + 60/7*x^14*e^10*b^3*a^7*A + 10/13*x^13*e*d^9*b^10*B + 450/13*x^13*e^2*d^8*b^9*a*B + 5400/13*x^13*e^3*d^7*b^8*a^2*B + 25200/13*x^13*e^4*d^6*b^7*a^3*B + 52920/13*x^13*e^5*d^5*b^6*a^4*B + 52920/13*x^13*e^6*d^4*b^5*a^5*B + 25200/13*x^13*e^7*d^3*b^4*a^6*B + 5400/13*x^13*e^8*d^2*b^3*a^7*B + 450/13*x^13*e^9*d*b^2*a^8*B + 10/13*x^13*e^10*b*a^9*B + 45/13*x^13*e^2*d^8*b^10*A + 1200/13*x^13*e^3*d^7*b^9*a*A + 9450/13*x^13*e^4*d^6*b^8*a^2*A + 30240/13*x^13*e^5*d^5*b^7*a^3*A + 44100/13*x^13*e^6*d^4*b^6*a^4*A + 30240/13*x^13*e^7*d^3*b^5*a^5*A + 9450/13*x^13*e^8*d^2*b^4*a^6*A + 1200/13*x^13*e^9*d*b^3*a^7*A + 45/13*x^13*e^10*b^2*a^8*A + 1/12*x^12*d^10*b^10*B + 25/3*x^12*e*d^9*b^9*a*B + 675/4*x^12*e^2*d^8*b^8*a^2*B + 1200*x^12*e^3*d^7*b^7*a^3*B + 3675*x^12*e^4*d^6*b^6*a^4*B + 5292*x^12*e^5*d^5*b^5*a^5*B + 3675*x^12*e^6*d^4*b^4*a^6*B + 1200*x^12*e^7*d^3*b^3*a^7*B + 675/4*x^12*e^8*d^2*b^2*a^8*B + 25/3*x^12*e^9*d*b*a^9*B + 1/12*x^12*e^10*a^10*B + 5/6*x^12*e*d^9*b^10*A + 75/2*x^12*e^2*d^8*b^9*a*A + 450*x^12*e^3*d^7*b^8*a^2*A + 2100*x^12*e^4*d^6*b^7*a^3*A + 4410*x^12*e^5*d^5*b^6*a^4*A + 4410*x^12*e^6*d^4*b^5*a^5*A + 2100*x^12*e^7*d^3*b^4*a^6*A + 450*x^12*e^8*d^2*b^3*a^7*A + 75/2*x^12*e^9*d*b^2*a^8*A + 5/6*x^12*e^10*b*a^9*A + 10/11*x^11*d^10*b^9*a*B + 450/11*x^11*e*d^9*b^8*a^2*B + 5400/11*x^11*e^2*d^8*b^7*a^3*B + 25200/11*x^11*e^3*d^7*b^6*a^4*B + 52920/11*x^11*e^4*d^6*b^5*a^5*B + 52920/11*x^11*e^5*d^5*b^4*a^6*B + 25200/11*x^11*e^6*d^4*b^3*a^7*B + 5400/11*x^11*e^7*d^3*b^2*a^8*B + 450/11*x^11*e^8*d^2*b*a^9*B + 10/11*x^11*e^9*d*a^10*B + 1/11*x^11*d^10*b^10*A + 100/11*x^11*e*d^9*b^9*a*A + 2025/11*x^11*e^2*d^8*b^8*a^2*A + 14400/11*x^11*e^3*d^7*b^7*a^3*A + 44100/11*x^11*e^4*d^6*b^6*a^4*A + 63504/11*x^11*e^5*d^5*b^5*a^5*A + 44100/11*x^11*e^6*d^4*b^4*a^6*A + 14400/11*x^11*e^7*d^3*b^3*a^7*A + 2025/11*x^11*e^8*d^2*b^2*a^8*A + 100/11*x^11*e^9*d*b*a^9*A + 1/11*x^11*e^10*a^10*A + 9/2*x^10*d^10*b^8*a^2*B + 120*x^10*e*d^9*b^7*a^3*B + 945*x^10*e^2*d^8*b^6*a^4*B + 3024*x^10*e^3*d^7*b^5*a^5*B + 4410*x^10*e^4*d^6*b^4*a^6*B + 3024*x^10*e^5*d^5*b^3*a^7*B + 945*x^10*e^6*d^4*b^2*a^8*B + 120*x^10*e^7*d^3*b*a^9*B + 9/2*x^10*e^8*d^2*a^10*B + x^10*d^10*b^9*a*A + 45*x^10*e*d^9*b^8*a^2*A + 540*x^10*e^2*d^8*b^7*a^3*A + 2520*x^10*e^3*d^7*b^6*a^4*A + 5292*x^10*e^4*d^6*b^5*a^5*A + 5292*x^10*e^5*d^5*b^4*a^6*A + 2520*x^10*e^6*d^4*b^3*a^7*A + 540*x^10*e^7*d^3*b^2*a^8*A + 45*x^10*e^8*d^2*b*a^9*A + x^10*e^9*d*a^10*A + 40/3*x^9*d^10*b^7*a^3*B + 700/3*x^9*e*d^9*b^6*a^4*B + 1260*x^9*e^2*d^8*b^5*a^5*B + 2800*x^9*e^3*d^7*b^4*a^6*B + 2800*x^9*e^4*d^6*b^3*a^7*B + 1260*x^9*e^5*d^5*b^2*a^8*B + 700/3*x^9*e^6*d^4*b*a^9*B + 40/3*x^9*e^7*d^3*a^10*B + 5*x^9*d^10*b^8*a^2*A + 400/3*x^9*e*d^9*b^7*a^3*A + 1050*x^9*e^2*d^8*b^6*a^4*A + 3360*x^9*e^3*d^7*b^5*a^5*A + 4900*x^9*e^4*d^6*b^4*a^6*A + 3360*x^9*e^5*d^5*b^3*a^7*A + 1050*x^9*e^6*d^4*b^2*a^8*A + 400/3*x^9*e^7*d^3*b*a^9*A + 5*x^9*e^8*d^2*a^10*A + 105/4*x^8*d^10*b^6*a^4*B + 315*x^8*e*d^9*b^5*a^5*B + 4725/4*x^8*e^2*d^8*b^4*a^6*B + 1800*x^8*e^3*d^7*b^3*a^7*B + 4725/4*x^8*e^4*d^6*b^2*a^8*B + 315*x^8*e^5*d^5*b*a^9*B + 105/4*x^8*e^6*d^4*a^10*B + 15*x^8*d^10*b^7*a^3*A + 525/2*x^8*e*d^9*b^6*a^4*A + 2835/2*x^8*e^2*d^8*b^5*a^5*A + 3150*x^8*e^3*d^7*b^4*a^6*A + 3150*x^8*e^4*d^6*b^3*a^7*A + 2835/2*x^8*e^5*d^5*b^2*a^8*A + 525/2*x^8*e^6*d^4*b*a^9*A + 15*x^8*e^7*d^3*a^10*A + 36*x^7*d^10*b^5*a^5*B + 300*x^7*e*d^9*b^4*a^6*B + 5400/7*x^7*e^2*d^8*b^3*a^7*B + 5400/7*x^7*e^3*d^7*b^2*a^8*B + 300*x^7*e^4*d^6*b*a^9*B + 36*x^7*e^5*d^5*a^10*B + 30*x^7*d^10*b^6*a^4*A + 360*x^7*e*d^9*b^5*a^5*A + 1350*x^7*e^2*d^8*b^4*a^6*A + 14400/7*x^7*e^3*d^7*b^3*a^7*A + 1350*x^7*e^4*d^6*b^2*a^8*A + 360*x^7*e^5*d^5*b*a^9*A + 30*x^7*e^6*d^4*a^10*A + 35*x^6*d^10*b^4*a^6*B + 200*x^6*e*d^9*b^3*a^7*B + 675/2*x^6*e^2*d^8*b^2*a^8*B + 200*x^6*e^3*d^7*b*a^9*B + 35*x^6*e^4*d^6*a^10*B + 42*x^6*d^10*b^5*a^5*A + 350*x^6*e*d^9*b^4*a^6*A + 900*x^6*e^2*d^8*b^3*a^7*A + 900*x^6*e^3*d^7*b^2*a^8*A + 350*x^6*e^4*d^6*b*a^9*A + 42*x^6*e^5*d^5*a^10*A + 24*x^5*d^10*b^3*a^7*B + 90*x^5*e*d^9*b^2*a^8*B + 90*x^5*e^2*d^8*b*a^9*B + 24*x^5*e^3*d^7*a^10*B + 42*x^5*d^10*b^4*a^6*A + 240*x^5*e*d^9*b^3*a^7*A + 405*x^5*e^2*d^8*b^2*a^8*A + 240*x^5*e^3*d^7*b*a^9*A + 42*x^5*e^4*d^6*a^10*A + 45/4*x^4*d^10*b^2*a^8*B + 25*x^4*e*d^9*b*a^9*B + 45/4*x^4*e^2*d^8*a^10*B + 30*x^4*d^10*b^3*a^7*A + 225/2*x^4*e*d^9*b^2*a^8*A + 225/2*x^4*e^2*d^8*b*a^9*A + 30*x^4*e^3*d^7*a^10*A + 10/3*x^3*d^10*b*a^9*B + 10/3*x^3*e*d^9*a^10*B + 15*x^3*d^10*b^2*a^8*A + 100/3*x^3*e*d^9*b*a^9*A + 15*x^3*e^2*d^8*a^10*A + 1/2*x^2*d^10*a^10*B + 5*x^2*d^10*b*a^9*A + 5*x^2*e*d^9*a^10*A + x*d^10*a^10*A","B",0
1079,1,3536,0,1.076820," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^9,x, algorithm=""fricas"")","\frac{1}{21} x^{21} e^{9} b^{10} B + \frac{9}{20} x^{20} e^{8} d b^{10} B + \frac{1}{2} x^{20} e^{9} b^{9} a B + \frac{1}{20} x^{20} e^{9} b^{10} A + \frac{36}{19} x^{19} e^{7} d^{2} b^{10} B + \frac{90}{19} x^{19} e^{8} d b^{9} a B + \frac{45}{19} x^{19} e^{9} b^{8} a^{2} B + \frac{9}{19} x^{19} e^{8} d b^{10} A + \frac{10}{19} x^{19} e^{9} b^{9} a A + \frac{14}{3} x^{18} e^{6} d^{3} b^{10} B + 20 x^{18} e^{7} d^{2} b^{9} a B + \frac{45}{2} x^{18} e^{8} d b^{8} a^{2} B + \frac{20}{3} x^{18} e^{9} b^{7} a^{3} B + 2 x^{18} e^{7} d^{2} b^{10} A + 5 x^{18} e^{8} d b^{9} a A + \frac{5}{2} x^{18} e^{9} b^{8} a^{2} A + \frac{126}{17} x^{17} e^{5} d^{4} b^{10} B + \frac{840}{17} x^{17} e^{6} d^{3} b^{9} a B + \frac{1620}{17} x^{17} e^{7} d^{2} b^{8} a^{2} B + \frac{1080}{17} x^{17} e^{8} d b^{7} a^{3} B + \frac{210}{17} x^{17} e^{9} b^{6} a^{4} B + \frac{84}{17} x^{17} e^{6} d^{3} b^{10} A + \frac{360}{17} x^{17} e^{7} d^{2} b^{9} a A + \frac{405}{17} x^{17} e^{8} d b^{8} a^{2} A + \frac{120}{17} x^{17} e^{9} b^{7} a^{3} A + \frac{63}{8} x^{16} e^{4} d^{5} b^{10} B + \frac{315}{4} x^{16} e^{5} d^{4} b^{9} a B + \frac{945}{4} x^{16} e^{6} d^{3} b^{8} a^{2} B + 270 x^{16} e^{7} d^{2} b^{7} a^{3} B + \frac{945}{8} x^{16} e^{8} d b^{6} a^{4} B + \frac{63}{4} x^{16} e^{9} b^{5} a^{5} B + \frac{63}{8} x^{16} e^{5} d^{4} b^{10} A + \frac{105}{2} x^{16} e^{6} d^{3} b^{9} a A + \frac{405}{4} x^{16} e^{7} d^{2} b^{8} a^{2} A + \frac{135}{2} x^{16} e^{8} d b^{7} a^{3} A + \frac{105}{8} x^{16} e^{9} b^{6} a^{4} A + \frac{28}{5} x^{15} e^{3} d^{6} b^{10} B + 84 x^{15} e^{4} d^{5} b^{9} a B + 378 x^{15} e^{5} d^{4} b^{8} a^{2} B + 672 x^{15} e^{6} d^{3} b^{7} a^{3} B + 504 x^{15} e^{7} d^{2} b^{6} a^{4} B + \frac{756}{5} x^{15} e^{8} d b^{5} a^{5} B + 14 x^{15} e^{9} b^{4} a^{6} B + \frac{42}{5} x^{15} e^{4} d^{5} b^{10} A + 84 x^{15} e^{5} d^{4} b^{9} a A + 252 x^{15} e^{6} d^{3} b^{8} a^{2} A + 288 x^{15} e^{7} d^{2} b^{7} a^{3} A + 126 x^{15} e^{8} d b^{6} a^{4} A + \frac{84}{5} x^{15} e^{9} b^{5} a^{5} A + \frac{18}{7} x^{14} e^{2} d^{7} b^{10} B + 60 x^{14} e^{3} d^{6} b^{9} a B + 405 x^{14} e^{4} d^{5} b^{8} a^{2} B + 1080 x^{14} e^{5} d^{4} b^{7} a^{3} B + 1260 x^{14} e^{6} d^{3} b^{6} a^{4} B + 648 x^{14} e^{7} d^{2} b^{5} a^{5} B + 135 x^{14} e^{8} d b^{4} a^{6} B + \frac{60}{7} x^{14} e^{9} b^{3} a^{7} B + 6 x^{14} e^{3} d^{6} b^{10} A + 90 x^{14} e^{4} d^{5} b^{9} a A + 405 x^{14} e^{5} d^{4} b^{8} a^{2} A + 720 x^{14} e^{6} d^{3} b^{7} a^{3} A + 540 x^{14} e^{7} d^{2} b^{6} a^{4} A + 162 x^{14} e^{8} d b^{5} a^{5} A + 15 x^{14} e^{9} b^{4} a^{6} A + \frac{9}{13} x^{13} e d^{8} b^{10} B + \frac{360}{13} x^{13} e^{2} d^{7} b^{9} a B + \frac{3780}{13} x^{13} e^{3} d^{6} b^{8} a^{2} B + \frac{15120}{13} x^{13} e^{4} d^{5} b^{7} a^{3} B + \frac{26460}{13} x^{13} e^{5} d^{4} b^{6} a^{4} B + \frac{21168}{13} x^{13} e^{6} d^{3} b^{5} a^{5} B + \frac{7560}{13} x^{13} e^{7} d^{2} b^{4} a^{6} B + \frac{1080}{13} x^{13} e^{8} d b^{3} a^{7} B + \frac{45}{13} x^{13} e^{9} b^{2} a^{8} B + \frac{36}{13} x^{13} e^{2} d^{7} b^{10} A + \frac{840}{13} x^{13} e^{3} d^{6} b^{9} a A + \frac{5670}{13} x^{13} e^{4} d^{5} b^{8} a^{2} A + \frac{15120}{13} x^{13} e^{5} d^{4} b^{7} a^{3} A + \frac{17640}{13} x^{13} e^{6} d^{3} b^{6} a^{4} A + \frac{9072}{13} x^{13} e^{7} d^{2} b^{5} a^{5} A + \frac{1890}{13} x^{13} e^{8} d b^{4} a^{6} A + \frac{120}{13} x^{13} e^{9} b^{3} a^{7} A + \frac{1}{12} x^{12} d^{9} b^{10} B + \frac{15}{2} x^{12} e d^{8} b^{9} a B + 135 x^{12} e^{2} d^{7} b^{8} a^{2} B + 840 x^{12} e^{3} d^{6} b^{7} a^{3} B + 2205 x^{12} e^{4} d^{5} b^{6} a^{4} B + 2646 x^{12} e^{5} d^{4} b^{5} a^{5} B + 1470 x^{12} e^{6} d^{3} b^{4} a^{6} B + 360 x^{12} e^{7} d^{2} b^{3} a^{7} B + \frac{135}{4} x^{12} e^{8} d b^{2} a^{8} B + \frac{5}{6} x^{12} e^{9} b a^{9} B + \frac{3}{4} x^{12} e d^{8} b^{10} A + 30 x^{12} e^{2} d^{7} b^{9} a A + 315 x^{12} e^{3} d^{6} b^{8} a^{2} A + 1260 x^{12} e^{4} d^{5} b^{7} a^{3} A + 2205 x^{12} e^{5} d^{4} b^{6} a^{4} A + 1764 x^{12} e^{6} d^{3} b^{5} a^{5} A + 630 x^{12} e^{7} d^{2} b^{4} a^{6} A + 90 x^{12} e^{8} d b^{3} a^{7} A + \frac{15}{4} x^{12} e^{9} b^{2} a^{8} A + \frac{10}{11} x^{11} d^{9} b^{9} a B + \frac{405}{11} x^{11} e d^{8} b^{8} a^{2} B + \frac{4320}{11} x^{11} e^{2} d^{7} b^{7} a^{3} B + \frac{17640}{11} x^{11} e^{3} d^{6} b^{6} a^{4} B + \frac{31752}{11} x^{11} e^{4} d^{5} b^{5} a^{5} B + \frac{26460}{11} x^{11} e^{5} d^{4} b^{4} a^{6} B + \frac{10080}{11} x^{11} e^{6} d^{3} b^{3} a^{7} B + \frac{1620}{11} x^{11} e^{7} d^{2} b^{2} a^{8} B + \frac{90}{11} x^{11} e^{8} d b a^{9} B + \frac{1}{11} x^{11} e^{9} a^{10} B + \frac{1}{11} x^{11} d^{9} b^{10} A + \frac{90}{11} x^{11} e d^{8} b^{9} a A + \frac{1620}{11} x^{11} e^{2} d^{7} b^{8} a^{2} A + \frac{10080}{11} x^{11} e^{3} d^{6} b^{7} a^{3} A + \frac{26460}{11} x^{11} e^{4} d^{5} b^{6} a^{4} A + \frac{31752}{11} x^{11} e^{5} d^{4} b^{5} a^{5} A + \frac{17640}{11} x^{11} e^{6} d^{3} b^{4} a^{6} A + \frac{4320}{11} x^{11} e^{7} d^{2} b^{3} a^{7} A + \frac{405}{11} x^{11} e^{8} d b^{2} a^{8} A + \frac{10}{11} x^{11} e^{9} b a^{9} A + \frac{9}{2} x^{10} d^{9} b^{8} a^{2} B + 108 x^{10} e d^{8} b^{7} a^{3} B + 756 x^{10} e^{2} d^{7} b^{6} a^{4} B + \frac{10584}{5} x^{10} e^{3} d^{6} b^{5} a^{5} B + 2646 x^{10} e^{4} d^{5} b^{4} a^{6} B + 1512 x^{10} e^{5} d^{4} b^{3} a^{7} B + 378 x^{10} e^{6} d^{3} b^{2} a^{8} B + 36 x^{10} e^{7} d^{2} b a^{9} B + \frac{9}{10} x^{10} e^{8} d a^{10} B + x^{10} d^{9} b^{9} a A + \frac{81}{2} x^{10} e d^{8} b^{8} a^{2} A + 432 x^{10} e^{2} d^{7} b^{7} a^{3} A + 1764 x^{10} e^{3} d^{6} b^{6} a^{4} A + \frac{15876}{5} x^{10} e^{4} d^{5} b^{5} a^{5} A + 2646 x^{10} e^{5} d^{4} b^{4} a^{6} A + 1008 x^{10} e^{6} d^{3} b^{3} a^{7} A + 162 x^{10} e^{7} d^{2} b^{2} a^{8} A + 9 x^{10} e^{8} d b a^{9} A + \frac{1}{10} x^{10} e^{9} a^{10} A + \frac{40}{3} x^{9} d^{9} b^{7} a^{3} B + 210 x^{9} e d^{8} b^{6} a^{4} B + 1008 x^{9} e^{2} d^{7} b^{5} a^{5} B + 1960 x^{9} e^{3} d^{6} b^{4} a^{6} B + 1680 x^{9} e^{4} d^{5} b^{3} a^{7} B + 630 x^{9} e^{5} d^{4} b^{2} a^{8} B + \frac{280}{3} x^{9} e^{6} d^{3} b a^{9} B + 4 x^{9} e^{7} d^{2} a^{10} B + 5 x^{9} d^{9} b^{8} a^{2} A + 120 x^{9} e d^{8} b^{7} a^{3} A + 840 x^{9} e^{2} d^{7} b^{6} a^{4} A + 2352 x^{9} e^{3} d^{6} b^{5} a^{5} A + 2940 x^{9} e^{4} d^{5} b^{4} a^{6} A + 1680 x^{9} e^{5} d^{4} b^{3} a^{7} A + 420 x^{9} e^{6} d^{3} b^{2} a^{8} A + 40 x^{9} e^{7} d^{2} b a^{9} A + x^{9} e^{8} d a^{10} A + \frac{105}{4} x^{8} d^{9} b^{6} a^{4} B + \frac{567}{2} x^{8} e d^{8} b^{5} a^{5} B + 945 x^{8} e^{2} d^{7} b^{4} a^{6} B + 1260 x^{8} e^{3} d^{6} b^{3} a^{7} B + \frac{2835}{4} x^{8} e^{4} d^{5} b^{2} a^{8} B + \frac{315}{2} x^{8} e^{5} d^{4} b a^{9} B + \frac{21}{2} x^{8} e^{6} d^{3} a^{10} B + 15 x^{8} d^{9} b^{7} a^{3} A + \frac{945}{4} x^{8} e d^{8} b^{6} a^{4} A + 1134 x^{8} e^{2} d^{7} b^{5} a^{5} A + 2205 x^{8} e^{3} d^{6} b^{4} a^{6} A + 1890 x^{8} e^{4} d^{5} b^{3} a^{7} A + \frac{2835}{4} x^{8} e^{5} d^{4} b^{2} a^{8} A + 105 x^{8} e^{6} d^{3} b a^{9} A + \frac{9}{2} x^{8} e^{7} d^{2} a^{10} A + 36 x^{7} d^{9} b^{5} a^{5} B + 270 x^{7} e d^{8} b^{4} a^{6} B + \frac{4320}{7} x^{7} e^{2} d^{7} b^{3} a^{7} B + 540 x^{7} e^{3} d^{6} b^{2} a^{8} B + 180 x^{7} e^{4} d^{5} b a^{9} B + 18 x^{7} e^{5} d^{4} a^{10} B + 30 x^{7} d^{9} b^{6} a^{4} A + 324 x^{7} e d^{8} b^{5} a^{5} A + 1080 x^{7} e^{2} d^{7} b^{4} a^{6} A + 1440 x^{7} e^{3} d^{6} b^{3} a^{7} A + 810 x^{7} e^{4} d^{5} b^{2} a^{8} A + 180 x^{7} e^{5} d^{4} b a^{9} A + 12 x^{7} e^{6} d^{3} a^{10} A + 35 x^{6} d^{9} b^{4} a^{6} B + 180 x^{6} e d^{8} b^{3} a^{7} B + 270 x^{6} e^{2} d^{7} b^{2} a^{8} B + 140 x^{6} e^{3} d^{6} b a^{9} B + 21 x^{6} e^{4} d^{5} a^{10} B + 42 x^{6} d^{9} b^{5} a^{5} A + 315 x^{6} e d^{8} b^{4} a^{6} A + 720 x^{6} e^{2} d^{7} b^{3} a^{7} A + 630 x^{6} e^{3} d^{6} b^{2} a^{8} A + 210 x^{6} e^{4} d^{5} b a^{9} A + 21 x^{6} e^{5} d^{4} a^{10} A + 24 x^{5} d^{9} b^{3} a^{7} B + 81 x^{5} e d^{8} b^{2} a^{8} B + 72 x^{5} e^{2} d^{7} b a^{9} B + \frac{84}{5} x^{5} e^{3} d^{6} a^{10} B + 42 x^{5} d^{9} b^{4} a^{6} A + 216 x^{5} e d^{8} b^{3} a^{7} A + 324 x^{5} e^{2} d^{7} b^{2} a^{8} A + 168 x^{5} e^{3} d^{6} b a^{9} A + \frac{126}{5} x^{5} e^{4} d^{5} a^{10} A + \frac{45}{4} x^{4} d^{9} b^{2} a^{8} B + \frac{45}{2} x^{4} e d^{8} b a^{9} B + 9 x^{4} e^{2} d^{7} a^{10} B + 30 x^{4} d^{9} b^{3} a^{7} A + \frac{405}{4} x^{4} e d^{8} b^{2} a^{8} A + 90 x^{4} e^{2} d^{7} b a^{9} A + 21 x^{4} e^{3} d^{6} a^{10} A + \frac{10}{3} x^{3} d^{9} b a^{9} B + 3 x^{3} e d^{8} a^{10} B + 15 x^{3} d^{9} b^{2} a^{8} A + 30 x^{3} e d^{8} b a^{9} A + 12 x^{3} e^{2} d^{7} a^{10} A + \frac{1}{2} x^{2} d^{9} a^{10} B + 5 x^{2} d^{9} b a^{9} A + \frac{9}{2} x^{2} e d^{8} a^{10} A + x d^{9} a^{10} A"," ",0,"1/21*x^21*e^9*b^10*B + 9/20*x^20*e^8*d*b^10*B + 1/2*x^20*e^9*b^9*a*B + 1/20*x^20*e^9*b^10*A + 36/19*x^19*e^7*d^2*b^10*B + 90/19*x^19*e^8*d*b^9*a*B + 45/19*x^19*e^9*b^8*a^2*B + 9/19*x^19*e^8*d*b^10*A + 10/19*x^19*e^9*b^9*a*A + 14/3*x^18*e^6*d^3*b^10*B + 20*x^18*e^7*d^2*b^9*a*B + 45/2*x^18*e^8*d*b^8*a^2*B + 20/3*x^18*e^9*b^7*a^3*B + 2*x^18*e^7*d^2*b^10*A + 5*x^18*e^8*d*b^9*a*A + 5/2*x^18*e^9*b^8*a^2*A + 126/17*x^17*e^5*d^4*b^10*B + 840/17*x^17*e^6*d^3*b^9*a*B + 1620/17*x^17*e^7*d^2*b^8*a^2*B + 1080/17*x^17*e^8*d*b^7*a^3*B + 210/17*x^17*e^9*b^6*a^4*B + 84/17*x^17*e^6*d^3*b^10*A + 360/17*x^17*e^7*d^2*b^9*a*A + 405/17*x^17*e^8*d*b^8*a^2*A + 120/17*x^17*e^9*b^7*a^3*A + 63/8*x^16*e^4*d^5*b^10*B + 315/4*x^16*e^5*d^4*b^9*a*B + 945/4*x^16*e^6*d^3*b^8*a^2*B + 270*x^16*e^7*d^2*b^7*a^3*B + 945/8*x^16*e^8*d*b^6*a^4*B + 63/4*x^16*e^9*b^5*a^5*B + 63/8*x^16*e^5*d^4*b^10*A + 105/2*x^16*e^6*d^3*b^9*a*A + 405/4*x^16*e^7*d^2*b^8*a^2*A + 135/2*x^16*e^8*d*b^7*a^3*A + 105/8*x^16*e^9*b^6*a^4*A + 28/5*x^15*e^3*d^6*b^10*B + 84*x^15*e^4*d^5*b^9*a*B + 378*x^15*e^5*d^4*b^8*a^2*B + 672*x^15*e^6*d^3*b^7*a^3*B + 504*x^15*e^7*d^2*b^6*a^4*B + 756/5*x^15*e^8*d*b^5*a^5*B + 14*x^15*e^9*b^4*a^6*B + 42/5*x^15*e^4*d^5*b^10*A + 84*x^15*e^5*d^4*b^9*a*A + 252*x^15*e^6*d^3*b^8*a^2*A + 288*x^15*e^7*d^2*b^7*a^3*A + 126*x^15*e^8*d*b^6*a^4*A + 84/5*x^15*e^9*b^5*a^5*A + 18/7*x^14*e^2*d^7*b^10*B + 60*x^14*e^3*d^6*b^9*a*B + 405*x^14*e^4*d^5*b^8*a^2*B + 1080*x^14*e^5*d^4*b^7*a^3*B + 1260*x^14*e^6*d^3*b^6*a^4*B + 648*x^14*e^7*d^2*b^5*a^5*B + 135*x^14*e^8*d*b^4*a^6*B + 60/7*x^14*e^9*b^3*a^7*B + 6*x^14*e^3*d^6*b^10*A + 90*x^14*e^4*d^5*b^9*a*A + 405*x^14*e^5*d^4*b^8*a^2*A + 720*x^14*e^6*d^3*b^7*a^3*A + 540*x^14*e^7*d^2*b^6*a^4*A + 162*x^14*e^8*d*b^5*a^5*A + 15*x^14*e^9*b^4*a^6*A + 9/13*x^13*e*d^8*b^10*B + 360/13*x^13*e^2*d^7*b^9*a*B + 3780/13*x^13*e^3*d^6*b^8*a^2*B + 15120/13*x^13*e^4*d^5*b^7*a^3*B + 26460/13*x^13*e^5*d^4*b^6*a^4*B + 21168/13*x^13*e^6*d^3*b^5*a^5*B + 7560/13*x^13*e^7*d^2*b^4*a^6*B + 1080/13*x^13*e^8*d*b^3*a^7*B + 45/13*x^13*e^9*b^2*a^8*B + 36/13*x^13*e^2*d^7*b^10*A + 840/13*x^13*e^3*d^6*b^9*a*A + 5670/13*x^13*e^4*d^5*b^8*a^2*A + 15120/13*x^13*e^5*d^4*b^7*a^3*A + 17640/13*x^13*e^6*d^3*b^6*a^4*A + 9072/13*x^13*e^7*d^2*b^5*a^5*A + 1890/13*x^13*e^8*d*b^4*a^6*A + 120/13*x^13*e^9*b^3*a^7*A + 1/12*x^12*d^9*b^10*B + 15/2*x^12*e*d^8*b^9*a*B + 135*x^12*e^2*d^7*b^8*a^2*B + 840*x^12*e^3*d^6*b^7*a^3*B + 2205*x^12*e^4*d^5*b^6*a^4*B + 2646*x^12*e^5*d^4*b^5*a^5*B + 1470*x^12*e^6*d^3*b^4*a^6*B + 360*x^12*e^7*d^2*b^3*a^7*B + 135/4*x^12*e^8*d*b^2*a^8*B + 5/6*x^12*e^9*b*a^9*B + 3/4*x^12*e*d^8*b^10*A + 30*x^12*e^2*d^7*b^9*a*A + 315*x^12*e^3*d^6*b^8*a^2*A + 1260*x^12*e^4*d^5*b^7*a^3*A + 2205*x^12*e^5*d^4*b^6*a^4*A + 1764*x^12*e^6*d^3*b^5*a^5*A + 630*x^12*e^7*d^2*b^4*a^6*A + 90*x^12*e^8*d*b^3*a^7*A + 15/4*x^12*e^9*b^2*a^8*A + 10/11*x^11*d^9*b^9*a*B + 405/11*x^11*e*d^8*b^8*a^2*B + 4320/11*x^11*e^2*d^7*b^7*a^3*B + 17640/11*x^11*e^3*d^6*b^6*a^4*B + 31752/11*x^11*e^4*d^5*b^5*a^5*B + 26460/11*x^11*e^5*d^4*b^4*a^6*B + 10080/11*x^11*e^6*d^3*b^3*a^7*B + 1620/11*x^11*e^7*d^2*b^2*a^8*B + 90/11*x^11*e^8*d*b*a^9*B + 1/11*x^11*e^9*a^10*B + 1/11*x^11*d^9*b^10*A + 90/11*x^11*e*d^8*b^9*a*A + 1620/11*x^11*e^2*d^7*b^8*a^2*A + 10080/11*x^11*e^3*d^6*b^7*a^3*A + 26460/11*x^11*e^4*d^5*b^6*a^4*A + 31752/11*x^11*e^5*d^4*b^5*a^5*A + 17640/11*x^11*e^6*d^3*b^4*a^6*A + 4320/11*x^11*e^7*d^2*b^3*a^7*A + 405/11*x^11*e^8*d*b^2*a^8*A + 10/11*x^11*e^9*b*a^9*A + 9/2*x^10*d^9*b^8*a^2*B + 108*x^10*e*d^8*b^7*a^3*B + 756*x^10*e^2*d^7*b^6*a^4*B + 10584/5*x^10*e^3*d^6*b^5*a^5*B + 2646*x^10*e^4*d^5*b^4*a^6*B + 1512*x^10*e^5*d^4*b^3*a^7*B + 378*x^10*e^6*d^3*b^2*a^8*B + 36*x^10*e^7*d^2*b*a^9*B + 9/10*x^10*e^8*d*a^10*B + x^10*d^9*b^9*a*A + 81/2*x^10*e*d^8*b^8*a^2*A + 432*x^10*e^2*d^7*b^7*a^3*A + 1764*x^10*e^3*d^6*b^6*a^4*A + 15876/5*x^10*e^4*d^5*b^5*a^5*A + 2646*x^10*e^5*d^4*b^4*a^6*A + 1008*x^10*e^6*d^3*b^3*a^7*A + 162*x^10*e^7*d^2*b^2*a^8*A + 9*x^10*e^8*d*b*a^9*A + 1/10*x^10*e^9*a^10*A + 40/3*x^9*d^9*b^7*a^3*B + 210*x^9*e*d^8*b^6*a^4*B + 1008*x^9*e^2*d^7*b^5*a^5*B + 1960*x^9*e^3*d^6*b^4*a^6*B + 1680*x^9*e^4*d^5*b^3*a^7*B + 630*x^9*e^5*d^4*b^2*a^8*B + 280/3*x^9*e^6*d^3*b*a^9*B + 4*x^9*e^7*d^2*a^10*B + 5*x^9*d^9*b^8*a^2*A + 120*x^9*e*d^8*b^7*a^3*A + 840*x^9*e^2*d^7*b^6*a^4*A + 2352*x^9*e^3*d^6*b^5*a^5*A + 2940*x^9*e^4*d^5*b^4*a^6*A + 1680*x^9*e^5*d^4*b^3*a^7*A + 420*x^9*e^6*d^3*b^2*a^8*A + 40*x^9*e^7*d^2*b*a^9*A + x^9*e^8*d*a^10*A + 105/4*x^8*d^9*b^6*a^4*B + 567/2*x^8*e*d^8*b^5*a^5*B + 945*x^8*e^2*d^7*b^4*a^6*B + 1260*x^8*e^3*d^6*b^3*a^7*B + 2835/4*x^8*e^4*d^5*b^2*a^8*B + 315/2*x^8*e^5*d^4*b*a^9*B + 21/2*x^8*e^6*d^3*a^10*B + 15*x^8*d^9*b^7*a^3*A + 945/4*x^8*e*d^8*b^6*a^4*A + 1134*x^8*e^2*d^7*b^5*a^5*A + 2205*x^8*e^3*d^6*b^4*a^6*A + 1890*x^8*e^4*d^5*b^3*a^7*A + 2835/4*x^8*e^5*d^4*b^2*a^8*A + 105*x^8*e^6*d^3*b*a^9*A + 9/2*x^8*e^7*d^2*a^10*A + 36*x^7*d^9*b^5*a^5*B + 270*x^7*e*d^8*b^4*a^6*B + 4320/7*x^7*e^2*d^7*b^3*a^7*B + 540*x^7*e^3*d^6*b^2*a^8*B + 180*x^7*e^4*d^5*b*a^9*B + 18*x^7*e^5*d^4*a^10*B + 30*x^7*d^9*b^6*a^4*A + 324*x^7*e*d^8*b^5*a^5*A + 1080*x^7*e^2*d^7*b^4*a^6*A + 1440*x^7*e^3*d^6*b^3*a^7*A + 810*x^7*e^4*d^5*b^2*a^8*A + 180*x^7*e^5*d^4*b*a^9*A + 12*x^7*e^6*d^3*a^10*A + 35*x^6*d^9*b^4*a^6*B + 180*x^6*e*d^8*b^3*a^7*B + 270*x^6*e^2*d^7*b^2*a^8*B + 140*x^6*e^3*d^6*b*a^9*B + 21*x^6*e^4*d^5*a^10*B + 42*x^6*d^9*b^5*a^5*A + 315*x^6*e*d^8*b^4*a^6*A + 720*x^6*e^2*d^7*b^3*a^7*A + 630*x^6*e^3*d^6*b^2*a^8*A + 210*x^6*e^4*d^5*b*a^9*A + 21*x^6*e^5*d^4*a^10*A + 24*x^5*d^9*b^3*a^7*B + 81*x^5*e*d^8*b^2*a^8*B + 72*x^5*e^2*d^7*b*a^9*B + 84/5*x^5*e^3*d^6*a^10*B + 42*x^5*d^9*b^4*a^6*A + 216*x^5*e*d^8*b^3*a^7*A + 324*x^5*e^2*d^7*b^2*a^8*A + 168*x^5*e^3*d^6*b*a^9*A + 126/5*x^5*e^4*d^5*a^10*A + 45/4*x^4*d^9*b^2*a^8*B + 45/2*x^4*e*d^8*b*a^9*B + 9*x^4*e^2*d^7*a^10*B + 30*x^4*d^9*b^3*a^7*A + 405/4*x^4*e*d^8*b^2*a^8*A + 90*x^4*e^2*d^7*b*a^9*A + 21*x^4*e^3*d^6*a^10*A + 10/3*x^3*d^9*b*a^9*B + 3*x^3*e*d^8*a^10*B + 15*x^3*d^9*b^2*a^8*A + 30*x^3*e*d^8*b*a^9*A + 12*x^3*e^2*d^7*a^10*A + 1/2*x^2*d^9*a^10*B + 5*x^2*d^9*b*a^9*A + 9/2*x^2*e*d^8*a^10*A + x*d^9*a^10*A","B",0
1080,1,3159,0,0.942731," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^8,x, algorithm=""fricas"")","\frac{1}{20} x^{20} e^{8} b^{10} B + \frac{8}{19} x^{19} e^{7} d b^{10} B + \frac{10}{19} x^{19} e^{8} b^{9} a B + \frac{1}{19} x^{19} e^{8} b^{10} A + \frac{14}{9} x^{18} e^{6} d^{2} b^{10} B + \frac{40}{9} x^{18} e^{7} d b^{9} a B + \frac{5}{2} x^{18} e^{8} b^{8} a^{2} B + \frac{4}{9} x^{18} e^{7} d b^{10} A + \frac{5}{9} x^{18} e^{8} b^{9} a A + \frac{56}{17} x^{17} e^{5} d^{3} b^{10} B + \frac{280}{17} x^{17} e^{6} d^{2} b^{9} a B + \frac{360}{17} x^{17} e^{7} d b^{8} a^{2} B + \frac{120}{17} x^{17} e^{8} b^{7} a^{3} B + \frac{28}{17} x^{17} e^{6} d^{2} b^{10} A + \frac{80}{17} x^{17} e^{7} d b^{9} a A + \frac{45}{17} x^{17} e^{8} b^{8} a^{2} A + \frac{35}{8} x^{16} e^{4} d^{4} b^{10} B + 35 x^{16} e^{5} d^{3} b^{9} a B + \frac{315}{4} x^{16} e^{6} d^{2} b^{8} a^{2} B + 60 x^{16} e^{7} d b^{7} a^{3} B + \frac{105}{8} x^{16} e^{8} b^{6} a^{4} B + \frac{7}{2} x^{16} e^{5} d^{3} b^{10} A + \frac{35}{2} x^{16} e^{6} d^{2} b^{9} a A + \frac{45}{2} x^{16} e^{7} d b^{8} a^{2} A + \frac{15}{2} x^{16} e^{8} b^{7} a^{3} A + \frac{56}{15} x^{15} e^{3} d^{5} b^{10} B + \frac{140}{3} x^{15} e^{4} d^{4} b^{9} a B + 168 x^{15} e^{5} d^{3} b^{8} a^{2} B + 224 x^{15} e^{6} d^{2} b^{7} a^{3} B + 112 x^{15} e^{7} d b^{6} a^{4} B + \frac{84}{5} x^{15} e^{8} b^{5} a^{5} B + \frac{14}{3} x^{15} e^{4} d^{4} b^{10} A + \frac{112}{3} x^{15} e^{5} d^{3} b^{9} a A + 84 x^{15} e^{6} d^{2} b^{8} a^{2} A + 64 x^{15} e^{7} d b^{7} a^{3} A + 14 x^{15} e^{8} b^{6} a^{4} A + 2 x^{14} e^{2} d^{6} b^{10} B + 40 x^{14} e^{3} d^{5} b^{9} a B + 225 x^{14} e^{4} d^{4} b^{8} a^{2} B + 480 x^{14} e^{5} d^{3} b^{7} a^{3} B + 420 x^{14} e^{6} d^{2} b^{6} a^{4} B + 144 x^{14} e^{7} d b^{5} a^{5} B + 15 x^{14} e^{8} b^{4} a^{6} B + 4 x^{14} e^{3} d^{5} b^{10} A + 50 x^{14} e^{4} d^{4} b^{9} a A + 180 x^{14} e^{5} d^{3} b^{8} a^{2} A + 240 x^{14} e^{6} d^{2} b^{7} a^{3} A + 120 x^{14} e^{7} d b^{6} a^{4} A + 18 x^{14} e^{8} b^{5} a^{5} A + \frac{8}{13} x^{13} e d^{7} b^{10} B + \frac{280}{13} x^{13} e^{2} d^{6} b^{9} a B + \frac{2520}{13} x^{13} e^{3} d^{5} b^{8} a^{2} B + \frac{8400}{13} x^{13} e^{4} d^{4} b^{7} a^{3} B + \frac{11760}{13} x^{13} e^{5} d^{3} b^{6} a^{4} B + \frac{7056}{13} x^{13} e^{6} d^{2} b^{5} a^{5} B + \frac{1680}{13} x^{13} e^{7} d b^{4} a^{6} B + \frac{120}{13} x^{13} e^{8} b^{3} a^{7} B + \frac{28}{13} x^{13} e^{2} d^{6} b^{10} A + \frac{560}{13} x^{13} e^{3} d^{5} b^{9} a A + \frac{3150}{13} x^{13} e^{4} d^{4} b^{8} a^{2} A + \frac{6720}{13} x^{13} e^{5} d^{3} b^{7} a^{3} A + \frac{5880}{13} x^{13} e^{6} d^{2} b^{6} a^{4} A + \frac{2016}{13} x^{13} e^{7} d b^{5} a^{5} A + \frac{210}{13} x^{13} e^{8} b^{4} a^{6} A + \frac{1}{12} x^{12} d^{8} b^{10} B + \frac{20}{3} x^{12} e d^{7} b^{9} a B + 105 x^{12} e^{2} d^{6} b^{8} a^{2} B + 560 x^{12} e^{3} d^{5} b^{7} a^{3} B + 1225 x^{12} e^{4} d^{4} b^{6} a^{4} B + 1176 x^{12} e^{5} d^{3} b^{5} a^{5} B + 490 x^{12} e^{6} d^{2} b^{4} a^{6} B + 80 x^{12} e^{7} d b^{3} a^{7} B + \frac{15}{4} x^{12} e^{8} b^{2} a^{8} B + \frac{2}{3} x^{12} e d^{7} b^{10} A + \frac{70}{3} x^{12} e^{2} d^{6} b^{9} a A + 210 x^{12} e^{3} d^{5} b^{8} a^{2} A + 700 x^{12} e^{4} d^{4} b^{7} a^{3} A + 980 x^{12} e^{5} d^{3} b^{6} a^{4} A + 588 x^{12} e^{6} d^{2} b^{5} a^{5} A + 140 x^{12} e^{7} d b^{4} a^{6} A + 10 x^{12} e^{8} b^{3} a^{7} A + \frac{10}{11} x^{11} d^{8} b^{9} a B + \frac{360}{11} x^{11} e d^{7} b^{8} a^{2} B + \frac{3360}{11} x^{11} e^{2} d^{6} b^{7} a^{3} B + \frac{11760}{11} x^{11} e^{3} d^{5} b^{6} a^{4} B + \frac{17640}{11} x^{11} e^{4} d^{4} b^{5} a^{5} B + \frac{11760}{11} x^{11} e^{5} d^{3} b^{4} a^{6} B + \frac{3360}{11} x^{11} e^{6} d^{2} b^{3} a^{7} B + \frac{360}{11} x^{11} e^{7} d b^{2} a^{8} B + \frac{10}{11} x^{11} e^{8} b a^{9} B + \frac{1}{11} x^{11} d^{8} b^{10} A + \frac{80}{11} x^{11} e d^{7} b^{9} a A + \frac{1260}{11} x^{11} e^{2} d^{6} b^{8} a^{2} A + \frac{6720}{11} x^{11} e^{3} d^{5} b^{7} a^{3} A + \frac{14700}{11} x^{11} e^{4} d^{4} b^{6} a^{4} A + \frac{14112}{11} x^{11} e^{5} d^{3} b^{5} a^{5} A + \frac{5880}{11} x^{11} e^{6} d^{2} b^{4} a^{6} A + \frac{960}{11} x^{11} e^{7} d b^{3} a^{7} A + \frac{45}{11} x^{11} e^{8} b^{2} a^{8} A + \frac{9}{2} x^{10} d^{8} b^{8} a^{2} B + 96 x^{10} e d^{7} b^{7} a^{3} B + 588 x^{10} e^{2} d^{6} b^{6} a^{4} B + \frac{7056}{5} x^{10} e^{3} d^{5} b^{5} a^{5} B + 1470 x^{10} e^{4} d^{4} b^{4} a^{6} B + 672 x^{10} e^{5} d^{3} b^{3} a^{7} B + 126 x^{10} e^{6} d^{2} b^{2} a^{8} B + 8 x^{10} e^{7} d b a^{9} B + \frac{1}{10} x^{10} e^{8} a^{10} B + x^{10} d^{8} b^{9} a A + 36 x^{10} e d^{7} b^{8} a^{2} A + 336 x^{10} e^{2} d^{6} b^{7} a^{3} A + 1176 x^{10} e^{3} d^{5} b^{6} a^{4} A + 1764 x^{10} e^{4} d^{4} b^{5} a^{5} A + 1176 x^{10} e^{5} d^{3} b^{4} a^{6} A + 336 x^{10} e^{6} d^{2} b^{3} a^{7} A + 36 x^{10} e^{7} d b^{2} a^{8} A + x^{10} e^{8} b a^{9} A + \frac{40}{3} x^{9} d^{8} b^{7} a^{3} B + \frac{560}{3} x^{9} e d^{7} b^{6} a^{4} B + 784 x^{9} e^{2} d^{6} b^{5} a^{5} B + \frac{3920}{3} x^{9} e^{3} d^{5} b^{4} a^{6} B + \frac{2800}{3} x^{9} e^{4} d^{4} b^{3} a^{7} B + 280 x^{9} e^{5} d^{3} b^{2} a^{8} B + \frac{280}{9} x^{9} e^{6} d^{2} b a^{9} B + \frac{8}{9} x^{9} e^{7} d a^{10} B + 5 x^{9} d^{8} b^{8} a^{2} A + \frac{320}{3} x^{9} e d^{7} b^{7} a^{3} A + \frac{1960}{3} x^{9} e^{2} d^{6} b^{6} a^{4} A + 1568 x^{9} e^{3} d^{5} b^{5} a^{5} A + \frac{4900}{3} x^{9} e^{4} d^{4} b^{4} a^{6} A + \frac{2240}{3} x^{9} e^{5} d^{3} b^{3} a^{7} A + 140 x^{9} e^{6} d^{2} b^{2} a^{8} A + \frac{80}{9} x^{9} e^{7} d b a^{9} A + \frac{1}{9} x^{9} e^{8} a^{10} A + \frac{105}{4} x^{8} d^{8} b^{6} a^{4} B + 252 x^{8} e d^{7} b^{5} a^{5} B + 735 x^{8} e^{2} d^{6} b^{4} a^{6} B + 840 x^{8} e^{3} d^{5} b^{3} a^{7} B + \frac{1575}{4} x^{8} e^{4} d^{4} b^{2} a^{8} B + 70 x^{8} e^{5} d^{3} b a^{9} B + \frac{7}{2} x^{8} e^{6} d^{2} a^{10} B + 15 x^{8} d^{8} b^{7} a^{3} A + 210 x^{8} e d^{7} b^{6} a^{4} A + 882 x^{8} e^{2} d^{6} b^{5} a^{5} A + 1470 x^{8} e^{3} d^{5} b^{4} a^{6} A + 1050 x^{8} e^{4} d^{4} b^{3} a^{7} A + 315 x^{8} e^{5} d^{3} b^{2} a^{8} A + 35 x^{8} e^{6} d^{2} b a^{9} A + x^{8} e^{7} d a^{10} A + 36 x^{7} d^{8} b^{5} a^{5} B + 240 x^{7} e d^{7} b^{4} a^{6} B + 480 x^{7} e^{2} d^{6} b^{3} a^{7} B + 360 x^{7} e^{3} d^{5} b^{2} a^{8} B + 100 x^{7} e^{4} d^{4} b a^{9} B + 8 x^{7} e^{5} d^{3} a^{10} B + 30 x^{7} d^{8} b^{6} a^{4} A + 288 x^{7} e d^{7} b^{5} a^{5} A + 840 x^{7} e^{2} d^{6} b^{4} a^{6} A + 960 x^{7} e^{3} d^{5} b^{3} a^{7} A + 450 x^{7} e^{4} d^{4} b^{2} a^{8} A + 80 x^{7} e^{5} d^{3} b a^{9} A + 4 x^{7} e^{6} d^{2} a^{10} A + 35 x^{6} d^{8} b^{4} a^{6} B + 160 x^{6} e d^{7} b^{3} a^{7} B + 210 x^{6} e^{2} d^{6} b^{2} a^{8} B + \frac{280}{3} x^{6} e^{3} d^{5} b a^{9} B + \frac{35}{3} x^{6} e^{4} d^{4} a^{10} B + 42 x^{6} d^{8} b^{5} a^{5} A + 280 x^{6} e d^{7} b^{4} a^{6} A + 560 x^{6} e^{2} d^{6} b^{3} a^{7} A + 420 x^{6} e^{3} d^{5} b^{2} a^{8} A + \frac{350}{3} x^{6} e^{4} d^{4} b a^{9} A + \frac{28}{3} x^{6} e^{5} d^{3} a^{10} A + 24 x^{5} d^{8} b^{3} a^{7} B + 72 x^{5} e d^{7} b^{2} a^{8} B + 56 x^{5} e^{2} d^{6} b a^{9} B + \frac{56}{5} x^{5} e^{3} d^{5} a^{10} B + 42 x^{5} d^{8} b^{4} a^{6} A + 192 x^{5} e d^{7} b^{3} a^{7} A + 252 x^{5} e^{2} d^{6} b^{2} a^{8} A + 112 x^{5} e^{3} d^{5} b a^{9} A + 14 x^{5} e^{4} d^{4} a^{10} A + \frac{45}{4} x^{4} d^{8} b^{2} a^{8} B + 20 x^{4} e d^{7} b a^{9} B + 7 x^{4} e^{2} d^{6} a^{10} B + 30 x^{4} d^{8} b^{3} a^{7} A + 90 x^{4} e d^{7} b^{2} a^{8} A + 70 x^{4} e^{2} d^{6} b a^{9} A + 14 x^{4} e^{3} d^{5} a^{10} A + \frac{10}{3} x^{3} d^{8} b a^{9} B + \frac{8}{3} x^{3} e d^{7} a^{10} B + 15 x^{3} d^{8} b^{2} a^{8} A + \frac{80}{3} x^{3} e d^{7} b a^{9} A + \frac{28}{3} x^{3} e^{2} d^{6} a^{10} A + \frac{1}{2} x^{2} d^{8} a^{10} B + 5 x^{2} d^{8} b a^{9} A + 4 x^{2} e d^{7} a^{10} A + x d^{8} a^{10} A"," ",0,"1/20*x^20*e^8*b^10*B + 8/19*x^19*e^7*d*b^10*B + 10/19*x^19*e^8*b^9*a*B + 1/19*x^19*e^8*b^10*A + 14/9*x^18*e^6*d^2*b^10*B + 40/9*x^18*e^7*d*b^9*a*B + 5/2*x^18*e^8*b^8*a^2*B + 4/9*x^18*e^7*d*b^10*A + 5/9*x^18*e^8*b^9*a*A + 56/17*x^17*e^5*d^3*b^10*B + 280/17*x^17*e^6*d^2*b^9*a*B + 360/17*x^17*e^7*d*b^8*a^2*B + 120/17*x^17*e^8*b^7*a^3*B + 28/17*x^17*e^6*d^2*b^10*A + 80/17*x^17*e^7*d*b^9*a*A + 45/17*x^17*e^8*b^8*a^2*A + 35/8*x^16*e^4*d^4*b^10*B + 35*x^16*e^5*d^3*b^9*a*B + 315/4*x^16*e^6*d^2*b^8*a^2*B + 60*x^16*e^7*d*b^7*a^3*B + 105/8*x^16*e^8*b^6*a^4*B + 7/2*x^16*e^5*d^3*b^10*A + 35/2*x^16*e^6*d^2*b^9*a*A + 45/2*x^16*e^7*d*b^8*a^2*A + 15/2*x^16*e^8*b^7*a^3*A + 56/15*x^15*e^3*d^5*b^10*B + 140/3*x^15*e^4*d^4*b^9*a*B + 168*x^15*e^5*d^3*b^8*a^2*B + 224*x^15*e^6*d^2*b^7*a^3*B + 112*x^15*e^7*d*b^6*a^4*B + 84/5*x^15*e^8*b^5*a^5*B + 14/3*x^15*e^4*d^4*b^10*A + 112/3*x^15*e^5*d^3*b^9*a*A + 84*x^15*e^6*d^2*b^8*a^2*A + 64*x^15*e^7*d*b^7*a^3*A + 14*x^15*e^8*b^6*a^4*A + 2*x^14*e^2*d^6*b^10*B + 40*x^14*e^3*d^5*b^9*a*B + 225*x^14*e^4*d^4*b^8*a^2*B + 480*x^14*e^5*d^3*b^7*a^3*B + 420*x^14*e^6*d^2*b^6*a^4*B + 144*x^14*e^7*d*b^5*a^5*B + 15*x^14*e^8*b^4*a^6*B + 4*x^14*e^3*d^5*b^10*A + 50*x^14*e^4*d^4*b^9*a*A + 180*x^14*e^5*d^3*b^8*a^2*A + 240*x^14*e^6*d^2*b^7*a^3*A + 120*x^14*e^7*d*b^6*a^4*A + 18*x^14*e^8*b^5*a^5*A + 8/13*x^13*e*d^7*b^10*B + 280/13*x^13*e^2*d^6*b^9*a*B + 2520/13*x^13*e^3*d^5*b^8*a^2*B + 8400/13*x^13*e^4*d^4*b^7*a^3*B + 11760/13*x^13*e^5*d^3*b^6*a^4*B + 7056/13*x^13*e^6*d^2*b^5*a^5*B + 1680/13*x^13*e^7*d*b^4*a^6*B + 120/13*x^13*e^8*b^3*a^7*B + 28/13*x^13*e^2*d^6*b^10*A + 560/13*x^13*e^3*d^5*b^9*a*A + 3150/13*x^13*e^4*d^4*b^8*a^2*A + 6720/13*x^13*e^5*d^3*b^7*a^3*A + 5880/13*x^13*e^6*d^2*b^6*a^4*A + 2016/13*x^13*e^7*d*b^5*a^5*A + 210/13*x^13*e^8*b^4*a^6*A + 1/12*x^12*d^8*b^10*B + 20/3*x^12*e*d^7*b^9*a*B + 105*x^12*e^2*d^6*b^8*a^2*B + 560*x^12*e^3*d^5*b^7*a^3*B + 1225*x^12*e^4*d^4*b^6*a^4*B + 1176*x^12*e^5*d^3*b^5*a^5*B + 490*x^12*e^6*d^2*b^4*a^6*B + 80*x^12*e^7*d*b^3*a^7*B + 15/4*x^12*e^8*b^2*a^8*B + 2/3*x^12*e*d^7*b^10*A + 70/3*x^12*e^2*d^6*b^9*a*A + 210*x^12*e^3*d^5*b^8*a^2*A + 700*x^12*e^4*d^4*b^7*a^3*A + 980*x^12*e^5*d^3*b^6*a^4*A + 588*x^12*e^6*d^2*b^5*a^5*A + 140*x^12*e^7*d*b^4*a^6*A + 10*x^12*e^8*b^3*a^7*A + 10/11*x^11*d^8*b^9*a*B + 360/11*x^11*e*d^7*b^8*a^2*B + 3360/11*x^11*e^2*d^6*b^7*a^3*B + 11760/11*x^11*e^3*d^5*b^6*a^4*B + 17640/11*x^11*e^4*d^4*b^5*a^5*B + 11760/11*x^11*e^5*d^3*b^4*a^6*B + 3360/11*x^11*e^6*d^2*b^3*a^7*B + 360/11*x^11*e^7*d*b^2*a^8*B + 10/11*x^11*e^8*b*a^9*B + 1/11*x^11*d^8*b^10*A + 80/11*x^11*e*d^7*b^9*a*A + 1260/11*x^11*e^2*d^6*b^8*a^2*A + 6720/11*x^11*e^3*d^5*b^7*a^3*A + 14700/11*x^11*e^4*d^4*b^6*a^4*A + 14112/11*x^11*e^5*d^3*b^5*a^5*A + 5880/11*x^11*e^6*d^2*b^4*a^6*A + 960/11*x^11*e^7*d*b^3*a^7*A + 45/11*x^11*e^8*b^2*a^8*A + 9/2*x^10*d^8*b^8*a^2*B + 96*x^10*e*d^7*b^7*a^3*B + 588*x^10*e^2*d^6*b^6*a^4*B + 7056/5*x^10*e^3*d^5*b^5*a^5*B + 1470*x^10*e^4*d^4*b^4*a^6*B + 672*x^10*e^5*d^3*b^3*a^7*B + 126*x^10*e^6*d^2*b^2*a^8*B + 8*x^10*e^7*d*b*a^9*B + 1/10*x^10*e^8*a^10*B + x^10*d^8*b^9*a*A + 36*x^10*e*d^7*b^8*a^2*A + 336*x^10*e^2*d^6*b^7*a^3*A + 1176*x^10*e^3*d^5*b^6*a^4*A + 1764*x^10*e^4*d^4*b^5*a^5*A + 1176*x^10*e^5*d^3*b^4*a^6*A + 336*x^10*e^6*d^2*b^3*a^7*A + 36*x^10*e^7*d*b^2*a^8*A + x^10*e^8*b*a^9*A + 40/3*x^9*d^8*b^7*a^3*B + 560/3*x^9*e*d^7*b^6*a^4*B + 784*x^9*e^2*d^6*b^5*a^5*B + 3920/3*x^9*e^3*d^5*b^4*a^6*B + 2800/3*x^9*e^4*d^4*b^3*a^7*B + 280*x^9*e^5*d^3*b^2*a^8*B + 280/9*x^9*e^6*d^2*b*a^9*B + 8/9*x^9*e^7*d*a^10*B + 5*x^9*d^8*b^8*a^2*A + 320/3*x^9*e*d^7*b^7*a^3*A + 1960/3*x^9*e^2*d^6*b^6*a^4*A + 1568*x^9*e^3*d^5*b^5*a^5*A + 4900/3*x^9*e^4*d^4*b^4*a^6*A + 2240/3*x^9*e^5*d^3*b^3*a^7*A + 140*x^9*e^6*d^2*b^2*a^8*A + 80/9*x^9*e^7*d*b*a^9*A + 1/9*x^9*e^8*a^10*A + 105/4*x^8*d^8*b^6*a^4*B + 252*x^8*e*d^7*b^5*a^5*B + 735*x^8*e^2*d^6*b^4*a^6*B + 840*x^8*e^3*d^5*b^3*a^7*B + 1575/4*x^8*e^4*d^4*b^2*a^8*B + 70*x^8*e^5*d^3*b*a^9*B + 7/2*x^8*e^6*d^2*a^10*B + 15*x^8*d^8*b^7*a^3*A + 210*x^8*e*d^7*b^6*a^4*A + 882*x^8*e^2*d^6*b^5*a^5*A + 1470*x^8*e^3*d^5*b^4*a^6*A + 1050*x^8*e^4*d^4*b^3*a^7*A + 315*x^8*e^5*d^3*b^2*a^8*A + 35*x^8*e^6*d^2*b*a^9*A + x^8*e^7*d*a^10*A + 36*x^7*d^8*b^5*a^5*B + 240*x^7*e*d^7*b^4*a^6*B + 480*x^7*e^2*d^6*b^3*a^7*B + 360*x^7*e^3*d^5*b^2*a^8*B + 100*x^7*e^4*d^4*b*a^9*B + 8*x^7*e^5*d^3*a^10*B + 30*x^7*d^8*b^6*a^4*A + 288*x^7*e*d^7*b^5*a^5*A + 840*x^7*e^2*d^6*b^4*a^6*A + 960*x^7*e^3*d^5*b^3*a^7*A + 450*x^7*e^4*d^4*b^2*a^8*A + 80*x^7*e^5*d^3*b*a^9*A + 4*x^7*e^6*d^2*a^10*A + 35*x^6*d^8*b^4*a^6*B + 160*x^6*e*d^7*b^3*a^7*B + 210*x^6*e^2*d^6*b^2*a^8*B + 280/3*x^6*e^3*d^5*b*a^9*B + 35/3*x^6*e^4*d^4*a^10*B + 42*x^6*d^8*b^5*a^5*A + 280*x^6*e*d^7*b^4*a^6*A + 560*x^6*e^2*d^6*b^3*a^7*A + 420*x^6*e^3*d^5*b^2*a^8*A + 350/3*x^6*e^4*d^4*b*a^9*A + 28/3*x^6*e^5*d^3*a^10*A + 24*x^5*d^8*b^3*a^7*B + 72*x^5*e*d^7*b^2*a^8*B + 56*x^5*e^2*d^6*b*a^9*B + 56/5*x^5*e^3*d^5*a^10*B + 42*x^5*d^8*b^4*a^6*A + 192*x^5*e*d^7*b^3*a^7*A + 252*x^5*e^2*d^6*b^2*a^8*A + 112*x^5*e^3*d^5*b*a^9*A + 14*x^5*e^4*d^4*a^10*A + 45/4*x^4*d^8*b^2*a^8*B + 20*x^4*e*d^7*b*a^9*B + 7*x^4*e^2*d^6*a^10*B + 30*x^4*d^8*b^3*a^7*A + 90*x^4*e*d^7*b^2*a^8*A + 70*x^4*e^2*d^6*b*a^9*A + 14*x^4*e^3*d^5*a^10*A + 10/3*x^3*d^8*b*a^9*B + 8/3*x^3*e*d^7*a^10*B + 15*x^3*d^8*b^2*a^8*A + 80/3*x^3*e*d^7*b*a^9*A + 28/3*x^3*e^2*d^6*a^10*A + 1/2*x^2*d^8*a^10*B + 5*x^2*d^8*b*a^9*A + 4*x^2*e*d^7*a^10*A + x*d^8*a^10*A","B",0
1081,1,2783,0,0.963743," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^7,x, algorithm=""fricas"")","\frac{1}{19} x^{19} e^{7} b^{10} B + \frac{7}{18} x^{18} e^{6} d b^{10} B + \frac{5}{9} x^{18} e^{7} b^{9} a B + \frac{1}{18} x^{18} e^{7} b^{10} A + \frac{21}{17} x^{17} e^{5} d^{2} b^{10} B + \frac{70}{17} x^{17} e^{6} d b^{9} a B + \frac{45}{17} x^{17} e^{7} b^{8} a^{2} B + \frac{7}{17} x^{17} e^{6} d b^{10} A + \frac{10}{17} x^{17} e^{7} b^{9} a A + \frac{35}{16} x^{16} e^{4} d^{3} b^{10} B + \frac{105}{8} x^{16} e^{5} d^{2} b^{9} a B + \frac{315}{16} x^{16} e^{6} d b^{8} a^{2} B + \frac{15}{2} x^{16} e^{7} b^{7} a^{3} B + \frac{21}{16} x^{16} e^{5} d^{2} b^{10} A + \frac{35}{8} x^{16} e^{6} d b^{9} a A + \frac{45}{16} x^{16} e^{7} b^{8} a^{2} A + \frac{7}{3} x^{15} e^{3} d^{4} b^{10} B + \frac{70}{3} x^{15} e^{4} d^{3} b^{9} a B + 63 x^{15} e^{5} d^{2} b^{8} a^{2} B + 56 x^{15} e^{6} d b^{7} a^{3} B + 14 x^{15} e^{7} b^{6} a^{4} B + \frac{7}{3} x^{15} e^{4} d^{3} b^{10} A + 14 x^{15} e^{5} d^{2} b^{9} a A + 21 x^{15} e^{6} d b^{8} a^{2} A + 8 x^{15} e^{7} b^{7} a^{3} A + \frac{3}{2} x^{14} e^{2} d^{5} b^{10} B + 25 x^{14} e^{3} d^{4} b^{9} a B + \frac{225}{2} x^{14} e^{4} d^{3} b^{8} a^{2} B + 180 x^{14} e^{5} d^{2} b^{7} a^{3} B + 105 x^{14} e^{6} d b^{6} a^{4} B + 18 x^{14} e^{7} b^{5} a^{5} B + \frac{5}{2} x^{14} e^{3} d^{4} b^{10} A + 25 x^{14} e^{4} d^{3} b^{9} a A + \frac{135}{2} x^{14} e^{5} d^{2} b^{8} a^{2} A + 60 x^{14} e^{6} d b^{7} a^{3} A + 15 x^{14} e^{7} b^{6} a^{4} A + \frac{7}{13} x^{13} e d^{6} b^{10} B + \frac{210}{13} x^{13} e^{2} d^{5} b^{9} a B + \frac{1575}{13} x^{13} e^{3} d^{4} b^{8} a^{2} B + \frac{4200}{13} x^{13} e^{4} d^{3} b^{7} a^{3} B + \frac{4410}{13} x^{13} e^{5} d^{2} b^{6} a^{4} B + \frac{1764}{13} x^{13} e^{6} d b^{5} a^{5} B + \frac{210}{13} x^{13} e^{7} b^{4} a^{6} B + \frac{21}{13} x^{13} e^{2} d^{5} b^{10} A + \frac{350}{13} x^{13} e^{3} d^{4} b^{9} a A + \frac{1575}{13} x^{13} e^{4} d^{3} b^{8} a^{2} A + \frac{2520}{13} x^{13} e^{5} d^{2} b^{7} a^{3} A + \frac{1470}{13} x^{13} e^{6} d b^{6} a^{4} A + \frac{252}{13} x^{13} e^{7} b^{5} a^{5} A + \frac{1}{12} x^{12} d^{7} b^{10} B + \frac{35}{6} x^{12} e d^{6} b^{9} a B + \frac{315}{4} x^{12} e^{2} d^{5} b^{8} a^{2} B + 350 x^{12} e^{3} d^{4} b^{7} a^{3} B + \frac{1225}{2} x^{12} e^{4} d^{3} b^{6} a^{4} B + 441 x^{12} e^{5} d^{2} b^{5} a^{5} B + \frac{245}{2} x^{12} e^{6} d b^{4} a^{6} B + 10 x^{12} e^{7} b^{3} a^{7} B + \frac{7}{12} x^{12} e d^{6} b^{10} A + \frac{35}{2} x^{12} e^{2} d^{5} b^{9} a A + \frac{525}{4} x^{12} e^{3} d^{4} b^{8} a^{2} A + 350 x^{12} e^{4} d^{3} b^{7} a^{3} A + \frac{735}{2} x^{12} e^{5} d^{2} b^{6} a^{4} A + 147 x^{12} e^{6} d b^{5} a^{5} A + \frac{35}{2} x^{12} e^{7} b^{4} a^{6} A + \frac{10}{11} x^{11} d^{7} b^{9} a B + \frac{315}{11} x^{11} e d^{6} b^{8} a^{2} B + \frac{2520}{11} x^{11} e^{2} d^{5} b^{7} a^{3} B + \frac{7350}{11} x^{11} e^{3} d^{4} b^{6} a^{4} B + \frac{8820}{11} x^{11} e^{4} d^{3} b^{5} a^{5} B + \frac{4410}{11} x^{11} e^{5} d^{2} b^{4} a^{6} B + \frac{840}{11} x^{11} e^{6} d b^{3} a^{7} B + \frac{45}{11} x^{11} e^{7} b^{2} a^{8} B + \frac{1}{11} x^{11} d^{7} b^{10} A + \frac{70}{11} x^{11} e d^{6} b^{9} a A + \frac{945}{11} x^{11} e^{2} d^{5} b^{8} a^{2} A + \frac{4200}{11} x^{11} e^{3} d^{4} b^{7} a^{3} A + \frac{7350}{11} x^{11} e^{4} d^{3} b^{6} a^{4} A + \frac{5292}{11} x^{11} e^{5} d^{2} b^{5} a^{5} A + \frac{1470}{11} x^{11} e^{6} d b^{4} a^{6} A + \frac{120}{11} x^{11} e^{7} b^{3} a^{7} A + \frac{9}{2} x^{10} d^{7} b^{8} a^{2} B + 84 x^{10} e d^{6} b^{7} a^{3} B + 441 x^{10} e^{2} d^{5} b^{6} a^{4} B + 882 x^{10} e^{3} d^{4} b^{5} a^{5} B + 735 x^{10} e^{4} d^{3} b^{4} a^{6} B + 252 x^{10} e^{5} d^{2} b^{3} a^{7} B + \frac{63}{2} x^{10} e^{6} d b^{2} a^{8} B + x^{10} e^{7} b a^{9} B + x^{10} d^{7} b^{9} a A + \frac{63}{2} x^{10} e d^{6} b^{8} a^{2} A + 252 x^{10} e^{2} d^{5} b^{7} a^{3} A + 735 x^{10} e^{3} d^{4} b^{6} a^{4} A + 882 x^{10} e^{4} d^{3} b^{5} a^{5} A + 441 x^{10} e^{5} d^{2} b^{4} a^{6} A + 84 x^{10} e^{6} d b^{3} a^{7} A + \frac{9}{2} x^{10} e^{7} b^{2} a^{8} A + \frac{40}{3} x^{9} d^{7} b^{7} a^{3} B + \frac{490}{3} x^{9} e d^{6} b^{6} a^{4} B + 588 x^{9} e^{2} d^{5} b^{5} a^{5} B + \frac{2450}{3} x^{9} e^{3} d^{4} b^{4} a^{6} B + \frac{1400}{3} x^{9} e^{4} d^{3} b^{3} a^{7} B + 105 x^{9} e^{5} d^{2} b^{2} a^{8} B + \frac{70}{9} x^{9} e^{6} d b a^{9} B + \frac{1}{9} x^{9} e^{7} a^{10} B + 5 x^{9} d^{7} b^{8} a^{2} A + \frac{280}{3} x^{9} e d^{6} b^{7} a^{3} A + 490 x^{9} e^{2} d^{5} b^{6} a^{4} A + 980 x^{9} e^{3} d^{4} b^{5} a^{5} A + \frac{2450}{3} x^{9} e^{4} d^{3} b^{4} a^{6} A + 280 x^{9} e^{5} d^{2} b^{3} a^{7} A + 35 x^{9} e^{6} d b^{2} a^{8} A + \frac{10}{9} x^{9} e^{7} b a^{9} A + \frac{105}{4} x^{8} d^{7} b^{6} a^{4} B + \frac{441}{2} x^{8} e d^{6} b^{5} a^{5} B + \frac{2205}{4} x^{8} e^{2} d^{5} b^{4} a^{6} B + 525 x^{8} e^{3} d^{4} b^{3} a^{7} B + \frac{1575}{8} x^{8} e^{4} d^{3} b^{2} a^{8} B + \frac{105}{4} x^{8} e^{5} d^{2} b a^{9} B + \frac{7}{8} x^{8} e^{6} d a^{10} B + 15 x^{8} d^{7} b^{7} a^{3} A + \frac{735}{4} x^{8} e d^{6} b^{6} a^{4} A + \frac{1323}{2} x^{8} e^{2} d^{5} b^{5} a^{5} A + \frac{3675}{4} x^{8} e^{3} d^{4} b^{4} a^{6} A + 525 x^{8} e^{4} d^{3} b^{3} a^{7} A + \frac{945}{8} x^{8} e^{5} d^{2} b^{2} a^{8} A + \frac{35}{4} x^{8} e^{6} d b a^{9} A + \frac{1}{8} x^{8} e^{7} a^{10} A + 36 x^{7} d^{7} b^{5} a^{5} B + 210 x^{7} e d^{6} b^{4} a^{6} B + 360 x^{7} e^{2} d^{5} b^{3} a^{7} B + 225 x^{7} e^{3} d^{4} b^{2} a^{8} B + 50 x^{7} e^{4} d^{3} b a^{9} B + 3 x^{7} e^{5} d^{2} a^{10} B + 30 x^{7} d^{7} b^{6} a^{4} A + 252 x^{7} e d^{6} b^{5} a^{5} A + 630 x^{7} e^{2} d^{5} b^{4} a^{6} A + 600 x^{7} e^{3} d^{4} b^{3} a^{7} A + 225 x^{7} e^{4} d^{3} b^{2} a^{8} A + 30 x^{7} e^{5} d^{2} b a^{9} A + x^{7} e^{6} d a^{10} A + 35 x^{6} d^{7} b^{4} a^{6} B + 140 x^{6} e d^{6} b^{3} a^{7} B + \frac{315}{2} x^{6} e^{2} d^{5} b^{2} a^{8} B + \frac{175}{3} x^{6} e^{3} d^{4} b a^{9} B + \frac{35}{6} x^{6} e^{4} d^{3} a^{10} B + 42 x^{6} d^{7} b^{5} a^{5} A + 245 x^{6} e d^{6} b^{4} a^{6} A + 420 x^{6} e^{2} d^{5} b^{3} a^{7} A + \frac{525}{2} x^{6} e^{3} d^{4} b^{2} a^{8} A + \frac{175}{3} x^{6} e^{4} d^{3} b a^{9} A + \frac{7}{2} x^{6} e^{5} d^{2} a^{10} A + 24 x^{5} d^{7} b^{3} a^{7} B + 63 x^{5} e d^{6} b^{2} a^{8} B + 42 x^{5} e^{2} d^{5} b a^{9} B + 7 x^{5} e^{3} d^{4} a^{10} B + 42 x^{5} d^{7} b^{4} a^{6} A + 168 x^{5} e d^{6} b^{3} a^{7} A + 189 x^{5} e^{2} d^{5} b^{2} a^{8} A + 70 x^{5} e^{3} d^{4} b a^{9} A + 7 x^{5} e^{4} d^{3} a^{10} A + \frac{45}{4} x^{4} d^{7} b^{2} a^{8} B + \frac{35}{2} x^{4} e d^{6} b a^{9} B + \frac{21}{4} x^{4} e^{2} d^{5} a^{10} B + 30 x^{4} d^{7} b^{3} a^{7} A + \frac{315}{4} x^{4} e d^{6} b^{2} a^{8} A + \frac{105}{2} x^{4} e^{2} d^{5} b a^{9} A + \frac{35}{4} x^{4} e^{3} d^{4} a^{10} A + \frac{10}{3} x^{3} d^{7} b a^{9} B + \frac{7}{3} x^{3} e d^{6} a^{10} B + 15 x^{3} d^{7} b^{2} a^{8} A + \frac{70}{3} x^{3} e d^{6} b a^{9} A + 7 x^{3} e^{2} d^{5} a^{10} A + \frac{1}{2} x^{2} d^{7} a^{10} B + 5 x^{2} d^{7} b a^{9} A + \frac{7}{2} x^{2} e d^{6} a^{10} A + x d^{7} a^{10} A"," ",0,"1/19*x^19*e^7*b^10*B + 7/18*x^18*e^6*d*b^10*B + 5/9*x^18*e^7*b^9*a*B + 1/18*x^18*e^7*b^10*A + 21/17*x^17*e^5*d^2*b^10*B + 70/17*x^17*e^6*d*b^9*a*B + 45/17*x^17*e^7*b^8*a^2*B + 7/17*x^17*e^6*d*b^10*A + 10/17*x^17*e^7*b^9*a*A + 35/16*x^16*e^4*d^3*b^10*B + 105/8*x^16*e^5*d^2*b^9*a*B + 315/16*x^16*e^6*d*b^8*a^2*B + 15/2*x^16*e^7*b^7*a^3*B + 21/16*x^16*e^5*d^2*b^10*A + 35/8*x^16*e^6*d*b^9*a*A + 45/16*x^16*e^7*b^8*a^2*A + 7/3*x^15*e^3*d^4*b^10*B + 70/3*x^15*e^4*d^3*b^9*a*B + 63*x^15*e^5*d^2*b^8*a^2*B + 56*x^15*e^6*d*b^7*a^3*B + 14*x^15*e^7*b^6*a^4*B + 7/3*x^15*e^4*d^3*b^10*A + 14*x^15*e^5*d^2*b^9*a*A + 21*x^15*e^6*d*b^8*a^2*A + 8*x^15*e^7*b^7*a^3*A + 3/2*x^14*e^2*d^5*b^10*B + 25*x^14*e^3*d^4*b^9*a*B + 225/2*x^14*e^4*d^3*b^8*a^2*B + 180*x^14*e^5*d^2*b^7*a^3*B + 105*x^14*e^6*d*b^6*a^4*B + 18*x^14*e^7*b^5*a^5*B + 5/2*x^14*e^3*d^4*b^10*A + 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2520/11*x^11*e^2*d^5*b^7*a^3*B + 7350/11*x^11*e^3*d^4*b^6*a^4*B + 8820/11*x^11*e^4*d^3*b^5*a^5*B + 4410/11*x^11*e^5*d^2*b^4*a^6*B + 840/11*x^11*e^6*d*b^3*a^7*B + 45/11*x^11*e^7*b^2*a^8*B + 1/11*x^11*d^7*b^10*A + 70/11*x^11*e*d^6*b^9*a*A + 945/11*x^11*e^2*d^5*b^8*a^2*A + 4200/11*x^11*e^3*d^4*b^7*a^3*A + 7350/11*x^11*e^4*d^3*b^6*a^4*A + 5292/11*x^11*e^5*d^2*b^5*a^5*A + 1470/11*x^11*e^6*d*b^4*a^6*A + 120/11*x^11*e^7*b^3*a^7*A + 9/2*x^10*d^7*b^8*a^2*B + 84*x^10*e*d^6*b^7*a^3*B + 441*x^10*e^2*d^5*b^6*a^4*B + 882*x^10*e^3*d^4*b^5*a^5*B + 735*x^10*e^4*d^3*b^4*a^6*B + 252*x^10*e^5*d^2*b^3*a^7*B + 63/2*x^10*e^6*d*b^2*a^8*B + x^10*e^7*b*a^9*B + x^10*d^7*b^9*a*A + 63/2*x^10*e*d^6*b^8*a^2*A + 252*x^10*e^2*d^5*b^7*a^3*A + 735*x^10*e^3*d^4*b^6*a^4*A + 882*x^10*e^4*d^3*b^5*a^5*A + 441*x^10*e^5*d^2*b^4*a^6*A + 84*x^10*e^6*d*b^3*a^7*A + 9/2*x^10*e^7*b^2*a^8*A + 40/3*x^9*d^7*b^7*a^3*B + 490/3*x^9*e*d^6*b^6*a^4*B + 588*x^9*e^2*d^5*b^5*a^5*B + 2450/3*x^9*e^3*d^4*b^4*a^6*B + 1400/3*x^9*e^4*d^3*b^3*a^7*B + 105*x^9*e^5*d^2*b^2*a^8*B + 70/9*x^9*e^6*d*b*a^9*B + 1/9*x^9*e^7*a^10*B + 5*x^9*d^7*b^8*a^2*A + 280/3*x^9*e*d^6*b^7*a^3*A + 490*x^9*e^2*d^5*b^6*a^4*A + 980*x^9*e^3*d^4*b^5*a^5*A + 2450/3*x^9*e^4*d^3*b^4*a^6*A + 280*x^9*e^5*d^2*b^3*a^7*A + 35*x^9*e^6*d*b^2*a^8*A + 10/9*x^9*e^7*b*a^9*A + 105/4*x^8*d^7*b^6*a^4*B + 441/2*x^8*e*d^6*b^5*a^5*B + 2205/4*x^8*e^2*d^5*b^4*a^6*B + 525*x^8*e^3*d^4*b^3*a^7*B + 1575/8*x^8*e^4*d^3*b^2*a^8*B + 105/4*x^8*e^5*d^2*b*a^9*B + 7/8*x^8*e^6*d*a^10*B + 15*x^8*d^7*b^7*a^3*A + 735/4*x^8*e*d^6*b^6*a^4*A + 1323/2*x^8*e^2*d^5*b^5*a^5*A + 3675/4*x^8*e^3*d^4*b^4*a^6*A + 525*x^8*e^4*d^3*b^3*a^7*A + 945/8*x^8*e^5*d^2*b^2*a^8*A + 35/4*x^8*e^6*d*b*a^9*A + 1/8*x^8*e^7*a^10*A + 36*x^7*d^7*b^5*a^5*B + 210*x^7*e*d^6*b^4*a^6*B + 360*x^7*e^2*d^5*b^3*a^7*B + 225*x^7*e^3*d^4*b^2*a^8*B + 50*x^7*e^4*d^3*b*a^9*B + 3*x^7*e^5*d^2*a^10*B + 30*x^7*d^7*b^6*a^4*A + 252*x^7*e*d^6*b^5*a^5*A + 630*x^7*e^2*d^5*b^4*a^6*A + 600*x^7*e^3*d^4*b^3*a^7*A + 225*x^7*e^4*d^3*b^2*a^8*A + 30*x^7*e^5*d^2*b*a^9*A + x^7*e^6*d*a^10*A + 35*x^6*d^7*b^4*a^6*B + 140*x^6*e*d^6*b^3*a^7*B + 315/2*x^6*e^2*d^5*b^2*a^8*B + 175/3*x^6*e^3*d^4*b*a^9*B + 35/6*x^6*e^4*d^3*a^10*B + 42*x^6*d^7*b^5*a^5*A + 245*x^6*e*d^6*b^4*a^6*A + 420*x^6*e^2*d^5*b^3*a^7*A + 525/2*x^6*e^3*d^4*b^2*a^8*A + 175/3*x^6*e^4*d^3*b*a^9*A + 7/2*x^6*e^5*d^2*a^10*A + 24*x^5*d^7*b^3*a^7*B + 63*x^5*e*d^6*b^2*a^8*B + 42*x^5*e^2*d^5*b*a^9*B + 7*x^5*e^3*d^4*a^10*B + 42*x^5*d^7*b^4*a^6*A + 168*x^5*e*d^6*b^3*a^7*A + 189*x^5*e^2*d^5*b^2*a^8*A + 70*x^5*e^3*d^4*b*a^9*A + 7*x^5*e^4*d^3*a^10*A + 45/4*x^4*d^7*b^2*a^8*B + 35/2*x^4*e*d^6*b*a^9*B + 21/4*x^4*e^2*d^5*a^10*B + 30*x^4*d^7*b^3*a^7*A + 315/4*x^4*e*d^6*b^2*a^8*A + 105/2*x^4*e^2*d^5*b*a^9*A + 35/4*x^4*e^3*d^4*a^10*A + 10/3*x^3*d^7*b*a^9*B + 7/3*x^3*e*d^6*a^10*B + 15*x^3*d^7*b^2*a^8*A + 70/3*x^3*e*d^6*b*a^9*A + 7*x^3*e^2*d^5*a^10*A + 1/2*x^2*d^7*a^10*B + 5*x^2*d^7*b*a^9*A + 7/2*x^2*e*d^6*a^10*A + x*d^7*a^10*A","B",0
1082,1,2407,0,1.079406," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^6,x, algorithm=""fricas"")","\frac{1}{18} x^{18} e^{6} b^{10} B + \frac{6}{17} x^{17} e^{5} d b^{10} B + \frac{10}{17} x^{17} e^{6} b^{9} a B + \frac{1}{17} x^{17} e^{6} b^{10} A + \frac{15}{16} x^{16} e^{4} d^{2} b^{10} B + \frac{15}{4} x^{16} e^{5} d b^{9} a B + \frac{45}{16} x^{16} e^{6} b^{8} a^{2} B + \frac{3}{8} x^{16} e^{5} d b^{10} A + \frac{5}{8} x^{16} e^{6} b^{9} a A + \frac{4}{3} x^{15} e^{3} d^{3} b^{10} B + 10 x^{15} e^{4} d^{2} b^{9} a B + 18 x^{15} e^{5} d b^{8} a^{2} B + 8 x^{15} e^{6} b^{7} a^{3} B + x^{15} e^{4} d^{2} b^{10} A + 4 x^{15} e^{5} d b^{9} a A + 3 x^{15} e^{6} b^{8} a^{2} A + \frac{15}{14} x^{14} e^{2} d^{4} b^{10} B + \frac{100}{7} x^{14} e^{3} d^{3} b^{9} a B + \frac{675}{14} x^{14} e^{4} d^{2} b^{8} a^{2} B + \frac{360}{7} x^{14} e^{5} d b^{7} a^{3} B + 15 x^{14} e^{6} b^{6} a^{4} B + \frac{10}{7} x^{14} e^{3} d^{3} b^{10} A + \frac{75}{7} x^{14} e^{4} d^{2} b^{9} a A + \frac{135}{7} x^{14} e^{5} d b^{8} a^{2} A + \frac{60}{7} x^{14} e^{6} b^{7} a^{3} A + \frac{6}{13} x^{13} e d^{5} b^{10} B + \frac{150}{13} x^{13} e^{2} d^{4} b^{9} a B + \frac{900}{13} x^{13} e^{3} d^{3} b^{8} a^{2} B + \frac{1800}{13} x^{13} e^{4} d^{2} b^{7} a^{3} B + \frac{1260}{13} x^{13} e^{5} d b^{6} a^{4} B + \frac{252}{13} x^{13} e^{6} b^{5} a^{5} B + \frac{15}{13} x^{13} e^{2} d^{4} b^{10} A + \frac{200}{13} x^{13} e^{3} d^{3} b^{9} a A + \frac{675}{13} x^{13} e^{4} d^{2} b^{8} a^{2} A + \frac{720}{13} x^{13} e^{5} d b^{7} a^{3} A + \frac{210}{13} x^{13} e^{6} b^{6} a^{4} A + \frac{1}{12} x^{12} d^{6} b^{10} B + 5 x^{12} e d^{5} b^{9} a B + \frac{225}{4} x^{12} e^{2} d^{4} b^{8} a^{2} B + 200 x^{12} e^{3} d^{3} b^{7} a^{3} B + \frac{525}{2} x^{12} e^{4} d^{2} b^{6} a^{4} B + 126 x^{12} e^{5} d b^{5} a^{5} B + \frac{35}{2} x^{12} e^{6} b^{4} a^{6} B + \frac{1}{2} x^{12} e d^{5} b^{10} A + \frac{25}{2} x^{12} e^{2} d^{4} b^{9} a A + 75 x^{12} e^{3} d^{3} b^{8} a^{2} A + 150 x^{12} e^{4} d^{2} b^{7} a^{3} A + 105 x^{12} e^{5} d b^{6} a^{4} A + 21 x^{12} e^{6} b^{5} a^{5} A + \frac{10}{11} x^{11} d^{6} b^{9} a B + \frac{270}{11} x^{11} e d^{5} b^{8} a^{2} B + \frac{1800}{11} x^{11} e^{2} d^{4} b^{7} a^{3} B + \frac{4200}{11} x^{11} e^{3} d^{3} b^{6} a^{4} B + \frac{3780}{11} x^{11} e^{4} d^{2} b^{5} a^{5} B + \frac{1260}{11} x^{11} e^{5} d b^{4} a^{6} B + \frac{120}{11} x^{11} e^{6} b^{3} a^{7} B + \frac{1}{11} x^{11} d^{6} b^{10} A + \frac{60}{11} x^{11} e d^{5} b^{9} a A + \frac{675}{11} x^{11} e^{2} d^{4} b^{8} a^{2} A + \frac{2400}{11} x^{11} e^{3} d^{3} b^{7} a^{3} A + \frac{3150}{11} x^{11} e^{4} d^{2} b^{6} a^{4} A + \frac{1512}{11} x^{11} e^{5} d b^{5} a^{5} A + \frac{210}{11} x^{11} e^{6} b^{4} a^{6} A + \frac{9}{2} x^{10} d^{6} b^{8} a^{2} B + 72 x^{10} e d^{5} b^{7} a^{3} B + 315 x^{10} e^{2} d^{4} b^{6} a^{4} B + 504 x^{10} e^{3} d^{3} b^{5} a^{5} B + 315 x^{10} e^{4} d^{2} b^{4} a^{6} B + 72 x^{10} e^{5} d b^{3} a^{7} B + \frac{9}{2} x^{10} e^{6} b^{2} a^{8} B + x^{10} d^{6} b^{9} a A + 27 x^{10} e d^{5} b^{8} a^{2} A + 180 x^{10} e^{2} d^{4} b^{7} a^{3} A + 420 x^{10} e^{3} d^{3} b^{6} a^{4} A + 378 x^{10} e^{4} d^{2} b^{5} a^{5} A + 126 x^{10} e^{5} d b^{4} a^{6} A + 12 x^{10} e^{6} b^{3} a^{7} A + \frac{40}{3} x^{9} d^{6} b^{7} a^{3} B + 140 x^{9} e d^{5} b^{6} a^{4} B + 420 x^{9} e^{2} d^{4} b^{5} a^{5} B + \frac{1400}{3} x^{9} e^{3} d^{3} b^{4} a^{6} B + 200 x^{9} e^{4} d^{2} b^{3} a^{7} B + 30 x^{9} e^{5} d b^{2} a^{8} B + \frac{10}{9} x^{9} e^{6} b a^{9} B + 5 x^{9} d^{6} b^{8} a^{2} A + 80 x^{9} e d^{5} b^{7} a^{3} A + 350 x^{9} e^{2} d^{4} b^{6} a^{4} A + 560 x^{9} e^{3} d^{3} b^{5} a^{5} A + 350 x^{9} e^{4} d^{2} b^{4} a^{6} A + 80 x^{9} e^{5} d b^{3} a^{7} A + 5 x^{9} e^{6} b^{2} a^{8} A + \frac{105}{4} x^{8} d^{6} b^{6} a^{4} B + 189 x^{8} e d^{5} b^{5} a^{5} B + \frac{1575}{4} x^{8} e^{2} d^{4} b^{4} a^{6} B + 300 x^{8} e^{3} d^{3} b^{3} a^{7} B + \frac{675}{8} x^{8} e^{4} d^{2} b^{2} a^{8} B + \frac{15}{2} x^{8} e^{5} d b a^{9} B + \frac{1}{8} x^{8} e^{6} a^{10} B + 15 x^{8} d^{6} b^{7} a^{3} A + \frac{315}{2} x^{8} e d^{5} b^{6} a^{4} A + \frac{945}{2} x^{8} e^{2} d^{4} b^{5} a^{5} A + 525 x^{8} e^{3} d^{3} b^{4} a^{6} A + 225 x^{8} e^{4} d^{2} b^{3} a^{7} A + \frac{135}{4} x^{8} e^{5} d b^{2} a^{8} A + \frac{5}{4} x^{8} e^{6} b a^{9} A + 36 x^{7} d^{6} b^{5} a^{5} B + 180 x^{7} e d^{5} b^{4} a^{6} B + \frac{1800}{7} x^{7} e^{2} d^{4} b^{3} a^{7} B + \frac{900}{7} x^{7} e^{3} d^{3} b^{2} a^{8} B + \frac{150}{7} x^{7} e^{4} d^{2} b a^{9} B + \frac{6}{7} x^{7} e^{5} d a^{10} B + 30 x^{7} d^{6} b^{6} a^{4} A + 216 x^{7} e d^{5} b^{5} a^{5} A + 450 x^{7} e^{2} d^{4} b^{4} a^{6} A + \frac{2400}{7} x^{7} e^{3} d^{3} b^{3} a^{7} A + \frac{675}{7} x^{7} e^{4} d^{2} b^{2} a^{8} A + \frac{60}{7} x^{7} e^{5} d b a^{9} A + \frac{1}{7} x^{7} e^{6} a^{10} A + 35 x^{6} d^{6} b^{4} a^{6} B + 120 x^{6} e d^{5} b^{3} a^{7} B + \frac{225}{2} x^{6} e^{2} d^{4} b^{2} a^{8} B + \frac{100}{3} x^{6} e^{3} d^{3} b a^{9} B + \frac{5}{2} x^{6} e^{4} d^{2} a^{10} B + 42 x^{6} d^{6} b^{5} a^{5} A + 210 x^{6} e d^{5} b^{4} a^{6} A + 300 x^{6} e^{2} d^{4} b^{3} a^{7} A + 150 x^{6} e^{3} d^{3} b^{2} a^{8} A + 25 x^{6} e^{4} d^{2} b a^{9} A + x^{6} e^{5} d a^{10} A + 24 x^{5} d^{6} b^{3} a^{7} B + 54 x^{5} e d^{5} b^{2} a^{8} B + 30 x^{5} e^{2} d^{4} b a^{9} B + 4 x^{5} e^{3} d^{3} a^{10} B + 42 x^{5} d^{6} b^{4} a^{6} A + 144 x^{5} e d^{5} b^{3} a^{7} A + 135 x^{5} e^{2} d^{4} b^{2} a^{8} A + 40 x^{5} e^{3} d^{3} b a^{9} A + 3 x^{5} e^{4} d^{2} a^{10} A + \frac{45}{4} x^{4} d^{6} b^{2} a^{8} B + 15 x^{4} e d^{5} b a^{9} B + \frac{15}{4} x^{4} e^{2} d^{4} a^{10} B + 30 x^{4} d^{6} b^{3} a^{7} A + \frac{135}{2} x^{4} e d^{5} b^{2} a^{8} A + \frac{75}{2} x^{4} e^{2} d^{4} b a^{9} A + 5 x^{4} e^{3} d^{3} a^{10} A + \frac{10}{3} x^{3} d^{6} b a^{9} B + 2 x^{3} e d^{5} a^{10} B + 15 x^{3} d^{6} b^{2} a^{8} A + 20 x^{3} e d^{5} b a^{9} A + 5 x^{3} e^{2} d^{4} a^{10} A + \frac{1}{2} x^{2} d^{6} a^{10} B + 5 x^{2} d^{6} b a^{9} A + 3 x^{2} e d^{5} a^{10} A + x d^{6} a^{10} A"," ",0,"1/18*x^18*e^6*b^10*B + 6/17*x^17*e^5*d*b^10*B + 10/17*x^17*e^6*b^9*a*B + 1/17*x^17*e^6*b^10*A + 15/16*x^16*e^4*d^2*b^10*B + 15/4*x^16*e^5*d*b^9*a*B + 45/16*x^16*e^6*b^8*a^2*B + 3/8*x^16*e^5*d*b^10*A + 5/8*x^16*e^6*b^9*a*A + 4/3*x^15*e^3*d^3*b^10*B + 10*x^15*e^4*d^2*b^9*a*B + 18*x^15*e^5*d*b^8*a^2*B + 8*x^15*e^6*b^7*a^3*B + x^15*e^4*d^2*b^10*A + 4*x^15*e^5*d*b^9*a*A + 3*x^15*e^6*b^8*a^2*A + 15/14*x^14*e^2*d^4*b^10*B + 100/7*x^14*e^3*d^3*b^9*a*B + 675/14*x^14*e^4*d^2*b^8*a^2*B + 360/7*x^14*e^5*d*b^7*a^3*B + 15*x^14*e^6*b^6*a^4*B + 10/7*x^14*e^3*d^3*b^10*A + 75/7*x^14*e^4*d^2*b^9*a*A + 135/7*x^14*e^5*d*b^8*a^2*A + 60/7*x^14*e^6*b^7*a^3*A + 6/13*x^13*e*d^5*b^10*B + 150/13*x^13*e^2*d^4*b^9*a*B + 900/13*x^13*e^3*d^3*b^8*a^2*B + 1800/13*x^13*e^4*d^2*b^7*a^3*B + 1260/13*x^13*e^5*d*b^6*a^4*B + 252/13*x^13*e^6*b^5*a^5*B + 15/13*x^13*e^2*d^4*b^10*A + 200/13*x^13*e^3*d^3*b^9*a*A + 675/13*x^13*e^4*d^2*b^8*a^2*A + 720/13*x^13*e^5*d*b^7*a^3*A + 210/13*x^13*e^6*b^6*a^4*A + 1/12*x^12*d^6*b^10*B + 5*x^12*e*d^5*b^9*a*B + 225/4*x^12*e^2*d^4*b^8*a^2*B + 200*x^12*e^3*d^3*b^7*a^3*B + 525/2*x^12*e^4*d^2*b^6*a^4*B + 126*x^12*e^5*d*b^5*a^5*B + 35/2*x^12*e^6*b^4*a^6*B + 1/2*x^12*e*d^5*b^10*A + 25/2*x^12*e^2*d^4*b^9*a*A + 75*x^12*e^3*d^3*b^8*a^2*A + 150*x^12*e^4*d^2*b^7*a^3*A + 105*x^12*e^5*d*b^6*a^4*A + 21*x^12*e^6*b^5*a^5*A + 10/11*x^11*d^6*b^9*a*B + 270/11*x^11*e*d^5*b^8*a^2*B + 1800/11*x^11*e^2*d^4*b^7*a^3*B + 4200/11*x^11*e^3*d^3*b^6*a^4*B + 3780/11*x^11*e^4*d^2*b^5*a^5*B + 1260/11*x^11*e^5*d*b^4*a^6*B + 120/11*x^11*e^6*b^3*a^7*B + 1/11*x^11*d^6*b^10*A + 60/11*x^11*e*d^5*b^9*a*A + 675/11*x^11*e^2*d^4*b^8*a^2*A + 2400/11*x^11*e^3*d^3*b^7*a^3*A + 3150/11*x^11*e^4*d^2*b^6*a^4*A + 1512/11*x^11*e^5*d*b^5*a^5*A + 210/11*x^11*e^6*b^4*a^6*A + 9/2*x^10*d^6*b^8*a^2*B + 72*x^10*e*d^5*b^7*a^3*B + 315*x^10*e^2*d^4*b^6*a^4*B + 504*x^10*e^3*d^3*b^5*a^5*B + 315*x^10*e^4*d^2*b^4*a^6*B + 72*x^10*e^5*d*b^3*a^7*B + 9/2*x^10*e^6*b^2*a^8*B + x^10*d^6*b^9*a*A + 27*x^10*e*d^5*b^8*a^2*A + 180*x^10*e^2*d^4*b^7*a^3*A + 420*x^10*e^3*d^3*b^6*a^4*A + 378*x^10*e^4*d^2*b^5*a^5*A + 126*x^10*e^5*d*b^4*a^6*A + 12*x^10*e^6*b^3*a^7*A + 40/3*x^9*d^6*b^7*a^3*B + 140*x^9*e*d^5*b^6*a^4*B + 420*x^9*e^2*d^4*b^5*a^5*B + 1400/3*x^9*e^3*d^3*b^4*a^6*B + 200*x^9*e^4*d^2*b^3*a^7*B + 30*x^9*e^5*d*b^2*a^8*B + 10/9*x^9*e^6*b*a^9*B + 5*x^9*d^6*b^8*a^2*A + 80*x^9*e*d^5*b^7*a^3*A + 350*x^9*e^2*d^4*b^6*a^4*A + 560*x^9*e^3*d^3*b^5*a^5*A + 350*x^9*e^4*d^2*b^4*a^6*A + 80*x^9*e^5*d*b^3*a^7*A + 5*x^9*e^6*b^2*a^8*A + 105/4*x^8*d^6*b^6*a^4*B + 189*x^8*e*d^5*b^5*a^5*B + 1575/4*x^8*e^2*d^4*b^4*a^6*B + 300*x^8*e^3*d^3*b^3*a^7*B + 675/8*x^8*e^4*d^2*b^2*a^8*B + 15/2*x^8*e^5*d*b*a^9*B + 1/8*x^8*e^6*a^10*B + 15*x^8*d^6*b^7*a^3*A + 315/2*x^8*e*d^5*b^6*a^4*A + 945/2*x^8*e^2*d^4*b^5*a^5*A + 525*x^8*e^3*d^3*b^4*a^6*A + 225*x^8*e^4*d^2*b^3*a^7*A + 135/4*x^8*e^5*d*b^2*a^8*A + 5/4*x^8*e^6*b*a^9*A + 36*x^7*d^6*b^5*a^5*B + 180*x^7*e*d^5*b^4*a^6*B + 1800/7*x^7*e^2*d^4*b^3*a^7*B + 900/7*x^7*e^3*d^3*b^2*a^8*B + 150/7*x^7*e^4*d^2*b*a^9*B + 6/7*x^7*e^5*d*a^10*B + 30*x^7*d^6*b^6*a^4*A + 216*x^7*e*d^5*b^5*a^5*A + 450*x^7*e^2*d^4*b^4*a^6*A + 2400/7*x^7*e^3*d^3*b^3*a^7*A + 675/7*x^7*e^4*d^2*b^2*a^8*A + 60/7*x^7*e^5*d*b*a^9*A + 1/7*x^7*e^6*a^10*A + 35*x^6*d^6*b^4*a^6*B + 120*x^6*e*d^5*b^3*a^7*B + 225/2*x^6*e^2*d^4*b^2*a^8*B + 100/3*x^6*e^3*d^3*b*a^9*B + 5/2*x^6*e^4*d^2*a^10*B + 42*x^6*d^6*b^5*a^5*A + 210*x^6*e*d^5*b^4*a^6*A + 300*x^6*e^2*d^4*b^3*a^7*A + 150*x^6*e^3*d^3*b^2*a^8*A + 25*x^6*e^4*d^2*b*a^9*A + x^6*e^5*d*a^10*A + 24*x^5*d^6*b^3*a^7*B + 54*x^5*e*d^5*b^2*a^8*B + 30*x^5*e^2*d^4*b*a^9*B + 4*x^5*e^3*d^3*a^10*B + 42*x^5*d^6*b^4*a^6*A + 144*x^5*e*d^5*b^3*a^7*A + 135*x^5*e^2*d^4*b^2*a^8*A + 40*x^5*e^3*d^3*b*a^9*A + 3*x^5*e^4*d^2*a^10*A + 45/4*x^4*d^6*b^2*a^8*B + 15*x^4*e*d^5*b*a^9*B + 15/4*x^4*e^2*d^4*a^10*B + 30*x^4*d^6*b^3*a^7*A + 135/2*x^4*e*d^5*b^2*a^8*A + 75/2*x^4*e^2*d^4*b*a^9*A + 5*x^4*e^3*d^3*a^10*A + 10/3*x^3*d^6*b*a^9*B + 2*x^3*e*d^5*a^10*B + 15*x^3*d^6*b^2*a^8*A + 20*x^3*e*d^5*b*a^9*A + 5*x^3*e^2*d^4*a^10*A + 1/2*x^2*d^6*a^10*B + 5*x^2*d^6*b*a^9*A + 3*x^2*e*d^5*a^10*A + x*d^6*a^10*A","B",0
1083,1,2032,0,0.781994," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^5,x, algorithm=""fricas"")","\frac{1}{17} x^{17} e^{5} b^{10} B + \frac{5}{16} x^{16} e^{4} d b^{10} B + \frac{5}{8} x^{16} e^{5} b^{9} a B + \frac{1}{16} x^{16} e^{5} b^{10} A + \frac{2}{3} x^{15} e^{3} d^{2} b^{10} B + \frac{10}{3} x^{15} e^{4} d b^{9} a B + 3 x^{15} e^{5} b^{8} a^{2} B + \frac{1}{3} x^{15} e^{4} d b^{10} A + \frac{2}{3} x^{15} e^{5} b^{9} a A + \frac{5}{7} x^{14} e^{2} d^{3} b^{10} B + \frac{50}{7} x^{14} e^{3} d^{2} b^{9} a B + \frac{225}{14} x^{14} e^{4} d b^{8} a^{2} B + \frac{60}{7} x^{14} e^{5} b^{7} a^{3} B + \frac{5}{7} x^{14} e^{3} d^{2} b^{10} A + \frac{25}{7} x^{14} e^{4} d b^{9} a A + \frac{45}{14} x^{14} e^{5} b^{8} a^{2} A + \frac{5}{13} x^{13} e d^{4} b^{10} B + \frac{100}{13} x^{13} e^{2} d^{3} b^{9} a B + \frac{450}{13} x^{13} e^{3} d^{2} b^{8} a^{2} B + \frac{600}{13} x^{13} e^{4} d b^{7} a^{3} B + \frac{210}{13} x^{13} e^{5} b^{6} a^{4} B + \frac{10}{13} x^{13} e^{2} d^{3} b^{10} A + \frac{100}{13} x^{13} e^{3} d^{2} b^{9} a A + \frac{225}{13} x^{13} e^{4} d b^{8} a^{2} A + \frac{120}{13} x^{13} e^{5} b^{7} a^{3} A + \frac{1}{12} x^{12} d^{5} b^{10} B + \frac{25}{6} x^{12} e d^{4} b^{9} a B + \frac{75}{2} x^{12} e^{2} d^{3} b^{8} a^{2} B + 100 x^{12} e^{3} d^{2} b^{7} a^{3} B + \frac{175}{2} x^{12} e^{4} d b^{6} a^{4} B + 21 x^{12} e^{5} b^{5} a^{5} B + \frac{5}{12} x^{12} e d^{4} b^{10} A + \frac{25}{3} x^{12} e^{2} d^{3} b^{9} a A + \frac{75}{2} x^{12} e^{3} d^{2} b^{8} a^{2} A + 50 x^{12} e^{4} d b^{7} a^{3} A + \frac{35}{2} x^{12} e^{5} b^{6} a^{4} A + \frac{10}{11} x^{11} d^{5} b^{9} a B + \frac{225}{11} x^{11} e d^{4} b^{8} a^{2} B + \frac{1200}{11} x^{11} e^{2} d^{3} b^{7} a^{3} B + \frac{2100}{11} x^{11} e^{3} d^{2} b^{6} a^{4} B + \frac{1260}{11} x^{11} e^{4} d b^{5} a^{5} B + \frac{210}{11} x^{11} e^{5} b^{4} a^{6} B + \frac{1}{11} x^{11} d^{5} b^{10} A + \frac{50}{11} x^{11} e d^{4} b^{9} a A + \frac{450}{11} x^{11} e^{2} d^{3} b^{8} a^{2} A + \frac{1200}{11} x^{11} e^{3} d^{2} b^{7} a^{3} A + \frac{1050}{11} x^{11} e^{4} d b^{6} a^{4} A + \frac{252}{11} x^{11} e^{5} b^{5} a^{5} A + \frac{9}{2} x^{10} d^{5} b^{8} a^{2} B + 60 x^{10} e d^{4} b^{7} a^{3} B + 210 x^{10} e^{2} d^{3} b^{6} a^{4} B + 252 x^{10} e^{3} d^{2} b^{5} a^{5} B + 105 x^{10} e^{4} d b^{4} a^{6} B + 12 x^{10} e^{5} b^{3} a^{7} B + x^{10} d^{5} b^{9} a A + \frac{45}{2} x^{10} e d^{4} b^{8} a^{2} A + 120 x^{10} e^{2} d^{3} b^{7} a^{3} A + 210 x^{10} e^{3} d^{2} b^{6} a^{4} A + 126 x^{10} e^{4} d b^{5} a^{5} A + 21 x^{10} e^{5} b^{4} a^{6} A + \frac{40}{3} x^{9} d^{5} b^{7} a^{3} B + \frac{350}{3} x^{9} e d^{4} b^{6} a^{4} B + 280 x^{9} e^{2} d^{3} b^{5} a^{5} B + \frac{700}{3} x^{9} e^{3} d^{2} b^{4} a^{6} B + \frac{200}{3} x^{9} e^{4} d b^{3} a^{7} B + 5 x^{9} e^{5} b^{2} a^{8} B + 5 x^{9} d^{5} b^{8} a^{2} A + \frac{200}{3} x^{9} e d^{4} b^{7} a^{3} A + \frac{700}{3} x^{9} e^{2} d^{3} b^{6} a^{4} A + 280 x^{9} e^{3} d^{2} b^{5} a^{5} A + \frac{350}{3} x^{9} e^{4} d b^{4} a^{6} A + \frac{40}{3} x^{9} e^{5} b^{3} a^{7} A + \frac{105}{4} x^{8} d^{5} b^{6} a^{4} B + \frac{315}{2} x^{8} e d^{4} b^{5} a^{5} B + \frac{525}{2} x^{8} e^{2} d^{3} b^{4} a^{6} B + 150 x^{8} e^{3} d^{2} b^{3} a^{7} B + \frac{225}{8} x^{8} e^{4} d b^{2} a^{8} B + \frac{5}{4} x^{8} e^{5} b a^{9} B + 15 x^{8} d^{5} b^{7} a^{3} A + \frac{525}{4} x^{8} e d^{4} b^{6} a^{4} A + 315 x^{8} e^{2} d^{3} b^{5} a^{5} A + \frac{525}{2} x^{8} e^{3} d^{2} b^{4} a^{6} A + 75 x^{8} e^{4} d b^{3} a^{7} A + \frac{45}{8} x^{8} e^{5} b^{2} a^{8} A + 36 x^{7} d^{5} b^{5} a^{5} B + 150 x^{7} e d^{4} b^{4} a^{6} B + \frac{1200}{7} x^{7} e^{2} d^{3} b^{3} a^{7} B + \frac{450}{7} x^{7} e^{3} d^{2} b^{2} a^{8} B + \frac{50}{7} x^{7} e^{4} d b a^{9} B + \frac{1}{7} x^{7} e^{5} a^{10} B + 30 x^{7} d^{5} b^{6} a^{4} A + 180 x^{7} e d^{4} b^{5} a^{5} A + 300 x^{7} e^{2} d^{3} b^{4} a^{6} A + \frac{1200}{7} x^{7} e^{3} d^{2} b^{3} a^{7} A + \frac{225}{7} x^{7} e^{4} d b^{2} a^{8} A + \frac{10}{7} x^{7} e^{5} b a^{9} A + 35 x^{6} d^{5} b^{4} a^{6} B + 100 x^{6} e d^{4} b^{3} a^{7} B + 75 x^{6} e^{2} d^{3} b^{2} a^{8} B + \frac{50}{3} x^{6} e^{3} d^{2} b a^{9} B + \frac{5}{6} x^{6} e^{4} d a^{10} B + 42 x^{6} d^{5} b^{5} a^{5} A + 175 x^{6} e d^{4} b^{4} a^{6} A + 200 x^{6} e^{2} d^{3} b^{3} a^{7} A + 75 x^{6} e^{3} d^{2} b^{2} a^{8} A + \frac{25}{3} x^{6} e^{4} d b a^{9} A + \frac{1}{6} x^{6} e^{5} a^{10} A + 24 x^{5} d^{5} b^{3} a^{7} B + 45 x^{5} e d^{4} b^{2} a^{8} B + 20 x^{5} e^{2} d^{3} b a^{9} B + 2 x^{5} e^{3} d^{2} a^{10} B + 42 x^{5} d^{5} b^{4} a^{6} A + 120 x^{5} e d^{4} b^{3} a^{7} A + 90 x^{5} e^{2} d^{3} b^{2} a^{8} A + 20 x^{5} e^{3} d^{2} b a^{9} A + x^{5} e^{4} d a^{10} A + \frac{45}{4} x^{4} d^{5} b^{2} a^{8} B + \frac{25}{2} x^{4} e d^{4} b a^{9} B + \frac{5}{2} x^{4} e^{2} d^{3} a^{10} B + 30 x^{4} d^{5} b^{3} a^{7} A + \frac{225}{4} x^{4} e d^{4} b^{2} a^{8} A + 25 x^{4} e^{2} d^{3} b a^{9} A + \frac{5}{2} x^{4} e^{3} d^{2} a^{10} A + \frac{10}{3} x^{3} d^{5} b a^{9} B + \frac{5}{3} x^{3} e d^{4} a^{10} B + 15 x^{3} d^{5} b^{2} a^{8} A + \frac{50}{3} x^{3} e d^{4} b a^{9} A + \frac{10}{3} x^{3} e^{2} d^{3} a^{10} A + \frac{1}{2} x^{2} d^{5} a^{10} B + 5 x^{2} d^{5} b a^{9} A + \frac{5}{2} x^{2} e d^{4} a^{10} A + x d^{5} a^{10} A"," ",0,"1/17*x^17*e^5*b^10*B + 5/16*x^16*e^4*d*b^10*B + 5/8*x^16*e^5*b^9*a*B + 1/16*x^16*e^5*b^10*A + 2/3*x^15*e^3*d^2*b^10*B + 10/3*x^15*e^4*d*b^9*a*B + 3*x^15*e^5*b^8*a^2*B + 1/3*x^15*e^4*d*b^10*A + 2/3*x^15*e^5*b^9*a*A + 5/7*x^14*e^2*d^3*b^10*B + 50/7*x^14*e^3*d^2*b^9*a*B + 225/14*x^14*e^4*d*b^8*a^2*B + 60/7*x^14*e^5*b^7*a^3*B + 5/7*x^14*e^3*d^2*b^10*A + 25/7*x^14*e^4*d*b^9*a*A + 45/14*x^14*e^5*b^8*a^2*A + 5/13*x^13*e*d^4*b^10*B + 100/13*x^13*e^2*d^3*b^9*a*B + 450/13*x^13*e^3*d^2*b^8*a^2*B + 600/13*x^13*e^4*d*b^7*a^3*B + 210/13*x^13*e^5*b^6*a^4*B + 10/13*x^13*e^2*d^3*b^10*A + 100/13*x^13*e^3*d^2*b^9*a*A + 225/13*x^13*e^4*d*b^8*a^2*A + 120/13*x^13*e^5*b^7*a^3*A + 1/12*x^12*d^5*b^10*B + 25/6*x^12*e*d^4*b^9*a*B + 75/2*x^12*e^2*d^3*b^8*a^2*B + 100*x^12*e^3*d^2*b^7*a^3*B + 175/2*x^12*e^4*d*b^6*a^4*B + 21*x^12*e^5*b^5*a^5*B + 5/12*x^12*e*d^4*b^10*A + 25/3*x^12*e^2*d^3*b^9*a*A + 75/2*x^12*e^3*d^2*b^8*a^2*A + 50*x^12*e^4*d*b^7*a^3*A + 35/2*x^12*e^5*b^6*a^4*A + 10/11*x^11*d^5*b^9*a*B + 225/11*x^11*e*d^4*b^8*a^2*B + 1200/11*x^11*e^2*d^3*b^7*a^3*B + 2100/11*x^11*e^3*d^2*b^6*a^4*B + 1260/11*x^11*e^4*d*b^5*a^5*B + 210/11*x^11*e^5*b^4*a^6*B + 1/11*x^11*d^5*b^10*A + 50/11*x^11*e*d^4*b^9*a*A + 450/11*x^11*e^2*d^3*b^8*a^2*A + 1200/11*x^11*e^3*d^2*b^7*a^3*A + 1050/11*x^11*e^4*d*b^6*a^4*A + 252/11*x^11*e^5*b^5*a^5*A + 9/2*x^10*d^5*b^8*a^2*B + 60*x^10*e*d^4*b^7*a^3*B + 210*x^10*e^2*d^3*b^6*a^4*B + 252*x^10*e^3*d^2*b^5*a^5*B + 105*x^10*e^4*d*b^4*a^6*B + 12*x^10*e^5*b^3*a^7*B + x^10*d^5*b^9*a*A + 45/2*x^10*e*d^4*b^8*a^2*A + 120*x^10*e^2*d^3*b^7*a^3*A + 210*x^10*e^3*d^2*b^6*a^4*A + 126*x^10*e^4*d*b^5*a^5*A + 21*x^10*e^5*b^4*a^6*A + 40/3*x^9*d^5*b^7*a^3*B + 350/3*x^9*e*d^4*b^6*a^4*B + 280*x^9*e^2*d^3*b^5*a^5*B + 700/3*x^9*e^3*d^2*b^4*a^6*B + 200/3*x^9*e^4*d*b^3*a^7*B + 5*x^9*e^5*b^2*a^8*B + 5*x^9*d^5*b^8*a^2*A + 200/3*x^9*e*d^4*b^7*a^3*A + 700/3*x^9*e^2*d^3*b^6*a^4*A + 280*x^9*e^3*d^2*b^5*a^5*A + 350/3*x^9*e^4*d*b^4*a^6*A + 40/3*x^9*e^5*b^3*a^7*A + 105/4*x^8*d^5*b^6*a^4*B + 315/2*x^8*e*d^4*b^5*a^5*B + 525/2*x^8*e^2*d^3*b^4*a^6*B + 150*x^8*e^3*d^2*b^3*a^7*B + 225/8*x^8*e^4*d*b^2*a^8*B + 5/4*x^8*e^5*b*a^9*B + 15*x^8*d^5*b^7*a^3*A + 525/4*x^8*e*d^4*b^6*a^4*A + 315*x^8*e^2*d^3*b^5*a^5*A + 525/2*x^8*e^3*d^2*b^4*a^6*A + 75*x^8*e^4*d*b^3*a^7*A + 45/8*x^8*e^5*b^2*a^8*A + 36*x^7*d^5*b^5*a^5*B + 150*x^7*e*d^4*b^4*a^6*B + 1200/7*x^7*e^2*d^3*b^3*a^7*B + 450/7*x^7*e^3*d^2*b^2*a^8*B + 50/7*x^7*e^4*d*b*a^9*B + 1/7*x^7*e^5*a^10*B + 30*x^7*d^5*b^6*a^4*A + 180*x^7*e*d^4*b^5*a^5*A + 300*x^7*e^2*d^3*b^4*a^6*A + 1200/7*x^7*e^3*d^2*b^3*a^7*A + 225/7*x^7*e^4*d*b^2*a^8*A + 10/7*x^7*e^5*b*a^9*A + 35*x^6*d^5*b^4*a^6*B + 100*x^6*e*d^4*b^3*a^7*B + 75*x^6*e^2*d^3*b^2*a^8*B + 50/3*x^6*e^3*d^2*b*a^9*B + 5/6*x^6*e^4*d*a^10*B + 42*x^6*d^5*b^5*a^5*A + 175*x^6*e*d^4*b^4*a^6*A + 200*x^6*e^2*d^3*b^3*a^7*A + 75*x^6*e^3*d^2*b^2*a^8*A + 25/3*x^6*e^4*d*b*a^9*A + 1/6*x^6*e^5*a^10*A + 24*x^5*d^5*b^3*a^7*B + 45*x^5*e*d^4*b^2*a^8*B + 20*x^5*e^2*d^3*b*a^9*B + 2*x^5*e^3*d^2*a^10*B + 42*x^5*d^5*b^4*a^6*A + 120*x^5*e*d^4*b^3*a^7*A + 90*x^5*e^2*d^3*b^2*a^8*A + 20*x^5*e^3*d^2*b*a^9*A + x^5*e^4*d*a^10*A + 45/4*x^4*d^5*b^2*a^8*B + 25/2*x^4*e*d^4*b*a^9*B + 5/2*x^4*e^2*d^3*a^10*B + 30*x^4*d^5*b^3*a^7*A + 225/4*x^4*e*d^4*b^2*a^8*A + 25*x^4*e^2*d^3*b*a^9*A + 5/2*x^4*e^3*d^2*a^10*A + 10/3*x^3*d^5*b*a^9*B + 5/3*x^3*e*d^4*a^10*B + 15*x^3*d^5*b^2*a^8*A + 50/3*x^3*e*d^4*b*a^9*A + 10/3*x^3*e^2*d^3*a^10*A + 1/2*x^2*d^5*a^10*B + 5*x^2*d^5*b*a^9*A + 5/2*x^2*e*d^4*a^10*A + x*d^5*a^10*A","B",0
1084,1,1656,0,0.812363," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^4,x, algorithm=""fricas"")","\frac{1}{16} x^{16} e^{4} b^{10} B + \frac{4}{15} x^{15} e^{3} d b^{10} B + \frac{2}{3} x^{15} e^{4} b^{9} a B + \frac{1}{15} x^{15} e^{4} b^{10} A + \frac{3}{7} x^{14} e^{2} d^{2} b^{10} B + \frac{20}{7} x^{14} e^{3} d b^{9} a B + \frac{45}{14} x^{14} e^{4} b^{8} a^{2} B + \frac{2}{7} x^{14} e^{3} d b^{10} A + \frac{5}{7} x^{14} e^{4} b^{9} a A + \frac{4}{13} x^{13} e d^{3} b^{10} B + \frac{60}{13} x^{13} e^{2} d^{2} b^{9} a B + \frac{180}{13} x^{13} e^{3} d b^{8} a^{2} B + \frac{120}{13} x^{13} e^{4} b^{7} a^{3} B + \frac{6}{13} x^{13} e^{2} d^{2} b^{10} A + \frac{40}{13} x^{13} e^{3} d b^{9} a A + \frac{45}{13} x^{13} e^{4} b^{8} a^{2} A + \frac{1}{12} x^{12} d^{4} b^{10} B + \frac{10}{3} x^{12} e d^{3} b^{9} a B + \frac{45}{2} x^{12} e^{2} d^{2} b^{8} a^{2} B + 40 x^{12} e^{3} d b^{7} a^{3} B + \frac{35}{2} x^{12} e^{4} b^{6} a^{4} B + \frac{1}{3} x^{12} e d^{3} b^{10} A + 5 x^{12} e^{2} d^{2} b^{9} a A + 15 x^{12} e^{3} d b^{8} a^{2} A + 10 x^{12} e^{4} b^{7} a^{3} A + \frac{10}{11} x^{11} d^{4} b^{9} a B + \frac{180}{11} x^{11} e d^{3} b^{8} a^{2} B + \frac{720}{11} x^{11} e^{2} d^{2} b^{7} a^{3} B + \frac{840}{11} x^{11} e^{3} d b^{6} a^{4} B + \frac{252}{11} x^{11} e^{4} b^{5} a^{5} B + \frac{1}{11} x^{11} d^{4} b^{10} A + \frac{40}{11} x^{11} e d^{3} b^{9} a A + \frac{270}{11} x^{11} e^{2} d^{2} b^{8} a^{2} A + \frac{480}{11} x^{11} e^{3} d b^{7} a^{3} A + \frac{210}{11} x^{11} e^{4} b^{6} a^{4} A + \frac{9}{2} x^{10} d^{4} b^{8} a^{2} B + 48 x^{10} e d^{3} b^{7} a^{3} B + 126 x^{10} e^{2} d^{2} b^{6} a^{4} B + \frac{504}{5} x^{10} e^{3} d b^{5} a^{5} B + 21 x^{10} e^{4} b^{4} a^{6} B + x^{10} d^{4} b^{9} a A + 18 x^{10} e d^{3} b^{8} a^{2} A + 72 x^{10} e^{2} d^{2} b^{7} a^{3} A + 84 x^{10} e^{3} d b^{6} a^{4} A + \frac{126}{5} x^{10} e^{4} b^{5} a^{5} A + \frac{40}{3} x^{9} d^{4} b^{7} a^{3} B + \frac{280}{3} x^{9} e d^{3} b^{6} a^{4} B + 168 x^{9} e^{2} d^{2} b^{5} a^{5} B + \frac{280}{3} x^{9} e^{3} d b^{4} a^{6} B + \frac{40}{3} x^{9} e^{4} b^{3} a^{7} B + 5 x^{9} d^{4} b^{8} a^{2} A + \frac{160}{3} x^{9} e d^{3} b^{7} a^{3} A + 140 x^{9} e^{2} d^{2} b^{6} a^{4} A + 112 x^{9} e^{3} d b^{5} a^{5} A + \frac{70}{3} x^{9} e^{4} b^{4} a^{6} A + \frac{105}{4} x^{8} d^{4} b^{6} a^{4} B + 126 x^{8} e d^{3} b^{5} a^{5} B + \frac{315}{2} x^{8} e^{2} d^{2} b^{4} a^{6} B + 60 x^{8} e^{3} d b^{3} a^{7} B + \frac{45}{8} x^{8} e^{4} b^{2} a^{8} B + 15 x^{8} d^{4} b^{7} a^{3} A + 105 x^{8} e d^{3} b^{6} a^{4} A + 189 x^{8} e^{2} d^{2} b^{5} a^{5} A + 105 x^{8} e^{3} d b^{4} a^{6} A + 15 x^{8} e^{4} b^{3} a^{7} A + 36 x^{7} d^{4} b^{5} a^{5} B + 120 x^{7} e d^{3} b^{4} a^{6} B + \frac{720}{7} x^{7} e^{2} d^{2} b^{3} a^{7} B + \frac{180}{7} x^{7} e^{3} d b^{2} a^{8} B + \frac{10}{7} x^{7} e^{4} b a^{9} B + 30 x^{7} d^{4} b^{6} a^{4} A + 144 x^{7} e d^{3} b^{5} a^{5} A + 180 x^{7} e^{2} d^{2} b^{4} a^{6} A + \frac{480}{7} x^{7} e^{3} d b^{3} a^{7} A + \frac{45}{7} x^{7} e^{4} b^{2} a^{8} A + 35 x^{6} d^{4} b^{4} a^{6} B + 80 x^{6} e d^{3} b^{3} a^{7} B + 45 x^{6} e^{2} d^{2} b^{2} a^{8} B + \frac{20}{3} x^{6} e^{3} d b a^{9} B + \frac{1}{6} x^{6} e^{4} a^{10} B + 42 x^{6} d^{4} b^{5} a^{5} A + 140 x^{6} e d^{3} b^{4} a^{6} A + 120 x^{6} e^{2} d^{2} b^{3} a^{7} A + 30 x^{6} e^{3} d b^{2} a^{8} A + \frac{5}{3} x^{6} e^{4} b a^{9} A + 24 x^{5} d^{4} b^{3} a^{7} B + 36 x^{5} e d^{3} b^{2} a^{8} B + 12 x^{5} e^{2} d^{2} b a^{9} B + \frac{4}{5} x^{5} e^{3} d a^{10} B + 42 x^{5} d^{4} b^{4} a^{6} A + 96 x^{5} e d^{3} b^{3} a^{7} A + 54 x^{5} e^{2} d^{2} b^{2} a^{8} A + 8 x^{5} e^{3} d b a^{9} A + \frac{1}{5} x^{5} e^{4} a^{10} A + \frac{45}{4} x^{4} d^{4} b^{2} a^{8} B + 10 x^{4} e d^{3} b a^{9} B + \frac{3}{2} x^{4} e^{2} d^{2} a^{10} B + 30 x^{4} d^{4} b^{3} a^{7} A + 45 x^{4} e d^{3} b^{2} a^{8} A + 15 x^{4} e^{2} d^{2} b a^{9} A + x^{4} e^{3} d a^{10} A + \frac{10}{3} x^{3} d^{4} b a^{9} B + \frac{4}{3} x^{3} e d^{3} a^{10} B + 15 x^{3} d^{4} b^{2} a^{8} A + \frac{40}{3} x^{3} e d^{3} b a^{9} A + 2 x^{3} e^{2} d^{2} a^{10} A + \frac{1}{2} x^{2} d^{4} a^{10} B + 5 x^{2} d^{4} b a^{9} A + 2 x^{2} e d^{3} a^{10} A + x d^{4} a^{10} A"," ",0,"1/16*x^16*e^4*b^10*B + 4/15*x^15*e^3*d*b^10*B + 2/3*x^15*e^4*b^9*a*B + 1/15*x^15*e^4*b^10*A + 3/7*x^14*e^2*d^2*b^10*B + 20/7*x^14*e^3*d*b^9*a*B + 45/14*x^14*e^4*b^8*a^2*B + 2/7*x^14*e^3*d*b^10*A + 5/7*x^14*e^4*b^9*a*A + 4/13*x^13*e*d^3*b^10*B + 60/13*x^13*e^2*d^2*b^9*a*B + 180/13*x^13*e^3*d*b^8*a^2*B + 120/13*x^13*e^4*b^7*a^3*B + 6/13*x^13*e^2*d^2*b^10*A + 40/13*x^13*e^3*d*b^9*a*A + 45/13*x^13*e^4*b^8*a^2*A + 1/12*x^12*d^4*b^10*B + 10/3*x^12*e*d^3*b^9*a*B + 45/2*x^12*e^2*d^2*b^8*a^2*B + 40*x^12*e^3*d*b^7*a^3*B + 35/2*x^12*e^4*b^6*a^4*B + 1/3*x^12*e*d^3*b^10*A + 5*x^12*e^2*d^2*b^9*a*A + 15*x^12*e^3*d*b^8*a^2*A + 10*x^12*e^4*b^7*a^3*A + 10/11*x^11*d^4*b^9*a*B + 180/11*x^11*e*d^3*b^8*a^2*B + 720/11*x^11*e^2*d^2*b^7*a^3*B + 840/11*x^11*e^3*d*b^6*a^4*B + 252/11*x^11*e^4*b^5*a^5*B + 1/11*x^11*d^4*b^10*A + 40/11*x^11*e*d^3*b^9*a*A + 270/11*x^11*e^2*d^2*b^8*a^2*A + 480/11*x^11*e^3*d*b^7*a^3*A + 210/11*x^11*e^4*b^6*a^4*A + 9/2*x^10*d^4*b^8*a^2*B + 48*x^10*e*d^3*b^7*a^3*B + 126*x^10*e^2*d^2*b^6*a^4*B + 504/5*x^10*e^3*d*b^5*a^5*B + 21*x^10*e^4*b^4*a^6*B + x^10*d^4*b^9*a*A + 18*x^10*e*d^3*b^8*a^2*A + 72*x^10*e^2*d^2*b^7*a^3*A + 84*x^10*e^3*d*b^6*a^4*A + 126/5*x^10*e^4*b^5*a^5*A + 40/3*x^9*d^4*b^7*a^3*B + 280/3*x^9*e*d^3*b^6*a^4*B + 168*x^9*e^2*d^2*b^5*a^5*B + 280/3*x^9*e^3*d*b^4*a^6*B + 40/3*x^9*e^4*b^3*a^7*B + 5*x^9*d^4*b^8*a^2*A + 160/3*x^9*e*d^3*b^7*a^3*A + 140*x^9*e^2*d^2*b^6*a^4*A + 112*x^9*e^3*d*b^5*a^5*A + 70/3*x^9*e^4*b^4*a^6*A + 105/4*x^8*d^4*b^6*a^4*B + 126*x^8*e*d^3*b^5*a^5*B + 315/2*x^8*e^2*d^2*b^4*a^6*B + 60*x^8*e^3*d*b^3*a^7*B + 45/8*x^8*e^4*b^2*a^8*B + 15*x^8*d^4*b^7*a^3*A + 105*x^8*e*d^3*b^6*a^4*A + 189*x^8*e^2*d^2*b^5*a^5*A + 105*x^8*e^3*d*b^4*a^6*A + 15*x^8*e^4*b^3*a^7*A + 36*x^7*d^4*b^5*a^5*B + 120*x^7*e*d^3*b^4*a^6*B + 720/7*x^7*e^2*d^2*b^3*a^7*B + 180/7*x^7*e^3*d*b^2*a^8*B + 10/7*x^7*e^4*b*a^9*B + 30*x^7*d^4*b^6*a^4*A + 144*x^7*e*d^3*b^5*a^5*A + 180*x^7*e^2*d^2*b^4*a^6*A + 480/7*x^7*e^3*d*b^3*a^7*A + 45/7*x^7*e^4*b^2*a^8*A + 35*x^6*d^4*b^4*a^6*B + 80*x^6*e*d^3*b^3*a^7*B + 45*x^6*e^2*d^2*b^2*a^8*B + 20/3*x^6*e^3*d*b*a^9*B + 1/6*x^6*e^4*a^10*B + 42*x^6*d^4*b^5*a^5*A + 140*x^6*e*d^3*b^4*a^6*A + 120*x^6*e^2*d^2*b^3*a^7*A + 30*x^6*e^3*d*b^2*a^8*A + 5/3*x^6*e^4*b*a^9*A + 24*x^5*d^4*b^3*a^7*B + 36*x^5*e*d^3*b^2*a^8*B + 12*x^5*e^2*d^2*b*a^9*B + 4/5*x^5*e^3*d*a^10*B + 42*x^5*d^4*b^4*a^6*A + 96*x^5*e*d^3*b^3*a^7*A + 54*x^5*e^2*d^2*b^2*a^8*A + 8*x^5*e^3*d*b*a^9*A + 1/5*x^5*e^4*a^10*A + 45/4*x^4*d^4*b^2*a^8*B + 10*x^4*e*d^3*b*a^9*B + 3/2*x^4*e^2*d^2*a^10*B + 30*x^4*d^4*b^3*a^7*A + 45*x^4*e*d^3*b^2*a^8*A + 15*x^4*e^2*d^2*b*a^9*A + x^4*e^3*d*a^10*A + 10/3*x^3*d^4*b*a^9*B + 4/3*x^3*e*d^3*a^10*B + 15*x^3*d^4*b^2*a^8*A + 40/3*x^3*e*d^3*b*a^9*A + 2*x^3*e^2*d^2*a^10*A + 1/2*x^2*d^4*a^10*B + 5*x^2*d^4*b*a^9*A + 2*x^2*e*d^3*a^10*A + x*d^4*a^10*A","B",0
1085,1,1279,0,1.072494," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{3} b^{10} B + \frac{3}{14} x^{14} e^{2} d b^{10} B + \frac{5}{7} x^{14} e^{3} b^{9} a B + \frac{1}{14} x^{14} e^{3} b^{10} A + \frac{3}{13} x^{13} e d^{2} b^{10} B + \frac{30}{13} x^{13} e^{2} d b^{9} a B + \frac{45}{13} x^{13} e^{3} b^{8} a^{2} B + \frac{3}{13} x^{13} e^{2} d b^{10} A + \frac{10}{13} x^{13} e^{3} b^{9} a A + \frac{1}{12} x^{12} d^{3} b^{10} B + \frac{5}{2} x^{12} e d^{2} b^{9} a B + \frac{45}{4} x^{12} e^{2} d b^{8} a^{2} B + 10 x^{12} e^{3} b^{7} a^{3} B + \frac{1}{4} x^{12} e d^{2} b^{10} A + \frac{5}{2} x^{12} e^{2} d b^{9} a A + \frac{15}{4} x^{12} e^{3} b^{8} a^{2} A + \frac{10}{11} x^{11} d^{3} b^{9} a B + \frac{135}{11} x^{11} e d^{2} b^{8} a^{2} B + \frac{360}{11} x^{11} e^{2} d b^{7} a^{3} B + \frac{210}{11} x^{11} e^{3} b^{6} a^{4} B + \frac{1}{11} x^{11} d^{3} b^{10} A + \frac{30}{11} x^{11} e d^{2} b^{9} a A + \frac{135}{11} x^{11} e^{2} d b^{8} a^{2} A + \frac{120}{11} x^{11} e^{3} b^{7} a^{3} A + \frac{9}{2} x^{10} d^{3} b^{8} a^{2} B + 36 x^{10} e d^{2} b^{7} a^{3} B + 63 x^{10} e^{2} d b^{6} a^{4} B + \frac{126}{5} x^{10} e^{3} b^{5} a^{5} B + x^{10} d^{3} b^{9} a A + \frac{27}{2} x^{10} e d^{2} b^{8} a^{2} A + 36 x^{10} e^{2} d b^{7} a^{3} A + 21 x^{10} e^{3} b^{6} a^{4} A + \frac{40}{3} x^{9} d^{3} b^{7} a^{3} B + 70 x^{9} e d^{2} b^{6} a^{4} B + 84 x^{9} e^{2} d b^{5} a^{5} B + \frac{70}{3} x^{9} e^{3} b^{4} a^{6} B + 5 x^{9} d^{3} b^{8} a^{2} A + 40 x^{9} e d^{2} b^{7} a^{3} A + 70 x^{9} e^{2} d b^{6} a^{4} A + 28 x^{9} e^{3} b^{5} a^{5} A + \frac{105}{4} x^{8} d^{3} b^{6} a^{4} B + \frac{189}{2} x^{8} e d^{2} b^{5} a^{5} B + \frac{315}{4} x^{8} e^{2} d b^{4} a^{6} B + 15 x^{8} e^{3} b^{3} a^{7} B + 15 x^{8} d^{3} b^{7} a^{3} A + \frac{315}{4} x^{8} e d^{2} b^{6} a^{4} A + \frac{189}{2} x^{8} e^{2} d b^{5} a^{5} A + \frac{105}{4} x^{8} e^{3} b^{4} a^{6} A + 36 x^{7} d^{3} b^{5} a^{5} B + 90 x^{7} e d^{2} b^{4} a^{6} B + \frac{360}{7} x^{7} e^{2} d b^{3} a^{7} B + \frac{45}{7} x^{7} e^{3} b^{2} a^{8} B + 30 x^{7} d^{3} b^{6} a^{4} A + 108 x^{7} e d^{2} b^{5} a^{5} A + 90 x^{7} e^{2} d b^{4} a^{6} A + \frac{120}{7} x^{7} e^{3} b^{3} a^{7} A + 35 x^{6} d^{3} b^{4} a^{6} B + 60 x^{6} e d^{2} b^{3} a^{7} B + \frac{45}{2} x^{6} e^{2} d b^{2} a^{8} B + \frac{5}{3} x^{6} e^{3} b a^{9} B + 42 x^{6} d^{3} b^{5} a^{5} A + 105 x^{6} e d^{2} b^{4} a^{6} A + 60 x^{6} e^{2} d b^{3} a^{7} A + \frac{15}{2} x^{6} e^{3} b^{2} a^{8} A + 24 x^{5} d^{3} b^{3} a^{7} B + 27 x^{5} e d^{2} b^{2} a^{8} B + 6 x^{5} e^{2} d b a^{9} B + \frac{1}{5} x^{5} e^{3} a^{10} B + 42 x^{5} d^{3} b^{4} a^{6} A + 72 x^{5} e d^{2} b^{3} a^{7} A + 27 x^{5} e^{2} d b^{2} a^{8} A + 2 x^{5} e^{3} b a^{9} A + \frac{45}{4} x^{4} d^{3} b^{2} a^{8} B + \frac{15}{2} x^{4} e d^{2} b a^{9} B + \frac{3}{4} x^{4} e^{2} d a^{10} B + 30 x^{4} d^{3} b^{3} a^{7} A + \frac{135}{4} x^{4} e d^{2} b^{2} a^{8} A + \frac{15}{2} x^{4} e^{2} d b a^{9} A + \frac{1}{4} x^{4} e^{3} a^{10} A + \frac{10}{3} x^{3} d^{3} b a^{9} B + x^{3} e d^{2} a^{10} B + 15 x^{3} d^{3} b^{2} a^{8} A + 10 x^{3} e d^{2} b a^{9} A + x^{3} e^{2} d a^{10} A + \frac{1}{2} x^{2} d^{3} a^{10} B + 5 x^{2} d^{3} b a^{9} A + \frac{3}{2} x^{2} e d^{2} a^{10} A + x d^{3} a^{10} A"," ",0,"1/15*x^15*e^3*b^10*B + 3/14*x^14*e^2*d*b^10*B + 5/7*x^14*e^3*b^9*a*B + 1/14*x^14*e^3*b^10*A + 3/13*x^13*e*d^2*b^10*B + 30/13*x^13*e^2*d*b^9*a*B + 45/13*x^13*e^3*b^8*a^2*B + 3/13*x^13*e^2*d*b^10*A + 10/13*x^13*e^3*b^9*a*A + 1/12*x^12*d^3*b^10*B + 5/2*x^12*e*d^2*b^9*a*B + 45/4*x^12*e^2*d*b^8*a^2*B + 10*x^12*e^3*b^7*a^3*B + 1/4*x^12*e*d^2*b^10*A + 5/2*x^12*e^2*d*b^9*a*A + 15/4*x^12*e^3*b^8*a^2*A + 10/11*x^11*d^3*b^9*a*B + 135/11*x^11*e*d^2*b^8*a^2*B + 360/11*x^11*e^2*d*b^7*a^3*B + 210/11*x^11*e^3*b^6*a^4*B + 1/11*x^11*d^3*b^10*A + 30/11*x^11*e*d^2*b^9*a*A + 135/11*x^11*e^2*d*b^8*a^2*A + 120/11*x^11*e^3*b^7*a^3*A + 9/2*x^10*d^3*b^8*a^2*B + 36*x^10*e*d^2*b^7*a^3*B + 63*x^10*e^2*d*b^6*a^4*B + 126/5*x^10*e^3*b^5*a^5*B + x^10*d^3*b^9*a*A + 27/2*x^10*e*d^2*b^8*a^2*A + 36*x^10*e^2*d*b^7*a^3*A + 21*x^10*e^3*b^6*a^4*A + 40/3*x^9*d^3*b^7*a^3*B + 70*x^9*e*d^2*b^6*a^4*B + 84*x^9*e^2*d*b^5*a^5*B + 70/3*x^9*e^3*b^4*a^6*B + 5*x^9*d^3*b^8*a^2*A + 40*x^9*e*d^2*b^7*a^3*A + 70*x^9*e^2*d*b^6*a^4*A + 28*x^9*e^3*b^5*a^5*A + 105/4*x^8*d^3*b^6*a^4*B + 189/2*x^8*e*d^2*b^5*a^5*B + 315/4*x^8*e^2*d*b^4*a^6*B + 15*x^8*e^3*b^3*a^7*B + 15*x^8*d^3*b^7*a^3*A + 315/4*x^8*e*d^2*b^6*a^4*A + 189/2*x^8*e^2*d*b^5*a^5*A + 105/4*x^8*e^3*b^4*a^6*A + 36*x^7*d^3*b^5*a^5*B + 90*x^7*e*d^2*b^4*a^6*B + 360/7*x^7*e^2*d*b^3*a^7*B + 45/7*x^7*e^3*b^2*a^8*B + 30*x^7*d^3*b^6*a^4*A + 108*x^7*e*d^2*b^5*a^5*A + 90*x^7*e^2*d*b^4*a^6*A + 120/7*x^7*e^3*b^3*a^7*A + 35*x^6*d^3*b^4*a^6*B + 60*x^6*e*d^2*b^3*a^7*B + 45/2*x^6*e^2*d*b^2*a^8*B + 5/3*x^6*e^3*b*a^9*B + 42*x^6*d^3*b^5*a^5*A + 105*x^6*e*d^2*b^4*a^6*A + 60*x^6*e^2*d*b^3*a^7*A + 15/2*x^6*e^3*b^2*a^8*A + 24*x^5*d^3*b^3*a^7*B + 27*x^5*e*d^2*b^2*a^8*B + 6*x^5*e^2*d*b*a^9*B + 1/5*x^5*e^3*a^10*B + 42*x^5*d^3*b^4*a^6*A + 72*x^5*e*d^2*b^3*a^7*A + 27*x^5*e^2*d*b^2*a^8*A + 2*x^5*e^3*b*a^9*A + 45/4*x^4*d^3*b^2*a^8*B + 15/2*x^4*e*d^2*b*a^9*B + 3/4*x^4*e^2*d*a^10*B + 30*x^4*d^3*b^3*a^7*A + 135/4*x^4*e*d^2*b^2*a^8*A + 15/2*x^4*e^2*d*b*a^9*A + 1/4*x^4*e^3*a^10*A + 10/3*x^3*d^3*b*a^9*B + x^3*e*d^2*a^10*B + 15*x^3*d^3*b^2*a^8*A + 10*x^3*e*d^2*b*a^9*A + x^3*e^2*d*a^10*A + 1/2*x^2*d^3*a^10*B + 5*x^2*d^3*b*a^9*A + 3/2*x^2*e*d^2*a^10*A + x*d^3*a^10*A","B",0
1086,1,904,0,0.882038," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e^{2} b^{10} B + \frac{2}{13} x^{13} e d b^{10} B + \frac{10}{13} x^{13} e^{2} b^{9} a B + \frac{1}{13} x^{13} e^{2} b^{10} A + \frac{1}{12} x^{12} d^{2} b^{10} B + \frac{5}{3} x^{12} e d b^{9} a B + \frac{15}{4} x^{12} e^{2} b^{8} a^{2} B + \frac{1}{6} x^{12} e d b^{10} A + \frac{5}{6} x^{12} e^{2} b^{9} a A + \frac{10}{11} x^{11} d^{2} b^{9} a B + \frac{90}{11} x^{11} e d b^{8} a^{2} B + \frac{120}{11} x^{11} e^{2} b^{7} a^{3} B + \frac{1}{11} x^{11} d^{2} b^{10} A + \frac{20}{11} x^{11} e d b^{9} a A + \frac{45}{11} x^{11} e^{2} b^{8} a^{2} A + \frac{9}{2} x^{10} d^{2} b^{8} a^{2} B + 24 x^{10} e d b^{7} a^{3} B + 21 x^{10} e^{2} b^{6} a^{4} B + x^{10} d^{2} b^{9} a A + 9 x^{10} e d b^{8} a^{2} A + 12 x^{10} e^{2} b^{7} a^{3} A + \frac{40}{3} x^{9} d^{2} b^{7} a^{3} B + \frac{140}{3} x^{9} e d b^{6} a^{4} B + 28 x^{9} e^{2} b^{5} a^{5} B + 5 x^{9} d^{2} b^{8} a^{2} A + \frac{80}{3} x^{9} e d b^{7} a^{3} A + \frac{70}{3} x^{9} e^{2} b^{6} a^{4} A + \frac{105}{4} x^{8} d^{2} b^{6} a^{4} B + 63 x^{8} e d b^{5} a^{5} B + \frac{105}{4} x^{8} e^{2} b^{4} a^{6} B + 15 x^{8} d^{2} b^{7} a^{3} A + \frac{105}{2} x^{8} e d b^{6} a^{4} A + \frac{63}{2} x^{8} e^{2} b^{5} a^{5} A + 36 x^{7} d^{2} b^{5} a^{5} B + 60 x^{7} e d b^{4} a^{6} B + \frac{120}{7} x^{7} e^{2} b^{3} a^{7} B + 30 x^{7} d^{2} b^{6} a^{4} A + 72 x^{7} e d b^{5} a^{5} A + 30 x^{7} e^{2} b^{4} a^{6} A + 35 x^{6} d^{2} b^{4} a^{6} B + 40 x^{6} e d b^{3} a^{7} B + \frac{15}{2} x^{6} e^{2} b^{2} a^{8} B + 42 x^{6} d^{2} b^{5} a^{5} A + 70 x^{6} e d b^{4} a^{6} A + 20 x^{6} e^{2} b^{3} a^{7} A + 24 x^{5} d^{2} b^{3} a^{7} B + 18 x^{5} e d b^{2} a^{8} B + 2 x^{5} e^{2} b a^{9} B + 42 x^{5} d^{2} b^{4} a^{6} A + 48 x^{5} e d b^{3} a^{7} A + 9 x^{5} e^{2} b^{2} a^{8} A + \frac{45}{4} x^{4} d^{2} b^{2} a^{8} B + 5 x^{4} e d b a^{9} B + \frac{1}{4} x^{4} e^{2} a^{10} B + 30 x^{4} d^{2} b^{3} a^{7} A + \frac{45}{2} x^{4} e d b^{2} a^{8} A + \frac{5}{2} x^{4} e^{2} b a^{9} A + \frac{10}{3} x^{3} d^{2} b a^{9} B + \frac{2}{3} x^{3} e d a^{10} B + 15 x^{3} d^{2} b^{2} a^{8} A + \frac{20}{3} x^{3} e d b a^{9} A + \frac{1}{3} x^{3} e^{2} a^{10} A + \frac{1}{2} x^{2} d^{2} a^{10} B + 5 x^{2} d^{2} b a^{9} A + x^{2} e d a^{10} A + x d^{2} a^{10} A"," ",0,"1/14*x^14*e^2*b^10*B + 2/13*x^13*e*d*b^10*B + 10/13*x^13*e^2*b^9*a*B + 1/13*x^13*e^2*b^10*A + 1/12*x^12*d^2*b^10*B + 5/3*x^12*e*d*b^9*a*B + 15/4*x^12*e^2*b^8*a^2*B + 1/6*x^12*e*d*b^10*A + 5/6*x^12*e^2*b^9*a*A + 10/11*x^11*d^2*b^9*a*B + 90/11*x^11*e*d*b^8*a^2*B + 120/11*x^11*e^2*b^7*a^3*B + 1/11*x^11*d^2*b^10*A + 20/11*x^11*e*d*b^9*a*A + 45/11*x^11*e^2*b^8*a^2*A + 9/2*x^10*d^2*b^8*a^2*B + 24*x^10*e*d*b^7*a^3*B + 21*x^10*e^2*b^6*a^4*B + x^10*d^2*b^9*a*A + 9*x^10*e*d*b^8*a^2*A + 12*x^10*e^2*b^7*a^3*A + 40/3*x^9*d^2*b^7*a^3*B + 140/3*x^9*e*d*b^6*a^4*B + 28*x^9*e^2*b^5*a^5*B + 5*x^9*d^2*b^8*a^2*A + 80/3*x^9*e*d*b^7*a^3*A + 70/3*x^9*e^2*b^6*a^4*A + 105/4*x^8*d^2*b^6*a^4*B + 63*x^8*e*d*b^5*a^5*B + 105/4*x^8*e^2*b^4*a^6*B + 15*x^8*d^2*b^7*a^3*A + 105/2*x^8*e*d*b^6*a^4*A + 63/2*x^8*e^2*b^5*a^5*A + 36*x^7*d^2*b^5*a^5*B + 60*x^7*e*d*b^4*a^6*B + 120/7*x^7*e^2*b^3*a^7*B + 30*x^7*d^2*b^6*a^4*A + 72*x^7*e*d*b^5*a^5*A + 30*x^7*e^2*b^4*a^6*A + 35*x^6*d^2*b^4*a^6*B + 40*x^6*e*d*b^3*a^7*B + 15/2*x^6*e^2*b^2*a^8*B + 42*x^6*d^2*b^5*a^5*A + 70*x^6*e*d*b^4*a^6*A + 20*x^6*e^2*b^3*a^7*A + 24*x^5*d^2*b^3*a^7*B + 18*x^5*e*d*b^2*a^8*B + 2*x^5*e^2*b*a^9*B + 42*x^5*d^2*b^4*a^6*A + 48*x^5*e*d*b^3*a^7*A + 9*x^5*e^2*b^2*a^8*A + 45/4*x^4*d^2*b^2*a^8*B + 5*x^4*e*d*b*a^9*B + 1/4*x^4*e^2*a^10*B + 30*x^4*d^2*b^3*a^7*A + 45/2*x^4*e*d*b^2*a^8*A + 5/2*x^4*e^2*b*a^9*A + 10/3*x^3*d^2*b*a^9*B + 2/3*x^3*e*d*a^10*B + 15*x^3*d^2*b^2*a^8*A + 20/3*x^3*e*d*b*a^9*A + 1/3*x^3*e^2*a^10*A + 1/2*x^2*d^2*a^10*B + 5*x^2*d^2*b*a^9*A + x^2*e*d*a^10*A + x*d^2*a^10*A","B",0
1087,1,529,0,0.930383," ","integrate((b*x+a)^10*(B*x+A)*(e*x+d),x, algorithm=""fricas"")","\frac{1}{13} x^{13} e b^{10} B + \frac{1}{12} x^{12} d b^{10} B + \frac{5}{6} x^{12} e b^{9} a B + \frac{1}{12} x^{12} e b^{10} A + \frac{10}{11} x^{11} d b^{9} a B + \frac{45}{11} x^{11} e b^{8} a^{2} B + \frac{1}{11} x^{11} d b^{10} A + \frac{10}{11} x^{11} e b^{9} a A + \frac{9}{2} x^{10} d b^{8} a^{2} B + 12 x^{10} e b^{7} a^{3} B + x^{10} d b^{9} a A + \frac{9}{2} x^{10} e b^{8} a^{2} A + \frac{40}{3} x^{9} d b^{7} a^{3} B + \frac{70}{3} x^{9} e b^{6} a^{4} B + 5 x^{9} d b^{8} a^{2} A + \frac{40}{3} x^{9} e b^{7} a^{3} A + \frac{105}{4} x^{8} d b^{6} a^{4} B + \frac{63}{2} x^{8} e b^{5} a^{5} B + 15 x^{8} d b^{7} a^{3} A + \frac{105}{4} x^{8} e b^{6} a^{4} A + 36 x^{7} d b^{5} a^{5} B + 30 x^{7} e b^{4} a^{6} B + 30 x^{7} d b^{6} a^{4} A + 36 x^{7} e b^{5} a^{5} A + 35 x^{6} d b^{4} a^{6} B + 20 x^{6} e b^{3} a^{7} B + 42 x^{6} d b^{5} a^{5} A + 35 x^{6} e b^{4} a^{6} A + 24 x^{5} d b^{3} a^{7} B + 9 x^{5} e b^{2} a^{8} B + 42 x^{5} d b^{4} a^{6} A + 24 x^{5} e b^{3} a^{7} A + \frac{45}{4} x^{4} d b^{2} a^{8} B + \frac{5}{2} x^{4} e b a^{9} B + 30 x^{4} d b^{3} a^{7} A + \frac{45}{4} x^{4} e b^{2} a^{8} A + \frac{10}{3} x^{3} d b a^{9} B + \frac{1}{3} x^{3} e a^{10} B + 15 x^{3} d b^{2} a^{8} A + \frac{10}{3} x^{3} e b a^{9} A + \frac{1}{2} x^{2} d a^{10} B + 5 x^{2} d b a^{9} A + \frac{1}{2} x^{2} e a^{10} A + x d a^{10} A"," ",0,"1/13*x^13*e*b^10*B + 1/12*x^12*d*b^10*B + 5/6*x^12*e*b^9*a*B + 1/12*x^12*e*b^10*A + 10/11*x^11*d*b^9*a*B + 45/11*x^11*e*b^8*a^2*B + 1/11*x^11*d*b^10*A + 10/11*x^11*e*b^9*a*A + 9/2*x^10*d*b^8*a^2*B + 12*x^10*e*b^7*a^3*B + x^10*d*b^9*a*A + 9/2*x^10*e*b^8*a^2*A + 40/3*x^9*d*b^7*a^3*B + 70/3*x^9*e*b^6*a^4*B + 5*x^9*d*b^8*a^2*A + 40/3*x^9*e*b^7*a^3*A + 105/4*x^8*d*b^6*a^4*B + 63/2*x^8*e*b^5*a^5*B + 15*x^8*d*b^7*a^3*A + 105/4*x^8*e*b^6*a^4*A + 36*x^7*d*b^5*a^5*B + 30*x^7*e*b^4*a^6*B + 30*x^7*d*b^6*a^4*A + 36*x^7*e*b^5*a^5*A + 35*x^6*d*b^4*a^6*B + 20*x^6*e*b^3*a^7*B + 42*x^6*d*b^5*a^5*A + 35*x^6*e*b^4*a^6*A + 24*x^5*d*b^3*a^7*B + 9*x^5*e*b^2*a^8*B + 42*x^5*d*b^4*a^6*A + 24*x^5*e*b^3*a^7*A + 45/4*x^4*d*b^2*a^8*B + 5/2*x^4*e*b*a^9*B + 30*x^4*d*b^3*a^7*A + 45/4*x^4*e*b^2*a^8*A + 10/3*x^3*d*b*a^9*B + 1/3*x^3*e*a^10*B + 15*x^3*d*b^2*a^8*A + 10/3*x^3*e*b*a^9*A + 1/2*x^2*d*a^10*B + 5*x^2*d*b*a^9*A + 1/2*x^2*e*a^10*A + x*d*a^10*A","B",0
1088,1,241,0,0.768888," ","integrate((b*x+a)^10*(B*x+A),x, algorithm=""fricas"")","\frac{1}{12} x^{12} b^{10} B + \frac{10}{11} x^{11} b^{9} a B + \frac{1}{11} x^{11} b^{10} A + \frac{9}{2} x^{10} b^{8} a^{2} B + x^{10} b^{9} a A + \frac{40}{3} x^{9} b^{7} a^{3} B + 5 x^{9} b^{8} a^{2} A + \frac{105}{4} x^{8} b^{6} a^{4} B + 15 x^{8} b^{7} a^{3} A + 36 x^{7} b^{5} a^{5} B + 30 x^{7} b^{6} a^{4} A + 35 x^{6} b^{4} a^{6} B + 42 x^{6} b^{5} a^{5} A + 24 x^{5} b^{3} a^{7} B + 42 x^{5} b^{4} a^{6} A + \frac{45}{4} x^{4} b^{2} a^{8} B + 30 x^{4} b^{3} a^{7} A + \frac{10}{3} x^{3} b a^{9} B + 15 x^{3} b^{2} a^{8} A + \frac{1}{2} x^{2} a^{10} B + 5 x^{2} b a^{9} A + x a^{10} A"," ",0,"1/12*x^12*b^10*B + 10/11*x^11*b^9*a*B + 1/11*x^11*b^10*A + 9/2*x^10*b^8*a^2*B + x^10*b^9*a*A + 40/3*x^9*b^7*a^3*B + 5*x^9*b^8*a^2*A + 105/4*x^8*b^6*a^4*B + 15*x^8*b^7*a^3*A + 36*x^7*b^5*a^5*B + 30*x^7*b^6*a^4*A + 35*x^6*b^4*a^6*B + 42*x^6*b^5*a^5*A + 24*x^5*b^3*a^7*B + 42*x^5*b^4*a^6*A + 45/4*x^4*b^2*a^8*B + 30*x^4*b^3*a^7*A + 10/3*x^3*b*a^9*B + 15*x^3*b^2*a^8*A + 1/2*x^2*a^10*B + 5*x^2*b*a^9*A + x*a^10*A","B",0
1089,1,1805,0,1.146046," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d),x, algorithm=""fricas"")","\frac{2520 \, B b^{10} e^{11} x^{11} - 2772 \, {\left(B b^{10} d e^{10} - {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 3080 \, {\left(B b^{10} d^{2} e^{9} - {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 3465 \, {\left(B b^{10} d^{3} e^{8} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 3960 \, {\left(B b^{10} d^{4} e^{7} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 4620 \, {\left(B b^{10} d^{5} e^{6} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 5544 \, {\left(B b^{10} d^{6} e^{5} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 6930 \, {\left(B b^{10} d^{7} e^{4} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 9240 \, {\left(B b^{10} d^{8} e^{3} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} - 13860 \, {\left(B b^{10} d^{9} e^{2} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 27720 \, {\left(B b^{10} d^{10} e - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 27720 \, {\left(B b^{10} d^{11} - A a^{10} e^{11} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 5 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 15 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 30 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10}\right)} \log\left(e x + d\right)}{27720 \, e^{12}}"," ",0,"1/27720*(2520*B*b^10*e^11*x^11 - 2772*(B*b^10*d*e^10 - (10*B*a*b^9 + A*b^10)*e^11)*x^10 + 3080*(B*b^10*d^2*e^9 - (10*B*a*b^9 + A*b^10)*d*e^10 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 3465*(B*b^10*d^3*e^8 - (10*B*a*b^9 + A*b^10)*d^2*e^9 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 3960*(B*b^10*d^4*e^7 - (10*B*a*b^9 + A*b^10)*d^3*e^8 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 4620*(B*b^10*d^5*e^6 - (10*B*a*b^9 + A*b^10)*d^4*e^7 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 5544*(B*b^10*d^6*e^5 - (10*B*a*b^9 + A*b^10)*d^5*e^6 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 6930*(B*b^10*d^7*e^4 - (10*B*a*b^9 + A*b^10)*d^6*e^5 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 9240*(B*b^10*d^8*e^3 - (10*B*a*b^9 + A*b^10)*d^7*e^4 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 13860*(B*b^10*d^9*e^2 - (10*B*a*b^9 + A*b^10)*d^8*e^3 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 27720*(B*b^10*d^10*e - (10*B*a*b^9 + A*b^10)*d^9*e^2 + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x - 27720*(B*b^10*d^11 - A*a^10*e^11 - (10*B*a*b^9 + A*b^10)*d^10*e + 5*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 15*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 30*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + (B*a^10 + 10*A*a^9*b)*d*e^10)*log(e*x + d))/e^12","B",0
1090,1,2329,0,1.238304," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{252 \, B b^{10} e^{11} x^{11} + 2520 \, B b^{10} d^{11} - 2520 \, A a^{10} e^{11} - 2520 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 12600 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 37800 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 75600 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 105840 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 105840 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 75600 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 37800 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 12600 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 2520 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 28 \, {\left(11 \, B b^{10} d e^{10} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 35 \, {\left(11 \, B b^{10} d^{2} e^{9} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 45 \, {\left(11 \, B b^{10} d^{3} e^{8} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 60 \, {\left(11 \, B b^{10} d^{4} e^{7} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 84 \, {\left(11 \, B b^{10} d^{5} e^{6} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 126 \, {\left(11 \, B b^{10} d^{6} e^{5} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 210 \, {\left(11 \, B b^{10} d^{7} e^{4} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 420 \, {\left(11 \, B b^{10} d^{8} e^{3} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} - 1260 \, {\left(11 \, B b^{10} d^{9} e^{2} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 2520 \, {\left(10 \, B b^{10} d^{10} e - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 40 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 105 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 180 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 210 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 168 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 90 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 30 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10}\right)} x + 2520 \, {\left(11 \, B b^{10} d^{11} - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + {\left(11 \, B b^{10} d^{10} e - 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x\right)} \log\left(e x + d\right)}{2520 \, {\left(e^{13} x + d e^{12}\right)}}"," ",0,"1/2520*(252*B*b^10*e^11*x^11 + 2520*B*b^10*d^11 - 2520*A*a^10*e^11 - 2520*(10*B*a*b^9 + A*b^10)*d^10*e + 12600*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 37800*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 75600*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 105840*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 105840*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 75600*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 37800*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 12600*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 2520*(B*a^10 + 10*A*a^9*b)*d*e^10 - 28*(11*B*b^10*d*e^10 - 10*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 35*(11*B*b^10*d^2*e^9 - 10*(10*B*a*b^9 + A*b^10)*d*e^10 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 45*(11*B*b^10*d^3*e^8 - 10*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 60*(11*B*b^10*d^4*e^7 - 10*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 84*(11*B*b^10*d^5*e^6 - 10*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 126*(11*B*b^10*d^6*e^5 - 10*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 210*(11*B*b^10*d^7*e^4 - 10*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 420*(11*B*b^10*d^8*e^3 - 10*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 1260*(11*B*b^10*d^9*e^2 - 10*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 2520*(10*B*b^10*d^10*e - 9*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 40*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 105*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 180*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 210*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 168*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 90*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 30*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10)*x + 2520*(11*B*b^10*d^11 - 10*(10*B*a*b^9 + A*b^10)*d^10*e + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + (B*a^10 + 10*A*a^9*b)*d*e^10 + (11*B*b^10*d^10*e - 10*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x)*log(e*x + d))/(e^13*x + d*e^12)","B",0
1091,1,2547,0,1.547431," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{56 \, B b^{10} e^{11} x^{11} - 5292 \, B b^{10} d^{11} - 252 \, A a^{10} e^{11} + 4788 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 21420 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 56700 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 98280 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 116424 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 95256 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 52920 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 18900 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 3780 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 252 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 7 \, {\left(11 \, B b^{10} d e^{10} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 10 \, {\left(11 \, B b^{10} d^{2} e^{9} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 15 \, {\left(11 \, B b^{10} d^{3} e^{8} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 24 \, {\left(11 \, B b^{10} d^{4} e^{7} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 42 \, {\left(11 \, B b^{10} d^{5} e^{6} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 84 \, {\left(11 \, B b^{10} d^{6} e^{5} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 210 \, {\left(11 \, B b^{10} d^{7} e^{4} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 840 \, {\left(11 \, B b^{10} d^{8} e^{3} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 252 \, {\left(144 \, B b^{10} d^{9} e^{2} - 116 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 455 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 1035 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 1500 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 1428 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 882 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 60 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10}\right)} x^{2} + 504 \, {\left(34 \, B b^{10} d^{10} e - 26 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 95 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 195 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 240 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 168 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 30 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 30 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} - {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 2520 \, {\left(11 \, B b^{10} d^{11} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + {\left(11 \, B b^{10} d^{9} e^{2} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 2 \, {\left(11 \, B b^{10} d^{10} e - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10}\right)} x\right)} \log\left(e x + d\right)}{504 \, {\left(e^{14} x^{2} + 2 \, d e^{13} x + d^{2} e^{12}\right)}}"," ",0,"1/504*(56*B*b^10*e^11*x^11 - 5292*B*b^10*d^11 - 252*A*a^10*e^11 + 4788*(10*B*a*b^9 + A*b^10)*d^10*e - 21420*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 56700*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 98280*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 116424*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 95256*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 52920*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 18900*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 3780*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 252*(B*a^10 + 10*A*a^9*b)*d*e^10 - 7*(11*B*b^10*d*e^10 - 9*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 10*(11*B*b^10*d^2*e^9 - 9*(10*B*a*b^9 + A*b^10)*d*e^10 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 15*(11*B*b^10*d^3*e^8 - 9*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 24*(11*B*b^10*d^4*e^7 - 9*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 42*(11*B*b^10*d^5*e^6 - 9*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 84*(11*B*b^10*d^6*e^5 - 9*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 210*(11*B*b^10*d^7*e^4 - 9*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 840*(11*B*b^10*d^8*e^3 - 9*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 252*(144*B*b^10*d^9*e^2 - 116*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 455*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 1035*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 1500*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 1428*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 882*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 60*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10)*x^2 + 504*(34*B*b^10*d^10*e - 26*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 95*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 195*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 240*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 168*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 30*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 30*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 - (B*a^10 + 10*A*a^9*b)*e^11)*x - 2520*(11*B*b^10*d^11 - 9*(10*B*a*b^9 + A*b^10)*d^10*e + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - (2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + (11*B*b^10*d^9*e^2 - 9*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - (2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 2*(11*B*b^10*d^10*e - 9*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - (2*B*a^9*b + 9*A*a^8*b^2)*d*e^10)*x)*log(e*x + d))/(e^14*x^2 + 2*d*e^13*x + d^2*e^12)","B",0
1092,1,2702,0,1.691893," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{21 \, B b^{10} e^{11} x^{11} + 8372 \, B b^{10} d^{11} - 56 \, A a^{10} e^{11} - 6776 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 26740 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 61320 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 89880 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 87024 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 55272 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 21840 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 4620 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 280 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 28 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 3 \, {\left(11 \, B b^{10} d e^{10} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 5 \, {\left(11 \, B b^{10} d^{2} e^{9} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 9 \, {\left(11 \, B b^{10} d^{3} e^{8} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 18 \, {\left(11 \, B b^{10} d^{4} e^{7} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 42 \, {\left(11 \, B b^{10} d^{5} e^{6} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 126 \, {\left(11 \, B b^{10} d^{6} e^{5} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 630 \, {\left(11 \, B b^{10} d^{7} e^{4} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} - 28 \, {\left(1516 \, B b^{10} d^{8} e^{3} - 1078 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 3665 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 7050 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 8340 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 6132 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 2646 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 540 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10}\right)} x^{3} - 84 \, {\left(526 \, B b^{10} d^{9} e^{2} - 358 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 1145 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 2010 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 2040 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 1092 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 126 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 180 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 90 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 84 \, {\left(31 \, B b^{10} d^{10} e + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} - 115 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 510 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} - 1110 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 1428 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} - 1134 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 540 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 135 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x + 2520 \, {\left(11 \, B b^{10} d^{11} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + {\left(11 \, B b^{10} d^{8} e^{3} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 3 \, {\left(11 \, B b^{10} d^{9} e^{2} - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10}\right)} x^{2} + 3 \, {\left(11 \, B b^{10} d^{10} e - 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9}\right)} x\right)} \log\left(e x + d\right)}{168 \, {\left(e^{15} x^{3} + 3 \, d e^{14} x^{2} + 3 \, d^{2} e^{13} x + d^{3} e^{12}\right)}}"," ",0,"1/168*(21*B*b^10*e^11*x^11 + 8372*B*b^10*d^11 - 56*A*a^10*e^11 - 6776*(10*B*a*b^9 + A*b^10)*d^10*e + 26740*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 61320*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 89880*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 87024*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 55272*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 21840*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 4620*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 280*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 28*(B*a^10 + 10*A*a^9*b)*d*e^10 - 3*(11*B*b^10*d*e^10 - 8*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 5*(11*B*b^10*d^2*e^9 - 8*(10*B*a*b^9 + A*b^10)*d*e^10 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 9*(11*B*b^10*d^3*e^8 - 8*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 18*(11*B*b^10*d^4*e^7 - 8*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 42*(11*B*b^10*d^5*e^6 - 8*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 126*(11*B*b^10*d^6*e^5 - 8*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 630*(11*B*b^10*d^7*e^4 - 8*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 - 28*(1516*B*b^10*d^8*e^3 - 1078*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 3665*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 7050*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 8340*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 6132*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 2646*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 540*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10)*x^3 - 84*(526*B*b^10*d^9*e^2 - 358*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 1145*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 2010*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 2040*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 1092*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 126*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 180*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 90*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 84*(31*B*b^10*d^10*e + 2*(10*B*a*b^9 + A*b^10)*d^9*e^2 - 115*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 510*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 - 1110*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 1428*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 - 1134*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 540*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 135*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x + 2520*(11*B*b^10*d^11 - 8*(10*B*a*b^9 + A*b^10)*d^10*e + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + (11*B*b^10*d^8*e^3 - 8*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 3*(11*B*b^10*d^9*e^2 - 8*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10)*x^2 + 3*(11*B*b^10*d^10*e - 8*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9)*x)*log(e*x + d))/(e^15*x^3 + 3*d*e^14*x^2 + 3*d^2*e^13*x + d^3*e^12)","B",0
1093,1,2808,0,1.410040," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, B b^{10} e^{11} x^{11} - 11837 \, B b^{10} d^{11} - 21 \, A a^{10} e^{11} + 8449 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 28875 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 55965 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 66990 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 50274 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 22638 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 5250 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 315 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 35 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 7 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 2 \, {\left(11 \, B b^{10} d e^{10} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 4 \, {\left(11 \, B b^{10} d^{2} e^{9} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 9 \, {\left(11 \, B b^{10} d^{3} e^{8} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 24 \, {\left(11 \, B b^{10} d^{4} e^{7} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 84 \, {\left(11 \, B b^{10} d^{5} e^{6} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 504 \, {\left(11 \, B b^{10} d^{6} e^{5} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 7 \, {\left(6559 \, B b^{10} d^{7} e^{4} - 4043 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 11625 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 18255 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 16680 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 8568 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 2016 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10}\right)} x^{4} + 28 \, {\left(2599 \, B b^{10} d^{8} e^{3} - 1523 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 4065 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 5655 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 4080 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 1008 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} - 504 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 42 \, {\left(619 \, B b^{10} d^{9} e^{2} - 263 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 285 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 645 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} - 2220 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 2772 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} - 1764 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 540 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 28 \, {\left(701 \, B b^{10} d^{10} e - 577 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 2235 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 4845 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 6420 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 5292 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 2604 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 660 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 2520 \, {\left(11 \, B b^{10} d^{11} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + {\left(11 \, B b^{10} d^{7} e^{4} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 4 \, {\left(11 \, B b^{10} d^{8} e^{3} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10}\right)} x^{3} + 6 \, {\left(11 \, B b^{10} d^{9} e^{2} - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9}\right)} x^{2} + 4 \, {\left(11 \, B b^{10} d^{10} e - 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8}\right)} x\right)} \log\left(e x + d\right)}{84 \, {\left(e^{16} x^{4} + 4 \, d e^{15} x^{3} + 6 \, d^{2} e^{14} x^{2} + 4 \, d^{3} e^{13} x + d^{4} e^{12}\right)}}"," ",0,"1/84*(12*B*b^10*e^11*x^11 - 11837*B*b^10*d^11 - 21*A*a^10*e^11 + 8449*(10*B*a*b^9 + A*b^10)*d^10*e - 28875*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 55965*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 66990*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 50274*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 22638*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 5250*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 315*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 35*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 7*(B*a^10 + 10*A*a^9*b)*d*e^10 - 2*(11*B*b^10*d*e^10 - 7*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 4*(11*B*b^10*d^2*e^9 - 7*(10*B*a*b^9 + A*b^10)*d*e^10 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 9*(11*B*b^10*d^3*e^8 - 7*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 24*(11*B*b^10*d^4*e^7 - 7*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 84*(11*B*b^10*d^5*e^6 - 7*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 504*(11*B*b^10*d^6*e^5 - 7*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 7*(6559*B*b^10*d^7*e^4 - 4043*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 11625*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 18255*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 16680*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 8568*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 2016*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10)*x^4 + 28*(2599*B*b^10*d^8*e^3 - 1523*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 4065*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 5655*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 4080*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 1008*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 - 504*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 42*(619*B*b^10*d^9*e^2 - 263*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 285*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 645*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 - 2220*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 2772*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 - 1764*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 540*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 28*(701*B*b^10*d^10*e - 577*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 2235*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 4845*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 6420*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 5292*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 2604*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 660*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x - 2520*(11*B*b^10*d^11 - 7*(10*B*a*b^9 + A*b^10)*d^10*e + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + (11*B*b^10*d^7*e^4 - 7*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - (4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 4*(11*B*b^10*d^8*e^3 - 7*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - (4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10)*x^3 + 6*(11*B*b^10*d^9*e^2 - 7*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9)*x^2 + 4*(11*B*b^10*d^10*e - 7*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8)*x)*log(e*x + d))/(e^16*x^4 + 4*d*e^15*x^3 + 6*d^2*e^14*x^2 + 4*d^3*e^13*x + d^4*e^12)","B",0
1094,1,2851,0,1.318662," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, B b^{10} e^{11} x^{11} + 15797 \, B b^{10} d^{11} - 12 \, A a^{10} e^{11} - 9762 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 28185 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 44580 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 41310 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 21924 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 5754 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 3 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 2 \, {\left(11 \, B b^{10} d e^{10} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 5 \, {\left(11 \, B b^{10} d^{2} e^{9} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 15 \, {\left(11 \, B b^{10} d^{3} e^{8} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 60 \, {\left(11 \, B b^{10} d^{4} e^{7} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 420 \, {\left(11 \, B b^{10} d^{5} e^{6} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} - {\left(47497 \, B b^{10} d^{6} e^{5} - 24762 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 58125 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 70500 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 45000 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 12600 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10}\right)} x^{5} - 5 \, {\left(19777 \, B b^{10} d^{7} e^{4} - 9642 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 20325 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 20100 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 7200 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 2520 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} - 2520 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} - 10 \, {\left(5917 \, B b^{10} d^{8} e^{3} - 2082 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 1425 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 5100 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} - 11700 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 10080 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} - 3780 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 10 \, {\left(3323 \, B b^{10} d^{9} e^{2} - 2958 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 11175 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 21900 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 24300 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 15120 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 4620 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 5 \, {\left(10253 \, B b^{10} d^{10} e - 6738 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 20625 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 34500 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 33750 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 18900 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 5250 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} - 3 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x + 2520 \, {\left(11 \, B b^{10} d^{11} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + {\left(11 \, B b^{10} d^{6} e^{5} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 5 \, {\left(11 \, B b^{10} d^{7} e^{4} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10}\right)} x^{4} + 10 \, {\left(11 \, B b^{10} d^{8} e^{3} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(11 \, B b^{10} d^{9} e^{2} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(11 \, B b^{10} d^{10} e - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{17} x^{5} + 5 \, d e^{16} x^{4} + 10 \, d^{2} e^{15} x^{3} + 10 \, d^{3} e^{14} x^{2} + 5 \, d^{4} e^{13} x + d^{5} e^{12}\right)}}"," ",0,"1/60*(10*B*b^10*e^11*x^11 + 15797*B*b^10*d^11 - 12*A*a^10*e^11 - 9762*(10*B*a*b^9 + A*b^10)*d^10*e + 28185*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 44580*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 41310*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 21924*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 5754*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 3*(B*a^10 + 10*A*a^9*b)*d*e^10 - 2*(11*B*b^10*d*e^10 - 6*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 5*(11*B*b^10*d^2*e^9 - 6*(10*B*a*b^9 + A*b^10)*d*e^10 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 15*(11*B*b^10*d^3*e^8 - 6*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 60*(11*B*b^10*d^4*e^7 - 6*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 420*(11*B*b^10*d^5*e^6 - 6*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 - (47497*B*b^10*d^6*e^5 - 24762*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 58125*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 70500*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 45000*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 12600*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10)*x^5 - 5*(19777*B*b^10*d^7*e^4 - 9642*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 20325*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 20100*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 7200*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 2520*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 - 2520*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 - 10*(5917*B*b^10*d^8*e^3 - 2082*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 1425*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 5100*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 - 11700*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 10080*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 - 3780*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 10*(3323*B*b^10*d^9*e^2 - 2958*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 11175*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 21900*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 24300*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 15120*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 4620*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 5*(10253*B*b^10*d^10*e - 6738*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 20625*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 34500*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 33750*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 18900*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 5250*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 - 3*(B*a^10 + 10*A*a^9*b)*e^11)*x + 2520*(11*B*b^10*d^11 - 6*(10*B*a*b^9 + A*b^10)*d^10*e + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + (11*B*b^10*d^6*e^5 - 6*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 5*(11*B*b^10*d^7*e^4 - 6*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10)*x^4 + 10*(11*B*b^10*d^8*e^3 - 6*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9)*x^3 + 10*(11*B*b^10*d^9*e^2 - 6*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8)*x^2 + 5*(11*B*b^10*d^10*e - 6*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7)*x)*log(e*x + d))/(e^17*x^5 + 5*d*e^16*x^4 + 10*d^2*e^15*x^3 + 10*d^3*e^14*x^2 + 5*d^4*e^13*x + d^5*e^12)","B",0
1095,1,2850,0,1.179057," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{12 \, B b^{10} e^{11} x^{11} - 20417 \, B b^{10} d^{11} - 10 \, A a^{10} e^{11} + 10655 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 25090 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 30690 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 20070 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 6174 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 2 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 3 \, {\left(11 \, B b^{10} d e^{10} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 10 \, {\left(11 \, B b^{10} d^{2} e^{9} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 45 \, {\left(11 \, B b^{10} d^{3} e^{8} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 360 \, {\left(11 \, B b^{10} d^{4} e^{7} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + {\left(47497 \, B b^{10} d^{5} e^{6} - 20215 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 36650 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 31050 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 10800 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10}\right)} x^{6} + 6 \, {\left(19777 \, B b^{10} d^{6} e^{5} - 7615 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 11450 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 5850 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} - 1800 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 2520 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 15 \, {\left(5917 \, B b^{10} d^{7} e^{4} - 1315 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} - 1150 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 6750 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} - 8100 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 3780 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} - 20 \, {\left(3323 \, B b^{10} d^{8} e^{3} - 2885 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 9550 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 15150 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 12300 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 4620 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} - 15 \, {\left(10253 \, B b^{10} d^{9} e^{2} - 6035 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 15850 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 21450 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 15450 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 5250 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 6 \, {\left(15797 \, B b^{10} d^{10} e - 8555 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 20890 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 26490 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 17970 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 5754 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 2 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 2520 \, {\left(11 \, B b^{10} d^{11} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + {\left(11 \, B b^{10} d^{5} e^{6} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 6 \, {\left(11 \, B b^{10} d^{6} e^{5} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10}\right)} x^{5} + 15 \, {\left(11 \, B b^{10} d^{7} e^{4} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9}\right)} x^{4} + 20 \, {\left(11 \, B b^{10} d^{8} e^{3} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8}\right)} x^{3} + 15 \, {\left(11 \, B b^{10} d^{9} e^{2} - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7}\right)} x^{2} + 6 \, {\left(11 \, B b^{10} d^{10} e - 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6}\right)} x\right)} \log\left(e x + d\right)}{60 \, {\left(e^{18} x^{6} + 6 \, d e^{17} x^{5} + 15 \, d^{2} e^{16} x^{4} + 20 \, d^{3} e^{15} x^{3} + 15 \, d^{4} e^{14} x^{2} + 6 \, d^{5} e^{13} x + d^{6} e^{12}\right)}}"," ",0,"1/60*(12*B*b^10*e^11*x^11 - 20417*B*b^10*d^11 - 10*A*a^10*e^11 + 10655*(10*B*a*b^9 + A*b^10)*d^10*e - 25090*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 30690*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 20070*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 6174*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 2*(B*a^10 + 10*A*a^9*b)*d*e^10 - 3*(11*B*b^10*d*e^10 - 5*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 10*(11*B*b^10*d^2*e^9 - 5*(10*B*a*b^9 + A*b^10)*d*e^10 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 45*(11*B*b^10*d^3*e^8 - 5*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 360*(11*B*b^10*d^4*e^7 - 5*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + (47497*B*b^10*d^5*e^6 - 20215*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 36650*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 31050*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 10800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10)*x^6 + 6*(19777*B*b^10*d^6*e^5 - 7615*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 11450*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 5850*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 - 1800*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 2520*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 15*(5917*B*b^10*d^7*e^4 - 1315*(10*B*a*b^9 + A*b^10)*d^6*e^5 - 1150*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 6750*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 - 8100*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 3780*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 - 20*(3323*B*b^10*d^8*e^3 - 2885*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 9550*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 15150*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 12300*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 4620*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 15*(10253*B*b^10*d^9*e^2 - 6035*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 15850*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 21450*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 15450*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 5250*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 6*(15797*B*b^10*d^10*e - 8555*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 20890*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 26490*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 17970*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 5754*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 2*(B*a^10 + 10*A*a^9*b)*e^11)*x - 2520*(11*B*b^10*d^11 - 5*(10*B*a*b^9 + A*b^10)*d^10*e + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + (11*B*b^10*d^5*e^6 - 5*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 6*(11*B*b^10*d^6*e^5 - 5*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10)*x^5 + 15*(11*B*b^10*d^7*e^4 - 5*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9)*x^4 + 20*(11*B*b^10*d^8*e^3 - 5*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8)*x^3 + 15*(11*B*b^10*d^9*e^2 - 5*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7)*x^2 + 6*(11*B*b^10*d^10*e - 5*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6)*x)*log(e*x + d))/(e^18*x^6 + 6*d*e^17*x^5 + 15*d^2*e^16*x^4 + 20*d^3*e^15*x^3 + 15*d^4*e^14*x^2 + 6*d^5*e^13*x + d^6*e^12)","B",0
1096,1,2783,0,1.424833," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^8,x, algorithm=""fricas"")","\frac{21 \, B b^{10} e^{11} x^{11} + 25961 \, B b^{10} d^{11} - 12 \, A a^{10} e^{11} - 11044 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 20094 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 17316 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 6534 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 4 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 2 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 7 \, {\left(11 \, B b^{10} d e^{10} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 35 \, {\left(11 \, B b^{10} d^{2} e^{9} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 315 \, {\left(11 \, B b^{10} d^{3} e^{8} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} - 49 \, {\left(937 \, B b^{10} d^{4} e^{7} - 308 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 390 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 180 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10}\right)} x^{7} - 49 \, {\left(2599 \, B b^{10} d^{5} e^{6} - 716 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 570 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 180 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} - 360 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 72 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} - 147 \, {\left(619 \, B b^{10} d^{6} e^{5} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} - 510 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 900 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} - 540 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 72 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 12 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 35 \, {\left(4907 \, B b^{10} d^{7} e^{4} - 3388 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 8610 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 9660 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 4620 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 35 \, {\left(11837 \, B b^{10} d^{8} e^{3} - 5908 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 12390 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 12180 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 5250 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} - 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 21 \, {\left(17381 \, B b^{10} d^{9} e^{2} - 7924 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 15414 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 14196 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 5754 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 4 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 7 \, {\left(22001 \, B b^{10} d^{10} e - 9604 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 17934 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 15876 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 6174 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 4 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} - 2 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x + 2520 \, {\left(11 \, B b^{10} d^{11} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + {\left(11 \, B b^{10} d^{4} e^{7} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 7 \, {\left(11 \, B b^{10} d^{5} e^{6} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10}\right)} x^{6} + 21 \, {\left(11 \, B b^{10} d^{6} e^{5} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9}\right)} x^{5} + 35 \, {\left(11 \, B b^{10} d^{7} e^{4} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8}\right)} x^{4} + 35 \, {\left(11 \, B b^{10} d^{8} e^{3} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7}\right)} x^{3} + 21 \, {\left(11 \, B b^{10} d^{9} e^{2} - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6}\right)} x^{2} + 7 \, {\left(11 \, B b^{10} d^{10} e - 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5}\right)} x\right)} \log\left(e x + d\right)}{84 \, {\left(e^{19} x^{7} + 7 \, d e^{18} x^{6} + 21 \, d^{2} e^{17} x^{5} + 35 \, d^{3} e^{16} x^{4} + 35 \, d^{4} e^{15} x^{3} + 21 \, d^{5} e^{14} x^{2} + 7 \, d^{6} e^{13} x + d^{7} e^{12}\right)}}"," ",0,"1/84*(21*B*b^10*e^11*x^11 + 25961*B*b^10*d^11 - 12*A*a^10*e^11 - 11044*(10*B*a*b^9 + A*b^10)*d^10*e + 20094*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 17316*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 6534*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 4*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 2*(B*a^10 + 10*A*a^9*b)*d*e^10 - 7*(11*B*b^10*d*e^10 - 4*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 35*(11*B*b^10*d^2*e^9 - 4*(10*B*a*b^9 + A*b^10)*d*e^10 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 315*(11*B*b^10*d^3*e^8 - 4*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 - 49*(937*B*b^10*d^4*e^7 - 308*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 390*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 180*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10)*x^7 - 49*(2599*B*b^10*d^5*e^6 - 716*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 570*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 180*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 - 360*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 72*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 - 147*(619*B*b^10*d^6*e^5 + 4*(10*B*a*b^9 + A*b^10)*d^5*e^6 - 510*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 900*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 - 540*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 72*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 12*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 35*(4907*B*b^10*d^7*e^4 - 3388*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 8610*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 9660*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 4620*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 35*(11837*B*b^10*d^8*e^3 - 5908*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 12390*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 12180*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 5250*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 - 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 21*(17381*B*b^10*d^9*e^2 - 7924*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 15414*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 14196*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 5754*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 4*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 7*(22001*B*b^10*d^10*e - 9604*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 17934*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 15876*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 6174*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 4*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 - 2*(B*a^10 + 10*A*a^9*b)*e^11)*x + 2520*(11*B*b^10*d^11 - 4*(10*B*a*b^9 + A*b^10)*d^10*e + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + (11*B*b^10*d^4*e^7 - 4*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 7*(11*B*b^10*d^5*e^6 - 4*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10)*x^6 + 21*(11*B*b^10*d^6*e^5 - 4*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9)*x^5 + 35*(11*B*b^10*d^7*e^4 - 4*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8)*x^4 + 35*(11*B*b^10*d^8*e^3 - 4*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7)*x^3 + 21*(11*B*b^10*d^9*e^2 - 4*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6)*x^2 + 7*(11*B*b^10*d^10*e - 4*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5)*x)*log(e*x + d))/(e^19*x^7 + 7*d*e^18*x^6 + 21*d^2*e^17*x^5 + 35*d^3*e^16*x^4 + 35*d^4*e^15*x^3 + 21*d^5*e^14*x^2 + 7*d^6*e^13*x + d^7*e^12)","B",0
1097,1,2677,0,1.453396," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^9,x, algorithm=""fricas"")","\frac{56 \, B b^{10} e^{11} x^{11} - 32891 \, B b^{10} d^{11} - 21 \, A a^{10} e^{11} + 10803 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 13827 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 6849 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 18 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 3 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 28 \, {\left(11 \, B b^{10} d e^{10} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 280 \, {\left(11 \, B b^{10} d^{2} e^{9} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 112 \, {\left(379 \, B b^{10} d^{3} e^{8} - 87 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 60 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10}\right)} x^{8} + 112 \, {\left(1052 \, B b^{10} d^{4} e^{7} - 156 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} - 60 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 180 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} - 45 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 392 \, {\left(62 \, B b^{10} d^{5} e^{6} + 114 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} - 330 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 270 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} - 45 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 9 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} - 784 \, {\left(598 \, B b^{10} d^{6} e^{5} - 294 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 510 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 330 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 45 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 9 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 3 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 140 \, {\left(7651 \, B b^{10} d^{7} e^{4} - 3003 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 4515 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 2625 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 315 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 63 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 21 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 9 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} - 56 \, {\left(20846 \, B b^{10} d^{8} e^{3} - 7518 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 10542 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 5754 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 18 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} - 28 \, {\left(25466 \, B b^{10} d^{9} e^{2} - 8778 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 11802 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 6174 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 18 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 8 \, {\left(29426 \, B b^{10} d^{10} e - 9858 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 12882 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 6534 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 18 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 5 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 3 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 2520 \, {\left(11 \, B b^{10} d^{11} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + {\left(11 \, B b^{10} d^{3} e^{8} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 8 \, {\left(11 \, B b^{10} d^{4} e^{7} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10}\right)} x^{7} + 28 \, {\left(11 \, B b^{10} d^{5} e^{6} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9}\right)} x^{6} + 56 \, {\left(11 \, B b^{10} d^{6} e^{5} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8}\right)} x^{5} + 70 \, {\left(11 \, B b^{10} d^{7} e^{4} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7}\right)} x^{4} + 56 \, {\left(11 \, B b^{10} d^{8} e^{3} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6}\right)} x^{3} + 28 \, {\left(11 \, B b^{10} d^{9} e^{2} - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5}\right)} x^{2} + 8 \, {\left(11 \, B b^{10} d^{10} e - 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4}\right)} x\right)} \log\left(e x + d\right)}{168 \, {\left(e^{20} x^{8} + 8 \, d e^{19} x^{7} + 28 \, d^{2} e^{18} x^{6} + 56 \, d^{3} e^{17} x^{5} + 70 \, d^{4} e^{16} x^{4} + 56 \, d^{5} e^{15} x^{3} + 28 \, d^{6} e^{14} x^{2} + 8 \, d^{7} e^{13} x + d^{8} e^{12}\right)}}"," ",0,"1/168*(56*B*b^10*e^11*x^11 - 32891*B*b^10*d^11 - 21*A*a^10*e^11 + 10803*(10*B*a*b^9 + A*b^10)*d^10*e - 13827*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 6849*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 18*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 5*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 3*(B*a^10 + 10*A*a^9*b)*d*e^10 - 28*(11*B*b^10*d*e^10 - 3*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 280*(11*B*b^10*d^2*e^9 - 3*(10*B*a*b^9 + A*b^10)*d*e^10 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 112*(379*B*b^10*d^3*e^8 - 87*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 60*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10)*x^8 + 112*(1052*B*b^10*d^4*e^7 - 156*(10*B*a*b^9 + A*b^10)*d^3*e^8 - 60*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 180*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 - 45*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 392*(62*B*b^10*d^5*e^6 + 114*(10*B*a*b^9 + A*b^10)*d^4*e^7 - 330*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 270*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 - 45*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 9*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 - 784*(598*B*b^10*d^6*e^5 - 294*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 510*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 330*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 45*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 9*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 3*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 140*(7651*B*b^10*d^7*e^4 - 3003*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 4515*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 2625*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 315*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 63*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 21*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 9*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 - 56*(20846*B*b^10*d^8*e^3 - 7518*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 10542*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 5754*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 18*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 28*(25466*B*b^10*d^9*e^2 - 8778*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 11802*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 6174*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 18*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 8*(29426*B*b^10*d^10*e - 9858*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 12882*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 6534*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 18*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 5*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 3*(B*a^10 + 10*A*a^9*b)*e^11)*x - 2520*(11*B*b^10*d^11 - 3*(10*B*a*b^9 + A*b^10)*d^10*e + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + (11*B*b^10*d^3*e^8 - 3*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 8*(11*B*b^10*d^4*e^7 - 3*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10)*x^7 + 28*(11*B*b^10*d^5*e^6 - 3*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9)*x^6 + 56*(11*B*b^10*d^6*e^5 - 3*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8)*x^5 + 70*(11*B*b^10*d^7*e^4 - 3*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7)*x^4 + 56*(11*B*b^10*d^8*e^3 - 3*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6)*x^3 + 28*(11*B*b^10*d^9*e^2 - 3*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5)*x^2 + 8*(11*B*b^10*d^10*e - 3*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4)*x)*log(e*x + d))/(e^20*x^8 + 8*d*e^19*x^7 + 28*d^2*e^18*x^6 + 56*d^3*e^17*x^5 + 70*d^4*e^16*x^4 + 56*d^5*e^15*x^3 + 28*d^6*e^14*x^2 + 8*d^7*e^13*x + d^8*e^12)","B",0
1098,1,2501,0,1.287586," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^10,x, algorithm=""fricas"")","\frac{252 \, B b^{10} e^{11} x^{11} + 42131 \, B b^{10} d^{11} - 56 \, A a^{10} e^{11} - 9722 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 7129 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 84 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 7 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 252 \, {\left(11 \, B b^{10} d e^{10} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} - 4536 \, {\left(8 \, B b^{10} d^{2} e^{9} - {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10}\right)} x^{9} - 1512 \, {\left(51 \, B b^{10} d^{3} e^{8} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} - 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 5 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 1512 \, {\left(126 \, B b^{10} d^{4} e^{7} - 72 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 90 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} - 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 3528 \, {\left(346 \, B b^{10} d^{5} e^{6} - 112 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 110 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} - 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 2 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 5292 \, {\left(511 \, B b^{10} d^{6} e^{5} - 142 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 125 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} - 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 2 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} - {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 756 \, {\left(4501 \, B b^{10} d^{7} e^{4} - 1162 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 959 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 140 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} - 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 14 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} - 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 4 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 252 \, {\left(10542 \, B b^{10} d^{8} e^{3} - 2604 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 2058 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 280 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} - 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 28 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} - 14 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} - 5 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 36 \, {\left(35586 \, B b^{10} d^{9} e^{2} - 8532 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 6534 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} - 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 84 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} - 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 9 \, {\left(39051 \, B b^{10} d^{10} e - 9162 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 6849 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} - 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 84 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} - 42 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 24 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} - 7 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x + 2520 \, {\left(11 \, B b^{10} d^{11} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + {\left(11 \, B b^{10} d^{2} e^{9} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 9 \, {\left(11 \, B b^{10} d^{3} e^{8} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10}\right)} x^{8} + 36 \, {\left(11 \, B b^{10} d^{4} e^{7} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9}\right)} x^{7} + 84 \, {\left(11 \, B b^{10} d^{5} e^{6} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8}\right)} x^{6} + 126 \, {\left(11 \, B b^{10} d^{6} e^{5} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7}\right)} x^{5} + 126 \, {\left(11 \, B b^{10} d^{7} e^{4} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6}\right)} x^{4} + 84 \, {\left(11 \, B b^{10} d^{8} e^{3} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5}\right)} x^{3} + 36 \, {\left(11 \, B b^{10} d^{9} e^{2} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4}\right)} x^{2} + 9 \, {\left(11 \, B b^{10} d^{10} e - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3}\right)} x\right)} \log\left(e x + d\right)}{504 \, {\left(e^{21} x^{9} + 9 \, d e^{20} x^{8} + 36 \, d^{2} e^{19} x^{7} + 84 \, d^{3} e^{18} x^{6} + 126 \, d^{4} e^{17} x^{5} + 126 \, d^{5} e^{16} x^{4} + 84 \, d^{6} e^{15} x^{3} + 36 \, d^{7} e^{14} x^{2} + 9 \, d^{8} e^{13} x + d^{9} e^{12}\right)}}"," ",0,"1/504*(252*B*b^10*e^11*x^11 + 42131*B*b^10*d^11 - 56*A*a^10*e^11 - 9722*(10*B*a*b^9 + A*b^10)*d^10*e + 7129*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 84*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 7*(B*a^10 + 10*A*a^9*b)*d*e^10 - 252*(11*B*b^10*d*e^10 - 2*(10*B*a*b^9 + A*b^10)*e^11)*x^10 - 4536*(8*B*b^10*d^2*e^9 - (10*B*a*b^9 + A*b^10)*d*e^10)*x^9 - 1512*(51*B*b^10*d^3*e^8 + 3*(10*B*a*b^9 + A*b^10)*d^2*e^9 - 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 5*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 1512*(126*B*b^10*d^4*e^7 - 72*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 90*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 - 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 3528*(346*B*b^10*d^5*e^6 - 112*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 110*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 - 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 2*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 5292*(511*B*b^10*d^6*e^5 - 142*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 125*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 - 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 2*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 - (5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 756*(4501*B*b^10*d^7*e^4 - 1162*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 959*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 140*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 - 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 14*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 - 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 4*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 252*(10542*B*b^10*d^8*e^3 - 2604*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 2058*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 280*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 - 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 28*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 - 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 - 5*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 36*(35586*B*b^10*d^9*e^2 - 8532*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 6534*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 - 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 84*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 - 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 9*(39051*B*b^10*d^10*e - 9162*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 6849*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 - 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 84*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 - 42*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 24*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 - 7*(B*a^10 + 10*A*a^9*b)*e^11)*x + 2520*(11*B*b^10*d^11 - 2*(10*B*a*b^9 + A*b^10)*d^10*e + (9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + (11*B*b^10*d^2*e^9 - 2*(10*B*a*b^9 + A*b^10)*d*e^10 + (9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 9*(11*B*b^10*d^3*e^8 - 2*(10*B*a*b^9 + A*b^10)*d^2*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10)*x^8 + 36*(11*B*b^10*d^4*e^7 - 2*(10*B*a*b^9 + A*b^10)*d^3*e^8 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9)*x^7 + 84*(11*B*b^10*d^5*e^6 - 2*(10*B*a*b^9 + A*b^10)*d^4*e^7 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8)*x^6 + 126*(11*B*b^10*d^6*e^5 - 2*(10*B*a*b^9 + A*b^10)*d^5*e^6 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7)*x^5 + 126*(11*B*b^10*d^7*e^4 - 2*(10*B*a*b^9 + A*b^10)*d^6*e^5 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6)*x^4 + 84*(11*B*b^10*d^8*e^3 - 2*(10*B*a*b^9 + A*b^10)*d^7*e^4 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5)*x^3 + 36*(11*B*b^10*d^9*e^2 - 2*(10*B*a*b^9 + A*b^10)*d^8*e^3 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4)*x^2 + 9*(11*B*b^10*d^10*e - 2*(10*B*a*b^9 + A*b^10)*d^9*e^2 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3)*x)*log(e*x + d))/(e^21*x^9 + 9*d*e^20*x^8 + 36*d^2*e^19*x^7 + 84*d^3*e^18*x^6 + 126*d^4*e^17*x^5 + 126*d^5*e^16*x^4 + 84*d^6*e^15*x^3 + 36*d^7*e^14*x^2 + 9*d^8*e^13*x + d^9*e^12)","B",0
1099,1,2309,0,1.303218," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^11,x, algorithm=""fricas"")","\frac{2520 \, B b^{10} e^{11} x^{11} + 25200 \, B b^{10} d e^{10} x^{10} - 55991 \, B b^{10} d^{11} - 252 \, A a^{10} e^{11} + 7381 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 420 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 35 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 28 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} - 12600 \, {\left(2 \, B b^{10} d^{2} e^{9} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} - 18900 \, {\left(39 \, B b^{10} d^{3} e^{8} - 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} - 25200 \, {\left(122 \, B b^{10} d^{4} e^{7} - 22 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 2 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} - 8820 \, {\left(775 \, B b^{10} d^{5} e^{6} - 125 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 30 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 3 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} - 10584 \, {\left(907 \, B b^{10} d^{6} e^{5} - 137 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 30 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 3 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 2 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} - 1260 \, {\left(7119 \, B b^{10} d^{7} e^{4} - 1029 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 210 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 70 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 14 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 10 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} - 360 \, {\left(15558 \, B b^{10} d^{8} e^{3} - 2178 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 420 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 140 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 42 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 20 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 15 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} - 45 \, {\left(50139 \, B b^{10} d^{9} e^{2} - 6849 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 420 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 35 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} - 10 \, {\left(53219 \, B b^{10} d^{10} e - 7129 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 420 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 35 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 28 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x - 2520 \, {\left(11 \, B b^{10} d^{11} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + {\left(11 \, B b^{10} d e^{10} - {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 10 \, {\left(11 \, B b^{10} d^{2} e^{9} - {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10}\right)} x^{9} + 45 \, {\left(11 \, B b^{10} d^{3} e^{8} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9}\right)} x^{8} + 120 \, {\left(11 \, B b^{10} d^{4} e^{7} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8}\right)} x^{7} + 210 \, {\left(11 \, B b^{10} d^{5} e^{6} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7}\right)} x^{6} + 252 \, {\left(11 \, B b^{10} d^{6} e^{5} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6}\right)} x^{5} + 210 \, {\left(11 \, B b^{10} d^{7} e^{4} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5}\right)} x^{4} + 120 \, {\left(11 \, B b^{10} d^{8} e^{3} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4}\right)} x^{3} + 45 \, {\left(11 \, B b^{10} d^{9} e^{2} - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3}\right)} x^{2} + 10 \, {\left(11 \, B b^{10} d^{10} e - {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2}\right)} x\right)} \log\left(e x + d\right)}{2520 \, {\left(e^{22} x^{10} + 10 \, d e^{21} x^{9} + 45 \, d^{2} e^{20} x^{8} + 120 \, d^{3} e^{19} x^{7} + 210 \, d^{4} e^{18} x^{6} + 252 \, d^{5} e^{17} x^{5} + 210 \, d^{6} e^{16} x^{4} + 120 \, d^{7} e^{15} x^{3} + 45 \, d^{8} e^{14} x^{2} + 10 \, d^{9} e^{13} x + d^{10} e^{12}\right)}}"," ",0,"1/2520*(2520*B*b^10*e^11*x^11 + 25200*B*b^10*d*e^10*x^10 - 55991*B*b^10*d^11 - 252*A*a^10*e^11 + 7381*(10*B*a*b^9 + A*b^10)*d^10*e - 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 420*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 35*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 28*(B*a^10 + 10*A*a^9*b)*d*e^10 - 12600*(2*B*b^10*d^2*e^9 - 2*(10*B*a*b^9 + A*b^10)*d*e^10 + (9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 - 18900*(39*B*b^10*d^3*e^8 - 9*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 - 25200*(122*B*b^10*d^4*e^7 - 22*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 2*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 - 8820*(775*B*b^10*d^5*e^6 - 125*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 3*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 - 10584*(907*B*b^10*d^6*e^5 - 137*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 3*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 2*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 - 1260*(7119*B*b^10*d^7*e^4 - 1029*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 210*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 70*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 14*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 10*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 - 360*(15558*B*b^10*d^8*e^3 - 2178*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 420*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 140*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 42*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 20*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 15*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 - 45*(50139*B*b^10*d^9*e^2 - 6849*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 420*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 35*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 - 10*(53219*B*b^10*d^10*e - 7129*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 420*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 35*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 28*(B*a^10 + 10*A*a^9*b)*e^11)*x - 2520*(11*B*b^10*d^11 - (10*B*a*b^9 + A*b^10)*d^10*e + (11*B*b^10*d*e^10 - (10*B*a*b^9 + A*b^10)*e^11)*x^10 + 10*(11*B*b^10*d^2*e^9 - (10*B*a*b^9 + A*b^10)*d*e^10)*x^9 + 45*(11*B*b^10*d^3*e^8 - (10*B*a*b^9 + A*b^10)*d^2*e^9)*x^8 + 120*(11*B*b^10*d^4*e^7 - (10*B*a*b^9 + A*b^10)*d^3*e^8)*x^7 + 210*(11*B*b^10*d^5*e^6 - (10*B*a*b^9 + A*b^10)*d^4*e^7)*x^6 + 252*(11*B*b^10*d^6*e^5 - (10*B*a*b^9 + A*b^10)*d^5*e^6)*x^5 + 210*(11*B*b^10*d^7*e^4 - (10*B*a*b^9 + A*b^10)*d^6*e^5)*x^4 + 120*(11*B*b^10*d^8*e^3 - (10*B*a*b^9 + A*b^10)*d^7*e^4)*x^3 + 45*(11*B*b^10*d^9*e^2 - (10*B*a*b^9 + A*b^10)*d^8*e^3)*x^2 + 10*(11*B*b^10*d^10*e - (10*B*a*b^9 + A*b^10)*d^9*e^2)*x)*log(e*x + d))/(e^22*x^10 + 10*d*e^21*x^9 + 45*d^2*e^20*x^8 + 120*d^3*e^19*x^7 + 210*d^4*e^18*x^6 + 252*d^5*e^17*x^5 + 210*d^6*e^16*x^4 + 120*d^7*e^15*x^3 + 45*d^8*e^14*x^2 + 10*d^9*e^13*x + d^10*e^12)","B",0
1100,1,2089,0,1.628568," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^12,x, algorithm=""fricas"")","\frac{83711 \, B b^{10} d^{11} - 2520 \, A a^{10} e^{11} - 2520 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e - 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} - 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} - 315 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} - 280 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} - 252 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 27720 \, {\left(11 \, B b^{10} d e^{10} - {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 69300 \, {\left(33 \, B b^{10} d^{2} e^{9} - 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} - {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 69300 \, {\left(121 \, B b^{10} d^{3} e^{8} - 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} - 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} - 2 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 69300 \, {\left(275 \, B b^{10} d^{4} e^{7} - 12 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} - 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} - 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} - 3 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 19404 \, {\left(1507 \, B b^{10} d^{5} e^{6} - 60 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} - 30 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} - 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} - 12 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 19404 \, {\left(1617 \, B b^{10} d^{6} e^{5} - 60 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} - 30 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} - 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} - 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} - 12 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} - 10 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 1980 \, {\left(11979 \, B b^{10} d^{7} e^{4} - 420 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} - 210 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} - 140 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} - 105 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} - 84 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} - 70 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} - 60 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 495 \, {\left(25113 \, B b^{10} d^{8} e^{3} - 840 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} - 420 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} - 280 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} - 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} - 168 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} - 140 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} - 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} - 105 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 55 \, {\left(78419 \, B b^{10} d^{9} e^{2} - 2520 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} - 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} - 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} - 315 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} - 280 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 11 \, {\left(81191 \, B b^{10} d^{10} e - 2520 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} - 1260 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} - 840 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} - 630 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} - 504 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} - 420 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} - 360 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} - 315 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} - 280 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} - 252 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x + 27720 \, {\left(B b^{10} e^{11} x^{11} + 11 \, B b^{10} d e^{10} x^{10} + 55 \, B b^{10} d^{2} e^{9} x^{9} + 165 \, B b^{10} d^{3} e^{8} x^{8} + 330 \, B b^{10} d^{4} e^{7} x^{7} + 462 \, B b^{10} d^{5} e^{6} x^{6} + 462 \, B b^{10} d^{6} e^{5} x^{5} + 330 \, B b^{10} d^{7} e^{4} x^{4} + 165 \, B b^{10} d^{8} e^{3} x^{3} + 55 \, B b^{10} d^{9} e^{2} x^{2} + 11 \, B b^{10} d^{10} e x + B b^{10} d^{11}\right)} \log\left(e x + d\right)}{27720 \, {\left(e^{23} x^{11} + 11 \, d e^{22} x^{10} + 55 \, d^{2} e^{21} x^{9} + 165 \, d^{3} e^{20} x^{8} + 330 \, d^{4} e^{19} x^{7} + 462 \, d^{5} e^{18} x^{6} + 462 \, d^{6} e^{17} x^{5} + 330 \, d^{7} e^{16} x^{4} + 165 \, d^{8} e^{15} x^{3} + 55 \, d^{9} e^{14} x^{2} + 11 \, d^{10} e^{13} x + d^{11} e^{12}\right)}}"," ",0,"1/27720*(83711*B*b^10*d^11 - 2520*A*a^10*e^11 - 2520*(10*B*a*b^9 + A*b^10)*d^10*e - 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 - 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 - 315*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 - 280*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 - 252*(B*a^10 + 10*A*a^9*b)*d*e^10 + 27720*(11*B*b^10*d*e^10 - (10*B*a*b^9 + A*b^10)*e^11)*x^10 + 69300*(33*B*b^10*d^2*e^9 - 2*(10*B*a*b^9 + A*b^10)*d*e^10 - (9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 69300*(121*B*b^10*d^3*e^8 - 6*(10*B*a*b^9 + A*b^10)*d^2*e^9 - 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 - 2*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 69300*(275*B*b^10*d^4*e^7 - 12*(10*B*a*b^9 + A*b^10)*d^3*e^8 - 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 - 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 - 3*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 19404*(1507*B*b^10*d^5*e^6 - 60*(10*B*a*b^9 + A*b^10)*d^4*e^7 - 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 - 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 - 12*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 19404*(1617*B*b^10*d^6*e^5 - 60*(10*B*a*b^9 + A*b^10)*d^5*e^6 - 30*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 - 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 - 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 - 12*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 - 10*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 1980*(11979*B*b^10*d^7*e^4 - 420*(10*B*a*b^9 + A*b^10)*d^6*e^5 - 210*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 - 140*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 - 105*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 - 84*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 - 70*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 - 60*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 495*(25113*B*b^10*d^8*e^3 - 840*(10*B*a*b^9 + A*b^10)*d^7*e^4 - 420*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 - 280*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 - 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 - 168*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 - 140*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 - 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 - 105*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 55*(78419*B*b^10*d^9*e^2 - 2520*(10*B*a*b^9 + A*b^10)*d^8*e^3 - 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 - 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 - 315*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 - 280*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 11*(81191*B*b^10*d^10*e - 2520*(10*B*a*b^9 + A*b^10)*d^9*e^2 - 1260*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 - 840*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 - 630*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 - 504*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 - 420*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 - 360*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 - 315*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 - 280*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 - 252*(B*a^10 + 10*A*a^9*b)*e^11)*x + 27720*(B*b^10*e^11*x^11 + 11*B*b^10*d*e^10*x^10 + 55*B*b^10*d^2*e^9*x^9 + 165*B*b^10*d^3*e^8*x^8 + 330*B*b^10*d^4*e^7*x^7 + 462*B*b^10*d^5*e^6*x^6 + 462*B*b^10*d^6*e^5*x^5 + 330*B*b^10*d^7*e^4*x^4 + 165*B*b^10*d^8*e^3*x^3 + 55*B*b^10*d^9*e^2*x^2 + 11*B*b^10*d^10*e*x + B*b^10*d^11)*log(e*x + d))/(e^23*x^11 + 11*d*e^22*x^10 + 55*d^2*e^21*x^9 + 165*d^3*e^20*x^8 + 330*d^4*e^19*x^7 + 462*d^5*e^18*x^6 + 462*d^6*e^17*x^5 + 330*d^7*e^16*x^4 + 165*d^8*e^15*x^3 + 55*d^9*e^14*x^2 + 11*d^10*e^13*x + d^11*e^12)","B",0
1101,1,1875,0,1.089059," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{132 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 11 \, A a^{10} e^{11} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 66 \, {\left(11 \, B b^{10} d e^{10} + {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 220 \, {\left(11 \, B b^{10} d^{2} e^{9} + {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 495 \, {\left(11 \, B b^{10} d^{3} e^{8} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 792 \, {\left(11 \, B b^{10} d^{4} e^{7} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 924 \, {\left(11 \, B b^{10} d^{5} e^{6} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 792 \, {\left(11 \, B b^{10} d^{6} e^{5} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 495 \, {\left(11 \, B b^{10} d^{7} e^{4} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 220 \, {\left(11 \, B b^{10} d^{8} e^{3} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 66 \, {\left(11 \, B b^{10} d^{9} e^{2} + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 12 \, {\left(11 \, B b^{10} d^{10} e + {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{132 \, {\left(e^{24} x^{12} + 12 \, d e^{23} x^{11} + 66 \, d^{2} e^{22} x^{10} + 220 \, d^{3} e^{21} x^{9} + 495 \, d^{4} e^{20} x^{8} + 792 \, d^{5} e^{19} x^{7} + 924 \, d^{6} e^{18} x^{6} + 792 \, d^{7} e^{17} x^{5} + 495 \, d^{8} e^{16} x^{4} + 220 \, d^{9} e^{15} x^{3} + 66 \, d^{10} e^{14} x^{2} + 12 \, d^{11} e^{13} x + d^{12} e^{12}\right)}}"," ",0,"-1/132*(132*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 11*A*a^10*e^11 + (10*B*a*b^9 + A*b^10)*d^10*e + (9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + (2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + (B*a^10 + 10*A*a^9*b)*d*e^10 + 66*(11*B*b^10*d*e^10 + (10*B*a*b^9 + A*b^10)*e^11)*x^10 + 220*(11*B*b^10*d^2*e^9 + (10*B*a*b^9 + A*b^10)*d*e^10 + (9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 495*(11*B*b^10*d^3*e^8 + (10*B*a*b^9 + A*b^10)*d^2*e^9 + (9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 792*(11*B*b^10*d^4*e^7 + (10*B*a*b^9 + A*b^10)*d^3*e^8 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 924*(11*B*b^10*d^5*e^6 + (10*B*a*b^9 + A*b^10)*d^4*e^7 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 792*(11*B*b^10*d^6*e^5 + (10*B*a*b^9 + A*b^10)*d^5*e^6 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 495*(11*B*b^10*d^7*e^4 + (10*B*a*b^9 + A*b^10)*d^6*e^5 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 220*(11*B*b^10*d^8*e^3 + (10*B*a*b^9 + A*b^10)*d^7*e^4 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 66*(11*B*b^10*d^9*e^2 + (10*B*a*b^9 + A*b^10)*d^8*e^3 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + (2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 12*(11*B*b^10*d^10*e + (10*B*a*b^9 + A*b^10)*d^9*e^2 + (9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + (8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + (7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + (6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + (5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + (4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + (3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + (2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + (B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^24*x^12 + 12*d*e^23*x^11 + 66*d^2*e^22*x^10 + 220*d^3*e^21*x^9 + 495*d^4*e^20*x^8 + 792*d^5*e^19*x^7 + 924*d^6*e^18*x^6 + 792*d^7*e^17*x^5 + 495*d^8*e^16*x^4 + 220*d^9*e^15*x^3 + 66*d^10*e^14*x^2 + 12*d^11*e^13*x + d^12*e^12)","B",0
1102,1,1951,0,1.297802," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^14,x, algorithm=""fricas"")","-\frac{858 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 132 \, A a^{10} e^{11} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 11 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 286 \, {\left(11 \, B b^{10} d e^{10} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 715 \, {\left(11 \, B b^{10} d^{2} e^{9} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 1287 \, {\left(11 \, B b^{10} d^{3} e^{8} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 1716 \, {\left(11 \, B b^{10} d^{4} e^{7} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 1716 \, {\left(11 \, B b^{10} d^{5} e^{6} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 1287 \, {\left(11 \, B b^{10} d^{6} e^{5} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 715 \, {\left(11 \, B b^{10} d^{7} e^{4} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 286 \, {\left(11 \, B b^{10} d^{8} e^{3} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 78 \, {\left(11 \, B b^{10} d^{9} e^{2} + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 13 \, {\left(11 \, B b^{10} d^{10} e + 2 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 3 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 4 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 5 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 6 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 7 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 8 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 9 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 10 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 11 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{1716 \, {\left(e^{25} x^{13} + 13 \, d e^{24} x^{12} + 78 \, d^{2} e^{23} x^{11} + 286 \, d^{3} e^{22} x^{10} + 715 \, d^{4} e^{21} x^{9} + 1287 \, d^{5} e^{20} x^{8} + 1716 \, d^{6} e^{19} x^{7} + 1716 \, d^{7} e^{18} x^{6} + 1287 \, d^{8} e^{17} x^{5} + 715 \, d^{9} e^{16} x^{4} + 286 \, d^{10} e^{15} x^{3} + 78 \, d^{11} e^{14} x^{2} + 13 \, d^{12} e^{13} x + d^{13} e^{12}\right)}}"," ",0,"-1/1716*(858*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 132*A*a^10*e^11 + 2*(10*B*a*b^9 + A*b^10)*d^10*e + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 11*(B*a^10 + 10*A*a^9*b)*d*e^10 + 286*(11*B*b^10*d*e^10 + 2*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 715*(11*B*b^10*d^2*e^9 + 2*(10*B*a*b^9 + A*b^10)*d*e^10 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 1287*(11*B*b^10*d^3*e^8 + 2*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 1716*(11*B*b^10*d^4*e^7 + 2*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 1716*(11*B*b^10*d^5*e^6 + 2*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 1287*(11*B*b^10*d^6*e^5 + 2*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 715*(11*B*b^10*d^7*e^4 + 2*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 286*(11*B*b^10*d^8*e^3 + 2*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 78*(11*B*b^10*d^9*e^2 + 2*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 13*(11*B*b^10*d^10*e + 2*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 3*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 4*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 5*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 6*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 7*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 8*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 9*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 10*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 11*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^25*x^13 + 13*d*e^24*x^12 + 78*d^2*e^23*x^11 + 286*d^3*e^22*x^10 + 715*d^4*e^21*x^9 + 1287*d^5*e^20*x^8 + 1716*d^6*e^19*x^7 + 1716*d^7*e^18*x^6 + 1287*d^8*e^17*x^5 + 715*d^9*e^16*x^4 + 286*d^10*e^15*x^3 + 78*d^11*e^14*x^2 + 13*d^12*e^13*x + d^13*e^12)","B",0
1103,1,1962,0,1.223532," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^15,x, algorithm=""fricas"")","-\frac{4004 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 858 \, A a^{10} e^{11} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 55 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 66 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 1001 \, {\left(11 \, B b^{10} d e^{10} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 2002 \, {\left(11 \, B b^{10} d^{2} e^{9} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 3003 \, {\left(11 \, B b^{10} d^{3} e^{8} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 3432 \, {\left(11 \, B b^{10} d^{4} e^{7} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 3003 \, {\left(11 \, B b^{10} d^{5} e^{6} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 2002 \, {\left(11 \, B b^{10} d^{6} e^{5} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 1001 \, {\left(11 \, B b^{10} d^{7} e^{4} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 364 \, {\left(11 \, B b^{10} d^{8} e^{3} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 91 \, {\left(11 \, B b^{10} d^{9} e^{2} + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 55 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 14 \, {\left(11 \, B b^{10} d^{10} e + 3 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 6 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 10 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 15 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 21 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 28 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 36 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 45 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 55 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 66 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{12012 \, {\left(e^{26} x^{14} + 14 \, d e^{25} x^{13} + 91 \, d^{2} e^{24} x^{12} + 364 \, d^{3} e^{23} x^{11} + 1001 \, d^{4} e^{22} x^{10} + 2002 \, d^{5} e^{21} x^{9} + 3003 \, d^{6} e^{20} x^{8} + 3432 \, d^{7} e^{19} x^{7} + 3003 \, d^{8} e^{18} x^{6} + 2002 \, d^{9} e^{17} x^{5} + 1001 \, d^{10} e^{16} x^{4} + 364 \, d^{11} e^{15} x^{3} + 91 \, d^{12} e^{14} x^{2} + 14 \, d^{13} e^{13} x + d^{14} e^{12}\right)}}"," ",0,"-1/12012*(4004*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 858*A*a^10*e^11 + 3*(10*B*a*b^9 + A*b^10)*d^10*e + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 55*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 66*(B*a^10 + 10*A*a^9*b)*d*e^10 + 1001*(11*B*b^10*d*e^10 + 3*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 2002*(11*B*b^10*d^2*e^9 + 3*(10*B*a*b^9 + A*b^10)*d*e^10 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 3003*(11*B*b^10*d^3*e^8 + 3*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 3432*(11*B*b^10*d^4*e^7 + 3*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 3003*(11*B*b^10*d^5*e^6 + 3*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 2002*(11*B*b^10*d^6*e^5 + 3*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 1001*(11*B*b^10*d^7*e^4 + 3*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 364*(11*B*b^10*d^8*e^3 + 3*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 91*(11*B*b^10*d^9*e^2 + 3*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 55*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 14*(11*B*b^10*d^10*e + 3*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 6*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 10*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 15*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 21*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 28*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 36*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 45*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 55*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 66*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^26*x^14 + 14*d*e^25*x^13 + 91*d^2*e^24*x^12 + 364*d^3*e^23*x^11 + 1001*d^4*e^22*x^10 + 2002*d^5*e^21*x^9 + 3003*d^6*e^20*x^8 + 3432*d^7*e^19*x^7 + 3003*d^8*e^18*x^6 + 2002*d^9*e^17*x^5 + 1001*d^10*e^16*x^4 + 364*d^11*e^15*x^3 + 91*d^12*e^14*x^2 + 14*d^13*e^13*x + d^14*e^12)","B",0
1104,1,1973,0,0.987297," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^16,x, algorithm=""fricas"")","-\frac{15015 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 4004 \, A a^{10} e^{11} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 165 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 220 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 286 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 3003 \, {\left(11 \, B b^{10} d e^{10} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 5005 \, {\left(11 \, B b^{10} d^{2} e^{9} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 6435 \, {\left(11 \, B b^{10} d^{3} e^{8} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 6435 \, {\left(11 \, B b^{10} d^{4} e^{7} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 5005 \, {\left(11 \, B b^{10} d^{5} e^{6} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 3003 \, {\left(11 \, B b^{10} d^{6} e^{5} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 1365 \, {\left(11 \, B b^{10} d^{7} e^{4} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 455 \, {\left(11 \, B b^{10} d^{8} e^{3} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 165 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 105 \, {\left(11 \, B b^{10} d^{9} e^{2} + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 165 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 220 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 15 \, {\left(11 \, B b^{10} d^{10} e + 4 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 10 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 20 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 35 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 56 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 84 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 120 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 165 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 220 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 286 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{60060 \, {\left(e^{27} x^{15} + 15 \, d e^{26} x^{14} + 105 \, d^{2} e^{25} x^{13} + 455 \, d^{3} e^{24} x^{12} + 1365 \, d^{4} e^{23} x^{11} + 3003 \, d^{5} e^{22} x^{10} + 5005 \, d^{6} e^{21} x^{9} + 6435 \, d^{7} e^{20} x^{8} + 6435 \, d^{8} e^{19} x^{7} + 5005 \, d^{9} e^{18} x^{6} + 3003 \, d^{10} e^{17} x^{5} + 1365 \, d^{11} e^{16} x^{4} + 455 \, d^{12} e^{15} x^{3} + 105 \, d^{13} e^{14} x^{2} + 15 \, d^{14} e^{13} x + d^{15} e^{12}\right)}}"," ",0,"-1/60060*(15015*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 4004*A*a^10*e^11 + 4*(10*B*a*b^9 + A*b^10)*d^10*e + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 165*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 220*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 286*(B*a^10 + 10*A*a^9*b)*d*e^10 + 3003*(11*B*b^10*d*e^10 + 4*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 5005*(11*B*b^10*d^2*e^9 + 4*(10*B*a*b^9 + A*b^10)*d*e^10 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 6435*(11*B*b^10*d^3*e^8 + 4*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 6435*(11*B*b^10*d^4*e^7 + 4*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 5005*(11*B*b^10*d^5*e^6 + 4*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 3003*(11*B*b^10*d^6*e^5 + 4*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 1365*(11*B*b^10*d^7*e^4 + 4*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 455*(11*B*b^10*d^8*e^3 + 4*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 165*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 105*(11*B*b^10*d^9*e^2 + 4*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 165*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 220*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 15*(11*B*b^10*d^10*e + 4*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 10*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 20*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 35*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 56*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 84*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 120*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 165*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 220*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 286*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^27*x^15 + 15*d*e^26*x^14 + 105*d^2*e^25*x^13 + 455*d^3*e^24*x^12 + 1365*d^4*e^23*x^11 + 3003*d^5*e^22*x^10 + 5005*d^6*e^21*x^9 + 6435*d^7*e^20*x^8 + 6435*d^8*e^19*x^7 + 5005*d^9*e^18*x^6 + 3003*d^10*e^17*x^5 + 1365*d^11*e^16*x^4 + 455*d^12*e^15*x^3 + 105*d^13*e^14*x^2 + 15*d^14*e^13*x + d^15*e^12)","B",0
1105,1,1984,0,1.368958," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^17,x, algorithm=""fricas"")","-\frac{48048 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 15015 \, A a^{10} e^{11} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 495 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 715 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 1001 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 8008 \, {\left(11 \, B b^{10} d e^{10} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 11440 \, {\left(11 \, B b^{10} d^{2} e^{9} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 12870 \, {\left(11 \, B b^{10} d^{3} e^{8} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 11440 \, {\left(11 \, B b^{10} d^{4} e^{7} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 8008 \, {\left(11 \, B b^{10} d^{5} e^{6} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 4368 \, {\left(11 \, B b^{10} d^{6} e^{5} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 1820 \, {\left(11 \, B b^{10} d^{7} e^{4} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 560 \, {\left(11 \, B b^{10} d^{8} e^{3} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 495 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 120 \, {\left(11 \, B b^{10} d^{9} e^{2} + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 495 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 715 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 16 \, {\left(11 \, B b^{10} d^{10} e + 5 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 15 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 35 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 70 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 126 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 210 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 330 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 495 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 715 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 1001 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{240240 \, {\left(e^{28} x^{16} + 16 \, d e^{27} x^{15} + 120 \, d^{2} e^{26} x^{14} + 560 \, d^{3} e^{25} x^{13} + 1820 \, d^{4} e^{24} x^{12} + 4368 \, d^{5} e^{23} x^{11} + 8008 \, d^{6} e^{22} x^{10} + 11440 \, d^{7} e^{21} x^{9} + 12870 \, d^{8} e^{20} x^{8} + 11440 \, d^{9} e^{19} x^{7} + 8008 \, d^{10} e^{18} x^{6} + 4368 \, d^{11} e^{17} x^{5} + 1820 \, d^{12} e^{16} x^{4} + 560 \, d^{13} e^{15} x^{3} + 120 \, d^{14} e^{14} x^{2} + 16 \, d^{15} e^{13} x + d^{16} e^{12}\right)}}"," ",0,"-1/240240*(48048*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 15015*A*a^10*e^11 + 5*(10*B*a*b^9 + A*b^10)*d^10*e + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 495*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 715*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 1001*(B*a^10 + 10*A*a^9*b)*d*e^10 + 8008*(11*B*b^10*d*e^10 + 5*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 11440*(11*B*b^10*d^2*e^9 + 5*(10*B*a*b^9 + A*b^10)*d*e^10 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 12870*(11*B*b^10*d^3*e^8 + 5*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 11440*(11*B*b^10*d^4*e^7 + 5*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 8008*(11*B*b^10*d^5*e^6 + 5*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 4368*(11*B*b^10*d^6*e^5 + 5*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 1820*(11*B*b^10*d^7*e^4 + 5*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 560*(11*B*b^10*d^8*e^3 + 5*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 495*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 120*(11*B*b^10*d^9*e^2 + 5*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 495*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 715*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 16*(11*B*b^10*d^10*e + 5*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 15*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 35*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 70*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 126*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 210*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 330*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 495*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 715*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 1001*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^28*x^16 + 16*d*e^27*x^15 + 120*d^2*e^26*x^14 + 560*d^3*e^25*x^13 + 1820*d^4*e^24*x^12 + 4368*d^5*e^23*x^11 + 8008*d^6*e^22*x^10 + 11440*d^7*e^21*x^9 + 12870*d^8*e^20*x^8 + 11440*d^9*e^19*x^7 + 8008*d^10*e^18*x^6 + 4368*d^11*e^17*x^5 + 1820*d^12*e^16*x^4 + 560*d^13*e^15*x^3 + 120*d^14*e^14*x^2 + 16*d^15*e^13*x + d^16*e^12)","B",0
1106,1,1995,0,1.249267," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^18,x, algorithm=""fricas"")","-\frac{136136 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 48048 \, A a^{10} e^{11} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 792 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 1287 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 2002 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 3003 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 19448 \, {\left(11 \, B b^{10} d e^{10} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 24310 \, {\left(11 \, B b^{10} d^{2} e^{9} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 24310 \, {\left(11 \, B b^{10} d^{3} e^{8} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 19448 \, {\left(11 \, B b^{10} d^{4} e^{7} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 12376 \, {\left(11 \, B b^{10} d^{5} e^{6} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 6188 \, {\left(11 \, B b^{10} d^{6} e^{5} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 2380 \, {\left(11 \, B b^{10} d^{7} e^{4} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 792 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 680 \, {\left(11 \, B b^{10} d^{8} e^{3} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 792 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 1287 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 136 \, {\left(11 \, B b^{10} d^{9} e^{2} + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 792 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 1287 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 2002 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 17 \, {\left(11 \, B b^{10} d^{10} e + 6 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 21 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 56 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 126 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 252 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 462 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 792 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 1287 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 2002 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 3003 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{816816 \, {\left(e^{29} x^{17} + 17 \, d e^{28} x^{16} + 136 \, d^{2} e^{27} x^{15} + 680 \, d^{3} e^{26} x^{14} + 2380 \, d^{4} e^{25} x^{13} + 6188 \, d^{5} e^{24} x^{12} + 12376 \, d^{6} e^{23} x^{11} + 19448 \, d^{7} e^{22} x^{10} + 24310 \, d^{8} e^{21} x^{9} + 24310 \, d^{9} e^{20} x^{8} + 19448 \, d^{10} e^{19} x^{7} + 12376 \, d^{11} e^{18} x^{6} + 6188 \, d^{12} e^{17} x^{5} + 2380 \, d^{13} e^{16} x^{4} + 680 \, d^{14} e^{15} x^{3} + 136 \, d^{15} e^{14} x^{2} + 17 \, d^{16} e^{13} x + d^{17} e^{12}\right)}}"," ",0,"-1/816816*(136136*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 48048*A*a^10*e^11 + 6*(10*B*a*b^9 + A*b^10)*d^10*e + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 3003*(B*a^10 + 10*A*a^9*b)*d*e^10 + 19448*(11*B*b^10*d*e^10 + 6*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 24310*(11*B*b^10*d^2*e^9 + 6*(10*B*a*b^9 + A*b^10)*d*e^10 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 24310*(11*B*b^10*d^3*e^8 + 6*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 19448*(11*B*b^10*d^4*e^7 + 6*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 12376*(11*B*b^10*d^5*e^6 + 6*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 6188*(11*B*b^10*d^6*e^5 + 6*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 2380*(11*B*b^10*d^7*e^4 + 6*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 680*(11*B*b^10*d^8*e^3 + 6*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 136*(11*B*b^10*d^9*e^2 + 6*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 17*(11*B*b^10*d^10*e + 6*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 21*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 56*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 126*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 252*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 462*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 792*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 1287*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 2002*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 3003*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^29*x^17 + 17*d*e^28*x^16 + 136*d^2*e^27*x^15 + 680*d^3*e^26*x^14 + 2380*d^4*e^25*x^13 + 6188*d^5*e^24*x^12 + 12376*d^6*e^23*x^11 + 19448*d^7*e^22*x^10 + 24310*d^8*e^21*x^9 + 24310*d^9*e^20*x^8 + 19448*d^10*e^19*x^7 + 12376*d^11*e^18*x^6 + 6188*d^12*e^17*x^5 + 2380*d^13*e^16*x^4 + 680*d^14*e^15*x^3 + 136*d^15*e^14*x^2 + 17*d^16*e^13*x + d^17*e^12)","B",0
1107,1,2006,0,0.962303," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^19,x, algorithm=""fricas"")","-\frac{350064 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 136136 \, A a^{10} e^{11} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 1716 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 3003 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 5005 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 8008 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 43758 \, {\left(11 \, B b^{10} d e^{10} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 48620 \, {\left(11 \, B b^{10} d^{2} e^{9} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 43758 \, {\left(11 \, B b^{10} d^{3} e^{8} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 31824 \, {\left(11 \, B b^{10} d^{4} e^{7} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 18564 \, {\left(11 \, B b^{10} d^{5} e^{6} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 8568 \, {\left(11 \, B b^{10} d^{6} e^{5} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 3060 \, {\left(11 \, B b^{10} d^{7} e^{4} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 1716 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 816 \, {\left(11 \, B b^{10} d^{8} e^{3} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 1716 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 3003 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 153 \, {\left(11 \, B b^{10} d^{9} e^{2} + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 1716 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 3003 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 5005 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 18 \, {\left(11 \, B b^{10} d^{10} e + 7 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 28 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 84 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 210 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 462 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 924 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 1716 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 3003 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 5005 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 8008 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{2450448 \, {\left(e^{30} x^{18} + 18 \, d e^{29} x^{17} + 153 \, d^{2} e^{28} x^{16} + 816 \, d^{3} e^{27} x^{15} + 3060 \, d^{4} e^{26} x^{14} + 8568 \, d^{5} e^{25} x^{13} + 18564 \, d^{6} e^{24} x^{12} + 31824 \, d^{7} e^{23} x^{11} + 43758 \, d^{8} e^{22} x^{10} + 48620 \, d^{9} e^{21} x^{9} + 43758 \, d^{10} e^{20} x^{8} + 31824 \, d^{11} e^{19} x^{7} + 18564 \, d^{12} e^{18} x^{6} + 8568 \, d^{13} e^{17} x^{5} + 3060 \, d^{14} e^{16} x^{4} + 816 \, d^{15} e^{15} x^{3} + 153 \, d^{16} e^{14} x^{2} + 18 \, d^{17} e^{13} x + d^{18} e^{12}\right)}}"," ",0,"-1/2450448*(350064*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 136136*A*a^10*e^11 + 7*(10*B*a*b^9 + A*b^10)*d^10*e + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 1716*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 3003*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 5005*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 8008*(B*a^10 + 10*A*a^9*b)*d*e^10 + 43758*(11*B*b^10*d*e^10 + 7*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 48620*(11*B*b^10*d^2*e^9 + 7*(10*B*a*b^9 + A*b^10)*d*e^10 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 43758*(11*B*b^10*d^3*e^8 + 7*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 31824*(11*B*b^10*d^4*e^7 + 7*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 18564*(11*B*b^10*d^5*e^6 + 7*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 8568*(11*B*b^10*d^6*e^5 + 7*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 3060*(11*B*b^10*d^7*e^4 + 7*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 1716*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 816*(11*B*b^10*d^8*e^3 + 7*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 1716*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 3003*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 153*(11*B*b^10*d^9*e^2 + 7*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 1716*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 3003*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 5005*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 18*(11*B*b^10*d^10*e + 7*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 28*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 84*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 210*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 462*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 924*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 1716*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 3003*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 5005*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 8008*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^30*x^18 + 18*d*e^29*x^17 + 153*d^2*e^28*x^16 + 816*d^3*e^27*x^15 + 3060*d^4*e^26*x^14 + 8568*d^5*e^25*x^13 + 18564*d^6*e^24*x^12 + 31824*d^7*e^23*x^11 + 43758*d^8*e^22*x^10 + 48620*d^9*e^21*x^9 + 43758*d^10*e^20*x^8 + 31824*d^11*e^19*x^7 + 18564*d^12*e^18*x^6 + 8568*d^13*e^17*x^5 + 3060*d^14*e^16*x^4 + 816*d^15*e^15*x^3 + 153*d^16*e^14*x^2 + 18*d^17*e^13*x + d^18*e^12)","B",0
1108,1,2017,0,0.808804," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^20,x, algorithm=""fricas"")","-\frac{831402 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 350064 \, A a^{10} e^{11} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 3432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 6435 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 11440 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 19448 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 92378 \, {\left(11 \, B b^{10} d e^{10} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 92378 \, {\left(11 \, B b^{10} d^{2} e^{9} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 75582 \, {\left(11 \, B b^{10} d^{3} e^{8} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 50388 \, {\left(11 \, B b^{10} d^{4} e^{7} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 27132 \, {\left(11 \, B b^{10} d^{5} e^{6} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 11628 \, {\left(11 \, B b^{10} d^{6} e^{5} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 3876 \, {\left(11 \, B b^{10} d^{7} e^{4} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 3432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 969 \, {\left(11 \, B b^{10} d^{8} e^{3} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 3432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 6435 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 171 \, {\left(11 \, B b^{10} d^{9} e^{2} + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 3432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 6435 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 11440 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 19 \, {\left(11 \, B b^{10} d^{10} e + 8 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 36 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 120 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 330 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 792 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 1716 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 3432 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 6435 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 11440 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 19448 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{6651216 \, {\left(e^{31} x^{19} + 19 \, d e^{30} x^{18} + 171 \, d^{2} e^{29} x^{17} + 969 \, d^{3} e^{28} x^{16} + 3876 \, d^{4} e^{27} x^{15} + 11628 \, d^{5} e^{26} x^{14} + 27132 \, d^{6} e^{25} x^{13} + 50388 \, d^{7} e^{24} x^{12} + 75582 \, d^{8} e^{23} x^{11} + 92378 \, d^{9} e^{22} x^{10} + 92378 \, d^{10} e^{21} x^{9} + 75582 \, d^{11} e^{20} x^{8} + 50388 \, d^{12} e^{19} x^{7} + 27132 \, d^{13} e^{18} x^{6} + 11628 \, d^{14} e^{17} x^{5} + 3876 \, d^{15} e^{16} x^{4} + 969 \, d^{16} e^{15} x^{3} + 171 \, d^{17} e^{14} x^{2} + 19 \, d^{18} e^{13} x + d^{19} e^{12}\right)}}"," ",0,"-1/6651216*(831402*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 350064*A*a^10*e^11 + 8*(10*B*a*b^9 + A*b^10)*d^10*e + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 3432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 6435*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 11440*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 19448*(B*a^10 + 10*A*a^9*b)*d*e^10 + 92378*(11*B*b^10*d*e^10 + 8*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 92378*(11*B*b^10*d^2*e^9 + 8*(10*B*a*b^9 + A*b^10)*d*e^10 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 75582*(11*B*b^10*d^3*e^8 + 8*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 50388*(11*B*b^10*d^4*e^7 + 8*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 27132*(11*B*b^10*d^5*e^6 + 8*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 11628*(11*B*b^10*d^6*e^5 + 8*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 3876*(11*B*b^10*d^7*e^4 + 8*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 3432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 969*(11*B*b^10*d^8*e^3 + 8*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 3432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 6435*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 171*(11*B*b^10*d^9*e^2 + 8*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 3432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 6435*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 11440*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 19*(11*B*b^10*d^10*e + 8*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 36*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 120*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 330*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 792*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 1716*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 3432*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 6435*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 11440*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 19448*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^31*x^19 + 19*d*e^30*x^18 + 171*d^2*e^29*x^17 + 969*d^3*e^28*x^16 + 3876*d^4*e^27*x^15 + 11628*d^5*e^26*x^14 + 27132*d^6*e^25*x^13 + 50388*d^7*e^24*x^12 + 75582*d^8*e^23*x^11 + 92378*d^9*e^22*x^10 + 92378*d^10*e^21*x^9 + 75582*d^11*e^20*x^8 + 50388*d^12*e^19*x^7 + 27132*d^13*e^18*x^6 + 11628*d^14*e^17*x^5 + 3876*d^15*e^16*x^4 + 969*d^16*e^15*x^3 + 171*d^17*e^14*x^2 + 19*d^18*e^13*x + d^19*e^12)","B",0
1109,1,2028,0,1.232167," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^21,x, algorithm=""fricas"")","-\frac{1847560 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 831402 \, A a^{10} e^{11} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 6435 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 12870 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 24310 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 43758 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 184756 \, {\left(11 \, B b^{10} d e^{10} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 167960 \, {\left(11 \, B b^{10} d^{2} e^{9} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 125970 \, {\left(11 \, B b^{10} d^{3} e^{8} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 77520 \, {\left(11 \, B b^{10} d^{4} e^{7} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 38760 \, {\left(11 \, B b^{10} d^{5} e^{6} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 15504 \, {\left(11 \, B b^{10} d^{6} e^{5} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 4845 \, {\left(11 \, B b^{10} d^{7} e^{4} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 6435 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 1140 \, {\left(11 \, B b^{10} d^{8} e^{3} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 6435 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 12870 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 190 \, {\left(11 \, B b^{10} d^{9} e^{2} + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 6435 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 12870 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 24310 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 20 \, {\left(11 \, B b^{10} d^{10} e + 9 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 45 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 165 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 495 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 1287 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 3003 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 6435 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 12870 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 24310 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 43758 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{16628040 \, {\left(e^{32} x^{20} + 20 \, d e^{31} x^{19} + 190 \, d^{2} e^{30} x^{18} + 1140 \, d^{3} e^{29} x^{17} + 4845 \, d^{4} e^{28} x^{16} + 15504 \, d^{5} e^{27} x^{15} + 38760 \, d^{6} e^{26} x^{14} + 77520 \, d^{7} e^{25} x^{13} + 125970 \, d^{8} e^{24} x^{12} + 167960 \, d^{9} e^{23} x^{11} + 184756 \, d^{10} e^{22} x^{10} + 167960 \, d^{11} e^{21} x^{9} + 125970 \, d^{12} e^{20} x^{8} + 77520 \, d^{13} e^{19} x^{7} + 38760 \, d^{14} e^{18} x^{6} + 15504 \, d^{15} e^{17} x^{5} + 4845 \, d^{16} e^{16} x^{4} + 1140 \, d^{17} e^{15} x^{3} + 190 \, d^{18} e^{14} x^{2} + 20 \, d^{19} e^{13} x + d^{20} e^{12}\right)}}"," ",0,"-1/16628040*(1847560*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 831402*A*a^10*e^11 + 9*(10*B*a*b^9 + A*b^10)*d^10*e + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 6435*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 12870*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 24310*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 43758*(B*a^10 + 10*A*a^9*b)*d*e^10 + 184756*(11*B*b^10*d*e^10 + 9*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 167960*(11*B*b^10*d^2*e^9 + 9*(10*B*a*b^9 + A*b^10)*d*e^10 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 125970*(11*B*b^10*d^3*e^8 + 9*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 77520*(11*B*b^10*d^4*e^7 + 9*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 38760*(11*B*b^10*d^5*e^6 + 9*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 15504*(11*B*b^10*d^6*e^5 + 9*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 4845*(11*B*b^10*d^7*e^4 + 9*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 6435*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 1140*(11*B*b^10*d^8*e^3 + 9*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 6435*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 12870*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 190*(11*B*b^10*d^9*e^2 + 9*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 6435*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 12870*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 24310*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 20*(11*B*b^10*d^10*e + 9*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 45*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 165*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 495*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 1287*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 3003*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 6435*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 12870*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 24310*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 43758*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^32*x^20 + 20*d*e^31*x^19 + 190*d^2*e^30*x^18 + 1140*d^3*e^29*x^17 + 4845*d^4*e^28*x^16 + 15504*d^5*e^27*x^15 + 38760*d^6*e^26*x^14 + 77520*d^7*e^25*x^13 + 125970*d^8*e^24*x^12 + 167960*d^9*e^23*x^11 + 184756*d^10*e^22*x^10 + 167960*d^11*e^21*x^9 + 125970*d^12*e^20*x^8 + 77520*d^13*e^19*x^7 + 38760*d^14*e^18*x^6 + 15504*d^15*e^17*x^5 + 4845*d^16*e^16*x^4 + 1140*d^17*e^15*x^3 + 190*d^18*e^14*x^2 + 20*d^19*e^13*x + d^20*e^12)","B",0
1110,1,2039,0,1.210013," ","integrate((b*x+a)^10*(B*x+A)/(e*x+d)^22,x, algorithm=""fricas"")","-\frac{3879876 \, B b^{10} e^{11} x^{11} + 11 \, B b^{10} d^{11} + 1847560 \, A a^{10} e^{11} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{10} e + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{9} e^{2} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{8} e^{3} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{7} e^{4} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{6} e^{5} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{5} e^{6} + 11440 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{4} e^{7} + 24310 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{3} e^{8} + 48620 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d^{2} e^{9} + 92378 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} d e^{10} + 352716 \, {\left(11 \, B b^{10} d e^{10} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} e^{11}\right)} x^{10} + 293930 \, {\left(11 \, B b^{10} d^{2} e^{9} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d e^{10} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} e^{11}\right)} x^{9} + 203490 \, {\left(11 \, B b^{10} d^{3} e^{8} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{2} e^{9} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d e^{10} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} e^{11}\right)} x^{8} + 116280 \, {\left(11 \, B b^{10} d^{4} e^{7} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{3} e^{8} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{2} e^{9} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d e^{10} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} e^{11}\right)} x^{7} + 54264 \, {\left(11 \, B b^{10} d^{5} e^{6} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{4} e^{7} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{3} e^{8} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{2} e^{9} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d e^{10} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} e^{11}\right)} x^{6} + 20349 \, {\left(11 \, B b^{10} d^{6} e^{5} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{5} e^{6} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{4} e^{7} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{3} e^{8} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{2} e^{9} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d e^{10} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} e^{11}\right)} x^{5} + 5985 \, {\left(11 \, B b^{10} d^{7} e^{4} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{6} e^{5} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{5} e^{6} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{4} e^{7} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{3} e^{8} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{2} e^{9} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d e^{10} + 11440 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} e^{11}\right)} x^{4} + 1330 \, {\left(11 \, B b^{10} d^{8} e^{3} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{7} e^{4} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{6} e^{5} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{5} e^{6} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{4} e^{7} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{3} e^{8} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{2} e^{9} + 11440 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d e^{10} + 24310 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} e^{11}\right)} x^{3} + 210 \, {\left(11 \, B b^{10} d^{9} e^{2} + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{8} e^{3} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{7} e^{4} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{6} e^{5} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{5} e^{6} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{4} e^{7} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{3} e^{8} + 11440 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{2} e^{9} + 24310 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d e^{10} + 48620 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} e^{11}\right)} x^{2} + 21 \, {\left(11 \, B b^{10} d^{10} e + 10 \, {\left(10 \, B a b^{9} + A b^{10}\right)} d^{9} e^{2} + 55 \, {\left(9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right)} d^{8} e^{3} + 220 \, {\left(8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right)} d^{7} e^{4} + 715 \, {\left(7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right)} d^{6} e^{5} + 2002 \, {\left(6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right)} d^{5} e^{6} + 5005 \, {\left(5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right)} d^{4} e^{7} + 11440 \, {\left(4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right)} d^{3} e^{8} + 24310 \, {\left(3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right)} d^{2} e^{9} + 48620 \, {\left(2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right)} d e^{10} + 92378 \, {\left(B a^{10} + 10 \, A a^{9} b\right)} e^{11}\right)} x}{38798760 \, {\left(e^{33} x^{21} + 21 \, d e^{32} x^{20} + 210 \, d^{2} e^{31} x^{19} + 1330 \, d^{3} e^{30} x^{18} + 5985 \, d^{4} e^{29} x^{17} + 20349 \, d^{5} e^{28} x^{16} + 54264 \, d^{6} e^{27} x^{15} + 116280 \, d^{7} e^{26} x^{14} + 203490 \, d^{8} e^{25} x^{13} + 293930 \, d^{9} e^{24} x^{12} + 352716 \, d^{10} e^{23} x^{11} + 352716 \, d^{11} e^{22} x^{10} + 293930 \, d^{12} e^{21} x^{9} + 203490 \, d^{13} e^{20} x^{8} + 116280 \, d^{14} e^{19} x^{7} + 54264 \, d^{15} e^{18} x^{6} + 20349 \, d^{16} e^{17} x^{5} + 5985 \, d^{17} e^{16} x^{4} + 1330 \, d^{18} e^{15} x^{3} + 210 \, d^{19} e^{14} x^{2} + 21 \, d^{20} e^{13} x + d^{21} e^{12}\right)}}"," ",0,"-1/38798760*(3879876*B*b^10*e^11*x^11 + 11*B*b^10*d^11 + 1847560*A*a^10*e^11 + 10*(10*B*a*b^9 + A*b^10)*d^10*e + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^9*e^2 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^8*e^3 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^7*e^4 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^6*e^5 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^5*e^6 + 11440*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^4*e^7 + 24310*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^3*e^8 + 48620*(2*B*a^9*b + 9*A*a^8*b^2)*d^2*e^9 + 92378*(B*a^10 + 10*A*a^9*b)*d*e^10 + 352716*(11*B*b^10*d*e^10 + 10*(10*B*a*b^9 + A*b^10)*e^11)*x^10 + 293930*(11*B*b^10*d^2*e^9 + 10*(10*B*a*b^9 + A*b^10)*d*e^10 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*e^11)*x^9 + 203490*(11*B*b^10*d^3*e^8 + 10*(10*B*a*b^9 + A*b^10)*d^2*e^9 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d*e^10 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*e^11)*x^8 + 116280*(11*B*b^10*d^4*e^7 + 10*(10*B*a*b^9 + A*b^10)*d^3*e^8 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^2*e^9 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d*e^10 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*e^11)*x^7 + 54264*(11*B*b^10*d^5*e^6 + 10*(10*B*a*b^9 + A*b^10)*d^4*e^7 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^3*e^8 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^2*e^9 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d*e^10 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*e^11)*x^6 + 20349*(11*B*b^10*d^6*e^5 + 10*(10*B*a*b^9 + A*b^10)*d^5*e^6 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^4*e^7 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^3*e^8 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^2*e^9 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d*e^10 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*e^11)*x^5 + 5985*(11*B*b^10*d^7*e^4 + 10*(10*B*a*b^9 + A*b^10)*d^6*e^5 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^5*e^6 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^4*e^7 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^3*e^8 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^2*e^9 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d*e^10 + 11440*(4*B*a^7*b^3 + 7*A*a^6*b^4)*e^11)*x^4 + 1330*(11*B*b^10*d^8*e^3 + 10*(10*B*a*b^9 + A*b^10)*d^7*e^4 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^6*e^5 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^5*e^6 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^4*e^7 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^3*e^8 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^2*e^9 + 11440*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d*e^10 + 24310*(3*B*a^8*b^2 + 8*A*a^7*b^3)*e^11)*x^3 + 210*(11*B*b^10*d^9*e^2 + 10*(10*B*a*b^9 + A*b^10)*d^8*e^3 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^7*e^4 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^6*e^5 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^5*e^6 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^4*e^7 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^3*e^8 + 11440*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^2*e^9 + 24310*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d*e^10 + 48620*(2*B*a^9*b + 9*A*a^8*b^2)*e^11)*x^2 + 21*(11*B*b^10*d^10*e + 10*(10*B*a*b^9 + A*b^10)*d^9*e^2 + 55*(9*B*a^2*b^8 + 2*A*a*b^9)*d^8*e^3 + 220*(8*B*a^3*b^7 + 3*A*a^2*b^8)*d^7*e^4 + 715*(7*B*a^4*b^6 + 4*A*a^3*b^7)*d^6*e^5 + 2002*(6*B*a^5*b^5 + 5*A*a^4*b^6)*d^5*e^6 + 5005*(5*B*a^6*b^4 + 6*A*a^5*b^5)*d^4*e^7 + 11440*(4*B*a^7*b^3 + 7*A*a^6*b^4)*d^3*e^8 + 24310*(3*B*a^8*b^2 + 8*A*a^7*b^3)*d^2*e^9 + 48620*(2*B*a^9*b + 9*A*a^8*b^2)*d*e^10 + 92378*(B*a^10 + 10*A*a^9*b)*e^11)*x)/(e^33*x^21 + 21*d*e^32*x^20 + 210*d^2*e^31*x^19 + 1330*d^3*e^30*x^18 + 5985*d^4*e^29*x^17 + 20349*d^5*e^28*x^16 + 54264*d^6*e^27*x^15 + 116280*d^7*e^26*x^14 + 203490*d^8*e^25*x^13 + 293930*d^9*e^24*x^12 + 352716*d^10*e^23*x^11 + 352716*d^11*e^22*x^10 + 293930*d^12*e^21*x^9 + 203490*d^13*e^20*x^8 + 116280*d^14*e^19*x^7 + 54264*d^15*e^18*x^6 + 20349*d^16*e^17*x^5 + 5985*d^17*e^16*x^4 + 1330*d^18*e^15*x^3 + 210*d^19*e^14*x^2 + 21*d^20*e^13*x + d^21*e^12)","B",0
1111,1,566,0,1.059568," ","integrate((B*x+A)*(e*x+d)^5/(b*x+a),x, algorithm=""fricas"")","\frac{10 \, B b^{6} e^{5} x^{6} + 12 \, {\left(5 \, B b^{6} d e^{4} - {\left(B a b^{5} - A b^{6}\right)} e^{5}\right)} x^{5} + 15 \, {\left(10 \, B b^{6} d^{2} e^{3} - 5 \, {\left(B a b^{5} - A b^{6}\right)} d e^{4} + {\left(B a^{2} b^{4} - A a b^{5}\right)} e^{5}\right)} x^{4} + 20 \, {\left(10 \, B b^{6} d^{3} e^{2} - 10 \, {\left(B a b^{5} - A b^{6}\right)} d^{2} e^{3} + 5 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d e^{4} - {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 30 \, {\left(5 \, B b^{6} d^{4} e - 10 \, {\left(B a b^{5} - A b^{6}\right)} d^{3} e^{2} + 10 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d^{2} e^{3} - 5 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d e^{4} + {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 60 \, {\left(B b^{6} d^{5} - 5 \, {\left(B a b^{5} - A b^{6}\right)} d^{4} e + 10 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d^{3} e^{2} - 10 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} d e^{4} - {\left(B a^{5} b - A a^{4} b^{2}\right)} e^{5}\right)} x - 60 \, {\left({\left(B a b^{5} - A b^{6}\right)} d^{5} - 5 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d^{4} e + 10 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{3} e^{2} - 10 \, {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} d^{2} e^{3} + 5 \, {\left(B a^{5} b - A a^{4} b^{2}\right)} d e^{4} - {\left(B a^{6} - A a^{5} b\right)} e^{5}\right)} \log\left(b x + a\right)}{60 \, b^{7}}"," ",0,"1/60*(10*B*b^6*e^5*x^6 + 12*(5*B*b^6*d*e^4 - (B*a*b^5 - A*b^6)*e^5)*x^5 + 15*(10*B*b^6*d^2*e^3 - 5*(B*a*b^5 - A*b^6)*d*e^4 + (B*a^2*b^4 - A*a*b^5)*e^5)*x^4 + 20*(10*B*b^6*d^3*e^2 - 10*(B*a*b^5 - A*b^6)*d^2*e^3 + 5*(B*a^2*b^4 - A*a*b^5)*d*e^4 - (B*a^3*b^3 - A*a^2*b^4)*e^5)*x^3 + 30*(5*B*b^6*d^4*e - 10*(B*a*b^5 - A*b^6)*d^3*e^2 + 10*(B*a^2*b^4 - A*a*b^5)*d^2*e^3 - 5*(B*a^3*b^3 - A*a^2*b^4)*d*e^4 + (B*a^4*b^2 - A*a^3*b^3)*e^5)*x^2 + 60*(B*b^6*d^5 - 5*(B*a*b^5 - A*b^6)*d^4*e + 10*(B*a^2*b^4 - A*a*b^5)*d^3*e^2 - 10*(B*a^3*b^3 - A*a^2*b^4)*d^2*e^3 + 5*(B*a^4*b^2 - A*a^3*b^3)*d*e^4 - (B*a^5*b - A*a^4*b^2)*e^5)*x - 60*((B*a*b^5 - A*b^6)*d^5 - 5*(B*a^2*b^4 - A*a*b^5)*d^4*e + 10*(B*a^3*b^3 - A*a^2*b^4)*d^3*e^2 - 10*(B*a^4*b^2 - A*a^3*b^3)*d^2*e^3 + 5*(B*a^5*b - A*a^4*b^2)*d*e^4 - (B*a^6 - A*a^5*b)*e^5)*log(b*x + a))/b^7","B",0
1112,1,403,0,1.196476," ","integrate((B*x+A)*(e*x+d)^4/(b*x+a),x, algorithm=""fricas"")","\frac{12 \, B b^{5} e^{4} x^{5} + 15 \, {\left(4 \, B b^{5} d e^{3} - {\left(B a b^{4} - A b^{5}\right)} e^{4}\right)} x^{4} + 20 \, {\left(6 \, B b^{5} d^{2} e^{2} - 4 \, {\left(B a b^{4} - A b^{5}\right)} d e^{3} + {\left(B a^{2} b^{3} - A a b^{4}\right)} e^{4}\right)} x^{3} + 30 \, {\left(4 \, B b^{5} d^{3} e - 6 \, {\left(B a b^{4} - A b^{5}\right)} d^{2} e^{2} + 4 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d e^{3} - {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 60 \, {\left(B b^{5} d^{4} - 4 \, {\left(B a b^{4} - A b^{5}\right)} d^{3} e + 6 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{3} + {\left(B a^{4} b - A a^{3} b^{2}\right)} e^{4}\right)} x - 60 \, {\left({\left(B a b^{4} - A b^{5}\right)} d^{4} - 4 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{3} e + 6 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{2} e^{2} - 4 \, {\left(B a^{4} b - A a^{3} b^{2}\right)} d e^{3} + {\left(B a^{5} - A a^{4} b\right)} e^{4}\right)} \log\left(b x + a\right)}{60 \, b^{6}}"," ",0,"1/60*(12*B*b^5*e^4*x^5 + 15*(4*B*b^5*d*e^3 - (B*a*b^4 - A*b^5)*e^4)*x^4 + 20*(6*B*b^5*d^2*e^2 - 4*(B*a*b^4 - A*b^5)*d*e^3 + (B*a^2*b^3 - A*a*b^4)*e^4)*x^3 + 30*(4*B*b^5*d^3*e - 6*(B*a*b^4 - A*b^5)*d^2*e^2 + 4*(B*a^2*b^3 - A*a*b^4)*d*e^3 - (B*a^3*b^2 - A*a^2*b^3)*e^4)*x^2 + 60*(B*b^5*d^4 - 4*(B*a*b^4 - A*b^5)*d^3*e + 6*(B*a^2*b^3 - A*a*b^4)*d^2*e^2 - 4*(B*a^3*b^2 - A*a^2*b^3)*d*e^3 + (B*a^4*b - A*a^3*b^2)*e^4)*x - 60*((B*a*b^4 - A*b^5)*d^4 - 4*(B*a^2*b^3 - A*a*b^4)*d^3*e + 6*(B*a^3*b^2 - A*a^2*b^3)*d^2*e^2 - 4*(B*a^4*b - A*a^3*b^2)*d*e^3 + (B*a^5 - A*a^4*b)*e^4)*log(b*x + a))/b^6","B",0
1113,1,269,0,1.055905," ","integrate((B*x+A)*(e*x+d)^3/(b*x+a),x, algorithm=""fricas"")","\frac{3 \, B b^{4} e^{3} x^{4} + 4 \, {\left(3 \, B b^{4} d e^{2} - {\left(B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + 6 \, {\left(3 \, B b^{4} d^{2} e - 3 \, {\left(B a b^{3} - A b^{4}\right)} d e^{2} + {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 12 \, {\left(B b^{4} d^{3} - 3 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e + 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{2} - {\left(B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x - 12 \, {\left({\left(B a b^{3} - A b^{4}\right)} d^{3} - 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 3 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - {\left(B a^{4} - A a^{3} b\right)} e^{3}\right)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*B*b^4*e^3*x^4 + 4*(3*B*b^4*d*e^2 - (B*a*b^3 - A*b^4)*e^3)*x^3 + 6*(3*B*b^4*d^2*e - 3*(B*a*b^3 - A*b^4)*d*e^2 + (B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 12*(B*b^4*d^3 - 3*(B*a*b^3 - A*b^4)*d^2*e + 3*(B*a^2*b^2 - A*a*b^3)*d*e^2 - (B*a^3*b - A*a^2*b^2)*e^3)*x - 12*((B*a*b^3 - A*b^4)*d^3 - 3*(B*a^2*b^2 - A*a*b^3)*d^2*e + 3*(B*a^3*b - A*a^2*b^2)*d*e^2 - (B*a^4 - A*a^3*b)*e^3)*log(b*x + a))/b^5","B",0
1114,1,158,0,1.121812," ","integrate((B*x+A)*(e*x+d)^2/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{2} x^{3} + 3 \, {\left(2 \, B b^{3} d e - {\left(B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 6 \, {\left(B b^{3} d^{2} - 2 \, {\left(B a b^{2} - A b^{3}\right)} d e + {\left(B a^{2} b - A a b^{2}\right)} e^{2}\right)} x - 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e + {\left(B a^{3} - A a^{2} b\right)} e^{2}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*B*b^3*e^2*x^3 + 3*(2*B*b^3*d*e - (B*a*b^2 - A*b^3)*e^2)*x^2 + 6*(B*b^3*d^2 - 2*(B*a*b^2 - A*b^3)*d*e + (B*a^2*b - A*a*b^2)*e^2)*x - 6*((B*a*b^2 - A*b^3)*d^2 - 2*(B*a^2*b - A*a*b^2)*d*e + (B*a^3 - A*a^2*b)*e^2)*log(b*x + a))/b^4","A",0
1115,1,75,0,0.924376," ","integrate((B*x+A)*(e*x+d)/(b*x+a),x, algorithm=""fricas"")","\frac{B b^{2} e x^{2} + 2 \, {\left(B b^{2} d - {\left(B a b - A b^{2}\right)} e\right)} x - 2 \, {\left({\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(B*b^2*e*x^2 + 2*(B*b^2*d - (B*a*b - A*b^2)*e)*x - 2*((B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e)*log(b*x + a))/b^3","A",0
1116,1,25,0,1.024509," ","integrate((B*x+A)/(b*x+a),x, algorithm=""fricas"")","\frac{B b x - {\left(B a - A b\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(B*b*x - (B*a - A*b)*log(b*x + a))/b^2","A",0
1117,1,53,0,1.101217," ","integrate((B*x+A)/(b*x+a)/(e*x+d),x, algorithm=""fricas"")","-\frac{{\left(B a - A b\right)} e \log\left(b x + a\right) - {\left(B b d - A b e\right)} \log\left(e x + d\right)}{b^{2} d e - a b e^{2}}"," ",0,"-((B*a - A*b)*e*log(b*x + a) - (B*b*d - A*b*e)*log(e*x + d))/(b^2*d*e - a*b*e^2)","A",0
1118,1,148,0,0.970424," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{B b d^{2} + A a e^{2} - {\left(B a + A b\right)} d e + {\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \log\left(b x + a\right) - {\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \log\left(e x + d\right)}{b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x}"," ",0,"-(B*b*d^2 + A*a*e^2 - (B*a + A*b)*d*e + ((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*log(b*x + a) - ((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*log(e*x + d))/(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x)","A",0
1119,1,343,0,0.878311," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{B b^{2} d^{3} - 3 \, A b^{2} d^{2} e - A a^{2} e^{3} - {\left(B a^{2} - 4 \, A a b\right)} d e^{2} + 2 \, {\left({\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x + 2 \, {\left({\left(B a b - A b^{2}\right)} e^{3} x^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e^{2} x + {\left(B a b - A b^{2}\right)} d^{2} e\right)} \log\left(b x + a\right) - 2 \, {\left({\left(B a b - A b^{2}\right)} e^{3} x^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e^{2} x + {\left(B a b - A b^{2}\right)} d^{2} e\right)} \log\left(e x + d\right)}{2 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{2} + 2 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x\right)}}"," ",0,"-1/2*(B*b^2*d^3 - 3*A*b^2*d^2*e - A*a^2*e^3 - (B*a^2 - 4*A*a*b)*d*e^2 + 2*((B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x + 2*((B*a*b - A*b^2)*e^3*x^2 + 2*(B*a*b - A*b^2)*d*e^2*x + (B*a*b - A*b^2)*d^2*e)*log(b*x + a) - 2*((B*a*b - A*b^2)*e^3*x^2 + 2*(B*a*b - A*b^2)*d*e^2*x + (B*a*b - A*b^2)*d^2*e)*log(e*x + d))/(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^2 + 2*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x)","B",0
1120,1,608,0,1.288135," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{2 \, B b^{3} d^{4} + 2 \, A a^{3} e^{4} + {\left(3 \, B a b^{2} - 11 \, A b^{3}\right)} d^{3} e - 6 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e^{2} + {\left(B a^{3} - 9 \, A a^{2} b\right)} d e^{3} + 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} d e^{3} - {\left(B a^{2} b - A a b^{2}\right)} e^{4}\right)} x^{2} + 3 \, {\left(5 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} - 6 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{3} + {\left(B a^{3} - A a^{2} b\right)} e^{4}\right)} x + 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} e^{4} x^{3} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} x^{2} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} x + {\left(B a b^{2} - A b^{3}\right)} d^{3} e\right)} \log\left(b x + a\right) - 6 \, {\left({\left(B a b^{2} - A b^{3}\right)} e^{4} x^{3} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} x^{2} + 3 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} x + {\left(B a b^{2} - A b^{3}\right)} d^{3} e\right)} \log\left(e x + d\right)}{6 \, {\left(b^{4} d^{7} e - 4 \, a b^{3} d^{6} e^{2} + 6 \, a^{2} b^{2} d^{5} e^{3} - 4 \, a^{3} b d^{4} e^{4} + a^{4} d^{3} e^{5} + {\left(b^{4} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} x^{3} + 3 \, {\left(b^{4} d^{5} e^{3} - 4 \, a b^{3} d^{4} e^{4} + 6 \, a^{2} b^{2} d^{3} e^{5} - 4 \, a^{3} b d^{2} e^{6} + a^{4} d e^{7}\right)} x^{2} + 3 \, {\left(b^{4} d^{6} e^{2} - 4 \, a b^{3} d^{5} e^{3} + 6 \, a^{2} b^{2} d^{4} e^{4} - 4 \, a^{3} b d^{3} e^{5} + a^{4} d^{2} e^{6}\right)} x\right)}}"," ",0,"-1/6*(2*B*b^3*d^4 + 2*A*a^3*e^4 + (3*B*a*b^2 - 11*A*b^3)*d^3*e - 6*(B*a^2*b - 3*A*a*b^2)*d^2*e^2 + (B*a^3 - 9*A*a^2*b)*d*e^3 + 6*((B*a*b^2 - A*b^3)*d*e^3 - (B*a^2*b - A*a*b^2)*e^4)*x^2 + 3*(5*(B*a*b^2 - A*b^3)*d^2*e^2 - 6*(B*a^2*b - A*a*b^2)*d*e^3 + (B*a^3 - A*a^2*b)*e^4)*x + 6*((B*a*b^2 - A*b^3)*e^4*x^3 + 3*(B*a*b^2 - A*b^3)*d*e^3*x^2 + 3*(B*a*b^2 - A*b^3)*d^2*e^2*x + (B*a*b^2 - A*b^3)*d^3*e)*log(b*x + a) - 6*((B*a*b^2 - A*b^3)*e^4*x^3 + 3*(B*a*b^2 - A*b^3)*d*e^3*x^2 + 3*(B*a*b^2 - A*b^3)*d^2*e^2*x + (B*a*b^2 - A*b^3)*d^3*e)*log(e*x + d))/(b^4*d^7*e - 4*a*b^3*d^6*e^2 + 6*a^2*b^2*d^5*e^3 - 4*a^3*b*d^4*e^4 + a^4*d^3*e^5 + (b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 6*a^2*b^2*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*x^3 + 3*(b^4*d^5*e^3 - 4*a*b^3*d^4*e^4 + 6*a^2*b^2*d^3*e^5 - 4*a^3*b*d^2*e^6 + a^4*d*e^7)*x^2 + 3*(b^4*d^6*e^2 - 4*a*b^3*d^5*e^3 + 6*a^2*b^2*d^4*e^4 - 4*a^3*b*d^3*e^5 + a^4*d^2*e^6)*x)","B",0
1121,1,922,0,1.058388," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{3 \, B b^{4} d^{5} - 3 \, A a^{4} e^{5} + 5 \, {\left(2 \, B a b^{3} - 5 \, A b^{4}\right)} d^{4} e - 6 \, {\left(3 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d^{3} e^{2} + 6 \, {\left(B a^{3} b - 6 \, A a^{2} b^{2}\right)} d^{2} e^{3} - {\left(B a^{4} - 16 \, A a^{3} b\right)} d e^{4} + 12 \, {\left({\left(B a b^{3} - A b^{4}\right)} d e^{4} - {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{5}\right)} x^{3} + 6 \, {\left(7 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{3} - 8 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{4} + {\left(B a^{3} b - A a^{2} b^{2}\right)} e^{5}\right)} x^{2} + 4 \, {\left(13 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e^{2} - 18 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{3} + 6 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{4} - {\left(B a^{4} - A a^{3} b\right)} e^{5}\right)} x + 12 \, {\left({\left(B a b^{3} - A b^{4}\right)} e^{5} x^{4} + 4 \, {\left(B a b^{3} - A b^{4}\right)} d e^{4} x^{3} + 6 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{3} x^{2} + 4 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e^{2} x + {\left(B a b^{3} - A b^{4}\right)} d^{4} e\right)} \log\left(b x + a\right) - 12 \, {\left({\left(B a b^{3} - A b^{4}\right)} e^{5} x^{4} + 4 \, {\left(B a b^{3} - A b^{4}\right)} d e^{4} x^{3} + 6 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{3} x^{2} + 4 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e^{2} x + {\left(B a b^{3} - A b^{4}\right)} d^{4} e\right)} \log\left(e x + d\right)}{12 \, {\left(b^{5} d^{9} e - 5 \, a b^{4} d^{8} e^{2} + 10 \, a^{2} b^{3} d^{7} e^{3} - 10 \, a^{3} b^{2} d^{6} e^{4} + 5 \, a^{4} b d^{5} e^{5} - a^{5} d^{4} e^{6} + {\left(b^{5} d^{5} e^{5} - 5 \, a b^{4} d^{4} e^{6} + 10 \, a^{2} b^{3} d^{3} e^{7} - 10 \, a^{3} b^{2} d^{2} e^{8} + 5 \, a^{4} b d e^{9} - a^{5} e^{10}\right)} x^{4} + 4 \, {\left(b^{5} d^{6} e^{4} - 5 \, a b^{4} d^{5} e^{5} + 10 \, a^{2} b^{3} d^{4} e^{6} - 10 \, a^{3} b^{2} d^{3} e^{7} + 5 \, a^{4} b d^{2} e^{8} - a^{5} d e^{9}\right)} x^{3} + 6 \, {\left(b^{5} d^{7} e^{3} - 5 \, a b^{4} d^{6} e^{4} + 10 \, a^{2} b^{3} d^{5} e^{5} - 10 \, a^{3} b^{2} d^{4} e^{6} + 5 \, a^{4} b d^{3} e^{7} - a^{5} d^{2} e^{8}\right)} x^{2} + 4 \, {\left(b^{5} d^{8} e^{2} - 5 \, a b^{4} d^{7} e^{3} + 10 \, a^{2} b^{3} d^{6} e^{4} - 10 \, a^{3} b^{2} d^{5} e^{5} + 5 \, a^{4} b d^{4} e^{6} - a^{5} d^{3} e^{7}\right)} x\right)}}"," ",0,"-1/12*(3*B*b^4*d^5 - 3*A*a^4*e^5 + 5*(2*B*a*b^3 - 5*A*b^4)*d^4*e - 6*(3*B*a^2*b^2 - 8*A*a*b^3)*d^3*e^2 + 6*(B*a^3*b - 6*A*a^2*b^2)*d^2*e^3 - (B*a^4 - 16*A*a^3*b)*d*e^4 + 12*((B*a*b^3 - A*b^4)*d*e^4 - (B*a^2*b^2 - A*a*b^3)*e^5)*x^3 + 6*(7*(B*a*b^3 - A*b^4)*d^2*e^3 - 8*(B*a^2*b^2 - A*a*b^3)*d*e^4 + (B*a^3*b - A*a^2*b^2)*e^5)*x^2 + 4*(13*(B*a*b^3 - A*b^4)*d^3*e^2 - 18*(B*a^2*b^2 - A*a*b^3)*d^2*e^3 + 6*(B*a^3*b - A*a^2*b^2)*d*e^4 - (B*a^4 - A*a^3*b)*e^5)*x + 12*((B*a*b^3 - A*b^4)*e^5*x^4 + 4*(B*a*b^3 - A*b^4)*d*e^4*x^3 + 6*(B*a*b^3 - A*b^4)*d^2*e^3*x^2 + 4*(B*a*b^3 - A*b^4)*d^3*e^2*x + (B*a*b^3 - A*b^4)*d^4*e)*log(b*x + a) - 12*((B*a*b^3 - A*b^4)*e^5*x^4 + 4*(B*a*b^3 - A*b^4)*d*e^4*x^3 + 6*(B*a*b^3 - A*b^4)*d^2*e^3*x^2 + 4*(B*a*b^3 - A*b^4)*d^3*e^2*x + (B*a*b^3 - A*b^4)*d^4*e)*log(e*x + d))/(b^5*d^9*e - 5*a*b^4*d^8*e^2 + 10*a^2*b^3*d^7*e^3 - 10*a^3*b^2*d^6*e^4 + 5*a^4*b*d^5*e^5 - a^5*d^4*e^6 + (b^5*d^5*e^5 - 5*a*b^4*d^4*e^6 + 10*a^2*b^3*d^3*e^7 - 10*a^3*b^2*d^2*e^8 + 5*a^4*b*d*e^9 - a^5*e^10)*x^4 + 4*(b^5*d^6*e^4 - 5*a*b^4*d^5*e^5 + 10*a^2*b^3*d^4*e^6 - 10*a^3*b^2*d^3*e^7 + 5*a^4*b*d^2*e^8 - a^5*d*e^9)*x^3 + 6*(b^5*d^7*e^3 - 5*a*b^4*d^6*e^4 + 10*a^2*b^3*d^5*e^5 - 10*a^3*b^2*d^4*e^6 + 5*a^4*b*d^3*e^7 - a^5*d^2*e^8)*x^2 + 4*(b^5*d^8*e^2 - 5*a*b^4*d^7*e^3 + 10*a^2*b^3*d^6*e^4 - 10*a^3*b^2*d^5*e^5 + 5*a^4*b*d^4*e^6 - a^5*d^3*e^7)*x)","B",0
1122,1,832,0,0.857005," ","integrate((B*x+A)*(e*x+d)^5/(b*x+a)^2,x, algorithm=""fricas"")","\frac{12 \, B b^{6} e^{5} x^{6} + 60 \, {\left(B a b^{5} - A b^{6}\right)} d^{5} - 300 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d^{4} e + 600 \, {\left(B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{3} e^{2} - 600 \, {\left(B a^{4} b^{2} - A a^{3} b^{3}\right)} d^{2} e^{3} + 300 \, {\left(B a^{5} b - A a^{4} b^{2}\right)} d e^{4} - 60 \, {\left(B a^{6} - A a^{5} b\right)} e^{5} + 3 \, {\left(25 \, B b^{6} d e^{4} - {\left(6 \, B a b^{5} - 5 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(40 \, B b^{6} d^{2} e^{3} - 5 \, {\left(5 \, B a b^{5} - 4 \, A b^{6}\right)} d e^{4} + {\left(6 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 10 \, {\left(30 \, B b^{6} d^{3} e^{2} - 10 \, {\left(4 \, B a b^{5} - 3 \, A b^{6}\right)} d^{2} e^{3} + 5 \, {\left(5 \, B a^{2} b^{4} - 4 \, A a b^{5}\right)} d e^{4} - {\left(6 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 30 \, {\left(10 \, B b^{6} d^{4} e - 10 \, {\left(3 \, B a b^{5} - 2 \, A b^{6}\right)} d^{3} e^{2} + 10 \, {\left(4 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} d^{2} e^{3} - 5 \, {\left(5 \, B a^{3} b^{3} - 4 \, A a^{2} b^{4}\right)} d e^{4} + {\left(6 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 60 \, {\left(5 \, B a b^{5} d^{4} e - 10 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} d^{3} e^{2} + 10 \, {\left(3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 5 \, {\left(4 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d e^{4} + {\left(5 \, B a^{5} b - 4 \, A a^{4} b^{2}\right)} e^{5}\right)} x + 60 \, {\left(B a b^{5} d^{5} - 5 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} d^{4} e + 10 \, {\left(3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} d^{3} e^{2} - 10 \, {\left(4 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d^{2} e^{3} + 5 \, {\left(5 \, B a^{5} b - 4 \, A a^{4} b^{2}\right)} d e^{4} - {\left(6 \, B a^{6} - 5 \, A a^{5} b\right)} e^{5} + {\left(B b^{6} d^{5} - 5 \, {\left(2 \, B a b^{5} - A b^{6}\right)} d^{4} e + 10 \, {\left(3 \, B a^{2} b^{4} - 2 \, A a b^{5}\right)} d^{3} e^{2} - 10 \, {\left(4 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} d^{2} e^{3} + 5 \, {\left(5 \, B a^{4} b^{2} - 4 \, A a^{3} b^{3}\right)} d e^{4} - {\left(6 \, B a^{5} b - 5 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \log\left(b x + a\right)}{60 \, {\left(b^{8} x + a b^{7}\right)}}"," ",0,"1/60*(12*B*b^6*e^5*x^6 + 60*(B*a*b^5 - A*b^6)*d^5 - 300*(B*a^2*b^4 - A*a*b^5)*d^4*e + 600*(B*a^3*b^3 - A*a^2*b^4)*d^3*e^2 - 600*(B*a^4*b^2 - A*a^3*b^3)*d^2*e^3 + 300*(B*a^5*b - A*a^4*b^2)*d*e^4 - 60*(B*a^6 - A*a^5*b)*e^5 + 3*(25*B*b^6*d*e^4 - (6*B*a*b^5 - 5*A*b^6)*e^5)*x^5 + 5*(40*B*b^6*d^2*e^3 - 5*(5*B*a*b^5 - 4*A*b^6)*d*e^4 + (6*B*a^2*b^4 - 5*A*a*b^5)*e^5)*x^4 + 10*(30*B*b^6*d^3*e^2 - 10*(4*B*a*b^5 - 3*A*b^6)*d^2*e^3 + 5*(5*B*a^2*b^4 - 4*A*a*b^5)*d*e^4 - (6*B*a^3*b^3 - 5*A*a^2*b^4)*e^5)*x^3 + 30*(10*B*b^6*d^4*e - 10*(3*B*a*b^5 - 2*A*b^6)*d^3*e^2 + 10*(4*B*a^2*b^4 - 3*A*a*b^5)*d^2*e^3 - 5*(5*B*a^3*b^3 - 4*A*a^2*b^4)*d*e^4 + (6*B*a^4*b^2 - 5*A*a^3*b^3)*e^5)*x^2 + 60*(5*B*a*b^5*d^4*e - 10*(2*B*a^2*b^4 - A*a*b^5)*d^3*e^2 + 10*(3*B*a^3*b^3 - 2*A*a^2*b^4)*d^2*e^3 - 5*(4*B*a^4*b^2 - 3*A*a^3*b^3)*d*e^4 + (5*B*a^5*b - 4*A*a^4*b^2)*e^5)*x + 60*(B*a*b^5*d^5 - 5*(2*B*a^2*b^4 - A*a*b^5)*d^4*e + 10*(3*B*a^3*b^3 - 2*A*a^2*b^4)*d^3*e^2 - 10*(4*B*a^4*b^2 - 3*A*a^3*b^3)*d^2*e^3 + 5*(5*B*a^5*b - 4*A*a^4*b^2)*d*e^4 - (6*B*a^6 - 5*A*a^5*b)*e^5 + (B*b^6*d^5 - 5*(2*B*a*b^5 - A*b^6)*d^4*e + 10*(3*B*a^2*b^4 - 2*A*a*b^5)*d^3*e^2 - 10*(4*B*a^3*b^3 - 3*A*a^2*b^4)*d^2*e^3 + 5*(5*B*a^4*b^2 - 4*A*a^3*b^3)*d*e^4 - (6*B*a^5*b - 5*A*a^4*b^2)*e^5)*x)*log(b*x + a))/(b^8*x + a*b^7)","B",0
1123,1,610,0,1.320539," ","integrate((B*x+A)*(e*x+d)^4/(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, B b^{5} e^{4} x^{5} + 12 \, {\left(B a b^{4} - A b^{5}\right)} d^{4} - 48 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{3} e + 72 \, {\left(B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{2} e^{2} - 48 \, {\left(B a^{4} b - A a^{3} b^{2}\right)} d e^{3} + 12 \, {\left(B a^{5} - A a^{4} b\right)} e^{4} + {\left(16 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} e^{4}\right)} x^{4} + 2 \, {\left(18 \, B b^{5} d^{2} e^{2} - 4 \, {\left(4 \, B a b^{4} - 3 \, A b^{5}\right)} d e^{3} + {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 6 \, {\left(8 \, B b^{5} d^{3} e - 6 \, {\left(3 \, B a b^{4} - 2 \, A b^{5}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} d e^{3} - {\left(5 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(4 \, B a b^{4} d^{3} e - 6 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} + 4 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d e^{3} - {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(B a b^{4} d^{4} - 4 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d^{3} e + 6 \, {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e^{2} - 4 \, {\left(4 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} d e^{3} + {\left(5 \, B a^{5} - 4 \, A a^{4} b\right)} e^{4} + {\left(B b^{5} d^{4} - 4 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(4 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d e^{3} + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*B*b^5*e^4*x^5 + 12*(B*a*b^4 - A*b^5)*d^4 - 48*(B*a^2*b^3 - A*a*b^4)*d^3*e + 72*(B*a^3*b^2 - A*a^2*b^3)*d^2*e^2 - 48*(B*a^4*b - A*a^3*b^2)*d*e^3 + 12*(B*a^5 - A*a^4*b)*e^4 + (16*B*b^5*d*e^3 - (5*B*a*b^4 - 4*A*b^5)*e^4)*x^4 + 2*(18*B*b^5*d^2*e^2 - 4*(4*B*a*b^4 - 3*A*b^5)*d*e^3 + (5*B*a^2*b^3 - 4*A*a*b^4)*e^4)*x^3 + 6*(8*B*b^5*d^3*e - 6*(3*B*a*b^4 - 2*A*b^5)*d^2*e^2 + 4*(4*B*a^2*b^3 - 3*A*a*b^4)*d*e^3 - (5*B*a^3*b^2 - 4*A*a^2*b^3)*e^4)*x^2 + 12*(4*B*a*b^4*d^3*e - 6*(2*B*a^2*b^3 - A*a*b^4)*d^2*e^2 + 4*(3*B*a^3*b^2 - 2*A*a^2*b^3)*d*e^3 - (4*B*a^4*b - 3*A*a^3*b^2)*e^4)*x + 12*(B*a*b^4*d^4 - 4*(2*B*a^2*b^3 - A*a*b^4)*d^3*e + 6*(3*B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e^2 - 4*(4*B*a^4*b - 3*A*a^3*b^2)*d*e^3 + (5*B*a^5 - 4*A*a^4*b)*e^4 + (B*b^5*d^4 - 4*(2*B*a*b^4 - A*b^5)*d^3*e + 6*(3*B*a^2*b^3 - 2*A*a*b^4)*d^2*e^2 - 4*(4*B*a^3*b^2 - 3*A*a^2*b^3)*d*e^3 + (5*B*a^4*b - 4*A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^7*x + a*b^6)","B",0
1124,1,417,0,0.913471," ","integrate((B*x+A)*(e*x+d)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, B b^{4} e^{3} x^{4} + 6 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} - 18 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 18 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{2} - 6 \, {\left(B a^{4} - A a^{3} b\right)} e^{3} + {\left(9 \, B b^{4} d e^{2} - {\left(4 \, B a b^{3} - 3 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(6 \, B b^{4} d^{2} e - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d e^{2} + {\left(4 \, B a^{2} b^{2} - 3 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 6 \, {\left(3 \, B a b^{3} d^{2} e - 3 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} d e^{2} + {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x + 6 \, {\left(B a b^{3} d^{3} - 3 \, {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} d^{2} e + 3 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{2} - {\left(4 \, B a^{4} - 3 \, A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{3} - 3 \, {\left(2 \, B a b^{3} - A b^{4}\right)} d^{2} e + 3 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d e^{2} - {\left(4 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/6*(2*B*b^4*e^3*x^4 + 6*(B*a*b^3 - A*b^4)*d^3 - 18*(B*a^2*b^2 - A*a*b^3)*d^2*e + 18*(B*a^3*b - A*a^2*b^2)*d*e^2 - 6*(B*a^4 - A*a^3*b)*e^3 + (9*B*b^4*d*e^2 - (4*B*a*b^3 - 3*A*b^4)*e^3)*x^3 + 3*(6*B*b^4*d^2*e - 3*(3*B*a*b^3 - 2*A*b^4)*d*e^2 + (4*B*a^2*b^2 - 3*A*a*b^3)*e^3)*x^2 + 6*(3*B*a*b^3*d^2*e - 3*(2*B*a^2*b^2 - A*a*b^3)*d*e^2 + (3*B*a^3*b - 2*A*a^2*b^2)*e^3)*x + 6*(B*a*b^3*d^3 - 3*(2*B*a^2*b^2 - A*a*b^3)*d^2*e + 3*(3*B*a^3*b - 2*A*a^2*b^2)*d*e^2 - (4*B*a^4 - 3*A*a^3*b)*e^3 + (B*b^4*d^3 - 3*(2*B*a*b^3 - A*b^4)*d^2*e + 3*(3*B*a^2*b^2 - 2*A*a*b^3)*d*e^2 - (4*B*a^3*b - 3*A*a^2*b^2)*e^3)*x)*log(b*x + a))/(b^6*x + a*b^5)","B",0
1125,1,249,0,1.106664," ","integrate((B*x+A)*(e*x+d)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B b^{3} e^{2} x^{3} + 2 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} - 4 \, {\left(B a^{2} b - A a b^{2}\right)} d e + 2 \, {\left(B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, B a b^{2} d e - {\left(2 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x + 2 \, {\left(B a b^{2} d^{2} - 2 \, {\left(2 \, B a^{2} b - A a b^{2}\right)} d e + {\left(3 \, B a^{3} - 2 \, A a^{2} b\right)} e^{2} + {\left(B b^{3} d^{2} - 2 \, {\left(2 \, B a b^{2} - A b^{3}\right)} d e + {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} e^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(B*b^3*e^2*x^3 + 2*(B*a*b^2 - A*b^3)*d^2 - 4*(B*a^2*b - A*a*b^2)*d*e + 2*(B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 - 2*A*b^3)*e^2)*x^2 + 2*(2*B*a*b^2*d*e - (2*B*a^2*b - A*a*b^2)*e^2)*x + 2*(B*a*b^2*d^2 - 2*(2*B*a^2*b - A*a*b^2)*d*e + (3*B*a^3 - 2*A*a^2*b)*e^2 + (B*b^3*d^2 - 2*(2*B*a*b^2 - A*b^3)*d*e + (3*B*a^2*b - 2*A*a*b^2)*e^2)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
1126,1,109,0,0.686267," ","integrate((B*x+A)*(e*x+d)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B b^{2} e x^{2} + B a b e x + {\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e + {\left(B a b d - {\left(2 \, B a^{2} - A a b\right)} e + {\left(B b^{2} d - {\left(2 \, B a b - A b^{2}\right)} e\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(B*b^2*e*x^2 + B*a*b*e*x + (B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e + (B*a*b*d - (2*B*a^2 - A*a*b)*e + (B*b^2*d - (2*B*a*b - A*b^2)*e)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
1127,1,37,0,1.000086," ","integrate((B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b x + B a\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"(B*a - A*b + (B*b*x + B*a)*log(b*x + a))/(b^3*x + a*b^2)","A",0
1128,1,157,0,1.006052," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{{\left(B a b - A b^{2}\right)} d - {\left(B a^{2} - A a b\right)} e + {\left(B a b d - A a b e + {\left(B b^{2} d - A b^{2} e\right)} x\right)} \log\left(b x + a\right) - {\left(B a b d - A a b e + {\left(B b^{2} d - A b^{2} e\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x}"," ",0,"((B*a*b - A*b^2)*d - (B*a^2 - A*a*b)*e + (B*a*b*d - A*a*b*e + (B*b^2*d - A*b^2*e)*x)*log(b*x + a) - (B*a*b*d - A*a*b*e + (B*b^2*d - A*b^2*e)*x)*log(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x)","A",0
1129,1,396,0,1.199052," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{2} d e - A a^{2} e^{2} - {\left(2 \, B a b - A b^{2}\right)} d^{2} - {\left(B b^{2} d^{2} - 2 \, A b^{2} d e - {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x - {\left(B a b d^{2} + {\left(B a^{2} - 2 \, A a b\right)} d e + {\left(B b^{2} d e + {\left(B a b - 2 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(B b^{2} d^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x\right)} \log\left(b x + a\right) + {\left(B a b d^{2} + {\left(B a^{2} - 2 \, A a b\right)} d e + {\left(B b^{2} d e + {\left(B a b - 2 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(B b^{2} d^{2} + 2 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 2 \, A a b\right)} e^{2}\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{4} - 3 \, a^{2} b^{2} d^{3} e + 3 \, a^{3} b d^{2} e^{2} - a^{4} d e^{3} + {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x^{2} + {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + 2 \, a^{3} b d e^{3} - a^{4} e^{4}\right)} x}"," ",0,"-(2*B*a^2*d*e - A*a^2*e^2 - (2*B*a*b - A*b^2)*d^2 - (B*b^2*d^2 - 2*A*b^2*d*e - (B*a^2 - 2*A*a*b)*e^2)*x - (B*a*b*d^2 + (B*a^2 - 2*A*a*b)*d*e + (B*b^2*d*e + (B*a*b - 2*A*b^2)*e^2)*x^2 + (B*b^2*d^2 + 2*(B*a*b - A*b^2)*d*e + (B*a^2 - 2*A*a*b)*e^2)*x)*log(b*x + a) + (B*a*b*d^2 + (B*a^2 - 2*A*a*b)*d*e + (B*b^2*d*e + (B*a*b - 2*A*b^2)*e^2)*x^2 + (B*b^2*d^2 + 2*(B*a*b - A*b^2)*d*e + (B*a^2 - 2*A*a*b)*e^2)*x)*log(e*x + d))/(a*b^3*d^4 - 3*a^2*b^2*d^3*e + 3*a^3*b*d^2*e^2 - a^4*d*e^3 + (b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x^2 + (b^4*d^4 - 2*a*b^3*d^3*e + 2*a^3*b*d*e^3 - a^4*e^4)*x)","B",0
1130,1,801,0,0.773148," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{A a^{3} e^{3} - {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} d^{3} + {\left(4 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{2} e + {\left(B a^{3} - 6 \, A a^{2} b\right)} d e^{2} - 2 \, {\left(B b^{3} d^{2} e + {\left(B a b^{2} - 3 \, A b^{3}\right)} d e^{2} - {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(3 \, B b^{3} d^{3} + {\left(4 \, B a b^{2} - 9 \, A b^{3}\right)} d^{2} e - {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} d e^{2} - {\left(2 \, B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x - 2 \, {\left(B a b^{2} d^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e + {\left(B b^{3} d e^{2} + {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} d e^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(B b^{3} d^{3} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(B a b^{2} d^{3} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e + {\left(B b^{3} d e^{2} + {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} d e^{2} + {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(B b^{3} d^{3} + {\left(4 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a b^{4} d^{6} - 4 \, a^{2} b^{3} d^{5} e + 6 \, a^{3} b^{2} d^{4} e^{2} - 4 \, a^{4} b d^{3} e^{3} + a^{5} d^{2} e^{4} + {\left(b^{5} d^{4} e^{2} - 4 \, a b^{4} d^{3} e^{3} + 6 \, a^{2} b^{3} d^{2} e^{4} - 4 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{3} + {\left(2 \, b^{5} d^{5} e - 7 \, a b^{4} d^{4} e^{2} + 8 \, a^{2} b^{3} d^{3} e^{3} - 2 \, a^{3} b^{2} d^{2} e^{4} - 2 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x^{2} + {\left(b^{5} d^{6} - 2 \, a b^{4} d^{5} e - 2 \, a^{2} b^{3} d^{4} e^{2} + 8 \, a^{3} b^{2} d^{3} e^{3} - 7 \, a^{4} b d^{2} e^{4} + 2 \, a^{5} d e^{5}\right)} x\right)}}"," ",0,"-1/2*(A*a^3*e^3 - (5*B*a*b^2 - 2*A*b^3)*d^3 + (4*B*a^2*b + 3*A*a*b^2)*d^2*e + (B*a^3 - 6*A*a^2*b)*d*e^2 - 2*(B*b^3*d^2*e + (B*a*b^2 - 3*A*b^3)*d*e^2 - (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 - (3*B*b^3*d^3 + (4*B*a*b^2 - 9*A*b^3)*d^2*e - (5*B*a^2*b - 6*A*a*b^2)*d*e^2 - (2*B*a^3 - 3*A*a^2*b)*e^3)*x - 2*(B*a*b^2*d^3 + (2*B*a^2*b - 3*A*a*b^2)*d^2*e + (B*b^3*d*e^2 + (2*B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 6*A*b^3)*d*e^2 + (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (B*b^3*d^3 + (4*B*a*b^2 - 3*A*b^3)*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2)*x)*log(b*x + a) + 2*(B*a*b^2*d^3 + (2*B*a^2*b - 3*A*a*b^2)*d^2*e + (B*b^3*d*e^2 + (2*B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 6*A*b^3)*d*e^2 + (2*B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (B*b^3*d^3 + (4*B*a*b^2 - 3*A*b^3)*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2)*x)*log(e*x + d))/(a*b^4*d^6 - 4*a^2*b^3*d^5*e + 6*a^3*b^2*d^4*e^2 - 4*a^4*b*d^3*e^3 + a^5*d^2*e^4 + (b^5*d^4*e^2 - 4*a*b^4*d^3*e^3 + 6*a^2*b^3*d^2*e^4 - 4*a^3*b^2*d*e^5 + a^4*b*e^6)*x^3 + (2*b^5*d^5*e - 7*a*b^4*d^4*e^2 + 8*a^2*b^3*d^3*e^3 - 2*a^3*b^2*d^2*e^4 - 2*a^4*b*d*e^5 + a^5*e^6)*x^2 + (b^5*d^6 - 2*a*b^4*d^5*e - 2*a^2*b^3*d^4*e^2 + 8*a^3*b^2*d^3*e^3 - 7*a^4*b*d^2*e^4 + 2*a^5*d*e^5)*x)","B",0
1131,1,1219,0,0.861099," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, A a^{4} e^{4} + {\left(17 \, B a b^{3} - 6 \, A b^{4}\right)} d^{4} - {\left(9 \, B a^{2} b^{2} + 20 \, A a b^{3}\right)} d^{3} e - 9 \, {\left(B a^{3} b - 4 \, A a^{2} b^{2}\right)} d^{2} e^{2} + {\left(B a^{4} - 12 \, A a^{3} b\right)} d e^{3} + 6 \, {\left(B b^{4} d^{2} e^{2} + 2 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} d e^{3} - {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(5 \, B b^{4} d^{3} e + {\left(11 \, B a b^{3} - 20 \, A b^{4}\right)} d^{2} e^{2} - {\left(13 \, B a^{2} b^{2} - 16 \, A a b^{3}\right)} d e^{3} - {\left(3 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(11 \, B b^{4} d^{4} + 2 \, {\left(15 \, B a b^{3} - 22 \, A b^{4}\right)} d^{3} e - 6 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(13 \, B a^{3} b - 18 \, A a^{2} b^{2}\right)} d e^{3} + {\left(3 \, B a^{4} - 4 \, A a^{3} b\right)} e^{4}\right)} x + 6 \, {\left(B a b^{3} d^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{3} e + {\left(B b^{4} d e^{3} + {\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} - 6 \, A b^{4}\right)} d e^{3} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(B b^{4} d^{3} e + 4 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{2} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d e^{3}\right)} x^{2} + {\left(B b^{4} d^{4} + 2 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d^{3} e + 3 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(B a b^{3} d^{4} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{3} e + {\left(B b^{4} d e^{3} + {\left(3 \, B a b^{3} - 4 \, A b^{4}\right)} e^{4}\right)} x^{4} + {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} - 6 \, A b^{4}\right)} d e^{3} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(B b^{4} d^{3} e + 4 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{2} + {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d e^{3}\right)} x^{2} + {\left(B b^{4} d^{4} + 2 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d^{3} e + 3 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a b^{5} d^{8} - 5 \, a^{2} b^{4} d^{7} e + 10 \, a^{3} b^{3} d^{6} e^{2} - 10 \, a^{4} b^{2} d^{5} e^{3} + 5 \, a^{5} b d^{4} e^{4} - a^{6} d^{3} e^{5} + {\left(b^{6} d^{5} e^{3} - 5 \, a b^{5} d^{4} e^{4} + 10 \, a^{2} b^{4} d^{3} e^{5} - 10 \, a^{3} b^{3} d^{2} e^{6} + 5 \, a^{4} b^{2} d e^{7} - a^{5} b e^{8}\right)} x^{4} + {\left(3 \, b^{6} d^{6} e^{2} - 14 \, a b^{5} d^{5} e^{3} + 25 \, a^{2} b^{4} d^{4} e^{4} - 20 \, a^{3} b^{3} d^{3} e^{5} + 5 \, a^{4} b^{2} d^{2} e^{6} + 2 \, a^{5} b d e^{7} - a^{6} e^{8}\right)} x^{3} + 3 \, {\left(b^{6} d^{7} e - 4 \, a b^{5} d^{6} e^{2} + 5 \, a^{2} b^{4} d^{5} e^{3} - 5 \, a^{4} b^{2} d^{3} e^{5} + 4 \, a^{5} b d^{2} e^{6} - a^{6} d e^{7}\right)} x^{2} + {\left(b^{6} d^{8} - 2 \, a b^{5} d^{7} e - 5 \, a^{2} b^{4} d^{6} e^{2} + 20 \, a^{3} b^{3} d^{5} e^{3} - 25 \, a^{4} b^{2} d^{4} e^{4} + 14 \, a^{5} b d^{3} e^{5} - 3 \, a^{6} d^{2} e^{6}\right)} x\right)}}"," ",0,"1/6*(2*A*a^4*e^4 + (17*B*a*b^3 - 6*A*b^4)*d^4 - (9*B*a^2*b^2 + 20*A*a*b^3)*d^3*e - 9*(B*a^3*b - 4*A*a^2*b^2)*d^2*e^2 + (B*a^4 - 12*A*a^3*b)*d*e^3 + 6*(B*b^4*d^2*e^2 + 2*(B*a*b^3 - 2*A*b^4)*d*e^3 - (3*B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(5*B*b^4*d^3*e + (11*B*a*b^3 - 20*A*b^4)*d^2*e^2 - (13*B*a^2*b^2 - 16*A*a*b^3)*d*e^3 - (3*B*a^3*b - 4*A*a^2*b^2)*e^4)*x^2 + (11*B*b^4*d^4 + 2*(15*B*a*b^3 - 22*A*b^4)*d^3*e - 6*(3*B*a^2*b^2 - 2*A*a*b^3)*d^2*e^2 - 2*(13*B*a^3*b - 18*A*a^2*b^2)*d*e^3 + (3*B*a^4 - 4*A*a^3*b)*e^4)*x + 6*(B*a*b^3*d^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*d^3*e + (B*b^4*d*e^3 + (3*B*a*b^3 - 4*A*b^4)*e^4)*x^4 + (3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 - 6*A*b^4)*d*e^3 + (3*B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(B*b^4*d^3*e + 4*(B*a*b^3 - A*b^4)*d^2*e^2 + (3*B*a^2*b^2 - 4*A*a*b^3)*d*e^3)*x^2 + (B*b^4*d^4 + 2*(3*B*a*b^3 - 2*A*b^4)*d^3*e + 3*(3*B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2)*x)*log(b*x + a) - 6*(B*a*b^3*d^4 + (3*B*a^2*b^2 - 4*A*a*b^3)*d^3*e + (B*b^4*d*e^3 + (3*B*a*b^3 - 4*A*b^4)*e^4)*x^4 + (3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 - 6*A*b^4)*d*e^3 + (3*B*a^2*b^2 - 4*A*a*b^3)*e^4)*x^3 + 3*(B*b^4*d^3*e + 4*(B*a*b^3 - A*b^4)*d^2*e^2 + (3*B*a^2*b^2 - 4*A*a*b^3)*d*e^3)*x^2 + (B*b^4*d^4 + 2*(3*B*a*b^3 - 2*A*b^4)*d^3*e + 3*(3*B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2)*x)*log(e*x + d))/(a*b^5*d^8 - 5*a^2*b^4*d^7*e + 10*a^3*b^3*d^6*e^2 - 10*a^4*b^2*d^5*e^3 + 5*a^5*b*d^4*e^4 - a^6*d^3*e^5 + (b^6*d^5*e^3 - 5*a*b^5*d^4*e^4 + 10*a^2*b^4*d^3*e^5 - 10*a^3*b^3*d^2*e^6 + 5*a^4*b^2*d*e^7 - a^5*b*e^8)*x^4 + (3*b^6*d^6*e^2 - 14*a*b^5*d^5*e^3 + 25*a^2*b^4*d^4*e^4 - 20*a^3*b^3*d^3*e^5 + 5*a^4*b^2*d^2*e^6 + 2*a^5*b*d*e^7 - a^6*e^8)*x^3 + 3*(b^6*d^7*e - 4*a*b^5*d^6*e^2 + 5*a^2*b^4*d^5*e^3 - 5*a^4*b^2*d^3*e^5 + 4*a^5*b*d^2*e^6 - a^6*d*e^7)*x^2 + (b^6*d^8 - 2*a*b^5*d^7*e - 5*a^2*b^4*d^6*e^2 + 20*a^3*b^3*d^5*e^3 - 25*a^4*b^2*d^4*e^4 + 14*a^5*b*d^3*e^5 - 3*a^6*d^2*e^6)*x)","B",0
1132,1,1702,0,0.652957," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{3 \, A a^{5} e^{5} - {\left(37 \, B a b^{4} - 12 \, A b^{5}\right)} d^{5} + {\left(8 \, B a^{2} b^{3} + 65 \, A a b^{4}\right)} d^{4} e + 12 \, {\left(3 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} d^{3} e^{2} - 4 \, {\left(2 \, B a^{4} b - 15 \, A a^{3} b^{2}\right)} d^{2} e^{3} + {\left(B a^{5} - 20 \, A a^{4} b\right)} d e^{4} - 12 \, {\left(B b^{5} d^{2} e^{3} + {\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} d e^{4} - {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} - 6 \, {\left(7 \, B b^{5} d^{3} e^{2} + {\left(22 \, B a b^{4} - 35 \, A b^{5}\right)} d^{2} e^{3} - 5 \, {\left(5 \, B a^{2} b^{3} - 6 \, A a b^{4}\right)} d e^{4} - {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} - 2 \, {\left(26 \, B b^{5} d^{4} e + {\left(89 \, B a b^{4} - 130 \, A b^{5}\right)} d^{3} e^{2} - 3 \, {\left(24 \, B a^{2} b^{3} - 25 \, A a b^{4}\right)} d^{2} e^{3} - {\left(47 \, B a^{3} b^{2} - 60 \, A a^{2} b^{3}\right)} d e^{4} + {\left(4 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} - {\left(25 \, B b^{5} d^{5} + {\left(104 \, B a b^{4} - 125 \, A b^{5}\right)} d^{4} e - 20 \, {\left(B a^{2} b^{3} + A a b^{4}\right)} d^{3} e^{2} - 4 \, {\left(34 \, B a^{3} b^{2} - 45 \, A a^{2} b^{3}\right)} d^{2} e^{3} + {\left(31 \, B a^{4} b - 40 \, A a^{3} b^{2}\right)} d e^{4} - {\left(4 \, B a^{5} - 5 \, A a^{4} b\right)} e^{5}\right)} x - 12 \, {\left(B a b^{4} d^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{4} e + {\left(B b^{5} d e^{4} + {\left(4 \, B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{5} d^{2} e^{3} + {\left(17 \, B a b^{4} - 20 \, A b^{5}\right)} d e^{4} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(3 \, B b^{5} d^{3} e^{2} + {\left(14 \, B a b^{4} - 15 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{4}\right)} x^{3} + 2 \, {\left(2 \, B b^{5} d^{4} e + {\left(11 \, B a b^{4} - 10 \, A b^{5}\right)} d^{3} e^{2} + 3 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e^{3}\right)} x^{2} + {\left(B b^{5} d^{5} + {\left(8 \, B a b^{4} - 5 \, A b^{5}\right)} d^{4} e + 4 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{3} e^{2}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(B a b^{4} d^{5} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{4} e + {\left(B b^{5} d e^{4} + {\left(4 \, B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(4 \, B b^{5} d^{2} e^{3} + {\left(17 \, B a b^{4} - 20 \, A b^{5}\right)} d e^{4} + {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(3 \, B b^{5} d^{3} e^{2} + {\left(14 \, B a b^{4} - 15 \, A b^{5}\right)} d^{2} e^{3} + 2 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{4}\right)} x^{3} + 2 \, {\left(2 \, B b^{5} d^{4} e + {\left(11 \, B a b^{4} - 10 \, A b^{5}\right)} d^{3} e^{2} + 3 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e^{3}\right)} x^{2} + {\left(B b^{5} d^{5} + {\left(8 \, B a b^{4} - 5 \, A b^{5}\right)} d^{4} e + 4 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a b^{6} d^{10} - 6 \, a^{2} b^{5} d^{9} e + 15 \, a^{3} b^{4} d^{8} e^{2} - 20 \, a^{4} b^{3} d^{7} e^{3} + 15 \, a^{5} b^{2} d^{6} e^{4} - 6 \, a^{6} b d^{5} e^{5} + a^{7} d^{4} e^{6} + {\left(b^{7} d^{6} e^{4} - 6 \, a b^{6} d^{5} e^{5} + 15 \, a^{2} b^{5} d^{4} e^{6} - 20 \, a^{3} b^{4} d^{3} e^{7} + 15 \, a^{4} b^{3} d^{2} e^{8} - 6 \, a^{5} b^{2} d e^{9} + a^{6} b e^{10}\right)} x^{5} + {\left(4 \, b^{7} d^{7} e^{3} - 23 \, a b^{6} d^{6} e^{4} + 54 \, a^{2} b^{5} d^{5} e^{5} - 65 \, a^{3} b^{4} d^{4} e^{6} + 40 \, a^{4} b^{3} d^{3} e^{7} - 9 \, a^{5} b^{2} d^{2} e^{8} - 2 \, a^{6} b d e^{9} + a^{7} e^{10}\right)} x^{4} + 2 \, {\left(3 \, b^{7} d^{8} e^{2} - 16 \, a b^{6} d^{7} e^{3} + 33 \, a^{2} b^{5} d^{6} e^{4} - 30 \, a^{3} b^{4} d^{5} e^{5} + 5 \, a^{4} b^{3} d^{4} e^{6} + 12 \, a^{5} b^{2} d^{3} e^{7} - 9 \, a^{6} b d^{2} e^{8} + 2 \, a^{7} d e^{9}\right)} x^{3} + 2 \, {\left(2 \, b^{7} d^{9} e - 9 \, a b^{6} d^{8} e^{2} + 12 \, a^{2} b^{5} d^{7} e^{3} + 5 \, a^{3} b^{4} d^{6} e^{4} - 30 \, a^{4} b^{3} d^{5} e^{5} + 33 \, a^{5} b^{2} d^{4} e^{6} - 16 \, a^{6} b d^{3} e^{7} + 3 \, a^{7} d^{2} e^{8}\right)} x^{2} + {\left(b^{7} d^{10} - 2 \, a b^{6} d^{9} e - 9 \, a^{2} b^{5} d^{8} e^{2} + 40 \, a^{3} b^{4} d^{7} e^{3} - 65 \, a^{4} b^{3} d^{6} e^{4} + 54 \, a^{5} b^{2} d^{5} e^{5} - 23 \, a^{6} b d^{4} e^{6} + 4 \, a^{7} d^{3} e^{7}\right)} x\right)}}"," ",0,"-1/12*(3*A*a^5*e^5 - (37*B*a*b^4 - 12*A*b^5)*d^5 + (8*B*a^2*b^3 + 65*A*a*b^4)*d^4*e + 12*(3*B*a^3*b^2 - 10*A*a^2*b^3)*d^3*e^2 - 4*(2*B*a^4*b - 15*A*a^3*b^2)*d^2*e^3 + (B*a^5 - 20*A*a^4*b)*d*e^4 - 12*(B*b^5*d^2*e^3 + (3*B*a*b^4 - 5*A*b^5)*d*e^4 - (4*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 - 6*(7*B*b^5*d^3*e^2 + (22*B*a*b^4 - 35*A*b^5)*d^2*e^3 - 5*(5*B*a^2*b^3 - 6*A*a*b^4)*d*e^4 - (4*B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 - 2*(26*B*b^5*d^4*e + (89*B*a*b^4 - 130*A*b^5)*d^3*e^2 - 3*(24*B*a^2*b^3 - 25*A*a*b^4)*d^2*e^3 - (47*B*a^3*b^2 - 60*A*a^2*b^3)*d*e^4 + (4*B*a^4*b - 5*A*a^3*b^2)*e^5)*x^2 - (25*B*b^5*d^5 + (104*B*a*b^4 - 125*A*b^5)*d^4*e - 20*(B*a^2*b^3 + A*a*b^4)*d^3*e^2 - 4*(34*B*a^3*b^2 - 45*A*a^2*b^3)*d^2*e^3 + (31*B*a^4*b - 40*A*a^3*b^2)*d*e^4 - (4*B*a^5 - 5*A*a^4*b)*e^5)*x - 12*(B*a*b^4*d^5 + (4*B*a^2*b^3 - 5*A*a*b^4)*d^4*e + (B*b^5*d*e^4 + (4*B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (4*B*b^5*d^2*e^3 + (17*B*a*b^4 - 20*A*b^5)*d*e^4 + (4*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 2*(3*B*b^5*d^3*e^2 + (14*B*a*b^4 - 15*A*b^5)*d^2*e^3 + 2*(4*B*a^2*b^3 - 5*A*a*b^4)*d*e^4)*x^3 + 2*(2*B*b^5*d^4*e + (11*B*a*b^4 - 10*A*b^5)*d^3*e^2 + 3*(4*B*a^2*b^3 - 5*A*a*b^4)*d^2*e^3)*x^2 + (B*b^5*d^5 + (8*B*a*b^4 - 5*A*b^5)*d^4*e + 4*(4*B*a^2*b^3 - 5*A*a*b^4)*d^3*e^2)*x)*log(b*x + a) + 12*(B*a*b^4*d^5 + (4*B*a^2*b^3 - 5*A*a*b^4)*d^4*e + (B*b^5*d*e^4 + (4*B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (4*B*b^5*d^2*e^3 + (17*B*a*b^4 - 20*A*b^5)*d*e^4 + (4*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 2*(3*B*b^5*d^3*e^2 + (14*B*a*b^4 - 15*A*b^5)*d^2*e^3 + 2*(4*B*a^2*b^3 - 5*A*a*b^4)*d*e^4)*x^3 + 2*(2*B*b^5*d^4*e + (11*B*a*b^4 - 10*A*b^5)*d^3*e^2 + 3*(4*B*a^2*b^3 - 5*A*a*b^4)*d^2*e^3)*x^2 + (B*b^5*d^5 + (8*B*a*b^4 - 5*A*b^5)*d^4*e + 4*(4*B*a^2*b^3 - 5*A*a*b^4)*d^3*e^2)*x)*log(e*x + d))/(a*b^6*d^10 - 6*a^2*b^5*d^9*e + 15*a^3*b^4*d^8*e^2 - 20*a^4*b^3*d^7*e^3 + 15*a^5*b^2*d^6*e^4 - 6*a^6*b*d^5*e^5 + a^7*d^4*e^6 + (b^7*d^6*e^4 - 6*a*b^6*d^5*e^5 + 15*a^2*b^5*d^4*e^6 - 20*a^3*b^4*d^3*e^7 + 15*a^4*b^3*d^2*e^8 - 6*a^5*b^2*d*e^9 + a^6*b*e^10)*x^5 + (4*b^7*d^7*e^3 - 23*a*b^6*d^6*e^4 + 54*a^2*b^5*d^5*e^5 - 65*a^3*b^4*d^4*e^6 + 40*a^4*b^3*d^3*e^7 - 9*a^5*b^2*d^2*e^8 - 2*a^6*b*d*e^9 + a^7*e^10)*x^4 + 2*(3*b^7*d^8*e^2 - 16*a*b^6*d^7*e^3 + 33*a^2*b^5*d^6*e^4 - 30*a^3*b^4*d^5*e^5 + 5*a^4*b^3*d^4*e^6 + 12*a^5*b^2*d^3*e^7 - 9*a^6*b*d^2*e^8 + 2*a^7*d*e^9)*x^3 + 2*(2*b^7*d^9*e - 9*a*b^6*d^8*e^2 + 12*a^2*b^5*d^7*e^3 + 5*a^3*b^4*d^6*e^4 - 30*a^4*b^3*d^5*e^5 + 33*a^5*b^2*d^4*e^6 - 16*a^6*b*d^3*e^7 + 3*a^7*d^2*e^8)*x^2 + (b^7*d^10 - 2*a*b^6*d^9*e - 9*a^2*b^5*d^8*e^2 + 40*a^3*b^4*d^7*e^3 - 65*a^4*b^3*d^6*e^4 + 54*a^5*b^2*d^5*e^5 - 23*a^6*b*d^4*e^6 + 4*a^7*d^3*e^7)*x)","B",0
1133,1,912,0,1.150484," ","integrate((B*x+A)*(e*x+d)^5/(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, B b^{6} e^{5} x^{6} - 6 \, {\left(B a b^{5} + A b^{6}\right)} d^{5} + 30 \, {\left(3 \, B a^{2} b^{4} - A a b^{5}\right)} d^{4} e - 60 \, {\left(5 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} d^{3} e^{2} + 60 \, {\left(7 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3}\right)} d^{2} e^{3} - 30 \, {\left(9 \, B a^{5} b - 7 \, A a^{4} b^{2}\right)} d e^{4} + 6 \, {\left(11 \, B a^{6} - 9 \, A a^{5} b\right)} e^{5} + 2 \, {\left(10 \, B b^{6} d e^{4} - {\left(3 \, B a b^{5} - 2 \, A b^{6}\right)} e^{5}\right)} x^{5} + 5 \, {\left(12 \, B b^{6} d^{2} e^{3} - 2 \, {\left(5 \, B a b^{5} - 3 \, A b^{6}\right)} d e^{4} + {\left(3 \, B a^{2} b^{4} - 2 \, A a b^{5}\right)} e^{5}\right)} x^{4} + 20 \, {\left(6 \, B b^{6} d^{3} e^{2} - 6 \, {\left(2 \, B a b^{5} - A b^{6}\right)} d^{2} e^{3} + 2 \, {\left(5 \, B a^{2} b^{4} - 3 \, A a b^{5}\right)} d e^{4} - {\left(3 \, B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} e^{5}\right)} x^{3} + 6 \, {\left(40 \, B a b^{5} d^{3} e^{2} - 10 \, {\left(11 \, B a^{2} b^{4} - 4 \, A a b^{5}\right)} d^{2} e^{3} + 5 \, {\left(21 \, B a^{3} b^{3} - 11 \, A a^{2} b^{4}\right)} d e^{4} - {\left(34 \, B a^{4} b^{2} - 21 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} - 12 \, {\left(B b^{6} d^{5} - 5 \, {\left(2 \, B a b^{5} - A b^{6}\right)} d^{4} e + 20 \, {\left(B a^{2} b^{4} - A a b^{5}\right)} d^{3} e^{2} - 10 \, {\left(B a^{3} b^{3} - 2 \, A a^{2} b^{4}\right)} d^{2} e^{3} - 5 \, {\left(B a^{4} b^{2} + A a^{3} b^{3}\right)} d e^{4} + {\left(4 \, B a^{5} b - A a^{4} b^{2}\right)} e^{5}\right)} x + 60 \, {\left(B a^{2} b^{4} d^{4} e - 2 \, {\left(3 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{3} e^{2} + 6 \, {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3}\right)} d^{2} e^{3} - 2 \, {\left(5 \, B a^{5} b - 3 \, A a^{4} b^{2}\right)} d e^{4} + {\left(3 \, B a^{6} - 2 \, A a^{5} b\right)} e^{5} + {\left(B b^{6} d^{4} e - 2 \, {\left(3 \, B a b^{5} - A b^{6}\right)} d^{3} e^{2} + 6 \, {\left(2 \, B a^{2} b^{4} - A a b^{5}\right)} d^{2} e^{3} - 2 \, {\left(5 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\right)} d e^{4} + {\left(3 \, B a^{4} b^{2} - 2 \, A a^{3} b^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(B a b^{5} d^{4} e - 2 \, {\left(3 \, B a^{2} b^{4} - A a b^{5}\right)} d^{3} e^{2} + 6 \, {\left(2 \, B a^{3} b^{3} - A a^{2} b^{4}\right)} d^{2} e^{3} - 2 \, {\left(5 \, B a^{4} b^{2} - 3 \, A a^{3} b^{3}\right)} d e^{4} + {\left(3 \, B a^{5} b - 2 \, A a^{4} b^{2}\right)} e^{5}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{2} + 2 \, a b^{8} x + a^{2} b^{7}\right)}}"," ",0,"1/12*(3*B*b^6*e^5*x^6 - 6*(B*a*b^5 + A*b^6)*d^5 + 30*(3*B*a^2*b^4 - A*a*b^5)*d^4*e - 60*(5*B*a^3*b^3 - 3*A*a^2*b^4)*d^3*e^2 + 60*(7*B*a^4*b^2 - 5*A*a^3*b^3)*d^2*e^3 - 30*(9*B*a^5*b - 7*A*a^4*b^2)*d*e^4 + 6*(11*B*a^6 - 9*A*a^5*b)*e^5 + 2*(10*B*b^6*d*e^4 - (3*B*a*b^5 - 2*A*b^6)*e^5)*x^5 + 5*(12*B*b^6*d^2*e^3 - 2*(5*B*a*b^5 - 3*A*b^6)*d*e^4 + (3*B*a^2*b^4 - 2*A*a*b^5)*e^5)*x^4 + 20*(6*B*b^6*d^3*e^2 - 6*(2*B*a*b^5 - A*b^6)*d^2*e^3 + 2*(5*B*a^2*b^4 - 3*A*a*b^5)*d*e^4 - (3*B*a^3*b^3 - 2*A*a^2*b^4)*e^5)*x^3 + 6*(40*B*a*b^5*d^3*e^2 - 10*(11*B*a^2*b^4 - 4*A*a*b^5)*d^2*e^3 + 5*(21*B*a^3*b^3 - 11*A*a^2*b^4)*d*e^4 - (34*B*a^4*b^2 - 21*A*a^3*b^3)*e^5)*x^2 - 12*(B*b^6*d^5 - 5*(2*B*a*b^5 - A*b^6)*d^4*e + 20*(B*a^2*b^4 - A*a*b^5)*d^3*e^2 - 10*(B*a^3*b^3 - 2*A*a^2*b^4)*d^2*e^3 - 5*(B*a^4*b^2 + A*a^3*b^3)*d*e^4 + (4*B*a^5*b - A*a^4*b^2)*e^5)*x + 60*(B*a^2*b^4*d^4*e - 2*(3*B*a^3*b^3 - A*a^2*b^4)*d^3*e^2 + 6*(2*B*a^4*b^2 - A*a^3*b^3)*d^2*e^3 - 2*(5*B*a^5*b - 3*A*a^4*b^2)*d*e^4 + (3*B*a^6 - 2*A*a^5*b)*e^5 + (B*b^6*d^4*e - 2*(3*B*a*b^5 - A*b^6)*d^3*e^2 + 6*(2*B*a^2*b^4 - A*a*b^5)*d^2*e^3 - 2*(5*B*a^3*b^3 - 3*A*a^2*b^4)*d*e^4 + (3*B*a^4*b^2 - 2*A*a^3*b^3)*e^5)*x^2 + 2*(B*a*b^5*d^4*e - 2*(3*B*a^2*b^4 - A*a*b^5)*d^3*e^2 + 6*(2*B*a^3*b^3 - A*a^2*b^4)*d^2*e^3 - 2*(5*B*a^4*b^2 - 3*A*a^3*b^3)*d*e^4 + (3*B*a^5*b - 2*A*a^4*b^2)*e^5)*x)*log(b*x + a))/(b^9*x^2 + 2*a*b^8*x + a^2*b^7)","B",0
1134,1,668,0,1.311719," ","integrate((B*x+A)*(e*x+d)^4/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{5} e^{4} x^{5} - 3 \, {\left(B a b^{4} + A b^{5}\right)} d^{4} + 12 \, {\left(3 \, B a^{2} b^{3} - A a b^{4}\right)} d^{3} e - 18 \, {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d^{2} e^{2} + 12 \, {\left(7 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} d e^{3} - 3 \, {\left(9 \, B a^{5} - 7 \, A a^{4} b\right)} e^{4} + {\left(12 \, B b^{5} d e^{3} - {\left(5 \, B a b^{4} - 3 \, A b^{5}\right)} e^{4}\right)} x^{4} + 4 \, {\left(9 \, B b^{5} d^{2} e^{2} - 6 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d e^{3} + {\left(5 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(24 \, B a b^{4} d^{2} e^{2} - 4 \, {\left(11 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} d e^{3} + {\left(21 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} - 6 \, {\left(B b^{5} d^{4} - 4 \, {\left(2 \, B a b^{4} - A b^{5}\right)} d^{3} e + 12 \, {\left(B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} - 4 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d e^{3} - {\left(B a^{4} b + A a^{3} b^{2}\right)} e^{4}\right)} x + 12 \, {\left(2 \, B a^{2} b^{3} d^{3} e - 3 \, {\left(3 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{4} b - A a^{3} b^{2}\right)} d e^{3} - {\left(5 \, B a^{5} - 3 \, A a^{4} b\right)} e^{4} + {\left(2 \, B b^{5} d^{3} e - 3 \, {\left(3 \, B a b^{4} - A b^{5}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{2} b^{3} - A a b^{4}\right)} d e^{3} - {\left(5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left(2 \, B a b^{4} d^{3} e - 3 \, {\left(3 \, B a^{2} b^{3} - A a b^{4}\right)} d^{2} e^{2} + 6 \, {\left(2 \, B a^{3} b^{2} - A a^{2} b^{3}\right)} d e^{3} - {\left(5 \, B a^{4} b - 3 \, A a^{3} b^{2}\right)} e^{4}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} x^{2} + 2 \, a b^{7} x + a^{2} b^{6}\right)}}"," ",0,"1/6*(2*B*b^5*e^4*x^5 - 3*(B*a*b^4 + A*b^5)*d^4 + 12*(3*B*a^2*b^3 - A*a*b^4)*d^3*e - 18*(5*B*a^3*b^2 - 3*A*a^2*b^3)*d^2*e^2 + 12*(7*B*a^4*b - 5*A*a^3*b^2)*d*e^3 - 3*(9*B*a^5 - 7*A*a^4*b)*e^4 + (12*B*b^5*d*e^3 - (5*B*a*b^4 - 3*A*b^5)*e^4)*x^4 + 4*(9*B*b^5*d^2*e^2 - 6*(2*B*a*b^4 - A*b^5)*d*e^3 + (5*B*a^2*b^3 - 3*A*a*b^4)*e^4)*x^3 + 3*(24*B*a*b^4*d^2*e^2 - 4*(11*B*a^2*b^3 - 4*A*a*b^4)*d*e^3 + (21*B*a^3*b^2 - 11*A*a^2*b^3)*e^4)*x^2 - 6*(B*b^5*d^4 - 4*(2*B*a*b^4 - A*b^5)*d^3*e + 12*(B*a^2*b^3 - A*a*b^4)*d^2*e^2 - 4*(B*a^3*b^2 - 2*A*a^2*b^3)*d*e^3 - (B*a^4*b + A*a^3*b^2)*e^4)*x + 12*(2*B*a^2*b^3*d^3*e - 3*(3*B*a^3*b^2 - A*a^2*b^3)*d^2*e^2 + 6*(2*B*a^4*b - A*a^3*b^2)*d*e^3 - (5*B*a^5 - 3*A*a^4*b)*e^4 + (2*B*b^5*d^3*e - 3*(3*B*a*b^4 - A*b^5)*d^2*e^2 + 6*(2*B*a^2*b^3 - A*a*b^4)*d*e^3 - (5*B*a^3*b^2 - 3*A*a^2*b^3)*e^4)*x^2 + 2*(2*B*a*b^4*d^3*e - 3*(3*B*a^2*b^3 - A*a*b^4)*d^2*e^2 + 6*(2*B*a^3*b^2 - A*a^2*b^3)*d*e^3 - (5*B*a^4*b - 3*A*a^3*b^2)*e^4)*x)*log(b*x + a))/(b^8*x^2 + 2*a*b^7*x + a^2*b^6)","B",0
1135,1,442,0,1.285039," ","integrate((B*x+A)*(e*x+d)^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{B b^{4} e^{3} x^{4} - {\left(B a b^{3} + A b^{4}\right)} d^{3} + 3 \, {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - 3 \, {\left(5 \, B a^{3} b - 3 \, A a^{2} b^{2}\right)} d e^{2} + {\left(7 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 2 \, {\left(3 \, B b^{4} d e^{2} - {\left(2 \, B a b^{3} - A b^{4}\right)} e^{3}\right)} x^{3} + {\left(12 \, B a b^{3} d e^{2} - {\left(11 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(B b^{4} d^{3} - 3 \, {\left(2 \, B a b^{3} - A b^{4}\right)} d^{2} e + 6 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{2} - {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x + 6 \, {\left(B a^{2} b^{2} d^{2} e - {\left(3 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + {\left(2 \, B a^{4} - A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{2} e - {\left(3 \, B a b^{3} - A b^{4}\right)} d e^{2} + {\left(2 \, B a^{2} b^{2} - A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{2} e - {\left(3 \, B a^{2} b^{2} - A a b^{3}\right)} d e^{2} + {\left(2 \, B a^{3} b - A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(B*b^4*e^3*x^4 - (B*a*b^3 + A*b^4)*d^3 + 3*(3*B*a^2*b^2 - A*a*b^3)*d^2*e - 3*(5*B*a^3*b - 3*A*a^2*b^2)*d*e^2 + (7*B*a^4 - 5*A*a^3*b)*e^3 + 2*(3*B*b^4*d*e^2 - (2*B*a*b^3 - A*b^4)*e^3)*x^3 + (12*B*a*b^3*d*e^2 - (11*B*a^2*b^2 - 4*A*a*b^3)*e^3)*x^2 - 2*(B*b^4*d^3 - 3*(2*B*a*b^3 - A*b^4)*d^2*e + 6*(B*a^2*b^2 - A*a*b^3)*d*e^2 - (B*a^3*b - 2*A*a^2*b^2)*e^3)*x + 6*(B*a^2*b^2*d^2*e - (3*B*a^3*b - A*a^2*b^2)*d*e^2 + (2*B*a^4 - A*a^3*b)*e^3 + (B*b^4*d^2*e - (3*B*a*b^3 - A*b^4)*d*e^2 + (2*B*a^2*b^2 - A*a*b^3)*e^3)*x^2 + 2*(B*a*b^3*d^2*e - (3*B*a^2*b^2 - A*a*b^3)*d*e^2 + (2*B*a^3*b - A*a^2*b^2)*e^3)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","B",0
1136,1,258,0,1.415564," ","integrate((B*x+A)*(e*x+d)^2/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, B b^{3} e^{2} x^{3} + 4 \, B a b^{2} e^{2} x^{2} - {\left(B a b^{2} + A b^{3}\right)} d^{2} + 2 \, {\left(3 \, B a^{2} b - A a b^{2}\right)} d e - {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} - 2 \, {\left(B b^{3} d^{2} - 2 \, {\left(2 \, B a b^{2} - A b^{3}\right)} d e + 2 \, {\left(B a^{2} b - A a b^{2}\right)} e^{2}\right)} x + 2 \, {\left(2 \, B a^{2} b d e - {\left(3 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d e - {\left(3 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(2 \, B a b^{2} d e - {\left(3 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*B*b^3*e^2*x^3 + 4*B*a*b^2*e^2*x^2 - (B*a*b^2 + A*b^3)*d^2 + 2*(3*B*a^2*b - A*a*b^2)*d*e - (5*B*a^3 - 3*A*a^2*b)*e^2 - 2*(B*b^3*d^2 - 2*(2*B*a*b^2 - A*b^3)*d*e + 2*(B*a^2*b - A*a*b^2)*e^2)*x + 2*(2*B*a^2*b*d*e - (3*B*a^3 - A*a^2*b)*e^2 + (2*B*b^3*d*e - (3*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(2*B*a*b^2*d*e - (3*B*a^2*b - A*a*b^2)*e^2)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","B",0
1137,1,110,0,1.247411," ","integrate((B*x+A)*(e*x+d)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(B a b + A b^{2}\right)} d - {\left(3 \, B a^{2} - A a b\right)} e + 2 \, {\left(B b^{2} d - {\left(2 \, B a b - A b^{2}\right)} e\right)} x - 2 \, {\left(B b^{2} e x^{2} + 2 \, B a b e x + B a^{2} e\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/2*((B*a*b + A*b^2)*d - (3*B*a^2 - A*a*b)*e + 2*(B*b^2*d - (2*B*a*b - A*b^2)*e)*x - 2*(B*b^2*e*x^2 + 2*B*a*b*e*x + B*a^2*e)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
1138,1,38,0,1.207295," ","integrate((B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, B b x + B a + A b}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*B*b*x + B*a + A*b)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
1139,1,361,0,1.417330," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{4 \, A a b^{2} d e - {\left(B a b^{2} + A b^{3}\right)} d^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{2} - 2 \, {\left(B b^{3} d^{2} + A a b^{2} e^{2} - {\left(B a b^{2} + A b^{3}\right)} d e\right)} x - 2 \, {\left(B a^{2} b d e - A a^{2} b e^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x^{2} + 2 \, {\left(B a b^{2} d e - A a b^{2} e^{2}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(B a^{2} b d e - A a^{2} b e^{2} + {\left(B b^{3} d e - A b^{3} e^{2}\right)} x^{2} + 2 \, {\left(B a b^{2} d e - A a b^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\left(b^{6} d^{3} - 3 \, a b^{5} d^{2} e + 3 \, a^{2} b^{4} d e^{2} - a^{3} b^{3} e^{3}\right)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}"," ",0,"1/2*(4*A*a*b^2*d*e - (B*a*b^2 + A*b^3)*d^2 + (B*a^3 - 3*A*a^2*b)*e^2 - 2*(B*b^3*d^2 + A*a*b^2*e^2 - (B*a*b^2 + A*b^3)*d*e)*x - 2*(B*a^2*b*d*e - A*a^2*b*e^2 + (B*b^3*d*e - A*b^3*e^2)*x^2 + 2*(B*a*b^2*d*e - A*a*b^2*e^2)*x)*log(b*x + a) + 2*(B*a^2*b*d*e - A*a^2*b*e^2 + (B*b^3*d*e - A*b^3*e^2)*x^2 + 2*(B*a*b^2*d*e - A*a*b^2*e^2)*x)*log(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (b^6*d^3 - 3*a*b^5*d^2*e + 3*a^2*b^4*d*e^2 - a^3*b^3*e^3)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x)","B",0
1140,1,803,0,1.617887," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, A a^{3} e^{3} + {\left(B a b^{2} + A b^{3}\right)} d^{3} + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e - {\left(5 \, B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + 2 \, {\left(2 \, B b^{3} d^{2} e - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e^{2} - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{3} + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d^{2} e - 2 \, {\left(2 \, B a^{2} b + 3 \, A a b^{2}\right)} d e^{2} - 3 \, {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x + 2 \, {\left(2 \, B a^{2} b d^{2} e + {\left(B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + {\left(2 \, B b^{3} d e^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, B a b^{2} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, B a^{2} b d^{2} e + {\left(B a^{3} - 3 \, A a^{2} b\right)} d e^{2} + {\left(2 \, B b^{3} d e^{2} + {\left(B a b^{2} - 3 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(2 \, B b^{3} d^{2} e + {\left(5 \, B a b^{2} - 3 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, B a b^{2} d^{2} e + 2 \, {\left(2 \, B a^{2} b - 3 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 3 \, A a^{2} b\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{5} - 4 \, a^{3} b^{3} d^{4} e + 6 \, a^{4} b^{2} d^{3} e^{2} - 4 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4} + {\left(b^{6} d^{4} e - 4 \, a b^{5} d^{3} e^{2} + 6 \, a^{2} b^{4} d^{2} e^{3} - 4 \, a^{3} b^{3} d e^{4} + a^{4} b^{2} e^{5}\right)} x^{3} + {\left(b^{6} d^{5} - 2 \, a b^{5} d^{4} e - 2 \, a^{2} b^{4} d^{3} e^{2} + 8 \, a^{3} b^{3} d^{2} e^{3} - 7 \, a^{4} b^{2} d e^{4} + 2 \, a^{5} b e^{5}\right)} x^{2} + {\left(2 \, a b^{5} d^{5} - 7 \, a^{2} b^{4} d^{4} e + 8 \, a^{3} b^{3} d^{3} e^{2} - 2 \, a^{4} b^{2} d^{2} e^{3} - 2 \, a^{5} b d e^{4} + a^{6} e^{5}\right)} x\right)}}"," ",0,"-1/2*(2*A*a^3*e^3 + (B*a*b^2 + A*b^3)*d^3 + 2*(2*B*a^2*b - 3*A*a*b^2)*d^2*e - (5*B*a^3 - 3*A*a^2*b)*d*e^2 + 2*(2*B*b^3*d^2*e - (B*a*b^2 + 3*A*b^3)*d*e^2 - (B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (2*B*b^3*d^3 + (5*B*a*b^2 - 3*A*b^3)*d^2*e - 2*(2*B*a^2*b + 3*A*a*b^2)*d*e^2 - 3*(B*a^3 - 3*A*a^2*b)*e^3)*x + 2*(2*B*a^2*b*d^2*e + (B*a^3 - 3*A*a^2*b)*d*e^2 + (2*B*b^3*d*e^2 + (B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 3*A*b^3)*d*e^2 + 2*(B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (4*B*a*b^2*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2 + (B*a^3 - 3*A*a^2*b)*e^3)*x)*log(b*x + a) - 2*(2*B*a^2*b*d^2*e + (B*a^3 - 3*A*a^2*b)*d*e^2 + (2*B*b^3*d*e^2 + (B*a*b^2 - 3*A*b^3)*e^3)*x^3 + (2*B*b^3*d^2*e + (5*B*a*b^2 - 3*A*b^3)*d*e^2 + 2*(B*a^2*b - 3*A*a*b^2)*e^3)*x^2 + (4*B*a*b^2*d^2*e + 2*(2*B*a^2*b - 3*A*a*b^2)*d*e^2 + (B*a^3 - 3*A*a^2*b)*e^3)*x)*log(e*x + d))/(a^2*b^4*d^5 - 4*a^3*b^3*d^4*e + 6*a^4*b^2*d^3*e^2 - 4*a^5*b*d^2*e^3 + a^6*d*e^4 + (b^6*d^4*e - 4*a*b^5*d^3*e^2 + 6*a^2*b^4*d^2*e^3 - 4*a^3*b^3*d*e^4 + a^4*b^2*e^5)*x^3 + (b^6*d^5 - 2*a*b^5*d^4*e - 2*a^2*b^4*d^3*e^2 + 8*a^3*b^3*d^2*e^3 - 7*a^4*b^2*d*e^4 + 2*a^5*b*e^5)*x^2 + (2*a*b^5*d^5 - 7*a^2*b^4*d^4*e + 8*a^3*b^3*d^3*e^2 - 2*a^4*b^2*d^2*e^3 - 2*a^5*b*d*e^4 + a^6*e^5)*x)","B",0
1141,1,1215,0,1.528569," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{9 \, B a^{3} b d^{2} e^{2} + A a^{4} e^{4} - {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(9 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d^{3} e + {\left(B a^{4} - 8 \, A a^{3} b\right)} d e^{3} - 6 \, {\left(B b^{4} d^{2} e^{2} - 2 \, A b^{4} d e^{3} - {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 9 \, {\left(B b^{4} d^{3} e - B a^{2} b^{2} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} - {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - 2 \, {\left(B b^{4} d^{4} - 12 \, A a b^{3} d^{2} e^{2} + {\left(7 \, B a b^{3} - 2 \, A b^{4}\right)} d^{3} e - {\left(7 \, B a^{3} b - 12 \, A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - 2 \, A a^{3} b\right)} e^{4}\right)} x - 6 \, {\left(B a^{2} b^{2} d^{3} e + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d^{2} e^{2} + {\left(B b^{4} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left(B b^{4} d^{2} e^{2} + 2 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} + {\left(B b^{4} d^{3} e + {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{3} e + 2 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(B a^{2} b^{2} d^{3} e + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d^{2} e^{2} + {\left(B b^{4} d e^{3} + {\left(B a b^{3} - 2 \, A b^{4}\right)} e^{4}\right)} x^{4} + 2 \, {\left(B b^{4} d^{2} e^{2} + 2 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{4}\right)} x^{3} + {\left(B b^{4} d^{3} e + {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} d e^{3} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} d^{3} e + 2 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{5} d^{7} - 5 \, a^{3} b^{4} d^{6} e + 10 \, a^{4} b^{3} d^{5} e^{2} - 10 \, a^{5} b^{2} d^{4} e^{3} + 5 \, a^{6} b d^{3} e^{4} - a^{7} d^{2} e^{5} + {\left(b^{7} d^{5} e^{2} - 5 \, a b^{6} d^{4} e^{3} + 10 \, a^{2} b^{5} d^{3} e^{4} - 10 \, a^{3} b^{4} d^{2} e^{5} + 5 \, a^{4} b^{3} d e^{6} - a^{5} b^{2} e^{7}\right)} x^{4} + 2 \, {\left(b^{7} d^{6} e - 4 \, a b^{6} d^{5} e^{2} + 5 \, a^{2} b^{5} d^{4} e^{3} - 5 \, a^{4} b^{3} d^{2} e^{5} + 4 \, a^{5} b^{2} d e^{6} - a^{6} b e^{7}\right)} x^{3} + {\left(b^{7} d^{7} - a b^{6} d^{6} e - 9 \, a^{2} b^{5} d^{5} e^{2} + 25 \, a^{3} b^{4} d^{4} e^{3} - 25 \, a^{4} b^{3} d^{3} e^{4} + 9 \, a^{5} b^{2} d^{2} e^{5} + a^{6} b d e^{6} - a^{7} e^{7}\right)} x^{2} + 2 \, {\left(a b^{6} d^{7} - 4 \, a^{2} b^{5} d^{6} e + 5 \, a^{3} b^{4} d^{5} e^{2} - 5 \, a^{5} b^{2} d^{3} e^{4} + 4 \, a^{6} b d^{2} e^{5} - a^{7} d e^{6}\right)} x\right)}}"," ",0,"1/2*(9*B*a^3*b*d^2*e^2 + A*a^4*e^4 - (B*a*b^3 + A*b^4)*d^4 - (9*B*a^2*b^2 - 8*A*a*b^3)*d^3*e + (B*a^4 - 8*A*a^3*b)*d*e^3 - 6*(B*b^4*d^2*e^2 - 2*A*b^4*d*e^3 - (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 - 9*(B*b^4*d^3*e - B*a^2*b^2*d*e^3 + (B*a*b^3 - 2*A*b^4)*d^2*e^2 - (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 - 2*(B*b^4*d^4 - 12*A*a*b^3*d^2*e^2 + (7*B*a*b^3 - 2*A*b^4)*d^3*e - (7*B*a^3*b - 12*A*a^2*b^2)*d*e^3 - (B*a^4 - 2*A*a^3*b)*e^4)*x - 6*(B*a^2*b^2*d^3*e + (B*a^3*b - 2*A*a^2*b^2)*d^2*e^2 + (B*b^4*d*e^3 + (B*a*b^3 - 2*A*b^4)*e^4)*x^4 + 2*(B*b^4*d^2*e^2 + 2*(B*a*b^3 - A*b^4)*d*e^3 + (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 + (B*b^4*d^3*e + (5*B*a*b^3 - 2*A*b^4)*d^2*e^2 + (5*B*a^2*b^2 - 8*A*a*b^3)*d*e^3 + (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 + 2*(B*a*b^3*d^3*e + 2*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + (B*a^3*b - 2*A*a^2*b^2)*d*e^3)*x)*log(b*x + a) + 6*(B*a^2*b^2*d^3*e + (B*a^3*b - 2*A*a^2*b^2)*d^2*e^2 + (B*b^4*d*e^3 + (B*a*b^3 - 2*A*b^4)*e^4)*x^4 + 2*(B*b^4*d^2*e^2 + 2*(B*a*b^3 - A*b^4)*d*e^3 + (B*a^2*b^2 - 2*A*a*b^3)*e^4)*x^3 + (B*b^4*d^3*e + (5*B*a*b^3 - 2*A*b^4)*d^2*e^2 + (5*B*a^2*b^2 - 8*A*a*b^3)*d*e^3 + (B*a^3*b - 2*A*a^2*b^2)*e^4)*x^2 + 2*(B*a*b^3*d^3*e + 2*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + (B*a^3*b - 2*A*a^2*b^2)*d*e^3)*x)*log(e*x + d))/(a^2*b^5*d^7 - 5*a^3*b^4*d^6*e + 10*a^4*b^3*d^5*e^2 - 10*a^5*b^2*d^4*e^3 + 5*a^6*b*d^3*e^4 - a^7*d^2*e^5 + (b^7*d^5*e^2 - 5*a*b^6*d^4*e^3 + 10*a^2*b^5*d^3*e^4 - 10*a^3*b^4*d^2*e^5 + 5*a^4*b^3*d*e^6 - a^5*b^2*e^7)*x^4 + 2*(b^7*d^6*e - 4*a*b^6*d^5*e^2 + 5*a^2*b^5*d^4*e^3 - 5*a^4*b^3*d^2*e^5 + 4*a^5*b^2*d*e^6 - a^6*b*e^7)*x^3 + (b^7*d^7 - a*b^6*d^6*e - 9*a^2*b^5*d^5*e^2 + 25*a^3*b^4*d^4*e^3 - 25*a^4*b^3*d^3*e^4 + 9*a^5*b^2*d^2*e^5 + a^6*b*d*e^6 - a^7*e^7)*x^2 + 2*(a*b^6*d^7 - 4*a^2*b^5*d^6*e + 5*a^3*b^4*d^5*e^2 - 5*a^5*b^2*d^3*e^4 + 4*a^6*b*d^2*e^5 - a^7*d*e^6)*x)","B",0
1142,1,1845,0,1.357377," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{2 \, A a^{5} e^{5} + 3 \, {\left(B a b^{4} + A b^{5}\right)} d^{5} + 2 \, {\left(22 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} d^{4} e - 4 \, {\left(9 \, B a^{3} b^{2} + 5 \, A a^{2} b^{3}\right)} d^{3} e^{2} - 12 \, {\left(B a^{4} b - 5 \, A a^{3} b^{2}\right)} d^{2} e^{3} + {\left(B a^{5} - 15 \, A a^{4} b\right)} d e^{4} + 12 \, {\left(2 \, B b^{5} d^{2} e^{3} + {\left(B a b^{4} - 5 \, A b^{5}\right)} d e^{4} - {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + 6 \, {\left(10 \, B b^{5} d^{3} e^{2} + {\left(11 \, B a b^{4} - 25 \, A b^{5}\right)} d^{2} e^{3} - 2 \, {\left(6 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d e^{4} - 3 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(22 \, B b^{5} d^{4} e + {\left(57 \, B a b^{4} - 55 \, A b^{5}\right)} d^{3} e^{2} - 6 \, {\left(B a^{2} b^{3} + 10 \, A a b^{4}\right)} d^{2} e^{3} - {\left(67 \, B a^{3} b^{2} - 105 \, A a^{2} b^{3}\right)} d e^{4} - 2 \, {\left(3 \, B a^{4} b - 5 \, A a^{3} b^{2}\right)} e^{5}\right)} x^{2} + {\left(6 \, B b^{5} d^{5} + {\left(73 \, B a b^{4} - 15 \, A b^{5}\right)} d^{4} e + 16 \, {\left(3 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} d^{3} e^{2} - 24 \, {\left(4 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 2 \, {\left(17 \, B a^{4} b - 30 \, A a^{3} b^{2}\right)} d e^{4} + {\left(3 \, B a^{5} - 5 \, A a^{4} b\right)} e^{5}\right)} x + 12 \, {\left(2 \, B a^{2} b^{3} d^{4} e + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{3} e^{2} + {\left(2 \, B b^{5} d e^{4} + {\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(6 \, B b^{5} d^{2} e^{3} + {\left(13 \, B a b^{4} - 15 \, A b^{5}\right)} d e^{4} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + {\left(6 \, B b^{5} d^{3} e^{2} + 3 \, {\left(7 \, B a b^{4} - 5 \, A b^{5}\right)} d^{2} e^{3} + 10 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} d e^{4} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, B b^{5} d^{4} e + 5 \, {\left(3 \, B a b^{4} - A b^{5}\right)} d^{3} e^{2} + 6 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d e^{4}\right)} x^{2} + {\left(4 \, B a b^{4} d^{4} e + 2 \, {\left(6 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{3} e^{2} + 3 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{2} e^{3}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(2 \, B a^{2} b^{3} d^{4} e + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{3} e^{2} + {\left(2 \, B b^{5} d e^{4} + {\left(3 \, B a b^{4} - 5 \, A b^{5}\right)} e^{5}\right)} x^{5} + {\left(6 \, B b^{5} d^{2} e^{3} + {\left(13 \, B a b^{4} - 15 \, A b^{5}\right)} d e^{4} + 2 \, {\left(3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} e^{5}\right)} x^{4} + {\left(6 \, B b^{5} d^{3} e^{2} + 3 \, {\left(7 \, B a b^{4} - 5 \, A b^{5}\right)} d^{2} e^{3} + 10 \, {\left(2 \, B a^{2} b^{3} - 3 \, A a b^{4}\right)} d e^{4} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, B b^{5} d^{4} e + 5 \, {\left(3 \, B a b^{4} - A b^{5}\right)} d^{3} e^{2} + 6 \, {\left(4 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{2} e^{3} + 3 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d e^{4}\right)} x^{2} + {\left(4 \, B a b^{4} d^{4} e + 2 \, {\left(6 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{3} e^{2} + 3 \, {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{2} b^{6} d^{9} - 6 \, a^{3} b^{5} d^{8} e + 15 \, a^{4} b^{4} d^{7} e^{2} - 20 \, a^{5} b^{3} d^{6} e^{3} + 15 \, a^{6} b^{2} d^{5} e^{4} - 6 \, a^{7} b d^{4} e^{5} + a^{8} d^{3} e^{6} + {\left(b^{8} d^{6} e^{3} - 6 \, a b^{7} d^{5} e^{4} + 15 \, a^{2} b^{6} d^{4} e^{5} - 20 \, a^{3} b^{5} d^{3} e^{6} + 15 \, a^{4} b^{4} d^{2} e^{7} - 6 \, a^{5} b^{3} d e^{8} + a^{6} b^{2} e^{9}\right)} x^{5} + {\left(3 \, b^{8} d^{7} e^{2} - 16 \, a b^{7} d^{6} e^{3} + 33 \, a^{2} b^{6} d^{5} e^{4} - 30 \, a^{3} b^{5} d^{4} e^{5} + 5 \, a^{4} b^{4} d^{3} e^{6} + 12 \, a^{5} b^{3} d^{2} e^{7} - 9 \, a^{6} b^{2} d e^{8} + 2 \, a^{7} b e^{9}\right)} x^{4} + {\left(3 \, b^{8} d^{8} e - 12 \, a b^{7} d^{7} e^{2} + 10 \, a^{2} b^{6} d^{6} e^{3} + 24 \, a^{3} b^{5} d^{5} e^{4} - 60 \, a^{4} b^{4} d^{4} e^{5} + 52 \, a^{5} b^{3} d^{3} e^{6} - 18 \, a^{6} b^{2} d^{2} e^{7} + a^{8} e^{9}\right)} x^{3} + {\left(b^{8} d^{9} - 18 \, a^{2} b^{6} d^{7} e^{2} + 52 \, a^{3} b^{5} d^{6} e^{3} - 60 \, a^{4} b^{4} d^{5} e^{4} + 24 \, a^{5} b^{3} d^{4} e^{5} + 10 \, a^{6} b^{2} d^{3} e^{6} - 12 \, a^{7} b d^{2} e^{7} + 3 \, a^{8} d e^{8}\right)} x^{2} + {\left(2 \, a b^{7} d^{9} - 9 \, a^{2} b^{6} d^{8} e + 12 \, a^{3} b^{5} d^{7} e^{2} + 5 \, a^{4} b^{4} d^{6} e^{3} - 30 \, a^{5} b^{3} d^{5} e^{4} + 33 \, a^{6} b^{2} d^{4} e^{5} - 16 \, a^{7} b d^{3} e^{6} + 3 \, a^{8} d^{2} e^{7}\right)} x\right)}}"," ",0,"-1/6*(2*A*a^5*e^5 + 3*(B*a*b^4 + A*b^5)*d^5 + 2*(22*B*a^2*b^3 - 15*A*a*b^4)*d^4*e - 4*(9*B*a^3*b^2 + 5*A*a^2*b^3)*d^3*e^2 - 12*(B*a^4*b - 5*A*a^3*b^2)*d^2*e^3 + (B*a^5 - 15*A*a^4*b)*d*e^4 + 12*(2*B*b^5*d^2*e^3 + (B*a*b^4 - 5*A*b^5)*d*e^4 - (3*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + 6*(10*B*b^5*d^3*e^2 + (11*B*a*b^4 - 25*A*b^5)*d^2*e^3 - 2*(6*B*a^2*b^3 - 5*A*a*b^4)*d*e^4 - 3*(3*B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 + 2*(22*B*b^5*d^4*e + (57*B*a*b^4 - 55*A*b^5)*d^3*e^2 - 6*(B*a^2*b^3 + 10*A*a*b^4)*d^2*e^3 - (67*B*a^3*b^2 - 105*A*a^2*b^3)*d*e^4 - 2*(3*B*a^4*b - 5*A*a^3*b^2)*e^5)*x^2 + (6*B*b^5*d^5 + (73*B*a*b^4 - 15*A*b^5)*d^4*e + 16*(3*B*a^2*b^3 - 10*A*a*b^4)*d^3*e^2 - 24*(4*B*a^3*b^2 - 5*A*a^2*b^3)*d^2*e^3 - 2*(17*B*a^4*b - 30*A*a^3*b^2)*d*e^4 + (3*B*a^5 - 5*A*a^4*b)*e^5)*x + 12*(2*B*a^2*b^3*d^4*e + (3*B*a^3*b^2 - 5*A*a^2*b^3)*d^3*e^2 + (2*B*b^5*d*e^4 + (3*B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (6*B*b^5*d^2*e^3 + (13*B*a*b^4 - 15*A*b^5)*d*e^4 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + (6*B*b^5*d^3*e^2 + 3*(7*B*a*b^4 - 5*A*b^5)*d^2*e^3 + 10*(2*B*a^2*b^3 - 3*A*a*b^4)*d*e^4 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 + (2*B*b^5*d^4*e + 5*(3*B*a*b^4 - A*b^5)*d^3*e^2 + 6*(4*B*a^2*b^3 - 5*A*a*b^4)*d^2*e^3 + 3*(3*B*a^3*b^2 - 5*A*a^2*b^3)*d*e^4)*x^2 + (4*B*a*b^4*d^4*e + 2*(6*B*a^2*b^3 - 5*A*a*b^4)*d^3*e^2 + 3*(3*B*a^3*b^2 - 5*A*a^2*b^3)*d^2*e^3)*x)*log(b*x + a) - 12*(2*B*a^2*b^3*d^4*e + (3*B*a^3*b^2 - 5*A*a^2*b^3)*d^3*e^2 + (2*B*b^5*d*e^4 + (3*B*a*b^4 - 5*A*b^5)*e^5)*x^5 + (6*B*b^5*d^2*e^3 + (13*B*a*b^4 - 15*A*b^5)*d*e^4 + 2*(3*B*a^2*b^3 - 5*A*a*b^4)*e^5)*x^4 + (6*B*b^5*d^3*e^2 + 3*(7*B*a*b^4 - 5*A*b^5)*d^2*e^3 + 10*(2*B*a^2*b^3 - 3*A*a*b^4)*d*e^4 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*e^5)*x^3 + (2*B*b^5*d^4*e + 5*(3*B*a*b^4 - A*b^5)*d^3*e^2 + 6*(4*B*a^2*b^3 - 5*A*a*b^4)*d^2*e^3 + 3*(3*B*a^3*b^2 - 5*A*a^2*b^3)*d*e^4)*x^2 + (4*B*a*b^4*d^4*e + 2*(6*B*a^2*b^3 - 5*A*a*b^4)*d^3*e^2 + 3*(3*B*a^3*b^2 - 5*A*a^2*b^3)*d^2*e^3)*x)*log(e*x + d))/(a^2*b^6*d^9 - 6*a^3*b^5*d^8*e + 15*a^4*b^4*d^7*e^2 - 20*a^5*b^3*d^6*e^3 + 15*a^6*b^2*d^5*e^4 - 6*a^7*b*d^4*e^5 + a^8*d^3*e^6 + (b^8*d^6*e^3 - 6*a*b^7*d^5*e^4 + 15*a^2*b^6*d^4*e^5 - 20*a^3*b^5*d^3*e^6 + 15*a^4*b^4*d^2*e^7 - 6*a^5*b^3*d*e^8 + a^6*b^2*e^9)*x^5 + (3*b^8*d^7*e^2 - 16*a*b^7*d^6*e^3 + 33*a^2*b^6*d^5*e^4 - 30*a^3*b^5*d^4*e^5 + 5*a^4*b^4*d^3*e^6 + 12*a^5*b^3*d^2*e^7 - 9*a^6*b^2*d*e^8 + 2*a^7*b*e^9)*x^4 + (3*b^8*d^8*e - 12*a*b^7*d^7*e^2 + 10*a^2*b^6*d^6*e^3 + 24*a^3*b^5*d^5*e^4 - 60*a^4*b^4*d^4*e^5 + 52*a^5*b^3*d^3*e^6 - 18*a^6*b^2*d^2*e^7 + a^8*e^9)*x^3 + (b^8*d^9 - 18*a^2*b^6*d^7*e^2 + 52*a^3*b^5*d^6*e^3 - 60*a^4*b^4*d^5*e^4 + 24*a^5*b^3*d^4*e^5 + 10*a^6*b^2*d^3*e^6 - 12*a^7*b*d^2*e^7 + 3*a^8*d*e^8)*x^2 + (2*a*b^7*d^9 - 9*a^2*b^6*d^8*e + 12*a^3*b^5*d^7*e^2 + 5*a^4*b^4*d^6*e^3 - 30*a^5*b^3*d^5*e^4 + 33*a^6*b^2*d^4*e^5 - 16*a^7*b*d^3*e^6 + 3*a^8*d^2*e^7)*x)","B",0
1143,1,54,0,0.955499," ","integrate((1-2*x)*(2+3*x)^8*(3+5*x),x, algorithm=""fricas"")","-\frac{65610}{11} x^{11} - \frac{356481}{10} x^{10} - 92421 x^{9} - 133164 x^{8} - 110160 x^{7} - 41328 x^{6} + \frac{62496}{5} x^{5} + 24576 x^{4} + \frac{42752}{3} x^{3} + 4480 x^{2} + 768 x"," ",0,"-65610/11*x^11 - 356481/10*x^10 - 92421*x^9 - 133164*x^8 - 110160*x^7 - 41328*x^6 + 62496/5*x^5 + 24576*x^4 + 42752/3*x^3 + 4480*x^2 + 768*x","A",0
1144,1,49,0,1.006888," ","integrate((1-2*x)*(2+3*x)^7*(3+5*x),x, algorithm=""fricas"")","-2187 x^{10} - 11583 x^{9} - \frac{207765}{8} x^{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac{15520}{3} x^{3} + 1952 x^{2} + 384 x"," ",0,"-2187*x^10 - 11583*x^9 - 207765/8*x^8 - 30942*x^7 - 18774*x^6 - 1512*x^5 + 6468*x^4 + 15520/3*x^3 + 1952*x^2 + 384*x","A",0
1145,1,44,0,1.021449," ","integrate((1-2*x)*(2+3*x)^6*(3+5*x),x, algorithm=""fricas"")","-810 x^{9} - \frac{29889}{8} x^{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264}{3} x^{3} + 832 x^{2} + 192 x"," ",0,"-810*x^9 - 29889/8*x^8 - 7047*x^7 - 6552*x^6 - 2268*x^5 + 1260*x^4 + 5264/3*x^3 + 832*x^2 + 192*x","A",0
1146,1,39,0,1.064091," ","integrate((1-2*x)*(2+3*x)^5*(3+5*x),x, algorithm=""fricas"")","-\frac{1215}{4} x^{8} - \frac{8343}{7} x^{7} - \frac{3627}{2} x^{6} - 1170 x^{5} + 30 x^{4} + \frac{1600}{3} x^{3} + 344 x^{2} + 96 x"," ",0,"-1215/4*x^8 - 8343/7*x^7 - 3627/2*x^6 - 1170*x^5 + 30*x^4 + 1600/3*x^3 + 344*x^2 + 96*x","A",0
1147,1,34,0,0.838612," ","integrate((1-2*x)*(2+3*x)^4*(3+5*x),x, algorithm=""fricas"")","-\frac{810}{7} x^{7} - \frac{747}{2} x^{6} - \frac{2133}{5} x^{5} - 132 x^{4} + \frac{392}{3} x^{3} + 136 x^{2} + 48 x"," ",0,"-810/7*x^7 - 747/2*x^6 - 2133/5*x^5 - 132*x^4 + 392/3*x^3 + 136*x^2 + 48*x","A",0
1148,1,29,0,1.195910," ","integrate((1-2*x)*(2+3*x)^3*(3+5*x),x, algorithm=""fricas"")","-45 x^{6} - \frac{567}{5} x^{5} - \frac{333}{4} x^{4} + \frac{46}{3} x^{3} + 50 x^{2} + 24 x"," ",0,"-45*x^6 - 567/5*x^5 - 333/4*x^4 + 46/3*x^3 + 50*x^2 + 24*x","A",0
1149,1,24,0,0.715335," ","integrate((1-2*x)*(2+3*x)^2*(3+5*x),x, algorithm=""fricas"")","-18 x^{5} - \frac{129}{4} x^{4} - \frac{25}{3} x^{3} + 16 x^{2} + 12 x"," ",0,"-18*x^5 - 129/4*x^4 - 25/3*x^3 + 16*x^2 + 12*x","A",0
1150,1,19,0,1.245956," ","integrate((1-2*x)*(2+3*x)*(3+5*x),x, algorithm=""fricas"")","-\frac{15}{2} x^{4} - \frac{23}{3} x^{3} + \frac{7}{2} x^{2} + 6 x"," ",0,"-15/2*x^4 - 23/3*x^3 + 7/2*x^2 + 6*x","A",0
1151,1,14,0,1.162995," ","integrate((1-2*x)*(3+5*x),x, algorithm=""fricas"")","-\frac{10}{3} x^{3} - \frac{1}{2} x^{2} + 3 x"," ",0,"-10/3*x^3 - 1/2*x^2 + 3*x","A",0
1152,1,17,0,1.331342," ","integrate((1-2*x)*(3+5*x)/(2+3*x),x, algorithm=""fricas"")","-\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \log\left(3 \, x + 2\right)"," ",0,"-5/3*x^2 + 17/9*x - 7/27*log(3*x + 2)","A",0
1153,1,32,0,1.474769," ","integrate((1-2*x)*(3+5*x)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{90 \, x^{2} - 37 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 60 \, x - 7}{27 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/27*(90*x^2 - 37*(3*x + 2)*log(3*x + 2) + 60*x - 7)/(3*x + 2)","A",0
1154,1,37,0,1.278835," ","integrate((1-2*x)*(3+5*x)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{20 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 222 \, x + 141}{54 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/54*(20*(9*x^2 + 12*x + 4)*log(3*x + 2) + 222*x + 141)/(9*x^2 + 12*x + 4)","A",0
1155,1,29,0,1.243384," ","integrate((1-2*x)*(3+5*x)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{540 \, x^{2} + 387 \, x + 32}{162 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/162*(540*x^2 + 387*x + 32)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1156,1,34,0,1.112259," ","integrate((1-2*x)*(3+5*x)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{540 \, x^{2} + 276 \, x - 35}{324 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/324*(540*x^2 + 276*x - 35)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1157,1,39,0,1.169072," ","integrate((1-2*x)*(3+5*x)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{1800 \, x^{2} + 735 \, x - 226}{1620 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/1620*(1800*x^2 + 735*x - 226)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1158,1,59,0,1.202674," ","integrate((1-2*x)*(2+3*x)^8*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{54675}{2} x^{12} - \frac{1979235}{11} x^{11} - \frac{2614194}{5} x^{10} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac{679008}{5} x^{5} + 127168 x^{4} + \frac{173056}{3} x^{3} + 15360 x^{2} + 2304 x"," ",0,"-54675/2*x^12 - 1979235/11*x^11 - 2614194/5*x^10 - 869103*x^9 - 881442*x^8 - 507600*x^7 - 71904*x^6 + 679008/5*x^5 + 127168*x^4 + 173056/3*x^3 + 15360*x^2 + 2304*x","A",0
1159,1,54,0,1.085687," ","integrate((1-2*x)*(2+3*x)^7*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{109350}{11} x^{11} - \frac{117369}{2} x^{10} - 150174 x^{9} - \frac{1706265}{8} x^{8} - 173286 x^{7} - 62622 x^{6} + 21336 x^{5} + 38804 x^{4} + \frac{66080}{3} x^{3} + 6816 x^{2} + 1152 x"," ",0,"-109350/11*x^11 - 117369/2*x^10 - 150174*x^9 - 1706265/8*x^8 - 173286*x^7 - 62622*x^6 + 21336*x^5 + 38804*x^4 + 66080/3*x^3 + 6816*x^2 + 1152*x","A",0
1160,1,49,0,1.122607," ","integrate((1-2*x)*(2+3*x)^6*(3+5*x)^2,x, algorithm=""fricas"")","-3645 x^{10} - 19035 x^{9} - 42039 x^{8} - 49221 x^{7} - 29106 x^{6} - 1764 x^{5} + 10360 x^{4} + \frac{24112}{3} x^{3} + 2976 x^{2} + 576 x"," ",0,"-3645*x^10 - 19035*x^9 - 42039*x^8 - 49221*x^7 - 29106*x^6 - 1764*x^5 + 10360*x^4 + 24112/3*x^3 + 2976*x^2 + 576*x","A",0
1161,1,44,0,0.982702," ","integrate((1-2*x)*(2+3*x)^5*(3+5*x)^2,x, algorithm=""fricas"")","-1350 x^{9} - \frac{49005}{8} x^{8} - \frac{79434}{7} x^{7} - \frac{20631}{2} x^{6} - 3390 x^{5} + 2090 x^{4} + \frac{8240}{3} x^{3} + 1272 x^{2} + 288 x"," ",0,"-1350*x^9 - 49005/8*x^8 - 79434/7*x^7 - 20631/2*x^6 - 3390*x^5 + 2090*x^4 + 8240/3*x^3 + 1272*x^2 + 288*x","A",0
1162,1,39,0,1.617124," ","integrate((1-2*x)*(2+3*x)^4*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2025}{4} x^{8} - \frac{13635}{7} x^{7} - 2898 x^{6} - \frac{9039}{5} x^{5} + 94 x^{4} + \frac{2536}{3} x^{3} + 528 x^{2} + 144 x"," ",0,"-2025/4*x^8 - 13635/7*x^7 - 2898*x^6 - 9039/5*x^5 + 94*x^4 + 2536/3*x^3 + 528*x^2 + 144*x","A",0
1163,1,34,0,1.086555," ","integrate((1-2*x)*(2+3*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1350}{7} x^{7} - \frac{1215}{2} x^{6} - \frac{3366}{5} x^{5} - \frac{769}{4} x^{4} + \frac{638}{3} x^{3} + 210 x^{2} + 72 x"," ",0,"-1350/7*x^7 - 1215/2*x^6 - 3366/5*x^5 - 769/4*x^4 + 638/3*x^3 + 210*x^2 + 72*x","A",0
1164,1,29,0,1.050805," ","integrate((1-2*x)*(2+3*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","-75 x^{6} - 183 x^{5} - 128 x^{4} + \frac{85}{3} x^{3} + 78 x^{2} + 36 x"," ",0,"-75*x^6 - 183*x^5 - 128*x^4 + 85/3*x^3 + 78*x^2 + 36*x","A",0
1165,1,24,0,1.036064," ","integrate((1-2*x)*(2+3*x)*(3+5*x)^2,x, algorithm=""fricas"")","-30 x^{5} - \frac{205}{4} x^{4} - \frac{34}{3} x^{3} + \frac{51}{2} x^{2} + 18 x"," ",0,"-30*x^5 - 205/4*x^4 - 34/3*x^3 + 51/2*x^2 + 18*x","A",0
1166,1,19,0,1.079082," ","integrate((1-2*x)*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{25}{2} x^{4} - \frac{35}{3} x^{3} + 6 x^{2} + 9 x"," ",0,"-25/2*x^4 - 35/3*x^3 + 6*x^2 + 9*x","A",0
1167,1,22,0,1.273027," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x),x, algorithm=""fricas"")","-\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \log\left(3 \, x + 2\right)"," ",0,"-50/9*x^3 - 5/18*x^2 + 118/27*x + 7/81*log(3*x + 2)","A",0
1168,1,37,0,1.253091," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{675 \, x^{3} - 405 \, x^{2} + 72 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 570 \, x + 7}{81 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/81*(675*x^3 - 405*x^2 + 72*(3*x + 2)*log(3*x + 2) - 570*x + 7)/(3*x + 2)","A",0
1169,1,47,0,1.373611," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{2700 \, x^{3} + 3600 \, x^{2} - 390 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 768 \, x - 281}{162 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/162*(2700*x^3 + 3600*x^2 - 390*(9*x^2 + 12*x + 4)*log(3*x + 2) + 768*x - 281)/(9*x^2 + 12*x + 4)","A",0
1170,1,52,0,1.186236," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{5265 \, x^{2} + 150 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 6696 \, x + 2131}{243 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/243*(5265*x^2 + 150*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 6696*x + 2131)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1171,1,39,0,0.796503," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","\frac{600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/36*(600*x^3 + 810*x^2 + 312*x + 25)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1172,1,44,0,1.383786," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","\frac{3375 \, x^{3} + 3825 \, x^{2} + 870 \, x - 127}{405 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/405*(3375*x^3 + 3825*x^2 + 870*x - 127)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1173,1,49,0,1.443003," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","\frac{27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/4860*(27000*x^3 + 27675*x^2 + 3492*x - 2042)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1174,1,54,0,1.211747," ","integrate((1-2*x)*(3+5*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","\frac{225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/54*(225*x^3 + 216*x^2 + 12*x - 22)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1175,1,64,0,1.116542," ","integrate((1-2*x)*(2+3*x)^8*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1640250}{13} x^{13} - \frac{3626775}{4} x^{12} - \frac{32079645}{11} x^{11} - \frac{54794799}{10} x^{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384}{5} x^{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x"," ",0,"-1640250/13*x^13 - 3626775/4*x^12 - 32079645/11*x^11 - 54794799/10*x^10 - 6524829*x^9 - 4865076*x^8 - 1830960*x^7 + 350128*x^6 + 4580384/5*x^5 + 597824*x^4 + 224256*x^3 + 51840*x^2 + 6912*x","A",0
1176,1,59,0,0.580896," ","integrate((1-2*x)*(2+3*x)^7*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{91125}{2} x^{12} - \frac{3262275}{11} x^{11} - \frac{1703673}{2} x^{10} - 1398447 x^{9} - \frac{11183805}{8} x^{8} - 788238 x^{7} - 98966 x^{6} + 219224 x^{5} + 199012 x^{4} + 88800 x^{3} + 23328 x^{2} + 3456 x"," ",0,"-91125/2*x^12 - 3262275/11*x^11 - 1703673/2*x^10 - 1398447*x^9 - 11183805/8*x^8 - 788238*x^7 - 98966*x^6 + 219224*x^5 + 199012*x^4 + 88800*x^3 + 23328*x^2 + 3456*x","A",0
1177,1,54,0,1.230631," ","integrate((1-2*x)*(2+3*x)^6*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{182250}{11} x^{11} - \frac{193185}{2} x^{10} - 243945 x^{9} - \frac{2731671}{8} x^{8} - 272403 x^{7} - 94668 x^{6} + 36148 x^{5} + 61220 x^{4} + 34032 x^{3} + 10368 x^{2} + 1728 x"," ",0,"-182250/11*x^11 - 193185/2*x^10 - 243945*x^9 - 2731671/8*x^8 - 272403*x^7 - 94668*x^6 + 36148*x^5 + 61220*x^4 + 34032*x^3 + 10368*x^2 + 1728*x","A",0
1178,1,49,0,1.126465," ","integrate((1-2*x)*(2+3*x)^5*(3+5*x)^3,x, algorithm=""fricas"")","-6075 x^{10} - 31275 x^{9} - \frac{544185}{8} x^{8} - \frac{547767}{7} x^{7} - \frac{90143}{2} x^{6} - 1810 x^{5} + 16570 x^{4} + 12480 x^{3} + 4536 x^{2} + 864 x"," ",0,"-6075*x^10 - 31275*x^9 - 544185/8*x^8 - 547767/7*x^7 - 90143/2*x^6 - 1810*x^5 + 16570*x^4 + 12480*x^3 + 4536*x^2 + 864*x","A",0
1179,1,44,0,1.246589," ","integrate((1-2*x)*(2+3*x)^4*(3+5*x)^3,x, algorithm=""fricas"")","-2250 x^{9} - \frac{80325}{8} x^{8} - \frac{127845}{7} x^{7} - \frac{32453}{2} x^{6} - \frac{25237}{5} x^{5} + 3452 x^{4} + 4296 x^{3} + 1944 x^{2} + 432 x"," ",0,"-2250*x^9 - 80325/8*x^8 - 127845/7*x^7 - 32453/2*x^6 - 25237/5*x^5 + 3452*x^4 + 4296*x^3 + 1944*x^2 + 432*x","A",0
1180,1,39,0,1.335468," ","integrate((1-2*x)*(2+3*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{3375}{4} x^{8} - \frac{22275}{7} x^{7} - \frac{9255}{2} x^{6} - \frac{13943}{5} x^{5} + \frac{883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x"," ",0,"-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 810*x^2 + 216*x","A",0
1181,1,34,0,0.947389," ","integrate((1-2*x)*(2+3*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{2250}{7} x^{7} - \frac{1975}{2} x^{6} - 1061 x^{5} - \frac{1111}{4} x^{4} + 345 x^{3} + 324 x^{2} + 108 x"," ",0,"-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x","A",0
1182,1,29,0,1.658149," ","integrate((1-2*x)*(2+3*x)*(3+5*x)^3,x, algorithm=""fricas"")","-125 x^{6} - 295 x^{5} - \frac{785}{4} x^{4} + 51 x^{3} + \frac{243}{2} x^{2} + 54 x"," ",0,"-125*x^6 - 295*x^5 - 785/4*x^4 + 51*x^3 + 243/2*x^2 + 54*x","A",0
1183,1,24,0,1.093820," ","integrate((1-2*x)*(3+5*x)^3,x, algorithm=""fricas"")","-50 x^{5} - \frac{325}{4} x^{4} - 15 x^{3} + \frac{81}{2} x^{2} + 27 x"," ",0,"-50*x^5 - 325/4*x^4 - 15*x^3 + 81/2*x^2 + 27*x","A",0
1184,1,27,0,1.548949," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x),x, algorithm=""fricas"")","-\frac{125}{6} \, x^{4} - \frac{475}{27} \, x^{3} + \frac{545}{54} \, x^{2} + \frac{1097}{81} \, x - \frac{7}{243} \, \log\left(3 \, x + 2\right)"," ",0,"-125/6*x^4 - 475/27*x^3 + 545/54*x^2 + 1097/81*x - 7/243*log(3*x + 2)","A",0
1185,1,42,0,1.458716," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{13500 \, x^{4} + 8325 \, x^{3} - 9360 \, x^{2} - 214 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 5940 \, x - 14}{486 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/486*(13500*x^4 + 8325*x^3 - 9360*x^2 - 214*(3*x + 2)*log(3*x + 2) - 5940*x - 14)/(3*x + 2)","A",0
1186,1,52,0,1.399670," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{20250 \, x^{4} - 1350 \, x^{3} - 28800 \, x^{2} + 1110 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 11958 \, x + 421}{486 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/486*(20250*x^4 - 1350*x^3 - 28800*x^2 + 1110*(9*x^2 + 12*x + 4)*log(3*x + 2) - 11958*x + 421)/(9*x^2 + 12*x + 4)","A",0
1187,1,62,0,1.349477," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{121500 \, x^{4} + 243000 \, x^{3} + 132030 \, x^{2} - 6150 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 2997 \, x - 12692}{1458 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/1458*(121500*x^4 + 243000*x^3 + 132030*x^2 - 6150*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 2997*x - 12692)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1188,1,67,0,1.353255," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{332100 \, x^{3} + 634230 \, x^{2} + 3000 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 404124 \, x + 85915}{2916 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/2916*(332100*x^3 + 634230*x^2 + 3000*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 404124*x + 85915)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1189,1,49,0,1.305969," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","\frac{405000 \, x^{4} + 803250 \, x^{3} + 559800 \, x^{2} + 153795 \, x + 11758}{4860 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/4860*(405000*x^4 + 803250*x^3 + 559800*x^2 + 153795*x + 11758)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1190,1,54,0,1.224049," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^7,x, algorithm=""fricas"")","\frac{607500 \, x^{4} + 1066500 \, x^{3} + 587925 \, x^{2} + 78048 \, x - 13198}{14580 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/14580*(607500*x^4 + 1066500*x^3 + 587925*x^2 + 78048*x - 13198)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1191,1,59,0,1.341585," ","integrate((1-2*x)*(3+5*x)^3/(2+3*x)^8,x, algorithm=""fricas"")","\frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/2916*(81000*x^4 + 132975*x^3 + 61938*x^2 + 642*x - 3688)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1192,1,54,0,1.670987," ","integrate((5-2*x)^6*(2+3*x)^3*(-16+33*x),x, algorithm=""fricas"")","5184 x^{11} - 76896 x^{10} + 452304 x^{9} - 1256376 x^{8} + 1235404 x^{7} + 1497230 x^{6} - 3816225 x^{5} - \frac{98125}{2} x^{4} + 3987500 x^{3} - 37500 x^{2} - 2000000 x"," ",0,"5184*x^11 - 76896*x^10 + 452304*x^9 - 1256376*x^8 + 1235404*x^7 + 1497230*x^6 - 3816225*x^5 - 98125/2*x^4 + 3987500*x^3 - 37500*x^2 - 2000000*x","B",0
1193,1,42,0,0.772238," ","integrate((1-2*x)*(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","-\frac{1458}{35} \, x^{7} - \frac{7047}{50} \, x^{6} - \frac{106677}{625} \, x^{5} - \frac{152469}{2500} \, x^{4} + \frac{152469}{3125} \, x^{3} + \frac{1777779}{31250} \, x^{2} + \frac{1666663}{78125} \, x + \frac{11}{390625} \, \log\left(5 \, x + 3\right)"," ",0,"-1458/35*x^7 - 7047/50*x^6 - 106677/625*x^5 - 152469/2500*x^4 + 152469/3125*x^3 + 1777779/31250*x^2 + 1666663/78125*x + 11/390625*log(5*x + 3)","A",0
1194,1,37,0,1.374548," ","integrate((1-2*x)*(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","-\frac{81}{5} \, x^{6} - \frac{5427}{125} \, x^{5} - \frac{17469}{500} \, x^{4} + \frac{2469}{625} \, x^{3} + \frac{127779}{6250} \, x^{2} + \frac{166663}{15625} \, x + \frac{11}{78125} \, \log\left(5 \, x + 3\right)"," ",0,"-81/5*x^6 - 5427/125*x^5 - 17469/500*x^4 + 2469/625*x^3 + 127779/6250*x^2 + 166663/15625*x + 11/78125*log(5*x + 3)","A",0
1195,1,32,0,1.435770," ","integrate((1-2*x)*(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","-\frac{162}{25} \, x^{5} - \frac{1269}{100} \, x^{4} - \frac{531}{125} \, x^{3} + \frac{7779}{1250} \, x^{2} + \frac{16663}{3125} \, x + \frac{11}{15625} \, \log\left(5 \, x + 3\right)"," ",0,"-162/25*x^5 - 1269/100*x^4 - 531/125*x^3 + 7779/1250*x^2 + 16663/3125*x + 11/15625*log(5*x + 3)","A",0
1196,1,27,0,1.199485," ","integrate((1-2*x)*(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{27}{10} \, x^{4} - \frac{81}{25} \, x^{3} + \frac{279}{250} \, x^{2} + \frac{1663}{625} \, x + \frac{11}{3125} \, \log\left(5 \, x + 3\right)"," ",0,"-27/10*x^4 - 81/25*x^3 + 279/250*x^2 + 1663/625*x + 11/3125*log(5*x + 3)","A",0
1197,1,22,0,1.141459," ","integrate((1-2*x)*(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","-\frac{6}{5} \, x^{3} - \frac{21}{50} \, x^{2} + \frac{163}{125} \, x + \frac{11}{625} \, \log\left(5 \, x + 3\right)"," ",0,"-6/5*x^3 - 21/50*x^2 + 163/125*x + 11/625*log(5*x + 3)","A",0
1198,1,17,0,0.937476," ","integrate((1-2*x)*(2+3*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \log\left(5 \, x + 3\right)"," ",0,"-3/5*x^2 + 13/25*x + 11/125*log(5*x + 3)","A",0
1199,1,12,0,1.388030," ","integrate((1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{2}{5} \, x + \frac{11}{25} \, \log\left(5 \, x + 3\right)"," ",0,"-2/5*x + 11/25*log(5*x + 3)","A",0
1200,1,17,0,1.164572," ","integrate((1-2*x)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{11}{5} \, \log\left(5 \, x + 3\right) - \frac{7}{3} \, \log\left(3 \, x + 2\right)"," ",0,"11/5*log(5*x + 3) - 7/3*log(3*x + 2)","A",0
1201,1,37,0,1.481332," ","integrate((1-2*x)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{33 \, {\left(3 \, x + 2\right)} \log\left(5 \, x + 3\right) - 33 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 7}{3 \, {\left(3 \, x + 2\right)}}"," ",0,"1/3*(33*(3*x + 2)*log(5*x + 3) - 33*(3*x + 2)*log(3*x + 2) + 7)/(3*x + 2)","A",0
1202,1,55,0,1.321075," ","integrate((1-2*x)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{330 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x + 3\right) - 330 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 198 \, x + 139}{6 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/6*(330*(9*x^2 + 12*x + 4)*log(5*x + 3) - 330*(9*x^2 + 12*x + 4)*log(3*x + 2) + 198*x + 139)/(9*x^2 + 12*x + 4)","A",0
1203,1,75,0,1.359433," ","integrate((1-2*x)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{8910 \, x^{2} + 4950 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(5 \, x + 3\right) - 4950 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 12177 \, x + 4172}{18 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/18*(8910*x^2 + 4950*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 4950*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 12177*x + 4172)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1204,1,95,0,1.006871," ","integrate((1-2*x)/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{89100 \, x^{3} + 181170 \, x^{2} + 16500 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(5 \, x + 3\right) - 16500 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 122892 \, x + 27815}{12 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/12*(89100*x^3 + 181170*x^2 + 16500*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(5*x + 3) - 16500*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 122892*x + 27815)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1205,1,115,0,1.490624," ","integrate((1-2*x)/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{2227500 \, x^{4} + 6014250 \, x^{3} + 6091800 \, x^{2} + 137500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(5 \, x + 3\right) - 137500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 2743565 \, x + 463586}{20 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/20*(2227500*x^4 + 6014250*x^3 + 6091800*x^2 + 137500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(5*x + 3) - 137500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 2743565*x + 463586)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1206,1,135,0,0.853062," ","integrate((1-2*x)/(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 6187500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(5 \, x + 3\right) - 6187500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 309504888 \, x + 41722762}{180 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/180*(300712500*x^5 + 1012398750*x^4 + 1363675500*x^3 + 918643275*x^2 + 6187500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(5*x + 3) - 6187500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 309504888*x + 41722762)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1207,1,62,0,1.337926," ","integrate((1-2*x)*(2+3*x)^7/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{6834375000 \, x^{8} + 27755156250 \, x^{7} + 43662543750 \, x^{6} + 28920898125 \, x^{5} - 1358398125 \, x^{4} - 14907422250 \, x^{3} - 9916639950 \, x^{2} - 6412 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 2333300760 \, x + 308}{54687500 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/54687500*(6834375000*x^8 + 27755156250*x^7 + 43662543750*x^6 + 28920898125*x^5 - 1358398125*x^4 - 14907422250*x^3 - 9916639950*x^2 - 6412*(5*x + 3)*log(5*x + 3) - 2333300760*x + 308)/(5*x + 3)","A",0
1208,1,57,0,1.253787," ","integrate((1-2*x)*(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{18984375 \, x^{7} + 63787500 \, x^{6} + 75481875 \, x^{5} + 22955625 \, x^{4} - 27546750 \, x^{3} - 29165850 \, x^{2} - 196 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 8332335 \, x + 11}{390625 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/390625*(18984375*x^7 + 63787500*x^6 + 75481875*x^5 + 22955625*x^4 - 27546750*x^3 - 29165850*x^2 - 196*(5*x + 3)*log(5*x + 3) - 8332335*x + 11)/(5*x + 3)","A",0
1209,1,52,0,1.210607," ","integrate((1-2*x)*(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{6075000 \, x^{6} + 16048125 \, x^{5} + 12076875 \, x^{4} - 3242250 \, x^{3} - 9163950 \, x^{2} - 652 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 3330000 \, x + 44}{312500 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/312500*(6075000*x^6 + 16048125*x^5 + 12076875*x^4 - 3242250*x^3 - 9163950*x^2 - 652*(5*x + 3)*log(5*x + 3) - 3330000*x + 44)/(5*x + 3)","A",0
1210,1,47,0,1.323967," ","integrate((1-2*x)*(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{253125 \, x^{5} + 478125 \, x^{4} + 101250 \, x^{3} - 332250 \, x^{2} - 260 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 165330 \, x + 22}{31250 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/31250*(253125*x^5 + 478125*x^4 + 101250*x^3 - 332250*x^2 - 260*(5*x + 3)*log(5*x + 3) - 165330*x + 22)/(5*x + 3)","A",0
1211,1,42,0,1.254861," ","integrate((1-2*x)*(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{22500 \, x^{4} + 23625 \, x^{3} - 20025 \, x^{2} - 194 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 15660 \, x + 22}{6250 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/6250*(22500*x^4 + 23625*x^3 - 20025*x^2 - 194*(5*x + 3)*log(5*x + 3) - 15660*x + 22)/(5*x + 3)","A",0
1212,1,37,0,1.383940," ","integrate((1-2*x)*(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1125 \, x^{3} - 150 \, x^{2} - 64 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 495 \, x + 11}{625 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/625*(1125*x^3 - 150*x^2 - 64*(5*x + 3)*log(5*x + 3) - 495*x + 11)/(5*x + 3)","A",0
1213,1,32,0,1.018195," ","integrate((1-2*x)*(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{150 \, x^{2} - 31 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 90 \, x + 11}{125 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/125*(150*x^2 - 31*(5*x + 3)*log(5*x + 3) + 90*x + 11)/(5*x + 3)","A",0
1214,1,24,0,1.236466," ","integrate((1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 11}{25 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/25*(2*(5*x + 3)*log(5*x + 3) + 11)/(5*x + 3)","A",0
1215,1,37,0,1.377748," ","integrate((1-2*x)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{35 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 35 \, {\left(5 \, x + 3\right)} \log\left(3 \, x + 2\right) + 11}{5 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/5*(35*(5*x + 3)*log(5*x + 3) - 35*(5*x + 3)*log(3*x + 2) + 11)/(5*x + 3)","A",0
1216,1,55,0,0.847948," ","integrate((1-2*x)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{68 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(5 \, x + 3\right) - 68 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(3 \, x + 2\right) + 68 \, x + 43}{15 \, x^{2} + 19 \, x + 6}"," ",0,"-(68*(15*x^2 + 19*x + 6)*log(5*x + 3) - 68*(15*x^2 + 19*x + 6)*log(3*x + 2) + 68*x + 43)/(15*x^2 + 19*x + 6)","A",0
1217,1,75,0,1.329169," ","integrate((1-2*x)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{3030 \, x^{2} + 1010 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(5 \, x + 3\right) - 1010 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(3 \, x + 2\right) + 3939 \, x + 1277}{2 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"-1/2*(3030*x^2 + 1010*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 1010*(45*x^3 + 87*x^2 + 56*x + 12)*log(3*x + 2) + 3939*x + 1277)/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1218,1,95,0,1.300184," ","integrate((1-2*x)/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{90450 \, x^{3} + 177885 \, x^{2} + 10050 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(5 \, x + 3\right) - 10050 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(3 \, x + 2\right) + 116513 \, x + 25413}{3 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"-1/3*(90450*x^3 + 177885*x^2 + 10050*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(5*x + 3) - 10050*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) + 116513*x + 25413)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1219,1,115,0,1.188544," ","integrate((1-2*x)/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 250500 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(5 \, x + 3\right) - 250500 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(3 \, x + 2\right) + 7708553 \, x + 1266855}{12 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"-1/12*(6763500*x^4 + 17810550*x^3 + 17580090*x^2 + 250500*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(5*x + 3) - 250500*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(3*x + 2) + 7708553*x + 1266855)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
1220,1,135,0,1.423521," ","integrate((1-2*x)/(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{151875000 \, x^{5} + 501187500 \, x^{4} + 661387500 \, x^{3} + 436271250 \, x^{2} + 1875000 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(5 \, x + 3\right) - 1875000 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(3 \, x + 2\right) + 143844850 \, x + 18964893}{15 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"-1/15*(151875000*x^5 + 501187500*x^4 + 661387500*x^3 + 436271250*x^2 + 1875000*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(5*x + 3) - 1875000*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(3*x + 2) + 143844850*x + 18964893)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","A",0
1221,1,155,0,0.761827," ","integrate((1-2*x)/(2+3*x)^7/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{3538687500 \, x^{6} + 14036793750 \, x^{5} + 23195441250 \, x^{4} + 20438672625 \, x^{3} + 10128331755 \, x^{2} + 14562500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(5 \, x + 3\right) - 14562500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(3 \, x + 2\right) + 2676272018 \, x + 294588002}{20 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)}}"," ",0,"-1/20*(3538687500*x^6 + 14036793750*x^5 + 23195441250*x^4 + 20438672625*x^3 + 10128331755*x^2 + 14562500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(5*x + 3) - 14562500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*x + 2) + 2676272018*x + 294588002)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)","A",0
1222,1,72,0,1.082671," ","integrate((1-2*x)*(2+3*x)^7/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1139062500 \, x^{8} + 4601812500 \, x^{7} + 7128253125 \, x^{6} + 4439846250 \, x^{5} - 753519375 \, x^{4} - 2916553500 \, x^{3} - 1694131200 \, x^{2} - 8148 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 333201880 \, x + 2770}{7812500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/7812500*(1139062500*x^8 + 4601812500*x^7 + 7128253125*x^6 + 4439846250*x^5 - 753519375*x^4 - 2916553500*x^3 - 1694131200*x^2 - 8148*(25*x^2 + 30*x + 9)*log(5*x + 3) - 333201880*x + 2770)/(25*x^2 + 30*x + 9)","A",0
1223,1,67,0,1.055349," ","integrate((1-2*x)*(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{91125000 \, x^{7} + 302990625 \, x^{6} + 345161250 \, x^{5} + 72883125 \, x^{4} - 174919500 \, x^{3} - 144220500 \, x^{2} - 5796 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 33238480 \, x + 2374}{1562500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/1562500*(91125000*x^7 + 302990625*x^6 + 345161250*x^5 + 72883125*x^4 - 174919500*x^3 - 144220500*x^2 - 5796*(25*x^2 + 30*x + 9)*log(5*x + 3) - 33238480*x + 2374)/(25*x^2 + 30*x + 9)","A",0
1224,1,62,0,1.282073," ","integrate((1-2*x)*(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{3796875 \, x^{6} + 9787500 \, x^{5} + 6412500 \, x^{4} - 4140000 \, x^{3} - 5897475 \, x^{2} - 1920 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 1634570 \, x + 989}{156250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/156250*(3796875*x^6 + 9787500*x^5 + 6412500*x^4 - 4140000*x^3 - 5897475*x^2 - 1920*(25*x^2 + 30*x + 9)*log(5*x + 3) - 1634570*x + 989)/(25*x^2 + 30*x + 9)","A",0
1225,1,57,0,1.290615," ","integrate((1-2*x)*(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{337500 \, x^{5} + 590625 \, x^{4} - 67500 \, x^{3} - 427275 \, x^{2} - 1140 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 146930 \, x + 791}{31250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/31250*(337500*x^5 + 590625*x^4 - 67500*x^3 - 427275*x^2 - 1140*(25*x^2 + 30*x + 9)*log(5*x + 3) - 146930*x + 791)/(25*x^2 + 30*x + 9)","A",0
1226,1,52,0,1.342249," ","integrate((1-2*x)*(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{33750 \, x^{4} + 20250 \, x^{3} - 12150 \, x^{2} - 558 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 6320 \, x + 593}{6250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/6250*(33750*x^4 + 20250*x^3 - 12150*x^2 - 558*(25*x^2 + 30*x + 9)*log(5*x + 3) - 6320*x + 593)/(25*x^2 + 30*x + 9)","A",0
1227,1,47,0,1.267500," ","integrate((1-2*x)*(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{4500 \, x^{3} + 5400 \, x^{2} - 174 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 2260 \, x + 395}{1250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/1250*(4500*x^3 + 5400*x^2 - 174*(25*x^2 + 30*x + 9)*log(5*x + 3) + 2260*x + 395)/(25*x^2 + 30*x + 9)","A",0
1228,1,37,0,1.297030," ","integrate((1-2*x)*(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 310 \, x + 197}{250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/250*(12*(25*x^2 + 30*x + 9)*log(5*x + 3) + 310*x + 197)/(25*x^2 + 30*x + 9)","A",0
1229,1,19,0,0.636289," ","integrate((1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{20 \, x + 1}{50 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/50*(20*x + 1)/(25*x^2 + 30*x + 9)","A",0
1230,1,55,0,0.803308," ","integrate((1-2*x)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{210 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 210 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(3 \, x + 2\right) + 350 \, x + 199}{10 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/10*(210*(25*x^2 + 30*x + 9)*log(5*x + 3) - 210*(25*x^2 + 30*x + 9)*log(3*x + 2) + 350*x + 199)/(25*x^2 + 30*x + 9)","A",0
1231,1,75,0,1.134724," ","integrate((1-2*x)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3090 \, x^{2} + 618 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(5 \, x + 3\right) - 618 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(3 \, x + 2\right) + 3811 \, x + 1172}{2 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/2*(3090*x^2 + 618*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 618*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) + 3811*x + 1172)/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1232,1,95,0,1.232248," ","integrate((1-2*x)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{91800 \, x^{3} + 174420 \, x^{2} + 6120 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(5 \, x + 3\right) - 6120 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(3 \, x + 2\right) + 110296 \, x + 23213}{2 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/2*(91800*x^3 + 174420*x^2 + 6120*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(5*x + 3) - 6120*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 110296*x + 23213)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1233,1,115,0,1.307261," ","integrate((1-2*x)/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2281500 \, x^{4} + 5855850 \, x^{3} + 5631080 \, x^{2} + 50700 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(5 \, x + 3\right) - 50700 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(3 \, x + 2\right) + 2404363 \, x + 384608}{2 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/2*(2281500*x^4 + 5855850*x^3 + 5631080*x^2 + 50700*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(5*x + 3) - 50700*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) + 2404363*x + 384608)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
1234,1,135,0,1.219738," ","integrate((1-2*x)/(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 757500 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(5 \, x + 3\right) - 757500 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(3 \, x + 2\right) + 89085434 \, x + 11492725}{4 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"1/4*(102262500*x^5 + 330648750*x^4 + 427381500*x^3 + 276035525*x^2 + 757500*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5*x + 3) - 757500*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(3*x + 2) + 89085434*x + 11492725)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","A",0
1235,1,155,0,1.328013," ","integrate((1-2*x)/(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","\frac{10707187500 \, x^{6} + 41758031250 \, x^{5} + 67828050000 \, x^{4} + 58733814375 \, x^{3} + 28595335800 \, x^{2} + 26437500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(5 \, x + 3\right) - 26437500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(3 \, x + 2\right) + 7421662135 \, x + 802214966}{20 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)}}"," ",0,"1/20*(10707187500*x^6 + 41758031250*x^5 + 67828050000*x^4 + 58733814375*x^3 + 28595335800*x^2 + 26437500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(5*x + 3) - 26437500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(3*x + 2) + 7421662135*x + 802214966)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)","A",0
1236,1,59,0,0.783859," ","integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm=""fricas"")","10935 x^{12} + \frac{647352}{11} x^{11} + \frac{1307097}{10} x^{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112}{5} x^{5} + 3200 x^{4} + \frac{24832}{3} x^{3} + 3712 x^{2} + 768 x"," ",0,"10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5 + 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x","A",0
1237,1,54,0,1.149628," ","integrate((1-2*x)^2*(2+3*x)^7*(3+5*x),x, algorithm=""fricas"")","\frac{43740}{11} x^{11} + \frac{93312}{5} x^{10} + 34587 x^{9} + \frac{225423}{8} x^{8} + 1242 x^{7} - 16254 x^{6} - \frac{59304}{5} x^{5} - 1292 x^{4} + \frac{7712}{3} x^{3} + 1568 x^{2} + 384 x"," ",0,"43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712/3*x^3 + 1568*x^2 + 384*x","A",0
1238,1,49,0,0.565120," ","integrate((1-2*x)^2*(2+3*x)^6*(3+5*x),x, algorithm=""fricas"")","1458 x^{10} + 5832 x^{9} + \frac{68769}{8} x^{8} + 4185 x^{7} - 2772 x^{6} - 4284 x^{5} - 1372 x^{4} + \frac{1936}{3} x^{3} + 640 x^{2} + 192 x"," ",0,"1458*x^10 + 5832*x^9 + 68769/8*x^8 + 4185*x^7 - 2772*x^6 - 4284*x^5 - 1372*x^4 + 1936/3*x^3 + 640*x^2 + 192*x","A",0
1239,1,44,0,1.056220," ","integrate((1-2*x)^2*(2+3*x)^5*(3+5*x),x, algorithm=""fricas"")","540 x^{9} + 1782 x^{8} + 1917 x^{7} + \frac{273}{2} x^{6} - 1218 x^{5} - 770 x^{4} + \frac{224}{3} x^{3} + 248 x^{2} + 96 x"," ",0,"540*x^9 + 1782*x^8 + 1917*x^7 + 273/2*x^6 - 1218*x^5 - 770*x^4 + 224/3*x^3 + 248*x^2 + 96*x","A",0
1240,1,39,0,1.149809," ","integrate((1-2*x)^2*(2+3*x)^4*(3+5*x),x, algorithm=""fricas"")","\frac{405}{2} x^{8} + \frac{3672}{7} x^{7} + \frac{675}{2} x^{6} - \frac{1077}{5} x^{5} - 328 x^{4} - \frac{152}{3} x^{3} + 88 x^{2} + 48 x"," ",0,"405/2*x^8 + 3672/7*x^7 + 675/2*x^6 - 1077/5*x^5 - 328*x^4 - 152/3*x^3 + 88*x^2 + 48*x","A",0
1241,1,34,0,1.091650," ","integrate((1-2*x)^2*(2+3*x)^3*(3+5*x),x, algorithm=""fricas"")","\frac{540}{7} x^{7} + 144 x^{6} + \frac{99}{5} x^{5} - \frac{425}{4} x^{4} - \frac{154}{3} x^{3} + 26 x^{2} + 24 x"," ",0,"540/7*x^7 + 144*x^6 + 99/5*x^5 - 425/4*x^4 - 154/3*x^3 + 26*x^2 + 24*x","A",0
1242,1,29,0,1.109553," ","integrate((1-2*x)^2*(2+3*x)^2*(3+5*x),x, algorithm=""fricas"")","30 x^{6} + \frac{168}{5} x^{5} - \frac{79}{4} x^{4} - \frac{89}{3} x^{3} + 4 x^{2} + 12 x"," ",0,"30*x^6 + 168/5*x^5 - 79/4*x^4 - 89/3*x^3 + 4*x^2 + 12*x","A",0
1243,1,24,0,0.915472," ","integrate((1-2*x)^2*(2+3*x)*(3+5*x),x, algorithm=""fricas"")","12 x^{5} + 4 x^{4} - \frac{37}{3} x^{3} - \frac{5}{2} x^{2} + 6 x"," ",0,"12*x^5 + 4*x^4 - 37/3*x^3 - 5/2*x^2 + 6*x","A",0
1244,1,19,0,0.955211," ","integrate((1-2*x)^2*(3+5*x),x, algorithm=""fricas"")","5 x^{4} - \frac{8}{3} x^{3} - \frac{7}{2} x^{2} + 3 x"," ",0,"5*x^4 - 8/3*x^3 - 7/2*x^2 + 3*x","A",0
1245,1,22,0,0.653144," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x),x, algorithm=""fricas"")","\frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{81} \, \log\left(3 \, x + 2\right)"," ",0,"20/9*x^3 - 32/9*x^2 + 65/27*x - 49/81*log(3*x + 2)","A",0
1246,1,37,0,1.149305," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{270 \, x^{3} - 756 \, x^{2} + 273 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 624 \, x + 49}{81 \, {\left(3 \, x + 2\right)}}"," ",0,"1/81*(270*x^3 - 756*x^2 + 273*(3*x + 2)*log(3*x + 2) - 624*x + 49)/(3*x + 2)","A",0
1247,1,47,0,1.289013," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{1080 \, x^{3} + 1440 \, x^{2} - 288 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 1158 \, x - 1043}{162 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/162*(1080*x^3 + 1440*x^2 - 288*(9*x^2 + 12*x + 4)*log(3*x + 2) - 1158*x - 1043)/(9*x^2 + 12*x + 4)","A",0
1248,1,52,0,1.206660," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{7776 \, x^{2} + 120 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 7911 \, x + 1916}{486 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/486*(7776*x^2 + 120*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 7911*x + 1916)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1249,1,39,0,1.237396," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{2160 \, x^{3} + 1728 \, x^{2} + 516 \, x + 167}{324 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/324*(2160*x^3 + 1728*x^2 + 516*x + 167)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1250,1,44,0,1.326909," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/540*(1800*x^3 + 720*x^2 - 75*x + 98)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1251,1,49,0,1.320333," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/2430*(5400*x^3 + 1080*x^2 - 846*x + 311)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1252,1,54,0,1.338678," ","integrate((1-2*x)^2*(3+5*x)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/810*(1350*x^3 + 108*x^2 - 291*x + 88)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1253,1,64,0,1.336106," ","integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x, algorithm=""fricas"")","\frac{656100}{13} x^{13} + 302535 x^{12} + \frac{8477541}{11} x^{11} + \frac{5207733}{5} x^{10} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac{338336}{5} x^{5} + 40640 x^{4} + \frac{111616}{3} x^{3} + 13056 x^{2} + 2304 x"," ",0,"656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x","A",0
1254,1,59,0,1.217564," ","integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^2,x, algorithm=""fricas"")","18225 x^{12} + \frac{1064340}{11} x^{11} + \frac{2116287}{10} x^{10} + 228996 x^{9} + \frac{719739}{8} x^{8} - 65934 x^{7} - 98182 x^{6} - \frac{203752}{5} x^{5} + 5764 x^{4} + \frac{38816}{3} x^{3} + 5664 x^{2} + 1152 x"," ",0,"18225*x^12 + 1064340/11*x^11 + 2116287/10*x^10 + 228996*x^9 + 719739/8*x^8 - 65934*x^7 - 98182*x^6 - 203752/5*x^5 + 5764*x^4 + 38816/3*x^3 + 5664*x^2 + 1152*x","A",0
1255,1,54,0,1.321107," ","integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm=""fricas"")","\frac{72900}{11} x^{11} + 30618 x^{10} + 55701 x^{9} + \frac{176391}{4} x^{8} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac{12208}{3} x^{3} + 2400 x^{2} + 576 x"," ",0,"72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x^3 + 2400*x^2 + 576*x","A",0
1256,1,49,0,0.540452," ","integrate((1-2*x)^2*(2+3*x)^5*(3+5*x)^2,x, algorithm=""fricas"")","2430 x^{10} + 9540 x^{9} + \frac{109863}{8} x^{8} + 6336 x^{7} - \frac{9331}{2} x^{6} - 6734 x^{5} - 2030 x^{4} + \frac{3152}{3} x^{3} + 984 x^{2} + 288 x"," ",0,"2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288*x","A",0
1257,1,44,0,1.235303," ","integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x, algorithm=""fricas"")","900 x^{9} + \frac{5805}{2} x^{8} + \frac{21141}{7} x^{7} + 115 x^{6} - \frac{9791}{5} x^{5} - 1174 x^{4} + \frac{424}{3} x^{3} + 384 x^{2} + 144 x"," ",0,"900*x^9 + 5805/2*x^8 + 21141/7*x^7 + 115*x^6 - 9791/5*x^5 - 1174*x^4 + 424/3*x^3 + 384*x^2 + 144*x","A",0
1258,1,39,0,1.071886," ","integrate((1-2*x)^2*(2+3*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","\frac{675}{2} x^{8} + \frac{5940}{7} x^{7} + \frac{1029}{2} x^{6} - \frac{1828}{5} x^{5} - \frac{2045}{4} x^{4} - \frac{202}{3} x^{3} + 138 x^{2} + 72 x"," ",0,"675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x","A",0
1259,1,34,0,1.079127," ","integrate((1-2*x)^2*(2+3*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","\frac{900}{7} x^{7} + 230 x^{6} + \frac{109}{5} x^{5} - \frac{341}{2} x^{4} - \frac{227}{3} x^{3} + 42 x^{2} + 36 x"," ",0,"900/7*x^7 + 230*x^6 + 109/5*x^5 - 341/2*x^4 - 227/3*x^3 + 42*x^2 + 36*x","A",0
1260,1,29,0,1.422739," ","integrate((1-2*x)^2*(2+3*x)*(3+5*x)^2,x, algorithm=""fricas"")","50 x^{6} + 52 x^{5} - \frac{137}{4} x^{4} - \frac{136}{3} x^{3} + \frac{15}{2} x^{2} + 18 x"," ",0,"50*x^6 + 52*x^5 - 137/4*x^4 - 136/3*x^3 + 15/2*x^2 + 18*x","A",0
1261,1,24,0,1.180831," ","integrate((1-2*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","20 x^{5} + 5 x^{4} - \frac{59}{3} x^{3} - 3 x^{2} + 9 x"," ",0,"20*x^5 + 5*x^4 - 59/3*x^3 - 3*x^2 + 9*x","A",0
1262,1,27,0,1.142370," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x),x, algorithm=""fricas"")","\frac{25}{3} \, x^{4} - \frac{140}{27} \, x^{3} - \frac{251}{54} \, x^{2} + \frac{340}{81} \, x + \frac{49}{243} \, \log\left(3 \, x + 2\right)"," ",0,"25/3*x^4 - 140/27*x^3 - 251/54*x^2 + 340/81*x + 49/243*log(3*x + 2)","A",0
1263,1,42,0,0.911492," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","\frac{2700 \, x^{4} - 2790 \, x^{3} + 801 \, x^{2} - 518 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 2574 \, x - 49}{243 \, {\left(3 \, x + 2\right)}}"," ",0,"1/243*(2700*x^4 - 2790*x^3 + 801*x^2 - 518*(3*x + 2)*log(3*x + 2) + 2574*x - 49)/(3*x + 2)","A",0
1264,1,52,0,0.720523," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","\frac{8100 \, x^{4} - 18360 \, x^{3} - 35280 \, x^{2} + 3018 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 9852 \, x + 2023}{486 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/486*(8100*x^4 - 18360*x^3 - 35280*x^2 + 3018*(9*x^2 + 12*x + 4)*log(3*x + 2) - 9852*x + 2023)/(9*x^2 + 12*x + 4)","A",0
1265,1,62,0,1.066723," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","\frac{24300 \, x^{4} + 48600 \, x^{3} - 8343 \, x^{2} - 2220 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 44793 \, x - 16603}{729 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/729*(24300*x^4 + 48600*x^3 - 8343*x^2 - 2220*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 44793*x - 16603)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1266,1,67,0,1.513492," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","\frac{239760 \, x^{3} + 398034 \, x^{2} + 1200 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 217248 \, x + 38821}{2916 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/2916*(239760*x^3 + 398034*x^2 + 1200*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 217248*x + 38821)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1267,1,49,0,1.051055," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/2430*(81000*x^4 + 116100*x^3 + 61470*x^2 + 19275*x + 4028)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1268,1,54,0,1.643610," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{243000 \, x^{4} + 248400 \, x^{3} + 52515 \, x^{2} + 8172 \, x + 8198}{14580 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/14580*(243000*x^4 + 248400*x^3 + 52515*x^2 + 8172*x + 8198)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1269,1,59,0,1.649279," ","integrate((1-2*x)^2*(3+5*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/3645*(40500*x^4 + 33075*x^3 - 1107*x^2 - 1461*x + 1423)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1270,1,79,0,1.557917," ","integrate((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x, algorithm=""fricas"")","\frac{7381125}{4} x^{16} + 14696640 x^{15} + \frac{734077485}{14} x^{14} + \frac{1417418757}{13} x^{13} + \frac{569034801}{4} x^{12} + \frac{1233925083}{11} x^{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac{154612896}{7} x^{7} - \frac{10627328}{3} x^{6} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x"," ",0,"7381125/4*x^16 + 14696640*x^15 + 734077485/14*x^14 + 1417418757/13*x^13 + 569034801/4*x^12 + 1233925083/11*x^11 + 36043704*x^10 - 26237700*x^9 - 40113468*x^8 - 154612896/7*x^7 - 10627328/3*x^6 + 3185792*x^5 + 2644160*x^4 + 1000704*x^3 + 221184*x^2 + 27648*x","A",0
1271,1,74,0,1.557014," ","integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm=""fricas"")","656100 x^{15} + \frac{33461100}{7} x^{14} + \frac{200077695}{13} x^{13} + \frac{113029263}{4} x^{12} + \frac{342976275}{11} x^{11} + \frac{182657511}{10} x^{10} - 180666 x^{9} - 9703638 x^{8} - \frac{55216512}{7} x^{7} - \frac{7363312}{3} x^{6} + \frac{2732864}{5} x^{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x"," ",0,"656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 - 180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*x^2 + 13824*x","A",0
1272,1,69,0,1.349908," ","integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1640250}{7} x^{14} + \frac{20120400}{13} x^{13} + \frac{17759655}{4} x^{12} + \frac{77509953}{11} x^{11} + \frac{62652123}{10} x^{10} + 2124195 x^{9} - 1660896 x^{8} - \frac{17018256}{7} x^{7} - \frac{3530000}{3} x^{6} - \frac{202208}{5} x^{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x"," ",0,"1640250/7*x^14 + 20120400/13*x^13 + 17759655/4*x^12 + 77509953/11*x^11 + 62652123/10*x^10 + 2124195*x^9 - 1660896*x^8 - 17018256/7*x^7 - 3530000/3*x^6 - 202208/5*x^5 + 261440*x^4 + 155136*x^3 + 44928*x^2 + 6912*x","A",0
1273,1,64,0,1.332439," ","integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1093500}{13} x^{13} + 498150 x^{12} + \frac{13774455}{11} x^{11} + \frac{16653681}{10} x^{10} + 1086843 x^{9} - \frac{148473}{8} x^{8} - 618582 x^{7} - \frac{1393018}{3} x^{6} - \frac{495976}{5} x^{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x"," ",0,"1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7 - 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x","A",0
1274,1,59,0,1.419288," ","integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x, algorithm=""fricas"")","30375 x^{12} + \frac{1749600}{11} x^{11} + \frac{685017}{2} x^{10} + 363093 x^{9} + \frac{1081971}{8} x^{8} - 110115 x^{7} - \frac{464744}{3} x^{6} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x"," ",0,"30375*x^12 + 1749600/11*x^11 + 685017/2*x^10 + 363093*x^9 + 1081971/8*x^8 - 110115*x^7 - 464744/3*x^6 - 61804*x^5 + 10172*x^4 + 20208*x^3 + 8640*x^2 + 1728*x","A",0
1275,1,54,0,0.561767," ","integrate((1-2*x)^2*(2+3*x)^5*(3+5*x)^3,x, algorithm=""fricas"")","\frac{121500}{11} x^{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349}{8} x^{8} - 987 x^{7} - \frac{252329}{6} x^{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x"," ",0,"121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*x^3 + 3672*x^2 + 864*x","A",0
1276,1,49,0,1.640049," ","integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm=""fricas"")","4050 x^{10} + 15600 x^{9} + \frac{175365}{8} x^{8} + \frac{66873}{7} x^{7} - \frac{46885}{6} x^{6} - \frac{52853}{5} x^{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x"," ",0,"4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^2 + 432*x","A",0
1277,1,44,0,1.537502," ","integrate((1-2*x)^2*(2+3*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","1500 x^{9} + 4725 x^{8} + \frac{33255}{7} x^{7} + \frac{121}{6} x^{6} - \frac{15709}{5} x^{5} - \frac{7145}{4} x^{4} + 258 x^{3} + 594 x^{2} + 216 x"," ",0,"1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x","A",0
1278,1,39,0,1.244958," ","integrate((1-2*x)^2*(2+3*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1125}{2} x^{8} + \frac{9600}{7} x^{7} + \frac{4685}{6} x^{6} - \frac{3083}{5} x^{5} - \frac{3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x"," ",0,"1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x","A",0
1279,1,34,0,1.584027," ","integrate((1-2*x)^2*(2+3*x)*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1500}{7} x^{7} + \frac{1100}{3} x^{6} + 19 x^{5} - \frac{1091}{4} x^{4} - 111 x^{3} + \frac{135}{2} x^{2} + 54 x"," ",0,"1500/7*x^7 + 1100/3*x^6 + 19*x^5 - 1091/4*x^4 - 111*x^3 + 135/2*x^2 + 54*x","A",0
1280,1,29,0,1.171645," ","integrate((1-2*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","\frac{250}{3} x^{6} + 80 x^{5} - \frac{235}{4} x^{4} - 69 x^{3} + \frac{27}{2} x^{2} + 27 x"," ",0,"250/3*x^6 + 80*x^5 - 235/4*x^4 - 69*x^3 + 27/2*x^2 + 27*x","A",0
1281,1,32,0,0.687577," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x),x, algorithm=""fricas"")","\frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log\left(3 \, x + 2\right)"," ",0,"100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(3*x + 2)","A",0
1282,1,47,0,1.680958," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","\frac{60750 \, x^{5} - 2700 \, x^{4} - 53505 \, x^{3} + 6408 \, x^{2} + 1526 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 15252 \, x + 98}{1458 \, {\left(3 \, x + 2\right)}}"," ",0,"1/1458*(60750*x^5 - 2700*x^4 - 53505*x^3 + 6408*x^2 + 1526*(3*x + 2)*log(3*x + 2) + 15252*x + 98)/(3*x + 2)","A",0
1283,1,57,0,1.292555," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","\frac{81000 \, x^{5} - 37800 \, x^{4} - 13410 \, x^{3} + 128520 \, x^{2} - 8198 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 59862 \, x - 3003}{1458 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/1458*(81000*x^5 - 37800*x^4 - 13410*x^3 + 128520*x^2 - 8198*(9*x^2 + 12*x + 4)*log(3*x + 2) + 59862*x - 3003)/(9*x^2 + 12*x + 4)","A",0
1284,1,67,0,1.376704," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","\frac{364500 \, x^{5} - 631800 \, x^{4} - 2235600 \, x^{3} - 1485054 \, x^{2} + 49710 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 114939 \, x + 93896}{4374 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/4374*(364500*x^5 - 631800*x^4 - 2235600*x^3 - 1485054*x^2 + 49710*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 114939*x + 93896)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1285,1,77,0,1.299457," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","\frac{1458000 \, x^{5} + 3888000 \, x^{4} + 1203660 \, x^{3} - 3419334 \, x^{2} - 45600 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) - 3005148 \, x - 702941}{8748 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/8748*(1458000*x^5 + 3888000*x^4 + 1203660*x^3 - 3419334*x^2 - 45600*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) - 3005148*x - 702941)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1286,1,82,0,1.613504," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","\frac{18468000 \, x^{4} + 42537150 \, x^{3} + 36564120 \, x^{2} + 30000 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 13889625 \, x + 1965218}{43740 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/43740*(18468000*x^4 + 42537150*x^3 + 36564120*x^2 + 30000*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 13889625*x + 1965218)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1287,1,59,0,1.599194," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{7290000 \, x^{5} + 15066000 \, x^{4} + 12249900 \, x^{3} + 5370435 \, x^{2} + 1510848 \, x + 233482}{43740 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/43740*(7290000*x^5 + 15066000*x^4 + 12249900*x^3 + 5370435*x^2 + 1510848*x + 233482)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1288,1,64,0,1.427371," ","integrate((1-2*x)^2*(3+5*x)^3/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{3645000 \, x^{5} + 5994000 \, x^{4} + 3139425 \, x^{3} + 652158 \, x^{2} + 210534 \, x + 76288}{43740 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/43740*(3645000*x^5 + 5994000*x^4 + 3139425*x^3 + 652158*x^2 + 210534*x + 76288)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1289,1,52,0,0.966643," ","integrate((1-2*x)^2*(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \log\left(5 \, x + 3\right)"," ",0,"972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/15625*x^5 - 20577159/62500*x^4 + 1327159/78125*x^3 + 80555569/781250*x^2 + 83333293/1953125*x + 121/9765625*log(5*x + 3)","A",0
1290,1,47,0,1.584956," ","integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \log\left(5 \, x + 3\right)"," ",0,"729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/156250*x^2 + 8333293/390625*x + 121/1953125*log(5*x + 3)","A",0
1291,1,42,0,1.253682," ","integrate((1-2*x)^2*(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{972}{35} \, x^{7} + \frac{1404}{25} \, x^{6} + \frac{7803}{625} \, x^{5} - \frac{102159}{2500} \, x^{4} - \frac{72841}{3125} \, x^{3} + \frac{305569}{31250} \, x^{2} + \frac{833293}{78125} \, x + \frac{121}{390625} \, \log\left(5 \, x + 3\right)"," ",0,"972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x + 121/390625*log(5*x + 3)","A",0
1292,1,37,0,1.278323," ","integrate((1-2*x)^2*(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{54}{5} \, x^{6} + \frac{1728}{125} \, x^{5} - \frac{3159}{500} \, x^{4} - \frac{7841}{625} \, x^{3} + \frac{5569}{6250} \, x^{2} + \frac{83293}{15625} \, x + \frac{121}{78125} \, \log\left(5 \, x + 3\right)"," ",0,"54/5*x^6 + 1728/125*x^5 - 3159/500*x^4 - 7841/625*x^3 + 5569/6250*x^2 + 83293/15625*x + 121/78125*log(5*x + 3)","A",0
1293,1,32,0,1.731576," ","integrate((1-2*x)^2*(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{108}{25} \, x^{5} + \frac{54}{25} \, x^{4} - \frac{591}{125} \, x^{3} - \frac{1931}{1250} \, x^{2} + \frac{8293}{3125} \, x + \frac{121}{15625} \, \log\left(5 \, x + 3\right)"," ",0,"108/25*x^5 + 54/25*x^4 - 591/125*x^3 - 1931/1250*x^2 + 8293/3125*x + 121/15625*log(5*x + 3)","A",0
1294,1,27,0,1.318128," ","integrate((1-2*x)^2*(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{9}{5} \, x^{4} - \frac{16}{25} \, x^{3} - \frac{431}{250} \, x^{2} + \frac{793}{625} \, x + \frac{121}{3125} \, \log\left(5 \, x + 3\right)"," ",0,"9/5*x^4 - 16/25*x^3 - 431/250*x^2 + 793/625*x + 121/3125*log(5*x + 3)","A",0
1295,1,22,0,1.515065," ","integrate((1-2*x)^2*(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log\left(5 \, x + 3\right)"," ",0,"4/5*x^3 - 28/25*x^2 + 43/125*x + 121/625*log(5*x + 3)","A",0
1296,1,17,0,1.502622," ","integrate((1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log\left(5 \, x + 3\right)"," ",0,"2/5*x^2 - 32/25*x + 121/125*log(5*x + 3)","A",0
1297,1,20,0,1.501059," ","integrate((1-2*x)^2/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{4}{15} \, x + \frac{121}{25} \, \log\left(5 \, x + 3\right) - \frac{49}{9} \, \log\left(3 \, x + 2\right)"," ",0,"4/15*x + 121/25*log(5*x + 3) - 49/9*log(3*x + 2)","A",0
1298,1,37,0,1.326596," ","integrate((1-2*x)^2/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{1089 \, {\left(3 \, x + 2\right)} \log\left(5 \, x + 3\right) - 1085 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 245}{45 \, {\left(3 \, x + 2\right)}}"," ",0,"1/45*(1089*(3*x + 2)*log(5*x + 3) - 1085*(3*x + 2)*log(3*x + 2) + 245)/(3*x + 2)","A",0
1299,1,55,0,1.306687," ","integrate((1-2*x)^2/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{2178 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x + 3\right) - 2178 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 1302 \, x + 917}{18 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/18*(2178*(9*x^2 + 12*x + 4)*log(5*x + 3) - 2178*(9*x^2 + 12*x + 4)*log(3*x + 2) + 1302*x + 917)/(9*x^2 + 12*x + 4)","A",0
1300,1,75,0,0.811210," ","integrate((1-2*x)^2/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{58806 \, x^{2} + 32670 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(5 \, x + 3\right) - 32670 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 80361 \, x + 27536}{54 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/54*(58806*x^2 + 32670*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 32670*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 80361*x + 27536)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1301,1,95,0,1.376254," ","integrate((1-2*x)^2/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{1764180 \, x^{3} + 3587166 \, x^{2} + 326700 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(5 \, x + 3\right) - 326700 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 2433252 \, x + 550739}{108 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/108*(1764180*x^3 + 3587166*x^2 + 326700*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(5*x + 3) - 326700*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 2433252*x + 550739)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1302,1,115,0,1.100827," ","integrate((1-2*x)^2/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{44104500 \, x^{4} + 119082150 \, x^{3} + 120617640 \, x^{2} + 2722500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(5 \, x + 3\right) - 2722500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 54322575 \, x + 9179006}{180 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/180*(44104500*x^4 + 119082150*x^3 + 120617640*x^2 + 2722500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(5*x + 3) - 2722500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 54322575*x + 9179006)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1303,1,135,0,1.338197," ","integrate((1-2*x)^2/(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 40837500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(5 \, x + 3\right) - 40837500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 2042732232 \, x + 275370238}{540 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/540*(1984702500*x^5 + 6681831750*x^4 + 9000258300*x^3 + 6063045615*x^2 + 40837500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(5*x + 3) - 40837500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 2042732232*x + 275370238)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1304,1,155,0,1.234527," ","integrate((1-2*x)^2/(2+3*x)^8/(3+5*x),x, algorithm=""fricas"")","\frac{29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 204187500 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(5 \, x + 3\right) - 204187500 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(3 \, x + 2\right) + 24557875626 \, x + 2753702432}{540 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/540*(29770537500*x^6 + 120074501250*x^5 + 201822192000*x^4 + 180948267225*x^3 + 91271440062*x^2 + 204187500*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(5*x + 3) - 204187500*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 24557875626*x + 2753702432)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1305,1,67,0,1.132403," ","integrate((1-2*x)^2*(2+3*x)^7/(3+5*x)^2,x, algorithm=""fricas"")","\frac{59800781250 \, x^{9} + 204461718750 \, x^{8} + 228457968750 \, x^{7} + 18948431250 \, x^{6} - 151420775625 \, x^{5} - 96641724375 \, x^{4} + 14907569250 \, x^{3} + 37916375350 \, x^{2} + 69916 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 11666311440 \, x - 3388}{273437500 \, {\left(5 \, x + 3\right)}}"," ",0,"1/273437500*(59800781250*x^9 + 204461718750*x^8 + 228457968750*x^7 + 18948431250*x^6 - 151420775625*x^5 - 96641724375*x^4 + 14907569250*x^3 + 37916375350*x^2 + 69916*(5*x + 3)*log(5*x + 3) + 11666311440*x - 3388)/(5*x + 3)","A",0
1306,1,62,0,1.346572," ","integrate((1-2*x)^2*(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","\frac{2278125000 \, x^{8} + 6150937500 \, x^{7} + 4135556250 \, x^{6} - 2688406875 \, x^{5} - 4202218125 \, x^{4} - 469838250 \, x^{3} + 1458208850 \, x^{2} + 29876 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 583181130 \, x - 1694}{27343750 \, {\left(5 \, x + 3\right)}}"," ",0,"1/27343750*(2278125000*x^8 + 6150937500*x^7 + 4135556250*x^6 - 2688406875*x^5 - 4202218125*x^4 - 469838250*x^3 + 1458208850*x^2 + 29876*(5*x + 3)*log(5*x + 3) + 583181130*x - 1694)/(5*x + 3)","A",0
1307,1,57,0,1.388830," ","integrate((1-2*x)^2*(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","\frac{50625000 \, x^{7} + 99225000 \, x^{6} + 14056875 \, x^{5} - 79681875 \, x^{4} - 35631750 \, x^{3} + 29137150 \, x^{2} + 7084 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 16630440 \, x - 484}{1562500 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1562500*(50625000*x^7 + 99225000*x^6 + 14056875*x^5 - 79681875*x^4 - 35631750*x^3 + 29137150*x^2 + 7084*(5*x + 3)*log(5*x + 3) + 16630440*x - 484)/(5*x + 3)","A",0
1308,1,52,0,1.158790," ","integrate((1-2*x)^2*(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{1012500 \, x^{6} + 1198125 \, x^{5} - 776250 \, x^{4} - 1131000 \, x^{3} + 410800 \, x^{2} + 1408 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 409425 \, x - 121}{78125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/78125*(1012500*x^6 + 1198125*x^5 - 776250*x^4 - 1131000*x^3 + 410800*x^2 + 1408*(5*x + 3)*log(5*x + 3) + 409425*x - 121)/(5*x + 3)","A",0
1309,1,47,0,1.171131," ","integrate((1-2*x)^2*(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{168750 \, x^{5} + 56250 \, x^{4} - 208125 \, x^{3} + 12125 \, x^{2} + 2090 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 72480 \, x - 242}{31250 \, {\left(5 \, x + 3\right)}}"," ",0,"1/31250*(168750*x^5 + 56250*x^4 - 208125*x^3 + 12125*x^2 + 2090*(5*x + 3)*log(5*x + 3) + 72480*x - 242)/(5*x + 3)","A",0
1310,1,42,0,1.274733," ","integrate((1-2*x)^2*(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{7500 \, x^{4} - 5250 \, x^{3} - 4925 \, x^{2} + 682 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 555 \, x - 121}{3125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/3125*(7500*x^4 - 5250*x^3 - 4925*x^2 + 682*(5*x + 3)*log(5*x + 3) + 555*x - 121)/(5*x + 3)","A",0
1311,1,37,0,1.191352," ","integrate((1-2*x)^2*(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{750 \, x^{3} - 1850 \, x^{2} + 319 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1380 \, x - 121}{625 \, {\left(5 \, x + 3\right)}}"," ",0,"1/625*(750*x^3 - 1850*x^2 + 319*(5*x + 3)*log(5*x + 3) - 1380*x - 121)/(5*x + 3)","A",0
1312,1,32,0,1.296657," ","integrate((1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{100 \, x^{2} - 44 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 60 \, x - 121}{125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/125*(100*x^2 - 44*(5*x + 3)*log(5*x + 3) + 60*x - 121)/(5*x + 3)","A",0
1313,1,37,0,1.180867," ","integrate((1-2*x)^2/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1221 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1225 \, {\left(5 \, x + 3\right)} \log\left(3 \, x + 2\right) + 363}{75 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/75*(1221*(5*x + 3)*log(5*x + 3) - 1225*(5*x + 3)*log(3*x + 2) + 363)/(5*x + 3)","A",0
1314,1,55,0,1.297330," ","integrate((1-2*x)^2/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2310 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(5 \, x + 3\right) - 2310 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(3 \, x + 2\right) + 2314 \, x + 1461}{15 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"-1/15*(2310*(15*x^2 + 19*x + 6)*log(5*x + 3) - 2310*(15*x^2 + 19*x + 6)*log(3*x + 2) + 2314*x + 1461)/(15*x^2 + 19*x + 6)","A",0
1315,1,75,0,0.948522," ","integrate((1-2*x)^2/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{20394 \, x^{2} + 6798 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(5 \, x + 3\right) - 6798 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(3 \, x + 2\right) + 26513 \, x + 8595}{6 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"-1/6*(20394*x^2 + 6798*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 6798*(45*x^3 + 87*x^2 + 56*x + 12)*log(3*x + 2) + 26513*x + 8595)/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1316,1,95,0,0.893601," ","integrate((1-2*x)^2/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{605880 \, x^{3} + 1191564 \, x^{2} + 67320 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(5 \, x + 3\right) - 67320 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(3 \, x + 2\right) + 780464 \, x + 170229}{9 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"-1/9*(605880*x^3 + 1191564*x^2 + 67320*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(5*x + 3) - 67320*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) + 780464*x + 170229)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1317,1,115,0,1.373254," ","integrate((1-2*x)^2/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{5019300 \, x^{4} + 13217490 \, x^{3} + 13046462 \, x^{2} + 185900 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(5 \, x + 3\right) - 185900 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(3 \, x + 2\right) + 5720639 \, x + 940153}{4 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"-1/4*(5019300*x^4 + 13217490*x^3 + 13046462*x^2 + 185900*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(5*x + 3) - 185900*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(3*x + 2) + 5720639*x + 940153)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
1318,1,135,0,1.242923," ","integrate((1-2*x)^2/(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{674932500 \, x^{5} + 2227277250 \, x^{4} + 2939206050 \, x^{3} + 1938789435 \, x^{2} + 8332500 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(5 \, x + 3\right) - 8332500 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(3 \, x + 2\right) + 639246515 \, x + 84279984}{30 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"-1/30*(674932500*x^5 + 2227277250*x^4 + 2939206050*x^3 + 1938789435*x^2 + 8332500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(5*x + 3) - 8332500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(3*x + 2) + 639246515*x + 84279984)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","A",0
1319,1,155,0,1.182184," ","integrate((1-2*x)^2/(2+3*x)^7/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{70667437500 \, x^{6} + 280314168750 \, x^{5} + 463211966250 \, x^{4} + 408159415125 \, x^{3} + 202262350455 \, x^{2} + 290812500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(5 \, x + 3\right) - 290812500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(3 \, x + 2\right) + 53445037346 \, x + 5882909754}{180 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)}}"," ",0,"-1/180*(70667437500*x^6 + 280314168750*x^5 + 463211966250*x^4 + 408159415125*x^3 + 202262350455*x^2 + 290812500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(5*x + 3) - 290812500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*x + 2) + 53445037346*x + 5882909754)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)","A",0
1320,1,175,0,1.238292," ","integrate((1-2*x)^2/(2+3*x)^8/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{100738687500 \, x^{7} + 466755918750 \, x^{6} + 926721303750 \, x^{5} + 1022059900125 \, x^{4} + 676227617505 \, x^{3} + 268408563588 \, x^{2} + 138187500 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)} \log\left(5 \, x + 3\right) - 138187500 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)} \log\left(3 \, x + 2\right) + 59178013234 \, x + 5590850403}{15 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)}}"," ",0,"-1/15*(100738687500*x^7 + 466755918750*x^6 + 926721303750*x^5 + 1022059900125*x^4 + 676227617505*x^3 + 268408563588*x^2 + 138187500*(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)*log(5*x + 3) - 138187500*(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)*log(3*x + 2) + 59178013234*x + 5590850403)/(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)","A",0
1321,1,82,0,0.880341," ","integrate((1-2*x)^2*(2+3*x)^8/(3+5*x)^3,x, algorithm=""fricas"")","\frac{448505859375 \, x^{10} + 1836738281250 \, x^{9} + 2748937500000 \, x^{8} + 1294582500000 \, x^{7} - 1049233500000 \, x^{6} - 1497169800000 \, x^{5} - 372682800000 \, x^{4} + 369438720000 \, x^{3} + 281928652425 \, x^{2} + 412160 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 58326747710 \, x - 120967}{683593750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/683593750*(448505859375*x^10 + 1836738281250*x^9 + 2748937500000*x^8 + 1294582500000*x^7 - 1049233500000*x^6 - 1497169800000*x^5 - 372682800000*x^4 + 369438720000*x^3 + 281928652425*x^2 + 412160*(25*x^2 + 30*x + 9)*log(5*x + 3) + 58326747710*x - 120967)/(25*x^2 + 30*x + 9)","A",0
1322,1,77,0,1.192829," ","integrate((1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x, algorithm=""fricas"")","\frac{68343750000 \, x^{9} + 230850000000 \, x^{8} + 248816812500 \, x^{7} + 2308753125 \, x^{6} - 181926753750 \, x^{5} - 99203619375 \, x^{4} + 35963686500 \, x^{3} + 47615255100 \, x^{2} + 614572 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 11656743280 \, x - 211442}{273437500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/273437500*(68343750000*x^9 + 230850000000*x^8 + 248816812500*x^7 + 2308753125*x^6 - 181926753750*x^5 - 99203619375*x^4 + 35963686500*x^3 + 47615255100*x^2 + 614572*(25*x^2 + 30*x + 9)*log(5*x + 3) + 11656743280*x - 211442)/(25*x^2 + 30*x + 9)","A",0
1323,1,72,0,1.092642," ","integrate((1-2*x)^2*(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","\frac{759375000 \, x^{8} + 2004750000 \, x^{7} + 1217278125 \, x^{6} - 1066983750 \, x^{5} - 1352649375 \, x^{4} + 96358500 \, x^{3} + 553151700 \, x^{2} + 62188 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 165647680 \, x - 25850}{7812500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/7812500*(759375000*x^8 + 2004750000*x^7 + 1217278125*x^6 - 1066983750*x^5 - 1352649375*x^4 + 96358500*x^3 + 553151700*x^2 + 62188*(25*x^2 + 30*x + 9)*log(5*x + 3) + 165647680*x - 25850)/(25*x^2 + 30*x + 9)","A",0
1324,1,67,0,1.191263," ","integrate((1-2*x)^2*(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{30375000 \, x^{7} + 56700000 \, x^{6} + 866250 \, x^{5} - 50518125 \, x^{4} - 10006500 \, x^{3} + 20730375 \, x^{2} + 20468 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 7990490 \, x - 10747}{781250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/781250*(30375000*x^7 + 56700000*x^6 + 866250*x^5 - 50518125*x^4 - 10006500*x^3 + 20730375*x^2 + 20468*(25*x^2 + 30*x + 9)*log(5*x + 3) + 7990490*x - 10747)/(25*x^2 + 30*x + 9)","A",0
1325,1,62,0,1.185377," ","integrate((1-2*x)^2*(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2531250 \, x^{6} + 2587500 \, x^{5} - 2615625 \, x^{4} - 1972500 \, x^{3} + 1053225 \, x^{2} + 12020 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 624470 \, x - 8569}{156250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/156250*(2531250*x^6 + 2587500*x^5 - 2615625*x^4 - 1972500*x^3 + 1053225*x^2 + 12020*(25*x^2 + 30*x + 9)*log(5*x + 3) + 624470*x - 8569)/(25*x^2 + 30*x + 9)","A",0
1326,1,52,0,1.048478," ","integrate((1-2*x)^2*(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{225000 \, x^{5} - 281250 \, x^{3} - 143100 \, x^{2} + 5750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 24220 \, x - 6391}{31250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/31250*(225000*x^5 - 281250*x^3 - 143100*x^2 + 5750*(25*x^2 + 30*x + 9)*log(5*x + 3) - 24220*x - 6391)/(25*x^2 + 30*x + 9)","A",0
1327,1,52,0,1.209549," ","integrate((1-2*x)^2*(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{22500 \, x^{4} - 39000 \, x^{3} - 71100 \, x^{2} + 1658 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 30580 \, x - 4213}{6250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/6250*(22500*x^4 - 39000*x^3 - 71100*x^2 + 1658*(25*x^2 + 30*x + 9)*log(5*x + 3) - 30580*x - 4213)/(25*x^2 + 30*x + 9)","A",0
1328,1,47,0,1.220623," ","integrate((1-2*x)^2*(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3000 \, x^{3} + 3600 \, x^{2} - 256 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 2110 \, x - 2035}{1250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1250*(3000*x^3 + 3600*x^2 - 256*(25*x^2 + 30*x + 9)*log(5*x + 3) - 2110*x - 2035)/(25*x^2 + 30*x + 9)","A",0
1329,1,37,0,1.198785," ","integrate((1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 440 \, x + 143}{250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/250*(8*(25*x^2 + 30*x + 9)*log(5*x + 3) + 440*x + 143)/(25*x^2 + 30*x + 9)","A",0
1330,1,55,0,1.281696," ","integrate((1-2*x)^2/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2450 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 2450 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(3 \, x + 2\right) + 4070 \, x + 2321}{50 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/50*(2450*(25*x^2 + 30*x + 9)*log(5*x + 3) - 2450*(25*x^2 + 30*x + 9)*log(3*x + 2) + 4070*x + 2321)/(25*x^2 + 30*x + 9)","A",0
1331,1,75,0,1.134093," ","integrate((1-2*x)^2/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{35350 \, x^{2} + 7070 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(5 \, x + 3\right) - 7070 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(3 \, x + 2\right) + 43597 \, x + 13408}{10 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/10*(35350*x^2 + 7070*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 7070*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) + 43597*x + 13408)/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1332,1,95,0,1.343994," ","integrate((1-2*x)^2/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{208020 \, x^{3} + 395238 \, x^{2} + 13868 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(5 \, x + 3\right) - 13868 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(3 \, x + 2\right) + 249932 \, x + 52601}{2 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/2*(208020*x^3 + 395238*x^2 + 13868*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(5*x + 3) - 13868*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 249932*x + 52601)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1333,1,115,0,1.186093," ","integrate((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 342660 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(5 \, x + 3\right) - 342660 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(3 \, x + 2\right) + 16250079 \, x + 2599404}{6 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/6*(15419700*x^4 + 39577230*x^3 + 38058104*x^2 + 342660*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(5*x + 3) - 342660*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) + 16250079*x + 2599404)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
1334,1,135,0,1.179324," ","integrate((1-2*x)^2/(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{688459500 \, x^{5} + 2226019050 \, x^{4} + 2877250740 \, x^{3} + 1858347679 \, x^{2} + 5099700 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(5 \, x + 3\right) - 5099700 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(3 \, x + 2\right) + 599747838 \, x + 77372211}{12 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"1/12*(688459500*x^5 + 2226019050*x^4 + 2877250740*x^3 + 1858347679*x^2 + 5099700*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5*x + 3) - 5099700*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(3*x + 2) + 599747838*x + 77372211)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","A",0
1335,1,155,0,0.992677," ","integrate((1-2*x)^2/(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","\frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 177487500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(5 \, x + 3\right) - 177487500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(3 \, x + 2\right) + 49825144515 \, x + 5385650262}{60 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)}}"," ",0,"1/60*(71882437500*x^6 + 280341506250*x^5 + 455361930000*x^4 + 394308004875*x^3 + 191974077080*x^2 + 177487500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(5*x + 3) - 177487500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(3*x + 2) + 49825144515*x + 5385650262)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)","A",0
1336,1,175,0,1.063723," ","integrate((1-2*x)^2/(2+3*x)^7/(3+5*x)^3,x, algorithm=""fricas"")","\frac{238595625000 \, x^{7} + 1089586687500 \, x^{6} + 2131807725000 \, x^{5} + 2316445391250 \, x^{4} + 1509746867100 \, x^{3} + 590188362770 \, x^{2} + 196375000 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)} \log\left(5 \, x + 3\right) - 196375000 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)} \log\left(3 \, x + 2\right) + 128130976648 \, x + 11917538647}{10 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)}}"," ",0,"1/10*(238595625000*x^7 + 1089586687500*x^6 + 2131807725000*x^5 + 2316445391250*x^4 + 1509746867100*x^3 + 590188362770*x^2 + 196375000*(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log(5*x + 3) - 196375000*(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log(3*x + 2) + 128130976648*x + 11917538647)/(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)","A",0
1337,1,195,0,1.279006," ","integrate((1-2*x)^2/(2+3*x)^8/(3+5*x)^3,x, algorithm=""fricas"")","\frac{4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1258250000 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)} \log\left(5 \, x + 3\right) - 1258250000 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)} \log\left(3 \, x + 2\right) + 1871049429619 \, x + 152720488888}{10 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)}}"," ",0,"1/10*(4586321250000*x^8 + 24001747875000*x^7 + 54940731300000*x^6 + 71845684942500*x^5 + 58705292494800*x^4 + 30691745453460*x^3 + 10026079791288*x^2 + 1258250000*(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)*log(5*x + 3) - 1258250000*(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)*log(3*x + 2) + 1871049429619*x + 152720488888)/(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)","A",0
1338,1,64,0,1.062171," ","integrate((1-2*x)^3*(2+3*x)^8*(3+5*x),x, algorithm=""fricas"")","-\frac{262440}{13} x^{13} - 96957 x^{12} - \frac{1966842}{11} x^{11} - \frac{1290573}{10} x^{10} + 38331 x^{9} + 128412 x^{8} + 67248 x^{7} - 17456 x^{6} - \frac{159712}{5} x^{5} - 9216 x^{4} + 3328 x^{3} + 2944 x^{2} + 768 x"," ",0,"-262440/13*x^13 - 96957*x^12 - 1966842/11*x^11 - 1290573/10*x^10 + 38331*x^9 + 128412*x^8 + 67248*x^7 - 17456*x^6 - 159712/5*x^5 - 9216*x^4 + 3328*x^3 + 2944*x^2 + 768*x","A",0
1339,1,59,0,0.700271," ","integrate((1-2*x)^3*(2+3*x)^7*(3+5*x),x, algorithm=""fricas"")","-7290 x^{12} - \frac{329508}{11} x^{11} - \frac{217971}{5} x^{10} - 15507 x^{9} + \frac{208035}{8} x^{8} + 29106 x^{7} + 3514 x^{6} - \frac{48968}{5} x^{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x"," ",0,"-7290*x^12 - 329508/11*x^11 - 217971/5*x^10 - 15507*x^9 + 208035/8*x^8 + 29106*x^7 + 3514*x^6 - 48968/5*x^5 - 5148*x^4 + 480*x^3 + 1184*x^2 + 384*x","A",0
1340,1,54,0,0.523874," ","integrate((1-2*x)^3*(2+3*x)^6*(3+5*x),x, algorithm=""fricas"")","-\frac{29160}{11} x^{11} - \frac{45198}{5} x^{10} - 9450 x^{9} + \frac{10179}{8} x^{8} + 8937 x^{7} + 4368 x^{6} - \frac{10444}{5} x^{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x"," ",0,"-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 10444/5*x^5 - 2340*x^4 - 208*x^3 + 448*x^2 + 192*x","A",0
1341,1,49,0,0.897726," ","integrate((1-2*x)^3*(2+3*x)^5*(3+5*x),x, algorithm=""fricas"")","-972 x^{10} - 2628 x^{9} - \frac{6291}{4} x^{8} + 1683 x^{7} + \frac{4333}{2} x^{6} + 14 x^{5} - 882 x^{4} - 256 x^{3} + 152 x^{2} + 96 x"," ",0,"-972*x^10 - 2628*x^9 - 6291/4*x^8 + 1683*x^7 + 4333/2*x^6 + 14*x^5 - 882*x^4 - 256*x^3 + 152*x^2 + 96*x","A",0
1342,1,44,0,1.145085," ","integrate((1-2*x)^3*(2+3*x)^4*(3+5*x),x, algorithm=""fricas"")","-360 x^{9} - \frac{1431}{2} x^{8} - 54 x^{7} + \frac{1393}{2} x^{6} + \frac{1547}{5} x^{5} - 252 x^{4} - 168 x^{3} + 40 x^{2} + 48 x"," ",0,"-360*x^9 - 1431/2*x^8 - 54*x^7 + 1393/2*x^6 + 1547/5*x^5 - 252*x^4 - 168*x^3 + 40*x^2 + 48*x","A",0
1343,1,39,0,0.797125," ","integrate((1-2*x)^3*(2+3*x)^3*(3+5*x),x, algorithm=""fricas"")","-135 x^{8} - \frac{1188}{7} x^{7} + 111 x^{6} + \frac{949}{5} x^{5} - \frac{117}{4} x^{4} - 86 x^{3} + 2 x^{2} + 24 x"," ",0,"-135*x^8 - 1188/7*x^7 + 111*x^6 + 949/5*x^5 - 117/4*x^4 - 86*x^3 + 2*x^2 + 24*x","A",0
1344,1,34,0,0.923310," ","integrate((1-2*x)^3*(2+3*x)^2*(3+5*x),x, algorithm=""fricas"")","-\frac{360}{7} x^{7} - 26 x^{6} + \frac{326}{5} x^{5} + \frac{99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x"," ",0,"-360/7*x^7 - 26*x^6 + 326/5*x^5 + 99/4*x^4 - 35*x^3 - 8*x^2 + 12*x","A",0
1345,1,29,0,1.105610," ","integrate((1-2*x)^3*(2+3*x)*(3+5*x),x, algorithm=""fricas"")","-20 x^{6} + \frac{28}{5} x^{5} + \frac{45}{2} x^{4} - 9 x^{3} - \frac{17}{2} x^{2} + 6 x"," ",0,"-20*x^6 + 28/5*x^5 + 45/2*x^4 - 9*x^3 - 17/2*x^2 + 6*x","A",0
1346,1,24,0,0.912848," ","integrate((1-2*x)^3*(3+5*x),x, algorithm=""fricas"")","-8 x^{5} + 9 x^{4} + 2 x^{3} - \frac{13}{2} x^{2} + 3 x"," ",0,"-8*x^5 + 9*x^4 + 2*x^3 - 13/2*x^2 + 3*x","A",0
1347,1,27,0,0.866236," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x),x, algorithm=""fricas"")","-\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{243} \, \log\left(3 \, x + 2\right)"," ",0,"-10/3*x^4 + 188/27*x^3 - 161/27*x^2 + 293/81*x - 343/243*log(3*x + 2)","A",0
1348,1,42,0,1.131038," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{1080 \, x^{4} - 2898 \, x^{3} + 5310 \, x^{2} - 2009 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 5148 \, x - 343}{243 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/243*(1080*x^4 - 2898*x^3 + 5310*x^2 - 2009*(3*x + 2)*log(3*x + 2) + 5148*x - 343)/(3*x + 2)","A",0
1349,1,52,0,1.182006," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{3240 \, x^{4} - 14472 \, x^{3} - 23616 \, x^{2} + 3108 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 3702 \, x + 7693}{486 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/486*(3240*x^4 - 14472*x^3 - 23616*x^2 + 3108*(9*x^2 + 12*x + 4)*log(3*x + 2) + 3702*x + 7693)/(9*x^2 + 12*x + 4)","A",0
1350,1,62,0,0.927882," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{19440 \, x^{4} + 38880 \, x^{3} - 57996 \, x^{2} - 2568 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 88047 \, x - 25928}{1458 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/1458*(19440*x^4 + 38880*x^3 - 57996*x^2 - 2568*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 88047*x - 25928)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1351,1,67,0,1.146410," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{138672 \, x^{3} + 193428 \, x^{2} + 480 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 97116 \, x + 18835}{2916 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/2916*(138672*x^3 + 193428*x^2 + 480*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 97116*x + 18835)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1352,1,49,0,1.317771," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/4860*(64800*x^4 + 57240*x^3 + 34920*x^2 + 16905*x + 1282)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1353,1,54,0,1.191755," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^7,x, algorithm=""fricas"")","\frac{48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/7290*(48600*x^4 + 14040*x^3 + 3375*x^2 + 7218*x - 413)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1354,1,59,0,1.102962," ","integrate((1-2*x)^3*(3+5*x)/(2+3*x)^8,x, algorithm=""fricas"")","\frac{32400 \, x^{4} - 270 \, x^{3} - 3024 \, x^{2} + 4593 \, x - 604}{7290 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/7290*(32400*x^4 - 270*x^3 - 3024*x^2 + 4593*x - 604)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1355,1,69,0,0.979084," ","integrate((1-2*x)^3*(2+3*x)^8*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{656100}{7} x^{14} - \frac{6604740}{13} x^{13} - \frac{2220777}{2} x^{12} - \frac{12353391}{11} x^{11} - \frac{1073412}{5} x^{10} + 685713 x^{9} + 679446 x^{8} + \frac{888528}{7} x^{7} - \frac{556384}{3} x^{6} - \frac{663456}{5} x^{5} - 15168 x^{4} + \frac{59392}{3} x^{3} + 10752 x^{2} + 2304 x"," ",0,"-656100/7*x^14 - 6604740/13*x^13 - 2220777/2*x^12 - 12353391/11*x^11 - 1073412/5*x^10 + 685713*x^9 + 679446*x^8 + 888528/7*x^7 - 556384/3*x^6 - 663456/5*x^5 - 15168*x^4 + 59392/3*x^3 + 10752*x^2 + 2304*x","A",0
1356,1,64,0,0.860342," ","integrate((1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{437400}{13} x^{13} - 159165 x^{12} - \frac{3168234}{11} x^{11} - \frac{2005641}{10} x^{10} + 69054 x^{9} + \frac{1642815}{8} x^{8} + 102378 x^{7} - \frac{90794}{3} x^{6} - \frac{249864}{5} x^{5} - 13644 x^{4} + \frac{16160}{3} x^{3} + 4512 x^{2} + 1152 x"," ",0,"-437400/13*x^13 - 159165*x^12 - 3168234/11*x^11 - 2005641/10*x^10 + 69054*x^9 + 1642815/8*x^8 + 102378*x^7 - 90794/3*x^6 - 249864/5*x^5 - 13644*x^4 + 16160/3*x^3 + 4512*x^2 + 1152*x","A",0
1357,1,59,0,1.076602," ","integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x, algorithm=""fricas"")","-12150 x^{12} - \frac{539460}{11} x^{11} - \frac{348219}{5} x^{10} - 22695 x^{9} + \frac{85833}{2} x^{8} + 45531 x^{7} + \frac{13202}{3} x^{6} - \frac{78132}{5} x^{5} - 7800 x^{4} + \frac{2608}{3} x^{3} + 1824 x^{2} + 576 x"," ",0,"-12150*x^12 - 539460/11*x^11 - 348219/5*x^10 - 22695*x^9 + 85833/2*x^8 + 45531*x^7 + 13202/3*x^6 - 78132/5*x^5 - 7800*x^4 + 2608/3*x^3 + 1824*x^2 + 576*x","A",0
1358,1,54,0,0.963416," ","integrate((1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{48600}{11} x^{11} - 14742 x^{10} - 14874 x^{9} + \frac{21159}{8} x^{8} + 14334 x^{7} + \frac{39347}{6} x^{6} - 3486 x^{5} - 3606 x^{4} - \frac{784}{3} x^{3} + 696 x^{2} + 288 x"," ",0,"-48600/11*x^11 - 14742*x^10 - 14874*x^9 + 21159/8*x^8 + 14334*x^7 + 39347/6*x^6 - 3486*x^5 - 3606*x^4 - 784/3*x^3 + 696*x^2 + 288*x","A",0
1359,1,49,0,1.032759," ","integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm=""fricas"")","-1620 x^{10} - 4260 x^{9} - \frac{9531}{4} x^{8} + 2823 x^{7} + \frac{10136}{3} x^{6} - \frac{399}{5} x^{5} - 1386 x^{4} - \frac{1112}{3} x^{3} + 240 x^{2} + 144 x"," ",0,"-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 144*x","A",0
1360,1,44,0,1.116678," ","integrate((1-2*x)^3*(2+3*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","-600 x^{9} - \frac{2295}{2} x^{8} - \frac{234}{7} x^{7} + \frac{6743}{6} x^{6} + \frac{2262}{5} x^{5} - \frac{1641}{4} x^{4} - \frac{754}{3} x^{3} + 66 x^{2} + 72 x"," ",0,"-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x","A",0
1361,1,39,0,1.147836," ","integrate((1-2*x)^3*(2+3*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","-225 x^{8} - \frac{1860}{7} x^{7} + \frac{581}{3} x^{6} + \frac{1473}{5} x^{5} - 57 x^{4} - \frac{395}{3} x^{3} + 6 x^{2} + 36 x"," ",0,"-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x","A",0
1362,1,34,0,1.020764," ","integrate((1-2*x)^3*(2+3*x)*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{600}{7} x^{7} - \frac{110}{3} x^{6} + \frac{534}{5} x^{5} + \frac{135}{4} x^{4} - \frac{166}{3} x^{3} - \frac{21}{2} x^{2} + 18 x"," ",0,"-600/7*x^7 - 110/3*x^6 + 534/5*x^5 + 135/4*x^4 - 166/3*x^3 - 21/2*x^2 + 18*x","A",0
1363,1,29,0,1.082677," ","integrate((1-2*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{100}{3} x^{6} + 12 x^{5} + \frac{69}{2} x^{4} - \frac{47}{3} x^{3} - 12 x^{2} + 9 x"," ",0,"-100/3*x^6 + 12*x^5 + 69/2*x^4 - 47/3*x^3 - 12*x^2 + 9*x","A",0
1364,1,32,0,0.776576," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x),x, algorithm=""fricas"")","-\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log\left(3 \, x + 2\right)"," ",0,"-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(3*x + 2)","A",0
1365,1,47,0,1.336942," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{12150 \, x^{5} - 18360 \, x^{4} + 7713 \, x^{3} - 4005 \, x^{2} + 3724 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 13938 \, x + 343}{729 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/729*(12150*x^5 - 18360*x^4 + 7713*x^3 - 4005*x^2 + 3724*(3*x + 2)*log(3*x + 2) - 13938*x + 343)/(3*x + 2)","A",0
1366,1,57,0,1.200632," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{32400 \, x^{5} - 68580 \, x^{4} + 115812 \, x^{3} + 284256 \, x^{2} - 23198 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 88968 \, x - 14553}{1458 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/1458*(32400*x^5 - 68580*x^4 + 115812*x^3 + 284256*x^2 - 23198*(9*x^2 + 12*x + 4)*log(3*x + 2) + 88968*x - 14553)/(9*x^2 + 12*x + 4)","A",0
1367,1,67,0,1.268628," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{72900 \, x^{5} - 286740 \, x^{4} - 767880 \, x^{3} - 241947 \, x^{2} + 24594 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 272646 \, x + 128359}{2187 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/2187*(72900*x^5 - 286740*x^4 - 767880*x^3 - 241947*x^2 + 24594*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 272646*x + 128359)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1368,1,77,0,1.746741," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{583200 \, x^{5} + 1555200 \, x^{4} - 1100952 \, x^{3} - 3994758 \, x^{2} - 26160 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) - 2635896 \, x - 537395}{8748 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/8748*(583200*x^5 + 1555200*x^4 - 1100952*x^3 - 3994758*x^2 - 26160*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) - 2635896*x - 537395)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1369,1,82,0,1.304704," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{2648700 \, x^{4} + 5403105 \, x^{3} + 4264965 \, x^{2} + 3000 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 1579785 \, x + 236399}{10935 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/10935*(2648700*x^4 + 5403105*x^3 + 4264965*x^2 + 3000*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 1579785*x + 236399)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1370,1,59,0,0.642952," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","\frac{2916000 \, x^{5} + 4422600 \, x^{4} + 3260520 \, x^{3} + 1801575 \, x^{2} + 550404 \, x + 39286}{43740 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/43740*(2916000*x^5 + 4422600*x^4 + 3260520*x^3 + 1801575*x^2 + 550404*x + 39286)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1371,1,64,0,1.064621," ","integrate((1-2*x)^3*(3+5*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","\frac{729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/21870*(729000*x^5 + 664200*x^4 + 191295*x^3 + 145044*x^2 + 61392*x - 3526)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1372,1,69,0,1.150032," ","integrate((1-2*x)^3*(2+3*x)^7*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1093500}{7} x^{14} - \frac{10862100}{13} x^{13} - \frac{3595185}{2} x^{12} - \frac{19532907}{11} x^{11} - \frac{2909493}{10} x^{10} + 1119837 x^{9} + \frac{8511675}{8} x^{8} + \frac{1241998}{7} x^{7} - 299014 x^{6} - \frac{1022472}{5} x^{5} - 20732 x^{4} + 31200 x^{3} + 16416 x^{2} + 3456 x"," ",0,"-1093500/7*x^14 - 10862100/13*x^13 - 3595185/2*x^12 - 19532907/11*x^11 - 2909493/10*x^10 + 1119837*x^9 + 8511675/8*x^8 + 1241998/7*x^7 - 299014*x^6 - 1022472/5*x^5 - 20732*x^4 + 31200*x^3 + 16416*x^2 + 3456*x","A",0
1373,1,64,0,1.155030," ","integrate((1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{729000}{13} x^{13} - 261225 x^{12} - \frac{5100570}{11} x^{11} - \frac{3110589}{10} x^{10} + 122655 x^{9} + \frac{2623581}{8} x^{8} + 155453 x^{7} - 51908 x^{6} - \frac{390396}{5} x^{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x"," ",0,"-729000/13*x^13 - 261225*x^12 - 5100570/11*x^11 - 3110589/10*x^10 + 122655*x^9 + 2623581/8*x^8 + 155453*x^7 - 51908*x^6 - 390396/5*x^5 - 20140*x^4 + 8688*x^3 + 6912*x^2 + 1728*x","A",0
1374,1,59,0,0.996416," ","integrate((1-2*x)^3*(2+3*x)^5*(3+5*x)^3,x, algorithm=""fricas"")","-20250 x^{12} - \frac{882900}{11} x^{11} - 111159 x^{10} - 32867 x^{9} + \frac{565167}{8} x^{8} + 71107 x^{7} + \frac{10297}{2} x^{6} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x"," ",0,"-20250*x^12 - 882900/11*x^11 - 111159*x^10 - 32867*x^9 + 565167/8*x^8 + 71107*x^7 + 10297/2*x^6 - 24882*x^5 - 11798*x^4 + 1536*x^3 + 2808*x^2 + 864*x","A",0
1375,1,54,0,0.891783," ","integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{81000}{11} x^{11} - 24030 x^{10} - 23370 x^{9} + \frac{41619}{8} x^{8} + 22949 x^{7} + \frac{19607}{2} x^{6} - \frac{28917}{5} x^{5} - 5548 x^{4} - 312 x^{3} + 1080 x^{2} + 432 x"," ",0,"-81000/11*x^11 - 24030*x^10 - 23370*x^9 + 41619/8*x^8 + 22949*x^7 + 19607/2*x^6 - 28917/5*x^5 - 5548*x^4 - 312*x^3 + 1080*x^2 + 432*x","A",0
1376,1,49,0,1.113037," ","integrate((1-2*x)^3*(2+3*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","-2700 x^{10} - 6900 x^{9} - \frac{14355}{4} x^{8} + \frac{33013}{7} x^{7} + \frac{10513}{2} x^{6} - \frac{1419}{5} x^{5} - \frac{8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x"," ",0,"-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2 + 216*x","A",0
1377,1,44,0,1.116317," ","integrate((1-2*x)^3*(2+3*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","-1000 x^{9} - \frac{3675}{2} x^{8} + \frac{230}{7} x^{7} + \frac{3617}{2} x^{6} + \frac{3279}{5} x^{5} - \frac{2659}{4} x^{4} - 375 x^{3} + 108 x^{2} + 108 x"," ",0,"-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x","A",0
1378,1,39,0,1.131198," ","integrate((1-2*x)^3*(2+3*x)*(3+5*x)^3,x, algorithm=""fricas"")","-375 x^{8} - \frac{2900}{7} x^{7} + 335 x^{6} + \frac{2277}{5} x^{5} - \frac{425}{4} x^{4} - 201 x^{3} + \frac{27}{2} x^{2} + 54 x"," ",0,"-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x","A",0
1379,1,34,0,0.933643," ","integrate((1-2*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1000}{7} x^{7} - 50 x^{6} + 174 x^{5} + \frac{179}{4} x^{4} - 87 x^{3} - \frac{27}{2} x^{2} + 27 x"," ",0,"-1000/7*x^7 - 50*x^6 + 174*x^5 + 179/4*x^4 - 87*x^3 - 27/2*x^2 + 27*x","A",0
1380,1,37,0,1.287799," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x),x, algorithm=""fricas"")","-\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \log\left(3 \, x + 2\right)"," ",0,"-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x - 343/2187*log(3*x + 2)","A",0
1381,1,52,0,1.735691," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{291600 \, x^{6} - 182250 \, x^{5} - 220320 \, x^{4} + 163269 \, x^{3} + 54000 \, x^{2} - 10878 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 27444 \, x - 686}{4374 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/4374*(291600*x^6 - 182250*x^5 - 220320*x^4 + 163269*x^3 + 54000*x^2 - 10878*(3*x + 2)*log(3*x + 2) - 27444*x - 686)/(3*x + 2)","A",0
1382,1,62,0,0.714489," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{364500 \, x^{6} - 340200 \, x^{5} - 67230 \, x^{4} - 81702 \, x^{3} - 782496 \, x^{2} + 60438 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 357438 \, x + 21413}{4374 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/4374*(364500*x^6 - 340200*x^5 - 67230*x^4 - 81702*x^3 - 782496*x^2 + 60438*(9*x^2 + 12*x + 4)*log(3*x + 2) - 357438*x + 21413)/(9*x^2 + 12*x + 4)","A",0
1383,1,72,0,1.327605," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{1458000 \, x^{6} - 2259900 \, x^{5} + 3727620 \, x^{4} + 17801640 \, x^{3} + 13015134 \, x^{2} - 397158 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 1468863 \, x - 693308}{13122 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/13122*(1458000*x^6 - 2259900*x^5 + 3727620*x^4 + 17801640*x^3 + 13015134*x^2 - 397158*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 1468863*x - 693308)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1384,1,82,0,1.221379," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{486000 \, x^{6} - 1652400 \, x^{5} - 6566400 \, x^{4} - 4903452 \, x^{3} + 1186182 \, x^{2} + 57560 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 2360364 \, x + 630195}{2916 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/2916*(486000*x^6 - 1652400*x^5 - 6566400*x^4 - 4903452*x^3 + 1186182*x^2 + 57560*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 2360364*x + 630195)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1385,1,92,0,1.344456," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{4860000 \, x^{6} + 16200000 \, x^{5} - 1711800 \, x^{4} - 41807430 \, x^{3} - 46054440 \, x^{2} - 74000 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) - 19824285 \, x - 3090594}{14580 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/14580*(4860000*x^6 + 16200000*x^5 - 1711800*x^4 - 41807430*x^3 - 46054440*x^2 - 74000*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) - 19824285*x - 3090594)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1386,1,97,0,1.421746," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{53946000 \, x^{5} + 144852300 \, x^{4} + 158427540 \, x^{3} + 89062425 \, x^{2} + 20000 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 25975248 \, x + 3165082}{43740 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/43740*(53946000*x^5 + 144852300*x^4 + 158427540*x^3 + 89062425*x^2 + 20000*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 25975248*x + 3165082)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1387,1,69,0,0.857929," ","integrate((1-2*x)^3*(3+5*x)^3/(2+3*x)^8,x, algorithm=""fricas"")","\frac{14580000 \, x^{6} + 31347000 \, x^{5} + 30601800 \, x^{4} + 19748745 \, x^{3} + 8660574 \, x^{2} + 1990182 \, x + 133304}{43740 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/43740*(14580000*x^6 + 31347000*x^5 + 30601800*x^4 + 19748745*x^3 + 8660574*x^2 + 1990182*x + 133304)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1388,1,52,0,1.596520," ","integrate((1-2*x)^3*(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","-\frac{648}{5} \, x^{9} - \frac{13851}{50} \, x^{8} - \frac{40338}{875} \, x^{7} + \frac{331713}{1250} \, x^{6} + \frac{2212083}{15625} \, x^{5} - \frac{5848749}{62500} \, x^{4} - \frac{17453753}{234375} \, x^{3} + \frac{11111259}{781250} \, x^{2} + \frac{41666223}{1953125} \, x + \frac{1331}{9765625} \, \log\left(5 \, x + 3\right)"," ",0,"-648/5*x^9 - 13851/50*x^8 - 40338/875*x^7 + 331713/1250*x^6 + 2212083/15625*x^5 - 5848749/62500*x^4 - 17453753/234375*x^3 + 11111259/781250*x^2 + 41666223/1953125*x + 1331/9765625*log(5*x + 3)","A",0
1389,1,47,0,1.400254," ","integrate((1-2*x)^3*(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","-\frac{243}{5} \, x^{8} - \frac{11988}{175} \, x^{7} + \frac{4419}{125} \, x^{6} + \frac{243333}{3125} \, x^{5} - \frac{73749}{12500} \, x^{4} - \frac{1703753}{46875} \, x^{3} - \frac{138741}{156250} \, x^{2} + \frac{4166223}{390625} \, x + \frac{1331}{1953125} \, \log\left(5 \, x + 3\right)"," ",0,"-243/5*x^8 - 11988/175*x^7 + 4419/125*x^6 + 243333/3125*x^5 - 73749/12500*x^4 - 1703753/46875*x^3 - 138741/156250*x^2 + 4166223/390625*x + 1331/1953125*log(5*x + 3)","A",0
1390,1,42,0,0.826889," ","integrate((1-2*x)^3*(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","-\frac{648}{35} \, x^{7} - \frac{306}{25} \, x^{6} + \frac{14958}{625} \, x^{5} + \frac{31251}{2500} \, x^{4} - \frac{128753}{9375} \, x^{3} - \frac{138741}{31250} \, x^{2} + \frac{416223}{78125} \, x + \frac{1331}{390625} \, \log\left(5 \, x + 3\right)"," ",0,"-648/35*x^7 - 306/25*x^6 + 14958/625*x^5 + 31251/2500*x^4 - 128753/9375*x^3 - 138741/31250*x^2 + 416223/78125*x + 1331/390625*log(5*x + 3)","A",0
1391,1,37,0,1.272628," ","integrate((1-2*x)^3*(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \, \log\left(5 \, x + 3\right)"," ",0,"-36/5*x^6 + 108/125*x^5 + 2313/250*x^4 - 5003/1875*x^3 - 26241/6250*x^2 + 41223/15625*x + 1331/78125*log(5*x + 3)","A",0
1392,1,32,0,1.353777," ","integrate((1-2*x)^3*(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","-\frac{72}{25} \, x^{5} + \frac{69}{25} \, x^{4} + \frac{622}{375} \, x^{3} - \frac{3741}{1250} \, x^{2} + \frac{3723}{3125} \, x + \frac{1331}{15625} \, \log\left(5 \, x + 3\right)"," ",0,"-72/25*x^5 + 69/25*x^4 + 622/375*x^3 - 3741/1250*x^2 + 3723/3125*x + 1331/15625*log(5*x + 3)","A",0
1393,1,27,0,1.192023," ","integrate((1-2*x)^3*(2+3*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{3125} \, \log\left(5 \, x + 3\right)"," ",0,"-6/5*x^4 + 172/75*x^3 - 183/125*x^2 - 27/625*x + 1331/3125*log(5*x + 3)","A",0
1394,1,22,0,1.166057," ","integrate((1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log\left(5 \, x + 3\right)"," ",0,"-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(5*x + 3)","A",0
1395,1,25,0,1.189314," ","integrate((1-2*x)^3/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log\left(5 \, x + 3\right) - \frac{343}{27} \, \log\left(3 \, x + 2\right)"," ",0,"-4/15*x^2 + 332/225*x + 1331/125*log(5*x + 3) - 343/27*log(3*x + 2)","A",0
1396,1,45,0,1.233166," ","integrate((1-2*x)^3/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","-\frac{360 \, x^{2} - 35937 \, {\left(3 \, x + 2\right)} \log\left(5 \, x + 3\right) + 35525 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 240 \, x - 8575}{675 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/675*(360*x^2 - 35937*(3*x + 2)*log(5*x + 3) + 35525*(3*x + 2)*log(3*x + 2) + 240*x - 8575)/(3*x + 2)","A",0
1397,1,55,0,1.346336," ","integrate((1-2*x)^3/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{71874 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x + 3\right) - 71890 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 42630 \, x + 30135}{270 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/270*(71874*(9*x^2 + 12*x + 4)*log(5*x + 3) - 71890*(9*x^2 + 12*x + 4)*log(3*x + 2) + 42630*x + 30135)/(9*x^2 + 12*x + 4)","A",0
1398,1,75,0,1.257698," ","integrate((1-2*x)^3/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{388206 \, x^{2} + 215622 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(5 \, x + 3\right) - 215622 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 530397 \, x + 181748}{162 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/162*(388206*x^2 + 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 530397*x + 181748)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1399,1,95,0,1.191796," ","integrate((1-2*x)^3/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{11643588 \, x^{3} + 23675382 \, x^{2} + 2156220 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(5 \, x + 3\right) - 2156220 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 16059444 \, x + 3634885}{324 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/324*(11643588*x^3 + 23675382*x^2 + 2156220*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(5*x + 3) - 2156220*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 16059444*x + 3634885)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1400,1,115,0,0.827179," ","integrate((1-2*x)^3/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 53905500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(5 \, x + 3\right) - 53905500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 1075586865 \, x + 181744346}{1620 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/1620*(873269100*x^4 + 2357826570*x^3 + 2388229560*x^2 + 53905500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(5*x + 3) - 53905500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 1075586865*x + 181744346)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1401,1,135,0,1.296165," ","integrate((1-2*x)^3/(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 269527500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(5 \, x + 3\right) - 269527500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 13482032616 \, x + 1817443594}{1620 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/1620*(13099036500*x^5 + 44100089550*x^4 + 59401704780*x^3 + 40016101275*x^2 + 269527500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(5*x + 3) - 269527500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 13482032616*x + 1817443594)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1402,1,155,0,1.203781," ","integrate((1-2*x)^3/(2+3*x)^8/(3+5*x),x, algorithm=""fricas"")","\frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 1347637500 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(5 \, x + 3\right) - 1347637500 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(3 \, x + 2\right) + 162081979026 \, x + 18174436072}{1620 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/1620*(196485547500*x^6 + 792491708250*x^5 + 1332026467200*x^4 + 1194258563685*x^3 + 602391504582*x^2 + 1347637500*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(5*x + 3) - 1347637500*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 162081979026*x + 18174436072)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1403,1,67,0,1.051151," ","integrate((1-2*x)^3*(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{9966796875 \, x^{9} + 20787890625 \, x^{8} + 2195859375 \, x^{7} - 20966006250 \, x^{6} - 9554422500 \, x^{5} + 8405985000 \, x^{4} + 5225318000 \, x^{3} - 2186822400 \, x^{2} - 162624 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1457504685 \, x + 9317}{68359375 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/68359375*(9966796875*x^9 + 20787890625*x^8 + 2195859375*x^7 - 20966006250*x^6 - 9554422500*x^5 + 8405985000*x^4 + 5225318000*x^3 - 2186822400*x^2 - 162624*(5*x + 3)*log(5*x + 3) - 1457504685*x + 9317)/(5*x + 3)","A",0
1404,1,62,0,1.250574," ","integrate((1-2*x)^3*(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{3037500000 \, x^{8} + 4066875000 \, x^{7} - 2589300000 \, x^{6} - 4732520625 \, x^{5} + 904395625 \, x^{4} + 2283475250 \, x^{3} - 435255450 \, x^{2} - 538692 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 580577760 \, x + 37268}{54687500 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/54687500*(3037500000*x^8 + 4066875000*x^7 - 2589300000*x^6 - 4732520625*x^5 + 904395625*x^4 + 2283475250*x^3 - 435255450*x^2 - 538692*(5*x + 3)*log(5*x + 3) - 580577760*x + 37268)/(5*x + 3)","A",0
1405,1,57,0,1.220492," ","integrate((1-2*x)^3*(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{16875000 \, x^{7} + 9450000 \, x^{6} - 23270625 \, x^{5} - 8448125 \, x^{4} + 14512750 \, x^{3} + 127050 \, x^{2} - 30492 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 4009770 \, x + 2662}{781250 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/781250*(16875000*x^7 + 9450000*x^6 - 23270625*x^5 - 8448125*x^4 + 14512750*x^3 + 127050*x^2 - 30492*(5*x + 3)*log(5*x + 3) - 4009770*x + 2662)/(5*x + 3)","A",0
1406,1,52,0,1.254991," ","integrate((1-2*x)^3*(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1350000 \, x^{6} - 371250 \, x^{5} - 1691250 \, x^{4} + 920125 \, x^{3} + 406275 \, x^{2} - 22506 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 299700 \, x + 2662}{156250 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/156250*(1350000*x^6 - 371250*x^5 - 1691250*x^4 + 920125*x^3 + 406275*x^2 - 22506*(5*x + 3)*log(5*x + 3) - 299700*x + 2662)/(5*x + 3)","A",0
1407,1,47,0,1.179833," ","integrate((1-2*x)^3*(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{56250 \, x^{5} - 68750 \, x^{4} - 8125 \, x^{3} + 61500 \, x^{2} - 7260 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 17685 \, x + 1331}{15625 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/15625*(56250*x^5 - 68750*x^4 - 8125*x^3 + 61500*x^2 - 7260*(5*x + 3)*log(5*x + 3) + 17685*x + 1331)/(5*x + 3)","A",0
1408,1,42,0,1.346335," ","integrate((1-2*x)^3*(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{5000 \, x^{4} - 12250 \, x^{3} + 18300 \, x^{2} - 3267 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 16470 \, x + 1331}{3125 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/3125*(5000*x^4 - 12250*x^3 + 18300*x^2 - 3267*(5*x + 3)*log(5*x + 3) + 16470*x + 1331)/(5*x + 3)","A",0
1409,1,37,0,1.252613," ","integrate((1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{500 \, x^{3} - 2400 \, x^{2} + 726 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1620 \, x + 1331}{625 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/625*(500*x^3 - 2400*x^2 + 726*(5*x + 3)*log(5*x + 3) - 1620*x + 1331)/(5*x + 3)","A",0
1410,1,45,0,1.287616," ","integrate((1-2*x)^3/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{600 \, x^{2} + 42471 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 42875 \, {\left(5 \, x + 3\right)} \log\left(3 \, x + 2\right) + 360 \, x + 11979}{1125 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/1125*(600*x^2 + 42471*(5*x + 3)*log(5*x + 3) - 42875*(5*x + 3)*log(3*x + 2) + 360*x + 11979)/(5*x + 3)","A",0
1411,1,55,0,1.275283," ","integrate((1-2*x)^3/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{78408 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(5 \, x + 3\right) - 78400 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(3 \, x + 2\right) + 78812 \, x + 49683}{225 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"-1/225*(78408*(15*x^2 + 19*x + 6)*log(5*x + 3) - 78400*(15*x^2 + 19*x + 6)*log(3*x + 2) + 78812*x + 49683)/(15*x^2 + 19*x + 6)","A",0
1412,1,75,0,0.955951," ","integrate((1-2*x)^3/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{686022 \, x^{2} + 228690 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(5 \, x + 3\right) - 228690 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(3 \, x + 2\right) + 891911 \, x + 289137}{90 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"-1/90*(686022*x^2 + 228690*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 228690*(45*x^3 + 87*x^2 + 56*x + 12)*log(3*x + 2) + 891911*x + 289137)/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1413,1,95,0,1.441463," ","integrate((1-2*x)^3/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{4057614 \, x^{3} + 7979967 \, x^{2} + 450846 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(5 \, x + 3\right) - 450846 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(3 \, x + 2\right) + 5226815 \, x + 1140033}{27 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"-1/27*(4057614*x^3 + 7979967*x^2 + 450846*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(5*x + 3) - 450846*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) + 5226815*x + 1140033)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1414,1,115,0,1.393755," ","integrate((1-2*x)^3/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{301674780 \, x^{4} + 794410254 \, x^{3} + 784130946 \, x^{2} + 11173140 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(5 \, x + 3\right) - 11173140 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(3 \, x + 2\right) + 343827337 \, x + 56505975}{108 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"-1/108*(301674780*x^4 + 794410254*x^3 + 784130946*x^2 + 11173140*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(5*x + 3) - 11173140*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(3*x + 2) + 343827337*x + 56505975)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
1415,1,135,0,1.354962," ","integrate((1-2*x)^3/(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2249329500 \, x^{5} + 7422787350 \, x^{4} + 9795413430 \, x^{3} + 6461351715 \, x^{2} + 27769500 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(5 \, x + 3\right) - 27769500 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(3 \, x + 2\right) + 2130399775 \, x + 280877649}{45 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"-1/45*(2249329500*x^5 + 7422787350*x^4 + 9795413430*x^3 + 6461351715*x^2 + 27769500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(5*x + 3) - 27769500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(3*x + 2) + 2130399775*x + 280877649)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","A",0
1416,1,155,0,1.422074," ","integrate((1-2*x)^3/(2+3*x)^7/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{470374492500 \, x^{6} + 1865818820250 \, x^{5} + 3083217691950 \, x^{4} + 2716778541015 \, x^{3} + 1346292632205 \, x^{2} + 1935697500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(5 \, x + 3\right) - 1935697500 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)} \log\left(3 \, x + 2\right) + 355739265638 \, x + 39157648662}{540 \, {\left(3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right)}}"," ",0,"-1/540*(470374492500*x^6 + 1865818820250*x^5 + 3083217691950*x^4 + 2716778541015*x^3 + 1346292632205*x^2 + 1935697500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(5*x + 3) - 1935697500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*x + 2) + 355739265638*x + 39157648662)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)","A",0
1417,1,175,0,1.449340," ","integrate((1-2*x)^3/(2+3*x)^8/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{4019022562500 \, x^{7} + 18621471206250 \, x^{6} + 36972030521250 \, x^{5} + 40775613627375 \, x^{4} + 26978454053595 \, x^{3} + 10708299857748 \, x^{2} + 5513062500 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)} \log\left(5 \, x + 3\right) - 5513062500 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)} \log\left(3 \, x + 2\right) + 2360937751874 \, x + 223049897418}{270 \, {\left(10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384\right)}}"," ",0,"-1/270*(4019022562500*x^7 + 18621471206250*x^6 + 36972030521250*x^5 + 40775613627375*x^4 + 26978454053595*x^3 + 10708299857748*x^2 + 5513062500*(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)*log(5*x + 3) - 5513062500*(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)*log(3*x + 2) + 2360937751874*x + 223049897418)/(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384)","A",0
1418,1,82,0,1.457551," ","integrate((1-2*x)^3*(2+3*x)^7/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{598007812500 \, x^{10} + 1651640625000 \, x^{9} + 972000000000 \, x^{8} - 1176752812500 \, x^{7} - 1425913453125 \, x^{6} + 126252393750 \, x^{5} + 660465159375 \, x^{4} + 73008617500 \, x^{3} - 179606439600 \, x^{2} - 6620460 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 58226341320 \, x + 2305534}{1367187500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/1367187500*(598007812500*x^10 + 1651640625000*x^9 + 972000000000*x^8 - 1176752812500*x^7 - 1425913453125*x^6 + 126252393750*x^5 + 660465159375*x^4 + 73008617500*x^3 - 179606439600*x^2 - 6620460*(25*x^2 + 30*x + 9)*log(5*x + 3) - 58226341320*x + 2305534)/(25*x^2 + 30*x + 9)","A",0
1419,1,77,0,1.274017," ","integrate((1-2*x)^3*(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{45562500000 \, x^{9} + 91884375000 \, x^{8} + 2156625000 \, x^{7} - 97871878125 \, x^{6} - 34147496250 \, x^{5} + 44330619375 \, x^{4} + 16106513500 \, x^{3} - 13430552100 \, x^{2} - 4668972 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 5756731680 \, x + 1970122}{273437500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/273437500*(45562500000*x^9 + 91884375000*x^8 + 2156625000*x^7 - 97871878125*x^6 - 34147496250*x^5 + 44330619375*x^4 + 16106513500*x^3 - 13430552100*x^2 - 4668972*(25*x^2 + 30*x + 9)*log(5*x + 3) - 5756731680*x + 1970122)/(25*x^2 + 30*x + 9)","A",0
1420,1,72,0,0.856609," ","integrate((1-2*x)^3*(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{253125000 \, x^{8} + 313875000 \, x^{7} - 255740625 \, x^{6} - 365767500 \, x^{5} + 138495000 \, x^{4} + 148862000 \, x^{3} - 57470475 \, x^{2} - 218064 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 38006490 \, x + 116765}{3906250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/3906250*(253125000*x^8 + 313875000*x^7 - 255740625*x^6 - 365767500*x^5 + 138495000*x^4 + 148862000*x^3 - 57470475*x^2 - 218064*(25*x^2 + 30*x + 9)*log(5*x + 3) - 38006490*x + 116765)/(25*x^2 + 30*x + 9)","A",0
1421,1,67,0,1.336826," ","integrate((1-2*x)^3*(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{20250000 \, x^{7} + 8268750 \, x^{6} - 29610000 \, x^{5} - 3163125 \, x^{4} + 16341500 \, x^{3} + 1532625 \, x^{2} - 126588 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 1958490 \, x + 92807}{781250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/781250*(20250000*x^7 + 8268750*x^6 - 29610000*x^5 - 3163125*x^4 + 16341500*x^3 + 1532625*x^2 - 126588*(25*x^2 + 30*x + 9)*log(5*x + 3) - 1958490*x + 92807)/(25*x^2 + 30*x + 9)","A",0
1422,1,62,0,1.795872," ","integrate((1-2*x)^3*(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1687500 \, x^{6} - 900000 \, x^{5} - 1743750 \, x^{4} + 1966250 \, x^{3} + 2371650 \, x^{2} - 59070 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 698880 \, x + 68849}{156250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/156250*(1687500*x^6 - 900000*x^5 - 1743750*x^4 + 1966250*x^3 + 2371650*x^2 - 59070*(25*x^2 + 30*x + 9)*log(5*x + 3) + 698880*x + 68849)/(25*x^2 + 30*x + 9)","A",0
1423,1,57,0,1.376657," ","integrate((1-2*x)^3*(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{150000 \, x^{5} - 262500 \, x^{4} + 267500 \, x^{3} + 734100 \, x^{2} - 15510 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 340620 \, x + 44891}{31250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/31250*(150000*x^5 - 262500*x^4 + 267500*x^3 + 734100*x^2 - 15510*(25*x^2 + 30*x + 9)*log(5*x + 3) + 340620*x + 44891)/(25*x^2 + 30*x + 9)","A",0
1424,1,52,0,1.278373," ","integrate((1-2*x)^3*(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{15000 \, x^{4} - 61000 \, x^{3} - 89400 \, x^{2} + 4092 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 4230 \, x + 20933}{6250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/6250*(15000*x^4 - 61000*x^3 - 89400*x^2 + 4092*(25*x^2 + 30*x + 9)*log(5*x + 3) + 4230*x + 20933)/(25*x^2 + 30*x + 9)","A",0
1425,1,47,0,0.935237," ","integrate((1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{2000 \, x^{3} + 2400 \, x^{2} - 264 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 6540 \, x - 3025}{1250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/1250*(2000*x^3 + 2400*x^2 - 264*(25*x^2 + 30*x + 9)*log(5*x + 3) - 6540*x - 3025)/(25*x^2 + 30*x + 9)","A",0
1426,1,55,0,1.264143," ","integrate((1-2*x)^3/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{85734 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 85750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(3 \, x + 2\right) + 141570 \, x + 80949}{750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/750*(85734*(25*x^2 + 30*x + 9)*log(5*x + 3) - 85750*(25*x^2 + 30*x + 9)*log(3*x + 2) + 141570*x + 80949)/(25*x^2 + 30*x + 9)","A",0
1427,1,75,0,0.814010," ","integrate((1-2*x)^3/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1212830 \, x^{2} + 242550 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(5 \, x + 3\right) - 242550 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(3 \, x + 2\right) + 1495689 \, x + 459996}{150 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/150*(1212830*x^2 + 242550*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 242550*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) + 1495689*x + 459996)/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1428,1,95,0,1.332749," ","integrate((1-2*x)^3/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{7068600 \, x^{3} + 13430348 \, x^{2} + 471240 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(5 \, x + 3\right) - 471240 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(3 \, x + 2\right) + 8492784 \, x + 1787403}{30 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/30*(7068600*x^3 + 13430348*x^2 + 471240*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(5*x + 3) - 471240*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 8492784*x + 1787403)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1429,1,115,0,1.127562," ","integrate((1-2*x)^3/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 2315412 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(5 \, x + 3\right) - 2315412 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(3 \, x + 2\right) + 109804551 \, x + 17564616}{18 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/18*(104193540*x^4 + 267430086*x^3 + 257165096*x^2 + 2315412*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(5*x + 3) - 2315412*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) + 109804551*x + 17564616)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
1430,1,135,0,1.422591," ","integrate((1-2*x)^3/(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1544726700 \, x^{5} + 4994616330 \, x^{4} + 6455813364 \, x^{3} + 4169655991 \, x^{2} + 11442420 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(5 \, x + 3\right) - 11442420 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(3 \, x + 2\right) + 1345680462 \, x + 173603415}{12 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"1/12*(1544726700*x^5 + 4994616330*x^4 + 6455813364*x^3 + 4169655991*x^2 + 11442420*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5*x + 3) - 11442420*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(3*x + 2) + 1345680462*x + 173603415)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","A",0
1431,1,155,0,1.412491," ","integrate((1-2*x)^3/(2+3*x)^6/(3+5*x)^3,x, algorithm=""fricas"")","\frac{160841092500 \, x^{6} + 627280260750 \, x^{5} + 1018898535600 \, x^{4} + 882286862985 \, x^{3} + 429553050280 \, x^{2} + 397138500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(5 \, x + 3\right) - 397138500 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \log\left(3 \, x + 2\right) + 111486629505 \, x + 12050702538}{60 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)}}"," ",0,"1/60*(160841092500*x^6 + 627280260750*x^5 + 1018898535600*x^4 + 882286862985*x^3 + 429553050280*x^2 + 397138500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(5*x + 3) - 397138500*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*log(3*x + 2) + 111486629505*x + 12050702538)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)","A",0
1432,1,175,0,1.026982," ","integrate((1-2*x)^3/(2+3*x)^7/(3+5*x)^3,x, algorithm=""fricas"")","\frac{4794860812500 \, x^{7} + 21896531043750 \, x^{6} + 42841193422500 \, x^{5} + 46551705341625 \, x^{4} + 30340145968110 \, x^{3} + 11860532030465 \, x^{2} + 3946387500 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)} \log\left(5 \, x + 3\right) - 3946387500 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)} \log\left(3 \, x + 2\right) + 2574943269792 \, x + 239497011063}{90 \, {\left(18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576\right)}}"," ",0,"1/90*(4794860812500*x^7 + 21896531043750*x^6 + 42841193422500*x^5 + 46551705341625*x^4 + 30340145968110*x^3 + 11860532030465*x^2 + 3946387500*(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log(5*x + 3) - 3946387500*(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)*log(3*x + 2) + 2574943269792*x + 239497011063)/(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576)","A",0
1433,1,195,0,0.868995," ","integrate((1-2*x)^3/(2+3*x)^8/(3+5*x)^3,x, algorithm=""fricas"")","\frac{30672675000000 \, x^{8} + 160520332500000 \, x^{7} + 367435926000000 \, x^{6} + 480493891350000 \, x^{5} + 392612784696000 \, x^{4} + 205262100529200 \, x^{3} + 67053019228048 \, x^{2} + 8415000000 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)} \log\left(5 \, x + 3\right) - 8415000000 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)} \log\left(3 \, x + 2\right) + 12513316868859 \, x + 1021373267628}{30 \, {\left(54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right)}}"," ",0,"1/30*(30672675000000*x^8 + 160520332500000*x^7 + 367435926000000*x^6 + 480493891350000*x^5 + 392612784696000*x^4 + 205262100529200*x^3 + 67053019228048*x^2 + 8415000000*(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)*log(5*x + 3) - 8415000000*(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)*log(3*x + 2) + 12513316868859*x + 1021373267628)/(54675*x^9 + 320760*x^8 + 836163*x^7 + 1271214*x^6 + 1242108*x^5 + 808920*x^4 + 351120*x^3 + 97952*x^2 + 15936*x + 1152)","A",0
1434,1,52,0,1.070112," ","integrate((2+3*x)^8*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{3645}{2} \, x^{9} - \frac{422091}{32} \, x^{8} - \frac{353565}{8} \, x^{7} - \frac{2929689}{32} \, x^{6} - \frac{21272139}{160} \, x^{5} - \frac{37722699}{256} \, x^{4} - \frac{17391129}{128} \, x^{3} - \frac{60332619}{512} \, x^{2} - \frac{63019595}{512} \, x - \frac{63412811}{1024} \, \log\left(2 \, x - 1\right)"," ",0,"-3645/2*x^9 - 422091/32*x^8 - 353565/8*x^7 - 2929689/32*x^6 - 21272139/160*x^5 - 37722699/256*x^4 - 17391129/128*x^3 - 60332619/512*x^2 - 63019595/512*x - 63412811/1024*log(2*x - 1)","A",0
1435,1,47,0,0.910326," ","integrate((2+3*x)^7*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{10935}{16} \, x^{8} - \frac{126117}{28} \, x^{7} - \frac{218943}{16} \, x^{6} - \frac{2053917}{80} \, x^{5} - \frac{4352157}{128} \, x^{4} - \frac{2257119}{64} \, x^{3} - \frac{8362653}{256} \, x^{2} - \frac{8960669}{256} \, x - \frac{9058973}{512} \, \log\left(2 \, x - 1\right)"," ",0,"-10935/16*x^8 - 126117/28*x^7 - 218943/16*x^6 - 2053917/80*x^5 - 4352157/128*x^4 - 2257119/64*x^3 - 8362653/256*x^2 - 8960669/256*x - 9058973/512*log(2*x - 1)","A",0
1436,1,42,0,0.801018," ","integrate((2+3*x)^6*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{3645}{14} \, x^{7} - \frac{12393}{8} \, x^{6} - \frac{169371}{40} \, x^{5} - \frac{458811}{64} \, x^{4} - \frac{279657}{32} \, x^{3} - \frac{1138491}{128} \, x^{2} - \frac{1269563}{128} \, x - \frac{1294139}{256} \, \log\left(2 \, x - 1\right)"," ",0,"-3645/14*x^7 - 12393/8*x^6 - 169371/40*x^5 - 458811/64*x^4 - 279657/32*x^3 - 1138491/128*x^2 - 1269563/128*x - 1294139/256*log(2*x - 1)","A",0
1437,1,37,0,1.788181," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \log\left(2 \, x - 1\right)"," ",0,"-405/4*x^6 - 10773/20*x^5 - 42093/32*x^4 - 32271/16*x^3 - 150573/64*x^2 - 178733/64*x - 184877/128*log(2*x - 1)","A",0
1438,1,32,0,1.028215," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log\left(2 \, x - 1\right)"," ",0,"-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(2*x - 1)","A",0
1439,1,27,0,1.473022," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \log\left(2 \, x - 1\right)"," ",0,"-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)","A",0
1440,1,22,0,1.364617," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \log\left(2 \, x - 1\right)"," ",0,"-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(2*x - 1)","A",0
1441,1,17,0,1.181581," ","integrate((2+3*x)*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{8} \, \log\left(2 \, x - 1\right)"," ",0,"-15/4*x^2 - 53/4*x - 77/8*log(2*x - 1)","A",0
1442,1,12,0,0.989017," ","integrate((3+5*x)/(1-2*x),x, algorithm=""fricas"")","-\frac{5}{2} \, x - \frac{11}{4} \, \log\left(2 \, x - 1\right)"," ",0,"-5/2*x - 11/4*log(2*x - 1)","A",0
1443,1,17,0,1.468906," ","integrate((3+5*x)/(1-2*x)/(2+3*x),x, algorithm=""fricas"")","-\frac{1}{21} \, \log\left(3 \, x + 2\right) - \frac{11}{14} \, \log\left(2 \, x - 1\right)"," ",0,"-1/21*log(3*x + 2) - 11/14*log(2*x - 1)","A",0
1444,1,37,0,1.362593," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{33 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 33 \, {\left(3 \, x + 2\right)} \log\left(2 \, x - 1\right) + 7}{147 \, {\left(3 \, x + 2\right)}}"," ",0,"1/147*(33*(3*x + 2)*log(3*x + 2) - 33*(3*x + 2)*log(2*x - 1) + 7)/(3*x + 2)","A",0
1445,1,55,0,1.488625," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{132 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 132 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x - 1\right) - 1386 \, x - 875}{2058 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/2058*(132*(9*x^2 + 12*x + 4)*log(3*x + 2) - 132*(9*x^2 + 12*x + 4)*log(2*x - 1) - 1386*x - 875)/(9*x^2 + 12*x + 4)","A",0
1446,1,75,0,1.460420," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{24948 \, x^{2} - 792 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 792 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(2 \, x - 1\right) + 47817 \, x + 20104}{43218 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/43218*(24948*x^2 - 792*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 792*(27*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 47817*x + 20104)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1447,1,95,0,1.375718," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{33264 \, x^{3} + 85932 \, x^{2} - 352 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 352 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(2 \, x - 1\right) + 85316 \, x + 27741}{67228 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/67228*(33264*x^3 + 85932*x^2 - 352*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 352*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x - 1) + 85316*x + 27741)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1448,1,115,0,1.018868," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{2993760 \, x^{4} + 9729720 \, x^{3} + 12834360 \, x^{2} - 10560 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 10560 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(2 \, x - 1\right) + 8876175 \, x + 2437582}{7058940 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/7058940*(2993760*x^4 + 9729720*x^3 + 12834360*x^2 - 10560*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 10560*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 8876175*x + 2437582)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1449,1,135,0,1.468792," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{26943840 \, x^{5} + 105530040 \, x^{4} + 173887560 \, x^{3} + 156891735 \, x^{2} - 31680 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 31680 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(2 \, x - 1\right) + 85783698 \, x + 21096187}{74118870 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/74118870*(26943840*x^5 + 105530040*x^4 + 173887560*x^3 + 156891735*x^2 - 31680*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 31680*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(2*x - 1) + 85783698*x + 21096187)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1450,1,155,0,1.342972," ","integrate((3+5*x)/(1-2*x)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{53887680 \, x^{6} + 246985200 \, x^{5} + 488481840 \, x^{4} + 545633550 \, x^{3} + 380756376 \, x^{2} - 21120 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(3 \, x + 2\right) + 21120 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(2 \, x - 1\right) + 177159213 \, x + 40677476}{172944030 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/172944030*(53887680*x^6 + 246985200*x^5 + 488481840*x^4 + 545633550*x^3 + 380756376*x^2 - 21120*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 21120*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(2*x - 1) + 177159213*x + 40677476)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1451,1,57,0,1.274220," ","integrate((2+3*x)^8*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{32805}{4} \, x^{10} - \frac{256365}{4} \, x^{9} - \frac{14907321}{64} \, x^{8} - \frac{8399295}{16} \, x^{7} - \frac{53031699}{64} \, x^{6} - \frac{316246329}{320} \, x^{5} - \frac{487203129}{512} \, x^{4} - \frac{204901139}{256} \, x^{3} - \frac{677093689}{1024} \, x^{2} - \frac{695181625}{1024} \, x - \frac{697540921}{2048} \, \log\left(2 \, x - 1\right)"," ",0,"-32805/4*x^10 - 256365/4*x^9 - 14907321/64*x^8 - 8399295/16*x^7 - 53031699/64*x^6 - 316246329/320*x^5 - 487203129/512*x^4 - 204901139/256*x^3 - 677093689/1024*x^2 - 695181625/1024*x - 697540921/2048*log(2*x - 1)","A",0
1452,1,52,0,1.298239," ","integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \, \log\left(2 \, x - 1\right)"," ",0,"-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(2*x - 1)","A",0
1453,1,47,0,0.654205," ","integrate((2+3*x)^6*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{18225}{16} \, x^{8} - \frac{207765}{28} \, x^{7} - \frac{356643}{16} \, x^{6} - \frac{3310281}{80} \, x^{5} - \frac{6947721}{128} \, x^{4} - \frac{3575427}{64} \, x^{3} - \frac{13178761}{256} \, x^{2} - \frac{14088073}{256} \, x - \frac{14235529}{512} \, \log\left(2 \, x - 1\right)"," ",0,"-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4 - 3575427/64*x^3 - 13178761/256*x^2 - 14088073/256*x - 14235529/512*log(2*x - 1)","A",0
1454,1,42,0,1.699368," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{6075}{14} \, x^{7} - \frac{20385}{8} \, x^{6} - \frac{275103}{40} \, x^{5} - \frac{736623}{64} \, x^{4} - \frac{444581}{32} \, x^{3} - \frac{1797103}{128} \, x^{2} - \frac{1996783}{128} \, x - \frac{2033647}{256} \, \log\left(2 \, x - 1\right)"," ",0,"-6075/14*x^7 - 20385/8*x^6 - 275103/40*x^5 - 736623/64*x^4 - 444581/32*x^3 - 1797103/128*x^2 - 1996783/128*x - 2033647/256*log(2*x - 1)","A",0
1455,1,37,0,1.348084," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{675}{4} \, x^{6} - \frac{3537}{4} \, x^{5} - \frac{68121}{32} \, x^{4} - \frac{51571}{16} \, x^{3} - \frac{238297}{64} \, x^{2} - \frac{281305}{64} \, x - \frac{290521}{128} \, \log\left(2 \, x - 1\right)"," ",0,"-675/4*x^6 - 3537/4*x^5 - 68121/32*x^4 - 51571/16*x^3 - 238297/64*x^2 - 281305/64*x - 290521/128*log(2*x - 1)","A",0
1456,1,32,0,1.618994," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \log\left(2 \, x - 1\right)"," ",0,"-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log(2*x - 1)","A",0
1457,1,27,0,1.488429," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{225}{8} \, x^{4} - \frac{455}{4} \, x^{3} - \frac{3529}{16} \, x^{2} - \frac{5353}{16} \, x - \frac{5929}{32} \, \log\left(2 \, x - 1\right)"," ",0,"-225/8*x^4 - 455/4*x^3 - 3529/16*x^2 - 5353/16*x - 5929/32*log(2*x - 1)","A",0
1458,1,22,0,1.107544," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \log\left(2 \, x - 1\right)"," ",0,"-25/2*x^3 - 355/8*x^2 - 703/8*x - 847/16*log(2*x - 1)","A",0
1459,1,17,0,1.209503," ","integrate((3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","-\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log\left(2 \, x - 1\right)"," ",0,"-25/4*x^2 - 85/4*x - 121/8*log(2*x - 1)","A",0
1460,1,20,0,1.041936," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x),x, algorithm=""fricas"")","-\frac{25}{6} \, x + \frac{1}{63} \, \log\left(3 \, x + 2\right) - \frac{121}{28} \, \log\left(2 \, x - 1\right)"," ",0,"-25/6*x + 1/63*log(3*x + 2) - 121/28*log(2*x - 1)","A",0
1461,1,37,0,1.251677," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{136 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 1089 \, {\left(3 \, x + 2\right)} \log\left(2 \, x - 1\right) + 14}{882 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/882*(136*(3*x + 2)*log(3*x + 2) + 1089*(3*x + 2)*log(2*x - 1) + 14)/(3*x + 2)","A",0
1462,1,55,0,1.402345," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{2178 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 2178 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x - 1\right) + 2856 \, x + 1855}{6174 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/6174*(2178*(9*x^2 + 12*x + 4)*log(3*x + 2) - 2178*(9*x^2 + 12*x + 4)*log(2*x - 1) + 2856*x + 1855)/(9*x^2 + 12*x + 4)","A",0
1463,1,75,0,1.354154," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{205821 \, x^{2} - 6534 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) + 6534 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(2 \, x - 1\right) + 259434 \, x + 81823}{64827 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/64827*(205821*x^2 - 6534*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 6534*(27*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 259434*x + 81823)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1464,1,95,0,1.453393," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{4939704 \, x^{3} + 12760902 \, x^{2} - 52272 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 52272 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(2 \, x - 1\right) + 10148376 \, x + 2564891}{1815156 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/1815156*(4939704*x^3 + 12760902*x^2 - 52272*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 52272*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x - 1) + 10148376*x + 2564891)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1465,1,115,0,1.540704," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{12349260 \, x^{4} + 40135095 \, x^{3} + 52941735 \, x^{2} - 43560 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 43560 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(2 \, x - 1\right) + 31099425 \, x + 6672617}{5294205 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/5294205*(12349260*x^4 + 40135095*x^3 + 52941735*x^2 - 43560*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 43560*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 31099425*x + 6672617)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1466,1,135,0,1.527527," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{889146720 \, x^{5} + 3482491320 \, x^{4} + 5738289480 \, x^{3} + 5177427255 \, x^{2} - 1045440 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 1045440 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(2 \, x - 1\right) + 2460267684 \, x + 469699846}{444713220 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/444713220*(889146720*x^5 + 3482491320*x^4 + 5738289480*x^3 + 5177427255*x^2 - 1045440*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 1045440*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(2*x - 1) + 2460267684*x + 469699846)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1467,1,155,0,1.254252," ","integrate((3+5*x)^2/(1-2*x)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{2667440160 \, x^{6} + 12225767400 \, x^{5} + 24179851080 \, x^{4} + 27008860725 \, x^{3} + 18847440612 \, x^{2} - 1045440 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(3 \, x + 2\right) + 1045440 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(2 \, x - 1\right) + 7688480856 \, x + 1354700662}{1556496270 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/1556496270*(2667440160*x^6 + 12225767400*x^5 + 24179851080*x^4 + 27008860725*x^3 + 18847440612*x^2 - 1045440*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 1045440*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(2*x - 1) + 7688480856*x + 1354700662)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1468,1,57,0,0.978723," ","integrate((2+3*x)^7*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{54675}{4} \, x^{10} - \frac{423225}{4} \, x^{9} - \frac{24381405}{64} \, x^{8} - \frac{95297877}{112} \, x^{7} - \frac{85228263}{64} \, x^{6} - \frac{504354357}{320} \, x^{5} - \frac{772025397}{512} \, x^{4} - \frac{969544757}{768} \, x^{3} - \frac{1065169973}{1024} \, x^{2} - \frac{1092596789}{1024} \, x - \frac{1096135733}{2048} \, \log\left(2 \, x - 1\right)"," ",0,"-54675/4*x^10 - 423225/4*x^9 - 24381405/64*x^8 - 95297877/112*x^7 - 85228263/64*x^6 - 504354357/320*x^5 - 772025397/512*x^4 - 969544757/768*x^3 - 1065169973/1024*x^2 - 1092596789/1024*x - 1096135733/2048*log(2*x - 1)","A",0
1469,1,52,0,1.302503," ","integrate((2+3*x)^6*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{10125}{2} \, x^{9} - \frac{1148175}{32} \, x^{8} - \frac{6596235}{56} \, x^{7} - \frac{7656993}{32} \, x^{6} - \frac{54600291}{160} \, x^{5} - \frac{95317731}{256} \, x^{4} - \frac{130251491}{384} \, x^{3} - \frac{149512931}{512} \, x^{2} - \frac{155706083}{512} \, x - \frac{156590819}{1024} \, \log\left(2 \, x - 1\right)"," ",0,"-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(2*x - 1)","A",0
1470,1,47,0,0.900254," ","integrate((2+3*x)^5*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{30375}{16} \, x^{8} - \frac{342225}{28} \, x^{7} - \frac{580815}{16} \, x^{6} - \frac{5333733}{80} \, x^{5} - \frac{11088453}{128} \, x^{4} - \frac{16987973}{192} \, x^{3} - \frac{20766533}{256} \, x^{2} - \frac{22148933}{256} \, x - \frac{22370117}{512} \, \log\left(2 \, x - 1\right)"," ",0,"-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^4 - 16987973/192*x^3 - 20766533/256*x^2 - 22148933/256*x - 22370117/512*log(2*x - 1)","A",0
1471,1,42,0,1.492010," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{10125}{14} \, x^{7} - \frac{33525}{8} \, x^{6} - \frac{89343}{8} \, x^{5} - \frac{1182291}{64} \, x^{4} - \frac{2119763}{96} \, x^{3} - \frac{2836307}{128} \, x^{2} - \frac{3140435}{128} \, x - \frac{3195731}{256} \, \log\left(2 \, x - 1\right)"," ",0,"-10125/14*x^7 - 33525/8*x^6 - 89343/8*x^5 - 1182291/64*x^4 - 2119763/96*x^3 - 2836307/128*x^2 - 3140435/128*x - 3195731/256*log(2*x - 1)","A",0
1472,1,37,0,1.411745," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \, \log\left(2 \, x - 1\right)"," ",0,"-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 442709/64*x - 456533/128*log(2*x - 1)","A",0
1473,1,32,0,1.039325," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log\left(2 \, x - 1\right)"," ",0,"-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*log(2*x - 1)","A",0
1474,1,27,0,1.278225," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \log\left(2 \, x - 1\right)"," ",0,"-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(2*x - 1)","A",0
1475,1,22,0,1.290099," ","integrate((3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","-\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log\left(2 \, x - 1\right)"," ",0,"-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(2*x - 1)","A",0
1476,1,25,0,1.317369," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x),x, algorithm=""fricas"")","-\frac{125}{12} \, x^{2} - \frac{1225}{36} \, x - \frac{1}{189} \, \log\left(3 \, x + 2\right) - \frac{1331}{56} \, \log\left(2 \, x - 1\right)"," ",0,"-125/12*x^2 - 1225/36*x - 1/189*log(3*x + 2) - 1331/56*log(2*x - 1)","A",0
1477,1,45,0,1.433480," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{110250 \, x^{2} - 412 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) + 35937 \, {\left(3 \, x + 2\right)} \log\left(2 \, x - 1\right) + 73500 \, x - 28}{5292 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/5292*(110250*x^2 - 412*(3*x + 2)*log(3*x + 2) + 35937*(3*x + 2)*log(2*x - 1) + 73500*x - 28)/(3*x + 2)","A",0
1478,1,55,0,1.351163," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{6938 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) + 35937 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x - 1\right) + 4326 \, x + 2835}{18522 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/18522*(6938*(9*x^2 + 12*x + 4)*log(3*x + 2) + 35937*(9*x^2 + 12*x + 4)*log(2*x - 1) + 4326*x + 2835)/(9*x^2 + 12*x + 4)","A",0
1479,1,75,0,0.830153," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{1311282 \, x^{2} + 215622 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 215622 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(2 \, x - 1\right) + 1702953 \, x + 553196}{388962 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/388962*(1311282*x^2 + 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 1702953*x + 553196)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1480,1,95,0,0.750703," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{81505116 \, x^{3} + 153831258 \, x^{2} - 862488 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) + 862488 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(2 \, x - 1\right) + 96858804 \, x + 20345549}{5445468 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/5445468*(81505116*x^3 + 153831258*x^2 - 862488*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) + 862488*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x - 1) + 96858804*x + 20345549)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1481,1,115,0,1.264771," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{2445153480 \, x^{4} + 7946748810 \, x^{3} + 9158912280 \, x^{2} - 8624880 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) + 8624880 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(2 \, x - 1\right) + 4525306275 \, x + 817640446}{190591380 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/190591380*(2445153480*x^4 + 7946748810*x^3 + 9158912280*x^2 - 8624880*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) + 8624880*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 4525306275*x + 817640446)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1482,1,135,0,1.537411," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{14670920880 \, x^{5} + 57461106780 \, x^{4} + 94681776420 \, x^{3} + 78478905645 \, x^{2} - 17249760 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) + 17249760 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(2 \, x - 1\right) + 32070746736 \, x + 5135298434}{1334139660 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/1334139660*(14670920880*x^5 + 57461106780*x^4 + 94681776420*x^3 + 78478905645*x^2 - 17249760*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) + 17249760*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(2*x - 1) + 32070746736*x + 5135298434)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1483,1,155,0,1.515068," ","integrate((3+5*x)^3/(1-2*x)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{88025525280 \, x^{6} + 403450324200 \, x^{5} + 797935085640 \, x^{4} + 891292403925 \, x^{3} + 583053133446 \, x^{2} - 34499520 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(3 \, x + 2\right) + 34499520 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(2 \, x - 1\right) + 206160259998 \, x + 30169587896}{9338977620 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/9338977620*(88025525280*x^6 + 403450324200*x^5 + 797935085640*x^4 + 891292403925*x^3 + 583053133446*x^2 - 34499520*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x + 2) + 34499520*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(2*x - 1) + 206160259998*x + 30169587896)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1484,1,207,0,1.767083," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{3} \log\left(d x + c\right) - {\left(b^{3} d^{3} e f^{2} - b^{3} c d^{2} f^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} e^{2} f - 3 \, a b^{2} d^{3} e f^{2} - {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} f^{3}\right)} x - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{3} e^{2} f + 3 \, a^{2} b d^{3} e f^{2} - a^{3} d^{3} f^{3}\right)} \log\left(f x + e\right)}{2 \, {\left(d^{4} e f^{3} - c d^{3} f^{4}\right)}}"," ",0,"-1/2*(2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^3*log(d*x + c) - (b^3*d^3*e*f^2 - b^3*c*d^2*f^3)*x^2 + 2*(b^3*d^3*e^2*f - 3*a*b^2*d^3*e*f^2 - (b^3*c^2*d - 3*a*b^2*c*d^2)*f^3)*x - 2*(b^3*d^3*e^3 - 3*a*b^2*d^3*e^2*f + 3*a^2*b*d^3*e*f^2 - a^3*d^3*f^3)*log(f*x + e))/(d^4*e*f^3 - c*d^3*f^4)","B",0
1485,1,50,0,1.486078," ","integrate((2+3*x)^8/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{6561}{70} \, x^{7} - \frac{114453}{200} \, x^{6} - \frac{8018271}{5000} \, x^{5} - \frac{111146499}{40000} \, x^{4} - \frac{345533877}{100000} \, x^{3} - \frac{7136193339}{2000000} \, x^{2} - \frac{40089855591}{10000000} \, x + \frac{1}{4296875} \, \log\left(5 \, x + 3\right) - \frac{5764801}{2816} \, \log\left(2 \, x - 1\right)"," ",0,"-6561/70*x^7 - 114453/200*x^6 - 8018271/5000*x^5 - 111146499/40000*x^4 - 345533877/100000*x^3 - 7136193339/2000000*x^2 - 40089855591/10000000*x + 1/4296875*log(5*x + 3) - 5764801/2816*log(2*x - 1)","A",0
1486,1,45,0,1.524036," ","integrate((2+3*x)^7/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{729}{20} \, x^{6} - \frac{99873}{500} \, x^{5} - \frac{2006937}{4000} \, x^{4} - \frac{7889751}{10000} \, x^{3} - \frac{187738857}{200000} \, x^{2} - \frac{1127138733}{1000000} \, x + \frac{1}{859375} \, \log\left(5 \, x + 3\right) - \frac{823543}{1408} \, \log\left(2 \, x - 1\right)"," ",0,"-729/20*x^6 - 99873/500*x^5 - 2006937/4000*x^4 - 7889751/10000*x^3 - 187738857/200000*x^2 - 1127138733/1000000*x + 1/859375*log(5*x + 3) - 823543/1408*log(2*x - 1)","A",0
1487,1,40,0,0.904910," ","integrate((2+3*x)^6/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{729}{50} \, x^{5} - \frac{28431}{400} \, x^{4} - \frac{159813}{1000} \, x^{3} - \frac{4693491}{20000} \, x^{2} - \frac{31289679}{100000} \, x + \frac{1}{171875} \, \log\left(5 \, x + 3\right) - \frac{117649}{704} \, \log\left(2 \, x - 1\right)"," ",0,"-729/50*x^5 - 28431/400*x^4 - 159813/1000*x^3 - 4693491/20000*x^2 - 31289679/100000*x + 1/171875*log(5*x + 3) - 117649/704*log(2*x - 1)","A",0
1488,1,35,0,1.403212," ","integrate((2+3*x)^5/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log\left(5 \, x + 3\right) - \frac{16807}{352} \, \log\left(2 \, x - 1\right)"," ",0,"-243/40*x^4 - 2619/100*x^3 - 107433/2000*x^2 - 848277/10000*x + 1/34375*log(5*x + 3) - 16807/352*log(2*x - 1)","A",0
1489,1,30,0,0.624059," ","integrate((2+3*x)^4/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{27}{10} \, x^{3} - \frac{2079}{200} \, x^{2} - \frac{21951}{1000} \, x + \frac{1}{6875} \, \log\left(5 \, x + 3\right) - \frac{2401}{176} \, \log\left(2 \, x - 1\right)"," ",0,"-27/10*x^3 - 2079/200*x^2 - 21951/1000*x + 1/6875*log(5*x + 3) - 2401/176*log(2*x - 1)","A",0
1490,1,25,0,1.062944," ","integrate((2+3*x)^3/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{27}{20} \, x^{2} - \frac{513}{100} \, x + \frac{1}{1375} \, \log\left(5 \, x + 3\right) - \frac{343}{88} \, \log\left(2 \, x - 1\right)"," ",0,"-27/20*x^2 - 513/100*x + 1/1375*log(5*x + 3) - 343/88*log(2*x - 1)","A",0
1491,1,20,0,1.213148," ","integrate((2+3*x)^2/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","-\frac{9}{10} \, x + \frac{1}{275} \, \log\left(5 \, x + 3\right) - \frac{49}{44} \, \log\left(2 \, x - 1\right)"," ",0,"-9/10*x + 1/275*log(5*x + 3) - 49/44*log(2*x - 1)","A",0
1492,1,17,0,1.448513," ","integrate((2+3*x)/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{55} \, \log\left(5 \, x + 3\right) - \frac{7}{22} \, \log\left(2 \, x - 1\right)"," ",0,"1/55*log(5*x + 3) - 7/22*log(2*x - 1)","A",0
1493,1,17,0,1.303263," ","integrate(1/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{11} \, \log\left(5 \, x + 3\right) - \frac{1}{11} \, \log\left(2 \, x - 1\right)"," ",0,"1/11*log(5*x + 3) - 1/11*log(2*x - 1)","A",0
1494,1,25,0,1.381279," ","integrate(1/(1-2*x)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{5}{11} \, \log\left(5 \, x + 3\right) - \frac{3}{7} \, \log\left(3 \, x + 2\right) - \frac{2}{77} \, \log\left(2 \, x - 1\right)"," ",0,"5/11*log(5*x + 3) - 3/7*log(3*x + 2) - 2/77*log(2*x - 1)","A",0
1495,1,50,0,1.606301," ","integrate(1/(1-2*x)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{1225 \, {\left(3 \, x + 2\right)} \log\left(5 \, x + 3\right) - 1221 \, {\left(3 \, x + 2\right)} \log\left(3 \, x + 2\right) - 4 \, {\left(3 \, x + 2\right)} \log\left(2 \, x - 1\right) + 231}{539 \, {\left(3 \, x + 2\right)}}"," ",0,"1/539*(1225*(3*x + 2)*log(5*x + 3) - 1221*(3*x + 2)*log(3*x + 2) - 4*(3*x + 2)*log(2*x - 1) + 231)/(3*x + 2)","A",0
1496,1,73,0,1.865481," ","integrate(1/(1-2*x)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{85750 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x + 3\right) - 85734 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(3 \, x + 2\right) - 16 \, {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x - 1\right) + 51282 \, x + 35805}{7546 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/7546*(85750*(9*x^2 + 12*x + 4)*log(5*x + 3) - 85734*(9*x^2 + 12*x + 4)*log(3*x + 2) - 16*(9*x^2 + 12*x + 4)*log(2*x - 1) + 51282*x + 35805)/(9*x^2 + 12*x + 4)","A",0
1497,1,98,0,1.582906," ","integrate(1/(1-2*x)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{5401242 \, x^{2} + 3001250 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(5 \, x + 3\right) - 3001218 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(3 \, x + 2\right) - 32 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(2 \, x - 1\right) + 7381143 \, x + 2527756}{52822 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/52822*(5401242*x^2 + 3001250*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 3001218*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 32*(27*x^3 + 54*x^2 + 36*x + 8)*log(2*x - 1) + 7381143*x + 2527756)/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1498,1,123,0,1.581383," ","integrate(1/(1-2*x)/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{1134460404 \, x^{3} + 2306729502 \, x^{2} + 210087500 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(5 \, x + 3\right) - 210087372 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(3 \, x + 2\right) - 128 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(2 \, x - 1\right) + 1564700676 \, x + 354136321}{739508 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/739508*(1134460404*x^3 + 2306729502*x^2 + 210087500*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(5*x + 3) - 210087372*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) - 128*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x - 1) + 1564700676*x + 354136321)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","B",0
1499,1,148,0,1.518802," ","integrate(1/(1-2*x)/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{595597699620 \, x^{4} + 1608113589390 \, x^{3} + 1628848849320 \, x^{2} + 36765312500 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(5 \, x + 3\right) - 36765311220 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(3 \, x + 2\right) - 1280 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(2 \, x - 1\right) + 733584557475 \, x + 123954940494}{25882780 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/25882780*(595597699620*x^4 + 1608113589390*x^3 + 1628848849320*x^2 + 36765312500*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(5*x + 3) - 36765311220*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(3*x + 2) - 1280*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log(2*x - 1) + 733584557475*x + 123954940494)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","B",0
1500,1,173,0,1.712882," ","integrate(1/(1-2*x)/(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{62537794385220 \, x^{5} + 210543906566070 \, x^{4} + 283597312285980 \, x^{3} + 191046007176255 \, x^{2} + 1286785937500 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(5 \, x + 3\right) - 1286785934940 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(3 \, x + 2\right) - 2560 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(2 \, x - 1\right) + 64366302153384 \, x + 8676887688546}{181179460 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/181179460*(62537794385220*x^5 + 210543906566070*x^4 + 283597312285980*x^3 + 191046007176255*x^2 + 1286785937500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(5*x + 3) - 1286785934940*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(3*x + 2) - 2560*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(2*x - 1) + 64366302153384*x + 8676887688546)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","B",0
1501,1,70,0,1.296929," ","integrate((2+3*x)^8/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{661567500000 \, x^{7} + 4075255800000 \, x^{6} + 11575887592500 \, x^{5} + 20540764282500 \, x^{4} + 26881371767250 \, x^{3} + 32416139725200 \, x^{2} - 34048 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 2251875390625 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 12994985849670 \, x + 1408}{6050000000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/6050000000*(661567500000*x^7 + 4075255800000*x^6 + 11575887592500*x^5 + 20540764282500*x^4 + 26881371767250*x^3 + 32416139725200*x^2 - 34048*(5*x + 3)*log(5*x + 3) + 2251875390625*(5*x + 3)*log(2*x - 1) + 12994985849670*x + 1408)/(5*x + 3)","A",0
1502,1,65,0,1.374964," ","integrate((2+3*x)^7/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{26462700000 \, x^{6} + 147088507500 \, x^{5} + 378490117500 \, x^{4} + 626065827750 \, x^{3} + 868095478800 \, x^{2} - 14912 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 64339296875 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 360222523650 \, x + 704}{605000000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/605000000*(26462700000*x^6 + 147088507500*x^5 + 378490117500*x^4 + 626065827750*x^3 + 868095478800*x^2 - 14912*(5*x + 3)*log(5*x + 3) + 64339296875*(5*x + 3)*log(2*x - 1) + 360222523650*x + 704)/(5*x + 3)","A",0
1503,1,60,0,1.363247," ","integrate((2+3*x)^6/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1102612500 \, x^{5} + 5513062500 \, x^{4} + 13047581250 \, x^{3} + 22313610000 \, x^{2} - 6400 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 1838265625 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 9738959670 \, x + 352}{60500000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/60500000*(1102612500*x^5 + 5513062500*x^4 + 13047581250*x^3 + 22313610000*x^2 - 6400*(5*x + 3)*log(5*x + 3) + 1838265625*(5*x + 3)*log(2*x - 1) + 9738959670*x + 352)/(5*x + 3)","A",0
1504,1,55,0,1.443403," ","integrate((2+3*x)^5/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{49005000 \, x^{4} + 222972750 \, x^{3} + 533827800 \, x^{2} - 2672 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 52521875 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 250611570 \, x + 176}{6050000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/6050000*(49005000*x^4 + 222972750*x^3 + 533827800*x^2 - 2672*(5*x + 3)*log(5*x + 3) + 52521875*(5*x + 3)*log(2*x - 1) + 250611570*x + 176)/(5*x + 3)","A",0
1505,1,50,0,1.436337," ","integrate((2+3*x)^4/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2450250 \, x^{3} + 11107800 \, x^{2} - 1072 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 1500625 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 5782590 \, x + 88}{605000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/605000*(2450250*x^3 + 11107800*x^2 - 1072*(5*x + 3)*log(5*x + 3) + 1500625*(5*x + 3)*log(2*x - 1) + 5782590*x + 88)/(5*x + 3)","A",0
1506,1,45,0,1.061090," ","integrate((2+3*x)^3/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{163350 \, x^{2} - 404 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) + 42875 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 98010 \, x + 44}{60500 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/60500*(163350*x^2 - 404*(5*x + 3)*log(5*x + 3) + 42875*(5*x + 3)*log(2*x - 1) + 98010*x + 44)/(5*x + 3)","A",0
1507,1,37,0,1.361817," ","integrate((2+3*x)^2/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{136 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1225 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) - 22}{6050 \, {\left(5 \, x + 3\right)}}"," ",0,"1/6050*(136*(5*x + 3)*log(5*x + 3) - 1225*(5*x + 3)*log(2*x - 1) - 22)/(5*x + 3)","A",0
1508,1,37,0,1.351532," ","integrate((2+3*x)/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{35 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 35 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) - 11}{605 \, {\left(5 \, x + 3\right)}}"," ",0,"1/605*(35*(5*x + 3)*log(5*x + 3) - 35*(5*x + 3)*log(2*x - 1) - 11)/(5*x + 3)","A",0
1509,1,37,0,1.481479," ","integrate(1/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 2 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) - 11}{121 \, {\left(5 \, x + 3\right)}}"," ",0,"1/121*(2*(5*x + 3)*log(5*x + 3) - 2*(5*x + 3)*log(2*x - 1) - 11)/(5*x + 3)","A",0
1510,1,50,0,1.315603," ","integrate(1/(1-2*x)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1085 \, {\left(5 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1089 \, {\left(5 \, x + 3\right)} \log\left(3 \, x + 2\right) + 4 \, {\left(5 \, x + 3\right)} \log\left(2 \, x - 1\right) + 385}{847 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/847*(1085*(5*x + 3)*log(5*x + 3) - 1089*(5*x + 3)*log(3*x + 2) + 4*(5*x + 3)*log(2*x - 1) + 385)/(5*x + 3)","A",0
1511,1,73,0,1.692927," ","integrate(1/(1-2*x)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{78400 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(5 \, x + 3\right) - 78408 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(3 \, x + 2\right) + 8 \, {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(2 \, x - 1\right) + 78540 \, x + 49819}{5929 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"-1/5929*(78400*(15*x^2 + 19*x + 6)*log(5*x + 3) - 78408*(15*x^2 + 19*x + 6)*log(3*x + 2) + 8*(15*x^2 + 19*x + 6)*log(2*x - 1) + 78540*x + 49819)/(15*x^2 + 19*x + 6)","A",0
1512,1,98,0,1.452854," ","integrate(1/(1-2*x)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{24954930 \, x^{2} + 8317750 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(5 \, x + 3\right) - 8317782 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(3 \, x + 2\right) + 32 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(2 \, x - 1\right) + 32442333 \, x + 10519355}{83006 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"-1/83006*(24954930*x^2 + 8317750*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 8317782*(45*x^3 + 87*x^2 + 56*x + 12)*log(3*x + 2) + 32*(45*x^3 + 87*x^2 + 56*x + 12)*log(2*x - 1) + 32442333*x + 10519355)/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1513,1,123,0,1.652717," ","integrate(1/(1-2*x)/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1755736290 \, x^{3} + 3452950809 \, x^{2} + 195081250 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(5 \, x + 3\right) - 195081282 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(3 \, x + 2\right) + 32 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(2 \, x - 1\right) + 2261654241 \, x + 493301347}{290521 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"-1/290521*(1755736290*x^3 + 3452950809*x^2 + 195081250*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(5*x + 3) - 195081282*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) + 32*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(2*x - 1) + 2261654241*x + 493301347)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","B",0
1514,1,148,0,1.212135," ","integrate(1/(1-2*x)/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{924595208460 \, x^{4} + 2434767448806 \, x^{3} + 2403262839978 \, x^{2} + 34244262500 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(5 \, x + 3\right) - 34244262756 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(3 \, x + 2\right) + 256 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(2 \, x - 1\right) + 1053787613109 \, x + 173183872939}{8134588 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"-1/8134588*(924595208460*x^4 + 2434767448806*x^3 + 2403262839978*x^2 + 34244262500*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(5*x + 3) - 34244262756*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(3*x + 2) + 256*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log(2*x - 1) + 1053787613109*x + 173183872939)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","B",0
1515,1,173,0,1.415584," ","integrate(1/(1-2*x)/(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{145921526219700 \, x^{5} + 481541037023970 \, x^{4} + 635461225889490 \, x^{3} + 419169494735145 \, x^{2} + 1801500312500 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(5 \, x + 3\right) - 1801500313140 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(3 \, x + 2\right) + 640 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(2 \, x - 1\right) + 138206158563165 \, x + 18221473659389}{71177645 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"-1/71177645*(145921526219700*x^5 + 481541037023970*x^4 + 635461225889490*x^3 + 419169494735145*x^2 + 1801500312500*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(5*x + 3) - 1801500313140*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(3*x + 2) + 640*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log(2*x - 1) + 138206158563165*x + 18221473659389)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","B",0
1516,1,85,0,1.416059," ","integrate((2+3*x)^8/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{4366345500000 \, x^{7} + 27253273162500 \, x^{6} + 79082602830000 \, x^{5} + 146338473723750 \, x^{4} + 215620841031750 \, x^{3} + 153403867608750 \, x^{2} - 1985536 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 2251875390625 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 37694322033170 \, x + 565664}{33275000000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/33275000000*(4366345500000*x^7 + 27253273162500*x^6 + 79082602830000*x^5 + 146338473723750*x^4 + 215620841031750*x^3 + 153403867608750*x^2 - 1985536*(25*x^2 + 30*x + 9)*log(5*x + 3) + 2251875390625*(25*x^2 + 30*x + 9)*log(2*x - 1) + 37694322033170*x + 565664)/(25*x^2 + 30*x + 9)","A",0
1517,1,80,0,1.555502," ","integrate((2+3*x)^7/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{181931062500 \, x^{6} + 1034985600000 \, x^{5} + 2783545256250 \, x^{4} + 5202285041250 \, x^{3} + 4012849402650 \, x^{2} - 746720 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 64339296875 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 1016146037830 \, x + 247984}{3327500000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/3327500000*(181931062500*x^6 + 1034985600000*x^5 + 2783545256250*x^4 + 5202285041250*x^3 + 4012849402650*x^2 - 746720*(25*x^2 + 30*x + 9)*log(5*x + 3) + 64339296875*(25*x^2 + 30*x + 9)*log(2*x - 1) + 1016146037830*x + 247984)/(25*x^2 + 30*x + 9)","A",0
1518,1,75,0,1.766880," ","integrate((2+3*x)^6/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{8085825000 \, x^{5} + 42450581250 \, x^{4} + 114414423750 \, x^{3} + 98436833550 \, x^{2} - 267760 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 1838265625 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 25994486210 \, x + 106568}{332750000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/332750000*(8085825000*x^5 + 42450581250*x^4 + 114414423750*x^3 + 98436833550*x^2 - 267760*(25*x^2 + 30*x + 9)*log(5*x + 3) + 1838265625*(25*x^2 + 30*x + 9)*log(2*x - 1) + 25994486210*x + 106568)/(25*x^2 + 30*x + 9)","A",0
1519,1,70,0,1.519480," ","integrate((2+3*x)^5/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{404291250 \, x^{4} + 2129267250 \, x^{3} + 2118486150 \, x^{2} - 89792 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 52521875 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 591955870 \, x + 44572}{33275000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/33275000*(404291250*x^4 + 2129267250*x^3 + 2118486150*x^2 - 89792*(25*x^2 + 30*x + 9)*log(5*x + 3) + 52521875*(25*x^2 + 30*x + 9)*log(2*x - 1) + 591955870*x + 44572)/(25*x^2 + 30*x + 9)","A",0
1520,1,65,0,1.022853," ","integrate((2+3*x)^4/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{26952750 \, x^{3} + 32343300 \, x^{2} - 27208 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 1500625 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 9732470 \, x + 17930}{3327500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/3327500*(26952750*x^3 + 32343300*x^2 - 27208*(25*x^2 + 30*x + 9)*log(5*x + 3) + 1500625*(25*x^2 + 30*x + 9)*log(2*x - 1) + 9732470*x + 17930)/(25*x^2 + 30*x + 9)","A",0
1521,1,55,0,0.749998," ","integrate((2+3*x)^3/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{6938 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 42875 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) - 11110 \, x - 6787}{332750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/332750*(6938*(25*x^2 + 30*x + 9)*log(5*x + 3) - 42875*(25*x^2 + 30*x + 9)*log(2*x - 1) - 11110*x - 6787)/(25*x^2 + 30*x + 9)","A",0
1522,1,55,0,1.660624," ","integrate((2+3*x)^2/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2450 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 2450 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) - 7480 \, x - 4609}{66550 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/66550*(2450*(25*x^2 + 30*x + 9)*log(5*x + 3) - 2450*(25*x^2 + 30*x + 9)*log(2*x - 1) - 7480*x - 4609)/(25*x^2 + 30*x + 9)","A",0
1523,1,55,0,1.658598," ","integrate((2+3*x)/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{140 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 140 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) - 3850 \, x - 2431}{13310 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/13310*(140*(25*x^2 + 30*x + 9)*log(5*x + 3) - 140*(25*x^2 + 30*x + 9)*log(2*x - 1) - 3850*x - 2431)/(25*x^2 + 30*x + 9)","A",0
1524,1,55,0,1.313510," ","integrate(1/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 8 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) - 220 \, x - 253}{2662 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/2662*(8*(25*x^2 + 30*x + 9)*log(5*x + 3) - 8*(25*x^2 + 30*x + 9)*log(2*x - 1) - 220*x - 253)/(25*x^2 + 30*x + 9)","A",0
1525,1,73,0,1.370512," ","integrate(1/(1-2*x)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{71890 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) - 71874 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(3 \, x + 2\right) - 16 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(2 \, x - 1\right) + 119350 \, x + 67375}{18634 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/18634*(71890*(25*x^2 + 30*x + 9)*log(5*x + 3) - 71874*(25*x^2 + 30*x + 9)*log(3*x + 2) - 16*(25*x^2 + 30*x + 9)*log(2*x - 1) + 119350*x + 67375)/(25*x^2 + 30*x + 9)","A",0
1526,1,98,0,1.322094," ","integrate(1/(1-2*x)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{38449950 \, x^{2} + 7690550 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(5 \, x + 3\right) - 7690518 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(3 \, x + 2\right) - 32 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(2 \, x - 1\right) + 47420065 \, x + 14580412}{130438 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/130438*(38449950*x^2 + 7690550*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 7690518*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) - 32*(75*x^3 + 140*x^2 + 87*x + 18)*log(2*x - 1) + 47420065*x + 14580412)/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1527,1,123,0,1.223494," ","integrate(1/(1-2*x)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{8154808200 \, x^{3} + 15494126340 \, x^{2} + 543655000 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(5 \, x + 3\right) - 543654936 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(3 \, x + 2\right) - 64 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(2 \, x - 1\right) + 9797832352 \, x + 2062044985}{913066 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/913066*(8154808200*x^3 + 15494126340*x^2 + 543655000*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(5*x + 3) - 543654936*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) - 64*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(2*x - 1) + 9797832352*x + 2062044985)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","B",0
1528,1,148,0,1.452307," ","integrate(1/(1-2*x)/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1435647836700 \, x^{4} + 3684829392090 \, x^{3} + 3543391400472 \, x^{2} + 31903287500 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(5 \, x + 3\right) - 31903287372 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(3 \, x + 2\right) - 128 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(2 \, x - 1\right) + 1512959972293 \, x + 242016815656}{6391462 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/6391462*(1435647836700*x^4 + 3684829392090*x^3 + 3543391400472*x^2 + 31903287500*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(5*x + 3) - 31903287372*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) - 128*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(2*x - 1) + 1512959972293*x + 242016815656)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","B",0
1529,1,173,0,1.411006," ","integrate(1/(1-2*x)/(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{454044255102900 \, x^{5} + 1468076424167430 \, x^{4} + 1897568655019884 \, x^{3} + 1225594367568417 \, x^{2} + 3363290787500 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(5 \, x + 3\right) - 3363290786988 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(3 \, x + 2\right) - 512 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(2 \, x - 1\right) + 395538240141506 \, x + 51027557612801}{89480468 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"1/89480468*(454044255102900*x^5 + 1468076424167430*x^4 + 1897568655019884*x^3 + 1225594367568417*x^2 + 3363290787500*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5*x + 3) - 3363290786988*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(3*x + 2) - 512*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(2*x - 1) + 395538240141506*x + 51027557612801)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","B",0
1530,1,174,0,0.837318," ","integrate((d*x+c)^4/(-b*x+a)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a b^{3} d^{4} x^{3} + 12 \, a b^{3} c d^{3} x^{2} + 6 \, {\left(6 \, a b^{3} c^{2} d^{2} + a^{3} b d^{4}\right)} x - 3 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(b x - a\right)}{6 \, a b^{5}}"," ",0,"-1/6*(2*a*b^3*d^4*x^3 + 12*a*b^3*c*d^3*x^2 + 6*(6*a*b^3*c^2*d^2 + a^3*b*d^4)*x - 3*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(b*x + a) + 3*(b^4*c^4 + 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + a^4*d^4)*log(b*x - a))/(a*b^5)","A",0
1531,1,119,0,1.666878," ","integrate((d*x+c)^3/(-b*x+a)/(b*x+a),x, algorithm=""fricas"")","-\frac{a b^{2} d^{3} x^{2} + 6 \, a b^{2} c d^{2} x - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(b x + a\right) + {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(b x - a\right)}{2 \, a b^{4}}"," ",0,"-1/2*(a*b^2*d^3*x^2 + 6*a*b^2*c*d^2*x - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x + a) + (b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*log(b*x - a))/(a*b^4)","A",0
1532,1,76,0,1.803847," ","integrate((d*x+c)^2/(-b*x+a)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a b d^{2} x - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x + a\right) + {\left(b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x - a\right)}{2 \, a b^{3}}"," ",0,"-1/2*(2*a*b*d^2*x - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x + a) + (b^2*c^2 + 2*a*b*c*d + a^2*d^2)*log(b*x - a))/(a*b^3)","A",0
1533,1,41,0,1.024971," ","integrate((d*x+c)/(-b*x+a)/(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b c - a d\right)} \log\left(b x + a\right) - {\left(b c + a d\right)} \log\left(b x - a\right)}{2 \, a b^{2}}"," ",0,"1/2*((b*c - a*d)*log(b*x + a) - (b*c + a*d)*log(b*x - a))/(a*b^2)","A",0
1534,1,25,0,1.144162," ","integrate(1/(-b*x+a)/(b*x+a),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right) - \log\left(b x - a\right)}{2 \, a b}"," ",0,"1/2*(log(b*x + a) - log(b*x - a))/(a*b)","A",0
1535,1,64,0,1.804277," ","integrate(1/(-b*x+a)/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, a d \log\left(d x + c\right) - {\left(b c + a d\right)} \log\left(b x + a\right) + {\left(b c - a d\right)} \log\left(b x - a\right)}{2 \, {\left(a b^{2} c^{2} - a^{3} d^{2}\right)}}"," ",0,"-1/2*(2*a*d*log(d*x + c) - (b*c + a*d)*log(b*x + a) + (b*c - a*d)*log(b*x - a))/(a*b^2*c^2 - a^3*d^2)","A",0
1536,1,244,0,3.044889," ","integrate(1/(-b*x+a)/(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, a b^{2} c^{2} d - 2 \, a^{3} d^{3} + {\left(b^{3} c^{3} + 2 \, 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\right)} \log\left(b x + a\right) - {\left(b^{3} c^{3} - 2 \, 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\right)} \log\left(b x - a\right) - 4 \, {\left(a b^{2} c d^{2} x + a b^{2} c^{2} d\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{4} c^{5} - 2 \, a^{3} b^{2} c^{3} d^{2} + a^{5} c d^{4} + {\left(a b^{4} c^{4} d - 2 \, a^{3} b^{2} c^{2} d^{3} + a^{5} d^{5}\right)} x\right)}}"," ",0,"1/2*(2*a*b^2*c^2*d - 2*a^3*d^3 + (b^3*c^3 + 2*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)*log(b*x + a) - (b^3*c^3 - 2*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)*log(b*x - a) - 4*(a*b^2*c*d^2*x + a*b^2*c^2*d)*log(d*x + c))/(a*b^4*c^5 - 2*a^3*b^2*c^3*d^2 + a^5*c*d^4 + (a*b^4*c^4*d - 2*a^3*b^2*c^2*d^3 + a^5*d^5)*x)","B",0
1537,1,605,0,17.026117," ","integrate(1/(-b*x+a)/(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{5 \, a b^{4} c^{4} d - 6 \, a^{3} b^{2} c^{2} d^{3} + a^{5} d^{5} + 4 \, {\left(a b^{4} c^{3} d^{2} - a^{3} b^{2} c d^{4}\right)} x + {\left(b^{5} c^{5} + 3 \, a b^{4} c^{4} d + 3 \, a^{2} b^{3} c^{3} d^{2} + a^{3} b^{2} c^{2} d^{3} + {\left(b^{5} c^{3} d^{2} + 3 \, a b^{4} c^{2} d^{3} + 3 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d + 3 \, a b^{4} c^{3} d^{2} + 3 \, a^{2} b^{3} c^{2} d^{3} + a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 3 \, a^{2} b^{3} c^{3} d^{2} - a^{3} b^{2} c^{2} d^{3} + {\left(b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} + 3 \, a^{2} b^{3} c d^{4} - a^{3} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d - 3 \, a b^{4} c^{3} d^{2} + 3 \, a^{2} b^{3} c^{2} d^{3} - a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x - a\right) - 2 \, {\left(3 \, a b^{4} c^{4} d + a^{3} b^{2} c^{2} d^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + a^{3} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(3 \, a b^{4} c^{3} d^{2} + a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{6} c^{8} - 3 \, a^{3} b^{4} c^{6} d^{2} + 3 \, a^{5} b^{2} c^{4} d^{4} - a^{7} c^{2} d^{6} + {\left(a b^{6} c^{6} d^{2} - 3 \, a^{3} b^{4} c^{4} d^{4} + 3 \, a^{5} b^{2} c^{2} d^{6} - a^{7} d^{8}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} d - 3 \, a^{3} b^{4} c^{5} d^{3} + 3 \, a^{5} b^{2} c^{3} d^{5} - a^{7} c d^{7}\right)} x\right)}}"," ",0,"1/2*(5*a*b^4*c^4*d - 6*a^3*b^2*c^2*d^3 + a^5*d^5 + 4*(a*b^4*c^3*d^2 - a^3*b^2*c*d^4)*x + (b^5*c^5 + 3*a*b^4*c^4*d + 3*a^2*b^3*c^3*d^2 + a^3*b^2*c^2*d^3 + (b^5*c^3*d^2 + 3*a*b^4*c^2*d^3 + 3*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + 2*(b^5*c^4*d + 3*a*b^4*c^3*d^2 + 3*a^2*b^3*c^2*d^3 + a^3*b^2*c*d^4)*x)*log(b*x + a) - (b^5*c^5 - 3*a*b^4*c^4*d + 3*a^2*b^3*c^3*d^2 - a^3*b^2*c^2*d^3 + (b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 + 3*a^2*b^3*c*d^4 - a^3*b^2*d^5)*x^2 + 2*(b^5*c^4*d - 3*a*b^4*c^3*d^2 + 3*a^2*b^3*c^2*d^3 - a^3*b^2*c*d^4)*x)*log(b*x - a) - 2*(3*a*b^4*c^4*d + a^3*b^2*c^2*d^3 + (3*a*b^4*c^2*d^3 + a^3*b^2*d^5)*x^2 + 2*(3*a*b^4*c^3*d^2 + a^3*b^2*c*d^4)*x)*log(d*x + c))/(a*b^6*c^8 - 3*a^3*b^4*c^6*d^2 + 3*a^5*b^2*c^4*d^4 - a^7*c^2*d^6 + (a*b^6*c^6*d^2 - 3*a^3*b^4*c^4*d^4 + 3*a^5*b^2*c^2*d^6 - a^7*d^8)*x^2 + 2*(a*b^6*c^7*d - 3*a^3*b^4*c^5*d^3 + 3*a^5*b^2*c^3*d^5 - a^7*c*d^7)*x)","B",0
1538,1,67,0,1.425656," ","integrate((2+3*x)^8*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{73483200 \, x^{9} + 545525280 \, x^{8} + 1896488640 \, x^{7} + 4156264224 \, x^{6} + 6612458328 \, x^{5} + 8581153140 \, x^{4} + 10604249460 \, x^{3} + 17048666670 \, x^{2} + 8618377495 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 12825383340 \, x - 2219448385}{35840 \, {\left(2 \, x - 1\right)}}"," ",0,"1/35840*(73483200*x^9 + 545525280*x^8 + 1896488640*x^7 + 4156264224*x^6 + 6612458328*x^5 + 8581153140*x^4 + 10604249460*x^3 + 17048666670*x^2 + 8618377495*(2*x - 1)*log(2*x - 1) - 12825383340*x - 2219448385)/(2*x - 1)","A",0
1539,1,62,0,0.724878," ","integrate((2+3*x)^7*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{13996800 \, x^{8} + 95333760 \, x^{7} + 304492608 \, x^{6} + 619554096 \, x^{5} + 945299880 \, x^{4} + 1283987880 \, x^{3} + 2148763260 \, x^{2} + 1095312190 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 1563377550 \, x - 317064055}{17920 \, {\left(2 \, x - 1\right)}}"," ",0,"1/17920*(13996800*x^8 + 95333760*x^7 + 304492608*x^6 + 619554096*x^5 + 945299880*x^4 + 1283987880*x^3 + 2148763260*x^2 + 1095312190*(2*x - 1)*log(2*x - 1) - 1563377550*x - 317064055)/(2*x - 1)","A",0
1540,1,57,0,0.930857," ","integrate((2+3*x)^6*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{388800 \, x^{7} + 2418336 \, x^{6} + 7101432 \, x^{5} + 13636260 \, x^{4} + 21239460 \, x^{3} + 37849590 \, x^{2} + 19580155 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 26464680 \, x - 6470695}{1280 \, {\left(2 \, x - 1\right)}}"," ",0,"1/1280*(388800*x^7 + 2418336*x^6 + 7101432*x^5 + 13636260*x^4 + 21239460*x^3 + 37849590*x^2 + 19580155*(2*x - 1)*log(2*x - 1) - 26464680*x - 6470695)/(2*x - 1)","A",0
1541,1,52,0,1.471323," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{15552 \, x^{6} + 88128 \, x^{5} + 240480 \, x^{4} + 459360 \, x^{3} + 904080 \, x^{2} + 480200 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 602934 \, x - 184877}{128 \, {\left(2 \, x - 1\right)}}"," ",0,"1/128*(15552*x^6 + 88128*x^5 + 240480*x^4 + 459360*x^3 + 904080*x^2 + 480200*(2*x - 1)*log(2*x - 1) - 602934*x - 184877)/(2*x - 1)","A",0
1542,1,47,0,1.081700," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{3240 \, x^{5} + 16812 \, x^{4} + 44460 \, x^{3} + 102786 \, x^{2} + 57281 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 64812 \, x - 26411}{64 \, {\left(2 \, x - 1\right)}}"," ",0,"1/64*(3240*x^5 + 16812*x^4 + 44460*x^3 + 102786*x^2 + 57281*(2*x - 1)*log(2*x - 1) - 64812*x - 26411)/(2*x - 1)","A",0
1543,1,42,0,1.393996," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 6354 \, x - 3773}{32 \, {\left(2 \, x - 1\right)}}"," ",0,"1/32*(720*x^4 + 3528*x^3 + 10764*x^2 + 6566*(2*x - 1)*log(2*x - 1) - 6354*x - 3773)/(2*x - 1)","A",0
1544,1,37,0,1.485007," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{180 \, x^{3} + 966 \, x^{2} + 707 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 528 \, x - 539}{16 \, {\left(2 \, x - 1\right)}}"," ",0,"1/16*(180*x^3 + 966*x^2 + 707*(2*x - 1)*log(2*x - 1) - 528*x - 539)/(2*x - 1)","A",0
1545,1,32,0,1.405471," ","integrate((2+3*x)*(3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{60 \, x^{2} + 68 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 30 \, x - 77}{8 \, {\left(2 \, x - 1\right)}}"," ",0,"1/8*(60*x^2 + 68*(2*x - 1)*log(2*x - 1) - 30*x - 77)/(2*x - 1)","A",0
1546,1,24,0,1.442772," ","integrate((3+5*x)/(1-2*x)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 11}{4 \, {\left(2 \, x - 1\right)}}"," ",0,"1/4*(5*(2*x - 1)*log(2*x - 1) - 11)/(2*x - 1)","A",0
1547,1,37,0,1.467502," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, x - 1\right)} \log\left(3 \, x + 2\right) - 2 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) + 77}{98 \, {\left(2 \, x - 1\right)}}"," ",0,"-1/98*(2*(2*x - 1)*log(3*x + 2) - 2*(2*x - 1)*log(2*x - 1) + 77)/(2*x - 1)","A",0
1548,1,49,0,1.337909," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","\frac{31 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(3 \, x + 2\right) - 31 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(2 \, x - 1\right) - 217 \, x - 161}{343 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/343*(31*(6*x^2 + x - 2)*log(3*x + 2) - 31*(6*x^2 + x - 2)*log(2*x - 1) - 217*x - 161)/(6*x^2 + x - 2)","A",0
1549,1,75,0,1.368248," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{5376 \, x^{2} - 256 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(3 \, x + 2\right) + 256 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(2 \, x - 1\right) + 4032 \, x + 413}{4802 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/4802*(5376*x^2 - 256*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) + 256*(18*x^3 + 15*x^2 - 4*x - 4)*log(2*x - 1) + 4032*x + 413)/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
1550,1,95,0,1.343662," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{146664 \, x^{3} + 207774 \, x^{2} - 2328 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(3 \, x + 2\right) + 2328 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(2 \, x - 1\right) + 48209 \, x - 15148}{100842 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/100842*(146664*x^3 + 207774*x^2 - 2328*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(3*x + 2) + 2328*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) + 48209*x - 15148)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
1551,1,115,0,1.351212," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{2358720 \, x^{4} + 4914000 \, x^{3} + 3003000 \, x^{2} - 12480 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(3 \, x + 2\right) + 12480 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(2 \, x - 1\right) - 64610 \, x - 370853}{1411788 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/1411788*(2358720*x^4 + 4914000*x^3 + 3003000*x^2 - 12480*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(3*x + 2) + 12480*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(2*x - 1) - 64610*x - 370853)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
1552,1,135,0,1.496192," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{88724160 \, x^{5} + 243991440 \, x^{4} + 236187000 \, x^{3} + 72875670 \, x^{2} - 156480 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(3 \, x + 2\right) + 156480 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(2 \, x - 1\right) - 24420823 \, x - 14729806}{49412580 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"-1/49412580*(88724160*x^5 + 243991440*x^4 + 236187000*x^3 + 72875670*x^2 - 156480*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2) + 156480*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*x - 1) - 24420823*x - 14729806)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","A",0
1553,1,140,0,1.405393," ","integrate((3+5*x)/(1-2*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{2177280 \, x^{6} + 7439040 \, x^{5} + 9787680 \, x^{4} + 5652360 \, x^{3} + 592956 \, x^{2} - 1280 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(3 \, x + 2\right) + 1280 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(2 \, x - 1\right) - 929404 \, x - 343917}{1176490 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)}}"," ",0,"-1/1176490*(2177280*x^6 + 7439040*x^5 + 9787680*x^4 + 5652360*x^3 + 592956*x^2 - 1280*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(3*x + 2) + 1280*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(2*x - 1) - 929404*x - 343917)/(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)","A",0
1554,1,72,0,0.999596," ","integrate((2+3*x)^8*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{653184000 \, x^{10} + 5209142400 \, x^{9} + 19476780480 \, x^{8} + 45754035840 \, x^{7} + 76962239424 \, x^{6} + 101724024528 \, x^{5} + 116681956440 \, x^{4} + 134531996760 \, x^{3} + 210532633220 \, x^{2} + 105899394370 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 163136074990 \, x - 24413932235}{71680 \, {\left(2 \, x - 1\right)}}"," ",0,"1/71680*(653184000*x^10 + 5209142400*x^9 + 19476780480*x^8 + 45754035840*x^7 + 76962239424*x^6 + 101724024528*x^5 + 116681956440*x^4 + 134531996760*x^3 + 210532633220*x^2 + 105899394370*(2*x - 1)*log(2*x - 1) - 163136074990*x - 24413932235)/(2*x - 1)","A",0
1555,1,67,0,1.017833," ","integrate((2+3*x)^7*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{122472000 \, x^{9} + 899877600 \, x^{8} + 3097258560 \, x^{7} + 6724111968 \, x^{6} + 10607727816 \, x^{5} + 13671721980 \, x^{4} + 16817757180 \, x^{3} + 26981935610 \, x^{2} + 13633754365 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 20333387200 \, x - 3487704605}{35840 \, {\left(2 \, x - 1\right)}}"," ",0,"1/35840*(122472000*x^9 + 899877600*x^8 + 3097258560*x^7 + 6724111968*x^6 + 10607727816*x^5 + 13671721980*x^4 + 16817757180*x^3 + 26981935610*x^2 + 13633754365*(2*x - 1)*log(2*x - 1) - 20333387200*x - 3487704605)/(2*x - 1)","A",0
1556,1,62,0,1.614126," ","integrate((2+3*x)^6*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{23328000 \, x^{8} + 157075200 \, x^{7} + 496202112 \, x^{6} + 999450144 \, x^{5} + 1511863920 \, x^{4} + 2040862320 \, x^{3} + 3404640680 \, x^{2} + 1734146260 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 2482127410 \, x - 498243515}{17920 \, {\left(2 \, x - 1\right)}}"," ",0,"1/17920*(23328000*x^8 + 157075200*x^7 + 496202112*x^6 + 999450144*x^5 + 1511863920*x^4 + 2040862320*x^3 + 3404640680*x^2 + 1734146260*(2*x - 1)*log(2*x - 1) - 2482127410*x - 498243515)/(2*x - 1)","A",0
1557,1,57,0,1.185656," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{129600 \, x^{7} + 795744 \, x^{6} + 2308392 \, x^{5} + 4385100 \, x^{4} + 6773580 \, x^{3} + 12013810 \, x^{2} + 6206585 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 8419604 \, x - 2033647}{256 \, {\left(2 \, x - 1\right)}}"," ",0,"1/256*(129600*x^7 + 795744*x^6 + 2308392*x^5 + 4385100*x^4 + 6773580*x^3 + 12013810*x^2 + 6206585*(2*x - 1)*log(2*x - 1) - 8419604*x - 2033647)/(2*x - 1)","A",0
1558,1,52,0,0.710273," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{25920 \, x^{6} + 144720 \, x^{5} + 389592 \, x^{4} + 735960 \, x^{3} + 1438276 \, x^{2} + 762146 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 961682 \, x - 290521}{128 \, {\left(2 \, x - 1\right)}}"," ",0,"1/128*(25920*x^6 + 144720*x^5 + 389592*x^4 + 735960*x^3 + 1438276*x^2 + 762146*(2*x - 1)*log(2*x - 1) - 961682*x - 290521)/(2*x - 1)","A",0
1559,1,47,0,1.437697," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 103784 \, x - 41503}{64 \, {\left(2 \, x - 1\right)}}"," ",0,"1/64*(5400*x^5 + 27540*x^4 + 71748*x^3 + 164134*x^2 + 91091*(2*x - 1)*log(2*x - 1) - 103784*x - 41503)/(2*x - 1)","A",0
1560,1,42,0,1.360981," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{1200 \, x^{4} + 5760 \, x^{3} + 17296 \, x^{2} + 10472 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 10238 \, x - 5929}{32 \, {\left(2 \, x - 1\right)}}"," ",0,"1/32*(1200*x^4 + 5760*x^3 + 17296*x^2 + 10472*(2*x - 1)*log(2*x - 1) - 10238*x - 5929)/(2*x - 1)","A",0
1561,1,37,0,1.382402," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{300 \, x^{3} + 1570 \, x^{2} + 1133 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 860 \, x - 847}{16 \, {\left(2 \, x - 1\right)}}"," ",0,"1/16*(300*x^3 + 1570*x^2 + 1133*(2*x - 1)*log(2*x - 1) - 860*x - 847)/(2*x - 1)","A",0
1562,1,32,0,1.285259," ","integrate((3+5*x)^2/(1-2*x)^2,x, algorithm=""fricas"")","\frac{100 \, x^{2} + 110 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 50 \, x - 121}{8 \, {\left(2 \, x - 1\right)}}"," ",0,"1/8*(100*x^2 + 110*(2*x - 1)*log(2*x - 1) - 50*x - 121)/(2*x - 1)","A",0
1563,1,37,0,1.567807," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, x - 1\right)} \log\left(3 \, x + 2\right) + 1221 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 2541}{588 \, {\left(2 \, x - 1\right)}}"," ",0,"1/588*(4*(2*x - 1)*log(3*x + 2) + 1221*(2*x - 1)*log(2*x - 1) - 2541)/(2*x - 1)","A",0
1564,1,49,0,1.460214," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{132 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(3 \, x + 2\right) - 132 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(2 \, x - 1\right) + 7651 \, x + 5068}{2058 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"-1/2058*(132*(6*x^2 + x - 2)*log(3*x + 2) - 132*(6*x^2 + x - 2)*log(2*x - 1) + 7651*x + 5068)/(6*x^2 + x - 2)","A",0
1565,1,75,0,1.127088," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{40194 \, x^{2} - 1914 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(3 \, x + 2\right) + 1914 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(2 \, x - 1\right) + 60158 \, x + 22127}{14406 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/14406*(40194*x^2 - 1914*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) + 1914*(18*x^3 + 15*x^2 - 4*x - 4)*log(2*x - 1) + 60158*x + 22127)/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
1566,1,95,0,1.383265," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{773388 \, x^{3} + 1095633 \, x^{2} - 12276 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(3 \, x + 2\right) + 12276 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(2 \, x - 1\right) + 464303 \, x + 50939}{151263 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/151263*(773388*x^3 + 1095633*x^2 - 12276*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(3*x + 2) + 12276*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) + 464303*x + 50939)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
1567,1,115,0,1.357803," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{9480240 \, x^{4} + 19750500 \, x^{3} + 12069750 \, x^{2} - 50160 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(3 \, x + 2\right) + 50160 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(2 \, x - 1\right) + 1210930 \, x - 583289}{1411788 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/1411788*(9480240*x^4 + 19750500*x^3 + 12069750*x^2 - 50160*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(3*x + 2) + 50160*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(2*x - 1) + 1210930*x - 583289)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
1568,1,135,0,1.118891," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{63866880 \, x^{5} + 175633920 \, x^{4} + 170016000 \, x^{3} + 52458560 \, x^{2} - 112640 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(3 \, x + 2\right) + 112640 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(2 \, x - 1\right) - 10716139 \, x - 6392708}{8235430 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"-1/8235430*(63866880*x^5 + 175633920*x^4 + 170016000*x^3 + 52458560*x^2 - 112640*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2) + 112640*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*x - 1) - 10716139*x - 6392708)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","A",0
1569,1,140,0,1.083667," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{1239416640 \, x^{6} + 4234673520 \, x^{5} + 5571636840 \, x^{4} + 3217605930 \, x^{3} + 337540203 \, x^{2} - 728640 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(3 \, x + 2\right) + 728640 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(2 \, x - 1\right) - 426120352 \, x - 132853546}{148237740 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)}}"," ",0,"-1/148237740*(1239416640*x^6 + 4234673520*x^5 + 5571636840*x^4 + 3217605930*x^3 + 337540203*x^2 - 728640*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(3*x + 2) + 728640*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(2*x - 1) - 426120352*x - 132853546)/(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)","A",0
1570,1,175,0,1.458616," ","integrate((3+5*x)^2/(1-2*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{5227104960 \, x^{7} + 21344011920 \, x^{6} + 35403956280 \, x^{5} + 29235085110 \, x^{4} + 10470141297 \, x^{3} - 1282240575 \, x^{2} - 1024320 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)} \log\left(3 \, x + 2\right) + 1024320 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)} \log\left(2 \, x - 1\right) - 2289114821 \, x - 535775051}{605304105 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)}}"," ",0,"-1/605304105*(5227104960*x^7 + 21344011920*x^6 + 35403956280*x^5 + 29235085110*x^4 + 10470141297*x^3 - 1282240575*x^2 - 1024320*(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)*log(3*x + 2) + 1024320*(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)*log(2*x - 1) - 2289114821*x - 535775051)/(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)","A",0
1571,1,77,0,1.030800," ","integrate((2+3*x)^8*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{5878656000 \, x^{11} + 50186304000 \, x^{10} + 201292257600 \, x^{9} + 507052003680 \, x^{8} + 909105215040 \, x^{7} + 1257998896224 \, x^{6} + 1446852761928 \, x^{5} + 1516182519740 \, x^{4} + 1666955952060 \, x^{3} + 2565503311770 \, x^{2} + 1286962999245 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 2037810393640 \, x - 268553254585}{143360 \, {\left(2 \, x - 1\right)}}"," ",0,"1/143360*(5878656000*x^11 + 50186304000*x^10 + 201292257600*x^9 + 507052003680*x^8 + 909105215040*x^7 + 1257998896224*x^6 + 1446852761928*x^5 + 1516182519740*x^4 + 1666955952060*x^3 + 2565503311770*x^2 + 1286962999245*(2*x - 1)*log(2*x - 1) - 2037810393640*x - 268553254585)/(2*x - 1)","A",0
1572,1,72,0,0.978014," ","integrate((2+3*x)^7*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{1088640000 \, x^{10} + 8600256000 \, x^{9} + 31861382400 \, x^{8} + 74191887360 \, x^{7} + 123787657728 \, x^{6} + 162468222336 \, x^{5} + 185355446080 \, x^{4} + 213008156480 \, x^{3} + 332899764960 \, x^{2} + 167409821040 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 258337866850 \, x - 38364750655}{71680 \, {\left(2 \, x - 1\right)}}"," ",0,"1/71680*(1088640000*x^10 + 8600256000*x^9 + 31861382400*x^8 + 74191887360*x^7 + 123787657728*x^6 + 162468222336*x^5 + 185355446080*x^4 + 213008156480*x^3 + 332899764960*x^2 + 167409821040*(2*x - 1)*log(2*x - 1) - 258337866850*x - 38364750655)/(2*x - 1)","A",0
1573,1,67,0,1.320901," ","integrate((2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{204120000 \, x^{9} + 1484244000 \, x^{8} + 5057380800 \, x^{7} + 10876051872 \, x^{6} + 17013246264 \, x^{5} + 21778294020 \, x^{4} + 26669020420 \, x^{3} + 42700132230 \, x^{2} + 21566826435 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 32234227060 \, x - 5480678665}{35840 \, {\left(2 \, x - 1\right)}}"," ",0,"1/35840*(204120000*x^9 + 1484244000*x^8 + 5057380800*x^7 + 10876051872*x^6 + 17013246264*x^5 + 21778294020*x^4 + 26669020420*x^3 + 42700132230*x^2 + 21566826435*(2*x - 1)*log(2*x - 1) - 32234227060*x - 5480678665)/(2*x - 1)","A",0
1574,1,62,0,1.505765," ","integrate((2+3*x)^5*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{7776000 \, x^{8} + 51753600 \, x^{7} + 161687232 \, x^{6} + 322377552 \, x^{5} + 483490840 \, x^{4} + 648677400 \, x^{3} + 1078815780 \, x^{2} + 549084690 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 788084318 \, x - 156590819}{3584 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3584*(7776000*x^8 + 51753600*x^7 + 161687232*x^6 + 322377552*x^5 + 483490840*x^4 + 648677400*x^3 + 1078815780*x^2 + 549084690*(2*x - 1)*log(2*x - 1) - 788084318*x - 156590819)/(2*x - 1)","A",0
1575,1,57,0,1.317300," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{216000 \, x^{7} + 1308960 \, x^{6} + 3750840 \, x^{5} + 7048772 \, x^{4} + 10798660 \, x^{3} + 19064166 \, x^{2} + 9836211 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 13391552 \, x - 3195731}{256 \, {\left(2 \, x - 1\right)}}"," ",0,"1/256*(216000*x^7 + 1308960*x^6 + 3750840*x^5 + 7048772*x^4 + 10798660*x^3 + 19064166*x^2 + 9836211*(2*x - 1)*log(2*x - 1) - 13391552*x - 3195731)/(2*x - 1)","A",0
1576,1,52,0,1.414573," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{43200 \, x^{6} + 237600 \, x^{5} + 630960 \, x^{4} + 1178768 \, x^{3} + 2287704 \, x^{2} + 1209516 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 1533614 \, x - 456533}{128 \, {\left(2 \, x - 1\right)}}"," ",0,"1/128*(43200*x^6 + 237600*x^5 + 630960*x^4 + 1178768*x^3 + 2287704*x^2 + 1209516*(2*x - 1)*log(2*x - 1) - 1533614*x - 456533)/(2*x - 1)","A",0
1577,1,47,0,0.922540," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{9000 \, x^{5} + 45100 \, x^{4} + 115740 \, x^{3} + 262026 \, x^{2} + 144837 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 166148 \, x - 65219}{64 \, {\left(2 \, x - 1\right)}}"," ",0,"1/64*(9000*x^5 + 45100*x^4 + 115740*x^3 + 262026*x^2 + 144837*(2*x - 1)*log(2*x - 1) - 166148*x - 65219)/(2*x - 1)","A",0
1578,1,42,0,1.776502," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{2000 \, x^{4} + 9400 \, x^{3} + 27780 \, x^{2} + 16698 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 16490 \, x - 9317}{32 \, {\left(2 \, x - 1\right)}}"," ",0,"1/32*(2000*x^4 + 9400*x^3 + 27780*x^2 + 16698*(2*x - 1)*log(2*x - 1) - 16490*x - 9317)/(2*x - 1)","A",0
1579,1,37,0,1.435836," ","integrate((3+5*x)^3/(1-2*x)^2,x, algorithm=""fricas"")","\frac{500 \, x^{3} + 2550 \, x^{2} + 1815 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 1400 \, x - 1331}{16 \, {\left(2 \, x - 1\right)}}"," ",0,"1/16*(500*x^3 + 2550*x^2 + 1815*(2*x - 1)*log(2*x - 1) - 1400*x - 1331)/(2*x - 1)","A",0
1580,1,45,0,1.634144," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x),x, algorithm=""fricas"")","\frac{73500 \, x^{2} - 8 \, {\left(2 \, x - 1\right)} \log\left(3 \, x + 2\right) + 78408 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 36750 \, x - 83853}{3528 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3528*(73500*x^2 - 8*(2*x - 1)*log(3*x + 2) + 78408*(2*x - 1)*log(2*x - 1) - 36750*x - 83853)/(2*x - 1)","A",0
1581,1,49,0,1.341281," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","\frac{404 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(3 \, x + 2\right) + 42471 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(2 \, x - 1\right) - 251503 \, x - 167734}{12348 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/12348*(404*(6*x^2 + x - 2)*log(3*x + 2) + 42471*(6*x^2 + x - 2)*log(2*x - 1) - 251503*x - 167734)/(6*x^2 + x - 2)","A",0
1582,1,75,0,1.329566," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{763161 \, x^{2} + 6534 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(3 \, x + 2\right) - 6534 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(2 \, x - 1\right) + 1007552 \, x + 332633}{43218 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/43218*(763161*x^2 + 6534*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) - 6534*(18*x^3 + 15*x^2 - 4*x - 4)*log(2*x - 1) + 1007552*x + 332633)/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
1583,1,95,0,1.489956," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{11114334 \, x^{3} + 25199244 \, x^{2} - 176418 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(3 \, x + 2\right) + 176418 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(2 \, x - 1\right) + 18674579 \, x + 4544792}{907578 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/907578*(11114334*x^3 + 25199244*x^2 - 176418*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(3*x + 2) + 176418*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) + 18674579*x + 4544792)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
1584,1,115,0,1.703224," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{296382240 \, x^{4} + 617463000 \, x^{3} + 465575250 \, x^{2} - 1568160 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(3 \, x + 2\right) + 1568160 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(2 \, x - 1\right) + 147766430 \, x + 16012787}{12706092 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/12706092*(296382240*x^4 + 617463000*x^3 + 465575250*x^2 - 1568160*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(3*x + 2) + 1568160*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(2*x - 1) + 147766430*x + 16012787)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
1585,1,135,0,1.707285," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{4593924720 \, x^{5} + 12633292980 \, x^{4} + 12229197750 \, x^{3} + 4545399390 \, x^{2} - 8102160 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(3 \, x + 2\right) + 8102160 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(2 \, x - 1\right) + 181895609 \, x - 165794902}{148237740 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"-1/148237740*(4593924720*x^5 + 12633292980*x^4 + 12229197750*x^3 + 4545399390*x^2 - 8102160*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2) + 8102160*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*x - 1) + 181895609*x - 165794902)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","A",0
1586,1,140,0,1.618946," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{16004640960 \, x^{6} + 54682523280 \, x^{5} + 71946788760 \, x^{4} + 41549085270 \, x^{3} + 6211643067 \, x^{2} - 9408960 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(3 \, x + 2\right) + 9408960 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)} \log\left(2 \, x - 1\right) - 3228815828 \, x - 1017833894}{444713220 \, {\left(1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64\right)}}"," ",0,"-1/444713220*(16004640960*x^6 + 54682523280*x^5 + 71946788760*x^4 + 41549085270*x^3 + 6211643067*x^2 - 9408960*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(3*x + 2) + 9408960*(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)*log(2*x - 1) - 3228815828*x - 1017833894)/(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64)","A",0
1587,1,175,0,1.521796," ","integrate((3+5*x)^3/(1-2*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{848245970880 \, x^{7} + 3463671047760 \, x^{6} + 5745295626840 \, x^{5} + 4744221388830 \, x^{4} + 1699077259341 \, x^{3} - 132416872350 \, x^{2} - 166224960 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)} \log\left(3 \, x + 2\right) + 166224960 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)} \log\left(2 \, x - 1\right) - 278976950938 \, x - 58668936928}{21790947780 \, {\left(4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right)}}"," ",0,"-1/21790947780*(848245970880*x^7 + 3463671047760*x^6 + 5745295626840*x^5 + 4744221388830*x^4 + 1699077259341*x^3 - 132416872350*x^2 - 166224960*(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)*log(3*x + 2) + 166224960*(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)*log(2*x - 1) - 278976950938*x - 58668936928)/(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)","A",0
1588,1,70,0,1.500494," ","integrate((2+3*x)^8/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{264627000000 \, x^{7} + 1688320260000 \, x^{6} + 5078633175000 \, x^{5} + 9963975928500 \, x^{4} + 15782492474100 \, x^{3} + 28400446856430 \, x^{2} + 256 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 14733698984375 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 19765652916240 \, x - 4954125859375}{2420000000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/2420000000*(264627000000*x^7 + 1688320260000*x^6 + 5078633175000*x^5 + 9963975928500*x^4 + 15782492474100*x^3 + 28400446856430*x^2 + 256*(2*x - 1)*log(5*x + 3) + 14733698984375*(2*x - 1)*log(2*x - 1) - 19765652916240*x - 4954125859375)/(2*x - 1)","A",0
1589,1,65,0,1.516918," ","integrate((2+3*x)^7/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{10585080000 \, x^{6} + 61746300000 \, x^{5} + 173066058000 \, x^{4} + 338044330800 \, x^{3} + 674996568840 \, x^{2} + 128 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 360300062500 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 447832551870 \, x - 141546453125}{242000000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/242000000*(10585080000*x^6 + 61746300000*x^5 + 173066058000*x^4 + 338044330800*x^3 + 674996568840*x^2 + 128*(2*x - 1)*log(5*x + 3) + 360300062500*(2*x - 1)*log(2*x - 1) - 447832551870*x - 141546453125)/(2*x - 1)","A",0
1590,1,60,0,1.344249," ","integrate((2+3*x)^6/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{441045000 \, x^{5} + 2366941500 \, x^{4} + 6448077900 \, x^{3} + 15229153170 \, x^{2} + 64 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 8561065625 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 9550029060 \, x - 4044184375}{24200000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/24200000*(441045000*x^5 + 2366941500*x^4 + 6448077900*x^3 + 15229153170*x^2 + 64*(2*x - 1)*log(5*x + 3) + 8561065625*(2*x - 1)*log(2*x - 1) - 9550029060*x - 4044184375)/(2*x - 1)","A",0
1591,1,55,0,1.445251," ","integrate((2+3*x)^5/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{19602000 \, x^{4} + 99970200 \, x^{3} + 314873460 \, x^{2} + 32 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 195081250 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 184879530 \, x - 115548125}{2420000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/2420000*(19602000*x^4 + 99970200*x^3 + 314873460*x^2 + 32*(2*x - 1)*log(5*x + 3) + 195081250*(2*x - 1)*log(2*x - 1) - 184879530*x - 115548125)/(2*x - 1)","A",0
1592,1,50,0,1.245335," ","integrate((2+3*x)^4/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{980100 \, x^{3} + 5521230 \, x^{2} + 16 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 4158875 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 3005640 \, x - 3301375}{242000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/242000*(980100*x^3 + 5521230*x^2 + 16*(2*x - 1)*log(5*x + 3) + 4158875*(2*x - 1)*log(2*x - 1) - 3005640*x - 3301375)/(2*x - 1)","A",0
1593,1,45,0,1.369857," ","integrate((2+3*x)^3/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{65340 \, x^{2} + 8 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 78400 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 32670 \, x - 94325}{24200 \, {\left(2 \, x - 1\right)}}"," ",0,"1/24200*(65340*x^2 + 8*(2*x - 1)*log(5*x + 3) + 78400*(2*x - 1)*log(2*x - 1) - 32670*x - 94325)/(2*x - 1)","A",0
1594,1,37,0,1.329914," ","integrate((2+3*x)^2/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) + 1085 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 2695}{2420 \, {\left(2 \, x - 1\right)}}"," ",0,"1/2420*(4*(2*x - 1)*log(5*x + 3) + 1085*(2*x - 1)*log(2*x - 1) - 2695)/(2*x - 1)","A",0
1595,1,37,0,0.740498," ","integrate((2+3*x)/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) - 2 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 77}{242 \, {\left(2 \, x - 1\right)}}"," ",0,"1/242*(2*(2*x - 1)*log(5*x + 3) - 2*(2*x - 1)*log(2*x - 1) - 77)/(2*x - 1)","A",0
1596,1,37,0,1.549510," ","integrate(1/(1-2*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{5 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) - 5 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 11}{121 \, {\left(2 \, x - 1\right)}}"," ",0,"1/121*(5*(2*x - 1)*log(5*x + 3) - 5*(2*x - 1)*log(2*x - 1) - 11)/(2*x - 1)","A",0
1597,1,50,0,1.657600," ","integrate(1/(1-2*x)^2/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{1225 \, {\left(2 \, x - 1\right)} \log\left(5 \, x + 3\right) - 1089 \, {\left(2 \, x - 1\right)} \log\left(3 \, x + 2\right) - 136 \, {\left(2 \, x - 1\right)} \log\left(2 \, x - 1\right) - 154}{5929 \, {\left(2 \, x - 1\right)}}"," ",0,"1/5929*(1225*(2*x - 1)*log(5*x + 3) - 1089*(2*x - 1)*log(3*x + 2) - 136*(2*x - 1)*log(2*x - 1) - 154)/(2*x - 1)","A",0
1598,1,65,0,1.467625," ","integrate(1/(1-2*x)^2/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{42875 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(5 \, x + 3\right) - 42471 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(3 \, x + 2\right) - 404 \, {\left(6 \, x^{2} + x - 2\right)} \log\left(2 \, x - 1\right) + 14322 \, x - 8239}{41503 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/41503*(42875*(6*x^2 + x - 2)*log(5*x + 3) - 42471*(6*x^2 + x - 2)*log(3*x + 2) - 404*(6*x^2 + x - 2)*log(2*x - 1) + 14322*x - 8239)/(6*x^2 + x - 2)","A",0
1599,1,98,0,1.308447," ","integrate(1/(1-2*x)^2/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{3556476 \, x^{2} + 3001250 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(5 \, x + 3\right) - 2999106 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(3 \, x + 2\right) - 2144 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(2 \, x - 1\right) + 686532 \, x - 1247477}{581042 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/581042*(3556476*x^2 + 3001250*(18*x^3 + 15*x^2 - 4*x - 4)*log(5*x + 3) - 2999106*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) - 2144*(18*x^3 + 15*x^2 - 4*x - 4)*log(2*x - 1) + 686532*x - 1247477)/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
1600,1,123,0,1.384950," ","integrate(1/(1-2*x)^2/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{377820828 \, x^{3} + 327259548 \, x^{2} + 105043750 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(5 \, x + 3\right) - 105038406 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(3 \, x + 2\right) - 5344 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(2 \, x - 1\right) - 81484557 \, x - 88405856}{4067294 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"1/4067294*(377820828*x^3 + 327259548*x^2 + 105043750*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(5*x + 3) - 105038406*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(3*x + 2) - 5344*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(2*x - 1) - 81484557*x - 88405856)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","B",0
1601,1,148,0,1.778938," ","integrate(1/(1-2*x)^2/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{79408236600 \, x^{4} + 121756635000 \, x^{3} + 28788432750 \, x^{2} + 7353062500 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(5 \, x + 3\right) - 7353036900 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(3 \, x + 2\right) - 25600 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(2 \, x - 1\right) - 29974871850 \, x - 12393745441}{56942116 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"1/56942116*(79408236600*x^4 + 121756635000*x^3 + 28788432750*x^2 + 7353062500*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(5*x + 3) - 7353036900*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(3*x + 2) - 25600*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log(2*x - 1) - 29974871850*x - 12393745441)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","B",0
1602,1,173,0,1.450533," ","integrate(1/(1-2*x)^2/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{41691695272920 \, x^{5} + 91721636594280 \, x^{4} + 57735061287750 \, x^{3} - 5658908734710 \, x^{2} + 1286785937500 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(5 \, x + 3\right) - 1286785639260 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(3 \, x + 2\right) - 298240 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(2 \, x - 1\right) - 16998574124301 \, x - 4338387945122}{1992974060 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"1/1992974060*(41691695272920*x^5 + 91721636594280*x^4 + 57735061287750*x^3 - 5658908734710*x^2 + 1286785937500*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(5*x + 3) - 1286785639260*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2) - 298240*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*x - 1) - 16998574124301*x - 4338387945122)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","B",0
1603,1,79,0,1.325911," ","integrate((2+3*x)^8/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{1746538200000 \, x^{7} + 11381607270000 \, x^{6} + 35550138195000 \, x^{5} + 75582410904000 \, x^{4} + 151398804021300 \, x^{3} - 7200755986050 \, x^{2} + 34304 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 12481823593750 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 71072602198741 \, x - 14862377576717}{13310000000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/13310000000*(1746538200000*x^7 + 11381607270000*x^6 + 35550138195000*x^5 + 75582410904000*x^4 + 151398804021300*x^3 - 7200755986050*x^2 + 34304*(10*x^2 + x - 3)*log(5*x + 3) + 12481823593750*(10*x^2 + x - 3)*log(2*x - 1) - 71072602198741*x - 14862377576717)/(10*x^2 + x - 3)","A",0
1604,1,74,0,1.479355," ","integrate((2+3*x)^7/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{72772425000 \, x^{6} + 440677462500 \, x^{5} + 1335778290000 \, x^{4} + 3278990706750 \, x^{3} - 66522621330 \, x^{2} + 15040 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 295960765625 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 1691007398993 \, x - 424639358671}{1331000000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1331000000*(72772425000*x^6 + 440677462500*x^5 + 1335778290000*x^4 + 3278990706750*x^3 - 66522621330*x^2 + 15040*(10*x^2 + x - 3)*log(5*x + 3) + 295960765625*(10*x^2 + x - 3)*log(2*x - 1) - 1691007398993*x - 424639358671)/(10*x^2 + x - 3)","A",0
1605,1,69,0,1.543046," ","integrate((2+3*x)^6/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{3234330000 \, x^{5} + 18759114000 \, x^{4} + 63910360800 \, x^{3} + 773004870 \, x^{2} + 6464 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 6722800000 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 39132050089 \, x - 12132552773}{133100000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/133100000*(3234330000*x^5 + 18759114000*x^4 + 63910360800*x^3 + 773004870*x^2 + 6464*(10*x^2 + x - 3)*log(5*x + 3) + 6722800000*(10*x^2 + x - 3)*log(2*x - 1) - 39132050089*x - 12132552773)/(10*x^2 + x - 3)","A",0
1606,1,64,0,1.559980," ","integrate((2+3*x)^5/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{161716500 \, x^{4} + 1029595050 \, x^{3} + 52827390 \, x^{2} + 2704 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 142559375 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 881767997 \, x - 346644199}{13310000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/13310000*(161716500*x^4 + 1029595050*x^3 + 52827390*x^2 + 2704*(10*x^2 + x - 3)*log(5*x + 3) + 142559375*(10*x^2 + x - 3)*log(2*x - 1) - 881767997*x - 346644199)/(10*x^2 + x - 3)","A",0
1607,1,59,0,1.303193," ","integrate((2+3*x)^4/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{10781100 \, x^{3} + 1078110 \, x^{2} + 1088 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 2658250 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 19741381 \, x - 9904037}{1331000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1331000*(10781100*x^3 + 1078110*x^2 + 1088*(10*x^2 + x - 3)*log(5*x + 3) + 2658250*(10*x^2 + x - 3)*log(2*x - 1) - 19741381*x - 9904037)/(10*x^2 + x - 3)","A",0
1608,1,49,0,1.317958," ","integrate((2+3*x)^3/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{412 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) + 35525 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 471713 \, x - 282931}{133100 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/133100*(412*(10*x^2 + x - 3)*log(5*x + 3) + 35525*(10*x^2 + x - 3)*log(2*x - 1) - 471713*x - 282931)/(10*x^2 + x - 3)","A",0
1609,1,49,0,1.527009," ","integrate((2+3*x)^2/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{140 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) - 140 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 13519 \, x - 8063}{13310 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/13310*(140*(10*x^2 + x - 3)*log(5*x + 3) - 140*(10*x^2 + x - 3)*log(2*x - 1) - 13519*x - 8063)/(10*x^2 + x - 3)","A",0
1610,1,49,0,1.497781," ","integrate((2+3*x)/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{37 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) - 37 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 407 \, x - 220}{1331 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1331*(37*(10*x^2 + x - 3)*log(5*x + 3) - 37*(10*x^2 + x - 3)*log(2*x - 1) - 407*x - 220)/(10*x^2 + x - 3)","A",0
1611,1,49,0,1.563341," ","integrate(1/(1-2*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{20 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) - 20 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) - 220 \, x - 11}{1331 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1331*(20*(10*x^2 + x - 3)*log(5*x + 3) - 20*(10*x^2 + x - 3)*log(2*x - 1) - 220*x - 11)/(10*x^2 + x - 3)","A",0
1612,1,65,0,1.142140," ","integrate(1/(1-2*x)^2/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{35525 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(5 \, x + 3\right) - 35937 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(3 \, x + 2\right) + 412 \, {\left(10 \, x^{2} + x - 3\right)} \log\left(2 \, x - 1\right) + 28490 \, x - 12551}{65219 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"-1/65219*(35525*(10*x^2 + x - 3)*log(5*x + 3) - 35937*(10*x^2 + x - 3)*log(3*x + 2) + 412*(10*x^2 + x - 3)*log(2*x - 1) + 28490*x - 12551)/(10*x^2 + x - 3)","A",0
1613,1,98,0,1.427101," ","integrate(1/(1-2*x)^2/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{5354580 \, x^{2} + 2658250 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \log\left(5 \, x + 3\right) - 2659338 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \log\left(3 \, x + 2\right) + 1088 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \log\left(2 \, x - 1\right) + 734888 \, x - 1694231}{456533 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)}}"," ",0,"-1/456533*(5354580*x^2 + 2658250*(30*x^3 + 23*x^2 - 7*x - 6)*log(5*x + 3) - 2659338*(30*x^3 + 23*x^2 - 7*x - 6)*log(3*x + 2) + 1088*(30*x^3 + 23*x^2 - 7*x - 6)*log(2*x - 1) + 734888*x - 1694231)/(30*x^3 + 23*x^2 - 7*x - 6)","A",0
1614,1,123,0,1.617578," ","integrate(1/(1-2*x)^2/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1711280340 \, x^{3} + 1369336584 \, x^{2} + 285118750 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \log\left(5 \, x + 3\right) - 285124158 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \log\left(3 \, x + 2\right) + 5408 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \log\left(2 \, x - 1\right) - 390771227 \, x - 360692563}{6391462 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)}}"," ",0,"-1/6391462*(1711280340*x^3 + 1369336584*x^2 + 285118750*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log(5*x + 3) - 285124158*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log(3*x + 2) + 5408*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log(2*x - 1) - 390771227*x - 360692563)/(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)","B",0
1615,1,148,0,1.445758," ","integrate(1/(1-2*x)^2/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{121012436160 \, x^{4} + 177486026256 \, x^{3} + 36888162696 \, x^{2} + 6722800000 \, {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)} \log\left(5 \, x + 3\right) - 6722806464 \, {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)} \log\left(3 \, x + 2\right) + 6464 \, {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)} \log\left(2 \, x - 1\right) - 43940321194 \, x - 17000329577}{22370117 \, {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)}}"," ",0,"-1/22370117*(121012436160*x^4 + 177486026256*x^3 + 36888162696*x^2 + 6722800000*(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)*log(5*x + 3) - 6722806464*(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)*log(3*x + 2) + 6464*(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)*log(2*x - 1) - 43940321194*x - 17000329577)/(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)","B",0
1616,1,173,0,1.264643," ","integrate(1/(1-2*x)^2/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{63927582226200 \, x^{5} + 136378873350720 \, x^{4} + 81993113952750 \, x^{3} - 10222048359600 \, x^{2} + 1183843062500 \, {\left(810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right)} \log\left(5 \, x + 3\right) - 1183843122660 \, {\left(810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right)} \log\left(3 \, x + 2\right) + 60160 \, {\left(810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right)} \log\left(2 \, x - 1\right) - 24455908667575 \, x - 5987073080219}{626363276 \, {\left(810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right)}}"," ",0,"-1/626363276*(63927582226200*x^5 + 136378873350720*x^4 + 81993113952750*x^3 - 10222048359600*x^2 + 1183843062500*(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48)*log(5*x + 3) - 1183843122660*(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48)*log(3*x + 2) + 60160*(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48)*log(2*x - 1) - 24455908667575*x - 5987073080219)/(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48)","B",0
1617,1,100,0,1.626287," ","integrate((2+3*x)^8/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{12007450125000 \, x^{7} + 80983580287500 \, x^{6} + 270968124487500 \, x^{5} + 698838044478750 \, x^{4} + 327005737947900 \, x^{3} - 298950055409445 \, x^{2} + 2019840 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 10229948203125 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) - 249835373577966 \, x - 44587132164487}{73205000000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/73205000000*(12007450125000*x^7 + 80983580287500*x^6 + 270968124487500*x^5 + 698838044478750*x^4 + 327005737947900*x^3 - 298950055409445*x^2 + 2019840*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 10229948203125*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) - 249835373577966*x - 44587132164487)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1618,1,95,0,1.573142," ","integrate((2+3*x)^7/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{533664450000 \, x^{6} + 3468818925000 \, x^{5} + 12781263577500 \, x^{4} + 6680945249550 \, x^{3} - 6674047531965 \, x^{2} + 761760 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 231621468750 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) - 6180073448472 \, x - 1273917828029}{7320500000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/7320500000*(533664450000*x^6 + 3468818925000*x^5 + 12781263577500*x^4 + 6680945249550*x^3 - 6674047531965*x^2 + 761760*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 231621468750*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) - 6180073448472*x - 1273917828029)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1619,1,90,0,1.668990," ","integrate((2+3*x)^6/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{26683222500 \, x^{5} + 189450879750 \, x^{4} + 113136863400 \, x^{3} - 146893374705 \, x^{2} + 274224 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 4884534375 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) - 152064641058 \, x - 36397551751}{732050000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/732050000*(26683222500*x^5 + 189450879750*x^4 + 113136863400*x^3 - 146893374705*x^2 + 274224*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 4884534375*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) - 152064641058*x - 36397551751)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1620,1,85,0,1.355997," ","integrate((2+3*x)^5/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1778881500 \, x^{4} + 1245217050 \, x^{3} - 3315783405 \, x^{2} + 92496 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 90037500 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) - 3786658260 \, x - 1039888025}{73205000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/73205000*(1778881500*x^4 + 1245217050*x^3 - 3315783405*x^2 + 92496*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 90037500*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) - 3786658260*x - 1039888025)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1621,1,75,0,1.220263," ","integrate((2+3*x)^4/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{82594215 \, x^{2} - 28296 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) - 1157625 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 99047718 \, x + 29694181}{7320500 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/7320500*(82594215*x^2 - 28296*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) - 1157625*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 99047718*x + 29694181)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1622,1,75,0,1.618854," ","integrate((2+3*x)^3/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{2380785 \, x^{2} - 7350 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 7350 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 2832258 \, x + 842006}{732050 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/732050*(2380785*x^2 - 7350*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 7350*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 2832258*x + 842006)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1623,1,75,0,1.498751," ","integrate((2+3*x)^2/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{150150 \, x^{2} - 2730 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 2730 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 163482 \, x + 43769}{146410 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/146410*(150150*x^2 - 2730*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 2730*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 163482*x + 43769)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1624,1,75,0,1.296495," ","integrate((2+3*x)/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{15840 \, x^{2} - 288 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 288 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 10296 \, x + 209}{29282 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/29282*(15840*x^2 - 288*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 288*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 10296*x + 209)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1625,1,75,0,1.365465," ","integrate(1/(1-2*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{6600 \, x^{2} - 120 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) + 120 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 4290 \, x - 1133}{29282 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/29282*(6600*x^2 - 120*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 120*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 4290*x - 1133)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1626,1,98,0,1.273678," ","integrate(1/(1-2*x)^2/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{7784700 \, x^{2} + 2374050 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(5 \, x + 3\right) - 2371842 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(3 \, x + 2\right) - 2208 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(2 \, x - 1\right) + 448140 \, x - 2207513}{1434818 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/1434818*(7784700*x^2 + 2374050*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) - 2371842*(50*x^3 + 35*x^2 - 12*x - 9)*log(3*x + 2) - 2208*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 448140*x - 2207513)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
1627,1,123,0,1.554085," ","integrate(1/(1-2*x)^2/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2584404900 \, x^{3} + 1894703580 \, x^{2} + 258536250 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \log\left(5 \, x + 3\right) - 258530778 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \log\left(3 \, x + 2\right) - 5472 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \log\left(2 \, x - 1\right) - 614007471 \, x - 489983648}{10043726 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)}}"," ",0,"1/10043726*(2584404900*x^3 + 1894703580*x^2 + 258536250*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log(5*x + 3) - 258530778*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log(3*x + 2) - 5472*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log(2*x - 1) - 614007471*x - 489983648)/(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)","B",0
1628,1,148,0,1.321650," ","integrate(1/(1-2*x)^2/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{553723770600 \, x^{4} + 775209508920 \, x^{3} + 139245535506 \, x^{2} + 18457687500 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \log\left(5 \, x + 3\right) - 18457674444 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \log\left(3 \, x + 2\right) - 13056 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \log\left(2 \, x - 1\right) - 192629430378 \, x - 70007419097}{70306082 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)}}"," ",0,"1/70306082*(553723770600*x^4 + 775209508920*x^3 + 139245535506*x^2 + 18457687500*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(5*x + 3) - 18457674444*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(3*x + 2) - 13056*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(2*x - 1) - 192629430378*x - 70007419097)/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)","B",0
1629,1,173,0,1.259395," ","integrate(1/(1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{98075099845800 \, x^{5} + 202688513402760 \, x^{4} + 116200773740898 \, x^{3} - 17675352484482 \, x^{2} + 1089723862500 \, {\left(1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right)} \log\left(5 \, x + 3\right) - 1089723832164 \, {\left(1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right)} \log\left(3 \, x + 2\right) - 30336 \, {\left(1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right)} \log\left(2 \, x - 1\right) - 35145131488467 \, x - 8266584593036}{492142574 \, {\left(1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right)}}"," ",0,"1/492142574*(98075099845800*x^5 + 202688513402760*x^4 + 116200773740898*x^3 - 17675352484482*x^2 + 1089723862500*(1350*x^6 + 3645*x^5 + 3366*x^4 + 769*x^3 - 638*x^2 - 420*x - 72)*log(5*x + 3) - 1089723832164*(1350*x^6 + 3645*x^5 + 3366*x^4 + 769*x^3 - 638*x^2 - 420*x - 72)*log(3*x + 2) - 30336*(1350*x^6 + 3645*x^5 + 3366*x^4 + 769*x^3 - 638*x^2 - 420*x - 72)*log(2*x - 1) - 35145131488467*x - 8266584593036)/(1350*x^6 + 3645*x^5 + 3366*x^4 + 769*x^3 - 638*x^2 - 420*x - 72)","B",0
1630,1,77,0,1.352810," ","integrate((2+3*x)^8*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{167961600 \, x^{9} + 1288638720 \, x^{8} + 4709643264 \, x^{7} + 11192743296 \, x^{6} + 20513437056 \, x^{5} + 34854109920 \, x^{4} + 77800605120 \, x^{3} - 118730138940 \, x^{2} + 29746373160 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 631530340 \, x + 15017306605}{71680 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/71680*(167961600*x^9 + 1288638720*x^8 + 4709643264*x^7 + 11192743296*x^6 + 20513437056*x^5 + 34854109920*x^4 + 77800605120*x^3 - 118730138940*x^2 + 29746373160*(4*x^2 - 4*x + 1)*log(2*x - 1) - 631530340*x + 15017306605)/(4*x^2 - 4*x + 1)","A",0
1631,1,72,0,1.488883," ","integrate((2+3*x)^7*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{4665600 \, x^{8} + 33219072 \, x^{7} + 113980608 \, x^{6} + 263003328 \, x^{5} + 512613360 \, x^{4} + 1218762720 \, x^{3} - 1777082220 \, x^{2} + 472948980 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 126674020 \, x + 267651475}{5120 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/5120*(4665600*x^8 + 33219072*x^7 + 113980608*x^6 + 263003328*x^5 + 512613360*x^4 + 1218762720*x^3 - 1777082220*x^2 + 472948980*(4*x^2 - 4*x + 1)*log(2*x - 1) - 126674020*x + 267651475)/(4*x^2 - 4*x + 1)","A",0
1632,1,67,0,0.939432," ","integrate((2+3*x)^6*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{186624 \, x^{7} + 1236384 \, x^{6} + 4056480 \, x^{5} + 9701640 \, x^{4} + 25485840 \, x^{3} - 35211672 \, x^{2} + 10156230 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 5937536 \, x + 6537923}{512 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/512*(186624*x^7 + 1236384*x^6 + 4056480*x^5 + 9701640*x^4 + 25485840*x^3 - 35211672*x^2 + 10156230*(4*x^2 - 4*x + 1)*log(2*x - 1) - 5937536*x + 6537923)/(4*x^2 - 4*x + 1)","A",0
1633,1,62,0,1.442266," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{38880 \, x^{6} + 242784 \, x^{5} + 804600 \, x^{4} + 2484720 \, x^{3} - 3221712 \, x^{2} + 1039290 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 1048088 \, x + 775523}{256 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/256*(38880*x^6 + 242784*x^5 + 804600*x^4 + 2484720*x^3 - 3221712*x^2 + 1039290*(4*x^2 - 4*x + 1)*log(2*x - 1) - 1048088*x + 775523)/(4*x^2 - 4*x + 1)","A",0
1634,1,57,0,1.579422," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{8640 \, x^{5} + 53136 \, x^{4} + 216864 \, x^{3} - 261036 \, x^{2} + 99372 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 160004 \, x + 88151}{128 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/128*(8640*x^5 + 53136*x^4 + 216864*x^3 - 261036*x^2 + 99372*(4*x^2 - 4*x + 1)*log(2*x - 1) - 160004*x + 88151)/(4*x^2 - 4*x + 1)","A",0
1635,1,52,0,1.339482," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{2160 \, x^{4} + 15552 \, x^{3} - 17172 \, x^{2} + 8568 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 21836 \, x + 9359}{64 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/64*(2160*x^4 + 15552*x^3 - 17172*x^2 + 8568*(4*x^2 - 4*x + 1)*log(2*x - 1) - 21836*x + 9359)/(4*x^2 - 4*x + 1)","A",0
1636,1,47,0,1.510759," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{720 \, x^{3} - 720 \, x^{2} + 618 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 2648 \, x + 875}{32 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/32*(720*x^3 - 720*x^2 + 618*(4*x^2 - 4*x + 1)*log(2*x - 1) - 2648*x + 875)/(4*x^2 - 4*x + 1)","A",0
1637,1,37,0,1.522882," ","integrate((2+3*x)*(3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{30 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 272 \, x + 59}{16 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/16*(30*(4*x^2 - 4*x + 1)*log(2*x - 1) - 272*x + 59)/(4*x^2 - 4*x + 1)","A",0
1638,1,19,0,1.338259," ","integrate((3+5*x)/(1-2*x)^3,x, algorithm=""fricas"")","\frac{20 \, x + 1}{8 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/8*(20*x + 1)/(4*x^2 - 4*x + 1)","A",0
1639,1,55,0,1.926111," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x),x, algorithm=""fricas"")","-\frac{12 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(3 \, x + 2\right) - 12 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 56 \, x - 511}{1372 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1372*(12*(4*x^2 - 4*x + 1)*log(3*x + 2) - 12*(4*x^2 - 4*x + 1)*log(2*x - 1) - 56*x - 511)/(4*x^2 - 4*x + 1)","A",0
1640,1,75,0,1.533209," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{2436 \, x^{2} - 174 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(3 \, x + 2\right) + 174 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(2 \, x - 1\right) - 1015 \, x - 1988}{4802 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"-1/4802*(2436*x^2 - 174*(12*x^3 - 4*x^2 - 5*x + 2)*log(3*x + 2) + 174*(12*x^3 - 4*x^2 - 5*x + 2)*log(2*x - 1) - 1015*x - 1988)/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
1641,1,95,0,0.822306," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{46872 \, x^{3} + 11718 \, x^{2} - 1116 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(3 \, x + 2\right) + 1116 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(2 \, x - 1\right) - 25606 \, x - 9191}{33614 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"-1/33614*(46872*x^3 + 11718*x^2 - 1116*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(3*x + 2) + 1116*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 25606*x - 9191)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
1642,1,115,0,1.514882," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{574560 \, x^{4} + 526680 \, x^{3} - 218120 \, x^{2} - 4560 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(3 \, x + 2\right) + 4560 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(2 \, x - 1\right) - 236075 \, x - 21616}{235298 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/235298*(574560*x^4 + 526680*x^3 - 218120*x^2 - 4560*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) + 4560*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 236075*x - 21616)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
1643,1,135,0,1.382162," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{11612160 \, x^{5} + 18385920 \, x^{4} + 2688000 \, x^{3} - 7710080 \, x^{2} - 30720 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(3 \, x + 2\right) + 30720 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(2 \, x - 1\right) - 2825088 \, x + 197925}{3294172 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"-1/3294172*(11612160*x^5 + 18385920*x^4 + 2688000*x^3 - 7710080*x^2 - 30720*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(3*x + 2) + 30720*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(2*x - 1) - 2825088*x + 197925)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
1644,1,155,0,1.193308," ","integrate((3+5*x)/(1-2*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{75116160 \, x^{6} + 169011360 \, x^{5} + 96677280 \, x^{4} - 38282580 \, x^{3} - 51524508 \, x^{2} - 66240 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)} \log\left(3 \, x + 2\right) + 66240 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)} \log\left(2 \, x - 1\right) - 7943257 \, x + 2669758}{16470860 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)}}"," ",0,"-1/16470860*(75116160*x^6 + 169011360*x^5 + 96677280*x^4 - 38282580*x^3 - 51524508*x^2 - 66240*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)*log(3*x + 2) + 66240*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)*log(2*x - 1) - 7943257*x + 2669758)/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)","A",0
1645,1,77,0,1.505379," ","integrate((2+3*x)^7*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{279936000 \, x^{9} + 2125958400 \, x^{8} + 7694383104 \, x^{7} + 18122662656 \, x^{6} + 32961712896 \, x^{5} + 55697987520 \, x^{4} + 123980115840 \, x^{3} - 189590514540 \, x^{2} + 47370193360 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 461405140 \, x + 23779804125}{71680 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/71680*(279936000*x^9 + 2125958400*x^8 + 7694383104*x^7 + 18122662656*x^6 + 32961712896*x^5 + 55697987520*x^4 + 123980115840*x^3 - 189590514540*x^2 + 47370193360*(4*x^2 - 4*x + 1)*log(2*x - 1) - 461405140*x + 23779804125)/(4*x^2 - 4*x + 1)","A",0
1646,1,72,0,1.232321," ","integrate((2+3*x)^6*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{1555200 \, x^{8} + 10948608 \, x^{7} + 37169280 \, x^{6} + 84963456 \, x^{5} + 164403360 \, x^{4} + 389263680 \, x^{3} - 568886292 \, x^{2} + 150878840 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 38266316 \, x + 84858543}{1024 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1024*(1555200*x^8 + 10948608*x^7 + 37169280*x^6 + 84963456*x^5 + 164403360*x^4 + 389263680*x^3 - 568886292*x^2 + 150878840*(4*x^2 - 4*x + 1)*log(2*x - 1) - 38266316*x + 84858543)/(4*x^2 - 4*x + 1)","A",0
1647,1,67,0,1.035320," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{311040 \, x^{7} + 2034720 \, x^{6} + 6598944 \, x^{5} + 15633000 \, x^{4} + 40819920 \, x^{3} - 56538312 \, x^{2} + 16234190 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 9197168 \, x + 10379523}{512 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/512*(311040*x^7 + 2034720*x^6 + 6598944*x^5 + 15633000*x^4 + 40819920*x^3 - 56538312*x^2 + 16234190*(4*x^2 - 4*x + 1)*log(2*x - 1) - 9197168*x + 10379523)/(4*x^2 - 4*x + 1)","A",0
1648,1,62,0,1.382926," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{64800 \, x^{6} + 398880 \, x^{5} + 1305576 \, x^{4} + 3996624 \, x^{3} - 5195496 \, x^{2} + 1665902 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 1640144 \, x + 1233771}{256 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/256*(64800*x^6 + 398880*x^5 + 1305576*x^4 + 3996624*x^3 - 5195496*x^2 + 1665902*(4*x^2 - 4*x + 1)*log(2*x - 1) - 1640144*x + 1233771)/(4*x^2 - 4*x + 1)","A",0
1649,1,57,0,1.687159," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{14400 \, x^{5} + 87120 \, x^{4} + 351072 \, x^{3} - 423612 \, x^{2} + 159908 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 252116 \, x + 140679}{128 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/128*(14400*x^5 + 87120*x^4 + 351072*x^3 - 423612*x^2 + 159908*(4*x^2 - 4*x + 1)*log(2*x - 1) - 252116*x + 140679)/(4*x^2 - 4*x + 1)","A",0
1650,1,52,0,1.499433," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{3600 \, x^{4} + 25440 \, x^{3} - 28140 \, x^{2} + 13868 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 34628 \, x + 15015}{64 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/64*(3600*x^4 + 25440*x^3 - 28140*x^2 + 13868*(4*x^2 - 4*x + 1)*log(2*x - 1) - 34628*x + 15015)/(4*x^2 - 4*x + 1)","A",0
1651,1,47,0,1.306349," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{1200 \, x^{3} - 1200 \, x^{2} + 1010 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 4232 \, x + 1419}{32 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/32*(1200*x^3 - 1200*x^2 + 1010*(4*x^2 - 4*x + 1)*log(2*x - 1) - 4232*x + 1419)/(4*x^2 - 4*x + 1)","A",0
1652,1,37,0,1.372765," ","integrate((3+5*x)^2/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{50 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 440 \, x + 99}{16 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/16*(50*(4*x^2 - 4*x + 1)*log(2*x - 1) - 440*x + 99)/(4*x^2 - 4*x + 1)","A",0
1653,1,55,0,1.552683," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x),x, algorithm=""fricas"")","\frac{8 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(3 \, x + 2\right) - 8 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) + 11396 \, x + 231}{2744 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/2744*(8*(4*x^2 - 4*x + 1)*log(3*x + 2) - 8*(4*x^2 - 4*x + 1)*log(2*x - 1) + 11396*x + 231)/(4*x^2 - 4*x + 1)","A",0
1654,1,75,0,1.583213," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","\frac{3584 \, x^{2} - 256 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(3 \, x + 2\right) + 256 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(2 \, x - 1\right) + 18515 \, x + 10598}{9604 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/9604*(3584*x^2 - 256*(12*x^3 - 4*x^2 - 5*x + 2)*log(3*x + 2) + 256*(12*x^3 - 4*x^2 - 5*x + 2)*log(2*x - 1) + 18515*x + 10598)/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
1655,1,95,0,1.330852," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{69636 \, x^{3} + 17409 \, x^{2} - 1658 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(3 \, x + 2\right) + 1658 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(2 \, x - 1\right) - 84728 \, x - 43323}{33614 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"-1/33614*(69636*x^3 + 17409*x^2 - 1658*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(3*x + 2) + 1658*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 84728*x - 43323)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
1656,1,115,0,1.504690," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{2173500 \, x^{4} + 1992375 \, x^{3} - 825125 \, x^{2} - 17250 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(3 \, x + 2\right) + 17250 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(2 \, x - 1\right) - 1260700 \, x - 310877}{352947 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/352947*(2173500*x^4 + 1992375*x^3 - 825125*x^2 - 17250*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) + 17250*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 1260700*x - 310877)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
1657,1,135,0,0.821026," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{109045440 \, x^{5} + 172655280 \, x^{4} + 25242000 \, x^{3} - 72402470 \, x^{2} - 288480 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(3 \, x + 2\right) + 288480 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(2 \, x - 1\right) - 34764772 \, x - 3224165}{9882516 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"-1/9882516*(109045440*x^5 + 172655280*x^4 + 25242000*x^3 - 72402470*x^2 - 288480*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(3*x + 2) + 288480*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(2*x - 1) - 34764772*x - 3224165)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
1658,1,155,0,1.610005," ","integrate((3+5*x)^2/(1-2*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{198948960 \, x^{6} + 447635160 \, x^{5} + 256054680 \, x^{4} - 101393355 \, x^{3} - 136465273 \, x^{2} - 175440 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)} \log\left(3 \, x + 2\right) + 175440 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)} \log\left(2 \, x - 1\right) - 29616692 \, x + 1806623}{12353145 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)}}"," ",0,"-1/12353145*(198948960*x^6 + 447635160*x^5 + 256054680*x^4 - 101393355*x^3 - 136465273*x^2 - 175440*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)*log(3*x + 2) + 175440*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)*log(2*x - 1) - 29616692*x + 1806623)/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)","A",0
1659,1,77,0,1.255460," ","integrate((2+3*x)^6*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) + 24774428 \, x + 7530594841}{14336 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/14336*(93312000*x^9 + 701395200*x^8 + 2513700864*x^7 + 5867430912*x^6 + 10590741504*x^5 + 17798780160*x^4 + 39510141440*x^3 - 60542035484*x^2 + 15085963200*(4*x^2 - 4*x + 1)*log(2*x - 1) + 24774428*x + 7530594841)/(4*x^2 - 4*x + 1)","A",0
1660,1,72,0,1.706362," ","integrate((2+3*x)^5*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{2592000 \, x^{8} + 18040320 \, x^{7} + 60592320 \, x^{6} + 137206464 \, x^{5} + 263583600 \, x^{4} + 621559520 \, x^{3} - 910451612 \, x^{2} + 240641940 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 57645748 \, x + 134511223}{1024 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1024*(2592000*x^8 + 18040320*x^7 + 60592320*x^6 + 137206464*x^5 + 263583600*x^4 + 621559520*x^3 - 910451612*x^2 + 240641940*(4*x^2 - 4*x + 1)*log(2*x - 1) - 57645748*x + 134511223)/(4*x^2 - 4*x + 1)","A",0
1661,1,67,0,1.686887," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{518400 \, x^{7} + 3348000 \, x^{6} + 10732320 \, x^{5} + 25184616 \, x^{4} + 65368784 \, x^{3} - 90766856 \, x^{2} + 25946382 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 14235184 \, x + 16476691}{512 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/512*(518400*x^7 + 3348000*x^6 + 10732320*x^5 + 25184616*x^4 + 65368784*x^3 - 90766856*x^2 + 25946382*(4*x^2 - 4*x + 1)*log(2*x - 1) - 14235184*x + 16476691)/(4*x^2 - 4*x + 1)","A",0
1662,1,62,0,1.455135," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{108000 \, x^{6} + 655200 \, x^{5} + 2117880 \, x^{4} + 6426992 \, x^{3} - 8376752 \, x^{2} + 2669898 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 2565496 \, x + 1962499}{256 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/256*(108000*x^6 + 655200*x^5 + 2117880*x^4 + 6426992*x^3 - 8376752*x^2 + 2669898*(4*x^2 - 4*x + 1)*log(2*x - 1) - 2565496*x + 1962499)/(4*x^2 - 4*x + 1)","A",0
1663,1,57,0,1.575353," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{24000 \, x^{5} + 142800 \, x^{4} + 568160 \, x^{3} - 687260 \, x^{2} + 257268 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 397108 \, x + 224455}{128 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/128*(24000*x^5 + 142800*x^4 + 568160*x^3 - 687260*x^2 + 257268*(4*x^2 - 4*x + 1)*log(2*x - 1) - 397108*x + 224455)/(4*x^2 - 4*x + 1)","A",0
1664,1,52,0,0.803432," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{6000 \, x^{4} + 41600 \, x^{3} - 46100 \, x^{2} + 22440 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 54892 \, x + 24079}{64 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/64*(6000*x^4 + 41600*x^3 - 46100*x^2 + 22440*(4*x^2 - 4*x + 1)*log(2*x - 1) - 54892*x + 24079)/(4*x^2 - 4*x + 1)","A",0
1665,1,47,0,1.752815," ","integrate((3+5*x)^3/(1-2*x)^3,x, algorithm=""fricas"")","-\frac{2000 \, x^{3} - 2000 \, x^{2} + 1650 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 6760 \, x + 2299}{32 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/32*(2000*x^3 - 2000*x^2 + 1650*(4*x^2 - 4*x + 1)*log(2*x - 1) - 6760*x + 2299)/(4*x^2 - 4*x + 1)","A",0
1666,1,55,0,1.679273," ","integrate((3+5*x)^3/(1-2*x)^3/(2+3*x),x, algorithm=""fricas"")","-\frac{16 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(3 \, x + 2\right) + 85734 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 731808 \, x + 170247}{16464 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/16464*(16*(4*x^2 - 4*x + 1)*log(3*x + 2) + 85734*(4*x^2 - 4*x + 1)*log(2*x - 1) - 731808*x + 170247)/(4*x^2 - 4*x + 1)","A",0
1667,1,75,0,1.211003," ","integrate((3+5*x)^3/(1-2*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","\frac{1189412 \, x^{2} + 792 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 792 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(2 \, x - 1\right) + 784945 \, x - 5026}{57624 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/57624*(1189412*x^2 + 792*(12*x^3 - 4*x^2 - 5*x + 2)*log(3*x + 2) - 792*(12*x^3 - 4*x^2 - 5*x + 2)*log(2*x - 1) + 784945*x - 5026)/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
1668,1,95,0,1.317823," ","integrate((3+5*x)^3/(1-2*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","\frac{515592 \, x^{3} + 2229773 \, x^{2} - 12276 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(3 \, x + 2\right) + 12276 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(2 \, x - 1\right) + 2239384 \, x + 655214}{201684 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/201684*(515592*x^3 + 2229773*x^2 - 12276*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(3*x + 2) + 12276*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) + 2239384*x + 655214)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
1669,1,115,0,0.880370," ","integrate((3+5*x)^3/(1-2*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{17588340 \, x^{4} + 16122645 \, x^{3} - 21383180 \, x^{2} - 139590 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(3 \, x + 2\right) + 139590 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(2 \, x - 1\right) - 28918225 \, x - 8476076}{2117682 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/2117682*(17588340*x^4 + 16122645*x^3 - 21383180*x^2 - 139590*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) + 139590*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 28918225*x - 8476076)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
1670,1,135,0,1.391387," ","integrate((3+5*x)^3/(1-2*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{267941520 \, x^{5} + 424240740 \, x^{4} + 62023500 \, x^{3} - 229375510 \, x^{2} - 708840 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(3 \, x + 2\right) + 708840 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(2 \, x - 1\right) - 149599856 \, x - 27940465}{9882516 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"-1/9882516*(267941520*x^5 + 424240740*x^4 + 62023500*x^3 - 229375510*x^2 - 708840*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(3*x + 2) + 708840*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log(2*x - 1) - 149599856*x - 27940465)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
1671,1,85,0,1.051559," ","integrate((2+3*x)^8/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{1397230560000 \, x^{7} + 9489524220000 \, x^{6} + 31855563036000 \, x^{5} + 77649212460600 \, x^{4} + 206501370522480 \, x^{3} - 283893518434680 \, x^{2} - 512 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) + 82637392906250 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 51350638082480 \, x + 53929198640625}{10648000000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/10648000000*(1397230560000*x^7 + 9489524220000*x^6 + 31855563036000*x^5 + 77649212460600*x^4 + 206501370522480*x^3 - 283893518434680*x^2 - 512*(4*x^2 - 4*x + 1)*log(5*x + 3) + 82637392906250*(4*x^2 - 4*x + 1)*log(2*x - 1) - 51350638082480*x + 53929198640625)/(4*x^2 - 4*x + 1)","A",0
1672,1,80,0,1.373480," ","integrate((2+3*x)^7/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{58217940000 \, x^{6} + 373888548000 \, x^{5} + 1269992017800 \, x^{4} + 3991792836240 \, x^{3} - 5149424229840 \, x^{2} - 256 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) + 1681645393750 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 1777812991240 \, x + 1273918078125}{1064800000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1064800000*(58217940000*x^6 + 373888548000*x^5 + 1269992017800*x^4 + 3991792836240*x^3 - 5149424229840*x^2 - 256*(4*x^2 - 4*x + 1)*log(5*x + 3) + 1681645393750*(4*x^2 - 4*x + 1)*log(2*x - 1) - 1777812991240*x + 1273918078125)/(4*x^2 - 4*x + 1)","A",0
1673,1,75,0,1.486801," ","integrate((2+3*x)^6/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{2587464000 \, x^{5} + 16430396400 \, x^{4} + 68774793120 \, x^{3} - 82391322420 \, x^{2} - 128 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) + 31903287500 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 53550930620 \, x + 28771483125}{106480000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/106480000*(2587464000*x^5 + 16430396400*x^4 + 68774793120*x^3 - 82391322420*x^2 - 128*(4*x^2 - 4*x + 1)*log(5*x + 3) + 31903287500*(4*x^2 - 4*x + 1)*log(2*x - 1) - 53550930620*x + 28771483125)/(4*x^2 - 4*x + 1)","A",0
1674,1,70,0,1.532090," ","integrate((2+3*x)^5/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{129373200 \, x^{4} + 965986560 \, x^{3} - 1063016460 \, x^{2} - 64 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) + 543655000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 1442875060 \, x + 604151625}{10648000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/10648000*(129373200*x^4 + 965986560*x^3 - 1063016460*x^2 - 64*(4*x^2 - 4*x + 1)*log(5*x + 3) + 543655000*(4*x^2 - 4*x + 1)*log(2*x - 1) - 1442875060*x + 604151625)/(4*x^2 - 4*x + 1)","A",0
1675,1,65,0,1.463374," ","integrate((2+3*x)^4/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","-\frac{8624880 \, x^{3} - 8624880 \, x^{2} - 32 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) + 7690550 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 34441880 \, x + 11036025}{1064800 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1064800*(8624880*x^3 - 8624880*x^2 - 32*(4*x^2 - 4*x + 1)*log(5*x + 3) + 7690550*(4*x^2 - 4*x + 1)*log(2*x - 1) - 34441880*x + 11036025)/(4*x^2 - 4*x + 1)","A",0
1676,1,55,0,1.476718," ","integrate((2+3*x)^3/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{16 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) - 71890 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) + 689920 \, x - 137445}{106480 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/106480*(16*(4*x^2 - 4*x + 1)*log(5*x + 3) - 71890*(4*x^2 - 4*x + 1)*log(2*x - 1) + 689920*x - 137445)/(4*x^2 - 4*x + 1)","A",0
1677,1,55,0,1.642228," ","integrate((2+3*x)^2/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{8 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) - 8 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) + 9548 \, x + 1155}{10648 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/10648*(8*(4*x^2 - 4*x + 1)*log(5*x + 3) - 8*(4*x^2 - 4*x + 1)*log(2*x - 1) + 9548*x + 1155)/(4*x^2 - 4*x + 1)","A",0
1678,1,55,0,1.125976," ","integrate((2+3*x)/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{20 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) - 20 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 88 \, x + 891}{5324 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/5324*(20*(4*x^2 - 4*x + 1)*log(5*x + 3) - 20*(4*x^2 - 4*x + 1)*log(2*x - 1) - 88*x + 891)/(4*x^2 - 4*x + 1)","A",0
1679,1,55,0,1.897566," ","integrate(1/(1-2*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{50 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) - 50 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 220 \, x + 231}{2662 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/2662*(50*(4*x^2 - 4*x + 1)*log(5*x + 3) - 50*(4*x^2 - 4*x + 1)*log(2*x - 1) - 220*x + 231)/(4*x^2 - 4*x + 1)","A",0
1680,1,73,0,1.361180," ","integrate(1/(1-2*x)^3/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{42875 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(5 \, x + 3\right) - 35937 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(3 \, x + 2\right) - 6938 \, {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(2 \, x - 1\right) - 20944 \, x + 16401}{456533 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/456533*(42875*(4*x^2 - 4*x + 1)*log(5*x + 3) - 35937*(4*x^2 - 4*x + 1)*log(3*x + 2) - 6938*(4*x^2 - 4*x + 1)*log(2*x - 1) - 20944*x + 16401)/(4*x^2 - 4*x + 1)","A",0
1681,1,98,0,1.593896," ","integrate(1/(1-2*x)^3/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{819588 \, x^{2} + 1500625 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(5 \, x + 3\right) - 1473417 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(3 \, x + 2\right) - 27208 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(2 \, x - 1\right) - 1001770 \, x + 337491}{3195731 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/3195731*(819588*x^2 + 1500625*(12*x^3 - 4*x^2 - 5*x + 2)*log(5*x + 3) - 1473417*(12*x^3 - 4*x^2 - 5*x + 2)*log(3*x + 2) - 27208*(12*x^3 - 4*x^2 - 5*x + 2)*log(2*x - 1) - 1001770*x + 337491)/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
1682,1,123,0,1.302995," ","integrate(1/(1-2*x)^3/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{244562472 \, x^{3} - 77517132 \, x^{2} + 105043750 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(5 \, x + 3\right) - 104864166 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(3 \, x + 2\right) - 179584 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(2 \, x - 1\right) - 108953306 \, x + 43866669}{44740234 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/44740234*(244562472*x^3 - 77517132*x^2 + 105043750*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(5*x + 3) - 104864166*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(3*x + 2) - 179584*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(2*x - 1) - 108953306*x + 43866669)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","B",0
1683,1,148,0,0.899758," ","integrate(1/(1-2*x)^3/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{26403549480 \, x^{4} + 9644189940 \, x^{3} - 17141334210 \, x^{2} + 3676531250 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(5 \, x + 3\right) - 3675995730 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(3 \, x + 2\right) - 535520 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(2 \, x - 1\right) - 3318409325 \, x + 3092859924}{313181638 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"1/313181638*(26403549480*x^4 + 9644189940*x^3 - 17141334210*x^2 + 3676531250*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(5*x + 3) - 3675995730*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) - 535520*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 3318409325*x + 3092859924)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","B",0
1684,1,100,0,0.992930," ","integrate((2+3*x)^8/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{9605960100000 \, x^{7} + 68309049600000 \, x^{6} + 252583384185000 \, x^{5} + 811024095717000 \, x^{4} - 468362848619160 \, x^{3} - 838544848893576 \, x^{2} - 69120 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 57673745718750 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) + 32898384865071 \, x + 132062840768441}{58564000000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/58564000000*(9605960100000*x^7 + 68309049600000*x^6 + 252583384185000*x^5 + 811024095717000*x^4 - 468362848619160*x^3 - 838544848893576*x^2 - 69120*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 57673745718750*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) + 32898384865071*x + 132062840768441)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1685,1,95,0,1.570339," ","integrate((2+3*x)^7/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{426931560000 \, x^{6} + 3009867498000 \, x^{5} + 13324533987600 \, x^{4} - 6947670741660 \, x^{3} - 17706353292408 \, x^{2} - 30336 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 1089723862500 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 647305946397 \, x + 2972475517033}{5856400000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/5856400000*(426931560000*x^6 + 3009867498000*x^5 + 13324533987600*x^4 - 6947670741660*x^3 - 17706353292408*x^2 - 30336*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 1089723862500*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 647305946397*x + 2972475517033)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1686,1,90,0,1.372886," ","integrate((2+3*x)^6/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{21346578000 \, x^{5} + 175041939600 \, x^{4} - 80903530620 \, x^{3} - 356854410264 \, x^{2} - 13056 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 18457687500 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 46529265321 \, x + 62049343829}{585640000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/585640000*(21346578000*x^5 + 175041939600*x^4 - 80903530620*x^3 - 356854410264*x^2 - 13056*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 18457687500*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 46529265321*x + 62049343829)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1687,1,85,0,1.064245," ","integrate((2+3*x)^5/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1423105200 \, x^{4} - 569242080 \, x^{3} - 6770697912 \, x^{2} - 5472 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 258536250 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 1684826253 \, x + 1119166477}{58564000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/58564000*(1423105200*x^4 - 569242080*x^3 - 6770697912*x^2 - 5472*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 258536250*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 1684826253*x + 1119166477)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1688,1,75,0,0.748308," ","integrate((2+3*x)^4/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{116962296 \, x^{2} + 2208 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) - 2374050 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) + 48012129 \, x - 13300001}{5856400 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/5856400*(116962296*x^2 + 2208*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) - 2374050*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) + 48012129*x - 13300001)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1689,1,75,0,1.014290," ","integrate((2+3*x)^3/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{1562748 \, x^{2} + 840 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) - 840 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) + 1194237 \, x + 153527}{585640 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/585640*(1562748*x^2 + 840*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) - 840*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) + 1194237*x + 153527)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1690,1,75,0,1.111702," ","integrate((2+3*x)^2/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{6336 \, x^{2} - 288 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 288 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 29205 \, x - 19591}{58564 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/58564*(6336*x^2 - 288*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 288*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 29205*x - 19591)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1691,1,75,0,1.192211," ","integrate((2+3*x)/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{8580 \, x^{2} - 390 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 390 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 3861 \, x - 4873}{29282 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/29282*(8580*x^2 - 390*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 390*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 3861*x - 4873)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1692,1,75,0,1.124903," ","integrate(1/(1-2*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{3300 \, x^{2} - 150 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) + 150 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 1485 \, x - 748}{14641 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/14641*(3300*x^2 - 150*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) + 150*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 1485*x - 748)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1693,1,98,0,1.233331," ","integrate(1/(1-2*x)^3/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{2203740 \, x^{2} + 1157625 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(5 \, x + 3\right) - 1185921 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(3 \, x + 2\right) + 28296 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(2 \, x - 1\right) - 1914066 \, x + 340879}{5021863 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/5021863*(2203740*x^2 + 1157625*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) - 1185921*(20*x^3 - 8*x^2 - 7*x + 3)*log(3*x + 2) + 28296*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) - 1914066*x + 340879)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
1694,1,123,0,1.588347," ","integrate(1/(1-2*x)^3/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{366624720 \, x^{3} - 130867968 \, x^{2} + 90037500 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \log\left(5 \, x + 3\right) - 90129996 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \log\left(3 \, x + 2\right) + 92496 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \log\left(2 \, x - 1\right) - 141681540 \, x + 57273139}{35153041 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)}}"," ",0,"-1/35153041*(366624720*x^3 - 130867968*x^2 + 90037500*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(5*x + 3) - 90129996*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(3*x + 2) + 92496*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(2*x - 1) - 141681540*x + 57273139)/(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)","B",0
1695,1,148,0,0.831518," ","integrate(1/(1-2*x)^3/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{117343999080 \, x^{4} + 35266545468 \, x^{3} - 73726130478 \, x^{2} + 9769068750 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \log\left(5 \, x + 3\right) - 9769617198 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \log\left(3 \, x + 2\right) + 548448 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \log\left(2 \, x - 1\right) - 11356433319 \, x + 12361039691}{492142574 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)}}"," ",0,"-1/492142574*(117343999080*x^4 + 35266545468*x^3 - 73726130478*x^2 + 9769068750*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log(5*x + 3) - 9769617198*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log(3*x + 2) + 548448*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log(2*x - 1) - 11356433319*x + 12361039691)/(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)","B",0
1696,1,173,0,1.291497," ","integrate(1/(1-2*x)^3/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","-\frac{8338852783800 \, x^{5} + 8061154974180 \, x^{4} - 3573065429010 \, x^{3} - 4298892128685 \, x^{2} + 231621468750 \, {\left(540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right)} \log\left(5 \, x + 3\right) - 231622230510 \, {\left(540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right)} \log\left(3 \, x + 2\right) + 761760 \, {\left(540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right)} \log\left(2 \, x - 1\right) + 342379099755 \, x + 585732955423}{1722499009 \, {\left(540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right)}}"," ",0,"-1/1722499009*(8338852783800*x^5 + 8061154974180*x^4 - 3573065429010*x^3 - 4298892128685*x^2 + 231621468750*(540*x^6 + 864*x^5 + 99*x^4 - 425*x^3 - 154*x^2 + 52*x + 24)*log(5*x + 3) - 231622230510*(540*x^6 + 864*x^5 + 99*x^4 - 425*x^3 - 154*x^2 + 52*x + 24)*log(3*x + 2) + 761760*(540*x^6 + 864*x^5 + 99*x^4 - 425*x^3 - 154*x^2 + 52*x + 24)*log(2*x - 1) + 342379099755*x + 585732955423)/(540*x^6 + 864*x^5 + 99*x^4 - 425*x^3 - 154*x^2 + 52*x + 24)","B",0
1697,1,120,0,1.177667," ","integrate((2+3*x)^9/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1584983416500000 \, x^{8} + 12362870648700000 \, x^{7} + 49530731765625000 \, x^{6} + 163943640232020000 \, x^{5} + 3373337816263800 \, x^{4} - 192223824266320440 \, x^{3} - 81487109015452107 \, x^{2} - 10498560 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 1977661307343750 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 25922683108313662 \, x + 13688249752028357}{3221020000000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/3221020000000*(1584983416500000*x^8 + 12362870648700000*x^7 + 49530731765625000*x^6 + 163943640232020000*x^5 + 3373337816263800*x^4 - 192223824266320440*x^3 - 81487109015452107*x^2 - 10498560*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 1977661307343750*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 25922683108313662*x + 13688249752028357)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1698,1,115,0,1.202676," ","integrate((2+3*x)^8/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{70443707400000 \, x^{7} + 545938732350000 \, x^{6} + 2559454702200000 \, x^{5} + 180911181221100 \, x^{4} - 3748001092791780 \, x^{3} - 1949701238862399 \, x^{2} - 4108800 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 37213849312500 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 437687139939434 \, x + 307014257976349}{322102000000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/322102000000*(70443707400000*x^7 + 545938732350000*x^6 + 2559454702200000*x^5 + 180911181221100*x^4 - 3748001092791780*x^3 - 1949701238862399*x^2 - 4108800*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 37213849312500*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 437687139939434*x + 307014257976349)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1699,1,110,0,1.383792," ","integrate((2+3*x)^7/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{3522185370000 \, x^{6} + 31464855972000 \, x^{5} + 4073994411300 \, x^{4} - 69316698060060 \, x^{3} - 44983390879251 \, x^{2} - 1553856 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 626480925000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 5655984161146 \, x + 6369590895041}{32210200000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/32210200000*(3522185370000*x^6 + 31464855972000*x^5 + 4073994411300*x^4 - 69316698060060*x^3 - 44983390879251*x^2 - 1553856*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 626480925000*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 5655984161146*x + 6369590895041)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1700,1,105,0,1.268688," ","integrate((2+3*x)^6/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{234812358000 \, x^{5} + 46962471600 \, x^{4} - 1213135417560 \, x^{3} - 988737742575 \, x^{2} - 561504 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 8688618750 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 12119848070 \, x + 113352927985}{3221020000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/3221020000*(234812358000*x^5 + 46962471600*x^4 - 1213135417560*x^3 - 988737742575*x^2 - 561504*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 8688618750*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 12119848070*x + 113352927985)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1701,1,95,0,1.200718," ","integrate((2+3*x)^5/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{19807648080 \, x^{3} + 20221158771 \, x^{2} + 190464 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) - 78461250 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 2872410794 \, x - 1277723381}{322102000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/322102000*(19807648080*x^3 + 20221158771*x^2 + 190464*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) - 78461250*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 2872410794*x - 1277723381)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1702,1,95,0,1.026608," ","integrate((2+3*x)^4/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{254434620 \, x^{3} + 359945091 \, x^{2} + 58800 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) - 58800 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) + 156855094 \, x + 19488359}{32210200 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/32210200*(254434620*x^3 + 359945091*x^2 + 58800*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) - 58800*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) + 156855094*x + 19488359)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1703,1,95,0,1.193497," ","integrate((2+3*x)^3/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1709400 \, x^{3} - 4091967 \, x^{2} - 15540 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 15540 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) - 6646838 \, x - 2144593}{3221020 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/3221020*(1709400*x^3 - 4091967*x^2 - 15540*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 15540*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 6646838*x - 2144593)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1704,1,95,0,1.184054," ","integrate((2+3*x)^2/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{331980 \, x^{3} + 49797 \, x^{2} - 3018 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 3018 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) - 261514 \, x - 102542}{322102 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/322102*(331980*x^3 + 49797*x^2 - 3018*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 3018*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 261514*x - 102542)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1705,1,95,0,1.363660," ","integrate((2+3*x)/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{244200 \, x^{3} + 36630 \, x^{2} - 2220 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 2220 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) - 121286 \, x - 30283}{322102 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/322102*(244200*x^3 + 36630*x^2 - 2220*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 2220*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 121286*x - 30283)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1706,1,95,0,1.162111," ","integrate(1/(1-2*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","-\frac{132000 \, x^{3} + 19800 \, x^{2} - 1200 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) + 1200 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) - 65560 \, x - 3311}{322102 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/322102*(132000*x^3 + 19800*x^2 - 1200*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 1200*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 65560*x - 3311)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
1707,1,123,0,1.286528," ","integrate(1/(1-2*x)^3/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{500854200 \, x^{3} - 229258260 \, x^{2} + 78461250 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x + 3\right) - 78270786 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(3 \, x + 2\right) - 190464 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x - 1\right) - 154059598 \, x + 73172407}{110480986 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/110480986*(500854200*x^3 - 229258260*x^2 + 78461250*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) - 78270786*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(3*x + 2) - 190464*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 154059598*x + 73172407)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","B",0
1708,1,148,0,0.634777," ","integrate(1/(1-2*x)^3/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{173575848600 \, x^{4} + 40392941820 \, x^{3} - 104891101854 \, x^{2} + 8688618750 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \log\left(5 \, x + 3\right) - 8688057246 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \log\left(3 \, x + 2\right) - 561504 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \log\left(2 \, x - 1\right) - 12253878175 \, x + 16462150012}{773366902 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)}}"," ",0,"1/773366902*(173575848600*x^4 + 40392941820*x^3 - 104891101854*x^2 + 8688618750*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*log(5*x + 3) - 8688057246*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*log(3*x + 2) - 561504*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*log(2*x - 1) - 12253878175*x + 16462150012)/(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)","B",0
1709,1,173,0,1.155098," ","integrate(1/(1-2*x)^3/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{37587223951200 \, x^{5} + 33827604204240 \, x^{4} - 16859483294808 \, x^{3} - 17801732753112 \, x^{2} + 626480925000 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \log\left(5 \, x + 3\right) - 626479371144 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \log\left(3 \, x + 2\right) - 1553856 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \log\left(2 \, x - 1\right) + 1786038929444 \, x + 2376093430249}{5413568314 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)}}"," ",0,"1/5413568314*(37587223951200*x^5 + 33827604204240*x^4 - 16859483294808*x^3 - 17801732753112*x^2 + 626480925000*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(5*x + 3) - 626479371144*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(3*x + 2) - 1553856*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(2*x - 1) + 1786038929444*x + 2376093430249)/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)","B",0
1710,1,198,0,1.203700," ","integrate(1/(1-2*x)^3/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{6698479933530000 \, x^{6} + 10494278110701000 \, x^{5} + 1014683641656300 \, x^{4} - 5175447127123350 \, x^{3} - 1796782743686700 \, x^{2} + 37213849312500 \, {\left(2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right)} \log\left(5 \, x + 3\right) - 37213845203700 \, {\left(2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right)} \log\left(3 \, x + 2\right) - 4108800 \, {\left(2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right)} \log\left(2 \, x - 1\right) + 635595472278305 \, x + 282301665291184}{37894978198 \, {\left(2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right)}}"," ",0,"1/37894978198*(6698479933530000*x^6 + 10494278110701000*x^5 + 1014683641656300*x^4 - 5175447127123350*x^3 - 1796782743686700*x^2 + 37213849312500*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72)*log(5*x + 3) - 37213845203700*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72)*log(3*x + 2) - 4108800*(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72)*log(2*x - 1) + 635595472278305*x + 282301665291184)/(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72)","B",0
1711,1,987,0,0.745010," ","integrate((b*x+a)^3*(d*x+c)^3*(f*x+e)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} f^{3} d^{3} b^{3} + \frac{1}{3} x^{9} f^{2} e d^{3} b^{3} + \frac{1}{3} x^{9} f^{3} d^{2} c b^{3} + \frac{1}{3} x^{9} f^{3} d^{3} b^{2} a + \frac{3}{8} x^{8} f e^{2} d^{3} b^{3} + \frac{9}{8} x^{8} f^{2} e d^{2} c b^{3} + \frac{3}{8} x^{8} f^{3} d c^{2} b^{3} + \frac{9}{8} x^{8} f^{2} e d^{3} b^{2} a + \frac{9}{8} x^{8} f^{3} d^{2} c b^{2} a + \frac{3}{8} x^{8} f^{3} d^{3} b a^{2} + \frac{1}{7} x^{7} e^{3} d^{3} b^{3} + \frac{9}{7} x^{7} f e^{2} d^{2} c b^{3} + \frac{9}{7} x^{7} f^{2} e d c^{2} b^{3} + \frac{1}{7} x^{7} f^{3} c^{3} b^{3} + \frac{9}{7} x^{7} f e^{2} d^{3} b^{2} a + \frac{27}{7} x^{7} f^{2} e d^{2} c b^{2} a + \frac{9}{7} x^{7} f^{3} d c^{2} b^{2} a + \frac{9}{7} x^{7} f^{2} e d^{3} b a^{2} + \frac{9}{7} x^{7} f^{3} d^{2} c b a^{2} + \frac{1}{7} x^{7} f^{3} d^{3} a^{3} + \frac{1}{2} x^{6} e^{3} d^{2} c b^{3} + \frac{3}{2} x^{6} f e^{2} d c^{2} b^{3} + \frac{1}{2} x^{6} f^{2} e c^{3} b^{3} + \frac{1}{2} x^{6} e^{3} d^{3} b^{2} a + \frac{9}{2} x^{6} f e^{2} d^{2} c b^{2} a + \frac{9}{2} x^{6} f^{2} e d c^{2} b^{2} a + \frac{1}{2} x^{6} f^{3} c^{3} b^{2} a + \frac{3}{2} x^{6} f e^{2} d^{3} b a^{2} + \frac{9}{2} x^{6} f^{2} e d^{2} c b a^{2} + \frac{3}{2} x^{6} f^{3} d c^{2} b a^{2} + \frac{1}{2} x^{6} f^{2} e d^{3} a^{3} + \frac{1}{2} x^{6} f^{3} d^{2} c a^{3} + \frac{3}{5} x^{5} e^{3} d c^{2} b^{3} + \frac{3}{5} x^{5} f e^{2} c^{3} b^{3} + \frac{9}{5} x^{5} e^{3} d^{2} c b^{2} a + \frac{27}{5} x^{5} f e^{2} d c^{2} b^{2} a + \frac{9}{5} x^{5} f^{2} e c^{3} b^{2} a + \frac{3}{5} x^{5} e^{3} d^{3} b a^{2} + \frac{27}{5} x^{5} f e^{2} d^{2} c b a^{2} + \frac{27}{5} x^{5} f^{2} e d c^{2} b a^{2} + \frac{3}{5} x^{5} f^{3} c^{3} b a^{2} + \frac{3}{5} x^{5} f e^{2} d^{3} a^{3} + \frac{9}{5} x^{5} f^{2} e d^{2} c a^{3} + \frac{3}{5} x^{5} f^{3} d c^{2} a^{3} + \frac{1}{4} x^{4} e^{3} c^{3} b^{3} + \frac{9}{4} x^{4} e^{3} d c^{2} b^{2} a + \frac{9}{4} x^{4} f e^{2} c^{3} b^{2} a + \frac{9}{4} x^{4} e^{3} d^{2} c b a^{2} + \frac{27}{4} x^{4} f e^{2} d c^{2} b a^{2} + \frac{9}{4} x^{4} f^{2} e c^{3} b a^{2} + \frac{1}{4} x^{4} e^{3} d^{3} a^{3} + \frac{9}{4} x^{4} f e^{2} d^{2} c a^{3} + \frac{9}{4} x^{4} f^{2} e d c^{2} a^{3} + \frac{1}{4} x^{4} f^{3} c^{3} a^{3} + x^{3} e^{3} c^{3} b^{2} a + 3 x^{3} e^{3} d c^{2} b a^{2} + 3 x^{3} f e^{2} c^{3} b a^{2} + x^{3} e^{3} d^{2} c a^{3} + 3 x^{3} f e^{2} d c^{2} a^{3} + x^{3} f^{2} e c^{3} a^{3} + \frac{3}{2} x^{2} e^{3} c^{3} b a^{2} + \frac{3}{2} x^{2} e^{3} d c^{2} a^{3} + \frac{3}{2} x^{2} f e^{2} c^{3} a^{3} + x e^{3} c^{3} a^{3}"," ",0,"1/10*x^10*f^3*d^3*b^3 + 1/3*x^9*f^2*e*d^3*b^3 + 1/3*x^9*f^3*d^2*c*b^3 + 1/3*x^9*f^3*d^3*b^2*a + 3/8*x^8*f*e^2*d^3*b^3 + 9/8*x^8*f^2*e*d^2*c*b^3 + 3/8*x^8*f^3*d*c^2*b^3 + 9/8*x^8*f^2*e*d^3*b^2*a + 9/8*x^8*f^3*d^2*c*b^2*a + 3/8*x^8*f^3*d^3*b*a^2 + 1/7*x^7*e^3*d^3*b^3 + 9/7*x^7*f*e^2*d^2*c*b^3 + 9/7*x^7*f^2*e*d*c^2*b^3 + 1/7*x^7*f^3*c^3*b^3 + 9/7*x^7*f*e^2*d^3*b^2*a + 27/7*x^7*f^2*e*d^2*c*b^2*a + 9/7*x^7*f^3*d*c^2*b^2*a + 9/7*x^7*f^2*e*d^3*b*a^2 + 9/7*x^7*f^3*d^2*c*b*a^2 + 1/7*x^7*f^3*d^3*a^3 + 1/2*x^6*e^3*d^2*c*b^3 + 3/2*x^6*f*e^2*d*c^2*b^3 + 1/2*x^6*f^2*e*c^3*b^3 + 1/2*x^6*e^3*d^3*b^2*a + 9/2*x^6*f*e^2*d^2*c*b^2*a + 9/2*x^6*f^2*e*d*c^2*b^2*a + 1/2*x^6*f^3*c^3*b^2*a + 3/2*x^6*f*e^2*d^3*b*a^2 + 9/2*x^6*f^2*e*d^2*c*b*a^2 + 3/2*x^6*f^3*d*c^2*b*a^2 + 1/2*x^6*f^2*e*d^3*a^3 + 1/2*x^6*f^3*d^2*c*a^3 + 3/5*x^5*e^3*d*c^2*b^3 + 3/5*x^5*f*e^2*c^3*b^3 + 9/5*x^5*e^3*d^2*c*b^2*a + 27/5*x^5*f*e^2*d*c^2*b^2*a + 9/5*x^5*f^2*e*c^3*b^2*a + 3/5*x^5*e^3*d^3*b*a^2 + 27/5*x^5*f*e^2*d^2*c*b*a^2 + 27/5*x^5*f^2*e*d*c^2*b*a^2 + 3/5*x^5*f^3*c^3*b*a^2 + 3/5*x^5*f*e^2*d^3*a^3 + 9/5*x^5*f^2*e*d^2*c*a^3 + 3/5*x^5*f^3*d*c^2*a^3 + 1/4*x^4*e^3*c^3*b^3 + 9/4*x^4*e^3*d*c^2*b^2*a + 9/4*x^4*f*e^2*c^3*b^2*a + 9/4*x^4*e^3*d^2*c*b*a^2 + 27/4*x^4*f*e^2*d*c^2*b*a^2 + 9/4*x^4*f^2*e*c^3*b*a^2 + 1/4*x^4*e^3*d^3*a^3 + 9/4*x^4*f*e^2*d^2*c*a^3 + 9/4*x^4*f^2*e*d*c^2*a^3 + 1/4*x^4*f^3*c^3*a^3 + x^3*e^3*c^3*b^2*a + 3*x^3*e^3*d*c^2*b*a^2 + 3*x^3*f*e^2*c^3*b*a^2 + x^3*e^3*d^2*c*a^3 + 3*x^3*f*e^2*d*c^2*a^3 + x^3*f^2*e*c^3*a^3 + 3/2*x^2*e^3*c^3*b*a^2 + 3/2*x^2*e^3*d*c^2*a^3 + 3/2*x^2*f*e^2*c^3*a^3 + x*e^3*c^3*a^3","B",0
1712,1,346,0,1.017555," ","integrate((b*x+a)^2*(d*x+c)^2*(f*x+e)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} f^{2} d^{2} b^{2} + \frac{1}{3} x^{6} f e d^{2} b^{2} + \frac{1}{3} x^{6} f^{2} d c b^{2} + \frac{1}{3} x^{6} f^{2} d^{2} b a + \frac{1}{5} x^{5} e^{2} d^{2} b^{2} + \frac{4}{5} x^{5} f e d c b^{2} + \frac{1}{5} x^{5} f^{2} c^{2} b^{2} + \frac{4}{5} x^{5} f e d^{2} b a + \frac{4}{5} x^{5} f^{2} d c b a + \frac{1}{5} x^{5} f^{2} d^{2} a^{2} + \frac{1}{2} x^{4} e^{2} d c b^{2} + \frac{1}{2} x^{4} f e c^{2} b^{2} + \frac{1}{2} x^{4} e^{2} d^{2} b a + 2 x^{4} f e d c b a + \frac{1}{2} x^{4} f^{2} c^{2} b a + \frac{1}{2} x^{4} f e d^{2} a^{2} + \frac{1}{2} x^{4} f^{2} d c a^{2} + \frac{1}{3} x^{3} e^{2} c^{2} b^{2} + \frac{4}{3} x^{3} e^{2} d c b a + \frac{4}{3} x^{3} f e c^{2} b a + \frac{1}{3} x^{3} e^{2} d^{2} a^{2} + \frac{4}{3} x^{3} f e d c a^{2} + \frac{1}{3} x^{3} f^{2} c^{2} a^{2} + x^{2} e^{2} c^{2} b a + x^{2} e^{2} d c a^{2} + x^{2} f e c^{2} a^{2} + x e^{2} c^{2} a^{2}"," ",0,"1/7*x^7*f^2*d^2*b^2 + 1/3*x^6*f*e*d^2*b^2 + 1/3*x^6*f^2*d*c*b^2 + 1/3*x^6*f^2*d^2*b*a + 1/5*x^5*e^2*d^2*b^2 + 4/5*x^5*f*e*d*c*b^2 + 1/5*x^5*f^2*c^2*b^2 + 4/5*x^5*f*e*d^2*b*a + 4/5*x^5*f^2*d*c*b*a + 1/5*x^5*f^2*d^2*a^2 + 1/2*x^4*e^2*d*c*b^2 + 1/2*x^4*f*e*c^2*b^2 + 1/2*x^4*e^2*d^2*b*a + 2*x^4*f*e*d*c*b*a + 1/2*x^4*f^2*c^2*b*a + 1/2*x^4*f*e*d^2*a^2 + 1/2*x^4*f^2*d*c*a^2 + 1/3*x^3*e^2*c^2*b^2 + 4/3*x^3*e^2*d*c*b*a + 4/3*x^3*f*e*c^2*b*a + 1/3*x^3*e^2*d^2*a^2 + 4/3*x^3*f*e*d*c*a^2 + 1/3*x^3*f^2*c^2*a^2 + x^2*e^2*c^2*b*a + x^2*e^2*d*c*a^2 + x^2*f*e*c^2*a^2 + x*e^2*c^2*a^2","A",0
1713,1,62,0,0.874959," ","integrate((b*x+a)*(d*x+c)*(f*x+e),x, algorithm=""fricas"")","\frac{1}{4} x^{4} f d b + \frac{1}{3} x^{3} e d b + \frac{1}{3} x^{3} f c b + \frac{1}{3} x^{3} f d a + \frac{1}{2} x^{2} e c b + \frac{1}{2} x^{2} e d a + \frac{1}{2} x^{2} f c a + x e c a"," ",0,"1/4*x^4*f*d*b + 1/3*x^3*e*d*b + 1/3*x^3*f*c*b + 1/3*x^3*f*d*a + 1/2*x^2*e*c*b + 1/2*x^2*e*d*a + 1/2*x^2*f*c*a + x*e*c*a","A",0
1714,1,112,0,14.514241," ","integrate(1/(b*x+a)/(d*x+c)/(f*x+e),x, algorithm=""fricas"")","\frac{{\left(b c - a d\right)} f \log\left(f x + e\right) + {\left(b d e - b c f\right)} \log\left(b x + a\right) - {\left(b d e - a d f\right)} \log\left(d x + c\right)}{{\left(b^{2} c d - a b d^{2}\right)} e^{2} - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} e f + {\left(a b c^{2} - a^{2} c d\right)} f^{2}}"," ",0,"((b*c - a*d)*f*log(f*x + e) + (b*d*e - b*c*f)*log(b*x + a) - (b*d*e - a*d*f)*log(d*x + c))/((b^2*c*d - a*b*d^2)*e^2 - (b^2*c^2 - a^2*d^2)*e*f + (a*b*c^2 - a^2*c*d)*f^2)","A",0
1715,-1,0,0,0.000000," ","integrate(1/(b*x+a)^2/(d*x+c)^2/(f*x+e)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1716,-1,0,0,0.000000," ","integrate(1/(b*x+a)^3/(d*x+c)^3/(f*x+e)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1717,1,1134,0,4.810789," ","integrate((d*x+c)^(3/2)/(b*x+a)^2/(f*x+e),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, a b d e - {\left(2 \, a b c + a^{2} d\right)} f + {\left(3 \, b^{2} d e - {\left(2 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left(a b d e - a b c f + {\left(b^{2} d e - b^{2} c f\right)} x\right)} \sqrt{-\frac{d e - c f}{f}} \log\left(\frac{d f x - d e + 2 \, c f - 2 \, \sqrt{d x + c} f \sqrt{-\frac{d e - c f}{f}}}{f x + e}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f\right)} \sqrt{d x + c}}{2 \, {\left(a b^{3} e^{2} - 2 \, a^{2} b^{2} e f + a^{3} b f^{2} + {\left(b^{4} e^{2} - 2 \, a b^{3} e f + a^{2} b^{2} f^{2}\right)} x\right)}}, -\frac{{\left(3 \, a b d e - {\left(2 \, a b c + a^{2} d\right)} f + {\left(3 \, b^{2} d e - {\left(2 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + {\left(a b d e - a b c f + {\left(b^{2} d e - b^{2} c f\right)} x\right)} \sqrt{-\frac{d e - c f}{f}} \log\left(\frac{d f x - d e + 2 \, c f - 2 \, \sqrt{d x + c} f \sqrt{-\frac{d e - c f}{f}}}{f x + e}\right) + {\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f\right)} \sqrt{d x + c}}{a b^{3} e^{2} - 2 \, a^{2} b^{2} e f + a^{3} b f^{2} + {\left(b^{4} e^{2} - 2 \, a b^{3} e f + a^{2} b^{2} f^{2}\right)} x}, -\frac{4 \, {\left(a b d e - a b c f + {\left(b^{2} d e - b^{2} c f\right)} x\right)} \sqrt{\frac{d e - c f}{f}} \arctan\left(-\frac{\sqrt{d x + c} f \sqrt{\frac{d e - c f}{f}}}{d e - c f}\right) + {\left(3 \, a b d e - {\left(2 \, a b c + a^{2} d\right)} f + {\left(3 \, b^{2} d e - {\left(2 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right) + 2 \, {\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f\right)} \sqrt{d x + c}}{2 \, {\left(a b^{3} e^{2} - 2 \, a^{2} b^{2} e f + a^{3} b f^{2} + {\left(b^{4} e^{2} - 2 \, a b^{3} e f + a^{2} b^{2} f^{2}\right)} x\right)}}, -\frac{{\left(3 \, a b d e - {\left(2 \, a b c + a^{2} d\right)} f + {\left(3 \, b^{2} d e - {\left(2 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right) + 2 \, {\left(a b d e - a b c f + {\left(b^{2} d e - b^{2} c f\right)} x\right)} \sqrt{\frac{d e - c f}{f}} \arctan\left(-\frac{\sqrt{d x + c} f \sqrt{\frac{d e - c f}{f}}}{d e - c f}\right) + {\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f\right)} \sqrt{d x + c}}{a b^{3} e^{2} - 2 \, a^{2} b^{2} e f + a^{3} b f^{2} + {\left(b^{4} e^{2} - 2 \, a b^{3} e f + a^{2} b^{2} f^{2}\right)} x}\right]"," ",0,"[-1/2*((3*a*b*d*e - (2*a*b*c + a^2*d)*f + (3*b^2*d*e - (2*b^2*c + a*b*d)*f)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*(a*b*d*e - a*b*c*f + (b^2*d*e - b^2*c*f)*x)*sqrt(-(d*e - c*f)/f)*log((d*f*x - d*e + 2*c*f - 2*sqrt(d*x + c)*f*sqrt(-(d*e - c*f)/f))/(f*x + e)) + 2*((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f)*sqrt(d*x + c))/(a*b^3*e^2 - 2*a^2*b^2*e*f + a^3*b*f^2 + (b^4*e^2 - 2*a*b^3*e*f + a^2*b^2*f^2)*x), -((3*a*b*d*e - (2*a*b*c + a^2*d)*f + (3*b^2*d*e - (2*b^2*c + a*b*d)*f)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + (a*b*d*e - a*b*c*f + (b^2*d*e - b^2*c*f)*x)*sqrt(-(d*e - c*f)/f)*log((d*f*x - d*e + 2*c*f - 2*sqrt(d*x + c)*f*sqrt(-(d*e - c*f)/f))/(f*x + e)) + ((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f)*sqrt(d*x + c))/(a*b^3*e^2 - 2*a^2*b^2*e*f + a^3*b*f^2 + (b^4*e^2 - 2*a*b^3*e*f + a^2*b^2*f^2)*x), -1/2*(4*(a*b*d*e - a*b*c*f + (b^2*d*e - b^2*c*f)*x)*sqrt((d*e - c*f)/f)*arctan(-sqrt(d*x + c)*f*sqrt((d*e - c*f)/f)/(d*e - c*f)) + (3*a*b*d*e - (2*a*b*c + a^2*d)*f + (3*b^2*d*e - (2*b^2*c + a*b*d)*f)*x)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d + 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)) + 2*((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f)*sqrt(d*x + c))/(a*b^3*e^2 - 2*a^2*b^2*e*f + a^3*b*f^2 + (b^4*e^2 - 2*a*b^3*e*f + a^2*b^2*f^2)*x), -((3*a*b*d*e - (2*a*b*c + a^2*d)*f + (3*b^2*d*e - (2*b^2*c + a*b*d)*f)*x)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)) + 2*(a*b*d*e - a*b*c*f + (b^2*d*e - b^2*c*f)*x)*sqrt((d*e - c*f)/f)*arctan(-sqrt(d*x + c)*f*sqrt((d*e - c*f)/f)/(d*e - c*f)) + ((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f)*sqrt(d*x + c))/(a*b^3*e^2 - 2*a^2*b^2*e*f + a^3*b*f^2 + (b^4*e^2 - 2*a*b^3*e*f + a^2*b^2*f^2)*x)]","A",0
1718,1,230,0,2.019958," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(99 \, B b e^{6} x^{6} + 8 \, B b d^{6} + 143 \, A a d^{4} e^{2} - 26 \, {\left(B a + A b\right)} d^{5} e + 9 \, {\left(40 \, B b d e^{5} + 13 \, {\left(B a + A b\right)} e^{6}\right)} x^{5} + {\left(458 \, B b d^{2} e^{4} + 143 \, A a e^{6} + 442 \, {\left(B a + A b\right)} d e^{5}\right)} x^{4} + 2 \, {\left(106 \, B b d^{3} e^{3} + 286 \, A a d e^{5} + 299 \, {\left(B a + A b\right)} d^{2} e^{4}\right)} x^{3} + 3 \, {\left(B b d^{4} e^{2} + 286 \, A a d^{2} e^{4} + 104 \, {\left(B a + A b\right)} d^{3} e^{3}\right)} x^{2} - {\left(4 \, B b d^{5} e - 572 \, A a d^{3} e^{3} - 13 \, {\left(B a + A b\right)} d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{1287 \, e^{3}}"," ",0,"2/1287*(99*B*b*e^6*x^6 + 8*B*b*d^6 + 143*A*a*d^4*e^2 - 26*(B*a + A*b)*d^5*e + 9*(40*B*b*d*e^5 + 13*(B*a + A*b)*e^6)*x^5 + (458*B*b*d^2*e^4 + 143*A*a*e^6 + 442*(B*a + A*b)*d*e^5)*x^4 + 2*(106*B*b*d^3*e^3 + 286*A*a*d*e^5 + 299*(B*a + A*b)*d^2*e^4)*x^3 + 3*(B*b*d^4*e^2 + 286*A*a*d^2*e^4 + 104*(B*a + A*b)*d^3*e^3)*x^2 - (4*B*b*d^5*e - 572*A*a*d^3*e^3 - 13*(B*a + A*b)*d^4*e^2)*x)*sqrt(e*x + d)/e^3","B",0
1719,1,189,0,2.135129," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B b e^{5} x^{5} + 8 \, B b d^{5} + 99 \, A a d^{3} e^{2} - 22 \, {\left(B a + A b\right)} d^{4} e + 7 \, {\left(23 \, B b d e^{4} + 11 \, {\left(B a + A b\right)} e^{5}\right)} x^{4} + {\left(113 \, B b d^{2} e^{3} + 99 \, A a e^{5} + 209 \, {\left(B a + A b\right)} d e^{4}\right)} x^{3} + 3 \, {\left(B b d^{3} e^{2} + 99 \, A a d e^{4} + 55 \, {\left(B a + A b\right)} d^{2} e^{3}\right)} x^{2} - {\left(4 \, B b d^{4} e - 297 \, A a d^{2} e^{3} - 11 \, {\left(B a + A b\right)} d^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*B*b*e^5*x^5 + 8*B*b*d^5 + 99*A*a*d^3*e^2 - 22*(B*a + A*b)*d^4*e + 7*(23*B*b*d*e^4 + 11*(B*a + A*b)*e^5)*x^4 + (113*B*b*d^2*e^3 + 99*A*a*e^5 + 209*(B*a + A*b)*d*e^4)*x^3 + 3*(B*b*d^3*e^2 + 99*A*a*d*e^4 + 55*(B*a + A*b)*d^2*e^3)*x^2 - (4*B*b*d^4*e - 297*A*a*d^2*e^3 - 11*(B*a + A*b)*d^3*e^2)*x)*sqrt(e*x + d)/e^3","B",0
1720,1,149,0,1.492246," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b e^{4} x^{4} + 8 \, B b d^{4} + 63 \, A a d^{2} e^{2} - 18 \, {\left(B a + A b\right)} d^{3} e + 5 \, {\left(10 \, B b d e^{3} + 9 \, {\left(B a + A b\right)} e^{4}\right)} x^{3} + 3 \, {\left(B b d^{2} e^{2} + 21 \, A a e^{4} + 24 \, {\left(B a + A b\right)} d e^{3}\right)} x^{2} - {\left(4 \, B b d^{3} e - 126 \, A a d e^{3} - 9 \, {\left(B a + A b\right)} d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*B*b*e^4*x^4 + 8*B*b*d^4 + 63*A*a*d^2*e^2 - 18*(B*a + A*b)*d^3*e + 5*(10*B*b*d*e^3 + 9*(B*a + A*b)*e^4)*x^3 + 3*(B*b*d^2*e^2 + 21*A*a*e^4 + 24*(B*a + A*b)*d*e^3)*x^2 - (4*B*b*d^3*e - 126*A*a*d*e^3 - 9*(B*a + A*b)*d^2*e^2)*x)*sqrt(e*x + d)/e^3","B",0
1721,1,108,0,1.443147," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b e^{3} x^{3} + 8 \, B b d^{3} + 35 \, A a d e^{2} - 14 \, {\left(B a + A b\right)} d^{2} e + 3 \, {\left(B b d e^{2} + 7 \, {\left(B a + A b\right)} e^{3}\right)} x^{2} - {\left(4 \, B b d^{2} e - 35 \, A a e^{3} - 7 \, {\left(B a + A b\right)} d e^{2}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*B*b*e^3*x^3 + 8*B*b*d^3 + 35*A*a*d*e^2 - 14*(B*a + A*b)*d^2*e + 3*(B*b*d*e^2 + 7*(B*a + A*b)*e^3)*x^2 - (4*B*b*d^2*e - 35*A*a*e^3 - 7*(B*a + A*b)*d*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1722,1,70,0,1.388384," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b e^{2} x^{2} + 8 \, B b d^{2} + 15 \, A a e^{2} - 10 \, {\left(B a + A b\right)} d e - {\left(4 \, B b d e - 5 \, {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*B*b*e^2*x^2 + 8*B*b*d^2 + 15*A*a*e^2 - 10*(B*a + A*b)*d*e - (4*B*b*d*e - 5*(B*a + A*b)*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1723,1,79,0,1.376941," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b e^{2} x^{2} - 8 \, B b d^{2} - 3 \, A a e^{2} + 6 \, {\left(B a + A b\right)} d e - {\left(4 \, B b d e - 3 \, {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(B*b*e^2*x^2 - 8*B*b*d^2 - 3*A*a*e^2 + 6*(B*a + A*b)*d*e - (4*B*b*d*e - 3*(B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
1724,1,91,0,1.436081," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b e^{2} x^{2} + 8 \, B b d^{2} - A a e^{2} - 2 \, {\left(B a + A b\right)} d e + 3 \, {\left(4 \, B b d e - {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*B*b*e^2*x^2 + 8*B*b*d^2 - A*a*e^2 - 2*(B*a + A*b)*d*e + 3*(4*B*b*d*e - (B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1725,1,101,0,1.579371," ","integrate((b*x+a)*(B*x+A)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B b e^{2} x^{2} + 8 \, B b d^{2} + 3 \, A a e^{2} + 2 \, {\left(B a + A b\right)} d e + 5 \, {\left(4 \, B b d e + {\left(B a + A b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*B*b*e^2*x^2 + 8*B*b*d^2 + 3*A*a*e^2 + 2*(B*a + A*b)*d*e + 5*(4*B*b*d*e + (B*a + A*b)*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1726,1,424,0,1.374737," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, B b^{2} e^{7} x^{7} - 16 \, B b^{2} d^{7} + 715 \, A a^{2} d^{4} e^{3} + 40 \, {\left(2 \, B a b + A b^{2}\right)} d^{6} e - 130 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5} e^{2} + 33 \, {\left(46 \, B b^{2} d e^{6} + 15 \, {\left(2 \, B a b + A b^{2}\right)} e^{7}\right)} x^{6} + 9 \, {\left(206 \, B b^{2} d^{2} e^{5} + 200 \, {\left(2 \, B a b + A b^{2}\right)} d e^{6} + 65 \, {\left(B a^{2} + 2 \, A a b\right)} e^{7}\right)} x^{5} + 5 \, {\left(160 \, B b^{2} d^{3} e^{4} + 143 \, A a^{2} e^{7} + 458 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{5} + 442 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{6}\right)} x^{4} + 5 \, {\left(B b^{2} d^{4} e^{3} + 572 \, A a^{2} d e^{6} + 212 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{4} + 598 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(2 \, B b^{2} d^{5} e^{2} - 1430 \, A a^{2} d^{2} e^{5} - 5 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e^{3} - 520 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{4}\right)} x^{2} + {\left(8 \, B b^{2} d^{6} e + 2860 \, A a^{2} d^{3} e^{4} - 20 \, {\left(2 \, B a b + A b^{2}\right)} d^{5} e^{2} + 65 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{4}}"," ",0,"2/6435*(429*B*b^2*e^7*x^7 - 16*B*b^2*d^7 + 715*A*a^2*d^4*e^3 + 40*(2*B*a*b + A*b^2)*d^6*e - 130*(B*a^2 + 2*A*a*b)*d^5*e^2 + 33*(46*B*b^2*d*e^6 + 15*(2*B*a*b + A*b^2)*e^7)*x^6 + 9*(206*B*b^2*d^2*e^5 + 200*(2*B*a*b + A*b^2)*d*e^6 + 65*(B*a^2 + 2*A*a*b)*e^7)*x^5 + 5*(160*B*b^2*d^3*e^4 + 143*A*a^2*e^7 + 458*(2*B*a*b + A*b^2)*d^2*e^5 + 442*(B*a^2 + 2*A*a*b)*d*e^6)*x^4 + 5*(B*b^2*d^4*e^3 + 572*A*a^2*d*e^6 + 212*(2*B*a*b + A*b^2)*d^3*e^4 + 598*(B*a^2 + 2*A*a*b)*d^2*e^5)*x^3 - 3*(2*B*b^2*d^5*e^2 - 1430*A*a^2*d^2*e^5 - 5*(2*B*a*b + A*b^2)*d^4*e^3 - 520*(B*a^2 + 2*A*a*b)*d^3*e^4)*x^2 + (8*B*b^2*d^6*e + 2860*A*a^2*d^3*e^4 - 20*(2*B*a*b + A*b^2)*d^5*e^2 + 65*(B*a^2 + 2*A*a*b)*d^4*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1727,1,356,0,1.396952," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, B b^{2} e^{6} x^{6} - 48 \, B b^{2} d^{6} + 1287 \, A a^{2} d^{3} e^{3} + 104 \, {\left(2 \, B a b + A b^{2}\right)} d^{5} e - 286 \, {\left(B a^{2} + 2 \, A a b\right)} d^{4} e^{2} + 63 \, {\left(27 \, B b^{2} d e^{5} + 13 \, {\left(2 \, B a b + A b^{2}\right)} e^{6}\right)} x^{5} + 7 \, {\left(159 \, B b^{2} d^{2} e^{4} + 299 \, {\left(2 \, B a b + A b^{2}\right)} d e^{5} + 143 \, {\left(B a^{2} + 2 \, A a b\right)} e^{6}\right)} x^{4} + {\left(15 \, B b^{2} d^{3} e^{3} + 1287 \, A a^{2} e^{6} + 1469 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{4} + 2717 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{5}\right)} x^{3} - 3 \, {\left(6 \, B b^{2} d^{4} e^{2} - 1287 \, A a^{2} d e^{5} - 13 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{3} - 715 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{4}\right)} x^{2} + {\left(24 \, B b^{2} d^{5} e + 3861 \, A a^{2} d^{2} e^{4} - 52 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e^{2} + 143 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{4}}"," ",0,"2/9009*(693*B*b^2*e^6*x^6 - 48*B*b^2*d^6 + 1287*A*a^2*d^3*e^3 + 104*(2*B*a*b + A*b^2)*d^5*e - 286*(B*a^2 + 2*A*a*b)*d^4*e^2 + 63*(27*B*b^2*d*e^5 + 13*(2*B*a*b + A*b^2)*e^6)*x^5 + 7*(159*B*b^2*d^2*e^4 + 299*(2*B*a*b + A*b^2)*d*e^5 + 143*(B*a^2 + 2*A*a*b)*e^6)*x^4 + (15*B*b^2*d^3*e^3 + 1287*A*a^2*e^6 + 1469*(2*B*a*b + A*b^2)*d^2*e^4 + 2717*(B*a^2 + 2*A*a*b)*d*e^5)*x^3 - 3*(6*B*b^2*d^4*e^2 - 1287*A*a^2*d*e^5 - 13*(2*B*a*b + A*b^2)*d^3*e^3 - 715*(B*a^2 + 2*A*a*b)*d^2*e^4)*x^2 + (24*B*b^2*d^5*e + 3861*A*a^2*d^2*e^4 - 52*(2*B*a*b + A*b^2)*d^4*e^2 + 143*(B*a^2 + 2*A*a*b)*d^3*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1728,1,289,0,1.443001," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{2} e^{5} x^{5} - 48 \, B b^{2} d^{5} + 693 \, A a^{2} d^{2} e^{3} + 88 \, {\left(2 \, B a b + A b^{2}\right)} d^{4} e - 198 \, {\left(B a^{2} + 2 \, A a b\right)} d^{3} e^{2} + 35 \, {\left(12 \, B b^{2} d e^{4} + 11 \, {\left(2 \, B a b + A b^{2}\right)} e^{5}\right)} x^{4} + 5 \, {\left(3 \, B b^{2} d^{2} e^{3} + 110 \, {\left(2 \, B a b + A b^{2}\right)} d e^{4} + 99 \, {\left(B a^{2} + 2 \, A a b\right)} e^{5}\right)} x^{3} - 3 \, {\left(6 \, B b^{2} d^{3} e^{2} - 231 \, A a^{2} e^{5} - 11 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{3} - 264 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{4}\right)} x^{2} + {\left(24 \, B b^{2} d^{4} e + 1386 \, A a^{2} d e^{4} - 44 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e^{2} + 99 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{4}}"," ",0,"2/3465*(315*B*b^2*e^5*x^5 - 48*B*b^2*d^5 + 693*A*a^2*d^2*e^3 + 88*(2*B*a*b + A*b^2)*d^4*e - 198*(B*a^2 + 2*A*a*b)*d^3*e^2 + 35*(12*B*b^2*d*e^4 + 11*(2*B*a*b + A*b^2)*e^5)*x^4 + 5*(3*B*b^2*d^2*e^3 + 110*(2*B*a*b + A*b^2)*d*e^4 + 99*(B*a^2 + 2*A*a*b)*e^5)*x^3 - 3*(6*B*b^2*d^3*e^2 - 231*A*a^2*e^5 - 11*(2*B*a*b + A*b^2)*d^2*e^3 - 264*(B*a^2 + 2*A*a*b)*d*e^4)*x^2 + (24*B*b^2*d^4*e + 1386*A*a^2*d*e^4 - 44*(2*B*a*b + A*b^2)*d^3*e^2 + 99*(B*a^2 + 2*A*a*b)*d^2*e^3)*x)*sqrt(e*x + d)/e^4","B",0
1729,1,220,0,1.244893," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{2} e^{4} x^{4} - 16 \, B b^{2} d^{4} + 105 \, A a^{2} d e^{3} + 24 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 42 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2} + 5 \, {\left(B b^{2} d e^{3} + 9 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} x^{3} - 3 \, {\left(2 \, B b^{2} d^{2} e^{2} - 3 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 21 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} x^{2} + {\left(8 \, B b^{2} d^{3} e + 105 \, A a^{2} e^{4} - 12 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 21 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*B*b^2*e^4*x^4 - 16*B*b^2*d^4 + 105*A*a^2*d*e^3 + 24*(2*B*a*b + A*b^2)*d^3*e - 42*(B*a^2 + 2*A*a*b)*d^2*e^2 + 5*(B*b^2*d*e^3 + 9*(2*B*a*b + A*b^2)*e^4)*x^3 - 3*(2*B*b^2*d^2*e^2 - 3*(2*B*a*b + A*b^2)*d*e^3 - 21*(B*a^2 + 2*A*a*b)*e^4)*x^2 + (8*B*b^2*d^3*e + 105*A*a^2*e^4 - 12*(2*B*a*b + A*b^2)*d^2*e^2 + 21*(B*a^2 + 2*A*a*b)*d*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1730,1,155,0,1.340340," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} e^{3} x^{3} - 48 \, B b^{2} d^{3} + 105 \, A a^{2} e^{3} + 56 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 70 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 3 \, {\left(6 \, B b^{2} d e^{2} - 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + {\left(24 \, B b^{2} d^{2} e - 28 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{4}}"," ",0,"2/105*(15*B*b^2*e^3*x^3 - 48*B*b^2*d^3 + 105*A*a^2*e^3 + 56*(2*B*a*b + A*b^2)*d^2*e - 70*(B*a^2 + 2*A*a*b)*d*e^2 - 3*(6*B*b^2*d*e^2 - 7*(2*B*a*b + A*b^2)*e^3)*x^2 + (24*B*b^2*d^2*e - 28*(2*B*a*b + A*b^2)*d*e^2 + 35*(B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1731,1,165,0,1.255680," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{2} e^{3} x^{3} + 48 \, B b^{2} d^{3} - 15 \, A a^{2} e^{3} - 40 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e + 30 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - {\left(6 \, B b^{2} d e^{2} - 5 \, {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + {\left(24 \, B b^{2} d^{2} e - 20 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + 15 \, {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/15*(3*B*b^2*e^3*x^3 + 48*B*b^2*d^3 - 15*A*a^2*e^3 - 40*(2*B*a*b + A*b^2)*d^2*e + 30*(B*a^2 + 2*A*a*b)*d*e^2 - (6*B*b^2*d*e^2 - 5*(2*B*a*b + A*b^2)*e^3)*x^2 + (24*B*b^2*d^2*e - 20*(2*B*a*b + A*b^2)*d*e^2 + 15*(B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1732,1,175,0,1.479400," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(B b^{2} e^{3} x^{3} - 16 \, B b^{2} d^{3} - A a^{2} e^{3} + 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} - 3 \, {\left(2 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} - 3 \, {\left(8 \, B b^{2} d^{2} e - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} + {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(B*b^2*e^3*x^3 - 16*B*b^2*d^3 - A*a^2*e^3 + 8*(2*B*a*b + A*b^2)*d^2*e - 2*(B*a^2 + 2*A*a*b)*d*e^2 - 3*(2*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 - 3*(8*B*b^2*d^2*e - 4*(2*B*a*b + A*b^2)*d*e^2 + (B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1733,1,188,0,1.081580," ","integrate((b*x+a)^2*(B*x+A)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B b^{2} e^{3} x^{3} + 48 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} - 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e - 2 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{2} + 15 \, {\left(6 \, B b^{2} d e^{2} - {\left(2 \, B a b + A b^{2}\right)} e^{3}\right)} x^{2} + 5 \, {\left(24 \, B b^{2} d^{2} e - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{2} - {\left(B a^{2} + 2 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/15*(15*B*b^2*e^3*x^3 + 48*B*b^2*d^3 - 3*A*a^2*e^3 - 8*(2*B*a*b + A*b^2)*d^2*e - 2*(B*a^2 + 2*A*a*b)*d*e^2 + 15*(6*B*b^2*d*e^2 - (2*B*a*b + A*b^2)*e^3)*x^2 + 5*(24*B*b^2*d^2*e - 4*(2*B*a*b + A*b^2)*d*e^2 - (B*a^2 + 2*A*a*b)*e^3)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1734,1,633,0,0.852091," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(6435 \, B b^{3} e^{8} x^{8} + 128 \, B b^{3} d^{8} + 12155 \, A a^{3} d^{4} e^{4} - 272 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{7} e + 2040 \, {\left(B a^{2} b + A a b^{2}\right)} d^{6} e^{2} - 2210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{5} e^{3} + 429 \, {\left(52 \, B b^{3} d e^{7} + 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{8}\right)} x^{7} + 33 \, {\left(802 \, B b^{3} d^{2} e^{6} + 782 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{7} + 765 \, {\left(B a^{2} b + A a b^{2}\right)} e^{8}\right)} x^{6} + 9 \, {\left(1212 \, B b^{3} d^{3} e^{5} + 3502 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{6} + 10200 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{7} + 1105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{8}\right)} x^{5} + 5 \, {\left(7 \, B b^{3} d^{4} e^{4} + 2431 \, A a^{3} e^{8} + 2720 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{5} + 23358 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{6} + 7514 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{7}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{5} e^{3} - 9724 \, A a^{3} d e^{7} - 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{4} - 10812 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{5} - 10166 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{6} e^{2} + 24310 \, A a^{3} d^{2} e^{6} - 34 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e^{3} + 255 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{4} + 8840 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{7} e - 48620 \, A a^{3} d^{3} e^{5} - 136 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{6} e^{2} + 1020 \, {\left(B a^{2} b + A a b^{2}\right)} d^{5} e^{3} - 1105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{109395 \, e^{5}}"," ",0,"2/109395*(6435*B*b^3*e^8*x^8 + 128*B*b^3*d^8 + 12155*A*a^3*d^4*e^4 - 272*(3*B*a*b^2 + A*b^3)*d^7*e + 2040*(B*a^2*b + A*a*b^2)*d^6*e^2 - 2210*(B*a^3 + 3*A*a^2*b)*d^5*e^3 + 429*(52*B*b^3*d*e^7 + 17*(3*B*a*b^2 + A*b^3)*e^8)*x^7 + 33*(802*B*b^3*d^2*e^6 + 782*(3*B*a*b^2 + A*b^3)*d*e^7 + 765*(B*a^2*b + A*a*b^2)*e^8)*x^6 + 9*(1212*B*b^3*d^3*e^5 + 3502*(3*B*a*b^2 + A*b^3)*d^2*e^6 + 10200*(B*a^2*b + A*a*b^2)*d*e^7 + 1105*(B*a^3 + 3*A*a^2*b)*e^8)*x^5 + 5*(7*B*b^3*d^4*e^4 + 2431*A*a^3*e^8 + 2720*(3*B*a*b^2 + A*b^3)*d^3*e^5 + 23358*(B*a^2*b + A*a*b^2)*d^2*e^6 + 7514*(B*a^3 + 3*A*a^2*b)*d*e^7)*x^4 - 5*(8*B*b^3*d^5*e^3 - 9724*A*a^3*d*e^7 - 17*(3*B*a*b^2 + A*b^3)*d^4*e^4 - 10812*(B*a^2*b + A*a*b^2)*d^3*e^5 - 10166*(B*a^3 + 3*A*a^2*b)*d^2*e^6)*x^3 + 3*(16*B*b^3*d^6*e^2 + 24310*A*a^3*d^2*e^6 - 34*(3*B*a*b^2 + A*b^3)*d^5*e^3 + 255*(B*a^2*b + A*a*b^2)*d^4*e^4 + 8840*(B*a^3 + 3*A*a^2*b)*d^3*e^5)*x^2 - (64*B*b^3*d^7*e - 48620*A*a^3*d^3*e^5 - 136*(3*B*a*b^2 + A*b^3)*d^6*e^2 + 1020*(B*a^2*b + A*a*b^2)*d^5*e^3 - 1105*(B*a^3 + 3*A*a^2*b)*d^4*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1735,1,539,0,1.257088," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, B b^{3} e^{7} x^{7} + 128 \, B b^{3} d^{7} + 6435 \, A a^{3} d^{3} e^{4} - 240 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{6} e + 1560 \, {\left(B a^{2} b + A a b^{2}\right)} d^{5} e^{2} - 1430 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{4} e^{3} + 231 \, {\left(31 \, B b^{3} d e^{6} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{7}\right)} x^{6} + 63 \, {\left(71 \, B b^{3} d^{2} e^{5} + 135 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{6} + 195 \, {\left(B a^{2} b + A a b^{2}\right)} e^{7}\right)} x^{5} + 35 \, {\left(B b^{3} d^{3} e^{4} + 159 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{5} + 897 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{6} + 143 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{7}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{4} e^{3} - 1287 \, A a^{3} e^{7} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{4} - 4407 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{5} - 2717 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{5} e^{2} + 6435 \, A a^{3} d e^{6} - 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{3} + 195 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{4} + 3575 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{6} e - 19305 \, A a^{3} d^{2} e^{5} - 120 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e^{2} + 780 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{3} - 715 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*B*b^3*e^7*x^7 + 128*B*b^3*d^7 + 6435*A*a^3*d^3*e^4 - 240*(3*B*a*b^2 + A*b^3)*d^6*e + 1560*(B*a^2*b + A*a*b^2)*d^5*e^2 - 1430*(B*a^3 + 3*A*a^2*b)*d^4*e^3 + 231*(31*B*b^3*d*e^6 + 15*(3*B*a*b^2 + A*b^3)*e^7)*x^6 + 63*(71*B*b^3*d^2*e^5 + 135*(3*B*a*b^2 + A*b^3)*d*e^6 + 195*(B*a^2*b + A*a*b^2)*e^7)*x^5 + 35*(B*b^3*d^3*e^4 + 159*(3*B*a*b^2 + A*b^3)*d^2*e^5 + 897*(B*a^2*b + A*a*b^2)*d*e^6 + 143*(B*a^3 + 3*A*a^2*b)*e^7)*x^4 - 5*(8*B*b^3*d^4*e^3 - 1287*A*a^3*e^7 - 15*(3*B*a*b^2 + A*b^3)*d^3*e^4 - 4407*(B*a^2*b + A*a*b^2)*d^2*e^5 - 2717*(B*a^3 + 3*A*a^2*b)*d*e^6)*x^3 + 3*(16*B*b^3*d^5*e^2 + 6435*A*a^3*d*e^6 - 30*(3*B*a*b^2 + A*b^3)*d^4*e^3 + 195*(B*a^2*b + A*a*b^2)*d^3*e^4 + 3575*(B*a^3 + 3*A*a^2*b)*d^2*e^5)*x^2 - (64*B*b^3*d^6*e - 19305*A*a^3*d^2*e^5 - 120*(3*B*a*b^2 + A*b^3)*d^5*e^2 + 780*(B*a^2*b + A*a*b^2)*d^4*e^3 - 715*(B*a^3 + 3*A*a^2*b)*d^3*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1736,1,446,0,1.128267," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B b^{3} e^{6} x^{6} + 128 \, B b^{3} d^{6} + 3003 \, A a^{3} d^{2} e^{4} - 208 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{5} e + 1144 \, {\left(B a^{2} b + A a b^{2}\right)} d^{4} e^{2} - 858 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{3} e^{3} + 105 \, {\left(14 \, B b^{3} d e^{5} + 13 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{6}\right)} x^{5} + 35 \, {\left(B b^{3} d^{2} e^{4} + 52 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{5} + 143 \, {\left(B a^{2} b + A a b^{2}\right)} e^{6}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{3} e^{3} - 13 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{4} - 1430 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{5} - 429 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{4} e^{2} + 1001 \, A a^{3} e^{6} - 26 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{3} + 143 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{4} + 1144 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{5} e - 6006 \, A a^{3} d e^{5} - 104 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e^{2} + 572 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{3} - 429 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{5}}"," ",0,"2/15015*(1155*B*b^3*e^6*x^6 + 128*B*b^3*d^6 + 3003*A*a^3*d^2*e^4 - 208*(3*B*a*b^2 + A*b^3)*d^5*e + 1144*(B*a^2*b + A*a*b^2)*d^4*e^2 - 858*(B*a^3 + 3*A*a^2*b)*d^3*e^3 + 105*(14*B*b^3*d*e^5 + 13*(3*B*a*b^2 + A*b^3)*e^6)*x^5 + 35*(B*b^3*d^2*e^4 + 52*(3*B*a*b^2 + A*b^3)*d*e^5 + 143*(B*a^2*b + A*a*b^2)*e^6)*x^4 - 5*(8*B*b^3*d^3*e^3 - 13*(3*B*a*b^2 + A*b^3)*d^2*e^4 - 1430*(B*a^2*b + A*a*b^2)*d*e^5 - 429*(B*a^3 + 3*A*a^2*b)*e^6)*x^3 + 3*(16*B*b^3*d^4*e^2 + 1001*A*a^3*e^6 - 26*(3*B*a*b^2 + A*b^3)*d^3*e^3 + 143*(B*a^2*b + A*a*b^2)*d^2*e^4 + 1144*(B*a^3 + 3*A*a^2*b)*d*e^5)*x^2 - (64*B*b^3*d^5*e - 6006*A*a^3*d*e^5 - 104*(3*B*a*b^2 + A*b^3)*d^4*e^2 + 572*(B*a^2*b + A*a*b^2)*d^3*e^3 - 429*(B*a^3 + 3*A*a^2*b)*d^2*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1737,1,353,0,1.555820," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B b^{3} e^{5} x^{5} + 128 \, B b^{3} d^{5} + 1155 \, A a^{3} d e^{4} - 176 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 792 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 462 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3} + 35 \, {\left(B b^{3} d e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} x^{4} - 5 \, {\left(8 \, B b^{3} d^{2} e^{3} - 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 297 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{3} e^{2} - 22 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 99 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 231 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} x^{2} - {\left(64 \, B b^{3} d^{4} e - 1155 \, A a^{3} e^{5} - 88 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} + 396 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} - 231 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*B*b^3*e^5*x^5 + 128*B*b^3*d^5 + 1155*A*a^3*d*e^4 - 176*(3*B*a*b^2 + A*b^3)*d^4*e + 792*(B*a^2*b + A*a*b^2)*d^3*e^2 - 462*(B*a^3 + 3*A*a^2*b)*d^2*e^3 + 35*(B*b^3*d*e^4 + 11*(3*B*a*b^2 + A*b^3)*e^5)*x^4 - 5*(8*B*b^3*d^2*e^3 - 11*(3*B*a*b^2 + A*b^3)*d*e^4 - 297*(B*a^2*b + A*a*b^2)*e^5)*x^3 + 3*(16*B*b^3*d^3*e^2 - 22*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 99*(B*a^2*b + A*a*b^2)*d*e^4 + 231*(B*a^3 + 3*A*a^2*b)*e^5)*x^2 - (64*B*b^3*d^4*e - 1155*A*a^3*e^5 - 88*(3*B*a*b^2 + A*b^3)*d^3*e^2 + 396*(B*a^2*b + A*a*b^2)*d^2*e^3 - 231*(B*a^3 + 3*A*a^2*b)*d*e^4)*x)*sqrt(e*x + d)/e^5","B",0
1738,1,263,0,1.085773," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B b^{3} e^{4} x^{4} + 128 \, B b^{3} d^{4} + 315 \, A a^{3} e^{4} - 144 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 504 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 5 \, {\left(8 \, B b^{3} d e^{3} - 9 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{2} e^{2} - 18 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 63 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{3} d^{3} e - 72 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 252 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*B*b^3*e^4*x^4 + 128*B*b^3*d^4 + 315*A*a^3*e^4 - 144*(3*B*a*b^2 + A*b^3)*d^3*e + 504*(B*a^2*b + A*a*b^2)*d^2*e^2 - 210*(B*a^3 + 3*A*a^2*b)*d*e^3 - 5*(8*B*b^3*d*e^3 - 9*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(16*B*b^3*d^2*e^2 - 18*(3*B*a*b^2 + A*b^3)*d*e^3 + 63*(B*a^2*b + A*a*b^2)*e^4)*x^2 - (64*B*b^3*d^3*e - 72*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 252*(B*a^2*b + A*a*b^2)*d*e^3 - 105*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/e^5","A",0
1739,1,272,0,1.398831," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} e^{4} x^{4} - 128 \, B b^{3} d^{4} - 35 \, A a^{3} e^{4} + 112 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 280 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} + 70 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(8 \, B b^{3} d e^{3} - 7 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + {\left(16 \, B b^{3} d^{2} e^{2} - 14 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 35 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - {\left(64 \, B b^{3} d^{3} e - 56 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 140 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 35 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/35*(5*B*b^3*e^4*x^4 - 128*B*b^3*d^4 - 35*A*a^3*e^4 + 112*(3*B*a*b^2 + A*b^3)*d^3*e - 280*(B*a^2*b + A*a*b^2)*d^2*e^2 + 70*(B*a^3 + 3*A*a^2*b)*d*e^3 - (8*B*b^3*d*e^3 - 7*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + (16*B*b^3*d^2*e^2 - 14*(3*B*a*b^2 + A*b^3)*d*e^3 + 35*(B*a^2*b + A*a*b^2)*e^4)*x^2 - (64*B*b^3*d^3*e - 56*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 140*(B*a^2*b + A*a*b^2)*d*e^3 - 35*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
1740,1,284,0,1.469351," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B b^{3} e^{4} x^{4} + 128 \, B b^{3} d^{4} - 5 \, A a^{3} e^{4} - 80 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e + 120 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 10 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - {\left(8 \, B b^{3} d e^{3} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(16 \, B b^{3} d^{2} e^{2} - 10 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 15 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} + 3 \, {\left(64 \, B b^{3} d^{3} e - 40 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} - 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*B*b^3*e^4*x^4 + 128*B*b^3*d^4 - 5*A*a^3*e^4 - 80*(3*B*a*b^2 + A*b^3)*d^3*e + 120*(B*a^2*b + A*a*b^2)*d^2*e^2 - 10*(B*a^3 + 3*A*a^2*b)*d*e^3 - (8*B*b^3*d*e^3 - 5*(3*B*a*b^2 + A*b^3)*e^4)*x^3 + 3*(16*B*b^3*d^2*e^2 - 10*(3*B*a*b^2 + A*b^3)*d*e^3 + 15*(B*a^2*b + A*a*b^2)*e^4)*x^2 + 3*(64*B*b^3*d^3*e - 40*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 60*(B*a^2*b + A*a*b^2)*d*e^3 - 5*(B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
1741,1,294,0,1.544399," ","integrate((b*x+a)^3*(B*x+A)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B b^{3} e^{4} x^{4} - 128 \, B b^{3} d^{4} - 3 \, A a^{3} e^{4} + 48 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e - 24 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{3} - 5 \, {\left(8 \, B b^{3} d e^{3} - 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{4}\right)} x^{3} - 15 \, {\left(16 \, B b^{3} d^{2} e^{2} - 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{3} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{4}\right)} x^{2} - 5 \, {\left(64 \, B b^{3} d^{3} e - 24 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{3} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*B*b^3*e^4*x^4 - 128*B*b^3*d^4 - 3*A*a^3*e^4 + 48*(3*B*a*b^2 + A*b^3)*d^3*e - 24*(B*a^2*b + A*a*b^2)*d^2*e^2 - 2*(B*a^3 + 3*A*a^2*b)*d*e^3 - 5*(8*B*b^3*d*e^3 - 3*(3*B*a*b^2 + A*b^3)*e^4)*x^3 - 15*(16*B*b^3*d^2*e^2 - 6*(3*B*a*b^2 + A*b^3)*d*e^3 + 3*(B*a^2*b + A*a*b^2)*e^4)*x^2 - 5*(64*B*b^3*d^3*e - 24*(3*B*a*b^2 + A*b^3)*d^2*e^2 + 12*(B*a^2*b + A*a*b^2)*d*e^3 + (B*a^3 + 3*A*a^2*b)*e^4)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
1742,1,865,0,1.409890," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left({\left(B a b^{3} - A b^{4}\right)} d^{3} e - 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - A a^{3} b\right)} e^{4}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(35 \, B b^{4} e^{4} x^{4} + 35 \, B b^{4} d^{4} - 528 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e + 1218 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} - 1050 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{3} + 315 \, {\left(B a^{4} - A a^{3} b\right)} e^{4} + 5 \, {\left(28 \, B b^{4} d e^{3} - 9 \, {\left(B a b^{3} - A b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(70 \, B b^{4} d^{2} e^{2} - 66 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + 21 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{4}\right)} x^{2} + {\left(140 \, B b^{4} d^{3} e - 366 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{2} + 336 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, b^{5} e}, \frac{2 \, {\left(315 \, {\left({\left(B a b^{3} - A b^{4}\right)} d^{3} e - 3 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} + 3 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - A a^{3} b\right)} e^{4}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(35 \, B b^{4} e^{4} x^{4} + 35 \, B b^{4} d^{4} - 528 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e + 1218 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e^{2} - 1050 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} d e^{3} + 315 \, {\left(B a^{4} - A a^{3} b\right)} e^{4} + 5 \, {\left(28 \, B b^{4} d e^{3} - 9 \, {\left(B a b^{3} - A b^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(70 \, B b^{4} d^{2} e^{2} - 66 \, {\left(B a b^{3} - A b^{4}\right)} d e^{3} + 21 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} e^{4}\right)} x^{2} + {\left(140 \, B b^{4} d^{3} e - 366 \, {\left(B a b^{3} - A b^{4}\right)} d^{2} e^{2} + 336 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d e^{3} - 105 \, {\left(B a^{3} b - A a^{2} b^{2}\right)} e^{4}\right)} x\right)} \sqrt{e x + d}\right)}}{315 \, b^{5} e}\right]"," ",0,"[-1/315*(315*((B*a*b^3 - A*b^4)*d^3*e - 3*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + 3*(B*a^3*b - A*a^2*b^2)*d*e^3 - (B*a^4 - A*a^3*b)*e^4)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(35*B*b^4*e^4*x^4 + 35*B*b^4*d^4 - 528*(B*a*b^3 - A*b^4)*d^3*e + 1218*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 - 1050*(B*a^3*b - A*a^2*b^2)*d*e^3 + 315*(B*a^4 - A*a^3*b)*e^4 + 5*(28*B*b^4*d*e^3 - 9*(B*a*b^3 - A*b^4)*e^4)*x^3 + 3*(70*B*b^4*d^2*e^2 - 66*(B*a*b^3 - A*b^4)*d*e^3 + 21*(B*a^2*b^2 - A*a*b^3)*e^4)*x^2 + (140*B*b^4*d^3*e - 366*(B*a*b^3 - A*b^4)*d^2*e^2 + 336*(B*a^2*b^2 - A*a*b^3)*d*e^3 - 105*(B*a^3*b - A*a^2*b^2)*e^4)*x)*sqrt(e*x + d))/(b^5*e), 2/315*(315*((B*a*b^3 - A*b^4)*d^3*e - 3*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 + 3*(B*a^3*b - A*a^2*b^2)*d*e^3 - (B*a^4 - A*a^3*b)*e^4)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (35*B*b^4*e^4*x^4 + 35*B*b^4*d^4 - 528*(B*a*b^3 - A*b^4)*d^3*e + 1218*(B*a^2*b^2 - A*a*b^3)*d^2*e^2 - 1050*(B*a^3*b - A*a^2*b^2)*d*e^3 + 315*(B*a^4 - A*a^3*b)*e^4 + 5*(28*B*b^4*d*e^3 - 9*(B*a*b^3 - A*b^4)*e^4)*x^3 + 3*(70*B*b^4*d^2*e^2 - 66*(B*a*b^3 - A*b^4)*d*e^3 + 21*(B*a^2*b^2 - A*a*b^3)*e^4)*x^2 + (140*B*b^4*d^3*e - 366*(B*a*b^3 - A*b^4)*d^2*e^2 + 336*(B*a^2*b^2 - A*a*b^3)*d*e^3 - 105*(B*a^3*b - A*a^2*b^2)*e^4)*x)*sqrt(e*x + d))/(b^5*e)]","B",0
1743,1,591,0,1.612088," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} e - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} + {\left(B a^{3} - A a^{2} b\right)} e^{3}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(15 \, B b^{3} e^{3} x^{3} + 15 \, B b^{3} d^{3} - 161 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e + 245 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} - 105 \, {\left(B a^{3} - A a^{2} b\right)} e^{3} + 3 \, {\left(15 \, B b^{3} d e^{2} - 7 \, {\left(B a b^{2} - A b^{3}\right)} e^{3}\right)} x^{2} + {\left(45 \, B b^{3} d^{2} e - 77 \, {\left(B a b^{2} - A b^{3}\right)} d e^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b^{4} e}, \frac{2 \, {\left(105 \, {\left({\left(B a b^{2} - A b^{3}\right)} d^{2} e - 2 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} + {\left(B a^{3} - A a^{2} b\right)} e^{3}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(15 \, B b^{3} e^{3} x^{3} + 15 \, B b^{3} d^{3} - 161 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e + 245 \, {\left(B a^{2} b - A a b^{2}\right)} d e^{2} - 105 \, {\left(B a^{3} - A a^{2} b\right)} e^{3} + 3 \, {\left(15 \, B b^{3} d e^{2} - 7 \, {\left(B a b^{2} - A b^{3}\right)} e^{3}\right)} x^{2} + {\left(45 \, B b^{3} d^{2} e - 77 \, {\left(B a b^{2} - A b^{3}\right)} d e^{2} + 35 \, {\left(B a^{2} b - A a b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, b^{4} e}\right]"," ",0,"[1/105*(105*((B*a*b^2 - A*b^3)*d^2*e - 2*(B*a^2*b - A*a*b^2)*d*e^2 + (B*a^3 - A*a^2*b)*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(15*B*b^3*e^3*x^3 + 15*B*b^3*d^3 - 161*(B*a*b^2 - A*b^3)*d^2*e + 245*(B*a^2*b - A*a*b^2)*d*e^2 - 105*(B*a^3 - A*a^2*b)*e^3 + 3*(15*B*b^3*d*e^2 - 7*(B*a*b^2 - A*b^3)*e^3)*x^2 + (45*B*b^3*d^2*e - 77*(B*a*b^2 - A*b^3)*d*e^2 + 35*(B*a^2*b - A*a*b^2)*e^3)*x)*sqrt(e*x + d))/(b^4*e), 2/105*(105*((B*a*b^2 - A*b^3)*d^2*e - 2*(B*a^2*b - A*a*b^2)*d*e^2 + (B*a^3 - A*a^2*b)*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (15*B*b^3*e^3*x^3 + 15*B*b^3*d^3 - 161*(B*a*b^2 - A*b^3)*d^2*e + 245*(B*a^2*b - A*a*b^2)*d*e^2 - 105*(B*a^3 - A*a^2*b)*e^3 + 3*(15*B*b^3*d*e^2 - 7*(B*a*b^2 - A*b^3)*e^3)*x^2 + (45*B*b^3*d^2*e - 77*(B*a*b^2 - A*b^3)*d*e^2 + 35*(B*a^2*b - A*a*b^2)*e^3)*x)*sqrt(e*x + d))/(b^4*e)]","B",0
1744,1,373,0,1.593586," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(B a b - A b^{2}\right)} d e - {\left(B a^{2} - A a b\right)} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} e^{2} x^{2} + 3 \, B b^{2} d^{2} - 20 \, {\left(B a b - A b^{2}\right)} d e + 15 \, {\left(B a^{2} - A a b\right)} e^{2} + {\left(6 \, B b^{2} d e - 5 \, {\left(B a b - A b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b^{3} e}, \frac{2 \, {\left(15 \, {\left({\left(B a b - A b^{2}\right)} d e - {\left(B a^{2} - A a b\right)} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(3 \, B b^{2} e^{2} x^{2} + 3 \, B b^{2} d^{2} - 20 \, {\left(B a b - A b^{2}\right)} d e + 15 \, {\left(B a^{2} - A a b\right)} e^{2} + {\left(6 \, B b^{2} d e - 5 \, {\left(B a b - A b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b^{3} e}\right]"," ",0,"[-1/15*(15*((B*a*b - A*b^2)*d*e - (B*a^2 - A*a*b)*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(3*B*b^2*e^2*x^2 + 3*B*b^2*d^2 - 20*(B*a*b - A*b^2)*d*e + 15*(B*a^2 - A*a*b)*e^2 + (6*B*b^2*d*e - 5*(B*a*b - A*b^2)*e^2)*x)*sqrt(e*x + d))/(b^3*e), 2/15*(15*((B*a*b - A*b^2)*d*e - (B*a^2 - A*a*b)*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (3*B*b^2*e^2*x^2 + 3*B*b^2*d^2 - 20*(B*a*b - A*b^2)*d*e + 15*(B*a^2 - A*a*b)*e^2 + (6*B*b^2*d*e - 5*(B*a*b - A*b^2)*e^2)*x)*sqrt(e*x + d))/(b^3*e)]","A",0
1745,1,211,0,1.824547," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a - A b\right)} e \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(B b e x + B b d - 3 \, {\left(B a - A b\right)} e\right)} \sqrt{e x + d}}{3 \, b^{2} e}, \frac{2 \, {\left(3 \, {\left(B a - A b\right)} e \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) + {\left(B b e x + B b d - 3 \, {\left(B a - A b\right)} e\right)} \sqrt{e x + d}\right)}}{3 \, b^{2} e}\right]"," ",0,"[-1/3*(3*(B*a - A*b)*e*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(B*b*e*x + B*b*d - 3*(B*a - A*b)*e)*sqrt(e*x + d))/(b^2*e), 2/3*(3*(B*a - A*b)*e*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) + (B*b*e*x + B*b*d - 3*(B*a - A*b)*e)*sqrt(e*x + d))/(b^2*e)]","A",0
1746,1,209,0,1.574002," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} d - a b e} {\left(B a - A b\right)} e \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(B b^{2} d - B a b e\right)} \sqrt{e x + d}}{b^{3} d e - a b^{2} e^{2}}, -\frac{2 \, {\left(\sqrt{-b^{2} d + a b e} {\left(B a - A b\right)} e \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(B b^{2} d - B a b e\right)} \sqrt{e x + d}\right)}}{b^{3} d e - a b^{2} e^{2}}\right]"," ",0,"[-(sqrt(b^2*d - a*b*e)*(B*a - A*b)*e*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(B*b^2*d - B*a*b*e)*sqrt(e*x + d))/(b^3*d*e - a*b^2*e^2), -2*(sqrt(-b^2*d + a*b*e)*(B*a - A*b)*e*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (B*b^2*d - B*a*b*e)*sqrt(e*x + d))/(b^3*d*e - a*b^2*e^2)]","A",0
1747,1,363,0,1.575109," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(B b^{2} d^{2} + A a b e^{2} - {\left(B a b + A b^{2}\right)} d e\right)} \sqrt{e x + d}}{b^{3} d^{3} e - 2 \, a b^{2} d^{2} e^{2} + a^{2} b d e^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x}, -\frac{2 \, {\left({\left({\left(B a - A b\right)} e^{2} x + {\left(B a - A b\right)} d e\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(B b^{2} d^{2} + A a b e^{2} - {\left(B a b + A b^{2}\right)} d e\right)} \sqrt{e x + d}\right)}}{b^{3} d^{3} e - 2 \, a b^{2} d^{2} e^{2} + a^{2} b d e^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x}\right]"," ",0,"[(((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(B*b^2*d^2 + A*a*b*e^2 - (B*a*b + A*b^2)*d*e)*sqrt(e*x + d))/(b^3*d^3*e - 2*a*b^2*d^2*e^2 + a^2*b*d*e^3 + (b^3*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)*x), -2*(((B*a - A*b)*e^2*x + (B*a - A*b)*d*e)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (B*b^2*d^2 + A*a*b*e^2 - (B*a*b + A*b^2)*d*e)*sqrt(e*x + d))/(b^3*d^3*e - 2*a*b^2*d^2*e^2 + a^2*b*d*e^3 + (b^3*d^2*e^2 - 2*a*b^2*d*e^3 + a^2*b*e^4)*x)]","B",0
1748,1,506,0,1.433272," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(B a - A b\right)} e^{3} x^{2} + 2 \, {\left(B a - A b\right)} d e^{2} x + {\left(B a - A b\right)} d^{2} e\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(B b d^{2} + A a e^{2} + 3 \, {\left(B a - A b\right)} e^{2} x + 2 \, {\left(B a - 2 \, A b\right)} d e\right)} \sqrt{e x + d}}{3 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left({\left(B a - A b\right)} e^{3} x^{2} + 2 \, {\left(B a - A b\right)} d e^{2} x + {\left(B a - A b\right)} d^{2} e\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(B b d^{2} + A a e^{2} + 3 \, {\left(B a - A b\right)} e^{2} x + 2 \, {\left(B a - 2 \, A b\right)} d e\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((B*a - A*b)*e^3*x^2 + 2*(B*a - A*b)*d*e^2*x + (B*a - A*b)*d^2*e)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(B*b*d^2 + A*a*e^2 + 3*(B*a - A*b)*e^2*x + 2*(B*a - 2*A*b)*d*e)*sqrt(e*x + d))/(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^2 + 2*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x), 2/3*(3*((B*a - A*b)*e^3*x^2 + 2*(B*a - A*b)*d*e^2*x + (B*a - A*b)*d^2*e)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (B*b*d^2 + A*a*e^2 + 3*(B*a - A*b)*e^2*x + 2*(B*a - 2*A*b)*d*e)*sqrt(e*x + d))/(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^2 + 2*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x)]","B",0
1749,1,902,0,0.937886," ","integrate((B*x+A)/(b*x+a)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(B a b - A b^{2}\right)} e^{4} x^{3} + 3 \, {\left(B a b - A b^{2}\right)} d e^{3} x^{2} + 3 \, {\left(B a b - A b^{2}\right)} d^{2} e^{2} x + {\left(B a b - A b^{2}\right)} d^{3} e\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} + 15 \, {\left(B a b - A b^{2}\right)} e^{3} x^{2} + {\left(14 \, B a b - 23 \, A b^{2}\right)} d^{2} e - {\left(2 \, B a^{2} - 11 \, A a b\right)} d e^{2} + 5 \, {\left(7 \, {\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x\right)}}, \frac{2 \, {\left(15 \, {\left({\left(B a b - A b^{2}\right)} e^{4} x^{3} + 3 \, {\left(B a b - A b^{2}\right)} d e^{3} x^{2} + 3 \, {\left(B a b - A b^{2}\right)} d^{2} e^{2} x + {\left(B a b - A b^{2}\right)} d^{3} e\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, B b^{2} d^{3} - 3 \, A a^{2} e^{3} + 15 \, {\left(B a b - A b^{2}\right)} e^{3} x^{2} + {\left(14 \, B a b - 23 \, A b^{2}\right)} d^{2} e - {\left(2 \, B a^{2} - 11 \, A a b\right)} d e^{2} + 5 \, {\left(7 \, {\left(B a b - A b^{2}\right)} d e^{2} - {\left(B a^{2} - A a b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/15*(15*((B*a*b - A*b^2)*e^4*x^3 + 3*(B*a*b - A*b^2)*d*e^3*x^2 + 3*(B*a*b - A*b^2)*d^2*e^2*x + (B*a*b - A*b^2)*d^3*e)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3*B*b^2*d^3 - 3*A*a^2*e^3 + 15*(B*a*b - A*b^2)*e^3*x^2 + (14*B*a*b - 23*A*b^2)*d^2*e - (2*B*a^2 - 11*A*a*b)*d*e^2 + 5*(7*(B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x)*sqrt(e*x + d))/(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^3 + 3*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^2 + 3*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x), 2/15*(15*((B*a*b - A*b^2)*e^4*x^3 + 3*(B*a*b - A*b^2)*d*e^3*x^2 + 3*(B*a*b - A*b^2)*d^2*e^2*x + (B*a*b - A*b^2)*d^3*e)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*B*b^2*d^3 - 3*A*a^2*e^3 + 15*(B*a*b - A*b^2)*e^3*x^2 + (14*B*a*b - 23*A*b^2)*d^2*e - (2*B*a^2 - 11*A*a*b)*d*e^2 + 5*(7*(B*a*b - A*b^2)*d*e^2 - (B*a^2 - A*a*b)*e^3)*x)*sqrt(e*x + d))/(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^3 + 3*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^2 + 3*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x)]","B",0
1750,1,1006,0,2.094400," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, B a b^{3} d^{3} - {\left(13 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d^{2} e + 2 \, {\left(10 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{2} - {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d^{3} - {\left(13 \, B a b^{3} - 7 \, A b^{4}\right)} d^{2} e + 2 \, {\left(10 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} - {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(30 \, B b^{4} e^{3} x^{4} + {\left(457 \, B a b^{3} - 105 \, A b^{4}\right)} d^{3} - 7 \, {\left(277 \, B a^{2} b^{2} - 161 \, A a b^{3}\right)} d^{2} e + 35 \, {\left(69 \, B a^{3} b - 49 \, A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + 6 \, {\left(22 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} e^{3}\right)} x^{3} + 2 \, {\left(122 \, B b^{4} d^{2} e - 2 \, {\left(79 \, B a b^{3} - 56 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(176 \, B b^{4} d^{3} - 2 \, {\left(345 \, B a b^{3} - 203 \, A b^{4}\right)} d^{2} e + 14 \, {\left(59 \, B a^{2} b^{2} - 42 \, A a b^{3}\right)} d e^{2} - 35 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{210 \, {\left(b^{6} x + a b^{5}\right)}}, -\frac{105 \, {\left(2 \, B a b^{3} d^{3} - {\left(13 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d^{2} e + 2 \, {\left(10 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{2} - {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + {\left(2 \, B b^{4} d^{3} - {\left(13 \, B a b^{3} - 7 \, A b^{4}\right)} d^{2} e + 2 \, {\left(10 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} d e^{2} - {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(30 \, B b^{4} e^{3} x^{4} + {\left(457 \, B a b^{3} - 105 \, A b^{4}\right)} d^{3} - 7 \, {\left(277 \, B a^{2} b^{2} - 161 \, A a b^{3}\right)} d^{2} e + 35 \, {\left(69 \, B a^{3} b - 49 \, A a^{2} b^{2}\right)} d e^{2} - 105 \, {\left(9 \, B a^{4} - 7 \, A a^{3} b\right)} e^{3} + 6 \, {\left(22 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 7 \, A b^{4}\right)} e^{3}\right)} x^{3} + 2 \, {\left(122 \, B b^{4} d^{2} e - 2 \, {\left(79 \, B a b^{3} - 56 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 7 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(176 \, B b^{4} d^{3} - 2 \, {\left(345 \, B a b^{3} - 203 \, A b^{4}\right)} d^{2} e + 14 \, {\left(59 \, B a^{2} b^{2} - 42 \, A a b^{3}\right)} d e^{2} - 35 \, {\left(9 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[1/210*(105*(2*B*a*b^3*d^3 - (13*B*a^2*b^2 - 7*A*a*b^3)*d^2*e + 2*(10*B*a^3*b - 7*A*a^2*b^2)*d*e^2 - (9*B*a^4 - 7*A*a^3*b)*e^3 + (2*B*b^4*d^3 - (13*B*a*b^3 - 7*A*b^4)*d^2*e + 2*(10*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 - (9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(30*B*b^4*e^3*x^4 + (457*B*a*b^3 - 105*A*b^4)*d^3 - 7*(277*B*a^2*b^2 - 161*A*a*b^3)*d^2*e + 35*(69*B*a^3*b - 49*A*a^2*b^2)*d*e^2 - 105*(9*B*a^4 - 7*A*a^3*b)*e^3 + 6*(22*B*b^4*d*e^2 - (9*B*a*b^3 - 7*A*b^4)*e^3)*x^3 + 2*(122*B*b^4*d^2*e - 2*(79*B*a*b^3 - 56*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 7*A*a*b^3)*e^3)*x^2 + 2*(176*B*b^4*d^3 - 2*(345*B*a*b^3 - 203*A*b^4)*d^2*e + 14*(59*B*a^2*b^2 - 42*A*a*b^3)*d*e^2 - 35*(9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^6*x + a*b^5), -1/105*(105*(2*B*a*b^3*d^3 - (13*B*a^2*b^2 - 7*A*a*b^3)*d^2*e + 2*(10*B*a^3*b - 7*A*a^2*b^2)*d*e^2 - (9*B*a^4 - 7*A*a^3*b)*e^3 + (2*B*b^4*d^3 - (13*B*a*b^3 - 7*A*b^4)*d^2*e + 2*(10*B*a^2*b^2 - 7*A*a*b^3)*d*e^2 - (9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (30*B*b^4*e^3*x^4 + (457*B*a*b^3 - 105*A*b^4)*d^3 - 7*(277*B*a^2*b^2 - 161*A*a*b^3)*d^2*e + 35*(69*B*a^3*b - 49*A*a^2*b^2)*d*e^2 - 105*(9*B*a^4 - 7*A*a^3*b)*e^3 + 6*(22*B*b^4*d*e^2 - (9*B*a*b^3 - 7*A*b^4)*e^3)*x^3 + 2*(122*B*b^4*d^2*e - 2*(79*B*a*b^3 - 56*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 7*A*a*b^3)*e^3)*x^2 + 2*(176*B*b^4*d^3 - 2*(345*B*a*b^3 - 203*A*b^4)*d^2*e + 14*(59*B*a^2*b^2 - 42*A*a*b^3)*d*e^2 - 35*(9*B*a^3*b - 7*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^6*x + a*b^5)]","B",0
1751,1,666,0,1.392702," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{2} d^{2} - {\left(9 \, B a^{2} b - 5 \, A a b^{2}\right)} d e + {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d^{2} - {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(6 \, B b^{3} e^{2} x^{3} + {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{2} - 10 \, {\left(17 \, B a^{2} b - 10 \, A a b^{2}\right)} d e + 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + 2 \, {\left(11 \, B b^{3} d e - {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{3} d^{2} - {\left(59 \, B a b^{2} - 35 \, A b^{3}\right)} d e + 5 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(2 \, B a b^{2} d^{2} - {\left(9 \, B a^{2} b - 5 \, A a b^{2}\right)} d e + {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + {\left(2 \, B b^{3} d^{2} - {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e + {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(6 \, B b^{3} e^{2} x^{3} + {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{2} - 10 \, {\left(17 \, B a^{2} b - 10 \, A a b^{2}\right)} d e + 15 \, {\left(7 \, B a^{3} - 5 \, A a^{2} b\right)} e^{2} + 2 \, {\left(11 \, B b^{3} d e - {\left(7 \, B a b^{2} - 5 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(23 \, B b^{3} d^{2} - {\left(59 \, B a b^{2} - 35 \, A b^{3}\right)} d e + 5 \, {\left(7 \, B a^{2} b - 5 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[-1/30*(15*(2*B*a*b^2*d^2 - (9*B*a^2*b - 5*A*a*b^2)*d*e + (7*B*a^3 - 5*A*a^2*b)*e^2 + (2*B*b^3*d^2 - (9*B*a*b^2 - 5*A*b^3)*d*e + (7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(6*B*b^3*e^2*x^3 + (61*B*a*b^2 - 15*A*b^3)*d^2 - 10*(17*B*a^2*b - 10*A*a*b^2)*d*e + 15*(7*B*a^3 - 5*A*a^2*b)*e^2 + 2*(11*B*b^3*d*e - (7*B*a*b^2 - 5*A*b^3)*e^2)*x^2 + 2*(23*B*b^3*d^2 - (59*B*a*b^2 - 35*A*b^3)*d*e + 5*(7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^5*x + a*b^4), -1/15*(15*(2*B*a*b^2*d^2 - (9*B*a^2*b - 5*A*a*b^2)*d*e + (7*B*a^3 - 5*A*a^2*b)*e^2 + (2*B*b^3*d^2 - (9*B*a*b^2 - 5*A*b^3)*d*e + (7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (6*B*b^3*e^2*x^3 + (61*B*a*b^2 - 15*A*b^3)*d^2 - 10*(17*B*a^2*b - 10*A*a*b^2)*d*e + 15*(7*B*a^3 - 5*A*a^2*b)*e^2 + 2*(11*B*b^3*d*e - (7*B*a*b^2 - 5*A*b^3)*e^2)*x^2 + 2*(23*B*b^3*d^2 - (59*B*a*b^2 - 35*A*b^3)*d*e + 5*(7*B*a^2*b - 5*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^5*x + a*b^4)]","A",0
1752,1,392,0,1.460203," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a b d - {\left(5 \, B a^{2} - 3 \, A a b\right)} e + {\left(2 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(2 \, B b^{2} e x^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d - 3 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} e + 2 \, {\left(4 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{3 \, {\left(2 \, B a b d - {\left(5 \, B a^{2} - 3 \, A a b\right)} e + {\left(2 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, B b^{2} e x^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d - 3 \, {\left(5 \, B a^{2} - 3 \, A a b\right)} e + 2 \, {\left(4 \, B b^{2} d - {\left(5 \, B a b - 3 \, A b^{2}\right)} e\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[1/6*(3*(2*B*a*b*d - (5*B*a^2 - 3*A*a*b)*e + (2*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(2*B*b^2*e*x^2 + (11*B*a*b - 3*A*b^2)*d - 3*(5*B*a^2 - 3*A*a*b)*e + 2*(4*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(e*x + d))/(b^4*x + a*b^3), -1/3*(3*(2*B*a*b*d - (5*B*a^2 - 3*A*a*b)*e + (2*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*B*b^2*e*x^2 + (11*B*a*b - 3*A*b^2)*d - 3*(5*B*a^2 - 3*A*a*b)*e + 2*(4*B*b^2*d - (5*B*a*b - 3*A*b^2)*e)*x)*sqrt(e*x + d))/(b^4*x + a*b^3)]","A",0
1753,1,393,0,1.575155," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a b d - {\left(3 \, B a^{2} - A a b\right)} e + {\left(2 \, B b^{2} d - {\left(3 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left({\left(3 \, B a b^{2} - A b^{3}\right)} d - {\left(3 \, B a^{2} b - A a b^{2}\right)} e + 2 \, {\left(B b^{3} d - B a b^{2} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d - a^{2} b^{3} e + {\left(b^{5} d - a b^{4} e\right)} x\right)}}, \frac{{\left(2 \, B a b d - {\left(3 \, B a^{2} - A a b\right)} e + {\left(2 \, B b^{2} d - {\left(3 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left({\left(3 \, B a b^{2} - A b^{3}\right)} d - {\left(3 \, B a^{2} b - A a b^{2}\right)} e + 2 \, {\left(B b^{3} d - B a b^{2} e\right)} x\right)} \sqrt{e x + d}}{a b^{4} d - a^{2} b^{3} e + {\left(b^{5} d - a b^{4} e\right)} x}\right]"," ",0,"[1/2*((2*B*a*b*d - (3*B*a^2 - A*a*b)*e + (2*B*b^2*d - (3*B*a*b - A*b^2)*e)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*((3*B*a*b^2 - A*b^3)*d - (3*B*a^2*b - A*a*b^2)*e + 2*(B*b^3*d - B*a*b^2*e)*x)*sqrt(e*x + d))/(a*b^4*d - a^2*b^3*e + (b^5*d - a*b^4*e)*x), ((2*B*a*b*d - (3*B*a^2 - A*a*b)*e + (2*B*b^2*d - (3*B*a*b - A*b^2)*e)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + ((3*B*a*b^2 - A*b^3)*d - (3*B*a^2*b - A*a*b^2)*e + 2*(B*b^3*d - B*a*b^2*e)*x)*sqrt(e*x + d))/(a*b^4*d - a^2*b^3*e + (b^5*d - a*b^4*e)*x)]","A",0
1754,1,397,0,1.429194," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, B a b d - {\left(B a^{2} + A a b\right)} e + {\left(2 \, B b^{2} d - {\left(B a b + A b^{2}\right)} e\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left({\left(B a b^{2} - A b^{3}\right)} d - {\left(B a^{2} b - A a b^{2}\right)} e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d^{2} - 2 \, a^{2} b^{3} d e + a^{3} b^{2} e^{2} + {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} x\right)}}, \frac{{\left(2 \, B a b d - {\left(B a^{2} + A a b\right)} e + {\left(2 \, B b^{2} d - {\left(B a b + A b^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left({\left(B a b^{2} - A b^{3}\right)} d - {\left(B a^{2} b - A a b^{2}\right)} e\right)} \sqrt{e x + d}}{a b^{4} d^{2} - 2 \, a^{2} b^{3} d e + a^{3} b^{2} e^{2} + {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} x}\right]"," ",0,"[1/2*((2*B*a*b*d - (B*a^2 + A*a*b)*e + (2*B*b^2*d - (B*a*b + A*b^2)*e)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*((B*a*b^2 - A*b^3)*d - (B*a^2*b - A*a*b^2)*e)*sqrt(e*x + d))/(a*b^4*d^2 - 2*a^2*b^3*d*e + a^3*b^2*e^2 + (b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*x), ((2*B*a*b*d - (B*a^2 + A*a*b)*e + (2*B*b^2*d - (B*a*b + A*b^2)*e)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + ((B*a*b^2 - A*b^3)*d - (B*a^2*b - A*a*b^2)*e)*sqrt(e*x + d))/(a*b^4*d^2 - 2*a^2*b^3*d*e + a^3*b^2*e^2 + (b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*x)]","B",0
1755,1,775,0,1.669160," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, B a b d^{2} + {\left(B a^{2} - 3 \, A a b\right)} d e + {\left(2 \, B b^{2} d e + {\left(B a b - 3 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, B b^{2} d^{2} + 3 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 3 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, A a^{2} b e^{2} + {\left(3 \, B a b^{2} - A b^{3}\right)} d^{2} - {\left(3 \, B a^{2} b + A a b^{2}\right)} d e + {\left(2 \, B b^{3} d^{2} - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{4} d^{4} - 3 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} - a^{4} b d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{2} + {\left(b^{5} d^{4} - 2 \, a b^{4} d^{3} e + 2 \, a^{3} b^{2} d e^{3} - a^{4} b e^{4}\right)} x\right)}}, \frac{{\left(2 \, B a b d^{2} + {\left(B a^{2} - 3 \, A a b\right)} d e + {\left(2 \, B b^{2} d e + {\left(B a b - 3 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(2 \, B b^{2} d^{2} + 3 \, {\left(B a b - A b^{2}\right)} d e + {\left(B a^{2} - 3 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, A a^{2} b e^{2} + {\left(3 \, B a b^{2} - A b^{3}\right)} d^{2} - {\left(3 \, B a^{2} b + A a b^{2}\right)} d e + {\left(2 \, B b^{3} d^{2} - {\left(B a b^{2} + 3 \, A b^{3}\right)} d e - {\left(B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{a b^{4} d^{4} - 3 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} - a^{4} b d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{2} + {\left(b^{5} d^{4} - 2 \, a b^{4} d^{3} e + 2 \, a^{3} b^{2} d e^{3} - a^{4} b e^{4}\right)} x}\right]"," ",0,"[-1/2*((2*B*a*b*d^2 + (B*a^2 - 3*A*a*b)*d*e + (2*B*b^2*d*e + (B*a*b - 3*A*b^2)*e^2)*x^2 + (2*B*b^2*d^2 + 3*(B*a*b - A*b^2)*d*e + (B*a^2 - 3*A*a*b)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*A*a^2*b*e^2 + (3*B*a*b^2 - A*b^3)*d^2 - (3*B*a^2*b + A*a*b^2)*d*e + (2*B*b^3*d^2 - (B*a*b^2 + 3*A*b^3)*d*e - (B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(a*b^4*d^4 - 3*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 - a^4*b*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^2 + (b^5*d^4 - 2*a*b^4*d^3*e + 2*a^3*b^2*d*e^3 - a^4*b*e^4)*x), ((2*B*a*b*d^2 + (B*a^2 - 3*A*a*b)*d*e + (2*B*b^2*d*e + (B*a*b - 3*A*b^2)*e^2)*x^2 + (2*B*b^2*d^2 + 3*(B*a*b - A*b^2)*d*e + (B*a^2 - 3*A*a*b)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*A*a^2*b*e^2 + (3*B*a*b^2 - A*b^3)*d^2 - (3*B*a^2*b + A*a*b^2)*d*e + (2*B*b^3*d^2 - (B*a*b^2 + 3*A*b^3)*d*e - (B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(a*b^4*d^4 - 3*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 - a^4*b*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^2 + (b^5*d^4 - 2*a*b^4*d^3*e + 2*a^3*b^2*d*e^3 - a^4*b*e^4)*x)]","B",0
1756,1,1106,0,1.637764," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, B a b d^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} d^{2} e + {\left(2 \, B b^{2} d e^{2} + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{2} d^{2} e + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e^{2} + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{2} d^{3} + {\left(7 \, B a b - 5 \, A b^{2}\right)} d^{2} e + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} d e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(2 \, A a^{2} e^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d^{2} + 2 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} d e + 3 \, {\left(2 \, B b^{2} d e + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B b^{2} d^{2} + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}, -\frac{3 \, {\left(2 \, B a b d^{3} + {\left(3 \, B a^{2} - 5 \, A a b\right)} d^{2} e + {\left(2 \, B b^{2} d e^{2} + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{2} d^{2} e + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e^{2} + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{3}\right)} x^{2} + {\left(2 \, B b^{2} d^{3} + {\left(7 \, B a b - 5 \, A b^{2}\right)} d^{2} e + 2 \, {\left(3 \, B a^{2} - 5 \, A a b\right)} d e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(2 \, A a^{2} e^{2} + {\left(11 \, B a b - 3 \, A b^{2}\right)} d^{2} + 2 \, {\left(2 \, B a^{2} - 7 \, A a b\right)} d e + 3 \, {\left(2 \, B b^{2} d e + {\left(3 \, B a b - 5 \, A b^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B b^{2} d^{2} + 2 \, {\left(4 \, B a b - 5 \, A b^{2}\right)} d e + {\left(3 \, B a^{2} - 5 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(2*B*a*b*d^3 + (3*B*a^2 - 5*A*a*b)*d^2*e + (2*B*b^2*d*e^2 + (3*B*a*b - 5*A*b^2)*e^3)*x^3 + (4*B*b^2*d^2*e + 2*(4*B*a*b - 5*A*b^2)*d*e^2 + (3*B*a^2 - 5*A*a*b)*e^3)*x^2 + (2*B*b^2*d^3 + (7*B*a*b - 5*A*b^2)*d^2*e + 2*(3*B*a^2 - 5*A*a*b)*d*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(2*A*a^2*e^2 + (11*B*a*b - 3*A*b^2)*d^2 + 2*(2*B*a^2 - 7*A*a*b)*d*e + 3*(2*B*b^2*d*e + (3*B*a*b - 5*A*b^2)*e^2)*x^2 + 2*(4*B*b^2*d^2 + 2*(4*B*a*b - 5*A*b^2)*d*e + (3*B*a^2 - 5*A*a*b)*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x), -1/3*(3*(2*B*a*b*d^3 + (3*B*a^2 - 5*A*a*b)*d^2*e + (2*B*b^2*d*e^2 + (3*B*a*b - 5*A*b^2)*e^3)*x^3 + (4*B*b^2*d^2*e + 2*(4*B*a*b - 5*A*b^2)*d*e^2 + (3*B*a^2 - 5*A*a*b)*e^3)*x^2 + (2*B*b^2*d^3 + (7*B*a*b - 5*A*b^2)*d^2*e + 2*(3*B*a^2 - 5*A*a*b)*d*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (2*A*a^2*e^2 + (11*B*a*b - 3*A*b^2)*d^2 + 2*(2*B*a^2 - 7*A*a*b)*d*e + 3*(2*B*b^2*d*e + (3*B*a*b - 5*A*b^2)*e^2)*x^2 + 2*(4*B*b^2*d^2 + 2*(4*B*a*b - 5*A*b^2)*d*e + (3*B*a^2 - 5*A*a*b)*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x)]","B",0
1757,1,1749,0,1.788675," ","integrate((B*x+A)/(b*x+a)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, B a b^{2} d^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{3} e + {\left(2 \, B b^{3} d e^{3} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{3} d^{2} e^{2} + {\left(17 \, B a b^{2} - 21 \, A b^{3}\right)} d e^{3} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, B b^{3} d^{3} e + 7 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{4} + {\left(11 \, B a b^{2} - 7 \, A b^{3}\right)} d^{3} e + 3 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(6 \, A a^{3} e^{3} - {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{3} - 4 \, {\left(12 \, B a^{2} b - 29 \, A a b^{2}\right)} d^{2} e + 4 \, {\left(B a^{3} - 8 \, A a^{2} b\right)} d e^{2} - 15 \, {\left(2 \, B b^{3} d e^{2} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} - 5 \, {\left(14 \, B b^{3} d^{2} e + {\left(39 \, B a b^{2} - 49 \, A b^{3}\right)} d e^{2} + 2 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(46 \, B b^{3} d^{3} + {\left(163 \, B a b^{2} - 161 \, A b^{3}\right)} d^{2} e + 4 \, {\left(29 \, B a^{2} b - 42 \, A a b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(2 \, B a b^{2} d^{4} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{3} e + {\left(2 \, B b^{3} d e^{3} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + {\left(6 \, B b^{3} d^{2} e^{2} + {\left(17 \, B a b^{2} - 21 \, A b^{3}\right)} d e^{3} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, B b^{3} d^{3} e + 7 \, {\left(B a b^{2} - A b^{3}\right)} d^{2} e^{2} + {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3}\right)} x^{2} + {\left(2 \, B b^{3} d^{4} + {\left(11 \, B a b^{2} - 7 \, A b^{3}\right)} d^{3} e + 3 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(6 \, A a^{3} e^{3} - {\left(61 \, B a b^{2} - 15 \, A b^{3}\right)} d^{3} - 4 \, {\left(12 \, B a^{2} b - 29 \, A a b^{2}\right)} d^{2} e + 4 \, {\left(B a^{3} - 8 \, A a^{2} b\right)} d e^{2} - 15 \, {\left(2 \, B b^{3} d e^{2} + {\left(5 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} - 5 \, {\left(14 \, B b^{3} d^{2} e + {\left(39 \, B a b^{2} - 49 \, A b^{3}\right)} d e^{2} + 2 \, {\left(5 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(46 \, B b^{3} d^{3} + {\left(163 \, B a b^{2} - 161 \, A b^{3}\right)} d^{2} e + 4 \, {\left(29 \, B a^{2} b - 42 \, A a b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/30*(15*(2*B*a*b^2*d^4 + (5*B*a^2*b - 7*A*a*b^2)*d^3*e + (2*B*b^3*d*e^3 + (5*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + (6*B*b^3*d^2*e^2 + (17*B*a*b^2 - 21*A*b^3)*d*e^3 + (5*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + 3*(2*B*b^3*d^3*e + 7*(B*a*b^2 - A*b^3)*d^2*e^2 + (5*B*a^2*b - 7*A*a*b^2)*d*e^3)*x^2 + (2*B*b^3*d^4 + (11*B*a*b^2 - 7*A*b^3)*d^3*e + 3*(5*B*a^2*b - 7*A*a*b^2)*d^2*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(6*A*a^3*e^3 - (61*B*a*b^2 - 15*A*b^3)*d^3 - 4*(12*B*a^2*b - 29*A*a*b^2)*d^2*e + 4*(B*a^3 - 8*A*a^2*b)*d*e^2 - 15*(2*B*b^3*d*e^2 + (5*B*a*b^2 - 7*A*b^3)*e^3)*x^3 - 5*(14*B*b^3*d^2*e + (39*B*a*b^2 - 49*A*b^3)*d*e^2 + 2*(5*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 - (46*B*b^3*d^3 + (163*B*a*b^2 - 161*A*b^3)*d^2*e + 4*(29*B*a^2*b - 42*A*a*b^2)*d*e^2 - 2*(5*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x), -1/15*(15*(2*B*a*b^2*d^4 + (5*B*a^2*b - 7*A*a*b^2)*d^3*e + (2*B*b^3*d*e^3 + (5*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + (6*B*b^3*d^2*e^2 + (17*B*a*b^2 - 21*A*b^3)*d*e^3 + (5*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + 3*(2*B*b^3*d^3*e + 7*(B*a*b^2 - A*b^3)*d^2*e^2 + (5*B*a^2*b - 7*A*a*b^2)*d*e^3)*x^2 + (2*B*b^3*d^4 + (11*B*a*b^2 - 7*A*b^3)*d^3*e + 3*(5*B*a^2*b - 7*A*a*b^2)*d^2*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (6*A*a^3*e^3 - (61*B*a*b^2 - 15*A*b^3)*d^3 - 4*(12*B*a^2*b - 29*A*a*b^2)*d^2*e + 4*(B*a^3 - 8*A*a^2*b)*d*e^2 - 15*(2*B*b^3*d*e^2 + (5*B*a*b^2 - 7*A*b^3)*e^3)*x^3 - 5*(14*B*b^3*d^2*e + (39*B*a*b^2 - 49*A*b^3)*d*e^2 + 2*(5*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 - (46*B*b^3*d^3 + (163*B*a*b^2 - 161*A*b^3)*d^2*e + 4*(29*B*a^2*b - 42*A*a*b^2)*d*e^2 - 2*(5*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x)]","B",0
1758,1,1060,0,1.683753," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{2} e - {\left(13 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + {\left(4 \, B b^{4} d^{2} e - {\left(13 \, B a b^{3} - 5 \, A b^{4}\right)} d e^{2} + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(4 \, B a b^{3} d^{2} e - {\left(13 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} d e^{2} + {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(24 \, B b^{4} e^{3} x^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(107 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e - 140 \, {\left(12 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 8 \, {\left(16 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 8 \, {\left(58 \, B b^{4} d^{2} e - 2 \, {\left(59 \, B a b^{3} - 25 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} - {\left(60 \, B b^{4} d^{3} - {\left(1303 \, B a b^{3} - 195 \, A b^{4}\right)} d^{2} e + 14 \, {\left(203 \, B a^{2} b^{2} - 85 \, A a b^{3}\right)} d e^{2} - 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{2} e - {\left(13 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + {\left(4 \, B b^{4} d^{2} e - {\left(13 \, B a b^{3} - 5 \, A b^{4}\right)} d e^{2} + {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(4 \, B a b^{3} d^{2} e - {\left(13 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} d e^{2} + {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(24 \, B b^{4} e^{3} x^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(107 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d^{2} e - 140 \, {\left(12 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(9 \, B a^{4} - 5 \, A a^{3} b\right)} e^{3} + 8 \, {\left(16 \, B b^{4} d e^{2} - {\left(9 \, B a b^{3} - 5 \, A b^{4}\right)} e^{3}\right)} x^{3} + 8 \, {\left(58 \, B b^{4} d^{2} e - 2 \, {\left(59 \, B a b^{3} - 25 \, A b^{4}\right)} d e^{2} + 7 \, {\left(9 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} - {\left(60 \, B b^{4} d^{3} - {\left(1303 \, B a b^{3} - 195 \, A b^{4}\right)} d^{2} e + 14 \, {\left(203 \, B a^{2} b^{2} - 85 \, A a b^{3}\right)} d e^{2} - 175 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{60 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/120*(105*(4*B*a^2*b^2*d^2*e - (13*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + (9*B*a^4 - 5*A*a^3*b)*e^3 + (4*B*b^4*d^2*e - (13*B*a*b^3 - 5*A*b^4)*d*e^2 + (9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + 2*(4*B*a*b^3*d^2*e - (13*B*a^2*b^2 - 5*A*a*b^3)*d*e^2 + (9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(24*B*b^4*e^3*x^4 - 30*(B*a*b^3 + A*b^4)*d^3 + 7*(107*B*a^2*b^2 - 15*A*a*b^3)*d^2*e - 140*(12*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(9*B*a^4 - 5*A*a^3*b)*e^3 + 8*(16*B*b^4*d*e^2 - (9*B*a*b^3 - 5*A*b^4)*e^3)*x^3 + 8*(58*B*b^4*d^2*e - 2*(59*B*a*b^3 - 25*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 - (60*B*b^4*d^3 - (1303*B*a*b^3 - 195*A*b^4)*d^2*e + 14*(203*B*a^2*b^2 - 85*A*a*b^3)*d*e^2 - 175*(9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/60*(105*(4*B*a^2*b^2*d^2*e - (13*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + (9*B*a^4 - 5*A*a^3*b)*e^3 + (4*B*b^4*d^2*e - (13*B*a*b^3 - 5*A*b^4)*d*e^2 + (9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + 2*(4*B*a*b^3*d^2*e - (13*B*a^2*b^2 - 5*A*a*b^3)*d*e^2 + (9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (24*B*b^4*e^3*x^4 - 30*(B*a*b^3 + A*b^4)*d^3 + 7*(107*B*a^2*b^2 - 15*A*a*b^3)*d^2*e - 140*(12*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(9*B*a^4 - 5*A*a^3*b)*e^3 + 8*(16*B*b^4*d*e^2 - (9*B*a*b^3 - 5*A*b^4)*e^3)*x^3 + 8*(58*B*b^4*d^2*e - 2*(59*B*a*b^3 - 25*A*b^4)*d*e^2 + 7*(9*B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 - (60*B*b^4*d^3 - (1303*B*a*b^3 - 195*A*b^4)*d^2*e + 14*(203*B*a^2*b^2 - 85*A*a*b^3)*d*e^2 - 175*(9*B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","B",0
1759,1,680,0,1.634099," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, B a^{2} b d e - {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(8 \, B b^{3} e^{2} x^{3} - 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(19 \, B a^{2} b - 3 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + 8 \, {\left(7 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} - {\left(12 \, B b^{3} d^{2} - {\left(163 \, B a b^{2} - 27 \, A b^{3}\right)} d e + 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{15 \, {\left(4 \, B a^{2} b d e - {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, B b^{3} e^{2} x^{3} - 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(19 \, B a^{2} b - 3 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 3 \, A a^{2} b\right)} e^{2} + 8 \, {\left(7 \, B b^{3} d e - {\left(7 \, B a b^{2} - 3 \, A b^{3}\right)} e^{2}\right)} x^{2} - {\left(12 \, B b^{3} d^{2} - {\left(163 \, B a b^{2} - 27 \, A b^{3}\right)} d e + 25 \, {\left(7 \, B a^{2} b - 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(15*(4*B*a^2*b*d*e - (7*B*a^3 - 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(8*B*b^3*e^2*x^3 - 6*(B*a*b^2 + A*b^3)*d^2 + 5*(19*B*a^2*b - 3*A*a*b^2)*d*e - 15*(7*B*a^3 - 3*A*a^2*b)*e^2 + 8*(7*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 - (12*B*b^3*d^2 - (163*B*a*b^2 - 27*A*b^3)*d*e + 25*(7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/12*(15*(4*B*a^2*b*d*e - (7*B*a^3 - 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*B*b^3*e^2*x^3 - 6*(B*a*b^2 + A*b^3)*d^2 + 5*(19*B*a^2*b - 3*A*a*b^2)*d*e - 15*(7*B*a^3 - 3*A*a^2*b)*e^2 + 8*(7*B*b^3*d*e - (7*B*a*b^2 - 3*A*b^3)*e^2)*x^2 - (12*B*b^3*d^2 - (163*B*a*b^2 - 27*A*b^3)*d*e + 25*(7*B*a^2*b - 3*A*a*b^2)*e^2)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
1760,1,703,0,0.907127," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a^{2} b d e - {\left(5 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(5 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(5 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(17 \, B a^{2} b^{2} - A a b^{3}\right)} d e + 3 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} e^{2} - 8 \, {\left(B b^{4} d e - B a b^{3} e^{2}\right)} x^{2} + {\left(4 \, B b^{4} d^{2} - {\left(29 \, B a b^{3} - 5 \, A b^{4}\right)} d e + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d - a^{3} b^{4} e + {\left(b^{7} d - a b^{6} e\right)} x^{2} + 2 \, {\left(a b^{6} d - a^{2} b^{5} e\right)} x\right)}}, \frac{3 \, {\left(4 \, B a^{2} b d e - {\left(5 \, B a^{3} - A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(5 \, B a b^{2} - A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(5 \, B a^{2} b - A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(17 \, B a^{2} b^{2} - A a b^{3}\right)} d e + 3 \, {\left(5 \, B a^{3} b - A a^{2} b^{2}\right)} e^{2} - 8 \, {\left(B b^{4} d e - B a b^{3} e^{2}\right)} x^{2} + {\left(4 \, B b^{4} d^{2} - {\left(29 \, B a b^{3} - 5 \, A b^{4}\right)} d e + 5 \, {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d - a^{3} b^{4} e + {\left(b^{7} d - a b^{6} e\right)} x^{2} + 2 \, {\left(a b^{6} d - a^{2} b^{5} e\right)} x\right)}}\right]"," ",0,"[1/8*(3*(4*B*a^2*b*d*e - (5*B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (5*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (5*B*a^2*b - A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*(B*a*b^3 + A*b^4)*d^2 - (17*B*a^2*b^2 - A*a*b^3)*d*e + 3*(5*B*a^3*b - A*a^2*b^2)*e^2 - 8*(B*b^4*d*e - B*a*b^3*e^2)*x^2 + (4*B*b^4*d^2 - (29*B*a*b^3 - 5*A*b^4)*d*e + 5*(5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d - a^3*b^4*e + (b^7*d - a*b^6*e)*x^2 + 2*(a*b^6*d - a^2*b^5*e)*x), 1/4*(3*(4*B*a^2*b*d*e - (5*B*a^3 - A*a^2*b)*e^2 + (4*B*b^3*d*e - (5*B*a*b^2 - A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (5*B*a^2*b - A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*(B*a*b^3 + A*b^4)*d^2 - (17*B*a^2*b^2 - A*a*b^3)*d*e + 3*(5*B*a^3*b - A*a^2*b^2)*e^2 - 8*(B*b^4*d*e - B*a*b^3*e^2)*x^2 + (4*B*b^4*d^2 - (29*B*a*b^3 - 5*A*b^4)*d*e + 5*(5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d - a^3*b^4*e + (b^7*d - a*b^6*e)*x^2 + 2*(a*b^6*d - a^2*b^5*e)*x)]","A",0
1761,1,721,0,0.788281," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{{\left(4 \, B a^{2} b d e - {\left(3 \, B a^{3} + A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(3 \, B a^{2} b + A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d e + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(9 \, B a b^{3} - A b^{4}\right)} d e + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{2} - 2 \, a^{3} b^{4} d e + a^{4} b^{3} e^{2} + {\left(b^{7} d^{2} - 2 \, a b^{6} d e + a^{2} b^{5} e^{2}\right)} x^{2} + 2 \, {\left(a b^{6} d^{2} - 2 \, a^{2} b^{5} d e + a^{3} b^{4} e^{2}\right)} x\right)}}, \frac{{\left(4 \, B a^{2} b d e - {\left(3 \, B a^{3} + A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(3 \, B a b^{2} + A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(3 \, B a^{2} b + A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(5 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d e + {\left(3 \, B a^{3} b + A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(9 \, B a b^{3} - A b^{4}\right)} d e + {\left(5 \, B a^{2} b^{2} - A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{2} - 2 \, a^{3} b^{4} d e + a^{4} b^{3} e^{2} + {\left(b^{7} d^{2} - 2 \, a b^{6} d e + a^{2} b^{5} e^{2}\right)} x^{2} + 2 \, {\left(a b^{6} d^{2} - 2 \, a^{2} b^{5} d e + a^{3} b^{4} e^{2}\right)} x\right)}}\right]"," ",0,"[1/8*((4*B*a^2*b*d*e - (3*B*a^3 + A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 + A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (3*B*a^2*b + A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*(B*a*b^3 + A*b^4)*d^2 - (5*B*a^2*b^2 + 3*A*a*b^3)*d*e + (3*B*a^3*b + A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (9*B*a*b^3 - A*b^4)*d*e + (5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^2 - 2*a^3*b^4*d*e + a^4*b^3*e^2 + (b^7*d^2 - 2*a*b^6*d*e + a^2*b^5*e^2)*x^2 + 2*(a*b^6*d^2 - 2*a^2*b^5*d*e + a^3*b^4*e^2)*x), 1/4*((4*B*a^2*b*d*e - (3*B*a^3 + A*a^2*b)*e^2 + (4*B*b^3*d*e - (3*B*a*b^2 + A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (3*B*a^2*b + A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*(B*a*b^3 + A*b^4)*d^2 - (5*B*a^2*b^2 + 3*A*a*b^3)*d*e + (3*B*a^3*b + A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (9*B*a*b^3 - A*b^4)*d*e + (5*B*a^2*b^2 - A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^2 - 2*a^3*b^4*d*e + a^4*b^3*e^2 + (b^7*d^2 - 2*a*b^6*d*e + a^2*b^5*e^2)*x^2 + 2*(a*b^6*d^2 - 2*a^2*b^5*d*e + a^3*b^4*e^2)*x)]","B",0
1762,1,808,0,1.030620," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, B a^{2} b d e - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(B a b^{2} + 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(B a^{2} b + 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(B a^{2} b^{2} + 7 \, A a b^{3}\right)} d e - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(5 \, B a b^{3} + 3 \, A b^{4}\right)} d e + {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{3} - 3 \, a^{3} b^{4} d^{2} e + 3 \, a^{4} b^{3} d e^{2} - a^{5} b^{2} e^{3} + {\left(b^{7} d^{3} - 3 \, a b^{6} d^{2} e + 3 \, a^{2} b^{5} d e^{2} - a^{3} b^{4} e^{3}\right)} x^{2} + 2 \, {\left(a b^{6} d^{3} - 3 \, a^{2} b^{5} d^{2} e + 3 \, a^{3} b^{4} d e^{2} - a^{4} b^{3} e^{3}\right)} x\right)}}, -\frac{{\left(4 \, B a^{2} b d e - {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{2} + {\left(4 \, B b^{3} d e - {\left(B a b^{2} + 3 \, A b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d e - {\left(B a^{2} b + 3 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, {\left(B a b^{3} + A b^{4}\right)} d^{2} - {\left(B a^{2} b^{2} + 7 \, A a b^{3}\right)} d e - {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{2} + {\left(4 \, B b^{4} d^{2} - {\left(5 \, B a b^{3} + 3 \, A b^{4}\right)} d e + {\left(B a^{2} b^{2} + 3 \, A a b^{3}\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{3} - 3 \, a^{3} b^{4} d^{2} e + 3 \, a^{4} b^{3} d e^{2} - a^{5} b^{2} e^{3} + {\left(b^{7} d^{3} - 3 \, a b^{6} d^{2} e + 3 \, a^{2} b^{5} d e^{2} - a^{3} b^{4} e^{3}\right)} x^{2} + 2 \, {\left(a b^{6} d^{3} - 3 \, a^{2} b^{5} d^{2} e + 3 \, a^{3} b^{4} d e^{2} - a^{4} b^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/8*((4*B*a^2*b*d*e - (B*a^3 + 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (B*a*b^2 + 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (B*a^2*b + 3*A*a*b^2)*e^2)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(2*(B*a*b^3 + A*b^4)*d^2 - (B*a^2*b^2 + 7*A*a*b^3)*d*e - (B*a^3*b - 5*A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (5*B*a*b^3 + 3*A*b^4)*d*e + (B*a^2*b^2 + 3*A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^3 - 3*a^3*b^4*d^2*e + 3*a^4*b^3*d*e^2 - a^5*b^2*e^3 + (b^7*d^3 - 3*a*b^6*d^2*e + 3*a^2*b^5*d*e^2 - a^3*b^4*e^3)*x^2 + 2*(a*b^6*d^3 - 3*a^2*b^5*d^2*e + 3*a^3*b^4*d*e^2 - a^4*b^3*e^3)*x), -1/4*((4*B*a^2*b*d*e - (B*a^3 + 3*A*a^2*b)*e^2 + (4*B*b^3*d*e - (B*a*b^2 + 3*A*b^3)*e^2)*x^2 + 2*(4*B*a*b^2*d*e - (B*a^2*b + 3*A*a*b^2)*e^2)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*(B*a*b^3 + A*b^4)*d^2 - (B*a^2*b^2 + 7*A*a*b^3)*d*e - (B*a^3*b - 5*A*a^2*b^2)*e^2 + (4*B*b^4*d^2 - (5*B*a*b^3 + 3*A*b^4)*d*e + (B*a^2*b^2 + 3*A*a*b^3)*e^2)*x)*sqrt(e*x + d))/(a^2*b^5*d^3 - 3*a^3*b^4*d^2*e + 3*a^4*b^3*d*e^2 - a^5*b^2*e^3 + (b^7*d^3 - 3*a*b^6*d^2*e + 3*a^2*b^5*d*e^2 - a^3*b^4*e^3)*x^2 + 2*(a*b^6*d^3 - 3*a^2*b^5*d^2*e + 3*a^3*b^4*d*e^2 - a^4*b^3*e^3)*x)]","B",0
1763,1,1410,0,1.343916," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, B a^{2} b d^{2} e + {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + {\left(4 \, B b^{3} d e^{2} + {\left(B a b^{2} - 5 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{3} d^{2} e + {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B a b^{2} d^{2} e + 2 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, A a^{3} b e^{3} + 2 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 11 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - {\left(13 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + 3 \, {\left(4 \, B b^{4} d^{2} e - {\left(3 \, B a b^{3} + 5 \, A b^{4}\right)} d e^{2} - {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + {\left(4 \, B b^{4} d^{3} + {\left(17 \, B a b^{3} - 5 \, A b^{4}\right)} d^{2} e - 4 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d e^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{5} d^{5} - 4 \, a^{3} b^{4} d^{4} e + 6 \, a^{4} b^{3} d^{3} e^{2} - 4 \, a^{5} b^{2} d^{2} e^{3} + a^{6} b d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{3} + {\left(b^{7} d^{5} - 2 \, a b^{6} d^{4} e - 2 \, a^{2} b^{5} d^{3} e^{2} + 8 \, a^{3} b^{4} d^{2} e^{3} - 7 \, a^{4} b^{3} d e^{4} + 2 \, a^{5} b^{2} e^{5}\right)} x^{2} + {\left(2 \, a b^{6} d^{5} - 7 \, a^{2} b^{5} d^{4} e + 8 \, a^{3} b^{4} d^{3} e^{2} - 2 \, a^{4} b^{3} d^{2} e^{3} - 2 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x\right)}}, -\frac{3 \, {\left(4 \, B a^{2} b d^{2} e + {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + {\left(4 \, B b^{3} d e^{2} + {\left(B a b^{2} - 5 \, A b^{3}\right)} e^{3}\right)} x^{3} + {\left(4 \, B b^{3} d^{2} e + {\left(9 \, B a b^{2} - 5 \, A b^{3}\right)} d e^{2} + 2 \, {\left(B a^{2} b - 5 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, B a b^{2} d^{2} e + 2 \, {\left(3 \, B a^{2} b - 5 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 5 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, A a^{3} b e^{3} + 2 \, {\left(B a b^{3} + A b^{4}\right)} d^{3} + 11 \, {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{2} e - {\left(13 \, B a^{3} b - A a^{2} b^{2}\right)} d e^{2} + 3 \, {\left(4 \, B b^{4} d^{2} e - {\left(3 \, B a b^{3} + 5 \, A b^{4}\right)} d e^{2} - {\left(B a^{2} b^{2} - 5 \, A a b^{3}\right)} e^{3}\right)} x^{2} + {\left(4 \, B b^{4} d^{3} + {\left(17 \, B a b^{3} - 5 \, A b^{4}\right)} d^{2} e - 4 \, {\left(4 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d e^{2} - 5 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{5} d^{5} - 4 \, a^{3} b^{4} d^{4} e + 6 \, a^{4} b^{3} d^{3} e^{2} - 4 \, a^{5} b^{2} d^{2} e^{3} + a^{6} b d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{3} + {\left(b^{7} d^{5} - 2 \, a b^{6} d^{4} e - 2 \, a^{2} b^{5} d^{3} e^{2} + 8 \, a^{3} b^{4} d^{2} e^{3} - 7 \, a^{4} b^{3} d e^{4} + 2 \, a^{5} b^{2} e^{5}\right)} x^{2} + {\left(2 \, a b^{6} d^{5} - 7 \, a^{2} b^{5} d^{4} e + 8 \, a^{3} b^{4} d^{3} e^{2} - 2 \, a^{4} b^{3} d^{2} e^{3} - 2 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(4*B*a^2*b*d^2*e + (B*a^3 - 5*A*a^2*b)*d*e^2 + (4*B*b^3*d*e^2 + (B*a*b^2 - 5*A*b^3)*e^3)*x^3 + (4*B*b^3*d^2*e + (9*B*a*b^2 - 5*A*b^3)*d*e^2 + 2*(B*a^2*b - 5*A*a*b^2)*e^3)*x^2 + (8*B*a*b^2*d^2*e + 2*(3*B*a^2*b - 5*A*a*b^2)*d*e^2 + (B*a^3 - 5*A*a^2*b)*e^3)*x)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e + 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*A*a^3*b*e^3 + 2*(B*a*b^3 + A*b^4)*d^3 + 11*(B*a^2*b^2 - A*a*b^3)*d^2*e - (13*B*a^3*b - A*a^2*b^2)*d*e^2 + 3*(4*B*b^4*d^2*e - (3*B*a*b^3 + 5*A*b^4)*d*e^2 - (B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + (4*B*b^4*d^3 + (17*B*a*b^3 - 5*A*b^4)*d^2*e - 4*(4*B*a^2*b^2 + 5*A*a*b^3)*d*e^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(a^2*b^5*d^5 - 4*a^3*b^4*d^4*e + 6*a^4*b^3*d^3*e^2 - 4*a^5*b^2*d^2*e^3 + a^6*b*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^3 + (b^7*d^5 - 2*a*b^6*d^4*e - 2*a^2*b^5*d^3*e^2 + 8*a^3*b^4*d^2*e^3 - 7*a^4*b^3*d*e^4 + 2*a^5*b^2*e^5)*x^2 + (2*a*b^6*d^5 - 7*a^2*b^5*d^4*e + 8*a^3*b^4*d^3*e^2 - 2*a^4*b^3*d^2*e^3 - 2*a^5*b^2*d*e^4 + a^6*b*e^5)*x), -1/4*(3*(4*B*a^2*b*d^2*e + (B*a^3 - 5*A*a^2*b)*d*e^2 + (4*B*b^3*d*e^2 + (B*a*b^2 - 5*A*b^3)*e^3)*x^3 + (4*B*b^3*d^2*e + (9*B*a*b^2 - 5*A*b^3)*d*e^2 + 2*(B*a^2*b - 5*A*a*b^2)*e^3)*x^2 + (8*B*a*b^2*d^2*e + 2*(3*B*a^2*b - 5*A*a*b^2)*d*e^2 + (B*a^3 - 5*A*a^2*b)*e^3)*x)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*A*a^3*b*e^3 + 2*(B*a*b^3 + A*b^4)*d^3 + 11*(B*a^2*b^2 - A*a*b^3)*d^2*e - (13*B*a^3*b - A*a^2*b^2)*d*e^2 + 3*(4*B*b^4*d^2*e - (3*B*a*b^3 + 5*A*b^4)*d*e^2 - (B*a^2*b^2 - 5*A*a*b^3)*e^3)*x^2 + (4*B*b^4*d^3 + (17*B*a*b^3 - 5*A*b^4)*d^2*e - 4*(4*B*a^2*b^2 + 5*A*a*b^3)*d*e^2 - 5*(B*a^3*b - 5*A*a^2*b^2)*e^3)*x)*sqrt(e*x + d))/(a^2*b^5*d^5 - 4*a^3*b^4*d^4*e + 6*a^4*b^3*d^3*e^2 - 4*a^5*b^2*d^2*e^3 + a^6*b*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^3 + (b^7*d^5 - 2*a*b^6*d^4*e - 2*a^2*b^5*d^3*e^2 + 8*a^3*b^4*d^2*e^3 - 7*a^4*b^3*d*e^4 + 2*a^5*b^2*e^5)*x^2 + (2*a*b^6*d^5 - 7*a^2*b^5*d^4*e + 8*a^3*b^4*d^3*e^2 - 2*a^4*b^3*d^2*e^3 - 2*a^5*b^2*d*e^4 + a^6*b*e^5)*x)]","B",0
1764,1,1776,0,1.542709," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, B a^{2} b d^{3} e + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d^{2} e^{2} + {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, B b^{3} d^{2} e^{2} + 7 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} + {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, B b^{3} d^{3} e + {\left(19 \, B a b^{2} - 7 \, A b^{3}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d^{3} e + 7 \, {\left(B a^{2} b - A a b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(8 \, A a^{3} e^{3} + 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{3} + {\left(83 \, B a^{2} b - 39 \, A a b^{2}\right)} d^{2} e + 16 \, {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + 15 \, {\left(4 \, B b^{3} d e^{2} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} + 5 \, {\left(16 \, B b^{3} d^{2} e + 4 \, {\left(8 \, B a b^{2} - 7 \, A b^{3}\right)} d e^{2} + 5 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(12 \, B b^{3} d^{3} + {\left(145 \, B a b^{2} - 21 \, A b^{3}\right)} d^{2} e + 2 \, {\left(67 \, B a^{2} b - 119 \, A a b^{2}\right)} d e^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}, \frac{15 \, {\left(4 \, B a^{2} b d^{3} e + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d^{2} e^{2} + {\left(4 \, B b^{3} d e^{3} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{4}\right)} x^{4} + 2 \, {\left(4 \, B b^{3} d^{2} e^{2} + 7 \, {\left(B a b^{2} - A b^{3}\right)} d e^{3} + {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{4}\right)} x^{3} + {\left(4 \, B b^{3} d^{3} e + {\left(19 \, B a b^{2} - 7 \, A b^{3}\right)} d^{2} e^{2} + 4 \, {\left(4 \, B a^{2} b - 7 \, A a b^{2}\right)} d e^{3} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{4}\right)} x^{2} + 2 \, {\left(4 \, B a b^{2} d^{3} e + 7 \, {\left(B a^{2} b - A a b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} d e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(8 \, A a^{3} e^{3} + 6 \, {\left(B a b^{2} + A b^{3}\right)} d^{3} + {\left(83 \, B a^{2} b - 39 \, A a b^{2}\right)} d^{2} e + 16 \, {\left(B a^{3} - 5 \, A a^{2} b\right)} d e^{2} + 15 \, {\left(4 \, B b^{3} d e^{2} + {\left(3 \, B a b^{2} - 7 \, A b^{3}\right)} e^{3}\right)} x^{3} + 5 \, {\left(16 \, B b^{3} d^{2} e + 4 \, {\left(8 \, B a b^{2} - 7 \, A b^{3}\right)} d e^{2} + 5 \, {\left(3 \, B a^{2} b - 7 \, A a b^{2}\right)} e^{3}\right)} x^{2} + {\left(12 \, B b^{3} d^{3} + {\left(145 \, B a b^{2} - 21 \, A b^{3}\right)} d^{2} e + 2 \, {\left(67 \, B a^{2} b - 119 \, A a b^{2}\right)} d e^{2} + 8 \, {\left(3 \, B a^{3} - 7 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}\right]"," ",0,"[-1/24*(15*(4*B*a^2*b*d^3*e + (3*B*a^3 - 7*A*a^2*b)*d^2*e^2 + (4*B*b^3*d*e^3 + (3*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + 2*(4*B*b^3*d^2*e^2 + 7*(B*a*b^2 - A*b^3)*d*e^3 + (3*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + (4*B*b^3*d^3*e + (19*B*a*b^2 - 7*A*b^3)*d^2*e^2 + 4*(4*B*a^2*b - 7*A*a*b^2)*d*e^3 + (3*B*a^3 - 7*A*a^2*b)*e^4)*x^2 + 2*(4*B*a*b^2*d^3*e + 7*(B*a^2*b - A*a*b^2)*d^2*e^2 + (3*B*a^3 - 7*A*a^2*b)*d*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(8*A*a^3*e^3 + 6*(B*a*b^2 + A*b^3)*d^3 + (83*B*a^2*b - 39*A*a*b^2)*d^2*e + 16*(B*a^3 - 5*A*a^2*b)*d*e^2 + 15*(4*B*b^3*d*e^2 + (3*B*a*b^2 - 7*A*b^3)*e^3)*x^3 + 5*(16*B*b^3*d^2*e + 4*(8*B*a*b^2 - 7*A*b^3)*d*e^2 + 5*(3*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 + (12*B*b^3*d^3 + (145*B*a*b^2 - 21*A*b^3)*d^2*e + 2*(67*B*a^2*b - 119*A*a*b^2)*d*e^2 + 8*(3*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x), 1/12*(15*(4*B*a^2*b*d^3*e + (3*B*a^3 - 7*A*a^2*b)*d^2*e^2 + (4*B*b^3*d*e^3 + (3*B*a*b^2 - 7*A*b^3)*e^4)*x^4 + 2*(4*B*b^3*d^2*e^2 + 7*(B*a*b^2 - A*b^3)*d*e^3 + (3*B*a^2*b - 7*A*a*b^2)*e^4)*x^3 + (4*B*b^3*d^3*e + (19*B*a*b^2 - 7*A*b^3)*d^2*e^2 + 4*(4*B*a^2*b - 7*A*a*b^2)*d*e^3 + (3*B*a^3 - 7*A*a^2*b)*e^4)*x^2 + 2*(4*B*a*b^2*d^3*e + 7*(B*a^2*b - A*a*b^2)*d^2*e^2 + (3*B*a^3 - 7*A*a^2*b)*d*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (8*A*a^3*e^3 + 6*(B*a*b^2 + A*b^3)*d^3 + (83*B*a^2*b - 39*A*a*b^2)*d^2*e + 16*(B*a^3 - 5*A*a^2*b)*d*e^2 + 15*(4*B*b^3*d*e^2 + (3*B*a*b^2 - 7*A*b^3)*e^3)*x^3 + 5*(16*B*b^3*d^2*e + 4*(8*B*a*b^2 - 7*A*b^3)*d*e^2 + 5*(3*B*a^2*b - 7*A*a*b^2)*e^3)*x^2 + (12*B*b^3*d^3 + (145*B*a*b^2 - 21*A*b^3)*d^2*e + 2*(67*B*a^2*b - 119*A*a*b^2)*d*e^2 + 8*(3*B*a^3 - 7*A*a^2*b)*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x)]","B",0
1765,1,2675,0,1.464877," ","integrate((B*x+A)/(b*x+a)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(4 \, B a^{2} b^{2} d^{4} e + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{3} e^{2} + {\left(4 \, B b^{4} d e^{4} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(12 \, B b^{4} d^{2} e^{3} + {\left(23 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{4} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(12 \, B b^{4} d^{3} e^{2} + 3 \, {\left(13 \, B a b^{3} - 9 \, A b^{4}\right)} d^{2} e^{3} + 2 \, {\left(17 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(4 \, B b^{4} d^{4} e + {\left(29 \, B a b^{3} - 9 \, A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{2} e^{3} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4}\right)} x^{2} + {\left(8 \, B a b^{3} d^{4} e + 2 \, {\left(11 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{3} e^{2} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(24 \, A a^{4} e^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(659 \, B a^{2} b^{2} - 255 \, A a b^{3}\right)} d^{3} e - 16 \, {\left(17 \, B a^{3} b - 54 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 8 \, {\left(2 \, B a^{4} - 21 \, A a^{3} b\right)} d e^{3} - 105 \, {\left(4 \, B b^{4} d e^{3} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{4}\right)} x^{4} - 35 \, {\left(28 \, B b^{4} d^{2} e^{2} + {\left(55 \, B a b^{3} - 63 \, A b^{4}\right)} d e^{3} + 5 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 7 \, {\left(92 \, B b^{4} d^{3} e + 9 \, {\left(39 \, B a b^{3} - 23 \, A b^{4}\right)} d^{2} e^{2} + 3 \, {\left(109 \, B a^{2} b^{2} - 177 \, A a b^{3}\right)} d e^{3} + 8 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(60 \, B b^{4} d^{4} + {\left(1183 \, B a b^{3} - 135 \, A b^{4}\right)} d^{3} e + 3 \, {\left(643 \, B a^{2} b^{2} - 831 \, A a b^{3}\right)} d^{2} e^{2} + 72 \, {\left(9 \, B a^{3} b - 17 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}, \frac{105 \, {\left(4 \, B a^{2} b^{2} d^{4} e + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{3} e^{2} + {\left(4 \, B b^{4} d e^{4} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{5}\right)} x^{5} + {\left(12 \, B b^{4} d^{2} e^{3} + {\left(23 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{4} + 2 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{5}\right)} x^{4} + {\left(12 \, B b^{4} d^{3} e^{2} + 3 \, {\left(13 \, B a b^{3} - 9 \, A b^{4}\right)} d^{2} e^{3} + 2 \, {\left(17 \, B a^{2} b^{2} - 27 \, A a b^{3}\right)} d e^{4} + {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{5}\right)} x^{3} + {\left(4 \, B b^{4} d^{4} e + {\left(29 \, B a b^{3} - 9 \, A b^{4}\right)} d^{3} e^{2} + 6 \, {\left(7 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{2} e^{3} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d e^{4}\right)} x^{2} + {\left(8 \, B a b^{3} d^{4} e + 2 \, {\left(11 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} d^{3} e^{2} + 3 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) + {\left(24 \, A a^{4} e^{4} - 30 \, {\left(B a b^{3} + A b^{4}\right)} d^{4} - {\left(659 \, B a^{2} b^{2} - 255 \, A a b^{3}\right)} d^{3} e - 16 \, {\left(17 \, B a^{3} b - 54 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 8 \, {\left(2 \, B a^{4} - 21 \, A a^{3} b\right)} d e^{3} - 105 \, {\left(4 \, B b^{4} d e^{3} + {\left(5 \, B a b^{3} - 9 \, A b^{4}\right)} e^{4}\right)} x^{4} - 35 \, {\left(28 \, B b^{4} d^{2} e^{2} + {\left(55 \, B a b^{3} - 63 \, A b^{4}\right)} d e^{3} + 5 \, {\left(5 \, B a^{2} b^{2} - 9 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 7 \, {\left(92 \, B b^{4} d^{3} e + 9 \, {\left(39 \, B a b^{3} - 23 \, A b^{4}\right)} d^{2} e^{2} + 3 \, {\left(109 \, B a^{2} b^{2} - 177 \, A a b^{3}\right)} d e^{3} + 8 \, {\left(5 \, B a^{3} b - 9 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(60 \, B b^{4} d^{4} + {\left(1183 \, B a b^{3} - 135 \, A b^{4}\right)} d^{3} e + 3 \, {\left(643 \, B a^{2} b^{2} - 831 \, A a b^{3}\right)} d^{2} e^{2} + 72 \, {\left(9 \, B a^{3} b - 17 \, A a^{2} b^{2}\right)} d e^{3} - 8 \, {\left(5 \, B a^{4} - 9 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{e x + d}}{60 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[1/120*(105*(4*B*a^2*b^2*d^4*e + (5*B*a^3*b - 9*A*a^2*b^2)*d^3*e^2 + (4*B*b^4*d*e^4 + (5*B*a*b^3 - 9*A*b^4)*e^5)*x^5 + (12*B*b^4*d^2*e^3 + (23*B*a*b^3 - 27*A*b^4)*d*e^4 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*e^5)*x^4 + (12*B*b^4*d^3*e^2 + 3*(13*B*a*b^3 - 9*A*b^4)*d^2*e^3 + 2*(17*B*a^2*b^2 - 27*A*a*b^3)*d*e^4 + (5*B*a^3*b - 9*A*a^2*b^2)*e^5)*x^3 + (4*B*b^4*d^4*e + (29*B*a*b^3 - 9*A*b^4)*d^3*e^2 + 6*(7*B*a^2*b^2 - 9*A*a*b^3)*d^2*e^3 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d*e^4)*x^2 + (8*B*a*b^3*d^4*e + 2*(11*B*a^2*b^2 - 9*A*a*b^3)*d^3*e^2 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(24*A*a^4*e^4 - 30*(B*a*b^3 + A*b^4)*d^4 - (659*B*a^2*b^2 - 255*A*a*b^3)*d^3*e - 16*(17*B*a^3*b - 54*A*a^2*b^2)*d^2*e^2 + 8*(2*B*a^4 - 21*A*a^3*b)*d*e^3 - 105*(4*B*b^4*d*e^3 + (5*B*a*b^3 - 9*A*b^4)*e^4)*x^4 - 35*(28*B*b^4*d^2*e^2 + (55*B*a*b^3 - 63*A*b^4)*d*e^3 + 5*(5*B*a^2*b^2 - 9*A*a*b^3)*e^4)*x^3 - 7*(92*B*b^4*d^3*e + 9*(39*B*a*b^3 - 23*A*b^4)*d^2*e^2 + 3*(109*B*a^2*b^2 - 177*A*a*b^3)*d*e^3 + 8*(5*B*a^3*b - 9*A*a^2*b^2)*e^4)*x^2 - (60*B*b^4*d^4 + (1183*B*a*b^3 - 135*A*b^4)*d^3*e + 3*(643*B*a^2*b^2 - 831*A*a*b^3)*d^2*e^2 + 72*(9*B*a^3*b - 17*A*a^2*b^2)*d*e^3 - 8*(5*B*a^4 - 9*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x), 1/60*(105*(4*B*a^2*b^2*d^4*e + (5*B*a^3*b - 9*A*a^2*b^2)*d^3*e^2 + (4*B*b^4*d*e^4 + (5*B*a*b^3 - 9*A*b^4)*e^5)*x^5 + (12*B*b^4*d^2*e^3 + (23*B*a*b^3 - 27*A*b^4)*d*e^4 + 2*(5*B*a^2*b^2 - 9*A*a*b^3)*e^5)*x^4 + (12*B*b^4*d^3*e^2 + 3*(13*B*a*b^3 - 9*A*b^4)*d^2*e^3 + 2*(17*B*a^2*b^2 - 27*A*a*b^3)*d*e^4 + (5*B*a^3*b - 9*A*a^2*b^2)*e^5)*x^3 + (4*B*b^4*d^4*e + (29*B*a*b^3 - 9*A*b^4)*d^3*e^2 + 6*(7*B*a^2*b^2 - 9*A*a*b^3)*d^2*e^3 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d*e^4)*x^2 + (8*B*a*b^3*d^4*e + 2*(11*B*a^2*b^2 - 9*A*a*b^3)*d^3*e^2 + 3*(5*B*a^3*b - 9*A*a^2*b^2)*d^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) + (24*A*a^4*e^4 - 30*(B*a*b^3 + A*b^4)*d^4 - (659*B*a^2*b^2 - 255*A*a*b^3)*d^3*e - 16*(17*B*a^3*b - 54*A*a^2*b^2)*d^2*e^2 + 8*(2*B*a^4 - 21*A*a^3*b)*d*e^3 - 105*(4*B*b^4*d*e^3 + (5*B*a*b^3 - 9*A*b^4)*e^4)*x^4 - 35*(28*B*b^4*d^2*e^2 + (55*B*a*b^3 - 63*A*b^4)*d*e^3 + 5*(5*B*a^2*b^2 - 9*A*a*b^3)*e^4)*x^3 - 7*(92*B*b^4*d^3*e + 9*(39*B*a*b^3 - 23*A*b^4)*d^2*e^2 + 3*(109*B*a^2*b^2 - 177*A*a*b^3)*d*e^3 + 8*(5*B*a^3*b - 9*A*a^2*b^2)*e^4)*x^2 - (60*B*b^4*d^4 + (1183*B*a*b^3 - 135*A*b^4)*d^3*e + 3*(643*B*a^2*b^2 - 831*A*a*b^3)*d^2*e^2 + 72*(9*B*a^3*b - 17*A*a^2*b^2)*d*e^3 - 8*(5*B*a^4 - 9*A*a^3*b)*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x)]","B",0
1766,1,591,0,1.307702," ","integrate((b*x+a)*(f*x+e)^(5/2)/(d*x+c),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(b c d^{2} - a d^{3}\right)} e^{2} f - 2 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{2} + {\left(b c^{3} - a c^{2} d\right)} f^{3}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) + 2 \, {\left(15 \, b d^{3} f^{3} x^{3} + 15 \, b d^{3} e^{3} - 161 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f + 245 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{2} - 105 \, {\left(b c^{3} - a c^{2} d\right)} f^{3} + 3 \, {\left(15 \, b d^{3} e f^{2} - 7 \, {\left(b c d^{2} - a d^{3}\right)} f^{3}\right)} x^{2} + {\left(45 \, b d^{3} e^{2} f - 77 \, {\left(b c d^{2} - a d^{3}\right)} e f^{2} + 35 \, {\left(b c^{2} d - a c d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}}{105 \, d^{4} f}, \frac{2 \, {\left(105 \, {\left({\left(b c d^{2} - a d^{3}\right)} e^{2} f - 2 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{2} + {\left(b c^{3} - a c^{2} d\right)} f^{3}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(15 \, b d^{3} f^{3} x^{3} + 15 \, b d^{3} e^{3} - 161 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f + 245 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{2} - 105 \, {\left(b c^{3} - a c^{2} d\right)} f^{3} + 3 \, {\left(15 \, b d^{3} e f^{2} - 7 \, {\left(b c d^{2} - a d^{3}\right)} f^{3}\right)} x^{2} + {\left(45 \, b d^{3} e^{2} f - 77 \, {\left(b c d^{2} - a d^{3}\right)} e f^{2} + 35 \, {\left(b c^{2} d - a c d^{2}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, d^{4} f}\right]"," ",0,"[1/105*(105*((b*c*d^2 - a*d^3)*e^2*f - 2*(b*c^2*d - a*c*d^2)*e*f^2 + (b*c^3 - a*c^2*d)*f^3)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f + 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) + 2*(15*b*d^3*f^3*x^3 + 15*b*d^3*e^3 - 161*(b*c*d^2 - a*d^3)*e^2*f + 245*(b*c^2*d - a*c*d^2)*e*f^2 - 105*(b*c^3 - a*c^2*d)*f^3 + 3*(15*b*d^3*e*f^2 - 7*(b*c*d^2 - a*d^3)*f^3)*x^2 + (45*b*d^3*e^2*f - 77*(b*c*d^2 - a*d^3)*e*f^2 + 35*(b*c^2*d - a*c*d^2)*f^3)*x)*sqrt(f*x + e))/(d^4*f), 2/105*(105*((b*c*d^2 - a*d^3)*e^2*f - 2*(b*c^2*d - a*c*d^2)*e*f^2 + (b*c^3 - a*c^2*d)*f^3)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (15*b*d^3*f^3*x^3 + 15*b*d^3*e^3 - 161*(b*c*d^2 - a*d^3)*e^2*f + 245*(b*c^2*d - a*c*d^2)*e*f^2 - 105*(b*c^3 - a*c^2*d)*f^3 + 3*(15*b*d^3*e*f^2 - 7*(b*c*d^2 - a*d^3)*f^3)*x^2 + (45*b*d^3*e^2*f - 77*(b*c*d^2 - a*d^3)*e*f^2 + 35*(b*c^2*d - a*c*d^2)*f^3)*x)*sqrt(f*x + e))/(d^4*f)]","B",0
1767,1,373,0,1.346990," ","integrate((b*x+a)*(f*x+e)^(3/2)/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b c d - a d^{2}\right)} e f - {\left(b c^{2} - a c d\right)} f^{2}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) - 2 \, {\left(3 \, b d^{2} f^{2} x^{2} + 3 \, b d^{2} e^{2} - 20 \, {\left(b c d - a d^{2}\right)} e f + 15 \, {\left(b c^{2} - a c d\right)} f^{2} + {\left(6 \, b d^{2} e f - 5 \, {\left(b c d - a d^{2}\right)} f^{2}\right)} x\right)} \sqrt{f x + e}}{15 \, d^{3} f}, \frac{2 \, {\left(15 \, {\left({\left(b c d - a d^{2}\right)} e f - {\left(b c^{2} - a c d\right)} f^{2}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(3 \, b d^{2} f^{2} x^{2} + 3 \, b d^{2} e^{2} - 20 \, {\left(b c d - a d^{2}\right)} e f + 15 \, {\left(b c^{2} - a c d\right)} f^{2} + {\left(6 \, b d^{2} e f - 5 \, {\left(b c d - a d^{2}\right)} f^{2}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, d^{3} f}\right]"," ",0,"[-1/15*(15*((b*c*d - a*d^2)*e*f - (b*c^2 - a*c*d)*f^2)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) - 2*(3*b*d^2*f^2*x^2 + 3*b*d^2*e^2 - 20*(b*c*d - a*d^2)*e*f + 15*(b*c^2 - a*c*d)*f^2 + (6*b*d^2*e*f - 5*(b*c*d - a*d^2)*f^2)*x)*sqrt(f*x + e))/(d^3*f), 2/15*(15*((b*c*d - a*d^2)*e*f - (b*c^2 - a*c*d)*f^2)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (3*b*d^2*f^2*x^2 + 3*b*d^2*e^2 - 20*(b*c*d - a*d^2)*e*f + 15*(b*c^2 - a*c*d)*f^2 + (6*b*d^2*e*f - 5*(b*c*d - a*d^2)*f^2)*x)*sqrt(f*x + e))/(d^3*f)]","A",0
1768,1,211,0,1.425382," ","integrate((b*x+a)*(f*x+e)^(1/2)/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c - a d\right)} f \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) - 2 \, {\left(b d f x + b d e - 3 \, {\left(b c - a d\right)} f\right)} \sqrt{f x + e}}{3 \, d^{2} f}, \frac{2 \, {\left(3 \, {\left(b c - a d\right)} f \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(b d f x + b d e - 3 \, {\left(b c - a d\right)} f\right)} \sqrt{f x + e}\right)}}{3 \, d^{2} f}\right]"," ",0,"[-1/3*(3*(b*c - a*d)*f*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) - 2*(b*d*f*x + b*d*e - 3*(b*c - a*d)*f)*sqrt(f*x + e))/(d^2*f), 2/3*(3*(b*c - a*d)*f*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (b*d*f*x + b*d*e - 3*(b*c - a*d)*f)*sqrt(f*x + e))/(d^2*f)]","A",0
1769,1,209,0,1.380950," ","integrate((b*x+a)/(d*x+c)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{d^{2} e - c d f} {\left(b c - a d\right)} f \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(b d^{2} e - b c d f\right)} \sqrt{f x + e}}{d^{3} e f - c d^{2} f^{2}}, -\frac{2 \, {\left(\sqrt{-d^{2} e + c d f} {\left(b c - a d\right)} f \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(b d^{2} e - b c d f\right)} \sqrt{f x + e}\right)}}{d^{3} e f - c d^{2} f^{2}}\right]"," ",0,"[-(sqrt(d^2*e - c*d*f)*(b*c - a*d)*f*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(b*d^2*e - b*c*d*f)*sqrt(f*x + e))/(d^3*e*f - c*d^2*f^2), -2*(sqrt(-d^2*e + c*d*f)*(b*c - a*d)*f*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (b*d^2*e - b*c*d*f)*sqrt(f*x + e))/(d^3*e*f - c*d^2*f^2)]","A",0
1770,1,363,0,1.424175," ","integrate((b*x+a)/(d*x+c)/(f*x+e)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b c - a d\right)} f^{2} x + {\left(b c - a d\right)} e f\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} \sqrt{f x + e}}{d^{3} e^{3} f - 2 \, c d^{2} e^{2} f^{2} + c^{2} d e f^{3} + {\left(d^{3} e^{2} f^{2} - 2 \, c d^{2} e f^{3} + c^{2} d f^{4}\right)} x}, -\frac{2 \, {\left({\left({\left(b c - a d\right)} f^{2} x + {\left(b c - a d\right)} e f\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) + {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} \sqrt{f x + e}\right)}}{d^{3} e^{3} f - 2 \, c d^{2} e^{2} f^{2} + c^{2} d e f^{3} + {\left(d^{3} e^{2} f^{2} - 2 \, c d^{2} e f^{3} + c^{2} d f^{4}\right)} x}\right]"," ",0,"[(((b*c - a*d)*f^2*x + (b*c - a*d)*e*f)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f + 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*sqrt(f*x + e))/(d^3*e^3*f - 2*c*d^2*e^2*f^2 + c^2*d*e*f^3 + (d^3*e^2*f^2 - 2*c*d^2*e*f^3 + c^2*d*f^4)*x), -2*(((b*c - a*d)*f^2*x + (b*c - a*d)*e*f)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) + (b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*sqrt(f*x + e))/(d^3*e^3*f - 2*c*d^2*e^2*f^2 + c^2*d*e*f^3 + (d^3*e^2*f^2 - 2*c*d^2*e*f^3 + c^2*d*f^4)*x)]","B",0
1771,1,506,0,1.353957," ","integrate((b*x+a)/(d*x+c)/(f*x+e)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b c - a d\right)} f^{3} x^{2} + 2 \, {\left(b c - a d\right)} e f^{2} x + {\left(b c - a d\right)} e^{2} f\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) + 2 \, {\left(b d e^{2} + a c f^{2} + 3 \, {\left(b c - a d\right)} f^{2} x + 2 \, {\left(b c - 2 \, a d\right)} e f\right)} \sqrt{f x + e}}{3 \, {\left(d^{2} e^{4} f - 2 \, c d e^{3} f^{2} + c^{2} e^{2} f^{3} + {\left(d^{2} e^{2} f^{3} - 2 \, c d e f^{4} + c^{2} f^{5}\right)} x^{2} + 2 \, {\left(d^{2} e^{3} f^{2} - 2 \, c d e^{2} f^{3} + c^{2} e f^{4}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left({\left(b c - a d\right)} f^{3} x^{2} + 2 \, {\left(b c - a d\right)} e f^{2} x + {\left(b c - a d\right)} e^{2} f\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) - {\left(b d e^{2} + a c f^{2} + 3 \, {\left(b c - a d\right)} f^{2} x + 2 \, {\left(b c - 2 \, a d\right)} e f\right)} \sqrt{f x + e}\right)}}{3 \, {\left(d^{2} e^{4} f - 2 \, c d e^{3} f^{2} + c^{2} e^{2} f^{3} + {\left(d^{2} e^{2} f^{3} - 2 \, c d e f^{4} + c^{2} f^{5}\right)} x^{2} + 2 \, {\left(d^{2} e^{3} f^{2} - 2 \, c d e^{2} f^{3} + c^{2} e f^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((b*c - a*d)*f^3*x^2 + 2*(b*c - a*d)*e*f^2*x + (b*c - a*d)*e^2*f)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f - 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) + 2*(b*d*e^2 + a*c*f^2 + 3*(b*c - a*d)*f^2*x + 2*(b*c - 2*a*d)*e*f)*sqrt(f*x + e))/(d^2*e^4*f - 2*c*d*e^3*f^2 + c^2*e^2*f^3 + (d^2*e^2*f^3 - 2*c*d*e*f^4 + c^2*f^5)*x^2 + 2*(d^2*e^3*f^2 - 2*c*d*e^2*f^3 + c^2*e*f^4)*x), 2/3*(3*((b*c - a*d)*f^3*x^2 + 2*(b*c - a*d)*e*f^2*x + (b*c - a*d)*e^2*f)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) - (b*d*e^2 + a*c*f^2 + 3*(b*c - a*d)*f^2*x + 2*(b*c - 2*a*d)*e*f)*sqrt(f*x + e))/(d^2*e^4*f - 2*c*d*e^3*f^2 + c^2*e^2*f^3 + (d^2*e^2*f^3 - 2*c*d*e*f^4 + c^2*f^5)*x^2 + 2*(d^2*e^3*f^2 - 2*c*d*e^2*f^3 + c^2*e*f^4)*x)]","B",0
1772,1,902,0,1.452279," ","integrate((b*x+a)/(d*x+c)/(f*x+e)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(b c d - a d^{2}\right)} f^{4} x^{3} + 3 \, {\left(b c d - a d^{2}\right)} e f^{3} x^{2} + 3 \, {\left(b c d - a d^{2}\right)} e^{2} f^{2} x + {\left(b c d - a d^{2}\right)} e^{3} f\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) - 2 \, {\left(3 \, b d^{2} e^{3} - 3 \, a c^{2} f^{3} + 15 \, {\left(b c d - a d^{2}\right)} f^{3} x^{2} + {\left(14 \, b c d - 23 \, a d^{2}\right)} e^{2} f - {\left(2 \, b c^{2} - 11 \, a c d\right)} e f^{2} + 5 \, {\left(7 \, {\left(b c d - a d^{2}\right)} e f^{2} - {\left(b c^{2} - a c d\right)} f^{3}\right)} x\right)} \sqrt{f x + e}}{15 \, {\left(d^{3} e^{6} f - 3 \, c d^{2} e^{5} f^{2} + 3 \, c^{2} d e^{4} f^{3} - c^{3} e^{3} f^{4} + {\left(d^{3} e^{3} f^{4} - 3 \, c d^{2} e^{2} f^{5} + 3 \, c^{2} d e f^{6} - c^{3} f^{7}\right)} x^{3} + 3 \, {\left(d^{3} e^{4} f^{3} - 3 \, c d^{2} e^{3} f^{4} + 3 \, c^{2} d e^{2} f^{5} - c^{3} e f^{6}\right)} x^{2} + 3 \, {\left(d^{3} e^{5} f^{2} - 3 \, c d^{2} e^{4} f^{3} + 3 \, c^{2} d e^{3} f^{4} - c^{3} e^{2} f^{5}\right)} x\right)}}, \frac{2 \, {\left(15 \, {\left({\left(b c d - a d^{2}\right)} f^{4} x^{3} + 3 \, {\left(b c d - a d^{2}\right)} e f^{3} x^{2} + 3 \, {\left(b c d - a d^{2}\right)} e^{2} f^{2} x + {\left(b c d - a d^{2}\right)} e^{3} f\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) - {\left(3 \, b d^{2} e^{3} - 3 \, a c^{2} f^{3} + 15 \, {\left(b c d - a d^{2}\right)} f^{3} x^{2} + {\left(14 \, b c d - 23 \, a d^{2}\right)} e^{2} f - {\left(2 \, b c^{2} - 11 \, a c d\right)} e f^{2} + 5 \, {\left(7 \, {\left(b c d - a d^{2}\right)} e f^{2} - {\left(b c^{2} - a c d\right)} f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, {\left(d^{3} e^{6} f - 3 \, c d^{2} e^{5} f^{2} + 3 \, c^{2} d e^{4} f^{3} - c^{3} e^{3} f^{4} + {\left(d^{3} e^{3} f^{4} - 3 \, c d^{2} e^{2} f^{5} + 3 \, c^{2} d e f^{6} - c^{3} f^{7}\right)} x^{3} + 3 \, {\left(d^{3} e^{4} f^{3} - 3 \, c d^{2} e^{3} f^{4} + 3 \, c^{2} d e^{2} f^{5} - c^{3} e f^{6}\right)} x^{2} + 3 \, {\left(d^{3} e^{5} f^{2} - 3 \, c d^{2} e^{4} f^{3} + 3 \, c^{2} d e^{3} f^{4} - c^{3} e^{2} f^{5}\right)} x\right)}}\right]"," ",0,"[1/15*(15*((b*c*d - a*d^2)*f^4*x^3 + 3*(b*c*d - a*d^2)*e*f^3*x^2 + 3*(b*c*d - a*d^2)*e^2*f^2*x + (b*c*d - a*d^2)*e^3*f)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f + 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) - 2*(3*b*d^2*e^3 - 3*a*c^2*f^3 + 15*(b*c*d - a*d^2)*f^3*x^2 + (14*b*c*d - 23*a*d^2)*e^2*f - (2*b*c^2 - 11*a*c*d)*e*f^2 + 5*(7*(b*c*d - a*d^2)*e*f^2 - (b*c^2 - a*c*d)*f^3)*x)*sqrt(f*x + e))/(d^3*e^6*f - 3*c*d^2*e^5*f^2 + 3*c^2*d*e^4*f^3 - c^3*e^3*f^4 + (d^3*e^3*f^4 - 3*c*d^2*e^2*f^5 + 3*c^2*d*e*f^6 - c^3*f^7)*x^3 + 3*(d^3*e^4*f^3 - 3*c*d^2*e^3*f^4 + 3*c^2*d*e^2*f^5 - c^3*e*f^6)*x^2 + 3*(d^3*e^5*f^2 - 3*c*d^2*e^4*f^3 + 3*c^2*d*e^3*f^4 - c^3*e^2*f^5)*x), 2/15*(15*((b*c*d - a*d^2)*f^4*x^3 + 3*(b*c*d - a*d^2)*e*f^3*x^2 + 3*(b*c*d - a*d^2)*e^2*f^2*x + (b*c*d - a*d^2)*e^3*f)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) - (3*b*d^2*e^3 - 3*a*c^2*f^3 + 15*(b*c*d - a*d^2)*f^3*x^2 + (14*b*c*d - 23*a*d^2)*e^2*f - (2*b*c^2 - 11*a*c*d)*e*f^2 + 5*(7*(b*c*d - a*d^2)*e*f^2 - (b*c^2 - a*c*d)*f^3)*x)*sqrt(f*x + e))/(d^3*e^6*f - 3*c*d^2*e^5*f^2 + 3*c^2*d*e^4*f^3 - c^3*e^3*f^4 + (d^3*e^3*f^4 - 3*c*d^2*e^2*f^5 + 3*c^2*d*e*f^6 - c^3*f^7)*x^3 + 3*(d^3*e^4*f^3 - 3*c*d^2*e^3*f^4 + 3*c^2*d*e^2*f^5 - c^3*e*f^6)*x^2 + 3*(d^3*e^5*f^2 - 3*c*d^2*e^4*f^3 + 3*c^2*d*e^3*f^4 - c^3*e^2*f^5)*x)]","B",0
1773,1,1396,0,1.290304," ","integrate((b*x+a)/(d*x+c)/(f*x+e)^(9/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(b c d^{2} - a d^{3}\right)} f^{5} x^{4} + 4 \, {\left(b c d^{2} - a d^{3}\right)} e f^{4} x^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(b c d^{2} - a d^{3}\right)} e^{3} f^{2} x + {\left(b c d^{2} - a d^{3}\right)} e^{4} f\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) + 2 \, {\left(15 \, b d^{3} e^{4} + 15 \, a c^{3} f^{4} + 105 \, {\left(b c d^{2} - a d^{3}\right)} f^{4} x^{3} + 4 \, {\left(29 \, b c d^{2} - 44 \, a d^{3}\right)} e^{3} f - 2 \, {\left(16 \, b c^{2} d - 61 \, a c d^{2}\right)} e^{2} f^{2} + 6 \, {\left(b c^{3} - 11 \, a c^{2} d\right)} e f^{3} + 35 \, {\left(10 \, {\left(b c d^{2} - a d^{3}\right)} e f^{3} - {\left(b c^{2} d - a c d^{2}\right)} f^{4}\right)} x^{2} + 7 \, {\left(58 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f^{2} - 16 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{3} + 3 \, {\left(b c^{3} - a c^{2} d\right)} f^{4}\right)} x\right)} \sqrt{f x + e}}{105 \, {\left(d^{4} e^{8} f - 4 \, c d^{3} e^{7} f^{2} + 6 \, c^{2} d^{2} e^{6} f^{3} - 4 \, c^{3} d e^{5} f^{4} + c^{4} e^{4} f^{5} + {\left(d^{4} e^{4} f^{5} - 4 \, c d^{3} e^{3} f^{6} + 6 \, c^{2} d^{2} e^{2} f^{7} - 4 \, c^{3} d e f^{8} + c^{4} f^{9}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{4} - 4 \, c d^{3} e^{4} f^{5} + 6 \, c^{2} d^{2} e^{3} f^{6} - 4 \, c^{3} d e^{2} f^{7} + c^{4} e f^{8}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{3} - 4 \, c d^{3} e^{5} f^{4} + 6 \, c^{2} d^{2} e^{4} f^{5} - 4 \, c^{3} d e^{3} f^{6} + c^{4} e^{2} f^{7}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{2} - 4 \, c d^{3} e^{6} f^{3} + 6 \, c^{2} d^{2} e^{5} f^{4} - 4 \, c^{3} d e^{4} f^{5} + c^{4} e^{3} f^{6}\right)} x\right)}}, \frac{2 \, {\left(105 \, {\left({\left(b c d^{2} - a d^{3}\right)} f^{5} x^{4} + 4 \, {\left(b c d^{2} - a d^{3}\right)} e f^{4} x^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f^{3} x^{2} + 4 \, {\left(b c d^{2} - a d^{3}\right)} e^{3} f^{2} x + {\left(b c d^{2} - a d^{3}\right)} e^{4} f\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) - {\left(15 \, b d^{3} e^{4} + 15 \, a c^{3} f^{4} + 105 \, {\left(b c d^{2} - a d^{3}\right)} f^{4} x^{3} + 4 \, {\left(29 \, b c d^{2} - 44 \, a d^{3}\right)} e^{3} f - 2 \, {\left(16 \, b c^{2} d - 61 \, a c d^{2}\right)} e^{2} f^{2} + 6 \, {\left(b c^{3} - 11 \, a c^{2} d\right)} e f^{3} + 35 \, {\left(10 \, {\left(b c d^{2} - a d^{3}\right)} e f^{3} - {\left(b c^{2} d - a c d^{2}\right)} f^{4}\right)} x^{2} + 7 \, {\left(58 \, {\left(b c d^{2} - a d^{3}\right)} e^{2} f^{2} - 16 \, {\left(b c^{2} d - a c d^{2}\right)} e f^{3} + 3 \, {\left(b c^{3} - a c^{2} d\right)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, {\left(d^{4} e^{8} f - 4 \, c d^{3} e^{7} f^{2} + 6 \, c^{2} d^{2} e^{6} f^{3} - 4 \, c^{3} d e^{5} f^{4} + c^{4} e^{4} f^{5} + {\left(d^{4} e^{4} f^{5} - 4 \, c d^{3} e^{3} f^{6} + 6 \, c^{2} d^{2} e^{2} f^{7} - 4 \, c^{3} d e f^{8} + c^{4} f^{9}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{4} - 4 \, c d^{3} e^{4} f^{5} + 6 \, c^{2} d^{2} e^{3} f^{6} - 4 \, c^{3} d e^{2} f^{7} + c^{4} e f^{8}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{3} - 4 \, c d^{3} e^{5} f^{4} + 6 \, c^{2} d^{2} e^{4} f^{5} - 4 \, c^{3} d e^{3} f^{6} + c^{4} e^{2} f^{7}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{2} - 4 \, c d^{3} e^{6} f^{3} + 6 \, c^{2} d^{2} e^{5} f^{4} - 4 \, c^{3} d e^{4} f^{5} + c^{4} e^{3} f^{6}\right)} x\right)}}\right]"," ",0,"[-1/105*(105*((b*c*d^2 - a*d^3)*f^5*x^4 + 4*(b*c*d^2 - a*d^3)*e*f^4*x^3 + 6*(b*c*d^2 - a*d^3)*e^2*f^3*x^2 + 4*(b*c*d^2 - a*d^3)*e^3*f^2*x + (b*c*d^2 - a*d^3)*e^4*f)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f - 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) + 2*(15*b*d^3*e^4 + 15*a*c^3*f^4 + 105*(b*c*d^2 - a*d^3)*f^4*x^3 + 4*(29*b*c*d^2 - 44*a*d^3)*e^3*f - 2*(16*b*c^2*d - 61*a*c*d^2)*e^2*f^2 + 6*(b*c^3 - 11*a*c^2*d)*e*f^3 + 35*(10*(b*c*d^2 - a*d^3)*e*f^3 - (b*c^2*d - a*c*d^2)*f^4)*x^2 + 7*(58*(b*c*d^2 - a*d^3)*e^2*f^2 - 16*(b*c^2*d - a*c*d^2)*e*f^3 + 3*(b*c^3 - a*c^2*d)*f^4)*x)*sqrt(f*x + e))/(d^4*e^8*f - 4*c*d^3*e^7*f^2 + 6*c^2*d^2*e^6*f^3 - 4*c^3*d*e^5*f^4 + c^4*e^4*f^5 + (d^4*e^4*f^5 - 4*c*d^3*e^3*f^6 + 6*c^2*d^2*e^2*f^7 - 4*c^3*d*e*f^8 + c^4*f^9)*x^4 + 4*(d^4*e^5*f^4 - 4*c*d^3*e^4*f^5 + 6*c^2*d^2*e^3*f^6 - 4*c^3*d*e^2*f^7 + c^4*e*f^8)*x^3 + 6*(d^4*e^6*f^3 - 4*c*d^3*e^5*f^4 + 6*c^2*d^2*e^4*f^5 - 4*c^3*d*e^3*f^6 + c^4*e^2*f^7)*x^2 + 4*(d^4*e^7*f^2 - 4*c*d^3*e^6*f^3 + 6*c^2*d^2*e^5*f^4 - 4*c^3*d*e^4*f^5 + c^4*e^3*f^6)*x), 2/105*(105*((b*c*d^2 - a*d^3)*f^5*x^4 + 4*(b*c*d^2 - a*d^3)*e*f^4*x^3 + 6*(b*c*d^2 - a*d^3)*e^2*f^3*x^2 + 4*(b*c*d^2 - a*d^3)*e^3*f^2*x + (b*c*d^2 - a*d^3)*e^4*f)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) - (15*b*d^3*e^4 + 15*a*c^3*f^4 + 105*(b*c*d^2 - a*d^3)*f^4*x^3 + 4*(29*b*c*d^2 - 44*a*d^3)*e^3*f - 2*(16*b*c^2*d - 61*a*c*d^2)*e^2*f^2 + 6*(b*c^3 - 11*a*c^2*d)*e*f^3 + 35*(10*(b*c*d^2 - a*d^3)*e*f^3 - (b*c^2*d - a*c*d^2)*f^4)*x^2 + 7*(58*(b*c*d^2 - a*d^3)*e^2*f^2 - 16*(b*c^2*d - a*c*d^2)*e*f^3 + 3*(b*c^3 - a*c^2*d)*f^4)*x)*sqrt(f*x + e))/(d^4*e^8*f - 4*c*d^3*e^7*f^2 + 6*c^2*d^2*e^6*f^3 - 4*c^3*d*e^5*f^4 + c^4*e^4*f^5 + (d^4*e^4*f^5 - 4*c*d^3*e^3*f^6 + 6*c^2*d^2*e^2*f^7 - 4*c^3*d*e*f^8 + c^4*f^9)*x^4 + 4*(d^4*e^5*f^4 - 4*c*d^3*e^4*f^5 + 6*c^2*d^2*e^3*f^6 - 4*c^3*d*e^2*f^7 + c^4*e*f^8)*x^3 + 6*(d^4*e^6*f^3 - 4*c*d^3*e^5*f^4 + 6*c^2*d^2*e^4*f^5 - 4*c^3*d*e^3*f^6 + c^4*e^2*f^7)*x^2 + 4*(d^4*e^7*f^2 - 4*c*d^3*e^6*f^3 + 6*c^2*d^2*e^5*f^4 - 4*c^3*d*e^4*f^5 + c^4*e^3*f^6)*x)]","B",0
1774,1,1068,0,1.159599," ","integrate((b*x+a)^2*(f*x+e)^(5/2)/(d*x+c),x, algorithm=""fricas"")","\left[\frac{315 \, {\left({\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e^{2} f^{2} - 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} e f^{3} + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} f^{4}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) + 2 \, {\left(35 \, b^{2} d^{4} f^{4} x^{4} - 10 \, b^{2} d^{4} e^{4} - 45 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e^{3} f + 483 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e^{2} f^{2} - 735 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} e f^{3} + 315 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} f^{4} + 5 \, {\left(19 \, b^{2} d^{4} e f^{3} - 9 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} f^{4}\right)} x^{3} + 3 \, {\left(25 \, b^{2} d^{4} e^{2} f^{2} - 45 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e f^{3} + 21 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} f^{4}\right)} x^{2} + {\left(5 \, b^{2} d^{4} e^{3} f - 135 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e^{2} f^{2} + 231 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e f^{3} - 105 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}}{315 \, d^{5} f^{2}}, -\frac{2 \, {\left(315 \, {\left({\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e^{2} f^{2} - 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} e f^{3} + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} f^{4}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) - {\left(35 \, b^{2} d^{4} f^{4} x^{4} - 10 \, b^{2} d^{4} e^{4} - 45 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e^{3} f + 483 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e^{2} f^{2} - 735 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} e f^{3} + 315 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} f^{4} + 5 \, {\left(19 \, b^{2} d^{4} e f^{3} - 9 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} f^{4}\right)} x^{3} + 3 \, {\left(25 \, b^{2} d^{4} e^{2} f^{2} - 45 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e f^{3} + 21 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} f^{4}\right)} x^{2} + {\left(5 \, b^{2} d^{4} e^{3} f - 135 \, {\left(b^{2} c d^{3} - 2 \, a b d^{4}\right)} e^{2} f^{2} + 231 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e f^{3} - 105 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{315 \, d^{5} f^{2}}\right]"," ",0,"[1/315*(315*((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e^2*f^2 - 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*e*f^3 + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*f^4)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) + 2*(35*b^2*d^4*f^4*x^4 - 10*b^2*d^4*e^4 - 45*(b^2*c*d^3 - 2*a*b*d^4)*e^3*f + 483*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e^2*f^2 - 735*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*e*f^3 + 315*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*f^4 + 5*(19*b^2*d^4*e*f^3 - 9*(b^2*c*d^3 - 2*a*b*d^4)*f^4)*x^3 + 3*(25*b^2*d^4*e^2*f^2 - 45*(b^2*c*d^3 - 2*a*b*d^4)*e*f^3 + 21*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*f^4)*x^2 + (5*b^2*d^4*e^3*f - 135*(b^2*c*d^3 - 2*a*b*d^4)*e^2*f^2 + 231*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e*f^3 - 105*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*f^4)*x)*sqrt(f*x + e))/(d^5*f^2), -2/315*(315*((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e^2*f^2 - 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*e*f^3 + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*f^4)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) - (35*b^2*d^4*f^4*x^4 - 10*b^2*d^4*e^4 - 45*(b^2*c*d^3 - 2*a*b*d^4)*e^3*f + 483*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e^2*f^2 - 735*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*e*f^3 + 315*(b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*f^4 + 5*(19*b^2*d^4*e*f^3 - 9*(b^2*c*d^3 - 2*a*b*d^4)*f^4)*x^3 + 3*(25*b^2*d^4*e^2*f^2 - 45*(b^2*c*d^3 - 2*a*b*d^4)*e*f^3 + 21*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*f^4)*x^2 + (5*b^2*d^4*e^3*f - 135*(b^2*c*d^3 - 2*a*b*d^4)*e^2*f^2 + 231*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e*f^3 - 105*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*f^4)*x)*sqrt(f*x + e))/(d^5*f^2)]","B",0
1775,1,694,0,1.424753," ","integrate((b*x+a)^2*(f*x+e)^(3/2)/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{3}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) - 2 \, {\left(15 \, b^{2} d^{3} f^{3} x^{3} - 6 \, b^{2} d^{3} e^{3} - 21 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} e^{2} f + 140 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} - 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{3} + 3 \, {\left(8 \, b^{2} d^{3} e f^{2} - 7 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} f^{3}\right)} x^{2} + {\left(3 \, b^{2} d^{3} e^{2} f - 42 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} e f^{2} + 35 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}}{105 \, d^{4} f^{2}}, -\frac{2 \, {\left(105 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{3}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) - {\left(15 \, b^{2} d^{3} f^{3} x^{3} - 6 \, b^{2} d^{3} e^{3} - 21 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} e^{2} f + 140 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} - 105 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{3} + 3 \, {\left(8 \, b^{2} d^{3} e f^{2} - 7 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} f^{3}\right)} x^{2} + {\left(3 \, b^{2} d^{3} e^{2} f - 42 \, {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} e f^{2} + 35 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, d^{4} f^{2}}\right]"," ",0,"[-1/105*(105*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^2 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^3)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f + 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) - 2*(15*b^2*d^3*f^3*x^3 - 6*b^2*d^3*e^3 - 21*(b^2*c*d^2 - 2*a*b*d^3)*e^2*f + 140*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^2 - 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^3 + 3*(8*b^2*d^3*e*f^2 - 7*(b^2*c*d^2 - 2*a*b*d^3)*f^3)*x^2 + (3*b^2*d^3*e^2*f - 42*(b^2*c*d^2 - 2*a*b*d^3)*e*f^2 + 35*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^3)*x)*sqrt(f*x + e))/(d^4*f^2), -2/105*(105*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^2 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^3)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) - (15*b^2*d^3*f^3*x^3 - 6*b^2*d^3*e^3 - 21*(b^2*c*d^2 - 2*a*b*d^3)*e^2*f + 140*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^2 - 105*(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^3 + 3*(8*b^2*d^3*e*f^2 - 7*(b^2*c*d^2 - 2*a*b*d^3)*f^3)*x^2 + (3*b^2*d^3*e^2*f - 42*(b^2*c*d^2 - 2*a*b*d^3)*e*f^2 + 35*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^3)*x)*sqrt(f*x + e))/(d^4*f^2)]","B",0
1776,1,402,0,1.478963," ","integrate((b*x+a)^2*(f*x+e)^(1/2)/(d*x+c),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) + 2 \, {\left(3 \, b^{2} d^{2} f^{2} x^{2} - 2 \, b^{2} d^{2} e^{2} - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} e f + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} + {\left(b^{2} d^{2} e f - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} f^{2}\right)} x\right)} \sqrt{f x + e}}{15 \, d^{3} f^{2}}, -\frac{2 \, {\left(15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) - {\left(3 \, b^{2} d^{2} f^{2} x^{2} - 2 \, b^{2} d^{2} e^{2} - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} e f + 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} + {\left(b^{2} d^{2} e f - 5 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} f^{2}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, d^{3} f^{2}}\right]"," ",0,"[1/15*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) + 2*(3*b^2*d^2*f^2*x^2 - 2*b^2*d^2*e^2 - 5*(b^2*c*d - 2*a*b*d^2)*e*f + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2 + (b^2*d^2*e*f - 5*(b^2*c*d - 2*a*b*d^2)*f^2)*x)*sqrt(f*x + e))/(d^3*f^2), -2/15*(15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) - (3*b^2*d^2*f^2*x^2 - 2*b^2*d^2*e^2 - 5*(b^2*c*d - 2*a*b*d^2)*e*f + 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2 + (b^2*d^2*e*f - 5*(b^2*c*d - 2*a*b*d^2)*f^2)*x)*sqrt(f*x + e))/(d^3*f^2)]","A",0
1777,1,375,0,1.716390," ","integrate((b*x+a)^2/(d*x+c)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{d^{2} e - c d f} f^{2} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(2 \, b^{2} d^{3} e^{2} + {\left(b^{2} c d^{2} - 6 \, a b d^{3}\right)} e f - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} f^{2} - {\left(b^{2} d^{3} e f - b^{2} c d^{2} f^{2}\right)} x\right)} \sqrt{f x + e}}{3 \, {\left(d^{4} e f^{2} - c d^{3} f^{3}\right)}}, \frac{2 \, {\left(3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-d^{2} e + c d f} f^{2} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(2 \, b^{2} d^{3} e^{2} + {\left(b^{2} c d^{2} - 6 \, a b d^{3}\right)} e f - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} f^{2} - {\left(b^{2} d^{3} e f - b^{2} c d^{2} f^{2}\right)} x\right)} \sqrt{f x + e}\right)}}{3 \, {\left(d^{4} e f^{2} - c d^{3} f^{3}\right)}}\right]"," ",0,"[1/3*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(d^2*e - c*d*f)*f^2*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(2*b^2*d^3*e^2 + (b^2*c*d^2 - 6*a*b*d^3)*e*f - 3*(b^2*c^2*d - 2*a*b*c*d^2)*f^2 - (b^2*d^3*e*f - b^2*c*d^2*f^2)*x)*sqrt(f*x + e))/(d^4*e*f^2 - c*d^3*f^3), 2/3*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-d^2*e + c*d*f)*f^2*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (2*b^2*d^3*e^2 + (b^2*c*d^2 - 6*a*b*d^3)*e*f - 3*(b^2*c^2*d - 2*a*b*c*d^2)*f^2 - (b^2*d^3*e*f - b^2*c*d^2*f^2)*x)*sqrt(f*x + e))/(d^4*e*f^2 - c*d^3*f^3)]","A",0
1778,1,600,0,1.738948," ","integrate((b*x+a)^2/(d*x+c)/(f*x+e)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{2}\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(2 \, b^{2} d^{3} e^{3} - a^{2} c d^{2} f^{3} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{2} f + {\left(b^{2} c^{2} d + 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} d^{3} e^{2} f - 2 \, b^{2} c d^{2} e f^{2} + b^{2} c^{2} d f^{3}\right)} x\right)} \sqrt{f x + e}}{d^{4} e^{3} f^{2} - 2 \, c d^{3} e^{2} f^{3} + c^{2} d^{2} e f^{4} + {\left(d^{4} e^{2} f^{3} - 2 \, c d^{3} e f^{4} + c^{2} d^{2} f^{5}\right)} x}, \frac{2 \, {\left({\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{2}\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) + {\left(2 \, b^{2} d^{3} e^{3} - a^{2} c d^{2} f^{3} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{2} f + {\left(b^{2} c^{2} d + 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} d^{3} e^{2} f - 2 \, b^{2} c d^{2} e f^{2} + b^{2} c^{2} d f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{d^{4} e^{3} f^{2} - 2 \, c d^{3} e^{2} f^{3} + c^{2} d^{2} e f^{4} + {\left(d^{4} e^{2} f^{3} - 2 \, c d^{3} e f^{4} + c^{2} d^{2} f^{5}\right)} x}\right]"," ",0,"[-(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^2)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f + 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(2*b^2*d^3*e^3 - a^2*c*d^2*f^3 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^2*f + (b^2*c^2*d + 2*a*b*c*d^2 + a^2*d^3)*e*f^2 + (b^2*d^3*e^2*f - 2*b^2*c*d^2*e*f^2 + b^2*c^2*d*f^3)*x)*sqrt(f*x + e))/(d^4*e^3*f^2 - 2*c*d^3*e^2*f^3 + c^2*d^2*e*f^4 + (d^4*e^2*f^3 - 2*c*d^3*e*f^4 + c^2*d^2*f^5)*x), 2*(((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^2)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) + (2*b^2*d^3*e^3 - a^2*c*d^2*f^3 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^2*f + (b^2*c^2*d + 2*a*b*c*d^2 + a^2*d^3)*e*f^2 + (b^2*d^3*e^2*f - 2*b^2*c*d^2*e*f^2 + b^2*c^2*d*f^3)*x)*sqrt(f*x + e))/(d^4*e^3*f^2 - 2*c*d^3*e^2*f^3 + c^2*d^2*e*f^4 + (d^4*e^2*f^3 - 2*c*d^3*e*f^4 + c^2*d^2*f^5)*x)]","B",0
1779,1,975,0,1.825050," ","integrate((b*x+a)^2/(d*x+c)/(f*x+e)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{4} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{2}\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(2 \, b^{2} d^{3} e^{4} - a^{2} c^{2} d f^{4} - {\left(7 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} e^{3} f + {\left(5 \, b^{2} c^{2} d + 2 \, a b c d^{2} - 4 \, a^{2} d^{3}\right)} e^{2} f^{2} - {\left(4 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} e f^{3} + 3 \, {\left(b^{2} d^{3} e^{3} f - 3 \, b^{2} c d^{2} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)} e f^{3} - {\left(2 \, a b c^{2} d - a^{2} c d^{2}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}}{3 \, {\left(d^{4} e^{5} f^{2} - 3 \, c d^{3} e^{4} f^{3} + 3 \, c^{2} d^{2} e^{3} f^{4} - c^{3} d e^{2} f^{5} + {\left(d^{4} e^{3} f^{4} - 3 \, c d^{3} e^{2} f^{5} + 3 \, c^{2} d^{2} e f^{6} - c^{3} d f^{7}\right)} x^{2} + 2 \, {\left(d^{4} e^{4} f^{3} - 3 \, c d^{3} e^{3} f^{4} + 3 \, c^{2} d^{2} e^{2} f^{5} - c^{3} d e f^{6}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{4} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{2}\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(2 \, b^{2} d^{3} e^{4} - a^{2} c^{2} d f^{4} - {\left(7 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} e^{3} f + {\left(5 \, b^{2} c^{2} d + 2 \, a b c d^{2} - 4 \, a^{2} d^{3}\right)} e^{2} f^{2} - {\left(4 \, a b c^{2} d - 5 \, a^{2} c d^{2}\right)} e f^{3} + 3 \, {\left(b^{2} d^{3} e^{3} f - 3 \, b^{2} c d^{2} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)} e f^{3} - {\left(2 \, a b c^{2} d - a^{2} c d^{2}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{3 \, {\left(d^{4} e^{5} f^{2} - 3 \, c d^{3} e^{4} f^{3} + 3 \, c^{2} d^{2} e^{3} f^{4} - c^{3} d e^{2} f^{5} + {\left(d^{4} e^{3} f^{4} - 3 \, c d^{3} e^{2} f^{5} + 3 \, c^{2} d^{2} e f^{6} - c^{3} d f^{7}\right)} x^{2} + 2 \, {\left(d^{4} e^{4} f^{3} - 3 \, c d^{3} e^{3} f^{4} + 3 \, c^{2} d^{2} e^{2} f^{5} - c^{3} d e f^{6}\right)} x\right)}}\right]"," ",0,"[1/3*(3*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^4*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2*f^2)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(2*b^2*d^3*e^4 - a^2*c^2*d*f^4 - (7*b^2*c*d^2 - 2*a*b*d^3)*e^3*f + (5*b^2*c^2*d + 2*a*b*c*d^2 - 4*a^2*d^3)*e^2*f^2 - (4*a*b*c^2*d - 5*a^2*c*d^2)*e*f^3 + 3*(b^2*d^3*e^3*f - 3*b^2*c*d^2*e^2*f^2 + (2*b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)*e*f^3 - (2*a*b*c^2*d - a^2*c*d^2)*f^4)*x)*sqrt(f*x + e))/(d^4*e^5*f^2 - 3*c*d^3*e^4*f^3 + 3*c^2*d^2*e^3*f^4 - c^3*d*e^2*f^5 + (d^4*e^3*f^4 - 3*c*d^3*e^2*f^5 + 3*c^2*d^2*e*f^6 - c^3*d*f^7)*x^2 + 2*(d^4*e^4*f^3 - 3*c*d^3*e^3*f^4 + 3*c^2*d^2*e^2*f^5 - c^3*d*e*f^6)*x), 2/3*(3*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^4*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2*f^2)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (2*b^2*d^3*e^4 - a^2*c^2*d*f^4 - (7*b^2*c*d^2 - 2*a*b*d^3)*e^3*f + (5*b^2*c^2*d + 2*a*b*c*d^2 - 4*a^2*d^3)*e^2*f^2 - (4*a*b*c^2*d - 5*a^2*c*d^2)*e*f^3 + 3*(b^2*d^3*e^3*f - 3*b^2*c*d^2*e^2*f^2 + (2*b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)*e*f^3 - (2*a*b*c^2*d - a^2*c*d^2)*f^4)*x)*sqrt(f*x + e))/(d^4*e^5*f^2 - 3*c*d^3*e^4*f^3 + 3*c^2*d^2*e^3*f^4 - c^3*d*e^2*f^5 + (d^4*e^3*f^4 - 3*c*d^3*e^2*f^5 + 3*c^2*d^2*e*f^6 - c^3*d*f^7)*x^2 + 2*(d^4*e^4*f^3 - 3*c*d^3*e^3*f^4 + 3*c^2*d^2*e^2*f^5 - c^3*d*e*f^6)*x)]","B",0
1780,1,1173,0,1.698910," ","integrate((b*x+a)^2/(d*x+c)/(f*x+e)^(7/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{5} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{4} x^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{3} f^{2}\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) + 2 \, {\left(2 \, b^{2} d^{2} e^{4} - 3 \, a^{2} c^{2} f^{4} - 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{4} x^{2} - 3 \, {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} e^{3} f - {\left(8 \, b^{2} c^{2} - 28 \, a b c d + 23 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(4 \, a b c^{2} - 11 \, a^{2} c d\right)} e f^{3} + 5 \, {\left(b^{2} d^{2} e^{3} f - 3 \, b^{2} c d e^{2} f^{2} - {\left(4 \, b^{2} c^{2} - 14 \, a b c d + 7 \, a^{2} d^{2}\right)} e f^{3} - {\left(2 \, a b c^{2} - a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{f x + e}}{15 \, {\left(d^{3} e^{6} f^{2} - 3 \, c d^{2} e^{5} f^{3} + 3 \, c^{2} d e^{4} f^{4} - c^{3} e^{3} f^{5} + {\left(d^{3} e^{3} f^{5} - 3 \, c d^{2} e^{2} f^{6} + 3 \, c^{2} d e f^{7} - c^{3} f^{8}\right)} x^{3} + 3 \, {\left(d^{3} e^{4} f^{4} - 3 \, c d^{2} e^{3} f^{5} + 3 \, c^{2} d e^{2} f^{6} - c^{3} e f^{7}\right)} x^{2} + 3 \, {\left(d^{3} e^{5} f^{3} - 3 \, c d^{2} e^{4} f^{4} + 3 \, c^{2} d e^{3} f^{5} - c^{3} e^{2} f^{6}\right)} x\right)}}, -\frac{2 \, {\left(15 \, {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{5} x^{3} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f^{4} x^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{3} x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{3} f^{2}\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) + {\left(2 \, b^{2} d^{2} e^{4} - 3 \, a^{2} c^{2} f^{4} - 15 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{4} x^{2} - 3 \, {\left(3 \, b^{2} c d - 2 \, a b d^{2}\right)} e^{3} f - {\left(8 \, b^{2} c^{2} - 28 \, a b c d + 23 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(4 \, a b c^{2} - 11 \, a^{2} c d\right)} e f^{3} + 5 \, {\left(b^{2} d^{2} e^{3} f - 3 \, b^{2} c d e^{2} f^{2} - {\left(4 \, b^{2} c^{2} - 14 \, a b c d + 7 \, a^{2} d^{2}\right)} e f^{3} - {\left(2 \, a b c^{2} - a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, {\left(d^{3} e^{6} f^{2} - 3 \, c d^{2} e^{5} f^{3} + 3 \, c^{2} d e^{4} f^{4} - c^{3} e^{3} f^{5} + {\left(d^{3} e^{3} f^{5} - 3 \, c d^{2} e^{2} f^{6} + 3 \, c^{2} d e f^{7} - c^{3} f^{8}\right)} x^{3} + 3 \, {\left(d^{3} e^{4} f^{4} - 3 \, c d^{2} e^{3} f^{5} + 3 \, c^{2} d e^{2} f^{6} - c^{3} e f^{7}\right)} x^{2} + 3 \, {\left(d^{3} e^{5} f^{3} - 3 \, c d^{2} e^{4} f^{4} + 3 \, c^{2} d e^{3} f^{5} - c^{3} e^{2} f^{6}\right)} x\right)}}\right]"," ",0,"[-1/15*(15*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^5*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^4*x^2 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^3*f^2)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f + 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) + 2*(2*b^2*d^2*e^4 - 3*a^2*c^2*f^4 - 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^4*x^2 - 3*(3*b^2*c*d - 2*a*b*d^2)*e^3*f - (8*b^2*c^2 - 28*a*b*c*d + 23*a^2*d^2)*e^2*f^2 - (4*a*b*c^2 - 11*a^2*c*d)*e*f^3 + 5*(b^2*d^2*e^3*f - 3*b^2*c*d*e^2*f^2 - (4*b^2*c^2 - 14*a*b*c*d + 7*a^2*d^2)*e*f^3 - (2*a*b*c^2 - a^2*c*d)*f^4)*x)*sqrt(f*x + e))/(d^3*e^6*f^2 - 3*c*d^2*e^5*f^3 + 3*c^2*d*e^4*f^4 - c^3*e^3*f^5 + (d^3*e^3*f^5 - 3*c*d^2*e^2*f^6 + 3*c^2*d*e*f^7 - c^3*f^8)*x^3 + 3*(d^3*e^4*f^4 - 3*c*d^2*e^3*f^5 + 3*c^2*d*e^2*f^6 - c^3*e*f^7)*x^2 + 3*(d^3*e^5*f^3 - 3*c*d^2*e^4*f^4 + 3*c^2*d*e^3*f^5 - c^3*e^2*f^6)*x), -2/15*(15*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^5*x^3 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f^4*x^2 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2*f^3*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^3*f^2)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) + (2*b^2*d^2*e^4 - 3*a^2*c^2*f^4 - 15*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^4*x^2 - 3*(3*b^2*c*d - 2*a*b*d^2)*e^3*f - (8*b^2*c^2 - 28*a*b*c*d + 23*a^2*d^2)*e^2*f^2 - (4*a*b*c^2 - 11*a^2*c*d)*e*f^3 + 5*(b^2*d^2*e^3*f - 3*b^2*c*d*e^2*f^2 - (4*b^2*c^2 - 14*a*b*c*d + 7*a^2*d^2)*e*f^3 - (2*a*b*c^2 - a^2*c*d)*f^4)*x)*sqrt(f*x + e))/(d^3*e^6*f^2 - 3*c*d^2*e^5*f^3 + 3*c^2*d*e^4*f^4 - c^3*e^3*f^5 + (d^3*e^3*f^5 - 3*c*d^2*e^2*f^6 + 3*c^2*d*e*f^7 - c^3*f^8)*x^3 + 3*(d^3*e^4*f^4 - 3*c*d^2*e^3*f^5 + 3*c^2*d*e^2*f^6 - c^3*e*f^7)*x^2 + 3*(d^3*e^5*f^3 - 3*c*d^2*e^4*f^4 + 3*c^2*d*e^3*f^5 - c^3*e^2*f^6)*x)]","B",0
1781,1,1799,0,1.025064," ","integrate((b*x+a)^2/(d*x+c)/(f*x+e)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{6} x^{4} + 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{5} x^{3} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{2} f^{4} x^{2} + 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{3} f^{3} x + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{4} f^{2}\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) - 2 \, {\left(6 \, b^{2} d^{3} e^{5} + 15 \, a^{2} c^{3} f^{5} - 105 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{5} x^{3} - 3 \, {\left(13 \, b^{2} c d^{2} - 10 \, a b d^{3}\right)} e^{4} f - 8 \, {\left(10 \, b^{2} c^{2} d - 29 \, a b c d^{2} + 22 \, a^{2} d^{3}\right)} e^{3} f^{2} + 2 \, {\left(4 \, b^{2} c^{3} - 32 \, a b c^{2} d + 61 \, a^{2} c d^{2}\right)} e^{2} f^{3} + 6 \, {\left(2 \, a b c^{3} - 11 \, a^{2} c^{2} d\right)} e f^{4} - 35 \, {\left(10 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{4} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{5}\right)} x^{2} + 7 \, {\left(3 \, b^{2} d^{3} e^{4} f - 12 \, b^{2} c d^{2} e^{3} f^{2} - 2 \, {\left(20 \, b^{2} c^{2} d - 58 \, a b c d^{2} + 29 \, a^{2} d^{3}\right)} e^{2} f^{3} + 4 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 4 \, a^{2} c d^{2}\right)} e f^{4} + 3 \, {\left(2 \, a b c^{3} - a^{2} c^{2} d\right)} f^{5}\right)} x\right)} \sqrt{f x + e}}{105 \, {\left(d^{4} e^{8} f^{2} - 4 \, c d^{3} e^{7} f^{3} + 6 \, c^{2} d^{2} e^{6} f^{4} - 4 \, c^{3} d e^{5} f^{5} + c^{4} e^{4} f^{6} + {\left(d^{4} e^{4} f^{6} - 4 \, c d^{3} e^{3} f^{7} + 6 \, c^{2} d^{2} e^{2} f^{8} - 4 \, c^{3} d e f^{9} + c^{4} f^{10}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{5} - 4 \, c d^{3} e^{4} f^{6} + 6 \, c^{2} d^{2} e^{3} f^{7} - 4 \, c^{3} d e^{2} f^{8} + c^{4} e f^{9}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{4} - 4 \, c d^{3} e^{5} f^{5} + 6 \, c^{2} d^{2} e^{4} f^{6} - 4 \, c^{3} d e^{3} f^{7} + c^{4} e^{2} f^{8}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{3} - 4 \, c d^{3} e^{6} f^{4} + 6 \, c^{2} d^{2} e^{5} f^{5} - 4 \, c^{3} d e^{4} f^{6} + c^{4} e^{3} f^{7}\right)} x\right)}}, -\frac{2 \, {\left(105 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{6} x^{4} + 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{5} x^{3} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{2} f^{4} x^{2} + 4 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{3} f^{3} x + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e^{4} f^{2}\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) + {\left(6 \, b^{2} d^{3} e^{5} + 15 \, a^{2} c^{3} f^{5} - 105 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} f^{5} x^{3} - 3 \, {\left(13 \, b^{2} c d^{2} - 10 \, a b d^{3}\right)} e^{4} f - 8 \, {\left(10 \, b^{2} c^{2} d - 29 \, a b c d^{2} + 22 \, a^{2} d^{3}\right)} e^{3} f^{2} + 2 \, {\left(4 \, b^{2} c^{3} - 32 \, a b c^{2} d + 61 \, a^{2} c d^{2}\right)} e^{2} f^{3} + 6 \, {\left(2 \, a b c^{3} - 11 \, a^{2} c^{2} d\right)} e f^{4} - 35 \, {\left(10 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} e f^{4} - {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} f^{5}\right)} x^{2} + 7 \, {\left(3 \, b^{2} d^{3} e^{4} f - 12 \, b^{2} c d^{2} e^{3} f^{2} - 2 \, {\left(20 \, b^{2} c^{2} d - 58 \, a b c d^{2} + 29 \, a^{2} d^{3}\right)} e^{2} f^{3} + 4 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 4 \, a^{2} c d^{2}\right)} e f^{4} + 3 \, {\left(2 \, a b c^{3} - a^{2} c^{2} d\right)} f^{5}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, {\left(d^{4} e^{8} f^{2} - 4 \, c d^{3} e^{7} f^{3} + 6 \, c^{2} d^{2} e^{6} f^{4} - 4 \, c^{3} d e^{5} f^{5} + c^{4} e^{4} f^{6} + {\left(d^{4} e^{4} f^{6} - 4 \, c d^{3} e^{3} f^{7} + 6 \, c^{2} d^{2} e^{2} f^{8} - 4 \, c^{3} d e f^{9} + c^{4} f^{10}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{5} - 4 \, c d^{3} e^{4} f^{6} + 6 \, c^{2} d^{2} e^{3} f^{7} - 4 \, c^{3} d e^{2} f^{8} + c^{4} e f^{9}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{4} - 4 \, c d^{3} e^{5} f^{5} + 6 \, c^{2} d^{2} e^{4} f^{6} - 4 \, c^{3} d e^{3} f^{7} + c^{4} e^{2} f^{8}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{3} - 4 \, c d^{3} e^{6} f^{4} + 6 \, c^{2} d^{2} e^{5} f^{5} - 4 \, c^{3} d e^{4} f^{6} + c^{4} e^{3} f^{7}\right)} x\right)}}\right]"," ",0,"[1/105*(105*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^6*x^4 + 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^5*x^3 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^2*f^4*x^2 + 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^3*f^3*x + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^4*f^2)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f - 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) - 2*(6*b^2*d^3*e^5 + 15*a^2*c^3*f^5 - 105*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^5*x^3 - 3*(13*b^2*c*d^2 - 10*a*b*d^3)*e^4*f - 8*(10*b^2*c^2*d - 29*a*b*c*d^2 + 22*a^2*d^3)*e^3*f^2 + 2*(4*b^2*c^3 - 32*a*b*c^2*d + 61*a^2*c*d^2)*e^2*f^3 + 6*(2*a*b*c^3 - 11*a^2*c^2*d)*e*f^4 - 35*(10*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^4 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^5)*x^2 + 7*(3*b^2*d^3*e^4*f - 12*b^2*c*d^2*e^3*f^2 - 2*(20*b^2*c^2*d - 58*a*b*c*d^2 + 29*a^2*d^3)*e^2*f^3 + 4*(b^2*c^3 - 8*a*b*c^2*d + 4*a^2*c*d^2)*e*f^4 + 3*(2*a*b*c^3 - a^2*c^2*d)*f^5)*x)*sqrt(f*x + e))/(d^4*e^8*f^2 - 4*c*d^3*e^7*f^3 + 6*c^2*d^2*e^6*f^4 - 4*c^3*d*e^5*f^5 + c^4*e^4*f^6 + (d^4*e^4*f^6 - 4*c*d^3*e^3*f^7 + 6*c^2*d^2*e^2*f^8 - 4*c^3*d*e*f^9 + c^4*f^10)*x^4 + 4*(d^4*e^5*f^5 - 4*c*d^3*e^4*f^6 + 6*c^2*d^2*e^3*f^7 - 4*c^3*d*e^2*f^8 + c^4*e*f^9)*x^3 + 6*(d^4*e^6*f^4 - 4*c*d^3*e^5*f^5 + 6*c^2*d^2*e^4*f^6 - 4*c^3*d*e^3*f^7 + c^4*e^2*f^8)*x^2 + 4*(d^4*e^7*f^3 - 4*c*d^3*e^6*f^4 + 6*c^2*d^2*e^5*f^5 - 4*c^3*d*e^4*f^6 + c^4*e^3*f^7)*x), -2/105*(105*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^6*x^4 + 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^5*x^3 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^2*f^4*x^2 + 4*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^3*f^3*x + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e^4*f^2)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) + (6*b^2*d^3*e^5 + 15*a^2*c^3*f^5 - 105*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*f^5*x^3 - 3*(13*b^2*c*d^2 - 10*a*b*d^3)*e^4*f - 8*(10*b^2*c^2*d - 29*a*b*c*d^2 + 22*a^2*d^3)*e^3*f^2 + 2*(4*b^2*c^3 - 32*a*b*c^2*d + 61*a^2*c*d^2)*e^2*f^3 + 6*(2*a*b*c^3 - 11*a^2*c^2*d)*e*f^4 - 35*(10*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*e*f^4 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*f^5)*x^2 + 7*(3*b^2*d^3*e^4*f - 12*b^2*c*d^2*e^3*f^2 - 2*(20*b^2*c^2*d - 58*a*b*c*d^2 + 29*a^2*d^3)*e^2*f^3 + 4*(b^2*c^3 - 8*a*b*c^2*d + 4*a^2*c*d^2)*e*f^4 + 3*(2*a*b*c^3 - a^2*c^2*d)*f^5)*x)*sqrt(f*x + e))/(d^4*e^8*f^2 - 4*c*d^3*e^7*f^3 + 6*c^2*d^2*e^6*f^4 - 4*c^3*d*e^5*f^5 + c^4*e^4*f^6 + (d^4*e^4*f^6 - 4*c*d^3*e^3*f^7 + 6*c^2*d^2*e^2*f^8 - 4*c^3*d*e*f^9 + c^4*f^10)*x^4 + 4*(d^4*e^5*f^5 - 4*c*d^3*e^4*f^6 + 6*c^2*d^2*e^3*f^7 - 4*c^3*d*e^2*f^8 + c^4*e*f^9)*x^3 + 6*(d^4*e^6*f^4 - 4*c*d^3*e^5*f^5 + 6*c^2*d^2*e^4*f^6 - 4*c^3*d*e^3*f^7 + c^4*e^2*f^8)*x^2 + 4*(d^4*e^7*f^3 - 4*c*d^3*e^6*f^4 + 6*c^2*d^2*e^5*f^5 - 4*c^3*d*e^4*f^6 + c^4*e^3*f^7)*x)]","B",0
1782,1,1741,0,1.769076," ","integrate((b*x+a)^3*(f*x+e)^(5/2)/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left({\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)} e^{2} f^{3} - 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} e f^{4} + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} f^{5}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) - 2 \, {\left(315 \, b^{3} d^{5} f^{5} x^{5} + 40 \, b^{3} d^{5} e^{5} + 110 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{4} f + 495 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e^{3} f^{2} - 5313 \, {\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)} e^{2} f^{3} + 8085 \, {\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)} e f^{4} - 3465 \, {\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)} f^{5} + 35 \, {\left(23 \, b^{3} d^{5} e f^{4} - 11 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} f^{5}\right)} x^{4} + 5 \, {\left(113 \, b^{3} d^{5} e^{2} f^{3} - 209 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e f^{4} + 99 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} f^{5}\right)} x^{3} + 3 \, {\left(5 \, b^{3} d^{5} e^{3} f^{2} - 275 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{2} f^{3} + 495 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e f^{4} - 231 \, {\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)} f^{5}\right)} x^{2} - {\left(20 \, b^{3} d^{5} e^{4} f + 55 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{3} f^{2} - 1485 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e^{2} f^{3} + 2541 \, {\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)} e f^{4} - 1155 \, {\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)} f^{5}\right)} x\right)} \sqrt{f x + e}}{3465 \, d^{6} f^{3}}, \frac{2 \, {\left(3465 \, {\left({\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)} e^{2} f^{3} - 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} e f^{4} + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} f^{5}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(315 \, b^{3} d^{5} f^{5} x^{5} + 40 \, b^{3} d^{5} e^{5} + 110 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{4} f + 495 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e^{3} f^{2} - 5313 \, {\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)} e^{2} f^{3} + 8085 \, {\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)} e f^{4} - 3465 \, {\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)} f^{5} + 35 \, {\left(23 \, b^{3} d^{5} e f^{4} - 11 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} f^{5}\right)} x^{4} + 5 \, {\left(113 \, b^{3} d^{5} e^{2} f^{3} - 209 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e f^{4} + 99 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} f^{5}\right)} x^{3} + 3 \, {\left(5 \, b^{3} d^{5} e^{3} f^{2} - 275 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{2} f^{3} + 495 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e f^{4} - 231 \, {\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)} f^{5}\right)} x^{2} - {\left(20 \, b^{3} d^{5} e^{4} f + 55 \, {\left(b^{3} c d^{4} - 3 \, a b^{2} d^{5}\right)} e^{3} f^{2} - 1485 \, {\left(b^{3} c^{2} d^{3} - 3 \, a b^{2} c d^{4} + 3 \, a^{2} b d^{5}\right)} e^{2} f^{3} + 2541 \, {\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)} e f^{4} - 1155 \, {\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)} f^{5}\right)} x\right)} \sqrt{f x + e}\right)}}{3465 \, d^{6} f^{3}}\right]"," ",0,"[-1/3465*(3465*((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)*e^2*f^3 - 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*e*f^4 + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*f^5)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) - 2*(315*b^3*d^5*f^5*x^5 + 40*b^3*d^5*e^5 + 110*(b^3*c*d^4 - 3*a*b^2*d^5)*e^4*f + 495*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e^3*f^2 - 5313*(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)*e^2*f^3 + 8085*(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)*e*f^4 - 3465*(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)*f^5 + 35*(23*b^3*d^5*e*f^4 - 11*(b^3*c*d^4 - 3*a*b^2*d^5)*f^5)*x^4 + 5*(113*b^3*d^5*e^2*f^3 - 209*(b^3*c*d^4 - 3*a*b^2*d^5)*e*f^4 + 99*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*f^5)*x^3 + 3*(5*b^3*d^5*e^3*f^2 - 275*(b^3*c*d^4 - 3*a*b^2*d^5)*e^2*f^3 + 495*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e*f^4 - 231*(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)*f^5)*x^2 - (20*b^3*d^5*e^4*f + 55*(b^3*c*d^4 - 3*a*b^2*d^5)*e^3*f^2 - 1485*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e^2*f^3 + 2541*(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)*e*f^4 - 1155*(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)*f^5)*x)*sqrt(f*x + e))/(d^6*f^3), 2/3465*(3465*((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)*e^2*f^3 - 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*e*f^4 + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*f^5)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (315*b^3*d^5*f^5*x^5 + 40*b^3*d^5*e^5 + 110*(b^3*c*d^4 - 3*a*b^2*d^5)*e^4*f + 495*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e^3*f^2 - 5313*(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)*e^2*f^3 + 8085*(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)*e*f^4 - 3465*(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)*f^5 + 35*(23*b^3*d^5*e*f^4 - 11*(b^3*c*d^4 - 3*a*b^2*d^5)*f^5)*x^4 + 5*(113*b^3*d^5*e^2*f^3 - 209*(b^3*c*d^4 - 3*a*b^2*d^5)*e*f^4 + 99*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*f^5)*x^3 + 3*(5*b^3*d^5*e^3*f^2 - 275*(b^3*c*d^4 - 3*a*b^2*d^5)*e^2*f^3 + 495*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e*f^4 - 231*(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)*f^5)*x^2 - (20*b^3*d^5*e^4*f + 55*(b^3*c*d^4 - 3*a*b^2*d^5)*e^3*f^2 - 1485*(b^3*c^2*d^3 - 3*a*b^2*c*d^4 + 3*a^2*b*d^5)*e^2*f^3 + 2541*(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)*e*f^4 - 1155*(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)*f^5)*x)*sqrt(f*x + e))/(d^6*f^3)]","B",0
1783,1,1165,0,1.350026," ","integrate((b*x+a)^3*(f*x+e)^(3/2)/(d*x+c),x, algorithm=""fricas"")","\left[\frac{315 \, {\left({\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)} e f^{3} - {\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)} f^{4}\right)} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) + 2 \, {\left(35 \, b^{3} d^{4} f^{4} x^{4} + 8 \, b^{3} d^{4} e^{4} + 18 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{3} f + 63 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} e^{2} f^{2} - 420 \, {\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)} e f^{3} + 315 \, {\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)} f^{4} + 5 \, {\left(10 \, b^{3} d^{4} e f^{3} - 9 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} f^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} f^{2} - 24 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e f^{3} + 21 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} f^{4}\right)} x^{2} - {\left(4 \, b^{3} d^{4} e^{3} f + 9 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{2} f^{2} - 126 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} e f^{3} + 105 \, {\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)} f^{4}\right)} x\right)} \sqrt{f x + e}}{315 \, d^{5} f^{3}}, \frac{2 \, {\left(315 \, {\left({\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)} e f^{3} - {\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)} f^{4}\right)} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(35 \, b^{3} d^{4} f^{4} x^{4} + 8 \, b^{3} d^{4} e^{4} + 18 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{3} f + 63 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} e^{2} f^{2} - 420 \, {\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)} e f^{3} + 315 \, {\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)} f^{4} + 5 \, {\left(10 \, b^{3} d^{4} e f^{3} - 9 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} f^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} f^{2} - 24 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e f^{3} + 21 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} f^{4}\right)} x^{2} - {\left(4 \, b^{3} d^{4} e^{3} f + 9 \, {\left(b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{2} f^{2} - 126 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} e f^{3} + 105 \, {\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)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{315 \, d^{5} f^{3}}\right]"," ",0,"[1/315*(315*((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 - (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^4)*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f + 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) + 2*(35*b^3*d^4*f^4*x^4 + 8*b^3*d^4*e^4 + 18*(b^3*c*d^3 - 3*a*b^2*d^4)*e^3*f + 63*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*e^2*f^2 - 420*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 + 315*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^4 + 5*(10*b^3*d^4*e*f^3 - 9*(b^3*c*d^3 - 3*a*b^2*d^4)*f^4)*x^3 + 3*(b^3*d^4*e^2*f^2 - 24*(b^3*c*d^3 - 3*a*b^2*d^4)*e*f^3 + 21*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*f^4)*x^2 - (4*b^3*d^4*e^3*f + 9*(b^3*c*d^3 - 3*a*b^2*d^4)*e^2*f^2 - 126*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*e*f^3 + 105*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*f^4)*x)*sqrt(f*x + e))/(d^5*f^3), 2/315*(315*((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 - (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^4)*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (35*b^3*d^4*f^4*x^4 + 8*b^3*d^4*e^4 + 18*(b^3*c*d^3 - 3*a*b^2*d^4)*e^3*f + 63*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*e^2*f^2 - 420*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 + 315*(b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^4 + 5*(10*b^3*d^4*e*f^3 - 9*(b^3*c*d^3 - 3*a*b^2*d^4)*f^4)*x^3 + 3*(b^3*d^4*e^2*f^2 - 24*(b^3*c*d^3 - 3*a*b^2*d^4)*e*f^3 + 21*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*f^4)*x^2 - (4*b^3*d^4*e^3*f + 9*(b^3*c*d^3 - 3*a*b^2*d^4)*e^2*f^2 - 126*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 3*a^2*b*d^4)*e*f^3 + 105*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*f^4)*x)*sqrt(f*x + e))/(d^5*f^3)]","B",0
1784,1,705,0,1.635943," ","integrate((b*x+a)^3*(f*x+e)^(1/2)/(d*x+c),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{3} \sqrt{\frac{d e - c f}{d}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{f x + e} d \sqrt{\frac{d e - c f}{d}}}{d x + c}\right) - 2 \, {\left(15 \, b^{3} d^{3} f^{3} x^{3} + 8 \, b^{3} d^{3} e^{3} + 14 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e^{2} f + 35 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} e f^{2} - 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{3} + 3 \, {\left(b^{3} d^{3} e f^{2} - 7 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} f^{3}\right)} x^{2} - {\left(4 \, b^{3} d^{3} e^{2} f + 7 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e f^{2} - 35 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}}{105 \, d^{4} f^{3}}, \frac{2 \, {\left(105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{3} \sqrt{-\frac{d e - c f}{d}} \arctan\left(-\frac{\sqrt{f x + e} d \sqrt{-\frac{d e - c f}{d}}}{d e - c f}\right) + {\left(15 \, b^{3} d^{3} f^{3} x^{3} + 8 \, b^{3} d^{3} e^{3} + 14 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e^{2} f + 35 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} e f^{2} - 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{3} + 3 \, {\left(b^{3} d^{3} e f^{2} - 7 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} f^{3}\right)} x^{2} - {\left(4 \, b^{3} d^{3} e^{2} f + 7 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e f^{2} - 35 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, d^{4} f^{3}}\right]"," ",0,"[-1/105*(105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^3*sqrt((d*e - c*f)/d)*log((d*f*x + 2*d*e - c*f - 2*sqrt(f*x + e)*d*sqrt((d*e - c*f)/d))/(d*x + c)) - 2*(15*b^3*d^3*f^3*x^3 + 8*b^3*d^3*e^3 + 14*(b^3*c*d^2 - 3*a*b^2*d^3)*e^2*f + 35*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*e*f^2 - 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^3 + 3*(b^3*d^3*e*f^2 - 7*(b^3*c*d^2 - 3*a*b^2*d^3)*f^3)*x^2 - (4*b^3*d^3*e^2*f + 7*(b^3*c*d^2 - 3*a*b^2*d^3)*e*f^2 - 35*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*f^3)*x)*sqrt(f*x + e))/(d^4*f^3), 2/105*(105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^3*sqrt(-(d*e - c*f)/d)*arctan(-sqrt(f*x + e)*d*sqrt(-(d*e - c*f)/d)/(d*e - c*f)) + (15*b^3*d^3*f^3*x^3 + 8*b^3*d^3*e^3 + 14*(b^3*c*d^2 - 3*a*b^2*d^3)*e^2*f + 35*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*e*f^2 - 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^3 + 3*(b^3*d^3*e*f^2 - 7*(b^3*c*d^2 - 3*a*b^2*d^3)*f^3)*x^2 - (4*b^3*d^3*e^2*f + 7*(b^3*c*d^2 - 3*a*b^2*d^3)*e*f^2 - 35*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*f^3)*x)*sqrt(f*x + e))/(d^4*f^3)]","A",0
1785,1,653,0,1.457485," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{d^{2} e - c d f} f^{3} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(8 \, b^{3} d^{4} e^{3} + 2 \, {\left(b^{3} c d^{3} - 15 \, a b^{2} d^{4}\right)} e^{2} f + 5 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 9 \, a^{2} b d^{4}\right)} e f^{2} - 15 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3}\right)} f^{3} + 3 \, {\left(b^{3} d^{4} e f^{2} - b^{3} c d^{3} f^{3}\right)} x^{2} - {\left(4 \, b^{3} d^{4} e^{2} f + {\left(b^{3} c d^{3} - 15 \, a b^{2} d^{4}\right)} e f^{2} - 5 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}}{15 \, {\left(d^{5} e f^{3} - c d^{4} f^{4}\right)}}, -\frac{2 \, {\left(15 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{-d^{2} e + c d f} f^{3} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(8 \, b^{3} d^{4} e^{3} + 2 \, {\left(b^{3} c d^{3} - 15 \, a b^{2} d^{4}\right)} e^{2} f + 5 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3} + 9 \, a^{2} b d^{4}\right)} e f^{2} - 15 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3}\right)} f^{3} + 3 \, {\left(b^{3} d^{4} e f^{2} - b^{3} c d^{3} f^{3}\right)} x^{2} - {\left(4 \, b^{3} d^{4} e^{2} f + {\left(b^{3} c d^{3} - 15 \, a b^{2} d^{4}\right)} e f^{2} - 5 \, {\left(b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} f^{3}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, {\left(d^{5} e f^{3} - c d^{4} f^{4}\right)}}\right]"," ",0,"[-1/15*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(d^2*e - c*d*f)*f^3*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(8*b^3*d^4*e^3 + 2*(b^3*c*d^3 - 15*a*b^2*d^4)*e^2*f + 5*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 9*a^2*b*d^4)*e*f^2 - 15*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3)*f^3 + 3*(b^3*d^4*e*f^2 - b^3*c*d^3*f^3)*x^2 - (4*b^3*d^4*e^2*f + (b^3*c*d^3 - 15*a*b^2*d^4)*e*f^2 - 5*(b^3*c^2*d^2 - 3*a*b^2*c*d^3)*f^3)*x)*sqrt(f*x + e))/(d^5*e*f^3 - c*d^4*f^4), -2/15*(15*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(-d^2*e + c*d*f)*f^3*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (8*b^3*d^4*e^3 + 2*(b^3*c*d^3 - 15*a*b^2*d^4)*e^2*f + 5*(b^3*c^2*d^2 - 3*a*b^2*c*d^3 + 9*a^2*b*d^4)*e*f^2 - 15*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3)*f^3 + 3*(b^3*d^4*e*f^2 - b^3*c*d^3*f^3)*x^2 - (4*b^3*d^4*e^2*f + (b^3*c*d^3 - 15*a*b^2*d^4)*e*f^2 - 5*(b^3*c^2*d^2 - 3*a*b^2*c*d^3)*f^3)*x)*sqrt(f*x + e))/(d^5*e*f^3 - c*d^4*f^4)]","A",0
1786,1,978,0,1.564265," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{3}\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(8 \, b^{3} d^{4} e^{4} + 3 \, a^{3} c d^{3} f^{4} - 2 \, {\left(5 \, b^{3} c d^{3} + 9 \, a b^{2} d^{4}\right)} e^{3} f - {\left(b^{3} c^{2} d^{2} - 27 \, a b^{2} c d^{3} - 9 \, a^{2} b d^{4}\right)} e^{2} f^{2} + 3 \, {\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)} e f^{3} - {\left(b^{3} d^{4} e^{2} f^{2} - 2 \, b^{3} c d^{3} e f^{3} + b^{3} c^{2} d^{2} f^{4}\right)} x^{2} + {\left(4 \, b^{3} d^{4} e^{3} f - {\left(5 \, b^{3} c d^{3} + 9 \, a b^{2} d^{4}\right)} e^{2} f^{2} - 2 \, {\left(b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3}\right)} e f^{3} + 3 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}}{3 \, {\left(d^{5} e^{3} f^{3} - 2 \, c d^{4} e^{2} f^{4} + c^{2} d^{3} e f^{5} + {\left(d^{5} e^{2} f^{4} - 2 \, c d^{4} e f^{5} + c^{2} d^{3} f^{6}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{3}\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) + {\left(8 \, b^{3} d^{4} e^{4} + 3 \, a^{3} c d^{3} f^{4} - 2 \, {\left(5 \, b^{3} c d^{3} + 9 \, a b^{2} d^{4}\right)} e^{3} f - {\left(b^{3} c^{2} d^{2} - 27 \, a b^{2} c d^{3} - 9 \, a^{2} b d^{4}\right)} e^{2} f^{2} + 3 \, {\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)} e f^{3} - {\left(b^{3} d^{4} e^{2} f^{2} - 2 \, b^{3} c d^{3} e f^{3} + b^{3} c^{2} d^{2} f^{4}\right)} x^{2} + {\left(4 \, b^{3} d^{4} e^{3} f - {\left(5 \, b^{3} c d^{3} + 9 \, a b^{2} d^{4}\right)} e^{2} f^{2} - 2 \, {\left(b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3}\right)} e f^{3} + 3 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2}\right)} f^{4}\right)} x\right)} \sqrt{f x + e}\right)}}{3 \, {\left(d^{5} e^{3} f^{3} - 2 \, c d^{4} e^{2} f^{4} + c^{2} d^{3} e f^{5} + {\left(d^{5} e^{2} f^{4} - 2 \, c d^{4} e f^{5} + c^{2} d^{3} f^{6}\right)} x\right)}}\right]"," ",0,"[1/3*(3*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^3)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f + 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(8*b^3*d^4*e^4 + 3*a^3*c*d^3*f^4 - 2*(5*b^3*c*d^3 + 9*a*b^2*d^4)*e^3*f - (b^3*c^2*d^2 - 27*a*b^2*c*d^3 - 9*a^2*b*d^4)*e^2*f^2 + 3*(b^3*c^3*d - 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 - (b^3*d^4*e^2*f^2 - 2*b^3*c*d^3*e*f^3 + b^3*c^2*d^2*f^4)*x^2 + (4*b^3*d^4*e^3*f - (5*b^3*c*d^3 + 9*a*b^2*d^4)*e^2*f^2 - 2*(b^3*c^2*d^2 - 9*a*b^2*c*d^3)*e*f^3 + 3*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^4)*x)*sqrt(f*x + e))/(d^5*e^3*f^3 - 2*c*d^4*e^2*f^4 + c^2*d^3*e*f^5 + (d^5*e^2*f^4 - 2*c*d^4*e*f^5 + c^2*d^3*f^6)*x), -2/3*(3*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^3)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) + (8*b^3*d^4*e^4 + 3*a^3*c*d^3*f^4 - 2*(5*b^3*c*d^3 + 9*a*b^2*d^4)*e^3*f - (b^3*c^2*d^2 - 27*a*b^2*c*d^3 - 9*a^2*b*d^4)*e^2*f^2 + 3*(b^3*c^3*d - 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 - a^3*d^4)*e*f^3 - (b^3*d^4*e^2*f^2 - 2*b^3*c*d^3*e*f^3 + b^3*c^2*d^2*f^4)*x^2 + (4*b^3*d^4*e^3*f - (5*b^3*c*d^3 + 9*a*b^2*d^4)*e^2*f^2 - 2*(b^3*c^2*d^2 - 9*a*b^2*c*d^3)*e*f^3 + 3*(b^3*c^3*d - 3*a*b^2*c^2*d^2)*f^4)*x)*sqrt(f*x + e))/(d^5*e^3*f^3 - 2*c*d^4*e^2*f^4 + c^2*d^3*e*f^5 + (d^5*e^2*f^4 - 2*c*d^4*e*f^5 + c^2*d^3*f^6)*x)]","B",0
1787,1,1435,0,1.687820," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{5} x^{2} + 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{3}\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(8 \, b^{3} d^{4} e^{5} + a^{3} c^{2} d^{2} f^{5} - 2 \, {\left(11 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{4} f + {\left(17 \, b^{3} c^{2} d^{2} + 21 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} e^{3} f^{2} - {\left(3 \, b^{3} c^{3} d + 15 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 4 \, a^{3} d^{4}\right)} e^{2} f^{3} + {\left(6 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} e f^{4} + 3 \, {\left(b^{3} d^{4} e^{3} f^{2} - 3 \, b^{3} c d^{3} e^{2} f^{3} + 3 \, b^{3} c^{2} d^{2} e f^{4} - b^{3} c^{3} d f^{5}\right)} x^{2} + 3 \, {\left(4 \, b^{3} d^{4} e^{4} f - {\left(11 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{3} f^{2} + 9 \, {\left(b^{3} c^{2} d^{2} + a b^{2} c d^{3}\right)} e^{2} f^{3} - {\left(2 \, b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} e f^{4} + {\left(3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} f^{5}\right)} x\right)} \sqrt{f x + e}}{3 \, {\left(d^{5} e^{5} f^{3} - 3 \, c d^{4} e^{4} f^{4} + 3 \, c^{2} d^{3} e^{3} f^{5} - c^{3} d^{2} e^{2} f^{6} + {\left(d^{5} e^{3} f^{5} - 3 \, c d^{4} e^{2} f^{6} + 3 \, c^{2} d^{3} e f^{7} - c^{3} d^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{5} e^{4} f^{4} - 3 \, c d^{4} e^{3} f^{5} + 3 \, c^{2} d^{3} e^{2} f^{6} - c^{3} d^{2} e f^{7}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{5} x^{2} + 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{3}\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(8 \, b^{3} d^{4} e^{5} + a^{3} c^{2} d^{2} f^{5} - 2 \, {\left(11 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{4} f + {\left(17 \, b^{3} c^{2} d^{2} + 21 \, a b^{2} c d^{3} - 3 \, a^{2} b d^{4}\right)} e^{3} f^{2} - {\left(3 \, b^{3} c^{3} d + 15 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - 4 \, a^{3} d^{4}\right)} e^{2} f^{3} + {\left(6 \, a^{2} b c^{2} d^{2} - 5 \, a^{3} c d^{3}\right)} e f^{4} + 3 \, {\left(b^{3} d^{4} e^{3} f^{2} - 3 \, b^{3} c d^{3} e^{2} f^{3} + 3 \, b^{3} c^{2} d^{2} e f^{4} - b^{3} c^{3} d f^{5}\right)} x^{2} + 3 \, {\left(4 \, b^{3} d^{4} e^{4} f - {\left(11 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{3} f^{2} + 9 \, {\left(b^{3} c^{2} d^{2} + a b^{2} c d^{3}\right)} e^{2} f^{3} - {\left(2 \, b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} e f^{4} + {\left(3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} f^{5}\right)} x\right)} \sqrt{f x + e}\right)}}{3 \, {\left(d^{5} e^{5} f^{3} - 3 \, c d^{4} e^{4} f^{4} + 3 \, c^{2} d^{3} e^{3} f^{5} - c^{3} d^{2} e^{2} f^{6} + {\left(d^{5} e^{3} f^{5} - 3 \, c d^{4} e^{2} f^{6} + 3 \, c^{2} d^{3} e f^{7} - c^{3} d^{2} f^{8}\right)} x^{2} + 2 \, {\left(d^{5} e^{4} f^{4} - 3 \, c d^{4} e^{3} f^{5} + 3 \, c^{2} d^{3} e^{2} f^{6} - c^{3} d^{2} e f^{7}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^5*x^2 + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^3)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(8*b^3*d^4*e^5 + a^3*c^2*d^2*f^5 - 2*(11*b^3*c*d^3 + 3*a*b^2*d^4)*e^4*f + (17*b^3*c^2*d^2 + 21*a*b^2*c*d^3 - 3*a^2*b*d^4)*e^3*f^2 - (3*b^3*c^3*d + 15*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 4*a^3*d^4)*e^2*f^3 + (6*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*e*f^4 + 3*(b^3*d^4*e^3*f^2 - 3*b^3*c*d^3*e^2*f^3 + 3*b^3*c^2*d^2*e*f^4 - b^3*c^3*d*f^5)*x^2 + 3*(4*b^3*d^4*e^4*f - (11*b^3*c*d^3 + 3*a*b^2*d^4)*e^3*f^2 + 9*(b^3*c^2*d^2 + a*b^2*c*d^3)*e^2*f^3 - (2*b^3*c^3*d + 6*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^4 + (3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^5)*x)*sqrt(f*x + e))/(d^5*e^5*f^3 - 3*c*d^4*e^4*f^4 + 3*c^2*d^3*e^3*f^5 - c^3*d^2*e^2*f^6 + (d^5*e^3*f^5 - 3*c*d^4*e^2*f^6 + 3*c^2*d^3*e*f^7 - c^3*d^2*f^8)*x^2 + 2*(d^5*e^4*f^4 - 3*c*d^4*e^3*f^5 + 3*c^2*d^3*e^2*f^6 - c^3*d^2*e*f^7)*x), -2/3*(3*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^5*x^2 + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^3)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (8*b^3*d^4*e^5 + a^3*c^2*d^2*f^5 - 2*(11*b^3*c*d^3 + 3*a*b^2*d^4)*e^4*f + (17*b^3*c^2*d^2 + 21*a*b^2*c*d^3 - 3*a^2*b*d^4)*e^3*f^2 - (3*b^3*c^3*d + 15*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - 4*a^3*d^4)*e^2*f^3 + (6*a^2*b*c^2*d^2 - 5*a^3*c*d^3)*e*f^4 + 3*(b^3*d^4*e^3*f^2 - 3*b^3*c*d^3*e^2*f^3 + 3*b^3*c^2*d^2*e*f^4 - b^3*c^3*d*f^5)*x^2 + 3*(4*b^3*d^4*e^4*f - (11*b^3*c*d^3 + 3*a*b^2*d^4)*e^3*f^2 + 9*(b^3*c^2*d^2 + a*b^2*c*d^3)*e^2*f^3 - (2*b^3*c^3*d + 6*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*e*f^4 + (3*a^2*b*c^2*d^2 - a^3*c*d^3)*f^5)*x)*sqrt(f*x + e))/(d^5*e^5*f^3 - 3*c*d^4*e^4*f^4 + 3*c^2*d^3*e^3*f^5 - c^3*d^2*e^2*f^6 + (d^5*e^3*f^5 - 3*c*d^4*e^2*f^6 + 3*c^2*d^3*e*f^7 - c^3*d^2*f^8)*x^2 + 2*(d^5*e^4*f^4 - 3*c*d^4*e^3*f^5 + 3*c^2*d^3*e^2*f^6 - c^3*d^2*e*f^7)*x)]","B",0
1788,1,2032,0,2.086261," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{6} x^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{5} x^{2} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{3} f^{3}\right)} \sqrt{d^{2} e - c d f} \log\left(\frac{d f x + 2 \, d e - c f + 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(8 \, b^{3} d^{4} e^{6} + 3 \, a^{3} c^{3} d f^{6} - 2 \, {\left(17 \, b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{5} f + {\left(59 \, b^{3} c^{2} d^{2} - 33 \, a b^{2} c d^{3} + 9 \, a^{2} b d^{4}\right)} e^{4} f^{2} - {\left(33 \, b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} - 33 \, a^{2} b c d^{3} + 23 \, a^{3} d^{4}\right)} e^{3} f^{3} + 2 \, {\left(12 \, a b^{2} c^{3} d - 24 \, a^{2} b c^{2} d^{2} + 17 \, a^{3} c d^{3}\right)} e^{2} f^{4} + 2 \, {\left(3 \, a^{2} b c^{3} d - 7 \, a^{3} c^{2} d^{2}\right)} e f^{5} + 15 \, {\left(b^{3} d^{4} e^{4} f^{2} - 4 \, b^{3} c d^{3} e^{3} f^{3} + 6 \, b^{3} c^{2} d^{2} e^{2} f^{4} - {\left(3 \, 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)} e f^{5} + {\left(3 \, a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{6}\right)} x^{2} + 5 \, {\left(4 \, b^{3} d^{4} e^{5} f - {\left(17 \, b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{4} f^{2} + 4 \, {\left(7 \, b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} e^{3} f^{3} - {\left(15 \, b^{3} c^{3} d + 3 \, a b^{2} c^{2} d^{2} - 21 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e^{2} f^{4} + 4 \, {\left(3 \, a b^{2} c^{3} d - 6 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} e f^{5} + {\left(3 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2}\right)} f^{6}\right)} x\right)} \sqrt{f x + e}}{15 \, {\left(d^{5} e^{7} f^{3} - 4 \, c d^{4} e^{6} f^{4} + 6 \, c^{2} d^{3} e^{5} f^{5} - 4 \, c^{3} d^{2} e^{4} f^{6} + c^{4} d e^{3} f^{7} + {\left(d^{5} e^{4} f^{6} - 4 \, c d^{4} e^{3} f^{7} + 6 \, c^{2} d^{3} e^{2} f^{8} - 4 \, c^{3} d^{2} e f^{9} + c^{4} d f^{10}\right)} x^{3} + 3 \, {\left(d^{5} e^{5} f^{5} - 4 \, c d^{4} e^{4} f^{6} + 6 \, c^{2} d^{3} e^{3} f^{7} - 4 \, c^{3} d^{2} e^{2} f^{8} + c^{4} d e f^{9}\right)} x^{2} + 3 \, {\left(d^{5} e^{6} f^{4} - 4 \, c d^{4} e^{5} f^{5} + 6 \, c^{2} d^{3} e^{4} f^{6} - 4 \, c^{3} d^{2} e^{3} f^{7} + c^{4} d e^{2} f^{8}\right)} x\right)}}, -\frac{2 \, {\left(15 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{6} x^{3} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{5} x^{2} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{3} f^{3}\right)} \sqrt{-d^{2} e + c d f} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) + {\left(8 \, b^{3} d^{4} e^{6} + 3 \, a^{3} c^{3} d f^{6} - 2 \, {\left(17 \, b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{5} f + {\left(59 \, b^{3} c^{2} d^{2} - 33 \, a b^{2} c d^{3} + 9 \, a^{2} b d^{4}\right)} e^{4} f^{2} - {\left(33 \, b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} - 33 \, a^{2} b c d^{3} + 23 \, a^{3} d^{4}\right)} e^{3} f^{3} + 2 \, {\left(12 \, a b^{2} c^{3} d - 24 \, a^{2} b c^{2} d^{2} + 17 \, a^{3} c d^{3}\right)} e^{2} f^{4} + 2 \, {\left(3 \, a^{2} b c^{3} d - 7 \, a^{3} c^{2} d^{2}\right)} e f^{5} + 15 \, {\left(b^{3} d^{4} e^{4} f^{2} - 4 \, b^{3} c d^{3} e^{3} f^{3} + 6 \, b^{3} c^{2} d^{2} e^{2} f^{4} - {\left(3 \, 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)} e f^{5} + {\left(3 \, a b^{2} c^{3} d - 3 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{6}\right)} x^{2} + 5 \, {\left(4 \, b^{3} d^{4} e^{5} f - {\left(17 \, b^{3} c d^{3} - 3 \, a b^{2} d^{4}\right)} e^{4} f^{2} + 4 \, {\left(7 \, b^{3} c^{2} d^{2} - 3 \, a b^{2} c d^{3}\right)} e^{3} f^{3} - {\left(15 \, b^{3} c^{3} d + 3 \, a b^{2} c^{2} d^{2} - 21 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e^{2} f^{4} + 4 \, {\left(3 \, a b^{2} c^{3} d - 6 \, a^{2} b c^{2} d^{2} + 2 \, a^{3} c d^{3}\right)} e f^{5} + {\left(3 \, a^{2} b c^{3} d - a^{3} c^{2} d^{2}\right)} f^{6}\right)} x\right)} \sqrt{f x + e}\right)}}{15 \, {\left(d^{5} e^{7} f^{3} - 4 \, c d^{4} e^{6} f^{4} + 6 \, c^{2} d^{3} e^{5} f^{5} - 4 \, c^{3} d^{2} e^{4} f^{6} + c^{4} d e^{3} f^{7} + {\left(d^{5} e^{4} f^{6} - 4 \, c d^{4} e^{3} f^{7} + 6 \, c^{2} d^{3} e^{2} f^{8} - 4 \, c^{3} d^{2} e f^{9} + c^{4} d f^{10}\right)} x^{3} + 3 \, {\left(d^{5} e^{5} f^{5} - 4 \, c d^{4} e^{4} f^{6} + 6 \, c^{2} d^{3} e^{3} f^{7} - 4 \, c^{3} d^{2} e^{2} f^{8} + c^{4} d e f^{9}\right)} x^{2} + 3 \, {\left(d^{5} e^{6} f^{4} - 4 \, c d^{4} e^{5} f^{5} + 6 \, c^{2} d^{3} e^{4} f^{6} - 4 \, c^{3} d^{2} e^{3} f^{7} + c^{4} d e^{2} f^{8}\right)} x\right)}}\right]"," ",0,"[1/15*(15*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^6*x^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^5*x^2 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^3*f^3)*sqrt(d^2*e - c*d*f)*log((d*f*x + 2*d*e - c*f + 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(8*b^3*d^4*e^6 + 3*a^3*c^3*d*f^6 - 2*(17*b^3*c*d^3 - 3*a*b^2*d^4)*e^5*f + (59*b^3*c^2*d^2 - 33*a*b^2*c*d^3 + 9*a^2*b*d^4)*e^4*f^2 - (33*b^3*c^3*d - 3*a*b^2*c^2*d^2 - 33*a^2*b*c*d^3 + 23*a^3*d^4)*e^3*f^3 + 2*(12*a*b^2*c^3*d - 24*a^2*b*c^2*d^2 + 17*a^3*c*d^3)*e^2*f^4 + 2*(3*a^2*b*c^3*d - 7*a^3*c^2*d^2)*e*f^5 + 15*(b^3*d^4*e^4*f^2 - 4*b^3*c*d^3*e^3*f^3 + 6*b^3*c^2*d^2*e^2*f^4 - (3*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*e*f^5 + (3*a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + a^3*c*d^3)*f^6)*x^2 + 5*(4*b^3*d^4*e^5*f - (17*b^3*c*d^3 - 3*a*b^2*d^4)*e^4*f^2 + 4*(7*b^3*c^2*d^2 - 3*a*b^2*c*d^3)*e^3*f^3 - (15*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 21*a^2*b*c*d^3 + 7*a^3*d^4)*e^2*f^4 + 4*(3*a*b^2*c^3*d - 6*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*e*f^5 + (3*a^2*b*c^3*d - a^3*c^2*d^2)*f^6)*x)*sqrt(f*x + e))/(d^5*e^7*f^3 - 4*c*d^4*e^6*f^4 + 6*c^2*d^3*e^5*f^5 - 4*c^3*d^2*e^4*f^6 + c^4*d*e^3*f^7 + (d^5*e^4*f^6 - 4*c*d^4*e^3*f^7 + 6*c^2*d^3*e^2*f^8 - 4*c^3*d^2*e*f^9 + c^4*d*f^10)*x^3 + 3*(d^5*e^5*f^5 - 4*c*d^4*e^4*f^6 + 6*c^2*d^3*e^3*f^7 - 4*c^3*d^2*e^2*f^8 + c^4*d*e*f^9)*x^2 + 3*(d^5*e^6*f^4 - 4*c*d^4*e^5*f^5 + 6*c^2*d^3*e^4*f^6 - 4*c^3*d^2*e^3*f^7 + c^4*d*e^2*f^8)*x), -2/15*(15*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^6*x^3 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^5*x^2 + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^3*f^3)*sqrt(-d^2*e + c*d*f)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) + (8*b^3*d^4*e^6 + 3*a^3*c^3*d*f^6 - 2*(17*b^3*c*d^3 - 3*a*b^2*d^4)*e^5*f + (59*b^3*c^2*d^2 - 33*a*b^2*c*d^3 + 9*a^2*b*d^4)*e^4*f^2 - (33*b^3*c^3*d - 3*a*b^2*c^2*d^2 - 33*a^2*b*c*d^3 + 23*a^3*d^4)*e^3*f^3 + 2*(12*a*b^2*c^3*d - 24*a^2*b*c^2*d^2 + 17*a^3*c*d^3)*e^2*f^4 + 2*(3*a^2*b*c^3*d - 7*a^3*c^2*d^2)*e*f^5 + 15*(b^3*d^4*e^4*f^2 - 4*b^3*c*d^3*e^3*f^3 + 6*b^3*c^2*d^2*e^2*f^4 - (3*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*e*f^5 + (3*a*b^2*c^3*d - 3*a^2*b*c^2*d^2 + a^3*c*d^3)*f^6)*x^2 + 5*(4*b^3*d^4*e^5*f - (17*b^3*c*d^3 - 3*a*b^2*d^4)*e^4*f^2 + 4*(7*b^3*c^2*d^2 - 3*a*b^2*c*d^3)*e^3*f^3 - (15*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 21*a^2*b*c*d^3 + 7*a^3*d^4)*e^2*f^4 + 4*(3*a*b^2*c^3*d - 6*a^2*b*c^2*d^2 + 2*a^3*c*d^3)*e*f^5 + (3*a^2*b*c^3*d - a^3*c^2*d^2)*f^6)*x)*sqrt(f*x + e))/(d^5*e^7*f^3 - 4*c*d^4*e^6*f^4 + 6*c^2*d^3*e^5*f^5 - 4*c^3*d^2*e^4*f^6 + c^4*d*e^3*f^7 + (d^5*e^4*f^6 - 4*c*d^4*e^3*f^7 + 6*c^2*d^3*e^2*f^8 - 4*c^3*d^2*e*f^9 + c^4*d*f^10)*x^3 + 3*(d^5*e^5*f^5 - 4*c*d^4*e^4*f^6 + 6*c^2*d^3*e^3*f^7 - 4*c^3*d^2*e^2*f^8 + c^4*d*e*f^9)*x^2 + 3*(d^5*e^6*f^4 - 4*c*d^4*e^5*f^5 + 6*c^2*d^3*e^4*f^6 - 4*c^3*d^2*e^3*f^7 + c^4*d*e^2*f^8)*x)]","B",0
1789,1,2284,0,1.903282," ","integrate((b*x+a)^3/(d*x+c)/(f*x+e)^(9/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{7} x^{4} + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{6} x^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{5} x^{2} + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{3} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{4} f^{3}\right)} \sqrt{\frac{d}{d e - c f}} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, {\left(d e - c f\right)} \sqrt{f x + e} \sqrt{\frac{d}{d e - c f}}}{d x + c}\right) + 2 \, {\left(8 \, b^{3} d^{3} e^{6} + 15 \, a^{3} c^{3} f^{6} + 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{6} x^{3} - 2 \, {\left(19 \, b^{3} c d^{2} - 9 \, a b^{2} d^{3}\right)} e^{5} f + 3 \, {\left(29 \, b^{3} c^{2} d - 39 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3}\right)} e^{4} f^{2} + 4 \, {\left(12 \, b^{3} c^{3} - 60 \, a b^{2} c^{2} d + 87 \, a^{2} b c d^{2} - 44 \, a^{3} d^{3}\right)} e^{3} f^{3} + 2 \, {\left(12 \, a b^{2} c^{3} - 48 \, a^{2} b c^{2} d + 61 \, a^{3} c d^{2}\right)} e^{2} f^{4} + 6 \, {\left(3 \, a^{2} b c^{3} - 11 \, a^{3} c^{2} d\right)} e f^{5} + 35 \, {\left(b^{3} d^{3} e^{4} f^{2} - 4 \, b^{3} c d^{2} e^{3} f^{3} + 6 \, b^{3} c^{2} d e^{2} f^{4} + 2 \, {\left(3 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} e f^{5} + {\left(3 \, a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{6}\right)} x^{2} + 7 \, {\left(4 \, b^{3} d^{3} e^{5} f - {\left(19 \, b^{3} c d^{2} - 9 \, a b^{2} d^{3}\right)} e^{4} f^{2} + 36 \, {\left(b^{3} c^{2} d - a b^{2} c d^{2}\right)} e^{3} f^{3} + 2 \, {\left(12 \, b^{3} c^{3} - 60 \, a b^{2} c^{2} d + 87 \, a^{2} b c d^{2} - 29 \, a^{3} d^{3}\right)} e^{2} f^{4} + 4 \, {\left(3 \, a b^{2} c^{3} - 12 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2}\right)} e f^{5} + 3 \, {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} f^{6}\right)} x\right)} \sqrt{f x + e}}{105 \, {\left(d^{4} e^{8} f^{3} - 4 \, c d^{3} e^{7} f^{4} + 6 \, c^{2} d^{2} e^{6} f^{5} - 4 \, c^{3} d e^{5} f^{6} + c^{4} e^{4} f^{7} + {\left(d^{4} e^{4} f^{7} - 4 \, c d^{3} e^{3} f^{8} + 6 \, c^{2} d^{2} e^{2} f^{9} - 4 \, c^{3} d e f^{10} + c^{4} f^{11}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{6} - 4 \, c d^{3} e^{4} f^{7} + 6 \, c^{2} d^{2} e^{3} f^{8} - 4 \, c^{3} d e^{2} f^{9} + c^{4} e f^{10}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{5} - 4 \, c d^{3} e^{5} f^{6} + 6 \, c^{2} d^{2} e^{4} f^{7} - 4 \, c^{3} d e^{3} f^{8} + c^{4} e^{2} f^{9}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{4} - 4 \, c d^{3} e^{6} f^{5} + 6 \, c^{2} d^{2} e^{5} f^{6} - 4 \, c^{3} d e^{4} f^{7} + c^{4} e^{3} f^{8}\right)} x\right)}}, \frac{2 \, {\left(105 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{7} x^{4} + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e f^{6} x^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{2} f^{5} x^{2} + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{3} f^{4} x + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} e^{4} f^{3}\right)} \sqrt{-\frac{d}{d e - c f}} \arctan\left(-\frac{{\left(d e - c f\right)} \sqrt{f x + e} \sqrt{-\frac{d}{d e - c f}}}{d f x + d e}\right) - {\left(8 \, b^{3} d^{3} e^{6} + 15 \, a^{3} c^{3} f^{6} + 105 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} f^{6} x^{3} - 2 \, {\left(19 \, b^{3} c d^{2} - 9 \, a b^{2} d^{3}\right)} e^{5} f + 3 \, {\left(29 \, b^{3} c^{2} d - 39 \, a b^{2} c d^{2} + 15 \, a^{2} b d^{3}\right)} e^{4} f^{2} + 4 \, {\left(12 \, b^{3} c^{3} - 60 \, a b^{2} c^{2} d + 87 \, a^{2} b c d^{2} - 44 \, a^{3} d^{3}\right)} e^{3} f^{3} + 2 \, {\left(12 \, a b^{2} c^{3} - 48 \, a^{2} b c^{2} d + 61 \, a^{3} c d^{2}\right)} e^{2} f^{4} + 6 \, {\left(3 \, a^{2} b c^{3} - 11 \, a^{3} c^{2} d\right)} e f^{5} + 35 \, {\left(b^{3} d^{3} e^{4} f^{2} - 4 \, b^{3} c d^{2} e^{3} f^{3} + 6 \, b^{3} c^{2} d e^{2} f^{4} + 2 \, {\left(3 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} e f^{5} + {\left(3 \, a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{6}\right)} x^{2} + 7 \, {\left(4 \, b^{3} d^{3} e^{5} f - {\left(19 \, b^{3} c d^{2} - 9 \, a b^{2} d^{3}\right)} e^{4} f^{2} + 36 \, {\left(b^{3} c^{2} d - a b^{2} c d^{2}\right)} e^{3} f^{3} + 2 \, {\left(12 \, b^{3} c^{3} - 60 \, a b^{2} c^{2} d + 87 \, a^{2} b c d^{2} - 29 \, a^{3} d^{3}\right)} e^{2} f^{4} + 4 \, {\left(3 \, a b^{2} c^{3} - 12 \, a^{2} b c^{2} d + 4 \, a^{3} c d^{2}\right)} e f^{5} + 3 \, {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} f^{6}\right)} x\right)} \sqrt{f x + e}\right)}}{105 \, {\left(d^{4} e^{8} f^{3} - 4 \, c d^{3} e^{7} f^{4} + 6 \, c^{2} d^{2} e^{6} f^{5} - 4 \, c^{3} d e^{5} f^{6} + c^{4} e^{4} f^{7} + {\left(d^{4} e^{4} f^{7} - 4 \, c d^{3} e^{3} f^{8} + 6 \, c^{2} d^{2} e^{2} f^{9} - 4 \, c^{3} d e f^{10} + c^{4} f^{11}\right)} x^{4} + 4 \, {\left(d^{4} e^{5} f^{6} - 4 \, c d^{3} e^{4} f^{7} + 6 \, c^{2} d^{2} e^{3} f^{8} - 4 \, c^{3} d e^{2} f^{9} + c^{4} e f^{10}\right)} x^{3} + 6 \, {\left(d^{4} e^{6} f^{5} - 4 \, c d^{3} e^{5} f^{6} + 6 \, c^{2} d^{2} e^{4} f^{7} - 4 \, c^{3} d e^{3} f^{8} + c^{4} e^{2} f^{9}\right)} x^{2} + 4 \, {\left(d^{4} e^{7} f^{4} - 4 \, c d^{3} e^{6} f^{5} + 6 \, c^{2} d^{2} e^{5} f^{6} - 4 \, c^{3} d e^{4} f^{7} + c^{4} e^{3} f^{8}\right)} x\right)}}\right]"," ",0,"[-1/105*(105*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^7*x^4 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^6*x^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^5*x^2 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^3*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^4*f^3)*sqrt(d/(d*e - c*f))*log((d*f*x + 2*d*e - c*f - 2*(d*e - c*f)*sqrt(f*x + e)*sqrt(d/(d*e - c*f)))/(d*x + c)) + 2*(8*b^3*d^3*e^6 + 15*a^3*c^3*f^6 + 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^6*x^3 - 2*(19*b^3*c*d^2 - 9*a*b^2*d^3)*e^5*f + 3*(29*b^3*c^2*d - 39*a*b^2*c*d^2 + 15*a^2*b*d^3)*e^4*f^2 + 4*(12*b^3*c^3 - 60*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 44*a^3*d^3)*e^3*f^3 + 2*(12*a*b^2*c^3 - 48*a^2*b*c^2*d + 61*a^3*c*d^2)*e^2*f^4 + 6*(3*a^2*b*c^3 - 11*a^3*c^2*d)*e*f^5 + 35*(b^3*d^3*e^4*f^2 - 4*b^3*c*d^2*e^3*f^3 + 6*b^3*c^2*d*e^2*f^4 + 2*(3*b^3*c^3 - 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 5*a^3*d^3)*e*f^5 + (3*a*b^2*c^3 - 3*a^2*b*c^2*d + a^3*c*d^2)*f^6)*x^2 + 7*(4*b^3*d^3*e^5*f - (19*b^3*c*d^2 - 9*a*b^2*d^3)*e^4*f^2 + 36*(b^3*c^2*d - a*b^2*c*d^2)*e^3*f^3 + 2*(12*b^3*c^3 - 60*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 29*a^3*d^3)*e^2*f^4 + 4*(3*a*b^2*c^3 - 12*a^2*b*c^2*d + 4*a^3*c*d^2)*e*f^5 + 3*(3*a^2*b*c^3 - a^3*c^2*d)*f^6)*x)*sqrt(f*x + e))/(d^4*e^8*f^3 - 4*c*d^3*e^7*f^4 + 6*c^2*d^2*e^6*f^5 - 4*c^3*d*e^5*f^6 + c^4*e^4*f^7 + (d^4*e^4*f^7 - 4*c*d^3*e^3*f^8 + 6*c^2*d^2*e^2*f^9 - 4*c^3*d*e*f^10 + c^4*f^11)*x^4 + 4*(d^4*e^5*f^6 - 4*c*d^3*e^4*f^7 + 6*c^2*d^2*e^3*f^8 - 4*c^3*d*e^2*f^9 + c^4*e*f^10)*x^3 + 6*(d^4*e^6*f^5 - 4*c*d^3*e^5*f^6 + 6*c^2*d^2*e^4*f^7 - 4*c^3*d*e^3*f^8 + c^4*e^2*f^9)*x^2 + 4*(d^4*e^7*f^4 - 4*c*d^3*e^6*f^5 + 6*c^2*d^2*e^5*f^6 - 4*c^3*d*e^4*f^7 + c^4*e^3*f^8)*x), 2/105*(105*((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^7*x^4 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e*f^6*x^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^2*f^5*x^2 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^3*f^4*x + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*e^4*f^3)*sqrt(-d/(d*e - c*f))*arctan(-(d*e - c*f)*sqrt(f*x + e)*sqrt(-d/(d*e - c*f))/(d*f*x + d*e)) - (8*b^3*d^3*e^6 + 15*a^3*c^3*f^6 + 105*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*f^6*x^3 - 2*(19*b^3*c*d^2 - 9*a*b^2*d^3)*e^5*f + 3*(29*b^3*c^2*d - 39*a*b^2*c*d^2 + 15*a^2*b*d^3)*e^4*f^2 + 4*(12*b^3*c^3 - 60*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 44*a^3*d^3)*e^3*f^3 + 2*(12*a*b^2*c^3 - 48*a^2*b*c^2*d + 61*a^3*c*d^2)*e^2*f^4 + 6*(3*a^2*b*c^3 - 11*a^3*c^2*d)*e*f^5 + 35*(b^3*d^3*e^4*f^2 - 4*b^3*c*d^2*e^3*f^3 + 6*b^3*c^2*d*e^2*f^4 + 2*(3*b^3*c^3 - 15*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 5*a^3*d^3)*e*f^5 + (3*a*b^2*c^3 - 3*a^2*b*c^2*d + a^3*c*d^2)*f^6)*x^2 + 7*(4*b^3*d^3*e^5*f - (19*b^3*c*d^2 - 9*a*b^2*d^3)*e^4*f^2 + 36*(b^3*c^2*d - a*b^2*c*d^2)*e^3*f^3 + 2*(12*b^3*c^3 - 60*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 29*a^3*d^3)*e^2*f^4 + 4*(3*a*b^2*c^3 - 12*a^2*b*c^2*d + 4*a^3*c*d^2)*e*f^5 + 3*(3*a^2*b*c^3 - a^3*c^2*d)*f^6)*x)*sqrt(f*x + e))/(d^4*e^8*f^3 - 4*c*d^3*e^7*f^4 + 6*c^2*d^2*e^6*f^5 - 4*c^3*d*e^5*f^6 + c^4*e^4*f^7 + (d^4*e^4*f^7 - 4*c*d^3*e^3*f^8 + 6*c^2*d^2*e^2*f^9 - 4*c^3*d*e*f^10 + c^4*f^11)*x^4 + 4*(d^4*e^5*f^6 - 4*c*d^3*e^4*f^7 + 6*c^2*d^2*e^3*f^8 - 4*c^3*d*e^2*f^9 + c^4*e*f^10)*x^3 + 6*(d^4*e^6*f^5 - 4*c*d^3*e^5*f^6 + 6*c^2*d^2*e^4*f^7 - 4*c^3*d*e^3*f^8 + c^4*e^2*f^9)*x^2 + 4*(d^4*e^7*f^4 - 4*c*d^3*e^6*f^5 + 6*c^2*d^2*e^5*f^6 - 4*c^3*d*e^4*f^7 + c^4*e^3*f^8)*x)]","B",0
1790,1,49,0,1.519144," ","integrate((2+3*x)^6*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{36465} \, {\left(15637050 \, x^{8} + 80999919 \, x^{7} + 181983186 \, x^{6} + 229582836 \, x^{5} + 173491920 \, x^{4} + 72883440 \, x^{3} + 5339712 \, x^{2} - 16666112 \, x - 23667392\right)} \sqrt{-2 \, x + 1}"," ",0,"1/36465*(15637050*x^8 + 80999919*x^7 + 181983186*x^6 + 229582836*x^5 + 173491920*x^4 + 72883440*x^3 + 5339712*x^2 - 16666112*x - 23667392)*sqrt(-2*x + 1)","A",0
1791,1,44,0,1.527952," ","integrate((2+3*x)^5*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{33} \, {\left(5346 \, x^{7} + 24057 \, x^{6} + 45765 \, x^{5} + 46875 \, x^{4} + 26220 \, x^{3} + 5172 \, x^{2} - 4120 \, x - 7288\right)} \sqrt{-2 \, x + 1}"," ",0,"1/33*(5346*x^7 + 24057*x^6 + 45765*x^5 + 46875*x^4 + 26220*x^3 + 5172*x^2 - 4120*x - 7288)*sqrt(-2*x + 1)","A",0
1792,1,39,0,1.500463," ","integrate((2+3*x)^4*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2145} \, {\left(133650 \, x^{6} + 509895 \, x^{5} + 791640 \, x^{4} + 614160 \, x^{3} + 200328 \, x^{2} - 60928 \, x - 163888\right)} \sqrt{-2 \, x + 1}"," ",0,"1/2145*(133650*x^6 + 509895*x^5 + 791640*x^4 + 614160*x^3 + 200328*x^2 - 60928*x - 163888)*sqrt(-2*x + 1)","A",0
1793,1,34,0,1.171545," ","integrate((2+3*x)^3*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{165} \, {\left(4050 \, x^{5} + 12645 \, x^{4} + 15075 \, x^{3} + 7527 \, x^{2} - 482 \, x - 4442\right)} \sqrt{-2 \, x + 1}"," ",0,"1/165*(4050*x^5 + 12645*x^4 + 15075*x^3 + 7527*x^2 - 482*x - 4442)*sqrt(-2*x + 1)","A",0
1794,1,29,0,1.210035," ","integrate((2+3*x)^2*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{105} \, {\left(1050 \, x^{4} + 2535 \, x^{3} + 2046 \, x^{2} + 244 \, x - 1016\right)} \sqrt{-2 \, x + 1}"," ",0,"1/105*(1050*x^4 + 2535*x^3 + 2046*x^2 + 244*x - 1016)*sqrt(-2*x + 1)","A",0
1795,1,24,0,1.469385," ","integrate((2+3*x)*(3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{105} \, {\left(450 \, x^{3} + 753 \, x^{2} + 257 \, x - 373\right)} \sqrt{-2 \, x + 1}"," ",0,"1/105*(450*x^3 + 753*x^2 + 257*x - 373)*sqrt(-2*x + 1)","A",0
1796,1,19,0,1.429347," ","integrate((3+5*x)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(6 \, x^{2} + 5 \, x - 4\right)} \sqrt{-2 \, x + 1}"," ",0,"1/3*(6*x^2 + 5*x - 4)*sqrt(-2*x + 1)","A",0
1797,1,52,0,1.503799," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{27} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + \frac{1}{9} \, {\left(10 \, x - 7\right)} \sqrt{-2 \, x + 1}"," ",0,"1/27*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 1/9*(10*x - 7)*sqrt(-2*x + 1)","A",0
1798,1,59,0,1.202539," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 7 \, {\left(10 \, x + 7\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(3 \, x + 2\right)}}"," ",0,"1/21*(4*sqrt(21)*(3*x + 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 7*(10*x + 7)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1799,1,70,0,1.639060," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{23 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(71 \, x + 45\right)} \sqrt{-2 \, x + 1}}{882 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/882*(23*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(71*x + 45)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1800,1,85,0,0.722725," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{17 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(153 \, x^{2} - 167 \, x - 163\right)} \sqrt{-2 \, x + 1}}{9261 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/9261*(17*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(153*x^2 - 167*x - 163)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1801,1,106,0,1.489944," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{15 \, \sqrt{7} \sqrt{3} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 7 \, {\left(1215 \, x^{3} + 3375 \, x^{2} - 1726 \, x - 2062\right)} \sqrt{-2 \, x + 1}}{57624 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/57624*(15*sqrt(7)*sqrt(3)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 7*(1215*x^3 + 3375*x^2 - 1726*x - 2062)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1802,1,115,0,0.765416," ","integrate((3+5*x)*(1-2*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{5 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(405 \, x^{4} + 1395 \, x^{3} + 2004 \, x^{2} - 864 \, x - 1019\right)} \sqrt{-2 \, x + 1}}{108045 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/108045*(5*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(405*x^4 + 1395*x^3 + 2004*x^2 - 864*x - 1019)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1803,1,44,0,1.684589," ","integrate((2+3*x)^4*(3+5*x)^2*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2145} \, {\left(579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right)} \sqrt{-2 \, x + 1}"," ",0,"1/2145*(579150*x^7 + 2561625*x^6 + 4787910*x^5 + 4814245*x^4 + 2635780*x^3 + 493524*x^2 - 426024*x - 734904)*sqrt(-2*x + 1)","A",0
1804,1,39,0,1.145283," ","integrate((2+3*x)^3*(3+5*x)^2*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2145} \, {\left(222750 \, x^{6} + 832275 \, x^{5} + 1264605 \, x^{4} + 958275 \, x^{3} + 301263 \, x^{2} - 99458 \, x - 253898\right)} \sqrt{-2 \, x + 1}"," ",0,"1/2145*(222750*x^6 + 832275*x^5 + 1264605*x^4 + 958275*x^3 + 301263*x^2 - 99458*x - 253898)*sqrt(-2*x + 1)","A",0
1805,1,34,0,1.321985," ","integrate((2+3*x)^2*(3+5*x)^2*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{1155} \, {\left(47250 \, x^{5} + 143675 \, x^{4} + 166580 \, x^{3} + 80313 \, x^{2} - 6518 \, x - 48098\right)} \sqrt{-2 \, x + 1}"," ",0,"1/1155*(47250*x^5 + 143675*x^4 + 166580*x^3 + 80313*x^2 - 6518*x - 48098)*sqrt(-2*x + 1)","A",0
1806,1,29,0,1.484463," ","integrate((2+3*x)*(3+5*x)^2*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{105} \, {\left(1750 \, x^{4} + 4075 \, x^{3} + 3159 \, x^{2} + 321 \, x - 1569\right)} \sqrt{-2 \, x + 1}"," ",0,"1/105*(1750*x^4 + 4075*x^3 + 3159*x^2 + 321*x - 1569)*sqrt(-2*x + 1)","A",0
1807,1,24,0,1.462654," ","integrate((3+5*x)^2*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{21} \, {\left(150 \, x^{3} + 237 \, x^{2} + 74 \, x - 115\right)} \sqrt{-2 \, x + 1}"," ",0,"1/21*(150*x^3 + 237*x^2 + 74*x - 115)*sqrt(-2*x + 1)","A",0
1808,1,56,0,1.641876," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{81} \, \sqrt{7} \sqrt{3} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + \frac{1}{27} \, {\left(90 \, x^{2} + 65 \, x - 53\right)} \sqrt{-2 \, x + 1}"," ",0,"1/81*sqrt(7)*sqrt(3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 1/27*(90*x^2 + 65*x - 53)*sqrt(-2*x + 1)","A",0
1809,1,65,0,1.367358," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{71 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(150 \, x^{2} - 35 \, x - 91\right)} \sqrt{-2 \, x + 1}}{567 \, {\left(3 \, x + 2\right)}}"," ",0,"1/567*(71*sqrt(21)*(3*x + 2)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(150*x^2 - 35*x - 91)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1810,1,74,0,1.520856," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{863 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(2100 \, x^{2} + 2941 \, x + 1025\right)} \sqrt{-2 \, x + 1}}{2646 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/2646*(863*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(2100*x^2 + 2941*x + 1025)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1811,1,85,0,0.814051," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{2381 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(22671 \, x^{2} + 28751 \, x + 9124\right)} \sqrt{-2 \, x + 1}}{55566 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/55566*(2381*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(22671*x^2 + 28751*x + 9124)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1812,1,100,0,1.180174," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{4625 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(124875 \, x^{3} - 64725 \, x^{2} - 225262 \, x - 85094\right)} \sqrt{-2 \, x + 1}}{1555848 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/1555848*(4625*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(124875*x^3 - 64725*x^2 - 225262*x - 85094)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1813,1,115,0,1.269544," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{155 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(12555 \, x^{4} + 43245 \, x^{3} + 3324 \, x^{2} - 33434 \, x - 13564\right)} \sqrt{-2 \, x + 1}}{370440 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/370440*(155*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(12555*x^4 + 43245*x^3 + 3324*x^2 - 33434*x - 13564)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1814,1,130,0,1.805092," ","integrate((3+5*x)^2*(1-2*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","\frac{8065 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1959795 \, x^{5} + 8056935 \, x^{4} + 14197626 \, x^{3} + 1791558 \, x^{2} - 7772840 \, x - 3136864\right)} \sqrt{-2 \, x + 1}}{108909360 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/108909360*(8065*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1959795*x^5 + 8056935*x^4 + 14197626*x^3 + 1791558*x^2 - 7772840*x - 3136864)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1815,1,49,0,1.660354," ","integrate((2+3*x)^4*(3+5*x)^3*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{109395} \, {\left(130308750 \, x^{8} + 655308225 \, x^{7} + 1428673950 \, x^{6} + 1747511955 \, x^{5} + 1277595710 \, x^{4} + 514265240 \, x^{3} + 26582592 \, x^{2} - 124054192 \, x - 171312832\right)} \sqrt{-2 \, x + 1}"," ",0,"1/109395*(130308750*x^8 + 655308225*x^7 + 1428673950*x^6 + 1747511955*x^5 + 1277595710*x^4 + 514265240*x^3 + 26582592*x^2 - 124054192*x - 171312832)*sqrt(-2*x + 1)","A",0
1816,1,44,0,1.505361," ","integrate((2+3*x)^3*(3+5*x)^3*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{6435} \, {\left(2895750 \, x^{7} + 12585375 \, x^{6} + 23107275 \, x^{5} + 22806620 \, x^{4} + 12220625 \, x^{3} + 2166357 \, x^{2} - 2030662 \, x - 3420622\right)} \sqrt{-2 \, x + 1}"," ",0,"1/6435*(2895750*x^7 + 12585375*x^6 + 23107275*x^5 + 22806620*x^4 + 12220625*x^3 + 2166357*x^2 - 2030662*x - 3420622)*sqrt(-2*x + 1)","A",0
1817,1,39,0,1.754742," ","integrate((2+3*x)^2*(3+5*x)^3*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{45045} \, {\left(7796250 \, x^{6} + 28515375 \, x^{5} + 42393400 \, x^{4} + 31374085 \, x^{3} + 9500136 \, x^{2} - 3396296 \, x - 8261156\right)} \sqrt{-2 \, x + 1}"," ",0,"1/45045*(7796250*x^6 + 28515375*x^5 + 42393400*x^4 + 31374085*x^3 + 9500136*x^2 - 3396296*x - 8261156)*sqrt(-2*x + 1)","A",0
1818,1,34,0,1.731220," ","integrate((2+3*x)*(3+5*x)^3*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{3465} \, {\left(236250 \, x^{5} + 699125 \, x^{4} + 788075 \, x^{3} + 366816 \, x^{2} - 36121 \, x - 223231\right)} \sqrt{-2 \, x + 1}"," ",0,"1/3465*(236250*x^5 + 699125*x^4 + 788075*x^3 + 366816*x^2 - 36121*x - 223231)*sqrt(-2*x + 1)","A",0
1819,1,29,0,1.562263," ","integrate((3+5*x)^3*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{63} \, {\left(1750 \, x^{4} + 3925 \, x^{3} + 2922 \, x^{2} + 247 \, x - 1454\right)} \sqrt{-2 \, x + 1}"," ",0,"1/63*(1750*x^4 + 3925*x^3 + 2922*x^2 + 247*x - 1454)*sqrt(-2*x + 1)","A",0
1820,1,62,0,1.671470," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{243} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + \frac{1}{567} \, {\left(6750 \, x^{3} + 10035 \, x^{2} + 2875 \, x - 4804\right)} \sqrt{-2 \, x + 1}"," ",0,"1/243*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 1/567*(6750*x^3 + 10035*x^2 + 2875*x - 4804)*sqrt(-2*x + 1)","A",0
1821,1,69,0,1.617452," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{106 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1350 \, x^{3} + 1725 \, x^{2} - 110 \, x - 439\right)} \sqrt{-2 \, x + 1}}{1701 \, {\left(3 \, x + 2\right)}}"," ",0,"1/1701*(106*sqrt(21)*(3*x + 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1350*x^3 + 1725*x^2 - 110*x - 439)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1822,1,80,0,1.423252," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{7559 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(31500 \, x^{3} + 7350 \, x^{2} - 32833 \, x - 15815\right)} \sqrt{-2 \, x + 1}}{23814 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/23814*(7559*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(31500*x^3 + 7350*x^2 - 32833*x - 15815)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1823,1,89,0,1.270874," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{46498 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(330750 \, x^{3} + 695043 \, x^{2} + 484618 \, x + 112187\right)} \sqrt{-2 \, x + 1}}{83349 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/83349*(46498*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(330750*x^3 + 695043*x^2 + 484618*x + 112187)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1824,1,100,0,1.753413," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{328715 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(9646695 \, x^{3} + 18358575 \, x^{2} + 11657098 \, x + 2469626\right)} \sqrt{-2 \, x + 1}}{4667544 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/4667544*(328715*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(9646695*x^3 + 18358575*x^2 + 11657098*x + 2469626)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1825,1,115,0,1.526211," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{56185 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(4550985 \, x^{4} + 240615 \, x^{3} - 10100352 \, x^{2} - 8471518 \, x - 1984928\right)} \sqrt{-2 \, x + 1}}{11668860 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/11668860*(56185*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(4550985*x^4 + 240615*x^3 - 10100352*x^2 - 8471518*x - 1984928)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1826,1,130,0,1.459021," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","\frac{219785 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(53407755 \, x^{5} + 219565215 \, x^{4} + 127601514 \, x^{3} - 139462938 \, x^{2} - 150340360 \, x - 36741296\right)} \sqrt{-2 \, x + 1}}{326728080 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/326728080*(219785*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(53407755*x^5 + 219565215*x^4 + 127601514*x^3 - 139462938*x^2 - 150340360*x - 36741296)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1827,1,145,0,1.536263," ","integrate((3+5*x)^3*(1-2*x)^(1/2)/(2+3*x)^8,x, algorithm=""fricas"")","\frac{118585 \, \sqrt{21} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(86448465 \, x^{6} + 413031555 \, x^{5} + 863203932 \, x^{4} + 473987484 \, x^{3} - 306463011 \, x^{2} - 361589428 \, x - 88036937\right)} \sqrt{-2 \, x + 1}}{1000604745 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/1000604745*(118585*sqrt(21)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(86448465*x^6 + 413031555*x^5 + 863203932*x^4 + 473987484*x^3 - 306463011*x^2 - 361589428*x - 88036937)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1828,1,66,0,1.520804," ","integrate((2+3*x)^4*(1-2*x)^(1/2)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{15625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{21875} \, {\left(78750 \, x^{4} + 203625 \, x^{3} + 177930 \, x^{2} + 27865 \, x - 88776\right)} \sqrt{-2 \, x + 1}"," ",0,"1/15625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/21875*(78750*x^4 + 203625*x^3 + 177930*x^2 + 27865*x - 88776)*sqrt(-2*x + 1)","A",0
1829,1,61,0,1.435130," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{3125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{4375} \, {\left(6750 \, x^{3} + 12555 \, x^{2} + 5115 \, x - 6526\right)} \sqrt{-2 \, x + 1}"," ",0,"1/3125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/4375*(6750*x^3 + 12555*x^2 + 5115*x - 6526)*sqrt(-2*x + 1)","A",0
1830,1,56,0,1.215443," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{125} \, {\left(90 \, x^{2} + 95 \, x - 68\right)} \sqrt{-2 \, x + 1}"," ",0,"1/625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/125*(90*x^2 + 95*x - 68)*sqrt(-2*x + 1)","A",0
1831,1,51,0,1.178414," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{25} \, {\left(10 \, x - 3\right)} \sqrt{-2 \, x + 1}"," ",0,"1/125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/25*(10*x - 3)*sqrt(-2*x + 1)","A",0
1832,1,46,0,1.544917," ","integrate((1-2*x)^(1/2)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{25} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{2}{5} \, \sqrt{-2 \, x + 1}"," ",0,"1/25*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 2/5*sqrt(-2*x + 1)","A",0
1833,1,74,0,0.806985," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{3} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right)"," ",0,"1/5*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/3*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2))","A",0
1834,1,90,0,1.375500," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{21 \, \sqrt{55} {\left(3 \, x + 2\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 34 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, \sqrt{-2 \, x + 1}}{21 \, {\left(3 \, x + 2\right)}}"," ",0,"1/21*(21*sqrt(55)*(3*x + 2)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 34*sqrt(21)*(3*x + 2)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*sqrt(-2*x + 1))/(3*x + 2)","A",0
1835,1,116,0,1.685385," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{793 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 490 \, \sqrt{55} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 7 \, {\left(207 \, x + 145\right)} \sqrt{-2 \, x + 1}}{98 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/98*(793*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 490*sqrt(55)*(9*x^2 + 12*x + 4)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 7*(207*x + 145)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1836,1,130,0,1.318617," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{25725 \, \sqrt{55} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 41632 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(10863 \, x^{2} + 14848 \, x + 5087\right)} \sqrt{-2 \, x + 1}}{1029 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/1029*(25725*sqrt(55)*(27*x^3 + 54*x^2 + 36*x + 8)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 41632*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(10863*x^2 + 14848*x + 5087)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1837,1,150,0,1.445949," ","integrate((1-2*x)^(1/2)/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{7203000 \, \sqrt{55} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 11656955 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(9124785 \, x^{3} + 18555225 \, x^{2} + 12587542 \, x + 2849254\right)} \sqrt{-2 \, x + 1}}{57624 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/57624*(7203000*sqrt(55)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 11656955*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(9124785*x^3 + 18555225*x^2 + 12587542*x + 2849254)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1838,1,79,0,1.754791," ","integrate((2+3*x)^5*(1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{1148 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(1181250 \, x^{5} + 3864375 \, x^{4} + 4760100 \, x^{3} + 2225760 \, x^{2} - 1133340 \, x - 862072\right)} \sqrt{-2 \, x + 1}}{6015625 \, {\left(5 \, x + 3\right)}}"," ",0,"1/6015625*(1148*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(1181250*x^5 + 3864375*x^4 + 4760100*x^3 + 2225760*x^2 - 1133340*x - 862072)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1839,1,74,0,1.566212," ","integrate((2+3*x)^4*(1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{917 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(101250 \, x^{4} + 258525 \, x^{3} + 206415 \, x^{2} - 52485 \, x - 63088\right)} \sqrt{-2 \, x + 1}}{1203125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1203125*(917*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(101250*x^4 + 258525*x^3 + 206415*x^2 - 52485*x - 63088)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1840,1,69,0,1.425379," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{98 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(1350 \, x^{3} + 2385 \, x^{2} - 90 \, x - 622\right)} \sqrt{-2 \, x + 1}}{34375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/34375*(98*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(1350*x^3 + 2385*x^2 - 90*x - 622)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1841,1,64,0,1.170276," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{13 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(30 \, x^{2} + 15 \, x - 2\right)} \sqrt{-2 \, x + 1}}{1375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1375*(13*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(30*x^2 + 15*x - 2)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1842,1,59,0,1.462574," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{32 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(30 \, x + 17\right)} \sqrt{-2 \, x + 1}}{1375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1375*(32*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(30*x + 17)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1843,1,54,0,1.375857," ","integrate((1-2*x)^(1/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, \sqrt{-2 \, x + 1}}{275 \, {\left(5 \, x + 3\right)}}"," ",0,"1/275*(sqrt(55)*(5*x + 3)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*sqrt(-2*x + 1))/(5*x + 3)","A",0
1844,1,90,0,1.639582," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{34 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, \sqrt{21} {\left(5 \, x + 3\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 55 \, \sqrt{-2 \, x + 1}}{55 \, {\left(5 \, x + 3\right)}}"," ",0,"1/55*(34*sqrt(55)*(5*x + 3)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*sqrt(21)*(5*x + 3)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 55*sqrt(-2*x + 1))/(5*x + 3)","A",0
1845,1,122,0,0.914253," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{469 \, \sqrt{11} \sqrt{5} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 759 \, \sqrt{7} \sqrt{3} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(30 \, x + 19\right)} \sqrt{-2 \, x + 1}}{77 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/77*(469*sqrt(11)*sqrt(5)*(15*x^2 + 19*x + 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 759*sqrt(7)*sqrt(3)*(15*x^2 + 19*x + 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(30*x + 19)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
1846,1,142,0,1.793130," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{49000 \, \sqrt{11} \sqrt{5} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 79299 \, \sqrt{7} \sqrt{3} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(9405 \, x^{2} + 12228 \, x + 3965\right)} \sqrt{-2 \, x + 1}}{1078 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/1078*(49000*sqrt(11)*sqrt(5)*(45*x^3 + 87*x^2 + 56*x + 12)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 79299*sqrt(7)*sqrt(3)*(45*x^3 + 87*x^2 + 56*x + 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(9405*x^2 + 12228*x + 3965)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1847,1,162,0,1.066222," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{2280950 \, \sqrt{11} \sqrt{5} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 3691369 \, \sqrt{7} \sqrt{3} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(1313415 \, x^{3} + 2583264 \, x^{2} + 1692159 \, x + 369116\right)} \sqrt{-2 \, x + 1}}{7546 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/7546*(2280950*sqrt(11)*sqrt(5)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 3691369*sqrt(7)*sqrt(3)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(1313415*x^3 + 2583264*x^2 + 1692159*x + 369116)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1848,1,84,0,1.499712," ","integrate((2+3*x)^4*(1-2*x)^(1/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{12803 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(445500 \, x^{4} + 1103850 \, x^{3} + 506880 \, x^{2} - 200305 \, x - 121976\right)} \sqrt{-2 \, x + 1}}{3781250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/3781250*(12803*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(445500*x^4 + 1103850*x^3 + 506880*x^2 - 200305*x - 121976)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1849,1,79,0,1.516372," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1267 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(9900 \, x^{3} + 12870 \, x^{2} + 4555 \, x + 236\right)} \sqrt{-2 \, x + 1}}{151250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/151250*(1267*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(9900*x^3 + 12870*x^2 + 4555*x + 236)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1850,1,74,0,1.180475," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{409 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(1980 \, x^{2} + 2245 \, x + 632\right)} \sqrt{-2 \, x + 1}}{30250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/30250*(409*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(1980*x^2 + 2245*x + 632)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1851,1,70,0,1.780293," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{67 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(325 \, x + 206\right)} \sqrt{-2 \, x + 1}}{30250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/30250*(67*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(325*x + 206)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1852,1,69,0,1.552603," ","integrate((1-2*x)^(1/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(5 \, x - 8\right)} \sqrt{-2 \, x + 1}}{6050 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/6050*(sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(5*x - 8)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1853,1,110,0,0.981499," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2243 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 3630 \, \sqrt{21} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 275 \, {\left(67 \, x + 38\right)} \sqrt{-2 \, x + 1}}{1210 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1210*(2243*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 3630*sqrt(21)*(25*x^2 + 30*x + 9)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 275*(67*x + 38)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1854,1,142,0,0.911759," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{46655 \, \sqrt{11} \sqrt{5} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 75504 \, \sqrt{7} \sqrt{3} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(14925 \, x^{2} + 18410 \, x + 5662\right)} \sqrt{-2 \, x + 1}}{1694 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/1694*(46655*sqrt(11)*sqrt(5)*(75*x^3 + 140*x^2 + 87*x + 18)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 75504*sqrt(7)*sqrt(3)*(75*x^3 + 140*x^2 + 87*x + 18)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(14925*x^2 + 18410*x + 5662)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1855,1,162,0,1.574345," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3249925 \, \sqrt{11} \sqrt{5} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5259507 \, \sqrt{7} \sqrt{3} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(3118950 \, x^{3} + 5926515 \, x^{2} + 3748007 \, x + 788875\right)} \sqrt{-2 \, x + 1}}{11858 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/11858*(3249925*sqrt(11)*sqrt(5)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5259507*sqrt(7)*sqrt(3)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(3118950*x^3 + 5926515*x^2 + 3748007*x + 788875)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1856,1,182,0,1.575966," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{189018725 \, \sqrt{11} \sqrt{5} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 305897922 \, \sqrt{7} \sqrt{3} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(544203225 \, x^{4} + 1396877220 \, x^{3} + 1343346156 \, x^{2} + 573620246 \, x + 91763734\right)} \sqrt{-2 \, x + 1}}{83006 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/83006*(189018725*sqrt(11)*sqrt(5)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 305897922*sqrt(7)*sqrt(3)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(544203225*x^4 + 1396877220*x^3 + 1343346156*x^2 + 573620246*x + 91763734)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
1857,1,54,0,1.303925," ","integrate((1-2*x)^(3/2)*(2+3*x)^6*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{230945} \, {\left(177219900 \, x^{9} + 806871780 \, x^{8} + 1489122063 \, x^{7} + 1322260632 \, x^{6} + 372044232 \, x^{5} - 342957860 \, x^{4} - 377036800 \, x^{3} - 136800176 \, x^{2} + 7336416 \, x + 51677856\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/230945*(177219900*x^9 + 806871780*x^8 + 1489122063*x^7 + 1322260632*x^6 + 372044232*x^5 - 342957860*x^4 - 377036800*x^3 - 136800176*x^2 + 7336416*x + 51677856)*sqrt(-2*x + 1)","A",0
1858,1,49,0,1.276939," ","integrate((1-2*x)^(3/2)*(2+3*x)^5*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{36465} \, {\left(10424700 \, x^{8} + 40216176 \, x^{7} + 59295159 \, x^{6} + 35057799 \, x^{5} - 5198095 \, x^{4} - 19014940 \, x^{3} - 9775332 \, x^{2} - 488008 \, x + 3012632\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/36465*(10424700*x^8 + 40216176*x^7 + 59295159*x^6 + 35057799*x^5 - 5198095*x^4 - 19014940*x^3 - 9775332*x^2 - 488008*x + 3012632)*sqrt(-2*x + 1)","A",0
1859,1,44,0,0.994348," ","integrate((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{2145} \, {\left(231660 \, x^{7} + 730620 \, x^{6} + 793395 \, x^{5} + 184090 \, x^{4} - 296840 \, x^{3} - 243312 \, x^{2} - 36368 \, x + 66592\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/2145*(231660*x^7 + 730620*x^6 + 793395*x^5 + 184090*x^4 - 296840*x^3 - 243312*x^2 - 36368*x + 66592)*sqrt(-2*x + 1)","A",0
1860,1,39,0,1.560420," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{715} \, {\left(29700 \, x^{6} + 72360 \, x^{5} + 48065 \, x^{4} - 15945 \, x^{3} - 31589 \, x^{2} - 8666 \, x + 8494\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/715*(29700*x^6 + 72360*x^5 + 48065*x^4 - 15945*x^3 - 31589*x^2 - 8666*x + 8494)*sqrt(-2*x + 1)","A",0
1861,1,34,0,1.280002," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{165} \, {\left(2700 \, x^{5} + 4580 \, x^{4} + 755 \, x^{3} - 2484 \, x^{2} - 1216 \, x + 764\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/165*(2700*x^5 + 4580*x^4 + 755*x^3 - 2484*x^2 - 1216*x + 764)*sqrt(-2*x + 1)","A",0
1862,1,29,0,1.653636," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(700 \, x^{4} + 640 \, x^{3} - 393 \, x^{2} - 437 \, x + 193\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/105*(700*x^4 + 640*x^3 - 393*x^2 - 437*x + 193)*sqrt(-2*x + 1)","A",0
1863,1,24,0,1.591576," ","integrate((1-2*x)^(3/2)*(3+5*x),x, algorithm=""fricas"")","-\frac{1}{35} \, {\left(100 \, x^{3} + 4 \, x^{2} - 79 \, x + 26\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/35*(100*x^3 + 4*x^2 - 79*x + 26)*sqrt(-2*x + 1)","A",0
1864,1,57,0,0.806815," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x),x, algorithm=""fricas"")","\frac{7}{81} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - \frac{1}{27} \, {\left(36 \, x^{2} - 40 \, x + 25\right)} \sqrt{-2 \, x + 1}"," ",0,"7/81*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 1/27*(36*x^2 - 40*x + 25)*sqrt(-2*x + 1)","A",0
1865,1,70,0,1.389086," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{38 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 3 \, {\left(60 \, x^{2} - 212 \, x - 175\right)} \sqrt{-2 \, x + 1}}{81 \, {\left(3 \, x + 2\right)}}"," ",0,"1/81*(38*sqrt(7)*sqrt(3)*(3*x + 2)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 3*(60*x^2 - 212*x - 175)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1866,1,75,0,1.524230," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{71 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(120 \, x^{2} + 235 \, x + 101\right)} \sqrt{-2 \, x + 1}}{378 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/378*(71*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(120*x^2 + 235*x + 101)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1867,1,84,0,1.719732," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{52 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(792 \, x^{2} + 664 \, x + 107\right)} \sqrt{-2 \, x + 1}}{3969 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/3969*(52*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(792*x^2 + 664*x + 107)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1868,1,99,0,1.447902," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{137 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(3699 \, x^{3} - 13245 \, x^{2} - 7990 \, x + 970\right)} \sqrt{-2 \, x + 1}}{222264 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/222264*(137*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(3699*x^3 - 13245*x^2 - 7990*x + 970)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1869,1,114,0,1.732049," ","integrate((1-2*x)^(3/2)*(3+5*x)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{85 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(6885 \, x^{4} + 23715 \, x^{3} - 48252 \, x^{2} - 23998 \, x + 7912\right)} \sqrt{-2 \, x + 1}}{1296540 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/1296540*(85*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(6885*x^4 + 23715*x^3 - 48252*x^2 - 23998*x + 7912)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1870,1,49,0,1.378897," ","integrate((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1}{109395} \, {\left(52123500 \, x^{8} + 197142660 \, x^{7} + 284055255 \, x^{6} + 161801280 \, x^{5} - 29120005 \, x^{4} - 90028420 \, x^{3} - 44740356 \, x^{2} - 1821784 \, x + 13931096\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/109395*(52123500*x^8 + 197142660*x^7 + 284055255*x^6 + 161801280*x^5 - 29120005*x^4 - 90028420*x^3 - 44740356*x^2 - 1821784*x + 13931096)*sqrt(-2*x + 1)","A",0
1871,1,44,0,0.929704," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1}{6435} \, {\left(1158300 \, x^{7} + 3564000 \, x^{6} + 3749895 \, x^{5} + 776255 \, x^{4} - 1436365 \, x^{3} - 1121793 \, x^{2} - 155842 \, x + 307478\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/6435*(1158300*x^7 + 3564000*x^6 + 3749895*x^5 + 776255*x^4 - 1436365*x^3 - 1121793*x^2 - 155842*x + 307478)*sqrt(-2*x + 1)","A",0
1872,1,39,0,1.436977," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1}{6435} \, {\left(445500 \, x^{6} + 1050300 \, x^{5} + 661435 \, x^{4} - 248990 \, x^{3} - 441543 \, x^{2} - 114182 \, x + 117478\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/6435*(445500*x^6 + 1050300*x^5 + 661435*x^4 - 248990*x^3 - 441543*x^2 - 114182*x + 117478)*sqrt(-2*x + 1)","A",0
1873,1,34,0,1.047198," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1}{3465} \, {\left(94500 \, x^{5} + 152600 \, x^{4} + 19385 \, x^{3} - 82617 \, x^{2} - 37753 \, x + 24617\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/3465*(94500*x^5 + 152600*x^4 + 19385*x^3 - 82617*x^2 - 37753*x + 24617)*sqrt(-2*x + 1)","A",0
1874,1,29,0,1.805742," ","integrate((1-2*x)^(3/2)*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{1}{315} \, {\left(3500 \, x^{4} + 2900 \, x^{3} - 1977 \, x^{2} - 1948 \, x + 887\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/315*(3500*x^4 + 2900*x^3 - 1977*x^2 - 1948*x + 887)*sqrt(-2*x + 1)","A",0
1875,1,61,0,1.764080," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x),x, algorithm=""fricas"")","\frac{7}{243} \, \sqrt{7} \sqrt{3} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - \frac{1}{567} \, {\left(2700 \, x^{3} - 144 \, x^{2} - 1853 \, x + 527\right)} \sqrt{-2 \, x + 1}"," ",0,"7/243*sqrt(7)*sqrt(3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 1/567*(2700*x^3 - 144*x^2 - 1853*x + 527)*sqrt(-2*x + 1)","A",0
1876,1,76,0,1.899664," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","\frac{73 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - 3 \, {\left(540 \, x^{3} - 300 \, x^{2} + 187 \, x + 425\right)} \sqrt{-2 \, x + 1}}{243 \, {\left(3 \, x + 2\right)}}"," ",0,"1/243*(73*sqrt(7)*sqrt(3)*(3*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 3*(540*x^3 - 300*x^2 + 187*x + 425)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1877,1,79,0,1.712357," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","\frac{2873 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1800 \, x^{3} - 5520 \, x^{2} - 10195 \, x - 3803\right)} \sqrt{-2 \, x + 1}}{3402 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/3402*(2873*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1800*x^3 - 5520*x^2 - 10195*x - 3803)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1878,1,90,0,1.778862," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","\frac{7559 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(37800 \, x^{3} + 100809 \, x^{2} + 82493 \, x + 21424\right)} \sqrt{-2 \, x + 1}}{23814 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/23814*(7559*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(37800*x^3 + 100809*x^2 + 82493*x + 21424)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1879,1,99,0,1.451494," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","\frac{14423 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(668979 \, x^{3} + 988035 \, x^{2} + 453730 \, x + 60890\right)} \sqrt{-2 \, x + 1}}{666792 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/666792*(14423*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(668979*x^3 + 988035*x^2 + 453730*x + 60890)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1880,1,114,0,0.869375," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","\frac{23465 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1900665 \, x^{4} - 5801265 \, x^{3} - 8540988 \, x^{2} - 2143262 \, x + 292028\right)} \sqrt{-2 \, x + 1}}{23337720 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/23337720*(23465*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1900665*x^4 - 5801265*x^3 - 8540988*x^2 - 2143262*x + 292028)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1881,1,129,0,1.680099," ","integrate((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","\frac{4955 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1204065 \, x^{5} + 4950045 \, x^{4} - 6094818 \, x^{3} - 9658494 \, x^{2} - 1262200 \, x + 858112\right)} \sqrt{-2 \, x + 1}}{46675440 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/46675440*(4955*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1204065*x^5 + 4950045*x^4 - 6094818*x^3 - 9658494*x^2 - 1262200*x + 858112)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1882,1,54,0,1.201738," ","integrate((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1}{692835} \, {\left(1476832500 \, x^{9} + 6503854500 \, x^{8} + 11568656385 \, x^{7} + 9793273050 \, x^{6} + 2388733575 \, x^{5} - 2741637820 \, x^{4} - 2751200080 \, x^{3} - 942365544 \, x^{2} + 70133984 \, x + 369438704\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/692835*(1476832500*x^9 + 6503854500*x^8 + 11568656385*x^7 + 9793273050*x^6 + 2388733575*x^5 - 2741637820*x^4 - 2751200080*x^3 - 942365544*x^2 + 70133984*x + 369438704)*sqrt(-2*x + 1)","A",0
1883,1,49,0,1.434668," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1}{36465} \, {\left(28957500 \, x^{8} + 107335800 \, x^{7} + 151076475 \, x^{6} + 82806465 \, x^{5} - 17644040 \, x^{4} - 47302655 \, x^{3} - 22736811 \, x^{2} - 717734 \, x + 7158706\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/36465*(28957500*x^8 + 107335800*x^7 + 151076475*x^6 + 82806465*x^5 - 17644040*x^4 - 47302655*x^3 - 22736811*x^2 - 717734*x + 7158706)*sqrt(-2*x + 1)","A",0
1884,1,44,0,1.376945," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1}{165} \, {\left(49500 \, x^{7} + 148500 \, x^{6} + 151275 \, x^{5} + 27520 \, x^{4} - 59255 \, x^{3} - 44166 \, x^{2} - 5684 \, x + 12136\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/165*(49500*x^7 + 148500*x^6 + 151275*x^5 + 27520*x^4 - 59255*x^3 - 44166*x^2 - 5684*x + 12136)*sqrt(-2*x + 1)","A",0
1885,1,39,0,1.402988," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1}{15015} \, {\left(1732500 \, x^{6} + 3948000 \, x^{5} + 2351825 \, x^{4} - 996295 \, x^{3} - 1597776 \, x^{2} - 389509 \, x + 421301\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/15015*(1732500*x^6 + 3948000*x^5 + 2351825*x^4 - 996295*x^3 - 1597776*x^2 - 389509*x + 421301)*sqrt(-2*x + 1)","A",0
1886,1,34,0,1.484610," ","integrate((1-2*x)^(3/2)*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{1}{1155} \, {\left(52500 \, x^{5} + 80500 \, x^{4} + 7225 \, x^{3} - 43482 \, x^{2} - 18593 \, x + 12592\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/1155*(52500*x^5 + 80500*x^4 + 7225*x^3 - 43482*x^2 - 18593*x + 12592)*sqrt(-2*x + 1)","A",0
1887,1,67,0,1.689235," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x),x, algorithm=""fricas"")","\frac{7}{729} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - \frac{1}{1701} \, {\left(31500 \, x^{4} + 23400 \, x^{3} - 17649 \, x^{2} - 15679 \, x + 7456\right)} \sqrt{-2 \, x + 1}"," ",0,"7/729*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 1/1701*(31500*x^4 + 23400*x^3 - 17649*x^2 - 15679*x + 7456)*sqrt(-2*x + 1)","A",0
1888,1,80,0,1.971842," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","\frac{28 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 3 \, {\left(1500 \, x^{4} + 780 \, x^{3} - 1005 \, x^{2} - 442 \, x + 85\right)} \sqrt{-2 \, x + 1}}{189 \, {\left(3 \, x + 2\right)}}"," ",0,"1/189*(28*sqrt(7)*sqrt(3)*(3*x + 2)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 3*(1500*x^4 + 780*x^3 - 1005*x^2 - 442*x + 85)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1889,1,80,0,1.458538," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","\frac{887 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1800 \, x^{4} + 570 \, x^{2} + 2965 \, x + 1367\right)} \sqrt{-2 \, x + 1}}{1134 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/1134*(887*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1800*x^4 + 570*x^2 + 2965*x + 1367)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1890,1,94,0,2.007951," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","\frac{18019 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(31500 \, x^{4} - 81900 \, x^{3} - 259614 \, x^{2} - 199243 \, x - 47939\right)} \sqrt{-2 \, x + 1}}{11907 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/11907*(18019*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(31500*x^4 - 81900*x^3 - 259614*x^2 - 199243*x - 47939)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1891,1,105,0,1.687632," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","\frac{13243 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(196000 \, x^{4} + 661639 \, x^{3} + 788415 \, x^{2} + 401850 \, x + 74810\right)} \sqrt{-2 \, x + 1}}{24696 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/24696*(13243*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(196000*x^4 + 661639*x^3 + 788415*x^2 + 401850*x + 74810)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1892,1,114,0,1.654690," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","\frac{34730 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(4904370 \, x^{4} + 10375830 \, x^{3} + 7992771 \, x^{2} + 2619854 \, x + 300049\right)} \sqrt{-2 \, x + 1}}{972405 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/972405*(34730*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(4904370*x^4 + 10375830*x^3 + 7992771*x^2 + 2619854*x + 300049)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1893,1,129,0,0.804393," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7,x, algorithm=""fricas"")","\frac{76565 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(18605295 \, x^{5} - 46991565 \, x^{4} - 122053374 \, x^{3} - 75153042 \, x^{2} - 10947400 \, x + 1660816\right)} \sqrt{-2 \, x + 1}}{46675440 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/46675440*(76565*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(18605295*x^5 - 46991565*x^4 - 122053374*x^3 - 75153042*x^2 - 10947400*x + 1660816)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1894,1,144,0,0.902270," ","integrate((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^8,x, algorithm=""fricas"")","\frac{21845 \, \sqrt{21} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(15925005 \, x^{6} + 76086135 \, x^{5} - 42669876 \, x^{4} - 182748162 \, x^{3} - 98441652 \, x^{2} + 606784 \, x + 7033976\right)} \sqrt{-2 \, x + 1}}{127060920 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/127060920*(21845*sqrt(21)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(15925005*x^6 + 76086135*x^5 - 42669876*x^4 - 182748162*x^3 - 98441652*x^2 + 606784*x + 7033976)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1895,1,81,0,1.456364," ","integrate((1-2*x)^(3/2)*(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{11}{1953125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{1173046875} \, {\left(45608062500 \, x^{7} + 150857437500 \, x^{6} + 174123928125 \, x^{5} + 49094797500 \, x^{4} - 61883481375 \, x^{3} - 56176961670 \, x^{2} - 9645684935 \, x + 15379193944\right)} \sqrt{-2 \, x + 1}"," ",0,"11/1953125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/1173046875*(45608062500*x^7 + 150857437500*x^6 + 174123928125*x^5 + 49094797500*x^4 - 61883481375*x^3 - 56176961670*x^2 - 9645684935*x + 15379193944)*sqrt(-2*x + 1)","A",0
1896,1,76,0,1.527546," ","integrate((1-2*x)^(3/2)*(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{11}{390625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{234609375} \, {\left(3508312500 \, x^{6} + 9100350000 \, x^{5} + 6683000625 \, x^{4} - 1659418875 \, x^{3} - 4276774170 \, x^{2} - 1321809935 \, x + 1180568944\right)} \sqrt{-2 \, x + 1}"," ",0,"11/390625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/234609375*(3508312500*x^6 + 9100350000*x^5 + 6683000625*x^4 - 1659418875*x^3 - 4276774170*x^2 - 1321809935*x + 1180568944)*sqrt(-2*x + 1)","A",0
1897,1,71,0,1.255606," ","integrate((1-2*x)^(3/2)*(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{11}{78125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{3609375} \, {\left(21262500 \, x^{5} + 39532500 \, x^{4} + 9559125 \, x^{3} - 21433590 \, x^{2} - 12144995 \, x + 7095688\right)} \sqrt{-2 \, x + 1}"," ",0,"11/78125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/3609375*(21262500*x^5 + 39532500*x^4 + 9559125*x^3 - 21433590*x^2 - 12144995*x + 7095688)*sqrt(-2*x + 1)","A",0
1898,1,66,0,1.203791," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{11}{15625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{65625} \, {\left(157500 \, x^{4} + 171000 \, x^{3} - 83565 \, x^{2} - 123295 \, x + 50858\right)} \sqrt{-2 \, x + 1}"," ",0,"11/15625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/65625*(157500*x^4 + 171000*x^3 - 83565*x^2 - 123295*x + 50858)*sqrt(-2*x + 1)","A",0
1899,1,61,0,1.641101," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{11}{3125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{13125} \, {\left(13500 \, x^{3} + 3060 \, x^{2} - 13045 \, x + 3608\right)} \sqrt{-2 \, x + 1}"," ",0,"11/3125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/13125*(13500*x^3 + 3060*x^2 - 13045*x + 3608)*sqrt(-2*x + 1)","A",0
1900,1,56,0,1.609049," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{11}{625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{1}{375} \, {\left(180 \, x^{2} - 160 \, x - 31\right)} \sqrt{-2 \, x + 1}"," ",0,"11/625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 1/375*(180*x^2 - 160*x - 31)*sqrt(-2*x + 1)","A",0
1901,1,51,0,1.521144," ","integrate((1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{11}{125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - \frac{4}{75} \, {\left(5 \, x - 19\right)} \sqrt{-2 \, x + 1}"," ",0,"11/125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 4/75*(5*x - 19)*sqrt(-2*x + 1)","A",0
1902,1,83,0,1.595328," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{11}{25} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{7}{9} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - \frac{4}{15} \, \sqrt{-2 \, x + 1}"," ",0,"11/25*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 7/9*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 4/15*sqrt(-2*x + 1)","A",0
1903,1,102,0,0.788709," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{99 \, \sqrt{11} \sqrt{5} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 160 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 105 \, \sqrt{-2 \, x + 1}}{45 \, {\left(3 \, x + 2\right)}}"," ",0,"1/45*(99*sqrt(11)*sqrt(5)*(3*x + 2)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 160*sqrt(7)*sqrt(3)*(3*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 105*sqrt(-2*x + 1))/(3*x + 2)","A",0
1904,1,110,0,1.365046," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{1386 \, \sqrt{55} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 2243 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(195 \, x + 137\right)} \sqrt{-2 \, x + 1}}{126 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/126*(1386*sqrt(55)*(9*x^2 + 12*x + 4)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 2243*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(195*x + 137)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1905,1,130,0,1.351546," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{24255 \, \sqrt{55} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 39253 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(10242 \, x^{2} + 13999 \, x + 4797\right)} \sqrt{-2 \, x + 1}}{441 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/441*(24255*sqrt(55)*(27*x^3 + 54*x^2 + 36*x + 8)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 39253*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(10242*x^2 + 13999*x + 4797)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1906,1,150,0,1.695045," ","integrate((1-2*x)^(3/2)/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{6791400 \, \sqrt{55} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 10990843 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(8603361 \, x^{3} + 17494905 \, x^{2} + 11868230 \, x + 2686470\right)} \sqrt{-2 \, x + 1}}{24696 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/24696*(6791400*sqrt(55)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 10990843*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(8603361*x^3 + 17494905*x^2 + 11868230*x + 2686470)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1907,1,170,0,1.062439," ","integrate((1-2*x)^(3/2)/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{297123750 \, \sqrt{55} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 480849385 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1129191435 \, x^{4} + 3049001415 \, x^{3} + 3088510878 \, x^{2} + 1391064622 \, x + 235067382\right)} \sqrt{-2 \, x + 1}}{216090 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/216090*(297123750*sqrt(55)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 480849385*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1129191435*x^4 + 3049001415*x^3 + 3088510878*x^2 + 1391064622*x + 235067382)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1908,1,90,0,1.231188," ","integrate((1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","\frac{12474 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 5 \, {\left(106312500 \, x^{6} + 270112500 \, x^{5} + 181738125 \, x^{4} - 76760550 \, x^{3} - 135193430 \, x^{2} - 2532130 \, x + 23061496\right)} \sqrt{-2 \, x + 1}}{30078125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/30078125*(12474*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 5*(106312500*x^6 + 270112500*x^5 + 181738125*x^4 - 76760550*x^3 - 135193430*x^2 - 2532130*x + 23061496)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1909,1,85,0,1.425679," ","integrate((1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{903 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 5 \, {\left(787500 \, x^{5} + 1395000 \, x^{4} + 157275 \, x^{3} - 924335 \, x^{2} - 143235 \, x + 161312\right)} \sqrt{-2 \, x + 1}}{546875 \, {\left(5 \, x + 3\right)}}"," ",0,"1/546875*(903*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 5*(787500*x^5 + 1395000*x^4 + 157275*x^3 - 924335*x^2 - 143235*x + 161312)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1910,1,80,0,1.046514," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{672 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 5 \, {\left(67500 \, x^{4} + 62100 \, x^{3} - 57165 \, x^{2} - 27640 \, x + 8738\right)} \sqrt{-2 \, x + 1}}{109375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/109375*(672*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 5*(67500*x^4 + 62100*x^3 - 57165*x^2 - 27640*x + 8738)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1911,1,75,0,1.503799," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{63 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 5 \, {\left(900 \, x^{3} - 160 \, x^{2} - 935 \, x - 298\right)} \sqrt{-2 \, x + 1}}{3125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/3125*(63*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 5*(900*x^3 - 160*x^2 - 935*x - 298)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1912,1,70,0,1.585461," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{6 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 5 \, {\left(20 \, x^{2} - 60 \, x - 41\right)} \sqrt{-2 \, x + 1}}{125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/125*(6*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 5*(20*x^2 - 60*x - 41)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1913,1,66,0,1.774461," ","integrate((1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) - 5 \, {\left(20 \, x + 23\right)} \sqrt{-2 \, x + 1}}{125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/125*(3*sqrt(11)*sqrt(5)*(5*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) - 5*(20*x + 23)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1914,1,102,0,1.075949," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{108 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 175 \, \sqrt{7} \sqrt{3} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 165 \, \sqrt{-2 \, x + 1}}{75 \, {\left(5 \, x + 3\right)}}"," ",0,"1/75*(108*sqrt(11)*sqrt(5)*(5*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 175*sqrt(7)*sqrt(3)*(5*x + 3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 165*sqrt(-2*x + 1))/(5*x + 3)","A",0
1915,1,122,0,1.527257," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{207 \, \sqrt{11} \sqrt{5} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 335 \, \sqrt{7} \sqrt{3} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 15 \, {\left(68 \, x + 43\right)} \sqrt{-2 \, x + 1}}{15 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/15*(207*sqrt(11)*sqrt(5)*(15*x^2 + 19*x + 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 335*sqrt(7)*sqrt(3)*(15*x^2 + 19*x + 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 15*(68*x + 43)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
1916,1,136,0,1.721756," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{2311 \, \sqrt{7} \sqrt{3} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + 1428 \, \sqrt{55} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 7 \, {\left(3015 \, x^{2} + 3920 \, x + 1271\right)} \sqrt{-2 \, x + 1}}{14 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/14*(2311*sqrt(7)*sqrt(3)*(45*x^3 + 87*x^2 + 56*x + 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 1428*sqrt(55)*(45*x^3 + 87*x^2 + 56*x + 12)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 7*(3015*x^2 + 3920*x + 1271)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1917,1,150,0,1.586264," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{198450 \, \sqrt{55} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 321161 \, \sqrt{21} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(418995 \, x^{3} + 824092 \, x^{2} + 539819 \, x + 117752\right)} \sqrt{-2 \, x + 1}}{294 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/294*(198450*sqrt(55)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 321161*sqrt(21)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(418995*x^3 + 824092*x^2 + 539819*x + 117752)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1918,1,170,0,1.646631," ","integrate((1-2*x)^(3/2)/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","\frac{34574400 \, \sqrt{55} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55953383 \, \sqrt{21} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(218994705 \, x^{4} + 576721848 \, x^{3} + 569295605 \, x^{2} + 249642200 \, x + 41029970\right)} \sqrt{-2 \, x + 1}}{8232 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"1/8232*(34574400*sqrt(55)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55953383*sqrt(21)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(218994705*x^4 + 576721848*x^3 + 569295605*x^2 + 249642200*x + 41029970)*sqrt(-2*x + 1))/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
1919,1,89,0,1.578319," ","integrate((1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{85953 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(2025000 \, x^{5} + 3267000 \, x^{4} - 496350 \, x^{3} - 2120880 \, x^{2} - 489445 \, x + 96776\right)} \sqrt{-2 \, x + 1}}{12031250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/12031250*(85953*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(2025000*x^5 + 3267000*x^4 - 496350*x^3 - 2120880*x^2 - 489445*x + 96776)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1920,1,84,0,1.737619," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{5943 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(27000 \, x^{4} + 14400 \, x^{3} - 37530 \, x^{2} - 36295 \, x - 8644\right)} \sqrt{-2 \, x + 1}}{343750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/343750*(5943*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(27000*x^4 + 14400*x^3 - 37530*x^2 - 36295*x - 8644)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1921,1,79,0,1.653424," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{357 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(600 \, x^{3} - 1320 \, x^{2} - 2105 \, x - 656\right)} \sqrt{-2 \, x + 1}}{13750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/13750*(357*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(600*x^3 - 1320*x^2 - 2105*x - 656)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1922,1,75,0,1.687789," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{39 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(120 \, x^{2} + 205 \, x + 82\right)} \sqrt{-2 \, x + 1}}{2750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/2750*(39*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(120*x^2 + 205*x + 82)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1923,1,69,0,1.390727," ","integrate((1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(25 \, x + 4\right)} \sqrt{-2 \, x + 1}}{2750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/2750*(3*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(25*x + 4)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1924,1,110,0,1.319663," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2379 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 3850 \, \sqrt{21} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 55 \, {\left(355 \, x + 202\right)} \sqrt{-2 \, x + 1}}{550 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/550*(2379*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 3850*sqrt(21)*(25*x^2 + 30*x + 9)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 55*(355*x + 202)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1925,1,130,0,1.523994," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{6933 \, \sqrt{55} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 11220 \, \sqrt{21} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 55 \, {\left(3105 \, x^{2} + 3830 \, x + 1178\right)} \sqrt{-2 \, x + 1}}{110 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/110*(6933*sqrt(55)*(75*x^3 + 140*x^2 + 87*x + 18)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 11220*sqrt(21)*(75*x^3 + 140*x^2 + 87*x + 18)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 55*(3105*x^2 + 3830*x + 1178)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1926,1,162,0,1.330547," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{95655 \, \sqrt{11} \sqrt{5} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 154803 \, \sqrt{7} \sqrt{3} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(91800 \, x^{3} + 174435 \, x^{2} + 110315 \, x + 23219\right)} \sqrt{-2 \, x + 1}}{154 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/154*(95655*sqrt(11)*sqrt(5)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 154803*sqrt(7)*sqrt(3)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(91800*x^3 + 174435*x^2 + 110315*x + 23219)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1927,1,182,0,1.417435," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{5530875 \, \sqrt{11} \sqrt{5} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 8950876 \, \sqrt{7} \sqrt{3} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(15923925 \, x^{4} + 40874010 \, x^{3} + 39307638 \, x^{2} + 16784696 \, x + 2685098\right)} \sqrt{-2 \, x + 1}}{1078 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/1078*(5530875*sqrt(11)*sqrt(5)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 8950876*sqrt(7)*sqrt(3)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(15923925*x^4 + 40874010*x^3 + 39307638*x^2 + 16784696*x + 2685098)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
1928,1,59,0,1.473262," ","integrate((1-2*x)^(5/2)*(2+3*x)^6*(3+5*x),x, algorithm=""fricas"")","\frac{1}{2909907} \, {\left(4040613720 \, x^{10} + 15971057388 \, x^{9} + 23013359226 \, x^{8} + 10299128697 \, x^{7} - 8457459318 \, x^{6} - 11546145324 \, x^{5} - 3037739768 \, x^{4} + 2155110064 \, x^{3} + 1656222432 \, x^{2} + 235056064 \, x - 323646080\right)} \sqrt{-2 \, x + 1}"," ",0,"1/2909907*(4040613720*x^10 + 15971057388*x^9 + 23013359226*x^8 + 10299128697*x^7 - 8457459318*x^6 - 11546145324*x^5 - 3037739768*x^4 + 2155110064*x^3 + 1656222432*x^2 + 235056064*x - 323646080)*sqrt(-2*x + 1)","A",0
1929,1,54,0,0.795211," ","integrate((1-2*x)^(5/2)*(2+3*x)^5*(3+5*x),x, algorithm=""fricas"")","\frac{1}{415701} \, {\left(212663880 \, x^{9} + 690949116 \, x^{8} + 717196194 \, x^{7} + 9461529 \, x^{6} - 486084375 \, x^{5} - 273280105 \, x^{4} + 53353244 \, x^{3} + 95863620 \, x^{2} + 21784712 \, x - 18122584\right)} \sqrt{-2 \, x + 1}"," ",0,"1/415701*(212663880*x^9 + 690949116*x^8 + 717196194*x^7 + 9461529*x^6 - 486084375*x^5 - 273280105*x^4 + 53353244*x^3 + 95863620*x^2 + 21784712*x - 18122584)*sqrt(-2*x + 1)","A",0
1930,1,49,0,1.275968," ","integrate((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x),x, algorithm=""fricas"")","\frac{1}{109395} \, {\left(20849400 \, x^{8} + 52864812 \, x^{7} + 31646538 \, x^{6} - 24298407 \, x^{5} - 32302900 \, x^{4} - 2705920 \, x^{3} + 9403464 \, x^{2} + 3351776 \, x - 1899184\right)} \sqrt{-2 \, x + 1}"," ",0,"1/109395*(20849400*x^8 + 52864812*x^7 + 31646538*x^6 - 24298407*x^5 - 32302900*x^4 - 2705920*x^3 + 9403464*x^2 + 3351776*x - 1899184)*sqrt(-2*x + 1)","A",0
1931,1,44,0,1.437991," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x),x, algorithm=""fricas"")","\frac{1}{1287} \, {\left(92664 \, x^{7} + 167508 \, x^{6} + 13446 \, x^{5} - 128237 \, x^{4} - 51767 \, x^{3} + 35349 \, x^{2} + 21850 \, x - 9038\right)} \sqrt{-2 \, x + 1}"," ",0,"1/1287*(92664*x^7 + 167508*x^6 + 13446*x^5 - 128237*x^4 - 51767*x^3 + 35349*x^2 + 21850*x - 9038)*sqrt(-2*x + 1)","A",0
1932,1,39,0,1.059752," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x),x, algorithm=""fricas"")","\frac{1}{1287} \, {\left(35640 \, x^{6} + 37692 \, x^{5} - 25678 \, x^{4} - 32875 \, x^{3} + 7302 \, x^{2} + 11732 \, x - 3712\right)} \sqrt{-2 \, x + 1}"," ",0,"1/1287*(35640*x^6 + 37692*x^5 - 25678*x^4 - 32875*x^3 + 7302*x^2 + 11732*x - 3712)*sqrt(-2*x + 1)","A",0
1933,1,34,0,1.723348," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x),x, algorithm=""fricas"")","\frac{1}{99} \, {\left(1080 \, x^{5} + 292 \, x^{4} - 1106 \, x^{3} - 129 \, x^{2} + 475 \, x - 119\right)} \sqrt{-2 \, x + 1}"," ",0,"1/99*(1080*x^5 + 292*x^4 - 1106*x^3 - 129*x^2 + 475*x - 119)*sqrt(-2*x + 1)","A",0
1934,1,29,0,1.531788," ","integrate((1-2*x)^(5/2)*(3+5*x),x, algorithm=""fricas"")","\frac{1}{63} \, {\left(280 \, x^{4} - 164 \, x^{3} - 174 \, x^{2} + 157 \, x - 32\right)} \sqrt{-2 \, x + 1}"," ",0,"1/63*(280*x^4 - 164*x^3 - 174*x^2 + 157*x - 32)*sqrt(-2*x + 1)","A",0
1935,1,62,0,1.674806," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x),x, algorithm=""fricas"")","\frac{49}{243} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + \frac{1}{2835} \, {\left(5400 \, x^{3} - 8604 \, x^{2} + 5534 \, x - 4721\right)} \sqrt{-2 \, x + 1}"," ",0,"49/243*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 1/2835*(5400*x^3 - 8604*x^2 + 5534*x - 4721)*sqrt(-2*x + 1)","A",0
1936,1,75,0,1.469011," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{280 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + 3 \, {\left(216 \, x^{3} - 516 \, x^{2} + 1474 \, x + 1325\right)} \sqrt{-2 \, x + 1}}{243 \, {\left(3 \, x + 2\right)}}"," ",0,"1/243*(280*sqrt(7)*sqrt(3)*(3*x + 2)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 3*(216*x^3 - 516*x^2 + 1474*x + 1325)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1937,1,86,0,1.634848," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{365 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 3 \, {\left(720 \, x^{3} - 4584 \, x^{2} - 8731 \, x - 3521\right)} \sqrt{-2 \, x + 1}}{486 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/486*(365*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 3*(720*x^3 - 4584*x^2 - 8731*x - 3521)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1938,1,89,0,0.729931," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{265 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1080 \, x^{3} + 3627 \, x^{2} + 2983 \, x + 713\right)} \sqrt{-2 \, x + 1}}{1701 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/1701*(265*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1080*x^3 + 3627*x^2 + 2983*x + 713)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1939,1,100,0,1.458303," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{695 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(41715 \, x^{3} + 43971 \, x^{2} + 18394 \, x + 4394\right)} \sqrt{-2 \, x + 1}}{95256 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/95256*(695*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(41715*x^3 + 43971*x^2 + 18394*x + 4394)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1940,1,115,0,1.377661," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{215 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(17415 \, x^{4} - 116415 \, x^{3} - 53772 \, x^{2} + 3322 \, x - 7018\right)} \sqrt{-2 \, x + 1}}{833490 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/833490*(215*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(17415*x^4 - 116415*x^3 - 53772*x^2 + 3322*x - 7018)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1941,1,130,0,1.286232," ","integrate((1-2*x)^(5/2)*(3+5*x)/(2+3*x)^7,x, algorithm=""fricas"")","\frac{205 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(49815 \, x^{5} + 204795 \, x^{4} - 824526 \, x^{3} - 176850 \, x^{2} + 154312 \, x - 51904\right)} \sqrt{-2 \, x + 1}}{9335088 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/9335088*(205*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(49815*x^5 + 204795*x^4 - 824526*x^3 - 176850*x^2 + 154312*x - 51904)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1942,1,54,0,1.285436," ","integrate((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^2,x, algorithm=""fricas"")","\frac{1}{2078505} \, {\left(1772199000 \, x^{9} + 5625863100 \, x^{8} + 5641824474 \, x^{7} - 121581999 \, x^{6} - 3896813214 \, x^{5} - 2072749175 \, x^{4} + 461747860 \, x^{3} + 739308228 \, x^{2} + 160311352 \, x - 138993368\right)} \sqrt{-2 \, x + 1}"," ",0,"1/2078505*(1772199000*x^9 + 5625863100*x^8 + 5641824474*x^7 - 121581999*x^6 - 3896813214*x^5 - 2072749175*x^4 + 461747860*x^3 + 739308228*x^2 + 160311352*x - 138993368)*sqrt(-2*x + 1)","A",0
1943,1,49,0,1.401067," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2,x, algorithm=""fricas"")","\frac{1}{21879} \, {\left(6949800 \, x^{8} + 17096508 \, x^{7} + 9599634 \, x^{6} - 8175663 \, x^{5} - 10040957 \, x^{4} - 608627 \, x^{3} + 2934177 \, x^{2} + 993442 \, x - 581846\right)} \sqrt{-2 \, x + 1}"," ",0,"1/21879*(6949800*x^8 + 17096508*x^7 + 9599634*x^6 - 8175663*x^5 - 10040957*x^4 - 608627*x^3 + 2934177*x^2 + 993442*x - 581846)*sqrt(-2*x + 1)","A",0
1944,1,44,0,0.864919," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2,x, algorithm=""fricas"")","\frac{1}{1287} \, {\left(154440 \, x^{7} + 267300 \, x^{6} + 9846 \, x^{5} - 205169 \, x^{4} - 75320 \, x^{3} + 56481 \, x^{2} + 32506 \, x - 13826\right)} \sqrt{-2 \, x + 1}"," ",0,"1/1287*(154440*x^7 + 267300*x^6 + 9846*x^5 - 205169*x^4 - 75320*x^3 + 56481*x^2 + 32506*x - 13826)*sqrt(-2*x + 1)","A",0
1945,1,39,0,1.651222," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2,x, algorithm=""fricas"")","\frac{1}{1287} \, {\left(59400 \, x^{6} + 58140 \, x^{5} - 44062 \, x^{4} - 49999 \, x^{3} + 12729 \, x^{2} + 17495 \, x - 5671\right)} \sqrt{-2 \, x + 1}"," ",0,"1/1287*(59400*x^6 + 58140*x^5 - 44062*x^4 - 49999*x^3 + 12729*x^2 + 17495*x - 5671)*sqrt(-2*x + 1)","A",0
1946,1,34,0,1.500988," ","integrate((1-2*x)^(5/2)*(3+5*x)^2,x, algorithm=""fricas"")","\frac{1}{693} \, {\left(12600 \, x^{5} + 2380 \, x^{4} - 12302 \, x^{3} - 867 \, x^{2} + 4966 \, x - 1271\right)} \sqrt{-2 \, x + 1}"," ",0,"1/693*(12600*x^5 + 2380*x^4 - 12302*x^3 - 867*x^2 + 4966*x - 1271)*sqrt(-2*x + 1)","A",0
1947,1,66,0,1.644298," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x),x, algorithm=""fricas"")","\frac{49}{729} \, \sqrt{7} \sqrt{3} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + \frac{1}{8505} \, {\left(63000 \, x^{4} - 42300 \, x^{3} - 30546 \, x^{2} + 29791 \, x - 2479\right)} \sqrt{-2 \, x + 1}"," ",0,"49/729*sqrt(7)*sqrt(3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 1/8505*(63000*x^4 - 42300*x^3 - 30546*x^2 + 29791*x - 2479)*sqrt(-2*x + 1)","A",0
1948,1,81,0,1.419278," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^2,x, algorithm=""fricas"")","\frac{1225 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 3 \, {\left(5400 \, x^{4} - 5508 \, x^{3} + 1002 \, x^{2} - 4471 \, x - 6239\right)} \sqrt{-2 \, x + 1}}{1701 \, {\left(3 \, x + 2\right)}}"," ",0,"1/1701*(1225*sqrt(7)*sqrt(3)*(3*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 3*(5400*x^4 - 5508*x^3 + 1002*x^2 - 4471*x - 6239)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1949,1,90,0,0.915324," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^3,x, algorithm=""fricas"")","\frac{1055 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + 3 \, {\left(2160 \, x^{4} - 3960 \, x^{3} + 12828 \, x^{2} + 25987 \, x + 10007\right)} \sqrt{-2 \, x + 1}}{486 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/486*(1055*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 3*(2160*x^4 - 3960*x^3 + 12828*x^2 + 25987*x + 10007)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1950,1,95,0,1.372708," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^4,x, algorithm=""fricas"")","\frac{4435 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(3600 \, x^{4} - 21240 \, x^{3} - 61353 \, x^{2} - 48697 \, x - 12212\right)} \sqrt{-2 \, x + 1}}{3402 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/3402*(4435*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(3600*x^4 - 21240*x^3 - 61353*x^2 - 48697*x - 12212)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1951,1,104,0,1.584367," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^5,x, algorithm=""fricas"")","\frac{24965 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(302400 \, x^{4} + 1231065 \, x^{3} + 1526937 \, x^{2} + 762598 \, x + 134558\right)} \sqrt{-2 \, x + 1}}{95256 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/95256*(24965*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(302400*x^4 + 1231065*x^3 + 1526937*x^2 + 762598*x + 134558)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1952,1,115,0,1.420427," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^6,x, algorithm=""fricas"")","\frac{40255 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(7323345 \, x^{4} + 12406455 \, x^{3} + 8277204 \, x^{2} + 2919346 \, x + 503276\right)} \sqrt{-2 \, x + 1}}{3333960 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/3333960*(40255*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(7323345*x^4 + 12406455*x^3 + 8277204*x^2 + 2919346*x + 503276)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1953,1,130,0,1.537246," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^7,x, algorithm=""fricas"")","\frac{1315 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(319545 \, x^{5} - 1979115 \, x^{4} - 2360850 \, x^{3} - 587502 \, x^{2} - 106808 \, x - 81568\right)} \sqrt{-2 \, x + 1}}{3111696 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/3111696*(1315*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(319545*x^5 - 1979115*x^4 - 2360850*x^3 - 587502*x^2 - 106808*x - 81568)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1954,1,145,0,1.256907," ","integrate((1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^8,x, algorithm=""fricas"")","\frac{2335 \, \sqrt{21} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1702215 \, x^{6} + 8132805 \, x^{5} - 24492348 \, x^{4} - 23950566 \, x^{3} + 1405308 \, x^{2} + 1415408 \, x - 1107536\right)} \sqrt{-2 \, x + 1}}{65345616 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/65345616*(2335*sqrt(21)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1702215*x^6 + 8132805*x^5 - 24492348*x^4 - 23950566*x^3 + 1405308*x^2 + 1415408*x - 1107536)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1955,1,59,0,1.264683," ","integrate((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1}{440895} \, {\left(1700595000 \, x^{10} + 6471211500 \, x^{9} + 8880844050 \, x^{8} + 3513142893 \, x^{7} - 3556515018 \, x^{6} - 4297543173 \, x^{5} - 970928350 \, x^{4} + 842946920 \, x^{3} + 588303696 \, x^{2} + 74758064 \, x - 115708576\right)} \sqrt{-2 \, x + 1}"," ",0,"1/440895*(1700595000*x^10 + 6471211500*x^9 + 8880844050*x^8 + 3513142893*x^7 - 3556515018*x^6 - 4297543173*x^5 - 970928350*x^4 + 842946920*x^3 + 588303696*x^2 + 74758064*x - 115708576)*sqrt(-2*x + 1)","A",0
1956,1,54,0,1.289491," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1}{741} \, {\left(1053000 \, x^{9} + 3264300 \, x^{8} + 3159234 \, x^{7} - 180615 \, x^{6} - 2223099 \, x^{5} - 1118224 \, x^{4} + 281231 \, x^{3} + 406155 \, x^{2} + 84038 \, x - 76018\right)} \sqrt{-2 \, x + 1}"," ",0,"1/741*(1053000*x^9 + 3264300*x^8 + 3159234*x^7 - 180615*x^6 - 2223099*x^5 - 1118224*x^4 + 281231*x^3 + 406155*x^2 + 84038*x - 76018)*sqrt(-2*x + 1)","A",0
1957,1,49,0,1.527941," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1}{221} \, {\left(117000 \, x^{8} + 278980 \, x^{7} + 146310 \, x^{6} - 138201 \, x^{5} - 157296 \, x^{4} - 5935 \, x^{3} + 46164 \, x^{2} + 14864 \, x - 9004\right)} \sqrt{-2 \, x + 1}"," ",0,"1/221*(117000*x^8 + 278980*x^7 + 146310*x^6 - 138201*x^5 - 157296*x^4 - 5935*x^3 + 46164*x^2 + 14864*x - 9004)*sqrt(-2*x + 1)","A",0
1958,1,44,0,0.965549," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1}{39} \, {\left(7800 \, x^{7} + 12900 \, x^{6} - 90 \, x^{5} - 9917 \, x^{4} - 3299 \, x^{3} + 2724 \, x^{2} + 1465 \, x - 641\right)} \sqrt{-2 \, x + 1}"," ",0,"1/39*(7800*x^7 + 12900*x^6 - 90*x^5 - 9917*x^4 - 3299*x^3 + 2724*x^2 + 1465*x - 641)*sqrt(-2*x + 1)","A",0
1959,1,39,0,1.484693," ","integrate((1-2*x)^(5/2)*(3+5*x)^3,x, algorithm=""fricas"")","\frac{1}{273} \, {\left(21000 \, x^{6} + 18900 \, x^{5} - 15890 \, x^{4} - 16061 \, x^{3} + 4614 \, x^{2} + 5533 \, x - 1838\right)} \sqrt{-2 \, x + 1}"," ",0,"1/273*(21000*x^6 + 18900*x^5 - 15890*x^4 - 16061*x^3 + 4614*x^2 + 5533*x - 1838)*sqrt(-2*x + 1)","A",0
1960,1,72,0,1.369785," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x),x, algorithm=""fricas"")","\frac{49}{2187} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + \frac{1}{280665} \, {\left(8505000 \, x^{5} + 913500 \, x^{4} - 7838550 \, x^{3} - 249219 \, x^{2} + 3024349 \, x - 830656\right)} \sqrt{-2 \, x + 1}"," ",0,"49/2187*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 1/280665*(8505000*x^5 + 913500*x^4 - 7838550*x^3 - 249219*x^2 + 3024349*x - 830656)*sqrt(-2*x + 1)","A",0
1961,1,85,0,1.245575," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2,x, algorithm=""fricas"")","\frac{5390 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + 3 \, {\left(189000 \, x^{5} - 17100 \, x^{4} - 159714 \, x^{3} + 25275 \, x^{2} + 65558 \, x + 13759\right)} \sqrt{-2 \, x + 1}}{15309 \, {\left(3 \, x + 2\right)}}"," ",0,"1/15309*(5390*sqrt(7)*sqrt(3)*(3*x + 2)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 3*(189000*x^5 - 17100*x^4 - 159714*x^3 + 25275*x^2 + 65558*x + 13759)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1962,1,96,0,1.263311," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3,x, algorithm=""fricas"")","\frac{6545 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 3 \, {\left(54000 \, x^{5} - 24120 \, x^{4} - 17460 \, x^{3} - 67962 \, x^{2} - 152833 \, x - 64943\right)} \sqrt{-2 \, x + 1}}{3402 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/3402*(6545*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 3*(54000*x^5 - 24120*x^4 - 17460*x^3 - 67962*x^2 - 152833*x - 64943)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1963,1,99,0,1.218970," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4,x, algorithm=""fricas"")","\frac{20680 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(16200 \, x^{5} - 20700 \, x^{4} + 87030 \, x^{3} + 289719 \, x^{2} + 229336 \, x + 56141\right)} \sqrt{-2 \, x + 1}}{5103 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/5103*(20680*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(16200*x^5 - 20700*x^4 + 87030*x^3 + 289719*x^2 + 229336*x + 56141)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1964,1,110,0,1.631100," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5,x, algorithm=""fricas"")","\frac{645865 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(1512000 \, x^{5} - 8215200 \, x^{4} - 32946525 \, x^{3} - 39158517 \, x^{2} - 19526798 \, x - 3553918\right)} \sqrt{-2 \, x + 1}}{285768 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/285768*(645865*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(1512000*x^5 - 8215200*x^4 - 32946525*x^3 - 39158517*x^2 - 19526798*x - 3553918)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1965,1,119,0,1.313161," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6,x, algorithm=""fricas"")","\frac{734855 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(26460000 \, x^{5} + 126578745 \, x^{4} + 207486855 \, x^{3} + 157178184 \, x^{2} + 56745266 \, x + 7933096\right)} \sqrt{-2 \, x + 1}}{1666980 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/1666980*(734855*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(26460000*x^5 + 126578745*x^4 + 207486855*x^3 + 157178184*x^2 + 56745266*x + 7933096)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1966,1,130,0,1.410821," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7,x, algorithm=""fricas"")","\frac{559625 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(308539125 \, x^{5} + 720187425 \, x^{4} + 687940758 \, x^{3} + 352611738 \, x^{2} + 102558856 \, x + 13847024\right)} \sqrt{-2 \, x + 1}}{28005264 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/28005264*(559625*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(308539125*x^5 + 720187425*x^4 + 687940758*x^3 + 352611738*x^2 + 102558856*x + 13847024)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1967,1,145,0,1.276940," ","integrate((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^8,x, algorithm=""fricas"")","\frac{33935 \, \sqrt{21} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(24738615 \, x^{6} - 141112395 \, x^{5} - 283697388 \, x^{4} - 164222766 \, x^{3} - 39606312 \, x^{2} - 12384752 \, x - 4005436\right)} \sqrt{-2 \, x + 1}}{49009212 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"1/49009212*(33935*sqrt(21)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(24738615*x^6 - 141112395*x^5 - 283697388*x^4 - 164222766*x^3 - 39606312*x^2 - 12384752*x - 4005436)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
1968,1,76,0,1.527541," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{121}{390625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{234609375} \, {\left(2338875000 \, x^{6} + 2842087500 \, x^{5} - 1540428750 \, x^{4} - 2556079875 \, x^{3} + 399578370 \, x^{2} + 960784285 \, x - 289133384\right)} \sqrt{-2 \, x + 1}"," ",0,"121/390625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/234609375*(2338875000*x^6 + 2842087500*x^5 - 1540428750*x^4 - 2556079875*x^3 + 399578370*x^2 + 960784285*x - 289133384)*sqrt(-2*x + 1)","A",0
1969,1,71,0,0.997697," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{121}{78125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{3609375} \, {\left(14175000 \, x^{5} + 6142500 \, x^{4} - 15572250 \, x^{3} - 3564885 \, x^{2} + 7726195 \, x - 1796318\right)} \sqrt{-2 \, x + 1}"," ",0,"121/78125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/3609375*(14175000*x^5 + 6142500*x^4 - 15572250*x^3 - 3564885*x^2 + 7726195*x - 1796318)*sqrt(-2*x + 1)","A",0
1970,1,66,0,1.327934," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{121}{15625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{65625} \, {\left(105000 \, x^{4} - 43500 \, x^{3} - 91410 \, x^{2} + 69995 \, x - 8188\right)} \sqrt{-2 \, x + 1}"," ",0,"121/15625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/65625*(105000*x^4 - 43500*x^3 - 91410*x^2 + 69995*x - 8188)*sqrt(-2*x + 1)","A",0
1971,1,61,0,1.641201," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{121}{3125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{13125} \, {\left(9000 \, x^{3} - 12660 \, x^{2} + 4370 \, x + 4937\right)} \sqrt{-2 \, x + 1}"," ",0,"121/3125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/13125*(9000*x^3 - 12660*x^2 + 4370*x + 4937)*sqrt(-2*x + 1)","A",0
1972,1,56,0,0.816943," ","integrate((1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{121}{625} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{2}{375} \, {\left(60 \, x^{2} - 170 \, x + 433\right)} \sqrt{-2 \, x + 1}"," ",0,"121/625*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 2/375*(60*x^2 - 170*x + 433)*sqrt(-2*x + 1)","A",0
1973,1,88,0,0.838316," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{121}{125} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{49}{27} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + \frac{4}{225} \, {\left(10 \, x - 73\right)} \sqrt{-2 \, x + 1}"," ",0,"121/125*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 49/27*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 4/225*(10*x - 73)*sqrt(-2*x + 1)","A",0
1974,1,107,0,1.401379," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{1089 \, \sqrt{11} \sqrt{5} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 1750 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 15 \, {\left(8 \, x + 87\right)} \sqrt{-2 \, x + 1}}{225 \, {\left(3 \, x + 2\right)}}"," ",0,"1/225*(1089*sqrt(11)*sqrt(5)*(3*x + 2)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1750*sqrt(7)*sqrt(3)*(3*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 15*(8*x + 87)*sqrt(-2*x + 1))/(3*x + 2)","A",0
1975,1,122,0,1.513635," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{726 \, \sqrt{11} \sqrt{5} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 1175 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 35 \, {\left(61 \, x + 43\right)} \sqrt{-2 \, x + 1}}{30 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/30*(726*sqrt(11)*sqrt(5)*(9*x^2 + 12*x + 4)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1175*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 35*(61*x + 43)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
1976,1,130,0,1.438140," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{22869 \, \sqrt{55} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 37010 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(9657 \, x^{2} + 13198 \, x + 4523\right)} \sqrt{-2 \, x + 1}}{189 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/189*(22869*sqrt(55)*(27*x^3 + 54*x^2 + 36*x + 8)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 37010*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(9657*x^2 + 13198*x + 4523)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
1977,1,150,0,2.410255," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x),x, algorithm=""fricas"")","\frac{2134440 \, \sqrt{55} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 3454265 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(2703915 \, x^{3} + 5498403 \, x^{2} + 3730002 \, x + 844322\right)} \sqrt{-2 \, x + 1}}{3528 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/3528*(2134440*sqrt(55)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 3454265*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(2703915*x^3 + 5498403*x^2 + 3730002*x + 844322)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
1978,1,170,0,1.544183," ","integrate((1-2*x)^(5/2)/(2+3*x)^6/(3+5*x),x, algorithm=""fricas"")","\frac{62254500 \, \sqrt{55} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 100749395 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 7 \, {\left(709777485 \, x^{4} + 1916515215 \, x^{3} + 1941349752 \, x^{2} + 874383298 \, x + 147756688\right)} \sqrt{-2 \, x + 1}}{20580 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/20580*(62254500*sqrt(55)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 100749395*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 7*(709777485*x^4 + 1916515215*x^3 + 1941349752*x^2 + 874383298*x + 147756688)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
1979,1,190,0,1.201283," ","integrate((1-2*x)^(5/2)/(2+3*x)^7/(3+5*x),x, algorithm=""fricas"")","\frac{15688134000 \, \sqrt{55} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 25388847535 \, \sqrt{21} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(178863925005 \, x^{5} + 602204446665 \, x^{4} + 811194684822 \, x^{3} + 546491397114 \, x^{2} + 184131053992 \, x + 24823128464\right)} \sqrt{-2 \, x + 1}}{1037232 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"1/1037232*(15688134000*sqrt(55)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 25388847535*sqrt(21)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(178863925005*x^5 + 602204446665*x^4 + 811194684822*x^3 + 546491397114*x^2 + 184131053992*x + 24823128464)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
1980,1,90,0,1.649740," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{322707 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(212625000 \, x^{6} + 237037500 \, x^{5} - 173598750 \, x^{4} - 214071975 \, x^{3} + 85482115 \, x^{2} + 50081215 \, x - 15982128\right)} \sqrt{-2 \, x + 1}}{90234375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/90234375*(322707*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(212625000*x^6 + 237037500*x^5 - 173598750*x^4 - 214071975*x^3 + 85482115*x^2 + 50081215*x - 15982128)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1981,1,85,0,0.809023," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{21714 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(1575000 \, x^{5} + 427500 \, x^{4} - 1858950 \, x^{3} + 152105 \, x^{2} + 680930 \, x + 16794\right)} \sqrt{-2 \, x + 1}}{1640625 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1640625*(21714*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(1575000*x^5 + 427500*x^4 - 1858950*x^3 + 152105*x^2 + 680930*x + 16794)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1982,1,80,0,1.582560," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{14091 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(135000 \, x^{4} - 96300 \, x^{3} - 75130 \, x^{2} + 173795 \, x + 90486\right)} \sqrt{-2 \, x + 1}}{328125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/328125*(14091*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(135000*x^4 - 96300*x^3 - 75130*x^2 + 173795*x + 90486)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1983,1,75,0,1.288430," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{924 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(1800 \, x^{3} - 3820 \, x^{2} + 8630 \, x + 6579\right)} \sqrt{-2 \, x + 1}}{9375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/9375*(924*sqrt(11)*sqrt(5)*(5*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(1800*x^3 - 3820*x^2 + 8630*x + 6579)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1984,1,71,0,1.276816," ","integrate((1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{33 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 5 \, {\left(40 \, x^{2} - 260 \, x - 243\right)} \sqrt{-2 \, x + 1}}{375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/375*(33*sqrt(11)*sqrt(5)*(5*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 5*(40*x^2 - 260*x - 243)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1985,1,107,0,1.468436," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{3762 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 6125 \, \sqrt{7} \sqrt{3} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) + 15 \, {\left(40 \, x - 339\right)} \sqrt{-2 \, x + 1}}{1125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1125*(3762*sqrt(11)*sqrt(5)*(5*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 6125*sqrt(7)*sqrt(3)*(5*x + 3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) + 15*(40*x - 339)*sqrt(-2*x + 1))/(5*x + 3)","A",0
1986,1,122,0,1.573904," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{7029 \, \sqrt{11} \sqrt{5} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 11375 \, \sqrt{7} \sqrt{3} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 15 \, {\left(2314 \, x + 1461\right)} \sqrt{-2 \, x + 1}}{225 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/225*(7029*sqrt(11)*sqrt(5)*(15*x^2 + 19*x + 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 11375*sqrt(7)*sqrt(3)*(15*x^2 + 19*x + 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 15*(2314*x + 1461)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
1987,1,142,0,0.934312," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{20592 \, \sqrt{11} \sqrt{5} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 33325 \, \sqrt{7} \sqrt{3} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 15 \, {\left(20289 \, x^{2} + 26380 \, x + 8553\right)} \sqrt{-2 \, x + 1}}{90 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/90*(20592*sqrt(11)*sqrt(5)*(45*x^3 + 87*x^2 + 56*x + 12)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 33325*sqrt(7)*sqrt(3)*(45*x^3 + 87*x^2 + 56*x + 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 15*(20289*x^2 + 26380*x + 8553)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
1988,1,150,0,1.074889," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^2,x, algorithm=""fricas"")","\frac{189882 \, \sqrt{55} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 307295 \, \sqrt{21} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(400905 \, x^{3} + 788512 \, x^{2} + 516513 \, x + 112668\right)} \sqrt{-2 \, x + 1}}{126 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/126*(189882*sqrt(55)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 307295*sqrt(21)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(400905*x^3 + 788512*x^2 + 516513*x + 112668)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
1989,1,170,0,1.918868," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^2,x, algorithm=""fricas"")","\frac{32986800 \, \sqrt{55} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 53384095 \, \sqrt{21} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(208938825 \, x^{4} + 550239720 \, x^{3} + 543154477 \, x^{2} + 238179048 \, x + 39145938\right)} \sqrt{-2 \, x + 1}}{3528 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"1/3528*(32986800*sqrt(55)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 53384095*sqrt(21)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(208938825*x^4 + 550239720*x^3 + 543154477*x^2 + 238179048*x + 39145938)*sqrt(-2*x + 1))/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
1990,1,190,0,1.523129," ","integrate((1-2*x)^(5/2)/(2+3*x)^6/(3+5*x)^2,x, algorithm=""fricas"")","\frac{6893271000 \, \sqrt{55} {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 11155705735 \, \sqrt{21} {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(130986207675 \, x^{5} + 432275892930 \, x^{4} + 570477768855 \, x^{3} + 376323861626 \, x^{2} + 124085884254 \, x + 16360698684\right)} \sqrt{-2 \, x + 1}}{123480 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"1/123480*(6893271000*sqrt(55)*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log((5*x - sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 11155705735*sqrt(21)*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(130986207675*x^5 + 432275892930*x^4 + 570477768855*x^3 + 376323861626*x^2 + 124085884254*x + 16360698684)*sqrt(-2*x + 1))/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","A",0
1991,1,100,0,1.764450," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{82341 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(15750000 \, x^{6} + 15075000 \, x^{5} - 16051500 \, x^{4} - 11139550 \, x^{3} + 9372960 \, x^{2} + 6891315 \, x + 871208\right)} \sqrt{-2 \, x + 1}}{5468750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/5468750*(82341*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(15750000*x^6 + 15075000*x^5 - 16051500*x^4 - 11139550*x^3 + 9372960*x^2 + 6891315*x + 871208)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1992,1,95,0,1.416716," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{38913 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(1350000 \, x^{5} - 27000 \, x^{4} - 1506900 \, x^{3} + 1651030 \, x^{2} + 2637795 \, x + 770444\right)} \sqrt{-2 \, x + 1}}{1093750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1093750*(38913*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(1350000*x^5 - 27000*x^4 - 1506900*x^3 + 1651030*x^2 + 2637795*x + 770444)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1993,1,90,0,1.351082," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1533 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(18000 \, x^{4} - 25400 \, x^{3} + 51980 \, x^{2} + 98595 \, x + 32504\right)} \sqrt{-2 \, x + 1}}{31250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/31250*(1533*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(18000*x^4 - 25400*x^3 + 51980*x^2 + 98595*x + 32504)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1994,1,86,0,1.531105," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{63 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 5 \, {\left(400 \, x^{3} - 2280 \, x^{2} - 3795 \, x - 1394\right)} \sqrt{-2 \, x + 1}}{1250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1250*(63*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 5*(400*x^3 - 2280*x^2 - 3795*x - 1394)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1995,1,80,0,1.527253," ","integrate((1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 5 \, {\left(80 \, x^{2} + 195 \, x + 64\right)} \sqrt{-2 \, x + 1}}{250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/250*(3*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 5*(80*x^2 + 195*x + 64)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1996,1,122,0,1.676221," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{7569 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 12250 \, \sqrt{7} \sqrt{3} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 165 \, {\left(375 \, x + 214\right)} \sqrt{-2 \, x + 1}}{750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/750*(7569*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 12250*sqrt(7)*sqrt(3)*(25*x^2 + 30*x + 9)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 165*(375*x + 214)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
1997,1,142,0,1.416827," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{21627 \, \sqrt{11} \sqrt{5} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 35000 \, \sqrt{7} \sqrt{3} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 15 \, {\left(35515 \, x^{2} + 43806 \, x + 13474\right)} \sqrt{-2 \, x + 1}}{150 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/150*(21627*sqrt(11)*sqrt(5)*(75*x^3 + 140*x^2 + 87*x + 18)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 35000*sqrt(7)*sqrt(3)*(75*x^3 + 140*x^2 + 87*x + 18)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 15*(35515*x^2 + 43806*x + 13474)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
1998,1,156,0,1.021417," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{14073 \, \sqrt{11} \sqrt{5} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 22775 \, \sqrt{21} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 5 \, {\left(207990 \, x^{3} + 395215 \, x^{2} + 249939 \, x + 52607\right)} \sqrt{-2 \, x + 1}}{10 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/10*(14073*sqrt(11)*sqrt(5)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 22775*sqrt(21)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 5*(207990*x^3 + 395215*x^2 + 249939*x + 52607)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
1999,1,170,0,1.292704," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^3,x, algorithm=""fricas"")","\frac{485415 \, \sqrt{55} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 785570 \, \sqrt{21} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(5124375 \, x^{4} + 13153400 \, x^{3} + 12649336 \, x^{2} + 5401374 \, x + 864074\right)} \sqrt{-2 \, x + 1}}{42 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/42*(485415*sqrt(55)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 785570*sqrt(21)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(5124375*x^4 + 13153400*x^3 + 12649336*x^2 + 5401374*x + 864074)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2000,1,190,0,1.417616," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^3,x, algorithm=""fricas"")","\frac{100944900 \, \sqrt{55} {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 163363895 \, \sqrt{21} {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(3196931625 \, x^{5} + 10337268075 \, x^{4} + 13362164665 \, x^{3} + 8630749831 \, x^{2} + 2785562634 \, x + 359378534\right)} \sqrt{-2 \, x + 1}}{1176 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"1/1176*(100944900*sqrt(55)*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 163363895*sqrt(21)*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(3196931625*x^5 + 10337268075*x^4 + 13362164665*x^3 + 8630749831*x^2 + 2785562634*x + 359378534)*sqrt(-2*x + 1))/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","A",0
2001,1,39,0,1.159789," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{429} \, {\left(40095 \, x^{6} + 208251 \, x^{5} + 488925 \, x^{4} + 698580 \, x^{3} + 707436 \, x^{2} + 597464 \, x + 638648\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/429*(40095*x^6 + 208251*x^5 + 488925*x^4 + 698580*x^3 + 707436*x^2 + 597464*x + 638648)*sqrt(-2*x + 1)","A",0
2002,1,34,0,1.073358," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{165} \, {\left(6075 \, x^{5} + 27630 \, x^{4} + 56520 \, x^{3} + 71136 \, x^{2} + 67664 \, x + 75584\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/165*(6075*x^5 + 27630*x^4 + 56520*x^3 + 71136*x^2 + 67664*x + 75584)*sqrt(-2*x + 1)","A",0
2003,1,29,0,1.402988," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(1575 \, x^{4} + 6165 \, x^{3} + 10881 \, x^{2} + 12434 \, x + 14954\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/105*(1575*x^4 + 6165*x^3 + 10881*x^2 + 12434*x + 14954)*sqrt(-2*x + 1)","A",0
2004,1,24,0,1.607952," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(675 \, x^{3} + 2232 \, x^{2} + 3448 \, x + 4708\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/105*(675*x^3 + 2232*x^2 + 3448*x + 4708)*sqrt(-2*x + 1)","A",0
2005,1,19,0,1.501122," ","integrate((2+3*x)*(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(9 \, x^{2} + 25 \, x + 43\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/3*(9*x^2 + 25*x + 43)*sqrt(-2*x + 1)","A",0
2006,1,14,0,0.960124," ","integrate((3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(5 \, x + 14\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/3*(5*x + 14)*sqrt(-2*x + 1)","A",0
2007,1,41,0,1.426694," ","integrate((3+5*x)/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{63} \, \sqrt{21} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - \frac{5}{3} \, \sqrt{-2 \, x + 1}"," ",0,"1/63*sqrt(21)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 5/3*sqrt(-2*x + 1)","A",0
2008,1,54,0,1.269531," ","integrate((3+5*x)/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{34 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, \sqrt{-2 \, x + 1}}{441 \, {\left(3 \, x + 2\right)}}"," ",0,"1/441*(34*sqrt(21)*(3*x + 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*sqrt(-2*x + 1))/(3*x + 2)","A",0
2009,1,69,0,1.527967," ","integrate((3+5*x)/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{67 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(201 \, x + 127\right)} \sqrt{-2 \, x + 1}}{6174 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/6174*(67*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(201*x + 127)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2010,1,84,0,1.214805," ","integrate((3+5*x)/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{50 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(450 \, x^{2} + 950 \, x + 417\right)} \sqrt{-2 \, x + 1}}{21609 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/21609*(50*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(450*x^2 + 950*x + 417)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2011,1,99,0,1.378719," ","integrate((3+5*x)/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{95 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(2565 \, x^{3} + 7125 \, x^{2} + 7942 \, x + 2790\right)} \sqrt{-2 \, x + 1}}{172872 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/172872*(95*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(2565*x^3 + 7125*x^2 + 7942*x + 2790)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2012,1,44,0,1.562577," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{429} \, {\left(173745 \, x^{7} + 1002375 \, x^{6} + 2632743 \, x^{5} + 4212525 \, x^{4} + 4694340 \, x^{3} + 4058988 \, x^{2} + 3152152 \, x + 3275704\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/429*(173745*x^7 + 1002375*x^6 + 2632743*x^5 + 4212525*x^4 + 4694340*x^3 + 4058988*x^2 + 3152152*x + 3275704)*sqrt(-2*x + 1)","A",0
2013,1,39,0,0.837967," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2145} \, {\left(334125 \, x^{6} + 1709100 \, x^{5} + 3954645 \, x^{4} + 5576580 \, x^{3} + 5587044 \, x^{2} + 4685656 \, x + 4994536\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/2145*(334125*x^6 + 1709100*x^5 + 3954645*x^4 + 5576580*x^3 + 5587044*x^2 + 4685656*x + 4994536)*sqrt(-2*x + 1)","A",0
2014,1,34,0,1.787710," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1155} \, {\left(70875 \, x^{5} + 316575 \, x^{4} + 636795 \, x^{3} + 790023 \, x^{2} + 743822 \, x + 826982\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/1155*(70875*x^5 + 316575*x^4 + 636795*x^3 + 790023*x^2 + 743822*x + 826982)*sqrt(-2*x + 1)","A",0
2015,1,29,0,1.418993," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{105} \, {\left(2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/105*(2625*x^4 + 10050*x^3 + 17391*x^2 + 19574*x + 23354)*sqrt(-2*x + 1)","A",0
2016,1,24,0,0.837084," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{21} \, {\left(225 \, x^{3} + 723 \, x^{2} + 1091 \, x + 1469\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/21*(225*x^3 + 723*x^2 + 1091*x + 1469)*sqrt(-2*x + 1)","A",0
2017,1,19,0,1.501151," ","integrate((3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} \, {\left(15 \, x^{2} + 40 \, x + 67\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/3*(15*x^2 + 40*x + 67)*sqrt(-2*x + 1)","A",0
2018,1,45,0,1.549566," ","integrate((3+5*x)^2/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{5}{9} \, {\left(5 \, x + 13\right)} \sqrt{-2 \, x + 1} + \frac{1}{189} \, \sqrt{21} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right)"," ",0,"-5/9*(5*x + 13)*sqrt(-2*x + 1) + 1/189*sqrt(21)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2))","A",0
2019,1,60,0,1.572882," ","integrate((3+5*x)^2/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{23 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(175 \, x + 117\right)} \sqrt{-2 \, x + 1}}{441 \, {\left(3 \, x + 2\right)}}"," ",0,"1/441*(23*sqrt(21)*(3*x + 2)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(175*x + 117)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2020,1,69,0,1.442616," ","integrate((3+5*x)^2/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{257 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 7 \, {\left(137 \, x + 89\right)} \sqrt{-2 \, x + 1}}{2058 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/2058*(257*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 7*(137*x + 89)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2021,1,84,0,1.487270," ","integrate((3+5*x)^2/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{2245 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(20205 \, x^{2} + 25505 \, x + 8056\right)} \sqrt{-2 \, x + 1}}{129654 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/129654*(2245*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(20205*x^2 + 25505*x + 8056)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2022,1,99,0,1.420685," ","integrate((3+5*x)^2/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{635 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(17145 \, x^{3} + 47625 \, x^{2} + 39366 \, x + 10190\right)} \sqrt{-2 \, x + 1}}{172872 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/172872*(635*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(17145*x^3 + 47625*x^2 + 39366*x + 10190)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2023,1,120,0,1.576404," ","integrate((3+5*x)^2/(2+3*x)^6/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1755 \, \sqrt{7} \sqrt{3} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(426465 \, x^{4} + 1468935 \, x^{3} + 2110212 \, x^{2} + 1327058 \, x + 298748\right)} \sqrt{-2 \, x + 1}}{2016840 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/2016840*(1755*sqrt(7)*sqrt(3)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(426465*x^4 + 1468935*x^3 + 2110212*x^2 + 1327058*x + 298748)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2024,1,44,0,1.085774," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2145} \, {\left(1447875 \, x^{7} + 8241750 \, x^{6} + 21369825 \, x^{5} + 33786160 \, x^{4} + 37260640 \, x^{3} + 31962552 \, x^{2} + 24706048 \, x + 25632688\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/2145*(1447875*x^7 + 8241750*x^6 + 21369825*x^5 + 33786160*x^4 + 37260640*x^3 + 31962552*x^2 + 24706048*x + 25632688)*sqrt(-2*x + 1)","A",0
2025,1,39,0,1.578754," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{5005} \, {\left(1299375 \, x^{6} + 6544125 \, x^{5} + 14921900 \, x^{4} + 20766885 \, x^{3} + 20586249 \, x^{2} + 17147586 \, x + 18228666\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/5005*(1299375*x^6 + 6544125*x^5 + 14921900*x^4 + 20766885*x^3 + 20586249*x^2 + 17147586*x + 18228666)*sqrt(-2*x + 1)","A",0
2026,1,34,0,1.469659," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1155} \, {\left(118125 \, x^{5} + 518000 \, x^{4} + 1024475 \, x^{3} + 1252938 \, x^{2} + 1167932 \, x + 1292672\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/1155*(118125*x^5 + 518000*x^4 + 1024475*x^3 + 1252938*x^2 + 1167932*x + 1292672)*sqrt(-2*x + 1)","A",0
2027,1,29,0,1.116666," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{21} \, {\left(875 \, x^{4} + 3275 \, x^{3} + 5556 \, x^{2} + 6161 \, x + 7295\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/21*(875*x^4 + 3275*x^3 + 5556*x^2 + 6161*x + 7295)*sqrt(-2*x + 1)","A",0
2028,1,24,0,1.381392," ","integrate((3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{7} \, {\left(125 \, x^{3} + 390 \, x^{2} + 575 \, x + 764\right)} \sqrt{-2 \, x + 1}"," ",0,"-1/7*(125*x^3 + 390*x^2 + 575*x + 764)*sqrt(-2*x + 1)","A",0
2029,1,51,0,1.502452," ","integrate((3+5*x)^3/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{5}{27} \, {\left(45 \, x^{2} + 115 \, x + 188\right)} \sqrt{-2 \, x + 1} + \frac{1}{567} \, \sqrt{21} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right)"," ",0,"-5/27*(45*x^2 + 115*x + 188)*sqrt(-2*x + 1) + 1/567*sqrt(21)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2))","A",0
2030,1,64,0,1.408571," ","integrate((3+5*x)^3/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{104 \, \sqrt{21} {\left(3 \, x + 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(2625 \, x^{2} + 8050 \, x + 4199\right)} \sqrt{-2 \, x + 1}}{3969 \, {\left(3 \, x + 2\right)}}"," ",0,"1/3969*(104*sqrt(21)*(3*x + 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(2625*x^2 + 8050*x + 4199)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2031,1,75,0,1.250370," ","integrate((3+5*x)^3/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{2381 \, \sqrt{21} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(36750 \, x^{2} + 49207 \, x + 16469\right)} \sqrt{-2 \, x + 1}}{18522 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/18522*(2381*sqrt(21)*(9*x^2 + 12*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(36750*x^2 + 49207*x + 16469)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2032,1,84,0,1.403466," ","integrate((3+5*x)^3/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{39355 \, \sqrt{21} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(31680 \, x^{2} + 41155 \, x + 13373\right)} \sqrt{-2 \, x + 1}}{194481 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/194481*(39355*sqrt(21)*(27*x^3 + 54*x^2 + 36*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(31680*x^2 + 41155*x + 13373)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2033,1,99,0,1.120795," ","integrate((3+5*x)^3/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{42995 \, \sqrt{21} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1160865 \, x^{3} + 2195625 \, x^{2} + 1385462 \, x + 291670\right)} \sqrt{-2 \, x + 1}}{1555848 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/1555848*(42995*sqrt(21)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1160865*x^3 + 2195625*x^2 + 1385462*x + 291670)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2034,1,114,0,1.610240," ","integrate((3+5*x)^3/(2+3*x)^6/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{26465 \, \sqrt{21} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(2143665 \, x^{4} + 7383735 \, x^{3} + 8806422 \, x^{2} + 4450198 \, x + 816938\right)} \sqrt{-2 \, x + 1}}{4537890 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"1/4537890*(26465*sqrt(21)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(2143665*x^4 + 7383735*x^3 + 8806422*x^2 + 4450198*x + 816938)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2035,1,701,0,1.632650," ","integrate((b*x+a)^2/(d*x+c)^2/(f*x+e)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{d^{2} e - c d f} {\left(4 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e f - {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2}\right)} f^{2} + {\left(4 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f - {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} f^{2}\right)} x\right)} \log\left(\frac{d f x + 2 \, d e - c f - 2 \, \sqrt{d^{2} e - c d f} \sqrt{f x + e}}{d x + c}\right) - 2 \, {\left(2 \, b^{2} c d^{3} e^{2} - {\left(5 \, b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e f + {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} f^{2} + 2 \, {\left(b^{2} d^{4} e^{2} - 2 \, b^{2} c d^{3} e f + b^{2} c^{2} d^{2} f^{2}\right)} x\right)} \sqrt{f x + e}}{2 \, {\left(c d^{5} e^{2} f - 2 \, c^{2} d^{4} e f^{2} + c^{3} d^{3} f^{3} + {\left(d^{6} e^{2} f - 2 \, c d^{5} e f^{2} + c^{2} d^{4} f^{3}\right)} x\right)}}, -\frac{\sqrt{-d^{2} e + c d f} {\left(4 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e f - {\left(3 \, b^{2} c^{3} - 2 \, a b c^{2} d - a^{2} c d^{2}\right)} f^{2} + {\left(4 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f - {\left(3 \, b^{2} c^{2} d - 2 \, a b c d^{2} - a^{2} d^{3}\right)} f^{2}\right)} x\right)} \arctan\left(\frac{\sqrt{-d^{2} e + c d f} \sqrt{f x + e}}{d f x + d e}\right) - {\left(2 \, b^{2} c d^{3} e^{2} - {\left(5 \, b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} e f + {\left(3 \, b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} f^{2} + 2 \, {\left(b^{2} d^{4} e^{2} - 2 \, b^{2} c d^{3} e f + b^{2} c^{2} d^{2} f^{2}\right)} x\right)} \sqrt{f x + e}}{c d^{5} e^{2} f - 2 \, c^{2} d^{4} e f^{2} + c^{3} d^{3} f^{3} + {\left(d^{6} e^{2} f - 2 \, c d^{5} e f^{2} + c^{2} d^{4} f^{3}\right)} x}\right]"," ",0,"[-1/2*(sqrt(d^2*e - c*d*f)*(4*(b^2*c^2*d - a*b*c*d^2)*e*f - (3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2)*f^2 + (4*(b^2*c*d^2 - a*b*d^3)*e*f - (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*f^2)*x)*log((d*f*x + 2*d*e - c*f - 2*sqrt(d^2*e - c*d*f)*sqrt(f*x + e))/(d*x + c)) - 2*(2*b^2*c*d^3*e^2 - (5*b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e*f + (3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*f^2 + 2*(b^2*d^4*e^2 - 2*b^2*c*d^3*e*f + b^2*c^2*d^2*f^2)*x)*sqrt(f*x + e))/(c*d^5*e^2*f - 2*c^2*d^4*e*f^2 + c^3*d^3*f^3 + (d^6*e^2*f - 2*c*d^5*e*f^2 + c^2*d^4*f^3)*x), -(sqrt(-d^2*e + c*d*f)*(4*(b^2*c^2*d - a*b*c*d^2)*e*f - (3*b^2*c^3 - 2*a*b*c^2*d - a^2*c*d^2)*f^2 + (4*(b^2*c*d^2 - a*b*d^3)*e*f - (3*b^2*c^2*d - 2*a*b*c*d^2 - a^2*d^3)*f^2)*x)*arctan(sqrt(-d^2*e + c*d*f)*sqrt(f*x + e)/(d*f*x + d*e)) - (2*b^2*c*d^3*e^2 - (5*b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*e*f + (3*b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*f^2 + 2*(b^2*d^4*e^2 - 2*b^2*c*d^3*e*f + b^2*c^2*d^2*f^2)*x)*sqrt(f*x + e))/(c*d^5*e^2*f - 2*c^2*d^4*e*f^2 + c^3*d^3*f^3 + (d^6*e^2*f - 2*c*d^5*e*f^2 + c^2*d^4*f^3)*x)]","B",0
2036,1,60,0,1.660728," ","integrate((2+3*x)^5/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{3}{21875} \, {\left(39375 \, x^{4} + 160875 \, x^{3} + 295290 \, x^{2} + 348095 \, x + 425872\right)} \sqrt{-2 \, x + 1} + \frac{1}{171875} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right)"," ",0,"-3/21875*(39375*x^4 + 160875*x^3 + 295290*x^2 + 348095*x + 425872)*sqrt(-2*x + 1) + 1/171875*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3))","A",0
2037,1,55,0,1.354364," ","integrate((2+3*x)^4/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{3}{4375} \, {\left(3375 \, x^{3} + 11790 \, x^{2} + 19095 \, x + 26872\right)} \sqrt{-2 \, x + 1} + \frac{1}{34375} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right)"," ",0,"-3/4375*(3375*x^3 + 11790*x^2 + 19095*x + 26872)*sqrt(-2*x + 1) + 1/34375*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3))","A",0
2038,1,50,0,1.519242," ","integrate((2+3*x)^3/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{9}{125} \, {\left(15 \, x^{2} + 45 \, x + 82\right)} \sqrt{-2 \, x + 1} + \frac{1}{6875} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right)"," ",0,"-9/125*(15*x^2 + 45*x + 82)*sqrt(-2*x + 1) + 1/6875*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3))","A",0
2039,1,45,0,1.222808," ","integrate((2+3*x)^2/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{3}{25} \, {\left(5 \, x + 16\right)} \sqrt{-2 \, x + 1} + \frac{1}{1375} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right)"," ",0,"-3/25*(5*x + 16)*sqrt(-2*x + 1) + 1/1375*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3))","A",0
2040,1,40,0,1.277560," ","integrate((2+3*x)/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{275} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - \frac{3}{5} \, \sqrt{-2 \, x + 1}"," ",0,"1/275*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 3/5*sqrt(-2*x + 1)","A",0
2041,1,30,0,1.291300," ","integrate(1/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{55} \, \sqrt{55} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right)"," ",0,"1/55*sqrt(55)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3))","A",0
2042,1,74,0,1.557669," ","integrate(1/(2+3*x)/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{11} \, \sqrt{11} \sqrt{5} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + \frac{1}{7} \, \sqrt{7} \sqrt{3} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right)"," ",0,"1/11*sqrt(11)*sqrt(5)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1/7*sqrt(7)*sqrt(3)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2))","A",0
2043,1,102,0,1.476861," ","integrate(1/(2+3*x)^2/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{245 \, \sqrt{11} \sqrt{5} {\left(3 \, x + 2\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 396 \, \sqrt{7} \sqrt{3} {\left(3 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 231 \, \sqrt{-2 \, x + 1}}{539 \, {\left(3 \, x + 2\right)}}"," ",0,"1/539*(245*sqrt(11)*sqrt(5)*(3*x + 2)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 396*sqrt(7)*sqrt(3)*(3*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 231*sqrt(-2*x + 1))/(3*x + 2)","A",0
2044,1,122,0,1.401488," ","integrate(1/(2+3*x)^3/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{17150 \, \sqrt{11} \sqrt{5} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 27753 \, \sqrt{7} \sqrt{3} {\left(9 \, x^{2} + 12 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 693 \, {\left(73 \, x + 51\right)} \sqrt{-2 \, x + 1}}{7546 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/7546*(17150*sqrt(11)*sqrt(5)*(9*x^2 + 12*x + 4)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 27753*sqrt(7)*sqrt(3)*(9*x^2 + 12*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 693*(73*x + 51)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2045,1,142,0,1.722430," ","integrate(1/(2+3*x)^4/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{300125 \, \sqrt{11} \sqrt{5} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 485705 \, \sqrt{7} \sqrt{3} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 231 \, {\left(11520 \, x^{2} + 15745 \, x + 5393\right)} \sqrt{-2 \, x + 1}}{26411 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/26411*(300125*sqrt(11)*sqrt(5)*(27*x^3 + 54*x^2 + 36*x + 8)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 485705*sqrt(7)*sqrt(3)*(27*x^3 + 54*x^2 + 36*x + 8)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 231*(11520*x^2 + 15745*x + 5393)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2046,1,162,0,1.347672," ","integrate(1/(2+3*x)^5/(3+5*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{245000 \, \sqrt{11} \sqrt{5} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 396495 \, \sqrt{7} \sqrt{3} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 231 \, {\left(28215 \, x^{3} + 57375 \, x^{2} + 38922 \, x + 8810\right)} \sqrt{-2 \, x + 1}}{4312 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/4312*(245000*sqrt(11)*sqrt(5)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 396495*sqrt(7)*sqrt(3)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 231*(28215*x^3 + 57375*x^2 + 38922*x + 8810)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2047,1,79,0,1.106086," ","integrate((2+3*x)^6/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1393 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(19490625 \, x^{5} + 92998125 \, x^{4} + 200942775 \, x^{3} + 273540465 \, x^{2} + 334366065 \, x + 135011752\right)} \sqrt{-2 \, x + 1}}{66171875 \, {\left(5 \, x + 3\right)}}"," ",0,"1/66171875*(1393*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(19490625*x^5 + 92998125*x^4 + 200942775*x^3 + 273540465*x^2 + 334366065*x + 135011752)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2048,1,74,0,1.478882," ","integrate((2+3*x)^5/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1162 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(1670625 \, x^{4} + 6994350 \, x^{3} + 13532310 \, x^{2} + 20175210 \, x + 8527768\right)} \sqrt{-2 \, x + 1}}{13234375 \, {\left(5 \, x + 3\right)}}"," ",0,"1/13234375*(1162*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(1670625*x^4 + 6994350*x^3 + 13532310*x^2 + 20175210*x + 8527768)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2049,1,69,0,1.352096," ","integrate((2+3*x)^4/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{133 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(22275 \, x^{3} + 82665 \, x^{2} + 171765 \, x + 78112\right)} \sqrt{-2 \, x + 1}}{378125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/378125*(133*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(22275*x^3 + 82665*x^2 + 171765*x + 78112)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2050,1,64,0,1.383038," ","integrate((2+3*x)^3/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(99 \, x^{2} + 396 \, x + 202\right)} \sqrt{-2 \, x + 1}}{3025 \, {\left(5 \, x + 3\right)}}"," ",0,"1/3025*(4*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(99*x^2 + 396*x + 202)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2051,1,59,0,1.506072," ","integrate((2+3*x)^2/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{67 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(495 \, x + 298\right)} \sqrt{-2 \, x + 1}}{15125 \, {\left(5 \, x + 3\right)}}"," ",0,"1/15125*(67*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(495*x + 298)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2052,1,54,0,1.561349," ","integrate((2+3*x)/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{34 \, \sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, \sqrt{-2 \, x + 1}}{3025 \, {\left(5 \, x + 3\right)}}"," ",0,"1/3025*(34*sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*sqrt(-2*x + 1))/(5*x + 3)","A",0
2053,1,53,0,1.200342," ","integrate(1/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(5 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, \sqrt{-2 \, x + 1}}{605 \, {\left(5 \, x + 3\right)}}"," ",0,"1/605*(sqrt(55)*(5*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*sqrt(-2*x + 1))/(5*x + 3)","A",0
2054,1,102,0,1.267294," ","integrate(1/(2+3*x)/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{224 \, \sqrt{11} \sqrt{5} {\left(5 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 363 \, \sqrt{7} \sqrt{3} {\left(5 \, x + 3\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 385 \, \sqrt{-2 \, x + 1}}{847 \, {\left(5 \, x + 3\right)}}"," ",0,"1/847*(224*sqrt(11)*sqrt(5)*(5*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 363*sqrt(7)*sqrt(3)*(5*x + 3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 385*sqrt(-2*x + 1))/(5*x + 3)","A",0
2055,1,122,0,1.422766," ","integrate(1/(2+3*x)^2/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{15925 \, \sqrt{11} \sqrt{5} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 25773 \, \sqrt{7} \sqrt{3} {\left(15 \, x^{2} + 19 \, x + 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(1020 \, x + 647\right)} \sqrt{-2 \, x + 1}}{5929 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/5929*(15925*sqrt(11)*sqrt(5)*(15*x^2 + 19*x + 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 25773*sqrt(7)*sqrt(3)*(15*x^2 + 19*x + 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(1020*x + 647)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
2056,1,142,0,1.352367," ","integrate(1/(2+3*x)^3/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1680700 \, \sqrt{11} \sqrt{5} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 2719959 \, \sqrt{7} \sqrt{3} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(322605 \, x^{2} + 419448 \, x + 136021\right)} \sqrt{-2 \, x + 1}}{83006 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/83006*(1680700*sqrt(11)*sqrt(5)*(45*x^3 + 87*x^2 + 56*x + 12)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 2719959*sqrt(7)*sqrt(3)*(45*x^3 + 87*x^2 + 56*x + 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(322605*x^2 + 419448*x + 136021)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
2057,1,162,0,1.109222," ","integrate(1/(2+3*x)^4/(3+5*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{78632750 \, \sqrt{11} \sqrt{5} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 127255095 \, \sqrt{7} \sqrt{3} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(45278325 \, x^{3} + 89054820 \, x^{2} + 58335165 \, x + 12724912\right)} \sqrt{-2 \, x + 1}}{581042 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/581042*(78632750*sqrt(11)*sqrt(5)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 127255095*sqrt(7)*sqrt(3)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(45278325*x^3 + 89054820*x^2 + 58335165*x + 12724912)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
2058,1,89,0,1.378062," ","integrate((2+3*x)^6/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{231483 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(551306250 \, x^{5} + 2690374500 \, x^{4} + 6078090150 \, x^{3} + 9876010320 \, x^{2} + 7254126105 \, x + 1804176536\right)} \sqrt{-2 \, x + 1}}{1455781250 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1455781250*(231483*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(551306250*x^5 + 2690374500*x^4 + 6078090150*x^3 + 9876010320*x^2 + 7254126105*x + 1804176536)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2059,1,84,0,1.454901," ","integrate((2+3*x)^5/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{22113 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(7350750 \, x^{4} + 32506650 \, x^{3} + 76970520 \, x^{2} + 63610155 \, x + 16525496\right)} \sqrt{-2 \, x + 1}}{41593750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/41593750*(22113*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(7350750*x^4 + 32506650*x^3 + 76970520*x^2 + 63610155*x + 16525496)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2060,1,79,0,1.545431," ","integrate((2+3*x)^4/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{2667 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(163350 \, x^{3} + 784080 \, x^{2} + 764745 \, x + 211864\right)} \sqrt{-2 \, x + 1}}{1663750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/1663750*(2667*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(163350*x^3 + 784080*x^2 + 764745*x + 211864)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2061,1,74,0,1.379580," ","integrate((2+3*x)^3/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1347 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(32670 \, x^{2} + 39405 \, x + 11884\right)} \sqrt{-2 \, x + 1}}{332750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/332750*(1347*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(32670*x^2 + 39405*x + 11884)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2062,1,69,0,1.232434," ","integrate((2+3*x)^2/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{2313 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(675 \, x + 416\right)} \sqrt{-2 \, x + 1}}{332750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/332750*(2313*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(675*x + 416)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2063,1,69,0,1.831125," ","integrate((2+3*x)/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{69 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(345 \, x + 218\right)} \sqrt{-2 \, x + 1}}{66550 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/66550*(69*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(345*x + 218)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2064,1,69,0,1.322429," ","integrate(1/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 275 \, {\left(3 \, x + 4\right)} \sqrt{-2 \, x + 1}}{13310 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/13310*(3*sqrt(55)*(25*x^2 + 30*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 275*(3*x + 4)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2065,1,122,0,1.649000," ","integrate(1/(2+3*x)/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{14805 \, \sqrt{11} \sqrt{5} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 23958 \, \sqrt{7} \sqrt{3} {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 385 \, {\left(315 \, x + 178\right)} \sqrt{-2 \, x + 1}}{18634 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/18634*(14805*sqrt(11)*sqrt(5)*(25*x^2 + 30*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 23958*sqrt(7)*sqrt(3)*(25*x^2 + 30*x + 9)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 385*(315*x + 178)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2066,1,142,0,1.157777," ","integrate(1/(2+3*x)^2/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1569225 \, \sqrt{11} \sqrt{5} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 2539548 \, \sqrt{7} \sqrt{3} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(501975 \, x^{2} + 619170 \, x + 190406\right)} \sqrt{-2 \, x + 1}}{130438 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"1/130438*(1569225*sqrt(11)*sqrt(5)*(75*x^3 + 140*x^2 + 87*x + 18)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 2539548*sqrt(7)*sqrt(3)*(75*x^3 + 140*x^2 + 87*x + 18)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(501975*x^2 + 619170*x + 190406)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
2067,1,162,0,1.566012," ","integrate(1/(2+3*x)^3/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{110385975 \, \sqrt{11} \sqrt{5} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 178642827 \, \sqrt{7} \sqrt{3} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(105937200 \, x^{3} + 201297915 \, x^{2} + 127303347 \, x + 26794499\right)} \sqrt{-2 \, x + 1}}{913066 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"1/913066*(110385975*sqrt(11)*sqrt(5)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 178642827*sqrt(7)*sqrt(3)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(105937200*x^3 + 201297915*x^2 + 127303347*x + 26794499)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
2068,1,182,0,1.556819," ","integrate(1/(2+3*x)^4/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{6458389875 \, \sqrt{11} \sqrt{5} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 10451917080 \, \sqrt{7} \sqrt{3} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(18594329625 \, x^{4} + 47728484550 \, x^{3} + 45899434890 \, x^{2} + 19599448500 \, x + 3135381218\right)} \sqrt{-2 \, x + 1}}{6391462 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"1/6391462*(6458389875*sqrt(11)*sqrt(5)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 10451917080*sqrt(7)*sqrt(3)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(18594329625*x^4 + 47728484550*x^3 + 45899434890*x^2 + 19599448500*x + 3135381218)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2069,1,56,0,1.136139," ","integrate((2+3*x)^7*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(104247 \, x^{8} + 697653 \, x^{7} + 2168775 \, x^{6} + 4220622 \, x^{5} + 5949090 \, x^{4} + 6921432 \, x^{3} + 8106616 \, x^{2} + 16881328 \, x - 16936240\right)} \sqrt{-2 \, x + 1}}{143 \, {\left(2 \, x - 1\right)}}"," ",0,"1/143*(104247*x^8 + 697653*x^7 + 2168775*x^6 + 4220622*x^5 + 5949090*x^4 + 6921432*x^3 + 8106616*x^2 + 16881328*x - 16936240)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2070,1,51,0,1.485461," ","integrate((2+3*x)^6*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(40095 \, x^{7} + 243486 \, x^{6} + 687420 \, x^{5} + 1230120 \, x^{4} + 1663632 \, x^{3} + 2109792 \, x^{2} + 4512448 \, x - 4539904\right)} \sqrt{-2 \, x + 1}}{143 \, {\left(2 \, x - 1\right)}}"," ",0,"1/143*(40095*x^7 + 243486*x^6 + 687420*x^5 + 1230120*x^4 + 1663632*x^3 + 2109792*x^2 + 4512448*x - 4539904)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2071,1,46,0,1.540075," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(1215 \, x^{6} + 6651 \, x^{5} + 17055 \, x^{4} + 28692 \, x^{3} + 41012 \, x^{2} + 91704 \, x - 92760\right)} \sqrt{-2 \, x + 1}}{11 \, {\left(2 \, x - 1\right)}}"," ",0,"1/11*(1215*x^6 + 6651*x^5 + 17055*x^4 + 28692*x^3 + 41012*x^2 + 91704*x - 92760)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2072,1,41,0,0.976029," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(1575 \, x^{5} + 7740 \, x^{4} + 18288 \, x^{3} + 31448 \, x^{2} + 75776 \, x - 77456\right)} \sqrt{-2 \, x + 1}}{35 \, {\left(2 \, x - 1\right)}}"," ",0,"1/35*(1575*x^5 + 7740*x^4 + 18288*x^3 + 31448*x^2 + 75776*x - 77456)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2073,1,36,0,1.516840," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(675 \, x^{4} + 2997 \, x^{3} + 6987 \, x^{2} + 19154 \, x - 19994\right)} \sqrt{-2 \, x + 1}}{35 \, {\left(2 \, x - 1\right)}}"," ",0,"1/35*(675*x^4 + 2997*x^3 + 6987*x^2 + 19154*x - 19994)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2074,1,30,0,1.243195," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(9 \, x^{3} + 38 \, x^{2} + 132 \, x - 144\right)} \sqrt{-2 \, x + 1}}{2 \, x - 1}"," ",0,"(9*x^3 + 38*x^2 + 132*x - 144)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2075,1,25,0,1.311428," ","integrate((2+3*x)*(3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, x^{2} + 29 \, x - 35\right)} \sqrt{-2 \, x + 1}}{2 \, x - 1}"," ",0,"(5*x^2 + 29*x - 35)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2076,1,20,0,1.435601," ","integrate((3+5*x)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, x - 8\right)} \sqrt{-2 \, x + 1}}{2 \, x - 1}"," ",0,"(5*x - 8)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2077,1,54,0,0.889127," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{21} {\left(2 \, x - 1\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 231 \, \sqrt{-2 \, x + 1}}{147 \, {\left(2 \, x - 1\right)}}"," ",0,"1/147*(sqrt(21)*(2*x - 1)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 231*sqrt(-2*x + 1))/(2*x - 1)","A",0
2078,1,65,0,1.712065," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{32 \, \sqrt{21} {\left(6 \, x^{2} + x - 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(64 \, x + 45\right)} \sqrt{-2 \, x + 1}}{1029 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/1029*(32*sqrt(21)*(6*x^2 + x - 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(64*x + 45)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2079,1,90,0,1.578279," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{65 \, \sqrt{7} \sqrt{3} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(1170 \, x^{2} + 1105 \, x + 233\right)} \sqrt{-2 \, x + 1}}{4802 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/4802*(65*sqrt(7)*sqrt(3)*(18*x^3 + 15*x^2 - 4*x - 4)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(1170*x^2 + 1105*x + 233)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2080,1,99,0,0.967536," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{5 \, \sqrt{21} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(90 \, x^{3} + 145 \, x^{2} + 57 \, x + 1\right)} \sqrt{-2 \, x + 1}}{1029 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"1/1029*(5*sqrt(21)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(90*x^3 + 145*x^2 + 57*x + 1)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2081,1,114,0,1.375242," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{655 \, \sqrt{21} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(35370 \, x^{4} + 80565 \, x^{3} + 60391 \, x^{2} + 10742 \, x - 2566\right)} \sqrt{-2 \, x + 1}}{403368 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"1/403368*(655*sqrt(21)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(35370*x^4 + 80565*x^3 + 60391*x^2 + 10742*x - 2566)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2082,1,135,0,1.384935," ","integrate((3+5*x)/(1-2*x)^(3/2)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{615 \, \sqrt{7} \sqrt{3} {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(298890 \, x^{5} + 880065 \, x^{4} + 964197 \, x^{3} + 430992 \, x^{2} + 8774 \, x - 32894\right)} \sqrt{-2 \, x + 1}}{1176490 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"1/1176490*(615*sqrt(7)*sqrt(3)*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(298890*x^5 + 880065*x^4 + 964197*x^3 + 430992*x^2 + 8774*x - 32894)*sqrt(-2*x + 1))/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","A",0
2083,1,51,0,1.265755," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(200475 \, x^{7} + 1201635 \, x^{6} + 3350637 \, x^{5} + 5928885 \, x^{4} + 7945164 \, x^{3} + 10015804 \, x^{2} + 21370088 \, x - 21493640\right)} \sqrt{-2 \, x + 1}}{429 \, {\left(2 \, x - 1\right)}}"," ",0,"1/429*(200475*x^7 + 1201635*x^6 + 3350637*x^5 + 5928885*x^4 + 7945164*x^3 + 10015804*x^2 + 21370088*x - 21493640)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2084,1,46,0,1.363977," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(212625 \, x^{6} + 1146600 \, x^{5} + 2899485 \, x^{4} + 4819932 \, x^{3} + 6831172 \, x^{2} + 15214664 \, x - 15380984\right)} \sqrt{-2 \, x + 1}}{1155 \, {\left(2 \, x - 1\right)}}"," ",0,"1/1155*(212625*x^6 + 1146600*x^5 + 2899485*x^4 + 4819932*x^3 + 6831172*x^2 + 15214664*x - 15380984)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2085,1,41,0,1.171231," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(7875 \, x^{5} + 38025 \, x^{4} + 88443 \, x^{3} + 150253 \, x^{2} + 359726 \, x - 367286\right)} \sqrt{-2 \, x + 1}}{105 \, {\left(2 \, x - 1\right)}}"," ",0,"1/105*(7875*x^5 + 38025*x^4 + 88443*x^3 + 150253*x^2 + 359726*x - 367286)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2086,1,36,0,1.248660," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(675 \, x^{4} + 2934 \, x^{3} + 6721 \, x^{2} + 18230 \, x - 18986\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(2 \, x - 1\right)}}"," ",0,"1/21*(675*x^4 + 2934*x^3 + 6721*x^2 + 18230*x - 18986)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2087,1,31,0,1.044649," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(45 \, x^{3} + 185 \, x^{2} + 631 \, x - 685\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3*(45*x^3 + 185*x^2 + 631*x - 685)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2088,1,26,0,1.572227," ","integrate((3+5*x)^2/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(25 \, x^{2} + 140 \, x - 167\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3*(25*x^2 + 140*x - 167)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2089,1,58,0,1.811653," ","integrate((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{21} {\left(2 \, x - 1\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(175 \, x - 269\right)} \sqrt{-2 \, x + 1}}{441 \, {\left(2 \, x - 1\right)}}"," ",0,"1/441*(sqrt(21)*(2*x - 1)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(175*x - 269)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2090,1,66,0,1.053581," ","integrate((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{67 \, \sqrt{21} {\left(6 \, x^{2} + x - 2\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(1091 \, x + 725\right)} \sqrt{-2 \, x + 1}}{3087 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/3087*(67*sqrt(21)*(6*x^2 + x - 2)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(1091*x + 725)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2091,1,84,0,1.222742," ","integrate((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{2045 \, \sqrt{21} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(12270 \, x^{2} + 17305 \, x + 6067\right)} \sqrt{-2 \, x + 1}}{43218 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/43218*(2045*sqrt(21)*(18*x^3 + 15*x^2 - 4*x - 4)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(12270*x^2 + 17305*x + 6067)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2092,1,99,0,1.171464," ","integrate((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{905 \, \sqrt{21} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(16290 \, x^{3} + 26245 \, x^{2} + 13747 \, x + 2316\right)} \sqrt{-2 \, x + 1}}{43218 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"1/43218*(905*sqrt(21)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(16290*x^3 + 26245*x^2 + 13747*x + 2316)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2093,1,114,0,1.480489," ","integrate((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{9145 \, \sqrt{21} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(493830 \, x^{4} + 1124835 \, x^{3} + 843169 \, x^{2} + 218578 \, x + 6486\right)} \sqrt{-2 \, x + 1}}{1210104 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"1/1210104*(9145*sqrt(21)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(493830*x^4 + 1124835*x^3 + 843169*x^2 + 218578*x + 6486)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2094,1,51,0,1.285644," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3898125 \, x^{7} + 23058000 \, x^{6} + 63495075 \, x^{5} + 111095730 \, x^{4} + 147527176 \, x^{3} + 184884496 \, x^{2} + 393552752 \, x - 395714912\right)} \sqrt{-2 \, x + 1}}{5005 \, {\left(2 \, x - 1\right)}}"," ",0,"1/5005*(3898125*x^7 + 23058000*x^6 + 63495075*x^5 + 111095730*x^4 + 147527176*x^3 + 184884496*x^2 + 393552752*x - 395714912)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2095,1,46,0,1.227549," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(118125 \, x^{6} + 627375 \, x^{5} + 1564350 \, x^{4} + 2569643 \, x^{3} + 3611453 \, x^{2} + 8012926 \, x - 8096086\right)} \sqrt{-2 \, x + 1}}{385 \, {\left(2 \, x - 1\right)}}"," ",0,"1/385*(118125*x^6 + 627375*x^5 + 1564350*x^4 + 2569643*x^3 + 3611453*x^2 + 8012926*x - 8096086)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2096,1,41,0,1.624974," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(875 \, x^{5} + 4150 \, x^{4} + 9501 \, x^{3} + 15948 \, x^{2} + 37944 \, x - 38700\right)} \sqrt{-2 \, x + 1}}{7 \, {\left(2 \, x - 1\right)}}"," ",0,"1/7*(875*x^5 + 4150*x^4 + 9501*x^3 + 15948*x^2 + 37944*x - 38700)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2097,1,36,0,0.960151," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(375 \, x^{4} + 1595 \, x^{3} + 3590 \, x^{2} + 9637 \, x - 10015\right)} \sqrt{-2 \, x + 1}}{7 \, {\left(2 \, x - 1\right)}}"," ",0,"1/7*(375*x^4 + 1595*x^3 + 3590*x^2 + 9637*x - 10015)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2098,1,30,0,1.073306," ","integrate((3+5*x)^3/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(25 \, x^{3} + 100 \, x^{2} + 335 \, x - 362\right)} \sqrt{-2 \, x + 1}}{2 \, x - 1}"," ",0,"(25*x^3 + 100*x^2 + 335*x - 362)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2099,1,64,0,1.072262," ","integrate((3+5*x)^3/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{21} {\left(2 \, x - 1\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(875 \, x^{2} + 4725 \, x - 5576\right)} \sqrt{-2 \, x + 1}}{1323 \, {\left(2 \, x - 1\right)}}"," ",0,"1/1323*(sqrt(21)*(2*x - 1)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(875*x^2 + 4725*x - 5576)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2100,1,70,0,1.114058," ","integrate((3+5*x)^3/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{34 \, \sqrt{21} {\left(6 \, x^{2} + x - 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(6125 \, x^{2} - 4968 \, x - 6035\right)} \sqrt{-2 \, x + 1}}{3087 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/3087*(34*sqrt(21)*(6*x^2 + x - 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(6125*x^2 - 4968*x - 6035)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2101,1,85,0,1.275095," ","integrate((3+5*x)^3/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{2245 \, \sqrt{21} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(72280 \, x^{2} + 95895 \, x + 31811\right)} \sqrt{-2 \, x + 1}}{43218 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/43218*(2245*sqrt(21)*(18*x^3 + 15*x^2 - 4*x - 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(72280*x^2 + 95895*x + 31811)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2102,1,99,0,1.271973," ","integrate((3+5*x)^3/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{4660 \, \sqrt{21} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(83880 \, x^{3} + 178015 \, x^{2} + 125154 \, x + 29177\right)} \sqrt{-2 \, x + 1}}{64827 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"1/64827*(4660*sqrt(21)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(83880*x^3 + 178015*x^2 + 125154*x + 29177)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2103,1,114,0,1.299521," ","integrate((3+5*x)^3/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{39185 \, \sqrt{21} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(2115990 \, x^{4} + 4819755 \, x^{3} + 4093057 \, x^{2} + 1534434 \, x + 213998\right)} \sqrt{-2 \, x + 1}}{1210104 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"1/1210104*(39185*sqrt(21)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(2115990*x^4 + 4819755*x^3 + 4093057*x^2 + 1534434*x + 213998)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2104,1,79,0,1.039824," ","integrate((2+3*x)^6/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{7 \, \sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(3898125 \, x^{5} + 19824750 \, x^{4} + 48323385 \, x^{3} + 85159800 \, x^{2} + 207964053 \, x - 213097384\right)} \sqrt{-2 \, x + 1}}{13234375 \, {\left(2 \, x - 1\right)}}"," ",0,"1/13234375*(7*sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(3898125*x^5 + 19824750*x^4 + 48323385*x^3 + 85159800*x^2 + 207964053*x - 213097384)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2105,1,74,0,1.330675," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{7 \, \sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(334125 \, x^{4} + 1545885 \, x^{3} + 3732300 \, x^{2} + 10459053 \, x - 10972384\right)} \sqrt{-2 \, x + 1}}{2646875 \, {\left(2 \, x - 1\right)}}"," ",0,"1/2646875*(7*sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(334125*x^4 + 1545885*x^3 + 3732300*x^2 + 10459053*x - 10972384)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2106,1,68,0,1.154138," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(4455 \, x^{3} + 19800 \, x^{2} + 71379 \, x - 78712\right)} \sqrt{-2 \, x + 1}}{75625 \, {\left(2 \, x - 1\right)}}"," ",0,"1/75625*(sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(4455*x^3 + 19800*x^2 + 71379*x - 78712)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2107,1,63,0,1.203301," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(495 \, x^{2} + 3069 \, x - 3802\right)} \sqrt{-2 \, x + 1}}{15125 \, {\left(2 \, x - 1\right)}}"," ",0,"1/15125*(sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(495*x^2 + 3069*x - 3802)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2108,1,58,0,1.177795," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(99 \, x - 172\right)} \sqrt{-2 \, x + 1}}{3025 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3025*(sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(99*x - 172)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2109,1,53,0,1.294525," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{\sqrt{55} {\left(2 \, x - 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 385 \, \sqrt{-2 \, x + 1}}{605 \, {\left(2 \, x - 1\right)}}"," ",0,"1/605*(sqrt(55)*(2*x - 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 385*sqrt(-2*x + 1))/(2*x - 1)","A",0
2110,1,59,0,1.253090," ","integrate(1/(1-2*x)^(3/2)/(3+5*x),x, algorithm=""fricas"")","\frac{\sqrt{11} \sqrt{5} {\left(2 \, x - 1\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 22 \, \sqrt{-2 \, x + 1}}{121 \, {\left(2 \, x - 1\right)}}"," ",0,"1/121*(sqrt(11)*sqrt(5)*(2*x - 1)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 22*sqrt(-2*x + 1))/(2*x - 1)","B",0
2111,1,102,0,1.223058," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{245 \, \sqrt{11} \sqrt{5} {\left(2 \, x - 1\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 363 \, \sqrt{7} \sqrt{3} {\left(2 \, x - 1\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - 308 \, \sqrt{-2 \, x + 1}}{5929 \, {\left(2 \, x - 1\right)}}"," ",0,"1/5929*(245*sqrt(11)*sqrt(5)*(2*x - 1)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 363*sqrt(7)*sqrt(3)*(2*x - 1)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 308*sqrt(-2*x + 1))/(2*x - 1)","B",0
2112,1,116,0,1.349420," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{8575 \, \sqrt{11} \sqrt{5} {\left(6 \, x^{2} + x - 2\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 13794 \, \sqrt{7} \sqrt{3} {\left(6 \, x^{2} + x - 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(174 \, x - 115\right)} \sqrt{-2 \, x + 1}}{41503 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/41503*(8575*sqrt(11)*sqrt(5)*(6*x^2 + x - 2)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 13794*sqrt(7)*sqrt(3)*(6*x^2 + x - 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(174*x - 115)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2113,1,142,0,0.807506," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{600250 \, \sqrt{11} \sqrt{5} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 971025 \, \sqrt{7} \sqrt{3} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(45450 \, x^{2} + 8625 \, x - 16067\right)} \sqrt{-2 \, x + 1}}{581042 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/581042*(600250*sqrt(11)*sqrt(5)*(18*x^3 + 15*x^2 - 4*x - 4)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 971025*sqrt(7)*sqrt(3)*(18*x^3 + 15*x^2 - 4*x - 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(45450*x^2 + 8625*x - 16067)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2114,1,162,0,1.344173," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{1500625 \, \sqrt{11} \sqrt{5} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 2428470 \, \sqrt{7} \sqrt{3} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(345330 \, x^{3} + 299115 \, x^{2} - 74556 \, x - 80863\right)} \sqrt{-2 \, x + 1}}{290521 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"1/290521*(1500625*sqrt(11)*sqrt(5)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 2428470*sqrt(7)*sqrt(3)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(345330*x^3 + 299115*x^2 - 74556*x - 80863)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2115,1,85,0,1.194486," ","integrate((2+3*x)^6/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{1407 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(55130625 \, x^{5} + 293294925 \, x^{4} + 795400155 \, x^{3} + 2195407665 \, x^{2} - 818846961 \, x - 1143572552\right)} \sqrt{-2 \, x + 1}}{145578125 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/145578125*(1407*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(55130625*x^5 + 293294925*x^4 + 795400155*x^3 + 2195407665*x^2 - 818846961*x - 1143572552)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2116,1,80,0,1.212836," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{168 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(735075 \, x^{4} + 3789720 \, x^{3} + 14309460 \, x^{2} - 6264264 \, x - 8186648\right)} \sqrt{-2 \, x + 1}}{4159375 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/4159375*(168*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(735075*x^4 + 3789720*x^3 + 14309460*x^2 - 6264264*x - 8186648)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2117,1,75,0,1.211401," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{27 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(16335 \, x^{3} + 114345 \, x^{2} - 68661 \, x - 78832\right)} \sqrt{-2 \, x + 1}}{166375 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/166375*(27*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(16335*x^3 + 114345*x^2 - 68661*x - 78832)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2118,1,70,0,0.926235," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{102 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(16335 \, x^{2} - 19806 \, x - 17762\right)} \sqrt{-2 \, x + 1}}{166375 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/166375*(102*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(16335*x^2 - 19806*x - 17762)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2119,1,65,0,1.384220," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{69 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(1227 \, x + 734\right)} \sqrt{-2 \, x + 1}}{33275 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/33275*(69*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(1227*x + 734)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2120,1,65,0,1.313920," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{36 \, \sqrt{55} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(72 \, x + 41\right)} \sqrt{-2 \, x + 1}}{6655 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/6655*(36*sqrt(55)*(10*x^2 + x - 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(72*x + 41)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2121,1,71,0,1.211364," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{11} \sqrt{5} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(30 \, x + 7\right)} \sqrt{-2 \, x + 1}}{1331 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1331*(3*sqrt(11)*sqrt(5)*(10*x^2 + x - 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(30*x + 7)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2122,1,116,0,1.579071," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{7350 \, \sqrt{11} \sqrt{5} {\left(10 \, x^{2} + x - 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 11979 \, \sqrt{7} \sqrt{3} {\left(10 \, x^{2} + x - 3\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(390 \, x - 151\right)} \sqrt{-2 \, x + 1}}{65219 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/65219*(7350*sqrt(11)*sqrt(5)*(10*x^2 + x - 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 11979*sqrt(7)*sqrt(3)*(10*x^2 + x - 3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(390*x - 151)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2123,1,142,0,1.512621," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{540225 \, \sqrt{11} \sqrt{5} {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 874467 \, \sqrt{7} \sqrt{3} {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(69660 \, x^{2} + 9696 \, x - 21955\right)} \sqrt{-2 \, x + 1}}{456533 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)}}"," ",0,"1/456533*(540225*sqrt(11)*sqrt(5)*(30*x^3 + 23*x^2 - 7*x - 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 874467*sqrt(7)*sqrt(3)*(30*x^3 + 23*x^2 - 7*x - 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(69660*x^2 + 9696*x - 21955)*sqrt(-2*x + 1))/(30*x^3 + 23*x^2 - 7*x - 6)","A",0
2124,1,162,0,1.311602," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{57624000 \, \sqrt{11} \sqrt{5} {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 93256515 \, \sqrt{7} \sqrt{3} {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(22127850 \, x^{3} + 17711235 \, x^{2} - 5050290 \, x - 4664333\right)} \sqrt{-2 \, x + 1}}{6391462 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)}}"," ",0,"1/6391462*(57624000*sqrt(11)*sqrt(5)*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 93256515*sqrt(7)*sqrt(3)*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(22127850*x^3 + 17711235*x^2 - 5050290*x - 4664333)*sqrt(-2*x + 1))/(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)","A",0
2125,1,99,0,1.129523," ","integrate((2+3*x)^6/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{33873 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(242574750 \, x^{5} + 1423105200 \, x^{4} + 5682717810 \, x^{3} + 762244410 \, x^{2} - 4150263077 \, x - 1702670584\right)} \sqrt{-2 \, x + 1}}{457531250 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/457531250*(33873*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(242574750*x^5 + 1423105200*x^4 + 5682717810*x^3 + 762244410*x^2 - 4150263077*x - 1702670584)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2126,1,94,0,1.150662," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{4557 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(5390550 \, x^{4} + 42046290 \, x^{3} - 764310 \, x^{2} - 41668993 \, x - 16342856\right)} \sqrt{-2 \, x + 1}}{18301250 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/18301250*(4557*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(5390550*x^4 + 42046290*x^3 - 764310*x^2 - 41668993*x - 16342856)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2127,1,89,0,1.422623," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{111 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 11 \, {\left(215622 \, x^{3} - 149298 \, x^{2} - 411911 \, x - 146824\right)} \sqrt{-2 \, x + 1}}{146410 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/146410*(111*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 11*(215622*x^3 - 149298*x^2 - 411911*x - 146824)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2128,1,84,0,1.162015," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{7143 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(430800 \, x^{2} + 514727 \, x + 153724\right)} \sqrt{-2 \, x + 1}}{3660250 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/3660250*(7143*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(430800*x^2 + 514727*x + 153724)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2129,1,84,0,1.332318," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{2589 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(25890 \, x^{2} + 29561 \, x + 8392\right)} \sqrt{-2 \, x + 1}}{732050 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/732050*(2589*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(25890*x^2 + 29561*x + 8392)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2130,1,84,0,1.070507," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{213 \, \sqrt{55} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(2130 \, x^{2} + 1775 \, x + 274\right)} \sqrt{-2 \, x + 1}}{146410 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/146410*(213*sqrt(55)*(50*x^3 + 35*x^2 - 12*x - 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(2130*x^2 + 1775*x + 274)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2131,1,90,0,1.334763," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{15 \, \sqrt{11} \sqrt{5} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(750 \, x^{2} + 625 \, x - 16\right)} \sqrt{-2 \, x + 1}}{29282 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/29282*(15*sqrt(11)*sqrt(5)*(50*x^3 + 35*x^2 - 12*x - 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(750*x^2 + 625*x - 16)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2132,1,142,0,1.315870," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{488775 \, \sqrt{11} \sqrt{5} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 790614 \, \sqrt{7} \sqrt{3} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(102450 \, x^{2} + 5515 \, x - 29338\right)} \sqrt{-2 \, x + 1}}{1434818 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/1434818*(488775*sqrt(11)*sqrt(5)*(50*x^3 + 35*x^2 - 12*x - 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 790614*sqrt(7)*sqrt(3)*(50*x^3 + 35*x^2 - 12*x - 9)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(102450*x^2 + 5515*x - 29338)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2133,1,162,0,1.378515," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{52761975 \, \sqrt{11} \sqrt{5} {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 85386312 \, \sqrt{7} \sqrt{3} {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(33745050 \, x^{3} + 24742935 \, x^{2} - 8019782 \, x - 6400750\right)} \sqrt{-2 \, x + 1}}{10043726 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)}}"," ",0,"1/10043726*(52761975*sqrt(11)*sqrt(5)*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 85386312*sqrt(7)*sqrt(3)*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(33745050*x^3 + 24742935*x^2 - 8019782*x - 6400750)*sqrt(-2*x + 1))/(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)","A",0
2134,1,182,0,1.346586," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{3748261125 \, \sqrt{11} \sqrt{5} {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 6065985915 \, \sqrt{7} \sqrt{3} {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(7194325500 \, x^{4} + 10073172600 \, x^{3} + 1810042755 \, x^{2} - 2503057145 \, x - 909821467\right)} \sqrt{-2 \, x + 1}}{70306082 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)}}"," ",0,"1/70306082*(3748261125*sqrt(11)*sqrt(5)*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 6065985915*sqrt(7)*sqrt(3)*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(7194325500*x^4 + 10073172600*x^3 + 1810042755*x^2 - 2503057145*x - 909821467)*sqrt(-2*x + 1))/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)","A",0
2135,1,51,0,1.038697," ","integrate((2+3*x)^5*(3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(2835 \, x^{6} + 16767 \, x^{5} + 49653 \, x^{4} + 114084 \, x^{3} + 412812 \, x^{2} - 844104 \, x + 280696\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/21*(2835*x^6 + 16767*x^5 + 49653*x^4 + 114084*x^3 + 412812*x^2 - 844104*x + 280696)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2136,1,46,0,1.152035," ","integrate((2+3*x)^4*(3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(6075 \, x^{5} + 33858 \, x^{4} + 105624 \, x^{3} + 435312 \, x^{2} - 909264 \, x + 301408\right)} \sqrt{-2 \, x + 1}}{105 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/105*(6075*x^5 + 33858*x^4 + 105624*x^3 + 435312*x^2 - 909264*x + 301408)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2137,1,41,0,1.079514," ","integrate((2+3*x)^3*(3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(81 \, x^{4} + 459 \, x^{3} + 2403 \, x^{2} - 5250 \, x + 1726\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(81*x^4 + 459*x^3 + 2403*x^2 - 5250*x + 1726)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2138,1,36,0,1.096192," ","integrate((2+3*x)^2*(3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(45 \, x^{3} + 396 \, x^{2} - 960 \, x + 308\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(45*x^3 + 396*x^2 - 960*x + 308)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2139,1,31,0,1.333278," ","integrate((2+3*x)*(3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(45 \, x^{2} - 147 \, x + 43\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(45*x^2 - 147*x + 43)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2140,1,26,0,1.323061," ","integrate((3+5*x)/(1-2*x)^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, x - 2\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/3*(15*x - 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2141,1,76,0,1.230870," ","integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{7} \sqrt{3} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 7 \, {\left(12 \, x + 71\right)} \sqrt{-2 \, x + 1}}{1029 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/1029*(3*sqrt(7)*sqrt(3)*(4*x^2 - 4*x + 1)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 7*(12*x + 71)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","B",0
2142,1,90,0,1.280069," ","integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{90 \, \sqrt{7} \sqrt{3} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(1080 \, x^{2} - 240 \, x - 689\right)} \sqrt{-2 \, x + 1}}{7203 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/7203*(90*sqrt(7)*sqrt(3)*(12*x^3 - 4*x^2 - 5*x + 2)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(1080*x^2 - 240*x - 689)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2143,1,105,0,1.216708," ","integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{135 \, \sqrt{7} \sqrt{3} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(4860 \, x^{3} + 2160 \, x^{2} - 2277 \, x - 1087\right)} \sqrt{-2 \, x + 1}}{14406 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/14406*(135*sqrt(7)*sqrt(3)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(4860*x^3 + 2160*x^2 - 2277*x - 1087)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2144,1,120,0,1.509376," ","integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{240 \, \sqrt{7} \sqrt{3} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(25920 \, x^{4} + 28800 \, x^{3} - 4464 \, x^{2} - 11280 \, x - 2237\right)} \sqrt{-2 \, x + 1}}{50421 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"1/50421*(240*sqrt(7)*sqrt(3)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(25920*x^4 + 28800*x^3 - 4464*x^2 - 11280*x - 2237)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2145,1,135,0,1.246424," ","integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{5805 \, \sqrt{7} \sqrt{3} {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(1880820 \, x^{5} + 3343680 \, x^{4} + 1069281 \, x^{3} - 1034451 \, x^{2} - 611202 \, x - 48490\right)} \sqrt{-2 \, x + 1}}{2823576 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"1/2823576*(5805*sqrt(7)*sqrt(3)*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(1880820*x^5 + 3343680*x^4 + 1069281*x^3 - 1034451*x^2 - 611202*x - 48490)*sqrt(-2*x + 1))/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
2146,1,56,0,1.185128," ","integrate((2+3*x)^5*(3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(127575 \, x^{7} + 806085 \, x^{6} + 2456001 \, x^{5} + 5121279 \, x^{4} + 9702012 \, x^{3} + 32450916 \, x^{2} - 65622552 \, x + 21852008\right)} \sqrt{-2 \, x + 1}}{231 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/231*(127575*x^7 + 806085*x^6 + 2456001*x^5 + 5121279*x^4 + 9702012*x^3 + 32450916*x^2 - 65622552*x + 21852008)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2147,1,51,0,1.179459," ","integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(23625 \, x^{6} + 137700 \, x^{5} + 402489 \, x^{4} + 915492 \, x^{3} + 3294996 \, x^{2} - 6731112 \, x + 2238664\right)} \sqrt{-2 \, x + 1}}{105 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/105*(23625*x^6 + 137700*x^5 + 402489*x^4 + 915492*x^3 + 3294996*x^2 - 6731112*x + 2238664)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2148,1,46,0,0.888725," ","integrate((2+3*x)^3*(3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(2025 \, x^{5} + 11097 \, x^{4} + 34137 \, x^{3} + 139497 \, x^{2} - 290838 \, x + 96442\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/21*(2025*x^5 + 11097*x^4 + 34137*x^3 + 139497*x^2 - 290838*x + 96442)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2149,1,41,0,1.195602," ","integrate((2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(135 \, x^{4} + 750 \, x^{3} + 3873 \, x^{2} - 8430 \, x + 2774\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(135*x^4 + 750*x^3 + 3873*x^2 - 8430*x + 2774)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2150,1,36,0,1.130450," ","integrate((2+3*x)*(3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(75 \, x^{3} + 645 \, x^{2} - 1551 \, x + 499\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(75*x^3 + 645*x^2 - 1551*x + 499)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2151,1,31,0,0.937369," ","integrate((3+5*x)^2/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(75 \, x^{2} - 240 \, x + 71\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(75*x^2 - 240*x + 71)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2152,1,68,0,1.398327," ","integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{21} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 77 \, {\left(111 \, x - 17\right)} \sqrt{-2 \, x + 1}}{1029 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/1029*(sqrt(21)*(4*x^2 - 4*x + 1)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 77*(111*x - 17)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2153,1,85,0,1.144752," ","integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{65 \, \sqrt{21} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 7 \, {\left(780 \, x^{2} + 2685 \, x + 1427\right)} \sqrt{-2 \, x + 1}}{7203 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/7203*(65*sqrt(21)*(12*x^3 - 4*x^2 - 5*x + 2)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 7*(780*x^2 + 2685*x + 1427)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2154,1,105,0,0.789438," ","integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{255 \, \sqrt{7} \sqrt{3} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 7 \, {\left(9180 \, x^{3} + 4080 \, x^{2} - 7731 \, x - 4231\right)} \sqrt{-2 \, x + 1}}{14406 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/14406*(255*sqrt(7)*sqrt(3)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 7*(9180*x^3 + 4080*x^2 - 7731*x - 4231)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2155,1,114,0,1.258291," ","integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{1415 \, \sqrt{21} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 7 \, {\left(152820 \, x^{4} + 169800 \, x^{3} - 26319 \, x^{2} - 83655 \, x - 23872\right)} \sqrt{-2 \, x + 1}}{100842 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"1/100842*(1415*sqrt(21)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 7*(152820*x^4 + 169800*x^3 - 26319*x^2 - 83655*x - 23872)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2156,1,129,0,1.344218," ","integrate((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{20465 \, \sqrt{21} {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 7 \, {\left(6630660 \, x^{5} + 11787840 \, x^{4} + 3769653 \, x^{3} - 3646863 \, x^{2} - 2528226 \, x - 401410\right)} \sqrt{-2 \, x + 1}}{2823576 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"1/2823576*(20465*sqrt(21)*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 7*(6630660*x^5 + 11787840*x^4 + 3769653*x^3 - 3646863*x^2 - 2528226*x - 401410)*sqrt(-2*x + 1))/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
2157,1,61,0,1.214889," ","integrate((2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(7016625 \, x^{8} + 47670525 \, x^{7} + 153878760 \, x^{6} + 324478899 \, x^{5} + 540496701 \, x^{4} + 905206628 \, x^{3} + 2892917004 \, x^{2} - 5818266408 \, x + 1938557272\right)} \sqrt{-2 \, x + 1}}{3003 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3003*(7016625*x^8 + 47670525*x^7 + 153878760*x^6 + 324478899*x^5 + 540496701*x^4 + 905206628*x^3 + 2892917004*x^2 - 5818266408*x + 1938557272)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2158,1,56,0,1.261465," ","integrate((2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(1063125 \, x^{7} + 6630750 \, x^{6} + 19961775 \, x^{5} + 41201532 \, x^{4} + 77493296 \, x^{3} + 258342648 \, x^{2} - 522173856 \, x + 173891632\right)} \sqrt{-2 \, x + 1}}{1155 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1155*(1063125*x^7 + 6630750*x^6 + 19961775*x^5 + 41201532*x^4 + 77493296*x^3 + 258342648*x^2 - 522173856*x + 173891632)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2159,1,51,0,1.334560," ","integrate((2+3*x)^3*(3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(7875 \, x^{6} + 45225 \, x^{5} + 130464 \, x^{4} + 293785 \, x^{3} + 1051833 \, x^{2} - 2146758 \, x + 714074\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/21*(7875*x^6 + 45225*x^5 + 130464*x^4 + 293785*x^3 + 1051833*x^2 - 2146758*x + 714074)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2160,1,46,0,1.202952," ","integrate((2+3*x)^2*(3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3375 \, x^{5} + 18180 \, x^{4} + 55145 \, x^{3} + 223458 \, x^{2} - 465060 \, x + 154264\right)} \sqrt{-2 \, x + 1}}{21 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/21*(3375*x^5 + 18180*x^4 + 55145*x^3 + 223458*x^2 - 465060*x + 154264)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2161,1,41,0,0.820632," ","integrate((2+3*x)*(3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(225 \, x^{4} + 1225 \, x^{3} + 6240 \, x^{2} - 13533 \, x + 4457\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(225*x^4 + 1225*x^3 + 6240*x^2 - 13533*x + 4457)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2162,1,36,0,1.298073," ","integrate((3+5*x)^3/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(125 \, x^{3} + 1050 \, x^{2} - 2505 \, x + 808\right)} \sqrt{-2 \, x + 1}}{3 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3*(125*x^3 + 1050*x^2 - 2505*x + 808)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2163,1,74,0,1.229711," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{21} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(6125 \, x^{2} - 19193 \, x + 5736\right)} \sqrt{-2 \, x + 1}}{3087 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/3087*(sqrt(21)*(4*x^2 - 4*x + 1)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(6125*x^2 - 19193*x + 5736)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2164,1,84,0,1.182332," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{100 \, \sqrt{21} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(42475 \, x^{2} + 21050 \, x - 4839\right)} \sqrt{-2 \, x + 1}}{21609 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/21609*(100*sqrt(21)*(12*x^3 - 4*x^2 - 5*x + 2)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(42475*x^2 + 21050*x - 4839)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2165,1,100,0,0.736376," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{905 \, \sqrt{21} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(\frac{3 \, x - \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) + 21 \, {\left(10860 \, x^{3} + 33410 \, x^{2} + 29593 \, x + 8103\right)} \sqrt{-2 \, x + 1}}{43218 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/43218*(905*sqrt(21)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log((3*x - sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) + 21*(10860*x^3 + 33410*x^2 + 29593*x + 8103)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2166,1,114,0,1.264213," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{3755 \, \sqrt{21} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(135180 \, x^{4} + 150200 \, x^{3} - 83306 \, x^{2} - 150295 \, x - 45383\right)} \sqrt{-2 \, x + 1}}{151263 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"1/151263*(3755*sqrt(21)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(135180*x^4 + 150200*x^3 - 83306*x^2 - 150295*x - 45383)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2167,1,129,0,1.182517," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{177635 \, \sqrt{21} {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(19184580 \, x^{5} + 34105920 \, x^{4} + 10906789 \, x^{3} - 12952519 \, x^{2} - 10307138 \, x - 2094250\right)} \sqrt{-2 \, x + 1}}{8470728 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"1/8470728*(177635*sqrt(21)*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(19184580*x^5 + 34105920*x^4 + 10906789*x^3 - 12952519*x^2 - 10307138*x - 2094250)*sqrt(-2*x + 1))/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
2168,1,144,0,1.390545," ","integrate((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^6,x, algorithm=""fricas"")","\frac{408685 \, \sqrt{21} {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)} \log\left(\frac{3 \, x + \sqrt{21} \sqrt{-2 \, x + 1} - 5}{3 \, x + 2}\right) - 21 \, {\left(132413940 \, x^{6} + 323678520 \, x^{5} + 232214817 \, x^{4} - 22641149 \, x^{3} - 99751837 \, x^{2} - 42553376 \, x - 5615203\right)} \sqrt{-2 \, x + 1}}{37059435 \, {\left(972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32\right)}}"," ",0,"1/37059435*(408685*sqrt(21)*(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)*log((3*x + sqrt(21)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - 21*(132413940*x^6 + 323678520*x^5 + 232214817*x^4 - 22641149*x^3 - 99751837*x^2 - 42553376*x - 5615203)*sqrt(-2*x + 1))/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32)","A",0
2169,1,89,0,1.230336," ","integrate((2+3*x)^6/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{21 \, \sqrt{55} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(33078375 \, x^{5} + 190531440 \, x^{4} + 611141355 \, x^{3} + 2562785082 \, x^{2} - 5374023537 \, x + 1780047848\right)} \sqrt{-2 \, x + 1}}{87346875 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/87346875*(21*sqrt(55)*(4*x^2 - 4*x + 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(33078375*x^5 + 190531440*x^4 + 611141355*x^3 + 2562785082*x^2 - 5374023537*x + 1780047848)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2170,1,84,0,1.345191," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(441045 \, x^{4} + 2597265 \, x^{3} + 13976226 \, x^{2} - 30775791 \, x + 10097264\right)} \sqrt{-2 \, x + 1}}{2495625 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/2495625*(3*sqrt(55)*(4*x^2 - 4*x + 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(441045*x^4 + 2597265*x^3 + 13976226*x^2 - 30775791*x + 10097264)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2171,1,79,0,1.148715," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(49005 \, x^{3} + 450846 \, x^{2} - 1111431 \, x + 354344\right)} \sqrt{-2 \, x + 1}}{499125 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/499125*(3*sqrt(55)*(4*x^2 - 4*x + 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(49005*x^3 + 450846*x^2 - 1111431*x + 354344)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2172,1,74,0,1.329607," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(9801 \, x^{2} - 33321 \, x + 9494\right)} \sqrt{-2 \, x + 1}}{99825 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/99825*(3*sqrt(55)*(4*x^2 - 4*x + 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(9801*x^2 - 33321*x + 9494)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2173,1,69,0,1.085181," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{55} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 385 \, {\left(93 \, x - 8\right)} \sqrt{-2 \, x + 1}}{19965 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/19965*(3*sqrt(55)*(4*x^2 - 4*x + 1)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 385*(93*x - 8)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2174,1,75,0,1.311943," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{11} \sqrt{5} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(12 \, x - 83\right)} \sqrt{-2 \, x + 1}}{3993 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/3993*(3*sqrt(11)*sqrt(5)*(4*x^2 - 4*x + 1)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(12*x - 83)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","B",0
2175,1,75,0,1.182713," ","integrate(1/(1-2*x)^(5/2)/(3+5*x),x, algorithm=""fricas"")","\frac{15 \, \sqrt{11} \sqrt{5} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 44 \, {\left(15 \, x - 13\right)} \sqrt{-2 \, x + 1}}{3993 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/3993*(15*sqrt(11)*sqrt(5)*(4*x^2 - 4*x + 1)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 44*(15*x - 13)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","B",0
2176,1,122,0,1.264127," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x),x, algorithm=""fricas"")","\frac{25725 \, \sqrt{11} \sqrt{5} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 35937 \, \sqrt{7} \sqrt{3} {\left(4 \, x^{2} - 4 \, x + 1\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) - 308 \, {\left(408 \, x - 281\right)} \sqrt{-2 \, x + 1}}{1369599 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/1369599*(25725*sqrt(11)*sqrt(5)*(4*x^2 - 4*x + 1)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 35937*sqrt(7)*sqrt(3)*(4*x^2 - 4*x + 1)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) - 308*(408*x - 281)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","B",0
2177,1,142,0,1.343320," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x),x, algorithm=""fricas"")","\frac{900375 \, \sqrt{11} \sqrt{5} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 1437480 \, \sqrt{7} \sqrt{3} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(24660 \, x^{2} - 39780 \, x + 15881\right)} \sqrt{-2 \, x + 1}}{9587193 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/9587193*(900375*sqrt(11)*sqrt(5)*(12*x^3 - 4*x^2 - 5*x + 2)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 1437480*sqrt(7)*sqrt(3)*(12*x^3 - 4*x^2 - 5*x + 2)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(24660*x^2 - 39780*x + 15881)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2178,1,162,0,1.145063," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x),x, algorithm=""fricas"")","\frac{9003750 \, \sqrt{11} \sqrt{5} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 14554485 \, \sqrt{7} \sqrt{3} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(1327860 \, x^{3} - 438840 \, x^{2} - 594687 \, x + 245383\right)} \sqrt{-2 \, x + 1}}{19174386 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/19174386*(9003750*sqrt(11)*sqrt(5)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 14554485*sqrt(7)*sqrt(3)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(1327860*x^3 - 438840*x^2 - 594687*x + 245383)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2179,1,182,0,1.199157," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^4/(3+5*x),x, algorithm=""fricas"")","\frac{157565625 \, \sqrt{11} \sqrt{5} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 254973015 \, \sqrt{7} \sqrt{3} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(72358920 \, x^{4} + 26376300 \, x^{3} - 47036214 \, x^{2} - 9083055 \, x + 8496203\right)} \sqrt{-2 \, x + 1}}{67110351 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"1/67110351*(157565625*sqrt(11)*sqrt(5)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 254973015*sqrt(7)*sqrt(3)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(72358920*x^4 + 26376300*x^3 - 47036214*x^2 - 9083055*x + 8496203)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2180,1,99,0,1.380124," ","integrate((2+3*x)^6/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{609 \, \sqrt{55} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(72772425 \, x^{5} + 480298005 \, x^{4} + 2644064775 \, x^{3} - 3837745731 \, x^{2} - 1434109759 \, x + 1035652776\right)} \sqrt{-2 \, x + 1}}{137259375 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/137259375*(609*sqrt(55)*(20*x^3 - 8*x^2 - 7*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(72772425*x^5 + 480298005*x^4 + 2644064775*x^3 - 3837745731*x^2 - 1434109759*x + 1035652776)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2181,1,94,0,1.194772," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{102 \, \sqrt{55} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(1617165 \, x^{4} + 16171650 \, x^{3} - 28677318 \, x^{2} - 10671002 \, x + 7204728\right)} \sqrt{-2 \, x + 1}}{5490375 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/5490375*(102*sqrt(55)*(20*x^3 - 8*x^2 - 7*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(1617165*x^4 + 16171650*x^3 - 28677318*x^2 - 10671002*x + 7204728)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2182,1,89,0,1.169026," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{411 \, \sqrt{55} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(1617165 \, x^{3} - 4634229 \, x^{2} - 1790101 \, x + 943584\right)} \sqrt{-2 \, x + 1}}{5490375 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/5490375*(411*sqrt(55)*(20*x^3 - 8*x^2 - 7*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(1617165*x^3 - 4634229*x^2 - 1790101*x + 943584)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2183,1,84,0,1.209920," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{312 \, \sqrt{55} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(106563 \, x^{2} + 57832 \, x - 3678\right)} \sqrt{-2 \, x + 1}}{1098075 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/1098075*(312*sqrt(55)*(20*x^3 - 8*x^2 - 7*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(106563*x^2 + 57832*x - 3678)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2184,1,84,0,0.868117," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{213 \, \sqrt{55} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(852 \, x^{2} - 2623 \, x - 1866\right)} \sqrt{-2 \, x + 1}}{219615 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/219615*(213*sqrt(55)*(20*x^3 - 8*x^2 - 7*x + 3)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(852*x^2 - 2623*x - 1866)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2185,1,90,0,1.408583," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{114 \, \sqrt{11} \sqrt{5} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(2280 \, x^{2} - 608 \, x - 1113\right)} \sqrt{-2 \, x + 1}}{43923 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/43923*(114*sqrt(11)*sqrt(5)*(20*x^3 - 8*x^2 - 7*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(2280*x^2 - 608*x - 1113)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2186,1,90,0,1.301055," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{75 \, \sqrt{11} \sqrt{5} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(1500 \, x^{2} - 400 \, x - 417\right)} \sqrt{-2 \, x + 1}}{43923 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/43923*(75*sqrt(11)*sqrt(5)*(20*x^3 - 8*x^2 - 7*x + 3)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(1500*x^2 - 400*x - 417)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2187,1,142,0,1.343108," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x)^2,x, algorithm=""fricas"")","\frac{720300 \, \sqrt{11} \sqrt{5} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 1185921 \, \sqrt{7} \sqrt{3} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(98220 \, x^{2} - 74108 \, x + 9111\right)} \sqrt{-2 \, x + 1}}{15065589 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/15065589*(720300*sqrt(11)*sqrt(5)*(20*x^3 - 8*x^2 - 7*x + 3)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 1185921*sqrt(7)*sqrt(3)*(20*x^3 - 8*x^2 - 7*x + 3)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(98220*x^2 - 74108*x + 9111)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2188,1,162,0,1.194936," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^2,x, algorithm=""fricas"")","\frac{54922875 \, \sqrt{11} \sqrt{5} {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 88944075 \, \sqrt{7} \sqrt{3} {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(14382000 \, x^{3} - 5028300 \, x^{2} - 5548760 \, x + 2209989\right)} \sqrt{-2 \, x + 1}}{105459123 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)}}"," ",0,"1/105459123*(54922875*sqrt(11)*sqrt(5)*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 88944075*sqrt(7)*sqrt(3)*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(14382000*x^3 - 5028300*x^2 - 5548760*x + 2209989)*sqrt(-2*x + 1))/(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)","A",0
2189,1,182,0,1.279311," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^2,x, algorithm=""fricas"")","\frac{120907500 \, \sqrt{11} \sqrt{5} {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \log\left(-\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} - 5 \, x + 8}{5 \, x + 3}\right) + 195676965 \, \sqrt{7} \sqrt{3} {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \log\left(\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} + 3 \, x - 5}{3 \, x + 2}\right) - 77 \, {\left(92936700 \, x^{4} + 27977220 \, x^{3} - 58371045 \, x^{2} - 9008764 \, x + 9784671\right)} \sqrt{-2 \, x + 1}}{30131178 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)}}"," ",0,"1/30131178*(120907500*sqrt(11)*sqrt(5)*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log(-(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) - 5*x + 8)/(5*x + 3)) + 195676965*sqrt(7)*sqrt(3)*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*log((sqrt(7)*sqrt(3)*sqrt(-2*x + 1) + 3*x - 5)/(3*x + 2)) - 77*(92936700*x^4 + 27977220*x^3 - 58371045*x^2 - 9008764*x + 9784671)*sqrt(-2*x + 1))/(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)","A",0
2190,1,109,0,1.732684," ","integrate((2+3*x)^6/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{20811 \, \sqrt{55} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(533664450 \, x^{5} + 5763576060 \, x^{4} - 6510290070 \, x^{3} - 9509366452 \, x^{2} + 253794537 \, x + 1463964312\right)} \sqrt{-2 \, x + 1}}{603941250 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/603941250*(20811*sqrt(55)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(533664450*x^5 + 5763576060*x^4 - 6510290070*x^3 - 9509366452*x^2 + 253794537*x + 1463964312)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2191,1,104,0,1.516666," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{14079 \, \sqrt{55} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(106732890 \, x^{4} - 248761830 \, x^{3} - 309826828 \, x^{2} - 10907307 \, x + 37428168\right)} \sqrt{-2 \, x + 1}}{120788250 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/120788250*(14079*sqrt(55)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(106732890*x^4 - 248761830*x^3 - 309826828*x^2 - 10907307*x + 37428168)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2192,1,99,0,1.183399," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{43269 \, \sqrt{55} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) + 55 \, {\left(34712250 \, x^{3} + 40823468 \, x^{2} + 11479257 \, x - 311208\right)} \sqrt{-2 \, x + 1}}{120788250 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/120788250*(43269*sqrt(55)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) + 55*(34712250*x^3 + 40823468*x^2 + 11479257*x - 311208)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2193,1,99,0,1.189836," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{22677 \, \sqrt{55} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(453540 \, x^{3} - 639434 \, x^{2} - 1242261 \, x - 417036\right)} \sqrt{-2 \, x + 1}}{24157650 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/24157650*(22677*sqrt(55)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(453540*x^3 - 639434*x^2 - 1242261*x - 417036)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2194,1,99,0,1.533619," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{8619 \, \sqrt{55} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right) - 55 \, {\left(172380 \, x^{3} + 57460 \, x^{2} - 107127 \, x - 47568\right)} \sqrt{-2 \, x + 1}}{4831530 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/4831530*(8619*sqrt(55)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((5*x + sqrt(55)*sqrt(-2*x + 1) - 8)/(5*x + 3)) - 55*(172380*x^3 + 57460*x^2 - 107127*x - 47568)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2195,1,105,0,1.414577," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1095 \, \sqrt{11} \sqrt{5} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(109500 \, x^{3} + 36500 \, x^{2} - 47961 \, x - 17466\right)} \sqrt{-2 \, x + 1}}{966306 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/966306*(1095*sqrt(11)*sqrt(5)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(109500*x^3 + 36500*x^2 - 47961*x - 17466)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2196,1,105,0,2.148061," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{525 \, \sqrt{11} \sqrt{5} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) - 11 \, {\left(52500 \, x^{3} + 17500 \, x^{2} - 22995 \, x - 4764\right)} \sqrt{-2 \, x + 1}}{966306 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/966306*(525*sqrt(11)*sqrt(5)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) - 11*(52500*x^3 + 17500*x^2 - 22995*x - 4764)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2197,1,162,0,1.609675," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{48440175 \, \sqrt{11} \sqrt{5} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 78270786 \, \sqrt{7} \sqrt{3} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(19550100 \, x^{3} - 9295580 \, x^{2} - 6032979 \, x + 2971158\right)} \sqrt{-2 \, x + 1}}{331442958 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/331442958*(48440175*sqrt(11)*sqrt(5)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 78270786*sqrt(7)*sqrt(3)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(19550100*x^3 - 9295580*x^2 - 6032979*x + 2971158)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2198,1,182,0,1.041442," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^3,x, algorithm=""fricas"")","\frac{5320315875 \, \sqrt{11} \sqrt{5} {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 8609786460 \, \sqrt{7} \sqrt{3} {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(6798820500 \, x^{4} + 1580768100 \, x^{3} - 4110847595 \, x^{2} - 479695050 \, x + 645558882\right)} \sqrt{-2 \, x + 1}}{2320100706 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)}}"," ",0,"1/2320100706*(5320315875*sqrt(11)*sqrt(5)*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 8609786460*sqrt(7)*sqrt(3)*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(6798820500*x^4 + 1580768100*x^3 - 4110847595*x^2 - 479695050*x + 645558882)*sqrt(-2*x + 1))/(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)","A",0
2199,1,202,0,1.310262," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^3,x, algorithm=""fricas"")","\frac{54531211875 \, \sqrt{11} \sqrt{5} {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \log\left(\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right) + 88250311215 \, \sqrt{7} \sqrt{3} {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \log\left(-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right) + 77 \, {\left(209324196000 \, x^{5} + 188418548700 \, x^{4} - 93885376440 \, x^{3} - 99160158305 \, x^{2} + 9944654283 \, x + 13236365823\right)} \sqrt{-2 \, x + 1}}{2320100706 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)}}"," ",0,"1/2320100706*(54531211875*sqrt(11)*sqrt(5)*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log((sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 88250311215*sqrt(7)*sqrt(3)*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(209324196000*x^5 + 188418548700*x^4 - 93885376440*x^3 - 99160158305*x^2 + 9944654283*x + 13236365823)*sqrt(-2*x + 1))/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)","A",0
2200,1,1044,0,1.589412," ","integrate((B*x+A)*(e*x+d)^(5/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(3 \, B b^{5} d^{5} - 5 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} e - 10 \, {\left(B a^{2} b^{3} - 4 \, A a b^{4}\right)} d^{3} e^{2} + 30 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 5 \, {\left(5 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(7 \, B a^{5} - 10 \, A a^{4} b\right)} e^{5}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(384 \, B b^{5} e^{5} x^{4} - 45 \, B b^{5} d^{4} e + 30 \, {\left(2 \, B a b^{4} + 5 \, A b^{5}\right)} d^{3} e^{2} - 2 \, {\left(173 \, B a^{2} b^{3} - 365 \, A a b^{4}\right)} d^{2} e^{3} + 10 \, {\left(34 \, B a^{3} b^{2} - 55 \, A a^{2} b^{3}\right)} d e^{4} - 15 \, {\left(7 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} e^{5} + 48 \, {\left(21 \, B b^{5} d e^{4} + {\left(B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} + 8 \, {\left(93 \, B b^{5} d^{2} e^{3} + 2 \, {\left(11 \, B a b^{4} + 85 \, A b^{5}\right)} d e^{4} - {\left(7 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(15 \, B b^{5} d^{3} e^{2} + {\left(109 \, B a b^{4} + 590 \, A b^{5}\right)} d^{2} e^{3} - 3 \, {\left(37 \, B a^{2} b^{3} - 60 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(7 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{7680 \, b^{5} e^{3}}, -\frac{15 \, {\left(3 \, B b^{5} d^{5} - 5 \, {\left(B a b^{4} + 2 \, A b^{5}\right)} d^{4} e - 10 \, {\left(B a^{2} b^{3} - 4 \, A a b^{4}\right)} d^{3} e^{2} + 30 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 5 \, {\left(5 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(7 \, B a^{5} - 10 \, A a^{4} b\right)} e^{5}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, B b^{5} e^{5} x^{4} - 45 \, B b^{5} d^{4} e + 30 \, {\left(2 \, B a b^{4} + 5 \, A b^{5}\right)} d^{3} e^{2} - 2 \, {\left(173 \, B a^{2} b^{3} - 365 \, A a b^{4}\right)} d^{2} e^{3} + 10 \, {\left(34 \, B a^{3} b^{2} - 55 \, A a^{2} b^{3}\right)} d e^{4} - 15 \, {\left(7 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} e^{5} + 48 \, {\left(21 \, B b^{5} d e^{4} + {\left(B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} + 8 \, {\left(93 \, B b^{5} d^{2} e^{3} + 2 \, {\left(11 \, B a b^{4} + 85 \, A b^{5}\right)} d e^{4} - {\left(7 \, B a^{2} b^{3} - 10 \, A a b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(15 \, B b^{5} d^{3} e^{2} + {\left(109 \, B a b^{4} + 590 \, A b^{5}\right)} d^{2} e^{3} - 3 \, {\left(37 \, B a^{2} b^{3} - 60 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(7 \, B a^{3} b^{2} - 10 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3840 \, b^{5} e^{3}}\right]"," ",0,"[-1/7680*(15*(3*B*b^5*d^5 - 5*(B*a*b^4 + 2*A*b^5)*d^4*e - 10*(B*a^2*b^3 - 4*A*a*b^4)*d^3*e^2 + 30*(B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e^3 - 5*(5*B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (7*B*a^5 - 10*A*a^4*b)*e^5)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(384*B*b^5*e^5*x^4 - 45*B*b^5*d^4*e + 30*(2*B*a*b^4 + 5*A*b^5)*d^3*e^2 - 2*(173*B*a^2*b^3 - 365*A*a*b^4)*d^2*e^3 + 10*(34*B*a^3*b^2 - 55*A*a^2*b^3)*d*e^4 - 15*(7*B*a^4*b - 10*A*a^3*b^2)*e^5 + 48*(21*B*b^5*d*e^4 + (B*a*b^4 + 10*A*b^5)*e^5)*x^3 + 8*(93*B*b^5*d^2*e^3 + 2*(11*B*a*b^4 + 85*A*b^5)*d*e^4 - (7*B*a^2*b^3 - 10*A*a*b^4)*e^5)*x^2 + 2*(15*B*b^5*d^3*e^2 + (109*B*a*b^4 + 590*A*b^5)*d^2*e^3 - 3*(37*B*a^2*b^3 - 60*A*a*b^4)*d*e^4 + 5*(7*B*a^3*b^2 - 10*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^3), -1/3840*(15*(3*B*b^5*d^5 - 5*(B*a*b^4 + 2*A*b^5)*d^4*e - 10*(B*a^2*b^3 - 4*A*a*b^4)*d^3*e^2 + 30*(B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e^3 - 5*(5*B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (7*B*a^5 - 10*A*a^4*b)*e^5)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(384*B*b^5*e^5*x^4 - 45*B*b^5*d^4*e + 30*(2*B*a*b^4 + 5*A*b^5)*d^3*e^2 - 2*(173*B*a^2*b^3 - 365*A*a*b^4)*d^2*e^3 + 10*(34*B*a^3*b^2 - 55*A*a^2*b^3)*d*e^4 - 15*(7*B*a^4*b - 10*A*a^3*b^2)*e^5 + 48*(21*B*b^5*d*e^4 + (B*a*b^4 + 10*A*b^5)*e^5)*x^3 + 8*(93*B*b^5*d^2*e^3 + 2*(11*B*a*b^4 + 85*A*b^5)*d*e^4 - (7*B*a^2*b^3 - 10*A*a*b^4)*e^5)*x^2 + 2*(15*B*b^5*d^3*e^2 + (109*B*a*b^4 + 590*A*b^5)*d^2*e^3 - 3*(37*B*a^2*b^3 - 60*A*a*b^4)*d*e^4 + 5*(7*B*a^3*b^2 - 10*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^3)]","A",0
2201,1,766,0,1.578625," ","integrate((B*x+A)*(e*x+d)^(3/2)*(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B b^{4} d^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} e - 6 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3} - {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(48 \, B b^{4} e^{4} x^{3} - 9 \, B b^{4} d^{3} e + 3 \, {\left(3 \, B a b^{3} + 8 \, A b^{4}\right)} d^{2} e^{2} - {\left(31 \, B a^{2} b^{2} - 64 \, A a b^{3}\right)} d e^{3} + 3 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(9 \, B b^{4} d e^{3} + {\left(B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} + 28 \, A b^{4}\right)} d e^{3} - {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{768 \, b^{4} e^{3}}, -\frac{3 \, {\left(3 \, B b^{4} d^{4} - 4 \, {\left(B a b^{3} + 2 \, A b^{4}\right)} d^{3} e - 6 \, {\left(B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2} + 12 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e^{3} - {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, B b^{4} e^{4} x^{3} - 9 \, B b^{4} d^{3} e + 3 \, {\left(3 \, B a b^{3} + 8 \, A b^{4}\right)} d^{2} e^{2} - {\left(31 \, B a^{2} b^{2} - 64 \, A a b^{3}\right)} d e^{3} + 3 \, {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(9 \, B b^{4} d e^{3} + {\left(B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(3 \, B b^{4} d^{2} e^{2} + 2 \, {\left(5 \, B a b^{3} + 28 \, A b^{4}\right)} d e^{3} - {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{384 \, b^{4} e^{3}}\right]"," ",0,"[1/768*(3*(3*B*b^4*d^4 - 4*(B*a*b^3 + 2*A*b^4)*d^3*e - 6*(B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2 + 12*(B*a^3*b - 2*A*a^2*b^2)*d*e^3 - (5*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(48*B*b^4*e^4*x^3 - 9*B*b^4*d^3*e + 3*(3*B*a*b^3 + 8*A*b^4)*d^2*e^2 - (31*B*a^2*b^2 - 64*A*a*b^3)*d*e^3 + 3*(5*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(9*B*b^4*d*e^3 + (B*a*b^3 + 8*A*b^4)*e^4)*x^2 + 2*(3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 + 28*A*b^4)*d*e^3 - (5*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^3), -1/384*(3*(3*B*b^4*d^4 - 4*(B*a*b^3 + 2*A*b^4)*d^3*e - 6*(B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2 + 12*(B*a^3*b - 2*A*a^2*b^2)*d*e^3 - (5*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(48*B*b^4*e^4*x^3 - 9*B*b^4*d^3*e + 3*(3*B*a*b^3 + 8*A*b^4)*d^2*e^2 - (31*B*a^2*b^2 - 64*A*a*b^3)*d*e^3 + 3*(5*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(9*B*b^4*d*e^3 + (B*a*b^3 + 8*A*b^4)*e^4)*x^2 + 2*(3*B*b^4*d^2*e^2 + 2*(5*B*a*b^3 + 28*A*b^4)*d*e^3 - (5*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^3)]","A",0
2202,1,528,0,1.407342," ","integrate((B*x+A)*(b*x+a)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} d^{3} - {\left(B a b^{2} + 2 \, A b^{3}\right)} d^{2} e - {\left(B a^{2} b - 4 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 2 \, A a^{2} b\right)} e^{3}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{3} e^{3} x^{2} - 3 \, B b^{3} d^{2} e + 2 \, {\left(B a b^{2} + 3 \, A b^{3}\right)} d e^{2} - 3 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} e^{3} + 2 \, {\left(B b^{3} d e^{2} + {\left(B a b^{2} + 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, b^{3} e^{3}}, -\frac{3 \, {\left(B b^{3} d^{3} - {\left(B a b^{2} + 2 \, A b^{3}\right)} d^{2} e - {\left(B a^{2} b - 4 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 2 \, A a^{2} b\right)} e^{3}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, B b^{3} e^{3} x^{2} - 3 \, B b^{3} d^{2} e + 2 \, {\left(B a b^{2} + 3 \, A b^{3}\right)} d e^{2} - 3 \, {\left(B a^{2} b - 2 \, A a b^{2}\right)} e^{3} + 2 \, {\left(B b^{3} d e^{2} + {\left(B a b^{2} + 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, b^{3} e^{3}}\right]"," ",0,"[-1/96*(3*(B*b^3*d^3 - (B*a*b^2 + 2*A*b^3)*d^2*e - (B*a^2*b - 4*A*a*b^2)*d*e^2 + (B*a^3 - 2*A*a^2*b)*e^3)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^3*e^3*x^2 - 3*B*b^3*d^2*e + 2*(B*a*b^2 + 3*A*b^3)*d*e^2 - 3*(B*a^2*b - 2*A*a*b^2)*e^3 + 2*(B*b^3*d*e^2 + (B*a*b^2 + 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^3), -1/48*(3*(B*b^3*d^3 - (B*a*b^2 + 2*A*b^3)*d^2*e - (B*a^2*b - 4*A*a*b^2)*d*e^2 + (B*a^3 - 2*A*a^2*b)*e^3)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(8*B*b^3*e^3*x^2 - 3*B*b^3*d^2*e + 2*(B*a*b^2 + 3*A*b^3)*d*e^2 - 3*(B*a^2*b - 2*A*a*b^2)*e^3 + 2*(B*b^3*d*e^2 + (B*a*b^2 + 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^3)]","A",0
2203,1,364,0,1.331126," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B b^{2} d^{2} - 2 \, {\left(B a b + 2 \, A b^{2}\right)} d e - {\left(B a^{2} - 4 \, A a b\right)} e^{2}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(2 \, B b^{2} e^{2} x - 3 \, B b^{2} d e + {\left(B a b + 4 \, A b^{2}\right)} e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{16 \, b^{2} e^{3}}, -\frac{{\left(3 \, B b^{2} d^{2} - 2 \, {\left(B a b + 2 \, A b^{2}\right)} d e - {\left(B a^{2} - 4 \, A a b\right)} e^{2}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, B b^{2} e^{2} x - 3 \, B b^{2} d e + {\left(B a b + 4 \, A b^{2}\right)} e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{8 \, b^{2} e^{3}}\right]"," ",0,"[1/16*((3*B*b^2*d^2 - 2*(B*a*b + 2*A*b^2)*d*e - (B*a^2 - 4*A*a*b)*e^2)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(2*B*b^2*e^2*x - 3*B*b^2*d*e + (B*a*b + 4*A*b^2)*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^3), -1/8*((3*B*b^2*d^2 - 2*(B*a*b + 2*A*b^2)*d*e - (B*a^2 - 4*A*a*b)*e^2)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(2*B*b^2*e^2*x - 3*B*b^2*d*e + (B*a*b + 4*A*b^2)*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^3)]","A",0
2204,1,358,0,2.794370," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B b d^{2} - {\left(B a + 2 \, A b\right)} d e + {\left(3 \, B b d e - {\left(B a + 2 \, A b\right)} e^{2}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(B b e^{2} x + 3 \, B b d e - 2 \, A b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{4 \, {\left(b e^{4} x + b d e^{3}\right)}}, \frac{{\left(3 \, B b d^{2} - {\left(B a + 2 \, A b\right)} d e + {\left(3 \, B b d e - {\left(B a + 2 \, A b\right)} e^{2}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(B b e^{2} x + 3 \, B b d e - 2 \, A b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b e^{4} x + b d e^{3}\right)}}\right]"," ",0,"[-1/4*((3*B*b*d^2 - (B*a + 2*A*b)*d*e + (3*B*b*d*e - (B*a + 2*A*b)*e^2)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(B*b*e^2*x + 3*B*b*d*e - 2*A*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^4*x + b*d*e^3), 1/2*((3*B*b*d^2 - (B*a + 2*A*b)*d*e + (3*B*b*d*e - (B*a + 2*A*b)*e^2)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(B*b*e^2*x + 3*B*b*d*e - 2*A*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^4*x + b*d*e^3)]","A",0
2205,1,515,0,5.724203," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B b d^{3} - B a d^{2} e + {\left(B b d e^{2} - B a e^{3}\right)} x^{2} + 2 \, {\left(B b d^{2} e - B a d e^{2}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(3 \, B b d^{2} - 2 \, B a d e - A a e^{2} + {\left(4 \, B b d e - {\left(3 \, B a + A b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{6 \, {\left(b d^{3} e^{2} - a d^{2} e^{3} + {\left(b d e^{4} - a e^{5}\right)} x^{2} + 2 \, {\left(b d^{2} e^{3} - a d e^{4}\right)} x\right)}}, -\frac{3 \, {\left(B b d^{3} - B a d^{2} e + {\left(B b d e^{2} - B a e^{3}\right)} x^{2} + 2 \, {\left(B b d^{2} e - B a d e^{2}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) + 2 \, {\left(3 \, B b d^{2} - 2 \, B a d e - A a e^{2} + {\left(4 \, B b d e - {\left(3 \, B a + A b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(b d^{3} e^{2} - a d^{2} e^{3} + {\left(b d e^{4} - a e^{5}\right)} x^{2} + 2 \, {\left(b d^{2} e^{3} - a d e^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*(B*b*d^3 - B*a*d^2*e + (B*b*d*e^2 - B*a*e^3)*x^2 + 2*(B*b*d^2*e - B*a*d*e^2)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(3*B*b*d^2 - 2*B*a*d*e - A*a*e^2 + (4*B*b*d*e - (3*B*a + A*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^3*e^2 - a*d^2*e^3 + (b*d*e^4 - a*e^5)*x^2 + 2*(b*d^2*e^3 - a*d*e^4)*x), -1/3*(3*(B*b*d^3 - B*a*d^2*e + (B*b*d*e^2 - B*a*e^3)*x^2 + 2*(B*b*d^2*e - B*a*d*e^2)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) + 2*(3*B*b*d^2 - 2*B*a*d*e - A*a*e^2 + (4*B*b*d*e - (3*B*a + A*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^3*e^2 - a*d^2*e^3 + (b*d*e^4 - a*e^5)*x^2 + 2*(b*d^2*e^3 - a*d*e^4)*x)]","B",0
2206,1,221,0,12.800939," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{2} e - {\left(3 \, B b^{2} d - {\left(5 \, B a b - 2 \, A b^{2}\right)} e\right)} x^{2} + {\left(2 \, B a^{2} - 5 \, A a b\right)} d - {\left({\left(B a b + 5 \, A b^{2}\right)} d - {\left(5 \, B a^{2} + A a b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(b^{2} d^{5} - 2 \, a b d^{4} e + a^{2} d^{3} e^{2} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{3} + 3 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x^{2} + 3 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3}\right)} x\right)}}"," ",0,"-2/15*(3*A*a^2*e - (3*B*b^2*d - (5*B*a*b - 2*A*b^2)*e)*x^2 + (2*B*a^2 - 5*A*a*b)*d - ((B*a*b + 5*A*b^2)*d - (5*B*a^2 + A*a*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*d^5 - 2*a*b*d^4*e + a^2*d^3*e^2 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^3 + 3*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x^2 + 3*(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3)*x)","B",0
2207,1,440,0,38.717868," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, A a^{3} e^{2} + 2 \, {\left(3 \, B b^{3} d e - {\left(7 \, B a b^{2} - 4 \, A b^{3}\right)} e^{2}\right)} x^{3} - 7 \, {\left(2 \, B a^{2} b - 5 \, A a b^{2}\right)} d^{2} + 6 \, {\left(B a^{3} - 7 \, A a^{2} b\right)} d e + {\left(21 \, B b^{3} d^{2} - 4 \, {\left(13 \, B a b^{2} - 7 \, A b^{3}\right)} d e + {\left(7 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2}\right)} x^{2} + {\left(7 \, {\left(B a b^{2} + 5 \, A b^{3}\right)} d^{2} - 2 \, {\left(26 \, B a^{2} b + 7 \, A a b^{2}\right)} d e + 3 \, {\left(7 \, B a^{3} + A a^{2} b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{105 \, {\left(b^{3} d^{7} - 3 \, a b^{2} d^{6} e + 3 \, a^{2} b d^{5} e^{2} - a^{3} d^{4} e^{3} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{4} + 4 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{3} + 6 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x^{2} + 4 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4}\right)} x\right)}}"," ",0,"2/105*(15*A*a^3*e^2 + 2*(3*B*b^3*d*e - (7*B*a*b^2 - 4*A*b^3)*e^2)*x^3 - 7*(2*B*a^2*b - 5*A*a*b^2)*d^2 + 6*(B*a^3 - 7*A*a^2*b)*d*e + (21*B*b^3*d^2 - 4*(13*B*a*b^2 - 7*A*b^3)*d*e + (7*B*a^2*b - 4*A*a*b^2)*e^2)*x^2 + (7*(B*a*b^2 + 5*A*b^3)*d^2 - 2*(26*B*a^2*b + 7*A*a*b^2)*d*e + 3*(7*B*a^3 + A*a^2*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^3*d^7 - 3*a*b^2*d^6*e + 3*a^2*b*d^5*e^2 - a^3*d^4*e^3 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^4 + 4*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^3 + 6*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x^2 + 4*(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4)*x)","B",0
2208,-1,0,0,0.000000," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2209,-1,0,0,0.000000," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2210,-1,0,0,0.000000," ","integrate((B*x+A)*(b*x+a)^(1/2)/(e*x+d)^(15/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2211,1,1384,0,2.183991," ","integrate((b*x+a)^(3/2)*(B*x+A)*(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(5 \, B b^{6} d^{6} - 6 \, {\left(3 \, B a b^{5} + 2 \, A b^{6}\right)} d^{5} e + 15 \, {\left(B a^{2} b^{4} + 4 \, A a b^{5}\right)} d^{4} e^{2} + 20 \, {\left(B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 15 \, {\left(3 \, B a^{4} b^{2} - 8 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 30 \, {\left(B a^{5} b - 2 \, A a^{4} b^{2}\right)} d e^{5} - {\left(7 \, B a^{6} - 12 \, A a^{5} b\right)} e^{6}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(1280 \, B b^{6} e^{6} x^{5} + 75 \, B b^{6} d^{5} e - 5 \, {\left(49 \, B a b^{5} + 36 \, A b^{6}\right)} d^{4} e^{2} + 30 \, {\left(5 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} d^{3} e^{3} - 6 \, {\left(91 \, B a^{3} b^{3} - 256 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 5 \, {\left(83 \, B a^{4} b^{2} - 168 \, A a^{3} b^{3}\right)} d e^{5} - 15 \, {\left(7 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} e^{6} + 128 \, {\left(25 \, B b^{6} d e^{5} + {\left(13 \, B a b^{5} + 12 \, A b^{6}\right)} e^{6}\right)} x^{4} + 16 \, {\left(135 \, B b^{6} d^{2} e^{4} + 2 \, {\left(139 \, B a b^{5} + 126 \, A b^{6}\right)} d e^{5} + 3 \, {\left(B a^{2} b^{4} + 44 \, A a b^{5}\right)} e^{6}\right)} x^{3} + 8 \, {\left(5 \, B b^{6} d^{3} e^{3} + 3 \, {\left(141 \, B a b^{5} + 124 \, A b^{6}\right)} d^{2} e^{4} + 3 \, {\left(9 \, B a^{2} b^{4} + 256 \, A a b^{5}\right)} d e^{5} - {\left(7 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{2} - 2 \, {\left(25 \, B b^{6} d^{4} e^{2} - 20 \, {\left(4 \, B a b^{5} + 3 \, A b^{6}\right)} d^{3} e^{3} - 6 \, {\left(29 \, B a^{2} b^{4} + 466 \, A a b^{5}\right)} d^{2} e^{4} + 4 \, {\left(34 \, B a^{3} b^{3} - 69 \, A a^{2} b^{4}\right)} d e^{5} - 5 \, {\left(7 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} e^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{30720 \, b^{5} e^{4}}, \frac{15 \, {\left(5 \, B b^{6} d^{6} - 6 \, {\left(3 \, B a b^{5} + 2 \, A b^{6}\right)} d^{5} e + 15 \, {\left(B a^{2} b^{4} + 4 \, A a b^{5}\right)} d^{4} e^{2} + 20 \, {\left(B a^{3} b^{3} - 6 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 15 \, {\left(3 \, B a^{4} b^{2} - 8 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 30 \, {\left(B a^{5} b - 2 \, A a^{4} b^{2}\right)} d e^{5} - {\left(7 \, B a^{6} - 12 \, A a^{5} b\right)} e^{6}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(1280 \, B b^{6} e^{6} x^{5} + 75 \, B b^{6} d^{5} e - 5 \, {\left(49 \, B a b^{5} + 36 \, A b^{6}\right)} d^{4} e^{2} + 30 \, {\left(5 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} d^{3} e^{3} - 6 \, {\left(91 \, B a^{3} b^{3} - 256 \, A a^{2} b^{4}\right)} d^{2} e^{4} + 5 \, {\left(83 \, B a^{4} b^{2} - 168 \, A a^{3} b^{3}\right)} d e^{5} - 15 \, {\left(7 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} e^{6} + 128 \, {\left(25 \, B b^{6} d e^{5} + {\left(13 \, B a b^{5} + 12 \, A b^{6}\right)} e^{6}\right)} x^{4} + 16 \, {\left(135 \, B b^{6} d^{2} e^{4} + 2 \, {\left(139 \, B a b^{5} + 126 \, A b^{6}\right)} d e^{5} + 3 \, {\left(B a^{2} b^{4} + 44 \, A a b^{5}\right)} e^{6}\right)} x^{3} + 8 \, {\left(5 \, B b^{6} d^{3} e^{3} + 3 \, {\left(141 \, B a b^{5} + 124 \, A b^{6}\right)} d^{2} e^{4} + 3 \, {\left(9 \, B a^{2} b^{4} + 256 \, A a b^{5}\right)} d e^{5} - {\left(7 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{2} - 2 \, {\left(25 \, B b^{6} d^{4} e^{2} - 20 \, {\left(4 \, B a b^{5} + 3 \, A b^{6}\right)} d^{3} e^{3} - 6 \, {\left(29 \, B a^{2} b^{4} + 466 \, A a b^{5}\right)} d^{2} e^{4} + 4 \, {\left(34 \, B a^{3} b^{3} - 69 \, A a^{2} b^{4}\right)} d e^{5} - 5 \, {\left(7 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} e^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15360 \, b^{5} e^{4}}\right]"," ",0,"[1/30720*(15*(5*B*b^6*d^6 - 6*(3*B*a*b^5 + 2*A*b^6)*d^5*e + 15*(B*a^2*b^4 + 4*A*a*b^5)*d^4*e^2 + 20*(B*a^3*b^3 - 6*A*a^2*b^4)*d^3*e^3 - 15*(3*B*a^4*b^2 - 8*A*a^3*b^3)*d^2*e^4 + 30*(B*a^5*b - 2*A*a^4*b^2)*d*e^5 - (7*B*a^6 - 12*A*a^5*b)*e^6)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(1280*B*b^6*e^6*x^5 + 75*B*b^6*d^5*e - 5*(49*B*a*b^5 + 36*A*b^6)*d^4*e^2 + 30*(5*B*a^2*b^4 + 28*A*a*b^5)*d^3*e^3 - 6*(91*B*a^3*b^3 - 256*A*a^2*b^4)*d^2*e^4 + 5*(83*B*a^4*b^2 - 168*A*a^3*b^3)*d*e^5 - 15*(7*B*a^5*b - 12*A*a^4*b^2)*e^6 + 128*(25*B*b^6*d*e^5 + (13*B*a*b^5 + 12*A*b^6)*e^6)*x^4 + 16*(135*B*b^6*d^2*e^4 + 2*(139*B*a*b^5 + 126*A*b^6)*d*e^5 + 3*(B*a^2*b^4 + 44*A*a*b^5)*e^6)*x^3 + 8*(5*B*b^6*d^3*e^3 + 3*(141*B*a*b^5 + 124*A*b^6)*d^2*e^4 + 3*(9*B*a^2*b^4 + 256*A*a*b^5)*d*e^5 - (7*B*a^3*b^3 - 12*A*a^2*b^4)*e^6)*x^2 - 2*(25*B*b^6*d^4*e^2 - 20*(4*B*a*b^5 + 3*A*b^6)*d^3*e^3 - 6*(29*B*a^2*b^4 + 466*A*a*b^5)*d^2*e^4 + 4*(34*B*a^3*b^3 - 69*A*a^2*b^4)*d*e^5 - 5*(7*B*a^4*b^2 - 12*A*a^3*b^3)*e^6)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^4), 1/15360*(15*(5*B*b^6*d^6 - 6*(3*B*a*b^5 + 2*A*b^6)*d^5*e + 15*(B*a^2*b^4 + 4*A*a*b^5)*d^4*e^2 + 20*(B*a^3*b^3 - 6*A*a^2*b^4)*d^3*e^3 - 15*(3*B*a^4*b^2 - 8*A*a^3*b^3)*d^2*e^4 + 30*(B*a^5*b - 2*A*a^4*b^2)*d*e^5 - (7*B*a^6 - 12*A*a^5*b)*e^6)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(1280*B*b^6*e^6*x^5 + 75*B*b^6*d^5*e - 5*(49*B*a*b^5 + 36*A*b^6)*d^4*e^2 + 30*(5*B*a^2*b^4 + 28*A*a*b^5)*d^3*e^3 - 6*(91*B*a^3*b^3 - 256*A*a^2*b^4)*d^2*e^4 + 5*(83*B*a^4*b^2 - 168*A*a^3*b^3)*d*e^5 - 15*(7*B*a^5*b - 12*A*a^4*b^2)*e^6 + 128*(25*B*b^6*d*e^5 + (13*B*a*b^5 + 12*A*b^6)*e^6)*x^4 + 16*(135*B*b^6*d^2*e^4 + 2*(139*B*a*b^5 + 126*A*b^6)*d*e^5 + 3*(B*a^2*b^4 + 44*A*a*b^5)*e^6)*x^3 + 8*(5*B*b^6*d^3*e^3 + 3*(141*B*a*b^5 + 124*A*b^6)*d^2*e^4 + 3*(9*B*a^2*b^4 + 256*A*a*b^5)*d*e^5 - (7*B*a^3*b^3 - 12*A*a^2*b^4)*e^6)*x^2 - 2*(25*B*b^6*d^4*e^2 - 20*(4*B*a*b^5 + 3*A*b^6)*d^3*e^3 - 6*(29*B*a^2*b^4 + 466*A*a*b^5)*d^2*e^4 + 4*(34*B*a^3*b^3 - 69*A*a^2*b^4)*d*e^5 - 5*(7*B*a^4*b^2 - 12*A*a^3*b^3)*e^6)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^4)]","B",0
2212,1,1036,0,2.326741," ","integrate((b*x+a)^(3/2)*(B*x+A)*(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B b^{5} d^{5} - {\left(3 \, B a b^{4} + 2 \, A b^{5}\right)} d^{4} e + 2 \, {\left(B a^{2} b^{3} + 4 \, A a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(B a^{3} b^{2} - 6 \, A a^{2} b^{3}\right)} d^{2} e^{3} - {\left(3 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 2 \, A a^{4} b\right)} e^{5}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(128 \, B b^{5} e^{5} x^{4} + 15 \, B b^{5} d^{4} e - 10 \, {\left(4 \, B a b^{4} + 3 \, A b^{5}\right)} d^{3} e^{2} + 2 \, {\left(9 \, B a^{2} b^{3} + 55 \, A a b^{4}\right)} d^{2} e^{3} - 10 \, {\left(4 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} d e^{4} + 15 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{5} + 16 \, {\left(11 \, B b^{5} d e^{4} + {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} + 8 \, {\left(B b^{5} d^{2} e^{3} + 2 \, {\left(17 \, B a b^{4} + 15 \, A b^{5}\right)} d e^{4} + {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} e^{5}\right)} x^{2} - 2 \, {\left(5 \, B b^{5} d^{3} e^{2} - {\left(13 \, B a b^{4} + 10 \, A b^{5}\right)} d^{2} e^{3} - {\left(13 \, B a^{2} b^{3} + 220 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{2560 \, b^{4} e^{4}}, \frac{15 \, {\left(B b^{5} d^{5} - {\left(3 \, B a b^{4} + 2 \, A b^{5}\right)} d^{4} e + 2 \, {\left(B a^{2} b^{3} + 4 \, A a b^{4}\right)} d^{3} e^{2} + 2 \, {\left(B a^{3} b^{2} - 6 \, A a^{2} b^{3}\right)} d^{2} e^{3} - {\left(3 \, B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(B a^{5} - 2 \, A a^{4} b\right)} e^{5}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(128 \, B b^{5} e^{5} x^{4} + 15 \, B b^{5} d^{4} e - 10 \, {\left(4 \, B a b^{4} + 3 \, A b^{5}\right)} d^{3} e^{2} + 2 \, {\left(9 \, B a^{2} b^{3} + 55 \, A a b^{4}\right)} d^{2} e^{3} - 10 \, {\left(4 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3}\right)} d e^{4} + 15 \, {\left(B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{5} + 16 \, {\left(11 \, B b^{5} d e^{4} + {\left(11 \, B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} + 8 \, {\left(B b^{5} d^{2} e^{3} + 2 \, {\left(17 \, B a b^{4} + 15 \, A b^{5}\right)} d e^{4} + {\left(B a^{2} b^{3} + 30 \, A a b^{4}\right)} e^{5}\right)} x^{2} - 2 \, {\left(5 \, B b^{5} d^{3} e^{2} - {\left(13 \, B a b^{4} + 10 \, A b^{5}\right)} d^{2} e^{3} - {\left(13 \, B a^{2} b^{3} + 220 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{1280 \, b^{4} e^{4}}\right]"," ",0,"[1/2560*(15*(B*b^5*d^5 - (3*B*a*b^4 + 2*A*b^5)*d^4*e + 2*(B*a^2*b^3 + 4*A*a*b^4)*d^3*e^2 + 2*(B*a^3*b^2 - 6*A*a^2*b^3)*d^2*e^3 - (3*B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (B*a^5 - 2*A*a^4*b)*e^5)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(128*B*b^5*e^5*x^4 + 15*B*b^5*d^4*e - 10*(4*B*a*b^4 + 3*A*b^5)*d^3*e^2 + 2*(9*B*a^2*b^3 + 55*A*a*b^4)*d^2*e^3 - 10*(4*B*a^3*b^2 - 11*A*a^2*b^3)*d*e^4 + 15*(B*a^4*b - 2*A*a^3*b^2)*e^5 + 16*(11*B*b^5*d*e^4 + (11*B*a*b^4 + 10*A*b^5)*e^5)*x^3 + 8*(B*b^5*d^2*e^3 + 2*(17*B*a*b^4 + 15*A*b^5)*d*e^4 + (B*a^2*b^3 + 30*A*a*b^4)*e^5)*x^2 - 2*(5*B*b^5*d^3*e^2 - (13*B*a*b^4 + 10*A*b^5)*d^2*e^3 - (13*B*a^2*b^3 + 220*A*a*b^4)*d*e^4 + 5*(B*a^3*b^2 - 2*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^4), 1/1280*(15*(B*b^5*d^5 - (3*B*a*b^4 + 2*A*b^5)*d^4*e + 2*(B*a^2*b^3 + 4*A*a*b^4)*d^3*e^2 + 2*(B*a^3*b^2 - 6*A*a^2*b^3)*d^2*e^3 - (3*B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (B*a^5 - 2*A*a^4*b)*e^5)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(128*B*b^5*e^5*x^4 + 15*B*b^5*d^4*e - 10*(4*B*a*b^4 + 3*A*b^5)*d^3*e^2 + 2*(9*B*a^2*b^3 + 55*A*a*b^4)*d^2*e^3 - 10*(4*B*a^3*b^2 - 11*A*a^2*b^3)*d*e^4 + 15*(B*a^4*b - 2*A*a^3*b^2)*e^5 + 16*(11*B*b^5*d*e^4 + (11*B*a*b^4 + 10*A*b^5)*e^5)*x^3 + 8*(B*b^5*d^2*e^3 + 2*(17*B*a*b^4 + 15*A*b^5)*d*e^4 + (B*a^2*b^3 + 30*A*a*b^4)*e^5)*x^2 - 2*(5*B*b^5*d^3*e^2 - (13*B*a*b^4 + 10*A*b^5)*d^2*e^3 - (13*B*a^2*b^3 + 220*A*a*b^4)*d*e^4 + 5*(B*a^3*b^2 - 2*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^4)]","A",0
2213,1,766,0,1.525711," ","integrate((b*x+a)^(3/2)*(B*x+A)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{4} d^{4} - 4 \, {\left(3 \, B a b^{3} + 2 \, A b^{4}\right)} d^{3} e + 6 \, {\left(B a^{2} b^{2} + 4 \, A a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(B a^{3} b - 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(48 \, B b^{4} e^{4} x^{3} + 15 \, B b^{4} d^{3} e - {\left(31 \, B a b^{3} + 24 \, A b^{4}\right)} d^{2} e^{2} + {\left(9 \, B a^{2} b^{2} + 64 \, A a b^{3}\right)} d e^{3} - 3 \, {\left(3 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(B b^{4} d e^{3} + {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{4} d^{2} e^{2} - 2 \, {\left(5 \, B a b^{3} + 4 \, A b^{4}\right)} d e^{3} - {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{768 \, b^{3} e^{4}}, \frac{3 \, {\left(5 \, B b^{4} d^{4} - 4 \, {\left(3 \, B a b^{3} + 2 \, A b^{4}\right)} d^{3} e + 6 \, {\left(B a^{2} b^{2} + 4 \, A a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(B a^{3} b - 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(3 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, B b^{4} e^{4} x^{3} + 15 \, B b^{4} d^{3} e - {\left(31 \, B a b^{3} + 24 \, A b^{4}\right)} d^{2} e^{2} + {\left(9 \, B a^{2} b^{2} + 64 \, A a b^{3}\right)} d e^{3} - 3 \, {\left(3 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(B b^{4} d e^{3} + {\left(9 \, B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} - 2 \, {\left(5 \, B b^{4} d^{2} e^{2} - 2 \, {\left(5 \, B a b^{3} + 4 \, A b^{4}\right)} d e^{3} - {\left(3 \, B a^{2} b^{2} + 56 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{384 \, b^{3} e^{4}}\right]"," ",0,"[1/768*(3*(5*B*b^4*d^4 - 4*(3*B*a*b^3 + 2*A*b^4)*d^3*e + 6*(B*a^2*b^2 + 4*A*a*b^3)*d^2*e^2 + 4*(B*a^3*b - 6*A*a^2*b^2)*d*e^3 - (3*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(48*B*b^4*e^4*x^3 + 15*B*b^4*d^3*e - (31*B*a*b^3 + 24*A*b^4)*d^2*e^2 + (9*B*a^2*b^2 + 64*A*a*b^3)*d*e^3 - 3*(3*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(B*b^4*d*e^3 + (9*B*a*b^3 + 8*A*b^4)*e^4)*x^2 - 2*(5*B*b^4*d^2*e^2 - 2*(5*B*a*b^3 + 4*A*b^4)*d*e^3 - (3*B*a^2*b^2 + 56*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^4), 1/384*(3*(5*B*b^4*d^4 - 4*(3*B*a*b^3 + 2*A*b^4)*d^3*e + 6*(B*a^2*b^2 + 4*A*a*b^3)*d^2*e^2 + 4*(B*a^3*b - 6*A*a^2*b^2)*d*e^3 - (3*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(48*B*b^4*e^4*x^3 + 15*B*b^4*d^3*e - (31*B*a*b^3 + 24*A*b^4)*d^2*e^2 + (9*B*a^2*b^2 + 64*A*a*b^3)*d*e^3 - 3*(3*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(B*b^4*d*e^3 + (9*B*a*b^3 + 8*A*b^4)*e^4)*x^2 - 2*(5*B*b^4*d^2*e^2 - 2*(5*B*a*b^3 + 4*A*b^4)*d*e^3 - (3*B*a^2*b^2 + 56*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^4)]","A",0
2214,1,540,0,1.645537," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b^{3} d^{3} - 3 \, {\left(3 \, B a b^{2} + 2 \, A b^{3}\right)} d^{2} e + 3 \, {\left(B a^{2} b + 4 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{3} e^{3} x^{2} + 15 \, B b^{3} d^{2} e - 2 \, {\left(11 \, B a b^{2} + 9 \, A b^{3}\right)} d e^{2} + 3 \, {\left(B a^{2} b + 10 \, A a b^{2}\right)} e^{3} - 2 \, {\left(5 \, B b^{3} d e^{2} - {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, b^{2} e^{4}}, \frac{3 \, {\left(5 \, B b^{3} d^{3} - 3 \, {\left(3 \, B a b^{2} + 2 \, A b^{3}\right)} d^{2} e + 3 \, {\left(B a^{2} b + 4 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, B b^{3} e^{3} x^{2} + 15 \, B b^{3} d^{2} e - 2 \, {\left(11 \, B a b^{2} + 9 \, A b^{3}\right)} d e^{2} + 3 \, {\left(B a^{2} b + 10 \, A a b^{2}\right)} e^{3} - 2 \, {\left(5 \, B b^{3} d e^{2} - {\left(7 \, B a b^{2} + 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, b^{2} e^{4}}\right]"," ",0,"[-1/96*(3*(5*B*b^3*d^3 - 3*(3*B*a*b^2 + 2*A*b^3)*d^2*e + 3*(B*a^2*b + 4*A*a*b^2)*d*e^2 + (B*a^3 - 6*A*a^2*b)*e^3)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^3*e^3*x^2 + 15*B*b^3*d^2*e - 2*(11*B*a*b^2 + 9*A*b^3)*d*e^2 + 3*(B*a^2*b + 10*A*a*b^2)*e^3 - 2*(5*B*b^3*d*e^2 - (7*B*a*b^2 + 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^4), 1/48*(3*(5*B*b^3*d^3 - 3*(3*B*a*b^2 + 2*A*b^3)*d^2*e + 3*(B*a^2*b + 4*A*a*b^2)*d*e^2 + (B*a^3 - 6*A*a^2*b)*e^3)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(8*B*b^3*e^3*x^2 + 15*B*b^3*d^2*e - 2*(11*B*a*b^2 + 9*A*b^3)*d*e^2 + 3*(B*a^2*b + 10*A*a*b^2)*e^3 - 2*(5*B*b^3*d*e^2 - (7*B*a*b^2 + 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^4)]","A",0
2215,1,572,0,3.135901," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(5 \, B b^{2} d^{3} - 2 \, {\left(3 \, B a b + 2 \, A b^{2}\right)} d^{2} e + {\left(B a^{2} + 4 \, A a b\right)} d e^{2} + {\left(5 \, B b^{2} d^{2} e - 2 \, {\left(3 \, B a b + 2 \, A b^{2}\right)} d e^{2} + {\left(B a^{2} + 4 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(2 \, B b^{2} e^{3} x^{2} - 15 \, B b^{2} d^{2} e - 8 \, A a b e^{3} + {\left(13 \, B a b + 12 \, A b^{2}\right)} d e^{2} - {\left(5 \, B b^{2} d e^{2} - {\left(5 \, B a b + 4 \, A b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{16 \, {\left(b e^{5} x + b d e^{4}\right)}}, -\frac{3 \, {\left(5 \, B b^{2} d^{3} - 2 \, {\left(3 \, B a b + 2 \, A b^{2}\right)} d^{2} e + {\left(B a^{2} + 4 \, A a b\right)} d e^{2} + {\left(5 \, B b^{2} d^{2} e - 2 \, {\left(3 \, B a b + 2 \, A b^{2}\right)} d e^{2} + {\left(B a^{2} + 4 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, B b^{2} e^{3} x^{2} - 15 \, B b^{2} d^{2} e - 8 \, A a b e^{3} + {\left(13 \, B a b + 12 \, A b^{2}\right)} d e^{2} - {\left(5 \, B b^{2} d e^{2} - {\left(5 \, B a b + 4 \, A b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{8 \, {\left(b e^{5} x + b d e^{4}\right)}}\right]"," ",0,"[1/16*(3*(5*B*b^2*d^3 - 2*(3*B*a*b + 2*A*b^2)*d^2*e + (B*a^2 + 4*A*a*b)*d*e^2 + (5*B*b^2*d^2*e - 2*(3*B*a*b + 2*A*b^2)*d*e^2 + (B*a^2 + 4*A*a*b)*e^3)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(2*B*b^2*e^3*x^2 - 15*B*b^2*d^2*e - 8*A*a*b*e^3 + (13*B*a*b + 12*A*b^2)*d*e^2 - (5*B*b^2*d*e^2 - (5*B*a*b + 4*A*b^2)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^5*x + b*d*e^4), -1/8*(3*(5*B*b^2*d^3 - 2*(3*B*a*b + 2*A*b^2)*d^2*e + (B*a^2 + 4*A*a*b)*d*e^2 + (5*B*b^2*d^2*e - 2*(3*B*a*b + 2*A*b^2)*d*e^2 + (B*a^2 + 4*A*a*b)*e^3)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(2*B*b^2*e^3*x^2 - 15*B*b^2*d^2*e - 8*A*a*b*e^3 + (13*B*a*b + 12*A*b^2)*d*e^2 - (5*B*b^2*d*e^2 - (5*B*a*b + 4*A*b^2)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^5*x + b*d*e^4)]","A",0
2216,1,537,0,5.386065," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B b d^{3} - {\left(3 \, B a + 2 \, A b\right)} d^{2} e + {\left(5 \, B b d e^{2} - {\left(3 \, B a + 2 \, A b\right)} e^{3}\right)} x^{2} + 2 \, {\left(5 \, B b d^{2} e - {\left(3 \, B a + 2 \, A b\right)} d e^{2}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(3 \, B b e^{2} x^{2} + 15 \, B b d^{2} - 2 \, A a e^{2} - 2 \, {\left(2 \, B a + 3 \, A b\right)} d e + 2 \, {\left(10 \, B b d e - {\left(3 \, B a + 4 \, A b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{12 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}, \frac{3 \, {\left(5 \, B b d^{3} - {\left(3 \, B a + 2 \, A b\right)} d^{2} e + {\left(5 \, B b d e^{2} - {\left(3 \, B a + 2 \, A b\right)} e^{3}\right)} x^{2} + 2 \, {\left(5 \, B b d^{2} e - {\left(3 \, B a + 2 \, A b\right)} d e^{2}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) + 2 \, {\left(3 \, B b e^{2} x^{2} + 15 \, B b d^{2} - 2 \, A a e^{2} - 2 \, {\left(2 \, B a + 3 \, A b\right)} d e + 2 \, {\left(10 \, B b d e - {\left(3 \, B a + 4 \, A b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{6 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}\right]"," ",0,"[-1/12*(3*(5*B*b*d^3 - (3*B*a + 2*A*b)*d^2*e + (5*B*b*d*e^2 - (3*B*a + 2*A*b)*e^3)*x^2 + 2*(5*B*b*d^2*e - (3*B*a + 2*A*b)*d*e^2)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(3*B*b*e^2*x^2 + 15*B*b*d^2 - 2*A*a*e^2 - 2*(2*B*a + 3*A*b)*d*e + 2*(10*B*b*d*e - (3*B*a + 4*A*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3), 1/6*(3*(5*B*b*d^3 - (3*B*a + 2*A*b)*d^2*e + (5*B*b*d*e^2 - (3*B*a + 2*A*b)*e^3)*x^2 + 2*(5*B*b*d^2*e - (3*B*a + 2*A*b)*d*e^2)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) + 2*(3*B*b*e^2*x^2 + 15*B*b*d^2 - 2*A*a*e^2 - 2*(2*B*a + 3*A*b)*d*e + 2*(10*B*b*d*e - (3*B*a + 4*A*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)]","A",0
2217,1,767,0,14.792691," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B b^{2} d^{4} - B a b d^{3} e + {\left(B b^{2} d e^{3} - B a b e^{4}\right)} x^{3} + 3 \, {\left(B b^{2} d^{2} e^{2} - B a b d e^{3}\right)} x^{2} + 3 \, {\left(B b^{2} d^{3} e - B a b d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(15 \, B b^{2} d^{3} - 10 \, B a b d^{2} e - 2 \, B a^{2} d e^{2} - 3 \, A a^{2} e^{3} + {\left(23 \, B b^{2} d e^{2} - {\left(20 \, B a b + 3 \, A b^{2}\right)} e^{3}\right)} x^{2} + {\left(35 \, B b^{2} d^{2} e - 24 \, B a b d e^{2} - {\left(5 \, B a^{2} + 6 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{30 \, {\left(b d^{4} e^{3} - a d^{3} e^{4} + {\left(b d e^{6} - a e^{7}\right)} x^{3} + 3 \, {\left(b d^{2} e^{5} - a d e^{6}\right)} x^{2} + 3 \, {\left(b d^{3} e^{4} - a d^{2} e^{5}\right)} x\right)}}, -\frac{15 \, {\left(B b^{2} d^{4} - B a b d^{3} e + {\left(B b^{2} d e^{3} - B a b e^{4}\right)} x^{3} + 3 \, {\left(B b^{2} d^{2} e^{2} - B a b d e^{3}\right)} x^{2} + 3 \, {\left(B b^{2} d^{3} e - B a b d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) + 2 \, {\left(15 \, B b^{2} d^{3} - 10 \, B a b d^{2} e - 2 \, B a^{2} d e^{2} - 3 \, A a^{2} e^{3} + {\left(23 \, B b^{2} d e^{2} - {\left(20 \, B a b + 3 \, A b^{2}\right)} e^{3}\right)} x^{2} + {\left(35 \, B b^{2} d^{2} e - 24 \, B a b d e^{2} - {\left(5 \, B a^{2} + 6 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(b d^{4} e^{3} - a d^{3} e^{4} + {\left(b d e^{6} - a e^{7}\right)} x^{3} + 3 \, {\left(b d^{2} e^{5} - a d e^{6}\right)} x^{2} + 3 \, {\left(b d^{3} e^{4} - a d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/30*(15*(B*b^2*d^4 - B*a*b*d^3*e + (B*b^2*d*e^3 - B*a*b*e^4)*x^3 + 3*(B*b^2*d^2*e^2 - B*a*b*d*e^3)*x^2 + 3*(B*b^2*d^3*e - B*a*b*d^2*e^2)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(15*B*b^2*d^3 - 10*B*a*b*d^2*e - 2*B*a^2*d*e^2 - 3*A*a^2*e^3 + (23*B*b^2*d*e^2 - (20*B*a*b + 3*A*b^2)*e^3)*x^2 + (35*B*b^2*d^2*e - 24*B*a*b*d*e^2 - (5*B*a^2 + 6*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^4*e^3 - a*d^3*e^4 + (b*d*e^6 - a*e^7)*x^3 + 3*(b*d^2*e^5 - a*d*e^6)*x^2 + 3*(b*d^3*e^4 - a*d^2*e^5)*x), -1/15*(15*(B*b^2*d^4 - B*a*b*d^3*e + (B*b^2*d*e^3 - B*a*b*e^4)*x^3 + 3*(B*b^2*d^2*e^2 - B*a*b*d*e^3)*x^2 + 3*(B*b^2*d^3*e - B*a*b*d^2*e^2)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) + 2*(15*B*b^2*d^3 - 10*B*a*b*d^2*e - 2*B*a^2*d*e^2 - 3*A*a^2*e^3 + (23*B*b^2*d*e^2 - (20*B*a*b + 3*A*b^2)*e^3)*x^2 + (35*B*b^2*d^2*e - 24*B*a*b*d*e^2 - (5*B*a^2 + 6*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^4*e^3 - a*d^3*e^4 + (b*d*e^6 - a*e^7)*x^3 + 3*(b*d^2*e^5 - a*d*e^6)*x^2 + 3*(b*d^3*e^4 - a*d^2*e^5)*x)]","B",0
2218,1,306,0,35.590213," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, A a^{3} e - {\left(5 \, B b^{3} d - {\left(7 \, B a b^{2} - 2 \, A b^{3}\right)} e\right)} x^{3} - {\left({\left(8 \, B a b^{2} + 7 \, A b^{3}\right)} d - {\left(14 \, B a^{2} b + A a b^{2}\right)} e\right)} x^{2} + {\left(2 \, B a^{3} - 7 \, A a^{2} b\right)} d - {\left({\left(B a^{2} b + 14 \, A a b^{2}\right)} d - {\left(7 \, B a^{3} + 8 \, A a^{2} b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{35 \, {\left(b^{2} d^{6} - 2 \, a b d^{5} e + a^{2} d^{4} e^{2} + {\left(b^{2} d^{2} e^{4} - 2 \, a b d e^{5} + a^{2} e^{6}\right)} x^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 2 \, a b d^{2} e^{4} + a^{2} d e^{5}\right)} x^{3} + 6 \, {\left(b^{2} d^{4} e^{2} - 2 \, a b d^{3} e^{3} + a^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(b^{2} d^{5} e - 2 \, a b d^{4} e^{2} + a^{2} d^{3} e^{3}\right)} x\right)}}"," ",0,"-2/35*(5*A*a^3*e - (5*B*b^3*d - (7*B*a*b^2 - 2*A*b^3)*e)*x^3 - ((8*B*a*b^2 + 7*A*b^3)*d - (14*B*a^2*b + A*a*b^2)*e)*x^2 + (2*B*a^3 - 7*A*a^2*b)*d - ((B*a^2*b + 14*A*a*b^2)*d - (7*B*a^3 + 8*A*a^2*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*d^6 - 2*a*b*d^5*e + a^2*d^4*e^2 + (b^2*d^2*e^4 - 2*a*b*d*e^5 + a^2*e^6)*x^4 + 4*(b^2*d^3*e^3 - 2*a*b*d^2*e^4 + a^2*d*e^5)*x^3 + 6*(b^2*d^4*e^2 - 2*a*b*d^3*e^3 + a^2*d^2*e^4)*x^2 + 4*(b^2*d^5*e - 2*a*b*d^4*e^2 + a^2*d^3*e^3)*x)","B",0
2219,1,567,0,142.533702," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{4} e^{2} + 2 \, {\left(5 \, B b^{4} d e - {\left(9 \, B a b^{3} - 4 \, A b^{4}\right)} e^{2}\right)} x^{4} + {\left(45 \, B b^{4} d^{2} - 2 \, {\left(43 \, B a b^{3} - 18 \, A b^{4}\right)} d e + {\left(9 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{2}\right)} x^{3} - 9 \, {\left(2 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d^{2} + 10 \, {\left(B a^{4} - 9 \, A a^{3} b\right)} d e + 3 \, {\left(3 \, {\left(8 \, B a b^{3} + 7 \, A b^{4}\right)} d^{2} - 2 \, {\left(32 \, B a^{2} b^{2} + 3 \, A a b^{3}\right)} d e + {\left(24 \, B a^{3} b + A a^{2} b^{2}\right)} e^{2}\right)} x^{2} + {\left(9 \, {\left(B a^{2} b^{2} + 14 \, A a b^{3}\right)} d^{2} - 2 \, {\left(43 \, B a^{3} b + 72 \, A a^{2} b^{2}\right)} d e + 5 \, {\left(9 \, B a^{4} + 10 \, A a^{3} b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{315 \, {\left(b^{3} d^{8} - 3 \, a b^{2} d^{7} e + 3 \, a^{2} b d^{6} e^{2} - a^{3} d^{5} e^{3} + {\left(b^{3} d^{3} e^{5} - 3 \, a b^{2} d^{2} e^{6} + 3 \, a^{2} b d e^{7} - a^{3} e^{8}\right)} x^{5} + 5 \, {\left(b^{3} d^{4} e^{4} - 3 \, a b^{2} d^{3} e^{5} + 3 \, a^{2} b d^{2} e^{6} - a^{3} d e^{7}\right)} x^{4} + 10 \, {\left(b^{3} d^{5} e^{3} - 3 \, a b^{2} d^{4} e^{4} + 3 \, a^{2} b d^{3} e^{5} - a^{3} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(b^{3} d^{6} e^{2} - 3 \, a b^{2} d^{5} e^{3} + 3 \, a^{2} b d^{4} e^{4} - a^{3} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(b^{3} d^{7} e - 3 \, a b^{2} d^{6} e^{2} + 3 \, a^{2} b d^{5} e^{3} - a^{3} d^{4} e^{4}\right)} x\right)}}"," ",0,"2/315*(35*A*a^4*e^2 + 2*(5*B*b^4*d*e - (9*B*a*b^3 - 4*A*b^4)*e^2)*x^4 + (45*B*b^4*d^2 - 2*(43*B*a*b^3 - 18*A*b^4)*d*e + (9*B*a^2*b^2 - 4*A*a*b^3)*e^2)*x^3 - 9*(2*B*a^3*b - 7*A*a^2*b^2)*d^2 + 10*(B*a^4 - 9*A*a^3*b)*d*e + 3*(3*(8*B*a*b^3 + 7*A*b^4)*d^2 - 2*(32*B*a^2*b^2 + 3*A*a*b^3)*d*e + (24*B*a^3*b + A*a^2*b^2)*e^2)*x^2 + (9*(B*a^2*b^2 + 14*A*a*b^3)*d^2 - 2*(43*B*a^3*b + 72*A*a^2*b^2)*d*e + 5*(9*B*a^4 + 10*A*a^3*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^3*d^8 - 3*a*b^2*d^7*e + 3*a^2*b*d^6*e^2 - a^3*d^5*e^3 + (b^3*d^3*e^5 - 3*a*b^2*d^2*e^6 + 3*a^2*b*d*e^7 - a^3*e^8)*x^5 + 5*(b^3*d^4*e^4 - 3*a*b^2*d^3*e^5 + 3*a^2*b*d^2*e^6 - a^3*d*e^7)*x^4 + 10*(b^3*d^5*e^3 - 3*a*b^2*d^4*e^4 + 3*a^2*b*d^3*e^5 - a^3*d^2*e^6)*x^3 + 10*(b^3*d^6*e^2 - 3*a*b^2*d^5*e^3 + 3*a^2*b*d^4*e^4 - a^3*d^3*e^5)*x^2 + 5*(b^3*d^7*e - 3*a*b^2*d^6*e^2 + 3*a^2*b*d^5*e^3 - a^3*d^4*e^4)*x)","B",0
2220,-1,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2221,-1,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(15/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2222,-1,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(B*x+A)/(e*x+d)^(17/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2223,1,1758,0,2.100782," ","integrate((b*x+a)^(5/2)*(B*x+A)*(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(B b^{7} d^{7} - {\left(5 \, B a b^{6} + 2 \, A b^{7}\right)} d^{6} e + 3 \, {\left(3 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} d^{5} e^{2} - 5 \, {\left(B a^{3} b^{4} + 6 \, A a^{2} b^{5}\right)} d^{4} e^{3} - 5 \, {\left(B a^{4} b^{3} - 8 \, A a^{3} b^{4}\right)} d^{3} e^{4} + 3 \, {\left(3 \, B a^{5} b^{2} - 10 \, A a^{4} b^{3}\right)} d^{2} e^{5} - {\left(5 \, B a^{6} b - 12 \, A a^{5} b^{2}\right)} d e^{6} + {\left(B a^{7} - 2 \, A a^{6} b\right)} e^{7}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(3072 \, B b^{7} e^{7} x^{6} - 105 \, B b^{7} d^{6} e + 70 \, {\left(7 \, B a b^{6} + 3 \, A b^{7}\right)} d^{5} e^{2} - 7 \, {\left(113 \, B a^{2} b^{5} + 170 \, A a b^{6}\right)} d^{4} e^{3} + 12 \, {\left(25 \, B a^{3} b^{4} + 231 \, A a^{2} b^{5}\right)} d^{3} e^{4} - 7 \, {\left(113 \, B a^{4} b^{3} - 396 \, A a^{3} b^{4}\right)} d^{2} e^{5} + 70 \, {\left(7 \, B a^{5} b^{2} - 17 \, A a^{4} b^{3}\right)} d e^{6} - 105 \, {\left(B a^{6} b - 2 \, A a^{5} b^{2}\right)} e^{7} + 256 \, {\left(29 \, B b^{7} d e^{6} + {\left(29 \, B a b^{6} + 14 \, A b^{7}\right)} e^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{7} d^{2} e^{5} + 2 \, {\left(73 \, B a b^{6} + 35 \, A b^{7}\right)} d e^{6} + {\left(37 \, B a^{2} b^{5} + 70 \, A a b^{6}\right)} e^{7}\right)} x^{4} + 16 \, {\left(3 \, B b^{7} d^{3} e^{4} + {\left(797 \, B a b^{6} + 378 \, A b^{7}\right)} d^{2} e^{5} + {\left(797 \, B a^{2} b^{5} + 1484 \, A a b^{6}\right)} d e^{6} + 3 \, {\left(B a^{3} b^{4} + 126 \, A a^{2} b^{5}\right)} e^{7}\right)} x^{3} - 8 \, {\left(7 \, B b^{7} d^{4} e^{3} - 2 \, {\left(16 \, B a b^{6} + 7 \, A b^{7}\right)} d^{3} e^{4} - 6 \, {\left(205 \, B a^{2} b^{5} + 371 \, A a b^{6}\right)} d^{2} e^{5} - 2 \, {\left(16 \, B a^{3} b^{4} + 1113 \, A a^{2} b^{5}\right)} d e^{6} + 7 \, {\left(B a^{4} b^{3} - 2 \, A a^{3} b^{4}\right)} e^{7}\right)} x^{2} + 2 \, {\left(35 \, B b^{7} d^{5} e^{2} - 7 \, {\left(23 \, B a b^{6} + 10 \, A b^{7}\right)} d^{4} e^{3} + 2 \, {\left(127 \, B a^{2} b^{5} + 196 \, A a b^{6}\right)} d^{3} e^{4} + 2 \, {\left(127 \, B a^{3} b^{4} + 4158 \, A a^{2} b^{5}\right)} d^{2} e^{5} - 7 \, {\left(23 \, B a^{4} b^{3} - 56 \, A a^{3} b^{4}\right)} d e^{6} + 35 \, {\left(B a^{5} b^{2} - 2 \, A a^{4} b^{3}\right)} e^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{86016 \, b^{5} e^{5}}, -\frac{105 \, {\left(B b^{7} d^{7} - {\left(5 \, B a b^{6} + 2 \, A b^{7}\right)} d^{6} e + 3 \, {\left(3 \, B a^{2} b^{5} + 4 \, A a b^{6}\right)} d^{5} e^{2} - 5 \, {\left(B a^{3} b^{4} + 6 \, A a^{2} b^{5}\right)} d^{4} e^{3} - 5 \, {\left(B a^{4} b^{3} - 8 \, A a^{3} b^{4}\right)} d^{3} e^{4} + 3 \, {\left(3 \, B a^{5} b^{2} - 10 \, A a^{4} b^{3}\right)} d^{2} e^{5} - {\left(5 \, B a^{6} b - 12 \, A a^{5} b^{2}\right)} d e^{6} + {\left(B a^{7} - 2 \, A a^{6} b\right)} e^{7}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(3072 \, B b^{7} e^{7} x^{6} - 105 \, B b^{7} d^{6} e + 70 \, {\left(7 \, B a b^{6} + 3 \, A b^{7}\right)} d^{5} e^{2} - 7 \, {\left(113 \, B a^{2} b^{5} + 170 \, A a b^{6}\right)} d^{4} e^{3} + 12 \, {\left(25 \, B a^{3} b^{4} + 231 \, A a^{2} b^{5}\right)} d^{3} e^{4} - 7 \, {\left(113 \, B a^{4} b^{3} - 396 \, A a^{3} b^{4}\right)} d^{2} e^{5} + 70 \, {\left(7 \, B a^{5} b^{2} - 17 \, A a^{4} b^{3}\right)} d e^{6} - 105 \, {\left(B a^{6} b - 2 \, A a^{5} b^{2}\right)} e^{7} + 256 \, {\left(29 \, B b^{7} d e^{6} + {\left(29 \, B a b^{6} + 14 \, A b^{7}\right)} e^{7}\right)} x^{5} + 128 \, {\left(37 \, B b^{7} d^{2} e^{5} + 2 \, {\left(73 \, B a b^{6} + 35 \, A b^{7}\right)} d e^{6} + {\left(37 \, B a^{2} b^{5} + 70 \, A a b^{6}\right)} e^{7}\right)} x^{4} + 16 \, {\left(3 \, B b^{7} d^{3} e^{4} + {\left(797 \, B a b^{6} + 378 \, A b^{7}\right)} d^{2} e^{5} + {\left(797 \, B a^{2} b^{5} + 1484 \, A a b^{6}\right)} d e^{6} + 3 \, {\left(B a^{3} b^{4} + 126 \, A a^{2} b^{5}\right)} e^{7}\right)} x^{3} - 8 \, {\left(7 \, B b^{7} d^{4} e^{3} - 2 \, {\left(16 \, B a b^{6} + 7 \, A b^{7}\right)} d^{3} e^{4} - 6 \, {\left(205 \, B a^{2} b^{5} + 371 \, A a b^{6}\right)} d^{2} e^{5} - 2 \, {\left(16 \, B a^{3} b^{4} + 1113 \, A a^{2} b^{5}\right)} d e^{6} + 7 \, {\left(B a^{4} b^{3} - 2 \, A a^{3} b^{4}\right)} e^{7}\right)} x^{2} + 2 \, {\left(35 \, B b^{7} d^{5} e^{2} - 7 \, {\left(23 \, B a b^{6} + 10 \, A b^{7}\right)} d^{4} e^{3} + 2 \, {\left(127 \, B a^{2} b^{5} + 196 \, A a b^{6}\right)} d^{3} e^{4} + 2 \, {\left(127 \, B a^{3} b^{4} + 4158 \, A a^{2} b^{5}\right)} d^{2} e^{5} - 7 \, {\left(23 \, B a^{4} b^{3} - 56 \, A a^{3} b^{4}\right)} d e^{6} + 35 \, {\left(B a^{5} b^{2} - 2 \, A a^{4} b^{3}\right)} e^{7}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{43008 \, b^{5} e^{5}}\right]"," ",0,"[1/86016*(105*(B*b^7*d^7 - (5*B*a*b^6 + 2*A*b^7)*d^6*e + 3*(3*B*a^2*b^5 + 4*A*a*b^6)*d^5*e^2 - 5*(B*a^3*b^4 + 6*A*a^2*b^5)*d^4*e^3 - 5*(B*a^4*b^3 - 8*A*a^3*b^4)*d^3*e^4 + 3*(3*B*a^5*b^2 - 10*A*a^4*b^3)*d^2*e^5 - (5*B*a^6*b - 12*A*a^5*b^2)*d*e^6 + (B*a^7 - 2*A*a^6*b)*e^7)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(3072*B*b^7*e^7*x^6 - 105*B*b^7*d^6*e + 70*(7*B*a*b^6 + 3*A*b^7)*d^5*e^2 - 7*(113*B*a^2*b^5 + 170*A*a*b^6)*d^4*e^3 + 12*(25*B*a^3*b^4 + 231*A*a^2*b^5)*d^3*e^4 - 7*(113*B*a^4*b^3 - 396*A*a^3*b^4)*d^2*e^5 + 70*(7*B*a^5*b^2 - 17*A*a^4*b^3)*d*e^6 - 105*(B*a^6*b - 2*A*a^5*b^2)*e^7 + 256*(29*B*b^7*d*e^6 + (29*B*a*b^6 + 14*A*b^7)*e^7)*x^5 + 128*(37*B*b^7*d^2*e^5 + 2*(73*B*a*b^6 + 35*A*b^7)*d*e^6 + (37*B*a^2*b^5 + 70*A*a*b^6)*e^7)*x^4 + 16*(3*B*b^7*d^3*e^4 + (797*B*a*b^6 + 378*A*b^7)*d^2*e^5 + (797*B*a^2*b^5 + 1484*A*a*b^6)*d*e^6 + 3*(B*a^3*b^4 + 126*A*a^2*b^5)*e^7)*x^3 - 8*(7*B*b^7*d^4*e^3 - 2*(16*B*a*b^6 + 7*A*b^7)*d^3*e^4 - 6*(205*B*a^2*b^5 + 371*A*a*b^6)*d^2*e^5 - 2*(16*B*a^3*b^4 + 1113*A*a^2*b^5)*d*e^6 + 7*(B*a^4*b^3 - 2*A*a^3*b^4)*e^7)*x^2 + 2*(35*B*b^7*d^5*e^2 - 7*(23*B*a*b^6 + 10*A*b^7)*d^4*e^3 + 2*(127*B*a^2*b^5 + 196*A*a*b^6)*d^3*e^4 + 2*(127*B*a^3*b^4 + 4158*A*a^2*b^5)*d^2*e^5 - 7*(23*B*a^4*b^3 - 56*A*a^3*b^4)*d*e^6 + 35*(B*a^5*b^2 - 2*A*a^4*b^3)*e^7)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^5), -1/43008*(105*(B*b^7*d^7 - (5*B*a*b^6 + 2*A*b^7)*d^6*e + 3*(3*B*a^2*b^5 + 4*A*a*b^6)*d^5*e^2 - 5*(B*a^3*b^4 + 6*A*a^2*b^5)*d^4*e^3 - 5*(B*a^4*b^3 - 8*A*a^3*b^4)*d^3*e^4 + 3*(3*B*a^5*b^2 - 10*A*a^4*b^3)*d^2*e^5 - (5*B*a^6*b - 12*A*a^5*b^2)*d*e^6 + (B*a^7 - 2*A*a^6*b)*e^7)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(3072*B*b^7*e^7*x^6 - 105*B*b^7*d^6*e + 70*(7*B*a*b^6 + 3*A*b^7)*d^5*e^2 - 7*(113*B*a^2*b^5 + 170*A*a*b^6)*d^4*e^3 + 12*(25*B*a^3*b^4 + 231*A*a^2*b^5)*d^3*e^4 - 7*(113*B*a^4*b^3 - 396*A*a^3*b^4)*d^2*e^5 + 70*(7*B*a^5*b^2 - 17*A*a^4*b^3)*d*e^6 - 105*(B*a^6*b - 2*A*a^5*b^2)*e^7 + 256*(29*B*b^7*d*e^6 + (29*B*a*b^6 + 14*A*b^7)*e^7)*x^5 + 128*(37*B*b^7*d^2*e^5 + 2*(73*B*a*b^6 + 35*A*b^7)*d*e^6 + (37*B*a^2*b^5 + 70*A*a*b^6)*e^7)*x^4 + 16*(3*B*b^7*d^3*e^4 + (797*B*a*b^6 + 378*A*b^7)*d^2*e^5 + (797*B*a^2*b^5 + 1484*A*a*b^6)*d*e^6 + 3*(B*a^3*b^4 + 126*A*a^2*b^5)*e^7)*x^3 - 8*(7*B*b^7*d^4*e^3 - 2*(16*B*a*b^6 + 7*A*b^7)*d^3*e^4 - 6*(205*B*a^2*b^5 + 371*A*a*b^6)*d^2*e^5 - 2*(16*B*a^3*b^4 + 1113*A*a^2*b^5)*d*e^6 + 7*(B*a^4*b^3 - 2*A*a^3*b^4)*e^7)*x^2 + 2*(35*B*b^7*d^5*e^2 - 7*(23*B*a*b^6 + 10*A*b^7)*d^4*e^3 + 2*(127*B*a^2*b^5 + 196*A*a*b^6)*d^3*e^4 + 2*(127*B*a^3*b^4 + 4158*A*a^2*b^5)*d^2*e^5 - 7*(23*B*a^4*b^3 - 56*A*a^3*b^4)*d*e^6 + 35*(B*a^5*b^2 - 2*A*a^4*b^3)*e^7)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^5)]","B",0
2224,1,1388,0,1.745837," ","integrate((b*x+a)^(5/2)*(B*x+A)*(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, B b^{6} d^{6} - 6 \, {\left(5 \, B a b^{5} + 2 \, A b^{6}\right)} d^{5} e + 15 \, {\left(3 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} d^{4} e^{2} - 20 \, {\left(B a^{3} b^{3} + 6 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 15 \, {\left(B a^{4} b^{2} - 8 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 6 \, {\left(3 \, B a^{5} b - 10 \, A a^{4} b^{2}\right)} d e^{5} - {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} e^{6}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(1280 \, B b^{6} e^{6} x^{5} - 105 \, B b^{6} d^{5} e + 5 \, {\left(83 \, B a b^{5} + 36 \, A b^{6}\right)} d^{4} e^{2} - 42 \, {\left(13 \, B a^{2} b^{4} + 20 \, A a b^{5}\right)} d^{3} e^{3} + 6 \, {\left(25 \, B a^{3} b^{3} + 256 \, A a^{2} b^{4}\right)} d^{2} e^{4} - 35 \, {\left(7 \, B a^{4} b^{2} - 24 \, A a^{3} b^{3}\right)} d e^{5} + 15 \, {\left(5 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} e^{6} + 128 \, {\left(13 \, B b^{6} d e^{5} + {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} e^{6}\right)} x^{4} + 16 \, {\left(3 \, B b^{6} d^{2} e^{4} + 2 \, {\left(139 \, B a b^{5} + 66 \, A b^{6}\right)} d e^{5} + 9 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} e^{6}\right)} x^{3} - 8 \, {\left(7 \, B b^{6} d^{3} e^{3} - 3 \, {\left(9 \, B a b^{5} + 4 \, A b^{6}\right)} d^{2} e^{4} - 3 \, {\left(141 \, B a^{2} b^{4} + 256 \, A a b^{5}\right)} d e^{5} - {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{2} + 2 \, {\left(35 \, B b^{6} d^{4} e^{2} - 4 \, {\left(34 \, B a b^{5} + 15 \, A b^{6}\right)} d^{3} e^{3} + 6 \, {\left(29 \, B a^{2} b^{4} + 46 \, A a b^{5}\right)} d^{2} e^{4} + 4 \, {\left(20 \, B a^{3} b^{3} + 699 \, A a^{2} b^{4}\right)} d e^{5} - 5 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} e^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{30720 \, b^{4} e^{5}}, -\frac{15 \, {\left(7 \, B b^{6} d^{6} - 6 \, {\left(5 \, B a b^{5} + 2 \, A b^{6}\right)} d^{5} e + 15 \, {\left(3 \, B a^{2} b^{4} + 4 \, A a b^{5}\right)} d^{4} e^{2} - 20 \, {\left(B a^{3} b^{3} + 6 \, A a^{2} b^{4}\right)} d^{3} e^{3} - 15 \, {\left(B a^{4} b^{2} - 8 \, A a^{3} b^{3}\right)} d^{2} e^{4} + 6 \, {\left(3 \, B a^{5} b - 10 \, A a^{4} b^{2}\right)} d e^{5} - {\left(5 \, B a^{6} - 12 \, A a^{5} b\right)} e^{6}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(1280 \, B b^{6} e^{6} x^{5} - 105 \, B b^{6} d^{5} e + 5 \, {\left(83 \, B a b^{5} + 36 \, A b^{6}\right)} d^{4} e^{2} - 42 \, {\left(13 \, B a^{2} b^{4} + 20 \, A a b^{5}\right)} d^{3} e^{3} + 6 \, {\left(25 \, B a^{3} b^{3} + 256 \, A a^{2} b^{4}\right)} d^{2} e^{4} - 35 \, {\left(7 \, B a^{4} b^{2} - 24 \, A a^{3} b^{3}\right)} d e^{5} + 15 \, {\left(5 \, B a^{5} b - 12 \, A a^{4} b^{2}\right)} e^{6} + 128 \, {\left(13 \, B b^{6} d e^{5} + {\left(25 \, B a b^{5} + 12 \, A b^{6}\right)} e^{6}\right)} x^{4} + 16 \, {\left(3 \, B b^{6} d^{2} e^{4} + 2 \, {\left(139 \, B a b^{5} + 66 \, A b^{6}\right)} d e^{5} + 9 \, {\left(15 \, B a^{2} b^{4} + 28 \, A a b^{5}\right)} e^{6}\right)} x^{3} - 8 \, {\left(7 \, B b^{6} d^{3} e^{3} - 3 \, {\left(9 \, B a b^{5} + 4 \, A b^{6}\right)} d^{2} e^{4} - 3 \, {\left(141 \, B a^{2} b^{4} + 256 \, A a b^{5}\right)} d e^{5} - {\left(5 \, B a^{3} b^{3} + 372 \, A a^{2} b^{4}\right)} e^{6}\right)} x^{2} + 2 \, {\left(35 \, B b^{6} d^{4} e^{2} - 4 \, {\left(34 \, B a b^{5} + 15 \, A b^{6}\right)} d^{3} e^{3} + 6 \, {\left(29 \, B a^{2} b^{4} + 46 \, A a b^{5}\right)} d^{2} e^{4} + 4 \, {\left(20 \, B a^{3} b^{3} + 699 \, A a^{2} b^{4}\right)} d e^{5} - 5 \, {\left(5 \, B a^{4} b^{2} - 12 \, A a^{3} b^{3}\right)} e^{6}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15360 \, b^{4} e^{5}}\right]"," ",0,"[1/30720*(15*(7*B*b^6*d^6 - 6*(5*B*a*b^5 + 2*A*b^6)*d^5*e + 15*(3*B*a^2*b^4 + 4*A*a*b^5)*d^4*e^2 - 20*(B*a^3*b^3 + 6*A*a^2*b^4)*d^3*e^3 - 15*(B*a^4*b^2 - 8*A*a^3*b^3)*d^2*e^4 + 6*(3*B*a^5*b - 10*A*a^4*b^2)*d*e^5 - (5*B*a^6 - 12*A*a^5*b)*e^6)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(1280*B*b^6*e^6*x^5 - 105*B*b^6*d^5*e + 5*(83*B*a*b^5 + 36*A*b^6)*d^4*e^2 - 42*(13*B*a^2*b^4 + 20*A*a*b^5)*d^3*e^3 + 6*(25*B*a^3*b^3 + 256*A*a^2*b^4)*d^2*e^4 - 35*(7*B*a^4*b^2 - 24*A*a^3*b^3)*d*e^5 + 15*(5*B*a^5*b - 12*A*a^4*b^2)*e^6 + 128*(13*B*b^6*d*e^5 + (25*B*a*b^5 + 12*A*b^6)*e^6)*x^4 + 16*(3*B*b^6*d^2*e^4 + 2*(139*B*a*b^5 + 66*A*b^6)*d*e^5 + 9*(15*B*a^2*b^4 + 28*A*a*b^5)*e^6)*x^3 - 8*(7*B*b^6*d^3*e^3 - 3*(9*B*a*b^5 + 4*A*b^6)*d^2*e^4 - 3*(141*B*a^2*b^4 + 256*A*a*b^5)*d*e^5 - (5*B*a^3*b^3 + 372*A*a^2*b^4)*e^6)*x^2 + 2*(35*B*b^6*d^4*e^2 - 4*(34*B*a*b^5 + 15*A*b^6)*d^3*e^3 + 6*(29*B*a^2*b^4 + 46*A*a*b^5)*d^2*e^4 + 4*(20*B*a^3*b^3 + 699*A*a^2*b^4)*d*e^5 - 5*(5*B*a^4*b^2 - 12*A*a^3*b^3)*e^6)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^5), -1/15360*(15*(7*B*b^6*d^6 - 6*(5*B*a*b^5 + 2*A*b^6)*d^5*e + 15*(3*B*a^2*b^4 + 4*A*a*b^5)*d^4*e^2 - 20*(B*a^3*b^3 + 6*A*a^2*b^4)*d^3*e^3 - 15*(B*a^4*b^2 - 8*A*a^3*b^3)*d^2*e^4 + 6*(3*B*a^5*b - 10*A*a^4*b^2)*d*e^5 - (5*B*a^6 - 12*A*a^5*b)*e^6)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(1280*B*b^6*e^6*x^5 - 105*B*b^6*d^5*e + 5*(83*B*a*b^5 + 36*A*b^6)*d^4*e^2 - 42*(13*B*a^2*b^4 + 20*A*a*b^5)*d^3*e^3 + 6*(25*B*a^3*b^3 + 256*A*a^2*b^4)*d^2*e^4 - 35*(7*B*a^4*b^2 - 24*A*a^3*b^3)*d*e^5 + 15*(5*B*a^5*b - 12*A*a^4*b^2)*e^6 + 128*(13*B*b^6*d*e^5 + (25*B*a*b^5 + 12*A*b^6)*e^6)*x^4 + 16*(3*B*b^6*d^2*e^4 + 2*(139*B*a*b^5 + 66*A*b^6)*d*e^5 + 9*(15*B*a^2*b^4 + 28*A*a*b^5)*e^6)*x^3 - 8*(7*B*b^6*d^3*e^3 - 3*(9*B*a*b^5 + 4*A*b^6)*d^2*e^4 - 3*(141*B*a^2*b^4 + 256*A*a*b^5)*d*e^5 - (5*B*a^3*b^3 + 372*A*a^2*b^4)*e^6)*x^2 + 2*(35*B*b^6*d^4*e^2 - 4*(34*B*a*b^5 + 15*A*b^6)*d^3*e^3 + 6*(29*B*a^2*b^4 + 46*A*a*b^5)*d^2*e^4 + 4*(20*B*a^3*b^3 + 699*A*a^2*b^4)*d*e^5 - 5*(5*B*a^4*b^2 - 12*A*a^3*b^3)*e^6)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^5)]","B",0
2225,1,1046,0,1.242175," ","integrate((b*x+a)^(5/2)*(B*x+A)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{5} d^{5} - 5 \, {\left(5 \, B a b^{4} + 2 \, A b^{5}\right)} d^{4} e + 10 \, {\left(3 \, B a^{2} b^{3} + 4 \, A a b^{4}\right)} d^{3} e^{2} - 10 \, {\left(B a^{3} b^{2} + 6 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 5 \, {\left(B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} e^{5}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(384 \, B b^{5} e^{5} x^{4} - 105 \, B b^{5} d^{4} e + 10 \, {\left(34 \, B a b^{4} + 15 \, A b^{5}\right)} d^{3} e^{2} - 2 \, {\left(173 \, B a^{2} b^{3} + 275 \, A a b^{4}\right)} d^{2} e^{3} + 10 \, {\left(6 \, B a^{3} b^{2} + 73 \, A a^{2} b^{3}\right)} d e^{4} - 15 \, {\left(3 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} e^{5} + 48 \, {\left(B b^{5} d e^{4} + {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{5} d^{2} e^{3} - 2 \, {\left(11 \, B a b^{4} + 5 \, A b^{5}\right)} d e^{4} - {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(35 \, B b^{5} d^{3} e^{2} - {\left(111 \, B a b^{4} + 50 \, A b^{5}\right)} d^{2} e^{3} + {\left(109 \, B a^{2} b^{3} + 180 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{7680 \, b^{3} e^{5}}, -\frac{15 \, {\left(7 \, B b^{5} d^{5} - 5 \, {\left(5 \, B a b^{4} + 2 \, A b^{5}\right)} d^{4} e + 10 \, {\left(3 \, B a^{2} b^{3} + 4 \, A a b^{4}\right)} d^{3} e^{2} - 10 \, {\left(B a^{3} b^{2} + 6 \, A a^{2} b^{3}\right)} d^{2} e^{3} - 5 \, {\left(B a^{4} b - 8 \, A a^{3} b^{2}\right)} d e^{4} + {\left(3 \, B a^{5} - 10 \, A a^{4} b\right)} e^{5}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(384 \, B b^{5} e^{5} x^{4} - 105 \, B b^{5} d^{4} e + 10 \, {\left(34 \, B a b^{4} + 15 \, A b^{5}\right)} d^{3} e^{2} - 2 \, {\left(173 \, B a^{2} b^{3} + 275 \, A a b^{4}\right)} d^{2} e^{3} + 10 \, {\left(6 \, B a^{3} b^{2} + 73 \, A a^{2} b^{3}\right)} d e^{4} - 15 \, {\left(3 \, B a^{4} b - 10 \, A a^{3} b^{2}\right)} e^{5} + 48 \, {\left(B b^{5} d e^{4} + {\left(21 \, B a b^{4} + 10 \, A b^{5}\right)} e^{5}\right)} x^{3} - 8 \, {\left(7 \, B b^{5} d^{2} e^{3} - 2 \, {\left(11 \, B a b^{4} + 5 \, A b^{5}\right)} d e^{4} - {\left(93 \, B a^{2} b^{3} + 170 \, A a b^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(35 \, B b^{5} d^{3} e^{2} - {\left(111 \, B a b^{4} + 50 \, A b^{5}\right)} d^{2} e^{3} + {\left(109 \, B a^{2} b^{3} + 180 \, A a b^{4}\right)} d e^{4} + 5 \, {\left(3 \, B a^{3} b^{2} + 118 \, A a^{2} b^{3}\right)} e^{5}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3840 \, b^{3} e^{5}}\right]"," ",0,"[-1/7680*(15*(7*B*b^5*d^5 - 5*(5*B*a*b^4 + 2*A*b^5)*d^4*e + 10*(3*B*a^2*b^3 + 4*A*a*b^4)*d^3*e^2 - 10*(B*a^3*b^2 + 6*A*a^2*b^3)*d^2*e^3 - 5*(B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (3*B*a^5 - 10*A*a^4*b)*e^5)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(384*B*b^5*e^5*x^4 - 105*B*b^5*d^4*e + 10*(34*B*a*b^4 + 15*A*b^5)*d^3*e^2 - 2*(173*B*a^2*b^3 + 275*A*a*b^4)*d^2*e^3 + 10*(6*B*a^3*b^2 + 73*A*a^2*b^3)*d*e^4 - 15*(3*B*a^4*b - 10*A*a^3*b^2)*e^5 + 48*(B*b^5*d*e^4 + (21*B*a*b^4 + 10*A*b^5)*e^5)*x^3 - 8*(7*B*b^5*d^2*e^3 - 2*(11*B*a*b^4 + 5*A*b^5)*d*e^4 - (93*B*a^2*b^3 + 170*A*a*b^4)*e^5)*x^2 + 2*(35*B*b^5*d^3*e^2 - (111*B*a*b^4 + 50*A*b^5)*d^2*e^3 + (109*B*a^2*b^3 + 180*A*a*b^4)*d*e^4 + 5*(3*B*a^3*b^2 + 118*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^5), -1/3840*(15*(7*B*b^5*d^5 - 5*(5*B*a*b^4 + 2*A*b^5)*d^4*e + 10*(3*B*a^2*b^3 + 4*A*a*b^4)*d^3*e^2 - 10*(B*a^3*b^2 + 6*A*a^2*b^3)*d^2*e^3 - 5*(B*a^4*b - 8*A*a^3*b^2)*d*e^4 + (3*B*a^5 - 10*A*a^4*b)*e^5)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(384*B*b^5*e^5*x^4 - 105*B*b^5*d^4*e + 10*(34*B*a*b^4 + 15*A*b^5)*d^3*e^2 - 2*(173*B*a^2*b^3 + 275*A*a*b^4)*d^2*e^3 + 10*(6*B*a^3*b^2 + 73*A*a^2*b^3)*d*e^4 - 15*(3*B*a^4*b - 10*A*a^3*b^2)*e^5 + 48*(B*b^5*d*e^4 + (21*B*a*b^4 + 10*A*b^5)*e^5)*x^3 - 8*(7*B*b^5*d^2*e^3 - 2*(11*B*a*b^4 + 5*A*b^5)*d*e^4 - (93*B*a^2*b^3 + 170*A*a*b^4)*e^5)*x^2 + 2*(35*B*b^5*d^3*e^2 - (111*B*a*b^4 + 50*A*b^5)*d^2*e^3 + (109*B*a^2*b^3 + 180*A*a*b^4)*d*e^4 + 5*(3*B*a^3*b^2 + 118*A*a^2*b^3)*e^5)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^5)]","A",0
2226,1,770,0,1.903569," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{4} d^{4} - 4 \, {\left(5 \, B a b^{3} + 2 \, A b^{4}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{2} + 4 \, A a b^{3}\right)} d^{2} e^{2} - 4 \, {\left(B a^{3} b + 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(48 \, B b^{4} e^{4} x^{3} - 105 \, B b^{4} d^{3} e + 5 \, {\left(53 \, B a b^{3} + 24 \, A b^{4}\right)} d^{2} e^{2} - {\left(191 \, B a^{2} b^{2} + 320 \, A a b^{3}\right)} d e^{3} + 3 \, {\left(5 \, B a^{3} b + 88 \, A a^{2} b^{2}\right)} e^{4} - 8 \, {\left(7 \, B b^{4} d e^{3} - {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{4} d^{2} e^{2} - 2 \, {\left(43 \, B a b^{3} + 20 \, A b^{4}\right)} d e^{3} + {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{768 \, b^{2} e^{5}}, -\frac{15 \, {\left(7 \, B b^{4} d^{4} - 4 \, {\left(5 \, B a b^{3} + 2 \, A b^{4}\right)} d^{3} e + 6 \, {\left(3 \, B a^{2} b^{2} + 4 \, A a b^{3}\right)} d^{2} e^{2} - 4 \, {\left(B a^{3} b + 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, B b^{4} e^{4} x^{3} - 105 \, B b^{4} d^{3} e + 5 \, {\left(53 \, B a b^{3} + 24 \, A b^{4}\right)} d^{2} e^{2} - {\left(191 \, B a^{2} b^{2} + 320 \, A a b^{3}\right)} d e^{3} + 3 \, {\left(5 \, B a^{3} b + 88 \, A a^{2} b^{2}\right)} e^{4} - 8 \, {\left(7 \, B b^{4} d e^{3} - {\left(17 \, B a b^{3} + 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(35 \, B b^{4} d^{2} e^{2} - 2 \, {\left(43 \, B a b^{3} + 20 \, A b^{4}\right)} d e^{3} + {\left(59 \, B a^{2} b^{2} + 104 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{384 \, b^{2} e^{5}}\right]"," ",0,"[-1/768*(15*(7*B*b^4*d^4 - 4*(5*B*a*b^3 + 2*A*b^4)*d^3*e + 6*(3*B*a^2*b^2 + 4*A*a*b^3)*d^2*e^2 - 4*(B*a^3*b + 6*A*a^2*b^2)*d*e^3 - (B*a^4 - 8*A*a^3*b)*e^4)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(48*B*b^4*e^4*x^3 - 105*B*b^4*d^3*e + 5*(53*B*a*b^3 + 24*A*b^4)*d^2*e^2 - (191*B*a^2*b^2 + 320*A*a*b^3)*d*e^3 + 3*(5*B*a^3*b + 88*A*a^2*b^2)*e^4 - 8*(7*B*b^4*d*e^3 - (17*B*a*b^3 + 8*A*b^4)*e^4)*x^2 + 2*(35*B*b^4*d^2*e^2 - 2*(43*B*a*b^3 + 20*A*b^4)*d*e^3 + (59*B*a^2*b^2 + 104*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^5), -1/384*(15*(7*B*b^4*d^4 - 4*(5*B*a*b^3 + 2*A*b^4)*d^3*e + 6*(3*B*a^2*b^2 + 4*A*a*b^3)*d^2*e^2 - 4*(B*a^3*b + 6*A*a^2*b^2)*d*e^3 - (B*a^4 - 8*A*a^3*b)*e^4)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(48*B*b^4*e^4*x^3 - 105*B*b^4*d^3*e + 5*(53*B*a*b^3 + 24*A*b^4)*d^2*e^2 - (191*B*a^2*b^2 + 320*A*a*b^3)*d*e^3 + 3*(5*B*a^3*b + 88*A*a^2*b^2)*e^4 - 8*(7*B*b^4*d*e^3 - (17*B*a*b^3 + 8*A*b^4)*e^4)*x^2 + 2*(35*B*b^4*d^2*e^2 - 2*(43*B*a*b^3 + 20*A*b^4)*d*e^3 + (59*B*a^2*b^2 + 104*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*e^5)]","A",0
2227,1,858,0,4.564746," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{3} d^{4} - 3 \, {\left(5 \, B a b^{2} + 2 \, A b^{3}\right)} d^{3} e + 3 \, {\left(3 \, B a^{2} b + 4 \, A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 6 \, A a^{2} b\right)} d e^{3} + {\left(7 \, B b^{3} d^{3} e - 3 \, {\left(5 \, B a b^{2} + 2 \, A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(3 \, B a^{2} b + 4 \, A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 6 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{3} e^{4} x^{3} + 105 \, B b^{3} d^{3} e - 48 \, A a^{2} b e^{4} - 10 \, {\left(19 \, B a b^{2} + 9 \, A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(27 \, B a^{2} b + 50 \, A a b^{2}\right)} d e^{3} - 2 \, {\left(7 \, B b^{3} d e^{3} - {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} e^{4}\right)} x^{2} + {\left(35 \, B b^{3} d^{2} e^{2} - 2 \, {\left(34 \, B a b^{2} + 15 \, A b^{3}\right)} d e^{3} + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, {\left(b e^{6} x + b d e^{5}\right)}}, \frac{15 \, {\left(7 \, B b^{3} d^{4} - 3 \, {\left(5 \, B a b^{2} + 2 \, A b^{3}\right)} d^{3} e + 3 \, {\left(3 \, B a^{2} b + 4 \, A a b^{2}\right)} d^{2} e^{2} - {\left(B a^{3} + 6 \, A a^{2} b\right)} d e^{3} + {\left(7 \, B b^{3} d^{3} e - 3 \, {\left(5 \, B a b^{2} + 2 \, A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(3 \, B a^{2} b + 4 \, A a b^{2}\right)} d e^{3} - {\left(B a^{3} + 6 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, B b^{3} e^{4} x^{3} + 105 \, B b^{3} d^{3} e - 48 \, A a^{2} b e^{4} - 10 \, {\left(19 \, B a b^{2} + 9 \, A b^{3}\right)} d^{2} e^{2} + 3 \, {\left(27 \, B a^{2} b + 50 \, A a b^{2}\right)} d e^{3} - 2 \, {\left(7 \, B b^{3} d e^{3} - {\left(13 \, B a b^{2} + 6 \, A b^{3}\right)} e^{4}\right)} x^{2} + {\left(35 \, B b^{3} d^{2} e^{2} - 2 \, {\left(34 \, B a b^{2} + 15 \, A b^{3}\right)} d e^{3} + 3 \, {\left(11 \, B a^{2} b + 18 \, A a b^{2}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, {\left(b e^{6} x + b d e^{5}\right)}}\right]"," ",0,"[-1/96*(15*(7*B*b^3*d^4 - 3*(5*B*a*b^2 + 2*A*b^3)*d^3*e + 3*(3*B*a^2*b + 4*A*a*b^2)*d^2*e^2 - (B*a^3 + 6*A*a^2*b)*d*e^3 + (7*B*b^3*d^3*e - 3*(5*B*a*b^2 + 2*A*b^3)*d^2*e^2 + 3*(3*B*a^2*b + 4*A*a*b^2)*d*e^3 - (B*a^3 + 6*A*a^2*b)*e^4)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^3*e^4*x^3 + 105*B*b^3*d^3*e - 48*A*a^2*b*e^4 - 10*(19*B*a*b^2 + 9*A*b^3)*d^2*e^2 + 3*(27*B*a^2*b + 50*A*a*b^2)*d*e^3 - 2*(7*B*b^3*d*e^3 - (13*B*a*b^2 + 6*A*b^3)*e^4)*x^2 + (35*B*b^3*d^2*e^2 - 2*(34*B*a*b^2 + 15*A*b^3)*d*e^3 + 3*(11*B*a^2*b + 18*A*a*b^2)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^6*x + b*d*e^5), 1/48*(15*(7*B*b^3*d^4 - 3*(5*B*a*b^2 + 2*A*b^3)*d^3*e + 3*(3*B*a^2*b + 4*A*a*b^2)*d^2*e^2 - (B*a^3 + 6*A*a^2*b)*d*e^3 + (7*B*b^3*d^3*e - 3*(5*B*a*b^2 + 2*A*b^3)*d^2*e^2 + 3*(3*B*a^2*b + 4*A*a*b^2)*d*e^3 - (B*a^3 + 6*A*a^2*b)*e^4)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(8*B*b^3*e^4*x^3 + 105*B*b^3*d^3*e - 48*A*a^2*b*e^4 - 10*(19*B*a*b^2 + 9*A*b^3)*d^2*e^2 + 3*(27*B*a^2*b + 50*A*a*b^2)*d*e^3 - 2*(7*B*b^3*d*e^3 - (13*B*a*b^2 + 6*A*b^3)*e^4)*x^2 + (35*B*b^3*d^2*e^2 - 2*(34*B*a*b^2 + 15*A*b^3)*d*e^3 + 3*(11*B*a^2*b + 18*A*a*b^2)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*e^6*x + b*d*e^5)]","A",0
2228,1,855,0,8.340315," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, B b^{2} d^{4} - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{3} e + {\left(3 \, B a^{2} + 4 \, A a b\right)} d^{2} e^{2} + {\left(7 \, B b^{2} d^{2} e^{2} - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d e^{3} + {\left(3 \, B a^{2} + 4 \, A a b\right)} e^{4}\right)} x^{2} + 2 \, {\left(7 \, B b^{2} d^{3} e - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{2} + 4 \, A a b\right)} d e^{3}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(6 \, B b^{2} e^{3} x^{3} - 105 \, B b^{2} d^{3} - 8 \, A a^{2} e^{3} + 5 \, {\left(23 \, B a b + 12 \, A b^{2}\right)} d^{2} e - 8 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} d e^{2} - 3 \, {\left(7 \, B b^{2} d e^{2} - {\left(9 \, B a b + 4 \, A b^{2}\right)} e^{3}\right)} x^{2} - 2 \, {\left(70 \, B b^{2} d^{2} e - {\left(79 \, B a b + 40 \, A b^{2}\right)} d e^{2} + 4 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}, -\frac{15 \, {\left(7 \, B b^{2} d^{4} - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{3} e + {\left(3 \, B a^{2} + 4 \, A a b\right)} d^{2} e^{2} + {\left(7 \, B b^{2} d^{2} e^{2} - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d e^{3} + {\left(3 \, B a^{2} + 4 \, A a b\right)} e^{4}\right)} x^{2} + 2 \, {\left(7 \, B b^{2} d^{3} e - 2 \, {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{2} e^{2} + {\left(3 \, B a^{2} + 4 \, A a b\right)} d e^{3}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) - 2 \, {\left(6 \, B b^{2} e^{3} x^{3} - 105 \, B b^{2} d^{3} - 8 \, A a^{2} e^{3} + 5 \, {\left(23 \, B a b + 12 \, A b^{2}\right)} d^{2} e - 8 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} d e^{2} - 3 \, {\left(7 \, B b^{2} d e^{2} - {\left(9 \, B a b + 4 \, A b^{2}\right)} e^{3}\right)} x^{2} - 2 \, {\left(70 \, B b^{2} d^{2} e - {\left(79 \, B a b + 40 \, A b^{2}\right)} d e^{2} + 4 \, {\left(3 \, B a^{2} + 7 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{24 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}\right]"," ",0,"[1/48*(15*(7*B*b^2*d^4 - 2*(5*B*a*b + 2*A*b^2)*d^3*e + (3*B*a^2 + 4*A*a*b)*d^2*e^2 + (7*B*b^2*d^2*e^2 - 2*(5*B*a*b + 2*A*b^2)*d*e^3 + (3*B*a^2 + 4*A*a*b)*e^4)*x^2 + 2*(7*B*b^2*d^3*e - 2*(5*B*a*b + 2*A*b^2)*d^2*e^2 + (3*B*a^2 + 4*A*a*b)*d*e^3)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(6*B*b^2*e^3*x^3 - 105*B*b^2*d^3 - 8*A*a^2*e^3 + 5*(23*B*a*b + 12*A*b^2)*d^2*e - 8*(2*B*a^2 + 5*A*a*b)*d*e^2 - 3*(7*B*b^2*d*e^2 - (9*B*a*b + 4*A*b^2)*e^3)*x^2 - 2*(70*B*b^2*d^2*e - (79*B*a*b + 40*A*b^2)*d*e^2 + 4*(3*B*a^2 + 7*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4), -1/24*(15*(7*B*b^2*d^4 - 2*(5*B*a*b + 2*A*b^2)*d^3*e + (3*B*a^2 + 4*A*a*b)*d^2*e^2 + (7*B*b^2*d^2*e^2 - 2*(5*B*a*b + 2*A*b^2)*d*e^3 + (3*B*a^2 + 4*A*a*b)*e^4)*x^2 + 2*(7*B*b^2*d^3*e - 2*(5*B*a*b + 2*A*b^2)*d^2*e^2 + (3*B*a^2 + 4*A*a*b)*d*e^3)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) - 2*(6*B*b^2*e^3*x^3 - 105*B*b^2*d^3 - 8*A*a^2*e^3 + 5*(23*B*a*b + 12*A*b^2)*d^2*e - 8*(2*B*a^2 + 5*A*a*b)*d*e^2 - 3*(7*B*b^2*d*e^2 - (9*B*a*b + 4*A*b^2)*e^3)*x^2 - 2*(70*B*b^2*d^2*e - (79*B*a*b + 40*A*b^2)*d*e^2 + 4*(3*B*a^2 + 7*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)]","A",0
2229,1,835,0,19.057806," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(7 \, B b^{2} d^{4} - {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{3} e + {\left(7 \, B b^{2} d e^{3} - {\left(5 \, B a b + 2 \, A b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(7 \, B b^{2} d^{2} e^{2} - {\left(5 \, B a b + 2 \, A b^{2}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(7 \, B b^{2} d^{3} e - {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(15 \, B b^{2} e^{3} x^{3} + 105 \, B b^{2} d^{3} - 6 \, A a^{2} e^{3} - 10 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} d^{2} e - 2 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} d e^{2} + {\left(161 \, B b^{2} d e^{2} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} e^{3}\right)} x^{2} + {\left(245 \, B b^{2} d^{2} e - 14 \, {\left(7 \, B a b + 5 \, A b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{60 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}, \frac{15 \, {\left(7 \, B b^{2} d^{4} - {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{3} e + {\left(7 \, B b^{2} d e^{3} - {\left(5 \, B a b + 2 \, A b^{2}\right)} e^{4}\right)} x^{3} + 3 \, {\left(7 \, B b^{2} d^{2} e^{2} - {\left(5 \, B a b + 2 \, A b^{2}\right)} d e^{3}\right)} x^{2} + 3 \, {\left(7 \, B b^{2} d^{3} e - {\left(5 \, B a b + 2 \, A b^{2}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) + 2 \, {\left(15 \, B b^{2} e^{3} x^{3} + 105 \, B b^{2} d^{3} - 6 \, A a^{2} e^{3} - 10 \, {\left(4 \, B a b + 3 \, A b^{2}\right)} d^{2} e - 2 \, {\left(2 \, B a^{2} + 5 \, A a b\right)} d e^{2} + {\left(161 \, B b^{2} d e^{2} - 2 \, {\left(35 \, B a b + 23 \, A b^{2}\right)} e^{3}\right)} x^{2} + {\left(245 \, B b^{2} d^{2} e - 14 \, {\left(7 \, B a b + 5 \, A b^{2}\right)} d e^{2} - 2 \, {\left(5 \, B a^{2} + 11 \, A a b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{30 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}\right]"," ",0,"[-1/60*(15*(7*B*b^2*d^4 - (5*B*a*b + 2*A*b^2)*d^3*e + (7*B*b^2*d*e^3 - (5*B*a*b + 2*A*b^2)*e^4)*x^3 + 3*(7*B*b^2*d^2*e^2 - (5*B*a*b + 2*A*b^2)*d*e^3)*x^2 + 3*(7*B*b^2*d^3*e - (5*B*a*b + 2*A*b^2)*d^2*e^2)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(15*B*b^2*e^3*x^3 + 105*B*b^2*d^3 - 6*A*a^2*e^3 - 10*(4*B*a*b + 3*A*b^2)*d^2*e - 2*(2*B*a^2 + 5*A*a*b)*d*e^2 + (161*B*b^2*d*e^2 - 2*(35*B*a*b + 23*A*b^2)*e^3)*x^2 + (245*B*b^2*d^2*e - 14*(7*B*a*b + 5*A*b^2)*d*e^2 - 2*(5*B*a^2 + 11*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4), 1/30*(15*(7*B*b^2*d^4 - (5*B*a*b + 2*A*b^2)*d^3*e + (7*B*b^2*d*e^3 - (5*B*a*b + 2*A*b^2)*e^4)*x^3 + 3*(7*B*b^2*d^2*e^2 - (5*B*a*b + 2*A*b^2)*d*e^3)*x^2 + 3*(7*B*b^2*d^3*e - (5*B*a*b + 2*A*b^2)*d^2*e^2)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) + 2*(15*B*b^2*e^3*x^3 + 105*B*b^2*d^3 - 6*A*a^2*e^3 - 10*(4*B*a*b + 3*A*b^2)*d^2*e - 2*(2*B*a^2 + 5*A*a*b)*d*e^2 + (161*B*b^2*d*e^2 - 2*(35*B*a*b + 23*A*b^2)*e^3)*x^2 + (245*B*b^2*d^2*e - 14*(7*B*a*b + 5*A*b^2)*d*e^2 - 2*(5*B*a^2 + 11*A*a*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)]","A",0
2230,1,1053,0,47.559661," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(B b^{3} d^{5} - B a b^{2} d^{4} e + {\left(B b^{3} d e^{4} - B a b^{2} e^{5}\right)} x^{4} + 4 \, {\left(B b^{3} d^{2} e^{3} - B a b^{2} d e^{4}\right)} x^{3} + 6 \, {\left(B b^{3} d^{3} e^{2} - B a b^{2} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(B b^{3} d^{4} e - B a b^{2} d^{3} e^{2}\right)} x\right)} \sqrt{\frac{b}{e}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e^{2} x + b d e + a e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{b}{e}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(105 \, B b^{3} d^{4} - 70 \, B a b^{2} d^{3} e - 14 \, B a^{2} b d^{2} e^{2} - 6 \, B a^{3} d e^{3} - 15 \, A a^{3} e^{4} + {\left(176 \, B b^{3} d e^{3} - {\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} e^{4}\right)} x^{3} + {\left(406 \, B b^{3} d^{2} e^{2} - 284 \, B a b^{2} d e^{3} - {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} e^{4}\right)} x^{2} + {\left(350 \, B b^{3} d^{3} e - 238 \, B a b^{2} d^{2} e^{2} - 46 \, B a^{2} b d e^{3} - 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{210 \, {\left(b d^{5} e^{4} - a d^{4} e^{5} + {\left(b d e^{8} - a e^{9}\right)} x^{4} + 4 \, {\left(b d^{2} e^{7} - a d e^{8}\right)} x^{3} + 6 \, {\left(b d^{3} e^{6} - a d^{2} e^{7}\right)} x^{2} + 4 \, {\left(b d^{4} e^{5} - a d^{3} e^{6}\right)} x\right)}}, -\frac{105 \, {\left(B b^{3} d^{5} - B a b^{2} d^{4} e + {\left(B b^{3} d e^{4} - B a b^{2} e^{5}\right)} x^{4} + 4 \, {\left(B b^{3} d^{2} e^{3} - B a b^{2} d e^{4}\right)} x^{3} + 6 \, {\left(B b^{3} d^{3} e^{2} - B a b^{2} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(B b^{3} d^{4} e - B a b^{2} d^{3} e^{2}\right)} x\right)} \sqrt{-\frac{b}{e}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{b}{e}}}{2 \, {\left(b^{2} e x^{2} + a b d + {\left(b^{2} d + a b e\right)} x\right)}}\right) + 2 \, {\left(105 \, B b^{3} d^{4} - 70 \, B a b^{2} d^{3} e - 14 \, B a^{2} b d^{2} e^{2} - 6 \, B a^{3} d e^{3} - 15 \, A a^{3} e^{4} + {\left(176 \, B b^{3} d e^{3} - {\left(161 \, B a b^{2} + 15 \, A b^{3}\right)} e^{4}\right)} x^{3} + {\left(406 \, B b^{3} d^{2} e^{2} - 284 \, B a b^{2} d e^{3} - {\left(77 \, B a^{2} b + 45 \, A a b^{2}\right)} e^{4}\right)} x^{2} + {\left(350 \, B b^{3} d^{3} e - 238 \, B a b^{2} d^{2} e^{2} - 46 \, B a^{2} b d e^{3} - 3 \, {\left(7 \, B a^{3} + 15 \, A a^{2} b\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{105 \, {\left(b d^{5} e^{4} - a d^{4} e^{5} + {\left(b d e^{8} - a e^{9}\right)} x^{4} + 4 \, {\left(b d^{2} e^{7} - a d e^{8}\right)} x^{3} + 6 \, {\left(b d^{3} e^{6} - a d^{2} e^{7}\right)} x^{2} + 4 \, {\left(b d^{4} e^{5} - a d^{3} e^{6}\right)} x\right)}}\right]"," ",0,"[1/210*(105*(B*b^3*d^5 - B*a*b^2*d^4*e + (B*b^3*d*e^4 - B*a*b^2*e^5)*x^4 + 4*(B*b^3*d^2*e^3 - B*a*b^2*d*e^4)*x^3 + 6*(B*b^3*d^3*e^2 - B*a*b^2*d^2*e^3)*x^2 + 4*(B*b^3*d^4*e - B*a*b^2*d^3*e^2)*x)*sqrt(b/e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e^2*x + b*d*e + a*e^2)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(b/e) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(105*B*b^3*d^4 - 70*B*a*b^2*d^3*e - 14*B*a^2*b*d^2*e^2 - 6*B*a^3*d*e^3 - 15*A*a^3*e^4 + (176*B*b^3*d*e^3 - (161*B*a*b^2 + 15*A*b^3)*e^4)*x^3 + (406*B*b^3*d^2*e^2 - 284*B*a*b^2*d*e^3 - (77*B*a^2*b + 45*A*a*b^2)*e^4)*x^2 + (350*B*b^3*d^3*e - 238*B*a*b^2*d^2*e^2 - 46*B*a^2*b*d*e^3 - 3*(7*B*a^3 + 15*A*a^2*b)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^5*e^4 - a*d^4*e^5 + (b*d*e^8 - a*e^9)*x^4 + 4*(b*d^2*e^7 - a*d*e^8)*x^3 + 6*(b*d^3*e^6 - a*d^2*e^7)*x^2 + 4*(b*d^4*e^5 - a*d^3*e^6)*x), -1/105*(105*(B*b^3*d^5 - B*a*b^2*d^4*e + (B*b^3*d*e^4 - B*a*b^2*e^5)*x^4 + 4*(B*b^3*d^2*e^3 - B*a*b^2*d*e^4)*x^3 + 6*(B*b^3*d^3*e^2 - B*a*b^2*d^2*e^3)*x^2 + 4*(B*b^3*d^4*e - B*a*b^2*d^3*e^2)*x)*sqrt(-b/e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-b/e)/(b^2*e*x^2 + a*b*d + (b^2*d + a*b*e)*x)) + 2*(105*B*b^3*d^4 - 70*B*a*b^2*d^3*e - 14*B*a^2*b*d^2*e^2 - 6*B*a^3*d*e^3 - 15*A*a^3*e^4 + (176*B*b^3*d*e^3 - (161*B*a*b^2 + 15*A*b^3)*e^4)*x^3 + (406*B*b^3*d^2*e^2 - 284*B*a*b^2*d*e^3 - (77*B*a^2*b + 45*A*a*b^2)*e^4)*x^2 + (350*B*b^3*d^3*e - 238*B*a*b^2*d^2*e^2 - 46*B*a^2*b*d*e^3 - 3*(7*B*a^3 + 15*A*a^2*b)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b*d^5*e^4 - a*d^4*e^5 + (b*d*e^8 - a*e^9)*x^4 + 4*(b*d^2*e^7 - a*d*e^8)*x^3 + 6*(b*d^3*e^6 - a*d^2*e^7)*x^2 + 4*(b*d^4*e^5 - a*d^3*e^6)*x)]","B",0
2231,1,391,0,152.732128," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, A a^{4} e - {\left(7 \, B b^{4} d - {\left(9 \, B a b^{3} - 2 \, A b^{4}\right)} e\right)} x^{4} - {\left({\left(19 \, B a b^{3} + 9 \, A b^{4}\right)} d - {\left(27 \, B a^{2} b^{2} + A a b^{3}\right)} e\right)} x^{3} - 3 \, {\left({\left(5 \, B a^{2} b^{2} + 9 \, A a b^{3}\right)} d - {\left(9 \, B a^{3} b + 5 \, A a^{2} b^{2}\right)} e\right)} x^{2} + {\left(2 \, B a^{4} - 9 \, A a^{3} b\right)} d - {\left({\left(B a^{3} b + 27 \, A a^{2} b^{2}\right)} d - {\left(9 \, B a^{4} + 19 \, A a^{3} b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{63 \, {\left(b^{2} d^{7} - 2 \, a b d^{6} e + a^{2} d^{5} e^{2} + {\left(b^{2} d^{2} e^{5} - 2 \, a b d e^{6} + a^{2} e^{7}\right)} x^{5} + 5 \, {\left(b^{2} d^{3} e^{4} - 2 \, a b d^{2} e^{5} + a^{2} d e^{6}\right)} x^{4} + 10 \, {\left(b^{2} d^{4} e^{3} - 2 \, a b d^{3} e^{4} + a^{2} d^{2} e^{5}\right)} x^{3} + 10 \, {\left(b^{2} d^{5} e^{2} - 2 \, a b d^{4} e^{3} + a^{2} d^{3} e^{4}\right)} x^{2} + 5 \, {\left(b^{2} d^{6} e - 2 \, a b d^{5} e^{2} + a^{2} d^{4} e^{3}\right)} x\right)}}"," ",0,"-2/63*(7*A*a^4*e - (7*B*b^4*d - (9*B*a*b^3 - 2*A*b^4)*e)*x^4 - ((19*B*a*b^3 + 9*A*b^4)*d - (27*B*a^2*b^2 + A*a*b^3)*e)*x^3 - 3*((5*B*a^2*b^2 + 9*A*a*b^3)*d - (9*B*a^3*b + 5*A*a^2*b^2)*e)*x^2 + (2*B*a^4 - 9*A*a^3*b)*d - ((B*a^3*b + 27*A*a^2*b^2)*d - (9*B*a^4 + 19*A*a^3*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*d^7 - 2*a*b*d^6*e + a^2*d^5*e^2 + (b^2*d^2*e^5 - 2*a*b*d*e^6 + a^2*e^7)*x^5 + 5*(b^2*d^3*e^4 - 2*a*b*d^2*e^5 + a^2*d*e^6)*x^4 + 10*(b^2*d^4*e^3 - 2*a*b*d^3*e^4 + a^2*d^2*e^5)*x^3 + 10*(b^2*d^5*e^2 - 2*a*b*d^4*e^3 + a^2*d^3*e^4)*x^2 + 5*(b^2*d^6*e - 2*a*b*d^5*e^2 + a^2*d^4*e^3)*x)","B",0
2232,-1,0,0,0.000000," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2233,-1,0,0,0.000000," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(15/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2234,-1,0,0,0.000000," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(17/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2235,-1,0,0,0.000000," ","integrate((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(19/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2236,1,772,0,1.683218," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B b^{4} d^{4} + 4 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} d^{3} e - 6 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(5 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(48 \, B b^{4} e^{4} x^{3} + 15 \, B b^{4} d^{3} e - {\left(191 \, B a b^{3} - 264 \, A b^{4}\right)} d^{2} e^{2} + 5 \, {\left(53 \, B a^{2} b^{2} - 64 \, A a b^{3}\right)} d e^{3} - 15 \, {\left(7 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(17 \, B b^{4} d e^{3} - {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(59 \, B b^{4} d^{2} e^{2} - 2 \, {\left(43 \, B a b^{3} - 52 \, A b^{4}\right)} d e^{3} + 5 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{768 \, b^{5} e^{2}}, \frac{15 \, {\left(B b^{4} d^{4} + 4 \, {\left(B a b^{3} - 2 \, A b^{4}\right)} d^{3} e - 6 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(5 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} d e^{3} - {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(48 \, B b^{4} e^{4} x^{3} + 15 \, B b^{4} d^{3} e - {\left(191 \, B a b^{3} - 264 \, A b^{4}\right)} d^{2} e^{2} + 5 \, {\left(53 \, B a^{2} b^{2} - 64 \, A a b^{3}\right)} d e^{3} - 15 \, {\left(7 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4} + 8 \, {\left(17 \, B b^{4} d e^{3} - {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} e^{4}\right)} x^{2} + 2 \, {\left(59 \, B b^{4} d^{2} e^{2} - 2 \, {\left(43 \, B a b^{3} - 52 \, A b^{4}\right)} d e^{3} + 5 \, {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{384 \, b^{5} e^{2}}\right]"," ",0,"[-1/768*(15*(B*b^4*d^4 + 4*(B*a*b^3 - 2*A*b^4)*d^3*e - 6*(3*B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2 + 4*(5*B*a^3*b - 6*A*a^2*b^2)*d*e^3 - (7*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(48*B*b^4*e^4*x^3 + 15*B*b^4*d^3*e - (191*B*a*b^3 - 264*A*b^4)*d^2*e^2 + 5*(53*B*a^2*b^2 - 64*A*a*b^3)*d*e^3 - 15*(7*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(17*B*b^4*d*e^3 - (7*B*a*b^3 - 8*A*b^4)*e^4)*x^2 + 2*(59*B*b^4*d^2*e^2 - 2*(43*B*a*b^3 - 52*A*b^4)*d*e^3 + 5*(7*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^2), 1/384*(15*(B*b^4*d^4 + 4*(B*a*b^3 - 2*A*b^4)*d^3*e - 6*(3*B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2 + 4*(5*B*a^3*b - 6*A*a^2*b^2)*d*e^3 - (7*B*a^4 - 8*A*a^3*b)*e^4)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(48*B*b^4*e^4*x^3 + 15*B*b^4*d^3*e - (191*B*a*b^3 - 264*A*b^4)*d^2*e^2 + 5*(53*B*a^2*b^2 - 64*A*a*b^3)*d*e^3 - 15*(7*B*a^3*b - 8*A*a^2*b^2)*e^4 + 8*(17*B*b^4*d*e^3 - (7*B*a*b^3 - 8*A*b^4)*e^4)*x^2 + 2*(59*B*b^4*d^2*e^2 - 2*(43*B*a*b^3 - 52*A*b^4)*d*e^3 + 5*(7*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e^2)]","A",0
2237,1,542,0,1.807358," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B b^{3} d^{3} + 3 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} d^{2} e - 3 \, {\left(3 \, B a^{2} b - 4 \, A a b^{2}\right)} d e^{2} + {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{3} e^{3} x^{2} + 3 \, B b^{3} d^{2} e - 2 \, {\left(11 \, B a b^{2} - 15 \, A b^{3}\right)} d e^{2} + 3 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} e^{3} + 2 \, {\left(7 \, B b^{3} d e^{2} - {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, b^{4} e^{2}}, \frac{3 \, {\left(B b^{3} d^{3} + 3 \, {\left(B a b^{2} - 2 \, A b^{3}\right)} d^{2} e - 3 \, {\left(3 \, B a^{2} b - 4 \, A a b^{2}\right)} d e^{2} + {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(8 \, B b^{3} e^{3} x^{2} + 3 \, B b^{3} d^{2} e - 2 \, {\left(11 \, B a b^{2} - 15 \, A b^{3}\right)} d e^{2} + 3 \, {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} e^{3} + 2 \, {\left(7 \, B b^{3} d e^{2} - {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, b^{4} e^{2}}\right]"," ",0,"[-1/96*(3*(B*b^3*d^3 + 3*(B*a*b^2 - 2*A*b^3)*d^2*e - 3*(3*B*a^2*b - 4*A*a*b^2)*d*e^2 + (5*B*a^3 - 6*A*a^2*b)*e^3)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^3*e^3*x^2 + 3*B*b^3*d^2*e - 2*(11*B*a*b^2 - 15*A*b^3)*d*e^2 + 3*(5*B*a^2*b - 6*A*a*b^2)*e^3 + 2*(7*B*b^3*d*e^2 - (5*B*a*b^2 - 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^2), 1/48*(3*(B*b^3*d^3 + 3*(B*a*b^2 - 2*A*b^3)*d^2*e - 3*(3*B*a^2*b - 4*A*a*b^2)*d*e^2 + (5*B*a^3 - 6*A*a^2*b)*e^3)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(8*B*b^3*e^3*x^2 + 3*B*b^3*d^2*e - 2*(11*B*a*b^2 - 15*A*b^3)*d*e^2 + 3*(5*B*a^2*b - 6*A*a*b^2)*e^3 + 2*(7*B*b^3*d*e^2 - (5*B*a*b^2 - 6*A*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e^2)]","A",0
2238,1,366,0,1.666458," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b^{2} d^{2} + 2 \, {\left(B a b - 2 \, A b^{2}\right)} d e - {\left(3 \, B a^{2} - 4 \, A a b\right)} e^{2}\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(2 \, B b^{2} e^{2} x + B b^{2} d e - {\left(3 \, B a b - 4 \, A b^{2}\right)} e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{16 \, b^{3} e^{2}}, \frac{{\left(B b^{2} d^{2} + 2 \, {\left(B a b - 2 \, A b^{2}\right)} d e - {\left(3 \, B a^{2} - 4 \, A a b\right)} e^{2}\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(2 \, B b^{2} e^{2} x + B b^{2} d e - {\left(3 \, B a b - 4 \, A b^{2}\right)} e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{8 \, b^{3} e^{2}}\right]"," ",0,"[1/16*((B*b^2*d^2 + 2*(B*a*b - 2*A*b^2)*d*e - (3*B*a^2 - 4*A*a*b)*e^2)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(2*B*b^2*e^2*x + B*b^2*d*e - (3*B*a*b - 4*A*b^2)*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^2), 1/8*((B*b^2*d^2 + 2*(B*a*b - 2*A*b^2)*d*e - (3*B*a^2 - 4*A*a*b)*e^2)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(2*B*b^2*e^2*x + B*b^2*d*e - (3*B*a*b - 4*A*b^2)*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^3*e^2)]","A",0
2239,1,251,0,1.406035," ","integrate((B*x+A)/(b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{b x + a} \sqrt{e x + d} B b e - {\left(B b d + {\left(B a - 2 \, A b\right)} e\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right)}{4 \, b^{2} e^{2}}, \frac{2 \, \sqrt{b x + a} \sqrt{e x + d} B b e + {\left(B b d + {\left(B a - 2 \, A b\right)} e\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{2 \, b^{2} e^{2}}\right]"," ",0,"[1/4*(4*sqrt(b*x + a)*sqrt(e*x + d)*B*b*e - (B*b*d + (B*a - 2*A*b)*e)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x))/(b^2*e^2), 1/2*(2*sqrt(b*x + a)*sqrt(e*x + d)*B*b*e + (B*b*d + (B*a - 2*A*b)*e)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)))/(b^2*e^2)]","A",0
2240,1,362,0,2.234072," ","integrate((B*x+A)/(e*x+d)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(B b d^{2} - B a d e + {\left(B b d e - B a e^{2}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(B b d e - A b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} d^{2} e^{2} - a b d e^{3} + {\left(b^{2} d e^{3} - a b e^{4}\right)} x\right)}}, -\frac{{\left(B b d^{2} - B a d e + {\left(B b d e - B a e^{2}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(B b d e - A b e^{2}\right)} \sqrt{b x + a} \sqrt{e x + d}}{b^{2} d^{2} e^{2} - a b d e^{3} + {\left(b^{2} d e^{3} - a b e^{4}\right)} x}\right]"," ",0,"[1/2*((B*b*d^2 - B*a*d*e + (B*b*d*e - B*a*e^2)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(B*b*d*e - A*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*d^2*e^2 - a*b*d*e^3 + (b^2*d*e^3 - a*b*e^4)*x), -((B*b*d^2 - B*a*d*e + (B*b*d*e - B*a*e^2)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) + 2*(B*b*d*e - A*b*e^2)*sqrt(b*x + a)*sqrt(e*x + d))/(b^2*d^2*e^2 - a*b*d*e^3 + (b^2*d*e^3 - a*b*e^4)*x)]","B",0
2241,1,140,0,3.685498," ","integrate((B*x+A)/(e*x+d)^(5/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a e + {\left(2 \, B a - 3 \, A b\right)} d - {\left(B b d - {\left(3 \, B a - 2 \, A b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)}}"," ",0,"-2/3*(A*a*e + (2*B*a - 3*A*b)*d - (B*b*d - (3*B*a - 2*A*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x)","A",0
2242,1,316,0,12.188212," ","integrate((B*x+A)/(e*x+d)^(7/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a^{2} e^{2} - 5 \, {\left(2 \, B a b - 3 \, A b^{2}\right)} d^{2} + 2 \, {\left(B a^{2} - 5 \, A a b\right)} d e + 2 \, {\left(B b^{2} d e - {\left(5 \, B a b - 4 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(5 \, B b^{2} d^{2} - 2 \, {\left(13 \, B a b - 10 \, A b^{2}\right)} d e + {\left(5 \, B a^{2} - 4 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}"," ",0,"2/15*(3*A*a^2*e^2 - 5*(2*B*a*b - 3*A*b^2)*d^2 + 2*(B*a^2 - 5*A*a*b)*d*e + 2*(B*b^2*d*e - (5*B*a*b - 4*A*b^2)*e^2)*x^2 + (5*B*b^2*d^2 - 2*(13*B*a*b - 10*A*b^2)*d*e + (5*B*a^2 - 4*A*a*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x)","B",0
2243,1,547,0,37.268478," ","integrate((B*x+A)/(e*x+d)^(9/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, A a^{3} e^{3} + 35 \, {\left(2 \, B a b^{2} - 3 \, A b^{3}\right)} d^{3} - 7 \, {\left(4 \, B a^{2} b - 15 \, A a b^{2}\right)} d^{2} e + 3 \, {\left(2 \, B a^{3} - 21 \, A a^{2} b\right)} d e^{2} - 8 \, {\left(B b^{3} d e^{2} - {\left(7 \, B a b^{2} - 6 \, A b^{3}\right)} e^{3}\right)} x^{3} - 4 \, {\left(7 \, B b^{3} d^{2} e - 2 \, {\left(25 \, B a b^{2} - 21 \, A b^{3}\right)} d e^{2} + {\left(7 \, B a^{2} b - 6 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(35 \, B b^{3} d^{3} - 7 \, {\left(37 \, B a b^{2} - 30 \, A b^{3}\right)} d^{2} e + {\left(101 \, B a^{2} b - 84 \, A a b^{2}\right)} d e^{2} - 3 \, {\left(7 \, B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{105 \, {\left(b^{4} d^{8} - 4 \, a b^{3} d^{7} e + 6 \, a^{2} b^{2} d^{6} e^{2} - 4 \, a^{3} b d^{5} e^{3} + a^{4} d^{4} e^{4} + {\left(b^{4} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} x^{4} + 4 \, {\left(b^{4} d^{5} e^{3} - 4 \, a b^{3} d^{4} e^{4} + 6 \, a^{2} b^{2} d^{3} e^{5} - 4 \, a^{3} b d^{2} e^{6} + a^{4} d e^{7}\right)} x^{3} + 6 \, {\left(b^{4} d^{6} e^{2} - 4 \, a b^{3} d^{5} e^{3} + 6 \, a^{2} b^{2} d^{4} e^{4} - 4 \, a^{3} b d^{3} e^{5} + a^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(b^{4} d^{7} e - 4 \, a b^{3} d^{6} e^{2} + 6 \, a^{2} b^{2} d^{5} e^{3} - 4 \, a^{3} b d^{4} e^{4} + a^{4} d^{3} e^{5}\right)} x\right)}}"," ",0,"-2/105*(15*A*a^3*e^3 + 35*(2*B*a*b^2 - 3*A*b^3)*d^3 - 7*(4*B*a^2*b - 15*A*a*b^2)*d^2*e + 3*(2*B*a^3 - 21*A*a^2*b)*d*e^2 - 8*(B*b^3*d*e^2 - (7*B*a*b^2 - 6*A*b^3)*e^3)*x^3 - 4*(7*B*b^3*d^2*e - 2*(25*B*a*b^2 - 21*A*b^3)*d*e^2 + (7*B*a^2*b - 6*A*a*b^2)*e^3)*x^2 - (35*B*b^3*d^3 - 7*(37*B*a*b^2 - 30*A*b^3)*d^2*e + (101*B*a^2*b - 84*A*a*b^2)*d*e^2 - 3*(7*B*a^3 - 6*A*a^2*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^4*d^8 - 4*a*b^3*d^7*e + 6*a^2*b^2*d^6*e^2 - 4*a^3*b*d^5*e^3 + a^4*d^4*e^4 + (b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 6*a^2*b^2*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*x^4 + 4*(b^4*d^5*e^3 - 4*a*b^3*d^4*e^4 + 6*a^2*b^2*d^3*e^5 - 4*a^3*b*d^2*e^6 + a^4*d*e^7)*x^3 + 6*(b^4*d^6*e^2 - 4*a*b^3*d^5*e^3 + 6*a^2*b^2*d^4*e^4 - 4*a^3*b*d^3*e^5 + a^4*d^2*e^6)*x^2 + 4*(b^4*d^7*e - 4*a*b^3*d^6*e^2 + 6*a^2*b^2*d^5*e^3 - 4*a^3*b*d^4*e^4 + a^4*d^3*e^5)*x)","B",0
2244,1,839,0,160.581887," ","integrate((B*x+A)/(e*x+d)^(11/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, A a^{4} e^{4} - 105 \, {\left(2 \, B a b^{3} - 3 \, A b^{4}\right)} d^{4} + 42 \, {\left(3 \, B a^{2} b^{2} - 10 \, A a b^{3}\right)} d^{3} e - 54 \, {\left(B a^{3} b - 7 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 10 \, {\left(B a^{4} - 18 \, A a^{3} b\right)} d e^{3} + 16 \, {\left(B b^{4} d e^{3} - {\left(9 \, B a b^{3} - 8 \, A b^{4}\right)} e^{4}\right)} x^{4} + 8 \, {\left(9 \, B b^{4} d^{2} e^{2} - 2 \, {\left(41 \, B a b^{3} - 36 \, A b^{4}\right)} d e^{3} + {\left(9 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 6 \, {\left(21 \, B b^{4} d^{3} e - 3 \, {\left(65 \, B a b^{3} - 56 \, A b^{4}\right)} d^{2} e^{2} + {\left(55 \, B a^{2} b^{2} - 48 \, A a b^{3}\right)} d e^{3} - {\left(9 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(105 \, B b^{4} d^{4} - 168 \, {\left(6 \, B a b^{3} - 5 \, A b^{4}\right)} d^{3} e + 18 \, {\left(33 \, B a^{2} b^{2} - 28 \, A a b^{3}\right)} d^{2} e^{2} - 8 \, {\left(31 \, B a^{3} b - 27 \, A a^{2} b^{2}\right)} d e^{3} + 5 \, {\left(9 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{315 \, {\left(b^{5} d^{10} - 5 \, a b^{4} d^{9} e + 10 \, a^{2} b^{3} d^{8} e^{2} - 10 \, a^{3} b^{2} d^{7} e^{3} + 5 \, a^{4} b d^{6} e^{4} - a^{5} d^{5} e^{5} + {\left(b^{5} d^{5} e^{5} - 5 \, a b^{4} d^{4} e^{6} + 10 \, a^{2} b^{3} d^{3} e^{7} - 10 \, a^{3} b^{2} d^{2} e^{8} + 5 \, a^{4} b d e^{9} - a^{5} e^{10}\right)} x^{5} + 5 \, {\left(b^{5} d^{6} e^{4} - 5 \, a b^{4} d^{5} e^{5} + 10 \, a^{2} b^{3} d^{4} e^{6} - 10 \, a^{3} b^{2} d^{3} e^{7} + 5 \, a^{4} b d^{2} e^{8} - a^{5} d e^{9}\right)} x^{4} + 10 \, {\left(b^{5} d^{7} e^{3} - 5 \, a b^{4} d^{6} e^{4} + 10 \, a^{2} b^{3} d^{5} e^{5} - 10 \, a^{3} b^{2} d^{4} e^{6} + 5 \, a^{4} b d^{3} e^{7} - a^{5} d^{2} e^{8}\right)} x^{3} + 10 \, {\left(b^{5} d^{8} e^{2} - 5 \, a b^{4} d^{7} e^{3} + 10 \, a^{2} b^{3} d^{6} e^{4} - 10 \, a^{3} b^{2} d^{5} e^{5} + 5 \, a^{4} b d^{4} e^{6} - a^{5} d^{3} e^{7}\right)} x^{2} + 5 \, {\left(b^{5} d^{9} e - 5 \, a b^{4} d^{8} e^{2} + 10 \, a^{2} b^{3} d^{7} e^{3} - 10 \, a^{3} b^{2} d^{6} e^{4} + 5 \, a^{4} b d^{5} e^{5} - a^{5} d^{4} e^{6}\right)} x\right)}}"," ",0,"2/315*(35*A*a^4*e^4 - 105*(2*B*a*b^3 - 3*A*b^4)*d^4 + 42*(3*B*a^2*b^2 - 10*A*a*b^3)*d^3*e - 54*(B*a^3*b - 7*A*a^2*b^2)*d^2*e^2 + 10*(B*a^4 - 18*A*a^3*b)*d*e^3 + 16*(B*b^4*d*e^3 - (9*B*a*b^3 - 8*A*b^4)*e^4)*x^4 + 8*(9*B*b^4*d^2*e^2 - 2*(41*B*a*b^3 - 36*A*b^4)*d*e^3 + (9*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x^3 + 6*(21*B*b^4*d^3*e - 3*(65*B*a*b^3 - 56*A*b^4)*d^2*e^2 + (55*B*a^2*b^2 - 48*A*a*b^3)*d*e^3 - (9*B*a^3*b - 8*A*a^2*b^2)*e^4)*x^2 + (105*B*b^4*d^4 - 168*(6*B*a*b^3 - 5*A*b^4)*d^3*e + 18*(33*B*a^2*b^2 - 28*A*a*b^3)*d^2*e^2 - 8*(31*B*a^3*b - 27*A*a^2*b^2)*d*e^3 + 5*(9*B*a^4 - 8*A*a^3*b)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(b^5*d^10 - 5*a*b^4*d^9*e + 10*a^2*b^3*d^8*e^2 - 10*a^3*b^2*d^7*e^3 + 5*a^4*b*d^6*e^4 - a^5*d^5*e^5 + (b^5*d^5*e^5 - 5*a*b^4*d^4*e^6 + 10*a^2*b^3*d^3*e^7 - 10*a^3*b^2*d^2*e^8 + 5*a^4*b*d*e^9 - a^5*e^10)*x^5 + 5*(b^5*d^6*e^4 - 5*a*b^4*d^5*e^5 + 10*a^2*b^3*d^4*e^6 - 10*a^3*b^2*d^3*e^7 + 5*a^4*b*d^2*e^8 - a^5*d*e^9)*x^4 + 10*(b^5*d^7*e^3 - 5*a*b^4*d^6*e^4 + 10*a^2*b^3*d^5*e^5 - 10*a^3*b^2*d^4*e^6 + 5*a^4*b*d^3*e^7 - a^5*d^2*e^8)*x^3 + 10*(b^5*d^8*e^2 - 5*a*b^4*d^7*e^3 + 10*a^2*b^3*d^6*e^4 - 10*a^3*b^2*d^5*e^5 + 5*a^4*b*d^4*e^6 - a^5*d^3*e^7)*x^2 + 5*(b^5*d^9*e - 5*a*b^4*d^8*e^2 + 10*a^2*b^3*d^7*e^3 - 10*a^3*b^2*d^6*e^4 + 5*a^4*b*d^5*e^5 - a^5*d^4*e^6)*x)","B",0
2245,1,872,0,2.728368," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(B a b^{3} d^{3} - 3 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{2} e + 3 \, {\left(5 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} d e^{2} - {\left(7 \, B a^{4} - 6 \, A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{3} - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e + 3 \, {\left(5 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d e^{2} - {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{4} e^{3} x^{3} + 3 \, {\left(27 \, B a b^{3} - 16 \, A b^{4}\right)} d^{2} e - 10 \, {\left(19 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d e^{2} + 15 \, {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} e^{3} + 2 \, {\left(13 \, B b^{4} d e^{2} - {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} e^{3}\right)} x^{2} + {\left(33 \, B b^{4} d^{2} e - 2 \, {\left(34 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{2} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, {\left(b^{6} e x + a b^{5} e\right)}}, -\frac{15 \, {\left(B a b^{3} d^{3} - 3 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{2} e + 3 \, {\left(5 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} d e^{2} - {\left(7 \, B a^{4} - 6 \, A a^{3} b\right)} e^{3} + {\left(B b^{4} d^{3} - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} d^{2} e + 3 \, {\left(5 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d e^{2} - {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, B b^{4} e^{3} x^{3} + 3 \, {\left(27 \, B a b^{3} - 16 \, A b^{4}\right)} d^{2} e - 10 \, {\left(19 \, B a^{2} b^{2} - 15 \, A a b^{3}\right)} d e^{2} + 15 \, {\left(7 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} e^{3} + 2 \, {\left(13 \, B b^{4} d e^{2} - {\left(7 \, B a b^{3} - 6 \, A b^{4}\right)} e^{3}\right)} x^{2} + {\left(33 \, B b^{4} d^{2} e - 2 \, {\left(34 \, B a b^{3} - 27 \, A b^{4}\right)} d e^{2} + 5 \, {\left(7 \, B a^{2} b^{2} - 6 \, A a b^{3}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, {\left(b^{6} e x + a b^{5} e\right)}}\right]"," ",0,"[-1/96*(15*(B*a*b^3*d^3 - 3*(3*B*a^2*b^2 - 2*A*a*b^3)*d^2*e + 3*(5*B*a^3*b - 4*A*a^2*b^2)*d*e^2 - (7*B*a^4 - 6*A*a^3*b)*e^3 + (B*b^4*d^3 - 3*(3*B*a*b^3 - 2*A*b^4)*d^2*e + 3*(5*B*a^2*b^2 - 4*A*a*b^3)*d*e^2 - (7*B*a^3*b - 6*A*a^2*b^2)*e^3)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^4*e^3*x^3 + 3*(27*B*a*b^3 - 16*A*b^4)*d^2*e - 10*(19*B*a^2*b^2 - 15*A*a*b^3)*d*e^2 + 15*(7*B*a^3*b - 6*A*a^2*b^2)*e^3 + 2*(13*B*b^4*d*e^2 - (7*B*a*b^3 - 6*A*b^4)*e^3)*x^2 + (33*B*b^4*d^2*e - 2*(34*B*a*b^3 - 27*A*b^4)*d*e^2 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^6*e*x + a*b^5*e), -1/48*(15*(B*a*b^3*d^3 - 3*(3*B*a^2*b^2 - 2*A*a*b^3)*d^2*e + 3*(5*B*a^3*b - 4*A*a^2*b^2)*d*e^2 - (7*B*a^4 - 6*A*a^3*b)*e^3 + (B*b^4*d^3 - 3*(3*B*a*b^3 - 2*A*b^4)*d^2*e + 3*(5*B*a^2*b^2 - 4*A*a*b^3)*d*e^2 - (7*B*a^3*b - 6*A*a^2*b^2)*e^3)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(8*B*b^4*e^3*x^3 + 3*(27*B*a*b^3 - 16*A*b^4)*d^2*e - 10*(19*B*a^2*b^2 - 15*A*a*b^3)*d*e^2 + 15*(7*B*a^3*b - 6*A*a^2*b^2)*e^3 + 2*(13*B*b^4*d*e^2 - (7*B*a*b^3 - 6*A*b^4)*e^3)*x^2 + (33*B*b^4*d^2*e - 2*(34*B*a*b^3 - 27*A*b^4)*d*e^2 + 5*(7*B*a^2*b^2 - 6*A*a*b^3)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^6*e*x + a*b^5*e)]","B",0
2246,1,584,0,3.115592," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a b^{2} d^{2} - 2 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} d e + {\left(5 \, B a^{3} - 4 \, A a^{2} b\right)} e^{2} + {\left(B b^{3} d^{2} - 2 \, {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} d e + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(2 \, B b^{3} e^{2} x^{2} + {\left(13 \, B a b^{2} - 8 \, A b^{3}\right)} d e - 3 \, {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2} + {\left(5 \, B b^{3} d e - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{16 \, {\left(b^{5} e x + a b^{4} e\right)}}, -\frac{3 \, {\left(B a b^{2} d^{2} - 2 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2}\right)} d e + {\left(5 \, B a^{3} - 4 \, A a^{2} b\right)} e^{2} + {\left(B b^{3} d^{2} - 2 \, {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} d e + {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, B b^{3} e^{2} x^{2} + {\left(13 \, B a b^{2} - 8 \, A b^{3}\right)} d e - 3 \, {\left(5 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2} + {\left(5 \, B b^{3} d e - {\left(5 \, B a b^{2} - 4 \, A b^{3}\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{8 \, {\left(b^{5} e x + a b^{4} e\right)}}\right]"," ",0,"[1/16*(3*(B*a*b^2*d^2 - 2*(3*B*a^2*b - 2*A*a*b^2)*d*e + (5*B*a^3 - 4*A*a^2*b)*e^2 + (B*b^3*d^2 - 2*(3*B*a*b^2 - 2*A*b^3)*d*e + (5*B*a^2*b - 4*A*a*b^2)*e^2)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(2*B*b^3*e^2*x^2 + (13*B*a*b^2 - 8*A*b^3)*d*e - 3*(5*B*a^2*b - 4*A*a*b^2)*e^2 + (5*B*b^3*d*e - (5*B*a*b^2 - 4*A*b^3)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e*x + a*b^4*e), -1/8*(3*(B*a*b^2*d^2 - 2*(3*B*a^2*b - 2*A*a*b^2)*d*e + (5*B*a^3 - 4*A*a^2*b)*e^2 + (B*b^3*d^2 - 2*(3*B*a*b^2 - 2*A*b^3)*d*e + (5*B*a^2*b - 4*A*a*b^2)*e^2)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(2*B*b^3*e^2*x^2 + (13*B*a*b^2 - 8*A*b^3)*d*e - 3*(5*B*a^2*b - 4*A*a*b^2)*e^2 + (5*B*b^3*d*e - (5*B*a*b^2 - 4*A*b^3)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*e*x + a*b^4*e)]","A",0
2247,1,366,0,2.575088," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(B a b d - {\left(3 \, B a^{2} - 2 \, A a b\right)} e + {\left(B b^{2} d - {\left(3 \, B a b - 2 \, A b^{2}\right)} e\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(B b^{2} e x + {\left(3 \, B a b - 2 \, A b^{2}\right)} e\right)} \sqrt{b x + a} \sqrt{e x + d}}{4 \, {\left(b^{4} e x + a b^{3} e\right)}}, -\frac{{\left(B a b d - {\left(3 \, B a^{2} - 2 \, A a b\right)} e + {\left(B b^{2} d - {\left(3 \, B a b - 2 \, A b^{2}\right)} e\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(B b^{2} e x + {\left(3 \, B a b - 2 \, A b^{2}\right)} e\right)} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{4} e x + a b^{3} e\right)}}\right]"," ",0,"[1/4*((B*a*b*d - (3*B*a^2 - 2*A*a*b)*e + (B*b^2*d - (3*B*a*b - 2*A*b^2)*e)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(B*b^2*e*x + (3*B*a*b - 2*A*b^2)*e)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e*x + a*b^3*e), -1/2*((B*a*b*d - (3*B*a^2 - 2*A*a*b)*e + (B*b^2*d - (3*B*a*b - 2*A*b^2)*e)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)) - 2*(B*b^2*e*x + (3*B*a*b - 2*A*b^2)*e)*sqrt(b*x + a)*sqrt(e*x + d))/(b^4*e*x + a*b^3*e)]","A",0
2248,1,360,0,2.235088," ","integrate((B*x+A)/(b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B a b - A b^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} e + {\left(B a b d - B a^{2} e + {\left(B b^{2} d - B a b e\right)} x\right)} \sqrt{b e} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b e x + b d + a e\right)} \sqrt{b e} \sqrt{b x + a} \sqrt{e x + d} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right)}{2 \, {\left(a b^{3} d e - a^{2} b^{2} e^{2} + {\left(b^{4} d e - a b^{3} e^{2}\right)} x\right)}}, \frac{2 \, {\left(B a b - A b^{2}\right)} \sqrt{b x + a} \sqrt{e x + d} e - {\left(B a b d - B a^{2} e + {\left(B b^{2} d - B a b e\right)} x\right)} \sqrt{-b e} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{-b e} \sqrt{b x + a} \sqrt{e x + d}}{2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{a b^{3} d e - a^{2} b^{2} e^{2} + {\left(b^{4} d e - a b^{3} e^{2}\right)} x}\right]"," ",0,"[1/2*(4*(B*a*b - A*b^2)*sqrt(b*x + a)*sqrt(e*x + d)*e + (B*a*b*d - B*a^2*e + (B*b^2*d - B*a*b*e)*x)*sqrt(b*e)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b*e*x + b*d + a*e)*sqrt(b*e)*sqrt(b*x + a)*sqrt(e*x + d) + 8*(b^2*d*e + a*b*e^2)*x))/(a*b^3*d*e - a^2*b^2*e^2 + (b^4*d*e - a*b^3*e^2)*x), (2*(B*a*b - A*b^2)*sqrt(b*x + a)*sqrt(e*x + d)*e - (B*a*b*d - B*a^2*e + (B*b^2*d - B*a*b*e)*x)*sqrt(-b*e)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(-b*e)*sqrt(b*x + a)*sqrt(e*x + d)/(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)))/(a*b^3*d*e - a^2*b^2*e^2 + (b^4*d*e - a*b^3*e^2)*x)]","B",0
2249,1,148,0,2.277793," ","integrate((B*x+A)/(b*x+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a e - {\left(2 \, B a - A b\right)} d - {\left(B b d + {\left(B a - 2 \, A b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{a b^{2} d^{3} - 2 \, a^{2} b d^{2} e + a^{3} d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + {\left(b^{3} d^{3} - a b^{2} d^{2} e - a^{2} b d e^{2} + a^{3} e^{3}\right)} x}"," ",0,"-2*(A*a*e - (2*B*a - A*b)*d - (B*b*d + (B*a - 2*A*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a*b^2*d^3 - 2*a^2*b*d^2*e + a^3*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + (b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2 + a^3*e^3)*x)","A",0
2250,1,336,0,8.391376," ","integrate((B*x+A)/(b*x+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(A a^{2} e^{2} + 3 \, {\left(2 \, B a b - A b^{2}\right)} d^{2} + 2 \, {\left(B a^{2} - 3 \, A a b\right)} d e + 2 \, {\left(B b^{2} d e + {\left(3 \, B a b - 4 \, A b^{2}\right)} e^{2}\right)} x^{2} + {\left(3 \, B b^{2} d^{2} + 2 \, {\left(5 \, B a b - 6 \, A b^{2}\right)} d e + {\left(3 \, B a^{2} - 4 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}"," ",0,"2/3*(A*a^2*e^2 + 3*(2*B*a*b - A*b^2)*d^2 + 2*(B*a^2 - 3*A*a*b)*d*e + 2*(B*b^2*d*e + (3*B*a*b - 4*A*b^2)*e^2)*x^2 + (3*B*b^2*d^2 + 2*(5*B*a*b - 6*A*b^2)*d*e + (3*B*a^2 - 4*A*a*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x)","B",0
2251,1,583,0,22.417552," ","integrate((B*x+A)/(b*x+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A a^{3} e^{3} - 15 \, {\left(2 \, B a b^{2} - A b^{3}\right)} d^{3} - 5 \, {\left(4 \, B a^{2} b - 9 \, A a b^{2}\right)} d^{2} e + {\left(2 \, B a^{3} - 15 \, A a^{2} b\right)} d e^{2} - 8 \, {\left(B b^{3} d e^{2} + {\left(5 \, B a b^{2} - 6 \, A b^{3}\right)} e^{3}\right)} x^{3} - 4 \, {\left(5 \, B b^{3} d^{2} e + 2 \, {\left(13 \, B a b^{2} - 15 \, A b^{3}\right)} d e^{2} + {\left(5 \, B a^{2} b - 6 \, A a b^{2}\right)} e^{3}\right)} x^{2} - {\left(15 \, B b^{3} d^{3} + 5 \, {\left(17 \, B a b^{2} - 18 \, A b^{3}\right)} d^{2} e + {\left(49 \, B a^{2} b - 60 \, A a b^{2}\right)} d e^{2} - {\left(5 \, B a^{3} - 6 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}"," ",0,"-2/15*(3*A*a^3*e^3 - 15*(2*B*a*b^2 - A*b^3)*d^3 - 5*(4*B*a^2*b - 9*A*a*b^2)*d^2*e + (2*B*a^3 - 15*A*a^2*b)*d*e^2 - 8*(B*b^3*d*e^2 + (5*B*a*b^2 - 6*A*b^3)*e^3)*x^3 - 4*(5*B*b^3*d^2*e + 2*(13*B*a*b^2 - 15*A*b^3)*d*e^2 + (5*B*a^2*b - 6*A*a*b^2)*e^3)*x^2 - (15*B*b^3*d^3 + 5*(17*B*a*b^2 - 18*A*b^3)*d^2*e + (49*B*a^2*b - 60*A*a*b^2)*d*e^2 - (5*B*a^3 - 6*A*a^2*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x)","B",0
2252,1,887,0,97.935901," ","integrate((B*x+A)/(b*x+a)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, A a^{4} e^{4} + 35 \, {\left(2 \, B a b^{3} - A b^{4}\right)} d^{4} + 70 \, {\left(B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{3} e - 14 \, {\left(B a^{3} b - 5 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(B a^{4} - 14 \, A a^{3} b\right)} d e^{3} + 16 \, {\left(B b^{4} d e^{3} + {\left(7 \, B a b^{3} - 8 \, A b^{4}\right)} e^{4}\right)} x^{4} + 8 \, {\left(7 \, B b^{4} d^{2} e^{2} + 2 \, {\left(25 \, B a b^{3} - 28 \, A b^{4}\right)} d e^{3} + {\left(7 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x^{3} + 2 \, {\left(35 \, B b^{4} d^{3} e + 7 \, {\left(37 \, B a b^{3} - 40 \, A b^{4}\right)} d^{2} e^{2} + {\left(97 \, B a^{2} b^{2} - 112 \, A a b^{3}\right)} d e^{3} - {\left(7 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} + {\left(35 \, B b^{4} d^{4} + 280 \, {\left(B a b^{3} - A b^{4}\right)} d^{3} e + 14 \, {\left(17 \, B a^{2} b^{2} - 20 \, A a b^{3}\right)} d^{2} e^{2} - 8 \, {\left(6 \, B a^{3} b - 7 \, A a^{2} b^{2}\right)} d e^{3} + {\left(7 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{35 \, {\left(a b^{5} d^{9} - 5 \, a^{2} b^{4} d^{8} e + 10 \, a^{3} b^{3} d^{7} e^{2} - 10 \, a^{4} b^{2} d^{6} e^{3} + 5 \, a^{5} b d^{5} e^{4} - a^{6} d^{4} e^{5} + {\left(b^{6} d^{5} e^{4} - 5 \, a b^{5} d^{4} e^{5} + 10 \, a^{2} b^{4} d^{3} e^{6} - 10 \, a^{3} b^{3} d^{2} e^{7} + 5 \, a^{4} b^{2} d e^{8} - a^{5} b e^{9}\right)} x^{5} + {\left(4 \, b^{6} d^{6} e^{3} - 19 \, a b^{5} d^{5} e^{4} + 35 \, a^{2} b^{4} d^{4} e^{5} - 30 \, a^{3} b^{3} d^{3} e^{6} + 10 \, a^{4} b^{2} d^{2} e^{7} + a^{5} b d e^{8} - a^{6} e^{9}\right)} x^{4} + 2 \, {\left(3 \, b^{6} d^{7} e^{2} - 13 \, a b^{5} d^{6} e^{3} + 20 \, a^{2} b^{4} d^{5} e^{4} - 10 \, a^{3} b^{3} d^{4} e^{5} - 5 \, a^{4} b^{2} d^{3} e^{6} + 7 \, a^{5} b d^{2} e^{7} - 2 \, a^{6} d e^{8}\right)} x^{3} + 2 \, {\left(2 \, b^{6} d^{8} e - 7 \, a b^{5} d^{7} e^{2} + 5 \, a^{2} b^{4} d^{6} e^{3} + 10 \, a^{3} b^{3} d^{5} e^{4} - 20 \, a^{4} b^{2} d^{4} e^{5} + 13 \, a^{5} b d^{3} e^{6} - 3 \, a^{6} d^{2} e^{7}\right)} x^{2} + {\left(b^{6} d^{9} - a b^{5} d^{8} e - 10 \, a^{2} b^{4} d^{7} e^{2} + 30 \, a^{3} b^{3} d^{6} e^{3} - 35 \, a^{4} b^{2} d^{5} e^{4} + 19 \, a^{5} b d^{4} e^{5} - 4 \, a^{6} d^{3} e^{6}\right)} x\right)}}"," ",0,"2/35*(5*A*a^4*e^4 + 35*(2*B*a*b^3 - A*b^4)*d^4 + 70*(B*a^2*b^2 - 2*A*a*b^3)*d^3*e - 14*(B*a^3*b - 5*A*a^2*b^2)*d^2*e^2 + 2*(B*a^4 - 14*A*a^3*b)*d*e^3 + 16*(B*b^4*d*e^3 + (7*B*a*b^3 - 8*A*b^4)*e^4)*x^4 + 8*(7*B*b^4*d^2*e^2 + 2*(25*B*a*b^3 - 28*A*b^4)*d*e^3 + (7*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x^3 + 2*(35*B*b^4*d^3*e + 7*(37*B*a*b^3 - 40*A*b^4)*d^2*e^2 + (97*B*a^2*b^2 - 112*A*a*b^3)*d*e^3 - (7*B*a^3*b - 8*A*a^2*b^2)*e^4)*x^2 + (35*B*b^4*d^4 + 280*(B*a*b^3 - A*b^4)*d^3*e + 14*(17*B*a^2*b^2 - 20*A*a*b^3)*d^2*e^2 - 8*(6*B*a^3*b - 7*A*a^2*b^2)*d*e^3 + (7*B*a^4 - 8*A*a^3*b)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a*b^5*d^9 - 5*a^2*b^4*d^8*e + 10*a^3*b^3*d^7*e^2 - 10*a^4*b^2*d^6*e^3 + 5*a^5*b*d^5*e^4 - a^6*d^4*e^5 + (b^6*d^5*e^4 - 5*a*b^5*d^4*e^5 + 10*a^2*b^4*d^3*e^6 - 10*a^3*b^3*d^2*e^7 + 5*a^4*b^2*d*e^8 - a^5*b*e^9)*x^5 + (4*b^6*d^6*e^3 - 19*a*b^5*d^5*e^4 + 35*a^2*b^4*d^4*e^5 - 30*a^3*b^3*d^3*e^6 + 10*a^4*b^2*d^2*e^7 + a^5*b*d*e^8 - a^6*e^9)*x^4 + 2*(3*b^6*d^7*e^2 - 13*a*b^5*d^6*e^3 + 20*a^2*b^4*d^5*e^4 - 10*a^3*b^3*d^4*e^5 - 5*a^4*b^2*d^3*e^6 + 7*a^5*b*d^2*e^7 - 2*a^6*d*e^8)*x^3 + 2*(2*b^6*d^8*e - 7*a*b^5*d^7*e^2 + 5*a^2*b^4*d^6*e^3 + 10*a^3*b^3*d^5*e^4 - 20*a^4*b^2*d^4*e^5 + 13*a^5*b*d^3*e^6 - 3*a^6*d^2*e^7)*x^2 + (b^6*d^9 - a*b^5*d^8*e - 10*a^2*b^4*d^7*e^2 + 30*a^3*b^3*d^6*e^3 - 35*a^4*b^2*d^5*e^4 + 19*a^5*b*d^4*e^5 - 4*a^6*d^3*e^6)*x)","B",0
2253,1,1271,0,9.542653," ","integrate((B*x+A)*(e*x+d)^(7/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(B a^{2} b^{3} d^{3} - {\left(5 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e + {\left(7 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} d e^{2} - {\left(3 \, B a^{5} - 2 \, A a^{4} b\right)} e^{3} + {\left(B b^{5} d^{3} - {\left(5 \, B a b^{4} - 2 \, A b^{5}\right)} d^{2} e + {\left(7 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} d e^{2} - {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(B a b^{4} d^{3} - {\left(5 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} d^{2} e + {\left(7 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} d e^{2} - {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{\frac{e}{b}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} - 4 \, {\left(2 \, b^{2} e x + b^{2} d + a b e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{e}{b}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) - 4 \, {\left(8 \, B b^{4} e^{3} x^{4} - 16 \, {\left(2 \, B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(49 \, B a^{2} b^{2} - 16 \, A a b^{3}\right)} d^{2} e - 70 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(3 \, B a^{4} - 2 \, A a^{3} b\right)} e^{3} + 2 \, {\left(19 \, B b^{4} d e^{2} - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(29 \, B b^{4} d^{2} e - 2 \, {\left(23 \, B a b^{3} - 13 \, A b^{4}\right)} d e^{2} + 7 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(24 \, B b^{4} d^{3} - {\left(239 \, B a b^{3} - 80 \, A b^{4}\right)} d^{2} e + 7 \, {\left(61 \, B a^{2} b^{2} - 34 \, A a b^{3}\right)} d e^{2} - 70 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{96 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(B a^{2} b^{3} d^{3} - {\left(5 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} d^{2} e + {\left(7 \, B a^{4} b - 4 \, A a^{3} b^{2}\right)} d e^{2} - {\left(3 \, B a^{5} - 2 \, A a^{4} b\right)} e^{3} + {\left(B b^{5} d^{3} - {\left(5 \, B a b^{4} - 2 \, A b^{5}\right)} d^{2} e + {\left(7 \, B a^{2} b^{3} - 4 \, A a b^{4}\right)} d e^{2} - {\left(3 \, B a^{3} b^{2} - 2 \, A a^{2} b^{3}\right)} e^{3}\right)} x^{2} + 2 \, {\left(B a b^{4} d^{3} - {\left(5 \, B a^{2} b^{3} - 2 \, A a b^{4}\right)} d^{2} e + {\left(7 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} d e^{2} - {\left(3 \, B a^{4} b - 2 \, A a^{3} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{e}{b}}}{2 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, B b^{4} e^{3} x^{4} - 16 \, {\left(2 \, B a b^{3} + A b^{4}\right)} d^{3} + 7 \, {\left(49 \, B a^{2} b^{2} - 16 \, A a b^{3}\right)} d^{2} e - 70 \, {\left(9 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{2} + 105 \, {\left(3 \, B a^{4} - 2 \, A a^{3} b\right)} e^{3} + 2 \, {\left(19 \, B b^{4} d e^{2} - 3 \, {\left(3 \, B a b^{3} - 2 \, A b^{4}\right)} e^{3}\right)} x^{3} + 3 \, {\left(29 \, B b^{4} d^{2} e - 2 \, {\left(23 \, B a b^{3} - 13 \, A b^{4}\right)} d e^{2} + 7 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} e^{3}\right)} x^{2} - 2 \, {\left(24 \, B b^{4} d^{3} - {\left(239 \, B a b^{3} - 80 \, A b^{4}\right)} d^{2} e + 7 \, {\left(61 \, B a^{2} b^{2} - 34 \, A a b^{3}\right)} d e^{2} - 70 \, {\left(3 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[-1/96*(105*(B*a^2*b^3*d^3 - (5*B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e + (7*B*a^4*b - 4*A*a^3*b^2)*d*e^2 - (3*B*a^5 - 2*A*a^4*b)*e^3 + (B*b^5*d^3 - (5*B*a*b^4 - 2*A*b^5)*d^2*e + (7*B*a^2*b^3 - 4*A*a*b^4)*d*e^2 - (3*B*a^3*b^2 - 2*A*a^2*b^3)*e^3)*x^2 + 2*(B*a*b^4*d^3 - (5*B*a^2*b^3 - 2*A*a*b^4)*d^2*e + (7*B*a^3*b^2 - 4*A*a^2*b^3)*d*e^2 - (3*B*a^4*b - 2*A*a^3*b^2)*e^3)*x)*sqrt(e/b)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 - 4*(2*b^2*e*x + b^2*d + a*b*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(e/b) + 8*(b^2*d*e + a*b*e^2)*x) - 4*(8*B*b^4*e^3*x^4 - 16*(2*B*a*b^3 + A*b^4)*d^3 + 7*(49*B*a^2*b^2 - 16*A*a*b^3)*d^2*e - 70*(9*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(3*B*a^4 - 2*A*a^3*b)*e^3 + 2*(19*B*b^4*d*e^2 - 3*(3*B*a*b^3 - 2*A*b^4)*e^3)*x^3 + 3*(29*B*b^4*d^2*e - 2*(23*B*a*b^3 - 13*A*b^4)*d*e^2 + 7*(3*B*a^2*b^2 - 2*A*a*b^3)*e^3)*x^2 - 2*(24*B*b^4*d^3 - (239*B*a*b^3 - 80*A*b^4)*d^2*e + 7*(61*B*a^2*b^2 - 34*A*a*b^3)*d*e^2 - 70*(3*B*a^3*b - 2*A*a^2*b^2)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/48*(105*(B*a^2*b^3*d^3 - (5*B*a^3*b^2 - 2*A*a^2*b^3)*d^2*e + (7*B*a^4*b - 4*A*a^3*b^2)*d*e^2 - (3*B*a^5 - 2*A*a^4*b)*e^3 + (B*b^5*d^3 - (5*B*a*b^4 - 2*A*b^5)*d^2*e + (7*B*a^2*b^3 - 4*A*a*b^4)*d*e^2 - (3*B*a^3*b^2 - 2*A*a^2*b^3)*e^3)*x^2 + 2*(B*a*b^4*d^3 - (5*B*a^2*b^3 - 2*A*a*b^4)*d^2*e + (7*B*a^3*b^2 - 4*A*a^2*b^3)*d*e^2 - (3*B*a^4*b - 2*A*a^3*b^2)*e^3)*x)*sqrt(-e/b)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-e/b)/(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)) - 2*(8*B*b^4*e^3*x^4 - 16*(2*B*a*b^3 + A*b^4)*d^3 + 7*(49*B*a^2*b^2 - 16*A*a*b^3)*d^2*e - 70*(9*B*a^3*b - 5*A*a^2*b^2)*d*e^2 + 105*(3*B*a^4 - 2*A*a^3*b)*e^3 + 2*(19*B*b^4*d*e^2 - 3*(3*B*a*b^3 - 2*A*b^4)*e^3)*x^3 + 3*(29*B*b^4*d^2*e - 2*(23*B*a*b^3 - 13*A*b^4)*d*e^2 + 7*(3*B*a^2*b^2 - 2*A*a*b^3)*e^3)*x^2 - 2*(24*B*b^4*d^3 - (239*B*a*b^3 - 80*A*b^4)*d^2*e + 7*(61*B*a^2*b^2 - 34*A*a*b^3)*d*e^2 - 70*(3*B*a^3*b - 2*A*a^2*b^2)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","B",0
2254,1,887,0,7.649857," ","integrate((B*x+A)*(e*x+d)^(5/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, B a^{2} b^{2} d^{2} - 2 \, {\left(5 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e + {\left(7 \, B a^{4} - 4 \, A a^{3} b\right)} e^{2} + {\left(3 \, B b^{4} d^{2} - 2 \, {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d e + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(3 \, B a b^{3} d^{2} - 2 \, {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d e + {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{2}\right)} x\right)} \sqrt{\frac{e}{b}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b^{2} e x + b^{2} d + a b e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{e}{b}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(6 \, B b^{3} e^{2} x^{3} - 8 \, {\left(2 \, B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(23 \, B a^{2} b - 8 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 4 \, A a^{2} b\right)} e^{2} + 3 \, {\left(9 \, B b^{3} d e - {\left(7 \, B a b^{2} - 4 \, A b^{3}\right)} e^{2}\right)} x^{2} - 2 \, {\left(12 \, B b^{3} d^{2} - {\left(79 \, B a b^{2} - 28 \, A b^{3}\right)} d e + 10 \, {\left(7 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{48 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{15 \, {\left(3 \, B a^{2} b^{2} d^{2} - 2 \, {\left(5 \, B a^{3} b - 2 \, A a^{2} b^{2}\right)} d e + {\left(7 \, B a^{4} - 4 \, A a^{3} b\right)} e^{2} + {\left(3 \, B b^{4} d^{2} - 2 \, {\left(5 \, B a b^{3} - 2 \, A b^{4}\right)} d e + {\left(7 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} e^{2}\right)} x^{2} + 2 \, {\left(3 \, B a b^{3} d^{2} - 2 \, {\left(5 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d e + {\left(7 \, B a^{3} b - 4 \, A a^{2} b^{2}\right)} e^{2}\right)} x\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{e}{b}}}{2 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)}}\right) - 2 \, {\left(6 \, B b^{3} e^{2} x^{3} - 8 \, {\left(2 \, B a b^{2} + A b^{3}\right)} d^{2} + 5 \, {\left(23 \, B a^{2} b - 8 \, A a b^{2}\right)} d e - 15 \, {\left(7 \, B a^{3} - 4 \, A a^{2} b\right)} e^{2} + 3 \, {\left(9 \, B b^{3} d e - {\left(7 \, B a b^{2} - 4 \, A b^{3}\right)} e^{2}\right)} x^{2} - 2 \, {\left(12 \, B b^{3} d^{2} - {\left(79 \, B a b^{2} - 28 \, A b^{3}\right)} d e + 10 \, {\left(7 \, B a^{2} b - 4 \, A a b^{2}\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[1/48*(15*(3*B*a^2*b^2*d^2 - 2*(5*B*a^3*b - 2*A*a^2*b^2)*d*e + (7*B*a^4 - 4*A*a^3*b)*e^2 + (3*B*b^4*d^2 - 2*(5*B*a*b^3 - 2*A*b^4)*d*e + (7*B*a^2*b^2 - 4*A*a*b^3)*e^2)*x^2 + 2*(3*B*a*b^3*d^2 - 2*(5*B*a^2*b^2 - 2*A*a*b^3)*d*e + (7*B*a^3*b - 4*A*a^2*b^2)*e^2)*x)*sqrt(e/b)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b^2*e*x + b^2*d + a*b*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(e/b) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(6*B*b^3*e^2*x^3 - 8*(2*B*a*b^2 + A*b^3)*d^2 + 5*(23*B*a^2*b - 8*A*a*b^2)*d*e - 15*(7*B*a^3 - 4*A*a^2*b)*e^2 + 3*(9*B*b^3*d*e - (7*B*a*b^2 - 4*A*b^3)*e^2)*x^2 - 2*(12*B*b^3*d^2 - (79*B*a*b^2 - 28*A*b^3)*d*e + 10*(7*B*a^2*b - 4*A*a*b^2)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/24*(15*(3*B*a^2*b^2*d^2 - 2*(5*B*a^3*b - 2*A*a^2*b^2)*d*e + (7*B*a^4 - 4*A*a^3*b)*e^2 + (3*B*b^4*d^2 - 2*(5*B*a*b^3 - 2*A*b^4)*d*e + (7*B*a^2*b^2 - 4*A*a*b^3)*e^2)*x^2 + 2*(3*B*a*b^3*d^2 - 2*(5*B*a^2*b^2 - 2*A*a*b^3)*d*e + (7*B*a^3*b - 4*A*a^2*b^2)*e^2)*x)*sqrt(-e/b)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-e/b)/(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)) - 2*(6*B*b^3*e^2*x^3 - 8*(2*B*a*b^2 + A*b^3)*d^2 + 5*(23*B*a^2*b - 8*A*a*b^2)*d*e - 15*(7*B*a^3 - 4*A*a^2*b)*e^2 + 3*(9*B*b^3*d*e - (7*B*a*b^2 - 4*A*b^3)*e^2)*x^2 - 2*(12*B*b^3*d^2 - (79*B*a*b^2 - 28*A*b^3)*d*e + 10*(7*B*a^2*b - 4*A*a*b^2)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
2255,1,561,0,6.166213," ","integrate((B*x+A)*(e*x+d)^(3/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, B a^{2} b d + {\left(3 \, B b^{3} d - {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} e\right)} x^{2} - {\left(5 \, B a^{3} - 2 \, A a^{2} b\right)} e + 2 \, {\left(3 \, B a b^{2} d - {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} e\right)} x\right)} \sqrt{\frac{e}{b}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b^{2} e x + b^{2} d + a b e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{e}{b}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(3 \, B b^{2} e x^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d + 3 \, {\left(5 \, B a^{2} - 2 \, A a b\right)} e - 2 \, {\left(3 \, B b^{2} d - 2 \, {\left(5 \, B a b - 2 \, A b^{2}\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{12 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{3 \, {\left(3 \, B a^{2} b d + {\left(3 \, B b^{3} d - {\left(5 \, B a b^{2} - 2 \, A b^{3}\right)} e\right)} x^{2} - {\left(5 \, B a^{3} - 2 \, A a^{2} b\right)} e + 2 \, {\left(3 \, B a b^{2} d - {\left(5 \, B a^{2} b - 2 \, A a b^{2}\right)} e\right)} x\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{e}{b}}}{2 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)}}\right) - 2 \, {\left(3 \, B b^{2} e x^{2} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d + 3 \, {\left(5 \, B a^{2} - 2 \, A a b\right)} e - 2 \, {\left(3 \, B b^{2} d - 2 \, {\left(5 \, B a b - 2 \, A b^{2}\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{6 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/12*(3*(3*B*a^2*b*d + (3*B*b^3*d - (5*B*a*b^2 - 2*A*b^3)*e)*x^2 - (5*B*a^3 - 2*A*a^2*b)*e + 2*(3*B*a*b^2*d - (5*B*a^2*b - 2*A*a*b^2)*e)*x)*sqrt(e/b)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b^2*e*x + b^2*d + a*b*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(e/b) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(3*B*b^2*e*x^2 - 2*(2*B*a*b + A*b^2)*d + 3*(5*B*a^2 - 2*A*a*b)*e - 2*(3*B*b^2*d - 2*(5*B*a*b - 2*A*b^2)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -1/6*(3*(3*B*a^2*b*d + (3*B*b^3*d - (5*B*a*b^2 - 2*A*b^3)*e)*x^2 - (5*B*a^3 - 2*A*a^2*b)*e + 2*(3*B*a*b^2*d - (5*B*a^2*b - 2*A*a*b^2)*e)*x)*sqrt(-e/b)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-e/b)/(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)) - 2*(3*B*b^2*e*x^2 - 2*(2*B*a*b + A*b^2)*d + 3*(5*B*a^2 - 2*A*a*b)*e - 2*(3*B*b^2*d - 2*(5*B*a*b - 2*A*b^2)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
2256,1,525,0,4.344394," ","integrate((B*x+A)*(e*x+d)^(1/2)/(b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B a^{2} b d - B a^{3} e + {\left(B b^{3} d - B a b^{2} e\right)} x^{2} + 2 \, {\left(B a b^{2} d - B a^{2} b e\right)} x\right)} \sqrt{\frac{e}{b}} \log\left(8 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 6 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b^{2} e x + b^{2} d + a b e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{\frac{e}{b}} + 8 \, {\left(b^{2} d e + a b e^{2}\right)} x\right) + 4 \, {\left(3 \, B a^{2} e - {\left(2 \, B a b + A b^{2}\right)} d - {\left(3 \, B b^{2} d - {\left(4 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{6 \, {\left(a^{2} b^{3} d - a^{3} b^{2} e + {\left(b^{5} d - a b^{4} e\right)} x^{2} + 2 \, {\left(a b^{4} d - a^{2} b^{3} e\right)} x\right)}}, -\frac{3 \, {\left(B a^{2} b d - B a^{3} e + {\left(B b^{3} d - B a b^{2} e\right)} x^{2} + 2 \, {\left(B a b^{2} d - B a^{2} b e\right)} x\right)} \sqrt{-\frac{e}{b}} \arctan\left(\frac{{\left(2 \, b e x + b d + a e\right)} \sqrt{b x + a} \sqrt{e x + d} \sqrt{-\frac{e}{b}}}{2 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)}}\right) - 2 \, {\left(3 \, B a^{2} e - {\left(2 \, B a b + A b^{2}\right)} d - {\left(3 \, B b^{2} d - {\left(4 \, B a b - A b^{2}\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(a^{2} b^{3} d - a^{3} b^{2} e + {\left(b^{5} d - a b^{4} e\right)} x^{2} + 2 \, {\left(a b^{4} d - a^{2} b^{3} e\right)} x\right)}}\right]"," ",0,"[1/6*(3*(B*a^2*b*d - B*a^3*e + (B*b^3*d - B*a*b^2*e)*x^2 + 2*(B*a*b^2*d - B*a^2*b*e)*x)*sqrt(e/b)*log(8*b^2*e^2*x^2 + b^2*d^2 + 6*a*b*d*e + a^2*e^2 + 4*(2*b^2*e*x + b^2*d + a*b*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(e/b) + 8*(b^2*d*e + a*b*e^2)*x) + 4*(3*B*a^2*e - (2*B*a*b + A*b^2)*d - (3*B*b^2*d - (4*B*a*b - A*b^2)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(a^2*b^3*d - a^3*b^2*e + (b^5*d - a*b^4*e)*x^2 + 2*(a*b^4*d - a^2*b^3*e)*x), -1/3*(3*(B*a^2*b*d - B*a^3*e + (B*b^3*d - B*a*b^2*e)*x^2 + 2*(B*a*b^2*d - B*a^2*b*e)*x)*sqrt(-e/b)*arctan(1/2*(2*b*e*x + b*d + a*e)*sqrt(b*x + a)*sqrt(e*x + d)*sqrt(-e/b)/(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)) - 2*(3*B*a^2*e - (2*B*a*b + A*b^2)*d - (3*B*b^2*d - (4*B*a*b - A*b^2)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d))/(a^2*b^3*d - a^3*b^2*e + (b^5*d - a*b^4*e)*x^2 + 2*(a*b^4*d - a^2*b^3*e)*x)]","B",0
2257,1,141,0,2.845232," ","integrate((B*x+A)/(b*x+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a e - {\left(2 \, B a + A b\right)} d - {\left(3 \, B b d - {\left(B a + 2 \, A b\right)} e\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(a^{2} b^{2} d^{2} - 2 \, a^{3} b d e + a^{4} e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2}\right)} x\right)}}"," ",0,"2/3*(3*A*a*e - (2*B*a + A*b)*d - (3*B*b*d - (B*a + 2*A*b)*e)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a^2*b^2*d^2 - 2*a^3*b*d*e + a^4*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x^2 + 2*(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2)*x)","A",0
2258,1,337,0,6.141561," ","integrate((B*x+A)/(b*x+a)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a^{2} e^{2} - {\left(2 \, B a b + A b^{2}\right)} d^{2} - 6 \, {\left(B a^{2} - A a b\right)} d e - 2 \, {\left(3 \, B b^{2} d e + {\left(B a b - 4 \, A b^{2}\right)} e^{2}\right)} x^{2} - {\left(3 \, B b^{2} d^{2} + 2 \, {\left(5 \, B a b - 2 \, A b^{2}\right)} d e + 3 \, {\left(B a^{2} - 4 \, A a b\right)} e^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(a^{2} b^{3} d^{4} - 3 \, a^{3} b^{2} d^{3} e + 3 \, a^{4} b d^{2} e^{2} - a^{5} d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{3} + {\left(b^{5} d^{4} - a b^{4} d^{3} e - 3 \, a^{2} b^{3} d^{2} e^{2} + 5 \, a^{3} b^{2} d e^{3} - 2 \, a^{4} b e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{4} - 5 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} + a^{4} b d e^{3} - a^{5} e^{4}\right)} x\right)}}"," ",0,"2/3*(3*A*a^2*e^2 - (2*B*a*b + A*b^2)*d^2 - 6*(B*a^2 - A*a*b)*d*e - 2*(3*B*b^2*d*e + (B*a*b - 4*A*b^2)*e^2)*x^2 - (3*B*b^2*d^2 + 2*(5*B*a*b - 2*A*b^2)*d*e + 3*(B*a^2 - 4*A*a*b)*e^2)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a^2*b^3*d^4 - 3*a^3*b^2*d^3*e + 3*a^4*b*d^2*e^2 - a^5*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^3 + (b^5*d^4 - a*b^4*d^3*e - 3*a^2*b^3*d^2*e^2 + 5*a^3*b^2*d*e^3 - 2*a^4*b*e^4)*x^2 + (2*a*b^4*d^4 - 5*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 + a^4*b*d*e^3 - a^5*e^4)*x)","B",0
2259,1,565,0,21.106395," ","integrate((B*x+A)/(b*x+a)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(A a^{3} e^{3} + {\left(2 \, B a b^{2} + A b^{3}\right)} d^{3} + 3 \, {\left(4 \, B a^{2} b - 3 \, A a b^{2}\right)} d^{2} e + {\left(2 \, B a^{3} - 9 \, A a^{2} b\right)} d e^{2} + 8 \, {\left(B b^{3} d e^{2} + {\left(B a b^{2} - 2 \, A b^{3}\right)} e^{3}\right)} x^{3} + 12 \, {\left(B b^{3} d^{2} e + 2 \, {\left(B a b^{2} - A b^{3}\right)} d e^{2} + {\left(B a^{2} b - 2 \, A a b^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(B b^{3} d^{3} + {\left(7 \, B a b^{2} - 2 \, A b^{3}\right)} d^{2} e + {\left(7 \, B a^{2} b - 12 \, A a b^{2}\right)} d e^{2} + {\left(B a^{3} - 2 \, A a^{2} b\right)} e^{3}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{3 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}"," ",0,"-2/3*(A*a^3*e^3 + (2*B*a*b^2 + A*b^3)*d^3 + 3*(4*B*a^2*b - 3*A*a*b^2)*d^2*e + (2*B*a^3 - 9*A*a^2*b)*d*e^2 + 8*(B*b^3*d*e^2 + (B*a*b^2 - 2*A*b^3)*e^3)*x^3 + 12*(B*b^3*d^2*e + 2*(B*a*b^2 - A*b^3)*d*e^2 + (B*a^2*b - 2*A*a*b^2)*e^3)*x^2 + 3*(B*b^3*d^3 + (7*B*a*b^2 - 2*A*b^3)*d^2*e + (7*B*a^2*b - 12*A*a*b^2)*d*e^2 + (B*a^3 - 2*A*a^2*b)*e^3)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x)","B",0
2260,1,916,0,150.345292," ","integrate((B*x+A)/(b*x+a)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, A a^{4} e^{4} - 5 \, {\left(2 \, B a b^{3} + A b^{4}\right)} d^{4} - 30 \, {\left(3 \, B a^{2} b^{2} - 2 \, A a b^{3}\right)} d^{3} e - 30 \, {\left(B a^{3} b - 3 \, A a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(B a^{4} - 10 \, A a^{3} b\right)} d e^{3} - 16 \, {\left(3 \, B b^{4} d e^{3} + {\left(5 \, B a b^{3} - 8 \, A b^{4}\right)} e^{4}\right)} x^{4} - 8 \, {\left(15 \, B b^{4} d^{2} e^{2} + 2 \, {\left(17 \, B a b^{3} - 20 \, A b^{4}\right)} d e^{3} + 3 \, {\left(5 \, B a^{2} b^{2} - 8 \, A a b^{3}\right)} e^{4}\right)} x^{3} - 6 \, {\left(15 \, B b^{4} d^{3} e + 5 \, {\left(11 \, B a b^{3} - 8 \, A b^{4}\right)} d^{2} e^{2} + {\left(53 \, B a^{2} b^{2} - 80 \, A a b^{3}\right)} d e^{3} + {\left(5 \, B a^{3} b - 8 \, A a^{2} b^{2}\right)} e^{4}\right)} x^{2} - {\left(15 \, B b^{4} d^{4} + 40 \, {\left(4 \, B a b^{3} - A b^{4}\right)} d^{3} e + 90 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} d^{2} e^{2} + 24 \, {\left(3 \, B a^{3} b - 5 \, A a^{2} b^{2}\right)} d e^{3} - {\left(5 \, B a^{4} - 8 \, A a^{3} b\right)} e^{4}\right)} x\right)} \sqrt{b x + a} \sqrt{e x + d}}{15 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}"," ",0,"2/15*(3*A*a^4*e^4 - 5*(2*B*a*b^3 + A*b^4)*d^4 - 30*(3*B*a^2*b^2 - 2*A*a*b^3)*d^3*e - 30*(B*a^3*b - 3*A*a^2*b^2)*d^2*e^2 + 2*(B*a^4 - 10*A*a^3*b)*d*e^3 - 16*(3*B*b^4*d*e^3 + (5*B*a*b^3 - 8*A*b^4)*e^4)*x^4 - 8*(15*B*b^4*d^2*e^2 + 2*(17*B*a*b^3 - 20*A*b^4)*d*e^3 + 3*(5*B*a^2*b^2 - 8*A*a*b^3)*e^4)*x^3 - 6*(15*B*b^4*d^3*e + 5*(11*B*a*b^3 - 8*A*b^4)*d^2*e^2 + (53*B*a^2*b^2 - 80*A*a*b^3)*d*e^3 + (5*B*a^3*b - 8*A*a^2*b^2)*e^4)*x^2 - (15*B*b^4*d^4 + 40*(4*B*a*b^3 - A*b^4)*d^3*e + 90*(3*B*a^2*b^2 - 4*A*a*b^3)*d^2*e^2 + 24*(3*B*a^3*b - 5*A*a^2*b^2)*d*e^3 - (5*B*a^4 - 8*A*a^3*b)*e^4)*x)*sqrt(b*x + a)*sqrt(e*x + d)/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x)","B",0
2261,-1,0,0,0.000000," ","integrate((B*x+A)/(b*x+a)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2262,1,82,0,1.504642," ","integrate((2+3*x)^4*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{51200000} \, {\left(691200000 \, x^{5} + 2218752000 \, x^{4} + 2739830400 \, x^{3} + 1468973920 \, x^{2} + 45781940 \, x - 518122939\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{4122385421}{1024000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/51200000*(691200000*x^5 + 2218752000*x^4 + 2739830400*x^3 + 1468973920*x^2 + 45781940*x - 518122939)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 4122385421/1024000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2263,1,77,0,1.778690," ","integrate((2+3*x)^3*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{1280000} \, {\left(6912000 \, x^{4} + 17366400 \, x^{3} + 14946720 \, x^{2} + 3002540 \, x - 4282349\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{39142411}{25600000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/1280000*(6912000*x^4 + 17366400*x^3 + 14946720*x^2 + 3002540*x - 4282349)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 39142411/25600000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2264,1,72,0,1.657993," ","integrate((2+3*x)^2*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{12800} \, {\left(28800 \, x^{3} + 51680 \, x^{2} + 22500 \, x - 13327\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{158873}{256000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/12800*(28800*x^3 + 51680*x^2 + 22500*x - 13327)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 158873/256000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2265,1,67,0,1.381833," ","integrate((2+3*x)*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{800} \, {\left(800 \, x^{2} + 820 \, x - 203\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{4477}{16000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/800*(800*x^2 + 820*x - 203)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 4477/16000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2266,1,62,0,0.823700," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{40} \, {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{121}{800} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/40*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 121/800*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2267,1,97,0,1.750846," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{37}{180} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + \frac{1}{3} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"1/9*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 37/180*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 1/3*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2268,1,116,0,1.311258," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{37 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{126 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/126*(37*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2269,1,86,0,1.381029," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{121 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{392 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/392*(121*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2270,1,101,0,1.836973," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{4477 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(3547 \, x^{2} + 4902 \, x + 1648\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5488 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/5488*(4477*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(3547*x^2 + 4902*x + 1648)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2271,1,116,0,1.695079," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{794365 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1875345 \, x^{3} + 3834760 \, x^{2} + 2617388 \, x + 594416\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{307328 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/307328*(794365*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1875345*x^3 + 3834760*x^2 + 2617388*x + 594416)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2272,1,131,0,1.710833," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{27958865 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(197947935 \, x^{4} + 536695650 \, x^{3} + 546004068 \, x^{2} + 247045192 \, x + 41933792\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3073280 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/3073280*(27958865*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(197947935*x^4 + 536695650*x^3 + 546004068*x^2 + 247045192*x + 41933792)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2273,1,146,0,1.670742," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{2944561015 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(62541041355 \, x^{5} + 211260697020 \, x^{4} + 285550790544 \, x^{3} + 193055073632 \, x^{2} + 65287037520 \, x + 8835086144\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{86051840 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/86051840*(2944561015*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(62541041355*x^5 + 211260697020*x^4 + 285550790544*x^3 + 193055073632*x^2 + 65287037520*x + 8835086144)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2274,1,87,0,1.514599," ","integrate((2+3*x)^4*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{4300800000} \, {\left(248832000000 \, x^{6} + 950400000000 \, x^{5} + 1480681728000 \, x^{4} + 1161696585600 \, x^{3} + 402838062880 \, x^{2} - 72932734340 \, x - 201521732121\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{70224051139}{4096000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/4300800000*(248832000000*x^6 + 950400000000*x^5 + 1480681728000*x^4 + 1161696585600*x^3 + 402838062880*x^2 - 72932734340*x - 201521732121)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 70224051139/4096000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2275,1,82,0,1.372844," ","integrate((2+3*x)^3*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{30720000} \, {\left(691200000 \, x^{5} + 2163456000 \, x^{4} + 2600899200 \, x^{3} + 1349400160 \, x^{2} + 21761620 \, x - 483864147\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1269748711}{204800000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/30720000*(691200000*x^5 + 2163456000*x^4 + 2600899200*x^3 + 1349400160*x^2 + 21761620*x - 483864147)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1269748711/204800000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2276,1,77,0,1.551722," ","integrate((2+3*x)^2*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{768000} \, {\left(6912000 \, x^{4} + 16790400 \, x^{3} + 13913120 \, x^{2} + 2552540 \, x - 4015809\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{11988317}{5120000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/768000*(6912000*x^4 + 16790400*x^3 + 13913120*x^2 + 2552540*x - 4015809)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 11988317/5120000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2277,1,72,0,1.396051," ","integrate((2+3*x)*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{38400} \, {\left(144000 \, x^{3} + 245600 \, x^{2} + 99380 \, x - 63387\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{240911}{256000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/38400*(144000*x^3 + 245600*x^2 + 99380*x - 63387)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 240911/256000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2278,1,67,0,1.693417," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{480} \, {\left(800 \, x^{2} + 740 \, x - 207\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1331}{3200} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/480*(800*x^2 + 740*x - 207)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1331/3200*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2279,1,102,0,1.085949," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{5}{72} \, {\left(12 \, x - 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1}{27} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{793}{4320} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"5/72*(12*x - 1)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1/27*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 793/4320*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2280,1,127,0,1.722371," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{287 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 214 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 84 \, {\left(15 \, x + 11\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{756 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/756*(287*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 214*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 84*(15*x + 11)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2281,1,136,0,1.574952," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{4091 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 1960 \, \sqrt{10} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(531 \, x + 340\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{10584 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/10584*(4091*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1960*sqrt(10)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(531*x + 340)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2282,1,101,0,1.445104," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{3993 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(4223 \, x^{2} + 4478 \, x + 1152\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{16464 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/16464*(3993*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(4223*x^2 + 4478*x + 1152)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2283,1,116,0,1.305775," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{459195 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1104135 \, x^{3} + 2269240 \, x^{2} + 1512052 \, x + 328464\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{921984 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/921984*(459195*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1104135*x^3 + 2269240*x^2 + 1512052*x + 328464)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2284,1,131,0,1.817326," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{11759385 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(83353815 \, x^{4} + 226052850 \, x^{3} + 230080132 \, x^{2} + 103856008 \, x + 17507808\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{9219840 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/9219840*(11759385*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(83353815*x^4 + 226052850*x^3 + 230080132*x^2 + 103856008*x + 17507808)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2285,1,146,0,0.948486," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{969680085 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(20597091345 \, x^{5} + 69576897780 \, x^{4} + 94045700016 \, x^{3} + 63585046048 \, x^{2} + 21497808880 \, x + 2906375616\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{258155520 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/258155520*(969680085*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(20597091345*x^5 + 69576897780*x^4 + 94045700016*x^3 + 63585046048*x^2 + 21497808880*x + 2906375616)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2286,1,92,0,1.471936," ","integrate((2+3*x)^4*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{27525120000} \, {\left(6967296000000 \, x^{7} + 30838579200000 \, x^{6} + 57746856960000 \, x^{5} + 58346097408000 \, x^{4} + 32457421737600 \, x^{3} + 6882844528480 \, x^{2} - 3991703112140 \, x - 5973304472091\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1988505613369}{26214400000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/27525120000*(6967296000000*x^7 + 30838579200000*x^6 + 57746856960000*x^5 + 58346097408000*x^4 + 32457421737600*x^3 + 6882844528480*x^2 - 3991703112140*x - 5973304472091)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1988505613369/26214400000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2287,1,87,0,1.506197," ","integrate((2+3*x)^3*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{172032000} \, {\left(16588800000 \, x^{6} + 62069760000 \, x^{5} + 94673664000 \, x^{4} + 72591427200 \, x^{3} + 24336990560 \, x^{2} - 4902803980 \, x - 12531569067\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{4343003753}{163840000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/172032000*(16588800000*x^6 + 62069760000*x^5 + 94673664000*x^4 + 72591427200*x^3 + 24336990560*x^2 - 4902803980*x - 12531569067)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 4343003753/163840000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2288,1,82,0,1.598931," ","integrate((2+3*x)^2*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{245760} \, {\left(9216000 \, x^{5} + 28108800 \, x^{4} + 32887680 \, x^{3} + 16507936 \, x^{2} + 17884 \, x - 6023169\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{15651229}{1638400} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/245760*(9216000*x^5 + 28108800*x^4 + 32887680*x^3 + 16507936*x^2 + 17884*x - 6023169)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 15651229/1638400*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2289,1,77,0,1.353802," ","integrate((2+3*x)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{153600} \, {\left(2304000 \, x^{4} + 5404800 \, x^{3} + 4310240 \, x^{2} + 718340 \, x - 1254087\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{3674891}{1024000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/153600*(2304000*x^4 + 5404800*x^3 + 4310240*x^2 + 718340*x - 1254087)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 3674891/1024000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2290,1,72,0,1.407971," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{1536} \, {\left(9600 \, x^{3} + 15520 \, x^{2} + 5836 \, x - 4005\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{14641}{10240} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/1536*(9600*x^3 + 15520*x^2 + 5836*x - 4005)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 14641/10240*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2291,1,113,0,1.294666," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{864} \, {\left(2400 \, x^{2} + 1980 \, x - 601\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{6553}{10368} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + \frac{1}{81} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/864*(2400*x^2 + 1980*x - 601)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 6553/10368*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 1/81*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2292,1,132,0,1.365847," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{1085 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 944 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 84 \, {\left(300 \, x^{2} + 135 \, x - 46\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6048 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/6048*(1085*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 944*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 84*(300*x^2 + 135*x - 46)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2293,1,147,0,1.373753," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{2450 \, \sqrt{5} \sqrt{2} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2119 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(700 \, x^{2} + 1039 \, x + 380\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3528 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/3528*(2450*sqrt(5)*sqrt(2)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2119*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(700*x^2 + 1039*x + 380)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2294,1,156,0,1.613252," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{250433 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 137200 \, \sqrt{10} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(124179 \, x^{2} + 159174 \, x + 51056\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{444528 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/444528*(250433*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 137200*sqrt(10)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(124179*x^2 + 159174*x + 51056)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2295,1,116,0,1.508785," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{219615 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(814395 \, x^{3} + 1285720 \, x^{2} + 654436 \, x + 105552\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{921984 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/921984*(219615*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(814395*x^3 + 1285720*x^2 + 654436*x + 105552)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2296,1,131,0,1.522588," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{3733455 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(27422145 \, x^{4} + 74915550 \, x^{3} + 74550556 \, x^{2} + 32206264 \, x + 5112864\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{9219840 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/9219840*(3733455*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(27422145*x^4 + 74915550*x^3 + 74550556*x^2 + 32206264*x + 5112864)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2297,1,146,0,1.681545," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{225544605 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(4803836985 \, x^{5} + 16234789140 \, x^{4} + 21960917808 \, x^{3} + 14818971424 \, x^{2} + 4978384240 \, x + 665270208\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{258155520 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/258155520*(225544605*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(4803836985*x^5 + 16234789140*x^4 + 21960917808*x^3 + 14818971424*x^2 + 4978384240*x + 665270208)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2298,1,161,0,1.054420," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{56038939935 \, \sqrt{7} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(3571458203385 \, x^{6} + 14445612678330 \, x^{5} + 24351227238888 \, x^{4} + 21898948566336 \, x^{3} + 11077661454896 \, x^{2} + 2987299350368 \, x + 335335888512\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{25299240960 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/25299240960*(56038939935*sqrt(7)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(3571458203385*x^6 + 14445612678330*x^5 + 24351227238888*x^4 + 21898948566336*x^3 + 11077661454896*x^2 + 2987299350368*x + 335335888512)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
2299,1,1358,0,21.214370," ","integrate((b*x+a)^(1/2)/(f*x+e)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \sqrt{\frac{b e - a f}{d e - c f}} \log\left(\frac{8 \, a^{2} c^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e^{2} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} e f + {\left(8 \, b^{2} d^{2} e^{2} - 8 \, {\left(b^{2} c d + a b d^{2}\right)} e f + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} f^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} f^{2} + {\left(b c d + a d^{2}\right)} e^{2} - {\left(b c^{2} + 3 \, a c d\right)} e f + {\left(2 \, b d^{2} e^{2} - {\left(3 \, b c d + a d^{2}\right)} e f + {\left(b c^{2} + a c d\right)} f^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b e - a f}{d e - c f}} + 2 \, {\left(4 \, {\left(b^{2} c d + a b d^{2}\right)} e^{2} - {\left(3 \, b^{2} c^{2} + 10 \, a b c d + 3 \, a^{2} d^{2}\right)} e f + 4 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2}\right)} x}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right)}{2 \, f}, -\frac{2 \, \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right) - \sqrt{\frac{b e - a f}{d e - c f}} \log\left(\frac{8 \, a^{2} c^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e^{2} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} e f + {\left(8 \, b^{2} d^{2} e^{2} - 8 \, {\left(b^{2} c d + a b d^{2}\right)} e f + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} f^{2}\right)} x^{2} - 4 \, {\left(2 \, a c^{2} f^{2} + {\left(b c d + a d^{2}\right)} e^{2} - {\left(b c^{2} + 3 \, a c d\right)} e f + {\left(2 \, b d^{2} e^{2} - {\left(3 \, b c d + a d^{2}\right)} e f + {\left(b c^{2} + a c d\right)} f^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b e - a f}{d e - c f}} + 2 \, {\left(4 \, {\left(b^{2} c d + a b d^{2}\right)} e^{2} - {\left(3 \, b^{2} c^{2} + 10 \, a b c d + 3 \, a^{2} d^{2}\right)} e f + 4 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2}\right)} x}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right)}{2 \, f}, \frac{2 \, \sqrt{-\frac{b e - a f}{d e - c f}} \arctan\left(-\frac{{\left(2 \, a c f - {\left(b c + a d\right)} e - {\left(2 \, b d e - {\left(b c + a d\right)} f\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b e - a f}{d e - c f}}}{2 \, {\left(a b c e - a^{2} c f + {\left(b^{2} d e - a b d f\right)} x^{2} + {\left({\left(b^{2} c + a b d\right)} e - {\left(a b c + a^{2} d\right)} f\right)} x\right)}}\right) + \sqrt{\frac{b}{d}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b d^{2} x + b c d + a d^{2}\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{b}{d}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{2 \, f}, \frac{\sqrt{-\frac{b e - a f}{d e - c f}} \arctan\left(-\frac{{\left(2 \, a c f - {\left(b c + a d\right)} e - {\left(2 \, b d e - {\left(b c + a d\right)} f\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b e - a f}{d e - c f}}}{2 \, {\left(a b c e - a^{2} c f + {\left(b^{2} d e - a b d f\right)} x^{2} + {\left({\left(b^{2} c + a b d\right)} e - {\left(a b c + a^{2} d\right)} f\right)} x\right)}}\right) - \sqrt{-\frac{b}{d}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{b}{d}}}{2 \, {\left(b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x\right)}}\right)}{f}\right]"," ",0,"[1/2*(sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x) + sqrt((b*e - a*f)/(d*e - c*f))*log((8*a^2*c^2*f^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e^2 - 8*(a*b*c^2 + a^2*c*d)*e*f + (8*b^2*d^2*e^2 - 8*(b^2*c*d + a*b*d^2)*e*f + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*f^2)*x^2 - 4*(2*a*c^2*f^2 + (b*c*d + a*d^2)*e^2 - (b*c^2 + 3*a*c*d)*e*f + (2*b*d^2*e^2 - (3*b*c*d + a*d^2)*e*f + (b*c^2 + a*c*d)*f^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt((b*e - a*f)/(d*e - c*f)) + 2*(4*(b^2*c*d + a*b*d^2)*e^2 - (3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*e*f + 4*(a*b*c^2 + a^2*c*d)*f^2)*x)/(f^2*x^2 + 2*e*f*x + e^2)))/f, -1/2*(2*sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)) - sqrt((b*e - a*f)/(d*e - c*f))*log((8*a^2*c^2*f^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e^2 - 8*(a*b*c^2 + a^2*c*d)*e*f + (8*b^2*d^2*e^2 - 8*(b^2*c*d + a*b*d^2)*e*f + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*f^2)*x^2 - 4*(2*a*c^2*f^2 + (b*c*d + a*d^2)*e^2 - (b*c^2 + 3*a*c*d)*e*f + (2*b*d^2*e^2 - (3*b*c*d + a*d^2)*e*f + (b*c^2 + a*c*d)*f^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt((b*e - a*f)/(d*e - c*f)) + 2*(4*(b^2*c*d + a*b*d^2)*e^2 - (3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*e*f + 4*(a*b*c^2 + a^2*c*d)*f^2)*x)/(f^2*x^2 + 2*e*f*x + e^2)))/f, 1/2*(2*sqrt(-(b*e - a*f)/(d*e - c*f))*arctan(-1/2*(2*a*c*f - (b*c + a*d)*e - (2*b*d*e - (b*c + a*d)*f)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-(b*e - a*f)/(d*e - c*f))/(a*b*c*e - a^2*c*f + (b^2*d*e - a*b*d*f)*x^2 + ((b^2*c + a*b*d)*e - (a*b*c + a^2*d)*f)*x)) + sqrt(b/d)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b*d^2*x + b*c*d + a*d^2)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(b/d) + 8*(b^2*c*d + a*b*d^2)*x))/f, (sqrt(-(b*e - a*f)/(d*e - c*f))*arctan(-1/2*(2*a*c*f - (b*c + a*d)*e - (2*b*d*e - (b*c + a*d)*f)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-(b*e - a*f)/(d*e - c*f))/(a*b*c*e - a^2*c*f + (b^2*d*e - a*b*d*f)*x^2 + ((b^2*c + a*b*d)*e - (a*b*c + a^2*d)*f)*x)) - sqrt(-b/d)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-b/d)/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x)))/f]","B",0
2300,1,1358,0,20.410108," ","integrate((d*x+c)^(1/2)/(f*x+e)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right) + \sqrt{\frac{d e - c f}{b e - a f}} \log\left(\frac{8 \, a^{2} c^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e^{2} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} e f + {\left(8 \, b^{2} d^{2} e^{2} - 8 \, {\left(b^{2} c d + a b d^{2}\right)} e f + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} f^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c f^{2} + {\left(b^{2} c + a b d\right)} e^{2} - {\left(3 \, a b c + a^{2} d\right)} e f + {\left(2 \, b^{2} d e^{2} - {\left(b^{2} c + 3 \, a b d\right)} e f + {\left(a b c + a^{2} d\right)} f^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d e - c f}{b e - a f}} + 2 \, {\left(4 \, {\left(b^{2} c d + a b d^{2}\right)} e^{2} - {\left(3 \, b^{2} c^{2} + 10 \, a b c d + 3 \, a^{2} d^{2}\right)} e f + 4 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2}\right)} x}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right)}{2 \, f}, \frac{2 \, \sqrt{-\frac{d e - c f}{b e - a f}} \arctan\left(-\frac{{\left(2 \, a c f - {\left(b c + a d\right)} e - {\left(2 \, b d e - {\left(b c + a d\right)} f\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d e - c f}{b e - a f}}}{2 \, {\left(a c d e - a c^{2} f + {\left(b d^{2} e - b c d f\right)} x^{2} + {\left({\left(b c d + a d^{2}\right)} e - {\left(b c^{2} + a c d\right)} f\right)} x\right)}}\right) + \sqrt{\frac{d}{b}} \log\left(8 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} d x + b^{2} c + a b d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d}{b}} + 8 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)}{2 \, f}, -\frac{2 \, \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right) - \sqrt{\frac{d e - c f}{b e - a f}} \log\left(\frac{8 \, a^{2} c^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} e^{2} - 8 \, {\left(a b c^{2} + a^{2} c d\right)} e f + {\left(8 \, b^{2} d^{2} e^{2} - 8 \, {\left(b^{2} c d + a b d^{2}\right)} e f + {\left(b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right)} f^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{2} c f^{2} + {\left(b^{2} c + a b d\right)} e^{2} - {\left(3 \, a b c + a^{2} d\right)} e f + {\left(2 \, b^{2} d e^{2} - {\left(b^{2} c + 3 \, a b d\right)} e f + {\left(a b c + a^{2} d\right)} f^{2}\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{d e - c f}{b e - a f}} + 2 \, {\left(4 \, {\left(b^{2} c d + a b d^{2}\right)} e^{2} - {\left(3 \, b^{2} c^{2} + 10 \, a b c d + 3 \, a^{2} d^{2}\right)} e f + 4 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2}\right)} x}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right)}{2 \, f}, \frac{\sqrt{-\frac{d e - c f}{b e - a f}} \arctan\left(-\frac{{\left(2 \, a c f - {\left(b c + a d\right)} e - {\left(2 \, b d e - {\left(b c + a d\right)} f\right)} x\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d e - c f}{b e - a f}}}{2 \, {\left(a c d e - a c^{2} f + {\left(b d^{2} e - b c d f\right)} x^{2} + {\left({\left(b c d + a d^{2}\right)} e - {\left(b c^{2} + a c d\right)} f\right)} x\right)}}\right) - \sqrt{-\frac{d}{b}} \arctan\left(\frac{{\left(2 \, b d x + b c + a d\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{-\frac{d}{b}}}{2 \, {\left(b d^{2} x^{2} + a c d + {\left(b c d + a d^{2}\right)} x\right)}}\right)}{f}\right]"," ",0,"[1/2*(sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x) + sqrt((d*e - c*f)/(b*e - a*f))*log((8*a^2*c^2*f^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e^2 - 8*(a*b*c^2 + a^2*c*d)*e*f + (8*b^2*d^2*e^2 - 8*(b^2*c*d + a*b*d^2)*e*f + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*f^2)*x^2 - 4*(2*a^2*c*f^2 + (b^2*c + a*b*d)*e^2 - (3*a*b*c + a^2*d)*e*f + (2*b^2*d*e^2 - (b^2*c + 3*a*b*d)*e*f + (a*b*c + a^2*d)*f^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt((d*e - c*f)/(b*e - a*f)) + 2*(4*(b^2*c*d + a*b*d^2)*e^2 - (3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*e*f + 4*(a*b*c^2 + a^2*c*d)*f^2)*x)/(f^2*x^2 + 2*e*f*x + e^2)))/f, 1/2*(2*sqrt(-(d*e - c*f)/(b*e - a*f))*arctan(-1/2*(2*a*c*f - (b*c + a*d)*e - (2*b*d*e - (b*c + a*d)*f)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-(d*e - c*f)/(b*e - a*f))/(a*c*d*e - a*c^2*f + (b*d^2*e - b*c*d*f)*x^2 + ((b*c*d + a*d^2)*e - (b*c^2 + a*c*d)*f)*x)) + sqrt(d/b)*log(8*b^2*d^2*x^2 + b^2*c^2 + 6*a*b*c*d + a^2*d^2 + 4*(2*b^2*d*x + b^2*c + a*b*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(d/b) + 8*(b^2*c*d + a*b*d^2)*x))/f, -1/2*(2*sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)) - sqrt((d*e - c*f)/(b*e - a*f))*log((8*a^2*c^2*f^2 + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*e^2 - 8*(a*b*c^2 + a^2*c*d)*e*f + (8*b^2*d^2*e^2 - 8*(b^2*c*d + a*b*d^2)*e*f + (b^2*c^2 + 6*a*b*c*d + a^2*d^2)*f^2)*x^2 - 4*(2*a^2*c*f^2 + (b^2*c + a*b*d)*e^2 - (3*a*b*c + a^2*d)*e*f + (2*b^2*d*e^2 - (b^2*c + 3*a*b*d)*e*f + (a*b*c + a^2*d)*f^2)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt((d*e - c*f)/(b*e - a*f)) + 2*(4*(b^2*c*d + a*b*d^2)*e^2 - (3*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*e*f + 4*(a*b*c^2 + a^2*c*d)*f^2)*x)/(f^2*x^2 + 2*e*f*x + e^2)))/f, (sqrt(-(d*e - c*f)/(b*e - a*f))*arctan(-1/2*(2*a*c*f - (b*c + a*d)*e - (2*b*d*e - (b*c + a*d)*f)*x)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-(d*e - c*f)/(b*e - a*f))/(a*c*d*e - a*c^2*f + (b*d^2*e - b*c*d*f)*x^2 + ((b*c*d + a*d^2)*e - (b*c^2 + a*c*d)*f)*x)) - sqrt(-d/b)*arctan(1/2*(2*b*d*x + b*c + a*d)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt(-d/b)/(b*d^2*x^2 + a*c*d + (b*c*d + a*d^2)*x)))/f]","B",0
2301,1,72,0,1.408893," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{64000} \, {\left(86400 \, x^{3} + 162720 \, x^{2} + 76140 \, x - 41789\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{525371}{1280000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/64000*(86400*x^3 + 162720*x^2 + 76140*x - 41789)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 525371/1280000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2302,1,67,0,1.288165," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{800} \, {\left(480 \, x^{2} + 540 \, x - 113\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{3047}{16000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/800*(480*x^2 + 540*x - 113)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 3047/16000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2303,1,62,0,1.616174," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{200} \, {\left(60 \, x + 11\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{451}{4000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/200*(60*x + 11)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 451/4000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2304,1,57,0,1.274887," ","integrate((1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{11}{100} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + \frac{1}{5} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"-11/100*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 1/5*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2305,1,87,0,1.465704," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{15} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{1}{3} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/15*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1/3*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2306,1,71,0,1.009674," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{11 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/14*(11*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2307,1,86,0,1.598968," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1177 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(309 \, x + 220\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{392 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/392*(1177*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(309*x + 220)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2308,1,101,0,1.303725," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{68959 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(54249 \, x^{2} + 74754 \, x + 25856\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5488 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/5488*(68959*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(54249*x^2 + 74754*x + 25856)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2309,1,116,0,1.579089," ","integrate((1-2*x)^(1/2)/(2+3*x)^5/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{16925425 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(39943125 \, x^{3} + 81668520 \, x^{2} + 55729116 \, x + 12696112\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{307328 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/307328*(16925425*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(39943125*x^3 + 81668520*x^2 + 55729116*x + 12696112)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2310,1,86,0,1.420798," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{10409 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(7200 \, x^{3} + 13140 \, x^{2} + 3825 \, x - 893\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{80000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/80000*(10409*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(7200*x^3 + 13140*x^2 + 3825*x - 893)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2311,1,81,0,1.301142," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{317 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(180 \, x^{2} + 165 \, x + 31\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/4000*(317*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(180*x^2 + 165*x + 31)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2312,1,76,0,1.489439," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{29 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(15 \, x + 7\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{500 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/500*(29*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(15*x + 7)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2313,1,76,0,1.463787," ","integrate((1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{5} \sqrt{2} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 10 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{25 \, {\left(5 \, x + 3\right)}}"," ",0,"1/25*(sqrt(5)*sqrt(2)*(5*x + 3)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 10*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","B",0
2314,1,69,0,1.290993," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{7} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5 \, x + 3}"," ",0,"(sqrt(7)*(5*x + 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2315,1,86,0,1.397376," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{103 \, \sqrt{7} {\left(15 \, x^{2} + 19 \, x + 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(45 \, x + 29\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/14*(103*sqrt(7)*(15*x^2 + 19*x + 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(45*x + 29)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
2316,1,101,0,1.328764," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{17951 \, \sqrt{7} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(23535 \, x^{2} + 30861 \, x + 10100\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{392 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/392*(17951*sqrt(7)*(45*x^3 + 87*x^2 + 56*x + 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(23535*x^2 + 30861*x + 10100)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
2317,1,116,0,1.301447," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1463447 \, \sqrt{7} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(5756085 \, x^{3} + 11385261 \, x^{2} + 7502166 \, x + 1646704\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5488 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/5488*(1463447*sqrt(7)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(5756085*x^3 + 11385261*x^2 + 7502166*x + 1646704)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
2318,1,101,0,1.589509," ","integrate((2+3*x)^4*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1171863 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(3564000 \, x^{4} + 8999100 \, x^{3} + 6384015 \, x^{2} + 995870 \, x - 218953\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{13200000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/13200000*(1171863*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(3564000*x^4 + 8999100*x^3 + 6384015*x^2 + 995870*x - 218953)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2319,1,96,0,1.568367," ","integrate((2+3*x)^3*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{35343 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(89100 \, x^{3} + 147015 \, x^{2} + 75470 \, x + 11567\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{660000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/660000*(35343*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(89100*x^3 + 147015*x^2 + 75470*x + 11567)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2320,1,91,0,1.597963," ","integrate((2+3*x)^2*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{99 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(297 \, x^{2} + 278 \, x + 59\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3300 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/3300*(99*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(297*x^2 + 278*x + 59)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2321,1,92,0,1.567252," ","integrate((2+3*x)*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{99 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 10 \, {\left(485 \, x + 302\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4125 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/4125*(99*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 10*(485*x + 302)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2322,1,33,0,1.534052," ","integrate((1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{5 \, x + 3} {\left(2 \, x - 1\right)} \sqrt{-2 \, x + 1}}{33 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"2/33*sqrt(5*x + 3)*(2*x - 1)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9)","B",0
2323,1,86,0,1.329216," ","integrate((1-2*x)^(1/2)/(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{99 \, \sqrt{7} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(505 \, x + 292\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{33 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/33*(99*sqrt(7)*(25*x^2 + 30*x + 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(505*x + 292)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2324,1,101,0,1.418103," ","integrate((1-2*x)^(1/2)/(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{17127 \, \sqrt{7} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(37425 \, x^{2} + 46580 \, x + 14453\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{462 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"-1/462*(17127*sqrt(7)*(75*x^3 + 140*x^2 + 87*x + 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(37425*x^2 + 46580*x + 14453)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
2325,1,116,0,1.053295," ","integrate((1-2*x)^(1/2)/(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{4174929 \, \sqrt{7} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(27368325 \, x^{3} + 52308690 \, x^{2} + 33277877 \, x + 7046540\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12936 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"-1/12936*(4174929*sqrt(7)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(27368325*x^3 + 52308690*x^2 + 33277877*x + 7046540)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
2326,1,131,0,1.435523," ","integrate((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{437126283 \, \sqrt{7} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(8596610325 \, x^{4} + 22161651840 \, x^{3} + 21406565457 \, x^{2} + 9181937962 \, x + 1475586688\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{181104 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"-1/181104*(437126283*sqrt(7)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(8596610325*x^4 + 22161651840*x^3 + 21406565457*x^2 + 9181937962*x + 1475586688)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2327,1,82,0,1.500702," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{76800000} \, {\left(691200000 \, x^{5} + 1251072000 \, x^{4} + 308534400 \, x^{3} - 623566880 \, x^{2} - 374573660 \, x + 81405921\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{452517373}{512000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/76800000*(691200000*x^5 + 1251072000*x^4 + 308534400*x^3 - 623566880*x^2 - 374573660*x + 81405921)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 452517373/512000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2328,1,77,0,1.459248," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1920000} \, {\left(6912000 \, x^{4} + 7286400 \, x^{3} - 3141280 \, x^{2} - 4872460 \, x + 382101\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{5487713}{12800000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/1920000*(6912000*x^4 + 7286400*x^3 - 3141280*x^2 - 4872460*x + 382101)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 5487713/12800000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2329,1,72,0,0.869361," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{19200} \, {\left(28800 \, x^{3} + 6880 \, x^{2} - 23420 \, x - 1959\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{30613}{128000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/19200*(28800*x^3 + 6880*x^2 - 23420*x - 1959)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 30613/128000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2330,1,67,0,1.585011," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1200} \, {\left(800 \, x^{2} - 580 \, x - 273\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1331}{8000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/1200*(800*x^2 - 580*x - 273)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1331/8000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2331,1,102,0,1.441762," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","-\frac{1}{180} \, {\left(60 \, x - 137\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + \frac{7}{27} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{4091}{10800} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/180*(60*x - 137)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 7/27*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 4091/10800*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2332,1,127,0,1.305955," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{107 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 205 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(6 \, x + 11\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{270 \, {\left(3 \, x + 2\right)}}"," ",0,"1/270*(107*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 205*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(6*x + 11)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2333,1,136,0,1.560777," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{793 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 112 \, \sqrt{10} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(135 \, x + 76\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1512 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/1512*(793*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 112*sqrt(10)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(135*x + 76)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2334,1,101,0,1.234710," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{3993 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(3103 \, x^{2} + 4366 \, x + 1488\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2352 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/2352*(3993*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(3103*x^2 + 4366*x + 1488)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2335,1,116,0,0.991126," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{722733 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1705089 \, x^{3} + 3485960 \, x^{2} + 2381420 \, x + 541680\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{131712 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/131712*(722733*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1705089*x^3 + 3485960*x^2 + 2381420*x + 541680)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2336,1,131,0,1.555209," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{179824755 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1273114845 \, x^{4} + 3451770150 \, x^{3} + 3511594796 \, x^{2} + 1588955864 \, x + 269759904\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{9219840 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/9219840*(179824755*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1273114845*x^4 + 3451770150*x^3 + 3511594796*x^2 + 1588955864*x + 269759904)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2337,1,87,0,1.036796," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{1}{716800000} \, {\left(27648000000 \, x^{6} + 67968000000 \, x^{5} + 46732032000 \, x^{4} - 12527113600 \, x^{3} - 28707557280 \, x^{2} - 9288436460 \, x + 3952411101\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{6219452877}{2048000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/716800000*(27648000000*x^6 + 67968000000*x^5 + 46732032000*x^4 - 12527113600*x^3 - 28707557280*x^2 - 9288436460*x + 3952411101)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 6219452877/2048000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2338,1,82,0,1.336229," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{1}{5120000} \, {\left(76800000 \, x^{5} + 132864000 \, x^{4} + 27804800 \, x^{3} - 66492960 \, x^{2} - 37288220 \, x + 8705457\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{136205223}{102400000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/5120000*(76800000*x^5 + 132864000*x^4 + 27804800*x^3 - 66492960*x^2 - 37288220*x + 8705457)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 136205223/102400000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2339,1,77,0,1.507357," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{1}{128000} \, {\left(768000 \, x^{4} + 745600 \, x^{3} - 364320 \, x^{2} - 489340 \, x + 46809\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1625151}{2560000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/128000*(768000*x^4 + 745600*x^3 - 364320*x^2 - 489340*x + 46809)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1625151/2560000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2340,1,72,0,1.269009," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{1}{6400} \, {\left(16000 \, x^{3} + 2400 \, x^{2} - 11980 \, x - 603\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{43923}{128000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/6400*(16000*x^3 + 2400*x^2 - 11980*x - 603)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 43923/128000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2341,1,107,0,0.917350," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","-\frac{1}{2160} \, {\left(2400 \, x^{2} - 1980 \, x - 271\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{7}{81} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{19573}{129600} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/2160*(2400*x^2 - 1980*x - 271)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 7/81*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 19573/129600*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2342,1,126,0,1.779671," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{1480 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 1649 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 60 \, {\left(60 \, x^{2} - 105 \, x - 106\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2160 \, {\left(3 \, x + 2\right)}}"," ",0,"1/2160*(1480*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1649*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 60*(60*x^2 - 105*x - 106)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2343,1,141,0,1.351303," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{1649 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 1036 \, \sqrt{10} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(120 \, x^{2} + 345 \, x + 172\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1512 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/1512*(1649*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1036*sqrt(10)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(120*x^2 + 345*x + 172)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2344,1,156,0,1.553546," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{19573 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 7840 \, \sqrt{10} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(19041 \, x^{2} + 21762 \, x + 6176\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{63504 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/63504*(19573*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 7840*sqrt(10)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(19041*x^2 + 21762*x + 6176)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2345,1,116,0,1.310939," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{43923 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(100159 \, x^{3} + 213240 \, x^{2} + 145940 \, x + 32400\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43904 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/43904*(43923*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(100159*x^3 + 213240*x^2 + 145940*x + 32400)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2346,1,131,0,1.363969," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{8125755 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(57469845 \, x^{4} + 155783350 \, x^{3} + 158785356 \, x^{2} + 71866904 \, x + 12157344\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3073280 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/3073280*(8125755*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(57469845*x^4 + 155783350*x^3 + 158785356*x^2 + 71866904*x + 12157344)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2347,1,146,0,1.484690," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{97289445 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(2066288865 \, x^{5} + 6979774260 \, x^{4} + 9434103472 \, x^{3} + 6379024416 \, x^{2} + 2157325040 \, x + 291805632\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12293120 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/12293120*(97289445*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(2066288865*x^5 + 6979774260*x^4 + 9434103472*x^3 + 6379024416*x^2 + 2157325040*x + 291805632)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2348,1,161,0,1.166088," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{31097264385 \, \sqrt{7} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1981465999335 \, x^{6} + 8014272743430 \, x^{5} + 13509190228248 \, x^{4} + 12147806104256 \, x^{3} + 6146173476816 \, x^{2} + 1658923773088 \, x + 186609267072\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1204725760 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/1204725760*(31097264385*sqrt(7)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1981465999335*x^6 + 8014272743430*x^5 + 13509190228248*x^4 + 12147806104256*x^3 + 6146173476816*x^2 + 1658923773088*x + 186609267072)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
2349,1,92,0,0.989699," ","integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1}{4587520000} \, {\left(774144000000 \, x^{7} + 2394316800000 \, x^{6} + 2554199040000 \, x^{5} + 592093952000 \, x^{4} - 910419721600 \, x^{3} - 749541131680 \, x^{2} - 138459209260 \, x + 116041578381\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{147858829437}{13107200000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/4587520000*(774144000000*x^7 + 2394316800000*x^6 + 2554199040000*x^5 + 592093952000*x^4 - 910419721600*x^3 - 749541131680*x^2 - 138459209260*x + 116041578381)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 147858829437/13107200000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2350,1,87,0,1.330432," ","integrate((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1}{28672000} \, {\left(1843200000 \, x^{6} + 4387840000 \, x^{5} + 2867456000 \, x^{4} - 887043200 \, x^{3} - 1789716960 \, x^{2} - 549624420 \, x + 247243887\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{378308799}{81920000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/28672000*(1843200000*x^6 + 4387840000*x^5 + 2867456000*x^4 - 887043200*x^3 - 1789716960*x^2 - 549624420*x + 247243887)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 378308799/81920000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2351,1,82,0,1.356629," ","integrate((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1}{204800} \, {\left(5120000 \, x^{5} + 8448000 \, x^{4} + 1456000 \, x^{3} - 4238560 \, x^{2} - 2224900 \, x + 555399\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{8213601}{4096000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/204800*(5120000*x^5 + 8448000*x^4 + 1456000*x^3 - 4238560*x^2 - 2224900*x + 555399)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 8213601/4096000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2352,1,77,0,1.497338," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1}{25600} \, {\left(256000 \, x^{4} + 227200 \, x^{3} - 124640 \, x^{2} - 147140 \, x + 16407\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{483153}{512000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/25600*(256000*x^4 + 227200*x^3 - 124640*x^2 - 147140*x + 16407)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 483153/512000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2353,1,112,0,1.121444," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","-\frac{1}{20736} \, {\left(86400 \, x^{3} + 5280 \, x^{2} - 58356 \, x - 2389\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + \frac{7}{243} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{648919}{1244160} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/20736*(86400*x^3 + 5280*x^2 - 58356*x - 2389)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 7/243*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 648919/1244160*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2354,1,137,0,1.641113," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{43 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 5792 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 12 \, {\left(7200 \, x^{3} - 1860 \, x^{2} - 3513 \, x + 730\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{15552 \, {\left(3 \, x + 2\right)}}"," ",0,"1/15552*(43*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 5792*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 12*(7200*x^3 - 1860*x^2 - 3513*x + 730)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2355,1,152,0,0.906994," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{13615 \, \sqrt{5} \sqrt{2} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 13658 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 84 \, {\left(900 \, x^{3} - 1095 \, x^{2} - 2985 \, x - 1232\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{9072 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/9072*(13615*sqrt(5)*sqrt(2)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 13658*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 84*(900*x^3 - 1095*x^2 - 2985*x - 1232)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2356,1,161,0,1.003416," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{326717 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 225400 \, \sqrt{10} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(75600 \, x^{3} + 286791 \, x^{2} + 275022 \, x + 78416\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{190512 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/190512*(326717*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 225400*sqrt(10)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(75600*x^3 + 286791*x^2 + 275022*x + 78416)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2357,1,176,0,1.574722," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{1922677 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 2195200 \, \sqrt{10} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(13290147 \, x^{3} + 23185560 \, x^{2} + 13434180 \, x + 2583760\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{10668672 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/10668672*(1922677*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 2195200*sqrt(10)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(13290147*x^3 + 23185560*x^2 + 13434180*x + 2583760)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2358,1,131,0,1.263274," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{2415765 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(15899035 \, x^{4} + 46076650 \, x^{3} + 47906548 \, x^{2} + 21437032 \, x + 3507552\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3073280 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/3073280*(2415765*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(15899035*x^4 + 46076650*x^3 + 47906548*x^2 + 21437032*x + 3507552)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2359,1,146,0,2.013581," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{21741885 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(460633945 \, x^{5} + 1555340180 \, x^{4} + 2108117296 \, x^{3} + 1428134688 \, x^{2} + 482263920 \, x + 64829376\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12293120 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/12293120*(21741885*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(460633945*x^5 + 1555340180*x^4 + 2108117296*x^3 + 1428134688*x^2 + 482263920*x + 64829376)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2360,1,161,0,1.279201," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{5524854555 \, \sqrt{7} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(351992877405 \, x^{6} + 1423652835490 \, x^{5} + 2399706883464 \, x^{4} + 2158260396608 \, x^{3} + 1092179419888 \, x^{2} + 294736348384 \, x + 33120084096\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1204725760 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/1204725760*(5524854555*sqrt(7)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(351992877405*x^6 + 1423652835490*x^5 + 2399706883464*x^4 + 2158260396608*x^3 + 1092179419888*x^2 + 294736348384*x + 33120084096)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
2361,1,77,0,1.674285," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3200000} \, {\left(6912000 \, x^{4} + 7862400 \, x^{3} - 2952480 \, x^{2} - 5372860 \, x + 314441\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{18648399}{64000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/3200000*(6912000*x^4 + 7862400*x^3 - 2952480*x^2 - 5372860*x + 314441)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 18648399/64000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2362,1,72,0,1.680726," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{32000} \, {\left(28800 \, x^{3} + 9440 \, x^{2} - 25020 \, x - 3383\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{109263}{640000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/32000*(28800*x^3 + 9440*x^2 - 25020*x - 3383)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 109263/640000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2363,1,67,0,1.663526," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{400} \, {\left(160 \, x^{2} - 100 \, x - 89\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1089}{8000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/400*(160*x^2 - 100*x - 89)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1089/8000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2364,1,62,0,0.976220," ","integrate((1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{100} \, {\left(20 \, x - 43\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{363}{2000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/100*(20*x - 43)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 363/2000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2365,1,103,0,1.207931," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{103}{450} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{7}{9} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{2}{15} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"103/450*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 7/9*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2/15*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2366,1,122,0,1.170367," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 145 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 210 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{90 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/90*(4*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 145*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 210*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2367,1,86,0,1.649506," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{363 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(95 \, x + 68\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{56 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/56*(363*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(95*x + 68)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2368,1,101,0,1.460475," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{21417 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(16847 \, x^{2} + 23214 \, x + 8032\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{784 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/784*(21417*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(16847*x^2 + 23214*x + 8032)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2369,1,116,0,1.556336," ","integrate((1-2*x)^(3/2)/(2+3*x)^5/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{5274027 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(12446391 \, x^{3} + 25448120 \, x^{2} + 17365300 \, x + 3956240\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43904 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/43904*(5274027*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(12446391*x^3 + 25448120*x^2 + 17365300*x + 3956240)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2370,1,131,0,1.205379," ","integrate((1-2*x)^(3/2)/(2+3*x)^6/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1666084695 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(11795595705 \, x^{4} + 31981229550 \, x^{3} + 32535654204 \, x^{2} + 14720806136 \, x + 2499608096\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3073280 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/3073280*(1666084695*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(11795595705*x^4 + 31981229550*x^3 + 32535654204*x^2 + 14720806136*x + 2499608096)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2371,1,91,0,1.527578," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{390621 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(432000 \, x^{4} + 439200 \, x^{3} - 287460 \, x^{2} - 317125 \, x - 46783\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3200000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/3200000*(390621*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(432000*x^4 + 439200*x^3 - 287460*x^2 - 317125*x - 46783)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2372,1,86,0,0.871691," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{3927 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2400 \, x^{3} + 180 \, x^{2} - 2575 \, x - 1021\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{40000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/40000*(3927*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2400*x^3 + 180*x^2 - 2575*x - 1021)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2373,1,81,0,1.448821," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{33 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(12 \, x^{2} - 17 \, x - 11\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{400 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/400*(33*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(12*x^2 - 17*x - 11)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2374,1,82,0,1.286216," ","integrate((1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{5} \sqrt{2} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(5 \, x + 14\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{250 \, {\left(5 \, x + 3\right)}}"," ",0,"1/250*(33*sqrt(5)*sqrt(2)*(5*x + 3)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(5*x + 14)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2375,1,122,0,1.433978," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{5} \sqrt{2} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 175 \, \sqrt{7} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 330 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{75 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/75*(2*sqrt(5)*sqrt(2)*(5*x + 3)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 175*sqrt(7)*(5*x + 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 330*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","B",0
2376,1,86,0,1.302679," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{7} {\left(15 \, x^{2} + 19 \, x + 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(101 \, x + 65\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/2*(33*sqrt(7)*(15*x^2 + 19*x + 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(101*x + 65)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
2377,1,101,0,1.523778," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{5709 \, \sqrt{7} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(7485 \, x^{2} + 9815 \, x + 3212\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{56 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/56*(5709*sqrt(7)*(45*x^3 + 87*x^2 + 56*x + 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(7485*x^2 + 9815*x + 3212)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
2378,1,116,0,0.937616," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{463881 \, \sqrt{7} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1824555 \, x^{3} + 3608883 \, x^{2} + 2378026 \, x + 521968\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{784 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/784*(463881*sqrt(7)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1824555*x^3 + 3608883*x^2 + 2378026*x + 521968)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
2379,1,131,0,1.814909," ","integrate((1-2*x)^(3/2)/(2+3*x)^5/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{145708761 \, \sqrt{7} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1719322065 \, x^{4} + 4546951839 \, x^{3} + 4508028900 \, x^{2} + 1985778980 \, x + 327908240\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43904 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"1/43904*(145708761*sqrt(7)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1719322065*x^4 + 4546951839*x^3 + 4508028900*x^2 + 1985778980*x + 327908240)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
2380,1,101,0,1.354325," ","integrate((1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{39459 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(108000 \, x^{4} + 83700 \, x^{3} - 118395 \, x^{2} - 129910 \, x - 31171\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{600000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/600000*(39459*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(108000*x^4 + 83700*x^3 - 118395*x^2 - 129910*x - 31171)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2381,1,96,0,0.872169," ","integrate((1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1029 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2700 \, x^{3} - 1845 \, x^{2} - 3610 \, x - 901\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{30000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/30000*(1029*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2700*x^3 - 1845*x^2 - 3610*x - 901)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2382,1,97,0,1.375894," ","integrate((1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{57 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(45 \, x^{2} + 145 \, x + 73\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/750*(57*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(45*x^2 + 145*x + 73)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2383,1,92,0,1.633158," ","integrate((1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 5 \, {\left(40 \, x + 13\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}\right)}}{375 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-2/375*(3*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 5*(40*x + 13)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2384,1,86,0,1.698970," ","integrate((1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{21 \, \sqrt{7} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(107 \, x + 62\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/3*(21*sqrt(7)*(25*x^2 + 30*x + 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(107*x + 62)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2385,1,101,0,1.429237," ","integrate((1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{507 \, \sqrt{7} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(7755 \, x^{2} + 9652 \, x + 2995\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"-1/6*(507*sqrt(7)*(75*x^3 + 140*x^2 + 87*x + 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(7755*x^2 + 9652*x + 2995)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
2386,1,116,0,0.953131," ","integrate((1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{122361 \, \sqrt{7} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(802125 \, x^{3} + 1533090 \, x^{2} + 975325 \, x + 206524\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{168 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"-1/168*(122361*sqrt(7)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(802125*x^3 + 1533090*x^2 + 975325*x + 206524)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
2387,1,131,0,1.591401," ","integrate((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{12740199 \, \sqrt{7} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(250551225 \, x^{4} + 645909120 \, x^{3} + 623901861 \, x^{2} + 267610802 \, x + 43006496\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2352 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"-1/2352*(12740199*sqrt(7)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(250551225*x^4 + 645909120*x^3 + 623901861*x^2 + 267610802*x + 43006496)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2388,1,87,0,1.155158," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{5376000000} \, {\left(82944000000 \, x^{6} + 97459200000 \, x^{5} - 52468992000 \, x^{4} - 85095638400 \, x^{3} + 9906627680 \, x^{2} + 29819034260 \, x - 679278531\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{3735929329}{5120000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/5376000000*(82944000000*x^6 + 97459200000*x^5 - 52468992000*x^4 - 85095638400*x^3 + 9906627680*x^2 + 29819034260*x - 679278531)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 3735929329/5120000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2389,1,82,0,1.321136," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{38400000} \, {\left(230400000 \, x^{5} + 94464000 \, x^{4} - 237187200 \, x^{3} - 61262560 \, x^{2} + 102523580 \, x + 9303927\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{105254149}{256000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/38400000*(230400000*x^5 + 94464000*x^4 - 237187200*x^3 - 61262560*x^2 + 102523580*x + 9303927)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 105254149/256000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2390,1,77,0,1.401997," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{960000} \, {\left(2304000 \, x^{4} - 931200 \, x^{3} - 1849760 \, x^{2} + 1108180 \, x + 355917\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1742279}{6400000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/960000*(2304000*x^4 - 931200*x^3 - 1849760*x^2 + 1108180*x + 355917)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1742279/6400000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2391,1,72,0,0.945581," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{9600} \, {\left(9600 \, x^{3} - 12640 \, x^{2} + 3020 \, x + 4443\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{14641}{64000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/9600*(9600*x^3 - 12640*x^2 + 3020*x + 4443)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 14641/64000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2392,1,107,0,1.214073," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{5400} \, {\left(2400 \, x^{2} - 5940 \, x + 8771\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + \frac{49}{81} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{250433}{324000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/5400*(2400*x^2 - 5940*x + 8771)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 49/81*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 250433/324000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2393,1,126,0,1.565340," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{3500 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2119 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 60 \, {\left(20 \, x^{2} - 79 \, x - 116\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1800 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/1800*(3500*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2119*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 60*(20*x^2 - 79*x - 116)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2394,1,147,0,1.403838," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{472 \, \sqrt{5} \sqrt{2} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 775 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(48 \, x^{2} + 435 \, x + 236\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1080 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/1080*(472*sqrt(5)*sqrt(2)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 775*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(48*x^2 + 435*x + 236)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2395,1,156,0,1.591354," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{32765 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 448 \, \sqrt{10} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(7689 \, x^{2} + 11106 \, x + 3856\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{9072 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/9072*(32765*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 448*sqrt(10)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(7689*x^2 + 11106*x + 3856)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2396,1,116,0,0.881164," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{219615 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(518715 \, x^{3} + 1059032 \, x^{2} + 723428 \, x + 164688\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{18816 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/18816*(219615*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(518715*x^3 + 1059032*x^2 + 723428*x + 164688)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2397,1,131,0,0.827431," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{55123365 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(390269835 \, x^{4} + 1058136330 \, x^{3} + 1076423732 \, x^{2} + 487066088 \, x + 82697568\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1317120 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/1317120*(55123365*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(390269835*x^4 + 1058136330*x^3 + 1076423732*x^2 + 487066088*x + 82697568)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2398,1,146,0,1.651616," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{1173842175 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(24931818675 \, x^{5} + 84218501340 \, x^{4} + 113834022672 \, x^{3} + 76960600672 \, x^{2} + 26026519504 \, x + 3522190656\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7375872 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/7375872*(1173842175*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(24931818675*x^5 + 84218501340*x^4 + 113834022672*x^3 + 76960600672*x^2 + 26026519504*x + 3522190656)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2399,1,92,0,0.821527," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1}{57344000000} \, {\left(3870720000000 \, x^{7} + 7105536000000 \, x^{6} + 808627200000 \, x^{5} - 5264367872000 \, x^{4} - 2347326614400 \, x^{3} + 1304824422880 \, x^{2} + 942468770660 \, x - 115416461871\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{355329559167}{163840000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/57344000000*(3870720000000*x^7 + 7105536000000*x^6 + 808627200000*x^5 - 5264367872000*x^4 - 2347326614400*x^3 + 1304824422880*x^2 + 942468770660*x - 115416461871)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 355329559167/163840000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2400,1,87,0,1.535588," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1}{358400000} \, {\left(9216000000 \, x^{6} + 10112000000 \, x^{5} - 6123776000 \, x^{4} - 8717155200 \, x^{3} + 1291331040 \, x^{2} + 2994263780 \, x - 104420943\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1104970911}{1024000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/358400000*(9216000000*x^6 + 10112000000*x^5 - 6123776000*x^4 - 8717155200*x^3 + 1291331040*x^2 + 2994263780*x - 104420943)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1104970911/1024000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2401,1,82,0,1.084488," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1}{2560000} \, {\left(25600000 \, x^{5} + 8448000 \, x^{4} - 25526400 \, x^{3} - 5162720 \, x^{2} + 10406460 \, x + 717399\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{30438639}{51200000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/2560000*(25600000*x^5 + 8448000*x^4 - 25526400*x^3 - 5162720*x^2 + 10406460*x + 717399)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 30438639/51200000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2402,1,77,0,1.256254," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1}{64000} \, {\left(256000 \, x^{4} - 124800 \, x^{3} - 177440 \, x^{2} + 116420 \, x + 29673\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{483153}{1280000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/64000*(256000*x^4 - 124800*x^3 - 177440*x^2 + 116420*x + 29673)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 483153/1280000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2403,1,112,0,1.459475," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{259200} \, {\left(432000 \, x^{3} - 607200 \, x^{2} + 230940 \, x + 59599\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{49}{243} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{1922677}{15552000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/259200*(432000*x^3 - 607200*x^2 + 230940*x + 59599)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 49/243*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1922677/15552000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2404,1,131,0,1.599689," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{322000 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 326717 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 60 \, {\left(7200 \, x^{3} - 13740 \, x^{2} + 17277 \, x + 21718\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{194400 \, {\left(3 \, x + 2\right)}}"," ",0,"1/194400*(322000*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 326717*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 60*(7200*x^3 - 13740*x^2 + 17277*x + 21718)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2405,1,146,0,1.645058," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{9725 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 6829 \, \sqrt{10} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(360 \, x^{3} - 1230 \, x^{2} - 3471 \, x - 1628\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3240 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/3240*(9725*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 6829*sqrt(10)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(360*x^3 - 1230*x^2 - 3471*x - 1628)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2406,1,161,0,0.946060," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{215 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20272 \, \sqrt{10} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(4320 \, x^{3} + 34341 \, x^{2} + 36234 \, x + 10304\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{27216 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/27216*(215*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20272*sqrt(10)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(4320*x^3 + 34341*x^2 + 36234*x + 10304)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2407,1,176,0,2.000178," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{3244595 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 125440 \, \sqrt{10} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(1790325 \, x^{3} + 4103592 \, x^{2} + 2947548 \, x + 677168\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1524096 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/1524096*(3244595*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 125440*sqrt(10)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(1790325*x^3 + 4103592*x^2 + 2947548*x + 677168)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2408,1,131,0,1.654636," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{2415765 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(17153435 \, x^{4} + 46327530 \, x^{3} + 47166452 \, x^{2} + 21361768 \, x + 3620448\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{439040 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/439040*(2415765*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(17153435*x^4 + 46327530*x^3 + 47166452*x^2 + 21361768*x + 3620448)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2409,1,146,0,1.730062," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{41068005 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(872316385 \, x^{5} + 2946673460 \, x^{4} + 3982356144 \, x^{3} + 2692519968 \, x^{2} + 910641904 \, x + 123208128\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2458624 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/2458624*(41068005*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(872316385*x^5 + 2946673460*x^4 + 3982356144*x^3 + 2692519968*x^2 + 910641904*x + 123208128)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2410,1,161,0,0.759492," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{1891543995 \, \sqrt{7} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(120526515645 \, x^{6} + 487483968610 \, x^{5} + 821723878536 \, x^{4} + 738910550592 \, x^{3} + 373848853744 \, x^{2} + 100906793184 \, x + 11351210112\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{34420736 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/34420736*(1891543995*sqrt(7)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(120526515645*x^6 + 487483968610*x^5 + 821723878536*x^4 + 738910550592*x^3 + 373848853744*x^2 + 100906793184*x + 11351210112)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
2411,1,97,0,0.959545," ","integrate((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{1}{137625600000} \, {\left(41287680000000 \, x^{8} + 102445056000000 \, x^{7} + 59625676800000 \, x^{6} - 46327577600000 \, x^{5} - 60250198784000 \, x^{4} - 5712426076800 \, x^{3} + 16445681555360 \, x^{2} + 6397508631020 \, x - 1496712721437\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{932023556783}{131072000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/137625600000*(41287680000000*x^8 + 102445056000000*x^7 + 59625676800000*x^6 - 46327577600000*x^5 - 60250198784000*x^4 - 5712426076800*x^3 + 16445681555360*x^2 + 6397508631020*x - 1496712721437)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 932023556783/131072000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2412,1,92,0,1.657618," ","integrate((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{1}{6881280000} \, {\left(774144000000 \, x^{7} + 1362124800000 \, x^{6} + 97008640000 \, x^{5} - 1013681408000 \, x^{4} - 413675529600 \, x^{3} + 252700365920 \, x^{2} + 169330465940 \, x - 22414998339\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{21331366001}{6553600000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/6881280000*(774144000000*x^7 + 1362124800000*x^6 + 97008640000*x^5 - 1013681408000*x^4 - 413675529600*x^3 + 252700365920*x^2 + 169330465940*x - 22414998339)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 21331366001/6553600000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2413,1,87,0,1.358983," ","integrate((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{1}{43008000} \, {\left(1843200000 \, x^{6} + 1879040000 \, x^{5} - 1272064000 \, x^{4} - 1600483200 \, x^{3} + 287177440 \, x^{2} + 540576580 \, x - 24901623\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{65547757}{40960000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/43008000*(1843200000*x^6 + 1879040000*x^5 - 1272064000*x^4 - 1600483200*x^3 + 287177440*x^2 + 540576580*x - 24901623)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 65547757/40960000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2414,1,82,0,1.103749," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{1}{307200} \, {\left(5120000 \, x^{5} + 1280000 \, x^{4} - 4905600 \, x^{3} - 748640 \, x^{2} + 1895020 \, x + 96003\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1771561}{2048000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/307200*(5120000*x^5 + 1280000*x^4 - 4905600*x^3 - 748640*x^2 + 1895020*x + 96003)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1771561/2048000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2415,1,117,0,0.967672," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","\frac{1}{3110400} \, {\left(20736000 \, x^{4} - 11836800 \, x^{3} - 11943840 \, x^{2} + 8506260 \, x + 2165117\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + \frac{49}{729} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{109715471}{186624000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/3110400*(20736000*x^4 - 11836800*x^3 - 11943840*x^2 + 8506260*x + 2165117)*sqrt(5*x + 3)*sqrt(-2*x + 1) + 49/729*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 109715471/186624000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2416,1,136,0,1.255893," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{1657600 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 660959 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 60 \, {\left(259200 \, x^{4} - 214560 \, x^{3} - 60348 \, x^{2} + 72849 \, x - 45658\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1866240 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/1866240*(1657600*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 660959*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 60*(259200*x^4 - 214560*x^3 - 60348*x^2 + 72849*x - 45658)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2417,1,157,0,1.462684," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{81733 \, \sqrt{5} \sqrt{2} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 87740 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 12 \, {\left(21600 \, x^{4} - 28980 \, x^{3} + 31731 \, x^{2} + 120534 \, x + 53204\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{23328 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/23328*(81733*sqrt(5)*sqrt(2)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 87740*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 12*(21600*x^4 - 28980*x^3 + 31731*x^2 + 120534*x + 53204)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2418,1,172,0,1.555057," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","\frac{307090 \, \sqrt{5} \sqrt{2} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 408665 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(32400 \, x^{4} - 93420 \, x^{3} - 420531 \, x^{2} - 391014 \, x - 107984\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{81648 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/81648*(307090*sqrt(5)*sqrt(2)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 408665*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(32400*x^4 - 93420*x^3 - 420531*x^2 - 391014*x - 107984)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2419,1,181,0,1.181413," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","\frac{3304795 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 5801600 \, \sqrt{10} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(3628800 \, x^{4} + 29475315 \, x^{3} + 45563928 \, x^{2} + 25998852 \, x + 5093072\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4572288 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"1/4572288*(3304795*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 5801600*sqrt(10)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(3628800*x^4 + 29475315*x^3 + 45563928*x^2 + 25998852*x + 5093072)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2420,1,196,0,1.406625," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{548577355 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 43904000 \, \sqrt{10} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(490413015 \, x^{4} + 1809469170 \, x^{3} + 2146957188 \, x^{2} + 1044006792 \, x + 180761312\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{320060160 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/320060160*(548577355*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 43904000*sqrt(10)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(490413015*x^4 + 1809469170*x^3 + 2146957188*x^2 + 1044006792*x + 180761312)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2421,1,146,0,1.191577," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7,x, algorithm=""fricas"")","-\frac{26573415 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(568572155 \, x^{5} + 1905431420 \, x^{4} + 2573967504 \, x^{3} + 1743189856 \, x^{2} + 589734736 \, x + 79536960\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7375872 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/7375872*(26573415*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(568572155*x^5 + 1905431420*x^4 + 2573967504*x^3 + 1743189856*x^2 + 589734736*x + 79536960)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2422,1,161,0,1.632429," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8,x, algorithm=""fricas"")","-\frac{983216355 \, \sqrt{7} {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(62659925205 \, x^{6} + 253441751890 \, x^{5} + 427105196104 \, x^{4} + 384048502848 \, x^{3} + 194338741616 \, x^{2} + 52456780256 \, x + 5897927808\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{103262208 \, {\left(2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right)}}"," ",0,"-1/103262208*(983216355*sqrt(7)*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(62659925205*x^6 + 253441751890*x^5 + 427105196104*x^4 + 384048502848*x^3 + 194338741616*x^2 + 52456780256*x + 5897927808)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)","A",0
2423,1,176,0,1.708811," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9,x, algorithm=""fricas"")","-\frac{319970490015 \, \sqrt{7} {\left(6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(61164463449195 \, x^{7} + 288163475473440 \, x^{6} + 581931572602156 \, x^{5} + 652979564561296 \, x^{4} + 439702534402320 \, x^{3} + 177688060285568 \, x^{2} + 39899303549504 \, x + 3840133416192\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11565367296 \, {\left(6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256\right)}}"," ",0,"-1/11565367296*(319970490015*sqrt(7)*(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^2 + 3072*x + 256)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(61164463449195*x^7 + 288163475473440*x^6 + 581931572602156*x^5 + 652979564561296*x^4 + 439702534402320*x^3 + 177688060285568*x^2 + 39899303549504*x + 3840133416192)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^2 + 3072*x + 256)","A",0
2424,1,87,0,1.686945," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{26880000000} \, {\left(248832000000 \, x^{6} + 311731200000 \, x^{5} - 147923712000 \, x^{4} - 275707382400 \, x^{3} + 23172376480 \, x^{2} + 98827130860 \, x - 920643741\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{12679836719}{25600000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/26880000000*(248832000000*x^6 + 311731200000*x^5 - 147923712000*x^4 - 275707382400*x^3 + 23172376480*x^2 + 98827130860*x - 920643741)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 12679836719/25600000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2425,1,82,0,1.751195," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{192000000} \, {\left(691200000 \, x^{5} + 338688000 \, x^{4} - 729302400 \, x^{3} - 233839520 \, x^{2} + 334643860 \, x + 39899709\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{368012183}{1280000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/192000000*(691200000*x^5 + 338688000*x^4 - 729302400*x^3 - 233839520*x^2 + 334643860*x + 39899709)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 368012183/1280000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2426,1,77,0,1.441170," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{4800000} \, {\left(6912000 \, x^{4} - 2217600 \, x^{3} - 6256480 \, x^{2} + 3384140 \, x + 1498491\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{6531217}{32000000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/4800000*(6912000*x^4 - 2217600*x^3 - 6256480*x^2 + 3384140*x + 1498491)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 6531217/32000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2427,1,72,0,0.903011," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{48000} \, {\left(28800 \, x^{3} - 35360 \, x^{2} + 2980 \, x + 21537\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{65219}{320000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/48000*(28800*x^3 - 35360*x^2 + 2980*x + 21537)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 65219/320000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2428,1,67,0,1.364796," ","integrate((1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{600} \, {\left(160 \, x^{2} - 380 \, x + 513\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1331}{4000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/600*(160*x^2 - 380*x + 513)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1331/4000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2429,1,102,0,1.119455," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{450} \, {\left(60 \, x - 269\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{49}{27} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + \frac{17687}{27000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/450*(60*x - 269)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 49/27*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 17687/27000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2430,1,127,0,1.329772," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{346 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4375 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(12 \, x + 253\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1350 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/1350*(346*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4375*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(12*x + 253)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2431,1,142,0,1.417695," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{32 \, \sqrt{5} \sqrt{2} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 15175 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 210 \, {\left(261 \, x + 188\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1080 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/1080*(32*sqrt(5)*sqrt(2)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 15175*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 210*(261*x + 188)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2432,1,101,0,1.239390," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{19965 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(15707 \, x^{2} + 21638 \, x + 7488\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{336 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/336*(19965*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(15707*x^2 + 21638*x + 7488)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2433,1,116,0,0.895102," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{4931355 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(11637735 \, x^{3} + 23794744 \, x^{2} + 16236916 \, x + 3699216\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{18816 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/18816*(4931355*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(11637735*x^3 + 23794744*x^2 + 16236916*x + 3699216)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2434,1,131,0,0.804257," ","integrate((1-2*x)^(5/2)/(2+3*x)^6/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1560604155 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(11048812245 \, x^{4} + 29956486710 \, x^{3} + 30475811404 \, x^{2} + 13788819736 \, x + 2341358496\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1317120 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/1317120*(1560604155*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(11048812245*x^4 + 29956486710*x^3 + 30475811404*x^2 + 13788819736*x + 2341358496)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2435,1,146,0,1.470187," ","integrate((1-2*x)^(5/2)/(2+3*x)^7/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{40175389815 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(853304772555 \, x^{5} + 2882422865340 \, x^{4} + 3896029345680 \, x^{3} + 2634024494432 \, x^{2} + 890768460368 \, x + 120549503808\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7375872 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/7375872*(40175389815*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(853304772555*x^5 + 2882422865340*x^4 + 3896029345680*x^3 + 2634024494432*x^2 + 890768460368*x + 120549503808)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2436,1,101,0,1.175690," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{1298595837 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(3456000000 \, x^{6} + 4043520000 \, x^{5} - 2530224000 \, x^{4} - 3673002400 \, x^{3} + 938891620 \, x^{2} + 1366129125 \, x + 168414751\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6400000000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/6400000000*(1298595837*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(3456000000*x^6 + 4043520000*x^5 - 2530224000*x^4 - 3673002400*x^3 + 938891620*x^2 + 1366129125*x + 168414751)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2437,1,96,0,1.233967," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{24319911 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(34560000 \, x^{5} + 12528000 \, x^{4} - 39487200 \, x^{3} - 4101140 \, x^{2} + 20337375 \, x + 6089453\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{160000000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/160000000*(24319911*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(34560000*x^5 + 12528000*x^4 - 39487200*x^3 - 4101140*x^2 + 20337375*x + 6089453)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2438,1,91,0,0.827245," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{236313 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(144000 \, x^{4} - 77600 \, x^{3} - 112620 \, x^{2} + 134625 \, x + 79699\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1600000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/1600000*(236313*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(144000*x^4 - 77600*x^3 - 112620*x^2 + 134625*x + 79699)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2439,1,86,0,1.353398," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2541 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(800 \, x^{3} - 1340 \, x^{2} + 1125 \, x + 943\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/20000*(2541*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(800*x^3 - 1340*x^2 + 1125*x + 943)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2440,1,81,0,1.209875," ","integrate((1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{363 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(20 \, x^{2} - 75 \, x - 149\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1000 \, {\left(5 \, x + 3\right)}}"," ",0,"1/1000*(363*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(20*x^2 - 75*x - 149)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2441,1,127,0,1.406832," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{169 \, \sqrt{5} \sqrt{2} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 6125 \, \sqrt{7} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(10 \, x - 357\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1125 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/1125*(169*sqrt(5)*sqrt(2)*(5*x + 3)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 6125*sqrt(7)*(5*x + 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(10*x - 357)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2442,1,142,0,1.351255," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{5} \sqrt{2} {\left(15 \, x^{2} + 19 \, x + 6\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 16625 \, \sqrt{7} {\left(15 \, x^{2} + 19 \, x + 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 30 \, {\left(3403 \, x + 2187\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{450 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/450*(8*sqrt(5)*sqrt(2)*(15*x^2 + 19*x + 6)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 16625*sqrt(7)*(15*x^2 + 19*x + 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 30*(3403*x + 2187)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
2443,1,101,0,1.385150," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1815 \, \sqrt{7} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(16657 \, x^{2} + 21843 \, x + 7148\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{8 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/8*(1815*sqrt(7)*(45*x^3 + 87*x^2 + 56*x + 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(16657*x^2 + 21843*x + 7148)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
2444,1,116,0,1.288439," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{147015 \, \sqrt{7} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(578245 \, x^{3} + 1143741 \, x^{2} + 753654 \, x + 165424\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{112 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/112*(147015*sqrt(7)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(578245*x^3 + 1143741*x^2 + 753654*x + 165424)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
2445,1,131,0,1.140128," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{46095555 \, \sqrt{7} {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(543914475 \, x^{4} + 1438446565 \, x^{3} + 1426133132 \, x^{2} + 628209228 \, x + 103735088\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6272 \, {\left(405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right)}}"," ",0,"1/6272*(46095555*sqrt(7)*(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(543914475*x^4 + 1438446565*x^3 + 1426133132*x^2 + 628209228*x + 103735088)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)","A",0
2446,1,146,0,1.007728," ","integrate((1-2*x)^(5/2)/(2+3*x)^6/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{17694048405 \, \sqrt{7} {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(626354259975 \, x^{5} + 2074037896035 \, x^{4} + 2746600901250 \, x^{3} + 1818284414692 \, x^{2} + 601741553688 \, x + 79638637088\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{439040 \, {\left(1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right)}}"," ",0,"1/439040*(17694048405*sqrt(7)*(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(626354259975*x^5 + 2074037896035*x^4 + 2746600901250*x^3 + 1818284414692*x^2 + 601741553688*x + 79638637088)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96)","A",0
2447,1,111,0,1.125732," ","integrate((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{264889779 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(1555200000 \, x^{6} + 1626480000 \, x^{5} - 1419228000 \, x^{4} - 1405199700 \, x^{3} + 865945995 \, x^{2} + 980658710 \, x + 210855251\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2400000000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/2400000000*(264889779*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(1555200000*x^6 + 1626480000*x^5 - 1419228000*x^4 - 1405199700*x^3 + 865945995*x^2 + 980658710*x + 210855251)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2448,1,106,0,1.362720," ","integrate((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2300529 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(6480000 \, x^{5} + 972000 \, x^{4} - 7724700 \, x^{3} + 3074745 \, x^{2} + 7876210 \, x + 2322001\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{24000000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/24000000*(2300529*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(6480000*x^5 + 972000*x^4 - 7724700*x^3 + 3074745*x^2 + 7876210*x + 2322001)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2449,1,101,0,1.420641," ","integrate((1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{10857 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(36000 \, x^{4} - 35100 \, x^{3} + 3585 \, x^{2} + 40930 \, x + 10633\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{300000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/300000*(10857*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(36000*x^4 - 35100*x^3 + 3585*x^2 + 40930*x + 10633)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2450,1,96,0,1.379032," ","integrate((1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{3003 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(900 \, x^{3} - 2715 \, x^{2} - 7970 \, x - 3707\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{15000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/15000*(3003*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(900*x^3 - 2715*x^2 - 7970*x - 3707)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2451,1,97,0,1.338270," ","integrate((1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{33 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 10 \, {\left(30 \, x^{2} + 190 \, x + 79\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{375 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/375*(33*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 10*(30*x^2 + 190*x + 79)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2452,1,142,0,1.405156," ","integrate((1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 6125 \, \sqrt{7} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 110 \, {\left(565 \, x + 328\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{375 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/375*(4*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 6125*sqrt(7)*(25*x^2 + 30*x + 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 110*(565*x + 328)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2453,1,101,0,1.361041," ","integrate((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1155 \, \sqrt{7} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(17667 \, x^{2} + 21988 \, x + 6823\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"-1/6*(1155*sqrt(7)*(75*x^3 + 140*x^2 + 87*x + 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(17667*x^2 + 21988*x + 6823)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
2454,1,116,0,1.134483," ","integrate((1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{39435 \, \sqrt{7} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 2 \, {\left(1809585 \, x^{3} + 3458634 \, x^{2} + 2200321 \, x + 465916\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{24 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"-1/24*(39435*sqrt(7)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 2*(1809585*x^3 + 3458634*x^2 + 2200321*x + 465916)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
2455,1,131,0,1.325252," ","integrate((1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{4083585 \, \sqrt{7} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(80308575 \, x^{4} + 207031680 \, x^{3} + 199977747 \, x^{2} + 85776638 \, x + 13784768\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{336 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"-1/336*(4083585*sqrt(7)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(80308575*x^4 + 207031680*x^3 + 199977747*x^2 + 85776638*x + 13784768)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2456,1,146,0,1.341106," ","integrate((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{1558263795 \, \sqrt{7} {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(91935354375 \, x^{5} + 298295199450 \, x^{4} + 386933096475 \, x^{3} + 250814924064 \, x^{2} + 81243850516 \, x + 10520317456\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{18816 \, {\left(2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right)}}"," ",0,"-1/18816*(1558263795*sqrt(7)*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(91935354375*x^5 + 298295199450*x^4 + 386933096475*x^3 + 250814924064*x^2 + 81243850516*x + 10520317456)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)","A",0
2457,1,161,0,1.359682," ","integrate((1-2*x)^(5/2)/(2+3*x)^6/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{704638763895 \, \sqrt{7} {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(124718063792625 \, x^{6} + 487807977825900 \, x^{5} + 794682454662945 \, x^{4} + 690189860794590 \, x^{3} + 337048538999244 \, x^{2} + 87747789308536 \, x + 9514465420576\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1317120 \, {\left(6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right)}}"," ",0,"-1/1317120*(704638763895*sqrt(7)*(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(124718063792625*x^6 + 487807977825900*x^5 + 794682454662945*x^4 + 690189860794590*x^3 + 337048538999244*x^2 + 87747789308536*x + 9514465420576)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288)","A",0
2458,1,77,0,1.966858," ","integrate((2+3*x)^4*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2560000} \, {\left(20736000 \, x^{4} + 82339200 \, x^{3} + 146144160 \, x^{2} + 163168620 \, x + 157419203\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1067352517}{51200000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/2560000*(20736000*x^4 + 82339200*x^3 + 146144160*x^2 + 163168620*x + 157419203)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1067352517/51200000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2459,1,72,0,1.109455," ","integrate((2+3*x)^3*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{5120} \, {\left(17280 \, x^{3} + 57888 \, x^{2} + 88092 \, x + 97295\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{677017}{102400} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/5120*(17280*x^3 + 57888*x^2 + 88092*x + 97295)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 677017/102400*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2460,1,67,0,1.125412," ","integrate((2+3*x)^2*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{1600} \, {\left(2400 \, x^{2} + 6660 \, x + 9401\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{68959}{32000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/1600*(2400*x^2 + 6660*x + 9401)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 68959/32000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2461,1,62,0,1.068222," ","integrate((2+3*x)*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{80} \, {\left(60 \, x + 143\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1177}{1600} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/80*(60*x + 143)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1177/1600*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2462,1,57,0,1.085677," ","integrate((3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{11}{40} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{1}{2} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"-11/40*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1/2*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2463,1,81,0,1.124099," ","integrate((3+5*x)^(1/2)/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{21} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{1}{6} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"1/21*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1/6*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2464,1,71,0,0.667333," ","integrate((3+5*x)^(1/2)/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{11 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{98 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/98*(11*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2465,1,86,0,1.227461," ","integrate((3+5*x)^(1/2)/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{451 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(87 \, x + 44\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2744 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/2744*(451*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(87*x + 44)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2466,1,101,0,1.353301," ","integrate((3+5*x)^(1/2)/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{15235 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(11685 \, x^{2} + 15930 \, x + 5296\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/38416*(15235*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(11685*x^2 + 15930*x + 5296)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2467,1,116,0,1.169600," ","integrate((3+5*x)^(1/2)/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{375265 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(883845 \, x^{3} + 1806120 \, x^{2} + 1230876 \, x + 278960\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{307328 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/307328*(375265*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(883845*x^3 + 1806120*x^2 + 1230876*x + 278960)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2468,1,77,0,0.850274," ","integrate((2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{512000} \, {\left(6912000 \, x^{4} + 26870400 \, x^{3} + 46785120 \, x^{2} + 51453140 \, x + 49229901\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{333216939}{10240000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/512000*(6912000*x^4 + 26870400*x^3 + 46785120*x^2 + 51453140*x + 49229901)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 333216939/10240000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2469,1,72,0,1.531955," ","integrate((2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{25600} \, {\left(144000 \, x^{3} + 469600 \, x^{2} + 698580 \, x + 760653\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{5274027}{512000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/25600*(144000*x^3 + 469600*x^2 + 698580*x + 760653)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 5274027/512000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2470,1,67,0,0.979318," ","integrate((2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{320} \, {\left(800 \, x^{2} + 2140 \, x + 2943\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{21417}{6400} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/320*(800*x^2 + 2140*x + 2943)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 21417/6400*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2471,1,62,0,0.925288," ","integrate((3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{5}{16} \, \sqrt{5 \, x + 3} {\left(4 \, x + 9\right)} \sqrt{-2 \, x + 1} - \frac{363}{320} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-5/16*sqrt(5*x + 3)*(4*x + 9)*sqrt(-2*x + 1) - 363/320*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2472,1,103,0,0.896955," ","integrate((3+5*x)^(3/2)/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{29}{72} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{1}{63} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{5}{6} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"-29/72*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 1/63*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 5/6*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2473,1,116,0,1.319179," ","integrate((3+5*x)^(3/2)/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{103 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 245 \, \sqrt{10} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{882 \, {\left(3 \, x + 2\right)}}"," ",0,"1/882*(103*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 245*sqrt(10)*(3*x + 2)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2474,1,86,0,1.255603," ","integrate((3+5*x)^(3/2)/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{363 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(169 \, x + 108\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2744 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/2744*(363*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(169*x + 108)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2475,1,101,0,1.190461," ","integrate((3+5*x)^(3/2)/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{5445 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(2195 \, x^{2} + 1830 \, x + 288\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/38416*(5445*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(2195*x^2 + 1830*x + 288)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2476,1,116,0,1.360516," ","integrate((3+5*x)^(3/2)/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{78045 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(172785 \, x^{3} + 346760 \, x^{2} + 226348 \, x + 48240\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{307328 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/307328*(78045*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(172785*x^3 + 346760*x^2 + 226348*x + 48240)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2477,1,131,0,1.203254," ","integrate((3+5*x)^(3/2)/(2+3*x)^6/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{13320285 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(93720915 \, x^{4} + 253769850 \, x^{3} + 257531412 \, x^{2} + 115804328 \, x + 19437408\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{21512960 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/21512960*(13320285*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(93720915*x^4 + 253769850*x^3 + 257531412*x^2 + 115804328*x + 19437408)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2478,1,82,0,1.141646," ","integrate((2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2457600} \, {\left(138240000 \, x^{5} + 615168000 \, x^{4} + 1229558400 \, x^{3} + 1505007200 \, x^{2} + 1362715220 \, x + 1202896557\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{2678359321}{16384000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/2457600*(138240000*x^5 + 615168000*x^4 + 1229558400*x^3 + 1505007200*x^2 + 1362715220*x + 1202896557)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 2678359321/16384000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2479,1,77,0,1.170164," ","integrate((2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{307200} \, {\left(6912000 \, x^{4} + 26294400 \, x^{3} + 44906720 \, x^{2} + 48658820 \, x + 46187289\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{104040277}{2048000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/307200*(6912000*x^4 + 26294400*x^3 + 44906720*x^2 + 48658820*x + 46187289)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 104040277/2048000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2480,1,72,0,1.250795," ","integrate((2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3072} \, {\left(28800 \, x^{3} + 91360 \, x^{2} + 132868 \, x + 142713\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{328757}{20480} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/3072*(28800*x^3 + 91360*x^2 + 132868*x + 142713)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 328757/20480*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2481,1,73,0,1.433890," ","integrate((3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{192} \, {\left(800 \, x^{2} + 2060 \, x + 2763\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{1331}{256} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/192*(800*x^2 + 2060*x + 2763)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 1331/256*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2482,1,108,0,1.376079," ","integrate((3+5*x)^(5/2)/(2+3*x)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{5}{144} \, {\left(60 \, x + 127\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{3035}{1728} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + \frac{1}{189} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-5/144*(60*x + 127)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 3035/1728*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 1/189*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2483,1,127,0,1.158206," ","integrate((3+5*x)^(5/2)/(2+3*x)^2/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{6125 \, \sqrt{5} \sqrt{2} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 692 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 84 \, {\left(525 \, x + 352\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{10584 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/10584*(6125*sqrt(5)*sqrt(2)*(3*x + 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 692*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 84*(525*x + 352)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2484,1,136,0,1.285711," ","integrate((3+5*x)^(5/2)/(2+3*x)^3/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{17687 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 34300 \, \sqrt{10} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 42 \, {\left(927 \, x + 604\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{74088 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/74088*(17687*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 34300*sqrt(10)*(9*x^2 + 12*x + 4)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 42*(927*x + 604)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2485,1,101,0,1.256671," ","integrate((3+5*x)^(5/2)/(2+3*x)^4/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{19965 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(37685 \, x^{2} + 48170 \, x + 15408\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{115248 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/115248*(19965*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(37685*x^2 + 48170*x + 15408)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2486,1,116,0,1.305120," ","integrate((3+5*x)^(5/2)/(2+3*x)^5/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{19965 \, \sqrt{7} {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(12945 \, x^{3} + 6920 \, x^{2} - 6484 \, x - 3600\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{131712 \, {\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)}}"," ",0,"-1/131712*(19965*sqrt(7)*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(12945*x^3 + 6920*x^2 - 6484*x - 3600)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)","A",0
2487,1,131,0,1.161540," ","integrate((3+5*x)^(5/2)/(2+3*x)^6/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{13995465 \, \sqrt{7} {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(87703335 \, x^{4} + 231277650 \, x^{3} + 222865988 \, x^{2} + 93291272 \, x + 14330592\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{64538880 \, {\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)}}"," ",0,"-1/64538880*(13995465*sqrt(7)*(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(87703335*x^4 + 231277650*x^3 + 222865988*x^2 + 93291272*x + 14330592)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)","A",0
2488,1,146,0,1.357610," ","integrate((3+5*x)^(5/2)/(2+3*x)^7/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{788597535 \, \sqrt{7} {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(16516390995 \, x^{5} + 55658284380 \, x^{4} + 74931979536 \, x^{3} + 50261760608 \, x^{2} + 16771747280 \, x + 2225100096\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1807088640 \, {\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)}}"," ",0,"-1/1807088640*(788597535*sqrt(7)*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(16516390995*x^5 + 55658284380*x^4 + 74931979536*x^3 + 50261760608*x^2 + 16771747280*x + 2225100096)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)","A",0
2489,1,72,0,1.030193," ","integrate((2+3*x)^4/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{3}{128000} \, {\left(86400 \, x^{3} + 297120 \, x^{2} + 462540 \, x + 518491\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{10866247}{2560000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-3/128000*(86400*x^3 + 297120*x^2 + 462540*x + 518491)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 10866247/2560000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2490,1,67,0,1.136274," ","integrate((2+3*x)^3/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{9}{1600} \, {\left(160 \, x^{2} + 460 \, x + 667\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{44437}{32000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-9/1600*(160*x^2 + 460*x + 667)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 44437/32000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2491,1,62,0,1.207708," ","integrate((2+3*x)^2/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{3}{400} \, {\left(60 \, x + 151\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{3827}{8000} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-3/400*(60*x + 151)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 3827/8000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2492,1,57,0,1.252398," ","integrate((2+3*x)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{37}{200} \, \sqrt{10} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - \frac{3}{10} \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}"," ",0,"-37/200*sqrt(10)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 3/10*sqrt(5*x + 3)*sqrt(-2*x + 1)","A",0
2493,1,46,0,1.310028," ","integrate(1/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{10} \, \sqrt{5} \sqrt{2} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/10*sqrt(5)*sqrt(2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","B",0
2494,1,40,0,1.468514," ","integrate(1/(2+3*x)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{7} \, \sqrt{7} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right)"," ",0,"-1/7*sqrt(7)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))","A",0
2495,1,71,0,1.473525," ","integrate(1/(2+3*x)^2/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{37 \, \sqrt{7} {\left(3 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{98 \, {\left(3 \, x + 2\right)}}"," ",0,"-1/98*(37*sqrt(7)*(3*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*sqrt(5*x + 3)*sqrt(-2*x + 1))/(3*x + 2)","A",0
2496,1,86,0,1.358848," ","integrate(1/(2+3*x)^3/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{3827 \, \sqrt{7} {\left(9 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 42 \, {\left(333 \, x + 236\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2744 \, {\left(9 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/2744*(3827*sqrt(7)*(9*x^2 + 12*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 42*(333*x + 236)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(9*x^2 + 12*x + 4)","A",0
2497,1,101,0,1.586945," ","integrate(1/(2+3*x)^4/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{222185 \, \sqrt{7} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 126 \, {\left(19415 \, x^{2} + 26750 \, x + 9248\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"-1/38416*(222185*sqrt(7)*(27*x^3 + 54*x^2 + 36*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 126*(19415*x^2 + 26750*x + 9248)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(27*x^3 + 54*x^2 + 36*x + 8)","A",0
2498,1,86,0,1.427997," ","integrate((2+3*x)^4/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1576113 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(237600 \, x^{3} + 849420 \, x^{2} + 1477575 \, x + 632101\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1760000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/1760000*(1576113*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(237600*x^3 + 849420*x^2 + 1477575*x + 632101)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2499,1,81,0,1.296939," ","integrate((2+3*x)^3/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{27423 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(5940 \, x^{2} + 19305 \, x + 9451\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{88000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/88000*(27423*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(5940*x^2 + 19305*x + 9451)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2500,1,76,0,0.786434," ","integrate((2+3*x)^2/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1353 \, \sqrt{10} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(495 \, x + 301\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11000 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/11000*(1353*sqrt(10)*(5*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(495*x + 301)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2501,1,77,0,0.706315," ","integrate((2+3*x)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{33 \, \sqrt{5} \sqrt{2} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{550 \, {\left(5 \, x + 3\right)}}"," ",0,"-1/550*(33*sqrt(5)*sqrt(2)*(5*x + 3)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","B",0
2502,1,16,0,1.278816," ","integrate(1/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-2 \, x + 1}}{11 \, \sqrt{5 \, x + 3}}"," ",0,"-2/11*sqrt(-2*x + 1)/sqrt(5*x + 3)","A",0
2503,1,71,0,1.219316," ","integrate(1/(2+3*x)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{7} {\left(5 \, x + 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 70 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{77 \, {\left(5 \, x + 3\right)}}"," ",0,"1/77*(33*sqrt(7)*(5*x + 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 70*sqrt(5*x + 3)*sqrt(-2*x + 1))/(5*x + 3)","A",0
2504,1,86,0,1.428166," ","integrate(1/(2+3*x)^2/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{3531 \, \sqrt{7} {\left(15 \, x^{2} + 19 \, x + 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1545 \, x + 997\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1078 \, {\left(15 \, x^{2} + 19 \, x + 6\right)}}"," ",0,"1/1078*(3531*sqrt(7)*(15*x^2 + 19*x + 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1545*x + 997)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(15*x^2 + 19*x + 6)","A",0
2505,1,101,0,1.343169," ","integrate(1/(2+3*x)^3/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{620631 \, \sqrt{7} {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(813735 \, x^{2} + 1067061 \, x + 349252\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{30184 \, {\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)}}"," ",0,"1/30184*(620631*sqrt(7)*(45*x^3 + 87*x^2 + 56*x + 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(813735*x^2 + 1067061*x + 349252)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(45*x^3 + 87*x^2 + 56*x + 12)","A",0
2506,1,116,0,0.895997," ","integrate(1/(2+3*x)^4/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","\frac{50776275 \, \sqrt{7} {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(199715625 \, x^{3} + 395028225 \, x^{2} + 260298990 \, x + 57135248\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{422576 \, {\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)}}"," ",0,"1/422576*(50776275*sqrt(7)*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(199715625*x^3 + 395028225*x^2 + 260298990*x + 57135248)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)","A",0
2507,1,101,0,1.116431," ","integrate((2+3*x)^5/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{167835591 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(117612000 \, x^{4} + 502791300 \, x^{3} + 1030526145 \, x^{2} + 795297410 \, x + 199549721\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{290400000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/290400000*(167835591*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(117612000*x^4 + 502791300*x^3 + 1030526145*x^2 + 795297410*x + 199549721)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2508,1,96,0,1.226886," ","integrate((2+3*x)^4/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{2950101 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2940300 \, x^{3} + 11712195 \, x^{2} + 10891910 \, x + 2953931\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14520000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/14520000*(2950101*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2940300*x^3 + 11712195*x^2 + 10891910*x + 2953931)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2509,1,91,0,1.160424," ","integrate((2+3*x)^3/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{29403 \, \sqrt{10} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(49005 \, x^{2} + 60010 \, x + 18373\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363000 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/363000*(29403*sqrt(10)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(49005*x^2 + 60010*x + 18373)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2510,1,92,0,1.298157," ","integrate((2+3*x)^2/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{3267 \, \sqrt{5} \sqrt{2} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(1010 \, x + 617\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{90750 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/90750*(3267*sqrt(5)*sqrt(2)*(25*x^2 + 30*x + 9)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(1010*x + 617)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2511,1,33,0,1.351920," ","integrate((2+3*x)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(103 \, x + 64\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-2/363*(103*x + 64)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9)","A",0
2512,1,33,0,1.247561," ","integrate(1/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(20 \, x + 23\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-2/363*(20*x + 23)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9)","A",0
2513,1,86,0,1.323670," ","integrate(1/(2+3*x)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{3267 \, \sqrt{7} {\left(25 \, x^{2} + 30 \, x + 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 70 \, {\left(475 \, x + 274\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2541 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"-1/2541*(3267*sqrt(7)*(25*x^2 + 30*x + 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 70*(475*x + 274)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(25*x^2 + 30*x + 9)","A",0
2514,1,101,0,0.914732," ","integrate(1/(2+3*x)^2/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{578259 \, \sqrt{7} {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1263525 \, x^{2} + 1572580 \, x + 487909\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{35574 \, {\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)}}"," ",0,"-1/35574*(578259*sqrt(7)*(75*x^3 + 140*x^2 + 87*x + 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1263525*x^2 + 1572580*x + 487909)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(75*x^3 + 140*x^2 + 87*x + 18)","A",0
2515,1,116,0,1.252799," ","integrate(1/(2+3*x)^3/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{142398729 \, \sqrt{7} {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(933479325 \, x^{3} + 1784145090 \, x^{2} + 1135041037 \, x + 240342364\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{996072 \, {\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)}}"," ",0,"-1/996072*(142398729*sqrt(7)*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(933479325*x^3 + 1784145090*x^2 + 1135041037*x + 240342364)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)","A",0
2516,1,131,0,1.350662," ","integrate(1/(2+3*x)^4/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","-\frac{14994762255 \, \sqrt{7} {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(294889892625 \, x^{4} + 760212086400 \, x^{3} + 734310313245 \, x^{2} + 314968389410 \, x + 50617099616\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{13945008 \, {\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)}}"," ",0,"-1/13945008*(14994762255*sqrt(7)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(294889892625*x^4 + 760212086400*x^3 + 734310313245*x^2 + 314968389410*x + 50617099616)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)","A",0
2517,1,208,0,1.569718," ","integrate(1/(f*x+e)/(b*x+a)^(1/2)/(b*f*x-a*f+2*b*e)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-f} \log\left(-\frac{b^{2} f^{2} x^{2} + 2 \, b^{2} e f x - b^{2} e^{2} + 4 \, a b e f - 2 \, a^{2} f^{2} + 2 \, \sqrt{b f x + 2 \, b e - a f} {\left(b e - a f\right)} \sqrt{b x + a} \sqrt{-f}}{f^{2} x^{2} + 2 \, e f x + e^{2}}\right)}{2 \, {\left(b e f - a f^{2}\right)}}, \frac{\sqrt{f} \arctan\left(-\frac{\sqrt{b f x + 2 \, b e - a f} {\left(b e - a f\right)} \sqrt{b x + a} \sqrt{f}}{b^{2} f^{2} x^{2} + 2 \, b^{2} e f x + 2 \, a b e f - a^{2} f^{2}}\right)}{b e f - a f^{2}}\right]"," ",0,"[1/2*sqrt(-f)*log(-(b^2*f^2*x^2 + 2*b^2*e*f*x - b^2*e^2 + 4*a*b*e*f - 2*a^2*f^2 + 2*sqrt(b*f*x + 2*b*e - a*f)*(b*e - a*f)*sqrt(b*x + a)*sqrt(-f))/(f^2*x^2 + 2*e*f*x + e^2))/(b*e*f - a*f^2), sqrt(f)*arctan(-sqrt(b*f*x + 2*b*e - a*f)*(b*e - a*f)*sqrt(b*x + a)*sqrt(f)/(b^2*f^2*x^2 + 2*b^2*e*f*x + 2*a*b*e*f - a^2*f^2))/(b*e*f - a*f^2)]","A",0
2518,1,96,0,0.722328," ","integrate((2+3*x)^5*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{35439958001 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(124416000 \, x^{5} + 613267200 \, x^{4} + 1429191360 \, x^{3} + 2297649240 \, x^{2} + 3810769458 \, x - 5389783159\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{102400000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/102400000*(35439958001*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(124416000*x^5 + 613267200*x^4 + 1429191360*x^3 + 2297649240*x^2 + 3810769458*x - 5389783159)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2519,1,91,0,1.331896," ","integrate((2+3*x)^4*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{92108287 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(518400 \, x^{4} + 2283840 \, x^{3} + 5020200 \, x^{2} + 9587886 \, x - 14050073\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1024000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/1024000*(92108287*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(518400*x^4 + 2283840*x^3 + 5020200*x^2 + 9587886*x - 14050073)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2520,1,86,0,1.352752," ","integrate((2+3*x)^3*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{1463447 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(14400 \, x^{3} + 57960 \, x^{2} + 142686 \, x - 224833\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{64000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/64000*(1463447*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(14400*x^3 + 57960*x^2 + 142686*x - 224833)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2521,1,81,0,1.235807," ","integrate((2+3*x)^2*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{17951 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(360 \, x^{2} + 1518 \, x - 2809\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3200 \, {\left(2 \, x - 1\right)}}"," ",0,"1/3200*(17951*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(360*x^2 + 1518*x - 2809)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2522,1,76,0,1.335316," ","integrate((2+3*x)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{103 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(6 \, x - 17\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{80 \, {\left(2 \, x - 1\right)}}"," ",0,"1/80*(103*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(6*x - 17)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2523,1,76,0,1.181741," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 4 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4 \, {\left(2 \, x - 1\right)}}"," ",0,"1/4*(sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 4*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","B",0
2524,1,70,0,1.010345," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{\sqrt{7} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{49 \, {\left(2 \, x - 1\right)}}"," ",0,"1/49*(sqrt(7)*(2*x - 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2525,1,82,0,1.288471," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{29 \, \sqrt{7} {\left(6 \, x^{2} + x - 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(18 \, x + 5\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{686 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"-1/686*(29*sqrt(7)*(6*x^2 + x - 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(18*x + 5)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2526,1,101,0,1.386869," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{1585 \, \sqrt{7} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(90 \, x^{2} - 405 \, x - 212\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{19208 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/19208*(1585*sqrt(7)*(18*x^3 + 15*x^2 - 4*x - 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(90*x^2 - 405*x - 212)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2527,1,116,0,0.996539," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{7435 \, \sqrt{7} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(10170 \, x^{3} + 8055 \, x^{2} - 3114 \, x - 2512\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/38416*(7435*sqrt(7)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(10170*x^3 + 8055*x^2 - 3114*x - 2512)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2528,1,131,0,1.319614," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{1244755 \, \sqrt{7} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(5791230 \, x^{4} + 8897265 \, x^{3} + 2075184 \, x^{2} - 2239092 \, x - 917264\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2151296 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/2151296*(1244755*sqrt(7)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(5791230*x^4 + 8897265*x^3 + 2075184*x^2 - 2239092*x - 917264)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2529,1,96,0,1.292491," ","integrate((2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{11199264087 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(41472000 \, x^{5} + 200966400 \, x^{4} + 461171520 \, x^{3} + 732415080 \, x^{2} + 1206337246 \, x - 1702927233\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20480000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/20480000*(11199264087*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(41472000*x^5 + 200966400*x^4 + 461171520*x^3 + 732415080*x^2 + 1206337246*x - 1702927233)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2530,1,91,0,1.384292," ","integrate((2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{145708761 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(864000 \, x^{4} + 3729600 \, x^{3} + 8057880 \, x^{2} + 15218818 \, x - 22217679\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1024000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/1024000*(145708761*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(864000*x^4 + 3729600*x^3 + 8057880*x^2 + 15218818*x - 22217679)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2531,1,86,0,1.166214," ","integrate((2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{463881 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(4800 \, x^{3} + 18840 \, x^{2} + 45538 \, x - 71199\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12800 \, {\left(2 \, x - 1\right)}}"," ",0,"1/12800*(463881*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(4800*x^3 + 18840*x^2 + 45538*x - 71199)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2532,1,81,0,1.283400," ","integrate((2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{5709 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(120 \, x^{2} + 490 \, x - 891\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{640 \, {\left(2 \, x - 1\right)}}"," ",0,"1/640*(5709*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(120*x^2 + 490*x - 891)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2533,1,82,0,0.941175," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(10 \, x - 27\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{16 \, {\left(2 \, x - 1\right)}}"," ",0,"1/16*(33*sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(10*x - 27)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2534,1,122,0,1.097272," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{245 \, \sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 4 \, \sqrt{7} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 924 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{588 \, {\left(2 \, x - 1\right)}}"," ",0,"1/588*(245*sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 4*sqrt(7)*(2*x - 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 924*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","B",0
2535,1,82,0,1.362679," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{33 \, \sqrt{7} {\left(6 \, x^{2} + x - 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(64 \, x + 45\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{686 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/686*(33*sqrt(7)*(6*x^2 + x - 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(64*x + 45)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2536,1,101,0,1.270913," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{825 \, \sqrt{7} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(2550 \, x^{2} + 2245 \, x + 396\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{19208 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/19208*(825*sqrt(7)*(18*x^3 + 15*x^2 - 4*x - 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(2550*x^2 + 2245*x + 396)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2537,1,116,0,1.211376," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{2805 \, \sqrt{7} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(2490 \, x^{3} + 6135 \, x^{2} + 3782 \, x + 576\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/38416*(2805*sqrt(7)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(2490*x^3 + 6135*x^2 + 3782*x + 576)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2538,1,131,0,1.283397," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{279015 \, \sqrt{7} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(917190 \, x^{4} + 1188045 \, x^{3} - 60048 \, x^{2} - 538276 \, x - 163152\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2151296 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/2151296*(279015*sqrt(7)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(917190*x^4 + 1188045*x^3 - 60048*x^2 - 538276*x - 163152)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2539,1,101,0,1.362194," ","integrate((2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{107121749031 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(276480000 \, x^{6} + 1479168000 \, x^{5} + 3687379200 \, x^{4} + 5945485120 \, x^{3} + 7755469800 \, x^{2} + 11734056318 \, x - 16267424049\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{32768000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/32768000*(107121749031*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(276480000*x^6 + 1479168000*x^5 + 3687379200*x^4 + 5945485120*x^3 + 7755469800*x^2 + 11734056318*x - 16267424049)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2540,1,96,0,1.286798," ","integrate((2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{3538809681 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(13824000 \, x^{5} + 65836800 \, x^{4} + 148751040 \, x^{3} + 233394520 \, x^{2} + 381820658 \, x - 538018839\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4096000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/4096000*(3538809681*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(13824000*x^5 + 65836800*x^4 + 148751040*x^3 + 233394520*x^2 + 381820658*x - 538018839)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2541,1,91,0,1.286248," ","integrate((2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{9219111 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(57600 \, x^{4} + 243520 \, x^{3} + 517096 \, x^{2} + 966014 \, x - 1405233\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{40960 \, {\left(2 \, x - 1\right)}}"," ",0,"1/40960*(9219111*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(57600*x^4 + 243520*x^3 + 517096*x^2 + 966014*x - 1405233)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2542,1,92,0,1.246622," ","integrate((2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{29403 \, \sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(1600 \, x^{3} + 6120 \, x^{2} + 14526 \, x - 22545\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{512 \, {\left(2 \, x - 1\right)}}"," ",0,"1/512*(29403*sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(1600*x^3 + 6120*x^2 + 14526*x - 22545)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2543,1,87,0,1.318869," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","\frac{1815 \, \sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(200 \, x^{2} + 790 \, x - 1413\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{128 \, {\left(2 \, x - 1\right)}}"," ",0,"1/128*(1815*sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(200*x^2 + 790*x - 1413)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2544,1,127,0,1.303343," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x),x, algorithm=""fricas"")","\frac{23275 \, \sqrt{5} \sqrt{2} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 16 \, \sqrt{7} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 84 \, {\left(350 \, x - 901\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7056 \, {\left(2 \, x - 1\right)}}"," ",0,"1/7056*(23275*sqrt(5)*sqrt(2)*(2*x - 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 16*sqrt(7)*(2*x - 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 84*(350*x - 901)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2545,1,136,0,1.334230," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{8575 \, \sqrt{5} \sqrt{2} {\left(6 \, x^{2} + x - 2\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 338 \, \sqrt{7} {\left(6 \, x^{2} + x - 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 84 \, {\left(1091 \, x + 725\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12348 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"1/12348*(8575*sqrt(5)*sqrt(2)*(6*x^2 + x - 2)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 338*sqrt(7)*(6*x^2 + x - 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 84*(1091*x + 725)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2546,1,101,0,1.261971," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{1815 \, \sqrt{7} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(8110 \, x^{2} + 11525 \, x + 4068\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{19208 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"1/19208*(1815*sqrt(7)*(18*x^3 + 15*x^2 - 4*x - 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(8110*x^2 + 11525*x + 4068)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2547,1,116,0,1.415114," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{1815 \, \sqrt{7} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(24670 \, x^{3} + 37405 \, x^{2} + 17666 \, x + 2448\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38416 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/38416*(1815*sqrt(7)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(24670*x^3 + 37405*x^2 + 17666*x + 2448)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2548,1,131,0,1.633803," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{168795 \, \sqrt{7} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(1002930 \, x^{4} + 2578615 \, x^{3} + 2184144 \, x^{2} + 687828 \, x + 53136\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2151296 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/2151296*(168795*sqrt(7)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(1002930*x^4 + 2578615*x^3 + 2184144*x^2 + 687828*x + 53136)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2549,1,146,0,1.098694," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^6,x, algorithm=""fricas"")","-\frac{17371365 \, \sqrt{7} {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(115230870 \, x^{5} + 180017865 \, x^{4} - 19738914 \, x^{3} - 164918884 \, x^{2} - 95331368 \, x - 16456032\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{150590720 \, {\left(486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right)}}"," ",0,"-1/150590720*(17371365*sqrt(7)*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(115230870*x^5 + 180017865*x^4 - 19738914*x^3 - 164918884*x^2 - 95331368*x - 16456032)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)","A",0
2550,1,91,0,1.589370," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{3202057551 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(17107200 \, x^{4} + 76887360 \, x^{3} + 171939240 \, x^{2} + 332129358 \, x - 488641609\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{56320000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/56320000*(3202057551*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(17107200*x^4 + 76887360*x^3 + 171939240*x^2 + 332129358*x - 488641609)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2551,1,86,0,1.640611," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{2031051 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(19008 \, x^{3} + 78408 \, x^{2} + 196614 \, x - 312365\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{140800 \, {\left(2 \, x - 1\right)}}"," ",0,"1/140800*(2031051*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(19008*x^3 + 78408*x^2 + 196614*x - 312365)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2552,1,81,0,0.998615," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{620631 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(11880 \, x^{2} + 51678 \, x - 97409\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{176000 \, {\left(2 \, x - 1\right)}}"," ",0,"1/176000*(620631*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(11880*x^2 + 51678*x - 97409)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2553,1,76,0,1.375615," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{3531 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(198 \, x - 589\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4400 \, {\left(2 \, x - 1\right)}}"," ",0,"1/4400*(3531*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(198*x - 589)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2554,1,71,0,1.541510," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{33 \, \sqrt{10} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 140 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{220 \, {\left(2 \, x - 1\right)}}"," ",0,"1/220*(33*sqrt(10)*(2*x - 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 140*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","B",0
2555,1,23,0,1.378855," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11 \, {\left(2 \, x - 1\right)}}"," ",0,"-2/11*sqrt(5*x + 3)*sqrt(-2*x + 1)/(2*x - 1)","A",0
2556,1,71,0,0.892092," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{33 \, \sqrt{7} {\left(2 \, x - 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 28 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{539 \, {\left(2 \, x - 1\right)}}"," ",0,"-1/539*(33*sqrt(7)*(2*x - 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 28*sqrt(5*x + 3)*sqrt(-2*x + 1))/(2*x - 1)","A",0
2557,1,82,0,1.027193," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1353 \, \sqrt{7} {\left(6 \, x^{2} + x - 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(174 \, x - 115\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7546 \, {\left(6 \, x^{2} + x - 2\right)}}"," ",0,"-1/7546*(1353*sqrt(7)*(6*x^2 + x - 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(174*x - 115)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(6*x^2 + x - 2)","A",0
2558,1,101,0,1.480513," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{137115 \, \sqrt{7} {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(70110 \, x^{2} + 13785 \, x - 25204\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{211288 \, {\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)}}"," ",0,"-1/211288*(137115*sqrt(7)*(18*x^3 + 15*x^2 - 4*x - 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(70110*x^2 + 13785*x - 25204)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(18*x^3 + 15*x^2 - 4*x - 4)","A",0
2559,1,116,0,1.256253," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{1125795 \, \sqrt{7} {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1767690 \, x^{3} + 1549935 \, x^{2} - 377658 \, x - 421184\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{422576 \, {\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)}}"," ",0,"-1/422576*(1125795*sqrt(7)*(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1767690*x^3 + 1549935*x^2 - 377658*x - 421184)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)","A",0
2560,1,131,0,1.405183," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^5/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{274145685 \, \sqrt{7} {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1293749010 \, x^{4} + 1998242055 \, x^{3} + 482249808 \, x^{2} - 491393004 \, x - 205593328\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{23664256 \, {\left(162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right)}}"," ",0,"-1/23664256*(274145685*sqrt(7)*(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1293749010*x^4 + 1998242055*x^3 + 482249808*x^2 - 491393004*x - 205593328)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16)","A",0
2561,1,97,0,1.358396," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{352281699 \, \sqrt{10} {\left(10 \, x^{2} + x - 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(15681600 \, x^{4} + 75663720 \, x^{3} + 208989990 \, x^{2} - 169670279 \, x - 162727423\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{38720000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/38720000*(352281699*sqrt(10)*(10*x^2 + x - 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(15681600*x^4 + 75663720*x^3 + 208989990*x^2 - 169670279*x - 162727423)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2562,1,92,0,1.311626," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{4289571 \, \sqrt{10} {\left(10 \, x^{2} + x - 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(392040 \, x^{3} + 1992870 \, x^{2} - 2323271 \, x - 2026687\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1936000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/1936000*(4289571*sqrt(10)*(10*x^2 + x - 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(392040*x^3 + 1992870*x^2 - 2323271*x - 2026687)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2563,1,87,0,1.359408," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{120879 \, \sqrt{10} {\left(10 \, x^{2} + x - 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(32670 \, x^{2} - 82499 \, x - 61243\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{242000 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/242000*(120879*sqrt(10)*(10*x^2 + x - 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(32670*x^2 - 82499*x - 61243)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2564,1,82,0,1.386141," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1089 \, \sqrt{10} {\left(10 \, x^{2} + x - 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(1229 \, x + 733\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{12100 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/12100*(1089*sqrt(10)*(10*x^2 + x - 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(1229*x + 733)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2565,1,31,0,1.068492," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{121 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"-2/121*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)","A",0
2566,1,31,0,1.394324," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{121 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"-2/121*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)","A",0
2567,1,82,0,1.382526," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{1089 \, \sqrt{7} {\left(10 \, x^{2} + x - 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(370 \, x - 163\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5929 \, {\left(10 \, x^{2} + x - 3\right)}}"," ",0,"1/5929*(1089*sqrt(7)*(10*x^2 + x - 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(370*x - 163)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(10*x^2 + x - 3)","A",0
2568,1,101,0,1.384883," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{120879 \, \sqrt{7} {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(106410 \, x^{2} + 15821 \, x - 34205\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{83006 \, {\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)}}"," ",0,"1/83006*(120879*sqrt(7)*(30*x^3 + 23*x^2 - 7*x - 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(106410*x^2 + 15821*x - 34205)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(30*x^3 + 23*x^2 - 7*x - 6)","A",0
2569,1,116,0,0.761363," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{21447855 \, \sqrt{7} {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(56260350 \, x^{3} + 45655035 \, x^{2} - 12730165 \, x - 12072596\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2324168 \, {\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)}}"," ",0,"1/2324168*(21447855*sqrt(7)*(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(56260350*x^3 + 45655035*x^2 - 12730165*x - 12072596)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)","A",0
2570,1,131,0,1.281510," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{251629785 \, \sqrt{7} {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1979479350 \, x^{4} + 2925598635 \, x^{3} + 622325745 \, x^{2} - 723664682 \, x - 283149136\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4648336 \, {\left(270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right)}}"," ",0,"1/4648336*(251629785*sqrt(7)*(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1979479350*x^4 + 2925598635*x^3 + 622325745*x^2 - 723664682*x - 283149136)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24)","A",0
2571,1,111,0,0.834415," ","integrate((2+3*x)^5/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{444504753 \, \sqrt{10} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(194059800 \, x^{4} + 1128781170 \, x^{3} - 612106475 \, x^{2} - 1785872944 \, x - 632498543\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{319440000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/319440000*(444504753*sqrt(10)*(50*x^3 + 35*x^2 - 12*x - 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(194059800*x^4 + 1128781170*x^3 - 612106475*x^2 - 1785872944*x - 632498543)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2572,1,106,0,1.565593," ","integrate((2+3*x)^4/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{2479653 \, \sqrt{10} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(3234330 \, x^{3} - 6746215 \, x^{2} - 11581424 \, x - 3821563\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7986000 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/7986000*(2479653*sqrt(10)*(50*x^3 + 35*x^2 - 12*x - 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(3234330*x^3 - 6746215*x^2 - 11581424*x - 3821563)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2573,1,101,0,1.494336," ","integrate((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{107811 \, \sqrt{10} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(649265 \, x^{2} + 772408 \, x + 229661\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1996500 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"1/1996500*(107811*sqrt(10)*(50*x^3 + 35*x^2 - 12*x - 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(649265*x^2 + 772408*x + 229661)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2574,1,43,0,1.546530," ","integrate((2+3*x)^2/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4091 \, x^{2} + 4456 \, x + 1196\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-2/3993*(4091*x^2 + 4456*x + 1196)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2575,1,43,0,0.952596," ","integrate((2+3*x)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2140 \, x^{2} + 1391 \, x + 40\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-2/3993*(2140*x^2 + 1391*x + 40)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2576,1,43,0,1.490421," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(800 \, x^{2} + 520 \, x - 97\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-2/3993*(800*x^2 + 520*x - 97)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2577,1,101,0,0.917470," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{107811 \, \sqrt{7} {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(155150 \, x^{2} + 11005 \, x - 45016\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{195657 \, {\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)}}"," ",0,"-1/195657*(107811*sqrt(7)*(50*x^3 + 35*x^2 - 12*x - 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(155150*x^2 + 11005*x - 45016)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(50*x^3 + 35*x^2 - 12*x - 9)","A",0
2578,1,116,0,1.660263," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{19513791 \, \sqrt{7} {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(85254450 \, x^{3} + 63467215 \, x^{2} - 20145298 \, x - 16461125\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{2739198 \, {\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)}}"," ",0,"-1/2739198*(19513791*sqrt(7)*(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(85254450*x^3 + 63467215*x^2 - 20145298*x - 16461125)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)","A",0
2579,1,131,0,1.396829," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{4855268385 \, \sqrt{7} {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(63655742250 \, x^{4} + 89836042575 \, x^{3} + 16567908760 \, x^{2} - 22311149965 \, x - 8194676012\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{76697544 \, {\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)}}"," ",0,"-1/76697544*(4855268385*sqrt(7)*(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(63655742250*x^4 + 89836042575*x^3 + 16567908760*x^2 - 22311149965*x - 8194676012)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)","A",0
2580,1,101,0,1.307135," ","integrate((2+3*x)^4*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{437126283 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2851200 \, x^{4} + 15040080 \, x^{3} + 52700868 \, x^{2} - 183672928 \, x + 66038637\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{4224000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/4224000*(437126283*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2851200*x^4 + 15040080*x^3 + 52700868*x^2 - 183672928*x + 66038637)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2581,1,96,0,1.600030," ","integrate((2+3*x)^3*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{4174929 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(71280 \, x^{3} + 431244 \, x^{2} - 1786144 \, x + 625431\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{211200 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/211200*(4174929*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(71280*x^3 + 431244*x^2 - 1786144*x + 625431)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2582,1,91,0,1.412867," ","integrate((2+3*x)^2*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{17127 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(1188 \, x^{2} - 7712 \, x + 2481\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{5280 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/5280*(17127*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(1188*x^2 - 7712*x + 2481)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2583,1,92,0,1.282136," ","integrate((2+3*x)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{99 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 4 \, {\left(268 \, x - 57\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{264 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/264*(99*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 4*(268*x - 57)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2584,1,28,0,1.262024," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{33 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"2/33*(5*x + 3)^(3/2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2585,1,86,0,1.355399," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","\frac{99 \, \sqrt{7} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(128 \, x - 141\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11319 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"1/11319*(99*sqrt(7)*(4*x^2 - 4*x + 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(128*x - 141)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2586,1,101,0,1.393840," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{2475 \, \sqrt{7} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(5100 \, x^{2} - 1460 \, x - 1623\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{158466 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"-1/158466*(2475*sqrt(7)*(12*x^3 - 4*x^2 - 5*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(5100*x^2 - 1460*x - 1623)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2587,1,116,0,1.332424," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{25245 \, \sqrt{7} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(14940 \, x^{3} + 19380 \, x^{2} - 8633 \, x - 6708\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{633864 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"-1/633864*(25245*sqrt(7)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(14940*x^3 + 19380*x^2 - 8633*x - 6708)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2588,1,131,0,1.482243," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{837045 \, \sqrt{7} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1834380 \, x^{4} + 235980 \, x^{3} - 1465461 \, x^{2} - 39530 \, x + 302352\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{8874096 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/8874096*(837045*sqrt(7)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1834380*x^4 + 235980*x^3 - 1465461*x^2 - 39530*x + 302352)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2589,1,106,0,1.346946," ","integrate((2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{4878634569 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(15552000 \, x^{5} + 83548800 \, x^{4} + 236669040 \, x^{3} + 633940524 \, x^{2} - 2034703904 \, x + 739060191\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6144000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/6144000*(4878634569*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(15552000*x^5 + 83548800*x^4 + 236669040*x^3 + 633940524*x^2 - 2034703904*x + 739060191)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2590,1,101,0,1.609021," ","integrate((2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{12740199 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(86400 \, x^{4} + 447120 \, x^{3} + 1544724 \, x^{2} - 5349344 \, x + 1925361\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{76800 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/76800*(12740199*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(86400*x^4 + 447120*x^3 + 1544724*x^2 - 5349344*x + 1925361)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2591,1,96,0,1.257312," ","integrate((2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{122361 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2160 \, x^{3} + 12780 \, x^{2} - 52256 \, x + 18351\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3840 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3840*(122361*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2160*x^3 + 12780*x^2 - 52256*x + 18351)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2592,1,97,0,1.275872," ","integrate((2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{507 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(180 \, x^{2} - 1136 \, x + 369\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{96 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/96*(507*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(180*x^2 - 1136*x + 369)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2593,1,92,0,0.862892," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 4 \, {\left(40 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{24 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/24*(15*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 4*(40*x - 9)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2594,1,86,0,0.944846," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{7} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(41 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1029 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/1029*(3*sqrt(7)*(4*x^2 - 4*x + 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(41*x + 18)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2595,1,101,0,0.846278," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","\frac{285 \, \sqrt{7} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(660 \, x^{2} - 310 \, x - 549\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14406 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"1/14406*(285*sqrt(7)*(12*x^3 - 4*x^2 - 5*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(660*x^2 - 310*x - 549)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2596,1,116,0,1.317991," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","-\frac{15 \, \sqrt{7} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(180 \, x^{3} + 60 \, x^{2} - 91 \, x - 36\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1176 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"-1/1176*(15*sqrt(7)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(180*x^3 + 60*x^2 - 91*x - 36)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2597,1,131,0,1.286909," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{28185 \, \sqrt{7} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(150660 \, x^{4} + 193860 \, x^{3} - 17127 \, x^{2} - 80510 \, x - 19296\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{806736 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/806736*(28185*sqrt(7)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(150660*x^4 + 193860*x^3 - 17127*x^2 - 80510*x - 19296)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2598,1,111,0,1.407562," ","integrate((2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{140927752779 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(248832000 \, x^{6} + 1423526400 \, x^{5} + 4002203520 \, x^{4} + 8217694800 \, x^{3} + 18987469764 \, x^{2} - 58600061024 \, x + 21368105901\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{24576000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/24576000*(140927752779*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(248832000*x^6 + 1423526400*x^5 + 4002203520*x^4 + 8217694800*x^3 + 18987469764*x^2 - 58600061024*x + 21368105901)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2599,1,106,0,0.804848," ","integrate((2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{311652759 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(1036800 \, x^{5} + 5477760 \, x^{4} + 15301008 \, x^{3} + 40614996 \, x^{2} - 129940960 \, x + 47216961\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{245760 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/245760*(311652759*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(1036800*x^5 + 5477760*x^4 + 15301008*x^3 + 40614996*x^2 - 129940960*x + 47216961)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2600,1,107,0,1.341556," ","integrate((2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{816717 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(28800 \, x^{4} + 146160 \, x^{3} + 497868 \, x^{2} - 1713440 \, x + 617319\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3072 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/3072*(816717*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(28800*x^4 + 146160*x^3 + 497868*x^2 - 1713440*x + 617319)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2601,1,102,0,1.651554," ","integrate((2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{39435 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(3600 \, x^{3} + 20820 \, x^{2} - 84064 \, x + 29601\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{768 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/768*(39435*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(3600*x^3 + 20820*x^2 - 84064*x + 29601)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2602,1,97,0,1.313175," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","-\frac{825 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 4 \, {\left(300 \, x^{2} - 1840 \, x + 603\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{96 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/96*(825*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 4*(300*x^2 - 1840*x + 603)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2603,1,142,0,1.666652," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x),x, algorithm=""fricas"")","-\frac{8575 \, \sqrt{5} \sqrt{2} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{5} \sqrt{2} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 8 \, \sqrt{7} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 308 \, {\left(292 \, x - 69\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{8232 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/8232*(8575*sqrt(5)*sqrt(2)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(5)*sqrt(2)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 8*sqrt(7)*(4*x^2 - 4*x + 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 308*(292*x - 69)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2604,1,101,0,1.169899," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^2,x, algorithm=""fricas"")","-\frac{165 \, \sqrt{7} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(3090 \, x^{2} + 3070 \, x + 657\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14406 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"-1/14406*(165*sqrt(7)*(12*x^3 - 4*x^2 - 5*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(3090*x^2 + 3070*x + 657)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2605,1,116,0,1.077657," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^3,x, algorithm=""fricas"")","\frac{2145 \, \sqrt{7} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(10260 \, x^{3} + 1620 \, x^{2} - 13627 \, x - 6732\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{57624 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"1/57624*(2145*sqrt(7)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(10260*x^3 + 1620*x^2 - 13627*x - 6732)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2606,1,131,0,1.700118," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm=""fricas"")","-\frac{7755 \, \sqrt{7} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(567180 \, x^{4} + 552780 \, x^{3} - 169221 \, x^{2} - 304730 \, x - 75888\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{806736 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/806736*(7755*sqrt(7)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(567180*x^4 + 552780*x^3 - 169221*x^2 - 304730*x - 75888)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2607,1,146,0,1.769798," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^5,x, algorithm=""fricas"")","-\frac{1643235 \, \sqrt{7} {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 14 \, {\left(45277380 \, x^{5} + 82071900 \, x^{4} + 25673409 \, x^{3} - 27318504 \, x^{2} - 18627988 \, x - 2906640\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{45177216 \, {\left(324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right)}}"," ",0,"-1/45177216*(1643235*sqrt(7)*(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 14*(45277380*x^5 + 82071900*x^4 + 25673409*x^3 - 27318504*x^2 - 18627988*x - 2906640)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16)","A",0
2608,1,101,0,1.424189," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{2998952451 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(18817920 \, x^{4} + 101146320 \, x^{3} + 359461476 \, x^{2} - 1261070176 \, x + 452899509\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{46464000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/46464000*(2998952451*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(18817920*x^4 + 101146320*x^3 + 359461476*x^2 - 1261070176*x + 452899509)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2609,1,96,0,1.471323," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{142398729 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(2352240 \, x^{3} + 14544684 \, x^{2} - 61036064 \, x + 21305631\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11616000 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/11616000*(142398729*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(2352240*x^3 + 14544684*x^2 - 61036064*x + 21305631)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2610,1,91,0,1.370768," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{578259 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(39204 \, x^{2} - 261664 \, x + 83301\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{290400 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/290400*(578259*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(39204*x^2 - 261664*x + 83301)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2611,1,86,0,1.539944," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{3267 \, \sqrt{10} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 140 \, {\left(256 \, x - 51\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14520 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/14520*(3267*sqrt(10)*(4*x^2 - 4*x + 1)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 140*(256*x - 51)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2612,1,33,0,1.482170," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(29 \, x + 24\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"2/363*(29*x + 24)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2613,1,33,0,1.629400," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(20 \, x - 21\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-2/363*(20*x - 21)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1)","A",0
2614,1,86,0,1.319296," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{3267 \, \sqrt{7} {\left(4 \, x^{2} - 4 \, x + 1\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 56 \, {\left(169 \, x - 123\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{124509 \, {\left(4 \, x^{2} - 4 \, x + 1\right)}}"," ",0,"-1/124509*(3267*sqrt(7)*(4*x^2 - 4*x + 1)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 56*(169*x - 123)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(4*x^2 - 4*x + 1)","A",0
2615,1,101,0,1.309943," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{147015 \, \sqrt{7} {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(26340 \, x^{2} - 39500 \, x + 15321\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1743126 \, {\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)}}"," ",0,"-1/1743126*(147015*sqrt(7)*(12*x^3 - 4*x^2 - 5*x + 2)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(26340*x^2 - 39500*x + 15321)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(12*x^3 - 4*x^2 - 5*x + 2)","A",0
2616,1,116,0,1.184263," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{2107215 \, \sqrt{7} {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(2073420 \, x^{3} - 676860 \, x^{2} - 945629 \, x + 391476\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{6972504 \, {\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)}}"," ",0,"-1/6972504*(2107215*sqrt(7)*(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(2073420*x^3 - 676860*x^2 - 945629*x + 391476)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)","A",0
2617,1,131,0,1.653235," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^4/(3+5*x)^(1/2),x, algorithm=""fricas"")","-\frac{119882565 \, \sqrt{7} {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(374883660 \, x^{4} + 140350860 \, x^{3} - 244982277 \, x^{2} - 48873610 \, x + 44829024\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{97615056 \, {\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)}}"," ",0,"-1/97615056*(119882565*sqrt(7)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(374883660*x^4 + 140350860*x^3 - 244982277*x^2 - 48873610*x + 44829024)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)","A",0
2618,1,111,0,1.663543," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{971053677 \, \sqrt{10} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(77623920 \, x^{4} + 536898780 \, x^{3} - 1790987404 \, x^{2} - 525679641 \, x + 435258129\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{127776000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/127776000*(971053677*sqrt(10)*(20*x^3 - 8*x^2 - 7*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(77623920*x^4 + 536898780*x^3 - 1790987404*x^2 - 525679641*x + 435258129)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2619,1,106,0,1.560137," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{19513791 \, \sqrt{10} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(6468660 \, x^{3} - 40488772 \, x^{2} - 12657123 \, x + 8379147\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{15972000 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/15972000*(19513791*sqrt(10)*(20*x^3 - 8*x^2 - 7*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(6468660*x^3 - 40488772*x^2 - 12657123*x + 8379147)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2620,1,101,0,1.518082," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{107811 \, \sqrt{10} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(298852 \, x^{2} + 124263 \, x - 33087\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{798600 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-1/798600*(107811*sqrt(10)*(20*x^3 - 8*x^2 - 7*x + 3)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(298852*x^2 + 124263*x - 33087)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2621,1,43,0,0.986965," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(793 \, x^{2} + 1440 \, x + 564\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"2/3993*(793*x^2 + 1440*x + 564)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2622,1,43,0,1.355386," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(820 \, x^{2} - 369 \, x - 444\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-2/3993*(820*x^2 - 369*x - 444)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2623,1,43,0,1.460341," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(800 \, x^{2} - 360 \, x - 141\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"-2/3993*(800*x^2 - 360*x - 141)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2624,1,101,0,1.474284," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{107811 \, \sqrt{7} {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(84460 \, x^{2} - 73944 \, x + 14163\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{1369599 \, {\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)}}"," ",0,"1/1369599*(107811*sqrt(7)*(20*x^3 - 8*x^2 - 7*x + 3)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(84460*x^2 - 73944*x + 14163)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(20*x^3 - 8*x^2 - 7*x + 3)","A",0
2625,1,116,0,0.766399," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{12398265 \, \sqrt{7} {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(22082700 \, x^{3} - 7613680 \, x^{2} - 8760465 \, x + 3499599\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{19174386 \, {\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)}}"," ",0,"1/19174386*(12398265*sqrt(7)*(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(22082700*x^3 - 7613680*x^2 - 8760465*x + 3499599)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)","A",0
2626,1,131,0,2.200196," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(3/2),x, algorithm=""fricas"")","\frac{317503395 \, \sqrt{7} {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(1667076300 \, x^{4} + 520073880 \, x^{3} - 1053213025 \, x^{2} - 169466391 \, x + 178740084\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{76697544 \, {\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)}}"," ",0,"1/76697544*(317503395*sqrt(7)*(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(1667076300*x^4 + 520073880*x^3 - 1053213025*x^2 - 169466391*x + 178740084)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)","A",0
2627,1,126,0,1.364416," ","integrate((2+3*x)^6/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{33097869189 \, \sqrt{10} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(12807946800 \, x^{5} + 97980793020 \, x^{4} - 252342435560 \, x^{3} - 274128335769 \, x^{2} + 19932058554 \, x + 44437106459\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{7027680000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/7027680000*(33097869189*sqrt(10)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(12807946800*x^5 + 97980793020*x^4 - 252342435560*x^3 - 274128335769*x^2 + 19932058554*x + 44437106459)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2628,1,121,0,1.437510," ","integrate((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{131637231 \, \sqrt{10} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) + 20 \, {\left(213465780 \, x^{4} - 1247811640 \, x^{3} - 1260430251 \, x^{2} + 19593966 \, x + 168318961\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{175692000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/175692000*(131637231*sqrt(10)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) + 20*(213465780*x^4 - 1247811640*x^3 - 1260430251*x^2 + 19593966*x + 168318961)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2629,1,116,0,1.362386," ","integrate((2+3*x)^4/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{3557763 \, \sqrt{10} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{\sqrt{10} {\left(20 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{20 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 20 \, {\left(49702040 \, x^{3} + 51334383 \, x^{2} + 7883562 \, x - 3014813\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923000 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/43923000*(3557763*sqrt(10)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*arctan(1/20*sqrt(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 20*(49702040*x^3 + 51334383*x^2 + 7883562*x - 3014813)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2630,1,53,0,1.651800," ","integrate((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(19573 \, x^{3} + 62232 \, x^{2} + 52044 \, x + 13040\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"2/43923*(19573*x^3 + 62232*x^2 + 52044*x + 13040)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2631,1,53,0,1.365226," ","integrate((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(32980 \, x^{3} + 4947 \, x^{2} - 24600 \, x - 9364\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-2/43923*(32980*x^3 + 4947*x^2 - 24600*x - 9364)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2632,1,53,0,1.355898," ","integrate((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(29600 \, x^{3} + 4440 \, x^{2} - 13209 \, x - 2864\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-2/43923*(29600*x^3 + 4440*x^2 - 13209*x - 2864)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2633,1,53,0,0.865642," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16000 \, x^{3} + 2400 \, x^{2} - 7140 \, x - 361\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-2/43923*(16000*x^3 + 2400*x^2 - 7140*x - 361)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2634,1,116,0,1.587526," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{3557763 \, \sqrt{7} {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(10015900 \, x^{3} - 4427220 \, x^{2} - 3234261 \, x + 1490582\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{15065589 \, {\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/15065589*(3557763*sqrt(7)*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(10015900*x^3 - 4427220*x^2 - 3234261*x + 1490582)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)","A",0
2635,1,131,0,1.547861," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{658186155 \, \sqrt{7} {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(5746984500 \, x^{4} + 1402439900 \, x^{3} - 3498236655 \, x^{2} - 429626520 \, x + 555141781\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{210918246 \, {\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)}}"," ",0,"-1/210918246*(658186155*sqrt(7)*(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(5746984500*x^4 + 1402439900*x^3 - 3498236655*x^2 - 429626520*x + 555141781)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)","A",0
2636,1,146,0,1.533767," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^3/(3+5*x)^(5/2),x, algorithm=""fricas"")","-\frac{23641335135 \, \sqrt{7} {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)} \arctan\left(\frac{\sqrt{7} {\left(37 \, x + 20\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{14 \, {\left(10 \, x^{2} + x - 3\right)}}\right) - 14 \, {\left(619886659500 \, x^{5} + 564878517900 \, x^{4} - 276089438305 \, x^{3} - 297937101390 \, x^{2} + 28838387211 \, x + 39900939556\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{843672984 \, {\left(900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right)}}"," ",0,"-1/843672984*(23641335135*sqrt(7)*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*arctan(1/14*sqrt(7)*(37*x + 20)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3)) - 14*(619886659500*x^5 + 564878517900*x^4 - 276089438305*x^3 - 297937101390*x^2 + 28838387211*x + 39900939556)*sqrt(5*x + 3)*sqrt(-2*x + 1))/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)","A",0
2637,0,0,0,1.704453," ","integrate(1/(b*x+a)^(1/2)/(c+b*(-1+c)*x/a)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} a^{2} \sqrt{\frac{a c + {\left(b c - b\right)} x}{a}} \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{3} c e - {\left(b^{3} c - b^{3} - {\left(b^{3} c - b^{3}\right)} e\right)} x^{3} - {\left(2 \, a b^{2} c - a b^{2} - {\left(3 \, a b^{2} c - 2 \, a b^{2}\right)} e\right)} x^{2} - {\left(a^{2} b c - {\left(3 \, a^{2} b c - a^{2} b\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*a^2*sqrt((a*c + (b*c - b)*x)/a)*sqrt((a*e + (b*e - b)*x)/a)/(a^3*c*e - (b^3*c - b^3 - (b^3*c - b^3)*e)*x^3 - (2*a*b^2*c - a*b^2 - (3*a*b^2*c - 2*a*b^2)*e)*x^2 - (a^2*b*c - (3*a^2*b*c - a^2*b)*e)*x), x)","F",0
2638,0,0,0,1.378222," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} a \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{2} c e + {\left(b^{2} d e - b^{2} d\right)} x^{3} - {\left(b^{2} c + a b d - {\left(b^{2} c + 2 \, a b d\right)} e\right)} x^{2} - {\left(a b c - {\left(2 \, a b c + a^{2} d\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*a*sqrt((a*e + (b*e - b)*x)/a)/(a^2*c*e + (b^2*d*e - b^2*d)*x^3 - (b^2*c + a*b*d - (b^2*c + 2*a*b*d)*e)*x^2 - (a*b*c - (2*a*b*c + a^2*d)*e)*x), x)","F",0
2639,0,0,0,1.506602," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b d f x^{3} + a c e + {\left(b d e + {\left(b c + a d\right)} f\right)} x^{2} + {\left(a c f + {\left(b c + a d\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b*d*f*x^3 + a*c*e + (b*d*e + (b*c + a*d)*f)*x^2 + (a*c*f + (b*c + a*d)*e)*x), x)","F",0
2640,0,0,0,1.379206," ","integrate((e+b*(-1+e)*x/a)^(1/2)/(b*x+a)^(1/2)/(c+b*(-1+c)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} a \sqrt{\frac{a c + {\left(b c - b\right)} x}{a}} \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{2} c + {\left(b^{2} c - b^{2}\right)} x^{2} + {\left(2 \, a b c - a b\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*a*sqrt((a*c + (b*c - b)*x)/a)*sqrt((a*e + (b*e - b)*x)/a)/(a^2*c + (b^2*c - b^2)*x^2 + (2*a*b*c - a*b)*x), x)","F",0
2641,0,0,0,1.842599," ","integrate((d*x+c)^(1/2)/(b*x+a)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} a \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{2} e + {\left(b^{2} e - b^{2}\right)} x^{2} + {\left(2 \, a b e - a b\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*a*sqrt((a*e + (b*e - b)*x)/a)/(a^2*e + (b^2*e - b^2)*x^2 + (2*a*b*e - a*b)*x), x)","F",0
2642,0,0,0,1.616197," ","integrate((b*x+a)^(1/2)/(c+b*(-1+c)*x/a)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} a^{2} \sqrt{\frac{a c + {\left(b c - b\right)} x}{a}} \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{2} c e - {\left(b^{2} c - b^{2} - {\left(b^{2} c - b^{2}\right)} e\right)} x^{2} - {\left(a b c - {\left(2 \, a b c - a b\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*a^2*sqrt((a*c + (b*c - b)*x)/a)*sqrt((a*e + (b*e - b)*x)/a)/(a^2*c*e - (b^2*c - b^2 - (b^2*c - b^2)*e)*x^2 - (a*b*c - (2*a*b*c - a*b)*e)*x), x)","F",0
2643,0,0,0,1.646155," ","integrate((f*x+e)^(1/2)/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
2644,0,0,0,1.152730," ","integrate(1/(d*x-c)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c} \sqrt{d x - c} \sqrt{f x + e}}{d^{2} f x^{3} + d^{2} e x^{2} - c^{2} f x - c^{2} e}, x\right)"," ",0,"integral(sqrt(d*x + c)*sqrt(d*x - c)*sqrt(f*x + e)/(d^2*f*x^3 + d^2*e*x^2 - c^2*f*x - c^2*e), x)","F",0
2645,0,0,0,1.324741," ","integrate((2+3*x)^(5/2)*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2646,0,0,0,1.374022," ","integrate((2+3*x)^(3/2)*(1-2*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1), x)","F",0
2647,0,0,0,1.299738," ","integrate((1-2*x)^(1/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2648,0,0,0,1.548256," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2649,0,0,0,1.288697," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2650,0,0,0,1.178526," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2651,0,0,0,1.494670," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2652,0,0,0,1.419652," ","integrate((1-2*x)^(1/2)*(3+5*x)^(1/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2653,0,0,0,1.541480," ","integrate((2+3*x)^(5/2)*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((45*x^3 + 87*x^2 + 56*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2654,0,0,0,1.455333," ","integrate((2+3*x)^(3/2)*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(15 \, x^{2} + 19 \, x + 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((15*x^2 + 19*x + 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2655,0,0,0,0.744360," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2656,0,0,0,0.891647," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2657,0,0,0,1.209882," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2658,0,0,0,1.494166," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2659,0,0,0,1.388805," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2660,0,0,0,0.970039," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2661,0,0,0,1.602854," ","integrate((3+5*x)^(3/2)*(1-2*x)^(1/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2662,0,0,0,1.512666," ","integrate((2+3*x)^(5/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2663,0,0,0,1.706912," ","integrate((2+3*x)^(3/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((75*x^3 + 140*x^2 + 87*x + 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2664,0,0,0,1.559850," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2665,0,0,0,1.384095," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2666,0,0,0,1.287117," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2667,0,0,0,1.390239," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2668,0,0,0,1.518861," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2669,0,0,0,1.397321," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2670,0,0,0,1.608108," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2671,0,0,0,1.468473," ","integrate((3+5*x)^(5/2)*(1-2*x)^(1/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2672,0,0,0,1.529470," ","integrate((f*x+e)^(1/2)/(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
2673,0,0,0,1.165703," ","integrate((f*x+e)^(1/2)/(b*x+a)^(3/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{2} d x^{3} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2} + {\left(2 \, a b c + a^{2} d\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^2*d*x^3 + a^2*c + (b^2*c + 2*a*b*d)*x^2 + (2*a*b*c + a^2*d)*x), x)","F",0
2674,0,0,0,1.519729," ","integrate((1-2*x)^(1/2)/(-3-5*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{3 \, x + 2} \sqrt{-2 \, x + 1} \sqrt{-5 \, x - 3}}{15 \, x^{2} + 19 \, x + 6}, x\right)"," ",0,"integral(-sqrt(3*x + 2)*sqrt(-2*x + 1)*sqrt(-5*x - 3)/(15*x^2 + 19*x + 6), x)","F",0
2675,0,0,0,1.486727," ","integrate((2+3*x)^(5/2)*(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2676,0,0,0,1.483222," ","integrate((2+3*x)^(3/2)*(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral((3*x + 2)^(3/2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2677,0,0,0,1.103519," ","integrate((1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral(sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2678,0,0,0,1.489125," ","integrate((1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{15 \, x^{2} + 19 \, x + 6}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(15*x^2 + 19*x + 6), x)","F",0
2679,0,0,0,1.523381," ","integrate((1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(45*x^3 + 87*x^2 + 56*x + 12), x)","F",0
2680,0,0,0,1.060920," ","integrate((1-2*x)^(1/2)/(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24), x)","F",0
2681,0,0,0,1.558796," ","integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48), x)","F",0
2682,0,0,0,1.782794," ","integrate((2+3*x)^(7/2)*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2683,0,0,0,1.207475," ","integrate((2+3*x)^(5/2)*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2684,0,0,0,1.349742," ","integrate((2+3*x)^(3/2)*(1-2*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2685,0,0,0,1.458371," ","integrate((1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2686,0,0,0,1.056759," ","integrate((1-2*x)^(1/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(75*x^3 + 140*x^2 + 87*x + 18), x)","F",0
2687,0,0,0,1.627241," ","integrate((1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36), x)","F",0
2688,0,0,0,1.215420," ","integrate((1-2*x)^(1/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72), x)","F",0
2689,0,0,0,1.346156," ","integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144), x)","F",0
2690,0,0,0,1.186893," ","integrate((2+3*x)^(9/2)*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2691,0,0,0,1.513371," ","integrate((2+3*x)^(7/2)*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2692,0,0,0,1.494884," ","integrate((2+3*x)^(5/2)*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2693,0,0,0,1.173340," ","integrate((2+3*x)^(3/2)*(1-2*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2694,0,0,0,1.288451," ","integrate((1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2695,0,0,0,1.428169," ","integrate((1-2*x)^(1/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{375 \, x^{4} + 925 \, x^{3} + 855 \, x^{2} + 351 \, x + 54}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(375*x^4 + 925*x^3 + 855*x^2 + 351*x + 54), x)","F",0
2696,0,0,0,1.255821," ","integrate((1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1125 \, x^{5} + 3525 \, x^{4} + 4415 \, x^{3} + 2763 \, x^{2} + 864 \, x + 108}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1125*x^5 + 3525*x^4 + 4415*x^3 + 2763*x^2 + 864*x + 108), x)","F",0
2697,0,0,0,1.319357," ","integrate((1-2*x)^(1/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{3375 \, x^{6} + 12825 \, x^{5} + 20295 \, x^{4} + 17119 \, x^{3} + 8118 \, x^{2} + 2052 \, x + 216}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(3375*x^6 + 12825*x^5 + 20295*x^4 + 17119*x^3 + 8118*x^2 + 2052*x + 216), x)","F",0
2698,0,0,0,1.402661," ","integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10125 \, x^{7} + 45225 \, x^{6} + 86535 \, x^{5} + 91947 \, x^{4} + 58592 \, x^{3} + 22392 \, x^{2} + 4752 \, x + 432}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10125*x^7 + 45225*x^6 + 86535*x^5 + 91947*x^4 + 58592*x^3 + 22392*x^2 + 4752*x + 432), x)","F",0
2699,0,0,0,1.350905," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(18*x^3 + 15*x^2 - 4*x - 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2700,0,0,0,1.369383," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(6 \, x^{2} + x - 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(6*x^2 + x - 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2701,0,0,0,1.434285," ","integrate((1-2*x)^(3/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2), x)","F",0
2702,0,0,0,1.066543," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(-2*x + 1)^(3/2)/sqrt(3*x + 2), x)","F",0
2703,0,0,0,1.325991," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(9*x^2 + 12*x + 4), x)","F",0
2704,0,0,0,1.645838," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2705,0,0,0,1.228130," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2706,0,0,0,1.419034," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2707,0,0,0,1.246843," ","integrate((1-2*x)^(3/2)*(3+5*x)^(1/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2708,0,0,0,1.343042," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2709,0,0,0,1.262317," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(30*x^3 + 23*x^2 - 7*x - 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2710,0,0,0,1.548112," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2711,0,0,0,1.260395," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2712,0,0,0,1.541884," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2713,0,0,0,1.294678," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2714,0,0,0,1.267239," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2715,0,0,0,1.687054," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2716,0,0,0,1.649572," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2717,0,0,0,1.739950," ","integrate((1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(10 \, x^{2} + x - 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral(-(10*x^2 + x - 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2718,0,0,0,1.399846," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2719,0,0,0,1.436825," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2720,0,0,0,1.576979," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2721,0,0,0,1.414662," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2722,0,0,0,1.491254," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2723,0,0,0,0.988691," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2724,0,0,0,1.349805," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2725,0,0,0,1.507882," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2726,0,0,0,1.488773," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2727,0,0,0,1.267149," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2728,0,0,0,1.339334," ","integrate((1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256}, x\right)"," ",0,"integral(-(50*x^3 + 35*x^2 - 12*x - 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^2 + 3072*x + 256), x)","F",0
2729,0,0,0,1.288604," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral(-(18*x^3 + 15*x^2 - 4*x - 4)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2730,0,0,0,0.878745," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(6 \, x^{2} + x - 2\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral(-(6*x^2 + x - 2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2731,0,0,0,1.306699," ","integrate((1-2*x)^(3/2)*(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral(sqrt(3*x + 2)*(-2*x + 1)^(3/2)/sqrt(5*x + 3), x)","F",0
2732,0,0,0,1.132970," ","integrate((1-2*x)^(3/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{15 \, x^{2} + 19 \, x + 6}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(15*x^2 + 19*x + 6), x)","F",0
2733,0,0,0,1.287895," ","integrate((1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(45*x^3 + 87*x^2 + 56*x + 12), x)","F",0
2734,0,0,0,1.204791," ","integrate((1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24), x)","F",0
2735,0,0,0,1.139970," ","integrate((1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48), x)","F",0
2736,0,0,0,1.245153," ","integrate((1-2*x)^(3/2)/(2+3*x)^(9/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96), x)","F",0
2737,0,0,0,1.447625," ","integrate((1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(-(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2738,0,0,0,1.367572," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(-(18*x^3 + 15*x^2 - 4*x - 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2739,0,0,0,1.292223," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(6 \, x^{2} + x - 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(-(6*x^2 + x - 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2740,0,0,0,1.039899," ","integrate((1-2*x)^(3/2)*(2+3*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(25*x^2 + 30*x + 9), x)","F",0
2741,0,0,0,0.807324," ","integrate((1-2*x)^(3/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(75*x^3 + 140*x^2 + 87*x + 18), x)","F",0
2742,0,0,0,1.205840," ","integrate((1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36), x)","F",0
2743,0,0,0,1.187625," ","integrate((1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72), x)","F",0
2744,0,0,0,1.622867," ","integrate((1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144), x)","F",0
2745,0,0,0,1.408555," ","integrate((1-2*x)^(3/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288), x)","F",0
2746,0,0,0,1.332892," ","integrate((1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(-(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2747,0,0,0,1.285155," ","integrate((1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(-(18*x^3 + 15*x^2 - 4*x - 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2748,0,0,0,0.923446," ","integrate((1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(6 \, x^{2} + x - 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(-(6*x^2 + x - 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2749,0,0,0,0.763603," ","integrate((1-2*x)^(3/2)*(2+3*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2750,0,0,0,1.294494," ","integrate((1-2*x)^(3/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{375 \, x^{4} + 925 \, x^{3} + 855 \, x^{2} + 351 \, x + 54}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(375*x^4 + 925*x^3 + 855*x^2 + 351*x + 54), x)","F",0
2751,0,0,0,1.282684," ","integrate((1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{1125 \, x^{5} + 3525 \, x^{4} + 4415 \, x^{3} + 2763 \, x^{2} + 864 \, x + 108}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(1125*x^5 + 3525*x^4 + 4415*x^3 + 2763*x^2 + 864*x + 108), x)","F",0
2752,0,0,0,1.253367," ","integrate((1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{3375 \, x^{6} + 12825 \, x^{5} + 20295 \, x^{4} + 17119 \, x^{3} + 8118 \, x^{2} + 2052 \, x + 216}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(3375*x^6 + 12825*x^5 + 20295*x^4 + 17119*x^3 + 8118*x^2 + 2052*x + 216), x)","F",0
2753,0,0,0,1.404054," ","integrate((1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} {\left(-2 \, x + 1\right)}^{\frac{3}{2}}}{10125 \, x^{7} + 45225 \, x^{6} + 86535 \, x^{5} + 91947 \, x^{4} + 58592 \, x^{3} + 22392 \, x^{2} + 4752 \, x + 432}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*(-2*x + 1)^(3/2)/(10125*x^7 + 45225*x^6 + 86535*x^5 + 91947*x^4 + 58592*x^3 + 22392*x^2 + 4752*x + 432), x)","F",0
2754,0,0,0,1.308157," ","integrate((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2755,0,0,0,1.385941," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((12*x^3 - 4*x^2 - 5*x + 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2756,0,0,0,1.390281," ","integrate((1-2*x)^(5/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2757,0,0,0,0.923296," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2758,0,0,0,1.408076," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2759,0,0,0,1.412550," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2760,0,0,0,1.223922," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2761,0,0,0,1.350977," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2762,0,0,0,1.198708," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2763,0,0,0,1.181628," ","integrate((1-2*x)^(5/2)*(3+5*x)^(1/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2764,0,0,0,1.135944," ","integrate((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2765,0,0,0,1.155166," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2766,0,0,0,1.185760," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2767,0,0,0,1.226957," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2768,0,0,0,0.894932," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2769,0,0,0,0.888533," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2770,0,0,0,0.853654," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2771,0,0,0,1.201727," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2772,0,0,0,1.147378," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2773,0,0,0,1.015366," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2774,0,0,0,0.904161," ","integrate((1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256}, x\right)"," ",0,"integral((20*x^3 - 8*x^2 - 7*x + 3)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^2 + 3072*x + 256), x)","F",0
2775,0,0,0,1.321634," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2776,0,0,0,1.067224," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)*(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1), x)","F",0
2777,0,0,0,1.025663," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{\sqrt{3 \, x + 2}}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(-2*x + 1)/sqrt(3*x + 2), x)","F",0
2778,0,0,0,0.657353," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9 \, x^{2} + 12 \, x + 4}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9*x^2 + 12*x + 4), x)","F",0
2779,0,0,0,1.050541," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27*x^3 + 54*x^2 + 36*x + 8), x)","F",0
2780,0,0,0,1.021657," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16), x)","F",0
2781,0,0,0,0.634893," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32), x)","F",0
2782,0,0,0,0.823925," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64), x)","F",0
2783,0,0,0,1.213839," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128), x)","F",0
2784,0,0,0,1.089287," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6561 \, x^{8} + 34992 \, x^{7} + 81648 \, x^{6} + 108864 \, x^{5} + 90720 \, x^{4} + 48384 \, x^{3} + 16128 \, x^{2} + 3072 \, x + 256}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6561*x^8 + 34992*x^7 + 81648*x^6 + 108864*x^5 + 90720*x^4 + 48384*x^3 + 16128*x^2 + 3072*x + 256), x)","F",0
2785,0,0,0,0.941420," ","integrate((1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{19683 \, x^{9} + 118098 \, x^{8} + 314928 \, x^{7} + 489888 \, x^{6} + 489888 \, x^{5} + 326592 \, x^{4} + 145152 \, x^{3} + 41472 \, x^{2} + 6912 \, x + 512}, x\right)"," ",0,"integral((100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(19683*x^9 + 118098*x^8 + 314928*x^7 + 489888*x^6 + 489888*x^5 + 326592*x^4 + 145152*x^3 + 41472*x^2 + 6912*x + 512), x)","F",0
2786,0,0,0,1.082563," ","integrate((1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral((36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2787,0,0,0,0.911316," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral((12*x^3 - 4*x^2 - 5*x + 2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2788,0,0,0,1.028319," ","integrate((1-2*x)^(5/2)*(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(3*x + 2)*sqrt(-2*x + 1)/sqrt(5*x + 3), x)","F",0
2789,0,0,0,0.911817," ","integrate((1-2*x)^(5/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{15 \, x^{2} + 19 \, x + 6}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(15*x^2 + 19*x + 6), x)","F",0
2790,0,0,0,0.985942," ","integrate((1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(45*x^3 + 87*x^2 + 56*x + 12), x)","F",0
2791,0,0,0,0.832268," ","integrate((1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24), x)","F",0
2792,0,0,0,0.954136," ","integrate((1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(405*x^5 + 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48), x)","F",0
2793,0,0,0,0.973397," ","integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1215*x^6 + 4779*x^5 + 7830*x^4 + 6840*x^3 + 3360*x^2 + 880*x + 96), x)","F",0
2794,0,0,0,0.977816," ","integrate((1-2*x)^(5/2)/(2+3*x)^(11/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192), x)","F",0
2795,0,0,0,1.124762," ","integrate((1-2*x)^(5/2)/(2+3*x)^(13/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10935 \, x^{8} + 57591 \, x^{7} + 132678 \, x^{6} + 174636 \, x^{5} + 143640 \, x^{4} + 75600 \, x^{3} + 24864 \, x^{2} + 4672 \, x + 384}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10935*x^8 + 57591*x^7 + 132678*x^6 + 174636*x^5 + 143640*x^4 + 75600*x^3 + 24864*x^2 + 4672*x + 384), x)","F",0
2796,0,0,0,1.095115," ","integrate((1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2797,0,0,0,0.820040," ","integrate((1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2798,0,0,0,1.208584," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((12*x^3 - 4*x^2 - 5*x + 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2799,0,0,0,0.958060," ","integrate((1-2*x)^(5/2)*(2+3*x)^(1/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(25*x^2 + 30*x + 9), x)","F",0
2800,0,0,0,1.154698," ","integrate((1-2*x)^(5/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(75*x^3 + 140*x^2 + 87*x + 18), x)","F",0
2801,0,0,0,1.313651," ","integrate((1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36), x)","F",0
2802,0,0,0,1.042003," ","integrate((1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72), x)","F",0
2803,0,0,0,0.970188," ","integrate((1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144), x)","F",0
2804,0,0,0,1.142744," ","integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6075*x^7 + 27540*x^6 + 53487*x^5 + 57690*x^4 + 37320*x^3 + 14480*x^2 + 3120*x + 288), x)","F",0
2805,0,0,0,1.035101," ","integrate((1-2*x)^(5/2)/(2+3*x)^(11/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(18225*x^8 + 94770*x^7 + 215541*x^6 + 280044*x^5 + 227340*x^4 + 118080*x^3 + 38320*x^2 + 7104*x + 576), x)","F",0
2806,0,0,0,1.181759," ","integrate((1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2807,0,0,0,1.046968," ","integrate((1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2808,0,0,0,1.286904," ","integrate((1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((12*x^3 - 4*x^2 - 5*x + 2)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2809,0,0,0,0.980416," ","integrate((1-2*x)^(5/2)*(2+3*x)^(1/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
2810,0,0,0,1.208833," ","integrate((1-2*x)^(5/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{375 \, x^{4} + 925 \, x^{3} + 855 \, x^{2} + 351 \, x + 54}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(375*x^4 + 925*x^3 + 855*x^2 + 351*x + 54), x)","F",0
2811,0,0,0,0.814272," ","integrate((1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1125 \, x^{5} + 3525 \, x^{4} + 4415 \, x^{3} + 2763 \, x^{2} + 864 \, x + 108}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1125*x^5 + 3525*x^4 + 4415*x^3 + 2763*x^2 + 864*x + 108), x)","F",0
2812,0,0,0,1.028574," ","integrate((1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{3375 \, x^{6} + 12825 \, x^{5} + 20295 \, x^{4} + 17119 \, x^{3} + 8118 \, x^{2} + 2052 \, x + 216}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(3375*x^6 + 12825*x^5 + 20295*x^4 + 17119*x^3 + 8118*x^2 + 2052*x + 216), x)","F",0
2813,0,0,0,0.740700," ","integrate((1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10125 \, x^{7} + 45225 \, x^{6} + 86535 \, x^{5} + 91947 \, x^{4} + 58592 \, x^{3} + 22392 \, x^{2} + 4752 \, x + 432}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10125*x^7 + 45225*x^6 + 86535*x^5 + 91947*x^4 + 58592*x^3 + 22392*x^2 + 4752*x + 432), x)","F",0
2814,0,0,0,1.101443," ","integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 4 \, x + 1\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{30375 \, x^{8} + 155925 \, x^{7} + 350055 \, x^{6} + 448911 \, x^{5} + 359670 \, x^{4} + 184360 \, x^{3} + 59040 \, x^{2} + 10800 \, x + 864}, x\right)"," ",0,"integral((4*x^2 - 4*x + 1)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(30375*x^8 + 155925*x^7 + 350055*x^6 + 448911*x^5 + 359670*x^4 + 184360*x^3 + 59040*x^2 + 10800*x + 864), x)","F",0
2815,0,0,0,1.231010," ","integrate((2+3*x)^(5/2)*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2816,0,0,0,0.823413," ","integrate((2+3*x)^(3/2)*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2817,0,0,0,1.457822," ","integrate((2+3*x)^(1/2)*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2818,0,0,0,0.928728," ","integrate((3+5*x)^(1/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6 \, x^{2} + x - 2}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6*x^2 + x - 2), x)","F",0
2819,0,0,0,1.094610," ","integrate((3+5*x)^(1/2)/(2+3*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(18*x^3 + 15*x^2 - 4*x - 4), x)","F",0
2820,0,0,0,0.925301," ","integrate((3+5*x)^(1/2)/(2+3*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8), x)","F",0
2821,0,0,0,0.740474," ","integrate((3+5*x)^(1/2)/(2+3*x)^(7/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16), x)","F",0
2822,0,0,0,1.058180," ","integrate((2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(45*x^3 + 87*x^2 + 56*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2823,0,0,0,1.178157," ","integrate((2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{2} + 19 \, x + 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(15*x^2 + 19*x + 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2824,0,0,0,0.728630," ","integrate((3+5*x)^(3/2)*(2+3*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2825,0,0,0,1.198185," ","integrate((3+5*x)^(3/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6 \, x^{2} + x - 2}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6*x^2 + x - 2), x)","F",0
2826,0,0,0,1.087664," ","integrate((3+5*x)^(3/2)/(2+3*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(18*x^3 + 15*x^2 - 4*x - 4), x)","F",0
2827,0,0,0,1.104020," ","integrate((3+5*x)^(3/2)/(2+3*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8), x)","F",0
2828,0,0,0,0.945601," ","integrate((3+5*x)^(3/2)/(2+3*x)^(7/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16), x)","F",0
2829,0,0,0,1.328105," ","integrate((3+5*x)^(3/2)/(2+3*x)^(9/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32), x)","F",0
2830,0,0,0,0.689825," ","integrate((2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2831,0,0,0,0.783556," ","integrate((2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2832,0,0,0,1.140894," ","integrate((2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(75*x^3 + 140*x^2 + 87*x + 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2833,0,0,0,1.263835," ","integrate((3+5*x)^(5/2)*(2+3*x)^(1/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2 \, x - 1}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2*x - 1), x)","F",0
2834,0,0,0,0.923958," ","integrate((3+5*x)^(5/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6 \, x^{2} + x - 2}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6*x^2 + x - 2), x)","F",0
2835,0,0,0,0.947152," ","integrate((3+5*x)^(5/2)/(2+3*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(18*x^3 + 15*x^2 - 4*x - 4), x)","F",0
2836,0,0,0,1.007252," ","integrate((3+5*x)^(5/2)/(2+3*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(54*x^4 + 81*x^3 + 18*x^2 - 20*x - 8), x)","F",0
2837,0,0,0,1.137794," ","integrate((3+5*x)^(5/2)/(2+3*x)^(7/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(162*x^5 + 351*x^4 + 216*x^3 - 24*x^2 - 64*x - 16), x)","F",0
2838,0,0,0,0.771920," ","integrate((3+5*x)^(5/2)/(2+3*x)^(9/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32), x)","F",0
2839,0,0,0,1.256243," ","integrate((3+5*x)^(5/2)/(2+3*x)^(11/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1458 \, x^{7} + 5103 \, x^{6} + 6804 \, x^{5} + 3780 \, x^{4} - 1008 \, x^{2} - 448 \, x - 64}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1458*x^7 + 5103*x^6 + 6804*x^5 + 3780*x^4 - 1008*x^2 - 448*x - 64), x)","F",0
2840,0,0,0,1.062636," ","integrate((3+5*x)^(5/2)/(2+3*x)^(13/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128), x)","F",0
2841,0,0,0,1.179064," ","integrate(1/(1+x)^(1/2)/(2+x)^(1/2)/(3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x + 3} \sqrt{x + 2} \sqrt{x + 1}}{x^{3} + 6 \, x^{2} + 11 \, x + 6}, x\right)"," ",0,"integral(sqrt(x + 3)*sqrt(x + 2)*sqrt(x + 1)/(x^3 + 6*x^2 + 11*x + 6), x)","F",0
2842,0,0,0,1.068805," ","integrate(1/(3-x)^(1/2)/(1+x)^(1/2)/(2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 2} \sqrt{x + 1} \sqrt{-x + 3}}{x^{3} - 7 \, x - 6}, x\right)"," ",0,"integral(-sqrt(x + 2)*sqrt(x + 1)*sqrt(-x + 3)/(x^3 - 7*x - 6), x)","F",0
2843,0,0,0,1.180968," ","integrate(1/(2-x)^(1/2)/(1+x)^(1/2)/(3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 3} \sqrt{x + 1} \sqrt{-x + 2}}{x^{3} + 2 \, x^{2} - 5 \, x - 6}, x\right)"," ",0,"integral(-sqrt(x + 3)*sqrt(x + 1)*sqrt(-x + 2)/(x^3 + 2*x^2 - 5*x - 6), x)","F",0
2844,0,0,0,1.028889," ","integrate(1/(2-x)^(1/2)/(3-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x + 1} \sqrt{-x + 3} \sqrt{-x + 2}}{x^{3} - 4 \, x^{2} + x + 6}, x\right)"," ",0,"integral(sqrt(x + 1)*sqrt(-x + 3)*sqrt(-x + 2)/(x^3 - 4*x^2 + x + 6), x)","F",0
2845,0,0,0,1.129934," ","integrate(1/(1-x)^(1/2)/(2+x)^(1/2)/(3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 3} \sqrt{x + 2} \sqrt{-x + 1}}{x^{3} + 4 \, x^{2} + x - 6}, x\right)"," ",0,"integral(-sqrt(x + 3)*sqrt(x + 2)*sqrt(-x + 1)/(x^3 + 4*x^2 + x - 6), x)","F",0
2846,0,0,0,0.918766," ","integrate(1/(1-x)^(1/2)/(3-x)^(1/2)/(2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x + 2} \sqrt{-x + 3} \sqrt{-x + 1}}{x^{3} - 2 \, x^{2} - 5 \, x + 6}, x\right)"," ",0,"integral(sqrt(x + 2)*sqrt(-x + 3)*sqrt(-x + 1)/(x^3 - 2*x^2 - 5*x + 6), x)","F",0
2847,0,0,0,0.726430," ","integrate(1/(1-x)^(1/2)/(2-x)^(1/2)/(3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x + 3} \sqrt{-x + 2} \sqrt{-x + 1}}{x^{3} - 7 \, x + 6}, x\right)"," ",0,"integral(sqrt(x + 3)*sqrt(-x + 2)*sqrt(-x + 1)/(x^3 - 7*x + 6), x)","F",0
2848,0,0,0,0.739660," ","integrate(1/(1-x)^(1/2)/(2-x)^(1/2)/(3-x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x + 3} \sqrt{-x + 2} \sqrt{-x + 1}}{x^{3} - 6 \, x^{2} + 11 \, x - 6}, x\right)"," ",0,"integral(-sqrt(-x + 3)*sqrt(-x + 2)*sqrt(-x + 1)/(x^3 - 6*x^2 + 11*x - 6), x)","F",0
2849,0,0,0,0.945232," ","integrate(1/(-3+x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x - 1} \sqrt{x - 2} \sqrt{x - 3}}{x^{3} - 6 \, x^{2} + 11 \, x - 6}, x\right)"," ",0,"integral(sqrt(x - 1)*sqrt(x - 2)*sqrt(x - 3)/(x^3 - 6*x^2 + 11*x - 6), x)","F",0
2850,0,0,0,1.082301," ","integrate(1/(-3-x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x - 1} \sqrt{x - 2} \sqrt{-x - 3}}{x^{3} - 7 \, x + 6}, x\right)"," ",0,"integral(-sqrt(x - 1)*sqrt(x - 2)*sqrt(-x - 3)/(x^3 - 7*x + 6), x)","F",0
2851,0,0,0,1.226827," ","integrate(1/(-2-x)^(1/2)/(-3+x)^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x - 1} \sqrt{x - 3} \sqrt{-x - 2}}{x^{3} - 2 \, x^{2} - 5 \, x + 6}, x\right)"," ",0,"integral(-sqrt(x - 1)*sqrt(x - 3)*sqrt(-x - 2)/(x^3 - 2*x^2 - 5*x + 6), x)","F",0
2852,0,0,0,1.022650," ","integrate(1/(-3-x)^(1/2)/(-2-x)^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x - 1} \sqrt{-x - 2} \sqrt{-x - 3}}{x^{3} + 4 \, x^{2} + x - 6}, x\right)"," ",0,"integral(sqrt(x - 1)*sqrt(-x - 2)*sqrt(-x - 3)/(x^3 + 4*x^2 + x - 6), x)","F",0
2853,0,0,0,1.016373," ","integrate(1/(-1-x)^(1/2)/(-3+x)^(1/2)/(-2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x - 2} \sqrt{x - 3} \sqrt{-x - 1}}{x^{3} - 4 \, x^{2} + x + 6}, x\right)"," ",0,"integral(-sqrt(x - 2)*sqrt(x - 3)*sqrt(-x - 1)/(x^3 - 4*x^2 + x + 6), x)","F",0
2854,0,0,0,0.890414," ","integrate(1/(-3-x)^(1/2)/(-1-x)^(1/2)/(-2+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x - 2} \sqrt{-x - 1} \sqrt{-x - 3}}{x^{3} + 2 \, x^{2} - 5 \, x - 6}, x\right)"," ",0,"integral(sqrt(x - 2)*sqrt(-x - 1)*sqrt(-x - 3)/(x^3 + 2*x^2 - 5*x - 6), x)","F",0
2855,0,0,0,1.124814," ","integrate(1/(-2-x)^(1/2)/(-1-x)^(1/2)/(-3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x - 3} \sqrt{-x - 1} \sqrt{-x - 2}}{x^{3} - 7 \, x - 6}, x\right)"," ",0,"integral(sqrt(x - 3)*sqrt(-x - 1)*sqrt(-x - 2)/(x^3 - 7*x - 6), x)","F",0
2856,0,0,0,1.121253," ","integrate(1/(-3-x)^(1/2)/(-2-x)^(1/2)/(-1-x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x - 1} \sqrt{-x - 2} \sqrt{-x - 3}}{x^{3} + 6 \, x^{2} + 11 \, x + 6}, x\right)"," ",0,"integral(-sqrt(-x - 1)*sqrt(-x - 2)*sqrt(-x - 3)/(x^3 + 6*x^2 + 11*x + 6), x)","F",0
2857,0,0,0,1.143481," ","integrate(1/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{2} d f x^{4} + a^{2} c e + {\left(b^{2} d e + {\left(b^{2} c + 2 \, a b d\right)} f\right)} x^{3} + {\left({\left(b^{2} c + 2 \, a b d\right)} e + {\left(2 \, a b c + a^{2} d\right)} f\right)} x^{2} + {\left(a^{2} c f + {\left(2 \, a b c + a^{2} d\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^2*d*f*x^4 + a^2*c*e + (b^2*d*e + (b^2*c + 2*a*b*d)*f)*x^3 + ((b^2*c + 2*a*b*d)*e + (2*a*b*c + a^2*d)*f)*x^2 + (a^2*c*f + (2*a*b*c + a^2*d)*e)*x), x)","F",0
2858,0,0,0,1.374927," ","integrate(1/(b*x+a)^(5/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e}}{b^{3} d f x^{5} + a^{3} c e + {\left(b^{3} d e + {\left(b^{3} c + 3 \, a b^{2} d\right)} f\right)} x^{4} + {\left({\left(b^{3} c + 3 \, a b^{2} d\right)} e + 3 \, {\left(a b^{2} c + a^{2} b d\right)} f\right)} x^{3} + {\left(3 \, {\left(a b^{2} c + a^{2} b d\right)} e + {\left(3 \, a^{2} b c + a^{3} d\right)} f\right)} x^{2} + {\left(a^{3} c f + {\left(3 \, a^{2} b c + a^{3} d\right)} e\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)/(b^3*d*f*x^5 + a^3*c*e + (b^3*d*e + (b^3*c + 3*a*b^2*d)*f)*x^4 + ((b^3*c + 3*a*b^2*d)*e + 3*(a*b^2*c + a^2*b*d)*f)*x^3 + (3*(a*b^2*c + a^2*b*d)*e + (3*a^2*b*c + a^3*d)*f)*x^2 + (a^3*c*f + (3*a^2*b*c + a^3*d)*e)*x), x)","F",0
2859,0,0,0,0.980145," ","integrate((2+3*x)^(7/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10 \, x^{2} + x - 3}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10*x^2 + x - 3), x)","F",0
2860,0,0,0,1.194774," ","integrate((2+3*x)^(5/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10 \, x^{2} + x - 3}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10*x^2 + x - 3), x)","F",0
2861,0,0,0,1.140120," ","integrate((2+3*x)^(3/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{10 \, x^{2} + x - 3}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(10*x^2 + x - 3), x)","F",0
2862,0,0,0,0.996590," ","integrate((2+3*x)^(1/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{10 \, x^{2} + x - 3}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(10*x^2 + x - 3), x)","F",0
2863,0,0,0,0.956858," ","integrate(1/(1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(30*x^3 + 23*x^2 - 7*x - 6), x)","F",0
2864,0,0,0,0.904399," ","integrate(1/(2+3*x)^(3/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(90*x^4 + 129*x^3 + 25*x^2 - 32*x - 12), x)","F",0
2865,0,0,0,1.285869," ","integrate(1/(2+3*x)^(5/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(270*x^5 + 567*x^4 + 333*x^3 - 46*x^2 - 100*x - 24), x)","F",0
2866,0,0,0,1.140033," ","integrate(1/(2+3*x)^(7/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(810*x^6 + 2241*x^5 + 2133*x^4 + 528*x^3 - 392*x^2 - 272*x - 48), x)","F",0
2867,0,0,0,0.996992," ","integrate((2+3*x)^(7/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9), x)","F",0
2868,0,0,0,0.655525," ","integrate((2+3*x)^(5/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9), x)","F",0
2869,0,0,0,1.206019," ","integrate((2+3*x)^(3/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9), x)","F",0
2870,0,0,0,0.966008," ","integrate((2+3*x)^(1/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(50*x^3 + 35*x^2 - 12*x - 9), x)","F",0
2871,0,0,0,0.985008," ","integrate(1/(3+5*x)^(3/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(150*x^4 + 205*x^3 + 34*x^2 - 51*x - 18), x)","F",0
2872,0,0,0,0.900532," ","integrate(1/(2+3*x)^(3/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(450*x^5 + 915*x^4 + 512*x^3 - 85*x^2 - 156*x - 36), x)","F",0
2873,0,0,0,1.107505," ","integrate(1/(2+3*x)^(5/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1350*x^6 + 3645*x^5 + 3366*x^4 + 769*x^3 - 638*x^2 - 420*x - 72), x)","F",0
2874,0,0,0,1.049856," ","integrate(1/(2+3*x)^(7/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4050 \, x^{7} + 13635 \, x^{6} + 17388 \, x^{5} + 9039 \, x^{4} - 376 \, x^{3} - 2536 \, x^{2} - 1056 \, x - 144}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4050*x^7 + 13635*x^6 + 17388*x^5 + 9039*x^4 - 376*x^3 - 2536*x^2 - 1056*x - 144), x)","F",0
2875,0,0,0,1.190283," ","integrate((2+3*x)^(9/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
2876,0,0,0,0.856715," ","integrate((2+3*x)^(7/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
2877,0,0,0,1.078417," ","integrate((2+3*x)^(5/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
2878,0,0,0,0.613304," ","integrate((2+3*x)^(3/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
2879,0,0,0,0.954964," ","integrate((2+3*x)^(1/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
2880,0,0,0,0.986372," ","integrate(1/(3+5*x)^(5/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{750 \, x^{5} + 1475 \, x^{4} + 785 \, x^{3} - 153 \, x^{2} - 243 \, x - 54}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(750*x^5 + 1475*x^4 + 785*x^3 - 153*x^2 - 243*x - 54), x)","F",0
2881,0,0,0,1.031601," ","integrate(1/(2+3*x)^(3/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2250 \, x^{6} + 5925 \, x^{5} + 5305 \, x^{4} + 1111 \, x^{3} - 1035 \, x^{2} - 648 \, x - 108}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2250*x^6 + 5925*x^5 + 5305*x^4 + 1111*x^3 - 1035*x^2 - 648*x - 108), x)","F",0
2882,0,0,0,1.000552," ","integrate(1/(2+3*x)^(5/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{6750 \, x^{7} + 22275 \, x^{6} + 27765 \, x^{5} + 13943 \, x^{4} - 883 \, x^{3} - 4014 \, x^{2} - 1620 \, x - 216}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(6750*x^7 + 22275*x^6 + 27765*x^5 + 13943*x^4 - 883*x^3 - 4014*x^2 - 1620*x - 216), x)","F",0
2883,0,0,0,0.931538," ","integrate(1/(2+3*x)^(7/2)/(3+5*x)^(5/2)/(1-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{20250 \, x^{8} + 80325 \, x^{7} + 127845 \, x^{6} + 97359 \, x^{5} + 25237 \, x^{4} - 13808 \, x^{3} - 12888 \, x^{2} - 3888 \, x - 432}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(20250*x^8 + 80325*x^7 + 127845*x^6 + 97359*x^5 + 25237*x^4 - 13808*x^3 - 12888*x^2 - 3888*x - 432), x)","F",0
2884,0,0,0,1.363020," ","integrate(x^(1/2)/(a+2*x)^(1/2)/(c+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a + 2 \, x} \sqrt{c + 2 \, x} \sqrt{x}}{a c + 2 \, {\left(a + c\right)} x + 4 \, x^{2}}, x\right)"," ",0,"integral(sqrt(a + 2*x)*sqrt(c + 2*x)*sqrt(x)/(a*c + 2*(a + c)*x + 4*x^2), x)","F",0
2885,0,0,0,1.137866," ","integrate(1/(4-x)^(1/2)/(5-x)^(1/2)/(-3+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x - 3} \sqrt{-x + 5} \sqrt{-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, x\right)"," ",0,"integral(sqrt(x - 3)*sqrt(-x + 5)*sqrt(-x + 4)/(x^3 - 12*x^2 + 47*x - 60), x)","F",0
2886,0,0,0,1.105146," ","integrate(1/(4-x)^(1/2)/((5-x)*(-3+x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, x\right)"," ",0,"integral(sqrt(-x^2 + 8*x - 15)*sqrt(-x + 4)/(x^3 - 12*x^2 + 47*x - 60), x)","F",0
2887,0,0,0,1.080198," ","integrate(1/(4-x)^(1/2)/(-x^2+8*x-15)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, x\right)"," ",0,"integral(sqrt(-x^2 + 8*x - 15)*sqrt(-x + 4)/(x^3 - 12*x^2 + 47*x - 60), x)","F",0
2888,0,0,0,0.823841," ","integrate(1/(6-x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x - 1} \sqrt{x - 2} \sqrt{-x + 6}}{x^{3} - 9 \, x^{2} + 20 \, x - 12}, x\right)"," ",0,"integral(-sqrt(x - 1)*sqrt(x - 2)*sqrt(-x + 6)/(x^3 - 9*x^2 + 20*x - 12), x)","F",0
2889,0,0,0,1.109061," ","integrate(1/((6-x)*(-2+x))^(1/2)/(-1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 8 \, x - 12} \sqrt{x - 1}}{x^{3} - 9 \, x^{2} + 20 \, x - 12}, x\right)"," ",0,"integral(-sqrt(-x^2 + 8*x - 12)*sqrt(x - 1)/(x^3 - 9*x^2 + 20*x - 12), x)","F",0
2890,0,0,0,1.027881," ","integrate(1/(-1+x)^(1/2)/(-x^2+8*x-12)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 8 \, x - 12} \sqrt{x - 1}}{x^{3} - 9 \, x^{2} + 20 \, x - 12}, x\right)"," ",0,"integral(-sqrt(-x^2 + 8*x - 12)*sqrt(x - 1)/(x^3 - 9*x^2 + 20*x - 12), x)","F",0
2891,0,0,0,0.750650," ","integrate((2+3*x)^(7/2)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2892,0,0,0,1.070844," ","integrate((2+3*x)^(5/2)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2893,0,0,0,0.771572," ","integrate((2+3*x)^(3/2)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2894,0,0,0,1.167435," ","integrate((2+3*x)^(1/2)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2895,0,0,0,0.693529," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(12*x^3 - 4*x^2 - 5*x + 2), x)","F",0
2896,0,0,0,1.143574," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4), x)","F",0
2897,0,0,0,0.881963," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8), x)","F",0
2898,0,0,0,0.965963," ","integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16), x)","F",0
2899,0,0,0,1.086432," ","integrate((2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2900,0,0,0,0.772333," ","integrate((2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((45*x^3 + 87*x^2 + 56*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2901,0,0,0,0.937705," ","integrate((2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(15 \, x^{2} + 19 \, x + 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((15*x^2 + 19*x + 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2902,0,0,0,1.056362," ","integrate((3+5*x)^(3/2)*(2+3*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2903,0,0,0,0.585983," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(12*x^3 - 4*x^2 - 5*x + 2), x)","F",0
2904,0,0,0,1.307249," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4), x)","F",0
2905,0,0,0,1.473588," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8), x)","F",0
2906,0,0,0,1.591700," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16), x)","F",0
2907,0,0,0,1.301927," ","integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32}, x\right)"," ",0,"integral((5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32), x)","F",0
2908,0,0,0,0.770651," ","integrate((2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2909,0,0,0,1.292597," ","integrate((2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2910,0,0,0,1.247407," ","integrate((2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((75*x^3 + 140*x^2 + 87*x + 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2911,0,0,0,1.371913," ","integrate((3+5*x)^(5/2)*(2+3*x)^(1/2)/(1-2*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4*x^2 - 4*x + 1), x)","F",0
2912,0,0,0,0.991629," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(12*x^3 - 4*x^2 - 5*x + 2), x)","F",0
2913,0,0,0,1.197139," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(36*x^4 + 12*x^3 - 23*x^2 - 4*x + 4), x)","F",0
2914,0,0,0,0.880274," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8), x)","F",0
2915,0,0,0,0.979457," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(324*x^6 + 540*x^5 + 81*x^4 - 264*x^3 - 104*x^2 + 32*x + 16), x)","F",0
2916,0,0,0,1.188666," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{972 \, x^{7} + 2268 \, x^{6} + 1323 \, x^{5} - 630 \, x^{4} - 840 \, x^{3} - 112 \, x^{2} + 112 \, x + 32}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(972*x^7 + 2268*x^6 + 1323*x^5 - 630*x^4 - 840*x^3 - 112*x^2 + 112*x + 32), x)","F",0
2917,0,0,0,1.379540," ","integrate((3+5*x)^(5/2)/(1-2*x)^(3/2)/(2+3*x)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2916 \, x^{8} + 8748 \, x^{7} + 8505 \, x^{6} + 756 \, x^{5} - 3780 \, x^{4} - 2016 \, x^{3} + 112 \, x^{2} + 320 \, x + 64}, x\right)"," ",0,"integral((25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2916*x^8 + 8748*x^7 + 8505*x^6 + 756*x^5 - 3780*x^4 - 2016*x^3 + 112*x^2 + 320*x + 64), x)","F",0
2918,0,0,0,1.272320," ","integrate((2+3*x)^(7/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3), x)","F",0
2919,0,0,0,1.224965," ","integrate((2+3*x)^(5/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3), x)","F",0
2920,0,0,0,1.306066," ","integrate((2+3*x)^(3/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3), x)","F",0
2921,0,0,0,0.716810," ","integrate((2+3*x)^(1/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(20*x^3 - 8*x^2 - 7*x + 3), x)","F",0
2922,0,0,0,1.237511," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{60 \, x^{4} + 16 \, x^{3} - 37 \, x^{2} - 5 \, x + 6}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(60*x^4 + 16*x^3 - 37*x^2 - 5*x + 6), x)","F",0
2923,0,0,0,1.330660," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(180*x^5 + 168*x^4 - 79*x^3 - 89*x^2 + 8*x + 12), x)","F",0
2924,0,0,0,1.317783," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(540*x^6 + 864*x^5 + 99*x^4 - 425*x^3 - 154*x^2 + 52*x + 24), x)","F",0
2925,0,0,0,1.346445," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1620 \, x^{7} + 3672 \, x^{6} + 2025 \, x^{5} - 1077 \, x^{4} - 1312 \, x^{3} - 152 \, x^{2} + 176 \, x + 48}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1620*x^7 + 3672*x^6 + 2025*x^5 - 1077*x^4 - 1312*x^3 - 152*x^2 + 176*x + 48), x)","F",0
2926,0,0,0,0.872697," ","integrate((2+3*x)^(9/2)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9}, x\right)"," ",0,"integral((81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9), x)","F",0
2927,0,0,0,1.287119," ","integrate((2+3*x)^(7/2)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9), x)","F",0
2928,0,0,0,1.291361," ","integrate((2+3*x)^(5/2)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9), x)","F",0
2929,0,0,0,1.138520," ","integrate((2+3*x)^(3/2)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9), x)","F",0
2930,0,0,0,0.929533," ","integrate((2+3*x)^(1/2)/(1-2*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9), x)","F",0
2931,0,0,0,1.189943," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(300*x^5 + 260*x^4 - 137*x^3 - 136*x^2 + 15*x + 18), x)","F",0
2932,0,0,0,0.895632," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36), x)","F",0
2933,0,0,0,1.282743," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(2700*x^7 + 5940*x^6 + 3087*x^5 - 1828*x^4 - 2045*x^3 - 202*x^2 + 276*x + 72), x)","F",0
2934,0,0,0,1.320814," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8100 \, x^{8} + 23220 \, x^{7} + 21141 \, x^{6} + 690 \, x^{5} - 9791 \, x^{4} - 4696 \, x^{3} + 424 \, x^{2} + 768 \, x + 144}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8100*x^8 + 23220*x^7 + 21141*x^6 + 690*x^5 - 9791*x^4 - 4696*x^3 + 424*x^2 + 768*x + 144), x)","F",0
2935,0,0,0,0.726623," ","integrate((2+3*x)^(11/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral((243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2936,0,0,0,1.440367," ","integrate((2+3*x)^(9/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral((81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2937,0,0,0,1.482198," ","integrate((2+3*x)^(7/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2938,0,0,0,1.239083," ","integrate((2+3*x)^(5/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2939,0,0,0,1.284963," ","integrate((2+3*x)^(3/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral(sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2940,0,0,0,1.331950," ","integrate((2+3*x)^(1/2)/(1-2*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{500 \, x^{5} + 400 \, x^{4} - 235 \, x^{3} - 207 \, x^{2} + 27 \, x + 27}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(500*x^5 + 400*x^4 - 235*x^3 - 207*x^2 + 27*x + 27), x)","F",0
2941,0,0,0,1.376008," ","integrate(1/(1-2*x)^(3/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1500 \, x^{6} + 2200 \, x^{5} + 95 \, x^{4} - 1091 \, x^{3} - 333 \, x^{2} + 135 \, x + 54}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1500*x^6 + 2200*x^5 + 95*x^4 - 1091*x^3 - 333*x^2 + 135*x + 54), x)","F",0
2942,0,0,0,0.761052," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{4500 \, x^{7} + 9600 \, x^{6} + 4685 \, x^{5} - 3083 \, x^{4} - 3181 \, x^{3} - 261 \, x^{2} + 432 \, x + 108}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(4500*x^7 + 9600*x^6 + 4685*x^5 - 3083*x^4 - 3181*x^3 - 261*x^2 + 432*x + 108), x)","F",0
2943,0,0,0,1.277622," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{13500 \, x^{8} + 37800 \, x^{7} + 33255 \, x^{6} + 121 \, x^{5} - 15709 \, x^{4} - 7145 \, x^{3} + 774 \, x^{2} + 1188 \, x + 216}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(13500*x^8 + 37800*x^7 + 33255*x^6 + 121*x^5 - 15709*x^4 - 7145*x^3 + 774*x^2 + 1188*x + 216), x)","F",0
2944,0,0,0,1.256297," ","integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{40500 \, x^{9} + 140400 \, x^{8} + 175365 \, x^{7} + 66873 \, x^{6} - 46885 \, x^{5} - 52853 \, x^{4} - 11968 \, x^{3} + 5112 \, x^{2} + 3024 \, x + 432}, x\right)"," ",0,"integral(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40500*x^9 + 140400*x^8 + 175365*x^7 + 66873*x^6 - 46885*x^5 - 52853*x^4 - 11968*x^3 + 5112*x^2 + 3024*x + 432), x)","F",0
2945,0,0,0,1.303518," ","integrate((2+3*x)^(9/2)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2946,0,0,0,1.225359," ","integrate((2+3*x)^(7/2)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2947,0,0,0,1.608371," ","integrate((2+3*x)^(5/2)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2948,0,0,0,1.222361," ","integrate((2+3*x)^(3/2)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2949,0,0,0,1.274223," ","integrate((2+3*x)^(1/2)*(3+5*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2950,0,0,0,0.753969," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{24 \, x^{4} - 20 \, x^{3} - 6 \, x^{2} + 9 \, x - 2}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(24*x^4 - 20*x^3 - 6*x^2 + 9*x - 2), x)","F",0
2951,0,0,0,0.721675," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{72 \, x^{5} - 12 \, x^{4} - 58 \, x^{3} + 15 \, x^{2} + 12 \, x - 4}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(72*x^5 - 12*x^4 - 58*x^3 + 15*x^2 + 12*x - 4), x)","F",0
2952,0,0,0,1.576361," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{216 \, x^{6} + 108 \, x^{5} - 198 \, x^{4} - 71 \, x^{3} + 66 \, x^{2} + 12 \, x - 8}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(216*x^6 + 108*x^5 - 198*x^4 - 71*x^3 + 66*x^2 + 12*x - 8), x)","F",0
2953,0,0,0,1.309094," ","integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{648 \, x^{7} + 756 \, x^{6} - 378 \, x^{5} - 609 \, x^{4} + 56 \, x^{3} + 168 \, x^{2} - 16}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(648*x^7 + 756*x^6 - 378*x^5 - 609*x^4 + 56*x^3 + 168*x^2 - 16), x)","F",0
2954,0,0,0,1.723479," ","integrate((2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2955,0,0,0,1.027689," ","integrate((2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(45*x^3 + 87*x^2 + 56*x + 12)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2956,0,0,0,1.213258," ","integrate((2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(15 \, x^{2} + 19 \, x + 6\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(15*x^2 + 19*x + 6)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2957,0,0,0,1.202857," ","integrate((3+5*x)^(3/2)*(2+3*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2958,0,0,0,1.053459," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{24 \, x^{4} - 20 \, x^{3} - 6 \, x^{2} + 9 \, x - 2}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(24*x^4 - 20*x^3 - 6*x^2 + 9*x - 2), x)","F",0
2959,0,0,0,1.157073," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{72 \, x^{5} - 12 \, x^{4} - 58 \, x^{3} + 15 \, x^{2} + 12 \, x - 4}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(72*x^5 - 12*x^4 - 58*x^3 + 15*x^2 + 12*x - 4), x)","F",0
2960,0,0,0,0.636034," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{216 \, x^{6} + 108 \, x^{5} - 198 \, x^{4} - 71 \, x^{3} + 66 \, x^{2} + 12 \, x - 8}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(216*x^6 + 108*x^5 - 198*x^4 - 71*x^3 + 66*x^2 + 12*x - 8), x)","F",0
2961,0,0,0,1.129604," ","integrate((3+5*x)^(3/2)/(1-2*x)^(5/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 3\right)}^{\frac{3}{2}} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{648 \, x^{7} + 756 \, x^{6} - 378 \, x^{5} - 609 \, x^{4} + 56 \, x^{3} + 168 \, x^{2} - 16}, x\right)"," ",0,"integral(-(5*x + 3)^(3/2)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(648*x^7 + 756*x^6 - 378*x^5 - 609*x^4 + 56*x^3 + 168*x^2 - 16), x)","F",0
2962,0,0,0,1.218626," ","integrate((2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2963,0,0,0,1.210346," ","integrate((2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2964,0,0,0,1.105448," ","integrate((2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(75*x^3 + 140*x^2 + 87*x + 18)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2965,0,0,0,1.196838," ","integrate((3+5*x)^(5/2)*(2+3*x)^(1/2)/(1-2*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{8 \, x^{3} - 12 \, x^{2} + 6 \, x - 1}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(8*x^3 - 12*x^2 + 6*x - 1), x)","F",0
2966,0,0,0,1.253398," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{24 \, x^{4} - 20 \, x^{3} - 6 \, x^{2} + 9 \, x - 2}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(24*x^4 - 20*x^3 - 6*x^2 + 9*x - 2), x)","F",0
2967,0,0,0,1.404324," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{72 \, x^{5} - 12 \, x^{4} - 58 \, x^{3} + 15 \, x^{2} + 12 \, x - 4}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(72*x^5 - 12*x^4 - 58*x^3 + 15*x^2 + 12*x - 4), x)","F",0
2968,0,0,0,1.747759," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{216 \, x^{6} + 108 \, x^{5} - 198 \, x^{4} - 71 \, x^{3} + 66 \, x^{2} + 12 \, x - 8}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(216*x^6 + 108*x^5 - 198*x^4 - 71*x^3 + 66*x^2 + 12*x - 8), x)","F",0
2969,0,0,0,1.168617," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{648 \, x^{7} + 756 \, x^{6} - 378 \, x^{5} - 609 \, x^{4} + 56 \, x^{3} + 168 \, x^{2} - 16}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(648*x^7 + 756*x^6 - 378*x^5 - 609*x^4 + 56*x^3 + 168*x^2 - 16), x)","F",0
2970,0,0,0,0.824032," ","integrate((3+5*x)^(5/2)/(1-2*x)^(5/2)/(2+3*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1944 \, x^{8} + 3564 \, x^{7} + 378 \, x^{6} - 2583 \, x^{5} - 1050 \, x^{4} + 616 \, x^{3} + 336 \, x^{2} - 48 \, x - 32}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1944*x^8 + 3564*x^7 + 378*x^6 - 2583*x^5 - 1050*x^4 + 616*x^3 + 336*x^2 - 48*x - 32), x)","F",0
2971,0,0,0,3.072979," ","integrate((2+3*x)^(9/2)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{40 \, x^{4} - 36 \, x^{3} - 6 \, x^{2} + 13 \, x - 3}, x\right)"," ",0,"integral(-(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40*x^4 - 36*x^3 - 6*x^2 + 13*x - 3), x)","F",0
2972,0,0,0,1.319414," ","integrate((2+3*x)^(7/2)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{40 \, x^{4} - 36 \, x^{3} - 6 \, x^{2} + 13 \, x - 3}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40*x^4 - 36*x^3 - 6*x^2 + 13*x - 3), x)","F",0
2973,0,0,0,1.297717," ","integrate((2+3*x)^(5/2)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{40 \, x^{4} - 36 \, x^{3} - 6 \, x^{2} + 13 \, x - 3}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40*x^4 - 36*x^3 - 6*x^2 + 13*x - 3), x)","F",0
2974,0,0,0,0.991283," ","integrate((2+3*x)^(3/2)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{40 \, x^{4} - 36 \, x^{3} - 6 \, x^{2} + 13 \, x - 3}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(40*x^4 - 36*x^3 - 6*x^2 + 13*x - 3), x)","F",0
2975,0,0,0,1.359724," ","integrate((2+3*x)^(1/2)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{40 \, x^{4} - 36 \, x^{3} - 6 \, x^{2} + 13 \, x - 3}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(40*x^4 - 36*x^3 - 6*x^2 + 13*x - 3), x)","F",0
2976,0,0,0,1.344223," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{120 \, x^{5} - 28 \, x^{4} - 90 \, x^{3} + 27 \, x^{2} + 17 \, x - 6}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(120*x^5 - 28*x^4 - 90*x^3 + 27*x^2 + 17*x - 6), x)","F",0
2977,0,0,0,1.345816," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{360 \, x^{6} + 156 \, x^{5} - 326 \, x^{4} - 99 \, x^{3} + 105 \, x^{2} + 16 \, x - 12}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(360*x^6 + 156*x^5 - 326*x^4 - 99*x^3 + 105*x^2 + 16*x - 12), x)","F",0
2978,0,0,0,1.346364," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1080 \, x^{7} + 1188 \, x^{6} - 666 \, x^{5} - 949 \, x^{4} + 117 \, x^{3} + 258 \, x^{2} - 4 \, x - 24}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1080*x^7 + 1188*x^6 - 666*x^5 - 949*x^4 + 117*x^3 + 258*x^2 - 4*x - 24), x)","F",0
2979,0,0,0,1.361841," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{3240 \, x^{8} + 5724 \, x^{7} + 378 \, x^{6} - 4179 \, x^{5} - 1547 \, x^{4} + 1008 \, x^{3} + 504 \, x^{2} - 80 \, x - 48}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(3240*x^8 + 5724*x^7 + 378*x^6 - 4179*x^5 - 1547*x^4 + 1008*x^3 + 504*x^2 - 80*x - 48), x)","F",0
2980,0,0,0,1.388005," ","integrate((2+3*x)^(11/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2981,0,0,0,1.328730," ","integrate((2+3*x)^(9/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2982,0,0,0,1.182269," ","integrate((2+3*x)^(7/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2983,0,0,0,1.347206," ","integrate((2+3*x)^(5/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2984,0,0,0,1.094053," ","integrate((2+3*x)^(3/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2985,0,0,0,1.161844," ","integrate((2+3*x)^(1/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{200 \, x^{5} - 60 \, x^{4} - 138 \, x^{3} + 47 \, x^{2} + 24 \, x - 9}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(200*x^5 - 60*x^4 - 138*x^3 + 47*x^2 + 24*x - 9), x)","F",0
2986,0,0,0,1.354997," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{600 \, x^{6} + 220 \, x^{5} - 534 \, x^{4} - 135 \, x^{3} + 166 \, x^{2} + 21 \, x - 18}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(600*x^6 + 220*x^5 - 534*x^4 - 135*x^3 + 166*x^2 + 21*x - 18), x)","F",0
2987,0,0,0,1.145923," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1800 \, x^{7} + 1860 \, x^{6} - 1162 \, x^{5} - 1473 \, x^{4} + 228 \, x^{3} + 395 \, x^{2} - 12 \, x - 36}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1800*x^7 + 1860*x^6 - 1162*x^5 - 1473*x^4 + 228*x^3 + 395*x^2 - 12*x - 36), x)","F",0
2988,0,0,0,1.276789," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{5400 \, x^{8} + 9180 \, x^{7} + 234 \, x^{6} - 6743 \, x^{5} - 2262 \, x^{4} + 1641 \, x^{3} + 754 \, x^{2} - 132 \, x - 72}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(5400*x^8 + 9180*x^7 + 234*x^6 - 6743*x^5 - 2262*x^4 + 1641*x^3 + 754*x^2 - 132*x - 72), x)","F",0
2989,0,0,0,1.191052," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{16200 \, x^{9} + 38340 \, x^{8} + 19062 \, x^{7} - 19761 \, x^{6} - 20272 \, x^{5} + 399 \, x^{4} + 5544 \, x^{3} + 1112 \, x^{2} - 480 \, x - 144}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(16200*x^9 + 38340*x^8 + 19062*x^7 - 19761*x^6 - 20272*x^5 + 399*x^4 + 5544*x^3 + 1112*x^2 - 480*x - 144), x)","F",0
2990,0,0,0,1.256946," ","integrate((2+3*x)^(13/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2991,0,0,0,1.358669," ","integrate((2+3*x)^(11/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-(243*x^5 + 810*x^4 + 1080*x^3 + 720*x^2 + 240*x + 32)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2992,0,0,0,1.180384," ","integrate((2+3*x)^(9/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2993,0,0,0,1.189093," ","integrate((2+3*x)^(7/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-(27*x^3 + 54*x^2 + 36*x + 8)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2994,0,0,0,1.372394," ","integrate((2+3*x)^(5/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(9 \, x^{2} + 12 \, x + 4\right)} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-(9*x^2 + 12*x + 4)*sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2995,0,0,0,1.167922," ","integrate((2+3*x)^(3/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} {\left(3 \, x + 2\right)}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*(3*x + 2)^(3/2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2996,0,0,0,1.233924," ","integrate((2+3*x)^(1/2)/(1-2*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{1000 \, x^{6} + 300 \, x^{5} - 870 \, x^{4} - 179 \, x^{3} + 261 \, x^{2} + 27 \, x - 27}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(1000*x^6 + 300*x^5 - 870*x^4 - 179*x^3 + 261*x^2 + 27*x - 27), x)","F",0
2997,0,0,0,1.377872," ","integrate(1/(1-2*x)^(5/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{3000 \, x^{7} + 2900 \, x^{6} - 2010 \, x^{5} - 2277 \, x^{4} + 425 \, x^{3} + 603 \, x^{2} - 27 \, x - 54}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(3000*x^7 + 2900*x^6 - 2010*x^5 - 2277*x^4 + 425*x^3 + 603*x^2 - 27*x - 54), x)","F",0
2998,0,0,0,1.237561," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{9000 \, x^{8} + 14700 \, x^{7} - 230 \, x^{6} - 10851 \, x^{5} - 3279 \, x^{4} + 2659 \, x^{3} + 1125 \, x^{2} - 216 \, x - 108}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(9000*x^8 + 14700*x^7 - 230*x^6 - 10851*x^5 - 3279*x^4 + 2659*x^3 + 1125*x^2 - 216*x - 108), x)","F",0
2999,0,0,0,1.216039," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{27000 \, x^{9} + 62100 \, x^{8} + 28710 \, x^{7} - 33013 \, x^{6} - 31539 \, x^{5} + 1419 \, x^{4} + 8693 \, x^{3} + 1602 \, x^{2} - 756 \, x - 216}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(27000*x^9 + 62100*x^8 + 28710*x^7 - 33013*x^6 - 31539*x^5 + 1419*x^4 + 8693*x^3 + 1602*x^2 - 756*x - 216), x)","F",0
3000,0,0,0,1.325990," ","integrate(1/(1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}{81000 \, x^{10} + 240300 \, x^{9} + 210330 \, x^{8} - 41619 \, x^{7} - 160643 \, x^{6} - 58821 \, x^{5} + 28917 \, x^{4} + 22192 \, x^{3} + 936 \, x^{2} - 2160 \, x - 432}, x\right)"," ",0,"integral(-sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)/(81000*x^10 + 240300*x^9 + 210330*x^8 - 41619*x^7 - 160643*x^6 - 58821*x^5 + 28917*x^4 + 22192*x^3 + 936*x^2 - 2160*x - 432), x)","F",0
3001,1,1857,0,1.996992," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)*(f*x+e)^2,x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} e^{2} - 6 \, {\left(4 \, b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} - 6 \, a^{2} b^{3} c d^{4} + 5 \, a^{3} b^{2} d^{5}\right)} e f + {\left(7 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 3 \, a^{2} b^{3} c^{2} d^{3} - 10 \, a^{3} b^{2} c d^{4} + 10 \, a^{4} b d^{5}\right)} f^{2}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d - 3 \, \left(b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} - 6 \, {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} e f + {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 10 \, a^{4} d^{4}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 4 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} - 6 \, {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} e f + {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 10 \, a^{4} d^{4}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(81 \, b^{5} d^{4} f^{2} x^{3} + 54 \, {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} e^{2} - 12 \, {\left(8 \, b^{5} c^{2} d^{2} - 4 \, a b^{4} c d^{3} + 5 \, a^{2} b^{3} d^{4}\right)} e f + {\left(28 \, b^{5} c^{3} d - 9 \, a b^{4} c^{2} d^{2} - 12 \, a^{2} b^{3} c d^{3} + 20 \, a^{3} b^{2} d^{4}\right)} f^{2} + 9 \, {\left(24 \, b^{5} d^{4} e f + {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} f^{2}\right)} x^{2} + 3 \, {\left(54 \, b^{5} d^{4} e^{2} + 12 \, {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} e f - {\left(7 \, b^{5} c^{2} d^{2} - 2 \, a b^{4} c d^{3} + 4 \, a^{2} b^{3} d^{4}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{972 \, b^{5} d^{4}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} + a^{2} b^{3} d^{5}\right)} e^{2} - 6 \, {\left(4 \, b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} - 6 \, a^{2} b^{3} c d^{4} + 5 \, a^{3} b^{2} d^{5}\right)} e f + {\left(7 \, b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} - 3 \, a^{2} b^{3} c^{2} d^{3} - 10 \, a^{3} b^{2} c d^{4} + 10 \, a^{4} b d^{5}\right)} f^{2}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} - 6 \, {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} e f + {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 10 \, a^{4} d^{4}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 4 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} - 6 \, {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} e f + {\left(7 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} - 10 \, a^{3} b c d^{3} + 10 \, a^{4} d^{4}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(81 \, b^{5} d^{4} f^{2} x^{3} + 54 \, {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} e^{2} - 12 \, {\left(8 \, b^{5} c^{2} d^{2} - 4 \, a b^{4} c d^{3} + 5 \, a^{2} b^{3} d^{4}\right)} e f + {\left(28 \, b^{5} c^{3} d - 9 \, a b^{4} c^{2} d^{2} - 12 \, a^{2} b^{3} c d^{3} + 20 \, a^{3} b^{2} d^{4}\right)} f^{2} + 9 \, {\left(24 \, b^{5} d^{4} e f + {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} f^{2}\right)} x^{2} + 3 \, {\left(54 \, b^{5} d^{4} e^{2} + 12 \, {\left(2 \, b^{5} c d^{3} + a b^{4} d^{4}\right)} e f - {\left(7 \, b^{5} c^{2} d^{2} - 2 \, a b^{4} c d^{3} + 4 \, a^{2} b^{3} d^{4}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{972 \, b^{5} d^{4}}\right]"," ",0,"[1/972*(6*sqrt(1/3)*(27*(b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*e^2 - 6*(4*b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 - 6*a^2*b^3*c*d^4 + 5*a^3*b^2*d^5)*e*f + (7*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 3*a^2*b^3*c^2*d^3 - 10*a^3*b^2*c*d^4 + 10*a^4*b*d^5)*f^2)*sqrt(-(b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d - 3*(b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b - 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(b^2*d)^(1/3)/d)) - 2*(b^2*d)^(2/3)*(27*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 - 6*(4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*e*f + (7*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 10*a^4*d^4)*f^2)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 4*(b^2*d)^(2/3)*(27*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 - 6*(4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*e*f + (7*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 10*a^4*d^4)*f^2)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) + 3*(81*b^5*d^4*f^2*x^3 + 54*(2*b^5*c*d^3 + a*b^4*d^4)*e^2 - 12*(8*b^5*c^2*d^2 - 4*a*b^4*c*d^3 + 5*a^2*b^3*d^4)*e*f + (28*b^5*c^3*d - 9*a*b^4*c^2*d^2 - 12*a^2*b^3*c*d^3 + 20*a^3*b^2*d^4)*f^2 + 9*(24*b^5*d^4*e*f + (2*b^5*c*d^3 + a*b^4*d^4)*f^2)*x^2 + 3*(54*b^5*d^4*e^2 + 12*(2*b^5*c*d^3 + a*b^4*d^4)*e*f - (7*b^5*c^2*d^2 - 2*a*b^4*c*d^3 + 4*a^2*b^3*d^4)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^5*d^4), -1/972*(12*sqrt(1/3)*(27*(b^5*c^2*d^3 - 2*a*b^4*c*d^4 + a^2*b^3*d^5)*e^2 - 6*(4*b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 - 6*a^2*b^3*c*d^4 + 5*a^3*b^2*d^5)*e*f + (7*b^5*c^4*d - 4*a*b^4*c^3*d^2 - 3*a^2*b^3*c^2*d^3 - 10*a^3*b^2*c*d^4 + 10*a^4*b*d^5)*f^2)*sqrt((b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + 2*(b^2*d)^(2/3)*(27*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 - 6*(4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*e*f + (7*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 10*a^4*d^4)*f^2)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 4*(b^2*d)^(2/3)*(27*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 - 6*(4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*e*f + (7*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 - 10*a^3*b*c*d^3 + 10*a^4*d^4)*f^2)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(81*b^5*d^4*f^2*x^3 + 54*(2*b^5*c*d^3 + a*b^4*d^4)*e^2 - 12*(8*b^5*c^2*d^2 - 4*a*b^4*c*d^3 + 5*a^2*b^3*d^4)*e*f + (28*b^5*c^3*d - 9*a*b^4*c^2*d^2 - 12*a^2*b^3*c*d^3 + 20*a^3*b^2*d^4)*f^2 + 9*(24*b^5*d^4*e*f + (2*b^5*c*d^3 + a*b^4*d^4)*f^2)*x^2 + 3*(54*b^5*d^4*e^2 + 12*(2*b^5*c*d^3 + a*b^4*d^4)*e*f - (7*b^5*c^2*d^2 - 2*a*b^4*c*d^3 + 4*a^2*b^3*d^4)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^5*d^4)]","A",0
3002,1,1196,0,1.366036," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)*(f*x+e),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e - {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} f\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d + 3 \, \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}\right) + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e - {\left(4 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e - {\left(4 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(18 \, b^{4} d^{3} f x^{2} + 9 \, {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e - {\left(8 \, b^{4} c^{2} d - 4 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} f + 3 \, {\left(9 \, b^{4} d^{3} e + {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} f\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, b^{4} d^{3}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e - {\left(4 \, b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} + 5 \, a^{3} b d^{4}\right)} f\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e - {\left(4 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e - {\left(4 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(18 \, b^{4} d^{3} f x^{2} + 9 \, {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e - {\left(8 \, b^{4} c^{2} d - 4 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} f + 3 \, {\left(9 \, b^{4} d^{3} e + {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} f\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, b^{4} d^{3}}\right]"," ",0,"[-1/162*(3*sqrt(1/3)*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e - (4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*f)*sqrt((-b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d + 3*(-b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b + 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((-b^2*d)^(1/3)/d)) + (-b^2*d)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e - (4*b^3*c^3 - 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 5*a^3*d^3)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(-b^2*d)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e - (4*b^3*c^3 - 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 5*a^3*d^3)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(18*b^4*d^3*f*x^2 + 9*(2*b^4*c*d^2 + a*b^3*d^3)*e - (8*b^4*c^2*d - 4*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*f + 3*(9*b^4*d^3*e + (2*b^4*c*d^2 + a*b^3*d^3)*f)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^3), -1/162*(6*sqrt(1/3)*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e - (4*b^4*c^3*d - 3*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 + 5*a^3*b*d^4)*f)*sqrt(-(-b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(-b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + (-b^2*d)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e - (4*b^3*c^3 - 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 5*a^3*d^3)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(-b^2*d)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e - (4*b^3*c^3 - 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 5*a^3*d^3)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(18*b^4*d^3*f*x^2 + 9*(2*b^4*c*d^2 + a*b^3*d^3)*e - (8*b^4*c^2*d - 4*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*f + 3*(9*b^4*d^3*e + (2*b^4*c*d^2 + a*b^3*d^3)*f)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^3)]","B",0
3003,1,716,0,1.221984," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d - 3 \, \left(b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(b^{2} d\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(b^{2} d\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(3 \, b^{3} d^{2} x + 2 \, b^{3} c d + a b^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, b^{3} d^{2}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(b^{2} d\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \left(b^{2} d\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(3 \, b^{3} d^{2} x + 2 \, b^{3} c d + a b^{2} d^{2}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, b^{3} d^{2}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*sqrt(-(b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d - 3*(b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b - 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(b^2*d)^(1/3)/d)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(b^2*d)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(b^2*d)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) + 3*(3*b^3*d^2*x + 2*b^3*c*d + a*b^2*d^2)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^2), -1/18*(6*sqrt(1/3)*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*sqrt((b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(b^2*d)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(b^2*d)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(3*b^3*d^2*x + 2*b^3*c*d + a*b^2*d^2)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^2)]","A",0
3004,1,2014,0,12.643559," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)/(f*x+e),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b^{2} d f - 6 \, \sqrt{3} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \arctan\left(\frac{2 \, \sqrt{3} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \sqrt{3} {\left(b c d e^{2} + a c^{2} f^{2} - {\left(b c^{2} + a c d\right)} e f + {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} x\right)}}{3 \, {\left(b c d e^{2} + a c^{2} f^{2} - {\left(b c^{2} + a c d\right)} e f + {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} x\right)}}\right) - 3 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \log\left(-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 6 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \log\left(-\frac{{\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e - {\left(2 \, b^{2} c d + a b d^{2}\right)} f\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d + 3 \, \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right)}{6 \, b^{2} d f^{2}}, \frac{6 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b^{2} d f - 6 \, \sqrt{3} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \arctan\left(\frac{2 \, \sqrt{3} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \sqrt{3} {\left(b c d e^{2} + a c^{2} f^{2} - {\left(b c^{2} + a c d\right)} e f + {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} x\right)}}{3 \, {\left(b c d e^{2} + a c^{2} f^{2} - {\left(b c^{2} + a c d\right)} e f + {\left(b d^{2} e^{2} + a c d f^{2} - {\left(b c d + a d^{2}\right)} e f\right)} x\right)}}\right) - 3 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \log\left(-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 6 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} b^{2} d \log\left(-\frac{{\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) - 6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e - {\left(2 \, b^{2} c d + a b d^{2}\right)} f\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right)}{6 \, b^{2} d f^{2}}\right]"," ",0,"[1/6*(6*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b^2*d*f - 6*sqrt(3)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*arctan(1/3*(2*sqrt(3)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + sqrt(3)*(b*c*d*e^2 + a*c^2*f^2 - (b*c^2 + a*c*d)*e*f + (b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*x))/(b*c*d*e^2 + a*c^2*f^2 - (b*c^2 + a*c*d)*e*f + (b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*x)) - 3*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*log(-((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 6*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*log(-((d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*x + c))/(d*x + c)) - 3*sqrt(1/3)*(3*b^2*d^2*e - (2*b^2*c*d + a*b*d^2)*f)*sqrt((-b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d + 3*(-b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b + 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((-b^2*d)^(1/3)/d)) - (-b^2*d)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(-b^2*d)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)))/(b^2*d*f^2), 1/6*(6*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b^2*d*f - 6*sqrt(3)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*arctan(1/3*(2*sqrt(3)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + sqrt(3)*(b*c*d*e^2 + a*c^2*f^2 - (b*c^2 + a*c*d)*e*f + (b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*x))/(b*c*d*e^2 + a*c^2*f^2 - (b*c^2 + a*c*d)*e*f + (b*d^2*e^2 + a*c*d*f^2 - (b*c*d + a*d^2)*e*f)*x)) - 3*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*log(-((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 6*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*b^2*d*log(-((d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*x + c))/(d*x + c)) - 6*sqrt(1/3)*(3*b^2*d^2*e - (2*b^2*c*d + a*b*d^2)*f)*sqrt(-(-b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(-b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) - (-b^2*d)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(-b^2*d)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)))/(b^2*d*f^2)]","B",0
3005,1,3608,0,17.985850," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)/(f*x+e)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e^{4} - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{3} f + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} e f^{3} + {\left(3 \, b^{2} d^{2} e^{3} f - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e f^{3} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f + 3 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - 6 \, \sqrt{3} {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \sqrt{3} {\left(b d^{2} x + b c d\right)}}{3 \, {\left(b d^{2} x + b c d\right)}}\right) - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d^{2} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 6 \, {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d + \left(-b d^{2}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) - 6 \, {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} d e^{4} f^{2} - a^{2} c e f^{5} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f^{3} + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{4} + {\left(b^{2} d e^{3} f^{3} - a^{2} c f^{6} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{4} + {\left(2 \, a b c + a^{2} d\right)} e f^{5}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e^{4} - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{3} f + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} e f^{3} + {\left(3 \, b^{2} d^{2} e^{3} f - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e f^{3} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + 6 \, \sqrt{3} {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \sqrt{3} {\left(b d^{2} x + b c d\right)}}{3 \, {\left(b d^{2} x + b c d\right)}}\right) + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d^{2} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 6 \, {\left(b^{2} d e^{4} - a^{2} c e f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{2} + {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} x\right)} \left(-b d^{2}\right)^{\frac{1}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d + \left(-b d^{2}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) + 6 \, {\left(b^{2} d e^{3} f - a^{2} c f^{4} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{2} + {\left(2 \, a b c + a^{2} d\right)} e f^{3}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} d e^{4} f^{2} - a^{2} c e f^{5} - {\left(b^{2} c + 2 \, a b d\right)} e^{3} f^{3} + {\left(2 \, a b c + a^{2} d\right)} e^{2} f^{4} + {\left(b^{2} d e^{3} f^{3} - a^{2} c f^{6} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f^{4} + {\left(2 \, a b c + a^{2} d\right)} e f^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*(3*b^2*d^2*e^4 - (4*b^2*c*d + 5*a*b*d^2)*e^3*f + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e^2*f^2 - (a*b*c^2 + 2*a^2*c*d)*e*f^3 + (3*b^2*d^2*e^3*f - (4*b^2*c*d + 5*a*b*d^2)*e^2*f^2 + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e*f^3 - (a*b*c^2 + 2*a^2*c*d)*f^4)*x)*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f + 3*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - 6*sqrt(3)*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(-b*d^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + sqrt(3)*(b*d^2*x + b*c*d))/(b*d^2*x + b*c*d)) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 3*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*d^2 - (-b*d^2)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*d + (-b*d^2)^(2/3)*(d*x + c))/(d*x + c)) + 6*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*d + (-b*d^2)^(1/3)*(d*x + c))/(d*x + c)) - 6*(b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d*e^4*f^2 - a^2*c*e*f^5 - (b^2*c + 2*a*b*d)*e^3*f^3 + (2*a*b*c + a^2*d)*e^2*f^4 + (b^2*d*e^3*f^3 - a^2*c*f^6 - (b^2*c + 2*a*b*d)*e^2*f^4 + (2*a*b*c + a^2*d)*e*f^5)*x), -1/6*(6*sqrt(1/3)*(3*b^2*d^2*e^4 - (4*b^2*c*d + 5*a*b*d^2)*e^3*f + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e^2*f^2 - (a*b*c^2 + 2*a^2*c*d)*e*f^3 + (3*b^2*d^2*e^3*f - (4*b^2*c*d + 5*a*b*d^2)*e^2*f^2 + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e*f^3 - (a*b*c^2 + 2*a^2*c*d)*f^4)*x)*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + 6*sqrt(3)*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*arctan(1/3*(2*sqrt(3)*(-b*d^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + sqrt(3)*(b*d^2*x + b*c*d))/(b*d^2*x + b*c*d)) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*d^2 - (-b*d^2)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*d + (-b*d^2)^(2/3)*(d*x + c))/(d*x + c)) - 6*(b^2*d*e^4 - a^2*c*e*f^3 - (b^2*c + 2*a*b*d)*e^3*f + (2*a*b*c + a^2*d)*e^2*f^2 + (b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*x)*(-b*d^2)^(1/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*d + (-b*d^2)^(1/3)*(d*x + c))/(d*x + c)) + 6*(b^2*d*e^3*f - a^2*c*f^4 - (b^2*c + 2*a*b*d)*e^2*f^2 + (2*a*b*c + a^2*d)*e*f^3)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d*e^4*f^2 - a^2*c*e*f^5 - (b^2*c + 2*a*b*d)*e^3*f^3 + (2*a*b*c + a^2*d)*e^2*f^4 + (b^2*d*e^3*f^3 - a^2*c*f^6 - (b^2*c + 2*a*b*d)*e^2*f^4 + (2*a*b*c + a^2*d)*e*f^5)*x)]","B",0
3006,1,3992,0,2.117675," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)/(f*x+e)^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{3} f + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} f^{2} + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e f^{3} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{2} f^{2} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e f^{3}\right)} x\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f + 3 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2}\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2}\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(3 \, a^{3} c^{2} f^{4} + {\left(2 \, b^{3} c d + a b^{2} d^{2}\right)} e^{4} - 2 \, {\left(b^{3} c^{2} + 4 \, a b^{2} c d + a^{2} b d^{2}\right)} e^{3} f + {\left(7 \, a b^{2} c^{2} + 10 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{2} - 4 \, {\left(2 \, a^{2} b c^{2} + a^{3} c d\right)} e f^{3} + {\left(3 \, b^{3} d^{2} e^{4} - 4 \, {\left(b^{3} c d + 2 \, a b^{2} d^{2}\right)} e^{3} f + {\left(b^{3} c^{2} + 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} e^{2} f^{2} - 2 \, {\left(a b^{2} c^{2} + 4 \, a^{2} b c d + a^{3} d^{2}\right)} e f^{3} + {\left(a^{2} b c^{2} + 2 \, a^{3} c d\right)} f^{4}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{3} d^{2} e^{7} - a^{3} c^{2} e^{2} f^{5} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{6} f + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{5} f^{2} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{4} f^{3} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e^{3} f^{4} + {\left(b^{3} d^{2} e^{5} f^{2} - a^{3} c^{2} f^{7} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{4} f^{3} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{3} f^{4} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{5} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e f^{6}\right)} x^{2} + 2 \, {\left(b^{3} d^{2} e^{6} f - a^{3} c^{2} e f^{6} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{5} f^{2} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{4} f^{3} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{3} f^{4} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e^{2} f^{5}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{3} f + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} f^{2} + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e f^{3} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{2} f^{2} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e f^{3}\right)} x\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2}\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} f^{2} x^{2} + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e f x + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} e^{2}\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(3 \, a^{3} c^{2} f^{4} + {\left(2 \, b^{3} c d + a b^{2} d^{2}\right)} e^{4} - 2 \, {\left(b^{3} c^{2} + 4 \, a b^{2} c d + a^{2} b d^{2}\right)} e^{3} f + {\left(7 \, a b^{2} c^{2} + 10 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{2} - 4 \, {\left(2 \, a^{2} b c^{2} + a^{3} c d\right)} e f^{3} + {\left(3 \, b^{3} d^{2} e^{4} - 4 \, {\left(b^{3} c d + 2 \, a b^{2} d^{2}\right)} e^{3} f + {\left(b^{3} c^{2} + 10 \, a b^{2} c d + 7 \, a^{2} b d^{2}\right)} e^{2} f^{2} - 2 \, {\left(a b^{2} c^{2} + 4 \, a^{2} b c d + a^{3} d^{2}\right)} e f^{3} + {\left(a^{2} b c^{2} + 2 \, a^{3} c d\right)} f^{4}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{3} d^{2} e^{7} - a^{3} c^{2} e^{2} f^{5} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{6} f + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{5} f^{2} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{4} f^{3} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e^{3} f^{4} + {\left(b^{3} d^{2} e^{5} f^{2} - a^{3} c^{2} f^{7} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{4} f^{3} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{3} f^{4} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{5} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e f^{6}\right)} x^{2} + 2 \, {\left(b^{3} d^{2} e^{6} f - a^{3} c^{2} e f^{6} - {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} e^{5} f^{2} + {\left(b^{3} c^{2} + 6 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} e^{4} f^{3} - {\left(3 \, a b^{2} c^{2} + 6 \, a^{2} b c d + a^{3} d^{2}\right)} e^{3} f^{4} + {\left(3 \, a^{2} b c^{2} + 2 \, a^{3} c d\right)} e^{2} f^{5}\right)} x\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e^3*f + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e^2*f^2 + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e*f^3 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f^4)*x^2 + 2*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e^2*f^2 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*f^3)*x)*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f + 3*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(3*a^3*c^2*f^4 + (2*b^3*c*d + a*b^2*d^2)*e^4 - 2*(b^3*c^2 + 4*a*b^2*c*d + a^2*b*d^2)*e^3*f + (7*a*b^2*c^2 + 10*a^2*b*c*d + a^3*d^2)*e^2*f^2 - 4*(2*a^2*b*c^2 + a^3*c*d)*e*f^3 + (3*b^3*d^2*e^4 - 4*(b^3*c*d + 2*a*b^2*d^2)*e^3*f + (b^3*c^2 + 10*a*b^2*c*d + 7*a^2*b*d^2)*e^2*f^2 - 2*(a*b^2*c^2 + 4*a^2*b*c*d + a^3*d^2)*e*f^3 + (a^2*b*c^2 + 2*a^3*c*d)*f^4)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^2*e^7 - a^3*c^2*e^2*f^5 - (2*b^3*c*d + 3*a*b^2*d^2)*e^6*f + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^5*f^2 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^4*f^3 + (3*a^2*b*c^2 + 2*a^3*c*d)*e^3*f^4 + (b^3*d^2*e^5*f^2 - a^3*c^2*f^7 - (2*b^3*c*d + 3*a*b^2*d^2)*e^4*f^3 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^3*f^4 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^2*f^5 + (3*a^2*b*c^2 + 2*a^3*c*d)*e*f^6)*x^2 + 2*(b^3*d^2*e^6*f - a^3*c^2*e*f^6 - (2*b^3*c*d + 3*a*b^2*d^2)*e^5*f^2 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^4*f^3 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^3*f^4 + (3*a^2*b*c^2 + 2*a^3*c*d)*e^2*f^5)*x), -1/18*(6*sqrt(1/3)*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e^3*f + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e^2*f^2 + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e*f^3 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f^4)*x^2 + 2*((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e^2*f^2 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*f^3)*x)*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*f^2*x^2 + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e*f*x + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*e^2)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 3*(3*a^3*c^2*f^4 + (2*b^3*c*d + a*b^2*d^2)*e^4 - 2*(b^3*c^2 + 4*a*b^2*c*d + a^2*b*d^2)*e^3*f + (7*a*b^2*c^2 + 10*a^2*b*c*d + a^3*d^2)*e^2*f^2 - 4*(2*a^2*b*c^2 + a^3*c*d)*e*f^3 + (3*b^3*d^2*e^4 - 4*(b^3*c*d + 2*a*b^2*d^2)*e^3*f + (b^3*c^2 + 10*a*b^2*c*d + 7*a^2*b*d^2)*e^2*f^2 - 2*(a*b^2*c^2 + 4*a^2*b*c*d + a^3*d^2)*e*f^3 + (a^2*b*c^2 + 2*a^3*c*d)*f^4)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^2*e^7 - a^3*c^2*e^2*f^5 - (2*b^3*c*d + 3*a*b^2*d^2)*e^6*f + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^5*f^2 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^4*f^3 + (3*a^2*b*c^2 + 2*a^3*c*d)*e^3*f^4 + (b^3*d^2*e^5*f^2 - a^3*c^2*f^7 - (2*b^3*c*d + 3*a*b^2*d^2)*e^4*f^3 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^3*f^4 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^2*f^5 + (3*a^2*b*c^2 + 2*a^3*c*d)*e*f^6)*x^2 + 2*(b^3*d^2*e^6*f - a^3*c^2*e*f^6 - (2*b^3*c*d + 3*a*b^2*d^2)*e^5*f^2 + (b^3*c^2 + 6*a*b^2*c*d + 3*a^2*b*d^2)*e^4*f^3 - (3*a*b^2*c^2 + 6*a^2*b*c*d + a^3*d^2)*e^3*f^4 + (3*a^2*b*c^2 + 2*a^3*c*d)*e^2*f^5)*x)]","B",0
3007,1,7932,0,5.991101," ","integrate((b*x+a)^(1/3)*(d*x+c)^(2/3)/(f*x+e)^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{6} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{5} f + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{4} f^{2} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e^{3} f^{3} + {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{3} f^{3} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{2} f^{4} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e f^{5} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} f^{6}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{4} f^{2} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{3} f^{3} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{2} f^{4} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e f^{5}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{5} f - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{4} f^{2} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{3} f^{3} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e^{2} f^{4}\right)} x\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f + 3 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{3} f + {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e f^{3} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} f^{4}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e f^{3}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{2} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{3} f + {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e f^{3} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} f^{4}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e f^{3}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{2} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(18 \, a^{4} c^{3} f^{6} + 9 \, {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e^{6} - {\left(28 \, b^{4} c^{2} d + 103 \, a b^{3} c d^{2} + 22 \, a^{2} b^{2} d^{3}\right)} e^{5} f + {\left(10 \, b^{4} c^{3} + 147 \, a b^{3} c^{2} d + 186 \, a^{2} b^{2} c d^{2} + 17 \, a^{3} b d^{3}\right)} e^{4} f^{2} - {\left(53 \, a b^{3} c^{3} + 258 \, a^{2} b^{2} c^{2} d + 135 \, a^{3} b c d^{2} + 4 \, a^{4} d^{3}\right)} e^{3} f^{3} + {\left(94 \, a^{2} b^{2} c^{3} + 187 \, a^{3} b c^{2} d + 34 \, a^{4} c d^{2}\right)} e^{2} f^{4} - 3 \, {\left(23 \, a^{3} b c^{3} + 16 \, a^{4} c^{2} d\right)} e f^{5} + {\left(9 \, b^{4} d^{3} e^{5} f - 15 \, {\left(b^{4} c d^{2} + 2 \, a b^{3} d^{3}\right)} e^{4} f^{2} + {\left(11 \, b^{4} c^{2} d + 38 \, a b^{3} c d^{2} + 41 \, a^{2} b^{2} d^{3}\right)} e^{3} f^{3} - {\left(5 \, b^{4} c^{3} + 18 \, a b^{3} c^{2} d + 39 \, a^{2} b^{2} c d^{2} + 28 \, a^{3} b d^{3}\right)} e^{2} f^{4} + {\left(10 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} + 8 \, a^{4} d^{3}\right)} e f^{5} - {\left(5 \, a^{2} b^{2} c^{3} - 4 \, a^{3} b c^{2} d + 8 \, a^{4} c d^{2}\right)} f^{6}\right)} x^{2} + {\left(27 \, b^{4} d^{3} e^{6} - 3 \, {\left(17 \, b^{4} c d^{2} + 31 \, a b^{3} d^{3}\right)} e^{5} f + {\left(37 \, b^{4} c^{2} d + 151 \, a b^{3} c d^{2} + 127 \, a^{2} b^{2} d^{3}\right)} e^{4} f^{2} - {\left(13 \, b^{4} c^{3} + 87 \, a b^{3} c^{2} d + 177 \, a^{2} b^{2} c d^{2} + 83 \, a^{3} b d^{3}\right)} e^{3} f^{3} + {\left(29 \, a b^{3} c^{3} + 69 \, a^{2} b^{2} c^{2} d + 105 \, a^{3} b c d^{2} + 22 \, a^{4} d^{3}\right)} e^{2} f^{4} - {\left(19 \, a^{2} b^{2} c^{3} + 25 \, a^{3} b c^{2} d + 28 \, a^{4} c d^{2}\right)} e f^{5} + 3 \, {\left(a^{3} b c^{3} + 2 \, a^{4} c^{2} d\right)} f^{6}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, {\left(b^{4} d^{3} e^{10} - a^{4} c^{3} e^{3} f^{7} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{9} f + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{8} f^{2} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{7} f^{3} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{6} f^{4} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{5} f^{5} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{4} f^{6} + {\left(b^{4} d^{3} e^{7} f^{3} - a^{4} c^{3} f^{10} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{6} f^{4} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{5} f^{5} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{4} f^{6} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{3} f^{7} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{2} f^{8} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e f^{9}\right)} x^{3} + 3 \, {\left(b^{4} d^{3} e^{8} f^{2} - a^{4} c^{3} e f^{9} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{7} f^{3} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{6} f^{4} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{5} f^{5} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{4} f^{6} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{3} f^{7} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{2} f^{8}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{9} f - a^{4} c^{3} e^{2} f^{8} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{8} f^{2} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{7} f^{3} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{6} f^{4} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{5} f^{5} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{4} f^{6} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{3} f^{7}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{6} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{5} f + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{4} f^{2} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e^{3} f^{3} + {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{3} f^{3} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{2} f^{4} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e f^{5} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} f^{6}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{4} f^{2} - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{3} f^{3} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{2} f^{4} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e f^{5}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{5} f - {\left(14 \, b^{4} c^{3} d - 15 \, a b^{3} c^{2} d^{2} - 12 \, a^{2} b^{2} c d^{3} + 13 \, a^{3} b d^{4}\right)} e^{4} f^{2} + {\left(5 \, b^{4} c^{4} + 8 \, a b^{3} c^{3} d - 27 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} + 4 \, a^{4} d^{4}\right)} e^{3} f^{3} - {\left(5 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d - 3 \, a^{3} b c^{2} d^{2} + 4 \, a^{4} c d^{3}\right)} e^{2} f^{4}\right)} x\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{3} f + {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e f^{3} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} f^{4}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e f^{3}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{2} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{3} f + {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e f^{3} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} f^{4}\right)} x^{3} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} f^{2} - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e f^{3}\right)} x^{2} + 3 \, {\left(9 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{3} f - {\left(5 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + 4 \, a^{3} d^{3}\right)} e^{2} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(18 \, a^{4} c^{3} f^{6} + 9 \, {\left(2 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e^{6} - {\left(28 \, b^{4} c^{2} d + 103 \, a b^{3} c d^{2} + 22 \, a^{2} b^{2} d^{3}\right)} e^{5} f + {\left(10 \, b^{4} c^{3} + 147 \, a b^{3} c^{2} d + 186 \, a^{2} b^{2} c d^{2} + 17 \, a^{3} b d^{3}\right)} e^{4} f^{2} - {\left(53 \, a b^{3} c^{3} + 258 \, a^{2} b^{2} c^{2} d + 135 \, a^{3} b c d^{2} + 4 \, a^{4} d^{3}\right)} e^{3} f^{3} + {\left(94 \, a^{2} b^{2} c^{3} + 187 \, a^{3} b c^{2} d + 34 \, a^{4} c d^{2}\right)} e^{2} f^{4} - 3 \, {\left(23 \, a^{3} b c^{3} + 16 \, a^{4} c^{2} d\right)} e f^{5} + {\left(9 \, b^{4} d^{3} e^{5} f - 15 \, {\left(b^{4} c d^{2} + 2 \, a b^{3} d^{3}\right)} e^{4} f^{2} + {\left(11 \, b^{4} c^{2} d + 38 \, a b^{3} c d^{2} + 41 \, a^{2} b^{2} d^{3}\right)} e^{3} f^{3} - {\left(5 \, b^{4} c^{3} + 18 \, a b^{3} c^{2} d + 39 \, a^{2} b^{2} c d^{2} + 28 \, a^{3} b d^{3}\right)} e^{2} f^{4} + {\left(10 \, a b^{3} c^{3} + 3 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} + 8 \, a^{4} d^{3}\right)} e f^{5} - {\left(5 \, a^{2} b^{2} c^{3} - 4 \, a^{3} b c^{2} d + 8 \, a^{4} c d^{2}\right)} f^{6}\right)} x^{2} + {\left(27 \, b^{4} d^{3} e^{6} - 3 \, {\left(17 \, b^{4} c d^{2} + 31 \, a b^{3} d^{3}\right)} e^{5} f + {\left(37 \, b^{4} c^{2} d + 151 \, a b^{3} c d^{2} + 127 \, a^{2} b^{2} d^{3}\right)} e^{4} f^{2} - {\left(13 \, b^{4} c^{3} + 87 \, a b^{3} c^{2} d + 177 \, a^{2} b^{2} c d^{2} + 83 \, a^{3} b d^{3}\right)} e^{3} f^{3} + {\left(29 \, a b^{3} c^{3} + 69 \, a^{2} b^{2} c^{2} d + 105 \, a^{3} b c d^{2} + 22 \, a^{4} d^{3}\right)} e^{2} f^{4} - {\left(19 \, a^{2} b^{2} c^{3} + 25 \, a^{3} b c^{2} d + 28 \, a^{4} c d^{2}\right)} e f^{5} + 3 \, {\left(a^{3} b c^{3} + 2 \, a^{4} c^{2} d\right)} f^{6}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, {\left(b^{4} d^{3} e^{10} - a^{4} c^{3} e^{3} f^{7} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{9} f + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{8} f^{2} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{7} f^{3} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{6} f^{4} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{5} f^{5} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{4} f^{6} + {\left(b^{4} d^{3} e^{7} f^{3} - a^{4} c^{3} f^{10} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{6} f^{4} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{5} f^{5} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{4} f^{6} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{3} f^{7} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{2} f^{8} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e f^{9}\right)} x^{3} + 3 \, {\left(b^{4} d^{3} e^{8} f^{2} - a^{4} c^{3} e f^{9} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{7} f^{3} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{6} f^{4} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{5} f^{5} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{4} f^{6} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{3} f^{7} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{2} f^{8}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{9} f - a^{4} c^{3} e^{2} f^{8} - {\left(3 \, b^{4} c d^{2} + 4 \, a b^{3} d^{3}\right)} e^{8} f^{2} + 3 \, {\left(b^{4} c^{2} d + 4 \, a b^{3} c d^{2} + 2 \, a^{2} b^{2} d^{3}\right)} e^{7} f^{3} - {\left(b^{4} c^{3} + 12 \, a b^{3} c^{2} d + 18 \, a^{2} b^{2} c d^{2} + 4 \, a^{3} b d^{3}\right)} e^{6} f^{4} + {\left(4 \, a b^{3} c^{3} + 18 \, a^{2} b^{2} c^{2} d + 12 \, a^{3} b c d^{2} + a^{4} d^{3}\right)} e^{5} f^{5} - 3 \, {\left(2 \, a^{2} b^{2} c^{3} + 4 \, a^{3} b c^{2} d + a^{4} c d^{2}\right)} e^{4} f^{6} + {\left(4 \, a^{3} b c^{3} + 3 \, a^{4} c^{2} d\right)} e^{3} f^{7}\right)} x\right)}}\right]"," ",0,"[1/162*(3*sqrt(1/3)*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^6 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^5*f + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^4*f^2 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e^3*f^3 + (9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^3*f^3 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^2*f^4 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e*f^5 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*f^6)*x^3 + 3*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^4*f^2 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^3*f^3 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^2*f^4 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e*f^5)*x^2 + 3*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^5*f - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^4*f^2 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^3*f^3 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e^2*f^4)*x)*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f + 3*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^3*f + (9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e*f^3 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*f^4)*x^3 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e*f^3)*x^2 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^2*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^3*f + (9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e*f^3 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*f^4)*x^3 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e*f^3)*x^2 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^2*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(18*a^4*c^3*f^6 + 9*(2*b^4*c*d^2 + a*b^3*d^3)*e^6 - (28*b^4*c^2*d + 103*a*b^3*c*d^2 + 22*a^2*b^2*d^3)*e^5*f + (10*b^4*c^3 + 147*a*b^3*c^2*d + 186*a^2*b^2*c*d^2 + 17*a^3*b*d^3)*e^4*f^2 - (53*a*b^3*c^3 + 258*a^2*b^2*c^2*d + 135*a^3*b*c*d^2 + 4*a^4*d^3)*e^3*f^3 + (94*a^2*b^2*c^3 + 187*a^3*b*c^2*d + 34*a^4*c*d^2)*e^2*f^4 - 3*(23*a^3*b*c^3 + 16*a^4*c^2*d)*e*f^5 + (9*b^4*d^3*e^5*f - 15*(b^4*c*d^2 + 2*a*b^3*d^3)*e^4*f^2 + (11*b^4*c^2*d + 38*a*b^3*c*d^2 + 41*a^2*b^2*d^3)*e^3*f^3 - (5*b^4*c^3 + 18*a*b^3*c^2*d + 39*a^2*b^2*c*d^2 + 28*a^3*b*d^3)*e^2*f^4 + (10*a*b^3*c^3 + 3*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 + 8*a^4*d^3)*e*f^5 - (5*a^2*b^2*c^3 - 4*a^3*b*c^2*d + 8*a^4*c*d^2)*f^6)*x^2 + (27*b^4*d^3*e^6 - 3*(17*b^4*c*d^2 + 31*a*b^3*d^3)*e^5*f + (37*b^4*c^2*d + 151*a*b^3*c*d^2 + 127*a^2*b^2*d^3)*e^4*f^2 - (13*b^4*c^3 + 87*a*b^3*c^2*d + 177*a^2*b^2*c*d^2 + 83*a^3*b*d^3)*e^3*f^3 + (29*a*b^3*c^3 + 69*a^2*b^2*c^2*d + 105*a^3*b*c*d^2 + 22*a^4*d^3)*e^2*f^4 - (19*a^2*b^2*c^3 + 25*a^3*b*c^2*d + 28*a^4*c*d^2)*e*f^5 + 3*(a^3*b*c^3 + 2*a^4*c^2*d)*f^6)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^3*e^10 - a^4*c^3*e^3*f^7 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^9*f + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^8*f^2 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^7*f^3 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^6*f^4 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^5*f^5 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^4*f^6 + (b^4*d^3*e^7*f^3 - a^4*c^3*f^10 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^6*f^4 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^5*f^5 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^4*f^6 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^3*f^7 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^2*f^8 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e*f^9)*x^3 + 3*(b^4*d^3*e^8*f^2 - a^4*c^3*e*f^9 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^7*f^3 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^6*f^4 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^5*f^5 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^4*f^6 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^3*f^7 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^2*f^8)*x^2 + 3*(b^4*d^3*e^9*f - a^4*c^3*e^2*f^8 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^8*f^2 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^7*f^3 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^6*f^4 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^5*f^5 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^4*f^6 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^3*f^7)*x), -1/162*(6*sqrt(1/3)*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^6 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^5*f + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^4*f^2 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e^3*f^3 + (9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^3*f^3 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^2*f^4 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e*f^5 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*f^6)*x^3 + 3*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^4*f^2 - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^3*f^3 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^2*f^4 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e*f^5)*x^2 + 3*(9*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^5*f - (14*b^4*c^3*d - 15*a*b^3*c^2*d^2 - 12*a^2*b^2*c*d^3 + 13*a^3*b*d^4)*e^4*f^2 + (5*b^4*c^4 + 8*a*b^3*c^3*d - 27*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 + 4*a^4*d^4)*e^3*f^3 - (5*a*b^3*c^4 - 6*a^2*b^2*c^3*d - 3*a^3*b*c^2*d^2 + 4*a^4*c*d^3)*e^2*f^4)*x)*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^3*f + (9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e*f^3 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*f^4)*x^3 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e*f^3)*x^2 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^2*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^4 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^3*f + (9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e*f^3 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*f^4)*x^3 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2*f^2 - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e*f^3)*x^2 + 3*(9*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^3*f - (5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 + 4*a^3*d^3)*e^2*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 3*(18*a^4*c^3*f^6 + 9*(2*b^4*c*d^2 + a*b^3*d^3)*e^6 - (28*b^4*c^2*d + 103*a*b^3*c*d^2 + 22*a^2*b^2*d^3)*e^5*f + (10*b^4*c^3 + 147*a*b^3*c^2*d + 186*a^2*b^2*c*d^2 + 17*a^3*b*d^3)*e^4*f^2 - (53*a*b^3*c^3 + 258*a^2*b^2*c^2*d + 135*a^3*b*c*d^2 + 4*a^4*d^3)*e^3*f^3 + (94*a^2*b^2*c^3 + 187*a^3*b*c^2*d + 34*a^4*c*d^2)*e^2*f^4 - 3*(23*a^3*b*c^3 + 16*a^4*c^2*d)*e*f^5 + (9*b^4*d^3*e^5*f - 15*(b^4*c*d^2 + 2*a*b^3*d^3)*e^4*f^2 + (11*b^4*c^2*d + 38*a*b^3*c*d^2 + 41*a^2*b^2*d^3)*e^3*f^3 - (5*b^4*c^3 + 18*a*b^3*c^2*d + 39*a^2*b^2*c*d^2 + 28*a^3*b*d^3)*e^2*f^4 + (10*a*b^3*c^3 + 3*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 + 8*a^4*d^3)*e*f^5 - (5*a^2*b^2*c^3 - 4*a^3*b*c^2*d + 8*a^4*c*d^2)*f^6)*x^2 + (27*b^4*d^3*e^6 - 3*(17*b^4*c*d^2 + 31*a*b^3*d^3)*e^5*f + (37*b^4*c^2*d + 151*a*b^3*c*d^2 + 127*a^2*b^2*d^3)*e^4*f^2 - (13*b^4*c^3 + 87*a*b^3*c^2*d + 177*a^2*b^2*c*d^2 + 83*a^3*b*d^3)*e^3*f^3 + (29*a*b^3*c^3 + 69*a^2*b^2*c^2*d + 105*a^3*b*c*d^2 + 22*a^4*d^3)*e^2*f^4 - (19*a^2*b^2*c^3 + 25*a^3*b*c^2*d + 28*a^4*c*d^2)*e*f^5 + 3*(a^3*b*c^3 + 2*a^4*c^2*d)*f^6)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^3*e^10 - a^4*c^3*e^3*f^7 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^9*f + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^8*f^2 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^7*f^3 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^6*f^4 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^5*f^5 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^4*f^6 + (b^4*d^3*e^7*f^3 - a^4*c^3*f^10 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^6*f^4 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^5*f^5 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^4*f^6 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^3*f^7 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^2*f^8 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e*f^9)*x^3 + 3*(b^4*d^3*e^8*f^2 - a^4*c^3*e*f^9 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^7*f^3 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^6*f^4 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^5*f^5 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^4*f^6 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^3*f^7 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^2*f^8)*x^2 + 3*(b^4*d^3*e^9*f - a^4*c^3*e^2*f^8 - (3*b^4*c*d^2 + 4*a*b^3*d^3)*e^8*f^2 + 3*(b^4*c^2*d + 4*a*b^3*c*d^2 + 2*a^2*b^2*d^3)*e^7*f^3 - (b^4*c^3 + 12*a*b^3*c^2*d + 18*a^2*b^2*c*d^2 + 4*a^3*b*d^3)*e^6*f^4 + (4*a*b^3*c^3 + 18*a^2*b^2*c^2*d + 12*a^3*b*c*d^2 + a^4*d^3)*e^5*f^5 - 3*(2*a^2*b^2*c^3 + 4*a^3*b*c^2*d + a^4*c*d^2)*e^4*f^6 + (4*a^3*b*c^3 + 3*a^4*c^2*d)*e^3*f^7)*x)]","B",0
3008,1,1400,0,1.647777," ","integrate((b*x+a)^(1/3)*(f*x+e)^2/(d*x+c)^(1/3),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{2} - 18 \, {\left(2 \, b^{4} c^{2} d^{2} - a b^{3} c d^{3} - a^{2} b^{2} d^{4}\right)} e f + {\left(14 \, b^{4} c^{3} d - 6 \, a b^{3} c^{2} d^{2} - 3 \, a^{2} b^{2} c d^{3} - 5 \, a^{3} b d^{4}\right)} f^{2}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d + 3 \, \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}\right) + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} - 18 \, {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} e f + {\left(14 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} - 18 \, {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} e f + {\left(14 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(18 \, b^{4} d^{3} f^{2} x^{2} + 54 \, b^{4} d^{3} e^{2} - 18 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} e f + {\left(28 \, b^{4} c^{2} d - 5 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} f^{2} + 3 \, {\left(18 \, b^{4} d^{3} e f - {\left(7 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, b^{4} d^{4}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{2} - 18 \, {\left(2 \, b^{4} c^{2} d^{2} - a b^{3} c d^{3} - a^{2} b^{2} d^{4}\right)} e f + {\left(14 \, b^{4} c^{3} d - 6 \, a b^{3} c^{2} d^{2} - 3 \, a^{2} b^{2} c d^{3} - 5 \, a^{3} b d^{4}\right)} f^{2}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} - 18 \, {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} e f + {\left(14 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} - 18 \, {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} e f + {\left(14 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(18 \, b^{4} d^{3} f^{2} x^{2} + 54 \, b^{4} d^{3} e^{2} - 18 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} e f + {\left(28 \, b^{4} c^{2} d - 5 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} f^{2} + 3 \, {\left(18 \, b^{4} d^{3} e f - {\left(7 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, b^{4} d^{4}}\right]"," ",0,"[-1/162*(3*sqrt(1/3)*(27*(b^4*c*d^3 - a*b^3*d^4)*e^2 - 18*(2*b^4*c^2*d^2 - a*b^3*c*d^3 - a^2*b^2*d^4)*e*f + (14*b^4*c^3*d - 6*a*b^3*c^2*d^2 - 3*a^2*b^2*c*d^3 - 5*a^3*b*d^4)*f^2)*sqrt((-b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d + 3*(-b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b + 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((-b^2*d)^(1/3)/d)) + (-b^2*d)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^2 - 18*(2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*e*f + (14*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f^2)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(-b^2*d)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^2 - 18*(2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*e*f + (14*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f^2)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(18*b^4*d^3*f^2*x^2 + 54*b^4*d^3*e^2 - 18*(4*b^4*c*d^2 - a*b^3*d^3)*e*f + (28*b^4*c^2*d - 5*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*f^2 + 3*(18*b^4*d^3*e*f - (7*b^4*c*d^2 - a*b^3*d^3)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^4), -1/162*(6*sqrt(1/3)*(27*(b^4*c*d^3 - a*b^3*d^4)*e^2 - 18*(2*b^4*c^2*d^2 - a*b^3*c*d^3 - a^2*b^2*d^4)*e*f + (14*b^4*c^3*d - 6*a*b^3*c^2*d^2 - 3*a^2*b^2*c*d^3 - 5*a^3*b*d^4)*f^2)*sqrt(-(-b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(-b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + (-b^2*d)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^2 - 18*(2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*e*f + (14*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f^2)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(-b^2*d)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^2 - 18*(2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*e*f + (14*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f^2)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(18*b^4*d^3*f^2*x^2 + 54*b^4*d^3*e^2 - 18*(4*b^4*c*d^2 - a*b^3*d^3)*e*f + (28*b^4*c^2*d - 5*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*f^2 + 3*(18*b^4*d^3*e*f - (7*b^4*c*d^2 - a*b^3*d^3)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^4)]","A",0
3009,1,892,0,1.163949," ","integrate((b*x+a)^(1/3)*(f*x+e)/(d*x+c)^(1/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e - {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} f\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d - 3 \, \left(b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - \left(b^{2} d\right)^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e - {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e - {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(3 \, b^{3} d^{2} f x + 6 \, b^{3} d^{2} e - {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, b^{3} d^{3}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e - {\left(2 \, b^{3} c^{2} d - a b^{2} c d^{2} - a^{2} b d^{3}\right)} f\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + \left(b^{2} d\right)^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e - {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e - {\left(2 \, b^{2} c^{2} - a b c d - a^{2} d^{2}\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(3 \, b^{3} d^{2} f x + 6 \, b^{3} d^{2} e - {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, b^{3} d^{3}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(3*(b^3*c*d^2 - a*b^2*d^3)*e - (2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*f)*sqrt(-(b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d - 3*(b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b - 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(b^2*d)^(1/3)/d)) - (b^2*d)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e - (2*b^2*c^2 - a*b*c*d - a^2*d^2)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(b^2*d)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e - (2*b^2*c^2 - a*b*c*d - a^2*d^2)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) + 3*(3*b^3*d^2*f*x + 6*b^3*d^2*e - (4*b^3*c*d - a*b^2*d^2)*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^3), -1/18*(6*sqrt(1/3)*(3*(b^3*c*d^2 - a*b^2*d^3)*e - (2*b^3*c^2*d - a*b^2*c*d^2 - a^2*b*d^3)*f)*sqrt((b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + (b^2*d)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e - (2*b^2*c^2 - a*b*c*d - a^2*d^2)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 2*(b^2*d)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e - (2*b^2*c^2 - a*b*c*d - a^2*d^2)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(3*b^3*d^2*f*x + 6*b^3*d^2*e - (4*b^3*c*d - a*b^2*d^2)*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^3)]","A",0
3010,1,618,0,1.494021," ","integrate((b*x+a)^(1/3)/(d*x+c)^(1/3),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b^{2} d - 3 \, \sqrt{\frac{1}{3}} {\left(b^{2} c d - a b d^{2}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d + 3 \, \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right)}{6 \, b^{2} d^{2}}, \frac{6 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b^{2} d - 6 \, \sqrt{\frac{1}{3}} {\left(b^{2} c d - a b d^{2}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b c - a d\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right)}{6 \, b^{2} d^{2}}\right]"," ",0,"[1/6*(6*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b^2*d - 3*sqrt(1/3)*(b^2*c*d - a*b*d^2)*sqrt((-b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d + 3*(-b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b + 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((-b^2*d)^(1/3)/d)) - (-b^2*d)^(2/3)*(b*c - a*d)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(-b^2*d)^(2/3)*(b*c - a*d)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)))/(b^2*d^2), 1/6*(6*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b^2*d - 6*sqrt(1/3)*(b^2*c*d - a*b*d^2)*sqrt(-(-b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(-b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) - (-b^2*d)^(2/3)*(b*c - a*d)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 2*(-b^2*d)^(2/3)*(b*c - a*d)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)))/(b^2*d^2)]","B",0
3011,1,509,0,1.759748," ","integrate((b*x+a)^(1/3)/(d*x+c)^(1/3)/(f*x+e),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{3 \, {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}\right) + 2 \, \sqrt{3} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d \left(-\frac{b}{d}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b d x + b c\right)}}{3 \, {\left(b d x + b c\right)}}\right) + \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) + \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{2}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) - 2 \, \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(d x + c\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right) - 2 \, \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right)}{2 \, f}"," ",0,"-1/2*(2*sqrt(3)*((b*e - a*f)/(d*e - c*f))^(1/3)*arctan(1/3*(2*sqrt(3)*(d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*((b*e - a*f)/(d*e - c*f))^(2/3) + sqrt(3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(b*c*e - a*c*f + (b*d*e - a*d*f)*x)) + 2*sqrt(3)*(-b/d)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*d*(-b/d)^(2/3) + sqrt(3)*(b*d*x + b*c))/(b*d*x + b*c)) + ((b*e - a*f)/(d*e - c*f))^(1/3)*log(((d*x + c)*((b*e - a*f)/(d*e - c*f))^(2/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3)*((b*e - a*f)/(d*e - c*f))^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) + (-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(2/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3)*(-b/d)^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) - 2*((b*e - a*f)/(d*e - c*f))^(1/3)*log(-((d*x + c)*((b*e - a*f)/(d*e - c*f))^(1/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)) - 2*(-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(1/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)))/f","A",0
3012,1,2504,0,2.169071," ","integrate((b*x+a)^(1/3)/(d*x+c)^(1/3)/(f*x+e)^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left({\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} e^{2} f + {\left(a b c^{2} - a^{2} c d\right)} e f^{2} + {\left({\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} e f^{2} + {\left(a b c^{2} - a^{2} c d\right)} f^{3}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f - 3 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b c - a d\right)} f x + {\left(b c - a d\right)} e\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b c - a d\right)} f x + {\left(b c - a d\right)} e\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 6 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} d^{2} e^{5} + a^{2} c^{2} e f^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} e^{4} f + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e^{3} f^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} e^{2} f^{3} + {\left(b^{2} d^{2} e^{4} f + a^{2} c^{2} f^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} e^{3} f^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} e f^{4}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left({\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} e^{2} f + {\left(a b c^{2} - a^{2} c d\right)} e f^{2} + {\left({\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} e f^{2} + {\left(a b c^{2} - a^{2} c d\right)} f^{3}\right)} x\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b c - a d\right)} f x + {\left(b c - a d\right)} e\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left({\left(b c - a d\right)} f x + {\left(b c - a d\right)} e\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 6 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{6 \, {\left(b^{2} d^{2} e^{5} + a^{2} c^{2} e f^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} e^{4} f + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e^{3} f^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} e^{2} f^{3} + {\left(b^{2} d^{2} e^{4} f + a^{2} c^{2} f^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} e^{3} f^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e^{2} f^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} e f^{4}\right)} x\right)}}\right]"," ",0,"[1/6*(3*sqrt(1/3)*((b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 - a^2*d^2)*e^2*f + (a*b*c^2 - a^2*c*d)*e*f^2 + ((b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 - a^2*d^2)*e*f^2 + (a*b*c^2 - a^2*c*d)*f^3)*x)*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f - 3*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b*c - a*d)*f*x + (b*c - a*d)*e)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b*c - a*d)*f*x + (b*c - a*d)*e)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 6*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d^2*e^5 + a^2*c^2*e*f^4 - 2*(b^2*c*d + a*b*d^2)*e^4*f + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^3*f^2 - 2*(a*b*c^2 + a^2*c*d)*e^2*f^3 + (b^2*d^2*e^4*f + a^2*c^2*f^5 - 2*(b^2*c*d + a*b*d^2)*e^3*f^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^2*f^3 - 2*(a*b*c^2 + a^2*c*d)*e*f^4)*x), -1/6*(6*sqrt(1/3)*((b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 - a^2*d^2)*e^2*f + (a*b*c^2 - a^2*c*d)*e*f^2 + ((b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 - a^2*d^2)*e*f^2 + (a*b*c^2 - a^2*c*d)*f^3)*x)*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b*c - a*d)*f*x + (b*c - a*d)*e)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*((b*c - a*d)*f*x + (b*c - a*d)*e)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 6*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d^2*e^5 + a^2*c^2*e*f^4 - 2*(b^2*c*d + a*b*d^2)*e^4*f + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^3*f^2 - 2*(a*b*c^2 + a^2*c*d)*e^2*f^3 + (b^2*d^2*e^4*f + a^2*c^2*f^5 - 2*(b^2*c*d + a*b*d^2)*e^3*f^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e^2*f^3 - 2*(a*b*c^2 + a^2*c*d)*e*f^4)*x)]","B",0
3013,1,4776,0,4.309879," ","integrate((b*x+a)^(1/3)/(d*x+c)^(1/3)/(f*x+e)^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{4} f + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e^{3} f^{2} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} e^{2} f^{3} + {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e f^{4} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} f^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e^{2} f^{3} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} e f^{4}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f - 3 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e^{2} f + {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e f^{2} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} f^{3}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e^{2} f + {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e f^{2} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} f^{3}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(6 \, b^{3} d^{2} e^{5} - 3 \, a^{3} c^{2} f^{5} - {\left(8 \, b^{3} c d + 19 \, a b^{2} d^{2}\right)} e^{4} f + 2 \, {\left(b^{3} c^{2} + 13 \, a b^{2} c d + 10 \, a^{2} b d^{2}\right)} e^{3} f^{2} - 7 \, {\left(a b^{2} c^{2} + 4 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{3} + 2 \, {\left(4 \, a^{2} b c^{2} + 5 \, a^{3} c d\right)} e f^{4} + {\left(3 \, b^{3} d^{2} e^{4} f - 2 \, {\left(b^{3} c d + 5 \, a b^{2} d^{2}\right)} e^{3} f^{2} - {\left(b^{3} c^{2} - 8 \, a b^{2} c d - 11 \, a^{2} b d^{2}\right)} e^{2} f^{3} + 2 \, {\left(a b^{2} c^{2} - 5 \, a^{2} b c d - 2 \, a^{3} d^{2}\right)} e f^{4} - {\left(a^{2} b c^{2} - 4 \, a^{3} c d\right)} f^{5}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{3} d^{3} e^{8} + a^{3} c^{3} e^{2} f^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{7} f + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{6} f^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{5} f^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{4} f^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e^{3} f^{5} + {\left(b^{3} d^{3} e^{6} f^{2} + a^{3} c^{3} f^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{5} f^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} f^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{3} f^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} f^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e f^{7}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} e^{7} f + a^{3} c^{3} e f^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{6} f^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{5} f^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{4} f^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{3} f^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e^{2} f^{6}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{4} f + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e^{3} f^{2} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} e^{2} f^{3} + {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e f^{4} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} f^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - {\left(4 \, b^{3} c^{2} d + a b^{2} c d^{2} - 5 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(b^{3} c^{3} + 5 \, a b^{2} c^{2} d - 4 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3}\right)} e^{2} f^{3} - {\left(a b^{2} c^{3} + a^{2} b c^{2} d - 2 \, a^{3} c d^{2}\right)} e f^{4}\right)} x\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e^{2} f + {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e f^{2} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} f^{3}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{3} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e^{2} f + {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e f^{2} - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} f^{3}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c d - a b d^{2}\right)} e^{2} f - {\left(b^{2} c^{2} + a b c d - 2 \, a^{2} d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(6 \, b^{3} d^{2} e^{5} - 3 \, a^{3} c^{2} f^{5} - {\left(8 \, b^{3} c d + 19 \, a b^{2} d^{2}\right)} e^{4} f + 2 \, {\left(b^{3} c^{2} + 13 \, a b^{2} c d + 10 \, a^{2} b d^{2}\right)} e^{3} f^{2} - 7 \, {\left(a b^{2} c^{2} + 4 \, a^{2} b c d + a^{3} d^{2}\right)} e^{2} f^{3} + 2 \, {\left(4 \, a^{2} b c^{2} + 5 \, a^{3} c d\right)} e f^{4} + {\left(3 \, b^{3} d^{2} e^{4} f - 2 \, {\left(b^{3} c d + 5 \, a b^{2} d^{2}\right)} e^{3} f^{2} - {\left(b^{3} c^{2} - 8 \, a b^{2} c d - 11 \, a^{2} b d^{2}\right)} e^{2} f^{3} + 2 \, {\left(a b^{2} c^{2} - 5 \, a^{2} b c d - 2 \, a^{3} d^{2}\right)} e f^{4} - {\left(a^{2} b c^{2} - 4 \, a^{3} c d\right)} f^{5}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{3} d^{3} e^{8} + a^{3} c^{3} e^{2} f^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{7} f + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{6} f^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{5} f^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{4} f^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e^{3} f^{5} + {\left(b^{3} d^{3} e^{6} f^{2} + a^{3} c^{3} f^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{5} f^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{4} f^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{3} f^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} f^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e f^{7}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} e^{7} f + a^{3} c^{3} e f^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{6} f^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{5} f^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{4} f^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{3} f^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} e^{2} f^{6}\right)} x\right)}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(3*(b^3*c*d^2 - a*b^2*d^3)*e^5 - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^4*f + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e^3*f^2 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*e^2*f^3 + (3*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^2*f^3 + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e*f^4 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*f^5)*x^2 + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^3*f^2 + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e^2*f^3 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*e*f^4)*x)*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f - 3*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e^2*f + (3*(b^2*c*d - a*b*d^2)*e*f^2 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*f^3)*x^2 + 2*(3*(b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e^2*f + (3*(b^2*c*d - a*b*d^2)*e*f^2 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*f^3)*x^2 + 2*(3*(b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(6*b^3*d^2*e^5 - 3*a^3*c^2*f^5 - (8*b^3*c*d + 19*a*b^2*d^2)*e^4*f + 2*(b^3*c^2 + 13*a*b^2*c*d + 10*a^2*b*d^2)*e^3*f^2 - 7*(a*b^2*c^2 + 4*a^2*b*c*d + a^3*d^2)*e^2*f^3 + 2*(4*a^2*b*c^2 + 5*a^3*c*d)*e*f^4 + (3*b^3*d^2*e^4*f - 2*(b^3*c*d + 5*a*b^2*d^2)*e^3*f^2 - (b^3*c^2 - 8*a*b^2*c*d - 11*a^2*b*d^2)*e^2*f^3 + 2*(a*b^2*c^2 - 5*a^2*b*c*d - 2*a^3*d^2)*e*f^4 - (a^2*b*c^2 - 4*a^3*c*d)*f^5)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^3*e^8 + a^3*c^3*e^2*f^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^7*f + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^6*f^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^5*f^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^4*f^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*e^3*f^5 + (b^3*d^3*e^6*f^2 + a^3*c^3*f^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^5*f^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^4*f^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^3*f^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^2*f^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*e*f^7)*x^2 + 2*(b^3*d^3*e^7*f + a^3*c^3*e*f^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^6*f^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^5*f^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^4*f^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^3*f^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*e^2*f^6)*x), -1/18*(6*sqrt(1/3)*(3*(b^3*c*d^2 - a*b^2*d^3)*e^5 - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^4*f + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e^3*f^2 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*e^2*f^3 + (3*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^2*f^3 + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e*f^4 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*f^5)*x^2 + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - (4*b^3*c^2*d + a*b^2*c*d^2 - 5*a^2*b*d^3)*e^3*f^2 + (b^3*c^3 + 5*a*b^2*c^2*d - 4*a^2*b*c*d^2 - 2*a^3*d^3)*e^2*f^3 - (a*b^2*c^3 + a^2*b*c^2*d - 2*a^3*c*d^2)*e*f^4)*x)*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e^2*f + (3*(b^2*c*d - a*b*d^2)*e*f^2 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*f^3)*x^2 + 2*(3*(b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(3*(b^2*c*d - a*b*d^2)*e^3 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e^2*f + (3*(b^2*c*d - a*b*d^2)*e*f^2 - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*f^3)*x^2 + 2*(3*(b^2*c*d - a*b*d^2)*e^2*f - (b^2*c^2 + a*b*c*d - 2*a^2*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 3*(6*b^3*d^2*e^5 - 3*a^3*c^2*f^5 - (8*b^3*c*d + 19*a*b^2*d^2)*e^4*f + 2*(b^3*c^2 + 13*a*b^2*c*d + 10*a^2*b*d^2)*e^3*f^2 - 7*(a*b^2*c^2 + 4*a^2*b*c*d + a^3*d^2)*e^2*f^3 + 2*(4*a^2*b*c^2 + 5*a^3*c*d)*e*f^4 + (3*b^3*d^2*e^4*f - 2*(b^3*c*d + 5*a*b^2*d^2)*e^3*f^2 - (b^3*c^2 - 8*a*b^2*c*d - 11*a^2*b*d^2)*e^2*f^3 + 2*(a*b^2*c^2 - 5*a^2*b*c*d - 2*a^3*d^2)*e*f^4 - (a^2*b*c^2 - 4*a^3*c*d)*f^5)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^3*e^8 + a^3*c^3*e^2*f^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^7*f + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^6*f^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^5*f^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^4*f^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*e^3*f^5 + (b^3*d^3*e^6*f^2 + a^3*c^3*f^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^5*f^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^4*f^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^3*f^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^2*f^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*e*f^7)*x^2 + 2*(b^3*d^3*e^7*f + a^3*c^3*e*f^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*e^6*f^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*e^5*f^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*e^4*f^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*e^3*f^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*e^2*f^6)*x)]","B",0
3014,1,9090,0,36.568680," ","integrate((b*x+a)^(1/3)/(d*x+c)^(1/3)/(f*x+e)^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{7} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{6} f + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{5} f^{2} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{4} f^{3} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e^{3} f^{4} + {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{4} f^{3} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{3} f^{4} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{2} f^{5} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e f^{6} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} f^{7}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{5} f^{2} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{4} f^{3} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{3} f^{4} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{2} f^{5} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e f^{6}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{6} f - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{5} f^{2} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{4} f^{3} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{3} f^{4} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e^{2} f^{5}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f - 3 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{4} f + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} f^{3} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e f^{4} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) + 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{4} f + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} f^{3} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e f^{4} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(54 \, b^{4} d^{3} e^{7} - 18 \, a^{4} c^{3} f^{7} - 18 \, {\left(5 \, b^{4} c d^{2} + 13 \, a b^{3} d^{3}\right)} e^{6} f + {\left(46 \, b^{4} c^{2} d + 409 \, a b^{3} c d^{2} + 373 \, a^{2} b^{2} d^{3}\right)} e^{5} f^{2} - 2 \, {\left(5 \, b^{4} c^{3} + 114 \, a b^{3} c^{2} d + 336 \, a^{2} b^{2} c d^{2} + 130 \, a^{3} b d^{3}\right)} e^{4} f^{3} + {\left(53 \, a b^{3} c^{3} + 393 \, a^{2} b^{2} c^{2} d + 477 \, a^{3} b c d^{2} + 67 \, a^{4} d^{3}\right)} e^{3} f^{4} - 2 \, {\left(47 \, a^{2} b^{2} c^{3} + 143 \, a^{3} b c^{2} d + 62 \, a^{4} c d^{2}\right)} e^{2} f^{5} + 3 \, {\left(23 \, a^{3} b c^{3} + 25 \, a^{4} c^{2} d\right)} e f^{6} + {\left(18 \, b^{4} d^{3} e^{5} f^{2} - 3 \, {\left(b^{4} c d^{2} + 29 \, a b^{3} d^{3}\right)} e^{4} f^{3} - 4 \, {\left(5 \, b^{4} c^{2} d - 13 \, a b^{3} c d^{2} - 37 \, a^{2} b^{2} d^{3}\right)} e^{3} f^{4} + {\left(5 \, b^{4} c^{3} + 45 \, a b^{3} c^{2} d - 123 \, a^{2} b^{2} c d^{2} - 107 \, a^{3} b d^{3}\right)} e^{2} f^{5} - 2 \, {\left(5 \, a b^{3} c^{3} + 15 \, a^{2} b^{2} c^{2} d - 51 \, a^{3} b c d^{2} - 14 \, a^{4} d^{3}\right)} e f^{6} + {\left(5 \, a^{2} b^{2} c^{3} + 5 \, a^{3} b c^{2} d - 28 \, a^{4} c d^{2}\right)} f^{7}\right)} x^{2} + {\left(54 \, b^{4} d^{3} e^{6} f - 3 \, {\left(13 \, b^{4} c d^{2} + 83 \, a b^{3} d^{3}\right)} e^{5} f^{2} - 7 \, {\left(4 \, b^{4} c^{2} d - 35 \, a b^{3} c d^{2} - 59 \, a^{2} b^{2} d^{3}\right)} e^{4} f^{3} + {\left(13 \, b^{4} c^{3} + 33 \, a b^{3} c^{2} d - 471 \, a^{2} b^{2} c d^{2} - 295 \, a^{3} b d^{3}\right)} e^{3} f^{4} - {\left(29 \, a b^{3} c^{3} - 39 \, a^{2} b^{2} c^{2} d - 363 \, a^{3} b c d^{2} - 77 \, a^{4} d^{3}\right)} e^{2} f^{5} + {\left(19 \, a^{2} b^{2} c^{3} - 65 \, a^{3} b c^{2} d - 98 \, a^{4} c d^{2}\right)} e f^{6} - 3 \, {\left(a^{3} b c^{3} - 7 \, a^{4} c^{2} d\right)} f^{7}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, {\left(b^{4} d^{4} e^{11} + a^{4} c^{4} e^{3} f^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{10} f + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{9} f^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{8} f^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{7} f^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{6} f^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{5} f^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{4} f^{7} + {\left(b^{4} d^{4} e^{8} f^{3} + a^{4} c^{4} f^{11} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{7} f^{4} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{6} f^{5} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{5} f^{6} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{4} f^{7} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{3} f^{8} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{2} f^{9} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e f^{10}\right)} x^{3} + 3 \, {\left(b^{4} d^{4} e^{9} f^{2} + a^{4} c^{4} e f^{10} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{8} f^{3} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{7} f^{4} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{6} f^{5} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{5} f^{6} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{4} f^{7} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{3} f^{8} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{2} f^{9}\right)} x^{2} + 3 \, {\left(b^{4} d^{4} e^{10} f + a^{4} c^{4} e^{2} f^{9} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{9} f^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{8} f^{3} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{7} f^{4} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{6} f^{5} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{5} f^{6} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{4} f^{7} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{3} f^{8}\right)} x\right)}}, -\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{7} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{6} f + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{5} f^{2} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{4} f^{3} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e^{3} f^{4} + {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{4} f^{3} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{3} f^{4} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{2} f^{5} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e f^{6} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} f^{7}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{5} f^{2} - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{4} f^{3} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{3} f^{4} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{2} f^{5} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e f^{6}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{6} f - 9 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} - 7 \, a^{2} b^{2} d^{4}\right)} e^{5} f^{2} + {\left(23 \, b^{4} c^{3} d + 66 \, a b^{3} c^{2} d^{2} - 39 \, a^{2} b^{2} c d^{3} - 50 \, a^{3} b d^{4}\right)} e^{4} f^{3} - {\left(5 \, b^{4} c^{4} + 26 \, a b^{3} c^{3} d + 27 \, a^{2} b^{2} c^{2} d^{2} - 44 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{3} f^{4} + {\left(5 \, a b^{3} c^{4} + 3 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} - 14 \, a^{4} c d^{3}\right)} e^{2} f^{5}\right)} x\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{4} f + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} f^{3} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e f^{4} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 2 \, {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{5} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{4} f + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} f^{3} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e f^{4} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{3} f^{2} - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{2} f^{3} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4}\right)} x^{2} + 3 \, {\left(27 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{4} f - 18 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} e^{3} f^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(b^{2} d e^{3} - a^{2} c f^{3} - {\left(b^{2} c + 2 \, a b d\right)} e^{2} f + {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(54 \, b^{4} d^{3} e^{7} - 18 \, a^{4} c^{3} f^{7} - 18 \, {\left(5 \, b^{4} c d^{2} + 13 \, a b^{3} d^{3}\right)} e^{6} f + {\left(46 \, b^{4} c^{2} d + 409 \, a b^{3} c d^{2} + 373 \, a^{2} b^{2} d^{3}\right)} e^{5} f^{2} - 2 \, {\left(5 \, b^{4} c^{3} + 114 \, a b^{3} c^{2} d + 336 \, a^{2} b^{2} c d^{2} + 130 \, a^{3} b d^{3}\right)} e^{4} f^{3} + {\left(53 \, a b^{3} c^{3} + 393 \, a^{2} b^{2} c^{2} d + 477 \, a^{3} b c d^{2} + 67 \, a^{4} d^{3}\right)} e^{3} f^{4} - 2 \, {\left(47 \, a^{2} b^{2} c^{3} + 143 \, a^{3} b c^{2} d + 62 \, a^{4} c d^{2}\right)} e^{2} f^{5} + 3 \, {\left(23 \, a^{3} b c^{3} + 25 \, a^{4} c^{2} d\right)} e f^{6} + {\left(18 \, b^{4} d^{3} e^{5} f^{2} - 3 \, {\left(b^{4} c d^{2} + 29 \, a b^{3} d^{3}\right)} e^{4} f^{3} - 4 \, {\left(5 \, b^{4} c^{2} d - 13 \, a b^{3} c d^{2} - 37 \, a^{2} b^{2} d^{3}\right)} e^{3} f^{4} + {\left(5 \, b^{4} c^{3} + 45 \, a b^{3} c^{2} d - 123 \, a^{2} b^{2} c d^{2} - 107 \, a^{3} b d^{3}\right)} e^{2} f^{5} - 2 \, {\left(5 \, a b^{3} c^{3} + 15 \, a^{2} b^{2} c^{2} d - 51 \, a^{3} b c d^{2} - 14 \, a^{4} d^{3}\right)} e f^{6} + {\left(5 \, a^{2} b^{2} c^{3} + 5 \, a^{3} b c^{2} d - 28 \, a^{4} c d^{2}\right)} f^{7}\right)} x^{2} + {\left(54 \, b^{4} d^{3} e^{6} f - 3 \, {\left(13 \, b^{4} c d^{2} + 83 \, a b^{3} d^{3}\right)} e^{5} f^{2} - 7 \, {\left(4 \, b^{4} c^{2} d - 35 \, a b^{3} c d^{2} - 59 \, a^{2} b^{2} d^{3}\right)} e^{4} f^{3} + {\left(13 \, b^{4} c^{3} + 33 \, a b^{3} c^{2} d - 471 \, a^{2} b^{2} c d^{2} - 295 \, a^{3} b d^{3}\right)} e^{3} f^{4} - {\left(29 \, a b^{3} c^{3} - 39 \, a^{2} b^{2} c^{2} d - 363 \, a^{3} b c d^{2} - 77 \, a^{4} d^{3}\right)} e^{2} f^{5} + {\left(19 \, a^{2} b^{2} c^{3} - 65 \, a^{3} b c^{2} d - 98 \, a^{4} c d^{2}\right)} e f^{6} - 3 \, {\left(a^{3} b c^{3} - 7 \, a^{4} c^{2} d\right)} f^{7}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{162 \, {\left(b^{4} d^{4} e^{11} + a^{4} c^{4} e^{3} f^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{10} f + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{9} f^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{8} f^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{7} f^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{6} f^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{5} f^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{4} f^{7} + {\left(b^{4} d^{4} e^{8} f^{3} + a^{4} c^{4} f^{11} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{7} f^{4} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{6} f^{5} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{5} f^{6} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{4} f^{7} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{3} f^{8} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{2} f^{9} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e f^{10}\right)} x^{3} + 3 \, {\left(b^{4} d^{4} e^{9} f^{2} + a^{4} c^{4} e f^{10} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{8} f^{3} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{7} f^{4} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{6} f^{5} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{5} f^{6} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{4} f^{7} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{3} f^{8} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{2} f^{9}\right)} x^{2} + 3 \, {\left(b^{4} d^{4} e^{10} f + a^{4} c^{4} e^{2} f^{9} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{9} f^{2} + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} e^{8} f^{3} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} e^{7} f^{4} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} e^{6} f^{5} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{5} f^{6} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{4} f^{7} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} e^{3} f^{8}\right)} x\right)}}\right]"," ",0,"[1/162*(3*sqrt(1/3)*(27*(b^4*c*d^3 - a*b^3*d^4)*e^7 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^6*f + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^5*f^2 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^4*f^3 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e^3*f^4 + (27*(b^4*c*d^3 - a*b^3*d^4)*e^4*f^3 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^3*f^4 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^2*f^5 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e*f^6 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*f^7)*x^3 + 3*(27*(b^4*c*d^3 - a*b^3*d^4)*e^5*f^2 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^4*f^3 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^3*f^4 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^2*f^5 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e*f^6)*x^2 + 3*(27*(b^4*c*d^3 - a*b^3*d^4)*e^6*f - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^5*f^2 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^4*f^3 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^3*f^4 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e^2*f^5)*x)*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f - 3*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^5 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^4*f + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^3*f^2 + (27*(b^3*c*d^2 - a*b^2*d^3)*e^2*f^3 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e*f^4 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^2*f^3 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4)*x^2 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^3*f^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) + 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^5 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^4*f + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^3*f^2 + (27*(b^3*c*d^2 - a*b^2*d^3)*e^2*f^3 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e*f^4 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^2*f^3 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4)*x^2 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^3*f^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(54*b^4*d^3*e^7 - 18*a^4*c^3*f^7 - 18*(5*b^4*c*d^2 + 13*a*b^3*d^3)*e^6*f + (46*b^4*c^2*d + 409*a*b^3*c*d^2 + 373*a^2*b^2*d^3)*e^5*f^2 - 2*(5*b^4*c^3 + 114*a*b^3*c^2*d + 336*a^2*b^2*c*d^2 + 130*a^3*b*d^3)*e^4*f^3 + (53*a*b^3*c^3 + 393*a^2*b^2*c^2*d + 477*a^3*b*c*d^2 + 67*a^4*d^3)*e^3*f^4 - 2*(47*a^2*b^2*c^3 + 143*a^3*b*c^2*d + 62*a^4*c*d^2)*e^2*f^5 + 3*(23*a^3*b*c^3 + 25*a^4*c^2*d)*e*f^6 + (18*b^4*d^3*e^5*f^2 - 3*(b^4*c*d^2 + 29*a*b^3*d^3)*e^4*f^3 - 4*(5*b^4*c^2*d - 13*a*b^3*c*d^2 - 37*a^2*b^2*d^3)*e^3*f^4 + (5*b^4*c^3 + 45*a*b^3*c^2*d - 123*a^2*b^2*c*d^2 - 107*a^3*b*d^3)*e^2*f^5 - 2*(5*a*b^3*c^3 + 15*a^2*b^2*c^2*d - 51*a^3*b*c*d^2 - 14*a^4*d^3)*e*f^6 + (5*a^2*b^2*c^3 + 5*a^3*b*c^2*d - 28*a^4*c*d^2)*f^7)*x^2 + (54*b^4*d^3*e^6*f - 3*(13*b^4*c*d^2 + 83*a*b^3*d^3)*e^5*f^2 - 7*(4*b^4*c^2*d - 35*a*b^3*c*d^2 - 59*a^2*b^2*d^3)*e^4*f^3 + (13*b^4*c^3 + 33*a*b^3*c^2*d - 471*a^2*b^2*c*d^2 - 295*a^3*b*d^3)*e^3*f^4 - (29*a*b^3*c^3 - 39*a^2*b^2*c^2*d - 363*a^3*b*c*d^2 - 77*a^4*d^3)*e^2*f^5 + (19*a^2*b^2*c^3 - 65*a^3*b*c^2*d - 98*a^4*c*d^2)*e*f^6 - 3*(a^3*b*c^3 - 7*a^4*c^2*d)*f^7)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^4*e^11 + a^4*c^4*e^3*f^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^10*f + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^9*f^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^8*f^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^7*f^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^6*f^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^5*f^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^4*f^7 + (b^4*d^4*e^8*f^3 + a^4*c^4*f^11 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^7*f^4 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^6*f^5 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^5*f^6 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^4*f^7 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^3*f^8 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^2*f^9 - 4*(a^3*b*c^4 + a^4*c^3*d)*e*f^10)*x^3 + 3*(b^4*d^4*e^9*f^2 + a^4*c^4*e*f^10 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^8*f^3 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^7*f^4 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^6*f^5 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^5*f^6 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^4*f^7 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^3*f^8 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^2*f^9)*x^2 + 3*(b^4*d^4*e^10*f + a^4*c^4*e^2*f^9 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^9*f^2 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^8*f^3 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^7*f^4 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^6*f^5 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^5*f^6 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^4*f^7 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^3*f^8)*x), -1/162*(6*sqrt(1/3)*(27*(b^4*c*d^3 - a*b^3*d^4)*e^7 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^6*f + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^5*f^2 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^4*f^3 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e^3*f^4 + (27*(b^4*c*d^3 - a*b^3*d^4)*e^4*f^3 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^3*f^4 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^2*f^5 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e*f^6 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*f^7)*x^3 + 3*(27*(b^4*c*d^3 - a*b^3*d^4)*e^5*f^2 - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^4*f^3 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^3*f^4 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^2*f^5 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e*f^6)*x^2 + 3*(27*(b^4*c*d^3 - a*b^3*d^4)*e^6*f - 9*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 - 7*a^2*b^2*d^4)*e^5*f^2 + (23*b^4*c^3*d + 66*a*b^3*c^2*d^2 - 39*a^2*b^2*c*d^3 - 50*a^3*b*d^4)*e^4*f^3 - (5*b^4*c^4 + 26*a*b^3*c^3*d + 27*a^2*b^2*c^2*d^2 - 44*a^3*b*c*d^3 - 14*a^4*d^4)*e^3*f^4 + (5*a*b^3*c^4 + 3*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 14*a^4*c*d^3)*e^2*f^5)*x)*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^5 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^4*f + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^3*f^2 + (27*(b^3*c*d^2 - a*b^2*d^3)*e^2*f^3 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e*f^4 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^2*f^3 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4)*x^2 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^3*f^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 2*(b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c*d^2 - a*b^2*d^3)*e^5 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^4*f + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^3*f^2 + (27*(b^3*c*d^2 - a*b^2*d^3)*e^2*f^3 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e*f^4 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^3*f^2 - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^2*f^3 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4)*x^2 + 3*(27*(b^3*c*d^2 - a*b^2*d^3)*e^4*f - 18*(b^3*c^2*d + a*b^2*c*d^2 - 2*a^2*b*d^3)*e^3*f^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 14*a^3*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d*e^3 - a^2*c*f^3 - (b^2*c + 2*a*b*d)*e^2*f + (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) - 3*(54*b^4*d^3*e^7 - 18*a^4*c^3*f^7 - 18*(5*b^4*c*d^2 + 13*a*b^3*d^3)*e^6*f + (46*b^4*c^2*d + 409*a*b^3*c*d^2 + 373*a^2*b^2*d^3)*e^5*f^2 - 2*(5*b^4*c^3 + 114*a*b^3*c^2*d + 336*a^2*b^2*c*d^2 + 130*a^3*b*d^3)*e^4*f^3 + (53*a*b^3*c^3 + 393*a^2*b^2*c^2*d + 477*a^3*b*c*d^2 + 67*a^4*d^3)*e^3*f^4 - 2*(47*a^2*b^2*c^3 + 143*a^3*b*c^2*d + 62*a^4*c*d^2)*e^2*f^5 + 3*(23*a^3*b*c^3 + 25*a^4*c^2*d)*e*f^6 + (18*b^4*d^3*e^5*f^2 - 3*(b^4*c*d^2 + 29*a*b^3*d^3)*e^4*f^3 - 4*(5*b^4*c^2*d - 13*a*b^3*c*d^2 - 37*a^2*b^2*d^3)*e^3*f^4 + (5*b^4*c^3 + 45*a*b^3*c^2*d - 123*a^2*b^2*c*d^2 - 107*a^3*b*d^3)*e^2*f^5 - 2*(5*a*b^3*c^3 + 15*a^2*b^2*c^2*d - 51*a^3*b*c*d^2 - 14*a^4*d^3)*e*f^6 + (5*a^2*b^2*c^3 + 5*a^3*b*c^2*d - 28*a^4*c*d^2)*f^7)*x^2 + (54*b^4*d^3*e^6*f - 3*(13*b^4*c*d^2 + 83*a*b^3*d^3)*e^5*f^2 - 7*(4*b^4*c^2*d - 35*a*b^3*c*d^2 - 59*a^2*b^2*d^3)*e^4*f^3 + (13*b^4*c^3 + 33*a*b^3*c^2*d - 471*a^2*b^2*c*d^2 - 295*a^3*b*d^3)*e^3*f^4 - (29*a*b^3*c^3 - 39*a^2*b^2*c^2*d - 363*a^3*b*c*d^2 - 77*a^4*d^3)*e^2*f^5 + (19*a^2*b^2*c^3 - 65*a^3*b*c^2*d - 98*a^4*c*d^2)*e*f^6 - 3*(a^3*b*c^3 - 7*a^4*c^2*d)*f^7)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^4*d^4*e^11 + a^4*c^4*e^3*f^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^10*f + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^9*f^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^8*f^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^7*f^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^6*f^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^5*f^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^4*f^7 + (b^4*d^4*e^8*f^3 + a^4*c^4*f^11 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^7*f^4 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^6*f^5 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^5*f^6 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^4*f^7 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^3*f^8 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^2*f^9 - 4*(a^3*b*c^4 + a^4*c^3*d)*e*f^10)*x^3 + 3*(b^4*d^4*e^9*f^2 + a^4*c^4*e*f^10 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^8*f^3 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^7*f^4 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^6*f^5 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^5*f^6 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^4*f^7 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^3*f^8 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^2*f^9)*x^2 + 3*(b^4*d^4*e^10*f + a^4*c^4*e^2*f^9 - 4*(b^4*c*d^3 + a*b^3*d^4)*e^9*f^2 + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*e^8*f^3 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*e^7*f^4 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*e^6*f^5 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*e^5*f^6 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^4*f^7 - 4*(a^3*b*c^4 + a^4*c^3*d)*e^3*f^8)*x)]","B",0
3015,1,1481,0,3.400667," ","integrate((f*x+e)^3/(b*x+a)^(1/3)/(d*x+c)^(2/3),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(81 \, b^{4} d^{4} e^{3} - 81 \, {\left(2 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{2} f + 27 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} e f^{2} - {\left(40 \, b^{4} c^{3} d + 15 \, a b^{3} c^{2} d^{2} + 12 \, a^{2} b^{2} c d^{3} + 14 \, a^{3} b d^{4}\right)} f^{3}\right)} \sqrt{-\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}} \log\left(-3 \, b d^{2} x - 2 \, b c d - a d^{2} + 3 \, \left(b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{-\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}}\right) + 2 \, {\left(81 \, b^{3} d^{3} e^{3} - 81 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{2} f + 27 \, {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} e f^{2} - {\left(40 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} + 14 \, a^{3} d^{3}\right)} f^{3}\right)} \left(b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) - {\left(81 \, b^{3} d^{3} e^{3} - 81 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{2} f + 27 \, {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} e f^{2} - {\left(40 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} + 14 \, a^{3} d^{3}\right)} f^{3}\right)} \left(b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right) - 3 \, {\left(18 \, b^{3} d^{4} f^{3} x^{2} + 162 \, b^{3} d^{4} e^{2} f - 27 \, {\left(5 \, b^{3} c d^{3} + 4 \, a b^{2} d^{4}\right)} e f^{2} + {\left(40 \, b^{3} c^{2} d^{2} + 31 \, a b^{2} c d^{3} + 28 \, a^{2} b d^{4}\right)} f^{3} + 3 \, {\left(27 \, b^{3} d^{4} e f^{2} - {\left(8 \, b^{3} c d^{3} + 7 \, a b^{2} d^{4}\right)} f^{3}\right)} x\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{162 \, b^{4} d^{5}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(81 \, b^{4} d^{4} e^{3} - 81 \, {\left(2 \, b^{4} c d^{3} + a b^{3} d^{4}\right)} e^{2} f + 27 \, {\left(5 \, b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} e f^{2} - {\left(40 \, b^{4} c^{3} d + 15 \, a b^{3} c^{2} d^{2} + 12 \, a^{2} b^{2} c d^{3} + 14 \, a^{3} b d^{4}\right)} f^{3}\right)} \sqrt{\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}}}{b d^{2} x + a d^{2}}\right) - 2 \, {\left(81 \, b^{3} d^{3} e^{3} - 81 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{2} f + 27 \, {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} e f^{2} - {\left(40 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} + 14 \, a^{3} d^{3}\right)} f^{3}\right)} \left(b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(81 \, b^{3} d^{3} e^{3} - 81 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e^{2} f + 27 \, {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} e f^{2} - {\left(40 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} + 14 \, a^{3} d^{3}\right)} f^{3}\right)} \left(b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right) + 3 \, {\left(18 \, b^{3} d^{4} f^{3} x^{2} + 162 \, b^{3} d^{4} e^{2} f - 27 \, {\left(5 \, b^{3} c d^{3} + 4 \, a b^{2} d^{4}\right)} e f^{2} + {\left(40 \, b^{3} c^{2} d^{2} + 31 \, a b^{2} c d^{3} + 28 \, a^{2} b d^{4}\right)} f^{3} + 3 \, {\left(27 \, b^{3} d^{4} e f^{2} - {\left(8 \, b^{3} c d^{3} + 7 \, a b^{2} d^{4}\right)} f^{3}\right)} x\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{162 \, b^{4} d^{5}}\right]"," ",0,"[-1/162*(3*sqrt(1/3)*(81*b^4*d^4*e^3 - 81*(2*b^4*c*d^3 + a*b^3*d^4)*e^2*f + 27*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*e*f^2 - (40*b^4*c^3*d + 15*a*b^3*c^2*d^2 + 12*a^2*b^2*c*d^3 + 14*a^3*b*d^4)*f^3)*sqrt(-(b*d^2)^(1/3)/b)*log(-3*b*d^2*x - 2*b*c*d - a*d^2 + 3*(b*d^2)^(1/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3)*d + 3*sqrt(1/3)*(2*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (b*d^2)^(1/3)*(b*d*x + a*d))*sqrt(-(b*d^2)^(1/3)/b)) + 2*(81*b^3*d^3*e^3 - 81*(2*b^3*c*d^2 + a*b^2*d^3)*e^2*f + 27*(5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*e*f^2 - (40*b^3*c^3 + 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 + 14*a^3*d^3)*f^3)*(b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b*d^2)^(2/3)*(b*x + a))/(b*x + a)) - (81*b^3*d^3*e^3 - 81*(2*b^3*c*d^2 + a*b^2*d^3)*e^2*f + 27*(5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*e*f^2 - (40*b^3*c^3 + 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 + 14*a^3*d^3)*f^3)*(b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)) - 3*(18*b^3*d^4*f^3*x^2 + 162*b^3*d^4*e^2*f - 27*(5*b^3*c*d^3 + 4*a*b^2*d^4)*e*f^2 + (40*b^3*c^2*d^2 + 31*a*b^2*c*d^3 + 28*a^2*b*d^4)*f^3 + 3*(27*b^3*d^4*e*f^2 - (8*b^3*c*d^3 + 7*a*b^2*d^4)*f^3)*x)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^4*d^5), 1/162*(6*sqrt(1/3)*(81*b^4*d^4*e^3 - 81*(2*b^4*c*d^3 + a*b^3*d^4)*e^2*f + 27*(5*b^4*c^2*d^2 + 2*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*e*f^2 - (40*b^4*c^3*d + 15*a*b^3*c^2*d^2 + 12*a^2*b^2*c*d^3 + 14*a^3*b*d^4)*f^3)*sqrt((b*d^2)^(1/3)/b)*arctan(sqrt(1/3)*(2*(b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))*sqrt((b*d^2)^(1/3)/b)/(b*d^2*x + a*d^2)) - 2*(81*b^3*d^3*e^3 - 81*(2*b^3*c*d^2 + a*b^2*d^3)*e^2*f + 27*(5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*e*f^2 - (40*b^3*c^3 + 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 + 14*a^3*d^3)*f^3)*(b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (81*b^3*d^3*e^3 - 81*(2*b^3*c*d^2 + a*b^2*d^3)*e^2*f + 27*(5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*e*f^2 - (40*b^3*c^3 + 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 + 14*a^3*d^3)*f^3)*(b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)) + 3*(18*b^3*d^4*f^3*x^2 + 162*b^3*d^4*e^2*f - 27*(5*b^3*c*d^3 + 4*a*b^2*d^4)*e*f^2 + (40*b^3*c^2*d^2 + 31*a*b^2*c*d^3 + 28*a^2*b*d^4)*f^3 + 3*(27*b^3*d^4*e*f^2 - (8*b^3*c*d^3 + 7*a*b^2*d^4)*f^3)*x)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^4*d^5)]","A",0
3016,1,1001,0,2.016419," ","integrate((f*x+e)^2/(b*x+a)^(1/3)/(d*x+c)^(2/3),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} d^{3} e^{2} - 6 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e f + {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} f^{2}\right)} \sqrt{\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}} \log\left(-3 \, b d^{2} x - 2 \, b c d - a d^{2} - 3 \, \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}}\right) - 2 \, {\left(9 \, b^{2} d^{2} e^{2} - 6 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} e f + {\left(5 \, b^{2} c^{2} + 2 \, a b c d + 2 \, a^{2} d^{2}\right)} f^{2}\right)} \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(9 \, b^{2} d^{2} e^{2} - 6 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} e f + {\left(5 \, b^{2} c^{2} + 2 \, a b c d + 2 \, a^{2} d^{2}\right)} f^{2}\right)} \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right) + 3 \, {\left(3 \, b^{2} d^{3} f^{2} x + 12 \, b^{2} d^{3} e f - {\left(5 \, b^{2} c d^{2} + 4 \, a b d^{3}\right)} f^{2}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{18 \, b^{3} d^{4}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} d^{3} e^{2} - 6 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} e f + {\left(5 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} f^{2}\right)} \sqrt{-\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{-\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}}}{b d^{2} x + a d^{2}}\right) - 2 \, {\left(9 \, b^{2} d^{2} e^{2} - 6 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} e f + {\left(5 \, b^{2} c^{2} + 2 \, a b c d + 2 \, a^{2} d^{2}\right)} f^{2}\right)} \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(9 \, b^{2} d^{2} e^{2} - 6 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} e f + {\left(5 \, b^{2} c^{2} + 2 \, a b c d + 2 \, a^{2} d^{2}\right)} f^{2}\right)} \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right) + 3 \, {\left(3 \, b^{2} d^{3} f^{2} x + 12 \, b^{2} d^{3} e f - {\left(5 \, b^{2} c d^{2} + 4 \, a b d^{3}\right)} f^{2}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{18 \, b^{3} d^{4}}\right]"," ",0,"[1/18*(3*sqrt(1/3)*(9*b^3*d^3*e^2 - 6*(2*b^3*c*d^2 + a*b^2*d^3)*e*f + (5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*f^2)*sqrt((-b*d^2)^(1/3)/b)*log(-3*b*d^2*x - 2*b*c*d - a*d^2 - 3*(-b*d^2)^(1/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3)*d - 3*sqrt(1/3)*(2*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b*d^2)^(1/3)*(b*d*x + a*d))*sqrt((-b*d^2)^(1/3)/b)) - 2*(9*b^2*d^2*e^2 - 6*(2*b^2*c*d + a*b*d^2)*e*f + (5*b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*f^2)*(-b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (9*b^2*d^2*e^2 - 6*(2*b^2*c*d + a*b*d^2)*e*f + (5*b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*f^2)*(-b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)) + 3*(3*b^2*d^3*f^2*x + 12*b^2*d^3*e*f - (5*b^2*c*d^2 + 4*a*b*d^3)*f^2)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^3*d^4), 1/18*(6*sqrt(1/3)*(9*b^3*d^3*e^2 - 6*(2*b^3*c*d^2 + a*b^2*d^3)*e*f + (5*b^3*c^2*d + 2*a*b^2*c*d^2 + 2*a^2*b*d^3)*f^2)*sqrt(-(-b*d^2)^(1/3)/b)*arctan(sqrt(1/3)*(2*(-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))*sqrt(-(-b*d^2)^(1/3)/b)/(b*d^2*x + a*d^2)) - 2*(9*b^2*d^2*e^2 - 6*(2*b^2*c*d + a*b*d^2)*e*f + (5*b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*f^2)*(-b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (9*b^2*d^2*e^2 - 6*(2*b^2*c*d + a*b*d^2)*e*f + (5*b^2*c^2 + 2*a*b*c*d + 2*a^2*d^2)*f^2)*(-b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)) + 3*(3*b^2*d^3*f^2*x + 12*b^2*d^3*e*f - (5*b^2*c*d^2 + 4*a*b*d^3)*f^2)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^3*d^4)]","A",0
3017,1,660,0,1.482053," ","integrate((f*x+e)/(b*x+a)^(1/3)/(d*x+c)^(2/3),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d^{2} f - 3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e - {\left(2 \, b^{2} c d + a b d^{2}\right)} f\right)} \sqrt{-\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}} \log\left(-3 \, b d^{2} x - 2 \, b c d - a d^{2} + 3 \, \left(b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{-\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}}\right) - 2 \, \left(b d^{2}\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + \left(b d^{2}\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right)}{6 \, b^{2} d^{3}}, \frac{6 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d^{2} f + 6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e - {\left(2 \, b^{2} c d + a b d^{2}\right)} f\right)} \sqrt{\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{\frac{\left(b d^{2}\right)^{\frac{1}{3}}}{b}}}{b d^{2} x + a d^{2}}\right) - 2 \, \left(b d^{2}\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + \left(b d^{2}\right)^{\frac{2}{3}} {\left(3 \, b d e - {\left(2 \, b c + a d\right)} f\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right)}{6 \, b^{2} d^{3}}\right]"," ",0,"[1/6*(6*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d^2*f - 3*sqrt(1/3)*(3*b^2*d^2*e - (2*b^2*c*d + a*b*d^2)*f)*sqrt(-(b*d^2)^(1/3)/b)*log(-3*b*d^2*x - 2*b*c*d - a*d^2 + 3*(b*d^2)^(1/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3)*d + 3*sqrt(1/3)*(2*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (b*d^2)^(1/3)*(b*d*x + a*d))*sqrt(-(b*d^2)^(1/3)/b)) - 2*(b*d^2)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (b*d^2)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)))/(b^2*d^3), 1/6*(6*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d^2*f + 6*sqrt(1/3)*(3*b^2*d^2*e - (2*b^2*c*d + a*b*d^2)*f)*sqrt((b*d^2)^(1/3)/b)*arctan(sqrt(1/3)*(2*(b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))*sqrt((b*d^2)^(1/3)/b)/(b*d^2*x + a*d^2)) - 2*(b*d^2)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (b*d^2)^(2/3)*(3*b*d*e - (2*b*c + a*d)*f)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)))/(b^2*d^3)]","A",0
3018,1,521,0,1.971689," ","integrate(1/(b*x+a)^(1/3)/(d*x+c)^(2/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} b d \sqrt{\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}} \log\left(-3 \, b d^{2} x - 2 \, b c d - a d^{2} - 3 \, \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} d - \sqrt{3} {\left(2 \, {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}}\right) - 2 \, \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right)}{2 \, b d^{2}}, \frac{2 \, \sqrt{3} b d \sqrt{-\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}} \arctan\left(\frac{\sqrt{3} {\left(2 \, \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}\right)} \sqrt{-\frac{\left(-b d^{2}\right)^{\frac{1}{3}}}{b}}}{3 \, {\left(b d^{2} x + a d^{2}\right)}}\right) - 2 \, \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + \left(-b d^{2}\right)^{\frac{2}{3}} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d + \left(-b d^{2}\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - \left(-b d^{2}\right)^{\frac{1}{3}} {\left(b d x + a d\right)}}{b x + a}\right)}{2 \, b d^{2}}\right]"," ",0,"[1/2*(sqrt(3)*b*d*sqrt((-b*d^2)^(1/3)/b)*log(-3*b*d^2*x - 2*b*c*d - a*d^2 - 3*(-b*d^2)^(1/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3)*d - sqrt(3)*(2*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b*d^2)^(1/3)*(b*d*x + a*d))*sqrt((-b*d^2)^(1/3)/b)) - 2*(-b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (-b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)))/(b*d^2), 1/2*(2*sqrt(3)*b*d*sqrt(-(-b*d^2)^(1/3)/b)*arctan(1/3*sqrt(3)*(2*(-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))*sqrt(-(-b*d^2)^(1/3)/b)/(b*d^2*x + a*d^2)) - 2*(-b*d^2)^(2/3)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b*d^2)^(2/3)*(b*x + a))/(b*x + a)) + (-b*d^2)^(2/3)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d + (-b*d^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2)^(1/3)*(b*d*x + a*d))/(b*x + a)))/(b*d^2)]","B",0
3019,1,1825,0,1.267086," ","integrate(1/(b*x+a)^(1/3)/(d*x+c)^(2/3)/(f*x+e),x, algorithm=""fricas"")","\left[-\frac{\sqrt{3} {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \log\left(\frac{3 \, a c^{2} f^{2} + {\left(2 \, b c d + a d^{2}\right)} e^{2} - 2 \, {\left(b c^{2} + 2 \, a c d\right)} e f + 3 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(3 \, b d^{2} e^{2} - 2 \, {\left(2 \, b c d + a d^{2}\right)} e f + {\left(b c^{2} + 2 \, a c d\right)} f^{2}\right)} x - \sqrt{3} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{f x + e}\right) + 2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right)}{2 \, {\left(b d^{2} e^{3} - a c^{2} f^{3} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f + {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}}, \frac{2 \, \sqrt{3} {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2} + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} x\right)}}\right) - 2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right)}{2 \, {\left(b d^{2} e^{3} - a c^{2} f^{3} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f + {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}}\right]"," ",0,"[-1/2*(sqrt(3)*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*log((3*a*c^2*f^2 + (2*b*c*d + a*d^2)*e^2 - 2*(b*c^2 + 2*a*c*d)*e*f + 3*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*e - c*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (3*b*d^2*e^2 - 2*(2*b*c*d + a*d^2)*e*f + (b*c^2 + 2*a*c*d)*f^2)*x - sqrt(3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f)))/(f*x + e)) + 2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)))/(b*d^2*e^3 - a*c^2*f^3 - (2*b*c*d + a*d^2)*e^2*f + (b*c^2 + 2*a*c*d)*e*f^2), 1/2*(2*sqrt(3)*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*arctan(1/3*sqrt(3)*(2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))/(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2 + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*x)) - 2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)))/(b*d^2*e^3 - a*c^2*f^3 - (2*b*c*d + a*d^2)*e^2*f + (b*c^2 + 2*a*c*d)*e*f^2)]","B",0
3020,1,2859,0,3.319251," ","integrate(1/(b*x+a)^(1/3)/(d*x+c)^(2/3)/(f*x+e)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e^{4} - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{3} f + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} e f^{3} + {\left(3 \, b^{2} d^{2} e^{3} f - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e f^{3} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \log\left(\frac{3 \, a c^{2} f^{2} + {\left(2 \, b c d + a d^{2}\right)} e^{2} - 2 \, {\left(b c^{2} + 2 \, a c d\right)} e f + 3 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(3 \, b d^{2} e^{2} - 2 \, {\left(2 \, b c d + a d^{2}\right)} e f + {\left(b c^{2} + 2 \, a c d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{f x + e}\right) + 2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right) + 6 \, {\left(b d^{2} e^{3} f - a c^{2} f^{4} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{6 \, {\left(b^{2} d^{3} e^{6} - a^{2} c^{3} e f^{5} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{5} f + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} e^{4} f^{2} - {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e^{3} f^{3} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} e^{2} f^{4} + {\left(b^{2} d^{3} e^{5} f - a^{2} c^{3} f^{6} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{4} f^{2} + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} e^{3} f^{3} - {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e^{2} f^{4} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} e f^{5}\right)} x\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(3 \, b^{2} d^{2} e^{4} - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{3} f + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e^{2} f^{2} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} e f^{3} + {\left(3 \, b^{2} d^{2} e^{3} f - {\left(4 \, b^{2} c d + 5 \, a b d^{2}\right)} e^{2} f^{2} + {\left(b^{2} c^{2} + 6 \, a b c d + 2 \, a^{2} d^{2}\right)} e f^{3} - {\left(a b c^{2} + 2 \, a^{2} c d\right)} f^{4}\right)} x\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2} + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} x}\right) - 2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(3 \, b d e^{2} - {\left(b c + 2 \, a d\right)} e f + {\left(3 \, b d e f - {\left(b c + 2 \, a d\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right) - 6 \, {\left(b d^{2} e^{3} f - a c^{2} f^{4} - {\left(2 \, b c d + a d^{2}\right)} e^{2} f^{2} + {\left(b c^{2} + 2 \, a c d\right)} e f^{3}\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{6 \, {\left(b^{2} d^{3} e^{6} - a^{2} c^{3} e f^{5} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{5} f + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} e^{4} f^{2} - {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e^{3} f^{3} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} e^{2} f^{4} + {\left(b^{2} d^{3} e^{5} f - a^{2} c^{3} f^{6} - {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} e^{4} f^{2} + {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} e^{3} f^{3} - {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} e^{2} f^{4} + {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} e f^{5}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*sqrt(1/3)*(3*b^2*d^2*e^4 - (4*b^2*c*d + 5*a*b*d^2)*e^3*f + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e^2*f^2 - (a*b*c^2 + 2*a^2*c*d)*e*f^3 + (3*b^2*d^2*e^3*f - (4*b^2*c*d + 5*a*b*d^2)*e^2*f^2 + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e*f^3 - (a*b*c^2 + 2*a^2*c*d)*f^4)*x)*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*log((3*a*c^2*f^2 + (2*b*c*d + a*d^2)*e^2 - 2*(b*c^2 + 2*a*c*d)*e*f + 3*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*e - c*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (3*b*d^2*e^2 - 2*(2*b*c*d + a*d^2)*e*f + (b*c^2 + 2*a*c*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f)))/(f*x + e)) + 2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)) + 6*(b*d^2*e^3*f - a*c^2*f^4 - (2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^2*d^3*e^6 - a^2*c^3*e*f^5 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^5*f + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*e^4*f^2 - (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*e^3*f^3 + (2*a*b*c^3 + 3*a^2*c^2*d)*e^2*f^4 + (b^2*d^3*e^5*f - a^2*c^3*f^6 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^4*f^2 + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*e^3*f^3 - (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*e^2*f^4 + (2*a*b*c^3 + 3*a^2*c^2*d)*e*f^5)*x), 1/6*(6*sqrt(1/3)*(3*b^2*d^2*e^4 - (4*b^2*c*d + 5*a*b*d^2)*e^3*f + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e^2*f^2 - (a*b*c^2 + 2*a^2*c*d)*e*f^3 + (3*b^2*d^2*e^3*f - (4*b^2*c*d + 5*a*b*d^2)*e^2*f^2 + (b^2*c^2 + 6*a*b*c*d + 2*a^2*d^2)*e*f^3 - (a*b*c^2 + 2*a^2*c*d)*f^4)*x)*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*arctan(sqrt(1/3)*(2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))/(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2 + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*x)) - 2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(3*b*d*e^2 - (b*c + 2*a*d)*e*f + (3*b*d*e*f - (b*c + 2*a*d)*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)) - 6*(b*d^2*e^3*f - a*c^2*f^4 - (2*b*c*d + a*d^2)*e^2*f^2 + (b*c^2 + 2*a*c*d)*e*f^3)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^2*d^3*e^6 - a^2*c^3*e*f^5 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^5*f + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*e^4*f^2 - (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*e^3*f^3 + (2*a*b*c^3 + 3*a^2*c^2*d)*e^2*f^4 + (b^2*d^3*e^5*f - a^2*c^3*f^6 - (3*b^2*c*d^2 + 2*a*b*d^3)*e^4*f^2 + (3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*e^3*f^3 - (b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*e^2*f^4 + (2*a*b*c^3 + 3*a^2*c^2*d)*e*f^5)*x)]","B",0
3021,1,5445,0,25.574029," ","integrate(1/(b*x+a)^(1/3)/(d*x+c)^(2/3)/(f*x+e)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} d^{3} e^{6} - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{5} f + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{4} f^{2} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e^{3} f^{3} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e^{2} f^{4} + {\left(9 \, b^{3} d^{3} e^{4} f^{2} - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{3} f^{3} + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{2} f^{4} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e f^{5} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} f^{6}\right)} x^{2} + 2 \, {\left(9 \, b^{3} d^{3} e^{5} f - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{4} f^{2} + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{3} f^{3} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e^{2} f^{4} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e f^{5}\right)} x\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \log\left(\frac{3 \, a c^{2} f^{2} + {\left(2 \, b c d + a d^{2}\right)} e^{2} - 2 \, {\left(b c^{2} + 2 \, a c d\right)} e f + 3 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(3 \, b d^{2} e^{2} - 2 \, {\left(2 \, b c d + a d^{2}\right)} e f + {\left(b c^{2} + 2 \, a c d\right)} f^{2}\right)} x - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{f x + e}\right) + 2 \, {\left(9 \, b^{2} d^{2} e^{4} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{3} f + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e^{2} f^{2} + {\left(9 \, b^{2} d^{2} e^{2} f^{2} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e f^{3} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(9 \, b^{2} d^{2} e^{3} f - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e f^{3}\right)} x\right)} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) - {\left(9 \, b^{2} d^{2} e^{4} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{3} f + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e^{2} f^{2} + {\left(9 \, b^{2} d^{2} e^{2} f^{2} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e f^{3} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(9 \, b^{2} d^{2} e^{3} f - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e f^{3}\right)} x\right)} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right) + 3 \, {\left(12 \, b^{2} d^{3} e^{5} f - 3 \, a^{2} c^{3} f^{6} - {\left(31 \, b^{2} c d^{2} + 20 \, a b d^{3}\right)} e^{4} f^{2} + 2 \, {\left(13 \, b^{2} c^{2} d + 25 \, a b c d^{2} + 4 \, a^{2} d^{3}\right)} e^{3} f^{3} - {\left(7 \, b^{2} c^{3} + 40 \, a b c^{2} d + 19 \, a^{2} c d^{2}\right)} e^{2} f^{4} + 2 \, {\left(5 \, a b c^{3} + 7 \, a^{2} c^{2} d\right)} e f^{5} + {\left(9 \, b^{2} d^{3} e^{4} f^{2} - 2 \, {\left(11 \, b^{2} c d^{2} + 7 \, a b d^{3}\right)} e^{3} f^{3} + {\left(17 \, b^{2} c^{2} d + 32 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} e^{2} f^{4} - 2 \, {\left(2 \, b^{2} c^{3} + 11 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} e f^{5} + {\left(4 \, a b c^{3} + 5 \, a^{2} c^{2} d\right)} f^{6}\right)} x\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{18 \, {\left(b^{3} d^{4} e^{9} - a^{3} c^{4} e^{2} f^{7} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{8} f + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{7} f^{2} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{6} f^{3} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{5} f^{4} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{4} f^{5} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e^{3} f^{6} + {\left(b^{3} d^{4} e^{7} f^{2} - a^{3} c^{4} f^{9} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{6} f^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{5} f^{4} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{4} f^{5} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{3} f^{6} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{2} f^{7} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e f^{8}\right)} x^{2} + 2 \, {\left(b^{3} d^{4} e^{8} f - a^{3} c^{4} e f^{8} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{7} f^{2} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{6} f^{3} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{5} f^{4} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{4} f^{5} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{3} f^{6} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e^{2} f^{7}\right)} x\right)}}, \frac{6 \, \sqrt{\frac{1}{3}} {\left(9 \, b^{3} d^{3} e^{6} - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{5} f + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{4} f^{2} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e^{3} f^{3} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e^{2} f^{4} + {\left(9 \, b^{3} d^{3} e^{4} f^{2} - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{3} f^{3} + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{2} f^{4} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e f^{5} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} f^{6}\right)} x^{2} + 2 \, {\left(9 \, b^{3} d^{3} e^{5} f - 3 \, {\left(5 \, b^{3} c d^{2} + 7 \, a b^{2} d^{3}\right)} e^{4} f^{2} + {\left(8 \, b^{3} c^{2} d + 29 \, a b^{2} c d^{2} + 17 \, a^{2} b d^{3}\right)} e^{3} f^{3} - {\left(2 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 19 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} e^{2} f^{4} + {\left(2 \, a b^{2} c^{3} + 2 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e f^{5}\right)} x\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}}}{b e - a f}}}{a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2} + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} x}\right) - 2 \, {\left(9 \, b^{2} d^{2} e^{4} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{3} f + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e^{2} f^{2} + {\left(9 \, b^{2} d^{2} e^{2} f^{2} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e f^{3} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(9 \, b^{2} d^{2} e^{3} f - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e f^{3}\right)} x\right)} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}}{b x + a}\right) + {\left(9 \, b^{2} d^{2} e^{4} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{3} f + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e^{2} f^{2} + {\left(9 \, b^{2} d^{2} e^{2} f^{2} - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e f^{3} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} f^{4}\right)} x^{2} + 2 \, {\left(9 \, b^{2} d^{2} e^{3} f - 6 \, {\left(b^{2} c d + 2 \, a b d^{2}\right)} e^{2} f^{2} + {\left(2 \, b^{2} c^{2} + 2 \, a b c d + 5 \, a^{2} d^{2}\right)} e f^{3}\right)} x\right)} {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b d^{2} e^{3} + a c^{2} f^{3} + {\left(2 \, b c d + a d^{2}\right)} e^{2} f - {\left(b c^{2} + 2 \, a c d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(a d e - a c f + {\left(b d e - b c f\right)} x\right)}}{b x + a}\right) - 3 \, {\left(12 \, b^{2} d^{3} e^{5} f - 3 \, a^{2} c^{3} f^{6} - {\left(31 \, b^{2} c d^{2} + 20 \, a b d^{3}\right)} e^{4} f^{2} + 2 \, {\left(13 \, b^{2} c^{2} d + 25 \, a b c d^{2} + 4 \, a^{2} d^{3}\right)} e^{3} f^{3} - {\left(7 \, b^{2} c^{3} + 40 \, a b c^{2} d + 19 \, a^{2} c d^{2}\right)} e^{2} f^{4} + 2 \, {\left(5 \, a b c^{3} + 7 \, a^{2} c^{2} d\right)} e f^{5} + {\left(9 \, b^{2} d^{3} e^{4} f^{2} - 2 \, {\left(11 \, b^{2} c d^{2} + 7 \, a b d^{3}\right)} e^{3} f^{3} + {\left(17 \, b^{2} c^{2} d + 32 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} e^{2} f^{4} - 2 \, {\left(2 \, b^{2} c^{3} + 11 \, a b c^{2} d + 5 \, a^{2} c d^{2}\right)} e f^{5} + {\left(4 \, a b c^{3} + 5 \, a^{2} c^{2} d\right)} f^{6}\right)} x\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{18 \, {\left(b^{3} d^{4} e^{9} - a^{3} c^{4} e^{2} f^{7} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{8} f + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{7} f^{2} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{6} f^{3} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{5} f^{4} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{4} f^{5} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e^{3} f^{6} + {\left(b^{3} d^{4} e^{7} f^{2} - a^{3} c^{4} f^{9} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{6} f^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{5} f^{4} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{4} f^{5} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{3} f^{6} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{2} f^{7} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e f^{8}\right)} x^{2} + 2 \, {\left(b^{3} d^{4} e^{8} f - a^{3} c^{4} e f^{8} - {\left(4 \, b^{3} c d^{3} + 3 \, a b^{2} d^{4}\right)} e^{7} f^{2} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + 4 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e^{6} f^{3} - {\left(4 \, b^{3} c^{3} d + 18 \, a b^{2} c^{2} d^{2} + 12 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} e^{5} f^{4} + {\left(b^{3} c^{4} + 12 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 4 \, a^{3} c d^{3}\right)} e^{4} f^{5} - 3 \, {\left(a b^{2} c^{4} + 4 \, a^{2} b c^{3} d + 2 \, a^{3} c^{2} d^{2}\right)} e^{3} f^{6} + {\left(3 \, a^{2} b c^{4} + 4 \, a^{3} c^{3} d\right)} e^{2} f^{7}\right)} x\right)}}\right]"," ",0,"[-1/18*(3*sqrt(1/3)*(9*b^3*d^3*e^6 - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^5*f + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^4*f^2 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e^3*f^3 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*e^2*f^4 + (9*b^3*d^3*e^4*f^2 - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^3*f^3 + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^2*f^4 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e*f^5 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*f^6)*x^2 + 2*(9*b^3*d^3*e^5*f - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^4*f^2 + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^3*f^3 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e^2*f^4 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*e*f^5)*x)*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*log((3*a*c^2*f^2 + (2*b*c*d + a*d^2)*e^2 - 2*(b*c^2 + 2*a*c*d)*e*f + 3*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(d*e - c*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (3*b*d^2*e^2 - 2*(2*b*c*d + a*d^2)*e*f + (b*c^2 + 2*a*c*d)*f^2)*x - 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt((-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f)))/(f*x + e)) + 2*(9*b^2*d^2*e^4 - 6*(b^2*c*d + 2*a*b*d^2)*e^3*f + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e^2*f^2 + (9*b^2*d^2*e^2*f^2 - 6*(b^2*c*d + 2*a*b*d^2)*e*f^3 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*f^4)*x^2 + 2*(9*b^2*d^2*e^3*f - 6*(b^2*c*d + 2*a*b*d^2)*e^2*f^2 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e*f^3)*x)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) - (9*b^2*d^2*e^4 - 6*(b^2*c*d + 2*a*b*d^2)*e^3*f + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e^2*f^2 + (9*b^2*d^2*e^2*f^2 - 6*(b^2*c*d + 2*a*b*d^2)*e*f^3 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*f^4)*x^2 + 2*(9*b^2*d^2*e^3*f - 6*(b^2*c*d + 2*a*b*d^2)*e^2*f^2 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e*f^3)*x)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)) + 3*(12*b^2*d^3*e^5*f - 3*a^2*c^3*f^6 - (31*b^2*c*d^2 + 20*a*b*d^3)*e^4*f^2 + 2*(13*b^2*c^2*d + 25*a*b*c*d^2 + 4*a^2*d^3)*e^3*f^3 - (7*b^2*c^3 + 40*a*b*c^2*d + 19*a^2*c*d^2)*e^2*f^4 + 2*(5*a*b*c^3 + 7*a^2*c^2*d)*e*f^5 + (9*b^2*d^3*e^4*f^2 - 2*(11*b^2*c*d^2 + 7*a*b*d^3)*e^3*f^3 + (17*b^2*c^2*d + 32*a*b*c*d^2 + 5*a^2*d^3)*e^2*f^4 - 2*(2*b^2*c^3 + 11*a*b*c^2*d + 5*a^2*c*d^2)*e*f^5 + (4*a*b*c^3 + 5*a^2*c^2*d)*f^6)*x)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^3*d^4*e^9 - a^3*c^4*e^2*f^7 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^8*f + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^7*f^2 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^6*f^3 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^5*f^4 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^4*f^5 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e^3*f^6 + (b^3*d^4*e^7*f^2 - a^3*c^4*f^9 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^6*f^3 + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^5*f^4 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^4*f^5 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^3*f^6 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^2*f^7 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e*f^8)*x^2 + 2*(b^3*d^4*e^8*f - a^3*c^4*e*f^8 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^7*f^2 + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^6*f^3 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^5*f^4 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^4*f^5 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^3*f^6 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e^2*f^7)*x), 1/18*(6*sqrt(1/3)*(9*b^3*d^3*e^6 - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^5*f + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^4*f^2 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e^3*f^3 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*e^2*f^4 + (9*b^3*d^3*e^4*f^2 - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^3*f^3 + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^2*f^4 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e*f^5 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*f^6)*x^2 + 2*(9*b^3*d^3*e^5*f - 3*(5*b^3*c*d^2 + 7*a*b^2*d^3)*e^4*f^2 + (8*b^3*c^2*d + 29*a*b^2*c*d^2 + 17*a^2*b*d^3)*e^3*f^3 - (2*b^3*c^3 + 10*a*b^2*c^2*d + 19*a^2*b*c*d^2 + 5*a^3*d^3)*e^2*f^4 + (2*a*b^2*c^3 + 2*a^2*b*c^2*d + 5*a^3*c*d^2)*e*f^5)*x)*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))*arctan(sqrt(1/3)*(2*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))*sqrt(-(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)/(b*e - a*f))/(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2 + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*x)) - 2*(9*b^2*d^2*e^4 - 6*(b^2*c*d + 2*a*b*d^2)*e^3*f + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e^2*f^2 + (9*b^2*d^2*e^2*f^2 - 6*(b^2*c*d + 2*a*b*d^2)*e*f^3 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*f^4)*x^2 + 2*(9*b^2*d^2*e^3*f - 6*(b^2*c*d + 2*a*b*d^2)*e^2*f^2 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e*f^3)*x)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a))/(b*x + a)) + (9*b^2*d^2*e^4 - 6*(b^2*c*d + 2*a*b*d^2)*e^3*f + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e^2*f^2 + (9*b^2*d^2*e^2*f^2 - 6*(b^2*c*d + 2*a*b*d^2)*e*f^3 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*f^4)*x^2 + 2*(9*b^2*d^2*e^3*f - 6*(b^2*c*d + 2*a*b*d^2)*e^2*f^2 + (2*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*e*f^3)*x)*(-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(2/3)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b*d^2*e^3 + a*c^2*f^3 + (2*b*c*d + a*d^2)*e^2*f - (b*c^2 + 2*a*c*d)*e*f^2)^(1/3)*(a*d*e - a*c*f + (b*d*e - b*c*f)*x))/(b*x + a)) - 3*(12*b^2*d^3*e^5*f - 3*a^2*c^3*f^6 - (31*b^2*c*d^2 + 20*a*b*d^3)*e^4*f^2 + 2*(13*b^2*c^2*d + 25*a*b*c*d^2 + 4*a^2*d^3)*e^3*f^3 - (7*b^2*c^3 + 40*a*b*c^2*d + 19*a^2*c*d^2)*e^2*f^4 + 2*(5*a*b*c^3 + 7*a^2*c^2*d)*e*f^5 + (9*b^2*d^3*e^4*f^2 - 2*(11*b^2*c*d^2 + 7*a*b*d^3)*e^3*f^3 + (17*b^2*c^2*d + 32*a*b*c*d^2 + 5*a^2*d^3)*e^2*f^4 - 2*(2*b^2*c^3 + 11*a*b*c^2*d + 5*a^2*c*d^2)*e*f^5 + (4*a*b*c^3 + 5*a^2*c^2*d)*f^6)*x)*(b*x + a)^(2/3)*(d*x + c)^(1/3))/(b^3*d^4*e^9 - a^3*c^4*e^2*f^7 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^8*f + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^7*f^2 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^6*f^3 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^5*f^4 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^4*f^5 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e^3*f^6 + (b^3*d^4*e^7*f^2 - a^3*c^4*f^9 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^6*f^3 + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^5*f^4 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^4*f^5 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^3*f^6 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^2*f^7 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e*f^8)*x^2 + 2*(b^3*d^4*e^8*f - a^3*c^4*e*f^8 - (4*b^3*c*d^3 + 3*a*b^2*d^4)*e^7*f^2 + 3*(2*b^3*c^2*d^2 + 4*a*b^2*c*d^3 + a^2*b*d^4)*e^6*f^3 - (4*b^3*c^3*d + 18*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3 + a^3*d^4)*e^5*f^4 + (b^3*c^4 + 12*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 4*a^3*c*d^3)*e^4*f^5 - 3*(a*b^2*c^4 + 4*a^2*b*c^3*d + 2*a^3*c^2*d^2)*e^3*f^6 + (3*a^2*b*c^4 + 4*a^3*c^3*d)*e^2*f^7)*x)]","B",0
3022,0,0,0,1.925549," ","integrate((b*x+a)^3/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} {\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{2 \, b d^{2} x^{2} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x}, x\right)"," ",0,"integral((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*(2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(2*b*d^2*x^2 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x), x)","F",0
3023,0,0,0,1.340702," ","integrate((b*x+a)^2/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} {\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{2 \, b d^{2} x^{2} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*(2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(2*b*d^2*x^2 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x), x)","F",0
3024,0,0,0,2.195252," ","integrate((b*x+a)/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(b x + a\right)} {\left(d x + c\right)}^{\frac{2}{3}}}{2 \, b d^{2} x^{2} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x}, x\right)"," ",0,"integral((2*b*d*x + b*c + a*d)^(2/3)*(b*x + a)*(d*x + c)^(2/3)/(2*b*d^2*x^2 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x), x)","F",0
3025,0,0,0,1.909407," ","integrate(1/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{2 \, b d^{2} x^{2} + b c^{2} + a c d + {\left(3 \, b c d + a d^{2}\right)} x}, x\right)"," ",0,"integral((2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(2*b*d^2*x^2 + b*c^2 + a*c*d + (3*b*c*d + a*d^2)*x), x)","F",0
3026,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3027,-1,0,0,0.000000," ","integrate(1/(b*x+a)^2/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3028,-1,0,0,0.000000," ","integrate(1/(b*x+a)^3/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3029,0,0,0,2.626836," ","integrate((b*x+a)^3/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} {\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{4 \, b^{2} d^{3} x^{3} + b^{2} c^{3} + 2 \, a b c^{2} d + a^{2} c d^{2} + 4 \, {\left(2 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2} + {\left(5 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x}, x\right)"," ",0,"integral((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*(2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(4*b^2*d^3*x^3 + b^2*c^3 + 2*a*b*c^2*d + a^2*c*d^2 + 4*(2*b^2*c*d^2 + a*b*d^3)*x^2 + (5*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x), x)","F",0
3030,0,0,0,2.295096," ","integrate((b*x+a)^2/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} {\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{4 \, b^{2} d^{3} x^{3} + b^{2} c^{3} + 2 \, a b c^{2} d + a^{2} c d^{2} + 4 \, {\left(2 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2} + {\left(5 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*(2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(4*b^2*d^3*x^3 + b^2*c^3 + 2*a*b*c^2*d + a^2*c*d^2 + 4*(2*b^2*c*d^2 + a*b*d^3)*x^2 + (5*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x), x)","F",0
3031,1,44,0,1.506253," ","integrate((b*x+a)/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{2 \, {\left(2 \, b d^{3} x + b c d^{2} + a d^{3}\right)}}"," ",0,"3/2*(2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(2*b*d^3*x + b*c*d^2 + a*d^3)","A",0
3032,0,0,0,1.481220," ","integrate(1/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, b d x + b c + a d\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{4 \, b^{2} d^{3} x^{3} + b^{2} c^{3} + 2 \, a b c^{2} d + a^{2} c d^{2} + 4 \, {\left(2 \, b^{2} c d^{2} + a b d^{3}\right)} x^{2} + {\left(5 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x}, x\right)"," ",0,"integral((2*b*d*x + b*c + a*d)^(2/3)*(d*x + c)^(2/3)/(4*b^2*d^3*x^3 + b^2*c^3 + 2*a*b*c^2*d + a^2*c*d^2 + 4*(2*b^2*c*d^2 + a*b*d^3)*x^2 + (5*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x), x)","F",0
3033,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3034,-1,0,0,0.000000," ","integrate(1/(b*x+a)^2/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3035,-1,0,0,0.000000," ","integrate(1/(b*x+a)^3/(d*x+c)^(1/3)/(2*b*d*x+a*d+b*c)^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3036,-1,0,0,0.000000," ","integrate(1/(-3*e*x+d)^(1/3)/(e*x+d)/(3*e*x+d)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3037,1,2267,0,2.035208," ","integrate((b*x+a)^(4/3)*(f*x+e)^2/(d*x+c)^(4/3),x, algorithm=""fricas"")","\left[\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{3} - a b^{3} c d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{4} c^{3} d^{2} - 8 \, a b^{3} c^{2} d^{3} + a^{2} b^{2} c d^{4}\right)} e f + {\left(35 \, b^{4} c^{4} d - 42 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4}\right)} f^{2} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{2} - 9 \, {\left(7 \, b^{4} c^{2} d^{3} - 8 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} e f + {\left(35 \, b^{4} c^{3} d^{2} - 42 \, a b^{3} c^{2} d^{3} + 6 \, a^{2} b^{2} c d^{4} + a^{3} b d^{5}\right)} f^{2}\right)} x\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d - 3 \, \left(b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}\right) - 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} e f + {\left(35 \, b^{3} c^{4} - 42 \, a b^{2} c^{3} d + 6 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e f + {\left(35 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) + 4 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} e f + {\left(35 \, b^{3} c^{4} - 42 \, a b^{2} c^{3} d + 6 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e f + {\left(35 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(9 \, b^{4} d^{4} f^{2} x^{3} + 27 \, {\left(4 \, b^{4} c d^{3} - 3 \, a b^{3} d^{4}\right)} e^{2} - 9 \, {\left(28 \, b^{4} c^{2} d^{2} - 25 \, a b^{3} c d^{3}\right)} e f + {\left(140 \, b^{4} c^{3} d - 133 \, a b^{3} c^{2} d^{2} + 2 \, a^{2} b^{2} c d^{3}\right)} f^{2} + 3 \, {\left(9 \, b^{4} d^{4} e f - 5 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{2}\right)} x^{2} + {\left(27 \, b^{4} d^{4} e^{2} - 63 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e f + {\left(35 \, b^{4} c^{2} d^{2} - 37 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{81 \, {\left(b^{3} d^{6} x + b^{3} c d^{5}\right)}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{3} - a b^{3} c d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{4} c^{3} d^{2} - 8 \, a b^{3} c^{2} d^{3} + a^{2} b^{2} c d^{4}\right)} e f + {\left(35 \, b^{4} c^{4} d - 42 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4}\right)} f^{2} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{2} - 9 \, {\left(7 \, b^{4} c^{2} d^{3} - 8 \, a b^{3} c d^{4} + a^{2} b^{2} d^{5}\right)} e f + {\left(35 \, b^{4} c^{3} d^{2} - 42 \, a b^{3} c^{2} d^{3} + 6 \, a^{2} b^{2} c d^{4} + a^{3} b d^{5}\right)} f^{2}\right)} x\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + 2 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} e f + {\left(35 \, b^{3} c^{4} - 42 \, a b^{2} c^{3} d + 6 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e f + {\left(35 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 4 \, \left(b^{2} d\right)^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} e f + {\left(35 \, b^{3} c^{4} - 42 \, a b^{2} c^{3} d + 6 \, a^{2} b c^{2} d^{2} + a^{3} c d^{3}\right)} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} - 9 \, {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} e f + {\left(35 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 6 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} f^{2}\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(9 \, b^{4} d^{4} f^{2} x^{3} + 27 \, {\left(4 \, b^{4} c d^{3} - 3 \, a b^{3} d^{4}\right)} e^{2} - 9 \, {\left(28 \, b^{4} c^{2} d^{2} - 25 \, a b^{3} c d^{3}\right)} e f + {\left(140 \, b^{4} c^{3} d - 133 \, a b^{3} c^{2} d^{2} + 2 \, a^{2} b^{2} c d^{3}\right)} f^{2} + 3 \, {\left(9 \, b^{4} d^{4} e f - 5 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{2}\right)} x^{2} + {\left(27 \, b^{4} d^{4} e^{2} - 63 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e f + {\left(35 \, b^{4} c^{2} d^{2} - 37 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} f^{2}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{81 \, {\left(b^{3} d^{6} x + b^{3} c d^{5}\right)}}\right]"," ",0,"[1/81*(6*sqrt(1/3)*(27*(b^4*c^2*d^3 - a*b^3*c*d^4)*e^2 - 9*(7*b^4*c^3*d^2 - 8*a*b^3*c^2*d^3 + a^2*b^2*c*d^4)*e*f + (35*b^4*c^4*d - 42*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 + a^3*b*c*d^4)*f^2 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^2 - 9*(7*b^4*c^2*d^3 - 8*a*b^3*c*d^4 + a^2*b^2*d^5)*e*f + (35*b^4*c^3*d^2 - 42*a*b^3*c^2*d^3 + 6*a^2*b^2*c*d^4 + a^3*b*d^5)*f^2)*x)*sqrt(-(b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d - 3*(b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b - 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(b^2*d)^(1/3)/d)) - 2*(b^2*d)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^2 - 9*(7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*e*f + (35*b^3*c^4 - 42*a*b^2*c^3*d + 6*a^2*b*c^2*d^2 + a^3*c*d^3)*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2 - 9*(7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*e*f + (35*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 + a^3*d^4)*f^2)*x)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) + 4*(b^2*d)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^2 - 9*(7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*e*f + (35*b^3*c^4 - 42*a*b^2*c^3*d + 6*a^2*b*c^2*d^2 + a^3*c*d^3)*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2 - 9*(7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*e*f + (35*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 + a^3*d^4)*f^2)*x)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) + 3*(9*b^4*d^4*f^2*x^3 + 27*(4*b^4*c*d^3 - 3*a*b^3*d^4)*e^2 - 9*(28*b^4*c^2*d^2 - 25*a*b^3*c*d^3)*e*f + (140*b^4*c^3*d - 133*a*b^3*c^2*d^2 + 2*a^2*b^2*c*d^3)*f^2 + 3*(9*b^4*d^4*e*f - 5*(b^4*c*d^3 - a*b^3*d^4)*f^2)*x^2 + (27*b^4*d^4*e^2 - 63*(b^4*c*d^3 - a*b^3*d^4)*e*f + (35*b^4*c^2*d^2 - 37*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^6*x + b^3*c*d^5), -1/81*(12*sqrt(1/3)*(27*(b^4*c^2*d^3 - a*b^3*c*d^4)*e^2 - 9*(7*b^4*c^3*d^2 - 8*a*b^3*c^2*d^3 + a^2*b^2*c*d^4)*e*f + (35*b^4*c^4*d - 42*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 + a^3*b*c*d^4)*f^2 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^2 - 9*(7*b^4*c^2*d^3 - 8*a*b^3*c*d^4 + a^2*b^2*d^5)*e*f + (35*b^4*c^3*d^2 - 42*a*b^3*c^2*d^3 + 6*a^2*b^2*c*d^4 + a^3*b*d^5)*f^2)*x)*sqrt((b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + 2*(b^2*d)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^2 - 9*(7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*e*f + (35*b^3*c^4 - 42*a*b^2*c^3*d + 6*a^2*b*c^2*d^2 + a^3*c*d^3)*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2 - 9*(7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*e*f + (35*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 + a^3*d^4)*f^2)*x)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 4*(b^2*d)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^2 - 9*(7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*e*f + (35*b^3*c^4 - 42*a*b^2*c^3*d + 6*a^2*b*c^2*d^2 + a^3*c*d^3)*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2 - 9*(7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*e*f + (35*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 6*a^2*b*c*d^3 + a^3*d^4)*f^2)*x)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(9*b^4*d^4*f^2*x^3 + 27*(4*b^4*c*d^3 - 3*a*b^3*d^4)*e^2 - 9*(28*b^4*c^2*d^2 - 25*a*b^3*c*d^3)*e*f + (140*b^4*c^3*d - 133*a*b^3*c^2*d^2 + 2*a^2*b^2*c*d^3)*f^2 + 3*(9*b^4*d^4*e*f - 5*(b^4*c*d^3 - a*b^3*d^4)*f^2)*x^2 + (27*b^4*d^4*e^2 - 63*(b^4*c*d^3 - a*b^3*d^4)*e*f + (35*b^4*c^2*d^2 - 37*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*f^2)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*d^6*x + b^3*c*d^5)]","B",0
3038,1,1386,0,1.915578," ","integrate((b*x+a)^(4/3)*(f*x+e)/(d*x+c)^(4/3),x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{\frac{1}{3}} {\left(6 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e - {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} f + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e - {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} f\right)} x\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \log\left(3 \, b^{2} d x + b^{2} c + 2 \, a b d + 3 \, \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e - {\left(7 \, b^{2} c^{3} - 8 \, a b c^{2} d + a^{2} c d^{2}\right)} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e - {\left(7 \, b^{2} c^{2} d - 8 \, a b c d^{2} + a^{2} d^{3}\right)} f\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 4 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e - {\left(7 \, b^{2} c^{3} - 8 \, a b c^{2} d + a^{2} c d^{2}\right)} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e - {\left(7 \, b^{2} c^{2} d - 8 \, a b c d^{2} + a^{2} d^{3}\right)} f\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(3 \, b^{3} d^{3} f x^{2} + 6 \, {\left(4 \, b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e - {\left(28 \, b^{3} c^{2} d - 25 \, a b^{2} c d^{2}\right)} f + {\left(6 \, b^{3} d^{3} e - 7 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(6 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e - {\left(7 \, b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + a^{2} b c d^{3}\right)} f + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e - {\left(7 \, b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + a^{2} b d^{4}\right)} f\right)} x\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}\right)} \sqrt{-\frac{\left(-b^{2} d\right)^{\frac{1}{3}}}{d}}}{b^{2} d x + b^{2} c}\right) + 2 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e - {\left(7 \, b^{2} c^{3} - 8 \, a b c^{2} d + a^{2} c d^{2}\right)} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e - {\left(7 \, b^{2} c^{2} d - 8 \, a b c d^{2} + a^{2} d^{3}\right)} f\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b d + \left(-b^{2} d\right)^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - \left(-b^{2} d\right)^{\frac{1}{3}} {\left(b d x + b c\right)}}{d x + c}\right) - 4 \, \left(-b^{2} d\right)^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e - {\left(7 \, b^{2} c^{3} - 8 \, a b c^{2} d + a^{2} c d^{2}\right)} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e - {\left(7 \, b^{2} c^{2} d - 8 \, a b c d^{2} + a^{2} d^{3}\right)} f\right)} x\right)} \log\left(\frac{{\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b d - \left(-b^{2} d\right)^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) - 3 \, {\left(3 \, b^{3} d^{3} f x^{2} + 6 \, {\left(4 \, b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e - {\left(28 \, b^{3} c^{2} d - 25 \, a b^{2} c d^{2}\right)} f + {\left(6 \, b^{3} d^{3} e - 7 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{2} d^{5} x + b^{2} c d^{4}\right)}}\right]"," ",0,"[-1/18*(6*sqrt(1/3)*(6*(b^3*c^2*d^2 - a*b^2*c*d^3)*e - (7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*f + (6*(b^3*c*d^3 - a*b^2*d^4)*e - (7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*f)*x)*sqrt((-b^2*d)^(1/3)/d)*log(3*b^2*d*x + b^2*c + 2*a*b*d + 3*(-b^2*d)^(1/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*b + 3*sqrt(1/3)*(2*(b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d - (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt((-b^2*d)^(1/3)/d)) + 2*(-b^2*d)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e - (7*b^2*c^3 - 8*a*b*c^2*d + a^2*c*d^2)*f + (6*(b^2*c*d^2 - a*b*d^3)*e - (7*b^2*c^2*d - 8*a*b*c*d^2 + a^2*d^3)*f)*x)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 4*(-b^2*d)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e - (7*b^2*c^3 - 8*a*b*c^2*d + a^2*c*d^2)*f + (6*(b^2*c*d^2 - a*b*d^3)*e - (7*b^2*c^2*d - 8*a*b*c*d^2 + a^2*d^3)*f)*x)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(3*b^3*d^3*f*x^2 + 6*(4*b^3*c*d^2 - 3*a*b^2*d^3)*e - (28*b^3*c^2*d - 25*a*b^2*c*d^2)*f + (6*b^3*d^3*e - 7*(b^3*c*d^2 - a*b^2*d^3)*f)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d^5*x + b^2*c*d^4), -1/18*(12*sqrt(1/3)*(6*(b^3*c^2*d^2 - a*b^2*c*d^3)*e - (7*b^3*c^3*d - 8*a*b^2*c^2*d^2 + a^2*b*c*d^3)*f + (6*(b^3*c*d^3 - a*b^2*d^4)*e - (7*b^3*c^2*d^2 - 8*a*b^2*c*d^3 + a^2*b*d^4)*f)*x)*sqrt(-(-b^2*d)^(1/3)/d)*arctan(sqrt(1/3)*(2*(-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))*sqrt(-(-b^2*d)^(1/3)/d)/(b^2*d*x + b^2*c)) + 2*(-b^2*d)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e - (7*b^2*c^3 - 8*a*b*c^2*d + a^2*c*d^2)*f + (6*(b^2*c*d^2 - a*b*d^3)*e - (7*b^2*c^2*d - 8*a*b*c*d^2 + a^2*d^3)*f)*x)*log(((b*x + a)^(2/3)*(d*x + c)^(1/3)*b*d + (-b^2*d)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d)^(1/3)*(b*d*x + b*c))/(d*x + c)) - 4*(-b^2*d)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e - (7*b^2*c^3 - 8*a*b*c^2*d + a^2*c*d^2)*f + (6*(b^2*c*d^2 - a*b*d^3)*e - (7*b^2*c^2*d - 8*a*b*c*d^2 + a^2*d^3)*f)*x)*log(((b*x + a)^(1/3)*(d*x + c)^(2/3)*b*d - (-b^2*d)^(2/3)*(d*x + c))/(d*x + c)) - 3*(3*b^3*d^3*f*x^2 + 6*(4*b^3*c*d^2 - 3*a*b^2*d^3)*e - (28*b^3*c^2*d - 25*a*b^2*c*d^2)*f + (6*b^3*d^3*e - 7*(b^3*c*d^2 - a*b^2*d^3)*f)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*d^5*x + b^2*c*d^4)]","B",0
3039,1,306,0,1.913733," ","integrate((b*x+a)^(4/3)/(d*x+c)^(4/3),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d \left(-\frac{b}{d}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b d x + b c\right)}}{3 \, {\left(b d x + b c\right)}}\right) + 2 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{2}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) - 4 \, {\left(b c^{2} - a c d + {\left(b c d - a d^{2}\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right) + 3 \, {\left(b d x + 4 \, b c - 3 \, a d\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{3 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/3*(4*sqrt(3)*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*(-b/d)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*d*(-b/d)^(2/3) + sqrt(3)*(b*d*x + b*c))/(b*d*x + b*c)) + 2*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*(-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(2/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3)*(-b/d)^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) - 4*(b*c^2 - a*c*d + (b*c*d - a*d^2)*x)*(-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(1/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)) + 3*(b*d*x + 4*b*c - 3*a*d)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(d^3*x + c*d^2)","A",0
3040,1,738,0,2.430649," ","integrate((b*x+a)^(4/3)/(d*x+c)^(4/3)/(f*x+e),x, algorithm=""fricas"")","\frac{6 \, {\left(b c - a d\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} f - 2 \, \sqrt{3} {\left(b c d e - a c d f + {\left(b d^{2} e - a d^{2} f\right)} x\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{3 \, {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}\right) - 2 \, \sqrt{3} {\left(b c d e - b c^{2} f + {\left(b d^{2} e - b c d f\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} d \left(-\frac{b}{d}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b d x + b c\right)}}{3 \, {\left(b d x + b c\right)}}\right) - {\left(b c d e - a c d f + {\left(b d^{2} e - a d^{2} f\right)} x\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) - {\left(b c d e - b c^{2} f + {\left(b d^{2} e - b c d f\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{2}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) + 2 \, {\left(b c d e - a c d f + {\left(b d^{2} e - a d^{2} f\right)} x\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(-\frac{{\left(d x + c\right)} \left(\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right) + 2 \, {\left(b c d e - b c^{2} f + {\left(b d^{2} e - b c d f\right)} x\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b}{d}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right)}{2 \, {\left(c d^{2} e f - c^{2} d f^{2} + {\left(d^{3} e f - c d^{2} f^{2}\right)} x\right)}}"," ",0,"1/2*(6*(b*c - a*d)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*f - 2*sqrt(3)*(b*c*d*e - a*c*d*f + (b*d^2*e - a*d^2*f)*x)*((b*e - a*f)/(d*e - c*f))^(1/3)*arctan(1/3*(2*sqrt(3)*(d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*((b*e - a*f)/(d*e - c*f))^(2/3) + sqrt(3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(b*c*e - a*c*f + (b*d*e - a*d*f)*x)) - 2*sqrt(3)*(b*c*d*e - b*c^2*f + (b*d^2*e - b*c*d*f)*x)*(-b/d)^(1/3)*arctan(1/3*(2*sqrt(3)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*d*(-b/d)^(2/3) + sqrt(3)*(b*d*x + b*c))/(b*d*x + b*c)) - (b*c*d*e - a*c*d*f + (b*d^2*e - a*d^2*f)*x)*((b*e - a*f)/(d*e - c*f))^(1/3)*log(((d*x + c)*((b*e - a*f)/(d*e - c*f))^(2/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3)*((b*e - a*f)/(d*e - c*f))^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) - (b*c*d*e - b*c^2*f + (b*d^2*e - b*c*d*f)*x)*(-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(2/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3)*(-b/d)^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) + 2*(b*c*d*e - a*c*d*f + (b*d^2*e - a*d^2*f)*x)*((b*e - a*f)/(d*e - c*f))^(1/3)*log(-((d*x + c)*((b*e - a*f)/(d*e - c*f))^(1/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)) + 2*(b*c*d*e - b*c^2*f + (b*d^2*e - b*c*d*f)*x)*(-b/d)^(1/3)*log(((d*x + c)*(-b/d)^(1/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)))/(c*d^2*e*f - c^2*d*f^2 + (d^3*e*f - c*d^2*f^2)*x)","B",0
3041,1,651,0,1.349739," ","integrate((b*x+a)^(4/3)/(d*x+c)^(4/3)/(f*x+e)^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} {\left({\left(b c d - a d^{2}\right)} f x^{2} + {\left(b c^{2} - a c d\right)} e + {\left({\left(b c d - a d^{2}\right)} e + {\left(b c^{2} - a c d\right)} f\right)} x\right)} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} {\left(d e - c f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} + \sqrt{3} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{3 \, {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}\right) + 2 \, {\left({\left(b c d - a d^{2}\right)} f x^{2} + {\left(b c^{2} - a c d\right)} e + {\left({\left(b c d - a d^{2}\right)} e + {\left(b c^{2} - a c d\right)} f\right)} x\right)} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{2}{3}} - {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}}}{d x + c}\right) - 4 \, {\left({\left(b c d - a d^{2}\right)} f x^{2} + {\left(b c^{2} - a c d\right)} e + {\left({\left(b c d - a d^{2}\right)} e + {\left(b c^{2} - a c d\right)} f\right)} x\right)} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} \log\left(\frac{{\left(d x + c\right)} \left(-\frac{b e - a f}{d e - c f}\right)^{\frac{1}{3}} + {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{d x + c}\right) - 3 \, {\left(a c f - {\left(4 \, b c - 3 \, a d\right)} e - {\left(b d e + {\left(3 \, b c - 4 \, a d\right)} f\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{3 \, {\left(c d^{2} e^{3} - 2 \, c^{2} d e^{2} f + c^{3} e f^{2} + {\left(d^{3} e^{2} f - 2 \, c d^{2} e f^{2} + c^{2} d f^{3}\right)} x^{2} + {\left(d^{3} e^{3} - c d^{2} e^{2} f - c^{2} d e f^{2} + c^{3} f^{3}\right)} x\right)}}"," ",0,"1/3*(4*sqrt(3)*((b*c*d - a*d^2)*f*x^2 + (b*c^2 - a*c*d)*e + ((b*c*d - a*d^2)*e + (b*c^2 - a*c*d)*f)*x)*(-(b*e - a*f)/(d*e - c*f))^(1/3)*arctan(1/3*(2*sqrt(3)*(d*e - c*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3)*(-(b*e - a*f)/(d*e - c*f))^(2/3) + sqrt(3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(b*c*e - a*c*f + (b*d*e - a*d*f)*x)) + 2*((b*c*d - a*d^2)*f*x^2 + (b*c^2 - a*c*d)*e + ((b*c*d - a*d^2)*e + (b*c^2 - a*c*d)*f)*x)*(-(b*e - a*f)/(d*e - c*f))^(1/3)*log(((d*x + c)*(-(b*e - a*f)/(d*e - c*f))^(2/3) - (b*x + a)^(1/3)*(d*x + c)^(2/3)*(-(b*e - a*f)/(d*e - c*f))^(1/3) + (b*x + a)^(2/3)*(d*x + c)^(1/3))/(d*x + c)) - 4*((b*c*d - a*d^2)*f*x^2 + (b*c^2 - a*c*d)*e + ((b*c*d - a*d^2)*e + (b*c^2 - a*c*d)*f)*x)*(-(b*e - a*f)/(d*e - c*f))^(1/3)*log(((d*x + c)*(-(b*e - a*f)/(d*e - c*f))^(1/3) + (b*x + a)^(1/3)*(d*x + c)^(2/3))/(d*x + c)) - 3*(a*c*f - (4*b*c - 3*a*d)*e - (b*d*e + (3*b*c - 4*a*d)*f)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(c*d^2*e^3 - 2*c^2*d*e^2*f + c^3*e*f^2 + (d^3*e^2*f - 2*c*d^2*e*f^2 + c^2*d*f^3)*x^2 + (d^3*e^3 - c*d^2*e^2*f - c^2*d*e*f^2 + c^3*f^3)*x)","B",0
3042,1,6825,0,4.602422," ","integrate((b*x+a)^(4/3)/(d*x+c)^(4/3)/(f*x+e)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{\frac{1}{3}} {\left(6 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} - {\left(5 \, b^{3} c^{3} d + 8 \, a b^{2} c^{2} d^{2} - 13 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} - 13 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} e^{2} f^{3} + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} - {\left(5 \, b^{3} c^{2} d^{2} + 8 \, a b^{2} c d^{3} - 13 \, a^{2} b d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{3} d - 13 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e f^{4} + {\left(a b^{2} c^{3} d - 8 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + {\left(12 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f - 2 \, {\left(2 \, b^{3} c^{2} d^{2} + 11 \, a b^{2} c d^{3} - 13 \, a^{2} b d^{4}\right)} e^{3} f^{2} - {\left(7 \, b^{3} c^{3} d - 18 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + 14 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} - 15 \, a b^{2} c^{3} d + 21 \, a^{2} b c^{2} d^{2} - 7 \, a^{3} c d^{3}\right)} e f^{4} + {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} f^{5}\right)} x^{2} + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + {\left(7 \, b^{3} c^{2} d^{2} - 20 \, a b^{2} c d^{3} + 13 \, a^{2} b d^{4}\right)} e^{4} f - {\left(11 \, b^{3} c^{3} d + 3 \, a b^{2} c^{2} d^{2} - 21 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e^{3} f^{2} - {\left(2 \, b^{3} c^{4} - 27 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} e^{2} f^{3} + 2 \, {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} e f^{4}\right)} x\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f + 3 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e^{3} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e^{2} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f^{2} + {\left(b^{2} c^{2} d - 8 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} f^{3}\right)} x^{3} + {\left(12 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{2} f + 2 \, {\left(4 \, b^{2} c^{2} d - 11 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} f^{3}\right)} x^{2} + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{3} + {\left(13 \, b^{2} c^{2} d - 20 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e^{2} f + 2 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 4 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e^{3} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e^{2} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f^{2} + {\left(b^{2} c^{2} d - 8 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} f^{3}\right)} x^{3} + {\left(12 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{2} f + 2 \, {\left(4 \, b^{2} c^{2} d - 11 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} f^{3}\right)} x^{2} + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{3} + {\left(13 \, b^{2} c^{2} d - 20 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e^{2} f + 2 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(3 \, a^{3} c^{3} f^{5} - 6 \, {\left(4 \, b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e^{5} + {\left(20 \, b^{3} c^{2} d + 43 \, a b^{2} c d^{2} - 36 \, a^{2} b d^{3}\right)} e^{4} f + 2 \, {\left(2 \, b^{3} c^{3} - 28 \, a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 9 \, a^{3} d^{3}\right)} e^{3} f^{2} - {\left(5 \, a b^{2} c^{3} - 52 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e^{2} f^{3} - 2 \, {\left(a^{2} b c^{3} + 8 \, a^{3} c^{2} d\right)} e f^{4} - {\left(3 \, b^{3} d^{3} e^{4} f + 2 \, {\left(11 \, b^{3} c d^{2} - 17 \, a b^{2} d^{3}\right)} e^{3} f^{2} - {\left(25 \, b^{3} c^{2} d + 16 \, a b^{2} c d^{2} - 59 \, a^{2} b d^{3}\right)} e^{2} f^{3} + 2 \, {\left(25 \, a b^{2} c^{2} d - 17 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4} - {\left(25 \, a^{2} b c^{2} d - 28 \, a^{3} c d^{2}\right)} f^{5}\right)} x^{2} - {\left(6 \, b^{3} d^{3} e^{5} + {\left(37 \, b^{3} c d^{2} - 61 \, a b^{2} d^{3}\right)} e^{4} f - 4 \, {\left(9 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 26 \, a^{2} b d^{3}\right)} e^{3} f^{2} - {\left(7 \, b^{3} c^{3} - 79 \, a b^{2} c^{2} d + 47 \, a^{2} b c d^{2} + 49 \, a^{3} d^{3}\right)} e^{2} f^{3} + 2 \, {\left(7 \, a b^{2} c^{3} - 25 \, a^{2} b c^{2} d + 21 \, a^{3} c d^{2}\right)} e f^{4} - 7 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f^{5}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{2} c d^{4} e^{8} + a^{2} c^{5} e^{2} f^{6} - 2 \, {\left(2 \, b^{2} c^{2} d^{3} + a b c d^{4}\right)} e^{7} f + {\left(6 \, b^{2} c^{3} d^{2} + 8 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} e^{6} f^{2} - 4 \, {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} e^{5} f^{3} + {\left(b^{2} c^{5} + 8 \, a b c^{4} d + 6 \, a^{2} c^{3} d^{2}\right)} e^{4} f^{4} - 2 \, {\left(a b c^{5} + 2 \, a^{2} c^{4} d\right)} e^{3} f^{5} + {\left(b^{2} d^{5} e^{6} f^{2} + a^{2} c^{4} d f^{8} - 2 \, {\left(2 \, b^{2} c d^{4} + a b d^{5}\right)} e^{5} f^{3} + {\left(6 \, b^{2} c^{2} d^{3} + 8 \, a b c d^{4} + a^{2} d^{5}\right)} e^{4} f^{4} - 4 \, {\left(b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} e^{3} f^{5} + {\left(b^{2} c^{4} d + 8 \, a b c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} e^{2} f^{6} - 2 \, {\left(a b c^{4} d + 2 \, a^{2} c^{3} d^{2}\right)} e f^{7}\right)} x^{3} + {\left(2 \, b^{2} d^{5} e^{7} f + a^{2} c^{5} f^{8} - {\left(7 \, b^{2} c d^{4} + 4 \, a b d^{5}\right)} e^{6} f^{2} + 2 \, {\left(4 \, b^{2} c^{2} d^{3} + 7 \, a b c d^{4} + a^{2} d^{5}\right)} e^{5} f^{3} - {\left(2 \, b^{2} c^{3} d^{2} + 16 \, a b c^{2} d^{3} + 7 \, a^{2} c d^{4}\right)} e^{4} f^{4} - 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} - 4 \, a^{2} c^{2} d^{3}\right)} e^{3} f^{5} + {\left(b^{2} c^{5} + 4 \, a b c^{4} d - 2 \, a^{2} c^{3} d^{2}\right)} e^{2} f^{6} - 2 \, {\left(a b c^{5} + a^{2} c^{4} d\right)} e f^{7}\right)} x^{2} + {\left(b^{2} d^{5} e^{8} + 2 \, a^{2} c^{5} e f^{7} - 2 \, {\left(b^{2} c d^{4} + a b d^{5}\right)} e^{7} f - {\left(2 \, b^{2} c^{2} d^{3} - 4 \, a b c d^{4} - a^{2} d^{5}\right)} e^{6} f^{2} + 2 \, {\left(4 \, b^{2} c^{3} d^{2} + 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} e^{5} f^{3} - {\left(7 \, b^{2} c^{4} d + 16 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} e^{4} f^{4} + 2 \, {\left(b^{2} c^{5} + 7 \, a b c^{4} d + 4 \, a^{2} c^{3} d^{2}\right)} e^{3} f^{5} - {\left(4 \, a b c^{5} + 7 \, a^{2} c^{4} d\right)} e^{2} f^{6}\right)} x\right)}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(6 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} - {\left(5 \, b^{3} c^{3} d + 8 \, a b^{2} c^{2} d^{2} - 13 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} - 13 \, a b^{2} c^{3} d + 5 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} e^{2} f^{3} + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} - {\left(5 \, b^{3} c^{2} d^{2} + 8 \, a b^{2} c d^{3} - 13 \, a^{2} b d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{3} d - 13 \, a b^{2} c^{2} d^{2} + 5 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e f^{4} + {\left(a b^{2} c^{3} d - 8 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + {\left(12 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f - 2 \, {\left(2 \, b^{3} c^{2} d^{2} + 11 \, a b^{2} c d^{3} - 13 \, a^{2} b d^{4}\right)} e^{3} f^{2} - {\left(7 \, b^{3} c^{3} d - 18 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + 14 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} - 15 \, a b^{2} c^{3} d + 21 \, a^{2} b c^{2} d^{2} - 7 \, a^{3} c d^{3}\right)} e f^{4} + {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} f^{5}\right)} x^{2} + {\left(6 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + {\left(7 \, b^{3} c^{2} d^{2} - 20 \, a b^{2} c d^{3} + 13 \, a^{2} b d^{4}\right)} e^{4} f - {\left(11 \, b^{3} c^{3} d + 3 \, a b^{2} c^{2} d^{2} - 21 \, a^{2} b c d^{3} + 7 \, a^{3} d^{4}\right)} e^{3} f^{2} - {\left(2 \, b^{3} c^{4} - 27 \, a b^{2} c^{3} d + 18 \, a^{2} b c^{2} d^{2} + 7 \, a^{3} c d^{3}\right)} e^{2} f^{3} + 2 \, {\left(a b^{2} c^{4} - 8 \, a^{2} b c^{3} d + 7 \, a^{3} c^{2} d^{2}\right)} e f^{4}\right)} x\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e^{3} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e^{2} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f^{2} + {\left(b^{2} c^{2} d - 8 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} f^{3}\right)} x^{3} + {\left(12 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{2} f + 2 \, {\left(4 \, b^{2} c^{2} d - 11 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} f^{3}\right)} x^{2} + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{3} + {\left(13 \, b^{2} c^{2} d - 20 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e^{2} f + 2 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 4 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(6 \, {\left(b^{2} c^{2} d - a b c d^{2}\right)} e^{3} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e^{2} f + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e f^{2} + {\left(b^{2} c^{2} d - 8 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} f^{3}\right)} x^{3} + {\left(12 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{2} f + 2 \, {\left(4 \, b^{2} c^{2} d - 11 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e f^{2} + {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} f^{3}\right)} x^{2} + {\left(6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} e^{3} + {\left(13 \, b^{2} c^{2} d - 20 \, a b c d^{2} + 7 \, a^{2} d^{3}\right)} e^{2} f + 2 \, {\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2}\right)} e f^{2}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(3 \, a^{3} c^{3} f^{5} - 6 \, {\left(4 \, b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e^{5} + {\left(20 \, b^{3} c^{2} d + 43 \, a b^{2} c d^{2} - 36 \, a^{2} b d^{3}\right)} e^{4} f + 2 \, {\left(2 \, b^{3} c^{3} - 28 \, a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 9 \, a^{3} d^{3}\right)} e^{3} f^{2} - {\left(5 \, a b^{2} c^{3} - 52 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e^{2} f^{3} - 2 \, {\left(a^{2} b c^{3} + 8 \, a^{3} c^{2} d\right)} e f^{4} - {\left(3 \, b^{3} d^{3} e^{4} f + 2 \, {\left(11 \, b^{3} c d^{2} - 17 \, a b^{2} d^{3}\right)} e^{3} f^{2} - {\left(25 \, b^{3} c^{2} d + 16 \, a b^{2} c d^{2} - 59 \, a^{2} b d^{3}\right)} e^{2} f^{3} + 2 \, {\left(25 \, a b^{2} c^{2} d - 17 \, a^{2} b c d^{2} - 14 \, a^{3} d^{3}\right)} e f^{4} - {\left(25 \, a^{2} b c^{2} d - 28 \, a^{3} c d^{2}\right)} f^{5}\right)} x^{2} - {\left(6 \, b^{3} d^{3} e^{5} + {\left(37 \, b^{3} c d^{2} - 61 \, a b^{2} d^{3}\right)} e^{4} f - 4 \, {\left(9 \, b^{3} c^{2} d + 8 \, a b^{2} c d^{2} - 26 \, a^{2} b d^{3}\right)} e^{3} f^{2} - {\left(7 \, b^{3} c^{3} - 79 \, a b^{2} c^{2} d + 47 \, a^{2} b c d^{2} + 49 \, a^{3} d^{3}\right)} e^{2} f^{3} + 2 \, {\left(7 \, a b^{2} c^{3} - 25 \, a^{2} b c^{2} d + 21 \, a^{3} c d^{2}\right)} e f^{4} - 7 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f^{5}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{18 \, {\left(b^{2} c d^{4} e^{8} + a^{2} c^{5} e^{2} f^{6} - 2 \, {\left(2 \, b^{2} c^{2} d^{3} + a b c d^{4}\right)} e^{7} f + {\left(6 \, b^{2} c^{3} d^{2} + 8 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} e^{6} f^{2} - 4 \, {\left(b^{2} c^{4} d + 3 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} e^{5} f^{3} + {\left(b^{2} c^{5} + 8 \, a b c^{4} d + 6 \, a^{2} c^{3} d^{2}\right)} e^{4} f^{4} - 2 \, {\left(a b c^{5} + 2 \, a^{2} c^{4} d\right)} e^{3} f^{5} + {\left(b^{2} d^{5} e^{6} f^{2} + a^{2} c^{4} d f^{8} - 2 \, {\left(2 \, b^{2} c d^{4} + a b d^{5}\right)} e^{5} f^{3} + {\left(6 \, b^{2} c^{2} d^{3} + 8 \, a b c d^{4} + a^{2} d^{5}\right)} e^{4} f^{4} - 4 \, {\left(b^{2} c^{3} d^{2} + 3 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} e^{3} f^{5} + {\left(b^{2} c^{4} d + 8 \, a b c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} e^{2} f^{6} - 2 \, {\left(a b c^{4} d + 2 \, a^{2} c^{3} d^{2}\right)} e f^{7}\right)} x^{3} + {\left(2 \, b^{2} d^{5} e^{7} f + a^{2} c^{5} f^{8} - {\left(7 \, b^{2} c d^{4} + 4 \, a b d^{5}\right)} e^{6} f^{2} + 2 \, {\left(4 \, b^{2} c^{2} d^{3} + 7 \, a b c d^{4} + a^{2} d^{5}\right)} e^{5} f^{3} - {\left(2 \, b^{2} c^{3} d^{2} + 16 \, a b c^{2} d^{3} + 7 \, a^{2} c d^{4}\right)} e^{4} f^{4} - 2 \, {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} - 4 \, a^{2} c^{2} d^{3}\right)} e^{3} f^{5} + {\left(b^{2} c^{5} + 4 \, a b c^{4} d - 2 \, a^{2} c^{3} d^{2}\right)} e^{2} f^{6} - 2 \, {\left(a b c^{5} + a^{2} c^{4} d\right)} e f^{7}\right)} x^{2} + {\left(b^{2} d^{5} e^{8} + 2 \, a^{2} c^{5} e f^{7} - 2 \, {\left(b^{2} c d^{4} + a b d^{5}\right)} e^{7} f - {\left(2 \, b^{2} c^{2} d^{3} - 4 \, a b c d^{4} - a^{2} d^{5}\right)} e^{6} f^{2} + 2 \, {\left(4 \, b^{2} c^{3} d^{2} + 2 \, a b c^{2} d^{3} - a^{2} c d^{4}\right)} e^{5} f^{3} - {\left(7 \, b^{2} c^{4} d + 16 \, a b c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3}\right)} e^{4} f^{4} + 2 \, {\left(b^{2} c^{5} + 7 \, a b c^{4} d + 4 \, a^{2} c^{3} d^{2}\right)} e^{3} f^{5} - {\left(4 \, a b c^{5} + 7 \, a^{2} c^{4} d\right)} e^{2} f^{6}\right)} x\right)}}\right]"," ",0,"[-1/18*(6*sqrt(1/3)*(6*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 - (5*b^3*c^3*d + 8*a*b^2*c^2*d^2 - 13*a^2*b*c*d^3)*e^4*f - (b^3*c^4 - 13*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*e^3*f^2 + (a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*e^2*f^3 + (6*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 - (5*b^3*c^2*d^2 + 8*a*b^2*c*d^3 - 13*a^2*b*d^4)*e^2*f^3 - (b^3*c^3*d - 13*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3 + 7*a^3*d^4)*e*f^4 + (a*b^2*c^3*d - 8*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*f^5)*x^3 + (12*(b^3*c*d^3 - a*b^2*d^4)*e^4*f - 2*(2*b^3*c^2*d^2 + 11*a*b^2*c*d^3 - 13*a^2*b*d^4)*e^3*f^2 - (7*b^3*c^3*d - 18*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + 14*a^3*d^4)*e^2*f^3 - (b^3*c^4 - 15*a*b^2*c^3*d + 21*a^2*b*c^2*d^2 - 7*a^3*c*d^3)*e*f^4 + (a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*f^5)*x^2 + (6*(b^3*c*d^3 - a*b^2*d^4)*e^5 + (7*b^3*c^2*d^2 - 20*a*b^2*c*d^3 + 13*a^2*b*d^4)*e^4*f - (11*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 21*a^2*b*c*d^3 + 7*a^3*d^4)*e^3*f^2 - (2*b^3*c^4 - 27*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*e^2*f^3 + 2*(a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*e*f^4)*x)*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f + 3*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x + 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e^3 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e^2*f + (6*(b^2*c*d^2 - a*b*d^3)*e*f^2 + (b^2*c^2*d - 8*a*b*c*d^2 + 7*a^2*d^3)*f^3)*x^3 + (12*(b^2*c*d^2 - a*b*d^3)*e^2*f + 2*(4*b^2*c^2*d - 11*a*b*c*d^2 + 7*a^2*d^3)*e*f^2 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*f^3)*x^2 + (6*(b^2*c*d^2 - a*b*d^3)*e^3 + (13*b^2*c^2*d - 20*a*b*c*d^2 + 7*a^2*d^3)*e^2*f + 2*(b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 4*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e^3 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e^2*f + (6*(b^2*c*d^2 - a*b*d^3)*e*f^2 + (b^2*c^2*d - 8*a*b*c*d^2 + 7*a^2*d^3)*f^3)*x^3 + (12*(b^2*c*d^2 - a*b*d^3)*e^2*f + 2*(4*b^2*c^2*d - 11*a*b*c*d^2 + 7*a^2*d^3)*e*f^2 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*f^3)*x^2 + (6*(b^2*c*d^2 - a*b*d^3)*e^3 + (13*b^2*c^2*d - 20*a*b*c*d^2 + 7*a^2*d^3)*e^2*f + 2*(b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(3*a^3*c^3*f^5 - 6*(4*b^3*c*d^2 - 3*a*b^2*d^3)*e^5 + (20*b^3*c^2*d + 43*a*b^2*c*d^2 - 36*a^2*b*d^3)*e^4*f + 2*(2*b^3*c^3 - 28*a*b^2*c^2*d - 7*a^2*b*c*d^2 + 9*a^3*d^3)*e^3*f^2 - (5*a*b^2*c^3 - 52*a^2*b*c^2*d + 5*a^3*c*d^2)*e^2*f^3 - 2*(a^2*b*c^3 + 8*a^3*c^2*d)*e*f^4 - (3*b^3*d^3*e^4*f + 2*(11*b^3*c*d^2 - 17*a*b^2*d^3)*e^3*f^2 - (25*b^3*c^2*d + 16*a*b^2*c*d^2 - 59*a^2*b*d^3)*e^2*f^3 + 2*(25*a*b^2*c^2*d - 17*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4 - (25*a^2*b*c^2*d - 28*a^3*c*d^2)*f^5)*x^2 - (6*b^3*d^3*e^5 + (37*b^3*c*d^2 - 61*a*b^2*d^3)*e^4*f - 4*(9*b^3*c^2*d + 8*a*b^2*c*d^2 - 26*a^2*b*d^3)*e^3*f^2 - (7*b^3*c^3 - 79*a*b^2*c^2*d + 47*a^2*b*c*d^2 + 49*a^3*d^3)*e^2*f^3 + 2*(7*a*b^2*c^3 - 25*a^2*b*c^2*d + 21*a^3*c*d^2)*e*f^4 - 7*(a^2*b*c^3 - a^3*c^2*d)*f^5)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*c*d^4*e^8 + a^2*c^5*e^2*f^6 - 2*(2*b^2*c^2*d^3 + a*b*c*d^4)*e^7*f + (6*b^2*c^3*d^2 + 8*a*b*c^2*d^3 + a^2*c*d^4)*e^6*f^2 - 4*(b^2*c^4*d + 3*a*b*c^3*d^2 + a^2*c^2*d^3)*e^5*f^3 + (b^2*c^5 + 8*a*b*c^4*d + 6*a^2*c^3*d^2)*e^4*f^4 - 2*(a*b*c^5 + 2*a^2*c^4*d)*e^3*f^5 + (b^2*d^5*e^6*f^2 + a^2*c^4*d*f^8 - 2*(2*b^2*c*d^4 + a*b*d^5)*e^5*f^3 + (6*b^2*c^2*d^3 + 8*a*b*c*d^4 + a^2*d^5)*e^4*f^4 - 4*(b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*e^3*f^5 + (b^2*c^4*d + 8*a*b*c^3*d^2 + 6*a^2*c^2*d^3)*e^2*f^6 - 2*(a*b*c^4*d + 2*a^2*c^3*d^2)*e*f^7)*x^3 + (2*b^2*d^5*e^7*f + a^2*c^5*f^8 - (7*b^2*c*d^4 + 4*a*b*d^5)*e^6*f^2 + 2*(4*b^2*c^2*d^3 + 7*a*b*c*d^4 + a^2*d^5)*e^5*f^3 - (2*b^2*c^3*d^2 + 16*a*b*c^2*d^3 + 7*a^2*c*d^4)*e^4*f^4 - 2*(b^2*c^4*d - 2*a*b*c^3*d^2 - 4*a^2*c^2*d^3)*e^3*f^5 + (b^2*c^5 + 4*a*b*c^4*d - 2*a^2*c^3*d^2)*e^2*f^6 - 2*(a*b*c^5 + a^2*c^4*d)*e*f^7)*x^2 + (b^2*d^5*e^8 + 2*a^2*c^5*e*f^7 - 2*(b^2*c*d^4 + a*b*d^5)*e^7*f - (2*b^2*c^2*d^3 - 4*a*b*c*d^4 - a^2*d^5)*e^6*f^2 + 2*(4*b^2*c^3*d^2 + 2*a*b*c^2*d^3 - a^2*c*d^4)*e^5*f^3 - (7*b^2*c^4*d + 16*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*e^4*f^4 + 2*(b^2*c^5 + 7*a*b*c^4*d + 4*a^2*c^3*d^2)*e^3*f^5 - (4*a*b*c^5 + 7*a^2*c^4*d)*e^2*f^6)*x), -1/18*(12*sqrt(1/3)*(6*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 - (5*b^3*c^3*d + 8*a*b^2*c^2*d^2 - 13*a^2*b*c*d^3)*e^4*f - (b^3*c^4 - 13*a*b^2*c^3*d + 5*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*e^3*f^2 + (a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*e^2*f^3 + (6*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 - (5*b^3*c^2*d^2 + 8*a*b^2*c*d^3 - 13*a^2*b*d^4)*e^2*f^3 - (b^3*c^3*d - 13*a*b^2*c^2*d^2 + 5*a^2*b*c*d^3 + 7*a^3*d^4)*e*f^4 + (a*b^2*c^3*d - 8*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*f^5)*x^3 + (12*(b^3*c*d^3 - a*b^2*d^4)*e^4*f - 2*(2*b^3*c^2*d^2 + 11*a*b^2*c*d^3 - 13*a^2*b*d^4)*e^3*f^2 - (7*b^3*c^3*d - 18*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + 14*a^3*d^4)*e^2*f^3 - (b^3*c^4 - 15*a*b^2*c^3*d + 21*a^2*b*c^2*d^2 - 7*a^3*c*d^3)*e*f^4 + (a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*f^5)*x^2 + (6*(b^3*c*d^3 - a*b^2*d^4)*e^5 + (7*b^3*c^2*d^2 - 20*a*b^2*c*d^3 + 13*a^2*b*d^4)*e^4*f - (11*b^3*c^3*d + 3*a*b^2*c^2*d^2 - 21*a^2*b*c*d^3 + 7*a^3*d^4)*e^3*f^2 - (2*b^3*c^4 - 27*a*b^2*c^3*d + 18*a^2*b*c^2*d^2 + 7*a^3*c*d^3)*e^2*f^3 + 2*(a*b^2*c^4 - 8*a^2*b*c^3*d + 7*a^3*c^2*d^2)*e*f^4)*x)*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e^3 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e^2*f + (6*(b^2*c*d^2 - a*b*d^3)*e*f^2 + (b^2*c^2*d - 8*a*b*c*d^2 + 7*a^2*d^3)*f^3)*x^3 + (12*(b^2*c*d^2 - a*b*d^3)*e^2*f + 2*(4*b^2*c^2*d - 11*a*b*c*d^2 + 7*a^2*d^3)*e*f^2 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*f^3)*x^2 + (6*(b^2*c*d^2 - a*b*d^3)*e^3 + (13*b^2*c^2*d - 20*a*b*c*d^2 + 7*a^2*d^3)*e^2*f + 2*(b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 4*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(6*(b^2*c^2*d - a*b*c*d^2)*e^3 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e^2*f + (6*(b^2*c*d^2 - a*b*d^3)*e*f^2 + (b^2*c^2*d - 8*a*b*c*d^2 + 7*a^2*d^3)*f^3)*x^3 + (12*(b^2*c*d^2 - a*b*d^3)*e^2*f + 2*(4*b^2*c^2*d - 11*a*b*c*d^2 + 7*a^2*d^3)*e*f^2 + (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*f^3)*x^2 + (6*(b^2*c*d^2 - a*b*d^3)*e^3 + (13*b^2*c^2*d - 20*a*b*c*d^2 + 7*a^2*d^3)*e^2*f + 2*(b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2)*e*f^2)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(3*a^3*c^3*f^5 - 6*(4*b^3*c*d^2 - 3*a*b^2*d^3)*e^5 + (20*b^3*c^2*d + 43*a*b^2*c*d^2 - 36*a^2*b*d^3)*e^4*f + 2*(2*b^3*c^3 - 28*a*b^2*c^2*d - 7*a^2*b*c*d^2 + 9*a^3*d^3)*e^3*f^2 - (5*a*b^2*c^3 - 52*a^2*b*c^2*d + 5*a^3*c*d^2)*e^2*f^3 - 2*(a^2*b*c^3 + 8*a^3*c^2*d)*e*f^4 - (3*b^3*d^3*e^4*f + 2*(11*b^3*c*d^2 - 17*a*b^2*d^3)*e^3*f^2 - (25*b^3*c^2*d + 16*a*b^2*c*d^2 - 59*a^2*b*d^3)*e^2*f^3 + 2*(25*a*b^2*c^2*d - 17*a^2*b*c*d^2 - 14*a^3*d^3)*e*f^4 - (25*a^2*b*c^2*d - 28*a^3*c*d^2)*f^5)*x^2 - (6*b^3*d^3*e^5 + (37*b^3*c*d^2 - 61*a*b^2*d^3)*e^4*f - 4*(9*b^3*c^2*d + 8*a*b^2*c*d^2 - 26*a^2*b*d^3)*e^3*f^2 - (7*b^3*c^3 - 79*a*b^2*c^2*d + 47*a^2*b*c*d^2 + 49*a^3*d^3)*e^2*f^3 + 2*(7*a*b^2*c^3 - 25*a^2*b*c^2*d + 21*a^3*c*d^2)*e*f^4 - 7*(a^2*b*c^3 - a^3*c^2*d)*f^5)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^2*c*d^4*e^8 + a^2*c^5*e^2*f^6 - 2*(2*b^2*c^2*d^3 + a*b*c*d^4)*e^7*f + (6*b^2*c^3*d^2 + 8*a*b*c^2*d^3 + a^2*c*d^4)*e^6*f^2 - 4*(b^2*c^4*d + 3*a*b*c^3*d^2 + a^2*c^2*d^3)*e^5*f^3 + (b^2*c^5 + 8*a*b*c^4*d + 6*a^2*c^3*d^2)*e^4*f^4 - 2*(a*b*c^5 + 2*a^2*c^4*d)*e^3*f^5 + (b^2*d^5*e^6*f^2 + a^2*c^4*d*f^8 - 2*(2*b^2*c*d^4 + a*b*d^5)*e^5*f^3 + (6*b^2*c^2*d^3 + 8*a*b*c*d^4 + a^2*d^5)*e^4*f^4 - 4*(b^2*c^3*d^2 + 3*a*b*c^2*d^3 + a^2*c*d^4)*e^3*f^5 + (b^2*c^4*d + 8*a*b*c^3*d^2 + 6*a^2*c^2*d^3)*e^2*f^6 - 2*(a*b*c^4*d + 2*a^2*c^3*d^2)*e*f^7)*x^3 + (2*b^2*d^5*e^7*f + a^2*c^5*f^8 - (7*b^2*c*d^4 + 4*a*b*d^5)*e^6*f^2 + 2*(4*b^2*c^2*d^3 + 7*a*b*c*d^4 + a^2*d^5)*e^5*f^3 - (2*b^2*c^3*d^2 + 16*a*b*c^2*d^3 + 7*a^2*c*d^4)*e^4*f^4 - 2*(b^2*c^4*d - 2*a*b*c^3*d^2 - 4*a^2*c^2*d^3)*e^3*f^5 + (b^2*c^5 + 4*a*b*c^4*d - 2*a^2*c^3*d^2)*e^2*f^6 - 2*(a*b*c^5 + a^2*c^4*d)*e*f^7)*x^2 + (b^2*d^5*e^8 + 2*a^2*c^5*e*f^7 - 2*(b^2*c*d^4 + a*b*d^5)*e^7*f - (2*b^2*c^2*d^3 - 4*a*b*c*d^4 - a^2*d^5)*e^6*f^2 + 2*(4*b^2*c^3*d^2 + 2*a*b*c^2*d^3 - a^2*c*d^4)*e^5*f^3 - (7*b^2*c^4*d + 16*a*b*c^3*d^2 + 2*a^2*c^2*d^3)*e^4*f^4 + 2*(b^2*c^5 + 7*a*b*c^4*d + 4*a^2*c^3*d^2)*e^3*f^5 - (4*a*b*c^5 + 7*a^2*c^4*d)*e^2*f^6)*x)]","B",0
3043,1,12725,0,29.747915," ","integrate((b*x+a)^(4/3)/(d*x+c)^(4/3)/(f*x+e)^4,x, algorithm=""fricas"")","\left[-\frac{6 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{3} - a b^{3} c d^{4}\right)} e^{7} - 18 \, {\left(b^{4} c^{3} d^{2} + 4 \, a b^{3} c^{2} d^{3} - 5 \, a^{2} b^{2} c d^{4}\right)} e^{6} f - 2 \, {\left(5 \, b^{4} c^{4} d - 42 \, a b^{3} c^{3} d^{2} - 12 \, a^{2} b^{2} c^{2} d^{3} + 49 \, a^{3} b c d^{4}\right)} e^{5} f^{2} + {\left(b^{4} c^{5} + 16 \, a b^{3} c^{4} d - 108 \, a^{2} b^{2} c^{3} d^{2} + 56 \, a^{3} b c^{2} d^{3} + 35 \, a^{4} c d^{4}\right)} e^{4} f^{3} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e^{3} f^{4} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{4} f^{3} - 18 \, {\left(b^{4} c^{2} d^{3} + 4 \, a b^{3} c d^{4} - 5 \, a^{2} b^{2} d^{5}\right)} e^{3} f^{4} - 2 \, {\left(5 \, b^{4} c^{3} d^{2} - 42 \, a b^{3} c^{2} d^{3} - 12 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{2} f^{5} + {\left(b^{4} c^{4} d + 16 \, a b^{3} c^{3} d^{2} - 108 \, a^{2} b^{2} c^{2} d^{3} + 56 \, a^{3} b c d^{4} + 35 \, a^{4} d^{5}\right)} e f^{6} - {\left(a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 42 \, a^{3} b c^{2} d^{3} + 35 \, a^{4} c d^{4}\right)} f^{7}\right)} x^{4} + {\left(81 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{5} f^{2} - 27 \, {\left(b^{4} c^{2} d^{3} + 9 \, a b^{3} c d^{4} - 10 \, a^{2} b^{2} d^{5}\right)} e^{4} f^{3} - 6 \, {\left(8 \, b^{4} c^{3} d^{2} - 30 \, a b^{3} c^{2} d^{3} - 27 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{3} f^{4} - {\left(7 \, b^{4} c^{4} d - 132 \, a b^{3} c^{3} d^{2} + 300 \, a^{2} b^{2} c^{2} d^{3} - 70 \, a^{3} b c d^{4} - 105 \, a^{4} d^{5}\right)} e^{2} f^{5} + {\left(b^{4} c^{5} + 13 \, a b^{3} c^{4} d - 126 \, a^{2} b^{2} c^{3} d^{2} + 182 \, a^{3} b c^{2} d^{3} - 70 \, a^{4} c d^{4}\right)} e f^{6} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} f^{7}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{6} f + 9 \, {\left(b^{4} c^{2} d^{3} - 11 \, a b^{3} c d^{4} + 10 \, a^{2} b^{2} d^{5}\right)} e^{5} f^{2} - 2 \, {\left(14 \, b^{4} c^{3} d^{2} - 6 \, a b^{3} c^{2} d^{3} - 57 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{4} f^{3} - {\left(9 \, b^{4} c^{4} d - 100 \, a b^{3} c^{3} d^{2} + 84 \, a^{2} b^{2} c^{2} d^{3} + 42 \, a^{3} b c d^{4} - 35 \, a^{4} d^{5}\right)} e^{3} f^{4} + {\left(b^{4} c^{5} + 15 \, a b^{3} c^{4} d - 114 \, a^{2} b^{2} c^{3} d^{2} + 98 \, a^{3} b c^{2} d^{3}\right)} e^{2} f^{5} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e f^{6}\right)} x^{2} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{7} + 9 \, {\left(7 \, b^{4} c^{2} d^{3} - 17 \, a b^{3} c d^{4} + 10 \, a^{2} b^{2} d^{5}\right)} e^{6} f - 2 \, {\left(32 \, b^{4} c^{3} d^{2} + 66 \, a b^{3} c^{2} d^{3} - 147 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{5} f^{2} - {\left(29 \, b^{4} c^{4} d - 268 \, a b^{3} c^{3} d^{2} + 36 \, a^{2} b^{2} c^{2} d^{3} + 238 \, a^{3} b c d^{4} - 35 \, a^{4} d^{5}\right)} e^{4} f^{3} + {\left(3 \, b^{4} c^{5} + 47 \, a b^{3} c^{4} d - 330 \, a^{2} b^{2} c^{3} d^{2} + 210 \, a^{3} b c^{2} d^{3} + 70 \, a^{4} c d^{4}\right)} e^{3} f^{4} - 3 \, {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e^{2} f^{5}\right)} x\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \log\left(-\frac{3 \, a^{2} c f^{2} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} - 2 \, {\left(2 \, a b c + a^{2} d\right)} e f + 3 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b e - a f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(3 \, b^{2} d e^{2} - 2 \, {\left(b^{2} c + 2 \, a b d\right)} e f + {\left(2 \, a b c + a^{2} d\right)} f^{2}\right)} x + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, {\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{f x + e}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} + 9 \, {\left(b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + 7 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} f^{3} + 9 \, {\left(b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e f^{4} - {\left(b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} - 42 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} f^{5}\right)} x^{4} + {\left(81 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} + 27 \, {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{2} f^{3} + 3 \, {\left(2 \, b^{3} c^{3} d - 30 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e f^{4} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f + 9 \, {\left(4 \, b^{3} c^{2} d^{2} - 11 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{3} f^{2} + {\left(8 \, b^{3} c^{3} d - 78 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e f^{4}\right)} x^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + 9 \, {\left(10 \, b^{3} c^{2} d^{2} - 17 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{4} f + {\left(26 \, b^{3} c^{3} d - 222 \, a b^{2} c^{2} d^{2} + 231 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{3} f^{2} - 3 \, {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 4 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} + 9 \, {\left(b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + 7 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} f^{3} + 9 \, {\left(b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e f^{4} - {\left(b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} - 42 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} f^{5}\right)} x^{4} + {\left(81 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} + 27 \, {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{2} f^{3} + 3 \, {\left(2 \, b^{3} c^{3} d - 30 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e f^{4} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f + 9 \, {\left(4 \, b^{3} c^{2} d^{2} - 11 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{3} f^{2} + {\left(8 \, b^{3} c^{3} d - 78 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e f^{4}\right)} x^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + 9 \, {\left(10 \, b^{3} c^{2} d^{2} - 17 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{4} f + {\left(26 \, b^{3} c^{3} d - 222 \, a b^{2} c^{2} d^{2} + 231 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{3} f^{2} - 3 \, {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(9 \, a^{4} c^{4} f^{7} - 27 \, {\left(4 \, b^{4} c d^{3} - 3 \, a b^{3} d^{4}\right)} e^{7} + 9 \, {\left(8 \, b^{4} c^{2} d^{2} + 37 \, a b^{3} c d^{3} - 27 \, a^{2} b^{2} d^{4}\right)} e^{6} f + {\left(40 \, b^{4} c^{3} d - 344 \, a b^{3} c^{2} d^{2} - 353 \, a^{2} b^{2} c d^{3} + 243 \, a^{3} b d^{4}\right)} e^{5} f^{2} - {\left(4 \, b^{4} c^{4} + 75 \, a b^{3} c^{3} d - 606 \, a^{2} b^{2} c^{2} d^{2} - 139 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}\right)} e^{4} f^{3} + {\left(5 \, a b^{3} c^{4} - 21 \, a^{2} b^{2} c^{3} d - 468 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e^{3} f^{4} + {\left(11 \, a^{2} b^{2} c^{4} + 107 \, a^{3} b c^{3} d + 134 \, a^{4} c^{2} d^{2}\right)} e^{2} f^{5} - 3 \, {\left(7 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} e f^{6} - {\left(9 \, b^{4} d^{4} e^{5} f^{2} + 15 \, {\left(8 \, b^{4} c d^{3} - 11 \, a b^{3} d^{4}\right)} e^{4} f^{3} - {\left(127 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} - 443 \, a^{2} b^{2} d^{4}\right)} e^{3} f^{4} - {\left(2 \, b^{4} c^{3} d - 387 \, a b^{3} c^{2} d^{2} + 48 \, a^{2} b^{2} c d^{3} + 427 \, a^{3} b d^{4}\right)} e^{2} f^{5} + {\left(4 \, a b^{3} c^{3} d - 393 \, a^{2} b^{2} c^{2} d^{2} + 294 \, a^{3} b c d^{3} + 140 \, a^{4} d^{4}\right)} e f^{6} - {\left(2 \, a^{2} b^{2} c^{3} d - 133 \, a^{3} b c^{2} d^{2} + 140 \, a^{4} c d^{3}\right)} f^{7}\right)} x^{3} - {\left(27 \, b^{4} d^{4} e^{6} f + 3 \, {\left(109 \, b^{4} c d^{3} - 154 \, a b^{3} d^{4}\right)} e^{5} f^{2} - {\left(317 \, b^{4} c^{2} d^{2} + 641 \, a b^{3} c d^{3} - 1228 \, a^{2} b^{2} d^{4}\right)} e^{4} f^{3} - {\left(35 \, b^{4} c^{3} d - 992 \, a b^{3} c^{2} d^{2} + 49 \, a^{2} b^{2} c d^{3} + 1178 \, a^{3} b d^{4}\right)} e^{3} f^{4} - {\left(2 \, b^{4} c^{4} - 107 \, a b^{3} c^{3} d + 1068 \, a^{2} b^{2} c^{2} d^{2} - 713 \, a^{3} b c d^{3} - 385 \, a^{4} d^{4}\right)} e^{2} f^{5} + {\left(4 \, a b^{3} c^{4} - 109 \, a^{2} b^{2} c^{3} d + 428 \, a^{3} b c^{2} d^{2} - 350 \, a^{4} c d^{3}\right)} e f^{6} - {\left(2 \, a^{2} b^{2} c^{4} - 37 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} f^{7}\right)} x^{2} - {\left(27 \, b^{4} d^{4} e^{7} + 9 \, {\left(31 \, b^{4} c d^{3} - 46 \, a b^{3} d^{4}\right)} e^{6} f - 2 \, {\left(104 \, b^{4} c^{2} d^{2} + 302 \, a b^{3} c d^{3} - 541 \, a^{2} b^{2} d^{4}\right)} e^{5} f^{2} - {\left(109 \, b^{4} c^{3} d - 733 \, a b^{3} c^{2} d^{2} - 136 \, a^{2} b^{2} c d^{3} + 1030 \, a^{3} b d^{4}\right)} e^{4} f^{3} + {\left(11 \, b^{4} c^{4} + 322 \, a b^{3} c^{3} d - 957 \, a^{2} b^{2} c^{2} d^{2} + 424 \, a^{3} b c d^{3} + 335 \, a^{4} d^{4}\right)} e^{3} f^{4} - {\left(37 \, a b^{3} c^{4} + 302 \, a^{2} b^{2} c^{3} d - 547 \, a^{3} b c^{2} d^{2} + 235 \, a^{4} c d^{3}\right)} e^{2} f^{5} + {\left(41 \, a^{2} b^{2} c^{4} + 74 \, a^{3} b c^{3} d - 115 \, a^{4} c^{2} d^{2}\right)} e f^{6} - 15 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} f^{7}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{81 \, {\left(b^{3} c d^{5} e^{11} + a^{3} c^{6} e^{3} f^{8} - {\left(5 \, b^{3} c^{2} d^{4} + 3 \, a b^{2} c d^{5}\right)} e^{10} f + {\left(10 \, b^{3} c^{3} d^{3} + 15 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5}\right)} e^{9} f^{2} - {\left(10 \, b^{3} c^{4} d^{2} + 30 \, a b^{2} c^{3} d^{3} + 15 \, a^{2} b c^{2} d^{4} + a^{3} c d^{5}\right)} e^{8} f^{3} + 5 \, {\left(b^{3} c^{5} d + 6 \, a b^{2} c^{4} d^{2} + 6 \, a^{2} b c^{3} d^{3} + a^{3} c^{2} d^{4}\right)} e^{7} f^{4} - {\left(b^{3} c^{6} + 15 \, a b^{2} c^{5} d + 30 \, a^{2} b c^{4} d^{2} + 10 \, a^{3} c^{3} d^{3}\right)} e^{6} f^{5} + {\left(3 \, a b^{2} c^{6} + 15 \, a^{2} b c^{5} d + 10 \, a^{3} c^{4} d^{2}\right)} e^{5} f^{6} - {\left(3 \, a^{2} b c^{6} + 5 \, a^{3} c^{5} d\right)} e^{4} f^{7} + {\left(b^{3} d^{6} e^{8} f^{3} + a^{3} c^{5} d f^{11} - {\left(5 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{7} f^{4} + {\left(10 \, b^{3} c^{2} d^{4} + 15 \, a b^{2} c d^{5} + 3 \, a^{2} b d^{6}\right)} e^{6} f^{5} - {\left(10 \, b^{3} c^{3} d^{3} + 30 \, a b^{2} c^{2} d^{4} + 15 \, a^{2} b c d^{5} + a^{3} d^{6}\right)} e^{5} f^{6} + 5 \, {\left(b^{3} c^{4} d^{2} + 6 \, a b^{2} c^{3} d^{3} + 6 \, a^{2} b c^{2} d^{4} + a^{3} c d^{5}\right)} e^{4} f^{7} - {\left(b^{3} c^{5} d + 15 \, a b^{2} c^{4} d^{2} + 30 \, a^{2} b c^{3} d^{3} + 10 \, a^{3} c^{2} d^{4}\right)} e^{3} f^{8} + {\left(3 \, a b^{2} c^{5} d + 15 \, a^{2} b c^{4} d^{2} + 10 \, a^{3} c^{3} d^{3}\right)} e^{2} f^{9} - {\left(3 \, a^{2} b c^{5} d + 5 \, a^{3} c^{4} d^{2}\right)} e f^{10}\right)} x^{4} + {\left(3 \, b^{3} d^{6} e^{9} f^{2} + a^{3} c^{6} f^{11} - {\left(14 \, b^{3} c d^{5} + 9 \, a b^{2} d^{6}\right)} e^{8} f^{3} + {\left(25 \, b^{3} c^{2} d^{4} + 42 \, a b^{2} c d^{5} + 9 \, a^{2} b d^{6}\right)} e^{7} f^{4} - {\left(20 \, b^{3} c^{3} d^{3} + 75 \, a b^{2} c^{2} d^{4} + 42 \, a^{2} b c d^{5} + 3 \, a^{3} d^{6}\right)} e^{6} f^{5} + {\left(5 \, b^{3} c^{4} d^{2} + 60 \, a b^{2} c^{3} d^{3} + 75 \, a^{2} b c^{2} d^{4} + 14 \, a^{3} c d^{5}\right)} e^{5} f^{6} + {\left(2 \, b^{3} c^{5} d - 15 \, a b^{2} c^{4} d^{2} - 60 \, a^{2} b c^{3} d^{3} - 25 \, a^{3} c^{2} d^{4}\right)} e^{4} f^{7} - {\left(b^{3} c^{6} + 6 \, a b^{2} c^{5} d - 15 \, a^{2} b c^{4} d^{2} - 20 \, a^{3} c^{3} d^{3}\right)} e^{3} f^{8} + {\left(3 \, a b^{2} c^{6} + 6 \, a^{2} b c^{5} d - 5 \, a^{3} c^{4} d^{2}\right)} e^{2} f^{9} - {\left(3 \, a^{2} b c^{6} + 2 \, a^{3} c^{5} d\right)} e f^{10}\right)} x^{3} + 3 \, {\left(b^{3} d^{6} e^{10} f + a^{3} c^{6} e f^{10} - {\left(4 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{9} f^{2} + {\left(5 \, b^{3} c^{2} d^{4} + 12 \, a b^{2} c d^{5} + 3 \, a^{2} b d^{6}\right)} e^{8} f^{3} - {\left(15 \, a b^{2} c^{2} d^{4} + 12 \, a^{2} b c d^{5} + a^{3} d^{6}\right)} e^{7} f^{4} - {\left(5 \, b^{3} c^{4} d^{2} - 15 \, a^{2} b c^{2} d^{4} - 4 \, a^{3} c d^{5}\right)} e^{6} f^{5} + {\left(4 \, b^{3} c^{5} d + 15 \, a b^{2} c^{4} d^{2} - 5 \, a^{3} c^{2} d^{4}\right)} e^{5} f^{6} - {\left(b^{3} c^{6} + 12 \, a b^{2} c^{5} d + 15 \, a^{2} b c^{4} d^{2}\right)} e^{4} f^{7} + {\left(3 \, a b^{2} c^{6} + 12 \, a^{2} b c^{5} d + 5 \, a^{3} c^{4} d^{2}\right)} e^{3} f^{8} - {\left(3 \, a^{2} b c^{6} + 4 \, a^{3} c^{5} d\right)} e^{2} f^{9}\right)} x^{2} + {\left(b^{3} d^{6} e^{11} + 3 \, a^{3} c^{6} e^{2} f^{9} - {\left(2 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{10} f - {\left(5 \, b^{3} c^{2} d^{4} - 6 \, a b^{2} c d^{5} - 3 \, a^{2} b d^{6}\right)} e^{9} f^{2} + {\left(20 \, b^{3} c^{3} d^{3} + 15 \, a b^{2} c^{2} d^{4} - 6 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} e^{8} f^{3} - {\left(25 \, b^{3} c^{4} d^{2} + 60 \, a b^{2} c^{3} d^{3} + 15 \, a^{2} b c^{2} d^{4} - 2 \, a^{3} c d^{5}\right)} e^{7} f^{4} + {\left(14 \, b^{3} c^{5} d + 75 \, a b^{2} c^{4} d^{2} + 60 \, a^{2} b c^{3} d^{3} + 5 \, a^{3} c^{2} d^{4}\right)} e^{6} f^{5} - {\left(3 \, b^{3} c^{6} + 42 \, a b^{2} c^{5} d + 75 \, a^{2} b c^{4} d^{2} + 20 \, a^{3} c^{3} d^{3}\right)} e^{5} f^{6} + {\left(9 \, a b^{2} c^{6} + 42 \, a^{2} b c^{5} d + 25 \, a^{3} c^{4} d^{2}\right)} e^{4} f^{7} - {\left(9 \, a^{2} b c^{6} + 14 \, a^{3} c^{5} d\right)} e^{3} f^{8}\right)} x\right)}}, -\frac{12 \, \sqrt{\frac{1}{3}} {\left(27 \, {\left(b^{4} c^{2} d^{3} - a b^{3} c d^{4}\right)} e^{7} - 18 \, {\left(b^{4} c^{3} d^{2} + 4 \, a b^{3} c^{2} d^{3} - 5 \, a^{2} b^{2} c d^{4}\right)} e^{6} f - 2 \, {\left(5 \, b^{4} c^{4} d - 42 \, a b^{3} c^{3} d^{2} - 12 \, a^{2} b^{2} c^{2} d^{3} + 49 \, a^{3} b c d^{4}\right)} e^{5} f^{2} + {\left(b^{4} c^{5} + 16 \, a b^{3} c^{4} d - 108 \, a^{2} b^{2} c^{3} d^{2} + 56 \, a^{3} b c^{2} d^{3} + 35 \, a^{4} c d^{4}\right)} e^{4} f^{3} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e^{3} f^{4} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{4} f^{3} - 18 \, {\left(b^{4} c^{2} d^{3} + 4 \, a b^{3} c d^{4} - 5 \, a^{2} b^{2} d^{5}\right)} e^{3} f^{4} - 2 \, {\left(5 \, b^{4} c^{3} d^{2} - 42 \, a b^{3} c^{2} d^{3} - 12 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{2} f^{5} + {\left(b^{4} c^{4} d + 16 \, a b^{3} c^{3} d^{2} - 108 \, a^{2} b^{2} c^{2} d^{3} + 56 \, a^{3} b c d^{4} + 35 \, a^{4} d^{5}\right)} e f^{6} - {\left(a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 42 \, a^{3} b c^{2} d^{3} + 35 \, a^{4} c d^{4}\right)} f^{7}\right)} x^{4} + {\left(81 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{5} f^{2} - 27 \, {\left(b^{4} c^{2} d^{3} + 9 \, a b^{3} c d^{4} - 10 \, a^{2} b^{2} d^{5}\right)} e^{4} f^{3} - 6 \, {\left(8 \, b^{4} c^{3} d^{2} - 30 \, a b^{3} c^{2} d^{3} - 27 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{3} f^{4} - {\left(7 \, b^{4} c^{4} d - 132 \, a b^{3} c^{3} d^{2} + 300 \, a^{2} b^{2} c^{2} d^{3} - 70 \, a^{3} b c d^{4} - 105 \, a^{4} d^{5}\right)} e^{2} f^{5} + {\left(b^{4} c^{5} + 13 \, a b^{3} c^{4} d - 126 \, a^{2} b^{2} c^{3} d^{2} + 182 \, a^{3} b c^{2} d^{3} - 70 \, a^{4} c d^{4}\right)} e f^{6} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} f^{7}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{6} f + 9 \, {\left(b^{4} c^{2} d^{3} - 11 \, a b^{3} c d^{4} + 10 \, a^{2} b^{2} d^{5}\right)} e^{5} f^{2} - 2 \, {\left(14 \, b^{4} c^{3} d^{2} - 6 \, a b^{3} c^{2} d^{3} - 57 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{4} f^{3} - {\left(9 \, b^{4} c^{4} d - 100 \, a b^{3} c^{3} d^{2} + 84 \, a^{2} b^{2} c^{2} d^{3} + 42 \, a^{3} b c d^{4} - 35 \, a^{4} d^{5}\right)} e^{3} f^{4} + {\left(b^{4} c^{5} + 15 \, a b^{3} c^{4} d - 114 \, a^{2} b^{2} c^{3} d^{2} + 98 \, a^{3} b c^{2} d^{3}\right)} e^{2} f^{5} - {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e f^{6}\right)} x^{2} + {\left(27 \, {\left(b^{4} c d^{4} - a b^{3} d^{5}\right)} e^{7} + 9 \, {\left(7 \, b^{4} c^{2} d^{3} - 17 \, a b^{3} c d^{4} + 10 \, a^{2} b^{2} d^{5}\right)} e^{6} f - 2 \, {\left(32 \, b^{4} c^{3} d^{2} + 66 \, a b^{3} c^{2} d^{3} - 147 \, a^{2} b^{2} c d^{4} + 49 \, a^{3} b d^{5}\right)} e^{5} f^{2} - {\left(29 \, b^{4} c^{4} d - 268 \, a b^{3} c^{3} d^{2} + 36 \, a^{2} b^{2} c^{2} d^{3} + 238 \, a^{3} b c d^{4} - 35 \, a^{4} d^{5}\right)} e^{4} f^{3} + {\left(3 \, b^{4} c^{5} + 47 \, a b^{3} c^{4} d - 330 \, a^{2} b^{2} c^{3} d^{2} + 210 \, a^{3} b c^{2} d^{3} + 70 \, a^{4} c d^{4}\right)} e^{3} f^{4} - 3 \, {\left(a b^{3} c^{5} + 6 \, a^{2} b^{2} c^{4} d - 42 \, a^{3} b c^{3} d^{2} + 35 \, a^{4} c^{2} d^{3}\right)} e^{2} f^{5}\right)} x\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}\right)} \sqrt{-\frac{{\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}}}{d e - c f}}}{b^{2} c e^{2} - 2 \, a b c e f + a^{2} c f^{2} + {\left(b^{2} d e^{2} - 2 \, a b d e f + a^{2} d f^{2}\right)} x}\right) + 2 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} + 9 \, {\left(b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + 7 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} f^{3} + 9 \, {\left(b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e f^{4} - {\left(b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} - 42 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} f^{5}\right)} x^{4} + {\left(81 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} + 27 \, {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{2} f^{3} + 3 \, {\left(2 \, b^{3} c^{3} d - 30 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e f^{4} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f + 9 \, {\left(4 \, b^{3} c^{2} d^{2} - 11 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{3} f^{2} + {\left(8 \, b^{3} c^{3} d - 78 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e f^{4}\right)} x^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + 9 \, {\left(10 \, b^{3} c^{2} d^{2} - 17 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{4} f + {\left(26 \, b^{3} c^{3} d - 222 \, a b^{2} c^{2} d^{2} + 231 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{3} f^{2} - 3 \, {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} + {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{1}{3}} {\left(b c e - a c f + {\left(b d e - a d f\right)} x\right)}}{d x + c}\right) - 4 \, {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(27 \, {\left(b^{3} c^{2} d^{2} - a b^{2} c d^{3}\right)} e^{5} + 9 \, {\left(b^{3} c^{3} d - 8 \, a b^{2} c^{2} d^{2} + 7 \, a^{2} b c d^{3}\right)} e^{4} f - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{3} f^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{2} f^{3} + 9 \, {\left(b^{3} c^{2} d^{2} - 8 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e f^{4} - {\left(b^{3} c^{3} d + 6 \, a b^{2} c^{2} d^{2} - 42 \, a^{2} b c d^{3} + 35 \, a^{3} d^{4}\right)} f^{5}\right)} x^{4} + {\left(81 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{3} f^{2} + 27 \, {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{2} f^{3} + 3 \, {\left(2 \, b^{3} c^{3} d - 30 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e f^{4} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} f^{5}\right)} x^{3} + 3 \, {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{4} f + 9 \, {\left(4 \, b^{3} c^{2} d^{2} - 11 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{3} f^{2} + {\left(8 \, b^{3} c^{3} d - 78 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{2} f^{3} - {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e f^{4}\right)} x^{2} + {\left(27 \, {\left(b^{3} c d^{3} - a b^{2} d^{4}\right)} e^{5} + 9 \, {\left(10 \, b^{3} c^{2} d^{2} - 17 \, a b^{2} c d^{3} + 7 \, a^{2} b d^{4}\right)} e^{4} f + {\left(26 \, b^{3} c^{3} d - 222 \, a b^{2} c^{2} d^{2} + 231 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} e^{3} f^{2} - 3 \, {\left(b^{3} c^{4} + 6 \, a b^{2} c^{3} d - 42 \, a^{2} b c^{2} d^{2} + 35 \, a^{3} c d^{3}\right)} e^{2} f^{3}\right)} x\right)} \log\left(\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(-b^{2} d e^{3} + a^{2} c f^{3} + {\left(b^{2} c + 2 \, a b d\right)} e^{2} f - {\left(2 \, a b c + a^{2} d\right)} e f^{2}\right)}^{\frac{2}{3}} {\left(d x + c\right)}}{d x + c}\right) + 3 \, {\left(9 \, a^{4} c^{4} f^{7} - 27 \, {\left(4 \, b^{4} c d^{3} - 3 \, a b^{3} d^{4}\right)} e^{7} + 9 \, {\left(8 \, b^{4} c^{2} d^{2} + 37 \, a b^{3} c d^{3} - 27 \, a^{2} b^{2} d^{4}\right)} e^{6} f + {\left(40 \, b^{4} c^{3} d - 344 \, a b^{3} c^{2} d^{2} - 353 \, a^{2} b^{2} c d^{3} + 243 \, a^{3} b d^{4}\right)} e^{5} f^{2} - {\left(4 \, b^{4} c^{4} + 75 \, a b^{3} c^{3} d - 606 \, a^{2} b^{2} c^{2} d^{2} - 139 \, a^{3} b c d^{3} + 81 \, a^{4} d^{4}\right)} e^{4} f^{3} + {\left(5 \, a b^{3} c^{4} - 21 \, a^{2} b^{2} c^{3} d - 468 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e^{3} f^{4} + {\left(11 \, a^{2} b^{2} c^{4} + 107 \, a^{3} b c^{3} d + 134 \, a^{4} c^{2} d^{2}\right)} e^{2} f^{5} - 3 \, {\left(7 \, a^{3} b c^{4} + 17 \, a^{4} c^{3} d\right)} e f^{6} - {\left(9 \, b^{4} d^{4} e^{5} f^{2} + 15 \, {\left(8 \, b^{4} c d^{3} - 11 \, a b^{3} d^{4}\right)} e^{4} f^{3} - {\left(127 \, b^{4} c^{2} d^{2} + 226 \, a b^{3} c d^{3} - 443 \, a^{2} b^{2} d^{4}\right)} e^{3} f^{4} - {\left(2 \, b^{4} c^{3} d - 387 \, a b^{3} c^{2} d^{2} + 48 \, a^{2} b^{2} c d^{3} + 427 \, a^{3} b d^{4}\right)} e^{2} f^{5} + {\left(4 \, a b^{3} c^{3} d - 393 \, a^{2} b^{2} c^{2} d^{2} + 294 \, a^{3} b c d^{3} + 140 \, a^{4} d^{4}\right)} e f^{6} - {\left(2 \, a^{2} b^{2} c^{3} d - 133 \, a^{3} b c^{2} d^{2} + 140 \, a^{4} c d^{3}\right)} f^{7}\right)} x^{3} - {\left(27 \, b^{4} d^{4} e^{6} f + 3 \, {\left(109 \, b^{4} c d^{3} - 154 \, a b^{3} d^{4}\right)} e^{5} f^{2} - {\left(317 \, b^{4} c^{2} d^{2} + 641 \, a b^{3} c d^{3} - 1228 \, a^{2} b^{2} d^{4}\right)} e^{4} f^{3} - {\left(35 \, b^{4} c^{3} d - 992 \, a b^{3} c^{2} d^{2} + 49 \, a^{2} b^{2} c d^{3} + 1178 \, a^{3} b d^{4}\right)} e^{3} f^{4} - {\left(2 \, b^{4} c^{4} - 107 \, a b^{3} c^{3} d + 1068 \, a^{2} b^{2} c^{2} d^{2} - 713 \, a^{3} b c d^{3} - 385 \, a^{4} d^{4}\right)} e^{2} f^{5} + {\left(4 \, a b^{3} c^{4} - 109 \, a^{2} b^{2} c^{3} d + 428 \, a^{3} b c^{2} d^{2} - 350 \, a^{4} c d^{3}\right)} e f^{6} - {\left(2 \, a^{2} b^{2} c^{4} - 37 \, a^{3} b c^{3} d + 35 \, a^{4} c^{2} d^{2}\right)} f^{7}\right)} x^{2} - {\left(27 \, b^{4} d^{4} e^{7} + 9 \, {\left(31 \, b^{4} c d^{3} - 46 \, a b^{3} d^{4}\right)} e^{6} f - 2 \, {\left(104 \, b^{4} c^{2} d^{2} + 302 \, a b^{3} c d^{3} - 541 \, a^{2} b^{2} d^{4}\right)} e^{5} f^{2} - {\left(109 \, b^{4} c^{3} d - 733 \, a b^{3} c^{2} d^{2} - 136 \, a^{2} b^{2} c d^{3} + 1030 \, a^{3} b d^{4}\right)} e^{4} f^{3} + {\left(11 \, b^{4} c^{4} + 322 \, a b^{3} c^{3} d - 957 \, a^{2} b^{2} c^{2} d^{2} + 424 \, a^{3} b c d^{3} + 335 \, a^{4} d^{4}\right)} e^{3} f^{4} - {\left(37 \, a b^{3} c^{4} + 302 \, a^{2} b^{2} c^{3} d - 547 \, a^{3} b c^{2} d^{2} + 235 \, a^{4} c d^{3}\right)} e^{2} f^{5} + {\left(41 \, a^{2} b^{2} c^{4} + 74 \, a^{3} b c^{3} d - 115 \, a^{4} c^{2} d^{2}\right)} e f^{6} - 15 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} f^{7}\right)} x\right)} {\left(b x + a\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}}}{81 \, {\left(b^{3} c d^{5} e^{11} + a^{3} c^{6} e^{3} f^{8} - {\left(5 \, b^{3} c^{2} d^{4} + 3 \, a b^{2} c d^{5}\right)} e^{10} f + {\left(10 \, b^{3} c^{3} d^{3} + 15 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5}\right)} e^{9} f^{2} - {\left(10 \, b^{3} c^{4} d^{2} + 30 \, a b^{2} c^{3} d^{3} + 15 \, a^{2} b c^{2} d^{4} + a^{3} c d^{5}\right)} e^{8} f^{3} + 5 \, {\left(b^{3} c^{5} d + 6 \, a b^{2} c^{4} d^{2} + 6 \, a^{2} b c^{3} d^{3} + a^{3} c^{2} d^{4}\right)} e^{7} f^{4} - {\left(b^{3} c^{6} + 15 \, a b^{2} c^{5} d + 30 \, a^{2} b c^{4} d^{2} + 10 \, a^{3} c^{3} d^{3}\right)} e^{6} f^{5} + {\left(3 \, a b^{2} c^{6} + 15 \, a^{2} b c^{5} d + 10 \, a^{3} c^{4} d^{2}\right)} e^{5} f^{6} - {\left(3 \, a^{2} b c^{6} + 5 \, a^{3} c^{5} d\right)} e^{4} f^{7} + {\left(b^{3} d^{6} e^{8} f^{3} + a^{3} c^{5} d f^{11} - {\left(5 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{7} f^{4} + {\left(10 \, b^{3} c^{2} d^{4} + 15 \, a b^{2} c d^{5} + 3 \, a^{2} b d^{6}\right)} e^{6} f^{5} - {\left(10 \, b^{3} c^{3} d^{3} + 30 \, a b^{2} c^{2} d^{4} + 15 \, a^{2} b c d^{5} + a^{3} d^{6}\right)} e^{5} f^{6} + 5 \, {\left(b^{3} c^{4} d^{2} + 6 \, a b^{2} c^{3} d^{3} + 6 \, a^{2} b c^{2} d^{4} + a^{3} c d^{5}\right)} e^{4} f^{7} - {\left(b^{3} c^{5} d + 15 \, a b^{2} c^{4} d^{2} + 30 \, a^{2} b c^{3} d^{3} + 10 \, a^{3} c^{2} d^{4}\right)} e^{3} f^{8} + {\left(3 \, a b^{2} c^{5} d + 15 \, a^{2} b c^{4} d^{2} + 10 \, a^{3} c^{3} d^{3}\right)} e^{2} f^{9} - {\left(3 \, a^{2} b c^{5} d + 5 \, a^{3} c^{4} d^{2}\right)} e f^{10}\right)} x^{4} + {\left(3 \, b^{3} d^{6} e^{9} f^{2} + a^{3} c^{6} f^{11} - {\left(14 \, b^{3} c d^{5} + 9 \, a b^{2} d^{6}\right)} e^{8} f^{3} + {\left(25 \, b^{3} c^{2} d^{4} + 42 \, a b^{2} c d^{5} + 9 \, a^{2} b d^{6}\right)} e^{7} f^{4} - {\left(20 \, b^{3} c^{3} d^{3} + 75 \, a b^{2} c^{2} d^{4} + 42 \, a^{2} b c d^{5} + 3 \, a^{3} d^{6}\right)} e^{6} f^{5} + {\left(5 \, b^{3} c^{4} d^{2} + 60 \, a b^{2} c^{3} d^{3} + 75 \, a^{2} b c^{2} d^{4} + 14 \, a^{3} c d^{5}\right)} e^{5} f^{6} + {\left(2 \, b^{3} c^{5} d - 15 \, a b^{2} c^{4} d^{2} - 60 \, a^{2} b c^{3} d^{3} - 25 \, a^{3} c^{2} d^{4}\right)} e^{4} f^{7} - {\left(b^{3} c^{6} + 6 \, a b^{2} c^{5} d - 15 \, a^{2} b c^{4} d^{2} - 20 \, a^{3} c^{3} d^{3}\right)} e^{3} f^{8} + {\left(3 \, a b^{2} c^{6} + 6 \, a^{2} b c^{5} d - 5 \, a^{3} c^{4} d^{2}\right)} e^{2} f^{9} - {\left(3 \, a^{2} b c^{6} + 2 \, a^{3} c^{5} d\right)} e f^{10}\right)} x^{3} + 3 \, {\left(b^{3} d^{6} e^{10} f + a^{3} c^{6} e f^{10} - {\left(4 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{9} f^{2} + {\left(5 \, b^{3} c^{2} d^{4} + 12 \, a b^{2} c d^{5} + 3 \, a^{2} b d^{6}\right)} e^{8} f^{3} - {\left(15 \, a b^{2} c^{2} d^{4} + 12 \, a^{2} b c d^{5} + a^{3} d^{6}\right)} e^{7} f^{4} - {\left(5 \, b^{3} c^{4} d^{2} - 15 \, a^{2} b c^{2} d^{4} - 4 \, a^{3} c d^{5}\right)} e^{6} f^{5} + {\left(4 \, b^{3} c^{5} d + 15 \, a b^{2} c^{4} d^{2} - 5 \, a^{3} c^{2} d^{4}\right)} e^{5} f^{6} - {\left(b^{3} c^{6} + 12 \, a b^{2} c^{5} d + 15 \, a^{2} b c^{4} d^{2}\right)} e^{4} f^{7} + {\left(3 \, a b^{2} c^{6} + 12 \, a^{2} b c^{5} d + 5 \, a^{3} c^{4} d^{2}\right)} e^{3} f^{8} - {\left(3 \, a^{2} b c^{6} + 4 \, a^{3} c^{5} d\right)} e^{2} f^{9}\right)} x^{2} + {\left(b^{3} d^{6} e^{11} + 3 \, a^{3} c^{6} e^{2} f^{9} - {\left(2 \, b^{3} c d^{5} + 3 \, a b^{2} d^{6}\right)} e^{10} f - {\left(5 \, b^{3} c^{2} d^{4} - 6 \, a b^{2} c d^{5} - 3 \, a^{2} b d^{6}\right)} e^{9} f^{2} + {\left(20 \, b^{3} c^{3} d^{3} + 15 \, a b^{2} c^{2} d^{4} - 6 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} e^{8} f^{3} - {\left(25 \, b^{3} c^{4} d^{2} + 60 \, a b^{2} c^{3} d^{3} + 15 \, a^{2} b c^{2} d^{4} - 2 \, a^{3} c d^{5}\right)} e^{7} f^{4} + {\left(14 \, b^{3} c^{5} d + 75 \, a b^{2} c^{4} d^{2} + 60 \, a^{2} b c^{3} d^{3} + 5 \, a^{3} c^{2} d^{4}\right)} e^{6} f^{5} - {\left(3 \, b^{3} c^{6} + 42 \, a b^{2} c^{5} d + 75 \, a^{2} b c^{4} d^{2} + 20 \, a^{3} c^{3} d^{3}\right)} e^{5} f^{6} + {\left(9 \, a b^{2} c^{6} + 42 \, a^{2} b c^{5} d + 25 \, a^{3} c^{4} d^{2}\right)} e^{4} f^{7} - {\left(9 \, a^{2} b c^{6} + 14 \, a^{3} c^{5} d\right)} e^{3} f^{8}\right)} x\right)}}\right]"," ",0,"[-1/81*(6*sqrt(1/3)*(27*(b^4*c^2*d^3 - a*b^3*c*d^4)*e^7 - 18*(b^4*c^3*d^2 + 4*a*b^3*c^2*d^3 - 5*a^2*b^2*c*d^4)*e^6*f - 2*(5*b^4*c^4*d - 42*a*b^3*c^3*d^2 - 12*a^2*b^2*c^2*d^3 + 49*a^3*b*c*d^4)*e^5*f^2 + (b^4*c^5 + 16*a*b^3*c^4*d - 108*a^2*b^2*c^3*d^2 + 56*a^3*b*c^2*d^3 + 35*a^4*c*d^4)*e^4*f^3 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e^3*f^4 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^4*f^3 - 18*(b^4*c^2*d^3 + 4*a*b^3*c*d^4 - 5*a^2*b^2*d^5)*e^3*f^4 - 2*(5*b^4*c^3*d^2 - 42*a*b^3*c^2*d^3 - 12*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^2*f^5 + (b^4*c^4*d + 16*a*b^3*c^3*d^2 - 108*a^2*b^2*c^2*d^3 + 56*a^3*b*c*d^4 + 35*a^4*d^5)*e*f^6 - (a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 42*a^3*b*c^2*d^3 + 35*a^4*c*d^4)*f^7)*x^4 + (81*(b^4*c*d^4 - a*b^3*d^5)*e^5*f^2 - 27*(b^4*c^2*d^3 + 9*a*b^3*c*d^4 - 10*a^2*b^2*d^5)*e^4*f^3 - 6*(8*b^4*c^3*d^2 - 30*a*b^3*c^2*d^3 - 27*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^3*f^4 - (7*b^4*c^4*d - 132*a*b^3*c^3*d^2 + 300*a^2*b^2*c^2*d^3 - 70*a^3*b*c*d^4 - 105*a^4*d^5)*e^2*f^5 + (b^4*c^5 + 13*a*b^3*c^4*d - 126*a^2*b^2*c^3*d^2 + 182*a^3*b*c^2*d^3 - 70*a^4*c*d^4)*e*f^6 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*f^7)*x^3 + 3*(27*(b^4*c*d^4 - a*b^3*d^5)*e^6*f + 9*(b^4*c^2*d^3 - 11*a*b^3*c*d^4 + 10*a^2*b^2*d^5)*e^5*f^2 - 2*(14*b^4*c^3*d^2 - 6*a*b^3*c^2*d^3 - 57*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^4*f^3 - (9*b^4*c^4*d - 100*a*b^3*c^3*d^2 + 84*a^2*b^2*c^2*d^3 + 42*a^3*b*c*d^4 - 35*a^4*d^5)*e^3*f^4 + (b^4*c^5 + 15*a*b^3*c^4*d - 114*a^2*b^2*c^3*d^2 + 98*a^3*b*c^2*d^3)*e^2*f^5 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e*f^6)*x^2 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^7 + 9*(7*b^4*c^2*d^3 - 17*a*b^3*c*d^4 + 10*a^2*b^2*d^5)*e^6*f - 2*(32*b^4*c^3*d^2 + 66*a*b^3*c^2*d^3 - 147*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^5*f^2 - (29*b^4*c^4*d - 268*a*b^3*c^3*d^2 + 36*a^2*b^2*c^2*d^3 + 238*a^3*b*c*d^4 - 35*a^4*d^5)*e^4*f^3 + (3*b^4*c^5 + 47*a*b^3*c^4*d - 330*a^2*b^2*c^3*d^2 + 210*a^3*b*c^2*d^3 + 70*a^4*c*d^4)*e^3*f^4 - 3*(a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e^2*f^5)*x)*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*log(-(3*a^2*c*f^2 + (b^2*c + 2*a*b*d)*e^2 - 2*(2*a*b*c + a^2*d)*e*f + 3*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*e - a*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (3*b^2*d*e^2 - 2*(b^2*c + 2*a*b*d)*e*f + (2*a*b*c + a^2*d)*f^2)*x + 3*sqrt(1/3)*(2*(b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt((-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f)))/(f*x + e)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 + 9*(b^3*c^3*d - 8*a*b^2*c^2*d^2 + 7*a^2*b*c*d^3)*e^4*f - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^3*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2*f^3 + 9*(b^3*c^2*d^2 - 8*a*b^2*c*d^3 + 7*a^2*b*d^4)*e*f^4 - (b^3*c^3*d + 6*a*b^2*c^2*d^2 - 42*a^2*b*c*d^3 + 35*a^3*d^4)*f^5)*x^4 + (81*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 + 27*(2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^2*f^3 + 3*(2*b^3*c^3*d - 30*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 - 35*a^3*d^4)*e*f^4 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^3 - a*b^2*d^4)*e^4*f + 9*(4*b^3*c^2*d^2 - 11*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^3*f^2 + (8*b^3*c^3*d - 78*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 - 35*a^3*d^4)*e^2*f^3 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e*f^4)*x^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^5 + 9*(10*b^3*c^2*d^2 - 17*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^4*f + (26*b^3*c^3*d - 222*a*b^2*c^2*d^2 + 231*a^2*b*c*d^3 - 35*a^3*d^4)*e^3*f^2 - 3*(b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 4*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 + 9*(b^3*c^3*d - 8*a*b^2*c^2*d^2 + 7*a^2*b*c*d^3)*e^4*f - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^3*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2*f^3 + 9*(b^3*c^2*d^2 - 8*a*b^2*c*d^3 + 7*a^2*b*d^4)*e*f^4 - (b^3*c^3*d + 6*a*b^2*c^2*d^2 - 42*a^2*b*c*d^3 + 35*a^3*d^4)*f^5)*x^4 + (81*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 + 27*(2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^2*f^3 + 3*(2*b^3*c^3*d - 30*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 - 35*a^3*d^4)*e*f^4 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^3 - a*b^2*d^4)*e^4*f + 9*(4*b^3*c^2*d^2 - 11*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^3*f^2 + (8*b^3*c^3*d - 78*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 - 35*a^3*d^4)*e^2*f^3 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e*f^4)*x^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^5 + 9*(10*b^3*c^2*d^2 - 17*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^4*f + (26*b^3*c^3*d - 222*a*b^2*c^2*d^2 + 231*a^2*b*c*d^3 - 35*a^3*d^4)*e^3*f^2 - 3*(b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(9*a^4*c^4*f^7 - 27*(4*b^4*c*d^3 - 3*a*b^3*d^4)*e^7 + 9*(8*b^4*c^2*d^2 + 37*a*b^3*c*d^3 - 27*a^2*b^2*d^4)*e^6*f + (40*b^4*c^3*d - 344*a*b^3*c^2*d^2 - 353*a^2*b^2*c*d^3 + 243*a^3*b*d^4)*e^5*f^2 - (4*b^4*c^4 + 75*a*b^3*c^3*d - 606*a^2*b^2*c^2*d^2 - 139*a^3*b*c*d^3 + 81*a^4*d^4)*e^4*f^3 + (5*a*b^3*c^4 - 21*a^2*b^2*c^3*d - 468*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e^3*f^4 + (11*a^2*b^2*c^4 + 107*a^3*b*c^3*d + 134*a^4*c^2*d^2)*e^2*f^5 - 3*(7*a^3*b*c^4 + 17*a^4*c^3*d)*e*f^6 - (9*b^4*d^4*e^5*f^2 + 15*(8*b^4*c*d^3 - 11*a*b^3*d^4)*e^4*f^3 - (127*b^4*c^2*d^2 + 226*a*b^3*c*d^3 - 443*a^2*b^2*d^4)*e^3*f^4 - (2*b^4*c^3*d - 387*a*b^3*c^2*d^2 + 48*a^2*b^2*c*d^3 + 427*a^3*b*d^4)*e^2*f^5 + (4*a*b^3*c^3*d - 393*a^2*b^2*c^2*d^2 + 294*a^3*b*c*d^3 + 140*a^4*d^4)*e*f^6 - (2*a^2*b^2*c^3*d - 133*a^3*b*c^2*d^2 + 140*a^4*c*d^3)*f^7)*x^3 - (27*b^4*d^4*e^6*f + 3*(109*b^4*c*d^3 - 154*a*b^3*d^4)*e^5*f^2 - (317*b^4*c^2*d^2 + 641*a*b^3*c*d^3 - 1228*a^2*b^2*d^4)*e^4*f^3 - (35*b^4*c^3*d - 992*a*b^3*c^2*d^2 + 49*a^2*b^2*c*d^3 + 1178*a^3*b*d^4)*e^3*f^4 - (2*b^4*c^4 - 107*a*b^3*c^3*d + 1068*a^2*b^2*c^2*d^2 - 713*a^3*b*c*d^3 - 385*a^4*d^4)*e^2*f^5 + (4*a*b^3*c^4 - 109*a^2*b^2*c^3*d + 428*a^3*b*c^2*d^2 - 350*a^4*c*d^3)*e*f^6 - (2*a^2*b^2*c^4 - 37*a^3*b*c^3*d + 35*a^4*c^2*d^2)*f^7)*x^2 - (27*b^4*d^4*e^7 + 9*(31*b^4*c*d^3 - 46*a*b^3*d^4)*e^6*f - 2*(104*b^4*c^2*d^2 + 302*a*b^3*c*d^3 - 541*a^2*b^2*d^4)*e^5*f^2 - (109*b^4*c^3*d - 733*a*b^3*c^2*d^2 - 136*a^2*b^2*c*d^3 + 1030*a^3*b*d^4)*e^4*f^3 + (11*b^4*c^4 + 322*a*b^3*c^3*d - 957*a^2*b^2*c^2*d^2 + 424*a^3*b*c*d^3 + 335*a^4*d^4)*e^3*f^4 - (37*a*b^3*c^4 + 302*a^2*b^2*c^3*d - 547*a^3*b*c^2*d^2 + 235*a^4*c*d^3)*e^2*f^5 + (41*a^2*b^2*c^4 + 74*a^3*b*c^3*d - 115*a^4*c^2*d^2)*e*f^6 - 15*(a^3*b*c^4 - a^4*c^3*d)*f^7)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*c*d^5*e^11 + a^3*c^6*e^3*f^8 - (5*b^3*c^2*d^4 + 3*a*b^2*c*d^5)*e^10*f + (10*b^3*c^3*d^3 + 15*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5)*e^9*f^2 - (10*b^3*c^4*d^2 + 30*a*b^2*c^3*d^3 + 15*a^2*b*c^2*d^4 + a^3*c*d^5)*e^8*f^3 + 5*(b^3*c^5*d + 6*a*b^2*c^4*d^2 + 6*a^2*b*c^3*d^3 + a^3*c^2*d^4)*e^7*f^4 - (b^3*c^6 + 15*a*b^2*c^5*d + 30*a^2*b*c^4*d^2 + 10*a^3*c^3*d^3)*e^6*f^5 + (3*a*b^2*c^6 + 15*a^2*b*c^5*d + 10*a^3*c^4*d^2)*e^5*f^6 - (3*a^2*b*c^6 + 5*a^3*c^5*d)*e^4*f^7 + (b^3*d^6*e^8*f^3 + a^3*c^5*d*f^11 - (5*b^3*c*d^5 + 3*a*b^2*d^6)*e^7*f^4 + (10*b^3*c^2*d^4 + 15*a*b^2*c*d^5 + 3*a^2*b*d^6)*e^6*f^5 - (10*b^3*c^3*d^3 + 30*a*b^2*c^2*d^4 + 15*a^2*b*c*d^5 + a^3*d^6)*e^5*f^6 + 5*(b^3*c^4*d^2 + 6*a*b^2*c^3*d^3 + 6*a^2*b*c^2*d^4 + a^3*c*d^5)*e^4*f^7 - (b^3*c^5*d + 15*a*b^2*c^4*d^2 + 30*a^2*b*c^3*d^3 + 10*a^3*c^2*d^4)*e^3*f^8 + (3*a*b^2*c^5*d + 15*a^2*b*c^4*d^2 + 10*a^3*c^3*d^3)*e^2*f^9 - (3*a^2*b*c^5*d + 5*a^3*c^4*d^2)*e*f^10)*x^4 + (3*b^3*d^6*e^9*f^2 + a^3*c^6*f^11 - (14*b^3*c*d^5 + 9*a*b^2*d^6)*e^8*f^3 + (25*b^3*c^2*d^4 + 42*a*b^2*c*d^5 + 9*a^2*b*d^6)*e^7*f^4 - (20*b^3*c^3*d^3 + 75*a*b^2*c^2*d^4 + 42*a^2*b*c*d^5 + 3*a^3*d^6)*e^6*f^5 + (5*b^3*c^4*d^2 + 60*a*b^2*c^3*d^3 + 75*a^2*b*c^2*d^4 + 14*a^3*c*d^5)*e^5*f^6 + (2*b^3*c^5*d - 15*a*b^2*c^4*d^2 - 60*a^2*b*c^3*d^3 - 25*a^3*c^2*d^4)*e^4*f^7 - (b^3*c^6 + 6*a*b^2*c^5*d - 15*a^2*b*c^4*d^2 - 20*a^3*c^3*d^3)*e^3*f^8 + (3*a*b^2*c^6 + 6*a^2*b*c^5*d - 5*a^3*c^4*d^2)*e^2*f^9 - (3*a^2*b*c^6 + 2*a^3*c^5*d)*e*f^10)*x^3 + 3*(b^3*d^6*e^10*f + a^3*c^6*e*f^10 - (4*b^3*c*d^5 + 3*a*b^2*d^6)*e^9*f^2 + (5*b^3*c^2*d^4 + 12*a*b^2*c*d^5 + 3*a^2*b*d^6)*e^8*f^3 - (15*a*b^2*c^2*d^4 + 12*a^2*b*c*d^5 + a^3*d^6)*e^7*f^4 - (5*b^3*c^4*d^2 - 15*a^2*b*c^2*d^4 - 4*a^3*c*d^5)*e^6*f^5 + (4*b^3*c^5*d + 15*a*b^2*c^4*d^2 - 5*a^3*c^2*d^4)*e^5*f^6 - (b^3*c^6 + 12*a*b^2*c^5*d + 15*a^2*b*c^4*d^2)*e^4*f^7 + (3*a*b^2*c^6 + 12*a^2*b*c^5*d + 5*a^3*c^4*d^2)*e^3*f^8 - (3*a^2*b*c^6 + 4*a^3*c^5*d)*e^2*f^9)*x^2 + (b^3*d^6*e^11 + 3*a^3*c^6*e^2*f^9 - (2*b^3*c*d^5 + 3*a*b^2*d^6)*e^10*f - (5*b^3*c^2*d^4 - 6*a*b^2*c*d^5 - 3*a^2*b*d^6)*e^9*f^2 + (20*b^3*c^3*d^3 + 15*a*b^2*c^2*d^4 - 6*a^2*b*c*d^5 - a^3*d^6)*e^8*f^3 - (25*b^3*c^4*d^2 + 60*a*b^2*c^3*d^3 + 15*a^2*b*c^2*d^4 - 2*a^3*c*d^5)*e^7*f^4 + (14*b^3*c^5*d + 75*a*b^2*c^4*d^2 + 60*a^2*b*c^3*d^3 + 5*a^3*c^2*d^4)*e^6*f^5 - (3*b^3*c^6 + 42*a*b^2*c^5*d + 75*a^2*b*c^4*d^2 + 20*a^3*c^3*d^3)*e^5*f^6 + (9*a*b^2*c^6 + 42*a^2*b*c^5*d + 25*a^3*c^4*d^2)*e^4*f^7 - (9*a^2*b*c^6 + 14*a^3*c^5*d)*e^3*f^8)*x), -1/81*(12*sqrt(1/3)*(27*(b^4*c^2*d^3 - a*b^3*c*d^4)*e^7 - 18*(b^4*c^3*d^2 + 4*a*b^3*c^2*d^3 - 5*a^2*b^2*c*d^4)*e^6*f - 2*(5*b^4*c^4*d - 42*a*b^3*c^3*d^2 - 12*a^2*b^2*c^2*d^3 + 49*a^3*b*c*d^4)*e^5*f^2 + (b^4*c^5 + 16*a*b^3*c^4*d - 108*a^2*b^2*c^3*d^2 + 56*a^3*b*c^2*d^3 + 35*a^4*c*d^4)*e^4*f^3 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e^3*f^4 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^4*f^3 - 18*(b^4*c^2*d^3 + 4*a*b^3*c*d^4 - 5*a^2*b^2*d^5)*e^3*f^4 - 2*(5*b^4*c^3*d^2 - 42*a*b^3*c^2*d^3 - 12*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^2*f^5 + (b^4*c^4*d + 16*a*b^3*c^3*d^2 - 108*a^2*b^2*c^2*d^3 + 56*a^3*b*c*d^4 + 35*a^4*d^5)*e*f^6 - (a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 42*a^3*b*c^2*d^3 + 35*a^4*c*d^4)*f^7)*x^4 + (81*(b^4*c*d^4 - a*b^3*d^5)*e^5*f^2 - 27*(b^4*c^2*d^3 + 9*a*b^3*c*d^4 - 10*a^2*b^2*d^5)*e^4*f^3 - 6*(8*b^4*c^3*d^2 - 30*a*b^3*c^2*d^3 - 27*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^3*f^4 - (7*b^4*c^4*d - 132*a*b^3*c^3*d^2 + 300*a^2*b^2*c^2*d^3 - 70*a^3*b*c*d^4 - 105*a^4*d^5)*e^2*f^5 + (b^4*c^5 + 13*a*b^3*c^4*d - 126*a^2*b^2*c^3*d^2 + 182*a^3*b*c^2*d^3 - 70*a^4*c*d^4)*e*f^6 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*f^7)*x^3 + 3*(27*(b^4*c*d^4 - a*b^3*d^5)*e^6*f + 9*(b^4*c^2*d^3 - 11*a*b^3*c*d^4 + 10*a^2*b^2*d^5)*e^5*f^2 - 2*(14*b^4*c^3*d^2 - 6*a*b^3*c^2*d^3 - 57*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^4*f^3 - (9*b^4*c^4*d - 100*a*b^3*c^3*d^2 + 84*a^2*b^2*c^2*d^3 + 42*a^3*b*c*d^4 - 35*a^4*d^5)*e^3*f^4 + (b^4*c^5 + 15*a*b^3*c^4*d - 114*a^2*b^2*c^3*d^2 + 98*a^3*b*c^2*d^3)*e^2*f^5 - (a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e*f^6)*x^2 + (27*(b^4*c*d^4 - a*b^3*d^5)*e^7 + 9*(7*b^4*c^2*d^3 - 17*a*b^3*c*d^4 + 10*a^2*b^2*d^5)*e^6*f - 2*(32*b^4*c^3*d^2 + 66*a*b^3*c^2*d^3 - 147*a^2*b^2*c*d^4 + 49*a^3*b*d^5)*e^5*f^2 - (29*b^4*c^4*d - 268*a*b^3*c^3*d^2 + 36*a^2*b^2*c^2*d^3 + 238*a^3*b*c*d^4 - 35*a^4*d^5)*e^4*f^3 + (3*b^4*c^5 + 47*a*b^3*c^4*d - 330*a^2*b^2*c^3*d^2 + 210*a^3*b*c^2*d^3 + 70*a^4*c*d^4)*e^3*f^4 - 3*(a*b^3*c^5 + 6*a^2*b^2*c^4*d - 42*a^3*b*c^3*d^2 + 35*a^4*c^2*d^3)*e^2*f^5)*x)*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))*arctan(sqrt(1/3)*(2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))*sqrt(-(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)/(d*e - c*f))/(b^2*c*e^2 - 2*a*b*c*e*f + a^2*c*f^2 + (b^2*d*e^2 - 2*a*b*d*e*f + a^2*d*f^2)*x)) + 2*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 + 9*(b^3*c^3*d - 8*a*b^2*c^2*d^2 + 7*a^2*b*c*d^3)*e^4*f - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^3*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2*f^3 + 9*(b^3*c^2*d^2 - 8*a*b^2*c*d^3 + 7*a^2*b*d^4)*e*f^4 - (b^3*c^3*d + 6*a*b^2*c^2*d^2 - 42*a^2*b*c*d^3 + 35*a^3*d^4)*f^5)*x^4 + (81*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 + 27*(2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^2*f^3 + 3*(2*b^3*c^3*d - 30*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 - 35*a^3*d^4)*e*f^4 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^3 - a*b^2*d^4)*e^4*f + 9*(4*b^3*c^2*d^2 - 11*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^3*f^2 + (8*b^3*c^3*d - 78*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 - 35*a^3*d^4)*e^2*f^3 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e*f^4)*x^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^5 + 9*(10*b^3*c^2*d^2 - 17*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^4*f + (26*b^3*c^3*d - 222*a*b^2*c^2*d^2 + 231*a^2*b*c*d^3 - 35*a^3*d^4)*e^3*f^2 - 3*(b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(2/3)*(d*x + c)^(1/3) + (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(1/3)*(b*c*e - a*c*f + (b*d*e - a*d*f)*x))/(d*x + c)) - 4*(-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(27*(b^3*c^2*d^2 - a*b^2*c*d^3)*e^5 + 9*(b^3*c^3*d - 8*a*b^2*c^2*d^2 + 7*a^2*b*c*d^3)*e^4*f - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^3*f^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^2*f^3 + 9*(b^3*c^2*d^2 - 8*a*b^2*c*d^3 + 7*a^2*b*d^4)*e*f^4 - (b^3*c^3*d + 6*a*b^2*c^2*d^2 - 42*a^2*b*c*d^3 + 35*a^3*d^4)*f^5)*x^4 + (81*(b^3*c*d^3 - a*b^2*d^4)*e^3*f^2 + 27*(2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^2*f^3 + 3*(2*b^3*c^3*d - 30*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 - 35*a^3*d^4)*e*f^4 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*f^5)*x^3 + 3*(27*(b^3*c*d^3 - a*b^2*d^4)*e^4*f + 9*(4*b^3*c^2*d^2 - 11*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^3*f^2 + (8*b^3*c^3*d - 78*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 - 35*a^3*d^4)*e^2*f^3 - (b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e*f^4)*x^2 + (27*(b^3*c*d^3 - a*b^2*d^4)*e^5 + 9*(10*b^3*c^2*d^2 - 17*a*b^2*c*d^3 + 7*a^2*b*d^4)*e^4*f + (26*b^3*c^3*d - 222*a*b^2*c^2*d^2 + 231*a^2*b*c*d^3 - 35*a^3*d^4)*e^3*f^2 - 3*(b^3*c^4 + 6*a*b^2*c^3*d - 42*a^2*b*c^2*d^2 + 35*a^3*c*d^3)*e^2*f^3)*x)*log(((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*(b*x + a)^(1/3)*(d*x + c)^(2/3) - (-b^2*d*e^3 + a^2*c*f^3 + (b^2*c + 2*a*b*d)*e^2*f - (2*a*b*c + a^2*d)*e*f^2)^(2/3)*(d*x + c))/(d*x + c)) + 3*(9*a^4*c^4*f^7 - 27*(4*b^4*c*d^3 - 3*a*b^3*d^4)*e^7 + 9*(8*b^4*c^2*d^2 + 37*a*b^3*c*d^3 - 27*a^2*b^2*d^4)*e^6*f + (40*b^4*c^3*d - 344*a*b^3*c^2*d^2 - 353*a^2*b^2*c*d^3 + 243*a^3*b*d^4)*e^5*f^2 - (4*b^4*c^4 + 75*a*b^3*c^3*d - 606*a^2*b^2*c^2*d^2 - 139*a^3*b*c*d^3 + 81*a^4*d^4)*e^4*f^3 + (5*a*b^3*c^4 - 21*a^2*b^2*c^3*d - 468*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e^3*f^4 + (11*a^2*b^2*c^4 + 107*a^3*b*c^3*d + 134*a^4*c^2*d^2)*e^2*f^5 - 3*(7*a^3*b*c^4 + 17*a^4*c^3*d)*e*f^6 - (9*b^4*d^4*e^5*f^2 + 15*(8*b^4*c*d^3 - 11*a*b^3*d^4)*e^4*f^3 - (127*b^4*c^2*d^2 + 226*a*b^3*c*d^3 - 443*a^2*b^2*d^4)*e^3*f^4 - (2*b^4*c^3*d - 387*a*b^3*c^2*d^2 + 48*a^2*b^2*c*d^3 + 427*a^3*b*d^4)*e^2*f^5 + (4*a*b^3*c^3*d - 393*a^2*b^2*c^2*d^2 + 294*a^3*b*c*d^3 + 140*a^4*d^4)*e*f^6 - (2*a^2*b^2*c^3*d - 133*a^3*b*c^2*d^2 + 140*a^4*c*d^3)*f^7)*x^3 - (27*b^4*d^4*e^6*f + 3*(109*b^4*c*d^3 - 154*a*b^3*d^4)*e^5*f^2 - (317*b^4*c^2*d^2 + 641*a*b^3*c*d^3 - 1228*a^2*b^2*d^4)*e^4*f^3 - (35*b^4*c^3*d - 992*a*b^3*c^2*d^2 + 49*a^2*b^2*c*d^3 + 1178*a^3*b*d^4)*e^3*f^4 - (2*b^4*c^4 - 107*a*b^3*c^3*d + 1068*a^2*b^2*c^2*d^2 - 713*a^3*b*c*d^3 - 385*a^4*d^4)*e^2*f^5 + (4*a*b^3*c^4 - 109*a^2*b^2*c^3*d + 428*a^3*b*c^2*d^2 - 350*a^4*c*d^3)*e*f^6 - (2*a^2*b^2*c^4 - 37*a^3*b*c^3*d + 35*a^4*c^2*d^2)*f^7)*x^2 - (27*b^4*d^4*e^7 + 9*(31*b^4*c*d^3 - 46*a*b^3*d^4)*e^6*f - 2*(104*b^4*c^2*d^2 + 302*a*b^3*c*d^3 - 541*a^2*b^2*d^4)*e^5*f^2 - (109*b^4*c^3*d - 733*a*b^3*c^2*d^2 - 136*a^2*b^2*c*d^3 + 1030*a^3*b*d^4)*e^4*f^3 + (11*b^4*c^4 + 322*a*b^3*c^3*d - 957*a^2*b^2*c^2*d^2 + 424*a^3*b*c*d^3 + 335*a^4*d^4)*e^3*f^4 - (37*a*b^3*c^4 + 302*a^2*b^2*c^3*d - 547*a^3*b*c^2*d^2 + 235*a^4*c*d^3)*e^2*f^5 + (41*a^2*b^2*c^4 + 74*a^3*b*c^3*d - 115*a^4*c^2*d^2)*e*f^6 - 15*(a^3*b*c^4 - a^4*c^3*d)*f^7)*x)*(b*x + a)^(1/3)*(d*x + c)^(2/3))/(b^3*c*d^5*e^11 + a^3*c^6*e^3*f^8 - (5*b^3*c^2*d^4 + 3*a*b^2*c*d^5)*e^10*f + (10*b^3*c^3*d^3 + 15*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5)*e^9*f^2 - (10*b^3*c^4*d^2 + 30*a*b^2*c^3*d^3 + 15*a^2*b*c^2*d^4 + a^3*c*d^5)*e^8*f^3 + 5*(b^3*c^5*d + 6*a*b^2*c^4*d^2 + 6*a^2*b*c^3*d^3 + a^3*c^2*d^4)*e^7*f^4 - (b^3*c^6 + 15*a*b^2*c^5*d + 30*a^2*b*c^4*d^2 + 10*a^3*c^3*d^3)*e^6*f^5 + (3*a*b^2*c^6 + 15*a^2*b*c^5*d + 10*a^3*c^4*d^2)*e^5*f^6 - (3*a^2*b*c^6 + 5*a^3*c^5*d)*e^4*f^7 + (b^3*d^6*e^8*f^3 + a^3*c^5*d*f^11 - (5*b^3*c*d^5 + 3*a*b^2*d^6)*e^7*f^4 + (10*b^3*c^2*d^4 + 15*a*b^2*c*d^5 + 3*a^2*b*d^6)*e^6*f^5 - (10*b^3*c^3*d^3 + 30*a*b^2*c^2*d^4 + 15*a^2*b*c*d^5 + a^3*d^6)*e^5*f^6 + 5*(b^3*c^4*d^2 + 6*a*b^2*c^3*d^3 + 6*a^2*b*c^2*d^4 + a^3*c*d^5)*e^4*f^7 - (b^3*c^5*d + 15*a*b^2*c^4*d^2 + 30*a^2*b*c^3*d^3 + 10*a^3*c^2*d^4)*e^3*f^8 + (3*a*b^2*c^5*d + 15*a^2*b*c^4*d^2 + 10*a^3*c^3*d^3)*e^2*f^9 - (3*a^2*b*c^5*d + 5*a^3*c^4*d^2)*e*f^10)*x^4 + (3*b^3*d^6*e^9*f^2 + a^3*c^6*f^11 - (14*b^3*c*d^5 + 9*a*b^2*d^6)*e^8*f^3 + (25*b^3*c^2*d^4 + 42*a*b^2*c*d^5 + 9*a^2*b*d^6)*e^7*f^4 - (20*b^3*c^3*d^3 + 75*a*b^2*c^2*d^4 + 42*a^2*b*c*d^5 + 3*a^3*d^6)*e^6*f^5 + (5*b^3*c^4*d^2 + 60*a*b^2*c^3*d^3 + 75*a^2*b*c^2*d^4 + 14*a^3*c*d^5)*e^5*f^6 + (2*b^3*c^5*d - 15*a*b^2*c^4*d^2 - 60*a^2*b*c^3*d^3 - 25*a^3*c^2*d^4)*e^4*f^7 - (b^3*c^6 + 6*a*b^2*c^5*d - 15*a^2*b*c^4*d^2 - 20*a^3*c^3*d^3)*e^3*f^8 + (3*a*b^2*c^6 + 6*a^2*b*c^5*d - 5*a^3*c^4*d^2)*e^2*f^9 - (3*a^2*b*c^6 + 2*a^3*c^5*d)*e*f^10)*x^3 + 3*(b^3*d^6*e^10*f + a^3*c^6*e*f^10 - (4*b^3*c*d^5 + 3*a*b^2*d^6)*e^9*f^2 + (5*b^3*c^2*d^4 + 12*a*b^2*c*d^5 + 3*a^2*b*d^6)*e^8*f^3 - (15*a*b^2*c^2*d^4 + 12*a^2*b*c*d^5 + a^3*d^6)*e^7*f^4 - (5*b^3*c^4*d^2 - 15*a^2*b*c^2*d^4 - 4*a^3*c*d^5)*e^6*f^5 + (4*b^3*c^5*d + 15*a*b^2*c^4*d^2 - 5*a^3*c^2*d^4)*e^5*f^6 - (b^3*c^6 + 12*a*b^2*c^5*d + 15*a^2*b*c^4*d^2)*e^4*f^7 + (3*a*b^2*c^6 + 12*a^2*b*c^5*d + 5*a^3*c^4*d^2)*e^3*f^8 - (3*a^2*b*c^6 + 4*a^3*c^5*d)*e^2*f^9)*x^2 + (b^3*d^6*e^11 + 3*a^3*c^6*e^2*f^9 - (2*b^3*c*d^5 + 3*a*b^2*d^6)*e^10*f - (5*b^3*c^2*d^4 - 6*a*b^2*c*d^5 - 3*a^2*b*d^6)*e^9*f^2 + (20*b^3*c^3*d^3 + 15*a*b^2*c^2*d^4 - 6*a^2*b*c*d^5 - a^3*d^6)*e^8*f^3 - (25*b^3*c^4*d^2 + 60*a*b^2*c^3*d^3 + 15*a^2*b*c^2*d^4 - 2*a^3*c*d^5)*e^7*f^4 + (14*b^3*c^5*d + 75*a*b^2*c^4*d^2 + 60*a^2*b*c^3*d^3 + 5*a^3*c^2*d^4)*e^6*f^5 - (3*b^3*c^6 + 42*a*b^2*c^5*d + 75*a^2*b*c^4*d^2 + 20*a^3*c^3*d^3)*e^5*f^6 + (9*a*b^2*c^6 + 42*a^2*b*c^5*d + 25*a^3*c^4*d^2)*e^4*f^7 - (9*a^2*b*c^6 + 14*a^3*c^5*d)*e^3*f^8)*x)]","B",0
3044,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(f*x+e)^(1/4)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3045,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(f*x+e)^(3/4)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3046,0,0,0,1.466979," ","integrate((b*x+a)^p*(B*x+A)*(e*x+d)^(-2-p),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{p} {\left(e x + d\right)}^{-p - 2}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^p*(e*x + d)^(-p - 2), x)","F",0
3047,0,0,0,1.488324," ","integrate((b*x+a)*(d*x+c)^n/((f*x+e)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} {\left(d x + c\right)}^{n}}{{\left(f x + e\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)*(d*x + c)^n/(f*x + e)^n, x)","F",0
3048,0,0,0,1.349540," ","integrate((b*x+a)*(d*x+c)^(-1+n)/((f*x+e)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} {\left(d x + c\right)}^{n - 1}}{{\left(f x + e\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)*(d*x + c)^(n - 1)/(f*x + e)^n, x)","F",0
3049,0,0,0,1.044084," ","integrate((b*x+a)*(d*x+c)^(-2+n)/((f*x+e)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} {\left(d x + c\right)}^{n - 2}}{{\left(f x + e\right)}^{n}}, x\right)"," ",0,"integral((b*x + a)*(d*x + c)^(n - 2)/(f*x + e)^n, x)","F",0
3050,1,324,0,1.183456," ","integrate((b*x+a)*(d*x+c)^(-3+n)/((f*x+e)^n),x, algorithm=""fricas"")","\frac{{\left(2 \, a c^{2} e f - {\left(2 \, b d^{2} e f - {\left(b c d + a d^{2}\right)} f^{2} - {\left(b d^{2} e f - b c d f^{2}\right)} n\right)} x^{3} - {\left(b c^{2} + a c d\right)} e^{2} - {\left(2 \, b d^{2} e^{2} + 2 \, b c d e f - {\left(b c^{2} + 3 \, a c d\right)} f^{2} - {\left(b d^{2} e^{2} + a d^{2} e f - {\left(b c^{2} + a c d\right)} f^{2}\right)} n\right)} x^{2} + {\left(a c d e^{2} - a c^{2} e f\right)} n + {\left(2 \, a c d e f + 2 \, a c^{2} f^{2} - {\left(3 \, b c d + a d^{2}\right)} e^{2} - {\left(b c^{2} e f + a c^{2} f^{2} - {\left(b c d + a d^{2}\right)} e^{2}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n - 3}}{{\left(2 \, d^{2} e^{2} - 4 \, c d e f + 2 \, c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} n^{2} - 3 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} n\right)} {\left(f x + e\right)}^{n}}"," ",0,"(2*a*c^2*e*f - (2*b*d^2*e*f - (b*c*d + a*d^2)*f^2 - (b*d^2*e*f - b*c*d*f^2)*n)*x^3 - (b*c^2 + a*c*d)*e^2 - (2*b*d^2*e^2 + 2*b*c*d*e*f - (b*c^2 + 3*a*c*d)*f^2 - (b*d^2*e^2 + a*d^2*e*f - (b*c^2 + a*c*d)*f^2)*n)*x^2 + (a*c*d*e^2 - a*c^2*e*f)*n + (2*a*c*d*e*f + 2*a*c^2*f^2 - (3*b*c*d + a*d^2)*e^2 - (b*c^2*e*f + a*c^2*f^2 - (b*c*d + a*d^2)*e^2)*n)*x)*(d*x + c)^(n - 3)/((2*d^2*e^2 - 4*c*d*e*f + 2*c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*n^2 - 3*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*n)*(f*x + e)^n)","B",0
3051,1,884,0,1.911536," ","integrate((b*x+a)*(d*x+c)^(-4+n)/((f*x+e)^n),x, algorithm=""fricas"")","-\frac{{\left(6 \, a c^{3} e f^{2} - {\left(3 \, b d^{3} e f^{2} - {\left(b c d^{2} + 2 \, a d^{3}\right)} f^{3} - {\left(b d^{3} e f^{2} - b c d^{2} f^{3}\right)} n\right)} x^{4} + {\left(b c^{2} d + 2 \, a c d^{2}\right)} e^{3} - 3 \, {\left(b c^{3} + 2 \, a c^{2} d\right)} e^{2} f - {\left(12 \, b c d^{2} e f^{2} - 4 \, {\left(b c^{2} d + 2 \, a c d^{2}\right)} f^{3} - {\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} n^{2} + {\left(3 \, b d^{3} e^{2} f - 2 \, {\left(4 \, b c d^{2} + a d^{3}\right)} e f^{2} + {\left(5 \, b c^{2} d + 2 \, a c d^{2}\right)} f^{3}\right)} n\right)} x^{3} + {\left(a c d^{2} e^{3} - 2 \, a c^{2} d e^{2} f + a c^{3} e f^{2}\right)} n^{2} + {\left(3 \, b d^{3} e^{3} - 9 \, b c d^{2} e^{2} f - 9 \, b c^{2} d e f^{2} + 3 \, {\left(b c^{3} + 4 \, a c^{2} d\right)} f^{3} + {\left(b d^{3} e^{3} - {\left(b c d^{2} - a d^{3}\right)} e^{2} f - {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(b c^{3} + a c^{2} d\right)} f^{3}\right)} n^{2} - {\left(4 \, b d^{3} e^{3} - {\left(4 \, b c d^{2} - a d^{3}\right)} e^{2} f - 4 \, {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(4 \, b c^{3} + 7 \, a c^{2} d\right)} f^{3}\right)} n\right)} x^{2} - {\left(5 \, a c^{3} e f^{2} + {\left(b c^{2} d + 3 \, a c d^{2}\right)} e^{3} - {\left(b c^{3} + 8 \, a c^{2} d\right)} e^{2} f\right)} n + {\left(6 \, a c^{2} d e f^{2} + 6 \, a c^{3} f^{3} + 2 \, {\left(2 \, b c d^{2} + a d^{3}\right)} e^{3} - 6 \, {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f + {\left(a c^{3} f^{3} + {\left(b c d^{2} + a d^{3}\right)} e^{3} - {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f + {\left(b c^{3} - a c^{2} d\right)} e f^{2}\right)} n^{2} - {\left(5 \, a c^{3} f^{3} + {\left(5 \, b c d^{2} + 3 \, a d^{3}\right)} e^{3} - {\left(8 \, b c^{2} d + 7 \, a c d^{2}\right)} e^{2} f + {\left(3 \, b c^{3} - a c^{2} d\right)} e f^{2}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n - 4}}{{\left(6 \, d^{3} e^{3} - 18 \, c d^{2} e^{2} f + 18 \, c^{2} d e f^{2} - 6 \, c^{3} f^{3} - {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} n^{3} + 6 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} n^{2} - 11 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} n\right)} {\left(f x + e\right)}^{n}}"," ",0,"-(6*a*c^3*e*f^2 - (3*b*d^3*e*f^2 - (b*c*d^2 + 2*a*d^3)*f^3 - (b*d^3*e*f^2 - b*c*d^2*f^3)*n)*x^4 + (b*c^2*d + 2*a*c*d^2)*e^3 - 3*(b*c^3 + 2*a*c^2*d)*e^2*f - (12*b*c*d^2*e*f^2 - 4*(b*c^2*d + 2*a*c*d^2)*f^3 - (b*d^3*e^2*f - 2*b*c*d^2*e*f^2 + b*c^2*d*f^3)*n^2 + (3*b*d^3*e^2*f - 2*(4*b*c*d^2 + a*d^3)*e*f^2 + (5*b*c^2*d + 2*a*c*d^2)*f^3)*n)*x^3 + (a*c*d^2*e^3 - 2*a*c^2*d*e^2*f + a*c^3*e*f^2)*n^2 + (3*b*d^3*e^3 - 9*b*c*d^2*e^2*f - 9*b*c^2*d*e*f^2 + 3*(b*c^3 + 4*a*c^2*d)*f^3 + (b*d^3*e^3 - (b*c*d^2 - a*d^3)*e^2*f - (b*c^2*d + 2*a*c*d^2)*e*f^2 + (b*c^3 + a*c^2*d)*f^3)*n^2 - (4*b*d^3*e^3 - (4*b*c*d^2 - a*d^3)*e^2*f - 4*(b*c^2*d + 2*a*c*d^2)*e*f^2 + (4*b*c^3 + 7*a*c^2*d)*f^3)*n)*x^2 - (5*a*c^3*e*f^2 + (b*c^2*d + 3*a*c*d^2)*e^3 - (b*c^3 + 8*a*c^2*d)*e^2*f)*n + (6*a*c^2*d*e*f^2 + 6*a*c^3*f^3 + 2*(2*b*c*d^2 + a*d^3)*e^3 - 6*(2*b*c^2*d + a*c*d^2)*e^2*f + (a*c^3*f^3 + (b*c*d^2 + a*d^3)*e^3 - (2*b*c^2*d + a*c*d^2)*e^2*f + (b*c^3 - a*c^2*d)*e*f^2)*n^2 - (5*a*c^3*f^3 + (5*b*c*d^2 + 3*a*d^3)*e^3 - (8*b*c^2*d + 7*a*c*d^2)*e^2*f + (3*b*c^3 - a*c^2*d)*e*f^2)*n)*x)*(d*x + c)^(n - 4)/((6*d^3*e^3 - 18*c*d^2*e^2*f + 18*c^2*d*e*f^2 - 6*c^3*f^3 - (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*n^3 + 6*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*n^2 - 11*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*n)*(f*x + e)^n)","B",0
3052,1,1741,0,1.352593," ","integrate((b*x+a)*(d*x+c)^(-5+n)/((f*x+e)^n),x, algorithm=""fricas"")","\frac{{\left(24 \, a c^{4} e f^{3} - 2 \, {\left(4 \, b d^{4} e f^{3} - {\left(b c d^{3} + 3 \, a d^{4}\right)} f^{4} - {\left(b d^{4} e f^{3} - b c d^{3} f^{4}\right)} n\right)} x^{5} - 2 \, {\left(b c^{2} d^{2} + 3 \, a c d^{3}\right)} e^{4} + 8 \, {\left(b c^{3} d + 3 \, a c^{2} d^{2}\right)} e^{3} f - 12 \, {\left(b c^{4} + 3 \, a c^{3} d\right)} e^{2} f^{2} - 2 \, {\left(20 \, b c d^{3} e f^{3} - 5 \, {\left(b c^{2} d^{2} + 3 \, a c d^{3}\right)} f^{4} - {\left(b d^{4} e^{2} f^{2} - 2 \, b c d^{3} e f^{3} + b c^{2} d^{2} f^{4}\right)} n^{2} + {\left(4 \, b d^{4} e^{2} f^{2} - {\left(10 \, b c d^{3} + 3 \, a d^{4}\right)} e f^{3} + 3 \, {\left(2 \, b c^{2} d^{2} + a c d^{3}\right)} f^{4}\right)} n\right)} x^{4} + {\left(a c d^{3} e^{4} - 3 \, a c^{2} d^{2} e^{3} f + 3 \, a c^{3} d e^{2} f^{2} - a c^{4} e f^{3}\right)} n^{3} - {\left(80 \, b c^{2} d^{2} e f^{3} - 20 \, {\left(b c^{3} d + 3 \, a c^{2} d^{2}\right)} f^{4} - {\left(b d^{4} e^{3} f - 3 \, b c d^{3} e^{2} f^{2} + 3 \, b c^{2} d^{2} e f^{3} - b c^{3} d f^{4}\right)} n^{3} + {\left(5 \, b d^{4} e^{3} f - {\left(20 \, b c d^{3} + 3 \, a d^{4}\right)} e^{2} f^{2} + {\left(25 \, b c^{2} d^{2} + 6 \, a c d^{3}\right)} e f^{3} - {\left(10 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} f^{4}\right)} n^{2} - {\left(4 \, b d^{4} e^{3} f - {\left(41 \, b c d^{3} + 3 \, a d^{4}\right)} e^{2} f^{2} + 6 \, {\left(11 \, b c^{2} d^{2} + 5 \, a c d^{3}\right)} e f^{3} - {\left(29 \, b c^{3} d + 27 \, a c^{2} d^{2}\right)} f^{4}\right)} n\right)} x^{3} + {\left(9 \, a c^{4} e f^{3} - {\left(b c^{2} d^{2} + 6 \, a c d^{3}\right)} e^{4} + {\left(2 \, b c^{3} d + 21 \, a c^{2} d^{2}\right)} e^{3} f - {\left(b c^{4} + 24 \, a c^{3} d\right)} e^{2} f^{2}\right)} n^{2} - {\left(8 \, b d^{4} e^{4} - 32 \, b c d^{3} e^{3} f + 48 \, b c^{2} d^{2} e^{2} f^{2} + 48 \, b c^{3} d e f^{3} - 12 \, {\left(b c^{4} + 5 \, a c^{3} d\right)} f^{4} - {\left(b d^{4} e^{4} - 3 \, a c d^{3} e^{2} f^{2} - {\left(2 \, b c d^{3} - a d^{4}\right)} e^{3} f + {\left(2 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} e f^{3} - {\left(b c^{4} + a c^{3} d\right)} f^{4}\right)} n^{3} + {\left(7 \, b d^{4} e^{4} - {\left(16 \, b c d^{3} - 3 \, a d^{4}\right)} e^{3} f + 3 \, {\left(b c^{2} d^{2} - 6 \, a c d^{3}\right)} e^{2} f^{2} + {\left(14 \, b c^{3} d + 27 \, a c^{2} d^{2}\right)} e f^{3} - 4 \, {\left(2 \, b c^{4} + 3 \, a c^{3} d\right)} f^{4}\right)} n^{2} - {\left(14 \, b d^{4} e^{4} - 2 \, {\left(23 \, b c d^{3} - a d^{4}\right)} e^{3} f + 15 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} e^{2} f^{2} + 12 \, {\left(3 \, b c^{3} d + 5 \, a c^{2} d^{2}\right)} e f^{3} - {\left(19 \, b c^{4} + 47 \, a c^{3} d\right)} f^{4}\right)} n\right)} x^{2} - {\left(26 \, a c^{4} e f^{3} - {\left(3 \, b c^{2} d^{2} + 11 \, a c d^{3}\right)} e^{4} + 2 \, {\left(5 \, b c^{3} d + 21 \, a c^{2} d^{2}\right)} e^{3} f - {\left(7 \, b c^{4} + 57 \, a c^{3} d\right)} e^{2} f^{2}\right)} n + {\left(24 \, a c^{3} d e f^{3} + 24 \, a c^{4} f^{4} - 2 \, {\left(5 \, b c d^{3} + 3 \, a d^{4}\right)} e^{4} + 8 \, {\left(5 \, b c^{2} d^{2} + 3 \, a c d^{3}\right)} e^{3} f - 12 \, {\left(5 \, b c^{3} d + 3 \, a c^{2} d^{2}\right)} e^{2} f^{2} + {\left(3 \, b c^{3} d e^{2} f^{2} - a c^{4} f^{4} + {\left(b c d^{3} + a d^{4}\right)} e^{4} - {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} e^{3} f - {\left(b c^{4} - 2 \, a c^{3} d\right)} e f^{3}\right)} n^{3} + {\left(9 \, a c^{4} f^{4} - 2 \, {\left(4 \, b c d^{3} + 3 \, a d^{4}\right)} e^{4} + {\left(23 \, b c^{2} d^{2} + 18 \, a c d^{3}\right)} e^{3} f - {\left(22 \, b c^{3} d + 9 \, a c^{2} d^{2}\right)} e^{2} f^{2} + {\left(7 \, b c^{4} - 12 \, a c^{3} d\right)} e f^{3}\right)} n^{2} - {\left(26 \, a c^{4} f^{4} - {\left(17 \, b c d^{3} + 11 \, a d^{4}\right)} e^{4} + 20 \, {\left(3 \, b c^{2} d^{2} + 2 \, a c d^{3}\right)} e^{3} f - 5 \, {\left(11 \, b c^{3} d + 9 \, a c^{2} d^{2}\right)} e^{2} f^{2} + 2 \, {\left(6 \, b c^{4} - 5 \, a c^{3} d\right)} e f^{3}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n - 5}}{{\left(24 \, d^{4} e^{4} - 96 \, c d^{3} e^{3} f + 144 \, c^{2} d^{2} e^{2} f^{2} - 96 \, c^{3} d e f^{3} + 24 \, c^{4} f^{4} + {\left(d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 6 \, c^{2} d^{2} e^{2} f^{2} - 4 \, c^{3} d e f^{3} + c^{4} f^{4}\right)} n^{4} - 10 \, {\left(d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 6 \, c^{2} d^{2} e^{2} f^{2} - 4 \, c^{3} d e f^{3} + c^{4} f^{4}\right)} n^{3} + 35 \, {\left(d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 6 \, c^{2} d^{2} e^{2} f^{2} - 4 \, c^{3} d e f^{3} + c^{4} f^{4}\right)} n^{2} - 50 \, {\left(d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 6 \, c^{2} d^{2} e^{2} f^{2} - 4 \, c^{3} d e f^{3} + c^{4} f^{4}\right)} n\right)} {\left(f x + e\right)}^{n}}"," ",0,"(24*a*c^4*e*f^3 - 2*(4*b*d^4*e*f^3 - (b*c*d^3 + 3*a*d^4)*f^4 - (b*d^4*e*f^3 - b*c*d^3*f^4)*n)*x^5 - 2*(b*c^2*d^2 + 3*a*c*d^3)*e^4 + 8*(b*c^3*d + 3*a*c^2*d^2)*e^3*f - 12*(b*c^4 + 3*a*c^3*d)*e^2*f^2 - 2*(20*b*c*d^3*e*f^3 - 5*(b*c^2*d^2 + 3*a*c*d^3)*f^4 - (b*d^4*e^2*f^2 - 2*b*c*d^3*e*f^3 + b*c^2*d^2*f^4)*n^2 + (4*b*d^4*e^2*f^2 - (10*b*c*d^3 + 3*a*d^4)*e*f^3 + 3*(2*b*c^2*d^2 + a*c*d^3)*f^4)*n)*x^4 + (a*c*d^3*e^4 - 3*a*c^2*d^2*e^3*f + 3*a*c^3*d*e^2*f^2 - a*c^4*e*f^3)*n^3 - (80*b*c^2*d^2*e*f^3 - 20*(b*c^3*d + 3*a*c^2*d^2)*f^4 - (b*d^4*e^3*f - 3*b*c*d^3*e^2*f^2 + 3*b*c^2*d^2*e*f^3 - b*c^3*d*f^4)*n^3 + (5*b*d^4*e^3*f - (20*b*c*d^3 + 3*a*d^4)*e^2*f^2 + (25*b*c^2*d^2 + 6*a*c*d^3)*e*f^3 - (10*b*c^3*d + 3*a*c^2*d^2)*f^4)*n^2 - (4*b*d^4*e^3*f - (41*b*c*d^3 + 3*a*d^4)*e^2*f^2 + 6*(11*b*c^2*d^2 + 5*a*c*d^3)*e*f^3 - (29*b*c^3*d + 27*a*c^2*d^2)*f^4)*n)*x^3 + (9*a*c^4*e*f^3 - (b*c^2*d^2 + 6*a*c*d^3)*e^4 + (2*b*c^3*d + 21*a*c^2*d^2)*e^3*f - (b*c^4 + 24*a*c^3*d)*e^2*f^2)*n^2 - (8*b*d^4*e^4 - 32*b*c*d^3*e^3*f + 48*b*c^2*d^2*e^2*f^2 + 48*b*c^3*d*e*f^3 - 12*(b*c^4 + 5*a*c^3*d)*f^4 - (b*d^4*e^4 - 3*a*c*d^3*e^2*f^2 - (2*b*c*d^3 - a*d^4)*e^3*f + (2*b*c^3*d + 3*a*c^2*d^2)*e*f^3 - (b*c^4 + a*c^3*d)*f^4)*n^3 + (7*b*d^4*e^4 - (16*b*c*d^3 - 3*a*d^4)*e^3*f + 3*(b*c^2*d^2 - 6*a*c*d^3)*e^2*f^2 + (14*b*c^3*d + 27*a*c^2*d^2)*e*f^3 - 4*(2*b*c^4 + 3*a*c^3*d)*f^4)*n^2 - (14*b*d^4*e^4 - 2*(23*b*c*d^3 - a*d^4)*e^3*f + 15*(b*c^2*d^2 - a*c*d^3)*e^2*f^2 + 12*(3*b*c^3*d + 5*a*c^2*d^2)*e*f^3 - (19*b*c^4 + 47*a*c^3*d)*f^4)*n)*x^2 - (26*a*c^4*e*f^3 - (3*b*c^2*d^2 + 11*a*c*d^3)*e^4 + 2*(5*b*c^3*d + 21*a*c^2*d^2)*e^3*f - (7*b*c^4 + 57*a*c^3*d)*e^2*f^2)*n + (24*a*c^3*d*e*f^3 + 24*a*c^4*f^4 - 2*(5*b*c*d^3 + 3*a*d^4)*e^4 + 8*(5*b*c^2*d^2 + 3*a*c*d^3)*e^3*f - 12*(5*b*c^3*d + 3*a*c^2*d^2)*e^2*f^2 + (3*b*c^3*d*e^2*f^2 - a*c^4*f^4 + (b*c*d^3 + a*d^4)*e^4 - (3*b*c^2*d^2 + 2*a*c*d^3)*e^3*f - (b*c^4 - 2*a*c^3*d)*e*f^3)*n^3 + (9*a*c^4*f^4 - 2*(4*b*c*d^3 + 3*a*d^4)*e^4 + (23*b*c^2*d^2 + 18*a*c*d^3)*e^3*f - (22*b*c^3*d + 9*a*c^2*d^2)*e^2*f^2 + (7*b*c^4 - 12*a*c^3*d)*e*f^3)*n^2 - (26*a*c^4*f^4 - (17*b*c*d^3 + 11*a*d^4)*e^4 + 20*(3*b*c^2*d^2 + 2*a*c*d^3)*e^3*f - 5*(11*b*c^3*d + 9*a*c^2*d^2)*e^2*f^2 + 2*(6*b*c^4 - 5*a*c^3*d)*e*f^3)*n)*x)*(d*x + c)^(n - 5)/((24*d^4*e^4 - 96*c*d^3*e^3*f + 144*c^2*d^2*e^2*f^2 - 96*c^3*d*e*f^3 + 24*c^4*f^4 + (d^4*e^4 - 4*c*d^3*e^3*f + 6*c^2*d^2*e^2*f^2 - 4*c^3*d*e*f^3 + c^4*f^4)*n^4 - 10*(d^4*e^4 - 4*c*d^3*e^3*f + 6*c^2*d^2*e^2*f^2 - 4*c^3*d*e*f^3 + c^4*f^4)*n^3 + 35*(d^4*e^4 - 4*c*d^3*e^3*f + 6*c^2*d^2*e^2*f^2 - 4*c^3*d*e*f^3 + c^4*f^4)*n^2 - 50*(d^4*e^4 - 4*c*d^3*e^3*f + 6*c^2*d^2*e^2*f^2 - 4*c^3*d*e*f^3 + c^4*f^4)*n)*(f*x + e)^n)","B",0
3053,0,0,0,1.235859," ","integrate((d*x+c)*(f*x+e)^n/((b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(f x + e\right)}^{n}}{{\left(b x + a\right)}^{n}}, x\right)"," ",0,"integral((d*x + c)*(f*x + e)^n/(b*x + a)^n, x)","F",0
3054,0,0,0,1.159496," ","integrate((d*x+c)*(f*x+e)^(-1+n)/((b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(f x + e\right)}^{n - 1}}{{\left(b x + a\right)}^{n}}, x\right)"," ",0,"integral((d*x + c)*(f*x + e)^(n - 1)/(b*x + a)^n, x)","F",0
3055,0,0,0,1.794719," ","integrate((d*x+c)*(f*x+e)^(-2+n)/((b*x+a)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(f x + e\right)}^{n - 2}}{{\left(b x + a\right)}^{n}}, x\right)"," ",0,"integral((d*x + c)*(f*x + e)^(n - 2)/(b*x + a)^n, x)","F",0
3056,1,326,0,1.024280," ","integrate((d*x+c)*(f*x+e)^(-3+n)/((b*x+a)^n),x, algorithm=""fricas"")","-\frac{{\left(a^{2} c e f - {\left(b^{2} d e f + {\left(b^{2} c - 2 \, a b d\right)} f^{2} - {\left(b^{2} d e f - a b d f^{2}\right)} n\right)} x^{3} - {\left(2 \, a b c - a^{2} d\right)} e^{2} - {\left(b^{2} d e^{2} - 2 \, a^{2} d f^{2} + {\left(3 \, b^{2} c - 2 \, a b d\right)} e f - {\left(b^{2} d e^{2} + b^{2} c e f - {\left(a b c + a^{2} d\right)} f^{2}\right)} n\right)} x^{2} + {\left(a b c e^{2} - a^{2} c e f\right)} n - {\left(2 \, b^{2} c e^{2} - a^{2} c f^{2} + {\left(2 \, a b c - 3 \, a^{2} d\right)} e f + {\left(a^{2} d e f + a^{2} c f^{2} - {\left(b^{2} c + a b d\right)} e^{2}\right)} n\right)} x\right)} {\left(f x + e\right)}^{n - 3}}{{\left(2 \, b^{2} e^{2} - 4 \, a b e f + 2 \, a^{2} f^{2} + {\left(b^{2} e^{2} - 2 \, a b e f + a^{2} f^{2}\right)} n^{2} - 3 \, {\left(b^{2} e^{2} - 2 \, a b e f + a^{2} f^{2}\right)} n\right)} {\left(b x + a\right)}^{n}}"," ",0,"-(a^2*c*e*f - (b^2*d*e*f + (b^2*c - 2*a*b*d)*f^2 - (b^2*d*e*f - a*b*d*f^2)*n)*x^3 - (2*a*b*c - a^2*d)*e^2 - (b^2*d*e^2 - 2*a^2*d*f^2 + (3*b^2*c - 2*a*b*d)*e*f - (b^2*d*e^2 + b^2*c*e*f - (a*b*c + a^2*d)*f^2)*n)*x^2 + (a*b*c*e^2 - a^2*c*e*f)*n - (2*b^2*c*e^2 - a^2*c*f^2 + (2*a*b*c - 3*a^2*d)*e*f + (a^2*d*e*f + a^2*c*f^2 - (b^2*c + a*b*d)*e^2)*n)*x)*(f*x + e)^(n - 3)/((2*b^2*e^2 - 4*a*b*e*f + 2*a^2*f^2 + (b^2*e^2 - 2*a*b*e*f + a^2*f^2)*n^2 - 3*(b^2*e^2 - 2*a*b*e*f + a^2*f^2)*n)*(b*x + a)^n)","B",0
3057,1,884,0,1.479385," ","integrate((d*x+c)*(f*x+e)^(-4+n)/((b*x+a)^n),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c e f^{2} + {\left(b^{3} d e f^{2} + {\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} f^{3} - {\left(b^{3} d e f^{2} - a b^{2} d f^{3}\right)} n\right)} x^{4} + 3 \, {\left(2 \, a b^{2} c - a^{2} b d\right)} e^{3} - {\left(6 \, a^{2} b c - a^{3} d\right)} e^{2} f + {\left(4 \, b^{3} d e^{2} f + 4 \, {\left(2 \, b^{3} c - 3 \, a b^{2} d\right)} e f^{2} + {\left(b^{3} d e^{2} f - 2 \, a b^{2} d e f^{2} + a^{2} b d f^{3}\right)} n^{2} - {\left(5 \, b^{3} d e^{2} f + 2 \, {\left(b^{3} c - 4 \, a b^{2} d\right)} e f^{2} - {\left(2 \, a b^{2} c - 3 \, a^{2} b d\right)} f^{3}\right)} n\right)} x^{3} + {\left(a b^{2} c e^{3} - 2 \, a^{2} b c e^{2} f + a^{3} c e f^{2}\right)} n^{2} + {\left(3 \, b^{3} d e^{3} - 9 \, a^{2} b d e f^{2} + 3 \, a^{3} d f^{3} + 3 \, {\left(4 \, b^{3} c - 3 \, a b^{2} d\right)} e^{2} f + {\left(b^{3} d e^{3} + {\left(b^{3} c - a b^{2} d\right)} e^{2} f - {\left(2 \, a b^{2} c + a^{2} b d\right)} e f^{2} + {\left(a^{2} b c + a^{3} d\right)} f^{3}\right)} n^{2} - {\left(4 \, b^{3} d e^{3} + {\left(7 \, b^{3} c - 4 \, a b^{2} d\right)} e^{2} f - 4 \, {\left(2 \, a b^{2} c + a^{2} b d\right)} e f^{2} + {\left(a^{2} b c + 4 \, a^{3} d\right)} f^{3}\right)} n\right)} x^{2} - {\left(3 \, a^{3} c e f^{2} + {\left(5 \, a b^{2} c - a^{2} b d\right)} e^{3} - {\left(8 \, a^{2} b c - a^{3} d\right)} e^{2} f\right)} n + {\left(6 \, b^{3} c e^{3} + 2 \, a^{3} c f^{3} + 6 \, {\left(a b^{2} c - 2 \, a^{2} b d\right)} e^{2} f - 2 \, {\left(3 \, a^{2} b c - 2 \, a^{3} d\right)} e f^{2} + {\left(a^{3} c f^{3} + {\left(b^{3} c + a b^{2} d\right)} e^{3} - {\left(a b^{2} c + 2 \, a^{2} b d\right)} e^{2} f - {\left(a^{2} b c - a^{3} d\right)} e f^{2}\right)} n^{2} - {\left(3 \, a^{3} c f^{3} + {\left(5 \, b^{3} c + 3 \, a b^{2} d\right)} e^{3} - {\left(a b^{2} c + 8 \, a^{2} b d\right)} e^{2} f - {\left(7 \, a^{2} b c - 5 \, a^{3} d\right)} e f^{2}\right)} n\right)} x\right)} {\left(f x + e\right)}^{n - 4}}{{\left(6 \, b^{3} e^{3} - 18 \, a b^{2} e^{2} f + 18 \, a^{2} b e f^{2} - 6 \, a^{3} f^{3} - {\left(b^{3} e^{3} - 3 \, a b^{2} e^{2} f + 3 \, a^{2} b e f^{2} - a^{3} f^{3}\right)} n^{3} + 6 \, {\left(b^{3} e^{3} - 3 \, a b^{2} e^{2} f + 3 \, a^{2} b e f^{2} - a^{3} f^{3}\right)} n^{2} - 11 \, {\left(b^{3} e^{3} - 3 \, a b^{2} e^{2} f + 3 \, a^{2} b e f^{2} - a^{3} f^{3}\right)} n\right)} {\left(b x + a\right)}^{n}}"," ",0,"(2*a^3*c*e*f^2 + (b^3*d*e*f^2 + (2*b^3*c - 3*a*b^2*d)*f^3 - (b^3*d*e*f^2 - a*b^2*d*f^3)*n)*x^4 + 3*(2*a*b^2*c - a^2*b*d)*e^3 - (6*a^2*b*c - a^3*d)*e^2*f + (4*b^3*d*e^2*f + 4*(2*b^3*c - 3*a*b^2*d)*e*f^2 + (b^3*d*e^2*f - 2*a*b^2*d*e*f^2 + a^2*b*d*f^3)*n^2 - (5*b^3*d*e^2*f + 2*(b^3*c - 4*a*b^2*d)*e*f^2 - (2*a*b^2*c - 3*a^2*b*d)*f^3)*n)*x^3 + (a*b^2*c*e^3 - 2*a^2*b*c*e^2*f + a^3*c*e*f^2)*n^2 + (3*b^3*d*e^3 - 9*a^2*b*d*e*f^2 + 3*a^3*d*f^3 + 3*(4*b^3*c - 3*a*b^2*d)*e^2*f + (b^3*d*e^3 + (b^3*c - a*b^2*d)*e^2*f - (2*a*b^2*c + a^2*b*d)*e*f^2 + (a^2*b*c + a^3*d)*f^3)*n^2 - (4*b^3*d*e^3 + (7*b^3*c - 4*a*b^2*d)*e^2*f - 4*(2*a*b^2*c + a^2*b*d)*e*f^2 + (a^2*b*c + 4*a^3*d)*f^3)*n)*x^2 - (3*a^3*c*e*f^2 + (5*a*b^2*c - a^2*b*d)*e^3 - (8*a^2*b*c - a^3*d)*e^2*f)*n + (6*b^3*c*e^3 + 2*a^3*c*f^3 + 6*(a*b^2*c - 2*a^2*b*d)*e^2*f - 2*(3*a^2*b*c - 2*a^3*d)*e*f^2 + (a^3*c*f^3 + (b^3*c + a*b^2*d)*e^3 - (a*b^2*c + 2*a^2*b*d)*e^2*f - (a^2*b*c - a^3*d)*e*f^2)*n^2 - (3*a^3*c*f^3 + (5*b^3*c + 3*a*b^2*d)*e^3 - (a*b^2*c + 8*a^2*b*d)*e^2*f - (7*a^2*b*c - 5*a^3*d)*e*f^2)*n)*x)*(f*x + e)^(n - 4)/((6*b^3*e^3 - 18*a*b^2*e^2*f + 18*a^2*b*e*f^2 - 6*a^3*f^3 - (b^3*e^3 - 3*a*b^2*e^2*f + 3*a^2*b*e*f^2 - a^3*f^3)*n^3 + 6*(b^3*e^3 - 3*a*b^2*e^2*f + 3*a^2*b*e*f^2 - a^3*f^3)*n^2 - 11*(b^3*e^3 - 3*a*b^2*e^2*f + 3*a^2*b*e*f^2 - a^3*f^3)*n)*(b*x + a)^n)","B",0
3058,1,1740,0,1.300648," ","integrate((d*x+c)*(f*x+e)^(-5+n)/((b*x+a)^n),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{4} c e f^{3} - 2 \, {\left(b^{4} d e f^{3} + {\left(3 \, b^{4} c - 4 \, a b^{3} d\right)} f^{4} - {\left(b^{4} d e f^{3} - a b^{3} d f^{4}\right)} n\right)} x^{5} - 12 \, {\left(2 \, a b^{3} c - a^{2} b^{2} d\right)} e^{4} + 4 \, {\left(9 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} e^{3} f - 2 \, {\left(12 \, a^{3} b c - a^{4} d\right)} e^{2} f^{2} - 2 \, {\left(5 \, b^{4} d e^{2} f^{2} + 5 \, {\left(3 \, b^{4} c - 4 \, a b^{3} d\right)} e f^{3} + {\left(b^{4} d e^{2} f^{2} - 2 \, a b^{3} d e f^{3} + a^{2} b^{2} d f^{4}\right)} n^{2} - {\left(6 \, b^{4} d e^{2} f^{2} + {\left(3 \, b^{4} c - 10 \, a b^{3} d\right)} e f^{3} - {\left(3 \, a b^{3} c - 4 \, a^{2} b^{2} d\right)} f^{4}\right)} n\right)} x^{4} + {\left(a b^{3} c e^{4} - 3 \, a^{2} b^{2} c e^{3} f + 3 \, a^{3} b c e^{2} f^{2} - a^{4} c e f^{3}\right)} n^{3} - {\left(20 \, b^{4} d e^{3} f + 20 \, {\left(3 \, b^{4} c - 4 \, a b^{3} d\right)} e^{2} f^{2} - {\left(b^{4} d e^{3} f - 3 \, a b^{3} d e^{2} f^{2} + 3 \, a^{2} b^{2} d e f^{3} - a^{3} b d f^{4}\right)} n^{3} + {\left(10 \, b^{4} d e^{3} f + {\left(3 \, b^{4} c - 25 \, a b^{3} d\right)} e^{2} f^{2} - 2 \, {\left(3 \, a b^{3} c - 10 \, a^{2} b^{2} d\right)} e f^{3} + {\left(3 \, a^{2} b^{2} c - 5 \, a^{3} b d\right)} f^{4}\right)} n^{2} - {\left(29 \, b^{4} d e^{3} f + 3 \, {\left(9 \, b^{4} c - 22 \, a b^{3} d\right)} e^{2} f^{2} - {\left(30 \, a b^{3} c - 41 \, a^{2} b^{2} d\right)} e f^{3} + {\left(3 \, a^{2} b^{2} c - 4 \, a^{3} b d\right)} f^{4}\right)} n\right)} x^{3} + {\left(6 \, a^{4} c e f^{3} - {\left(9 \, a b^{3} c - a^{2} b^{2} d\right)} e^{4} + 2 \, {\left(12 \, a^{2} b^{2} c - a^{3} b d\right)} e^{3} f - {\left(21 \, a^{3} b c - a^{4} d\right)} e^{2} f^{2}\right)} n^{2} - {\left(12 \, b^{4} d e^{4} - 48 \, a^{2} b^{2} d e^{2} f^{2} + 32 \, a^{3} b d e f^{3} - 8 \, a^{4} d f^{4} + 12 \, {\left(5 \, b^{4} c - 4 \, a b^{3} d\right)} e^{3} f - {\left(b^{4} d e^{4} - 3 \, a b^{3} c e^{2} f^{2} + {\left(b^{4} c - 2 \, a b^{3} d\right)} e^{3} f + {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} b d\right)} e f^{3} - {\left(a^{3} b c + a^{4} d\right)} f^{4}\right)} n^{3} + {\left(8 \, b^{4} d e^{4} + 2 \, {\left(6 \, b^{4} c - 7 \, a b^{3} d\right)} e^{3} f - 3 \, {\left(9 \, a b^{3} c + a^{2} b^{2} d\right)} e^{2} f^{2} + 2 \, {\left(9 \, a^{2} b^{2} c + 8 \, a^{3} b d\right)} e f^{3} - {\left(3 \, a^{3} b c + 7 \, a^{4} d\right)} f^{4}\right)} n^{2} - {\left(19 \, b^{4} d e^{4} + {\left(47 \, b^{4} c - 36 \, a b^{3} d\right)} e^{3} f - 15 \, {\left(4 \, a b^{3} c + a^{2} b^{2} d\right)} e^{2} f^{2} + {\left(15 \, a^{2} b^{2} c + 46 \, a^{3} b d\right)} e f^{3} - 2 \, {\left(a^{3} b c + 7 \, a^{4} d\right)} f^{4}\right)} n\right)} x^{2} - {\left(11 \, a^{4} c e f^{3} - {\left(26 \, a b^{3} c - 7 \, a^{2} b^{2} d\right)} e^{4} + {\left(57 \, a^{2} b^{2} c - 10 \, a^{3} b d\right)} e^{3} f - 3 \, {\left(14 \, a^{3} b c - a^{4} d\right)} e^{2} f^{2}\right)} n - {\left(24 \, b^{4} c e^{4} - 6 \, a^{4} c f^{4} + 12 \, {\left(2 \, a b^{3} c - 5 \, a^{2} b^{2} d\right)} e^{3} f - 4 \, {\left(9 \, a^{2} b^{2} c - 10 \, a^{3} b d\right)} e^{2} f^{2} + 2 \, {\left(12 \, a^{3} b c - 5 \, a^{4} d\right)} e f^{3} - {\left(3 \, a^{3} b d e^{2} f^{2} - a^{4} c f^{4} + {\left(b^{4} c + a b^{3} d\right)} e^{4} - {\left(2 \, a b^{3} c + 3 \, a^{2} b^{2} d\right)} e^{3} f + {\left(2 \, a^{3} b c - a^{4} d\right)} e f^{3}\right)} n^{3} - {\left(6 \, a^{4} c f^{4} - {\left(9 \, b^{4} c + 7 \, a b^{3} d\right)} e^{4} + 2 \, {\left(6 \, a b^{3} c + 11 \, a^{2} b^{2} d\right)} e^{3} f + {\left(9 \, a^{2} b^{2} c - 23 \, a^{3} b d\right)} e^{2} f^{2} - 2 \, {\left(9 \, a^{3} b c - 4 \, a^{4} d\right)} e f^{3}\right)} n^{2} + {\left(11 \, a^{4} c f^{4} - 2 \, {\left(13 \, b^{4} c + 6 \, a b^{3} d\right)} e^{4} + 5 \, {\left(2 \, a b^{3} c + 11 \, a^{2} b^{2} d\right)} e^{3} f + 15 \, {\left(3 \, a^{2} b^{2} c - 4 \, a^{3} b d\right)} e^{2} f^{2} - {\left(40 \, a^{3} b c - 17 \, a^{4} d\right)} e f^{3}\right)} n\right)} x\right)} {\left(f x + e\right)}^{n - 5}}{{\left(24 \, b^{4} e^{4} - 96 \, a b^{3} e^{3} f + 144 \, a^{2} b^{2} e^{2} f^{2} - 96 \, a^{3} b e f^{3} + 24 \, a^{4} f^{4} + {\left(b^{4} e^{4} - 4 \, a b^{3} e^{3} f + 6 \, a^{2} b^{2} e^{2} f^{2} - 4 \, a^{3} b e f^{3} + a^{4} f^{4}\right)} n^{4} - 10 \, {\left(b^{4} e^{4} - 4 \, a b^{3} e^{3} f + 6 \, a^{2} b^{2} e^{2} f^{2} - 4 \, a^{3} b e f^{3} + a^{4} f^{4}\right)} n^{3} + 35 \, {\left(b^{4} e^{4} - 4 \, a b^{3} e^{3} f + 6 \, a^{2} b^{2} e^{2} f^{2} - 4 \, a^{3} b e f^{3} + a^{4} f^{4}\right)} n^{2} - 50 \, {\left(b^{4} e^{4} - 4 \, a b^{3} e^{3} f + 6 \, a^{2} b^{2} e^{2} f^{2} - 4 \, a^{3} b e f^{3} + a^{4} f^{4}\right)} n\right)} {\left(b x + a\right)}^{n}}"," ",0,"-(6*a^4*c*e*f^3 - 2*(b^4*d*e*f^3 + (3*b^4*c - 4*a*b^3*d)*f^4 - (b^4*d*e*f^3 - a*b^3*d*f^4)*n)*x^5 - 12*(2*a*b^3*c - a^2*b^2*d)*e^4 + 4*(9*a^2*b^2*c - 2*a^3*b*d)*e^3*f - 2*(12*a^3*b*c - a^4*d)*e^2*f^2 - 2*(5*b^4*d*e^2*f^2 + 5*(3*b^4*c - 4*a*b^3*d)*e*f^3 + (b^4*d*e^2*f^2 - 2*a*b^3*d*e*f^3 + a^2*b^2*d*f^4)*n^2 - (6*b^4*d*e^2*f^2 + (3*b^4*c - 10*a*b^3*d)*e*f^3 - (3*a*b^3*c - 4*a^2*b^2*d)*f^4)*n)*x^4 + (a*b^3*c*e^4 - 3*a^2*b^2*c*e^3*f + 3*a^3*b*c*e^2*f^2 - a^4*c*e*f^3)*n^3 - (20*b^4*d*e^3*f + 20*(3*b^4*c - 4*a*b^3*d)*e^2*f^2 - (b^4*d*e^3*f - 3*a*b^3*d*e^2*f^2 + 3*a^2*b^2*d*e*f^3 - a^3*b*d*f^4)*n^3 + (10*b^4*d*e^3*f + (3*b^4*c - 25*a*b^3*d)*e^2*f^2 - 2*(3*a*b^3*c - 10*a^2*b^2*d)*e*f^3 + (3*a^2*b^2*c - 5*a^3*b*d)*f^4)*n^2 - (29*b^4*d*e^3*f + 3*(9*b^4*c - 22*a*b^3*d)*e^2*f^2 - (30*a*b^3*c - 41*a^2*b^2*d)*e*f^3 + (3*a^2*b^2*c - 4*a^3*b*d)*f^4)*n)*x^3 + (6*a^4*c*e*f^3 - (9*a*b^3*c - a^2*b^2*d)*e^4 + 2*(12*a^2*b^2*c - a^3*b*d)*e^3*f - (21*a^3*b*c - a^4*d)*e^2*f^2)*n^2 - (12*b^4*d*e^4 - 48*a^2*b^2*d*e^2*f^2 + 32*a^3*b*d*e*f^3 - 8*a^4*d*f^4 + 12*(5*b^4*c - 4*a*b^3*d)*e^3*f - (b^4*d*e^4 - 3*a*b^3*c*e^2*f^2 + (b^4*c - 2*a*b^3*d)*e^3*f + (3*a^2*b^2*c + 2*a^3*b*d)*e*f^3 - (a^3*b*c + a^4*d)*f^4)*n^3 + (8*b^4*d*e^4 + 2*(6*b^4*c - 7*a*b^3*d)*e^3*f - 3*(9*a*b^3*c + a^2*b^2*d)*e^2*f^2 + 2*(9*a^2*b^2*c + 8*a^3*b*d)*e*f^3 - (3*a^3*b*c + 7*a^4*d)*f^4)*n^2 - (19*b^4*d*e^4 + (47*b^4*c - 36*a*b^3*d)*e^3*f - 15*(4*a*b^3*c + a^2*b^2*d)*e^2*f^2 + (15*a^2*b^2*c + 46*a^3*b*d)*e*f^3 - 2*(a^3*b*c + 7*a^4*d)*f^4)*n)*x^2 - (11*a^4*c*e*f^3 - (26*a*b^3*c - 7*a^2*b^2*d)*e^4 + (57*a^2*b^2*c - 10*a^3*b*d)*e^3*f - 3*(14*a^3*b*c - a^4*d)*e^2*f^2)*n - (24*b^4*c*e^4 - 6*a^4*c*f^4 + 12*(2*a*b^3*c - 5*a^2*b^2*d)*e^3*f - 4*(9*a^2*b^2*c - 10*a^3*b*d)*e^2*f^2 + 2*(12*a^3*b*c - 5*a^4*d)*e*f^3 - (3*a^3*b*d*e^2*f^2 - a^4*c*f^4 + (b^4*c + a*b^3*d)*e^4 - (2*a*b^3*c + 3*a^2*b^2*d)*e^3*f + (2*a^3*b*c - a^4*d)*e*f^3)*n^3 - (6*a^4*c*f^4 - (9*b^4*c + 7*a*b^3*d)*e^4 + 2*(6*a*b^3*c + 11*a^2*b^2*d)*e^3*f + (9*a^2*b^2*c - 23*a^3*b*d)*e^2*f^2 - 2*(9*a^3*b*c - 4*a^4*d)*e*f^3)*n^2 + (11*a^4*c*f^4 - 2*(13*b^4*c + 6*a*b^3*d)*e^4 + 5*(2*a*b^3*c + 11*a^2*b^2*d)*e^3*f + 15*(3*a^2*b^2*c - 4*a^3*b*d)*e^2*f^2 - (40*a^3*b*c - 17*a^4*d)*e*f^3)*n)*x)*(f*x + e)^(n - 5)/((24*b^4*e^4 - 96*a*b^3*e^3*f + 144*a^2*b^2*e^2*f^2 - 96*a^3*b*e*f^3 + 24*a^4*f^4 + (b^4*e^4 - 4*a*b^3*e^3*f + 6*a^2*b^2*e^2*f^2 - 4*a^3*b*e*f^3 + a^4*f^4)*n^4 - 10*(b^4*e^4 - 4*a*b^3*e^3*f + 6*a^2*b^2*e^2*f^2 - 4*a^3*b*e*f^3 + a^4*f^4)*n^3 + 35*(b^4*e^4 - 4*a*b^3*e^3*f + 6*a^2*b^2*e^2*f^2 - 4*a^3*b*e*f^3 + a^4*f^4)*n^2 - 50*(b^4*e^4 - 4*a*b^3*e^3*f + 6*a^2*b^2*e^2*f^2 - 4*a^3*b*e*f^3 + a^4*f^4)*n)*(b*x + a)^n)","B",0
3059,0,0,0,1.534721," ","integrate((b*x+a)^m*(f*x+e)^p/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(f x + e\right)}^{p}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m*(f*x + e)^p/(d*x + c)^m, x)","F",0
3060,0,0,0,1.285465," ","integrate((5-4*x)^4*(2+3*x)^m/((1+2*x)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(256 \, x^{4} - 1280 \, x^{3} + 2400 \, x^{2} - 2000 \, x + 625\right)} {\left(3 \, x + 2\right)}^{m}}{{\left(2 \, x + 1\right)}^{m}}, x\right)"," ",0,"integral((256*x^4 - 1280*x^3 + 2400*x^2 - 2000*x + 625)*(3*x + 2)^m/(2*x + 1)^m, x)","F",0
3061,0,0,0,1.810958," ","integrate((b*x+a)^m*(f*x+e)^3/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} {\left(b x + a\right)}^{m}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*(b*x + a)^m/(d*x + c)^m, x)","F",0
3062,0,0,0,1.262614," ","integrate((b*x+a)^m*(f*x+e)^2/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m/(d*x + c)^m, x)","F",0
3063,0,0,0,0.915716," ","integrate((b*x+a)^m*(f*x+e)/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)} {\left(b x + a\right)}^{m}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m/(d*x + c)^m, x)","F",0
3064,0,0,0,1.555660," ","integrate((b*x+a)^m/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m/(d*x + c)^m, x)","F",0
3065,0,0,0,1.426819," ","integrate((b*x+a)^m/((d*x+c)^m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{{\left(f x + e\right)} {\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m/((f*x + e)*(d*x + c)^m), x)","F",0
3066,0,0,0,1.172498," ","integrate((b*x+a)^m/((d*x+c)^m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{{\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m/((f^2*x^2 + 2*e*f*x + e^2)*(d*x + c)^m), x)","F",0
3067,0,0,0,1.482893," ","integrate((b*x+a)^m/((d*x+c)^m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{{\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} {\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m/((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*(d*x + c)^m), x)","F",0
3068,0,0,0,1.763082," ","integrate((b*x+a)^m/((d*x+c)^m)/(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{{\left(f^{4} x^{4} + 4 \, e f^{3} x^{3} + 6 \, e^{2} f^{2} x^{2} + 4 \, e^{3} f x + e^{4}\right)} {\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((b*x + a)^m/((f^4*x^4 + 4*e*f^3*x^3 + 6*e^2*f^2*x^2 + 4*e^3*f*x + e^4)*(d*x + c)^m), x)","F",0
3069,0,0,0,1.336503," ","integrate((2+3*x)^m/(5-4*x)^5/((1+2*x)^m),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m}}{{\left(1024 \, x^{5} - 6400 \, x^{4} + 16000 \, x^{3} - 20000 \, x^{2} + 12500 \, x - 3125\right)} {\left(2 \, x + 1\right)}^{m}}, x\right)"," ",0,"integral(-(3*x + 2)^m/((1024*x^5 - 6400*x^4 + 16000*x^3 - 20000*x^2 + 12500*x - 3125)*(2*x + 1)^m), x)","F",0
3070,0,0,0,1.647279," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1)*(f*x + e)^p, x)","F",0
3071,0,0,0,1.065031," ","integrate((5-4*x)^3*(1+2*x)^(-1-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(64 \, x^{3} - 240 \, x^{2} + 300 \, x - 125\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 1}, x\right)"," ",0,"integral(-(64*x^3 - 240*x^2 + 300*x - 125)*(3*x + 2)^m*(2*x + 1)^(-m - 1), x)","F",0
3072,0,0,0,1.245924," ","integrate((5-4*x)^2*(1+2*x)^(-1-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(16 \, x^{2} - 40 \, x + 25\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 1}, x\right)"," ",0,"integral((16*x^2 - 40*x + 25)*(3*x + 2)^m*(2*x + 1)^(-m - 1), x)","F",0
3073,0,0,0,1.030551," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m*(d*x + c)^(-m - 1), x)","F",0
3074,0,0,0,1.402107," ","integrate((b*x+a)^m*(d*x+c)^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1), x)","F",0
3075,0,0,0,1.424802," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1)/(f*x + e), x)","F",0
3076,0,0,0,1.698188," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3077,0,0,0,1.096148," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3078,0,0,0,1.935412," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)/(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}}{f^{4} x^{4} + 4 \, e f^{3} x^{3} + 6 \, e^{2} f^{2} x^{2} + 4 \, e^{3} f x + e^{4}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 1)/(f^4*x^4 + 4*e*f^3*x^3 + 6*e^2*f^2*x^2 + 4*e^3*f*x + e^4), x)","F",0
3079,0,0,0,1.563568," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 2)*(f*x + e)^p, x)","F",0
3080,0,0,0,1.412121," ","integrate((5-4*x)^3*(1+2*x)^(-2-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(64 \, x^{3} - 240 \, x^{2} + 300 \, x - 125\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 2}, x\right)"," ",0,"integral(-(64*x^3 - 240*x^2 + 300*x - 125)*(3*x + 2)^m*(2*x + 1)^(-m - 2), x)","F",0
3081,0,0,0,0.894246," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m*(d*x + c)^(-m - 2), x)","F",0
3082,0,0,0,1.263473," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m*(d*x + c)^(-m - 2), x)","F",0
3083,1,58,0,1.403480," ","integrate((b*x+a)^m*(d*x+c)^(-2-m),x, algorithm=""fricas"")","\frac{{\left(b d x^{2} + a c + {\left(b c + a d\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{b c - a d + {\left(b c - a d\right)} m}"," ",0,"(b*d*x^2 + a*c + (b*c + a*d)*x)*(b*x + a)^m*(d*x + c)^(-m - 2)/(b*c - a*d + (b*c - a*d)*m)","A",0
3084,0,0,0,0.781857," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 2)/(f*x + e), x)","F",0
3085,0,0,0,0.983068," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3086,0,0,0,1.486506," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 2)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3087,0,0,0,1.194074," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 3)*(f*x + e)^p, x)","F",0
3088,0,0,0,1.181151," ","integrate((5-4*x)^4*(1+2*x)^(-3-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(256 \, x^{4} - 1280 \, x^{3} + 2400 \, x^{2} - 2000 \, x + 625\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 3}, x\right)"," ",0,"integral((256*x^4 - 1280*x^3 + 2400*x^2 - 2000*x + 625)*(3*x + 2)^m*(2*x + 1)^(-m - 3), x)","F",0
3089,0,0,0,1.385316," ","integrate((5-4*x)^3*(1+2*x)^(-3-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(64 \, x^{3} - 240 \, x^{2} + 300 \, x - 125\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 3}, x\right)"," ",0,"integral(-(64*x^3 - 240*x^2 + 300*x - 125)*(3*x + 2)^m*(2*x + 1)^(-m - 3), x)","F",0
3090,0,0,0,1.291464," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m*(d*x + c)^(-m - 3), x)","F",0
3091,1,336,0,1.240743," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)*(f*x+e),x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{2} f - {\left(b^{2} d^{2} e + {\left(b^{2} c d - a b d^{2}\right)} f m + {\left(b^{2} c d - 2 \, a b d^{2}\right)} f\right)} x^{3} - {\left(a b c^{2} - a^{2} c d\right)} e m - {\left(3 \, b^{2} c d e + {\left(b^{2} c^{2} - 2 \, a b c d - 2 \, a^{2} d^{2}\right)} f + {\left({\left(b^{2} c d - a b d^{2}\right)} e + {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f\right)} m\right)} x^{2} - {\left(2 \, a b c^{2} - a^{2} c d\right)} e + {\left(3 \, a^{2} c d f - {\left(2 \, b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2}\right)} e - {\left({\left(b^{2} c^{2} - a^{2} d^{2}\right)} e + {\left(a b c^{2} - a^{2} c d\right)} f\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}}{2 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m}"," ",0,"-(a^2*c^2*f - (b^2*d^2*e + (b^2*c*d - a*b*d^2)*f*m + (b^2*c*d - 2*a*b*d^2)*f)*x^3 - (a*b*c^2 - a^2*c*d)*e*m - (3*b^2*c*d*e + (b^2*c^2 - 2*a*b*c*d - 2*a^2*d^2)*f + ((b^2*c*d - a*b*d^2)*e + (b^2*c^2 - a^2*d^2)*f)*m)*x^2 - (2*a*b*c^2 - a^2*c*d)*e + (3*a^2*c*d*f - (2*b^2*c^2 + 2*a*b*c*d - a^2*d^2)*e - ((b^2*c^2 - a^2*d^2)*e + (a*b*c^2 - a^2*c*d)*f)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 3)/(2*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m^2 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m)","B",0
3092,1,205,0,1.683144," ","integrate((b*x+a)^m*(d*x+c)^(-3-m),x, algorithm=""fricas"")","\frac{{\left(b^{2} d^{2} x^{3} + 2 \, a b c^{2} - a^{2} c d + {\left(3 \, b^{2} c d + {\left(b^{2} c d - a b d^{2}\right)} m\right)} x^{2} + {\left(a b c^{2} - a^{2} c d\right)} m + {\left(2 \, b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} + {\left(b^{2} c^{2} - a^{2} d^{2}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}}{2 \, b^{2} c^{2} - 4 \, a b c d + 2 \, a^{2} d^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m^{2} + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m}"," ",0,"(b^2*d^2*x^3 + 2*a*b*c^2 - a^2*c*d + (3*b^2*c*d + (b^2*c*d - a*b*d^2)*m)*x^2 + (a*b*c^2 - a^2*c*d)*m + (2*b^2*c^2 + 2*a*b*c*d - a^2*d^2 + (b^2*c^2 - a^2*d^2)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 3)/(2*b^2*c^2 - 4*a*b*c*d + 2*a^2*d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m^2 + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m)","B",0
3093,0,0,0,0.971550," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 3)/(f*x + e), x)","F",0
3094,0,0,0,1.661061," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 3)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3095,0,0,0,1.569915," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 4)*(f*x + e)^p, x)","F",0
3096,0,0,0,1.146066," ","integrate((5-4*x)^4*(1+2*x)^(-4-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(256 \, x^{4} - 1280 \, x^{3} + 2400 \, x^{2} - 2000 \, x + 625\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 4}, x\right)"," ",0,"integral((256*x^4 - 1280*x^3 + 2400*x^2 - 2000*x + 625)*(3*x + 2)^m*(2*x + 1)^(-m - 4), x)","F",0
3097,0,0,0,1.436109," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)*(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}, x\right)"," ",0,"integral((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*(b*x + a)^m*(d*x + c)^(-m - 4), x)","F",0
3098,1,1292,0,1.363869," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)*(f*x+e)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} c^{3} f^{2} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} m^{2} + {\left(2 \, b^{3} d^{3} e^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{2} m^{2} + 2 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e f + 2 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f^{2} + {\left(2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e f + {\left(3 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} f^{2}\right)} m\right)} x^{4} + {\left(8 \, b^{3} c d^{2} e^{2} + 8 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} e f + 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} f^{2} + {\left(2 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e f + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{2}\right)} m^{2} + {\left(2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e^{2} + 2 \, {\left(5 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} e f + {\left(3 \, b^{3} c^{3} - 7 \, a b^{2} c^{2} d - a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f^{2}\right)} m\right)} x^{3} + 2 \, {\left(3 \, a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e^{2} - 2 \, {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} e f + {\left(12 \, b^{3} c^{2} d e^{2} + 12 \, a^{3} c d^{2} f^{2} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e f + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} + 2 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e f + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2}\right)} m^{2} + {\left({\left(7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e^{2} + 8 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e f + {\left(a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 7 \, a^{3} c d^{2}\right)} f^{2}\right)} m\right)} x^{2} + {\left({\left(5 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} e^{2} - 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} e f\right)} m + {\left(8 \, a^{3} c^{2} d f^{2} + 2 \, {\left(3 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{2} - 8 \, {\left(3 \, a^{2} b c^{2} d - a^{3} c d^{2}\right)} e f + {\left({\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e^{2} + 2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e f\right)} m^{2} + {\left({\left(5 \, b^{3} c^{3} - a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} e^{2} + 2 \, {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e f - 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f^{2}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{6 \, b^{3} c^{3} - 18 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 6 \, a^{3} d^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{2} + 11 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m}"," ",0,"(2*a^3*c^3*f^2 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e^2*m^2 + (2*b^3*d^3*e^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*f^2*m^2 + 2*(b^3*c*d^2 - 3*a*b^2*d^3)*e*f + 2*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*f^2 + (2*(b^3*c*d^2 - a*b^2*d^3)*e*f + (3*b^3*c^2*d - 8*a*b^2*c*d^2 + 5*a^2*b*d^3)*f^2)*m)*x^4 + (8*b^3*c*d^2*e^2 + 8*(b^3*c^2*d - 3*a*b^2*c*d^2)*e*f + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 3*a^3*d^3)*f^2 + (2*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e*f + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f^2)*m^2 + (2*(b^3*c*d^2 - a*b^2*d^3)*e^2 + 2*(5*b^3*c^2*d - 8*a*b^2*c*d^2 + 3*a^2*b*d^3)*e*f + (3*b^3*c^3 - 7*a*b^2*c^2*d - a^2*b*c*d^2 + 5*a^3*d^3)*f^2)*m)*x^3 + 2*(3*a*b^2*c^3 - 3*a^2*b*c^2*d + a^3*c*d^2)*e^2 - 2*(3*a^2*b*c^3 - a^3*c^2*d)*e*f + (12*b^3*c^2*d*e^2 + 12*a^3*c*d^2*f^2 + 6*(b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*e*f + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e^2 + 2*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e*f + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f^2)*m^2 + ((7*b^3*c^2*d - 8*a*b^2*c*d^2 + a^2*b*d^3)*e^2 + 8*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e*f + (a*b^2*c^3 - 8*a^2*b*c^2*d + 7*a^3*c*d^2)*f^2)*m)*x^2 + ((5*a*b^2*c^3 - 8*a^2*b*c^2*d + 3*a^3*c*d^2)*e^2 - 2*(a^2*b*c^3 - a^3*c^2*d)*e*f)*m + (8*a^3*c^2*d*f^2 + 2*(3*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*e^2 - 8*(3*a^2*b*c^2*d - a^3*c*d^2)*e*f + ((b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e^2 + 2*(a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*f)*m^2 + ((5*b^3*c^3 - a*b^2*c^2*d - 7*a^2*b*c*d^2 + 3*a^3*d^3)*e^2 + 2*(3*a*b^2*c^3 - 8*a^2*b*c^2*d + 5*a^3*c*d^2)*e*f - 2*(a^2*b*c^3 - a^3*c^2*d)*f^2)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 4)/(6*b^3*c^3 - 18*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 6*a^3*d^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^2 + 11*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m)","B",0
3099,1,902,0,1.353045," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)*(f*x+e),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, b^{3} d^{3} e + {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f m + {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} f\right)} x^{4} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e m^{2} + {\left(8 \, b^{3} c d^{2} e + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f m^{2} + 4 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} f + {\left(2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e + {\left(5 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f\right)} m\right)} x^{3} + {\left(12 \, b^{3} c^{2} d e + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} m^{2} + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f + {\left({\left(7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e + 4 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} m\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e - {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} f + {\left({\left(5 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} e - {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f\right)} m + {\left({\left({\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f\right)} m^{2} + 2 \, {\left(3 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e - 4 \, {\left(3 \, a^{2} b c^{2} d - a^{3} c d^{2}\right)} f + {\left({\left(5 \, b^{3} c^{3} - a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} e + {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} f\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{6 \, b^{3} c^{3} - 18 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 6 \, a^{3} d^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{2} + 11 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m}"," ",0,"((2*b^3*d^3*e + (b^3*c*d^2 - a*b^2*d^3)*f*m + (b^3*c*d^2 - 3*a*b^2*d^3)*f)*x^4 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*m^2 + (8*b^3*c*d^2*e + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*f*m^2 + 4*(b^3*c^2*d - 3*a*b^2*c*d^2)*f + (2*(b^3*c*d^2 - a*b^2*d^3)*e + (5*b^3*c^2*d - 8*a*b^2*c*d^2 + 3*a^2*b*d^3)*f)*m)*x^3 + (12*b^3*c^2*d*e + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f)*m^2 + 3*(b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*f + ((7*b^3*c^2*d - 8*a*b^2*c*d^2 + a^2*b*d^3)*e + 4*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f)*m)*x^2 + 2*(3*a*b^2*c^3 - 3*a^2*b*c^2*d + a^3*c*d^2)*e - (3*a^2*b*c^3 - a^3*c^2*d)*f + ((5*a*b^2*c^3 - 8*a^2*b*c^2*d + 3*a^3*c*d^2)*e - (a^2*b*c^3 - a^3*c^2*d)*f)*m + (((b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f)*m^2 + 2*(3*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*e - 4*(3*a^2*b*c^2*d - a^3*c*d^2)*f + ((5*b^3*c^3 - a*b^2*c^2*d - 7*a^2*b*c*d^2 + 3*a^3*d^3)*e + (3*a*b^2*c^3 - 8*a^2*b*c^2*d + 5*a^3*c*d^2)*f)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 4)/(6*b^3*c^3 - 18*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 6*a^3*d^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^2 + 11*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m)","B",0
3100,1,507,0,0.894731," ","integrate((b*x+a)^m*(d*x+c)^(-4-m),x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} d^{3} x^{4} + 6 \, a b^{2} c^{3} - 6 \, a^{2} b c^{2} d + 2 \, a^{3} c d^{2} + 2 \, {\left(4 \, b^{3} c d^{2} + {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} m\right)} x^{3} + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} m^{2} + {\left(12 \, b^{3} c^{2} d + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} m^{2} + {\left(7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} m\right)} x^{2} + {\left(5 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} m + {\left(6 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} m^{2} + {\left(5 \, b^{3} c^{3} - a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{6 \, b^{3} c^{3} - 18 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 6 \, a^{3} d^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{2} + 11 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m}"," ",0,"(2*b^3*d^3*x^4 + 6*a*b^2*c^3 - 6*a^2*b*c^2*d + 2*a^3*c*d^2 + 2*(4*b^3*c*d^2 + (b^3*c*d^2 - a*b^2*d^3)*m)*x^3 + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*m^2 + (12*b^3*c^2*d + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*m^2 + (7*b^3*c^2*d - 8*a*b^2*c*d^2 + a^2*b*d^3)*m)*x^2 + (5*a*b^2*c^3 - 8*a^2*b*c^2*d + 3*a^3*c*d^2)*m + (6*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*m^2 + (5*b^3*c^3 - a*b^2*c^2*d - 7*a^2*b*c*d^2 + 3*a^3*d^3)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 4)/(6*b^3*c^3 - 18*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 6*a^3*d^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^2 + 11*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m)","B",0
3101,0,0,0,1.356796," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 4)/(f*x + e), x)","F",0
3102,0,0,0,1.647017," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 4)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3103,0,0,0,1.920786," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 5)*(f*x + e)^p, x)","F",0
3104,0,0,0,1.434170," ","integrate((5-4*x)^5*(1+2*x)^(-5-m)*(2+3*x)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(1024 \, x^{5} - 6400 \, x^{4} + 16000 \, x^{3} - 20000 \, x^{2} + 12500 \, x - 3125\right)} {\left(3 \, x + 2\right)}^{m} {\left(2 \, x + 1\right)}^{-m - 5}, x\right)"," ",0,"integral(-(1024*x^5 - 6400*x^4 + 16000*x^3 - 20000*x^2 + 12500*x - 3125)*(3*x + 2)^m*(2*x + 1)^(-m - 5), x)","F",0
3105,0,0,0,1.146408," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{4} x^{4} + 4 \, e f^{3} x^{3} + 6 \, e^{2} f^{2} x^{2} + 4 \, e^{3} f x + e^{4}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}, x\right)"," ",0,"integral((f^4*x^4 + 4*e*f^3*x^3 + 6*e^2*f^2*x^2 + 4*e^3*f*x + e^4)*(b*x + a)^m*(d*x + c)^(-m - 5), x)","F",0
3106,1,3421,0,1.773923," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e)^3,x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{4} c^{4} f^{3} - {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e^{3} m^{3} - {\left(6 \, b^{4} d^{4} e^{3} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} f^{3} m^{3} + 6 \, {\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} e^{2} f + 6 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3} + 6 \, a^{2} b^{2} d^{4}\right)} e f^{2} + 6 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} f^{3} + 3 \, {\left({\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e f^{2} + {\left(2 \, b^{4} c^{3} d - 7 \, a b^{3} c^{2} d^{2} + 8 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} f^{3}\right)} m^{2} + {\left(6 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{2} f + 3 \, {\left(3 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + 7 \, a^{2} b^{2} d^{4}\right)} e f^{2} + {\left(11 \, b^{4} c^{3} d - 42 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} - 26 \, a^{3} b d^{4}\right)} f^{3}\right)} m\right)} x^{5} - {\left(30 \, b^{4} c d^{3} e^{3} + 30 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3}\right)} e^{2} f + 30 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3}\right)} e f^{2} + 6 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - 4 \, a^{4} d^{4}\right)} f^{3} + {\left(3 \, {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e f^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} f^{3}\right)} m^{3} + 3 \, {\left(2 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} f + {\left(8 \, b^{4} c^{3} d - 23 \, a b^{3} c^{2} d^{2} + 22 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} e f^{2} + {\left(2 \, b^{4} c^{4} - 6 \, a b^{3} c^{3} d + 3 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} f^{3}\right)} m^{2} + {\left(6 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{3} + 12 \, {\left(3 \, b^{4} c^{2} d^{2} - 5 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} e^{2} f + 3 \, {\left(17 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 55 \, a^{2} b^{2} c d^{3} - 12 \, a^{3} b d^{4}\right)} e f^{2} + {\left(11 \, b^{4} c^{4} - 40 \, a b^{3} c^{3} d + 45 \, a^{2} b^{2} c^{2} d^{2} + 10 \, a^{3} b c d^{3} - 26 \, a^{4} d^{4}\right)} f^{3}\right)} m\right)} x^{4} - 6 \, {\left(4 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e^{3} + 6 \, {\left(6 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e^{2} f - 6 \, {\left(4 \, a^{3} b c^{4} - a^{4} c^{3} d\right)} e f^{2} - {\left(60 \, b^{4} c^{2} d^{2} e^{3} - 60 \, a^{4} c d^{3} f^{3} + 60 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2}\right)} e^{2} f + 12 \, {\left(2 \, b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 12 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} e f^{2} + {\left(3 \, {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{2} f + 3 \, {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e f^{2} + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} f^{3}\right)} m^{3} + 3 \, {\left({\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{3} + 5 \, {\left(2 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} + 4 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{2} f + {\left(7 \, b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 3 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 8 \, a^{4} d^{4}\right)} e f^{2} + {\left(a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 9 \, a^{3} b c^{2} d^{2} - 4 \, a^{4} c d^{3}\right)} f^{3}\right)} m^{2} + {\left(3 \, {\left(9 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{3} + 3 \, {\left(29 \, b^{4} c^{3} d - 66 \, a b^{3} c^{2} d^{2} + 41 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} e^{2} f + 3 \, {\left(14 \, b^{4} c^{4} - 46 \, a b^{3} c^{3} d + 15 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 19 \, a^{4} d^{4}\right)} e f^{2} + {\left(2 \, a b^{3} c^{4} - 15 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 47 \, a^{4} c d^{3}\right)} f^{3}\right)} m\right)} x^{3} - 3 \, {\left({\left(3 \, a b^{3} c^{4} - 8 \, a^{2} b^{2} c^{3} d + 7 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} e^{3} - {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e^{2} f\right)} m^{2} - {\left(60 \, b^{4} c^{3} d e^{3} - 60 \, a^{4} c^{2} d^{2} f^{3} + 12 \, {\left(3 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e^{2} f + 60 \, {\left(4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e f^{2} + {\left({\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{3} + 3 \, {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e^{2} f + 3 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e f^{2}\right)} m^{3} + 3 \, {\left({\left(4 \, b^{4} c^{3} d - 9 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{3} + {\left(8 \, b^{4} c^{4} - 14 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} e^{2} f + 5 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b^{2} c^{3} d + 5 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} e f^{2} - {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f^{3}\right)} m^{2} + {\left({\left(47 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 15 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} e^{3} + 3 \, {\left(19 \, b^{4} c^{4} - 36 \, a b^{3} c^{3} d - 15 \, a^{2} b^{2} c^{2} d^{2} + 46 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e^{2} f + 3 \, {\left(4 \, a b^{3} c^{4} - 41 \, a^{2} b^{2} c^{3} d + 66 \, a^{3} b c^{2} d^{2} - 29 \, a^{4} c d^{3}\right)} e f^{2} - 3 \, {\left(a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 9 \, a^{4} c^{2} d^{2}\right)} f^{3}\right)} m\right)} x^{2} - {\left({\left(26 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d + 42 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e^{3} - 3 \, {\left(7 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e^{2} f + 6 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} e f^{2}\right)} m + {\left(30 \, a^{4} c^{3} d f^{3} - 6 \, {\left(4 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e^{3} + 30 \, {\left(6 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e^{2} f - 30 \, {\left(4 \, a^{3} b c^{3} d - a^{4} c^{2} d^{2}\right)} e f^{2} - {\left({\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e^{3} + 3 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e^{2} f\right)} m^{3} - 3 \, {\left({\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 6 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e^{3} + {\left(7 \, a b^{3} c^{4} - 22 \, a^{2} b^{2} c^{3} d + 23 \, a^{3} b c^{2} d^{2} - 8 \, a^{4} c d^{3}\right)} e^{2} f - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e f^{2}\right)} m^{2} - {\left({\left(26 \, b^{4} c^{4} - 10 \, a b^{3} c^{3} d - 45 \, a^{2} b^{2} c^{2} d^{2} + 40 \, a^{3} b c d^{3} - 11 \, a^{4} d^{4}\right)} e^{3} + 3 \, {\left(12 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 17 \, a^{4} c d^{3}\right)} e^{2} f - 12 \, {\left(2 \, a^{2} b^{2} c^{4} - 5 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e f^{2} + 6 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} f^{3}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{24 \, b^{4} c^{4} - 96 \, a b^{3} c^{3} d + 144 \, a^{2} b^{2} c^{2} d^{2} - 96 \, a^{3} b c d^{3} + 24 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{4} + 10 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{3} + 35 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{2} + 50 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m}"," ",0,"-(6*a^4*c^4*f^3 - (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e^3*m^3 - (6*b^4*d^4*e^3 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*f^3*m^3 + 6*(b^4*c*d^3 - 4*a*b^3*d^4)*e^2*f + 6*(b^4*c^2*d^2 - 4*a*b^3*c*d^3 + 6*a^2*b^2*d^4)*e*f^2 + 6*(b^4*c^3*d - 4*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*f^3 + 3*((b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e*f^2 + (2*b^4*c^3*d - 7*a*b^3*c^2*d^2 + 8*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*f^3)*m^2 + (6*(b^4*c*d^3 - a*b^3*d^4)*e^2*f + 3*(3*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + 7*a^2*b^2*d^4)*e*f^2 + (11*b^4*c^3*d - 42*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 - 26*a^3*b*d^4)*f^3)*m)*x^5 - (30*b^4*c*d^3*e^3 + 30*(b^4*c^2*d^2 - 4*a*b^3*c*d^3)*e^2*f + 30*(b^4*c^3*d - 4*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3)*e*f^2 + 6*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - 4*a^4*d^4)*f^3 + (3*(b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e*f^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*f^3)*m^3 + 3*(2*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2*f + (8*b^4*c^3*d - 23*a*b^3*c^2*d^2 + 22*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*e*f^2 + (2*b^4*c^4 - 6*a*b^3*c^3*d + 3*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - 3*a^4*d^4)*f^3)*m^2 + (6*(b^4*c*d^3 - a*b^3*d^4)*e^3 + 12*(3*b^4*c^2*d^2 - 5*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*e^2*f + 3*(17*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 55*a^2*b^2*c*d^3 - 12*a^3*b*d^4)*e*f^2 + (11*b^4*c^4 - 40*a*b^3*c^3*d + 45*a^2*b^2*c^2*d^2 + 10*a^3*b*c*d^3 - 26*a^4*d^4)*f^3)*m)*x^4 - 6*(4*a*b^3*c^4 - 6*a^2*b^2*c^3*d + 4*a^3*b*c^2*d^2 - a^4*c*d^3)*e^3 + 6*(6*a^2*b^2*c^4 - 4*a^3*b*c^3*d + a^4*c^2*d^2)*e^2*f - 6*(4*a^3*b*c^4 - a^4*c^3*d)*e*f^2 - (60*b^4*c^2*d^2*e^3 - 60*a^4*c*d^3*f^3 + 60*(b^4*c^3*d - 4*a*b^3*c^2*d^2)*e^2*f + 12*(2*b^4*c^4 - 8*a*b^3*c^3*d + 12*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 3*a^4*d^4)*e*f^2 + (3*(b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e^2*f + 3*(b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e*f^2 + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*f^3)*m^3 + 3*((b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^3 + 5*(2*b^4*c^3*d - 5*a*b^3*c^2*d^2 + 4*a^2*b^2*c*d^3 - a^3*b*d^4)*e^2*f + (7*b^4*c^4 - 16*a*b^3*c^3*d + 3*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 8*a^4*d^4)*e*f^2 + (a*b^3*c^4 - 6*a^2*b^2*c^3*d + 9*a^3*b*c^2*d^2 - 4*a^4*c*d^3)*f^3)*m^2 + (3*(9*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + a^2*b^2*d^4)*e^3 + 3*(29*b^4*c^3*d - 66*a*b^3*c^2*d^2 + 41*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*e^2*f + 3*(14*b^4*c^4 - 46*a*b^3*c^3*d + 15*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 19*a^4*d^4)*e*f^2 + (2*a*b^3*c^4 - 15*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 47*a^4*c*d^3)*f^3)*m)*x^3 - 3*((3*a*b^3*c^4 - 8*a^2*b^2*c^3*d + 7*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*e^3 - (a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*e^2*f)*m^2 - (60*b^4*c^3*d*e^3 - 60*a^4*c^2*d^2*f^3 + 12*(3*b^4*c^4 - 12*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 - 2*a^4*d^4)*e^2*f + 60*(4*a^3*b*c^2*d^2 - a^4*c*d^3)*e*f^2 + ((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e^3 + 3*(b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e^2*f + 3*(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e*f^2)*m^3 + 3*((4*b^4*c^3*d - 9*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - a^3*b*d^4)*e^3 + (8*b^4*c^4 - 14*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 - 7*a^4*d^4)*e^2*f + 5*(a*b^3*c^4 - 4*a^2*b^2*c^3*d + 5*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*e*f^2 - (a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*f^3)*m^2 + ((47*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 15*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*e^3 + 3*(19*b^4*c^4 - 36*a*b^3*c^3*d - 15*a^2*b^2*c^2*d^2 + 46*a^3*b*c*d^3 - 14*a^4*d^4)*e^2*f + 3*(4*a*b^3*c^4 - 41*a^2*b^2*c^3*d + 66*a^3*b*c^2*d^2 - 29*a^4*c*d^3)*e*f^2 - 3*(a^2*b^2*c^4 - 10*a^3*b*c^3*d + 9*a^4*c^2*d^2)*f^3)*m)*x^2 - ((26*a*b^3*c^4 - 57*a^2*b^2*c^3*d + 42*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e^3 - 3*(7*a^2*b^2*c^4 - 10*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e^2*f + 6*(a^3*b*c^4 - a^4*c^3*d)*e*f^2)*m + (30*a^4*c^3*d*f^3 - 6*(4*b^4*c^4 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*e^3 + 30*(6*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2 + a^4*c*d^3)*e^2*f - 30*(4*a^3*b*c^3*d - a^4*c^2*d^2)*e*f^2 - ((b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e^3 + 3*(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e^2*f)*m^3 - 3*((3*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 6*a^3*b*c*d^3 - 2*a^4*d^4)*e^3 + (7*a*b^3*c^4 - 22*a^2*b^2*c^3*d + 23*a^3*b*c^2*d^2 - 8*a^4*c*d^3)*e^2*f - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*e*f^2)*m^2 - ((26*b^4*c^4 - 10*a*b^3*c^3*d - 45*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 - 11*a^4*d^4)*e^3 + 3*(12*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 17*a^4*c*d^3)*e^2*f - 12*(2*a^2*b^2*c^4 - 5*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e*f^2 + 6*(a^3*b*c^4 - a^4*c^3*d)*f^3)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 5)/(24*b^4*c^4 - 96*a*b^3*c^3*d + 144*a^2*b^2*c^2*d^2 - 96*a^3*b*c*d^3 + 24*a^4*d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^4 + 10*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^3 + 35*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^2 + 50*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m)","B",0
3107,1,2662,0,1.686511," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e)^2,x, algorithm=""fricas"")","\frac{{\left({\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e^{2} m^{3} + {\left(6 \, b^{4} d^{4} e^{2} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} f^{2} m^{2} + 4 \, {\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} e f + 2 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3} + 6 \, a^{2} b^{2} d^{4}\right)} f^{2} + {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e f + {\left(3 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + 7 \, a^{2} b^{2} d^{4}\right)} f^{2}\right)} m\right)} x^{5} + {\left(30 \, b^{4} c d^{3} e^{2} + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} f^{2} m^{3} + 20 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3}\right)} e f + 10 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3}\right)} f^{2} + {\left(4 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e f + {\left(8 \, b^{4} c^{3} d - 23 \, a b^{3} c^{2} d^{2} + 22 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} f^{2}\right)} m^{2} + {\left(6 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e^{2} + 8 \, {\left(3 \, b^{4} c^{2} d^{2} - 5 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} e f + {\left(17 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 55 \, a^{2} b^{2} c d^{3} - 12 \, a^{3} b d^{4}\right)} f^{2}\right)} m\right)} x^{4} + {\left(60 \, b^{4} c^{2} d^{2} e^{2} + {\left(2 \, {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e f + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} f^{2}\right)} m^{3} + 40 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2}\right)} e f + 4 \, {\left(2 \, b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 12 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} f^{2} + {\left(3 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} + 10 \, {\left(2 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} + 4 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e f + {\left(7 \, b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 3 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 8 \, a^{4} d^{4}\right)} f^{2}\right)} m^{2} + {\left(3 \, {\left(9 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e^{2} + 2 \, {\left(29 \, b^{4} c^{3} d - 66 \, a b^{3} c^{2} d^{2} + 41 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} e f + {\left(14 \, b^{4} c^{4} - 46 \, a b^{3} c^{3} d + 15 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 19 \, a^{4} d^{4}\right)} f^{2}\right)} m\right)} x^{3} + 6 \, {\left(4 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e^{2} - 4 \, {\left(6 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e f + 2 \, {\left(4 \, a^{3} b c^{4} - a^{4} c^{3} d\right)} f^{2} + {\left(3 \, {\left(3 \, a b^{3} c^{4} - 8 \, a^{2} b^{2} c^{3} d + 7 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} e^{2} - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e f\right)} m^{2} + {\left(60 \, b^{4} c^{3} d e^{2} + {\left({\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{2} + 2 \, {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e f + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} f^{2}\right)} m^{3} + 8 \, {\left(3 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e f + 20 \, {\left(4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} f^{2} + {\left(3 \, {\left(4 \, b^{4} c^{3} d - 9 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e^{2} + 2 \, {\left(8 \, b^{4} c^{4} - 14 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} e f + 5 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b^{2} c^{3} d + 5 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} f^{2}\right)} m^{2} + {\left({\left(47 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 15 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} e^{2} + 2 \, {\left(19 \, b^{4} c^{4} - 36 \, a b^{3} c^{3} d - 15 \, a^{2} b^{2} c^{2} d^{2} + 46 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e f + {\left(4 \, a b^{3} c^{4} - 41 \, a^{2} b^{2} c^{3} d + 66 \, a^{3} b c^{2} d^{2} - 29 \, a^{4} c d^{3}\right)} f^{2}\right)} m\right)} x^{2} + {\left({\left(26 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d + 42 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e^{2} - 2 \, {\left(7 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e f + 2 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} f^{2}\right)} m + {\left({\left({\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e^{2} + 2 \, {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e f\right)} m^{3} + 6 \, {\left(4 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e^{2} - 20 \, {\left(6 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e f + 10 \, {\left(4 \, a^{3} b c^{3} d - a^{4} c^{2} d^{2}\right)} f^{2} + {\left(3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 6 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e^{2} + 2 \, {\left(7 \, a b^{3} c^{4} - 22 \, a^{2} b^{2} c^{3} d + 23 \, a^{3} b c^{2} d^{2} - 8 \, a^{4} c d^{3}\right)} e f - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f^{2}\right)} m^{2} + {\left({\left(26 \, b^{4} c^{4} - 10 \, a b^{3} c^{3} d - 45 \, a^{2} b^{2} c^{2} d^{2} + 40 \, a^{3} b c d^{3} - 11 \, a^{4} d^{4}\right)} e^{2} + 2 \, {\left(12 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 17 \, a^{4} c d^{3}\right)} e f - 4 \, {\left(2 \, a^{2} b^{2} c^{4} - 5 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{24 \, b^{4} c^{4} - 96 \, a b^{3} c^{3} d + 144 \, a^{2} b^{2} c^{2} d^{2} - 96 \, a^{3} b c d^{3} + 24 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{4} + 10 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{3} + 35 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{2} + 50 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m}"," ",0,"((a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e^2*m^3 + (6*b^4*d^4*e^2 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*f^2*m^2 + 4*(b^4*c*d^3 - 4*a*b^3*d^4)*e*f + 2*(b^4*c^2*d^2 - 4*a*b^3*c*d^3 + 6*a^2*b^2*d^4)*f^2 + (4*(b^4*c*d^3 - a*b^3*d^4)*e*f + (3*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + 7*a^2*b^2*d^4)*f^2)*m)*x^5 + (30*b^4*c*d^3*e^2 + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*f^2*m^3 + 20*(b^4*c^2*d^2 - 4*a*b^3*c*d^3)*e*f + 10*(b^4*c^3*d - 4*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3)*f^2 + (4*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e*f + (8*b^4*c^3*d - 23*a*b^3*c^2*d^2 + 22*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*f^2)*m^2 + (6*(b^4*c*d^3 - a*b^3*d^4)*e^2 + 8*(3*b^4*c^2*d^2 - 5*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*e*f + (17*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 55*a^2*b^2*c*d^3 - 12*a^3*b*d^4)*f^2)*m)*x^4 + (60*b^4*c^2*d^2*e^2 + (2*(b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e*f + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*f^2)*m^3 + 40*(b^4*c^3*d - 4*a*b^3*c^2*d^2)*e*f + 4*(2*b^4*c^4 - 8*a*b^3*c^3*d + 12*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 3*a^4*d^4)*f^2 + (3*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 + 10*(2*b^4*c^3*d - 5*a*b^3*c^2*d^2 + 4*a^2*b^2*c*d^3 - a^3*b*d^4)*e*f + (7*b^4*c^4 - 16*a*b^3*c^3*d + 3*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 8*a^4*d^4)*f^2)*m^2 + (3*(9*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + a^2*b^2*d^4)*e^2 + 2*(29*b^4*c^3*d - 66*a*b^3*c^2*d^2 + 41*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*e*f + (14*b^4*c^4 - 46*a*b^3*c^3*d + 15*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 19*a^4*d^4)*f^2)*m)*x^3 + 6*(4*a*b^3*c^4 - 6*a^2*b^2*c^3*d + 4*a^3*b*c^2*d^2 - a^4*c*d^3)*e^2 - 4*(6*a^2*b^2*c^4 - 4*a^3*b*c^3*d + a^4*c^2*d^2)*e*f + 2*(4*a^3*b*c^4 - a^4*c^3*d)*f^2 + (3*(3*a*b^3*c^4 - 8*a^2*b^2*c^3*d + 7*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*e^2 - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*e*f)*m^2 + (60*b^4*c^3*d*e^2 + ((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e^2 + 2*(b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e*f + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*f^2)*m^3 + 8*(3*b^4*c^4 - 12*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 - 2*a^4*d^4)*e*f + 20*(4*a^3*b*c^2*d^2 - a^4*c*d^3)*f^2 + (3*(4*b^4*c^3*d - 9*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - a^3*b*d^4)*e^2 + 2*(8*b^4*c^4 - 14*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 - 7*a^4*d^4)*e*f + 5*(a*b^3*c^4 - 4*a^2*b^2*c^3*d + 5*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*f^2)*m^2 + ((47*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 15*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*e^2 + 2*(19*b^4*c^4 - 36*a*b^3*c^3*d - 15*a^2*b^2*c^2*d^2 + 46*a^3*b*c*d^3 - 14*a^4*d^4)*e*f + (4*a*b^3*c^4 - 41*a^2*b^2*c^3*d + 66*a^3*b*c^2*d^2 - 29*a^4*c*d^3)*f^2)*m)*x^2 + ((26*a*b^3*c^4 - 57*a^2*b^2*c^3*d + 42*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e^2 - 2*(7*a^2*b^2*c^4 - 10*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e*f + 2*(a^3*b*c^4 - a^4*c^3*d)*f^2)*m + (((b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e^2 + 2*(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e*f)*m^3 + 6*(4*b^4*c^4 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*e^2 - 20*(6*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2 + a^4*c*d^3)*e*f + 10*(4*a^3*b*c^3*d - a^4*c^2*d^2)*f^2 + (3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 6*a^3*b*c*d^3 - 2*a^4*d^4)*e^2 + 2*(7*a*b^3*c^4 - 22*a^2*b^2*c^3*d + 23*a^3*b*c^2*d^2 - 8*a^4*c*d^3)*e*f - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*f^2)*m^2 + ((26*b^4*c^4 - 10*a*b^3*c^3*d - 45*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 - 11*a^4*d^4)*e^2 + 2*(12*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 17*a^4*c*d^3)*e*f - 4*(2*a^2*b^2*c^4 - 5*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 5)/(24*b^4*c^4 - 96*a*b^3*c^3*d + 144*a^2*b^2*c^2*d^2 - 96*a^3*b*c*d^3 + 24*a^4*d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^4 + 10*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^3 + 35*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^2 + 50*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m)","B",0
3108,1,1777,0,1.369596," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(3 \, b^{4} d^{4} e + {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f m + {\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} f\right)} x^{5} + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e m^{3} + 2 \, {\left(15 \, b^{4} c d^{3} e + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} f m^{2} + 5 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3}\right)} f + {\left(3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e + 2 \, {\left(3 \, b^{4} c^{2} d^{2} - 5 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} f\right)} m\right)} x^{4} + {\left(60 \, b^{4} c^{2} d^{2} e + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} f m^{3} + {\left(3 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e + 5 \, {\left(2 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} + 4 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} f\right)} m^{2} + 20 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2}\right)} f + {\left(3 \, {\left(9 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e + {\left(29 \, b^{4} c^{3} d - 66 \, a b^{3} c^{2} d^{2} + 41 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} f\right)} m\right)} x^{3} + {\left(3 \, {\left(3 \, a b^{3} c^{4} - 8 \, a^{2} b^{2} c^{3} d + 7 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} e - {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f\right)} m^{2} + {\left(60 \, b^{4} c^{3} d e + {\left({\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} f\right)} m^{3} + {\left(3 \, {\left(4 \, b^{4} c^{3} d - 9 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e + {\left(8 \, b^{4} c^{4} - 14 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} f\right)} m^{2} + 4 \, {\left(3 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} f + {\left({\left(47 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 15 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} e + {\left(19 \, b^{4} c^{4} - 36 \, a b^{3} c^{3} d - 15 \, a^{2} b^{2} c^{2} d^{2} + 46 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} f\right)} m\right)} x^{2} + 6 \, {\left(4 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e - 2 \, {\left(6 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f + {\left({\left(26 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d + 42 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e - {\left(7 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f\right)} m + {\left({\left({\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} f\right)} m^{3} + {\left(3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 6 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e + {\left(7 \, a b^{3} c^{4} - 22 \, a^{2} b^{2} c^{3} d + 23 \, a^{3} b c^{2} d^{2} - 8 \, a^{4} c d^{3}\right)} f\right)} m^{2} + 6 \, {\left(4 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e - 10 \, {\left(6 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f + {\left({\left(26 \, b^{4} c^{4} - 10 \, a b^{3} c^{3} d - 45 \, a^{2} b^{2} c^{2} d^{2} + 40 \, a^{3} b c d^{3} - 11 \, a^{4} d^{4}\right)} e + {\left(12 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 17 \, a^{4} c d^{3}\right)} f\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{24 \, b^{4} c^{4} - 96 \, a b^{3} c^{3} d + 144 \, a^{2} b^{2} c^{2} d^{2} - 96 \, a^{3} b c d^{3} + 24 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{4} + 10 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{3} + 35 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{2} + 50 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m}"," ",0,"(2*(3*b^4*d^4*e + (b^4*c*d^3 - a*b^3*d^4)*f*m + (b^4*c*d^3 - 4*a*b^3*d^4)*f)*x^5 + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*e*m^3 + 2*(15*b^4*c*d^3*e + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*f*m^2 + 5*(b^4*c^2*d^2 - 4*a*b^3*c*d^3)*f + (3*(b^4*c*d^3 - a*b^3*d^4)*e + 2*(3*b^4*c^2*d^2 - 5*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*f)*m)*x^4 + (60*b^4*c^2*d^2*e + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*f*m^3 + (3*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e + 5*(2*b^4*c^3*d - 5*a*b^3*c^2*d^2 + 4*a^2*b^2*c*d^3 - a^3*b*d^4)*f)*m^2 + 20*(b^4*c^3*d - 4*a*b^3*c^2*d^2)*f + (3*(9*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + a^2*b^2*d^4)*e + (29*b^4*c^3*d - 66*a*b^3*c^2*d^2 + 41*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*f)*m)*x^3 + (3*(3*a*b^3*c^4 - 8*a^2*b^2*c^3*d + 7*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*e - (a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*f)*m^2 + (60*b^4*c^3*d*e + ((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*e + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*f)*m^3 + (3*(4*b^4*c^3*d - 9*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - a^3*b*d^4)*e + (8*b^4*c^4 - 14*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 - 7*a^4*d^4)*f)*m^2 + 4*(3*b^4*c^4 - 12*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 - 2*a^4*d^4)*f + ((47*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 15*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*e + (19*b^4*c^4 - 36*a*b^3*c^3*d - 15*a^2*b^2*c^2*d^2 + 46*a^3*b*c*d^3 - 14*a^4*d^4)*f)*m)*x^2 + 6*(4*a*b^3*c^4 - 6*a^2*b^2*c^3*d + 4*a^3*b*c^2*d^2 - a^4*c*d^3)*e - 2*(6*a^2*b^2*c^4 - 4*a^3*b*c^3*d + a^4*c^2*d^2)*f + ((26*a*b^3*c^4 - 57*a^2*b^2*c^3*d + 42*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e - (7*a^2*b^2*c^4 - 10*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f)*m + (((b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*f)*m^3 + (3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 6*a^3*b*c*d^3 - 2*a^4*d^4)*e + (7*a*b^3*c^4 - 22*a^2*b^2*c^3*d + 23*a^3*b*c^2*d^2 - 8*a^4*c*d^3)*f)*m^2 + 6*(4*b^4*c^4 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*e - 10*(6*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2 + a^4*c*d^3)*f + ((26*b^4*c^4 - 10*a*b^3*c^3*d - 45*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 - 11*a^4*d^4)*e + (12*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 17*a^4*c*d^3)*f)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 5)/(24*b^4*c^4 - 96*a*b^3*c^3*d + 144*a^2*b^2*c^2*d^2 - 96*a^3*b*c*d^3 + 24*a^4*d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^4 + 10*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^3 + 35*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^2 + 50*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m)","B",0
3109,1,954,0,1.237059," ","integrate((b*x+a)^m*(d*x+c)^(-5-m),x, algorithm=""fricas"")","\frac{{\left(6 \, b^{4} d^{4} x^{5} + 24 \, a b^{3} c^{4} - 36 \, a^{2} b^{2} c^{3} d + 24 \, a^{3} b c^{2} d^{2} - 6 \, a^{4} c d^{3} + 6 \, {\left(5 \, b^{4} c d^{3} + {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} m\right)} x^{4} + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} m^{3} + 3 \, {\left(20 \, b^{4} c^{2} d^{2} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} m^{2} + {\left(9 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} m\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c^{4} - 8 \, a^{2} b^{2} c^{3} d + 7 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} m^{2} + {\left(60 \, b^{4} c^{3} d + {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} m^{3} + 3 \, {\left(4 \, b^{4} c^{3} d - 9 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} m^{2} + {\left(47 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 15 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} m\right)} x^{2} + {\left(26 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d + 42 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} m + {\left(24 \, b^{4} c^{4} + 24 \, a b^{3} c^{3} d - 36 \, a^{2} b^{2} c^{2} d^{2} + 24 \, a^{3} b c d^{3} - 6 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} m^{3} + 3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 6 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} m^{2} + {\left(26 \, b^{4} c^{4} - 10 \, a b^{3} c^{3} d - 45 \, a^{2} b^{2} c^{2} d^{2} + 40 \, a^{3} b c d^{3} - 11 \, a^{4} d^{4}\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{24 \, b^{4} c^{4} - 96 \, a b^{3} c^{3} d + 144 \, a^{2} b^{2} c^{2} d^{2} - 96 \, a^{3} b c d^{3} + 24 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{4} + 10 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{3} + 35 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{2} + 50 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m}"," ",0,"(6*b^4*d^4*x^5 + 24*a*b^3*c^4 - 36*a^2*b^2*c^3*d + 24*a^3*b*c^2*d^2 - 6*a^4*c*d^3 + 6*(5*b^4*c*d^3 + (b^4*c*d^3 - a*b^3*d^4)*m)*x^4 + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*m^3 + 3*(20*b^4*c^2*d^2 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*m^2 + (9*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + a^2*b^2*d^4)*m)*x^3 + 3*(3*a*b^3*c^4 - 8*a^2*b^2*c^3*d + 7*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*m^2 + (60*b^4*c^3*d + (b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*m^3 + 3*(4*b^4*c^3*d - 9*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - a^3*b*d^4)*m^2 + (47*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 15*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*m)*x^2 + (26*a*b^3*c^4 - 57*a^2*b^2*c^3*d + 42*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*m + (24*b^4*c^4 + 24*a*b^3*c^3*d - 36*a^2*b^2*c^2*d^2 + 24*a^3*b*c*d^3 - 6*a^4*d^4 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*m^3 + 3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 6*a^3*b*c*d^3 - 2*a^4*d^4)*m^2 + (26*b^4*c^4 - 10*a*b^3*c^3*d - 45*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 - 11*a^4*d^4)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 5)/(24*b^4*c^4 - 96*a*b^3*c^3*d + 144*a^2*b^2*c^2*d^2 - 96*a^3*b*c*d^3 + 24*a^4*d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^4 + 10*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^3 + 35*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^2 + 50*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m)","B",0
3110,0,0,0,1.181655," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 5)/(f*x + e), x)","F",0
3111,0,0,0,1.431668," ","integrate((b*x+a)^m*(d*x+c)^(1-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)*(f*x + e)^p, x)","F",0
3112,0,0,0,1.143157," ","integrate((b*x+a)^m*(d*x+c)^(1-m)*(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}, x\right)"," ",0,"integral((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*(b*x + a)^m*(d*x + c)^(-m + 1), x)","F",0
3113,0,0,0,1.151781," ","integrate((b*x+a)^m*(d*x+c)^(1-m)*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m*(d*x + c)^(-m + 1), x)","F",0
3114,0,0,0,0.945354," ","integrate((b*x+a)^m*(d*x+c)^(1-m)*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m*(d*x + c)^(-m + 1), x)","F",0
3115,0,0,0,1.391199," ","integrate((b*x+a)^m*(d*x+c)^(1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1), x)","F",0
3116,0,0,0,1.119580," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f*x + e), x)","F",0
3117,0,0,0,1.200686," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3118,0,0,0,1.182975," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3119,0,0,0,1.479051," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f^{4} x^{4} + 4 \, e f^{3} x^{3} + 6 \, e^{2} f^{2} x^{2} + 4 \, e^{3} f x + e^{4}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f^4*x^4 + 4*e*f^3*x^3 + 6*e^2*f^2*x^2 + 4*e^3*f*x + e^4), x)","F",0
3120,0,0,0,1.695887," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e)^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f^{5} x^{5} + 5 \, e f^{4} x^{4} + 10 \, e^{2} f^{3} x^{3} + 10 \, e^{3} f^{2} x^{2} + 5 \, e^{4} f x + e^{5}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f^5*x^5 + 5*e*f^4*x^4 + 10*e^2*f^3*x^3 + 10*e^3*f^2*x^2 + 5*e^4*f*x + e^5), x)","F",0
3121,0,0,0,1.617213," ","integrate((b*x+a)^m*(d*x+c)^(1-m)/(f*x+e)^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}}{f^{6} x^{6} + 6 \, e f^{5} x^{5} + 15 \, e^{2} f^{4} x^{4} + 20 \, e^{3} f^{3} x^{3} + 15 \, e^{4} f^{2} x^{2} + 6 \, e^{5} f x + e^{6}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 1)/(f^6*x^6 + 6*e*f^5*x^5 + 15*e^2*f^4*x^4 + 20*e^3*f^3*x^3 + 15*e^4*f^2*x^2 + 6*e^5*f*x + e^6), x)","F",0
3122,0,0,0,1.188752," ","integrate((b*x+a)^m*(d*x+c)^(2-m)*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)*(f*x + e)^p, x)","F",0
3123,0,0,0,0.953912," ","integrate((b*x+a)^m*(d*x+c)^(2-m)*(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}, x\right)"," ",0,"integral((f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3)*(b*x + a)^m*(d*x + c)^(-m + 2), x)","F",0
3124,0,0,0,0.937837," ","integrate((b*x+a)^m*(d*x+c)^(2-m)*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m*(d*x + c)^(-m + 2), x)","F",0
3125,0,0,0,1.212831," ","integrate((b*x+a)^m*(d*x+c)^(2-m)*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m*(d*x + c)^(-m + 2), x)","F",0
3126,0,0,0,0.919640," ","integrate((b*x+a)^m*(d*x+c)^(2-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2), x)","F",0
3127,0,0,0,1.177290," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f*x + e), x)","F",0
3128,0,0,0,1.004597," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3129,0,0,0,1.041486," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3130,0,0,0,1.394034," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{4} x^{4} + 4 \, e f^{3} x^{3} + 6 \, e^{2} f^{2} x^{2} + 4 \, e^{3} f x + e^{4}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^4*x^4 + 4*e*f^3*x^3 + 6*e^2*f^2*x^2 + 4*e^3*f*x + e^4), x)","F",0
3131,0,0,0,1.605983," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{5} x^{5} + 5 \, e f^{4} x^{4} + 10 \, e^{2} f^{3} x^{3} + 10 \, e^{3} f^{2} x^{2} + 5 \, e^{4} f x + e^{5}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^5*x^5 + 5*e*f^4*x^4 + 10*e^2*f^3*x^3 + 10*e^3*f^2*x^2 + 5*e^4*f*x + e^5), x)","F",0
3132,0,0,0,1.967263," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{6} x^{6} + 6 \, e f^{5} x^{5} + 15 \, e^{2} f^{4} x^{4} + 20 \, e^{3} f^{3} x^{3} + 15 \, e^{4} f^{2} x^{2} + 6 \, e^{5} f x + e^{6}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^6*x^6 + 6*e*f^5*x^5 + 15*e^2*f^4*x^4 + 20*e^3*f^3*x^3 + 15*e^4*f^2*x^2 + 6*e^5*f*x + e^6), x)","F",0
3133,0,0,0,1.628228," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(f*x+e)^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{f^{7} x^{7} + 7 \, e f^{6} x^{6} + 21 \, e^{2} f^{5} x^{5} + 35 \, e^{3} f^{4} x^{4} + 35 \, e^{4} f^{3} x^{3} + 21 \, e^{5} f^{2} x^{2} + 7 \, e^{6} f x + e^{7}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(f^7*x^7 + 7*e*f^6*x^6 + 21*e^2*f^5*x^5 + 35*e^3*f^4*x^4 + 35*e^4*f^3*x^3 + 21*e^5*f^2*x^2 + 7*e^6*f*x + e^7), x)","F",0
3134,0,0,0,1.210487," ","integrate((b*x+a)^m*(d*x+c)^(3-m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 3}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 3)/(f*x + e), x)","F",0
3135,0,0,0,0.986863," ","integrate((b*x+a)^m*(d*x+c)^(3-m)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 3}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 3)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3136,0,0,0,1.290231," ","integrate((b*x+a)^m*(d*x+c)^(3-m)/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 3}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 3)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3137,0,0,0,0.774523," ","integrate((b*x+a)^(1-n)*(d*x+c)^(1+n)/(2*b*d*x+a*d+b*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{-n + 1} {\left(d x + c\right)}^{n + 1}}{2 \, b d x + b c + a d}, x\right)"," ",0,"integral((b*x + a)^(-n + 1)*(d*x + c)^(n + 1)/(2*b*d*x + b*c + a*d), x)","F",0
3138,0,0,0,0.846168," ","integrate((b*x+a)^(1-n)*(d*x+c)^(1+n)/(2*b*d*x+a*d+b*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{-n + 1} {\left(d x + c\right)}^{n + 1}}{4 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2} + 4 \, {\left(b^{2} c d + a b d^{2}\right)} x}, x\right)"," ",0,"integral((b*x + a)^(-n + 1)*(d*x + c)^(n + 1)/(4*b^2*d^2*x^2 + b^2*c^2 + 2*a*b*c*d + a^2*d^2 + 4*(b^2*c*d + a*b*d^2)*x), x)","F",0
3139,0,0,0,1.146156," ","integrate((b*x+a)^(1-n)*(d*x+c)^(1+n)/(2*b*d*x+a*d+b*c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{-n + 1} {\left(d x + c\right)}^{n + 1}}{8 \, b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3} + 12 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}, x\right)"," ",0,"integral((b*x + a)^(-n + 1)*(d*x + c)^(n + 1)/(8*b^3*d^3*x^3 + b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3 + 12*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 6*(b^3*c^2*d + 2*a*b^2*c*d^2 + a^2*b*d^3)*x), x)","F",0
3140,0,0,0,1.364304," ","integrate((b*x+a)^(1-n)*(d*x+c)^(1+n)/(2*b*d*x+a*d+b*c)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{-n + 1} {\left(d x + c\right)}^{n + 1}}{16 \, b^{4} d^{4} x^{4} + b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + a^{4} d^{4} + 32 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 24 \, {\left(b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 8 \, {\left(b^{4} c^{3} d + 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x}, x\right)"," ",0,"integral((b*x + a)^(-n + 1)*(d*x + c)^(n + 1)/(16*b^4*d^4*x^4 + b^4*c^4 + 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + a^4*d^4 + 32*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 24*(b^4*c^2*d^2 + 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 8*(b^4*c^3*d + 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 + a^3*b*d^4)*x), x)","F",0
3141,0,0,0,1.687464," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(2*b*d*x+a*d+b*c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{2 \, b d x + b c + a d}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(2*b*d*x + b*c + a*d), x)","F",0
3142,0,0,0,1.082869," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(2*b*d*x+a*d+b*c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{4 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2} + 4 \, {\left(b^{2} c d + a b d^{2}\right)} x}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(4*b^2*d^2*x^2 + b^2*c^2 + 2*a*b*c*d + a^2*d^2 + 4*(b^2*c*d + a*b*d^2)*x), x)","F",0
3143,0,0,0,0.796821," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(2*b*d*x+a*d+b*c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{8 \, b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3} + 12 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(8*b^3*d^3*x^3 + b^3*c^3 + 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3 + 12*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 6*(b^3*c^2*d + 2*a*b^2*c*d^2 + a^2*b*d^3)*x), x)","F",0
3144,0,0,0,1.191080," ","integrate((b*x+a)^m*(d*x+c)^(2-m)/(2*b*d*x+a*d+b*c)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 2}}{16 \, b^{4} d^{4} x^{4} + b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} + a^{4} d^{4} + 32 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 24 \, {\left(b^{4} c^{2} d^{2} + 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 8 \, {\left(b^{4} c^{3} d + 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m + 2)/(16*b^4*d^4*x^4 + b^4*c^4 + 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 + a^4*d^4 + 32*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 24*(b^4*c^2*d^2 + 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 8*(b^4*c^3*d + 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 + a^3*b*d^4)*x), x)","F",0
3145,0,0,0,1.755583," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(n+p),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n + p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n + p), x)","F",0
3146,0,0,0,1.244389," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(1+n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n + 1}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n + 1), x)","F",0
3147,0,0,0,1.166680," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^n, x)","F",0
3148,0,0,0,1.823697," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(-1+n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n - 1}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n - 1), x)","F",0
3149,0,0,0,1.354960," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(-2+n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n - 2}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n - 2), x)","F",0
3150,0,0,0,2.383225," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(-3+n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n - 3}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n - 3), x)","F",0
3151,0,0,0,2.142377," ","integrate((b*x+a)^m*(d*x+c)^(-m-n)*(f*x+e)^(-4+n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - n} {\left(f x + e\right)}^{n - 4}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - n)*(f*x + e)^(n - 4), x)","F",0
3152,1,332,0,1.384572," ","integrate((b*x+a)^m*(d*x+c)^n*((a*d*f*m+b*c*f*n+a*d*f+b*c*f)/b/d/(2+m+n)+f*x)^(-3-m-n),x, algorithm=""fricas"")","\frac{{\left(a^{2} c d m + a b c^{2} n + a b c^{2} + a^{2} c d + {\left(b^{2} d^{2} m + b^{2} d^{2} n + 2 \, b^{2} d^{2}\right)} x^{3} + {\left(3 \, b^{2} c d + 3 \, a b d^{2} + {\left(b^{2} c d + 2 \, a b d^{2}\right)} m + {\left(2 \, b^{2} c d + a b d^{2}\right)} n\right)} x^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2} + {\left(2 \, a b c d + a^{2} d^{2}\right)} m + {\left(b^{2} c^{2} + 2 \, a b c d\right)} n\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} \left(\frac{a d f m + b c f n + {\left(b c + a d\right)} f + {\left(b d f m + b d f n + 2 \, b d f\right)} x}{b d m + b d n + 2 \, b d}\right)^{-m - n - 3}}{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} m\right)} n}"," ",0,"(a^2*c*d*m + a*b*c^2*n + a*b*c^2 + a^2*c*d + (b^2*d^2*m + b^2*d^2*n + 2*b^2*d^2)*x^3 + (3*b^2*c*d + 3*a*b*d^2 + (b^2*c*d + 2*a*b*d^2)*m + (2*b^2*c*d + a*b*d^2)*n)*x^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2 + (2*a*b*c*d + a^2*d^2)*m + (b^2*c^2 + 2*a*b*c*d)*n)*x)*(b*x + a)^m*(d*x + c)^n*((a*d*f*m + b*c*f*n + (b*c + a*d)*f + (b*d*f*m + b*d*f*n + 2*b*d*f)*x)/(b*d*m + b*d*n + 2*b*d))^(-m - n - 3)/(b^2*c^2 - 2*a*b*c*d + a^2*d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*m)*n)","B",0
3153,1,225,0,1.580838," ","integrate((b*x+a)^m*(d*x+c)^(-1-d*(-a*f+b*e)*(1+m)/b/(-c*f+d*e))*(f*x+e)^(-1+(-a*d+b*c)*f*(1+m)/b/(-c*f+d*e)),x, algorithm=""fricas"")","\frac{{\left(b^{2} d f x^{3} + a b c e + {\left(b^{2} d e + {\left(b^{2} c + a b d\right)} f\right)} x^{2} + {\left(a b c f + {\left(b^{2} c + a b d\right)} e\right)} x\right)} {\left(b x + a\right)}^{m}}{{\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f + {\left({\left(b^{2} c - a b d\right)} e - {\left(a b c - a^{2} d\right)} f\right)} m\right)} {\left(d x + c\right)}^{\frac{2 \, b d e - {\left(b c + a d\right)} f + {\left(b d e - a d f\right)} m}{b d e - b c f}} {\left(f x + e\right)}^{\frac{b d e - {\left(b c - a d\right)} f m - {\left(2 \, b c - a d\right)} f}{b d e - b c f}}}"," ",0,"(b^2*d*f*x^3 + a*b*c*e + (b^2*d*e + (b^2*c + a*b*d)*f)*x^2 + (a*b*c*f + (b^2*c + a*b*d)*e)*x)*(b*x + a)^m/(((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f + ((b^2*c - a*b*d)*e - (a*b*c - a^2*d)*f)*m)*(d*x + c)^((2*b*d*e - (b*c + a*d)*f + (b*d*e - a*d*f)*m)/(b*d*e - b*c*f))*(f*x + e)^((b*d*e - (b*c - a*d)*f*m - (2*b*c - a*d)*f)/(b*d*e - b*c*f)))","B",0
3154,0,0,0,1.103404," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^(-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n), x)","F",0
3155,0,0,0,1.762764," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^(-1-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 1}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 1), x)","F",0
3156,0,0,0,1.974639," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^(-2-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 2}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 2), x)","F",0
3157,0,0,0,2.144857," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^(-3-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 3}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 3), x)","F",0
3158,0,0,0,3.196511," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^(-4-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 4}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 4), x)","F",0
3159,0,0,0,1.421767," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
3160,0,0,0,1.104233," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(f^{2} x^{2} + 2 \, e f x + e^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)*(b*x + a)^m*(d*x + c)^n, x)","F",0
3161,0,0,0,1.084566," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((f*x + e)*(b*x + a)^m*(d*x + c)^n, x)","F",0
3162,0,0,0,1.250834," ","integrate((b*x+a)^m*(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n, x)","F",0
3163,0,0,0,1.225351," ","integrate((b*x+a)^m*(d*x+c)^n/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}}{f x + e}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n/(f*x + e), x)","F",0
3164,0,0,0,1.255640," ","integrate((b*x+a)^m*(d*x+c)^n/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3165,0,0,0,1.176835," ","integrate((b*x+a)^m*(d*x+c)^n/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
3166,0,0,0,0.747232," ","integrate((3+4*x)^n/(1-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, x + 3\right)}^{n} \sqrt{x + 1} \sqrt{-x + 1}}{x^{2} - 1}, x\right)"," ",0,"integral(-(4*x + 3)^n*sqrt(x + 1)*sqrt(-x + 1)/(x^2 - 1), x)","F",0
3167,0,0,0,1.167597," ","integrate((3-4*x)^n/(1-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 1} \sqrt{-x + 1} {\left(-4 \, x + 3\right)}^{n}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(x + 1)*sqrt(-x + 1)*(-4*x + 3)^n/(x^2 - 1), x)","F",0
3168,0,0,0,0.863129," ","integrate((-3+4*x)^n/(1-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, x - 3\right)}^{n} \sqrt{x + 1} \sqrt{-x + 1}}{x^{2} - 1}, x\right)"," ",0,"integral(-(4*x - 3)^n*sqrt(x + 1)*sqrt(-x + 1)/(x^2 - 1), x)","F",0
3169,0,0,0,1.125505," ","integrate((-3-4*x)^n/(1-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x + 1} \sqrt{-x + 1} {\left(-4 \, x - 3\right)}^{n}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(x + 1)*sqrt(-x + 1)*(-4*x - 3)^n/(x^2 - 1), x)","F",0
3170,-1,0,0,0.000000," ","integrate((b*x+a)^(4/3)/(f*x+e)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3171,-1,0,0,0.000000," ","integrate((d*x+c)^(2/5)*(f*x+e)^(3/5)/(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3172,0,0,0,1.584867," ","integrate((f*x+e)^n*(b*x+a)^(1/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} {\left(f x + e\right)}^{n}}{\sqrt{d x + c}}, x\right)"," ",0,"integral(sqrt(b*x + a)*(f*x + e)^n/sqrt(d*x + c), x)","F",0
3173,0,0,0,1.640063," ","integrate((f*x+e)^n*(d*x+c)^(1/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c} {\left(f x + e\right)}^{n}}{\sqrt{b x + a}}, x\right)"," ",0,"integral(sqrt(d*x + c)*(f*x + e)^n/sqrt(b*x + a), x)","F",0
3174,0,0,0,1.575552," ","integrate((f*x+e)^n/(d*x+c)^(3/2)/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} {\left(f x + e\right)}^{n}}{b d^{2} x^{3} + a c^{2} + {\left(2 \, b c d + a d^{2}\right)} x^{2} + {\left(b c^{2} + 2 \, a c d\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*(f*x + e)^n/(b*d^2*x^3 + a*c^2 + (2*b*c*d + a*d^2)*x^2 + (b*c^2 + 2*a*c*d)*x), x)","F",0
3175,0,0,0,1.525634," ","integrate((f*x+e)^n/(b*x+a)^(3/2)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} {\left(f x + e\right)}^{n}}{b^{2} d x^{3} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} x^{2} + {\left(2 \, a b c + a^{2} d\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*(f*x + e)^n/(b^2*d*x^3 + a^2*c + (b^2*c + 2*a*b*d)*x^2 + (2*a*b*c + a^2*d)*x), x)","F",0
3176,-1,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/3)/(f*x+e),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3177,-1,0,0,0.000000," ","integrate((b*x+a)^(1/3)*(d*x+c)^(1/2)/(f*x+e),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3178,-1,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/3)*(f*x+e)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3179,-1,0,0,0.000000," ","integrate((b*x+a)^(1/3)*(d*x+c)^(1/2)*(f*x+e)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3180,1,2274,0,2.028080," ","integrate((b*x+a)^4*(B*x+A)*(e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(A a^{4} d e^{5} m^{5} - 120 \, B b^{4} d^{6} + 720 \, A a^{4} d e^{5} + 144 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e - 360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 480 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 360 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4} + {\left(B b^{4} e^{6} m^{5} + 15 \, B b^{4} e^{6} m^{4} + 85 \, B b^{4} e^{6} m^{3} + 225 \, B b^{4} e^{6} m^{2} + 274 \, B b^{4} e^{6} m + 120 \, B b^{4} e^{6}\right)} x^{6} + {\left(144 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6} + {\left(B b^{4} d e^{5} + {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{5} + 2 \, {\left(5 \, B b^{4} d e^{5} + 8 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{4} + 5 \, {\left(7 \, B b^{4} d e^{5} + 19 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{3} + 10 \, {\left(5 \, B b^{4} d e^{5} + 26 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m^{2} + 12 \, {\left(2 \, B b^{4} d e^{5} + 27 \, {\left(4 \, B a b^{3} + A b^{4}\right)} e^{6}\right)} m\right)} x^{5} + {\left(20 \, A a^{4} d e^{5} - {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{4} + {\left(360 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6} + {\left({\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} + 2 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{5} - {\left(5 \, B b^{4} d^{2} e^{4} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 34 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{4} - {\left(30 \, B b^{4} d^{2} e^{4} - 47 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 214 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{3} - {\left(55 \, B b^{4} d^{2} e^{4} - 72 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 614 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m^{2} - 6 \, {\left(5 \, B b^{4} d^{2} e^{4} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d e^{5} - 132 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} e^{6}\right)} m\right)} x^{4} + {\left(155 \, A a^{4} d e^{5} + 4 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 18 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{3} + 2 \, {\left(240 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6} + {\left({\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{5} - 2 \, {\left({\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} - 7 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} - 9 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{4} + {\left(10 \, B b^{4} d^{3} e^{3} - 18 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 65 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 121 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{3} + 2 \, {\left(15 \, B b^{4} d^{3} e^{3} - 20 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 56 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 186 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m^{2} + 4 \, {\left(5 \, B b^{4} d^{3} e^{3} - 6 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{2} e^{4} + 15 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d e^{5} + 127 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} e^{6}\right)} m\right)} x^{3} + {\left(580 \, A a^{4} d e^{5} - 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 60 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 119 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m^{2} + {\left(360 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6} + {\left(2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} + {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{5} - {\left(6 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 32 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 19 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{4} + {\left(12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} - 72 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} + 178 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} + 137 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{3} - {\left(60 \, B b^{4} d^{4} e^{2} - 84 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} + 246 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 388 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 461 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m^{2} - 6 \, {\left(10 \, B b^{4} d^{4} e^{2} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{3} e^{3} + 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{2} e^{4} - 40 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d e^{5} - 117 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} e^{6}\right)} m\right)} x^{2} + 2 \, {\left(522 \, A a^{4} d e^{5} + 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{5} e - 66 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{4} e^{2} + 148 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{3} e^{3} - 171 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d^{2} e^{4}\right)} m + {\left(720 \, A a^{4} e^{6} + {\left(A a^{4} e^{6} + {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{5} + 2 \, {\left(10 \, A a^{4} e^{6} - 2 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 9 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{4} + {\left(155 \, A a^{4} e^{6} + 12 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 60 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 119 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{3} + 2 \, {\left(290 \, A a^{4} e^{6} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{2} + 66 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 148 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 171 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m^{2} + 12 \, {\left(10 \, B b^{4} d^{5} e + 87 \, A a^{4} e^{6} - 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} d^{4} e^{2} + 30 \, {\left(3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right)} d^{3} e^{3} - 40 \, {\left(2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right)} d^{2} e^{4} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} d e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(A*a^4*d*e^5*m^5 - 120*B*b^4*d^6 + 720*A*a^4*d*e^5 + 144*(4*B*a*b^3 + A*b^4)*d^5*e - 360*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 480*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 360*(B*a^4 + 4*A*a^3*b)*d^2*e^4 + (B*b^4*e^6*m^5 + 15*B*b^4*e^6*m^4 + 85*B*b^4*e^6*m^3 + 225*B*b^4*e^6*m^2 + 274*B*b^4*e^6*m + 120*B*b^4*e^6)*x^6 + (144*(4*B*a*b^3 + A*b^4)*e^6 + (B*b^4*d*e^5 + (4*B*a*b^3 + A*b^4)*e^6)*m^5 + 2*(5*B*b^4*d*e^5 + 8*(4*B*a*b^3 + A*b^4)*e^6)*m^4 + 5*(7*B*b^4*d*e^5 + 19*(4*B*a*b^3 + A*b^4)*e^6)*m^3 + 10*(5*B*b^4*d*e^5 + 26*(4*B*a*b^3 + A*b^4)*e^6)*m^2 + 12*(2*B*b^4*d*e^5 + 27*(4*B*a*b^3 + A*b^4)*e^6)*m)*x^5 + (20*A*a^4*d*e^5 - (B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^4 + (360*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6 + ((4*B*a*b^3 + A*b^4)*d*e^5 + 2*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^5 - (5*B*b^4*d^2*e^4 - 12*(4*B*a*b^3 + A*b^4)*d*e^5 - 34*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^4 - (30*B*b^4*d^2*e^4 - 47*(4*B*a*b^3 + A*b^4)*d*e^5 - 214*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^3 - (55*B*b^4*d^2*e^4 - 72*(4*B*a*b^3 + A*b^4)*d*e^5 - 614*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m^2 - 6*(5*B*b^4*d^2*e^4 - 6*(4*B*a*b^3 + A*b^4)*d*e^5 - 132*(3*B*a^2*b^2 + 2*A*a*b^3)*e^6)*m)*x^4 + (155*A*a^4*d*e^5 + 4*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 18*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^3 + 2*(240*(2*B*a^3*b + 3*A*a^2*b^2)*e^6 + ((3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + (2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^5 - 2*((4*B*a*b^3 + A*b^4)*d^2*e^4 - 7*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 - 9*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^4 + (10*B*b^4*d^3*e^3 - 18*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 65*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 121*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^3 + 2*(15*B*b^4*d^3*e^3 - 20*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 56*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 186*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m^2 + 4*(5*B*b^4*d^3*e^3 - 6*(4*B*a*b^3 + A*b^4)*d^2*e^4 + 15*(3*B*a^2*b^2 + 2*A*a*b^3)*d*e^5 + 127*(2*B*a^3*b + 3*A*a^2*b^2)*e^6)*m)*x^3 + (580*A*a^4*d*e^5 - 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 119*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m^2 + (360*(B*a^4 + 4*A*a^3*b)*e^6 + (2*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + (B*a^4 + 4*A*a^3*b)*e^6)*m^5 - (6*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 32*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 19*(B*a^4 + 4*A*a^3*b)*e^6)*m^4 + (12*(4*B*a*b^3 + A*b^4)*d^3*e^3 - 72*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 + 178*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 + 137*(B*a^4 + 4*A*a^3*b)*e^6)*m^3 - (60*B*b^4*d^4*e^2 - 84*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 246*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 388*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 461*(B*a^4 + 4*A*a^3*b)*e^6)*m^2 - 6*(10*B*b^4*d^4*e^2 - 12*(4*B*a*b^3 + A*b^4)*d^3*e^3 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^2*e^4 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*d*e^5 - 117*(B*a^4 + 4*A*a^3*b)*e^6)*m)*x^2 + 2*(522*A*a^4*d*e^5 + 12*(4*B*a*b^3 + A*b^4)*d^5*e - 66*(3*B*a^2*b^2 + 2*A*a*b^3)*d^4*e^2 + 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^3*e^3 - 171*(B*a^4 + 4*A*a^3*b)*d^2*e^4)*m + (720*A*a^4*e^6 + (A*a^4*e^6 + (B*a^4 + 4*A*a^3*b)*d*e^5)*m^5 + 2*(10*A*a^4*e^6 - 2*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 9*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^4 + (155*A*a^4*e^6 + 12*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 60*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 119*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^3 + 2*(290*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 66*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 148*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 171*(B*a^4 + 4*A*a^3*b)*d*e^5)*m^2 + 12*(10*B*b^4*d^5*e + 87*A*a^4*e^6 - 12*(4*B*a*b^3 + A*b^4)*d^4*e^2 + 30*(3*B*a^2*b^2 + 2*A*a*b^3)*d^3*e^3 - 40*(2*B*a^3*b + 3*A*a^2*b^2)*d^2*e^4 + 30*(B*a^4 + 4*A*a^3*b)*d*e^5)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
3181,1,1282,0,1.080973," ","integrate((b*x+a)^3*(B*x+A)*(e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(A a^{3} d e^{4} m^{4} + 24 \, B b^{3} d^{5} + 120 \, A a^{3} d e^{4} - 30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 120 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3} + {\left(B b^{3} e^{5} m^{4} + 10 \, B b^{3} e^{5} m^{3} + 35 \, B b^{3} e^{5} m^{2} + 50 \, B b^{3} e^{5} m + 24 \, B b^{3} e^{5}\right)} x^{5} + {\left(30 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5} + {\left(B b^{3} d e^{4} + {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{4} + {\left(6 \, B b^{3} d e^{4} + 11 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{3} + {\left(11 \, B b^{3} d e^{4} + 41 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m^{2} + {\left(6 \, B b^{3} d e^{4} + 61 \, {\left(3 \, B a b^{2} + A b^{3}\right)} e^{5}\right)} m\right)} x^{4} + {\left(14 \, A a^{3} d e^{4} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m^{3} + {\left(120 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5} + {\left({\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} + 3 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{4} - 4 \, {\left(B b^{3} d^{2} e^{3} - 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 9 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{3} - {\left(12 \, B b^{3} d^{2} e^{3} - 17 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 147 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m^{2} - 2 \, {\left(4 \, B b^{3} d^{2} e^{3} - 5 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d e^{4} - 117 \, {\left(B a^{2} b + A a b^{2}\right)} e^{5}\right)} m\right)} x^{3} + {\left(71 \, A a^{3} d e^{4} + 6 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m^{2} + {\left(60 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5} + {\left(3 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{4} - {\left(3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} - 30 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} - 13 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{3} + {\left(12 \, B b^{3} d^{3} e^{2} - 18 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 87 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 59 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m^{2} + {\left(12 \, B b^{3} d^{3} e^{2} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{2} e^{3} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d e^{4} + 107 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} e^{5}\right)} m\right)} x^{2} + {\left(154 \, A a^{3} d e^{4} - 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{4} e + 54 \, {\left(B a^{2} b + A a b^{2}\right)} d^{3} e^{2} - 47 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{2} e^{3}\right)} m + {\left(120 \, A a^{3} e^{5} + {\left(A a^{3} e^{5} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{4} + 2 \, {\left(7 \, A a^{3} e^{5} - 3 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} + 6 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{3} + {\left(71 \, A a^{3} e^{5} + 6 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} - 54 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} + 47 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m^{2} - 2 \, {\left(12 \, B b^{3} d^{4} e - 77 \, A a^{3} e^{5} - 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} d^{3} e^{2} + 60 \, {\left(B a^{2} b + A a b^{2}\right)} d^{2} e^{3} - 30 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(A*a^3*d*e^4*m^4 + 24*B*b^3*d^5 + 120*A*a^3*d*e^4 - 30*(3*B*a*b^2 + A*b^3)*d^4*e + 120*(B*a^2*b + A*a*b^2)*d^3*e^2 - 60*(B*a^3 + 3*A*a^2*b)*d^2*e^3 + (B*b^3*e^5*m^4 + 10*B*b^3*e^5*m^3 + 35*B*b^3*e^5*m^2 + 50*B*b^3*e^5*m + 24*B*b^3*e^5)*x^5 + (30*(3*B*a*b^2 + A*b^3)*e^5 + (B*b^3*d*e^4 + (3*B*a*b^2 + A*b^3)*e^5)*m^4 + (6*B*b^3*d*e^4 + 11*(3*B*a*b^2 + A*b^3)*e^5)*m^3 + (11*B*b^3*d*e^4 + 41*(3*B*a*b^2 + A*b^3)*e^5)*m^2 + (6*B*b^3*d*e^4 + 61*(3*B*a*b^2 + A*b^3)*e^5)*m)*x^4 + (14*A*a^3*d*e^4 - (B*a^3 + 3*A*a^2*b)*d^2*e^3)*m^3 + (120*(B*a^2*b + A*a*b^2)*e^5 + ((3*B*a*b^2 + A*b^3)*d*e^4 + 3*(B*a^2*b + A*a*b^2)*e^5)*m^4 - 4*(B*b^3*d^2*e^3 - 2*(3*B*a*b^2 + A*b^3)*d*e^4 - 9*(B*a^2*b + A*a*b^2)*e^5)*m^3 - (12*B*b^3*d^2*e^3 - 17*(3*B*a*b^2 + A*b^3)*d*e^4 - 147*(B*a^2*b + A*a*b^2)*e^5)*m^2 - 2*(4*B*b^3*d^2*e^3 - 5*(3*B*a*b^2 + A*b^3)*d*e^4 - 117*(B*a^2*b + A*a*b^2)*e^5)*m)*x^3 + (71*A*a^3*d*e^4 + 6*(B*a^2*b + A*a*b^2)*d^3*e^2 - 12*(B*a^3 + 3*A*a^2*b)*d^2*e^3)*m^2 + (60*(B*a^3 + 3*A*a^2*b)*e^5 + (3*(B*a^2*b + A*a*b^2)*d*e^4 + (B*a^3 + 3*A*a^2*b)*e^5)*m^4 - (3*(3*B*a*b^2 + A*b^3)*d^2*e^3 - 30*(B*a^2*b + A*a*b^2)*d*e^4 - 13*(B*a^3 + 3*A*a^2*b)*e^5)*m^3 + (12*B*b^3*d^3*e^2 - 18*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 87*(B*a^2*b + A*a*b^2)*d*e^4 + 59*(B*a^3 + 3*A*a^2*b)*e^5)*m^2 + (12*B*b^3*d^3*e^2 - 15*(3*B*a*b^2 + A*b^3)*d^2*e^3 + 60*(B*a^2*b + A*a*b^2)*d*e^4 + 107*(B*a^3 + 3*A*a^2*b)*e^5)*m)*x^2 + (154*A*a^3*d*e^4 - 6*(3*B*a*b^2 + A*b^3)*d^4*e + 54*(B*a^2*b + A*a*b^2)*d^3*e^2 - 47*(B*a^3 + 3*A*a^2*b)*d^2*e^3)*m + (120*A*a^3*e^5 + (A*a^3*e^5 + (B*a^3 + 3*A*a^2*b)*d*e^4)*m^4 + 2*(7*A*a^3*e^5 - 3*(B*a^2*b + A*a*b^2)*d^2*e^3 + 6*(B*a^3 + 3*A*a^2*b)*d*e^4)*m^3 + (71*A*a^3*e^5 + 6*(3*B*a*b^2 + A*b^3)*d^3*e^2 - 54*(B*a^2*b + A*a*b^2)*d^2*e^3 + 47*(B*a^3 + 3*A*a^2*b)*d*e^4)*m^2 - 2*(12*B*b^3*d^4*e - 77*A*a^3*e^5 - 15*(3*B*a*b^2 + A*b^3)*d^3*e^2 + 60*(B*a^2*b + A*a*b^2)*d^2*e^3 - 30*(B*a^3 + 3*A*a^2*b)*d*e^4)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
3182,1,660,0,1.285479," ","integrate((b*x+a)^2*(B*x+A)*(e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(A a^{2} d e^{3} m^{3} - 6 \, B b^{2} d^{4} + 24 \, A a^{2} d e^{3} + 8 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 12 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2} + {\left(B b^{2} e^{4} m^{3} + 6 \, B b^{2} e^{4} m^{2} + 11 \, B b^{2} e^{4} m + 6 \, B b^{2} e^{4}\right)} x^{4} + {\left(8 \, {\left(2 \, B a b + A b^{2}\right)} e^{4} + {\left(B b^{2} d e^{3} + {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m^{3} + {\left(3 \, B b^{2} d e^{3} + 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m^{2} + 2 \, {\left(B b^{2} d e^{3} + 7 \, {\left(2 \, B a b + A b^{2}\right)} e^{4}\right)} m\right)} x^{3} + {\left(9 \, A a^{2} d e^{3} - {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2}\right)} m^{2} + {\left(12 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4} + {\left({\left(2 \, B a b + A b^{2}\right)} d e^{3} + {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m^{3} - {\left(3 \, B b^{2} d^{2} e^{2} - 5 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 8 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m^{2} - {\left(3 \, B b^{2} d^{2} e^{2} - 4 \, {\left(2 \, B a b + A b^{2}\right)} d e^{3} - 19 \, {\left(B a^{2} + 2 \, A a b\right)} e^{4}\right)} m\right)} x^{2} + {\left(26 \, A a^{2} d e^{3} + 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{3} e - 7 \, {\left(B a^{2} + 2 \, A a b\right)} d^{2} e^{2}\right)} m + {\left(24 \, A a^{2} e^{4} + {\left(A a^{2} e^{4} + {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m^{3} + {\left(9 \, A a^{2} e^{4} - 2 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 7 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m^{2} + 2 \, {\left(3 \, B b^{2} d^{3} e + 13 \, A a^{2} e^{4} - 4 \, {\left(2 \, B a b + A b^{2}\right)} d^{2} e^{2} + 6 \, {\left(B a^{2} + 2 \, A a b\right)} d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(A*a^2*d*e^3*m^3 - 6*B*b^2*d^4 + 24*A*a^2*d*e^3 + 8*(2*B*a*b + A*b^2)*d^3*e - 12*(B*a^2 + 2*A*a*b)*d^2*e^2 + (B*b^2*e^4*m^3 + 6*B*b^2*e^4*m^2 + 11*B*b^2*e^4*m + 6*B*b^2*e^4)*x^4 + (8*(2*B*a*b + A*b^2)*e^4 + (B*b^2*d*e^3 + (2*B*a*b + A*b^2)*e^4)*m^3 + (3*B*b^2*d*e^3 + 7*(2*B*a*b + A*b^2)*e^4)*m^2 + 2*(B*b^2*d*e^3 + 7*(2*B*a*b + A*b^2)*e^4)*m)*x^3 + (9*A*a^2*d*e^3 - (B*a^2 + 2*A*a*b)*d^2*e^2)*m^2 + (12*(B*a^2 + 2*A*a*b)*e^4 + ((2*B*a*b + A*b^2)*d*e^3 + (B*a^2 + 2*A*a*b)*e^4)*m^3 - (3*B*b^2*d^2*e^2 - 5*(2*B*a*b + A*b^2)*d*e^3 - 8*(B*a^2 + 2*A*a*b)*e^4)*m^2 - (3*B*b^2*d^2*e^2 - 4*(2*B*a*b + A*b^2)*d*e^3 - 19*(B*a^2 + 2*A*a*b)*e^4)*m)*x^2 + (26*A*a^2*d*e^3 + 2*(2*B*a*b + A*b^2)*d^3*e - 7*(B*a^2 + 2*A*a*b)*d^2*e^2)*m + (24*A*a^2*e^4 + (A*a^2*e^4 + (B*a^2 + 2*A*a*b)*d*e^3)*m^3 + (9*A*a^2*e^4 - 2*(2*B*a*b + A*b^2)*d^2*e^2 + 7*(B*a^2 + 2*A*a*b)*d*e^3)*m^2 + 2*(3*B*b^2*d^3*e + 13*A*a^2*e^4 - 4*(2*B*a*b + A*b^2)*d^2*e^2 + 6*(B*a^2 + 2*A*a*b)*d*e^3)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
3183,1,256,0,1.096727," ","integrate((b*x+a)*(B*x+A)*(e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(A a d e^{2} m^{2} + 2 \, B b d^{3} + 6 \, A a d e^{2} - 3 \, {\left(B a + A b\right)} d^{2} e + {\left(B b e^{3} m^{2} + 3 \, B b e^{3} m + 2 \, B b e^{3}\right)} x^{3} + {\left(3 \, {\left(B a + A b\right)} e^{3} + {\left(B b d e^{2} + {\left(B a + A b\right)} e^{3}\right)} m^{2} + {\left(B b d e^{2} + 4 \, {\left(B a + A b\right)} e^{3}\right)} m\right)} x^{2} + {\left(5 \, A a d e^{2} - {\left(B a + A b\right)} d^{2} e\right)} m + {\left(6 \, A a e^{3} + {\left(A a e^{3} + {\left(B a + A b\right)} d e^{2}\right)} m^{2} - {\left(2 \, B b d^{2} e - 5 \, A a e^{3} - 3 \, {\left(B a + A b\right)} d e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(A*a*d*e^2*m^2 + 2*B*b*d^3 + 6*A*a*d*e^2 - 3*(B*a + A*b)*d^2*e + (B*b*e^3*m^2 + 3*B*b*e^3*m + 2*B*b*e^3)*x^3 + (3*(B*a + A*b)*e^3 + (B*b*d*e^2 + (B*a + A*b)*e^3)*m^2 + (B*b*d*e^2 + 4*(B*a + A*b)*e^3)*m)*x^2 + (5*A*a*d*e^2 - (B*a + A*b)*d^2*e)*m + (6*A*a*e^3 + (A*a*e^3 + (B*a + A*b)*d*e^2)*m^2 - (2*B*b*d^2*e - 5*A*a*e^3 - 3*(B*a + A*b)*d*e^2)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","B",0
3184,1,83,0,1.083151," ","integrate((B*x+A)*(e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(A d e m - B d^{2} + 2 \, A d e + {\left(B e^{2} m + B e^{2}\right)} x^{2} + {\left(2 \, A e^{2} + {\left(B d e + A e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{2} m^{2} + 3 \, e^{2} m + 2 \, e^{2}}"," ",0,"(A*d*e*m - B*d^2 + 2*A*d*e + (B*e^2*m + B*e^2)*x^2 + (2*A*e^2 + (B*d*e + A*e^2)*m)*x)*(e*x + d)^m/(e^2*m^2 + 3*e^2*m + 2*e^2)","A",0
3185,0,0,0,1.098681," ","integrate((B*x+A)*(e*x+d)^m/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b x + a}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(b*x + a), x)","F",0
3186,0,0,0,1.130984," ","integrate((B*x+A)*(e*x+d)^m/(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((B*x + A)*(e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
3187,1,175,0,1.247961," ","integrate((1-2*x)*(2+3*x)^m*(3+5*x)^3,x, algorithm=""fricas"")","-\frac{{\left(20250 \, {\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} x^{5} + 675 \, {\left(59 \, m^{4} + 549 \, m^{3} + 1819 \, m^{2} + 2499 \, m + 1170\right)} x^{4} - 1458 \, m^{4} + 45 \, {\left(471 \, m^{4} + 3292 \, m^{3} + 8199 \, m^{2} + 8618 \, m + 3240\right)} x^{3} - 17496 \, m^{3} - 9 \, {\left(459 \, m^{4} + 10677 \, m^{3} + 50581 \, m^{2} + 84103 \, m + 43740\right)} x^{2} - 66366 \, m^{2} - 3 \, {\left(2187 \, m^{4} + 28782 \, m^{3} + 114405 \, m^{2} + 175346 \, m + 87480\right)} x - 99240 \, m - 48800\right)} {\left(3 \, x + 2\right)}^{m}}{81 \, {\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)}}"," ",0,"-1/81*(20250*(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*x^5 + 675*(59*m^4 + 549*m^3 + 1819*m^2 + 2499*m + 1170)*x^4 - 1458*m^4 + 45*(471*m^4 + 3292*m^3 + 8199*m^2 + 8618*m + 3240)*x^3 - 17496*m^3 - 9*(459*m^4 + 10677*m^3 + 50581*m^2 + 84103*m + 43740)*x^2 - 66366*m^2 - 3*(2187*m^4 + 28782*m^3 + 114405*m^2 + 175346*m + 87480)*x - 99240*m - 48800)*(3*x + 2)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)","B",0
3188,1,120,0,1.125401," ","integrate((1-2*x)*(2+3*x)^m*(3+5*x)^2,x, algorithm=""fricas"")","-\frac{{\left(1350 \, {\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} x^{4} + 45 \, {\left(41 \, m^{3} + 207 \, m^{2} + 334 \, m + 168\right)} x^{3} - 162 \, m^{3} + 18 \, {\left(17 \, m^{3} - 69 \, m^{2} - 302 \, m - 216\right)} x^{2} - 1314 \, m^{2} - 3 \, {\left(153 \, m^{3} + 1513 \, m^{2} + 3290 \, m + 1944\right)} x - 2644 \, m - 1520\right)} {\left(3 \, x + 2\right)}^{m}}{27 \, {\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)}}"," ",0,"-1/27*(1350*(m^3 + 6*m^2 + 11*m + 6)*x^4 + 45*(41*m^3 + 207*m^2 + 334*m + 168)*x^3 - 162*m^3 + 18*(17*m^3 - 69*m^2 - 302*m - 216)*x^2 - 1314*m^2 - 3*(153*m^3 + 1513*m^2 + 3290*m + 1944)*x - 2644*m - 1520)*(3*x + 2)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","A",0
3189,1,75,0,1.088915," ","integrate((1-2*x)*(2+3*x)^m*(3+5*x),x, algorithm=""fricas"")","-\frac{{\left(270 \, {\left(m^{2} + 3 \, m + 2\right)} x^{3} + 9 \, {\left(23 \, m^{2} + 32 \, m + 9\right)} x^{2} - 54 \, m^{2} - 3 \, {\left(21 \, m^{2} + 197 \, m + 162\right)} x - 282 \, m - 200\right)} {\left(3 \, x + 2\right)}^{m}}{27 \, {\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)}}"," ",0,"-1/27*(270*(m^2 + 3*m + 2)*x^3 + 9*(23*m^2 + 32*m + 9)*x^2 - 54*m^2 - 3*(21*m^2 + 197*m + 162)*x - 282*m - 200)*(3*x + 2)^m/(m^3 + 6*m^2 + 11*m + 6)","A",0
3190,0,0,0,1.105202," ","integrate((1-2*x)*(2+3*x)^m/(3+5*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m} {\left(2 \, x - 1\right)}}{5 \, x + 3}, x\right)"," ",0,"integral(-(3*x + 2)^m*(2*x - 1)/(5*x + 3), x)","F",0
3191,0,0,0,1.124580," ","integrate((1-2*x)*(2+3*x)^m/(3+5*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m} {\left(2 \, x - 1\right)}}{25 \, x^{2} + 30 \, x + 9}, x\right)"," ",0,"integral(-(3*x + 2)^m*(2*x - 1)/(25*x^2 + 30*x + 9), x)","F",0
3192,0,0,0,1.023822," ","integrate((1-2*x)*(2+3*x)^m/(3+5*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m} {\left(2 \, x - 1\right)}}{125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27}, x\right)"," ",0,"integral(-(3*x + 2)^m*(2*x - 1)/(125*x^3 + 225*x^2 + 135*x + 27), x)","F",0
3193,0,0,0,1.125064," ","integrate((2+3*x)^m*(3+5*x)^3/(1-2*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(125 \, x^{3} + 225 \, x^{2} + 135 \, x + 27\right)} {\left(3 \, x + 2\right)}^{m}}{2 \, x - 1}, x\right)"," ",0,"integral(-(125*x^3 + 225*x^2 + 135*x + 27)*(3*x + 2)^m/(2*x - 1), x)","F",0
3194,0,0,0,1.405219," ","integrate((2+3*x)^m*(3+5*x)^2/(1-2*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 30 \, x + 9\right)} {\left(3 \, x + 2\right)}^{m}}{2 \, x - 1}, x\right)"," ",0,"integral(-(25*x^2 + 30*x + 9)*(3*x + 2)^m/(2*x - 1), x)","F",0
3195,0,0,0,1.064294," ","integrate((2+3*x)^m*(3+5*x)/(1-2*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m} {\left(5 \, x + 3\right)}}{2 \, x - 1}, x\right)"," ",0,"integral(-(3*x + 2)^m*(5*x + 3)/(2*x - 1), x)","F",0
3196,0,0,0,1.072877," ","integrate((2+3*x)^m/(1-2*x)/(3+5*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m}}{10 \, x^{2} + x - 3}, x\right)"," ",0,"integral(-(3*x + 2)^m/(10*x^2 + x - 3), x)","F",0
3197,0,0,0,1.132681," ","integrate((2+3*x)^m/(1-2*x)/(3+5*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right)"," ",0,"integral(-(3*x + 2)^m/(50*x^3 + 35*x^2 - 12*x - 9), x)","F",0
3198,0,0,0,1.001594," ","integrate((2+3*x)^m/(1-2*x)/(3+5*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, x + 2\right)}^{m}}{250 \, x^{4} + 325 \, x^{3} + 45 \, x^{2} - 81 \, x - 27}, x\right)"," ",0,"integral(-(3*x + 2)^m/(250*x^4 + 325*x^3 + 45*x^2 - 81*x - 27), x)","F",0
3199,0,0,0,0.703790," ","integrate((b*x+a)^m/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b*x + a)^m/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
3200,0,0,0,1.061170," ","integrate((b*x+a)^m/(d*x+c)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{d f^{2} x^{3} + c e^{2} + {\left(2 \, d e f + c f^{2}\right)} x^{2} + {\left(d e^{2} + 2 \, c e f\right)} x}, x\right)"," ",0,"integral((b*x + a)^m/(d*f^2*x^3 + c*e^2 + (2*d*e*f + c*f^2)*x^2 + (d*e^2 + 2*c*e*f)*x), x)","F",0
3201,0,0,0,1.031561," ","integrate((b*x+a)^m/(d*x+c)^2/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{d^{2} f^{2} x^{4} + c^{2} e^{2} + 2 \, {\left(d^{2} e f + c d f^{2}\right)} x^{3} + {\left(d^{2} e^{2} + 4 \, c d e f + c^{2} f^{2}\right)} x^{2} + 2 \, {\left(c d e^{2} + c^{2} e f\right)} x}, x\right)"," ",0,"integral((b*x + a)^m/(d^2*f^2*x^4 + c^2*e^2 + 2*(d^2*e*f + c*d*f^2)*x^3 + (d^2*e^2 + 4*c*d*e*f + c^2*f^2)*x^2 + 2*(c*d*e^2 + c^2*e*f)*x), x)","F",0
